Related papers: Algebraic entropy of sign-stable mutation loops

In statistical physics, entropy is generally logarithm of probability. Therefore, if dynamics is decomposed by log, entropy production should be decomposed properly. In the present work, log-decomposition of dynamics is introduced. By which…

We study the dynamic scaling properties of an aggregation model in which particles obey both diffusive and driven ballistic dynamics. The diffusion constant and the velocity of a cluster of size $s$ follow $D(s) \sim s^\gamma$ and $v(s)…

In this paper, we consider a resource-consumer model taking into account a mutation effect between species (with constant mutation rate). The corresponding mutation operator is a discretization of the Laplacian in such a way that the…

Let $G=\left\langle S|R_{A}\right\rangle $ be a semigroup with generating set $ S$ and equivalences $R_{A}$ among $S$ determined by a matrix $A$. This paper investigates the complexity of $G$-shift spaces by yielding the topological…

Kleinberg introduced three natural clustering properties, or axioms, and showed they cannot be simultaneously satisfied by any clustering algorithm. We present a new clustering property, Monotonic Consistency, which avoids the well-known…

Let $K = \{0,1,...,q-1\}$. We use a special class of translation invariant measures on $K^\mathbb{Z}$ called algebraic measures to study the entropy rate of a hidden Markov processes. Under some irreducibility assumptions of the Markov…

We study ergodic properties of a family of traffic maps acting in the space of bi-infinite sequences of real numbers. The corresponding dynamics mimics the motion of vehicles in a simple traffic flow, which explains the name. Using…

We develop analytical methods for computing the structure constant for three heavy operators, starting from the recently proposed hexagon approach. Such a structure constant is a semiclassical object, with the scale set by the inverse…

Numerical computation of the time evolution of the mass transfer rate in a close binary can be and, in particular, has been a computational challenge. Using a simple physical model to calculate the mass transfer rate, we show that for a…

We study polynomial and exponential stability for $C_{0}$-semigroups using the recently developed theory of operator-valued $(L^{p},L^{q})$ Fourier multipliers. We characterize polynomial decay of orbits of a $C_{0}$-semigroup in terms of…

The metastable states of a glass are counted by adding a weak pinning field which explicitly breaks the ergodicity. Their entropy, that is the logarithm of their number, is extensive in a range of temperatures $T_G < T < T_C$ only, where…

To describe the small-scale intermittency of turbulence, a self-similarity is assumed for the probability density function of a logarithm of the rate of energy dissipation smoothed over a length scale among those in the inertial range. The…

Motivated by the ubiquitous sampled-data setup in applied control, we examine the stability of a class of difference equations that arises by sampling a right- or left-invariant flow on a matrix Lie group. The map defining such a difference…

As a service for the solid mechanics community we gather in this paper constitutive properties of a collective list of isotropic elastic energies for compressible materials. Of interest to us are the invertibility and monotonicity of…

While macroscopic properties of spin glasses have been thoroughly investigated, their manifestation in the corresponding microscopic configurations is much less understood. Cases where both descriptions have been provided, such as…

We introduce a class of commutative superalgebras generalizing cluster algebras. A cluster superalgebra is defined by a hypergraph called an "extended quiver", and transformations called mutations. We prove the super analog of the "Laurent…

We generalise surface cluster algebras to the case of infinite surfaces where the surface contains finitely many accumulation points of boundary marked points. To connect different triangulations of an infinite surface, we consider infinite…

Direct numerical simulation of homogeneous isotropic turbulence shows pronounced clustering of inertial particles in the inertial subrange at high Reynolds number, in addition to the clustering typically observed in the near dissipation…

We study the stability of quantum pure states and, more generally, subspaces for stochastic dynamics that describe continuously--monitored systems. We show that the target subspace is almost surely invariant if and only if it is invariant…

The sign coherence of $c$-vectors is one of the fundamental theorems of cluster algebras with principal coefficients. In 2019, Gekhtman and Nakanishi posed the asymptotic sign coherence conjecture for arbitrary cluster algebras of geometric…