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Universidad EAFIT
Carrera 49 # 7 sur -50 Medellín Antioquia Colombia
Carrera 12 # 96-23, oficina 304 Bogotá Cundinamarca Colombia
(57)(4) 2619500 contacto@eafit.edu.co
EAFITProgramas académicosPosgradosPhD in Mathematical EngineeringSeminar of the PhD in Mathematical Engineering

Seminar of the PhD in Mathematical Engineering

​​​​​​​​​​​​​​​​​​​​​​

2019-2

Date​

​​​Talk

​2019-11-11
Speaker: TBA

Affiliation: Post doctoral researcher at Research Group in Spatial Econometrics RiSE, Universidad EAFIT

Title: TBA

Abstract: TBA.

Slides: [ ]

Video: [  ]

Place: TBA
Time: 9 a.m. - 10 a.m.
​2019-11-04
Speaker: TBA

Affiliation: Post doctoral researcher at Research Group in Spatial Econometrics RiSE, Universidad EAFIT

Title: TBA

Abstract: TBA.

Slides: [ ]

Video: [  ]

Place: TBA
Time: 9 a.m. - 10 a.m.
​2019-10-28
Speaker: Jhon Edinson Hinestroza

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematical Modelling, Universidad EAFIT

Title: TBA

Abstract: TBA.

Slides: [ ]

Video: [  ]

Place: TBA
Time: 9 a.m. - 10 a.m.
​2019-10-21
Speaker: Andrés Giovanny Pérez Coronado 

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematical Modelling, Universidad EAFIT

Title: TBA

Abstract: TBA.

Slides: [ ]

Video: [  ]

Place: TBA
Time: 9 a.m. - 10 a.m.
​2019-10-07
Speaker: Jorge Eliécer Agudelo

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematics and its Applications, Universidad EAFIT

Title: TBA

Abstract: TBA.

Slides: [ ]

Video: [  ]

Place: TBA
Time: 9 a.m. - 10 a.m.
​2019-09-30
Speaker: Jhon Willington Bernal Vera

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematics and its applications, Universidad EAFIT

Title: TBA

Abstract: TBA.

Slides: [ ]

Video: [  ]

Place: TBA
Time: 9 a.m. - 10 a.m.

Date​

​​​Talk

​2019-09-23
Speaker: Juan Carlos Arango parra

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematics and its applictions.

Title: TBA

Abstract: TBA.

Slides: [ ]

Video: [  ]

Place: TBA
Time: 9 a.m. - 10 a.m.
​2019-09-09
Speaker: Juan David Palacio

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematical Modelling, Universidad EAFIT

Title: TBA

Abstract: TBA.

Slides: [ ]

Video: [  ]

Place: TBA
Time: 9 a.m. - 10 a.m.
​2019-09-02
Speaker: Andrés Yarce Botero 

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematical Modelling, Universidad EAFIT

Title: TBA

Abstract: TBA.

Slides: [ ]

Video: [  ]

Place: TBA
Time: 9 a.m. - 10 a.m.
​2019-08-26
Speaker: Santiago López-Restrepo 

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematical Modelling, Universidad EAFIT

Title: TBA

Abstract: TBA.

Slides: [ ]

Video: [  ]

Place: TBA
Time: 9 a.m. - 10 a.m.
​2019-08-12
Speaker: Diana Paola Lizarralde

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematics and its Applications, Universidad EAFIT

Title: TBA

Abstract: TBA.

Slides: [ ]

Video: [  ]

Place: TBA
Time: 9 a.m. - 10 a.m.
​2019-08-05
Speaker: Leandro Fabio Ariza-Jimenez 

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematical Modelling, Universidad EAFIT

Title: TBA

Abstract: TBA.

Slides: [ ]

Video: [  ]

Place: TBA
Time: 9 a.m. - 10 a.m.




2019-1


Date​

​​​Talk

​2019-06-07
Speaker: Juan Carlos Arango Parra

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematics and Applications, Universidad EAFIT

Title: Solution to the heat equation way symmetry analysis

Abstract: [ pdf ]

Slides: [ pdf ]

Video: N/A

Place: 38-108
Time: 11 a.m. - 12 m.
​2019-05-31
Speaker: Jhon Willington Bernal Vera

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematics and Applications, Universidad EAFIT

Title: Detecting Minimal Morse Functions in Poincaré's homology sphere via the heat equation.

Abstract: Let (M,g) be a closed, connected riemannian manifold that is locally homogeneous, i.e. such that each pair of points p, q M have isometric neighborhoods. It has been conjectured that for each "generic" initial condition f_0, the solution to ∂f/∂t = ∆_gf, f (·,0) = f_0 is such that for sufficiently large t, f (·, t) is a minimal Morse function, i.e. a Morse function whose total number of critical points is the least possible on M. In this talk we will present some new results obtained by applying an algorithm for detecting critical points to eigenfunctions of the first nonzero eigenvalue of the Laplace-Beltrami operator of the Poincaré's Homology Sphere. These results indicate that a refinement of the conjecture´s statement, possibly involving the Ricci flow, is necessary.

Slides: [ pdf ]

Video: N/A

Place: 38-108
Time: 11 a.m. - 12 m.
​2019-05-24
Speaker: Jhon Edinson Hinestroza Ramírez

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematical Modeling - GRIMMAT, Universidad EAFIT

Title: Study of the algorithmic complexity of the Ensemble Kalman Filter and its efficient implementations

Abstract: This seminar will explore from a mathematical and statistical point of view, the data assimilation classical algorithm Ensemble Kalman Filter (EnKF) and will provide insights about its overall performance. We will address a few analysis of its efficient implementations such as SVD, Cholesky decomposition, and the Sherman-Morrison. 

Slides: [ pdf ]

Video: [ link ]

Place: 38-108
Time: 11 a.m. - 12 m.
​2019-05-17
Speaker: Andrés Giovanny Pérez Coronado

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematical Modeling - GRIMMAT, Universidad EAFIT

Title: Crime prediction using Mahalanobis distance applied in Villavicencio (Meta)

Abstract: Interpolation techniques in crimen prediction frecuently use Euclidean distance, that is equivalent in meters on the field. However, this distance has some limitations because doesn't take into account the dependence structure of the variables. So, we propose to use Mahalanobis distance to take advance of correlation between variables in Inverse Distance Interpolation.

Slides: [ pdf ]

Video: [ link ]

Place: 38-108
Time: 11 a.m. - 12 m.
​2019-05-03
Speaker:  Juan Pablo Fernández Gutiérrez

Affiliation: PhD(C) in Modeling and Sientific Computing, Universidad de Medellín

Title: A MCLP Based Optimization of Complex Processes: A Novel Computational Approach

Abstract: This Ph.D. article-based thesis discusses a novel computational approach to the extended Maximal Covering Location Problem (MCLP). We consider a fuzzy-type formulation of the generic MCLP and develop the necessary theoretical and numerical aspects of the proposed Separation Method (SM). A specific structure of the originally given MCLP makes it possible to reduce it to two auxiliary Knapsack-type problems. The equivalent separation we propose reduces essentially the complexity of the resulting  computational algorithms. This algorithm also incorporates a conventional relaxation technique and the scalarizing method applied to an auxiliary multiobjective optimization problem. The proposed solution methodology is next applied to Supply Chain optimization in the presence of incomplete information. We study two illustrative examples and give a rigorous analysis of the obtained results.

The previous result is extended to a newly developed computational optimization approach to a specific class of Maximal Covering Location Problems (MCLPs) with a switched dynamic structure. Most of the results obtained for the conventional MCLP address the “static” case where an optimal decision is determined on a fixed time-period. In our contribution we consider a dynamic MCLP based optimal decision making and propose an effective computational method for the numerical treatment of the switched-type Dynamic Maximal Covering Location Problem (DMCLP). A generic geometrical structure of the constraints under consideration makes it possible to separate the originally given dynamic optimization problem and reduce it to a specific family of relative simple auxiliary problems. The generalized Separation Method (SM) for the DMCLP with a switched structure finally leads to a computational solution scheme. The resulting numerical algorithm also includes the classic Lagrange relaxation. We present a rigorous formal analysis of the DMCLP optimization methodology and also discuss computational aspects. The proposed SM based algorithm is finally applied to a practically oriented example, namely, to an optimal design of a (dynamic) mobile network configuration.

Slides: N/A

Video: [ link ]

Place: 38-108
Time: 11 a.m. - 12 m.
​2019-04-12
Speaker: Jorge Eliécer Agudelo Quiceno

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematics and Applications, Universidad EAFIT

Title: Lagrangian-Eulerian method for two-dimensional hyperbolic conservation laws

Abstract: We propose a new two-dimensional scheme to solve 2D hyperbolic laws in square meshes and show that it is capable of capturing correct qualitative solutions for linear and nonlinear problems without the use of sophisticated tools, which makes it easy to implement, and without excessively increasing the computational cost.

Slides: [ pdf ]

Video: [ link ]

Place: 38-108
Time: 11 a.m. - 12 m.


2018-2


Date​

​​​Talk

​2018-11-30
Speaker: William Guerrero Rueda

Affiliation: Professor, Universidad de la Sabana, Bogotá

Title: Research experiences in humanitarian and hospital operations - Advances and challenges of multidisciplinary work

Abstract: Two research experiences associated with the application of mathematical modeling techniques and logistics optimization in specific cases of non-commercial logistics are presented. First, the context of the blood donation system using mobile units is analyzed. For this scenario, an optimization model based on two-stage stochastic programming is presented. Secondly, the context of the system of immediate response to natural disasters is analyzed. For this scenario, an optimization model is presented based on mixed integer programming that can be applied in the case of the Mocoa disaster in 2017. From both contexts we see how mathematical programming can help plan the operation of the vehicles required to respond to logistical needs in contexts other than commercial logistics. Finally, perspectives of research and multidisciplinary work in these contexts are presented. 

Keywords: logistics, operations research, health, natural disasters, vehicle routing

Slides: [ pdf ]

Video: [ link ]

Place: 38-204
Time: 11 a.m. - 12 m.
​2018-11-27
Speaker: Elias D. Nino-Ruiz

Affiliation: Associate Professor, Chair, Department of Computer Science, Universidad del Norte, Barranquilla

Title: BACKGROUND ERROR ESTIMATION IN SEQUENTIAL DATA ASSIMILATION METHODS

Abstract: In sequential data assimilation, imperfect numerical forecasts are adjusted according to real, noisy observations. In practice, the assimilation of observations can be sensitive to some issues: spurious correlations owing to small ensemble sizes, few observations during assimilation stages (sparse observational networks), and huge operational model resolutions. This talk covers different methodologies to overcome/counteract these situations. Efficient and practical covariance matrix estimators are discussed for their use in the context of high-dimensional spaces and even more, parallel resources can be exploited to speed-up algebraic computations. Two well-known covariance matrix estimators are highlighted from the statistical literature: the Rao-Blackwell Ledoit and Wolf estimator and the modified Cholesky decomposition for inverse covariance matrix estimation, their efficient use under ensemble Kalman filter formulations are presented as well. Some comparative examples for the discussed methods are shown making use of an Atmospheric General Circulation Model (AT-GCM) and the Lorenz 96 model. The numerical results reveal that the use of regularized covariance matrix estimation in the context of ensemble Kalman filtering can improve the quality of background error estimates and therefore, the impact of spurious correlations can be mitigated during the assimilation of observations. Even more, the proposed methods are attractive since their practical and parallel implementations are straightforward when observation operators are linear.

Keywords: ensemble Kalman filter, modified Cholesky decomposition, shrinkage covariance matrix estimation.

Slides: [ pdf ]

Video: [ link ]

Place: 38-302
Time: 11 a.m. - 12 m.
​​2018-11-16
Speaker: Juan Carlos Arango Parra

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematics and Applications, Universidad EAFIT

Title: Discretization of Laplacian operator

Abstract: [ pdf ]

Slides: [ pdf ]
Video: [ link ]

Place: 38-302
Time: 11 a.m. - 12 m.
​2018-11-09
Speaker: Santiago Lopez Restrepo

Affiliation: Research assistant, research group in mathematical modeling - GRIMMATUniversidad EAFIT

Title: Ensemble-based Data Assimilation For High-uncertainty systems: Case of study, PM10 and PM2.5 in the Aburrá Valley

Abstract: It has been proved that Ensemble-based data assimilation is suitable to be implemented in many cases showing an important improvement of the model performance. The Kalman Filter is a well-known, easy to implement  and optimal method when  different assumptions about the statistical behavior of the uncertainties are met. But in many real applications of data assimilation there are not enough information to characterize the system uncertainties or there are too many uncertainties sources, causing that the Kalman Filter will not be optimal and even, do not present a proper performance. This issues can be worst for high-dimensional where often is used  a ensemble approximation of the Kalman Filter (like the Ensemble Kalman Filter) that in the best of the cases, does not guarantee the optimability. For this reason, in this work is proposed a three-year plan to develop a Ensemble-based data assimilation scheme capable to lead with high-uncertainty and high-dimensional systems. The scheme will be focus in three important aspects of the data assimilation process: i) to implement a ensemble robust filter to evaluate its performance in a high-uncertainty system, ii) to develop a covariance localization technique to avoid the issues of use an ensemble to represent approximate the robust filter, that incorporates knowledge about the system and iii) to develop an uncertainty propagation model using phenomenological knowledge of the parameters to be estimated. The developed Ensemble-based data assimilation scheme will be tested in a real application that consist in the implementation of the LOTOS-EUROS to represent the PM10 and PM2.5 behavior over the Aburrá Valley.

Slides: [ pdf ]
Video: [ link ]

Place: 38-302
Time: 11 a.m. - 12 m.
​2018-11-02
Speaker: Juan David Palacio Domínguez

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematical Modeling - GRIMMAT, Universidad EAFIT

Title: Dealing with feasibility and solution quality in a Rebalacing Vehicle Routing Problem 

Abstract: A Bicycle Sharing System (BSS) is mainly composed by a set available bicycles for users and a set of stations with limited capacity distributed along an urban area. Routing problems for rebalancing operations in BSS are modeled as a Pickup and Delivery Traveling Salesman Problem (PDTSP). This talk is devoted to show some exact and heuristic methods able to improve the number of feasible solutions and solution quality within a Greedy Randomized Adaptive Search Procedure. More precisely, we present ideas inspired on hybrid procedures that include new mixed-integer linear programming models.

Slides: [ pdf ]
Video: N/A

Place: 38-302
Time: 11 a.m. - 12 m.
​2018-10-26

​​Speaker: Jhon Willington Bernal Vera
Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematics and Applications, Universidad EAFIT

Title: Exploring Critical Points And Critical Regions

Abstract: Current approaches to detect critical points are generally limited to isolated critical points. Functions in several variables often contain regions of constant value. We present a method (algorithm) that detects critical points, corresponding critical regions for functions of two and three variables that are interpolated bilinear or trilinearly by sections on a uniform rectilinear grid.

Slides: [ pdf ]

Video: [ link ]

Place: 38-302
Time: 11 a.m. - 12 m.
​2018-10-19
Speaker: Jhon Edinson Hinestroza Ramírez

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematical Modeling - GRIMMAT, Universidad EAFIT

Title: Non linearity and non-gaussianity in atmospheric dynamics

Abstract: The air quality is a critical preoccupation. For this reason, to study its dynamic is always relevant. This research seeks to study and to understand the dynamic behind of the atmospheric variables and meteorology using the Weather Research and Forecasting (WRF) model. It pretends to determine and improve the model performance in the Valley of Aburrá River. Based on this, the aim is to identify, measure, and model significant sources of uncertainty in the meteorological forecast with the WRF model. After this, it pretends to develop a methodology for decreasing uncertainty in the model, using nonlinear data assimilation via particle filters. Several challenges arise on our purpose. In this first seminar, It will be shown a first theoretical approximation and the importance of the problem solution.

