FRIDAY, April 30, Irakli Loladze, Department
of Mathematics
FRIDAY, May 7, Victor Padron
TALKS GIVEN
FRIDAY, Feb. 12, Dritan
Zela, Department of Mathematics
"Predicting the Financial Market using Technical
Analysis and Neural Networks"
ABSTRACT: A host of methods to predict the behavior
of financial markets will be presented.
There are two basic approaches to financial prediction,
trend and price prediction and the first
one is presented. The trend prediction is used to determine
when the trend is going to change
direction and the price prediction approach is
used to predict what the price will be during a
given time frame usually the next day. Ever since there
have been markets to trade, there have been
speculators attempting to predict their direction. In
recent years, the researchers and developers,
by using the back-propagation algorithm, have been
able to show that neural
networks can be used to solve 'real life' problems.
One such real-life problem is financial prediction.
Our financial markets have clearly demonstrated
through the years that they trend in
cycles. A trend prediction net can be used to develop
a position trading system. A price prediction net
can be used to develop a day trading system. Loosely
defined, day trading is when a trade
is opened and closed all in the same day, whereas position
trading is when a trade is opened and held,
possibly for many days or weeks, until it is determined
that it is time to close the trade. Futures data was
used to verify the techniques in this project. The real
challenge in using neural networks for
financial prediction is not the construction of the nets
themselves, but rather the construction of the
transformations used to feed data into the net and the
methods used to interpret the results that come out
of the net and that is the key to success.
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TUESDAY, February 16, 1999
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COLLOQUIUM
(Faculty Candidate in MathBio) PSH 103 3:00
p.m.
David Earn,
Cambridge University
"Homogeneity and Synchrony in Population Dynamics"
ABSTRACT:
The simplest population models for predator-prey
interactions
and epidemics of disease are based on the
assumption
that populations are homogeneously mixed. However,
recent studies
of measles epidemics have concluded that
age-related
heterogeneities have a profound dynamical effect and
that homogeneous
models cannot explain observed epidemics.
I will show
that, in fact, the aggregate behaviour of
age-structured
epidemic models is effectively equivalent to that
of a homogeneous
model with external forcing, and I will argue
that seasonal
variation in contact rates is the key determinant
of the temporal
pattern of measles epidemics. I will also
discuss some
new results concerning synchronization of
population
dynamics in different spatial locations, and the
potential
importance of synchronization in vaccination programs.
Refreshments will be served in PSA 206 after the talk.
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FRIDAY, Feb. 19, Eric Stemmons, Department of Mathematics
"Competition in a Chemostat with Wall Growth"
FRIDAY, Feb. 26, Eugene Izhikevich, Department of Mathematics
joint dynamical systems + math. biol. seminar
Title: "Bifurcations in Neurons Dynamics, Excitability and Spiking"
We discuss a bifurcational mechanism of generation of
action potentials (spikes)
by biological neurons. In particular, we elaborate the
classification
of neural excitability suggested by Hodgkin in 1948.
We show
that Class 1 excitable neurons (i.e., those that can
fire with arbitrary
small frequency) exhibit saddle-node on limit cycle bifurcation,
whereas Class 2 excitable neurons (i.e., those that can
fire only in a certain
frequency range) exhibit Andronov-Hopf bifurcation.
The bifurcational point of view explains some biological
phenomena.
For example, class 1 neurons are integrators (their response
to input is proportional to
the frequency of the input); they can generate quite
irregular spike trains,
and they are difficult to synchronize. In contrast, Class
2 neurons are resonators
(they respond selectively only to inputs having certain
frequency), they generate
quite regular spike trains, and they are easy to synchronize.
FRIDAY, March 5, Gilbert
G. Walter, Professor of Mathematics, visiting
from University of Wisconsin-Milwaukee
Complexity vs. Stability in Ecosystem Models
A recurring problem is ecology is the relation between the complexity
of an ecosystem and its stability. Most ecologists in the past assumed
that the two went together, but May showed in the 1970’s that for some
models this is not the case. However, the favorite sort of model
used by ecologists, namely a compartmental model, was not the type he used.
In this talk we shall explore the relation between complexity and stability
of such compartmental models. We first give a brief introduction
to the subject and then will discuss various measures of complexity.
These measures are related to the structure, while stability is related
to the dynamical properties of the system. We shall show that
in some cases the two are indeed related as expected.
