We consider the problem of estimating the partition function Z(β) = ∑ x exp(−β(H(x)) of a Gibbs distribution with a Hamilton H(·), or more precisely the logarithm of the ratio q = lnZ(0)/Z(β). It has been recently shown how to approximate q with high probability assuming the existence of an oracle that produces samples from the Gibbs distribution for a given parameter value in [0, β]. The curre...

We investigate several algorithms related to the parsing problem for weighted automata, under the assumption that the input is a string rather than a tree. This assumption is motivated by several natural language processing applications. We provide algorithms for the computation of parse-forests, best tree probability, inside probability (called partition function), and prefix probability. Our ...

gates on a single integrated circuit, so you have to partition the gates between separate circuits. Let's assume that you are forced to place exactly n/2 gates each on two integrated circuits. The connections between the gates across the partition are slow, energy consuming, and heat producing, while the cost associated with connections inside an integrated circuit are negligible. So, you want ...

An instance of the asymmetric matrix partition problem consists of a matrix A ∈ Rn×m + and a probability distribution p over its columns. The goal is to find a partition scheme that maximizes the resulting partition value. A partition scheme S = {S1, . . . ,Sn} consists of a partition Si of [m] for each row i of the matrix. The partition Si can be interpreted as a smoothing operator on row i, w...

We introduce a new isomorphism-invariant notion of entropy for measure-preserving actions arbitrary countable groups on probability spaces, which we call orbital Rokhlin entropy. It employs Danilenko’s approach to partition, and it is motivated by Seward’s recent generalization Rokhlin’s characterization from amenable general groups. A key ingredient in our the use an auxiliary probability-meas...

A bstract It is argued that the supersymmetric index of a certain system branes in M-theory equal to partition function an integrable three-dimensional lattice model. The local Boltzmann weights model satisfy generalization Zamolodchikov’s tetrahedron equation. In special case described by solution equation discovered Kapranov and Voevodsky Bazhanov Sergeev.

A new sharp upper bound for the probability of error of the likelihood ratio test is given for the detection in white Gaussian noise of any random vector whose norm is greater than, or equal to, a given value and whose probability of presence is less than, or equal to, one half. Also, a new test for the detection of such vectors is described. This test does not depend on the distribution of the...

Using BKP neutral fermions, we derive a product expression for the generating function of volume-weighted plane partitions that satisfy two conditions. If we call a set of adjacent equal height-h columns, h > 0, an h-path, then 1. Every h-path can assume one of two possible colours. 2. There is a unique way to move along an h-path from any column to another. In [1], Okounkov and Reshetikhin obs...

In the present paper, a new method for partitioning a circle in cells is presented. Cells have equal areas and shapes, so the method is termed the Isocell method. Its most interesting property is that cell centres are uniformly distributed inside the circle. Among possible applications of the Isocell method, the calculation of view factors by ray-tracing (image rendering, radiative heat transfe...

The n-dimensional hypercube network Qn is one of the most popular interconnection networks since it has simple structure and is easy to implement. The n-dimensional augmented cube, denoted by AQn, an important variation of the hypercube, possesses several embedding properties that hypercubes and other variations do not possess. The advantages of AQn are that the diameter is only about half of t...