An investigation is carried out to formulate some theoretical results regarding the behavior of a genetic-algorithm-based pattern classification methodology, for an infinitely large number of training data points n, in an N-dimensional space RN. It is proved that for nPR, and for a sufficiently large number of iterations, the performance of this classifier (when hyperplanes are considered to ge...

This paper investigates from the physical layer security (PLS) perspective the fundamental issues of mode selection and spectrum partition in cellular networks with inband device-to-device (D2D) communication. We consider a mode selection scheme allowing each D2D pair to probabilistically switch between the underlay and overlay modes, and also a spectrum partition scheme where the system spectr...

An overview is presented of the construction and use of algebraic partition functions to represent the equilibrium statistical mechanics of multimolecular complexes and their action within a larger regulatory network. Unlike many applications of equilibrium statistical mechanics, multimolecular complexes may operate with various subsets of their components present and connected to the others, t...

A random partition of the positive integers is called partially exchangeable if for each finite sequence of positive integers n,, ... , nk, the probability that the partition breaks the first n1 + + nk integers into k particular classes, of sizes nl,.. . ., nk in order of their first elements, has the same value p(nl,...,nk) for every possible choice of classes subject to the sizes constraint. ...

We consider a (sub-)critical Galton–Watson process with neutral mutations (infinite alleles model), and decompose the entire population into clusters of individuals carrying the same allele. We specify the law of this allelic partition in terms of the distribution of the number of clone-children and the number of mutant-children of a typical individual. The approach combines an extension of Har...

Let κ be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti (1974) and Dubins (1975), subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that κ is not a weakly inaccessible cardinal, we show that each probability that is not κ-­‐ additive has conditional probabilities that fail to be conglomerable i...

Using the geodesic distance on the n-dimensional sphere, we study the expected radius function of the Delaunay mosaic of a random set of points. Specifically, we consider the partition of the mosaic into intervals of the radius function and determine the expected number of intervals whose radii are less than or equal to a given threshold. Assuming the points are not contained in a hemisphere, t...

In the United States electoral system, a candidate is elected indirectly by winning a majority of electoral votes cast by individual states, the election usually being decided by the votes cast by a small number of " swing states " where the two candidates historically have roughly equal probabilities of winning. The effective value of a swing state in deciding the election is determined not on...

The object of the first part of this course was to introduce the principles of statistical mechanics which provide a bridge between the fundamental laws of microscopic physics, and observed phenomena at macroscopic scales. Microscopic Physics is characterized by large numbers of degrees of freedom; for example, the set of positions and momenta {~ pi, ~qi}, of particles in a gas, configurations ...

We present an algorithm which partitions a data set in two parts with equal size and experimentally nearly the same distribution measured through the likelihood of a Parzen kernel density estimator. The generation of the partition takes O( 1 2 N(N − 1)) operations (N number of data) and is 2 orders of magnitude faster than the state of the art. 1 Generating an equi-distributed bipartition 1.1 P...