Related papers: Walsh coefficients and circuits for several allele…
A mathematical development of the Walsh transform, Walsh basis, and Walsh coefficients is given. The author was prompted to write this by a wish to give a unified treatment of epistatic coordinates as they are used in evolutionary biology.…
A popular measure of association is the tail dependence coefficient which measures the strength of dependence in either the lower-left or upper-right tail of a bivariate distribution. In this paper, we develop the idea of quantile…
For extreme value copulas with a known upper tail dependence coefficient we find pointwise upper and lower bounds, which are used to establish upper and lower bounds of the Spearman and Kendall correlation coefficients. We shown that in all…
Defining the extent of epistasis - the non-independence of the effects of mutations - is essential for understanding the relationship of genotype, phenotype, and fitness in biological systems. The applications cover many areas of biological…
Circular variables such as phase or orientation have received considerable attention throughout the scientific and engineering communities and have recently been quite prominent in the field of neuroscience. While many analytic techniques…
It is argued that polydispersed systems like colloids provide a direct example where Tsallis' statistical distribution is useful for describing the heirarchical nature of the system based on particle size.
The partial correlation coefficient is a commonly used measure to assess the conditional dependence between two random variables. We provide a thorough explanation of the partial copula, which is a natural generalization of the partial…
We propose a methodology to explore and measure the pairwise correlations that exist between variables in a dataset. The methodology leverages copulas for encoding dependence between two variables, state-of-the-art optimal transport for…
Phase separation, crucial for spatially segregating biomolecules in cells, is well-understood in the simple case of a few components with pairwise interactions. Yet, biological cells challenge the simple picture in at least two ways: First,…
"Oscillations" occur in quite different kinds of many-particle-systems when two groups of particles with different directions of motion meet or intersect at a certain spot. We present a model of pedestrian motion that is able to reproduce…
An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We…
In this paper, we propose efficient probabilistic algorithms for several problems regarding the autocorrelation spectrum. First, we present a quantum algorithm that samples from the Walsh spectrum of any derivative of $f()$. Informally, the…
We present an algorithm to express Wilson lines that are defined on piecewise linear paths in function of their individual segments, reducing the number of diagrams needed to be calculated. The important step lies in the observation that…
A number of coupling strategies are presented for stochastically modeled biochemical processes with time-dependent parameters. In particular, the stacked coupling is introduced and is shown via a number of examples to provide an…
Genetic interactions confer robustness on cells in response to genetic perturbations. This often occurs through molecular buffering mechanisms that can be predicted using, among other features, the degree of coexpression between genes,…
The width of the distribution of species in a polydisperse system is employed in a small-variable expansion, to obtain a well-controlled and compact scheme by which to calculate phase equilibria in multi-phase systems. General and universal…
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 investigate the clustering ability in bipartite networks where cycles of size three are absent and therefore the standard definition of clustering coefficient cannot be used. Instead, we use another coefficient given by the fraction of…
A study of correlations in tractable multiparticle cascade models in terms of wavelets reveals many promising features. The selfsimilar construction of the wavelet basis functions and their multiscale localization properties provide a new…
Complex systems, such as economic, social, biological, and ecological systems, usually feature interactions not only between pairwise entities but also among three or more entities. These multi-entity interactions are known as higher-order…