Related papers: Interfacing biology, category theory and mathemati…
This paper introduces a novel decomposition framework to explain heterogeneity in causal effects observed across different studies, considering both observational and randomized settings. We present a formal decomposition of between-study…
In filtering, each output is produced by a certain number of different inputs. We explore the statistics of this degeneracy in an explicitly treatable filtering problem in which filtering performs the maximal compression of relevant…
A vast array of transformative technologies developed over the past decade has enabled measurement and perturbation at ever increasing scale, yet our understanding of many systems remains limited by experimental capacity. Overcoming this…
Mathematical modelling allows us to concisely describe fundamental principles in biology. Analysis of models can help to both explain known phenomena, and predict the existence of new, unseen behaviours. Model analysis is often a complex…
Mathematical models play an increasingly important role in the interpretation of biological experiments. Studies often present a model that generates the observations, connecting hypothesized process to an observed pattern. Such generative…
Systems biology models are useful models of complex biological systems that may require a large amount of experimental data to fit each model's parameters or to approximate a likelihood function. These models range from a few to thousands…
Can machine learning help discover new mathematical structures? In this article we discuss an approach to doing this which one can call "mathematical data science". In this paradigm, one studies mathematical objects collectively rather than…
Cellular heterogeneity is an immanent property of biological systems that covers very different aspects of life ranging from genetic diversity to cell-to-cell variability driven by stochastic molecular interactions, and noise induced cell…
Based on a case study on 3D printing, we have been experimenting on the sonification of multidimensional data for peripheral process monitoring. In a previous paper, we tested the effectiveness of a soundscape which combined intentionally…
This paper introduces a Bayesian framework to detect multiple signals embedded in noisy observations from a sensor array. For various states of knowledge on the communication channel and the noise at the receiving sensors, a marginalization…
We derive a general statistical model of interactions, starting from probabilistic principles and elementary requirements. Prevailing interaction models in biomedical researches diverge both mathematically and practically. In particular,…
We consider the problem of signal estimation (denoising) from a statistical mechanical perspective, using a relationship between the minimum mean square error (MMSE), of estimating a signal, and the mutual information between this signal…
The clustering of categories in a multivariate categorical data set is investigated, where the problem separates into that of merging categories of the same variables (i.e., within-variable categories), and combining categories of different…
This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the…
We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of multiple objects of…
Motivated by genome-wide association studies, we consider a standard linear model with one additional random effect in situations where many predictors have been collected on the same subjects and each predictor is analyzed separately.…
Entanglement detection criteria are developed within the framework of the majorization formulation of uncertainty. The primary results are two theorems asserting linear and nonlinear separability criteria based on majorization relations,…
We provide a brief overview of both Bayes and classical model selection. We argue tentatively that model selection has at least two major goals, that of finding the correct model or predicting well, and that in general both these goals may…
Understanding how genes interact and relate to each other is a fundamental question in biology. However, current practices for describing these relationships, such as drawing diagrams or graphs in a somewhat arbitrary manner, limit our…
During the past few years the development of experimental techniques has allowed the quantitative analysis of biological systems ranging from neurobiology and molecular biology. This work focuses on the quantitative description of these…