Daniel Berend

Multi-invariant sets on tori

Given a compact metric group G, we are interested in those semigroups L of continuous endomorphisms of G, possessing the following property: The only infinite, closed, :-invariant subset of G is G itself. Generalizing a one-dimensional result of Furstenberg, we give here a full characterization-for the case of finitedimensional tori-of those commutative semigroups with the aforementioned property.

Polynomials with roots modulo every integer

Given a polynomial with integer coefficients, we calculate the density of the set of primes modulo which the polynomial has a root. We also give a simple criterion to decide whether or not the polynomial has a root modulo every non-zero integer.

Monotonicity in Condorcet’s Jury Theorem with dependent voters

Condorcet’s Jury Theorem (CJT) provides a theoretical basis of public choice theory and political science. This paper provides an extension of CJT for random subcommittees consisting of dependent heterogeneous experts. Necessary and sufficient conditions for beneficial augmentation (reduction) of the size of a random subcommittee are provided. These results are applied in several dependency models.

Multi-invariant sets on compact abelian groups

Let G be a finite-dimensional connected compact abelian group. Gener- alizing previous results, dealing with the case of finite-dimensional tori, a full characterization is given herewith of those commutative semigroups 2 of continuous endomorphisms of C which satisfy the following property: The only infinite closed 2-invariant subset of G is G itself.

Analysis of Airplane Boarding Times

We model and analyze the process of passengers boarding an airplane. We show how the model yields closed-form estimates for the expected boarding time in many cases of interest. Comparison of our computations with previous work, based on discrete-event simulations, shows a high degree of agreement. Analysis of the model reveals a clear link between the efficiency of various airline boarding policies and a congestion parameter that is related to interior airplane design parameters, such as distance between rows. In particular, as congestion increases, random boarding becomes more attractive among row-based policies.

Computability by finite automata and Pisot bases

We prove that the function of normalization in base θ, which maps any θ-representation of a real number onto its θ-development, obtained by a greedy algorithm, is a function computable by a finite automaton over any alphabet if and only if θ is a Pisot number.

Monotonicity in Condorcet Jury Theorem

Abstract.Consider a committee of experts dealing with dichotomous choice problem, where the correctness probabilities are all greater than We prove that, if a random subcommittee of odd size m is selected randomly, and entrusted to make a decision by majority vote, its probability of deciding correctly increases with m. This includes a result of Ben-Yashar and Paroush (2000), who proved that a random subcommittee of size m≥3 is preferable to a random single expert.

An introduction to alysidal algebra (IV)

Purpose – Deontical impure systems are systems whose object set is formed by an s-impure set, whose elements are perceptuales significances (relative beings) of material and/or energetic objects (absolute beings) and whose relational set is freeways of relations, formed by sheaves of relations going in two-way directions and at least one of its relations has deontical properties such as permission, prohibition, obligation and faculty. The paper aims to discuss these issues. Design/methodology/approach – Mathematical and logical development of human society ethical and normative structure. Findings – Existence of relations with positive imperative modality (obligation) would constitute the skeleton of the system. Negative imperative modality (prohibition) would be the immunological system of protection of the system. Modality permission the muscular system, that gives the necessary flexibility. Four theorems have been formulated based on Godels theorem demonstrating the inconsistency or incompleteness of ...

Joint ergodicity and mixing

The study of jointly ergodic measure preserving transformations of probability spaces, begun in [1], is continued, and notions of joint weak and strong mixing are introduced. Various properties of ergodic and mixing transformations are shown to admit analogues for several transformations. The case of endomorphisms of compact abelian groups is particularly emphasized. The main result is that, given such commuting endomorphisms σ1σ2,...,σ, ofG, the sequence ((1/N)Σn=0N−1σ1nf1·σ2nf2· ··· · σsnfsconverges inL2(G) for everyf1,f2,…,fs∈L∞(G). If, moreover, the endomorphisms are jointly ergodic, i.e., if the limit of any sequence as above is Πi=1s∫Gf1dμ, where μ is the Haar measure, then the convergence holds also μ-a.e.

Minimum KL-Divergence on Complements of

Pinskers widely used inequality upper-bounds the total variation distance ∥P - Q∥1 in terms of the Kullback-Leibler divergence D(P∥Q). Although, in general, a bound in the reverse direction is impossible, in many applications the quantity of interest is actually D*(v, Q)-defined, for an arbitrary fixed Q, as the infimum of D(P∥Q) over all distributions P that are at least v-far away from Q in total variation. We show that D*(v, Q) ≤ Cv2 + O(v3), where C = C(Q) = 1/2 for balanced distributions, thereby providing a kind of reverse Pinsker inequality. Some of the structural results obtained in the course of the proof may be of independent interest. An application to large deviations is given.