一种简单神经Mealy机的构造

构造一种新型神经Mealy机,神经Mealy机具有一定的学习能力,它主要通过学习来获得(von Newman)计算机结构,可以较好地避免普通计算机那样损毁一条电路就带来灾难性后果的情况.其本质是将递归神经网络通过BP优化算法,对Mealy机进行模拟得到,并通过实验对该网络的学习性能进行研究分析.基于形式文法和自动机的等价性,用神经网络来实现文法推导.先采用神经网络对样本集进行学习,这些样本可由一个经典Mealy机生成,然后从训练完的神经网络提取出自动机.     

The smallest nontoroidal chiral maps

In this paper, we display those chiral maps which have fewest edges among those of genus greater than one. One of these is a branched covering of a regular map on the torus, and the other is its dual.     

Mealy Morphisms of Enriched Categories

We define and study the properties of a notion of morphism of enriched categories, intermediate between strong functor and profunctor. Suggested by bicategorical considerations, it turns out to be a generalization of Mealy machine, well-known since the 1950’s in the theory of computation. When the base category is closed we construct a classifying category for Mealy morphisms, as we call them. This is also seen to give the free tensor completion of an enriched category.     

The smallest moufang loop revisited

We derive presentations for Moufang loops of type M _2n(G, 2), defined by Chein, with G finite, two-generated. We then use G = S ₃ to visualize the smallest non-associative Moufang loop.     

The smallest point of a polytope

This note suggests new ways for calculating the point of smallest Euclidean norm in the convex hull of a given set of points inR ⁿ . It is shown that the problem can be formulated as a linear least-square problem with nonnegative variables or as a least-distance problem. Numerical experiments illustrate that the least-square problem is solved efficiently by the active set method. The advantage of the new approach lies in the solution of large sparse problems. In this case, the new formulation permits the use of row relaxation methods. In particular, the least-distance problem can be solved by Hildreth's method.     

Discontinuous cellular automaton method for crack growth analysis without remeshing

A numerical technical of discontinuous cellular automaton method for crack growth analysis without remeshing is developed. In this method, the level set method is employed to track the crack location and its growth path, where the level set functions and calculation grids are independent, so no explicit meshing for crack surface and no remeshing for crack growth are needed. Then, the discontinuous enrichment shape functions which are enriched by the Heaviside function and the exact near-tip asymptotic field functions are constructed to model the discontinuity of cracks. Finally, a discontinuous cellular automaton theory is proposed, which are composed of cell, neighborhood and updating rules for discontinuous case. There is an advantage that the calculation is only applied on local cell, so no assembled stiffness matrix but only cell stiffness is needed, which can overcome the stiffness matrix assembling difficulty caused by unequal degrees of nodal freedom for different cells, and much easier to consider the local properties of cells. Besides, the present method requires much less computer memory than that of XFEM because of it local property.     

Three-dimensional cellular automaton simulation of tumour growth in inhomogeneous oxygen environment

Cellular automaton theory has previously been used to study cell growth. In this study, we present a three-dimensional cellular automaton model performing the growth simulation of normal and cancerous cells. The necessary nutrient supply is provided by an artificial arterial tree which is generated by constrained constructive optimization. Spatial oxygen diffusion is approximated again by a cellular automaton model. All results could be illustrated dynamically by three-dimensional volume visualization. Because of the chosen modelling approach, an extension of the model to simulate angiogenic processes is possible.     

Semigroups of matrices of intermediate growth

Finitely generated linear semigroups over a field K that have intermediate growth are considered. New classes of such semigroups are found and a conjecture on the equivalence of the subexponential growth of a finitely generated linear semigroup S and the nonexistence of free noncommutative subsemigroups in S, or equivalently the existence of a nontrivial identity satisfied in S, is stated. This ‘growth alternative’ conjecture is proved for linear semigroups of degree 2, 3 or 4. Certain results supporting the general conjecture are obtained. As the main tool, a new combinatorial property of groups is introduced and studied.     

Distinguishing graphs with intermediate growth

A graph G is said to be 2-distinguishable if there is a 2-labeling of its vertices which is not preserved by any nontrivial automorphism of G. We show that every locally finte graph with infinite nite motion and growth at most \(\mathcal{O}\left( {2^{(1 - \varepsilon )\tfrac{{\sqrt n }}{2}} } \right)\) is 2-distinguishable. Infinite motion means that every automorphism moves infinitely many vertices and growth refers to the cardinality of balls of radius n.     

The semigroup of a strongly connected automaton

We show that each member of a class of strongly connected automata (containing all the finite ones) whose input semigroup is the semigroup of the automaton is isomorphic to an automaton (A,S,) where S is a semigroup of row-monomial matrices over a group G, A is a set of equivalence classes of monomial vectors over G and is the usual product of a matrix acting on a vector.     

The smallest eigenvalue of the signless Laplacian

Recently the signless Laplacian matrix of graphs has been intensively investigated. While there are many results about the largest eigenvalue of the signless Laplacian, the properties of its smallest eigenvalue are less well studied. The present paper surveys the known results and presents some new ones about the smallest eigenvalue of the signless Laplacian.     

The smallest regular polytopes of given rank

An abstract polytope is called regular   if its automorphism group has a single orbit on flags (maximal chains). In this paper, the regular n$n$-polytopes with the smallest number of flags are found, for every rank n>1$n>1$. With a few small exceptions, the smallest regular n$n$-polytopes come from a family of ‘tight’ polytopes with 2⋅4ⁿ⁻¹$2\cdot 4^{n-1}$ flags, one for each n$n$, with Schläfli symbol {4∣4∣?∣4}$\{4\mid 4\mid ?\mid 4\}$. Also with few exceptions, these have both the smallest number of elements, and the smallest number of edges in their Hasse diagram.     

The smallest values of algebraic connectivity for trees

The algebraic connectivity of a graph G is the second smallest eigenvalue of its Laplacian matrix. Let ■n be the set of all trees of order n. In this paper, we will provide the ordering of trees in ■n up to the last eight trees according to their smallest algebraic connectivities when n ≥ 13. This extends the result of Shao et al. [The ordering of trees and connected graphs by algebraic connectivity. Linear Algebra Appl., 428, 1421-1438 (2008)].     

The smallest graphs with certain adjacency properties

A graph is said to have property P₁,_n if for every sequence of n + 1 points, there is another point adjacent only to the first point. It has previously been shown that almost all graphs have property P₁,_n. It is easy to verify that for each n, there is a cube with this property. A more delicate question asks for the construction of the smallest graphs having property P₁,_n. We find that this problem is intimately related with the discovery of the highly symmetric graphs known as cages, and are thereby enabled to resolve this question for 1?n?6.     

The smallest basically disconnected preimage of a space

We show that for each space X, there exists a smallest basically disconnected perfect irreducible preimage ΛX. A corollary of the existence of ΛX is that each locally compact and basically disconnected space X has a smallest basically disconnected compactification.     

The smallest positive eigenvalue of graphs under perturbation

The effect on the smallest positive eigenvalue of a bipartite graph is studied when the graph is perturbed by attaching a pendant vertex at one of its vertices. Let $${\widehat{T}}(v)$$ be the graph obtained by attaching a pendant at vertex v of T. We characterize the vertices v such that the smallest positive eigenvalue of $${\widehat{T}}(v)$$ is equal or greater than that of T. As an application, we obtain the pairs of nonisomorphic noncospectral trees having the same smallest positive eigenvalue.