Slides: [ pdf ]

Video: [ link ]

Place: 38-304
Time: 10 a.m. - 11 a.m.
​2018-10-12
Speaker: Andrés Ya​rce Botero

Affiliation: Research assistant, Research Group in Mathematical Modeling - GRIMMAT, Universidad EAFIT

​​Title: Adjoint-free variational data assimilation and model order reduce techniques

Abstract: Variational data assimilation (Var DA) is a mathematical technique used to combine the results of a large scale model with available measurements to obtain an optimal reconstruction of the state and parameters of the system, minimizing a given cost function.  Var DA requires implementation of the adjoint model, which is very difficult to generate and maintain for high dimension nonlinear models. That is the reason why alternative variational and model order reduction (MOR) techniques appeared, to simplify the model before data assimilation is implemented. In this opportunity, an overview of some modified, adjoint free Var DA and MOR techniques will be presented.

Slides: [ pdf ]
Video: [ link ]

Place: 38-302
Time: 11 a.m. - 12 m.
​2018-09-28

​​Speaker: Arnold Heemink
Affiliation: Professor Department of Applied Mathematics, Delft University of Technology (TU Delft)

Title: The importance of mathematical modeling in air quality: case of study China dust air pollution

Abstract: N/A

Slides: N/A
Video: N/A

Place: 27-103
Time: 10:00 a.m. - 10:45 a.m.
​2018-08-31
​Speaker: Alexander Quintero Vélez

Affiliation: Universidad Nacional, seccional Medellín

Title: The Algebra and Geometry of Nonlinear Partial Differential Equations

Abstract: In this talk I will discuss the remarkable interaction between the applied mathematical subject of nonlinear partial differential equations and the pure mathematical subject of algebraic geometry.

Slides: [ pdf ]
Video: [ link ]

Place: 38-302
Time: 11 a.m. - 12 m.
​2018-08-03
Speaker: Juan David Palacio Domínguez

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematical Modeling - GRIMMAT, Universidad EAFIT

Title: The International Spring School on Integrated Operational Problems: What a PhD Student can Learn?

Abstract: The International Spring School on Integrated Operational Problems was a three-days event for PhD students and researches who wish to acquire knowledge on optimization and operational research applied to logistics. Lectures on scheduling and vehicle routing problems were presented as well as methodologies to solve them (metaheuristics, column generation, exact approaches and constraint programming). In this talk, I briefly summarize some of the main ideas, problems, methodologies and experiences that senior researches shared with the PhD students who attended this event two months ago in Troyes, France.

Slides: [ pdf ]
Video: N/A

Place: 38-302
Time: 11 a.m. - 12 m.
​2018-07-27

Speaker: Ralph Baker Kearfott
Affiliation: Professor Applied Mathematics, University of Louisiana, Lafayette, Louisiana USA

Title: Interval arithmetic: Fundamentals, Successes and Pitfalls

Abstract: In this tutorial survey, we introduce the underlying motivations for interval arithmetic, along with the basic operations.  We give a history of interval arithmetic, we highlight notable successes in scientific and engineering problems, and we mention problems and pitfalls. We also discuss IEEE 1788-2015, the standard for interval arithmetic, and we list available software for various tasks.

Slides: [ pdf ]
Video: [ link ]

Place: 38-304
Time: 11 a.m. - 12 m.
​2018-07-13

​Speaker: Jenny Díaz Ramírez
Affiliation: Universidad de Monterrey, México

Title: A Comparison of Ambulance Location Models in Two Mexican Cases

Abstract: The development of several ambulance location models have been discussed in the academic literature. Most of these models have been further extended to consider more realistic situations into account and the use of different assessment criteria. However, there is not an exhaustive literature that takes the existing standard models to compare them according to the criteria used in practice, especially when comparisons use real data. It is even scarcer when data comes from developing countries. In this work, we undertake the task of comparing the performance of several ambulance location models on coverage and response time criteria. The results of this work are important to help emergency medical organizations to define their most adequate model for defining their ambulance base structure. The comparison of the models is carried out in two Mexican emergency operations of the Red Cross located in the cities of Monterrey and Tijuana.

Slides: [ pdf ]
Video: [ link ]

Place: 38-108
Time: 11 a.m. - 12 m.


2018-1


Date​

​​​Talk

​2018-06-22
Speaker: Juan David Palacio Domínguez

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematical Modeling - GRIMMAT, Universidad EAFIT

Title: Hybrid approaches to the Repositioning Problem in Bicycle-sharing Systems
Abstract: The Repositioning Problem in Bicycle-sharing Systems (BSS) aims to find a set of routes able to serve all the system stations by picking up or delivering bicycles according to a previous demand estimation and a fixed number of available bicycles. In our work, we model the BSS vehicle operation as a Traveling Salesman Problem (TSP) with pick up and deliveries (PDTSP). Given the NP-hardness nature of the problem, we develop a metaheuristic approach based on a Greedy Randomized Adaptive Search Procedure (GRASP) and Variable Neighborhood Descent (VND). In this talk, we present new local search operators for our heuristic approach and we also show some hybrid strategies (matheuristics) to deal with the PDTSP. Our ideas include mixed-integer programming models (MILPs) as local search operators, post-optimization procedures and PDTSP decomposition.

Slides: [ pdf ]
Video: N/A

Place: 29-205
Time: 11 a.m. - 12 m.
​2018-06-15
Speaker: Mónica Patricia Hernández Lordui

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematics and Applications, Universidad EAFIT

Title: Robust Optimization Applied to the Dose Calculation in Radiation Therapy for Breast Cancer. An Introduction to the Problem

Abstract: In radiation therapy for cancer treatments, the border delineation of the clinical target volume (CTV) and organs at risk (OAR) should be precise so that the dose distribution applied to the patient does not generate toxicity in the healthy organs and allows for the greatest coverage of the diseased volume. The success or failure of the treatment plan depends on the precision previously mentioned. The problem is that the CTV and the OAR represent moving targets in the treatment plan that calculates the dose distribution applied, which directly impacts the quality of the solution generated by the optimization algorithm that calculates the dose. The movement of the targets is caused by position errors and the respiratory dynamic of each patient, which are added to the dose as sources of uncertainty in the problem.  In effect, the dose acquires the condition of aleatory variable with some associated distribution. The dose distribution denotes the objective function in the optimization problem that will be solved. The convexity or non-convexity and the linearity or non-linearity of the objective function should be studied to propose a robust optimal solver due to the implications of the said uncertainties. This presentation will introduce the declared problem and will mention some optimization methods used by the scientific communities that work in that field.

Slides: [ pdf ]
Video: N/A

Place: 29-205
Time: 11 a.m. - 12 m.
​2018-06-08
Speaker: Andrés Giovanny Pérez Coronado

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematical Modeling - GRIMMAT, Universidad EAFIT

Title: Non-parametric space-time prediction for organized crime, based on social media, police data and open sources
Abstract: The crime prediction from non-parametric methods are currently linking Twitter with Kernel Density Estimation (KDE) of crime statistics as Matthew Gerber proposed it, and this improves the predicting accuracy. In this way, we propose to complement the previous method, with intelligence reports and open sources, for instance, google trends, to strengthen the prediction in Colombian context.

We begin from criminal phenomenon of organized crime instead of the specific geographic location, usually cities. So, we analyze the
System of Illicit Drugs (SID), this is how Colombian public safety agencies understand the drug trafficking.

We based in Gerber’s analytical approach, we are going to try to change the interpolation method from Inverse Distance Weighted (IDW)
to Thin Plate Spline (TPS), and as well as explore the shrinkage of the covariance matrix.

Slides: [ pdf ]
Video: N/A

Place: 29-205
Time: 11 a.m. - 12 m.
​2018-06-01
Speaker: Andrés Ya​rce Botero

Affiliation: Research assistant, Research Group in Mathematical Modeling - GRIMMAT, Universidad EAFIT

Title: Conciliating models with reality: The Variational data assimilation technique

Abstract: When the physical dynamics of a problem are highly nonlinear, the parameters are unknown, or the number of model states involved is very large, model outputs usually do not correspond to the values of the real phenomena. Data assimilation techniques are then important as a solution to conciliate model outputs with the reality and reduce uncertainty. One of these approaches, the variational data assimilation technique, was born from optimal control theory. It is a methodology that searches through analysis of successive time interval windowing steps how to minimize a cost function. Different methods are used to find the minimum of the cost function by establishing an expression for the gradient, which implies to know the tangent linear model also known as the adjoint model, which in turn constitutes the big problem due to the frequent impossibility of generating it. In this presentation, the standard methodology of variational data assimilation is explained using a chaotic model for which the adjoint exist, explaining all the processes necessary for the assimilation with synthetic data, and finishing with an overview of the more representative adjoint-free modified variational techniques available to deal with this problem.

Slides: [ pdf ]
Video: [ link ]

Place: 29-205
Time: 11 a.m. - 12 m.
​​2018-05-30

Speaker: Jhon Willington Bernal Vera
Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematics and ApplicationsUniversidad EAFIT

Title: Minimal Morse Functions via the Heat Equation in Locally Homogeneous Riemannian Manifolds
Abstract: [ pdf ]

Slides: [ pdf ]
Video: N/A

Place: 29-205
Time: 9 a.m. - 10 a.m.
​2018-05-25
Speaker: Santiago Lopez Restrepo

Affiliation: Research assistant, research group in mathematical modeling - GRIMMATUniversidad EAFIT

Title: Covariance Localization and Parameter Estimation using Ensemble-Based Data Assimilation

Abstract: Data assimilation is a mathematical process that provides integration between measured values (observations) and a dynamical model, to improve the accuracy the model. The output value provided by the model has a smaller error than the output value provided by the model without observations. The data assimilation has two key objectives, to improve the operation in predictions of model states and estimate unknown parameters of the model. The Ensemble-Based data assimilation is a family of methods that uses an ensemble to model the statics of the first guess (background). In each assimilation step, a forecast from the previous model simulation is used as a first guess, using the available observation this forecast is modified in better agreement with these observations. Because its easily implementations and relative low computational cost (compare with other data assimilation techniques) and very general statistical formulation, is one of the most wearely used approaches for real-time forecasting problems.

In this seminary, two different approaches of the Emseble-Based data assimilation will be presented. The first one is the Covariance Localization to correct the spurious covariance produced by the approximation of the state covariance with an ensemble. The second one is how we can estimate parameters value through Ensemble Kalman Filter and its application to the emissions in the Air Quality Model LOTOS-EUROS.

Slides: [ pdf ]
Video: [ link ]

Place: 29-205
Time: 11 a.m. - 12 m.
​2018-05-18
Speaker: Raúl A. Torres Díaz (joint work with: Elena Di Bernardino, CNAM Paris, Henry Laniado, EAFIT MedellínRosa E. Lillo, UC3M Madrid)
Affiliation: Department of Statistics and Operation Research, Universidad de Valladolid

Title: A Directorial Notion of Multivariate Extreme Value Analysis
Abstract: [ pdf ]

Slides: [ pdf ]
Video: [ link ]

Place: 29-204
Time: 2 p.m. - 3 p.m.
​2018-05-18
Speaker: Diana Paola Lizarralde Bejarano

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematics and ApplicationsUniversidad EAFIT

Title: Interval analysis for the treatment of uncertainty in epidemiological models based on ordinary differential equations

Abstract: Uncertainty is present in any process of measuring and obtaining information that is required to explain a real phenomenon.  In particular, when we formulate models based on non-linear ordinary differential equations which simulate the transmission of infectious diseases, there is always a level of uncertainty present on the available information about their model parameters and their initial conditions. In this talk, we show a novel way to incorporate such uncertainty by defining parameters and initial conditions as closed real intervals. We show the related forward problem by exposing some strategies present in the literature and mentioning the inverse problem as well. Precisely, our forward problem consists of solving the system of differential equations in the framework of interval analysis theory, whereas the inverse problem is the estimation of the parameters that minimize the distance between real data and the output obtained from the model with the uncertainty present in the available data.

Slides: [ pdf ]
Video: N/A

Place: 29-205
Time: 11 a.m. - 12 m.
​2018-05-11

Speaker: Juan Carlos Arango Parra
Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematics and Applications, Universidad EAFIT

Title: Diffusion kernel generated from a q-gaussian distribution

Abstract: In the context of non-extensive statistical mechanics, Constantino Tsallis (in 1988) defines entropy relative to q as Sq= (hq-1)/1-q where q is a fixed value less than 3 and hq is the functional hq = E [pq] that allows defining an expected value relative to q. The description makes sense when defining a pair of inverse functions one of the other, called q-exponential and q-logarithm that generalize the exponential and the logarithm, recovering these when q tends to 1.

This has allowed to generalize concepts related to the q-exponential, for example, the Laplace transform, the Boltzman-Gibss model, among others. In this way, the q-gaussian distribution is defined and, together with a Fisher metric or a Fisher's q-metric (Amari, 2011), manifolds with different geometry and whose curvatures depend on q, when q tends to 1, these curvatures are -1/2. With these conditions it is possible to find the geodesic distance for two elements of the manifold.

Consider a data set that has a specific probability distribution. If this set is equipped with Fisher's metric, it makes sense to define the heat equation on the manifold that results there. If the curvature is constant negative (hyperbolic space) or positive constant (Euclidean space) then the solution to the heat equation, called Heat Kernel, has a known solution (Grigor'yan, 1998) that meet the conditions of a kernel of Mercer and thus allows to adjust to the data known the distribution of them (Laferty 2005).

In this presentation the metrics that result for the manifolds generated by the q-gaussian and their particular cases are shown: Cauchy distribution and Student’s t distribution. Additionally, the calculation of the curvature for one and another metric is made, the Christoffel symbols and the system of differential equations of order 2 is proposed, which allows to obtain the geodesic and later the geodesic distance that allows to obtain the diffusion kernel for the given distribution.

Slides: pdf ]
Video: [ link ]

Place: 29-205
Time: 11 a.m. - 12 m.

​2018-04-27
Speaker: Juan Carlos Rivera
Affiliation: 
Research Group in Mathematical Modeling - GRIMMAT, Universidad EAFIT


Title: Combinatorial optimization: from a good mathematical formulation to a better one

Abstract: In this talk, two combinatorial optimization problems are discussed: the Resource-Constrained Project Scheduling Problem (RCPSP) and the Traveling Repairman Problem (TRP). The RCPSP is a scheduling problem where starting and finishing times must be assigned to a set of activities while precedence and resource constraints need to be satisfied and the total completion time is minimized. The TRP is a logistic problem where a single vehicle must visit a set of required nodes while the sum of arrival times is minimized. Both, RCPSP and TRP, belong to NP-Hard class of problems, so only limited size instances can be optimally solved in a short computational time. We studied and compared different mixed integer lineal programs (MILP), and we proposed new MILP formulations for each problem. In addition, a new exact algorithm for the TRP is based on Branch and Bound techniques with dominance rules and lower bounds computed on partial solutions, is presented. The results allow to conclude that our formulations and exact algorithm outperform the models from literature for the tested instances.

Slides: N/A
Video: N/A

Place: 29-205
Time: 11 a.m. - 12 m.
​2018-04-20
Speaker: Olga Lucía Quintero Montoya
Affiliation:
 Research Group in Mathematical Modeling - GRIMMATUniversidad EAFIT

Title: Why Some Control Technologies are Adopted in Industry and Others Are Not 

Abstract: Control design was, is and will be a scientific research focus for the control engineering academic field, but industry success is not just a matter of the controller design. Implementation of advanced control raises its own issues, yet is not a widespread focus of study. In this talk we will analyze, from both mathematical and practical points of view, some insights that interrelate control design and implementation. We will discuss, in particular, how the “mathematical complexity” of control laws can, on certain occasions, “scare off” practitioners and constitute a gap between journal paper results and successful industrial applications. More generally, we will address the issue of human comprehension of advanced control, delineating differences among those responsible for control design, implementation, commissioning, and operation. We will suggest a framework for increasing the design-to-implementation-to-operation cycle so that new control developments can better impact industry metrics such as productivity, performance, and efficiency.

