## Control and estimation theory:

**Research line I:** control, estimation theory and signal analysis.

**Director (s):**

Olga Lucía Quintero Montoya.

Carlos Mario Vélez Sánchez.

**Joint director (s):**

María Eugenia Puerta Yepes.

Leonel Francisco Castañeda Heredia.

José Ignacio Marulanda Bernal.

Control theory, developed by mathematicians in the 50s, has played a relevant role in the design and implementation of worldwide advances in areas of engineering, military, economics, finances, health, among others. More...

**Research line II: **artificial intelligence and machine learning.

**Director:**

Olga Lucia Quintero Montoya.

**Joint director (s):**

Leonel Francisco Castañeda Heredia.

Helmuth Trefftz Gómez.

Javier Correa Álvarez.

María Alejandra Gonzalez-Perez.

With the advent of the age of automation, the natural question arose about giving intelligence to machines, devices and tools in order to improve its ability to “reason” and therefore, perform better on tasks where human beings are experts and perform very accurately in.

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## Optimization:

**Research line I:** optimization in epidemiology.

**Director (s):**

María Eugenia Yepes Puerta.

**Joint director (s): ** Sair Arboleda.

Definition of mathematical models of disease transmission and an estimation of its parameters with biological significance, through mathematical methods of optimization and the use of additional necessary information.

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**Research line II:** optimization.

**Director (s):**

María Gulnara Baldoquín de la Peña.

**Joint director (s): ** Juan Carlos Rivera Agudelo.

Models and solution methods in optimal route designs and definition frequencies of integrated multi-modal transportation system in Colombia.

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## Numerical solution of differential equations:

**Research line I:** solution of differential equations.

**Director (s):**

Jairo Alberto Villegas Gutiérrez.

José Albeiro Sánchez Cano.

Orlando García Jaimes.

Jorge Iván Castaño Bedoya.

**Joint director (s):**

Manuel Julio García Ruiz.

Juan Diego Jaramillo Fernández.

Numerical solutions to differential equations using the Petrov Galerkin- Wavelet transform and pseudo-differential operators with applicability in geophysics.

#### Research groups:

## Geometry and information:

It seeks to show new evidence of the power that diffusion processes have to simplify in terms of functional information defined on a differentiable manifold M, and therefore obtain the best results; results obtained by mathematical characteristics or advantages of interpretations in a specific context where diffusion processes are used to model.

Research line I: simplification of Morse functions through diffusion equations.

**Director (s):**

Carlos Alberto Cadavid Moreno.

**Joint director (s):**

Oscar Eduardo Ruiz Salguero.

Jorge León David Caro.

For hyperbolic, three-dimensional, closed and allied, Riemannian manifolds, we intend to find more experimental evidence that the diffusion process of heat recuperates, on his own, minimal Morse functions and the number of critical numerals, which are very important due to the fact that they concisely describe, without unnecessary complexities, the topology of a differential manifold.

**Research line II:** non-conventional statistical mechanics of markets.

**Director (s):**

Gabriel Ignacio Loaiza Ossa.

**Joint director (s):**

Jhon Jairo García Rendón.

Andrés Ramírez Hassan.

We initiate the study of entropy sets, searching for the simplest, for which the diffusion process in the porous medium is the fastest descent. The above will potentially be addressed given the Tsallis and/or Kaniadakis entropies.

Finally we study a problem, not strictly a diffusion type, which raises theoretical tools that can lead to consider a variety of statistical information, in addition to solving important questions raised in a specific context and enhance the formulation of diffusion processes. We aim to characterize the Colombian electricity sector market as a non- extensive system within the framework of statistical mechanics of Tsallis.

#### Research groups:

## Computer science:

**Logic, Languages and Algorithms**

Performs activities focused on building models for computability and to establish relationships with existing models; in addition to introducing the different possibilities offered by quantum physics and modern physics, for constructing new models of computation and programming. Likewise, the group’s work is focused on constructing deductive systems from classical propositional calculus using operators of alternating claims ( in contrast to the usual or classic claims - AC statement), alternating negation ( in contrast to the usual or classical negation - AC denial), and operators of incompatibility and determinability between pairs of operators ( negations versus claims). The group develops methods for correction, debugging, writing, processing and verification of logic and/or functional programs by using formal techniques.

**Research line I:** Declarative debugging

The working on the development of methods for testing, debugging and correction of logical and/or functional programs, by employing formal techniques.

**Research line II:** Logics for functional programs

Seeks to build deductive systems from classical propositional calculus, using operators of alternating claims ( in contrast to the usual or classic claims - AC statement), alternating negation ( in contrast to the usual or classical negation - AC denial), and operators of incompatibility and determinability between pairs of operators ( negations versus claims).

#### Research groups: