A. Nieves-González's web page
Here you can find some useful information. Of note: this webpage is under
construction. Thus, it is "constantly" evolving.
Fall 2017 (Primer Semestre 2017-2018)
Courses taught during previous semesters can be found here.
- Métodos cuantitativos para administración de empresas II: MECU 3032.
- Métodos cuantitativos para administración de empresas I: MECU 3035.
Departmental exams given during previous semesters can be
Broadly, the research fields that currently are more appealling to me are
(presentation about research):
- Mathematical/computational models of complex systems.
- Applied dynamical systems and bifurcation theory.
- Power spectrum analysis and wavelets.
- Parallel computing.
Computational models of complex systems
Many complex systems, e.g. biological systems and financial systems, can
be described by differential equations. Such equations are mathematical
objects that embody different principles or "laws of nature".
By describing the system with these equations and properly solving them, one can
get an understanding of the inner workings of the system being considered. Moreover,
math provides a precise language in which hypothesis about the system of
interest can be formulated.
The following is a list of the complex systems that we study using mathematical models.
One of our project consists on modeling a segment of the nephron, called the Thick Ascending Limb
(TAL) at the cellular and segmental level. The nephrons are tubules that are the functional
unit of the kidney. This means that a nephron is the smallest part of that organ that carries
out the functions of the organ as a whole (filtration, reabsorption, secretion and
excretion). In particular the TAL segment is responsible of actively reabsorbing NaCl from the
tubular fluid, hence it is a component of paramount importance that enhances the passive reabsorption
of water that occurs across other segment of the nephron (collecting duct) whose outflow is the
urine that eventually will get excreted from the human body. In addition,
as one moves deeper into medullary regions of the kidney, TAL cells find themselves in a
physiologically harsh environment in terms of osmotic challenges and
oxygen availability. Thereby, through mathematical modeling our goal is to understand the
different processes that occur in TAL cells, different aspects of their function including
transport efficiency, and how the properties of these cells give rise to the
physiological features of the segment as a whole.
- The kidney, (renal physiology).
Renal physiology, image from unckidneycenter.org
The system depicted above can be described with a system of conservation laws, for example
the thick ascending limb (TAL), which is a segment of the nephron can be described by
is a matrix operator, Ca
concentrations in different compartments, and V
are cell volume.
Another project involves the development of a mathematical model of the
population of coral polyps and its interactions with an unspecified pathogen and/or
its environment. The model, besides being solved numerically, is going to be rigurously
analyzed in order to gain insight of the physical system by studying its equilibria, and
its bifurcations (local and global).
High frequency time series of stock prices
We study high frequency time series of stock prices using methods
commonly used to analyze time series or time dependent signals in
engineering and applied sciences. By high frequency, what is meant is
that the elapsed time between subsequent observations is 1 minute or
less. The autospectral, autocorrelation, and the coherence function is
computed for each time series in order to characterize the time series
in terms of periodicity, time delay, and linearity. Additionally we
do a wavelet analysis of the time series. The wavelet analysis will
allow us to detect transient oscillatory phenomena as well as to uncover
phenomena within the time series that occurs at different time scales.
All of the aforementioned analysis will allow us to better understand the
mechanisms that underlie the system or process driving the changes
in stock prices.
Given the ubiquitous presence of multicore CPU's in computer systems, from cell phones
to supercomputers, it is advantageous to tap into the computational power that nowadays is readily
available. Thereby, we are interested in the parellized implementation and development
of numerical methods used to solve the models of the complex systems described above.
Interesting stuff to read, watch or listen to...
Disclaimer: for good or ill I, the author, is the sole responsible of this website and its contents.