Intersection problem for Droms RAAGs

We solve the subgroup intersection problem (SIP) for any RAAG [Formula: see text] of Droms type (i.e. with defining graph not containing induced squares or paths of length [Formula: see text]): there is an algorithm which, given finite sets of generators for two subgroups [Formula: see text], decides whether [Formula: see text] is finitely generated or not, and, in the affirmative case, it computes a set of generators for [Formula: see text]. Taking advantage of the recursive characterization of Droms groups, the proof consists in separately showing that the solvability of SIP passes through free products, and through direct products with free-abelian groups. We note that most of RAAGs are not Howson, and many (e.g. [Formula: see text]) even have unsolvable SIP.

Embeddability of right-angled Artin groups on the complements of linear forests

In this paper, we prove that embeddings of right-angled Artin group [Formula: see text] on the complement of a linear forest into another right-angled Artin group [Formula: see text] can be reduced to full embeddings of the defining graph of [Formula: see text] into the extension graph of the defining graph of [Formula: see text].

Modeling Software Architecture Evolution for Electronic Commerce System Based on Graph Representation

With the rapid development of mobil internent and internet of things,most of electronic commerce systems need to be improved.Software architecture evolution for electronic commerce system provides an important technology measure for its improvement work. This paper try to model software architecture evolution of e-commerce based on graph representation.Firstly the paper apply a graph to represent SA of a e-commerce system,and give its formulazation description.Then establish some basic evolution rules for software architecture evolution of electronic commerce system on the basis of defining graph transformation rule,software architecture evolution operations for electronic commerce can be carryed out according to these evolution rules.Finally through an evolution case, the sophisticated process of software architecture evolution for the electronic commerce system is described.This research work can help to upgrade the electronic commerce. system.

Combinatorial Methods for Detecting Surface Subgroups in Right-Angled Artin Groups

We give a short proof of the following theorem of Sang-hyun Kim: if is a right-angled Artin group with defining graph , then contains a hyperbolic surface subgroup if contains an induced subgraph for some , where denotes the complement graph of an -cycle. Furthermore, we give a new proof of Kim's cocontraction theorem.

ON SOLVABLE SUBGROUPS OF AUTOMORPHISM GROUPS OF RIGHT-ANGLED ARTIN GROUPS

For any right-angled Artin group, we show that its outer automorphism group contains either a finite-index nilpotent subgroup or a nonabelian free subgroup. This is a weak Tits alternative theorem. We find a criterion on the defining graph that determines which case holds. We also consider some examples of solvable subgroups, including one that is not virtually nilpotent and is embedded in a non-obvious way.

POISSON PROCESSES FOR SUBSYSTEMS OF FINITE TYPE IN SYMBOLIC DYNAMICS

Let Δ ⊊ V be a proper subset of the vertices V of the defining graph of an irreducible and aperiodic shift of finite type [Formula: see text]. Let ΣΔ be the subshift of allowable paths in the graph of [Formula: see text] which only passes through the vertices of Δ. For a random point x chosen with respect to an equilibrium state μ of a Hölder potential φ on [Formula: see text], let τn be the point process defined as the sum of Dirac point masses at the times k > 0, suitably rescaled, for which the first n-symbols of Tkx belong to Δ. We prove that this point process converges in law to a marked Poisson point process of constant parameter measure. The scale is related to the pressure of the restriction of φ to ΣΔ and the parameters of the limit law are explicitly computed.

A Graph Grammar Approach to Generate Neural Network Topologies

Neural networks are increasingly becoming a useful and popular choice for process modeling. The success of neural networks in effectively modeling a certain problem depends on the topology of the neural network. Generating topologies manually relies on previous neural network experience and is tedious and difficult. Hence there is a rising need for a method that generates neural network topologies for different problems automatically. Current methods such as growing, pruning and using genetic algorithms for this task are very complicated and do not explore all the possible topologies. This paper presents a novel method of automatically generating neural networks using a graph grammar. The approach involves representing the neural network as a graph and defining graph transformation rules to generate the topologies. The approach is simple, efficient and has the ability to create topologies of varying complexity. Two example problems are presented to demonstrate the power of our approach.

On outward and inward productions in the categorical graph-grammar approach and Δ-grammars

We consider the relationship between three ways of defining graph derivability. That the traditional double-pushout approach and Banach's inward version are equivalent in the case of injective left-hand sides is proved in a purely categorical setting. In the case of noninjective left-hand sides, equivalence can be shown in special categories if the right-hand side is injective. Both approaches have the same generative power in the category of graphs if the pushout connecting the outward production with the inward one is a pullback as well. Finally, it is shown that Banach's point of view establishes a close relationship between the categorical approach and Kaplan's Δ-grammars, allowing a slight generalization of Δ-grammars and making them an operational description of the categorical approach.