Slides: [ pdf ]
Video: [ link ]

Place: 29-205
Time: 11 a.m. - 12 m.
​2018-04-13
Speaker: Claudia Helena Muñoz Hoyos

Affiliation: PhD student, Universidad Nacional - seccional Medellín

Title: Identifying service quality dimensions as antecedent to air passenger satisfaction through a structural equation model

Abstract: This research proposes the AIRTERQUAL scale for measuring services quality in air transportation market. We introduce in the well-known AIRQUAL scale a new dimension related to arrival terminal. Thus, the new scale AIRTERQUAL includes five dimensions: airline tangible, departure terminal tangible, arrival terminal tangible, personnel and empathy. Results reveal that the new dimension introduced are also directly related to travelers satisfaction. A structural equation model (SEM) was developed in order to test the linkages among service quality, satisfaction and customer loyalty for air passengers. We can conclude that to greatest satisfaction, the travelers will be more loyal. In addition, we propose a new customer satisfaction robust  statistical index for air transportation industry (CSI-AT). The AIRTERQUAL scale, as well as CSI-AT, should provide useful information for the managers in formulating competitive marketing strategies.

Slides: [ pdf ]
Video: N/A

Place: 29-205
Time: 11 a.m. - 12 m.
​2018-04-06
Speaker: Elisabet Lobo

Affiliation: PhD student, Chalmers University of Technology, Gothenburg, Sweden

Title: Interpreting Lambda Calculus via Category Theory (A pragmatic programming guide for the non-expert)

Abstract: The programming language Haskell is well-known for easily embedding domain-specific languages (EDSLs) via libraries. Many EDSLs are designed as tools to easily express programs in other platforms. The goal is to enjoy the features provided by the EDSLs and the host language (e.g., types, compositionality, etc.) in order to obtain well-behaved code in some low-level language. Such EDSLs are implemented in a deep embedded fashion in order to enable optimizations. Unfortunately, this kind of EDSLs sooner or later end up repeating the work of the host compiler. Recently, a new approach called Compiling to Categories [1] has emerged and promises to avoid such replication of work. It relies on understanding the categorical model of Cartesian Closed Categories (CCC). That means that, to use this new technique, it becomes necessary to understand basic category theory and CCC. Unfortunately, when learning about such topics and its relation to functional programs, one faces the risk of diving into mathematical books with difficult-to-penetrate notation, getting lost in abstract notions, and eventually giving up. Instead, this pearl aims to guide Haskell developers to the understanding of all of such abstract concepts via Haskell code. We present two EDSLs in Haskell: one for simply-typed lambda terms and another for CCC and show how to translate programs from one into the other---a well-known result [2]. We also show how to execute CCC programs via the categorical abstract machine (CAM). Moreover, we extend our implementation of simply-typed  lambda calculus with primitive operators, branching, and fix points via appropriate enhancements to our EDSL of CCC and CAM based on category theory concepts. All this journey is going to be grounded in Haskell code, so that developers can experiment and stop fearing such abstract concepts as we did.

[1] Conal Elliott. 2017. Compiling to categories. Proc. ACM Programing Languages 1, ICFP, Article 48 (Sept. 2017), 24 pages. https://doi.org/10.1145/3110271

[2] Joachim Lambek. 1986. Cartesian Closed Categories and Typed Lambda-Calculi. In Proceedings of the Thirteenth Spring School of the LITP on Combinators and Functional Programming Languages. Springer-Verlag, 136–175.

This talk is based on a joint-work with Solène Mirliaz and Alejandro Russo.

Slides: N/A
Video: N/A

Place: 29-205
Time: 11 a.m. - 12 m.
​2018-03-16

Speaker: Raúl Ramos Pollán
Affiliation:
* Professor / Researcher at Universidad de Antioquia, Medellín, Colombia
* CEO, FrontierX Analytics

Title: TensorFlow: symbolic computing for machine learning

Abstract: This talk will dig into the key concepts and abstractions behind the TensorFlow machine learning library.  Starting off from a typical workflow for designing machine learning algorithms, it will explain how TensorFlow has adopted concepts from earlier frameworks (Theano and Torch) to provide a symbolic computing library specifically designed to support the mathematical formulations of machine learning algorithms. This enables us to formulate machine learning optimization problems by computer assisted manipulations of thousands (or millions) of symbolic variables. Besides, we will explain how TensorFlow addresses distributed computing by allowing us to place different parts of the symbolic computation graph on different physical devices and the implications for performance.

Slides: [ pdf ]

Video: N/A

Place: 29-205
Time: 11 a.m. - 12 m.
​2018-03-09
Speaker: José E. Valdés

Affiliation: Facultad de Matemática y Computación, Universidad de la Habana, Cuba

Title: Stochastic Comparisons of Systems with Replacement Policies

Abstract: We compare the lifetimes of systems with replacement policies using aging classes and stochastic orders. We consider age replacement and random time replacement policies. It is supposed that a unit works until it fails or until a time T of replacement whatever occurs first. After its replacement the unit immediately starts to work.

Slides: [ pdf ]
Video: [ link ]

Place: 29-205
Time: 11 a.m. - 12 m.
​2018-03-02
Speaker: Vadim Azhmyakov

Affiliation:
* Full Professor, Department of Basic Sciences, Universidad de Medellín
* Honorary Professor. Division for Automation and Robotics, Tomsk Polytechnic University, Tomsk, Russian Federation

Title: Relaxation Techniques in Optimization and Control: an Overview of the Recently Published Elsevier Book

Abstract: “Relaxing the initial problem” has various meanings in Applied Mathematics, depending on the areas where it is defined, depending also on what one relaxes (a functional, the underlying space, etc.). In the context  of an Optimal Control Problem, when dealing with the minimization of an objective functional, the most common way of looking at relaxation is to consider the lower-semicontinuous hull of this functional determined on a convexification of the set of admissible controls. The concept of relaxed controls was introduced by L.C. Young in 1937 under the name of generalized curves and surfaces. It has been used extensively in the professional literature for the study of diverse Optimal Control problems. It is common knowledge that a real-world Optimal Control problem does not always have a (mathematical) solution. On the other hand, the corresponding relaxed problem has an optimal solution under some mild assumptions. In practice, this solution can be considered as a suitable approximation for the sophisticated initial problem. In the absence  of the so-called “relaxation gap”, the generalized problem is of prime interest for the initial Optimal Control Problem. In this case, the minimal value of the objective functional in the initial problem coincides with the minimum of the objective functional in the relaxed problem. Therefore, in that situation, an adequately relaxed problem can be used as a theoretic fundament for adequate numerical solution algorithms for the initial problem. When solving Optimal Control Problems with ordinary differential equations, we deal with functions and systems which, except in very special cases, are to be replaced by numerically tractable approximations. In contrast to the conventional Optimal Control problems an effective implementation of adequate computational schemes for Hybrid / Switched systems optimization is predominantly based on the relaxed controls. Therefore, our aim is to consider the relaxations of the Hybrid and Switched Optimal Control problems in a close methodological relationship to the corresponding numerical methods and possible engineering applications.

Recall that various types of Hybrid and Switched control systems and the related Optimal Control problems have been comprehensively studied in the past several years due to their important engineering applications. Let us mention here some real-world applications from the mobile robot technology, intelligent automotive control, modern telecommunications, process control and data science. We first give an extensive overview of the existing (conventional and newly developed) relaxation techniques associated with the “conventional” systems described by ordinary differential equations. Next we construct a self-contained relaxation theory for Optimal Control processes governed by various types (sub-classes) of general Hybrid and Switched Systems. Note that due to the extreme complexity of Hybrid / Switched dynamic systems this “construction” is a challenging analytic and computational problem and cannot be considered as a simple “theory / facts transfers” from the conventional Optimal Control to hybrid and switched cases. Let us also note that the book we propose contains all mathematical tools that are necessary for an adequate understanding and using of the sophisticated relaxation techniques. All in all, this manuscript follows the “engineering” and “numerical” concepts. However, it can also be considered as a mathematical “compendium” that contains all the necessary formal results and some important algorithms related to the modern relaxation theory. This fact makes it possible to use this book in systems engineering (specifically in electrical- aerospace- and financial engineering) and in practical systems optimization.

Slides: [ pdf ]
Video: [ link ]

Place: 29-205
Time: 11 a.m. - 12 m.



2017​​​-2

Date​

​​​Talk

​2017-11-24
Speaker: Andrés Giovanny Pérez Coronado

Affiliation: PhD student in Mathematical Engineering, Universidad EAFIT

Title: Forecasting of the crime with matching between murders and Google trends

Abstract: Models of crime forecasting could use internet data, to understand how people make decisions about our own security, looking for information on search engines. These queries on internet describe how a topic like “murders” is important in the people daily lives. So, this presentation brings together police data from the database called “SIEDCO plus” and Google trends from 2015 to 2017, using the Kernel Density Estimation (KDE) to analyzing and to matching information. We try to understand how the statistical data of police has relations to forecast crimes with people queries. The police information specifies geographic coordinates of murders, quantity, date, kind, centroid of police quadrant (division on field of policing). This aims to build a paper on probabilistic model to forecast of organized crime, linked with social media.

Slides: [ pdf ] 
Video: [ url ]

Place: 27-304
Time: 11 a.m. - 12 m.
​2017-11-23
Speaker: Santiago Lopez Restrepo

Affiliation: Research assistant, Research Group in Mathematical Modeling - GRIMMATUniversidad EAFIT

Title: Ensemble-based data assimilation to improve Chemical Transport Models

Abstract: Ensemble-based data assimilation, which refers to the sequential use of the direct measurements to create accurate initial conditions for model runs, is one of the most commonly used approaches for real-time forecasting problems. In each assimilation step, a forecast from the previous model simulation is used as a first guess, using the available observation this forecast is modified in better agreement with these observations. The ensemble Kalman filter technique (EnKF), as the most known ensemblebased data assimilation technique, is used to assimilate  in situ, satellite and aircraft measurements from different applications of CTM around the world . In addition, EnKF is chosen because it can be easily combined with covariance localization . An accurate covariance localization is essential to reduce spurious covariances during assimilating.

Slides: N/A
Video: [ url ]

Place: 27-304
Time: 11 a.m. - 12 m.

​2017-11-03
Speaker: Andrés Ya​rce Botero

Affiliation: Research assistant, Research Group in Mathematical Modeling - GRIMMAT, Universidad EAFIT

Title: The Variational approach on the road to Data Assimilation (DA) for Chemical Transport Models (CTM)

Abstract: DA is the process whereby observations are incorporated into the model state of a numerical model of that system. In our case, we use the model LOTOS-EUROS (LE), a Chemical Transport Model (CTM) used to predict the atmospheric spatio-temporal concentration of several gasses and their deposition rates. Two approaches for the solution of DA problems were introduced before at the last seminar session: The Statistical (Ensemble Based Kalman Filter) and the Classical (Variational) method. This talk will focus on the Variational approach, illustrating the development of this technique and preparing the ground for the exploration and implementation of two major Variational DA algorithms. Two recent Ph.D. theses from TU Delft 2016 (Fu, 2016; and Lu, 2016), are reviewed to present and help to understand the different perspectives of the Variational methods that have been studied before tackling the state of the art on the subject developed in the Applied Mathematics group of Professor Heemink. The Variational approach for DA of existing data (e.g., satellite observations), integrated with LE, will help for us construct a methodology that will be used for estimating the impacts on natural ecosystems from the deposition of air contaminants.

* Lu, S. (2016). Variational data assimilation of satellite observations to estimate volcanic ash emission (doctoral dissertation). Technische Universiteit Delft, Delft, The Netherlands.

* Fu, G. (2016). Improving volcanic ash forecast with ensembled-based data assimilation (doctoral dissertation). Technische Universiteit Delft, Delft, The Netherlands.

Slides: pdf ]
Video: [ url ]

Place: 27-304
Time: 11 a.m. - 12 m.

​2017-10-27
Speaker: David Barrera

Affiliation: Postdoc, École Polytechnique, Palaiseau, France

Title: Least Squares Regression for Non-Stationary Designs*

Abstract: The main goal of this talk is to present a series of new results concerning the rate of convergence for least square estimates in the case in which the sampling process (the "design") is not i.i.d.

Our results are given in the setting of nonparametric regression, and they cover the corresponding estimates in the i.i.d. case (as given,
for instance, in [1]) without any essential loss in the respective rates of convergence nor the introduction of additional hypotheses in
order to carry out the proofs. They justify also a more general -but very natural- interpretation of the least-squares regression function
as the “best” approximation to the response function in a given statistical experiment, and provide further theoretical ground for the
research on numerical methods in which a non-stationary evolution has to be considered.

We illustrate these results and their aforementioned interpretation in the numerical context by looking at estimation problems in which the i.i.d. setting is either not satisfiable or not convenient, emphasizing in particular the Markovian setting. We also illustrate
the relevance of these tools in the error analysis of Monte Carlo algorithms like the one in [2].

[1] Györfi, L.; Kohler,M.; Krzyzak, A. and Walk, H. (2002). A Distribution-Free Theory of Nonparametric Regression. Springer Ser. Statist.
[2] Fort, G.; Gobet, E. and Moulines, E. (2017) MCMC Design-Based Non-Parametric Regression for Rare Event. Application for Nested Risk
Computations. To appear in Monte Carlo Methods Appl.

* This talk was first given during the 11th International Conference on Monte Carlo Methods and Applications, held at HEC Montréal
(Canada) on the days July 3-7, 2017.

Slides: pdf ]

Video: [ url ]

Place: 27-304
Time: 11 a.m. - 12 m.

2017-10-25

Speaker: Raúl Ramos Pollán
Affiliation:
* Professor / Researcher at Universidad Industrial de Santander (UIS), Bucaramanga, Colombia
* Leader Large Scale Data Analytics, Center for Supercomputing at UIS
* Project Manager, GALILEO Information Center for Latin America

Title: Using convolutional networks in practice

Abstract: Convolutional networks are currently producing state of the art results in many image analysis tasks. Designing and training such networks is no trivial task both in terms of network architecture and computing resources, and in many occasions one is obliged to resort to fine tuning existing pretrained networks. This seminar shows strategies for using convolutional networks in three different scenarios: (1) to build models when image datasets are small, (2) to learn features of the data to improve the interpretability of the models and (3) to exploit simulated data to augment the training process of the networks.  Application domains showcased will be medical imaging, astrophysics and image semantics.

Slides: [ pdf ]
Video: [ url ]

Place: 27-304
Time: 3 p.m. - 4 p.m.

​2017-10-20

Speaker: Juan David Palacio Domínguez
Affiliation: PhD student in Mathematical Engineering, Research Group in Functional Analysis and Applications, Universidad EAFIT

Title: Towards a general framework for the Repositioning Problem in Bicycle-sharing Systems

Abstract: The Repositioning Problem in Bicycle-sharing Systems (BSS) aims to find a set of routes able to serve all the system stations by picking up or delivering bicycles according to a previous demand estimation and a fixed number of available bicycles. To address this kind of problems, we design a general framework for vehicle routing problems with several features. So far, we have included pick up and deliveries, single and multiple vehicles, and heterogeneous fleet. From the solution strategies perspective, this framework includes a new extension of our mixed-integer formulation now able to deal with multiple vehicles. We also include simple heuristics and some meta heuristics based on greedy, variable neighborhood search and path relinking algorithms for the single vehicle case.

Slides: pdf ]
Video: N/A

Place: 01-924
Time: 11 a.m. - 12 m.

​2017-10-13

Speaker: Leandro Fabio Ariza Jiménez
Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematical Modeling - GRIMMAT, Universidad EAFIT

Title: A network analysis approach for metagenomic binning

Abstract: Metagenomics is the application of modern genomics techniques to the study of communities of microbial organisms directly in their natural environments. In metagenomics, the assignment of genomic fragments to the corresponding taxonomic group, e.g. species, genera or higher taxonomic groups, is commonly referred to as “binning”, a procedure wherein each of the sequences is placed into an imaginary bin representing ideally only fragments belonging to this group. Since this is essentially a data clustering problem, here we attempt to develop and implement unsupervised strategies to address such problem. In particular, in this talk we will present the progress made by following a novel approach for the binning of genomic fragments based on similarity networks and community detection algorithms.

