Related papers: Positive crossratios, barycenters, trees and appli…
We study a special class of graphs with a strong transience feature called uniform transience. We characterize uniform transience via a Feller-type property and via validity of an isoperimetric inequality. We then give a further…
We generalize the notion of isoperimetric profiles of finitely generated groups to their actions by measuring the boundary of finite subgraphings of the orbit graphing. We prove that like the classical isoperimetric profiles for groups,…
We identify a link between regular matroids and torus representations all of whose isotropy groups have an odd number of components. Applying Seymour's 1980 classification of the former objects, we obtain a classification of the latter. In…
In \cite{FGLNP}, Fox, Gromov, Lafforgue, Naor and Pach, in a respond to a question of Gromov \cite{G}, constructed bounded degree geometric expanders, namely, simplical complexes having the affine overlapping property. Their explicit…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
We study a question that lies at the intersection of classical research subjects in Topological Graph Theory and Graph Drawing: Computing a drawing of a graph with a prescribed number of crossings on a given set $S$ of points, while…
We consider the problem of translating between irreducible closed sets and implicational bases in closure systems. To date, the complexity status of this problem is widely open, and it is further known to generalize the notorious hypergraph…
How can we effectively find the best structures in tree models? Tree models have been favored over complex black box models in domains where interpretability is crucial for making irreversible decisions. However, searching for a tree…
The problem of how to estimate diffusion on a graph effectively is of importance both theoretically and practically. In this paper, we make use of two widely studied indices, geodesic distance and mean first-passage time ($MFPT$) for random…
We work with attracting subshifts generated by substitutions which are also irreducible parageometric automorphisms of free groups. For such a dynamical system, we construct a tree substitution to approximate the repelling real tree of the…
Understanding collective phenomena calls for tractable descriptions of correlations in assemblies of strongly interacting constituents. Capturing the essence of their self-consistency is central. The parquet theory admits a maximum level of…
We consider the response of a multicomponent body to $n$ fields, such as electric fields, magnetic fields, temperature gradients, concentration gradients, etc., where each component, which is possibly anisotropic, may cross couple the…
We derive an exact contrast-expansion formalism for the effective conductivity of heterogeneous materials (media) with local properties described by arbitrary continuous random fields, significantly generalizing the widely used binary-field…
We generalize the notion of tight geodesics in the curve complex to tight trees. We then use tight trees to construct model geometries for certain surface bundles over graphs. This extends some aspects of the combinatorial model for doubly…
Many classical objects on a surface S can be interpreted as cross-ratio functions on the circle at infinity of the universal covering. This includes closed curves considered up to homotopy, metrics of negative curvature considered up to…
All of 320 layer groups, distributed into 80 clusters - single/double ordinary/gray groups - are used to complete systematization of linear (in all directions) band crossings and corresponding effective Hamiltonians in high-symmetry…
We re-examine the constraints imposed by causality and unitarity on the low-energy effective field theory expansion of four-particle scattering amplitudes, exposing a hidden "totally positive" structure strikingly similar to the positive…
Taking a Feynman categorical perspective, several key aspects of the geometry of surfaces are deduced from combinatorial constructions with graphs. This provides a direct route from combinatorics of graphs to string topology operations via…
We find the complete set of conditions satisfied by the forward $2\to2$ scattering amplitude in unitarity and causal theories. These are based on an infinite set of energy dependent quantities -- the arcs -- which are dispersively expressed…
Under the hypotheses of analyticity, locality, Lorentz covariance, and Poincare invariance of the deformations, combined with the requirement that the interaction vertices contain at most two space-time derivatives of the fields, we…