相关论文: Spiders' webs in the punctured plane

We introduce the Webworld model, which links together the ecological modelling of food web structure with the evolutionary modelling of speciation and extinction events. The model describes dynamics of ecological communities on an…

Regarding the Specht modules associated to the two-row partition $(n,n)$, we provide a combinatorial path model to study the transitioning matrix from the tableau basis to the $A_1$-web basis (i.e. cup diagrams), and prove that the entries…

We show that the points that converge to infinity under iteration of the exponential map form a connected subset of the complex plane.

We investigate in detail the model of a trophic web proposed by Amaral and Meyer [Phys. Rev. Lett. 82, 652 (1999)]. We focused on small-size systems that are relevant for real biological food webs and for which the fluctuations are playing…

The sl_3 spider is a diagrammatic category used to study the representation theory of the quantum group U_q(sl_3). The morphisms in this category are generated by a basis of non-elliptic webs. Khovanov- Kuperberg observed that non-elliptic…

Collectives are often able to process information in a distributed fashion, surpassing each individual member's processing capacity. In fission-fusion dynamics, where group members come together and split from others often, sharing…

We study the geometry of simply connected wandering domains for entire functions and we prove that every bounded connected regular open set, whose closure has a connected complement, is a wandering domain of some entire function. In…

Intelligence analysts have long struggled with an abundance of data that must be investigated on a daily basis. In the U.S. Army, this activity involves reconciling information from various sources, a process that has been automated to a…

In this paper, we prove that escaping set of transcendental semigroup is S-forward invariant. We also prove that if holomorphic semigroup is abelian, then Fatou set, Julia set and escaping set are S-completely invariant. We see certain…

The concept of the cosmic web, viewing the Universe as a set of discrete galaxies held together by gravity, is deeply engrained in cosmology. Yet, little is known about the most effective construction and the characteristics of the…

Food webs, networks of feeding relationships among organisms, provide fundamental insights into mechanisms that determine ecosystem stability and persistence. Despite long-standing interest in the compartmental structure of food webs, past…

We consider a special type of self-similar sets, called fractal squares, and give a brief review on recent results and unsolved issues with an emphasis on their topological properties.

In holomorphic semigroup dynamics, Julia set is in general backward invariant and so some fundamental results of classical complex dynamics can not be generalized to semigroup dynamics. In this paper, we define completely invariant Julia…

By means of theory group analysis, some algebraic and geometrical properties of quaternion analogs of \emph{Julia} sets are investigated. We argue that symmetries, intrinsic to quaternions, give rise to the class of identical \emph{Julia}…

Webs are planar graphs with boundary that describe morphisms in a diagrammatic representation category for $\mathfrak{sl}_k$. They are studied extensively by knot theorists because braiding maps provide a categorical way to express link…

Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism…

We present the SpineWeb framework for the topological analysis of the Cosmic Web and the identification of its walls, filaments and cluster nodes. Based on the watershed segmentation of the cosmic density field, the SpineWeb method invokes…

Codimension one webs are configurations of finitely many codimension one foliations in general position. Much of the classical theory evolved around the concept of abelian relation: a functional relation among the first integrals of the…

We consider crossbar switching networks with base $b$ (that is, constructed from $b\times b$ crossbar switches), scale $k$ (that is, with $b^k$ inputs, $b^k$ outputs and $b^k$ links between each consecutive pair of stages) and depth $l$…

We use Bowen's definition of topological entropy and Ahlfors five islands theorem, as well as the theory of polynomial-like mappings, to show that the topological entropy of any entire transcendental function is infinity. In addition the…