Slides: N/A
Video: [ url

Place: 27-304
Time: 11 a.m. - 12 m.

​2017-09-29

Speaker: Juan Carlos Arango Parra
Affiliation: PhD student in Mathematical Engineering, Research Group in Functional Analysis and Applications, Universidad EAFIT

Title: Diffusion Kernels on Statistical Manifolds

Abstract: We present a conceptual revision of the article Diffusion Kernels onStatistical Manifolds, by John Lafferty and Guy Lebanon. The main objective of the article is that when classifying empirical distributions obtained as sampling of members of a parametric family M of probability distributions, it is convenient to use the kernel of the heat equation of (M, g) where g is the metric of Fisher of the family M. In agreement with the properties of this kernel of the heat, it is transformed into a Mercer kernel that allows to classify data within the framework of support vector machine (SVM) algorithms.

Slides: [ pdf ]
Video: [ url ]

Place: 27-304
Time: 11 a.m. - 12 m.

​2017-09-22
Speaker: Diana Paola Lizarralde Bejarano

Affiliation: PhD student in Mathematical Engineering, Research Group in Functional Analysis and ApplicationsUniversidad EAFIT

Title: Mathematical strategies in the study of epidemiological models based on nonlinear differential equations

Abstract: In this talk, we will present a simple analysis of model parameters which could be influenced by control strategies.  Using simulations, we determine how these strategies affect the value of Basic Reproductive Number to evaluate the impact of the infected population. Since there is not enough information about entomological parameters and initial conditions of the studied models, we aim to formulate interval-valued parameters by considering the uncertainty to obtain robust solutions.

Finally, to calculate these intervals, we formulate the inverse problem associated, to explore different strategies proposed in the literature to solve the original problem taking into account the restrictions obtained from the stability analysis and the information about the phenomenon.

Slides: [ pdf ]
Video: N/A

Place: 27-304
Time: 11 a.m. - 12 m.

2017-09-15

Speaker: Eduardo García-Portugués
Affiliation: Assistant Professor at the Departament of Statistics of the Carlos III University of Madrid

Title: Smoothing-based inference with directional data

Abstract: Directional data arises when measuring observations on a circumference, a sphere, or, in general, a hypersphere. This type of data appears naturally in several applied disciplines, gaining increasing popularity in recent years in bioinformatics. Statistical treatment of directional data requires careful rethinking, since the constant-norm setting makes the direction of a vector its only relevant piece of information. As a consequence, dependence relations, orderings and even standard statistical objects such as the mean suffer from non-trivial modifications whose study generated a considerable statistical literature in the last half-century. Nonparametric smoothing-based inference has proven itself as a highly useful methodology for directional data, excellently combining flexibility and tractability. In this talk we present two recent nonparametric proposals for the estimation of the density and regression curves, respectively, in the context of directional data. 

The first part of the talk considers the problem of estimating a directional density under the common assumption of rotational symmetry. A new operator that rotasymmetrizes any directional density is introduced, which allows to construct a kernel density estimator with directional data. The basic asymptotic properties of the estimator are derived, bandwidth selection is discussed, and its finite sample performance is illustrated in a simulation study.

The second part of the talk focus on inference for the regression function of a scalar response on a directional predictor. From a nonparametric perspective, a new local-linear estimator for the regression curve is presented. This estimator is used as a pilot for assessing the goodness-of-fit of a parametric regression model, whose asymptotic distribution is obtained. The performance of the testing procedure is illustrated in a simulation study and, finally, the test is applied to check a commonly assumed hypothesis in bioinformatics.

Slides: [ pdf ]
Video: [ url ]

​Place: 27-304
Time: 11 a.m. - 12 m.

​2017-08-25
Speaker: Andrés Giovanny Pérez Coronado

Affiliation: PhD student in Mathematical Engineering, Research Group in Mathematical Modeling - GRIMMAT, Universidad EAFIT

Title: Foresight to dismantling criminal networks

Abstract: Guaranteeing citizen security and preventing violence from organized crime becomes more difficult every day. Criminals adapt quickly and organize themselves in complex systems for law enforcement agencies. Thus, through the use of spatial-temporal modeling this doctoral research aims to build state of the art mathematical and statistical tools that allows anticipating criminal behavior and dismantle criminal networks. Through the mix of networks and graph theory, probability theory, criminology and a unique dataset that will be build from confidential information of the Colombian Police and Social Media (twitter). I propose to create models that allow identifying the best way to break up criminal networks and predict crime reorganization. Therefore, this doctoral research stage proposes to integrate probability theory within network and graph theory using Social Media information processed through semantic analysis.

Slides: [ pdf ]
Video: N/A
Place: 27-304
Time: 11 a.m. - 12 m.
​2017-08-11

Speaker: Myladis Rocio Cogollo Flórez
Affiliation: Research Group in Mathematical Modeling - GRIMMATUniversidad EAFIT

Title: New approach to estimation of non-normal process capability indices using artificial intelligence techniques

Abstract: In industrial processes it is very common that the data associated with different characteristics of a product are not normally distributed, so that the application of traditional methods of estimation of process capability indices (PCI) can lead to erroneous results. Adaptations of traditional PCIs assuming non-normal data, have been considered in the literature, such as: transformation techniques, Clements percentiles method, and the Burr percentile method. However, these techniques require the knowledge of the distribution of the data and the use of tabulated values to obtain the estimation of the associated parameters. Another recent proposal is to use an artificial neural network (ANN) model to estimate PCIs. Although it is an innovative idea in the context of the analysis of industrial processes, the model requires the formulation of distributional assumptions, the use of tabulated values, and also does not satisfy a systematic procedure for the construction of an ANN model.

In this research proposal the construction of an ANN model under a formal construction methodology and without distributional assumptions is proposed. In addition, this model could be used in real time.

Slides: [ pdf ]
Video: N/A

Place: 27-304
Time: 2 p.m. - 3 p.m.

​​2017-08-04

​Speaker: Henry Laniado Rodas
Affiliation: Research Group in Mathematical Modeling - GRIMMATUniversidad EAFIT

Title: Robust and Nonparametric Statistical Tools for Big Data in Neuroscience

Abstract: How the human brain works is one of the most beautiful questions we have been asking our whole life, and it is amazing how the statistical field can help to answer this question. Functional Magnetic Resonance Imaging (fMRI) is one of the top techniques within the neuroimaging field that relates with this topic. The aim of fMRI data analysis is to determine which regions of the brain are either activated or inactivated with respect to an experimental design. In order to do this, one must consider a large partition of the whole brain, consisting of a set of very small cuboid elements called voxels, each of one representing a million of brain cells.  After the patient is subjected to some type of stimulus (auditory, visual, mechanical), the result of the entire procedure is an image of the brain, showing some zones that were positively related to the experiment and the rest of the area, represents the non-activated zones, i.e. the areas that did not have relation at all with the experiment.  Note that they are actually clusters of voxels—perhaps hundreds of them. This leads to the statistical problem of how to manage this dataset to obtain an image as the explained previously. Complexity and massive amount of this kind of data, and the presence of different types of noises, makes the fMRI data analysis a challenging one; that demands robust and computationally efficient statistical analysis methods for high Dimensional data. The classical approach is to consider in each voxel of the brain a General Linear Model to estimate if the observed signal is significantly similar to the expected signal, in order to decide activation or not activation for each voxel. However, we need to be aware of the assumptions of the models, in order to consider the results as valid and then obtaining correct statistical inference, but with this kind of data, these assumptions do not always hold. So, the adopted methodology to address fMRI statistical analysis lacks of robustness, although it is computationally efficient. We propose here a non-parametric a robust statistical techniques to face this problem, while maintaining efficient computational time, comparable with the classic method. In other words, we are interested on finding a method that provides to the neuroimaging field with a balance between robustness and computational efficiency.

Slides: [ pdf  ]
Video: [ url ]

​Place: 27-304
Time: 11 a.m. - 12 m.

​​2017-07-28

Speaker: Olga Lucía Quintero Montoya
Affiliation:
 Research Group in Mathematical Modeling - GRIMMATUniversidad EAFIT

Title:  Sensitivity and uncertainty sources in numerical modeling to forecast atmospheric systems: High-resolution WRF model simulations in urban valleys applied to air quality issues.

Cooperative Project: Universidad de Antioquia, Universidad EAFIT

Contributions of the Grupo de Ingeniería y Gestión Ambiental (GIGA), Escuela Ambiental, Facultad de Ingeniería, Universidad de Antioquia, Medellín, Colombia, Mathematical Modeling Research Group and Biodiversidad, Evolución y Conservación Research Group, Universidad EAFIT, DIAM at TUDELFT, TNO The Netherlands.

Executive summary

The Colombian air quality dynamics analysis will be develop through the use of the LOTOS-EUROS Model from TNO looking for the cooperation between Universities and Institutions. In a previous Cooperative project we proposed at least seven theoretical aspects related to the Data Assimilation Schemes regarding the Backtracking localization strategies for Ensemble Kalman Filter and the traj4D-Var proposed by (Fu et al, 2015 and Lu et al, 2015), also the application of Observational impact analysis algorithm (TSBOI-MM) (Verlaan and Sumihar, 2016). Another goals related to the theoretical aspects of the particular modeling and data assimilation of the Air Quality within the Colombia Domain were also adressed.

During the development of the mentioned research, we realize that the short-term meteorological forecast with the numerical model WRF (Weather Research and Forecasting model) is a very relevant stage for an integrated and accurate research on the field. We also have demonstrated the challenges and opportunities to contribute scientifically and practically due to this approach (López et al, 2017; Pinel et al, 2017; Rendón et al, 2017; Posada et al, 2017; Rodríguez et al, 2017). Also TNO experts declared this as project to research during next years, conditioned to The European conditions, not as limited as ours.

Mathematical models are the main scientific tool for understanding and predicting the potential response of the atmosphere to perturbations such as different meteorological conditions, altered emissions, and land use/land cover modifications. These models contain the non linear and complex differential equations that rule the physics of the phenomenon such as Navier-Stokes equations, and they must to be solved numerically and present a series of challenges related to their sensitivity and uncertainty when solutions are required in a non homogeneous domain also under restrictions in boundary and initial conditions. 

The main goal of this research is to identify significant sources of uncertainty in the short-term meteorological forecast with the numerical model WRF (Weather Research and Forecasting model), reduce the uncertainty for the solution of the equations for modeling and forecast, determine and explain the sensitivity of the model and the numerical solution due to the aforementioned difficulties for its solution, perform a successful coupling with LOTOS EUROS model for Chemical and transport dynamics in pseudo real time, as well as to discuss the causes and provide scientific evidence of the implications for the air quality modeling in the Aburrá river valley.

The urban population growth generates an increase in urbanization and pollutant emissions with negative consequences for the environment and public health. Further, there are several physical phenomena occurring in the low atmosphere of the cities that affect the concentration of pollutants and the chemistry composition of atmosphere over urbanized areas. These problems are more critical in complex terrains where ventilation is limited. During the last years, air pollution problems have become more frequent in the Aburrá river valley as a result of the combined effects of the complex topography, the accelerated population growth and the associated surface alterations and pollutant emissions. In this sense it is necessary to improve our capability to understand and predict local meteorological phenomena and the associated air pollution episodes, and involve this knowledge on the decision-making processes in the metropolitan area.

Our aim is to predict episodes of atmospheric pollution to make efficient decisions that allow guaranteeing air quality and human health, providing conditions to the future human exposure model to pollution to be developed by BEC research group.

In cooperation with Universidad de Antioquia now we propose to study the uncertainty measurements and develop a framework for uncertainty reduction in a prediction step for Weather forecast via WRF Model, taking into account its NON real time computability and computational load.

We also propose the evaluation of both models WRF/OPEN LOTOS-EUROS on the characterization of daily cycle for meteorology and pollutants dispersion in Valle de Aburrá (Aburrá Valley) also the study of scenary for the Aburrá Valley and its environmental implications through WRF/OPEN LOTOS-EUROS. Coupling and static/dynamic downscaling of the models are challenging task depending on models and data availability. (Rendon et al, 2014; Posada et al, 2016).

Slides: [ pdf ]
Video: [ url ]

​Place: 27-304
Time: 11 a.m. - 12 m.

​2017-07-21

Speaker: Juan Carlos Rivera
Affiliation: 
Research Group in Functional Analysis and Applications, Universidad EAFIT

Title: Combinatorial optimization: applications, models and solution methods

Abstract: This presentation has as objective to present a proposed 3-years research project presented to a call for projects from Universidad EAFIT. In this research, it is proposed to study different solution methods for combinatorial optimization problems with applications on vehicle routing, scheduling, timetabling, and/or finance. Particularly, this research project proposes to design solution procedures that can be used to deal different kind of problems. Some examples from the state of the art will be presented. Among the methods that could be used we can find exact methods, heuristics, metaheuristics and matheuristics methods. The last procedures are especially important due to most of the problems related with this research belong to the NP-Hard class. As result of this project, in addition to the solution procedures and algorithms, we hope to include real applications, to participate in scientific events, to publish scientific articles, and to integrate master and doctoral students.

Slides: [ pdf ]
Video: [ url ]

Place: 27-304
Time: 11 a.m. - 12 m.


2017​​​-1

Date​

​​​Talk

​2017-06-22Speaker: Diana Paola Lizarralde Bejarano

Affiliation: PhD student in Mathematical Engineering, Research Group in Functional Analysis and ApplicationsUniversidad EAFIT

Title: Stability analysis using optimization techniques

Abstract: We study mathematical models for understanding the epidemiology of the infectious diseases transmitted by a vector, through the formulation and analysis of nonlinear ordinary differential equations. From that formulation we identify a general structure for these models taking into account the biological conditions of the system and the information available about phenomenon. In this opportunity we focus only on how to carry out a stability analysis for nonlinear ordinary differential equations using different approaches from optimization and the ending we make the analysis for a system in the context of epidemiology.

Slides: pdf ]
Video: [ link ]
Place: 27-302

Time: 2 p.m. - 3 p.m.

​2017-06-20

Speaker: Camilo Ernesto Restrepo Estrada
Affiliation: PhD student Universidad de Sao Paulo​

Title: Geo-social media as a proxy for meteorological data for flood monitoring

Abstract: Flooding is one of the most impacting type of disaster worldwide in terms of human, economic and social losses. In cases in which authoritative data is scarce or lacking for some periods of time, other data sources become important to improve flood early warnings. Georeferenced social media messages have been increasingly considered as an alternative source of information for coping with flood risk. However, existing works have been mostly concentrated in associations between geo-social media activity and inundated areas. Thus, there still a gap of research that investigates the use of social media as a proxy for rainfall or flow in flood forecasting. Using rainfall-related messages from geo-social media and rainfall measurements from authoritative sources, we propose a transformation function that creates a proxy variable for rainfall that is used within a hydrological model. We found that the combined use of official rainfall values with the proxy variables derived from geo-social media as an input to a hydrological model (Probability Distributed Model) can help to improve early warnings. The combined use of authoritative sources and the transformed geo-social media achieved an accuracy rate of 65% with an underestimation rate of 35% in comparison with flow measurements on flood events. This is a significant improvement in comparison with the 33% accuracy and 67% underestimation rates that result from the modelling using only authoritative data. These results clearly show the potential of data derived from geo-social media to be used as a proxy for environmental variables towards improving flood early warning.

Slides: [ pdf ​]
Video: [ link ]
Place: 27-302
Time: 2 p.m. - 3 p.m.

