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Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these groups may overlap. Group memberships are generated through the bipartite configuration model.…
The phase behavior of charged rods in the presence of inter-rod linkers is studied theoretically as a model for the equilibrium behavior underlying the organization of actin filaments by linker proteins in the cytoskeleton. The presence of…
This paper introduces a new shape-matching methodology, combinative matching, to combine interlocking parts for geometric shape assembly. Previous methods for geometric assembly typically rely on aligning parts by finding identical surfaces…
First we introduce a generalization of symmetric spaces to parabolic geometries. We provide construction of such parabolic geometries starting with classical symmetric spaces and we show that all regular parabolic geometries with smooth…
Mean-field techniques provide a rather accurate description of single-chain conformations in spatially inhomogeneous polymer systems containing interfaces or surfaces. Intermolecular correlations, however, are not described by the…
The human connectome has been widely studied over the past decade. A principal finding is that it can be decomposed into communities of densely interconnected brain regions. This result, however, may be limited methodologically. Past…
We develop and analyze a new algorithm to find the connected components of a compact set $I$ from a Lie group $G$ endowed with a left-invariant Riemannian distance. For a given $\delta>0$, the algorithm finds the largest cover of $I$ such…
We introduce a new algebraic structure for multi-dimensional compositional embeddings, built on directional non-commutative monoidal operators. The core contribution of this work is this novel framework, which exhibits appealing theoretical…
Let $S$ be a surface, $G$ a simply-connected classical group, and $G'$ the associated adjoint form of the group. In \cite{FG1}, it was shown that the moduli spaces of framed local systems $\X_{G',S}$ and $\A_{G,S}$ have the structure of…
We present a fine-structure entanglement classification under stochastic local operation and classical communication (SLOCC) for multiqubit pure states. To this end, we employ specific algebraic-geometry tools that are SLOCC invariants,…
We seek to understand the interplay between amino acid sequence and local structure in proteins. Are some amino acids unique in their ability to fit harmoniously into certain local structures? What is the role of sequence in sculpting the…
We revisit the classic stability problem of the buckling of an inextensible, axially compressed beam on a nonlinear elastic foundation with a semi-analytical approach to understand how spatially localized deformation solutions emerge in…
We elaborate on a general method that we recently introduced for characterizing the "natural" structures in complex physical systems via a multiscale network based approach for the data mining of such structures. The approach is based on…
A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…
The cluster analysis of very large objects is an important problem, which spans several theoretical as well as applied branches of mathematics and computer science. Here we suggest a novel approach: under assumption of local convergence of…
Human brain anatomy and function display a combination of modular and hierarchical organization, suggesting the importance of both cohesive structures and variable resolutions in the facilitation of healthy cognitive processes. However,…
Generalized contact bundles are odd dimensional analogues of generalized complex manifolds. They have been introduced recently and very little is known about them. In this paper we study their local structure. Specifically, we prove a local…
Neural circuits contain heterogeneous groups of neurons that differ in type, location, connectivity, and basic response properties. However, traditional methods for dimensionality reduction and clustering are ill-suited to recovering the…
A key topic in network science is the detection of intermediate or meso-scale structures. Community, core-periphery, disassortative and other partitions allow us to understand the organisation and function of large networks. In this work we…
Simplicial complexes are generalized network structures able to encode interactions occurring between more than two nodes. Simplicial complexes describe a large variety of complex interacting systems ranging from brain networks, to social…