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Analysis of a mathematical model of syntrophic bacteria in a chemostat
Syntrophic relationship Mathematical modelling Coexistence Asymptotic stability Anaerobic digestion
2011/9/23
Abstract: A mathematical model involving a syntrophic relationship between two populations of bacteria in a continuous culture is proposed. A detailed qualitative analysis is carried out. The local an...
Dense properties of the space of the circle diffeomorphisms with a Liouville rotation number
circle diffeomorphism rotation number Liouville number conjugacy invariant measure fast approximation by conjugation
2011/9/23
Abstract: Given any Liouville number $\alpha$, it is shown that various subspaces are $C^\infty$-dense in the space of the orientation preserving $C^\infty$ diffeomorphisms of the circle with rotation...
Asymptotic stability of ground states in some Hamiltonian PDEs with symmetry
Asymptotic stability of ground states Hamiltonian PDEs symmetry
2011/9/22
Abstract: We consider a ground state (soliton) of a Hamiltonian PDE. We prove that if the soliton is orbitally stable then it is also asymptotically stable. The main assumptions are transversal nondeg...
Lee-Yang-Fisher zeros for DHL and 2D rational dynamics, II. Global Pluripotential Interpretation
Lee-Yang-Fisher zeros 2D rational dynamics Global Pluripotential Interpretation
2011/9/22
Abstract: In a classical work of the 1950's, Lee and Yang proved that for fixed nonnegative temperature, the zeros of the partition functions of a ferromagnetic Ising model always lie on the unit circ...
Fractal bodies invisible in 2 and 3 directions
Billiards invisible bodies shape optimization geometrical optics problems of minimal resistance
2011/9/22
Abstract: We study the problem of invisibility for bodies with a mirror surface in the framework of geometrical optics. We show that for any two given directions it is possible to construct a two-dime...
Multiple steady states in a mathematical model for interactions between T cells and macrophages
mathematical model T cells and macrophages Cell Behavior
2011/10/9
Abstract: The aim of this paper is to prove results about the existence and stability of multiple steady states in a system of ordinary differential equations introduced by R. Lev Bar-Or to model the ...
On Thouvenot's ergodic proof of Roth's theorem
Thouvenot's ergodic proof Roth's theorem Dynamical Systems
2011/9/21
Abstract: We present a lecture note on Thouvenot's proof of the Roth-Furstenberg theorem and joining proofs of Furstenberg's theorems on multiple progression average mixing for weakly mixing transform...
Existence of complete Lyapunov functions for semiflows on separable metric spaces
Lyapunov functions Semiflows Separable metric space
2011/9/23
Abstract: The aim of this short note is to show how to construct a complete Lyapunov function of a semiflow by using a complete Lyapunov function of its time-one map. As a byproduct we assure the exis...
Non-Uniform Cellular Automata: classes, dynamics, and decidability
cellular automata non-uniform cellular automata decidability symbolic dynamics
2011/10/9
Abstract: The dynamical behavior of non-uniform cellular automata is compared with the one of classical cellular automata. Several differences and similarities are pointed out by a series of examples....
A Mathematical model for Astrocytes mediated LTP at Single Hippocampal Synapses
Mathematical model Astrocytes LTP Hippocampal Synapses
2011/10/9
Abstract: Many contemporary studies have shown that astrocytes play a significant role in modulating both short and long form of synaptic plasticity. There are very few experimental models which eluci...
Hierarchy of graph matchbox manifolds
matchbox manifold laminations ends of leaves growth of leaves theory of levels GromovHausdorff metric
2011/9/21
Abstract: We study a class of graph foliated spaces, or graph matchbox manifold, initially constructed by Kenyon and Ghys. For graph foliated spaces we introduce a quantifier of dynamical complexity w...
Almost periodic structures and the semiconjugacy problem
periodic structures semiconjugacy problem Dynamical Systems
2011/9/20
Abstract: The description of almost periodic or quasiperiodic structures has a long tradition in mathematical physics, in particular since the discovery of quasicrystals in the early 80's. Frequently,...
Variational Gaussian Process Dynamical Systems
Gaussian Dynamical Systems Machine Learning
2011/10/9
Abstract: High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphi...
Open problems in local discrete holomorphic dynamics
local discrete holomorphic dynamics Dynamical Systems
2011/9/20
Abstract: This paper contains a selection, dictated by personal taste and by no means complete, of open problems in local discrete holomorphic dynamics.
Stable Configurations of repelling points on compact hyperbolic Manifolds
compact hyperbolic Manifolds Dynamical Systems
2011/9/20
Abstract: It is shown that on compact hyperbolic manifolds, certain stable configurations of points which mutually repel along all interconnecting geodesics become equidistributed as the number of poi...