Interacting Modified Variable Chaplygin Gas in Non-flat Universe

A unified model of dark energy and matter is presented using the modified variable Chaplygin gas for interacting dark energy in a non-flat universe. The two entities interact with each other non-gravitationally which involves a coupling constant. Due to dynamic interaction, the variation in this constant arises that henceforth changes the equations of state of these quantities. We have derived the effective equations of state corresponding to matter and dark energy in this interacting model. Moreover, the case of phantom energy is deduced by putting constraints on the parameters involved.Comment: 9 pages; Accepted for publication in European Physical Journal

Interacting new agegraphic Phantom model of dark energy in non-flat universe

In this paper we consider the new agegraphic model of interacting dark energy in non-flat universe. We show that the interacting agegraphic dark energy can be described by a phantom scalar field. Then we show this phantomic description of the agegraphic dark energy and reconstruct the potential of the phantom scalar field.Comment: 8 pages, no figur

Transport and the Order Parameter of Superconducting UPt3

We calculate the ultrasonic absorption and the thermal conductivity in the superconducting state of UPt$_{3}$ as functions of temperature and direction of propagation and polarization. Two leading candidates for the superconducting order parameter are considered: the $E_{1g}$ and $E_{2u}$ representations. Both can fit the data except for the ultrasonic absorption in the $A$ phase. To do that, it is necessary to suppose that the system has only a single domain, and that must be chosen as the most favorable one. However, the $E_{2u}$ theory requires fine-tuning of parameters to fit the low temperature thermal conductivity. Thus, transport data favor the $E_{1g}$ theory. Measurements of the thermal conductivity as a function of pressure at low temperature could help to further distinguish the two theories.Comment: 7 pages, 4 figure

A simpler and more efficient algorithm for the next-to-shortest path problem

Given an undirected graph $G=(V,E)$ with positive edge lengths and two vertices $s$ and $t$, the next-to-shortest path problem is to find an $st$-path which length is minimum amongst all $st$-paths strictly longer than the shortest path length. In this paper we show that the problem can be solved in linear time if the distances from $s$ and $t$ to all other vertices are given. Particularly our new algorithm runs in $O(|V|\log |V|+|E|)$ time for general graphs, which improves the previous result of $O(|V|^2)$ time for sparse graphs, and takes only linear time for unweighted graphs, planar graphs, and graphs with positive integer edge lengths.Comment: Partial result appeared in COCOA201

Statefinder diagnostic and stability of modified gravity consistent with holographic and new agegraphic dark energy

Recently one of us derived the action of modified gravity consistent with the holographic and new-agegraphic dark energy. In this paper, we investigate the stability of the Lagrangians of the modified gravity as discussed in [M. R. Setare, Int. J. Mod. Phys. D 17 (2008) 2219; M. R. Setare, Astrophys. Space Sci. 326 (2010) 27]. We also calculate the statefinder parameters which classify our dark energy model.Comment: 12 pages, 2 figures, accepted by Gen. Relativ. Gravi

Techniques of replica symmetry breaking and the storage problem of the McCulloch-Pitts neuron

In this article the framework for Parisi's spontaneous replica symmetry breaking is reviewed, and subsequently applied to the example of the statistical mechanical description of the storage properties of a McCulloch-Pitts neuron. The technical details are reviewed extensively, with regard to the wide range of systems where the method may be applied. Parisi's partial differential equation and related differential equations are discussed, and a Green function technique introduced for the calculation of replica averages, the key to determining the averages of physical quantities. The ensuing graph rules involve only tree graphs, as appropriate for a mean-field-like model. The lowest order Ward-Takahashi identity is recovered analytically and is shown to lead to the Goldstone modes in continuous replica symmetry breaking phases. The need for a replica symmetry breaking theory in the storage problem of the neuron has arisen due to the thermodynamical instability of formerly given solutions. Variational forms for the neuron's free energy are derived in terms of the order parameter function x(q), for different prior distribution of synapses. Analytically in the high temperature limit and numerically in generic cases various phases are identified, among them one similar to the Parisi phase in the Sherrington-Kirkpatrick model. Extensive quantities like the error per pattern change slightly with respect to the known unstable solutions, but there is a significant difference in the distribution of non-extensive quantities like the synaptic overlaps and the pattern storage stability parameter. A simulation result is also reviewed and compared to the prediction of the theory.Comment: 103 Latex pages (with REVTeX 3.0), including 15 figures (ps, epsi, eepic), accepted for Physics Report

Interacting new agegraphic viscous dark energy with varying GG

We consider the new agegraphic model of dark energy with a varying gravitational constant, $G$, in a non-flat universe. We obtain the equation of state and the deceleration parameters for both interacting and noninteracting new agegraphic dark energy. We also present the equation of motion determining the evolution behavior of the dark energy density with a time variable gravitational constant. Finally, we generalize our study to the case of viscous new agegraphic dark energy in the presence of an interaction term between both dark components.Comment: 12 pages, accepted for publication in IJTP (2010

Holographic dark energy with time varying c2c^2 parameter

We consider the holographic dark energy model in which the model parameter $c^2$ evolves slowly with time. First we calculate the evolution of EoS parameter as well as the deceleration parameter in this generalized version of holographic dark energy (GHDE). Depending on the parameter $c^2$, the phantom regime can be achieved earlier or later compare with original version of holographic dark energy. The evolution of energy density of GHDE model is investigated in terms of parameter $c^2$. We also show that the time-dependency of $c^2$ can effect on the transition epoch from decelerated phase to accelerated expansion. Finally, we perform the statefinder diagnostic for GHDE model and show that the evolutionary trajectories of the model in $s-r$ plane are strongly depend on the parameter $c^2$.Comment: 16 pages, 4 figures, accepted by Astrophys Space Sc

New Agegraphic Dark Energy in f(R)f(R) Gravity

In this paper we study cosmological application of new agegraphic dark energy density in the $f(R)$ gravity framework. We employ the new agegraphic model of dark energy to obtain the equation of state for the new agegraphic energy density in spatially flat universe. Our calculation show, taking $n<0$, it is possible to have $w_{\rm \Lambda}$ crossing -1. This implies that one can generate phantom-like equation of state from a new agegraphic dark energy model in flat universe in the modified gravity cosmology framework. Also we develop a reconstruction scheme for the modified gravity with $f(R)$ action.Comment: 8 pages, no figur

The Intrinsic Dimensionality of Attractiveness: A Study in Face Profiles

The study of human attractiveness with pattern analysis techniques is an emerging research field. One still largely unresolved problem is which are the facial features relevant to attractiveness, how they combine together, and the number of independent parameters required for describing and identifying harmonious faces. In this paper, we present a first study about this problem, applied to face profiles. First, according to several empirical results, we hypothesize the existence of two well separated manifolds of attractive and unattractive face profiles. Then, we analyze with manifold learning techniques their intrinsic dimensionality. Finally, we show that the profile data can be reduced, with various techniques, to the intrinsic dimensions, largely without loosing their ability to discriminate between attractive and unattractive face