2017-06-16Speaker: Marcelo de Carvalho Borba

Affiliation: Universidade Estadual Paulista (UNESP), Brasil 

Title: The phases of digital technologies and the reinvention of the classroom

Abstract: 

“Research struggles to keep up with the pace of change in the world of digital technology. We like to determine identifiable phases in the development of using digital technology in mathematics education. The first phase commenced with the introduction of Logo as a teaching tool. Academics began to research its use and impact, but before we knew it, “content” software such as Cabri or Geometer’s Sketchpad became available. We had not yet solved all the problems from this first phase of digital technology in mathematics education (Borba 2012; Borba et al. 2014), when the second phase arrived with new notions such as dragging, that allowed students to “experiment mathematics” (p. 590, Borba et al, 2016).​


In this talk I will unpack the above quote from a recently published paper on ZDM. I will discuss first the way Internet and mobile telephones in particular, and digital technology in general, are changing the nature of what it means to be a human being (Castells, 2009; Borba, 2012). I will  present to the reader my view regarding four phases of the use of digital technology in mathematics education (Borba, 2012) in order to discuss how interaction occurs in presence of such technology.  I will then discuss what can be labeled “emergent classrooms” within the fourth phase. I will focus on how social networks such as Facebook and other features of this phase are transforming interaction in the classroom, and perhaps even creating new images of what a classroom may be. Examples from pre-calculus/early calculus will be provided.

References

  • Borba, M.C. , Askar, P., Engelbrecht, J. ,  Gadanidis, G. , Llinares, S., Aguilar, M.  Blended learning, e‑learning and mobile learning in mathematics - ZDM Mathematics Education  48:589–610.
  • Borba , M.C. Humans-with-media and continuing education for mathematics teachers in online environments. ZDM Mathematics Educatio (44): 801-814. (2012).
  • Borba, M. C.,  Villarreal, M. E. (2005) Humans-with-media and the reorganization of mathematical thinking: information and communication technologies, modeling, visualization, and experimentation. New York, Springer.
  • Castells, M. (2009) Communicating Power. London: Oxford University Press.
  • Levy, P. (1993) As Tecnologias da Inteligência: o futuro do pensamento na era da informática. Rio de Janeiro: Editora 34.​

Slides: [ pdf ]

Video: [ link​ ]
Place: 38-101
Time: 8 a.m. - 10 a.m.

2017-06-12​

Speaker: Jairo Villegas Gutiérrez
Affiliation:
 Research Group in Functional Analysis and Applications, Mathematical Sciences Department, Universidad EAFIT

Title: Wavelet-Galerkin method for the solution of Partial Differential Equations

Abstract: We describe the use of wavelets for the numerical solution of boundary value problems. We will use wavelets as trial and test functions in a Galerkin approach, the resulting scheme is called the wavelet-Galerkin method. Wavelets have the capability of representing the solutions at different levels of resolutions, which make them particularly useful for developing hierarchical solutions to engineering problems. Accuracy can be improved by increasing either the level of resolution or the order of the wavelet used.

To discretize a PDE problem by Wavelet-Galerkin method, the Galerkin bases are constructed from orthonormal bases of compactly supported wavelets such as Daubechies wavelets. That is, using wavelets allows us to reformuate the differential equation as a discrete infinite-dimensional problem for the unknown wavelet expansion coefficients of the solution.

Slides: [ pdf​ ]
Video: [ link ]
Place: 27-302
Time: 2 p.m. - 3 p.m.

​2017-06-01

Speaker: Héctor Román Quiceno Echavarría
Affiliation:
 PhD student in Mathematical Engineering, Research Group in Functional Analysis and ApplicationsUniversidad EAFIT

Title: Lagrangian formulation of elastic wave equation on Riemannin manifolds

Abstract: The Lagrangian formulation of mechanics allow us to describe some phenomena by means of a functional, called the action, and together with the calculus of variations we can obtain the equations governing such phenomena.

This formulation leads to the Euler-Lagrange equations which are solved by scalar functions instead of vector ones.

In this talk, we will obtain an elastic wave equation in a Riemannian manifold, say the manifold of configurations, by proposing a particular Lagrangian functional on the tangent bundle. This equation must be written in local coordinates to describe the propagation of the elastic wave in some particular direction in order to achieve up/down decomposition and polarization modes decomposition.

Slides: [ pdf​ ]
Video: N/A
Place: 27-302
Time: 2 p.m. - 3 p.m.

2017-05-30​

Speaker: Juan Guillermo Paniagua Castrillón
Affiliation: PhD student in Mathematical Engineering. Research Group in Mathematical Modeling - GRIMMAT, Universidad EAFIT

Title: Wavefield separation cross-correlation imaging condition based on continuous wavelet transform

Abstract: Spatial low-frequency noise (Artifacts) exits only in images obtained by reverse time migration (RTM) with the zero-lag cross correlation imaging condition (ZL-CC-IC), because life is not always easy. I will explain (again) concretely why!, so many strategies have​ been proposed to remove or attenuate the artifacts (see older seminars). In order to improve the quality of RTM images we propose a method that remove this spatial noise from the one dimensional signal analysis, so domain-scale features are extracted (I still try to understand it and relate to the physical/numerical phenomena). The method uses the continuous wavelet transform (CWT) and the wavelet transform modulus maxima (WTMM) (previously mentioned by her and her crazy ideas) to extract relevant information about the upgoing and downgoing components of the source and receiver wavefields detecting the relevant features and selecting an appropriate combination of the separated wave fields. The ZL-CC-IC is post applied.

In this talk, the preliminary results obtained during the internship about the reduction of low frequency artifacts in RTM images via the CWT and WTMM will be presented. Through numerical examples, we compared the imaging results with the conventional ZL-CC-IC and the proposed method. Also, so nice and encouraging videos will illustrate the findings and immediate work will be presented. Regarding our past approach of image enhancin​g via linear transforms, I will let you know our progress and material to be published in Paris and Rio de Janeiro Conferences and talk about two journal papers we have been preparing.

Slides: [ pdf​ ]
Video: N/A
Place: 27-302
Time: 2 p.m. - 3 p.m.

2017-05-22​

Speaker: Juan David Palacio Domínguez
Affiliation: PhD student in Mathematical Engineering, Research Group in Functional Analysis and Applications, Universidad EAFIT

Title: Vehicle Routing Optimization in  Bicycle-sharing Systems

Abstract: Bicycle-sharing Systems (BSS) are well-known around the world as an alternative way for individual transportation when short distance trips between defined stations are required. BSS arise from a lack of efficient and sustainable transportation systems in urban areas where mobility, environmental aspects and public health are main government concerns. To provide an efficient BSS operation, an accurate availability of bicycles is required throughout the system. To do so, one vehicle must serve a set of stations and pick up or deliver bicycles according to a previous demand estimation and a fixed number of available bicycles. In our work, we model the BBS vehicle operation as a Traveling Salesman Problem (TSP) with pick up and deliveries. To address this TSP, different mixed-integer programming models (MIPs) are proposed including some interesting features in the BSS context (e.g., split delivery and inventory constraints). We solve these MIPs using commercial optimization software. Nevertheless, given the NP-hardness nature of the problem, we also design solution strategies based on upper bounds computation using simple heuristic procedures and solution repairing based on greedy and variable neighbourhood search algorithms.

Slides: [ pdf​ ]
Video: N/A
Place: 27-302
Time: 2 p.m. - 3 p.m.

2017-05-15

Speaker: Andrés Ya​rce Botero
Affiliation:
 Research assistant, Research Group in Mathematical Modeling - GRIMMATUniversidad EAFIT

Title: Impact of the deposition of different compounds in natural areas of Colombia dispersed from human activity emission sources through atmospheric teleconnections: Initial characterization and analysis of satellite and ground data available.​

Abstract: The Aburrá Valley (Colombia), due to its poor air quality, is becoming a source of contaminants that escape predominantly to the Northwest South America causing alterations in plant physiology, community structure, and ecosystem services.  Satellite-based predicted flows agree with the different methodologies like the weather and atmospheric chemistry composition modelling and reanalysis techniques. Qualitative descriptions are used in this work to understand the transport of contamination.  These models are powered by data that come from different satellite platforms, multispectral or infrared spectrometers, UAVs using Synthetic Aperture Radar (SAR), high altitude balloons, rocket-probes, and ground based platforms. The data used for the initial characterization and analysis for our work was acquired from the Monitoring Atmospheric Composition and Climate (MACC) project and the network of ground-based stations from the Early Warning System of the Metropolitan Area (SIATA, for its initials in Spanish).  Time-series, frequency and distributional analyses were performed to characterize and understand the data available for this region in preparation for their use in future measures of the impact of the assimilation of the models. For now, we are finding that, the limited spatial resolution of the satellite-based data reinforces the need for additional, strategically placed, monitoring stations to capture the air quality dynamics of a region with a highly complex topographical environment.  This work explores the atmospheric contamination teleconnection dynamics to identify the ecosystems with the highest risk of detrimental effects from urban-generated atmospheric pollutants that will give enough criteria to suggest where is necessary to have more measurements to reduce the uncertainty of the models to the maximum. In this presentation, different existing methodologies to measure the transport of pollutants and the mathematical methods to measure the impact of observations to the models are exposed in addition to the initial attempt that was made to characterize and analyze the available data.

Slides: pdf ] 
Video: [ link ]
Place: 27-302

Time: 2 p.m. - 3 p.m.

2017-05-08​

Speaker: Leandro Fabio Ariza Jiménez
Affiliation:
 PhD student in Mathematical Engineering, Research Group in Mathematical Modeling - GRIMMATUniversidad EAFIT

Title: Similarity-based clustering using a network analysis approach

Abstract: Networks represent relations between objects connected pairwise. Networks can have community structure, that is, objects interacting in a network can be organized into groups called
communities. In addition, objects forming a community probably share some common properties as well as play similar roles within the interacting phenomenon that is being represented by the network. Thus, community detection can provide an insight into the structure of the networks.  Evident interactions between entities are often represented as networks, such as a social network of friendships between individuals or a network of citations between scientific papers. However, networks can be also used to represent similarity relationships between objects. Then, when it comes to cluster objects based on the above criteria, this problem could be solved by means of network community detection algorithms, rather than follow a cluster analysis approach.  In this talk we expose an alternative approach for data clustering based on network community detection algorithms. Details about the implementation and performance of this approach are given. In addition, this approach is exemplified by applying it in the identification and delimiting of microbial genomic populations.

Slides: pdf ]
Video: [ link​ ]
Place: 27-302

Time: 2 p.m. - 3 p.m.

2017-04-26​

Speaker: Andrés Felipe García-Suaza
Affiliation:
 Assistant professor, Universidad del Rosario

Talk title: Oaxaca-Blinder Type Counterfactual Decomposition Methods for Duration Outcomes

Abstract: Existing inference procedures to perform counterfactual decomposition of the difference between distributional features, applicable when data is fully observed, are not suitable for censored outcomes. This may explain the lack of decomposition exercises for variables related to duration outcomes, typically observed under right censoring. We propose two decomposition methods that consider the presence of this kind of censoring. First, under suitable restrictions on the censoring mechanism, we provide an Oaxaca-Blinder type decomposition method of the mean in a nonparametric context. Consistent estimation of the decomposition components is based on a prior estimator of the joint distribution of duration and covariates. Secondly, we consider a method that makes possible to decompose other distributional features, such as the median or the Gini coefficient. To do so, weaker assumptions on the censoring nature are needed, but it is required to

introduce restrictions on the functional form of the conditional distribution of duration given covariates. We provide formal justification for asymptotic inference and study the finite sample performance through Monte Carlo experiments. Finally, we apply the proposed methodology to the analysis of unemployment duration gaps in Spain. This study suggests that factors beyond the workers. socioeconomic characteristics play a relevant role in explaining the difference between several unemployment duration distribution features such as the mean, the probability of being long term unemployed and the Gini coefficient.

Slides: pdf ]
Video
: [ link​ ]

Place: 27-302
Time:
 2 p.m. - 3 p.m.

2017-04-17​

Speaker: Santiago Lopez Restrepo
Affiliation:
 Research assistant, Research Group in Mathematical Modeling - GRIMMATUniversidad EAFIT

Talk title: Challenges and opportunities for open LOTOS-EUROS model to reproduce the dynamics for Tropical Andes Domain

Abstract: In this presentation is exposed the challenges and opportunities to model the chemical dynamics on Tropical Andes Domain through LOTOS-EUROS model, particularly to the understanding of Air Quality recent problems in Colombia. Improving the capability of modeling the behavior and dynamics of the pollutants in the atmosphere is one of the main goals of the meteorological and air quality community. Few works about the implementation of air quality models on South Americ have been developed, most of these over Southern South America (South of Brasil and Perú, Argentina and Chile). Through analysis and comparison between the LOTOS-EUROS outputs and data retrieved from ensembles and reanalysis from Copernicus Project (ECMWF, MACC2), is presented the challenges and opportunities for the successful implementation and development of LOTOS-EUROS model as an alternativet o model the dynamics of pollutants on Tropical Andes Domain.

Slides: pdf​ ]
Video: [ link ]
Place: 27-302
Time: 2 p.m. - 3 p.m.

2017-03-09

Speaker: Andreas Abel
Affiliation: 
Senior Lecturer, Chalmers University of Technology, Gothenburg, Sweden

Talk title: Normalization by Evaluation

Abstract: In computer systems that manipulate syntactic objects, like computeralgebra systems, compilers, and theorem provers, we find algorithms that check whether two expressions are equal.  Some expression classes admit normal forms.  For objects of these classes, equality can be decided by checking that the expressions under consideration have the same normal form. Conversion to normal form is called normalization.

In this talk, I show how normalizers can be obtained from interpreters in a principled and elegant way.  The process of normalizing an expression via an interpreter is called normalization by evaluation. I will demonstrate normalization by evaluation for two structures: monoids and lambda-calculus.

Normalization by evaluation is applied in type-directed partial evaluation of functional programs, in implementation of proofassistants, and in foundational studies of Type Theory.

Slides: [ pdf ]
Video: [ link ]
Place: 27-302
Time: 2 p.m. - 3 p.m.​

2017-03-07​

Speaker: Daniele Pretolani
Affiliation: 
Associate Professor DISMI, Dipartimento di Scienze e Metodi dell'Ingegneria, Università degli Studi di Modena e Reggio Emilia, Italia 

Talk title: Apportionments with minimum Gini index of disproportionality

Abstract: A proportional apportionment is a fair distribution of parliamentary seats among parties – or equivalently among states in a federal system. The Gini index is a classical measure of inequality, often used in economics and social sciences.  In our work, we adopt the Gini index as a measure of disproportionality, i.e., unequal distribution of political representation among citizens.  In particular, we present a method that returns an apportionment with minimum Gini index (among those satisfying the "quota" property).  This method combines Boolean Programming with a non-trivial decomposition technique, leading to a particular case of the quadratic knapsack problem, which turns out to be effective in practical cases (such as, notably, the US House of Representatives). We also present ongoing research on possible extensions and variants.

Slides: pdf ]
Video
: N/A
Place: 27-302
Time:
 2 p.m. - 3 p.m.​

2017-02-13​

​Speaker: Alejandro Gomez-Londoño
Affiliation:
 ​Proof Engineer at Data61/CSIRO, Australia

Talk title: seL4: Formal verification of an OS kernel [1] (A proof engineer perspective)

​​Abstract: The seL4 microkernel is "The world's first operating-system kernel with an end-to-end proof of implementation correctness and security enforcement" [2]. In this talk, we present a high-level overview of seL4s specification and proofs, along with user cases and future challenges of the seL4 project.

[1] seL4: Formal verification of an OS kernel​. Gerwin Klein et al, ACM Symposium on Operating Systems Principles 2009.

[2] seL4 project website

Slides: pdf ]
Video
link ]

Place: 27-302
Time:
 2 p.m. - 3 p.m.

2017-01-30

​Speaker: Juan F. Paniagua-Arroyave
Affiliation:
* Ph.D. Candidate, Geomorphology Laboratory, Department of Geological Sciences, University of Florida, Gainesville, FL, USA

* Professor in Formation, Marine Sciences Group, Department of Earth Sciences, Universidad EAFIT, MedellÍn, Antioquia, Colombia

Talk title: Signal processing applied to ocean hydrodynamics: wave dissipation and nonlinear interactions via Fourier and wavelet transforms

​​Abstract: Field-oriented studies in nearshore physics typically comprise the analysis of ocean waves. These analyses are based on the direct water motion measuring and subsequent signal processing of discrete data. For example, Fourier and wavelet transforms of spatially-fixed time series of water pressure and velocity allow the quantification of wave statistics (height, period, and direction), and the characterization of wave dissipation and nonlinear interactions that exert control on the energy balance and particulate transport. This talk focus on analyses performed to data collected at the inner-shelf near Cape Canaveral, Florida. Three processes are considered: oscillations at tidal (periods of 12 and 24 hours), infragravity (periods between 20 and 500 s), and sea-swell (periods between 3 and 20 s) frequencies. Our results highlight the influence of inner-shelf complicated topography on the sea-swell transformation and dissipation, as well as on the interaction between tidal and infragravity motions. Signal processing techniques applied to nearshore studies decisively inform communities regarding coastal hazards such as erosion and flooding, and help scientists in exploring connections among processes that remain not well understood.

