We study approximate decimations in SU(N) LGT that connect the short to long distance regimes. Simple ‘bond-moving’ decimations turn out to provide both upper and lower bounds on the exact partition function. This leads to a representation of the exact partition function in terms of successive decimations whose effective couplings flows are related to those of the easily computable bond-moving ...

Let G be a finite and simple graph with vertex set V (G), and let f : V (G) → {−1, 1} be a two-valued function. If ∑ x∈N[v] f (x) ≥ 1 for each v ∈ V (G), where N[v] is the closed neighborhood of v, then f is a signed dominating function on G. A set {f1, f2, . . . , fd} of signed dominating functions on Gwith the property that ∑d i=1 fi(x) ≤ 1 for each x ∈ V (G), is called a signed dominating fa...

In this paper, we present a method for reducing a regular, discrete-time Markov chain (DTMC) to another DTMC with a given, typically much smaller number of states. The cost of reduction is defined as the Kullback–Leibler divergence rate between a projection of the original process through a partition function and a DTMC on the correspondingly partitioned state space. Finding the reduced model w...

A derivation is given from first principles of the fact that the SU(2) gauge theory is in a confining phase for all values of the coupling 0 < g < ∞ defined at lattice spacing (UV regulator) a, and space-time dimension d ≤ 4. The strategy is to employ approximate RG decimation transformations of the potential moving type which give both upper and lower bounds on the partition function at each s...

We introduce a novel method for estimating the partition function and marginals of distributions defined using graphical models. The method uses the entropy chain rule to obtain an upper bound on the entropy of a distribution given marginal distributions of variable subsets. The structure of the bound is determined by a permutation, or elimination order, of the model variables. Optimizing this ...

Given a sparse undirected graph G with weights on the edges, a k-plex partition of G is a partition of its set of nodes such that each component is a k-plex. A subset of nodes S is a k-plex if the degree of every node in the associated induced subgraph is at least |S|  k. The maximum edge-weight k-plex partitioning (Max-EkPP) problem is to find a k-plex partition with maximum total weight, whe...

The power system restoration control has a higher uncertainty level than the preventive of cascading failures. In order to ensure feasibility decision support control, framework for adaptive transmission is proposed, which can coordinated multiple partitions, units and loads, coordination multi-partition decision-making process actual process. proposed divided into two layers, global layer part...

A tree-partition of a graph G is a proper partition of its vertex set into ‘bags’, such that identifying the vertices in each bag produces a forest. The treepartition-width of G is the minimum number of vertices in a bag in a tree-partition of G. An anonymous referee of the paper by Ding and Oporowski [J. Graph Theory, 1995] proved that every graph with tree-width k ≥ 3 and maximum degree ∆ ≥ 1...

Computing the partition function of an arbitrary graphical model is generally intractable. As a result, approximate inference techniques such as loopy belief propagation and expectation propagation are used to compute an approximation to the true partition function. However, due to general issues of intractability in the continuous case, our understanding of these approximations is relatively l...