Related papers: Piecewise Linear Phase Transitions
Phase Transition is associated with a drastic change in some observable (ordered parameter) of the system when the controlled parameter is tuned smoothly. Lee-Yang theory of phase transition is discussed which is related to the accumulation…
The intrinsic nature of a problem usually suggests a first suitable method to deal with it. Unfortunately, the apparent ease of application of these initial approaches may make their possible flaws seem to be inherent to the problem and…
The cluster distributions of different systems are examined to search for signatures of a continuous phase transition. In a system known to possess such a phase transition, both sensitive and insensitive signatures are present; while in…
The past few years have seen many advances in our understanding of the dynamics of polymeric fluids. These include improvements on the successful reptation theory; an emerging molecular theory of semiflexible chain dynamics; and an…
Certain geometric properties of submanifolds of configuration space are numerically investigated for classical lattice phi^4 models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the…
We analyze the pattern formation in systems of active particles with chiral forces in the context of pedestrian dynamics. To describe the interparticle interactions, we use the standard social force model and supplement it with a new type…
A simple approach is presented to study the asymptotic behavior of some algorithms with an underlying tree structure. It is shown that some asymptotic oscillating behaviors can be precisely analyzed without resorting to complex analysis…
In this paper we define "piecewise scalable frames". This new scaling process allows us to alter many frames to Parseval frames which is impossible by the previous standard scaling. We give necessary and sufficient conditions for a frame to…
Most existing interpretable methods explain a black-box model in a post-hoc manner, which uses simpler models or data analysis techniques to interpret the predictions after the model is learned. However, they (a) may derive contradictory…
In the first part we associate a periodic sequence to a partition and study the connection the distribution of elements of uniform limit of the sequences. Then some facts of statistical independence of these limits are proved
The topological theory of phase transitions has its strong point in two theorems proving that, for a wide class of physical systems, phase transitions necessarily stem from topological changes of some submanifolds of configuration space. It…
We extend the theory of transience to general dynamical systems with no Markov structure assumed. This is linked to the theory of phase transitions. We also provide examples of new kinds of transient behaviour.
Particle filtering is a popular method for inferring latent states in stochastic dynamical systems, whose theoretical properties have been well studied in machine learning and statistics communities. In many control problems, e.g.,…
In this paper, we study the phase transition behavior emerging from the interactions among multiple agents in the presence of noise. We propose a simple discrete-time model in which a group of non-mobile agents form either a fixed connected…
This article discusses a partially adapted particle filter for estimating the likelihood of a nonlinear structural econometric state space models whose state transition density cannot be expressed in closed form. The filter generates the…
We characterize the non equilibrium stationary states in two classes of systems where phase transitions are present. We prove that the interface in the limit is a plane which separates the two phases.
Many classic questions of structural theory concern discrete changes, such as the formation or dissolution of groups, role turnover, or faction realignment. Here, we consider a basic framework combining prior work on change paths and recent…
We study in further detail particle models displaying a boundary-induced absorbing state phase transition [Phys. Rev. E. {\bf 65}, 046104 (2002) and Phys. Rev. Lett. {\bf 100}, 165701 (2008)] . These are one-dimensional systems consisting…
The group of piecewise projective homeomorphisms of the line provides straightforward counter-examples to the so-called von Neumann conjecture. The examples are so simple that many additional properties can be established.
Linear Parameter-Varying (LPV) systems with piecewise differentiable parameters is a class of LPV systems for which no proper analysis conditions have been obtained so far. To fill this gap, we propose an approach based on the theory of…