Slides: pdf ]
Video
link ]
Place:
 27-302
Time:
 2 p.m. - 3 p.m.



2016​​​-2


Date

Talk

2016​-11-21

​Speaker: Diana Paola Lizarralde Bejarano
Affiliation:
PhD student in Mathematical Engineering, Universidad EAFIT

Talk title: Stability Analysis Methodology for Epidemiological Models

​​Abstract: The transmission of infectious diseases frequently is modeled through nonlinear ordinary differential equations. We aware that in general, it is not possible to find an analytic solution to this kind of systems and we must focus on the qualitative properties of such a systems to understand the behavior of  the solutions. In order to understand the evolution of solutions of those systems, a stability analysis around the equilibrium points of the system from the model will be carried out. For this reason, we made the state-of-art of the most frequent approach to analyzing the stability of a nonlinear equations system that works for transmission infectious diseases. Later on, we will incorporate explicitly the uncertainty associated with the parameters involve into the model taking into account  the results of the stability analysis.

Slides: [ pdf ]

Video: [ link ]

Place: 38-118

Time: 2 pm - 3 pm

2016-10-24

Speaker: Héctor Román Quiceno Echavarría
Affiliation:
 PhD student in Mathematical Engineering, Research Group in Functional Analysis and ApplicationsUniversidad EAFIT

Talk title: Analysis of the Von Neumann stability criteria for a finite difference scheme for solving the 2D Riemannian wave equation​

Abstract: The Riemannian 2D acoustic wave equation has been used to model wave propagation in scenarios that are best described by a more general non-cartesian geometry. This approach has showed an improvement of the imaging methods for rugged topography and curvilinear layering in the subsurface; nevertheless the stabilty condition for an RTM finite difference scheme, has not been analized from a numerical theory. In this talk, we are going to show the implementation of the Von Neumman stability criteria for the 2D Riemannian wave equation and show that this stability condition generalizes the Courant criterion and then is better than the heuristic one proposed by Shragge.

Slides: [ pdf ]
Video:
 N/A
Place:
 38-118
Time:
 2 p.m.​ - 3 p.m.

2016-10-03

Speaker: Nicolás Pinel Peláez
Affiliation:
Research group in Biodiversity, Evolution and Conservation (BEC), Universidad EAFIT

Speaker: Olga Lucía Quintero Montoya
Affiliation:
 Research Group in Mathematical Modeling - GRIMMATUniversidad EAFIT

Talk title: Data Assimilation Schemes in Colombian Geodynamics

Abstract: This seminar addresses the research project for the improvement and development of new Data Assimilation Schemes from Mathematical point of view for two applications regarding the GeoSciences, Geophysics and Environmental issues. The use of the Open DA library developed and supported by Deltares makes feasible not only the traditional Data Assimilation schemes but also provides a hydrodynamic modeling frame​work to include this kind of applications. Colombian air quality dynamics analysis through the use of the LOTOS-EUROS Model from TNO and the History Matching problem with Statoil will be the applicability fields in which this proposal relies, looking for the cooperation between Universities and Institutions. We propose at least seven theoretical aspects related to the Data Assimilation Schemes regarding the Backtracking localization strategies for Ensemble Kalman Filter and the traj4D-Var proposed by (Fu et al, 2015 and Lu et al, 2015), also the application of Observational impact analysis algorithm (TSBOI-MM) (Verlaan and Sumihar, 2016) in order to establish a research plan for new PhD students that will be able to follow a co-supervised Doctoral formation between TU Delft Applied Mathematics PhD programme and Universidad EAFIT Mathematical Engineering Ph Programme. Master from the Applied Mathematics Programme and undergraduate students of the School of Sciences at Universidad EAFIT will be involved in activities within the framework of this research.​

Slides: [ pdf ]
Video:
 [ link ]
Place:
 38-118

Time: 2 p.m - 3 p.m

2016-09-19

​Speaker: Juan Guillermo Paniagua Castrillón
Affiliation:
PhD student in Mathematical Engineering, Research Group in Mathematical Modeling - GRIMMATUniversidad EAFIT

Talk title: Enhancing images in seismic migration is not an easy task​

Abstract: We demonstrated that, under a good Reverse Time Migration RTM (acoustic wave propagation) algorithm and the zero-lag cross correlation imaging condition, it is possible to improve the traditional post processing methodologies. But, in our race to generalize our achievements we found that this is not completely true for a kind of special velocity field models. Sadly, we are looking for the reasons why, under a very singular function of the velocity fields, our Laguerre-Gauss (LG) filter does not work very well. This seminar will show you different approximations for the analysis of the phenomenon under research and we will present some hypothesis and the path to the future research. We are going to use some concepts from Fourier Analysis, because we already solved the problem for wave propagation in time domain for huge and massive data, and present some frequencies spectrum from the zero-lag cross correlation image and its LG transformation.

Slides: [ pdf​ ]
Video: 
[ link ]
Place: 
38-118
Time: 2 p.m - 3 p.m

2016-09-05

Speaker: Maria​ Gulnara Baldoquin de la Peña
Affiliation:
 Research Group in Functional Analysis and Applications, Universidad EAFIT

Talk title: Models and methods for solving an assignment and vehicle scheduling problem

Abstract: In this proposed project, a real life problem will be considered, derived from the operation of some Integrated Mass Transit System (SITM) in Colombia. Mathematical models associated belong to the class of Multi Depot Vehicle Scheduling Problems (MDVSP). Different approaches to model the MDVSP, solution methods and extensions for a better representation of real public transit systems, have been developed. However, the literature reviewed doesn’t consider some requirements and restrictions derived of SITM in Colombia. The new models and solution methods to consider will be more complex.  It will be exposed some challenges in this research work.

Slides:pdf ]
Video:
[ ​link ]
Place:
 38-118
Time: 
2 p.m - 3 p.m

2016-08-22​

Speaker: Leandro Fabio Ariza Jiménez
Affiliation:
 PhD student in Mathematical Engineering, Research Group in Mathematical Modeling - GRIMMATUniversidad EAFIT

Talk title: Transfer Learning on an Autoencoder-​based Deep Network

​Abstract: It is widely known that deep neural networks can be difficult to train in practice, since in order to obtain state-of-the-art results we need a great amount of data and computing power. However, we can overcome this issue either using autoencoders as way to “pre-train” deep neural networks or following a “transfer learning” approach. In particular, here we carried out several experiments to study how both approaches can benefit the training of deep networks.​

Slides: [ pdf ]
Video:
[ link​ ]
Place:
 38-118
Time:
 2 p.m - 3 p.m

2016-08-01

Speaker: Daniel Cabarcas Jaramillo
Affiliation:
 Departamento de Matemáticas, Universidad Nacional de Colombia - seccional Medellín

Talk title: Pos-quantum cryptography based on lattices and on multivariate polynomial equations

Abstract: The security of all public key cryptography in use today is supported on the hardness of factoring and finding discrete logarithms. This assumptions is no longer valid in the presence of quantum computers. Hence it is imperative to develop new cryptographic primitives based on assumptions that resist quantum computer attacks. The quest for new hard problems to support cryptographic constructions has yield new powerful functionalities such as fully homomorphic encryption. In this talk I will discuss about two pos-quantum alternatives: cryptography based on lattice theory, and based on multivariate polynomial equations.

Slides: [ pdf ]​
Video:
[ link​ ]
Place:
 38-118
Time: 
2 pm - 3 pm

2016-07-18

Speaker: Peter Dybjer

Affiliation: Department of Computer Science and Engineering, Chalmers University of Technology, Gothenburg, Sweden

Talk title: Martin-Löf's Intuitionistic Type Theory and the Agda System

Abstract: Intuitionistic type theory (also constructive type theory or Martin-Löf type theory) is a formal logical system and philosophical foundation for constructive mathematics. It is a full-scale system which aims to play a similar role for constructive mathematics as Zermelo-Fraenkel Set Theory does for classical mathematics. It is based on the propositions-as-types principle and clarifies the Brouwer-Heyting-Kolmogorov interpretation of intuitionistic logic. It extends this interpretation to the more general setting of intuitionistic type theory and thus provides a general conception not only of what a constructive proof is, but also of what a constructive mathematical object is. The main idea is that mathematical concepts such as elements, sets and functions are explained in terms of concepts from programming such as data structures, data types and programs.

There are several proof assistants which are based on intutionistic type theory. The most well-known ones are the systems Coq and Agda. Coq was recently awarded the ACM Software System Award because of several impressive examples of computer assistested formal proofs: e g Gonthier's proof of the four colour theorem and of the Feit Thompson theorem in finite group theory, and Leroy's construction of a provably correct compiler for a significant subset of the C language. I will say something about the connection between the foundational intuitionistic type theory and these proof assistants.

Slides: N/A
Video:
N/A
Place:
 38-118​​
Time:
 2 p.m - 3 p.m


2016​​​-1


Date

Talk

2016-05-31

Speaker: Rosa Elvira Lillo Rodríguez
Affiliation:
 Department of Statistics, Universidad Carlos III de Madrid

Talk title: Scalable Statistical Tools for Social Data Analysis

Abstract: Online Social Networks (OSNs) such as Facebook, Twitter or Google+ have rapidly become one of the most used online services, through which hundreds of millions of users intensively interact every day. This makes OSNs an invaluable channel of information for different sectors such as advertising, marketing, or politics. Given the scale of popular OSNs, a still unsolved problem of key importance for the previous actors is the identification of relevant users. These will be the users to be addressed in order to advertise a product, 2016propagate a message, improve the image of a company or whatever goal has been set. In the specific context of online social networks the research community has focused its effort in identifying metrics that best define influential (or relevant) users. However, most existing works pre-define the properties of the target users to be found, and based on such definition establish ad-hoc mechanisms to find the target users. These supervised techniques have two main drawbacks: first, they require a considerable manual analysis of the problem and the data, and second, their effectiveness is fully tied with the definition of the target users profile: if such definition is inaccurate or incorrect the results would be likewise inaccurate or incorrect. Therefore, to advance the state-of-the-art in this important field, unsupervised methods for the detection of relevant users are required. In this work, we propose an unsupervised scalable method to identify outliers (some of them can be considered relevant users) based on functional data analysis (FDA). This method is suitable to be used in OSN data. We have evaluated the method with a dataset of 5.6 millions of Google+ users and the outliers identified by the method (in a few hours) have in fact interesting features.

Slides: [ pdf ]
Video:
 N/A
Place:
 38-103

Time: 4 p.m - 5 p.m

2016-05-16

Speaker: Luz Marleny Morales Mira
Affiliation:
 In the application process to the PhD in Mathematical Engineering, Universidad EAFIT

Talk title: Towards the development of a mathematical model for prediction of the magnetic and structural properties of iron ferrites obtained by mechanosynthesis

Abstract: In this talk I am going to introduce a method used to produce powders whose particle sizes are in order of nanometers, having a high magnetization in these scales. Such powders are produced by milling one or more precursor powders, which through a planetary mill, reach the energy levels needed to react chemically to form a product very different to the initial precursor, but with structural and magnetic characteristics convenient for technological applications.

The aim of the research is to develop a model of the milling process that optimizes production of some products of interest, such as nanostructured iron ferrites.

Slides: [ pdf ]
Video: 
link ]
Place:
 38-118
Time:
 2 p.m - 3 p.m

2016-05-02

Speaker: Héctor Román Quiceno Echavarría
Affiliation:
 PhD student in Mathematical Engineering, Research Group in Functional Analysis and ApplicationsUniversidad EAFIT

Talk title: Optimization approximation with separable variables for the one-way wave operator

Abstract: In this talk we present a review of a new method which approximates the one-way wave operator by products of functions in space variables and functions in wave number variables by means of optimization approximation with separable variables. This approximation enables us to use FFT algorithm which is independent of space variables while suffering no problem of branch points present in the generalized-screen method.

Slides: [ pdf ]
Video:
 [ link ]
Place:
 38-119
Time:
 2 pm - 3 pm

2016-04-25

Speaker: Leandro Fabio Ariza Jiménez
Affiliation: 
PhD student in Mathematical Engineering, Research Group in Mathematical Modeling - GRIMMATUniversidad EAFIT

Talk title: On the relation between Big Data and Machine Learning

Abstract: Recently the term “Big Data” was coined to capture the meaning of a data-explosion trend from diverse sources and domains, which society has been exposed due to technological advances since the second half of the 20th century. Machine Learning (ML) is a sophisticated analytical technology that can be used to provide us with intelligent analysis of Big Data. In this talk the relation between Big Data and ML is discussed, and two approaches of ML are presented: Clustering, and Deep Learning. The fundamental concepts of, and problems with Clustering will be discussed, followed by a description of some traditional algorithms and the presentation of experimental results in artificial datasets. With regard to Deep Learning, an introduction is given and future work in relation with big data is described.

Slides: pdf ]
Video:
 [ link​ ]

Place: 38-118
Time: 
2 pm - 3 pm

2016-04-11

Speaker: César Augusto Arias Chica
Affiliation: 
PhD student in Physics, Universidad de Antioquia

Talk title: Full wave inversion in Riemannian manifolds for zones with rugged topography

Abstract: Full waveform inversion (FWI) is a method that has been recently used to estimate subsurface parameters, such as the velocity model. This method, however, suffers of a number of drawbacks when applied to zones with rugged topography, due to the forced application of a Cartesian mesh to a curved surface. In this work, we present a simple coordinate transformation that allows the construction of a curved mesh. The proposed transformation is more suitable for rugged surfaces and it allows mapping a physical domain into a uniform rectangular grid, where the acoustic FWI can be applied in the traditional way by introducing a modified Laplacian. We show that the proposed approximation is somehow general, and it produces precise near surface velocity models without increasing the computing time of the FWI.

Slides: [ pdf ]
Video: 
N/A
Place: 
38-118
Time:
 2 p.m - 3 p.m

2016-03-28

Speaker: Olga Lucía Quintero Montoya
Affiliation:
 Research Group in Mathematical Modeling - GRIMMATUniversidad EAFIT

Talk title: Wavelet as affine group, practical evidence and theoretical hypothesis

Abstract: The coherent states associated with the ax+b-group, which are now called wavelets, were first constructed by Alasken and Kauder (1968, 1969), as the result of the action of operators U(a,b) on a given function f. This results on the fact that any function f in L2(R) can be approximated by wavelets superposition. It happens, that these results can summarized on the fact that the continuous wavelet transform can map isometrically the L2(R) in a subspace H subset of Hilbert space. And also, if we choose a subset of L2(R), H2 (Hardy) we can interpreter the same transform as a isometry from H2 to Bergman space and any function of this Bergman space is associated to a function in H2. In this case, result obvious (for some people), that its values of certain discrete families of points completely determine the function.

The group structure proposed by Alasken and Klauder was not exploited so much, because of people went to the discretely labeled wavelet families and these do not correspond to subgroups of the ax+b-group. However we will discuss why it is fascinating to me to find a relationship between the continuous representation theory using the affine group (that inherits the singularity spectrum obtained by continuous wavelet transform and Holder exponent calculus) and the capability of the discrete approximations via multiresolution analysis to describe a dynamical behavior of a system.

