We analyze random walks on a class of semigroups called ``left-regular bands.'' These walks include the hyperplane chamber walks of Bidigare, Hanlon, and Rockmore. Using methods of ring theory, we show that the transition matrices are diagonalizable and we calculate the eigenvalues and multiplicities. The methods lead to explicit formulas for the projections onto the eigenspaces. As examples of...

We present an artificially simulated dataset (TIED) constructed so that there are many minimal sets of variables with maximal predictivity (i.e., Markov boundaries) and likewise many sets of variables that are statistically indistinguishable from the set of direct causes and direct effects of the response variable. This dataset was used in the Potluck Causality Challenge to determine all statis...

Sensitive tests of Lorentz invariance can emerge from the study of neutrino oscillations, particularly for atmospheric neutrinos where the effect is conveniently near-maximal and has been observed over a wide range of energies. We assume these oscillations to be described in terms of two neutrinos with different masses and (possibly) different maximal attainable velocities (MAVs). It suffices t...

Supply chain and industrial cluster are the results of competition economy. Clustering analysis enable more efficient supply chain management practices. In this paper, we focus our discussion on the rough set theory for clustering supplier chain management. We propose ROSMAN (ROugh Set approach for clustering Supplier chain MANagement), an alternative algorithm for clustering supplier base mana...

We propose to exploit three-valued abstraction to stochastic systems in a compositional way. This combines the strengths of an aggressive state-based abstraction technique with compositional modeling. Applying this principle to interactive Markov chains yields abstract models that combine interval Markov chains and modal transition systems in a natural and orthogonal way. We prove the correctne...

We study occurrences of patterns on clusters of size n in random fields on Z. We prove that for a given pattern, there is a constant a > 0 such that the probability that this pattern occurs at most an times on a cluster of size n is exponentially small. Moreover, for random fields obeying a certain Markov property, we show that the ratio between the numbers of occurrences of two distinct patter...

A computably enumerable (c.e.) degree is a maximal contiguous degree if it is contiguous and no c.e. degree strictly above it is contiguous. We show that there are infinitely many maximal contiguous degrees. Since the contiguous degrees are definable, the class of maximal contiguous degrees provides the first example of a definable infinite anti-chain in the c.e. degrees. In addition, we show t...

in this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. some results about existence of maximal m-open setsare given. moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.our results are supported by examples and counterexamples.

The heavy and light chains of botulinum A toxin were separated by anion exchange chromatography. Their intracellular actions were studied using bovine adrenal chromaffin cells permeabilized with streptolysin O. Purified light chain inhibited the Ca2+-stimulated [3H]noradrenaline release with a half-maximal effect at about 1.8 nM. The inhibition was incomplete. Heavy chain up to 28 nM was neithe...

polypeptide consisting of two myosin heavy chain (MHC) and four myosin light chain (MLC) subunits. Each MHC is associated with one essential light chain (ELC) and one regulatory light chain (RLC; also called alkali light chain). All vertebrates, including humans, express a family of MHC, ELC and RLC isoforms in their skeletal muscles. In a given species, variable expression of multiple MHC and ...