A differential method of maximum entropy

We consider a differential method of maximum entropy that is based on the linearity of Fourier transform and involves reconstruction of images from the differences of the visibility function. The efficiency of the method is demonstrated with respect to the recovery of source images with bright components against the background of a sufficiently weak extended base. The simulation results are given along with the maps of an extragalactic radio source 0059+581, which were obtained using the standard and differential methods of maximum entropy for three observation dates and show that the principle of differential mapping allows us to increase considerably the dynamic interval of images.Comment: Latex, 6 pages with 4 Postscript figure

Duality and zero-point length of spacetime

The action for a relativistic free particle of mass $m$ receives a contribution $-mds$ from a path segment of infinitesimal length $ds$. Using this action in a path integral, one can obtain the Feynman propagator for a spinless particle of mass $m$. If one of the effects of quantizing gravity is to introduce a minimum length scale $L_P$ in the spacetime, then one would expect the segments of paths with lengths less than $L_P$ to be suppressed in the path integral. Assuming that the path integral amplitude is invariant under the `duality' transformation $ds\to L_P^2/ds$, one can calculate the modified Feynman propagator. I show that this propagator is the same as the one obtained by assuming that: quantum effects of gravity leads to modification of the spacetime interval $(x-y)^2$ to $(x-y)^2+L_P^2$. This equivalence suggests a deep relationship between introducing a `zero-point-length' to the spacetime and postulating invariance of path integral amplitudes under duality transformations.Comment: Revtex document; 4 page

Expansions of the solutions of the general Heun equation governed by two-term recurrence relations for coefficients

We examine the expansions of the solutions of the general Heun equation in terms of the Gauss hypergeometric functions. We present several expansions using functions, the forms of which differ from those applied before. In general, the coefficients of the expansions obey three-term recurrence relations. However, there exist certain choices of the parameters for which the recurrence relations become two-term. The coefficients of the expansions are then explicitly expressed in terms of the gamma functions. Discussing the termination of the presented series, we show that the finite-sum solutions of the general Heun equation in terms of generally irreducible hypergeometric functions have a representation through a single generalized hypergeometric function. Consequently, the power-series expansion of the Heun function for any such case is governed by a two-term recurrence relation

Single and pair production of heavy leptons in E6E_6 model

We investigate the single and pair production of new heavy leptons via string inspired $E_{6}$ model at future linear colliders. Signal and corresponding backgrounds for these leptons are studied. We have found that single production of heavy leptons is more relevant than that of pair production, as expected. For a maximal mixing value of 0.1, the upper mass limits of 2750 GeV in the single case and 1250 GeV in the pair production case are obtained at $\sqrt{s}=3$ TeV collider option.Comment: 14 pages, 10 figure

Reciprocity in Social Networks with Capacity Constraints

Directed links -- representing asymmetric social ties or interactions (e.g., "follower-followee") -- arise naturally in many social networks and other complex networks, giving rise to directed graphs (or digraphs) as basic topological models for these networks. Reciprocity, defined for a digraph as the percentage of edges with a reciprocal edge, is a key metric that has been used in the literature to compare different directed networks and provide "hints" about their structural properties: for example, are reciprocal edges generated randomly by chance or are there other processes driving their generation? In this paper we study the problem of maximizing achievable reciprocity for an ensemble of digraphs with the same prescribed in- and out-degree sequences. We show that the maximum reciprocity hinges crucially on the in- and out-degree sequences, which may be intuitively interpreted as constraints on some "social capacities" of nodes and impose fundamental limits on achievable reciprocity. We show that it is NP-complete to decide the achievability of a simple upper bound on maximum reciprocity, and provide conditions for achieving it. We demonstrate that many real networks exhibit reciprocities surprisingly close to the upper bound, which implies that users in these social networks are in a sense more "social" than suggested by the empirical reciprocity alone in that they are more willing to reciprocate, subject to their "social capacity" constraints. We find some surprising linear relationships between empirical reciprocity and the bound. We also show that a particular type of small network motifs that we call 3-paths are the major source of loss in reciprocity for real networks

Pairing and realistic shell-model interactions

This paper starts with a brief historical overview of pairing in nuclei, which fulfills the purpose of properly framing the main subject. This concerns the pairing properties of a realistic shell-model effective interaction which has proved very successful in describing nuclei around doubly magic 132Sn. We focus attention on the two nuclei 134Te and 134Sn with two valence protons and neutrons, respectively. Our study brings out the key role of one particle-one hole excitations in producing a significant difference between proton and neutron pairing in this region

Glycerol as an Energy Source for Ruminants: a Meta-Analysis of in Vitro Experiments

Glycerol or glycerin is generally recognized as a safe compound to be used in animal feed, especially for ruminants. A number of in vitro studies related to glycerol supplementation in ruminant ration have been published but to date the results have not been summarized. The objective of this study was, therefore, to evaluate in vitro digestibility, ruminal fermentation characteristics, total gas and methane production through the meta-analysis approach. Meta-analysis was applied to 13 experiments and 42 treatments dealing with glycerol supplementation in ruminants. Data were analyzed by general linear model procedure in which the glycerol levels and the different studies were treated as fixed effects. Results revealed that glycerol supplementation did not affect the in vitro digestibility and total VFA production, but significantly decreased molar proportion of acetate and iso-valerate (P<0.05). In contrast, molar proportion of propionate, butyrate, and valerate significantly increased, and thus the ratio of acetate to propionate declined linearly (P<0.05). Methane production decreased linearly and accompanied with an increase of total gas production with increasing levels of glycerol supplementation (P<0.05). It is concluded that the use of glycerol as an energy substitution in animal feed has no detrimental effects in the rumen and environmentally friendly