Slides: [ pdf ]
Video:
 [ link ] 
Place: 
38-118
Time:
 2 pm - 3 pm

2016-03-07

Speaker: Juan Guillermo Paniagua Castrillón
Affiliation: 
PhD student in Mathematical Engineering, Research Group in Mathematical Modeling - GRIMMATUniversidad EAFIT

Talk title: Reverse time migration image improvement using integral transforms

Abstract: Linear integral transforms can be described as a representation of one space into another space. These integral transforms have been used in different fields of knowledge such as applied mathematics, mathematical physics and engineering science. They have been applied in solving several problems in fluid mechanics, signal processing, electronics, quantum mechanics, viscoelaticity, seismic signal analysis, among other areas. Some problems in Geophysics (Such as Phase shift migration and Kirchhoff migration) can be solved through the use of integral transforms. The imaging condition in reverse time migration (RTM) is one of them.

RTM is achieved by a forward and a reverse time propagation of source and receiver wavefields respectively, obtained by modeling the acoustic wave equation and followed by applying some criteria known as imaging condition. The cross-correlation in time between source and receiver wavefields is the commonly used imaging condition. This imaging condition produces spatial low frequency noise (Artifacts) due to the backscattered correlation between the source and receiver wave-fields. Different techniques and other imaging conditions have been used to remove these artifacts (Valenciano and Biondi, 2003 Kaelin et al, 2006, Guitton, 2007, Liu, 2011, Whitmore, 2012, Pestana et al, 2013, Shragge, 2014, Youn, 2001, Guitton et al, 2006, among others).

In this seminar, we propose a post-imaging approach, based on linear integral transforms, the Riesz and Laguerre-Gauss transforms, which excludes high frequency spatial components and the low frequency noise, reducing artifacts and enhance the edges on a reflective events in the RTM images. The Laguerre-Gauss spatial filter allows for performing a Radial Hilbert transform with high contrastive and isotropic edge enhancement without resolution loss. The spatial low frequency noise around the enhanced edges is largely suppressed.

Slides: [ pdf ]
Video:
 [ link​ ] 
Place: 
38-118
Time: 
2 p.m - 3 p.m

2016-02-22

Speaker: Omar Andres Zapata Mesa

Affiliation: Grupo de Fenomenología de Interacciones Fundamentales, Instituto de Física, Universidad de Antioquia

Talk title: Data Analysis in High Energy Physics

Abstract: CERN (European Center for Nuclear Research) is the largest laboratory in fundamental particles in the world, the LHC (Large Hadron Collider) is a particle collider where was discovered the Higgs particle and it can produce more 25GB / s and it has a network of computers (grid) in 34 countries with over 250K cores and 150PB storage. The LHC experiments face one of the biggest challenges in the data processing world, for which was developed the ROOT project a C++ framework for data analysis, that allows processing large volumes of data efficiently, using different data mining approaches, some of which will be presented at this seminar.

Slides: [ pdf ]
Video:
 [ link ]
Place:
 38-118
Time:
 2 p.m - 3 p.m

2016-02-08

Speaker: Esteban Vélez Ramírez

Studies: Master in Complex System Science, Ecole Polytechnique, Paris, France and University of Gothenburg, Gothenburg, Sweden

Talk title: Introduction to complex systems (II)

Abstract: The new interdisciplinary field of complex systems focuses on systems of many interacting parts, sometimes called agents, which interact in a nonlinear way and produce an emergent collective behaviour that can not be easily predicted based on the behaviour of the individual parts. Therefore, from this perspective, it seems like a perfect scenario to apply ideas from statistical physics. The main purpose of this talk is to analyse some examples of complex systems, such as an ant colony, the irreversibility in physical systems and collective motion in active mater, using ideas and techniques from statistical physics.

Slides: [ pdf ]
Video:
 [ li​​nk ]
Place:
 38-118
Time:
 2 p.m - 3 p.m

2016-01-25

Speaker: José E. Valdés
Affiliation:
 Facultad de Matemática y Computación, Universidad de la Habana, Cuba

Talk title: Some stochastic models and its application

Abstract: We consider stochastic models and its applications to reliability analysis of repairable systems and to the study of inventory systems and queuing systems. The value of the stochastic simulation in the study of these systems is considered. Some practical examples are discussed.

Slides: N/A
Video:
 [ link ]
Place: 
38-118
Time: 
2 p.m - 3 p.m


2015​​-2


Date

Talk

2015-12-07

Speaker: Esteban Vélez Ramírez
Studies: 
Master in Complex System Science, Ecole Polytechnique, Paris, France and University of Gothenburg, Gothenburg, Sweden

Talk title: Introduction to complex systems (I)

Abstract: During the last thirty years the study of complex systems has consolidated as an interdisciplinary approach to understand our modern world and human societies, but also, it has become a powerful tool to analyse old theories and paradigms inside natural science, such us biological evolution, the origin of life, irreversibility in physical systems, anomalous behaviour in the movements of group of animals, neuroscience, cognition among many others. But what exactly are complex systems? what about their properties? How can we identify a complex system? what can we use them for? The purpose of this talk is try to answer these questions and emphasise on the relevance of this new discipline in the future of science.

Slides: link ]
Video:
 [ li​nk ]
Place:
 16-201
Time:
 2 p.m - 3 p.m

2015-11-23

Speaker: Patricia Gómez Palacio

Studies: Doctor en Ciencias Matemáticas, Universidad Politécnica de Valencia, España

Affiliation: Research Group in Functional Analysis and Applications, Universidad EAFIT

Talk title: The Wavelet Galerkin Method

Abstract: The Wavelet Galerkin Method is a numerical technique used to obtain approximate solutions of partial differential equations. In this seminar we will discuss the algorithmic structure of the method and some of the difficulties in its implementation. In particular we will refer to the work of A. Latto and others, on the evaluation of connection coefficients.

Slides: [ pdf ]

Video: N/A

Place: 38-118

Time: 2 p.m - 3 p.m

2015-11-09

Speaker: Jairo Villegas Gutiérrez
Affiliation:
 Research Group in Functional Analysis and Applications, Universidad EAFIT

Talk title: Representation of differential operators in wavelet basis

Abstract: The development of numerical techniques for obtaining approximate solutions of partial differential equations has very much increased in the last decades. Among these techniques are the finite element methods and finite difference. Wavelets methods are applied to the numerical solution of partial differential equations, pioneer works in this direction are those of Beylkin, Dahmen, Jaffard and Glowinski, among others. In this work, we employ the representation of differential operators in wavelet basis, in the numerical solution of evolution equation.

Slides: [ pdf ]
Video:
 N/A
Place:
 38-118
Time:
 2 p.m - 3 p.m

2015-10-19

Speaker: Carlos Alberto Cadavid Moreno
Affiliation:
 Research Group in Functional Analysis and Applications, Universidad EAFIT

Talk title: The q-exponential behaviour of expected aggregated supply curves in deregulated electricity markets

Abstract: This talk has the intention of presenting some evidence of the presence of q-exponentiallity in the expected supply curve associated to perhaps the simplest idealized deregulated electricity markets, namely, those markets composed of N generating firms, each capable of producing, at zero cost, one electricity unit per day, where each firm is free to choose, every day, the selling price of its electricity unit, out of an interval [0,\overline{p}], where \overline{p} is the highest unit price allowed by the government, and where it is assumed that each firm knows everything about the other firms, except for the particular selling prices they choose every day. It is also assumed that the demand is a discrete random variables, which takes values i=1,...,N, with Pr(demand=i)=\pi_i, and that all of this is known to each one of the firms.

Slides: N/A
Video:
 [ li​nk ]
Place: 
38-118
Time:
 2 pm - 3 pm

2015-10-05

Speaker: Juan Carlos Rivera
Affiliation: 
Research Group in Functional Analysis and Applications, Universidad EAFIT

Talk title: Optimization techniques to solve vehicle routing problems applied to humanitarian response operations

Abstract: In this research project mathematical models are proposed in order to optimize short term response operations after a humanitarian disaster, for instance relief distribution. Different optimization techniques are proposed to deal with the resulting NP-Hard problems. Some of the challenges in humanitarian applications are, for instance, different functions to optimize as service-based objective functions which better reflect the strategic goal under the urgency situation, the presence of uncertainties which are not possible to estimate, and specific constraints due to the emergency conditions. Other fields of application are also introduced in commercial applications.

Slides: pdf ]
Video: 
li​nk ]
Place:
 38-118
Time:
 2 pm - 3 pm

2015-09-21

Speaker: Andrés Sica​rd Ramírez
Affiliation: 
Research Group in Logic and Computation, Universidad EAFIT

Talk title: First-Order Proof Reconstruction (Research Proposal - 2016)

Abstract: In a previous research, we proposed a first-order theory for reasoning about functional programs by combining interactive proofs performed in the Agda proof assistant and automatic proofs performed by off-the-shelf first-order automatic theorem provers (ATPs). Our approach can be used with other first-order theories too. We have used it with other first-order theories such as Group Theory and Peano Arithmetic, and we had encouraging results. In our approach, we use the ATPs as oracles via a Haskell program called Apia, that is, we trust the ATPs when they tell us that a proof exists. In consequence, the consistency of our approach relies on the correct implementation of both the Apia program and the ATPs. We propose strengthen the consistency of our approach by reconstructing in Agda the first-order proofs automatically produced.

Slides: [ pdf ]
Video:
 N/A
Place:
 38-118
Time: 
2 pm - 3 pm

2015-09-07

Speaker: Héctor Román Quiceno Echavarría
Affiliation:
 PhD student in Mathematical Engineering, Research Group in Functional Analysis and ApplicationsUniversidad EAFIT

Talk title: Some Basic Aspects of Elastic Wave Equation in General Media

Abstract: The equation which best describes the propagation of seismic waves in the earth is the elastic wave equation, when neglecting absorption, moreover, to characterize reservoirs, the exploration focus on vertical fractures embedded in a isotropic rock matrix, since these fractures may give rise to increased permeability and are therefore of great interest for production from hydrocarbon reservoirs. This equation is framed in terms of tensor operators acting on vector quantities, and this is one motivation for considering a general frame in which we can write the elastic wave equation in a covariant manner. In this talk we show some basic aspects of differential geometry applied to propagation in continuous media and give some general forms of the tensors associated to a general and complex media. 

Slides: [ pdf ]
Video:
 [ link ]
Place:
 38-216
Time:
 2 pm - 3 pm

2015-08-24

Speaker: Raúl Andrés Torres Díaz (joint work with Henry Laniado and Rosa E. Lillo)
Affiliation: 
PhD student in Mathematical Engineering, Universidad Carlos III de Madrid, España

Talk title: A notion of multivariate Value at Risk from a directional perspective

Abstract: The univariate Value at Risk (VaR) is a risk measure frequently implemented by the financial industry since it is basically the quantile of losses distribution, whereby it meets good properties and its interpretation is straightforward. However, the extension of VaR to the multivariate framework is more complicated because in the literature there are many definitions of multivariate quantile. Therefore, researchers have tried to generalize the concept of VaR through the natural extensions of those multivariate quantiles. So, these extensions only consider level sets built from the cumulative distribution or the survival function. In this talk, we introduce a multivariate VaR with a directional approach as a vector-valued risk measure. The directional approach allows that the investor considers external information or risk preferences in her/his analysis. We provide the main properties of this financial risk measure and the relationship with some families of copulas where one is able to obtain closed expressions for this new measure. We also will present a nonparametric procedure for its estimation, as well as, its performance in terms of robustness regarding to another multivariate VaR that has been recently introduced in the literature.

Keywords: Multivariate quantiles; Value at risk; Copulas.

References:

  • Laniado, H., Lillo, R., Pellerey, F. and Romo, J. (2012). Portfolio selection through an extremality stochastic order. Insurance: Mathematics and Economics 51, 1-9.
  • Torres, R., Lillo, R. E., Laniado, H. (2015) A directional Multivariate Value at Risk, arXiv:1502.00908 Quantitative Finance and Risk Management.

Slides:
 [ pdf ]
Video:
 N/A

Place: 38-118
Time: 
2 p.m - 3 p.m

2015-08-10

Speaker: Christian Andrés Díaz León
Studies:
 Doctor en Ingeniería, Universidad EAFIT

Talk title: Handling Heterogeneity in Collaborative Networked Virtual Surgical Simulators

Abstract: Stand-alone and networked surgical virtual reality based simulators have been proposed as means to train surgical skills with or without a supervisor nearby the student or trainee. However, surgical skills teaching in medicine schools and hospitals is changing, requiring the development of new tools to focus on: (i) importance of mentors role, (ii) teamwork skills and (iii) remote training support. For these reasons, a surgical simulator should not only allow the training involving a student and an instructor that are located remotely, but also the collaborative training of users adopting different medical roles during the training session. Collaborative Networked Virtual Surgical Simulators (CNVSS) allow collaborative training of surgical procedures where remotely located users with different surgical roles can take part in the training session. To provide successful training involving good collaborative performance, CNVSS should handle heterogeneity factors such as users’ machine capabilities and network conditions, among others.

Several systems for collaborative training of surgical procedures have been developed as research projects. To the best of our knowledge none has focused on handling heterogeneity in CNVSS. Handling heterogeneity in this type of collaborative sessions is important because not all remotely located users have homogeneous internet connections, nor the same interaction devices and displays, nor the same computational resources, among other factors. Additionally, if heterogeneity is not handled properly, it will have an adverse impact on the performance of each user during the collaborative session. In this document, the development of a context-aware architecture for collaborative networked virtual surgical simulators, in order to handle the heterogeneity involved in the collaboration session, is proposed. To achieve this, the following main contributions are accomplished in this thesis: (i) Which and how infrastructure heterogeneity factors affect the collaboration of two users performing a virtual surgical procedure were determined and analyzed through a set of experiments involving users collaborating, (ii) a context-aware software architecture for a CNVSS was proposed and implemented. The architecture handles heterogeneity factors affecting collaboration, applying various adaptation mechanisms and finally, (iii) A mechanism for handling heterogeneity factors involved in a CNVSS is described, implemented and validated in a set of testing scenarios.

Slides: pdf ]
Video: 
lin​k ]
Place:
 38-118
Time:
 2 pm - 3 pm

2015-07-27

Speaker: Juan Guillermo Paniagua Castrillón
Affiliation:
 PhD student in Mathematical Engineering. Research Group in Mathematical Modeling - GRIMMATUniversidad EAFIT

Talk title: Estudio del uso de las transformaciones tiempo, frecuencia y escala en problemas de migración sísmica

Abstract: Actualmente, la industria petrolera se enfrenta a varios retos:

La exploración en aguas profundas, yacimientos pequeños en zonas conocidas, yacimientos profundos y más complejos y la disminución del riesgo de exploración.

En la exploración petrolera es de vital importancia saber con certeza la ubicación del pozo para su posterior perforación. Para ello, se hace una adquisición de datos aplicando el método sísmico y posteriormente un procesamiento de ellos que conducen a la obtención de imágenes de la estructura del subsuelo a través de un método llamado Migración Sísmica.

En la migración de datos sísmicos es necesario conocer el modelo de velocidad de la propagación de la onda sísmica en profundidad. Estos modelos son construidos a partir de estudios geológicos de la región donde se desea explorar, lo cual genera cierto grado de incertidumbre al momento de interpretar las imágenes obtenidas a través de estos debido a la heterogeneidad de las estructuras del subsuelo. Los métodos de migración sísmica utilizan diferentes dominios en los cuales los datos son procesados: Tiempo, frecuencia, tiempo-escala. En el dominio del tiempo los métodos usados están basados en la solución integral de la ecuación de onda (Solución integral de Kirchhoff), esquemas en diferencias infinitas que propagan y retropropagan las ondas para obtener imágenes a través de la suma de imágenes parciales (Reverse time migration) y aquellos que hacen inversión de onda completa (Full wave inversión). En el dominio de la frecuencia, o los métodos están basados en la transformación de los datos al espacio de la frecuencia compleja, a través de una transformada de Fourier, y en la extrapolación del campo de onda bajo las consideraciones de linealidad (suma de fases, superposición de señales) y velocidad constante en diferenciales de distancia y profundidad (Phase shift, PSPI, Split step, entre otros).

