This paper describes the use of Bernoulli mixture models for extracting boolean rules from data. Bernoulli mixtures identify high data density areas on the corners of a hypercube. One corner represents a conjunction of literals in a boolean clause and the set of all identified corners, of the hypercube, indicates disjuncts of clauses to form a rule. Further class labels can be used to select fe...

A uniformly p to one endomorphism is a measure preserving map with entropy log p which is a.e. p to 1 and for which the conditional expectation of each preimage is precisely 1/p. The standard example of this is one sided p-shift with uniform i.i.d. Bernoulli measure. We give a characterization of those uniformly finite to one endomorphisms conjugate to this standard example by a condition on th...

A countable group Γ is called shift-minimal if every non-trivial measure preserving action of Γ weakly contained in the Bernoulli shift Γ y ([0, 1] , λ ) is free. We show that any group Γ whose reduced C∗-algebra Cr(Γ) admits a unique tracial state is shift-minimal, and that any group Γ admitting a free measure preserving action of cost> 1 contains a finite normal subgroup N such that Γ/N is sh...

It was recently shown that there exists a family Z 2 Markov random elds which are K but are not isomorphic to Bernoulli shifts 6]. In this paper we show that most distinct members of this family are not isomorphic. This implies that there is a two parameter family of Z 2 Markov random elds of the same entropy, no two of which are isomorphic.

We consider crossed product II1 factors M = N ⋊σ G, with G discrete ICC groups that contain infinite normal subgroups with the relative property (T) and σ trace preserving actions of G on finite von Neumann algebras N that are “malleable” and mixing. Examples are the actions of G by Bernoulli shifts (classical and non-classical), and by Bogoliubov shifts. We prove a rigidity result for isomorph...

Abstract : We study a model of random electric networks with Bernoulli resistances. In the case of the lattice Z, we show that the point-to-point effective resistance has a small variance compared to its expected value, whereas for Z, d 6= 2, expectation and variance are of the same order. Similar results are obtained in the context of p-resistance. The proofs rely on a modified Poincaré inequa...

Abstract Recently, B. A. Kupershmidt have constructed a reflection symmetries of q-Bernoulli polynomials (see [9]). In this paper we give another construction of a q-Bernoulli polynomials, which form Barnes’ multiple Bernoulli polynomials at q = 1, cf. [1, 13, 14]. By using q-Volkenborn integration, we can also investigate the properties of the reflection symmetries of these’ q-Bernoulli polyno...

This paper deals with the measure-theoretical entropy of a linear cellular automaton (LCA) Tf @-l,rD :m Ø m , generated by a bipermutative local rule f Ix-l, ... , xrM  ⁄i-l r ai xi Hmod mL (m ¥ 2 and l, r œ +), with respect to the Bernoulli measure mp on m  defined by a probability vector p  Ip0, p1, ... , pm-1M. We prove that the measure entropy of the one-dimensional LCA Tf @-l,rD wi...

In this paper, we give a short new proof of a recent result due to Schumacher concerning an extension of Faulhaber’s identity for the Bernoulli numbers. Our approach follows from basic manipulations involving the ordinary generating function for the Bernoulli polynomials in the context of the Zeon algebra.

It has equilibrium (and in fact reversible) measure μ the product Bernoulli measure of density p on {0, 1}Z. It can also be constructed by attaching a Poisson process clock to every site in Z. Every time a clock rings, the site is refreshed to a Bernoulli variable of parameter p, but only if its right neighbour is empty. This constraint creates the ”bubbles” one can see on the picture. A natura...