Lorentz Violation for Photons and Ultra-High Energy Cosmic Rays

Lorentz symmetry breaking at very high energies may lead to photon dispersion relations of the form omega^2=k^2+xi_n k^2(k/M_Pl)^n with new terms suppressed by a power n of the Planck mass M_Pl. We show that first and second order terms of size xi_1 > 10^(-14) and xi_2 < -10^(-6), respectively, would lead to a photon component in cosmic rays above 10^(19) eV that should already have been detected, if corresponding terms for electrons and positrons are significantly smaller. This suggests that Lorentz invariance breakings suppressed up to second order in the Planck scale are unlikely to be phenomenologically viable for photons.Comment: 4 revtex pages, 3 postscript figures included, version published in PR

Rank Maximal Matchings -- Structure and Algorithms

Let G = (A U P, E) be a bipartite graph where A denotes a set of agents, P denotes a set of posts and ranks on the edges denote preferences of the agents over posts. A matching M in G is rank-maximal if it matches the maximum number of applicants to their top-rank post, subject to this, the maximum number of applicants to their second rank post and so on. In this paper, we develop a switching graph characterization of rank-maximal matchings, which is a useful tool that encodes all rank-maximal matchings in an instance. The characterization leads to simple and efficient algorithms for several interesting problems. In particular, we give an efficient algorithm to compute the set of rank-maximal pairs in an instance. We show that the problem of counting the number of rank-maximal matchings is #P-Complete and also give an FPRAS for the problem. Finally, we consider the problem of deciding whether a rank-maximal matching is popular among all the rank-maximal matchings in a given instance, and give an efficient algorithm for the problem

Cosmological Origin of the Stellar Velocity Dispersions in Massive Early-Type Galaxies

We show that the observed upper bound on the line-of-sight velocity dispersion of the stars in an early-type galaxy, sigma<400km/s, may have a simple dynamical origin within the LCDM cosmological model, under two main hypotheses. The first is that most of the stars now in the luminous parts of a giant elliptical formed at redshift z>6. Subsequently, the stars behaved dynamically just as an additional component of the dark matter. The second hypothesis is that the mass distribution characteristic of a newly formed dark matter halo forgets such details of the initial conditions as the stellar "collisionless matter" that was added to the dense parts of earlier generations of halos. We also assume that the stellar velocity dispersion does not evolve much at z<6, because a massive host halo grows mainly by the addition of material at large radii well away from the stellar core of the galaxy. These assumptions lead to a predicted number density of ellipticals as a function of stellar velocity dispersion that is in promising agreement with the Sloan Digital Sky Survey data.Comment: ApJ, in press (2003); matches published versio

Canonical transformations in three-dimensional phase space

Canonical transformation in a three-dimensional phase space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed as based on canonoid transformations. It is shown that generating functions, transformed Hamilton functions and the transformation itself for given generating functions can be determined by solving Pfaffian differential equations corresponding to that quantities. Types of the generating functions are introduced and all of them is listed. Infinitesimal canonical transformations are also discussed. Finally, we show that decomposition of canonical transformations is also possible in three-dimensional phase space as in the usual two-dimensional one.Comment: 19 pages, 1 table, no figures. Accepted for publication in Int. J. Mod. Phys.

A necklace of Wulff shapes

In a probabilistic model of a film over a disordered substrate, Monte-Carlo simulations show that the film hangs from peaks of the substrate. The film profile is well approximated by a necklace of Wulff shapes. Such a necklace can be obtained as the infimum of a collection of Wulff shapes resting on the substrate. When the random substrate is given by iid heights with exponential distribution, we prove estimates on the probability density of the resulting peaks, at small density

Integrating the EGC, EF, and ECS Trio Approaches to Ensure Security and Load Balancing in the Cloud

According to data protection studies, "Distributed Denial-of-Service (DDoS)" threats have cost governments and businesses throughout the globe a large number of financial resources. Despite this, the existing practices fall short of the standards set by "Cloud Computing (CC)" monitoring technology. They ignore the "Intrusion Detection Systems (IDS)" techniques, which take advantage of the CC's multiple tenants and elasticity qualities, and also the hardware limitations. Attackers are finding increasing ways to effectively exploit them because of their rising complexity. DDoS assaults of this scale have never been observed online before 2018. As online services get more popular, so does the amount of DDoS assaults and malevolent hackers leading to terrible. Numerous IDS for DDoS are already in place to address this problem. One of the most challenging aspects of virtualization is establishing a "Trust Model (TM)" between the many "Virtual Machines (VMs)". The lack of a standard formulation for generating a TM would be the primary reason. As a consequence, the integrity of every VM might not have been recognized by an independent trust, which might lead to a decrease in trust value. In this research for TM creation, "Enhanced Graph Based Clustering (EGC)" is proposed, while "Enhanced Fuzzy (EF)" is used for detecting attacks, and the "Enhanced Cuckoo Search (ECS)" method is used to find the ideal "Load Balancing (LB)" distribution. By creating a new TM, the proposed (EGC-EF-ECS) system strengthens trust value. To expand the CC model's stability, it optimizes attacker recognition percentage and makes better use of resources by restricting each VM's processing, bandwidth, and storage requirements. The proposed EGC-EF-ECS outperformed the previously used BPA-SAB, and DCRI-RI approaches in terms of the "Intrusion-Detection-Rate (IDR)", "Load-Balancing-Efficiency (LBE)", and "Data-Accessing-Time (DAT)" evaluation metrics

The Moduli Space of BPS Domain Walls

N=2 SQED with several flavors admits multiple, static BPS domain wall solutions. We determine the explicit two-kink metric and examine the dynamics of colliding domain walls. The multi-kink metric has a toric Kahler structure and we reduce the Kahler potential to quadrature. In the second part of this paper, we consider semi-local vortices compactified on circle. We argue that, in the presence of a suitable Wilson line, the vortices separate into domain wall constituents. These play the role of fractional instantons in two-dimensional gauge theories and sigma-models.Comment: 16 pages, LaTex, 2 figures; factors of zeta corrected, meaning of cross-terms elucidated, further clarifying comments; (more) references adde