Related papers: On stable patterns and properties on permutations …
We initiate a probabilistic study of forward stability for products of Schubert polynomials through the record statistic (left-to-right maxima) of permutations. Building on the explicit record formula for forward stability obtained by Hardt…
Group synchronization arises when two or more synchronization patterns coexist in a network formed of oscillators of different types, with the systems in each group synchronizing on the same time-evolution, but systems in different groups…
The paper investigates the stability properties of restrictions of irreducible representations of the symmetric group to the hyperoctahedral subgroup. A stability result is obtained, analogous to the classical Murnaghan theorem on the…
We consider a model of stable edge sets (``matchings'') in a bipartite graph $G=(V,E)$ in which the preferences for vertices of one side (``firms'') are given via choice functions subject to standard axioms of consistency, substitutability…
Scattering transforms are non-trainable deep convolutional architectures that exploit the multi-scale resolution of a wavelet filter bank to obtain an appropriate representation of data. More importantly, they are proven invariant to…
We study joint distributions of cycles and patterns in permutations written in standard cycle form. We explore both classical and generalised patterns of length 2 and 3. Many extensions of classical theory are achieved; bivariate generating…
In this work, we present a generalization of extended persistent homology to filtrations of graded sub-groups by defining relative homology in this setting. Our work provides a more comprehensive and flexible approach to get an algebraic…
We introduce the notion of symmetric covariation, which is a new measure of dependence between two components of a symmetric $\alpha$-stable random vector, where the stability parameter $\alpha$ measures the heavy-tailedness of its…
Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…
The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
Focusing on the bipartite Stable Marriage problem, we investigate different robustness measures related to stable matchings. We analyze the computational complexity of computing them and analyze their behavior in extensive experiments on…
Motivated by data on coauthorships in scientific publications, we analyze a team formation process that generalizes matching models and network formation models, allowing for overlapping teams of heterogeneous size. We apply different…
In this paper, We study an one--dimensional morphogenesis model considered by C. Stinner et al. in (Math. Meth. Appl. Sci. 2012,35 (445-465). Under homogeneous boundary conditions, we prove the existence of nonconstant positive steady…
We study relationships between permutation statistics and pattern-functions, counting the number of times particular patterns occur in a permutation. This allows us to write several familiar statistics as linear combinations of pattern…
We introduce and study a new notion of patterns in Stirling and $k$-Stirling permutations, which we call block patterns. We prove a general result which allows us to compute generating functions for the occurrences of various block patterns…
By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend this notion to a measure. Given a space of perturbations, we assign to each homology class of the intersection its…
Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…
In this article, we study feature attributions of Machine Learning (ML) models originating from linear game values and coalitional values defined as operators on appropriate functional spaces. The main focus is on random games based on the…
We illustrate how to extend the concept of structural stability through applying it to the front propagation speed selection problem. This consideration leads us to a renormalization group study of the problem. The study illustrates two…