相关论文: Dimer-monomer model on the generalized Tower of Ha…

We obtain the entropy of flexible linear chains composed of M monomers placed on the square lattice using a transfer matrix approach. An excluded volume interaction is included by considering the chains to be self-and mutually avoiding, and…

We provide proofs of the following theorems by considering the entropy of random walks: Theorem 1.(Alon, Hoory and Linial) Let G be an undirected simple graph with n vertices, girth g, minimum degree at least 2 and average degree d: Odd…

We study partition functions for the dimer model on families of finite graphs converging to infinite self-similar graphs and forming approximation sequences to certain well-known fractals. The graphs that we consider are provided by actions…

Let $f$ be a $C^r$ ($r>1$) diffeomorphism on a compact surface $M$ with $h_{\rm top}(f)\geq\frac{\lambda^{+}(f)}{r}$ where $\lambda^{+}(f):=\lim_{n\to+\infty}\frac{1}{n}\max_{x\in M}\log \left\|Df^{n}_{x}\right\|$. We establish an…

On a finite weighted graph, the dimer model is a probability measure on its dimer covers, that assigns to any cover a probability proportional to the product of the weights of its edges. For planar bipartite graphs, dimer correlations are…

The entropy of a graph is an information-theoretic quantity which expresses the complexity of a graph \cite{DM1,M}. After Shannon introduced the definition of entropy to information and communication, many generalizations of the entropy…

Let $G$ be a large (simple, unlabeled) dense graph on $n$ vertices. Suppose that we only know, or can estimate, the empirical distribution of the number of subgraphs $F$ that each vertex in $G$ participates in, for some fixed small graph…

The entropy density is an intuitive and powerful concept to study the complicated nonlinear processes derived from physical systems. We develop the minimum entropy density method (MEDM) to detect the structure scale of a given time series,…

We derive an entropy-area law for the future horizon of an observer in diamonds inside the static patch of de Sitter spacetime, taking into account the backreaction of quantum matter fields. We prove positivity and convexity of the relative…

Carbon nanotube Y-junctions are of great interest to the next generation of innovative multi-terminal nanodevices. Topological indices are graph-theoretically based parameters that describe various structural properties of a chemical…

We derive a unified closed-form expression for the Frame-Stewart algorithm in the multi-peg Tower of Hanoi: M(p,n) = 2^(i(p,n)+1)*n - sum_{k=0}^{i(p,n)} 2^k * C(p+k-2, k), where i(p,n) = min{ j >= 0 : n <= C(p-1+j, j+1) }. and prove it…

The bead model is a random point field on $\mathbb{Z}\times\mathbb{R}$ which can be viewed as a scaling limit of dimer model. We prove that, in the scaling limit, the normalized height function of a uniformly chosen random bead…

In the theory of surface diffeomorphisms relative to homoclinic and heteroclinic orbits, it is possible to compute a one-dimensional representative map for any irreducible isotopy class. The topological entropy of this graph representative…

We present the numbers of ice model and eight-vertex model configurations (with Boltzmann factors equal to one), I(n) and E(n) respectively, on the two-dimensional Sierpinski gasket SG(n) at stage $n$. For the eight-vertex model, the number…

Many complex systems can be modeled by temporal networks, whose organization often evolves through distinct structural phases. Detecting the change points that delimit these phases is both important and challenging. In this work, we extend…

We study properties of the Potts model partition function $Z(H_m,q,v)$ on $m$'th iterates of Hanoi graphs, $H_m$, and use the results to draw inferences about the $m \to \infty$ limit that yields a self-similar Hanoi fractal, $H_\infty$. We…

We introduce a many-body topological invariant, called the topological disorder parameter (TDP), to characterize gapped quantum phases with global internal symmetry in (2+1)d. TDP is defined as the constant correction that appears in the…

The R\'{e}nyi $\alpha$-entropy $H_{\alpha}$ of complete antisymmetric directed graphs (i.e., tournaments) is explored. We optimize $H_{\alpha}$ when $\alpha = 2$ and $3$, and find that as $\alpha$ increases $H_{\alpha}$'s sensitivity to…

In this paper, we develop the notion of entropy for uniform hypergraphs via tensor theory. We employ the probability distribution of the generalized singular values, calculated from the higher-order singular value decomposition of the…

Let $H_d(n,p)$ signify a random $d$-uniform hypergraph with $n$ vertices in which each of the ${n}\choose{d}$ possible edges is present with probability $p=p(n)$ independently, and let $H_d(n,m)$ denote a uniformly distributed with $n$…