En el dominio tiempo-escala existen algunos trabajos en migración o (Kirchhoff, phase shift) que utilizan otras transformaciones como la transformada wavelet y que han mostrado mejoras en la calidad de las imágenes obtenidas y el tiempo de cómputo.

En este seminario se pretende mostrar una aproximación de los métodos utilizados históricamente para la obtención de imágenes sísmicas y la posible línea de formación doctoral e indagar por otras transformaciones con el fin de encontrar el campo de velocidad en profundidad del subsuelo de tal manera que se puedan obtener imágenes de migración con alta resolución, disminuyendo así la incertidumbre en la interpretación y posterior perforación de pozos. Además, buscar metodologías que permitan el manejo de datos sísmicos masivos y el procesamiento de datos a través de computación de alto desempeño. Finalmente, se presentarán los avances en el seminario de investigación 1 donde se trabajó en la apropiación de los aspectos teóricos y prácticos de las aproximaciones de funciones a través de bases ortogonales, como el dominio del sistema Haar y la evaluación de la transformada discreta como una representación del fenómeno en dos dimensiones y se responde a la pregunta de por qué no usar esta transformación en migración Phase-Shift.

Slides: pdf ]
Video:
 [ lin​k ]
Place:
 38-118
Time:
 2 pm - 3 pm

2015​​-1


Date

Talk

2015-06-07

Speaker: Juan Guillermo Paniagua Castrillón
Affiliation: 
PhD student in Mathematical Engineering, Research Group in Mathematical Modeling - GRIMMATUniversidad EAFIT

Talk title: Estudio del uso de las transformaciones tiempo, frecuencia y escala en problemas de migración sísmica

Abstract: Actualmente, la industria petrolera se enfrenta a varios retos: la exploración en aguas profundas, yacimientos pequeños en zonas conocidas, yacimientos profundos y más complejos y la disminución del riesgo de exploración.

En la exploración petrolera es de vital importancia saber con certeza la ubicación del pozo para su posterior perforación. Para ello, se hace una adquisición de datos aplicando el método sísmico y posteriormente un procesamiento de ellos que conducen a la obtención de imágenes de la estructura del subsuelo a través de un método llamado Migración Sísmica.

En la migración de datos sísmicos es necesario conocer el modelo de velocidad de la propagación de la onda sísmica en profundidad. Estos modelos son construidos a partir de estudios geológicos de la región donde se desea explorar, lo cual genera cierto grado de incertidumbre al momento de interpretar las imágenes obtenidas a través de estos debido a la heterogeneidad de las estructuras del subsuelo. Los métodos de migración sísmica utilizan diferentes dominios en los cuales los datos son procesados: Tiempo, frecuencia, tiempo-escala. En el dominio del tiempo los métodos usados están basados en la solución integral de la ecuación de onda (Solución integral de Kirchhoff), esquemas en diferencias infinitas que propagan y retropropagan las ondas para obtener imágenes a través suma de imágenes parciales (Reverse time migration) y aquellos que hacen inversión de onda completa (Full wave inversión). En el dominio de la frecuencia, los métodos están basados en la transformación de los datos al espacio de la frecuencia, a través de una transformada de Fourier, y en la extrapolación del campo de onda bajo las consideraciones de linealidad (suma de fases, superposición de señales) y velocidad constante en diferenciales de distancia y profundidad (Phase shift, PSPI, Split step, entre otros). En el dominio tiempo-escala existen algunos trabajos en migración (Kirchhoff, phase shift) que utilizan otras transformaciones como la transformada wavelet y que han mostrado mejoras en la calidad de las imágenes obtenidas y el tiempo de cómputo.

En este seminario se pretende mostrar una aproximación de los métodos utilizados históricamente para la obtención de imágenes sísmicas y la posible línea de formación doctoral en indagar por otras transformaciones con el fin de encontrar el campo de velocidad en profundidad del subsuelo de tal manera que se puedan obtener imágenes de migración con alta resolución, disminuyendo así la incertidumbre en la interpretación y posterior perforación de pozos. Además, buscar metodologías que permitan el manejo de datos sísmicos masivos y el procesamiento de datos a través de computación de alto desempeño.

Slides: [ pdf ]
Video:
 [ li​nk ]

2015-05-11

Speaker: Héctor Román Quiceno Echavarría
Affiliation:
 PhD student in Mathematical Engineering, Research Group in Functional Analysis and ApplicationsUniversidad EAFIT

Talk title: Riemannian Wavefield Extrapolation

Abstract: In this talk, we show some extrapolation methods based on one way wave equation (OWWE), and how they lead to the general setting of pseudo-differential operators. The idea of extrapolate the wave field in the depth direction is constrained by the hypothesis that this direction (Z-direction) is the prefered direction of propagation, but that would not be true for turning waves or waves on anisotropic media, so the direction of extrapolation should response for the intrinsic properties of the media. The generalized acoustic Helmholtz equation in Riemannian coordinates is proposed to fit these issues and we show the extrapolation methods which has used this equation along with its limits and the research proposal for my thesis.

Slides: pdf ]
Video:
 [ 
lin​k ]

2015-04-27

Speaker: Diego A. Gutiérrez Isaza
Affiliation: 
Instituto Tecnológico Metropolitano

Talk title: From forward modeling of acoustic wave equation towards to reverse time migration (RTM)

Abstract: RTM uses modeling of an elastic wave equation that propagates in the inner of the earth to get a seismic imaging of the geological structures. Obtain RTM implies propagate a wavefield from the source to inner reflector (exploding reflector model), so a good starting point would be the forward modeling of an elastic wave that propagates in the earth subsurface (around 10 km of depth) but to further simplify our modeling of the complex inner of the Earth we begin with the acoustic limit of the Hooke's law presenting highlights and perspectives towards to the best seismic imaging.

Slides: [ pdf ]
Video:
 N/A

2015-04-13

Speaker: Henry Laniado Rodas
Affiliation:
 Postdoctoral fellow, Facultad de Minas, Universidad Nacional de Colombia, Sede Medellín

Talk title: On The Portfolio Selection Problem

Abstract: The portfolio selection problem was considered by Markowitz, where the philosophy is that an investor should hold a portfolio on the set of risk-return couples that cannot be improved simultaneously. This set in R2 is denoted commonly in the literature as the efficient frontier. Since Markowitz (1952) several criteria have been studied for the portfolio selection, in fact, the determination of optimal allocations of wealth among risks in single period portfolio problems still follows being an interesting topic of investigation. In this talk will be introduced what is the specific problem and will be discussed different approaches of the same problem as well as some methodologies of solution. Finally, I will present the main conclusions and some future research lines whose work is currently underway.

References: Markowitz, H. M., 1952. Mean-variance analysis in portfolio choice and capital markets. Journal of Finance 7, 77-91.

Slides: [ pdf ]
Video:
 [ lin​k ]

2015-03-02

Speaker: Javier Correa Alvarez
Affiliation:
 Research Group in Biological Sciences (CIBIOP), Universidad EAFIT

Speaker: Sergio Pulido Tamayo
Affiliation:
 PhD student, Bioinformatics, Ghent University, Belgium

Talk title: Computational biology; towards understanding of complex biological systems

Abstract: Computational biology is the science of using biological data to develop algorithms and relations among various biological systems. Sometimes referred as to bioinformatics, it is more than the use of tools and specialized software for resolving questions in biology. This discipline was critical to complete the Human Genome Project, helping to organize the 3 billion of nucleotides of our genome. Nowadays, six subareas are the most developed and all them have inherent to this field the use of mathematics, computing science and biology. They are: computational biomodeling, computational neuroscience, computational pharmacology, cancer computational biology, computational evolutionary biology, computational genomics. Being the last one my major area, in this lecture I am going to present, in a retrospective history, how the genomics evolved and some of the researches done with pathogenic microorganisms and the interaction with their hosts.

Slides: pdf ]
Video: 
lin​k ]

2015-02-16

Speaker: Daniel Esteban Sierra Sosa
Affiliation:
 Research Group in Mathematical Modeling - GRIMMAT, research group in apply optics, Universidad EAFIT

Talk title: Phase singularities study with metrology applications

Abstract: Singular optics is a contemporary branch from optics and photonics, where converges recent developments in optics, electromagnetism, quantum mechanics, topology, among others. In particular, our scope is focused in phase singularities, also known as optical vortices or screw dislocations; these singularities are located where the field intensity is null and phase is undefined. Currently, there is growing interest in analog and digital techniques appropriation for phase singularities generation, synthesis and analysis in optical fields; applications, statistic and physical properties are studied as well.

The study from these phase singularities in optical speckle fields’ summary will be presented. Speckle fields are obtained by the coherent superposition from independent contributions associated with the dispersive loci from a diffuser surface. From these fields complex-valued function are assigned by using linear integral transforms. This study is focused to optical vortex metrology applications.

Slides: [ link ]
Video: 
[ lin​k ]

​​2015-02-02

Speaker: Jayson A. Gutiérrez Betancur
Affiliation:
 Ghent University, Belgium

Talk title: Evolutionary systems biology: a multidisciplinary field to study biological phenomena in the light of evolution

Abstract: Evolutionary systems biology is an emerging multidisciplinary research field, which aims to understand genotype-phenotype relationships (or genotype-phenotype mapping problems) in the context of complex cellular information processing systems, such as gene regulatory networks, signal transduction pathways and metabolic reaction cascades, by means of a great variety of network modeling approaches. Two different types of modeling approaches are widely implemented in evolutionary systems biology to study the genotype-phenotype map of cellular information processing systems: 1) top-down approaches (coarse-grained network models) encompassing, for instance, Boolean networks and flux balance analysis, which are suitable for studying global properties of genome-wide gene regulatory networks and metabolic pathways; and 2) bottom-up approaches (fine-grained network models) encompassing, for instance, kinetic and thermodynamic modeling of prototypical small regulatory circuits (e.g. network motifs). What makes these network modeling approaches so appealing and powerful is that they allow us to create mathematical representations of complex molecular networks, which can then be systematically interrogated via computer simulations (in silico experiments) with the aim of revealing regularities/patterns/properties of particular genotype-phenotype mapping problems. For instance, having created a computer replica of a given molecular network one can then interrogate systematically the behavior of the system under different sorts of perturbations mimicking e.g. small and large-scale genetic lesions. In silico experiments such as these provide a wealth of interesting information on robust and fragile system features, which can then be verified experimentally. This would eventually narrow down our set of hypothesis on how molecular networks could be perturbed in order to effectively manipulate their behavior for particular purposes. Moreover, by offering the opportunity to gain mechanistic insight into the inner workings (i.e. operative rules) of cellular information processing systems, evolutionary systems biology approaches become a powerful predictive tool to investigate the origin of emergent system properties, such as network robustness, fragility and modularity, as well as the potential of biological systems to evolve novel properties (evolvability) and to adapt to new environments (plasticity). In addition, evolutionary systems biology provides guidelines for the rational design and optimization of biological functions, the primary goals of many research disciplines in the life sciences, such as synthetic biology, plant biotechnology (e.g. applied to crop design), metabolic engineering, evolutionary medicine, microbiology, etc. Moreover, gaining insights into the mechanistic underpinnings of cellular information processing networks is crucial to understanding the origin of complex diseases such as cancer, which is itself the result of an intricate evolutionary process operating on somatic cells within tissues, whereby natural selection acts upon the phenotypic variation generated by the accumulation of genetic, genomic and epigenetic alterations. Finally, from a basic research point of view, understanding the inner workings of molecular networks, and how evolution steers in them and shapes them at the same time, is crucial to address long-standing evolutionary questions, such as the origin of species diversity, the evolution of biological complexity, phenotypic innovation and survival of mass extinction events. In this sense, evolutionary systems biology offers the opportunity to recreate past evolutionary events, to reconstruct evolutionary trajectories and to assess their repeatability under similar conditions, as well as to assess how different starting conditions could impact on the outcome of evolution.

Slides: [ link ]
​Video: N/A



2014​-2


Date

Talk

2014-11-24

Speaker: Carlos Mario Vélez Sánchez
Affiliation:
 Research Group in Mathematical Modeling - GRIMMATUniversidad EAFIT

Talk title: Modelado matemático, estimación y control de sistemas dinámicos

Abstract: Se indican las áreas y oportunidades de aplicación de los sistemas dinámicos en diferentes áreas de la ciencia y la ingeniería, y se dan ejemplos de los desarrollos del grupo con miras a aplicar los métodos, resultados y preguntas en otras áreas y sectores.

Slides: pdf ]
Video:
 N/A

2014-11-10

Speaker: Nicanor Quijano Silva
Affiliation:
 Universidad de los Andes

Talk title: Evolutionary Games and Distributed Control: Theory and Applications

Abstract: Game theory is the methodology used to model and analyze situations where there is a need to make a decision (e.g., resource allocation problems). In these situations, there are several decision-makers (usually called players), which have different objectives and each of the decisions taken by the players affect all of them. Basically, the classical game-theoretical approach assumes that the decision is taken instantly without any information of past moves that would help to take the decision. In order to take into account these past behaviors, we use the methodology introduced in dynamic games, especially the evolutionary games. In this talk we focus our attention to a special type of evolutionary game called the replicator dynamics, which allows to model decisions in large-scale systems that possess distributed elements. Some examples in dynamic resource allocation problems (e.g., energy, water distribution) are shown in order to illustrate the fact that the architecture of a distributed control is similar to the one that is proposed here.

Slides: pdf ]
Video: N/A

2014-10-20

Speaker: Freddy Hernán Marín Sánchez
Affiliation:
 Research group in Mathematical Modeling - GRIMMATUniversidad EAFIT

Talk title: Stochastic modeling of electricity prices in the Colombian market: A perspective for the valuation of financial derivatives

Abstract: In this work the construction of a stochastic model (stochastic differential equation) that can be used to simulate and predict the short term, the dynamic behaviour of daily prices of electricity traded in high demand times is shown. Likewise a perspective arises, following the approach of Black-Scholes, for the valuation of financial derivatives on energy.

Slides: [ pdf ]
Video:
 N/A

2014-10-06

Speaker: Manuel Hernando Sierra Aristizábal
Affiliation:
 Research Group in Logic and Computation, Universidad EAFIT

Talk title: Aprendizaje ¿y-lógica?

Abstract: Pregunta: ¿Cómo se podría iniciar una aproximación, a la caracterización deductiva de cierta noción de aprendizaje? Conjetura: formalizando la relación de accesibilidad de la semántica de mundos posibles encajados, la cual se encuentra asociada a sistemas específicos de lógica multi-modal, en donde las inferencias tienen restricciones sobre la complejidad de las fórmulas.

Slides: pdf ]
Video:
 N/A
Animaciones didácticas: 
link ]

2014-09-22

Speaker: Carlos Alberto Cadavid Moreno
Affiliation:
 Research Group in Functional Analysis and Applications, Universidad EAFIT

Talk title: Minimal Morse function via the heat equation

Abstract: In this talk I will present some results about the intriguing ability of the heat equation to simplify complicated functions defined on manifolds endowed with "nice metrics".

Slides: pptx ]
Video:
 N/A

2014-09-08

Speaker: Andrés Sica​​rd Ramírez
Affiliation:
 Research Group in Logic and Computation, Universidad EAFIT

Talk title: Reasoning about Functional Programs by Combining Interactive and Automatic Proofs

Abstract: We propose a new approach to computer-assisted verification of lazy functional programs where functions can be defined by general recursion. We work in first-order theories of functional programs which are obtained by translating Dybjer's programming logic into a first-order theory, and by extending this programming logic with new (co-)inductive predicates. Rather than building a special purpose system, we formalise our theories in Agda, a proof assistant for dependent type theory which can be used as a generic theorem prover. Agda provides support for interactive reasoning by representing first-order theories using the propositions-as-types principle. Further support is provided by off-the-shelf automatic theorem provers for first-order-logic called by a Haskell program that translates our Agda representations of first-order formulae into the TPTP language understood by the provers. We show some examples where we combine interactive and automatic reasoning, covering both proofs by induction and co-induction.

Slides: [ pdf ]
Video:
 N/A

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Última modificación: 21/06/2019 12:19