Related papers: Entropy along W_{1,+}-geodesics on graphs

We consider skew tent maps $T_{{\alpha}, {\beta}}(x)$ such that $({\alpha}, {\beta})\in[0,1]^{2}$ is the turning point of $T {_ {{\alpha}, {\beta}}}$, that is, $T_{{\alpha}, {\beta}}=\frac{{\beta}}{{\alpha}}x$ for $0\leq x \leq {\alpha}$…

Entropy is a natural geometric quantity measuring the complexity of a surface embedded in $\mathbb{R}^3$. For dynamical reasons relating to mean curvature flow, Colding-Ilmanen-Minicozzi-White conjectured that the entropy of any closed…

We endow the set of probability measures on a weighted graph with a Monge--Kantorovich metric, induced by a function defined on the set of vertices. The graph is assumed to have $n$ vertices and so, the boundary of the probability simplex…

We introduce an algorithmic model of heat conduction, the thermodynamic graph. The thermodynamic graph is analogous to meshes in the finite difference method in the sense that the calculation of temperature is carried out at the vertices of…

Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…

We define a number of natural (from geometric and combinatorial points of view) deformation spaces of valuations on finite graphs, and study functions over these deformation spaces. These functions include both direct metric invariants…

The main purpose of this thesis is to study the interplay between geometric properties of infinite graphs and analytic and probabilistic objects such as transition operators, harmonic functions and random walks on these graphs. For a…

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…

We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…

In this note we study some properties of topological entropy for noncompact non-metrizable spaces.

Incompressible fluids on curved surfaces are considered with respect to the interplay between topology, geometry and fluid properties using a surface vorticity-stream function formulation, which is solved using parametric finite elements.…

In the article, we generalize some recent results of Colding and Minicozzi on generic singularities of mean curvature flow to curved ambient spaces. To do so, we make use of a weighted monotonicity formula to derive an "almost monotonicity"…

We study the entropy of Sinai-Ruelle-Bowen measure of the geodesic flow on convex real projective surfaces, and shows that the Hilbert area tends to infinity if the entropy tends to zero. For the Blaschke metric, the area tends to infinity…

Let $G=(V,E)$ be a finite, connected graph. We consider a greedy selection of vertices: given a list of vertices $x_1, \dots, x_k$, take $x_{k+1}$ to be any vertex maximizing the sum of distances to the existing vertices and iterate: we…

Topological entropy is a widely studied indicator of chaos in topological dynamics. Here we give a generalized definition of topological entropy which may be applied to set-valued functions. We demonstrate that some of the well-known…

Entropy functionals (i.e. convex integral functionals) and extensions of these functionals are minimized on convex sets. This paper is aimed at reducing as much as possible the assumptions on the constraint set. Dual equalities and…

In this work we study a class of random convex sets that "interpolate" between polytopes and zonotopes. These sets arise from considering a $q^{th}$-moment ($q\geq 1$) of an average of order statistics of $1$-dimensional marginals of a…

We present a method to derive an upper bound for the entropy density of coupled map lattices with local interactions from local observations. To do this, we use an embedding technique being a combination of time delay and spatial embedding.…

Immersions of graphs to the projective plane are studied. A classification of immersions up to regular homotopy is given. A complete invariant of immersions up to regular homotopy is constructed. Equivalence classes are described.

We locate the relevant degrees of freedom for the entanglement entropy on some 2+1 fuzzy models. It is found that the entropy is stored in the near boundary degrees of freedom. We give a simple analytical derivation for the area law using…