Deformed Symmetry in Snyder Space and Relativistic Particle Dynamics

We describe the deformed Poincare-conformal symmetries implying the covariance of the noncommutative space obeying Snyder's algebra. Relativistic particle models invariant under these deformed symmetries are presented. A gauge (reparametrisation) independent derivation of Snyder's algebra from such models is given. The algebraic transformations relating the deformed symmetries with the usual (undeformed) ones are provided. Finally, an alternative form of an action yielding Snyder's algebra is discussed where the mass of a relativistic particle gets identified with the inverse of the noncommutativity parameter.Comment: 19 pages; Latex; title changed, 3 new references added and minor changes; to appear in JHE

Inhomogeneous chiral symmetry breaking in noncommutative four fermion interactions

The generalization of the Gross-Neveu model for noncommutative 3+1 space-time has been analyzed. We find indications that the chiral symmetry breaking occurs for an inhomogeneous background as in the LOFF phase in condensed matter.Comment: 17 pages, 2 figures, published version, minor correction

Probing Noncommutative Space-Time in the Laboratory Frame

The phenomenological investigation of noncommutative space-time in the laboratory frame are presented. We formulate the apparent time variation of noncommutativity parameter $\theta_{\mu\nu}$ in the laboratory frame due to the earth's rotation. Furthermore, in the noncommutative QED, we discuss how to probe the electric-like component $\overrightarrow{\theta_{E}}=(\theta_{01},\theta_{02},\theta_{03})$ by the process $e^-e^+\to\gamma\gamma$ at future $e^-e^+$ linear collider. We may determine the magnitude and the direction of $\overrightarrow{\theta_{E}}$ by detailed study of the apparent time variation of total cross section. In case of us observing no signal, the upper limit on the magnitude of $\overrightarrow{\theta_E^{}}$ can be determined independently of its direction.Comment: 12 pages, 7 figures, typos are corrected, one graph have been added in figure

Cooperation and Self-Regulation in a Model of Agents Playing Different Games

A simple model for cooperation between "selfish" agents, which play an extended version of the Prisoner's Dilemma(PD) game, in which they use arbitrary payoffs, is presented and studied. A continuous variable, representing the probability of cooperation, $p_k(t) \in$ [0,1], is assigned to each agent $k$ at time $t$. At each time step $t$ a pair of agents, chosen at random, interact by playing the game. The players update their $p_k(t)$ using a criteria based on the comparison of their utilities with the simplest estimate for expected income. The agents have no memory and use strategies not based on direct reciprocity nor 'tags'. Depending on the payoff matrix, the systems self-organizes - after a transient - into stationary states characterized by their average probability of cooperation $\bar{p}_{eq}$ and average equilibrium per-capita-income $\bar{p}_{eq},\bar{U}_\infty$. It turns out that the model exhibit some results that contradict the intuition. In particular, some games which - {\it a priory}- seems to favor defection most, may produce a relatively high degree of cooperation. Conversely, other games, which one would bet that lead to maximum cooperation, indeed are not the optimal for producing cooperation.Comment: 11 pages, 3 figures, keybords: Complex adaptive systems, Agent-based models, Social system

Incidence and progression of hand osteoarthritis in a large community-based cohort: the Johnston County Osteoarthritis Project

Objective: To describe the incidence and progression of radiographic and symptomatic hand osteoarthritis (rHOA and sxHOA) in a large community-based cohort. Design: Data were from the Johnston County OA Project (1999–2015, 12 ± 1.2 years follow-up, age 45+). Participants had bilateral hand radiographs each visit, read for Kellgren–Lawrence grade (KLG) at 30 joints. We defined rHOA as KLG ≥2 in ≥1 joint. SxHOA was defined in a hand/joint with rHOA and self-reported symptoms or tenderness on exam. Incidence was assessed in those without, while progression was assessed in those with, baseline rHOA. Proportions or medians are reported; differences by sex and race were assessed using models appropriate for dichotomous or continuous definitions, additionally adjusted for age, education, body mass index (BMI), and weight change. Results: Of 800 participants (68% women, 32% African American, mean age 60 years), 327 had baseline rHOA and were older, more often white and female, than those without rHOA (n = 473). The incidence of HOA was high, for rHOA (60%) and for sxHOA (13%). Women were more likely than men to have incident HOA, particularly for distal interphalangeal joint radiographic osteoarthritis (DIP rOA) (adjusted odds ratios (aOR) 1.60 95% confidence intervals (95% CI) [1.03, 2.49]) and sxHOA (aOR 2.98 [1.50, 5.91]). Progressive HOA was more similar by sex, although thumb base rOA progressed more frequently in women than in men (aOR 2.56 [1.44, 4.55]). Particularly HOA incidence, but also progression, was more frequent among whites compared with African Americans. Conclusion: This study provides much needed information about the natural history of HOA, a common and frequently debilitating condition, in the general population

Bifurcation and stability for Nonlinear Schroedinger equations with double well potential in the semiclassical limit

We consider the stationary solutions for a class of Schroedinger equations with a symmetric double-well potential and a nonlinear perturbation. Here, in the semiclassical limit we prove that the reduction to a finite-mode approximation give the stationary solutions, up to an exponentially small term, and that symmetry-breaking bifurcation occurs at a given value for the strength of the nonlinear term. The kind of bifurcation picture only depends on the non-linearity power. We then discuss the stability/instability properties of each branch of the stationary solutions. Finally, we consider an explicit one-dimensional toy model where the double well potential is given by means of a couple of attractive Dirac's delta pointwise interactions.Comment: 46 pages, 4 figure

π+π+\pi^+\pi^+ and π+π−\pi^+\pi^- colliding in noncommutative space

By studying the scattering process of scalar particle pion on the noncommutative scalar quantum electrodynamics, the non-commutative amendment of differential scattering cross-section is found, which is dependent of polar-angle and the results are significantly different from that in the commutative scalar quantum electrodynamics, particularly when $\cos\theta\sim \pm 1$. The non-commutativity of space is expected to be explored at around $\Lambda_{NC}\sim$TeV.Comment: Latex, 12 page