Research

RESEARCH MISSION

  • Attract a pool of competitive and experienced mathematicians and computer scientists who provide students and young scholars with a stimulating research environment.
  • Support the natural and experimental sciences with training and computational tools for high resolution and large-scale modeling.
  • Interdisciplinary cooperation with national and foreign universities, public research laboratories and private companies.
  • Delve into the study of fundamental mathematics, numerical analysis, stochastic processes, theoretical computer science, artificial intelligence, software development, and systems engineering.

RESEARCH LINES

 

  • Ordinary and/or Partial Differential Equations
  • Mathematical and Numerical Analysis
  • Control and/or Synchronization Theory
  • Dynamic Systems
  • Probability and Statistics
  • Algebra and Geometry
  • Topology
  • Discrete Mathematics and Logic
  • Complex Analysis
  • Didactics of Mathematics

Hypotheses about a system often involve the rate of change of one or more variables. This leads to the fact that the mathematical statement of all these hypotheses can be one or more equations where derivatives intervene. Thus, a deterministic mathematical model is an equation or a system of differential equations, which can be ordinary or partial, depending on the number of variables present in the phenomenon studied.

In most of these models, the existence of solutions is established by means of some theorem from Mathematical Analysis, which deals with the study of the favorable conditioning factors to be able to establish these results in both finite and infinite dimensional spaces. However, in most cases, obtaining the solution is reduced to approximations using computational algorithms.

Hence, both the theoretical and computational study of the problem addressed is important. Also, many phenomena that take place in the real world, such as biological systems, weather, economics, and finance, behave randomly; and the dynamic nature of these processes cannot be determined using deterministic models, because there are variables that cannot be included in the modeling, while incorporating a stochastic structure can help to quantify this uncertainty.

In both cases, deterministic or non-deterministic, when enabling conditions are considered, it is important to take into account algebraic and geometric structures inherent to the problem. Moreover, Mathematical Logic and Discrete Mathematics tools are useful for modeling and solving problems coming from different important domains. This includes challenging problems in Artificial Intelligence, Symbolic Models, Decision Theory, Social Choice Theory, Axiomatic Set Theory and Functional Systems.

Additionally, modern university mathematics teaching, particularly the use of textbooks, requires an intelligent balance between 1) the obviously important purely mathematical concepts, 2) the possibility of using the ever-increasing computational resources, and 3) the use of interesting application examples. This puts the didactics of mathematics in tune with the elements that make up the line of research.

Definitely, the line focuses on a multidisciplinary spirit, thus fostering the relationship with other schools of our university and abroad, both nationally and internationally.

 

 

  • Data Analysis
  • Databases
  • Multivariate Statistical Analysis
  • Computational Statistics
  • Data Mining
  • Data Visualization

Data Science is a new paradigm and potentially one of the most significant advances of the early 21st century. The field of data science has emerged due to the intersection of several sciences, including: mathematics, statistics, data engineering, pattern recognition and learning, advanced computing, uncertainty modeling and visualization, data storage and high-performance computation with the goal of extracting insights from data and creating new products from the data. In today’s world, there is no doubt that a data scientist is among the most sought after experts due to the nature of their jobs.

 

  • Artificial Intelligence
  • Machine Learning
  • Deep Learning
  • Computer Vision
  • Reinforcement Learning
  • Agents

The branch of computational intelligence encompasses the creation or replication of intelligence by computational means. The goal is to create innovative algorithms and agents, capable of learning complex problems on their own, such as driving a car, playing chess, administering exact doses of medicine or a bipedal robot that starts crawling and ends up upright.

This is unsupervised learning as the programmer only creates the conditions and access to an environment and the machine has to figure things out for itself. The intellectual capacities of humans remain as a frontier of human knowledge. For this reason, it is of interest to be able to replicate human and collective intelligences in such a way that we can understand, replicate and extend these intelligences. This development has great repercussions on society and the economic activities of the immediate future.

 

  • Modeling and Simulation
  • High Performance Computing
  • Algorithms
  • Numerical Analysis
  • Computing Theory
  • Discrete Structures
  • Scientific Visualization
  • Internet of things (loT)

Scientific Computing is the science of computer problem solving, and from this point of view, it is undoubtedly the most widespread scientific area that establishes precise, efficient and realistic algorithms, methods and models that model our world, store its data, and establish and process their sets.

These data can be geospatial and scientific, and their applications have an effect on every citizen in all their activities: from natural and artificial disaster prevention, monitoring and warning systems coupled with physical, chemical or biological meters and sensors. Topics covered include self-driving cars, drones with visual auto-return, and smart homes that protect themselves from dangerous chemical intruders and flooding.

These elements are unified through web platforms that allow communication and taking data from common things (loT) such as refrigerators, plants, etc. Scientific computing provides tools that allow molecular elements to be modeled, which allows solving problems such as protein folding, which in turn leads to the production of drugs and the possible control of viral epidemics such as covid-19 and other diseases.

 

  • Computational Agriculture
  • Intelligent Transportation Systems
  • Computer Security
  • Networks and Communications
  • Software

Information Technologies are found transversally in the daily lives of societies. They have revolutionized social, economic, political and industrial processes, being catalysts for Industry 4.0 and the knowledge society. Modern society has seen its reality transformed by digitization processes in all its areas, including: communication, education, social behavior, transportation, industry and commerce.

The use of a wide range of technologies allows us to be agents of change in all these sectors, increasing productivity and reducing risks. This line of research aims to propose transformative changes for Ecuador.