We prove that certain Gibbs measures on subshifts of finite type are nonsingular and ergodic for certain countable equivalence relations, including the orbit relation of the adic transformation (the same as equality after a permutation of finitely many coordinates). The relations we consider are defined by cocycles taking values in groups, including some nonabelian ones. This generalizes (half ...

In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...

Sporulation in the filamentous bacteria Streptomyces coelicolor is a tightly regulated process involving aerial hyphae growth, chromosome segregation, septation and spore maturation. Genetic studies have identified numerous genes that regulate sporulation, including WhiA and the sigma factor WhiG. WhiA, which has been postulated to be a transcriptional regulator, contains two regions typically ...

sigma B is a secondary sigma factor of Bacillus subtilis. RNA polymerase containing sigma B transcribes a subset of genes that are expressed after heat shock or the onset of the stationary phase of growth. Three genes (rsbV, rsbW, and rsbX), cotranscribed with the sigma B structural gene (sigB), regulate sigma B-dependent gene expression. RsbW is the primary inhibitor of this system with the ot...

sigma(32) is the first alternative sigma factor discovered in Escherichia coli and can direct transcription of many genes in response to heat shock stress. To define the physiological role of sigma(32), we have used transcription profiling experiments to identify, on a genome-wide basis, genes under the control of sigma(32) in E. coli by moderate induction of a plasmid-borne rpoH gene under def...

Let $M_R$ be a non-zero‎ ‎module and ${mathcal F}‎: ‎sigma[M_R]times sigma[M_R]‎ ‎rightarrow$ Mod-$Bbb{Z}$ a bifunctor‎. ‎The‎ ‎$mathcal{F}$-reversibility of $M$ is defined by ${mathcal‎ ‎F}(X,Y)=0 Rightarrow {mathcal F}(Y,X)=0$ for all non-zero $X,Y$‎ ‎in $sigma[M_R]$‎. ‎Hom (resp‎. ‎Rej)-reversibility of $M$ is‎ ‎characterized in different ways‎. ‎Among other things‎, ‎it is shown‎ ‎th...

A frame $L$ is called {it coz-dense} if $Sigma_{coz(alpha)}=emptyset$ implies $alpha=mathbf 0$. Let $mathcal RL$ be the ring of real-valued continuous functions on a coz-dense and completely regular frame $L$. We present a description of the socle of the ring $mathcal RL$ based on minimal ideals of $mathcal RL$ and zero sets in pointfree topology. We show that socle of $mathcal RL$ is an essent...

Variable selection via penalized estimation is appealing for dimension reduction. For penalized linear regression, Efron, et al. (2004) introduced the LARS algorithm. Recently, the coordinate descent (CD) algorithm was developed by Friedman, et al. (2007) for penalized linear regression and penalized logistic regression and was shown to gain computational superiority. This paper explores...