FRIDAY, March 12, Marcos
Lizana, Department of Mathematics, visiting from Universidad de Los Andes,
M\'erida , Venezuela
Stable Periodic Orbits for a PREDATOR-PREY MODEL with
Delay
In this talk, we will consider
a predator-prey model
with delay and non-constant death rate, described by
the following
integro-differential system
\begin{eqnarray}\label{1}
N' &=& N\left[\frac{\varepsilon}{K}(K-
N)-
\frac{ aP}{ \beta+N}\right]\quad, \nonumber\\
\\
P' &=& P\left[ -M(P)+\frac{bQ}{\beta+Q}\right]\quad,
\nonumber
\end{eqnarray}
where the function $Q(t)$ is given by the following integral
\begin{equation}\label{2}
Q(t):=\int_{-\infty}^t \alpha N(\tau) \exp{(-\alpha(t-\tau))}
d\tau \quad, \quad \alpha>0\quad.
\end{equation}
We show that when the model has exactly one non-trivial
unstable and hyperbolic
equilibrium there exists
a stable periodic
orbit . This is a joint work with Mario Cavani
and Hal Smith.
FRIDAY, March 26, Frank Raebiger, University
of Tuebingen, Germany
Asymptotic Properties of Solutions of Nonautonomous, Semilinear,
Retarded Differential Equations
ABSTRACT: We consider the
nonautonomous, semilinear, retarded
differential equation $${d\over
dt} w(t) = Bw(t) + K(t,w_t),\quad
t\in J (= {\bf R}\ {\rm
or}\ {\bf R}_+), \leqno{(NSR)}$$ on the
Banach space $E = C([-1,0],Y_0)$,
where $B$ is a Hille-Yosida
operator on a Banach space
$Y$ such that $\overline{D(B)} = Y_0$
and $K: J\times E \to Y$
is a nonlinearity satisfying certain
conditions. We derive a
principle of linearized stability for
$(NSR)$ and discuss when
$(NSR)$ has a unique mild solution
belonging to one of the
spaces $C_0({\bf R},Y_0),\ C_b({\bf
R},Y_0),\ P_q({\bf R},Y_0)$,\
or $AP({\bf R},Y_0)$.
FRIDAY, April 2, Patrick Nelson, IMA,
University of Minnesota
Mathematical Analysis of HIV Dynamics in Vivo.
Mathematical models have proven valuable in understanding
the dynamics
of HIV-1 infection in vivo. By comparing
these models to data obtained
from patients undergoing antiretroviral drug therapy,
it has been
possible to determine many quantitative features
of the interaction
between HIV-1, the virus that causes AIDS, and
the cells that are
infected by the virus. The most dramatic
finding has been that even
though AIDS is a disease that occurs on a time
scale of about 10 years,
there are very rapid dynamical processes that occur
on time scales of
hours to days, as well as slower processes that
occur on time scales of
weeks to months. We show how dynamical modeling
and parameter estimation
techniques have uncovered these important features
of HIV pathogenesis
and impacted the way in which AIDS patients are
treated with potent
antiretroviral drugs. We will discuss variations
of these models
which include a constant and a continuous delay
process and present
detailed analysis these delay differential equation
models and their
impact on the parameter estimations.
FRIDAY, April 9, Bingtuan Li,
IMA, University of Minnesota
Exploitative Competition in a Chemostat for Two
Complementary Resources
A model of the chemostat involving $n$ species of microorganisms
competing
for two perfectly complementary, growth-limiting nutrients
will be presented.
A general class of monotone increasing functions is used
for nutrient
uptake. We will discuss various conditions that guarantee
competitive exclusion and coexistence of two species.
MONDAY, April 12, 1999
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ASU NATIONAL
MATHEMATICS AWARENESS MONTH DISTINGUISHED LECTURE
Murdock Hall 101 7:30 p.m.
James P. Keener,
University of Utah
"The Mathematics of Sudden Cardiac Death, or Heart Attacks
can Give you Mathematics"
ABSTRACT: Heart attacks kill
hundreds of people daily in the
United States-many more than
are killed by math anxiety!
A heart attack occurs
when there is an occlusion of a coronary
artery, leading to tissue damage.
A heart attack is fatal when
there is a subsequent disruption
of the normal electrical signal
of the heart, leading to fibrillation.
There is very little
understanding of why this occurs,
and there are essentially no
reliable predictors of the onset
of fibrillation.
In this talk, I
will give an overview of some of the ways
that mathematics can help our
understanding of cardiac arrhythmias,
how they occur, what they are,
and how they can be eliminated.
The main emphasis will be on
how mathematics can be used to give
us insight that could not be
found without mathematics.
This talk will be
accessible to a general audience
Refreshments will be served after the talk.