Related papers: Walsh coefficients and circuits for several allele…
Conditional copulas are flexible statistical tools that couple joint conditional and marginal conditional distributions. In a linear regression setting with more than one covariate and two dependent outcomes, we propose the use of additive…
Recursion relations for integrals of amplitudes over the phase space, i.e. for partial wave amplitudes, are introduced. In their simplest form these integrals are proportional to the s-wave amplitudes and represent rigorous lower bounds on…
The clustering coefficient is a valuable tool for understanding the structure of complex networks. It is widely used to analyze social networks, biological networks, and other complex systems. While there is generally a single common…
Interaction graphs provide an important qualitative modeling approach for System Biology. This paper presents a novel approach for construction of interaction graph with the help of Boolean function decomposition. Each decomposition part…
In multiplex networks, cycles cannot be characterized only by their length, as edges may occur in different layers in different combinations. We define a classification of cycles by the number of edges in each layer and the number of…
The self-assembly of functionalized (patchy) particles with directional interactions into target structures is still a challenge, despite the significant experimental advances on their synthesis. The self-assembly pathways are typically…
This paper reviews stability analysis techniques by using the Nyquist and Nichols charts. The relationship between the Nyquist and Nichols stability criteria is fully described by using the crossing concept. The results are demonstrated…
We study coamoebas of polynomials supported on circuits. Our results include an explicit description of the space of coamoebas, a relation between connected components of the coamoeba complement and critical points of the polynomial, an…
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…
For one-dimensional many-body systems interacting via the \textit{Coulomb force} and with \textit{arbitrary} external potential energy, we derive (\textit{i}) the \textit{node coalescence condition} for the wave function. This condition…
This article is a survey on recent contributions to an effective version of Bautin's theory about the bifurcation of periodic orbits (limit cycles). The analysis of Hopf bifurcations of higher order is possible by use of the return mapping.…
Modelling multivariate circular time series is considered. The cross-sectional and serial dependence is described by circulas, which are analogs of copulas for circular distributions. In order to obtain a simple expression of the dependence…
We present a weighted estimator of the covariance and correlation in bipartite complex systems with a double layer of heterogeneity. The advantage provided by the weighted estimators lies in the fact that the unweighted sample covariance…
In probability and statistics, copulas play important roles theoretically as well as to address a wide range of problems in various application areas. We introduce the concept of multivariate discrete copulas, discuss their equivalence to…
High-order, beyond-pairwise interdependencies are at the core of biological, economic, and social complex systems, and their adequate analysis is paramount to understand, engineer, and control such systems. This paper presents a framework…
A new empirical Bayes approach to variable selection in the context of generalized linear models is developed. The proposed algorithm scales to situations in which the number of putative explanatory variables is very large, possibly much…
In this work we are interested in identifying clusters of "positional equivalent" actors, i.e. actors who play a similar role in a system. In particular, we analyze weighted bipartite networks that describes the relationships between actors…
Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as…
Pairwise interactions between perturbations to a system can provide evidence for the causal dependencies of the underlying underlying mechanisms of a system. When observations are low dimensional, hand crafted measurements, detecting…
In this paper we consider the extreme behavior of the extremal eigenvalues of white Wishart matrices, which plays an important role in multivariate analysis. In particular, we focus on the case when the dimension of the feature p is much…