Directed graphs and Lie superalgebras of matrices

No abstract

On the Jacobson radical of strongly group graded rings

summary:For any non-torsion group $G$ with identity $e$, we construct a strongly $G$-graded ring $R$ such that the Jacobson radical $J(R_e)$ is locally nilpotent, but $J(R)$ is not locally nilpotent. This answers a question posed by Puczy{\l}owski

On congruences of automata defined by directed graphs

Graphs and various objects derived from them are basic essential tools that have been actively used in various branches of modern theoretical computer science. In particular, graph grammars and graph transformations have been very well explored in the literature. We consider finite state automata defined by directed graphs, characterize all their congruences, and give a complete description of all automata of this type satisfying three properties for congruences introduced and considered in the literature by analogy with classical semisimplicity conditions that play important roles in structure theory

Ideal bases in constructions defined by directed graphs

The present article continues the investigation of visible ideal bases in constructions defined using directed graphs. Our main theorem establishes that, for every balanced digraph D and each idempotent semiring R with 1, the incidence semiring ID(R) of the digraph D has a convenient visible ideal basis BD(R). It also shows that the elements of BD(R) can always be used to generate two-sided ideals with the largest possible weight among the weights of all two-sided ideals in the incidence semiring

Automatic generation of meta classifiers with large levels for distributed computing and networking

This paper is devoted to a case study of a new construction of classifiers. These classifiers are called automatically generated multi-level meta classifiers, AGMLMC. The construction combines diverse meta classifiers in a new way to create a unified system. This original construction can be generated automatically producing classifiers with large levels. Different meta classifiers are incorporated as low-level integral parts of another meta classifier at the top level. It is intended for the distributed computing and networking. The AGMLMC classifiers are unified classifiers with many parts that can operate in parallel. This make it easy to adopt them in distributed applications. This paper introduces new construction of classifiers and undertakes an experimental study of their performance. We look at a case study of their effectiveness in the special case of the detection and filtering of phishing emails. This is a possible important application area for such large and distributed classification systems. Our experiments investigate the effectiveness of combining diverse meta classifiers into one AGMLMC classifier in the case study of detection and filtering of phishing emails. The results show that new classifiers with large levels achieved better performance compared to the base classifiers and simple meta classifiers classifiers. This demonstrates that the new technique can be applied to increase the performance if diverse meta classifiers are included in the system

A new model for classifying DNA code inspired by neural networks and FSA

This paper introduces a new model of classifiers CL(V,E,l,r) designed for classifying DNA sequences and combining the flexibility of neural networks and the generality of finite state automata. Our careful and thorough verification demonstrates that the classifiers CL(V,E,l,r) are general enough and will be capable of solving all classification tasks for any given DNA dataset. We develop a minimisation algorithm for these classifiers and include several open questions which could benefit from contributions of various researchers throughout the world