Torsional-space Monte Carlo simulations of flexible molecules are usually based on the assumption that all values of dihedral angles have equal probability in the absence of atomic interactions. In the present paper it is shown that this assumption is not valid. Thermodynamic sampling using dihedral angles or other internal coordinates has to account for both the correct metric in conformationa...

We introduce a non-partisan probability distribution on congressional redistricting of North Carolina which emphasizes the equal partition of the population and the compactness of districts. When random districts are drawn and the results of the 2012 election were re-tabulated under the drawn districtings, we find that an average of 7.6 democratic representatives are elected. 95% of the randoml...

We propose an optimal bit allocation strategy for a joint source/channel video codec over noisy channel when the average channel state is assumed to be known. Our approach is to partition source and channel coding bits in such a way that the expected distortion is minimized. The particular source coding algorithm we use is rate scalable and is based on 3D subband coding with multi-rate quantiza...

We derive the limit shape of Young diagrams, associated with growing integer partitions, with respect to multiplicative probability measures underpinned by the generating functions of the form F(z) = ∞l=1F0(zl) (which entails equal weighting among possible parts l ∈ N). Under mild technical assumptions on the function H0(u) = ln(F0(u)), we show that the limit shape ω∗(x) exists and is given by ...

Tree structured modeling is a data mining technique used to recursively partition a dataset into relatively homogeneous subgroups in order to make more accurate predictions on generated classes. One of the classification tree induction algorithms, GUIDE, is a nonparametric method with suitable accuracy and low bias selection, which is used for predicting binary classes based on many predictors....

We investigate the performance of a randomized coordination mechanism for resource access in an autonomous decentralized system. Given n users and r resources, each user decides to access a resource with probability a, and each resource is selected with equal likelihood. The goal i s to select a so that mutually conjicting decisions, where multiple users try to access the same resource, are min...

The probability that the commutator of two group elements is equal to a given element has been introduced in literature few years ago. Several authors have investigated this notion with methods of the representation theory and with combinatorial techniques. Here we illustrate that a wider context may be considered and show some structural restrictions on the group.

Recently, George Beck posed many interesting partition problems considering the number of ones in partitions. In this paper, we first consider crank generating function weighted by and obtain analytic formulas for under conditions being less than or equal to some specific integer. We connect these cumulative point functions partitions with certain sizes Durfee rectangles. then a generalization ...

Let P be a planar n-point set. A k-partition of P is a subdivision of P into dn/ke parts of roughly equal size and a sequence of triangles such that each part is contained in a triangle. A line is k-shallow if it has at most k points of P below it. The crossing number of a k-partition is the maximum number of triangles in the partition that any k-shallow line intersects. We give a lower bound o...

We announce a new four parameter partition theorem from which the (big) theorem of Göllnitz follows by setting any one of the parameters equal to 0. This settles a problem of Andrews who asked whether there exists a result that goes beyond the partition theorem of Göllnitz. We state a four parameter q-series identity (key identity) which is the generating function form of this theorem. In a sub...