A partition of a set N of n distinct numbers is called nested if there do not exist four numbers a < b < c < d in N such that a and c are in one part while b and d in another. A partition is called a p-partition if the number of parts is specified at p, and a shape-partition if the sizes of the p parts are also specified. There are exponentially many p-partitions but only polynomially many nest...

2 Computing the Partition Function From Nested Sampling The μVT system enforces a constant chemical potential, constant volume, and constant temperature. Unlike the the canonical or isothermal-isobaric systems the μVT system is allowed to exchange particles with the external bath, i.e. the number of particles within the constant volume of our system is allowed to change. The partition function ...

A technique, permitting automatic finding coarse grained parallelism in algorithms presented with arbitrary nested loops, is presented. The technique is based on finding affine space partition mappings. The main advantage of this technique is that it allows us to form constraints for finding mappings directly in a linear form while known techniques result in building non-linear constraints whic...

Distributed Model Checking avoids the state explosion problem by using the computational resources of parallel environments LTL model checking mainly entails detecting accepting cycles in a state transition graph. The nested depth-rst search algorithm used for this purpose is diicult to parallelize since it is based on the depth-rst search traver-sal order which is inherently sequential. Propos...

There are three papers in a series of discussions related to the partitioning capabilities on nested rectangular decision regions using multi-layer perceptrons. We propose a constructive algorithm, called the up-down algorithm, to realize the nested rectangular decision regions. The algorithm determines the weights easily and can be generalized to solve other decision regions with the propertie...

We propose a class of graphs that would occur naturally in finite-element and finitedifference problems and we prove a bound on separators for this class of graphs. Graphs in this class are embedded in d-dimensional space in a certain manner. For d-dimensional graphs our separator bound is O(n(d−1)/d), which is the best possible bound. We also propose a simple randomized algorithm to find this ...

Clustering is an unsupervised technique dealing with problems of organizing a collection of patterns into clusters based on similarity. Most clustering algorithms are based on hierarchical and partitional approaches. Algorithms based on an hierarchical approach generate a dendrogram representing the nested grouping of patterns and similarity levels at which groupings change [19]. Partitional cl...

This paper describes a clustering methodology for temporal data using hidden Markov model(HMM) representation. The proposed method improves upon existing HMM based clustering methods in two ways: (i) it enables HMMs to dynamically change its model structure to obtain a better t model for data during clustering process, and (ii) it provides objective criterion function to automatically select th...

This paper proposed a clustering methodology for sequence data using hidden Markov model(HMM) representation. The proposed methodology improves upon existing HMM based clustering methods in two ways: (i) it enables HMMs to dynamically change its model structure to obtain a better t model for data during clustering process, and (ii) it provides objective criterion function to select the optimal ...

We present a PCFG parsing algorithm that uses a multilevel coarse-to-fine (mlctf) scheme to improve the efficiency of search for the best parse. Our approach requires the user to specify a sequence of nested partitions or equivalence classes of the PCFG nonterminals. We define a sequence of PCFGs corresponding to each partition, where the nonterminals of each PCFG are clusters of nonterminals o...