If L = ZD is a D-dimensional lattice, and A is a finite set, then A is a compact space; a cellular automaton (CA) is a continuous transformation Φ : A−→A that commutes with all shift maps. If μ is a probability measure on A, then Φ asymptotically randomizes μ if wk− lim N→∞ 1 N N ∑ n=1 Φμ = η, where η is the uniform Bernoulli measure on A. If μ has long range correlations, and Φ is μ-a.e. injec...

Let Ω be a set with n elements. A transformation monoid on Ω is a set of maps from Ω to itself which is closed under composition and contains the identity. A transformation monoid M is synchronizing if it contains a map with rank 1 (that is, whose image has only one element). The notion comes from automata theory. A (finite deterministic) automaton consists of a set Ω of states and a set S of t...

Abstract. The structure of transformation semigroups on a finite set is analyzed by introducing a hierarchy of functions mapping subsets to subsets. The resulting hierarchy of semigroups has a corresponding hierarchy of minimal ideals, or kernels. This kernel hierarchy produces a set of tools that provides direct access to computations of interest in probability limit theorems; in particular, f...

a $p$-group $g$ is called a $mathcal{cac}$-$p$-group if $c_g(h)/h$ is ‎cyclic for every non-cyclic abelian subgroup $h$ in $g$ with $hnleq‎ ‎z(g)$‎. ‎in this paper‎, ‎we give a complete classification of‎ ‎finite $mathcal{cac}$-$p$-groups‎.

A linear rank inequality is a that holds by dimensions of vector spaces over any finite field. characteristic-dependent also involves but this fields determined characteristics, and does not in general hold other characteristics. In paper, using as guide binary matrices whose ranks depend on the field where they are defined, we show theorem which explicitly produces inequalities; generalizes re...

Recently, the Factorized Hidden Layer (FHL) adaptation is proposed for speaker adaptation of deep neural network (DNN) based acoustic models. In addition to the standard affine transformation, an FHL contains a speaker-dependent (SD) transformation matrix using a linear combination of rank-1 matrices and an SD bias using a linear combination of vectors. In this work, we extend the FHL based ada...