99,920 research outputs found
Mixtures of Spatial Spline Regressions
We present an extension of the functional data analysis framework for
univariate functions to the analysis of surfaces: functions of two variables.
The spatial spline regression (SSR) approach developed can be used to model
surfaces that are sampled over a rectangular domain. Furthermore, combining SSR
with linear mixed effects models (LMM) allows for the analysis of populations
of surfaces, and combining the joint SSR-LMM method with finite mixture models
allows for the analysis of populations of surfaces with sub-family structures.
Through the mixtures of spatial splines regressions (MSSR) approach developed,
we present methodologies for clustering surfaces into sub-families, and for
performing surface-based discriminant analysis. The effectiveness of our
methodologies, as well as the modeling capabilities of the SSR model are
assessed through an application to handwritten character recognition
Spreading of sexually transmitted diseases in heterosexual populations
The spread of sexually transmitted diseases (e.g. Chlamydia, Syphilis,
Gonorrhea, HIV) across populations is a major concern for scientists and health
agencies. In this context, both data collection on sexual contact networks and
the modeling of disease spreading, are intensively contributing to the search
for effective immunization policies. Here, the spreading of sexually
transmitted diseases on bipartite scale-free graphs, representing heterosexual
contact networks, is considered. We analytically derive the expression for the
epidemic threshold and its dependence with the system size in finite
populations. We show that the epidemic outbreak in bipartite populations, with
number of sexual partners distributed as in empirical observations from
national sex surveys, takes place for larger spreading rates than for the case
in which the bipartite nature of the network is not taken into account.
Numerical simulations confirm the validity of the theoretical results. Our
findings indicate that the restriction to crossed infections between the two
classes of individuals (males and females) has to be taken into account in the
design of efficient immunization strategies for sexually transmitted diseases.Comment: 7 pages, 3 figures and 2 table
Error control for the FEM approximation of an upscaled thermo-diffusion system with Smoluchowski interactions
We analyze a coupled system of evolution equations that describes the effect
of thermal gradients on the motion and deposition of populations of
colloidal species diffusing and interacting together through Smoluchowski
production terms. This class of systems is particularly useful in studying drug
delivery, contaminant transportin complex media, as well as heat shocks
thorough permeable media. The particularity lies in the modeling of the
nonlinear and nonlocal coupling between diffusion and thermal conduction. We
investigate the semidiscrete as well as the fully discrete em a priori error
analysis of the finite elements approximation of the weak solution to a
thermo-diffusion reaction system posed in a macroscopic domain. The
mathematical techniques include energy-like estimates and compactness
arguments
Quasi-stationary states of game-driven systems: a dynamical approach
Evolutionary game theory is a framework to formalize the evolution of
collectives ("populations") of competing agents that are playing a game and,
after every round, update their strategies to maximize individual payoffs.
There are two complementary approaches to modeling evolution of player
populations. The first addresses essentially finite populations by implementing
the apparatus of Markov chains. The second assumes that the populations are
infinite and operates with a system of mean-field deterministic differential
equations. By using a model of two antagonistic populations, which are playing
a game with stationary or periodically varying payoffs, we demonstrate that it
exhibits metastable dynamics that is reducible neither to an immediate
transition to a fixation (extinction of all but one strategy in a finite-size
population) nor to the mean-field picture. In the case of stationary payoffs,
this dynamics can be captured with a system of stochastic differential
equations and interpreted as a stochastic Hopf bifurcation. In the case of
varying payoffs, the metastable dynamics is much more complex than the dynamics
of the means
Local/global analysis of the stationary solutions of some neural field equations
Neural or cortical fields are continuous assemblies of mesoscopic models,
also called neural masses, of neural populations that are fundamental in the
modeling of macroscopic parts of the brain. Neural fields are described by
nonlinear integro-differential equations. The solutions of these equations
represent the state of activity of these populations when submitted to inputs
from neighbouring brain areas. Understanding the properties of these solutions
is essential in advancing our understanding of the brain. In this paper we
study the dependency of the stationary solutions of the neural fields equations
with respect to the stiffness of the nonlinearity and the contrast of the
external inputs. This is done by using degree theory and bifurcation theory in
the context of functional, in particular infinite dimensional, spaces. The
joint use of these two theories allows us to make new detailed predictions
about the global and local behaviours of the solutions. We also provide a
generic finite dimensional approximation of these equations which allows us to
study in great details two models. The first model is a neural mass model of a
cortical hypercolumn of orientation sensitive neurons, the ring model. The
second model is a general neural field model where the spatial connectivity
isdescribed by heterogeneous Gaussian-like functions.Comment: 38 pages, 9 figure
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