Related papers: Interfacing biology, category theory and mathemati…
The molecular biology revolution of the last seventy five years has transformed our view of living systems. Scientific explanations of biological phenomena are now synonymous with the identification of the genes, proteins, and signaling…
Bi-clustering is a useful approach in analyzing biological data when observations come from heterogeneous groups and have a large number of features. We outline a general Bayesian approach in tackling bi-clustering problems in moderate to…
Modelling, analysing and inferring triggering mechanisms in population reproduction is fundamental in many biological applications. It is also an active and growing research domain in mathematical biology. In this chapter, we review the…
A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging…
Measuring the statistical dependence between observed signals is a primary tool for scientific discovery. However, biological systems often exhibit complex non-linear interactions that currently cannot be captured without a priori knowledge…
This paper considers the problem of appearance indication of useful acoustic signal in the signal/noise mixture. Various information characteristics (information entropy, Jensen-Shannon divergence, spectral information divergence and…
We introduce and investigate a new notion of the theory of approximation-the so-called degenerate approximation, i.e. approximation of the function of two (and more) variables (kernel) by means of degenerate function (kernel). We apply…
Genetic data are frequently categorical and have complex dependence structures that are not always well understood. For this reason, clustering and classification based on genetic data, while highly relevant, are challenging statistical…
Causality and causal inference have emerged as core research areas at the interface of modern statistics and domains including biomedical sciences, social sciences, computer science, and beyond. The field's inherently interdisciplinary…
Let Y be a random variable whose moment-generating function exists in some neighborhood of the origin. While probabilistic Stirling numbers of the first and second kind have been introduced, early definitions often failed to satisfy…
This is an essay in what might be called ``mathematical metaphysics.'' There is a fundamental duality that run through mathematics and the natural sciences. The duality starts as the logical level; it is represented by the Boolean logic of…
We explore a definition of complexity based on logic functions, which are widely used as compact descriptions of rules in diverse fields of contemporary science. Detailed numerical analysis shows that (i) logic complexity is effective in…
A family of information theoretic models of communication was introduced more than a decade ago to explain the origins of Zipf's law for word frequencies. The family is a based on a combination of two information theoretic principles:…
Computing Granger causal relations among bivariate experimentally observed time series has received increasing attention over the past few years. Such causal relations, if correctly estimated, can yield significant insights into the…
Score-based divergences have been widely used in machine learning and statistics applications. Despite their empirical success, a blindness problem has been observed when using these for multi-modal distributions. In this work, we discuss…
We study the application of a Bayesian method to extract relevant information from data for the case of a signal consisting of two or more decaying particles and its background. The method takes advantage of the dependence that exists in…
Gene-gene and gene-environment interactions are widely believed to play significant roles in explaining the variability of complex traits. While substantial research exists in this area, a comprehensive statistical framework that addresses…
The discipline of `theoretical biology' has been developing from its inception several decades ago almost in parallel with the advances in biology, so much so that the latter is often considered to be almost exclusively an empirical…
The present article is the first of a series whose goal is to define a logical formalism in which it is possible to reason about genetics. In this paper, we introduce the main concepts of our language whose domain of discourse consists of a…
Over the past two decades, the rapid surge in data-intensive computational techniques for statistical modeling may have had the effect of diminishing the use of applied mathematics in causal scientific inquiry. In this paper, co-authored by…