Related papers: Interfacing biology, category theory and mathemati…
In this paper, we evolve from sparsity, a key concept in robust statistics, to concepts and theoretical results of what we call the mathematics of resilience, at the interface between category theory, the theory of dynamical systems,…
Diagnostic testing is germane to a variety of scenarios in medicine, pandemic tracking, threat detection, and signal processing. This is an expository paper with some original results. Here we first set up a mathematical architecture for…
A critical task in systems biology is the identification of genes that interact to control cellular processes by transcriptional activation of a set of target genes. Many methods have been developed to use statistical correlations in…
We use elementary methods to establish three key recurrence relations: one for derangement numbers, a second for harmonic numbers, and a third for degenerate harmonic numbers. Our results not only contribute to the understanding of the…
Considerable interest has recently been focused on studying multiple phenotypes simultaneously in both epidemiological and genomic studies, either to capture the multidimensionality of complex disorders or to understand shared etiology of…
Diversity indices are useful single-number metrics for characterizing a complex distribution of a set of attributes across a population of interest. The utility of these different metrics or sets of metrics depend on the context and…
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…
Three variants of the statistical complexity function, which is used as a criterion in the problem of detection of a useful signal in the signal-noise mixture, are considered. The probability distributions maximizing the considered variants…
We define the concept of dependence among multiple variables using maximum entropy techniques and introduce a graphical notation to denote the dependencies. Direct inference of information theoretic quantities from data uncovers…
This paper is Part II of a two-part series devoting to the study of systematic measures in a complex bio-network modeled by a system of ordinary differential equations. In this part, we quantify several systematic measures of a biological…
In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…
Recent methodological advances are enabling better examination of speciation and extinction processes and patterns. A major open question is the origin of large discrepancies in species number between groups of the same age. Existing…
The large-sample behavior of non-degenerate multivariate $U$-statistics of arbitrary degree is investigated under the assumption that their kernel depends on parameters that can be estimated consistently. Mild regularity conditions are…
Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the…
Randomness is one of the important key concepts of statistics. In epidemiology or medical science, we investigate our hypotheses and interpret results through this statistical randomness. We hypothesized by imposing some conditions to this…
We provide a unifying view of statistical information measures, multi-way Bayesian hypothesis testing, loss functions for multi-class classification problems, and multi-distribution $f$-divergences, elaborating equivalence results between…
There is a growing proportion of people with several disease conditions ("multimorbidity"), placing increasing demands on healthcare systems. One hypothesis is that clusters of diseases may arise from shared underlying disease processes…
A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in…