相关论文: Growth and Structure of Stochastic Sequences
This article investigates integer sequences that partition the sequence into blocks of various lengths - irregular arrays. The main result of the article is explicit formulas for numbering of irregular arrays. A generalization of Cantor…
Appealing to several multivariate information measures---some familiar, some new here---we analyze the information embedded in discrete-valued stochastic time series. We dissect the uncertainty of a single observation to demonstrate how the…
A Galileo sequence \((a_n)\) is a sequence of positive integers whose partial sums $S_n$ satisfy $S_{2n}=kS_n$ for some $k>1$. In this paper we prove that every polynomial Galileo sequence is given by first differences of the form \(a_n=…
One calls attention to the fact that the stochastic physical systems are not random completely. They have both random and regular components of their evolution. Dynamic system is considered to be a special case of physical system with…
We introduce the notion of numerical semigroups generated by concatenation of arithmetic sequences and show that this class of numerical semigroups exhibit multiple interesting behaviours.
It is known that learning of players who interact in a repeated game can be interpreted as an evolutionary process in a population of ideas. These analogies have so far mostly been established in deterministic models, and memory loss in…
In the setting of nonstandard analysis we introduce the notion of flexible sequence. The terms of flexible sequences are external numbers. These are a sort of analogue for the classical \emph{O$ (\cdot ) $} and \emph{o$ (\cdot ) $} notation…
We consider arithmetic sequences, here defined as ordered lists of positive integers. Any such a sequence can be cast onto a quantum state, enabling the quantification of its `surprise' through von Neumann entropy. We identify typical…
Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
We consider the problem of sequencing a set of positive numbers. We try to find the optimal sequence to maximize the variance of its partial sums. The optimal sequence is shown to have a beautiful structure. It is interesting to note that…
It has long been noticed that high dimension data exhibits strange patterns. This has been variously interpreted as either a "blessing" or a "curse", causing uncomfortable inconsistencies in the literature. We propose that these patterns…
A composition of a nonnegative integer (n) is a sequence of positive integers whose sum is (n). A composition is palindromic if it is unchanged when its terms are read in reverse order. We provide a generating function for the number of…
We define a class of probabilistic models in terms of an operator algebra of stochastic processes, and a representation for this class in terms of stochastic parameterized grammars. A syntactic specification of a grammar is mapped to…
Single-cell gene expression measurements encode variability spanning molecular noise, cell-to-cell heterogeneity, and technical artifacts. Mechanistic stochastic models provide powerful approaches to disentangle these sources, yet inferring…
We determine the distributions of lengths of runs in random sequences of elements from a totally ordered set (total order) or partially ordered set (partial order). In particular, we produce novel formulae for the expected value, variance,…
We model stochastic choice as environment-dependent switching among a small library of deterministic decision rules. A Random Rule Model generates menu-level choice probabilities via named, interpretable rules weighted by observable menu…
A person is given a numbered sequence of positions on a sheet of paper. The person is asked, "Which will be the next (or the next after that) position?" Everyone has an opinion as to how he or she would proceed. There are regular sequences…
The growth of a population divided among spatial sites, with migration between the sites, is sometimes modelled by a product of random matrices, with each diagonal elements representing the growth rate in a given time period, and…
We present the formalism of sequential and asynchronous processes defined in terms of random or quantum grammars and argue that these processes have relevance in genomics. To make the article accessible to the non-mathematicians, we keep…