A quasi-elastic regime for vibrated granular gases

Using simple scaling arguments and two-dimensional numerical simulations of a granular gas excited by vibrating one of the container boundaries, we study a double limit of small $1-r$ and large $L$, where $r$ is the restitution coefficient and $L$ the size of the container. We show that if the particle density $n_0$ and $(1-r^2)(n_0 Ld)$ where $d$ is the particle diameter, are kept constant and small enough, the granular temperature, i.e. the mean value of the kinetic energy per particle, $/N$, tends to a constant whereas the mean dissipated power per particle, $/N$, decreases like $1/\sqrt{N}$ when $N$ increases, provided that $(1-r^2)(n_0 Ld)^2 < 1$. The relative fluctuations of $E$, $D$ and the power injected by the moving boundary, $I$, have simple properties in that regime. In addition, the granular temperature can be determined from the fluctuations of the power $I(t)$ injected by the moving boundary.

Comparing instance-averaging with instance-saving learning algorithms

The goal of our research is to understand the power and appropriateness of instance-based representations and their associated acquisition methods. This paper concerns two methods for reducing storage requirements for instance-based learning algorithms. The first method, termed instance-saving, represents concept descriptions by selecting and storing a representative subset of the given training instances. We provide an analysis for instance-saving techniques and specify one general class of concepts that instance-saving algorithms are capable of learning. The second method, termed instance-averaging, represents concept descriptions by averaging together some training instances while simply saving others. We describe why analyses for instance-averaging algorithms are difficult to produce. Our empirical results indicate that storage requirements for these two methods are roughly equivalent. We outline the assumptions of instance-averaging algorithms and describe how their violation might degrade performance. To mitigate the effects of non-convex concepts, a dynamic thresholding technique is introduced and applied in both the averaging and non-averaging learning algorithms. Thresholding increases the storage requirements but also increases the quality of the resulting concept descriptions

Algorithm Instance Games

This paper introduces algorithm instance games (AIGs) as a conceptual classification applying to games in which outcomes are resolved from joint strategies algorithmically. For such games, a fundamental question asks: How do the details of the algorithm's description influence agents' strategic behavior? We analyze two versions of an AIG based on the set-cover optimization problem. In these games, joint strategies correspond to instances of the set-cover problem, with each subset (of a given universe of elements) representing the strategy of a single agent. Outcomes are covers computed from the joint strategies by a set-cover algorithm. In one variant of this game, outcomes are computed by a deterministic greedy algorithm, and the other variant utilizes a non-deterministic form of the greedy algorithm. We characterize Nash equilibrium strategies for both versions of the game, finding that agents' strategies can vary considerably between the two settings. In particular, we find that the version of the game based on the deterministic algorithm only admits Nash equilibrium in which agents choose strategies (i.e., subsets) containing at most one element, with no two agents picking the same element. On the other hand, in the version of the game based on the non-deterministic algorithm, Nash equilibrium strategies can include agents with zero, one, or every element, and the same element can appear in the strategies of multiple agents.Comment: 14 page

Realistic Neutrino Masses from Multi-brane Extensions of the Randall-Sundrum Model?

Scenarios based on the existence of large or warped (Randall-Sundrum model) extra dimensions have been proposed for addressing the long standing puzzle of gauge hierarchy problem. Within the contexts of both those scenarios, a novel and original type of mechanism generating small (Dirac) neutrino masses, which relies on the presence of additional right-handed neutrinos that propagate in the bulk, has arisen. The main objective of the present study is to determine whether this geometrical mechanism can produce reasonable neutrino masses also in the interesting multi-brane extensions of the Randall-Sundrum model. We demonstrate that, in some multi-brane extensions, neutrino masses in agreement with all relevant experimental bounds can indeed be generated but at the price of a constraint (stronger than the existing ones) on the bulk geometry, and that the other multi-brane models even conflict with those experimental bounds.Comment: 29 pages, 3 figures, Latex file. References added, study extende

Iterative Instance Segmentation

Existing methods for pixel-wise labelling tasks generally disregard the underlying structure of labellings, often leading to predictions that are visually implausible. While incorporating structure into the model should improve prediction quality, doing so is challenging - manually specifying the form of structural constraints may be impractical and inference often becomes intractable even if structural constraints are given. We sidestep this problem by reducing structured prediction to a sequence of unconstrained prediction problems and demonstrate that this approach is capable of automatically discovering priors on shape, contiguity of region predictions and smoothness of region contours from data without any a priori specification. On the instance segmentation task, this method outperforms the state-of-the-art, achieving a mean $\mathrm{AP}^{r}$ of 63.6% at 50% overlap and 43.3% at 70% overlap.Comment: 13 pages, 10 figures; IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 201

Parity realization in Vector-like theories from Fermion Bilinears

We reconsider in this paper the old aim of trying to understand if the observed realization of discrete symmetries as Parity or CP in the QCD vacuum can be satisfied from first principles. We show how under the appropriate assumptions implicitely done by Vafa and Witten in their old paper on parity realization in vector-like theories, all parity and CP odd operators constructed from fermion bilinears of the form $\bar\psi\tilde O\psi$ should take a vanishing vacuum expectation value in a vector-like theory with N degenerate flavours (N>1). In our analysis the Vafa-Witten theorem on the impossibility to break spontaneously the flavour symmetry in a vector-like theory plays a fundamental role.Comment: 12 pages, no figures To be published in JHE