Related papers: No-Go Theorems for Distributive Laws
We describe and develop three recent novelties in network research which are particularly useful for studying social systems. The first one concerns the discovery of some basic dynamical laws that enable the emergence of the fundamental…
In a recent paper by Hellerstein [15], a tight relationship was conjectured between the number of strata of a Datalog${}^\neg$ program and the number of "coordination stages" required for its distributed computation. Indeed, Ameloot et al.…
We study, with the help of a computer program, the Polish Algorithm for finite terms satisfying various algebraic laws, e.g., left distributivity a(bc) = (ab)(ac). While the termination of the algorithm for left distributivity remains open…
A standard belief on emerging collective behavior is that it emerges from simple individual rules. Most of the mathematical research on such collective behavior starts from imperative individual rules, like always go to the center. But how…
We investigate two problems for a class C of regular word languages. The C-membership problem asks for an algorithm to decide whether an input language belongs to C. The C-separation problem asks for an algorithm that, given as input two…
We prove that every finitely generated convex set of finitely supported probability distributions has a unique base, and use this result to show that the monad of convex sets of probability distributions is presented by the algebraic theory…
Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized…
A fruitful way of studying physical theories is via the question whether the possible physical states and different kinds of correlations in each theory can be shared to different parties. Over the past few years it has become clear that…
We formulate conditions on a set of log-concave sequences, under which any linear combination of those sequences is log-concave, and further, of conditions under which linear combinations of log-concave sequences that have been transformed…
(doctoral thesis of Michal Bilek, finished on June 19, 2015) MOND is an observational rule for predicting the acceleration of stars and galaxies from the distribution of the visible matter. It possibly stems from a new law of physics. I…
Interpreting entwining structures as special instances of J. Beck's distributive law, the concept of entwining module can be generalized for the setting of arbitrary monoidal category. In this paper, we use the distributive law formalism to…
The frequency of the preferred order for a noun phrase formed by demonstrative, numeral, adjective and noun has received significant attention over the last two decades. We investigate the actual distribution of the 24 possible orders.…
Despite its importance, in the introductory disciplines of exact science courses, the demonstration of the Maxwell-Boltzmann velocity distribution law is not explained, only its final equation is shown. In order to fill this deficiency, in…
We discuss the role of the notion of information in the description of physical reality. We consider theories for which dynamics is linear with respect to stochastic mixing. We point out that the no-cloning and no-deleting principles emerge…
We develop a discrete-time version of the blended dynamics theorem for the use of designing distributed computation algorithms. The blended dynamics theorem enables to predict the behavior of heterogeneous multi-agent systems. Therefore,…
In this paper, we study compound bi-free Poisson distributions for {\sl two-faced families of random variables}. We prove a Poisson limit theorem for compound bi-free Poisson distributions. Furthermore, a bi-free infinitely divisible…
Any Quantum Key Distribution (QKD) protocol consists first of sequences of measurements that produce some correlation between classical data. We show that these correlation data must violate some Bell inequality in order to contain…
We investigate the existence of maximal collections of mutually noncrossing $k$-element subsets of $\left\{ 1, \dots, n \right\}$ that are invariant under adding $k\pmod n$ to all indices. Our main result is that such a collection exists if…
The occurrence of digits one through nine as the leftmost nonzero digit of numbers from real world sources is often not uniformly distributed, but instead, is distributed according to a logarithmic law, known as Benford's law. Here, we…
The well-known three distance theorem states that there are at most three distinct gaps between consecutive elements in the set of the first n multiples of any real number. We generalise this theorem to higher dimensions under a suitable…