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Conformal invariance of critical lattice models in two-dimensional has been vigorously studied for decades. The first example where the conformal invariance was rigorously verified was the planar unif...
Topology and entanglement are two powerful principles for characterizing the structure of complex quantum states. In a new paper in the journal Physical Review X, researchers from the University of Pe...
Our aim here is to describe a direct and natural connection between the representation theory of GLn and the Schubert calculus, which goes via the Chern-Weil theory of characteristic classes. Indeed,...
The Burton–Cabrera–Frank (BCF) theory of step flow has been recognized as a valuable tool for describing nanoscale evolution of crystal surfaces. We formally derive a single-step BCF-type model from a...
We consider a Markov process on a connected graph, with edges labeled with transition rates between the adjacent vertices. The distribution of the Markov process converges to the uniform distribution ...
Morse Decomposition for Dynamical Systems on compact metric spaces : φ : R × X → X, initiated by Morse, was established by Morse, Smale, ect by using the gradient–like flows for Morse decomposition...
In 1974 Cvetkovi\'c and Simi\'c showed which graphs $G$ are the bipartite complements of line graphs. In 2002 Borovi\'canin showed which line graphs $L(H)$ have third largest eigenvalue $\lambda_3\leq...
A path in an edge-colored graph is called {\em rainbow} if no two edges of it are colored the same. For an $\ell$-connected graph $G$ and an integer $k$ with $1\leq k\leq \ell$, the {\em rainbow $k$-c...
Abstract: The Gauss-Manin connection for nonabelian cohomology spaces is the isomonodromy flow. We write down explicitly the vector fields of the isomonodromy flow and calculate its induced vector fie...
We study a wireless relay network, with a single source and a single destination.Our main result is to show that an appropriate compress-and-forward scheme supports essentially the same reliable data ...
Motivated by the study of billiards in polygons, we prove fine results for the distribution of gaps of directions of saddle connections on translation surfaces.
A vertex-colored graph is rainbow vertex-connected if any two ver-tices are connected by a path whose internal vertices have distinct colors, which was introduced by Krivelevich and Yuster.
We define the concept of Levi Civita truncation for a Lagrangian in the Palatini formulation with an arbitrary connection, and show that its consistency uniquely identifies the Lovelock Lagrangians.
For a graph G, Chartrand et al. defined the rainbow connection number rc(G)and the strong rainbow connection number src(G) in “G. Charand, G.L. John,K.A. Mckeon, P. Zhang, Rainbow connection in graphs...
An edge-colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of G, denoted rc(G), is the minimum number of c...

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