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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some Results on Partial Inverse Spanning Tree Problems
部分逆生成树 有权函数 非循环边子集
2023/11/6
Given a graph G with weight function w and an acyclic edge subset E', the partial inverse spanning tree problem on (G, w; E') is to find a new weight function w* so that E' can be extended to a maximu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Connection probabilities for random-cluster model and uniform spanning treeConnection probabilities for random-cluster model and uniform spanning tree
随机 聚类模型 均匀生成树 连接概率
2023/5/16
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...
Ising models on locally tree-like graphs
Ising model random sparse graphs cavity method Bethe measures belief propagation local weak convergence
2015/8/21
We consider Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the...
The weak limit of Ising models on locally tree-like graphs
Ising model the temperature the last beta sequence
2015/8/20
We consider the Ising model with inverse temperature β and without external field on sequences of graphs Gn which converge locally to the k-regular tree. We show that for such graphs the Ising m...
FACTOR MODELS ON LOCALLY TREE-LIKE GRAPHS
Factor models random graphs belief propagation Bethe measures Potts model independent set Gibbs measures free energy density local weak convergence
2015/8/20
We consider homogeneous factor models on uniformly sparse graph sequences converg-ing locally to a (unimodular) random tree T, and study the existence of the free energy density ,the limit of the log...
THE SANDPILE GROUP OF A TREE
SANDPILE GROUP TREE
2015/8/14
A wired tree is a graph obtained from a tree by collapsing the leaves to a single vertex. We describe a pair of short exact sequences relating the sandpile group of a wired tree to the sandpile groups...
How Close a Bataknese One Another?: Study of Indonesian Batak’s Family Tree
family tree batak customary law scale-free network
2015/7/28
The paper conjectures some alternative acquisitions of mathematical models to see the Batak family tree that could enrich our understanding of the anthropological study of Bataknese people. We discuss...
Minimum Latency Aggregation Scheduling for Arbitrary Tree Topologies under the SINR Model
Minimum Latency Tree undeer Topologies SINR Model
2012/12/4
Almost all the existing wireless data aggregation approaches；need a topology construction step before scheduling. These solutions assume the availability of flexible topology controls. However, in rea...
Semi-infinite paths of the 2d-Radial Spanning Tree
stochastic geometry random tree semi-infinite path asymptotic direction competition interface
2012/6/9
We study semi-infinite paths of the radial spanning tree (RST) of a Poisson point process in the plane. We first show that the expectation of the number of intersection points between semi-infinite pa...
A quasi-tree expansion of the Krushkal polynomial
quasi-tree expansion Krushkal polynomial Combinatorics
2012/5/24
We introduce a generalization of the Krushkal polynomial to nonorientable surfaces, and prove that this polynomial has a natural quasi-tree expansion. This generalized Krushkal polynomial contains the...
We study the bilipschitz equivalence type of tree-graded spaces, showing that asymptotic cones of relatively hyperbolic groups (resp. asymptotic cones of groups containing a cut-point) only depend on ...
Theories without the tree property of the second kind
Theories the tree property of the second kind Logic
2012/4/23
We initiate a systematic study of the class of theories without the tree property of the second kind -- NTP2. Most importantly, we show: the burden is "sub-multiplicative" in arbitrary theories (in pa...
Tree Codes Improve Convergence Rate of Consensus Over Erasure Channels
Tree Codes Convergence Rate of Consensus Erasure Channels Optimization and Control
2012/4/17
We study the problem of achieving average consensus between a group of agents over a network with erasure links. In the context of consensus problems, the unreliability of communication links between ...
Record process on the Continuum Random Tree
continuum random tree, records, cutting down a tree
2011/9/14
Abstract: We consider the number of cuts $X_n^*$ needed to isolate the root of the sub-tree spanned by $n$ leaves uniformly chosen at random in Aldous's continuum random tree $\ct$. We prove the almos...
Divergent directions in some periodic wind-tree models
Divergent directions periodic wind-tree models Dynamical Systems
2011/9/5
Abstract: The periodic wind-tree model is a family T(a,b) of billiards in the plane in which identical rectangular scatterers of size axb are disposed at each integer point. It was proven by P. Hubert...