The minimal density of a letter in an infinite ternary square-free word is 883/3215.
The minimal density of a letter in an infinite ternary square-free word is .
The monadic second-order logic of graphs III : tree-decompositions, minors and complexity issues
The multiplicity problem for indecomposable decompositions of modules over domestic canonical algebras
Given a module M over a domestic canonical algebra Λ and a classifying set X for the indecomposable Λ-modules, the problem of determining the vector such that is studied. A precise formula for , for any postprojective indecomposable module X, is computed in Theorem 2.3, and interrelations between various structures on the set of all postprojective roots are described in Theorem 2.4. It is proved in Theorem 2.2 that a general method of finding vectors m(M) presented by the authors in Colloq....
The multiplicity problem for indecomposable decompositions of modules over a finite-dimensional algebra. Algorithms and a computer algebra approach
Given a module M over an algebra Λ and a complete set of pairwise nonisomorphic indecomposable Λ-modules, the problem of determining the vector such that is studied. A general method of finding the vectors m(M) is presented (Corollary 2.1, Theorem 2.2 and Corollary 2.3). It is discussed and applied in practice for two classes of algebras: string algebras of finite representation type and hereditary algebras of type . In the second case detailed algorithms are given (Algorithms 4.5 and 5.5).
The Mumford-Shah conjecture in image processing
The MX/M/1 queue with working breakdown
In this paper, we consider a batch arrival MX/M/1 queue model with working breakdown. The server may be subject to a service breakdown when it is busy, rather than completely stoping service, it will decrease its service rate. For this model, we analyze a two-dimensional Markov chain and give its quasi upper triangle transition probability matrix. Under the system stability condition, we derive the probability generating function (PGF) of the stationary queue length, and then obtain its stochastic...
The NP-completeness of automorphic colorings
Given a graph G, an automorphic edge(vertex)-coloring of G is a proper edge(vertex)-coloring such that each automorphism of the graph preserves the coloring. The automorphic chromatic index (number) is the least integer k for which G admits an automorphic edge(vertex)-coloring with k colors. We show that it is NP-complete to determine the automorphic chromatic index and the automorphic chromatic number of an arbitrary graph.
The number of automata, boundedly determined functions and hereditary properties of automata
The number of binary rotation words
We consider binary rotation words generated by partitions of the unit circle to two intervals and give a precise formula for the number of such words of length n. We also give the precise asymptotics for it, which happens to be Θ(n4). The result continues the line initiated by the formula for the number of all Sturmian words obtained by Lipatov [Problemy Kibernet. 39 (1982) 67–84], then independently by Mignosi [Theoret. Comput. Sci. 82 (1991) 71–84], and others.
The Number of Non-Isomorphic Hamiltonian Circuits in an -Dimensional Cube
The number of positions starting a square in binary words.
The number of ternary words avoiding abelian cubes grows exponentially.
The observational predicate calculus and complexity of computations (Preliminary communication)
The online specialization problem.
The onset of necrosis in a 3D cellular automaton model of EMT6 multi-cellular spheroids
A 3-dimensional (3D) extension to a previously reported scaled 2-dimensional Cellular Automaton (CA) model of avascular multi-cellular spheroid growth is presented and analysed for the EMT6/Ro cell line. The model outputs are found to compare favourably with reported experimentally obtained data for in vitro spheroids of the same cell line. Necrosis (unprogrammed central cell death) is observed to be delayed when compared with the experimental data. Furthermore, it is found that necrosis arises...
The optimal lower bound for generators of invariant rings without finite SAGBI bases with respect to any admissible order.
The optimization of feed forward neural networks structure using genetic algorithms.
The order of node removals in influence diagram
The Orthogonal Convex Skull Problem.