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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nonlinear Schrodinger equations on metric graphs
度量图 非线性 薛定谔方程
2023/5/12
This talk will introduce some topics related to the study of nonlinear Schr?dinger equation on metric graphs, and then show the existence result of concentrated solutions to NLS equations on compact g...
Pathlength scaling in graphs with incomplete navigational information
Graph routing, Geometric routing, Navigability
2011/9/1
The graph-navigability problem concerns how one can nd as short paths as possible between a pair of vertices, given an incomplete picture of a graph.We study the navigability of graphs where the vert...
Stationary Nonlinear Schrodinger Equation on Simplest Graphs: Boundary conditions and exact solutions
Nonlinear Schrodinger Equation Simplest Graphs Mathematical Physics
2011/9/29
Abstract: We treat the stationary (cubic) nonlinear Schr\"odinger equation (NSLE) on simplest graphs. Formulation of the problem and exact analytical solutions of NLSE are presented for star graphs co...
Non-equilibrium Steady States of Quantum Systems on Star Graphs
Non-equilibrium Steady States Quantum Systems Star Graphs
2011/7/27
Abstract: Non-equilibrium steady states of quantum fields on star graphs are explicitly constructed. These states are parametrized by the temperature and the chemical potential, associated with each e...
Uniform existence of the integrated density of states on metric Cayley graphs
random Schrodinger operator metric graph quantum graph integrated density of states
2011/7/27
Abstract: Given a finitely generated amenable group we consider ergodic random Schr\"odinger operators on a Cayley graph with random potentials and random boundary conditions. We show that the normali...
Systems of Kowalevski type, discriminantly separable polynomials and quad-graphs
Systems of Kowalevski type discriminantly separable polynomials quad-graphs
2011/7/27
Systems of Kowalevski type, discriminantly separable polynomials and quad-graphs.
Motif based hierarchical random graphs: structural properties and critical points of an Ising model
amenability degree distribution clustering small-world graph Ising model critical point
2011/7/26
Motif based hierarchical random graphs: structural properties and critical points of an Ising model.
Motif based hierarchical random graphs: structural properties and critical points of an Ising model
amenability, degree distribution, clustering, small-world graph, Ising model, critical point
2011/9/15
A class of random graphs is introduced and studied. The graphs are constructed in an algorithmic way from five motifs which were found in [Milo R., Shen-Orr S., Itzkovitz S., Kashtan N., Chklovskii D....
Numerical evidence against a conjecture on the cover time of planar graphs
Numerical evidence the cover times of planar graphs Statistical Mechanics
2011/7/28
Abstract: We investigate a conjecture on the cover times of planar graphs by means of large Monte Carlo simulations. The conjecture states that the cover time $\tau(G_{N})$ of a planar graph $G_{N}$ o...
Real complex systems are inherently time-varying. Thanks to new communication systems and novel technologies, it is today possible to produce and analyze social and biological networks with detailed i...
Surrogate Parenthood: Protected and Informative Graphs
Surrogate Parenthood Protected Informative Graphs
2011/9/14
Many applications, including provenance and some analyses of social networks, require path-based queries over graphstructured data. When these graphs contain sensitive information, paths may be broken...
Finite propagation speed for solutions of the wave equation on metric graphs
Metric graphs Laplace operators wave equation finite propagation speed
2011/7/25
Abstract: We provide a class of self-adjoint Laplace operators on metric graphs with the property that the solutions of the associated wave equation satisfy the finite propagation speed property. The ...
Phase transitions for the cavity approach to the clique problem on random graphs
Phase transitions the cavity graphs
2010/11/17
We give a rigorous proof of two phase transitions for a disordered system designed to find large cliques inside Erdos random graphs. Such a system is associated with a conservative probabilistic cellu...
Efficient Triangle Counting in Large Graphs via Degree-based Vertex Partitioning
Efficient Triangle Counting Graphs Degree-based Vertex Partitioning
2010/11/17
The number of triangles is a computationally expensive graph statistic which is frequently used in complex network analysis (e.g., transitivity ratio), in various random graph models (e.g., exponenti...
Finding structural anomalies in graphs by means of quantum walks
structural anomalies in graphs quantum walks
2010/10/18
We explore the possibility of using quantum walks on graphs to find structural anomalies, such as extra edges or loops, on a graph. We focus our attention on star graphs, whose edges are like spokes c...