相关论文: Abelian networks III. The critical group

We study information processing in populations of Boolean networks with evolving connectivity and systematically explore the interplay between the learning capability, robustness, the network topology, and the task complexity. We solve a…

We study the critical behavior of the dissipative abelian sandpile model on Z with dissipative sites at arbitrary positions (x_k). This is equivalent to studying whether the expected stopping time of a trapped random walk on Z is finite.…

Let G be a finite graph, and let G_n be the n-th iterated cone over G. We study the structure of the critical group of G_n arising in divisor and sandpile theory.

The Jacobian group (also known as the critical group or sandpile group) is an important invariant of a finite, connected graph $X$; it is a finite abelian group whose cardinality is equal to the number of spanning trees of $X$ (Kirchhoff's…

The $\textit{Abelian Sandpile}$ model is a well-known model used in exploring $\textit{self-organized criticality}$. Despite a large amount of work on other aspects of sandpiles, there have been limited results in efficiently computing the…

The commuting graph of a non-abelian group is a simple graph in which the vertices are the non-central elements of the group, and two distinct vertices are adjacent if and only if they commute. In this paper, we classify (up to isomorphism)…

Cubelike graphs are the Cayley graphs of the elementary abelian group (Z_2)^n (e.g., the hypercube is a cubelike graph). We give conditions for perfect state transfer between two particles in quantum networks modeled by a large class of…

We show that to correctly describe the position of the critical line in the Kauffman random boolean networks one must take into account percolation phenomena underlying the process of damage spreading. For this reason, since the issue of…

A new model of self-organized criticality is proposed. An algebra of operators is introduced which is similar to that used for the Abelian sandpile model. The structure of the configurational space is determined and the number of recurrent…

A popular theory of self-organized criticality relates the critical behavior of driven dissipative systems to that of systems with conservation. In particular, this theory predicts that the stationary density of the abelian sandpile model…

Sandpile groups are a subtle graph isomorphism invariant, in the form of a finite abelian group, whose cardinality is the number of spanning trees in the graph. We study their group structure for graphs obtained by attaching a cone vertex…

Elliptic curves are planar curves which can be used to define an abelian group. The efficient computation of discrete logarithms over this group is a longstanding problem relevant to cryptography. It may be possible to efficiently compute…

Boolean Networks have been used to study numerous phenomena, including gene regulation, neural networks, social interactions, and biological evolution. Here, we propose a general method for determining the critical behavior of Boolean…

This paper describes a quantum algorithm for efficiently decomposing finite Abelian groups. Such a decomposition is needed in order to apply the Abelian hidden subgroup algorithm. Such a decomposition (assuming the Generalized Riemann…

In complex systems, external parameters often determine the phase in which the system operates, i.e., its macroscopic behavior. For nearly a century, statistical physics has extensively studied systems' transitions across phases,…

We consider abelain subgroups of small index in finite groups. More generally, we consider subgroups such that the product of their index by the index of their centralizer is small.

We discuss functions from edges and vertices of an undirected graph to an Abelian group. Such functions, when the sum of their values along any cycle is zero, are called balanced labelings. The set of balanced labelings forms an Abelian…

Let G be an additive, finite abelian group. The critical number $\mathsf{cr}(G)$ of $G$ is the smallest positive integer $\ell$ such that for every subset $S \subset G \setminus \{0\}$ with $|S| \ge \ell$ the following holds: Every element…

This paper contains an analysis of a simple neural network that exhibits self-organized criticality. Such criticality follows from the combination of a simple neural network with an excitatory feedback loop that generates bistability, in…

A classification of critical behavior is provided in systems for which the renormalization group equations are control-parameter dependent. It describes phase transitions in networks with a recursive, hierarchical structure but appears to…