Small-World Networks: Links with long-tailed distributions

Small-world networks (SWN), obtained by randomly adding to a regular structure additional links (AL), are of current interest. In this article we explore (based on physical models) a new variant of SWN, in which the probability of realizing an AL depends on the chemical distance between the connected sites. We assume a power-law probability distribution and study random walkers on the network, focussing especially on their probability of being at the origin. We connect the results to L\'evy Flights, which follow from a mean field variant of our model.Comment: 11 pages, 4 figures, to appear in Phys.Rev.

Stable Equilibrium Based on L\'evy Statistics: Stochastic Collision Models Approach

We investigate equilibrium properties of two very different stochastic collision models: (i) the Rayleigh particle and (ii) the driven Maxwell gas. For both models the equilibrium velocity distribution is a L\'evy distribution, the Maxwell distribution being a special case. We show how these models are related to fractional kinetic equations. Our work demonstrates that a stable power-law equilibrium, which is independent of details of the underlying models, is a natural generalization of Maxwell's velocity distribution.Comment: PRE Rapid Communication (in press

Transport signatures of quasiparticle poisoning in a Majorana island

We investigate effects of quasiparticle poisoning in a Majorana island with strong tunnel coupling to normal-metal leads. In addition to the main Coulomb blockade diamonds, "shadow" diamonds appear, shifted by 1e in gate voltage, consistent with transport through an excited (poisoned) state of the island. Comparison to a simple model yields an estimate of parity lifetime for the strongly coupled island (~ 1 {\mu}s) and sets a bound for a weakly coupled island (> 10 {\mu}s). Fluctuations in the gate-voltage spacing of Coulomb peaks at high field, reflecting Majorana hybridization, are enhanced by the reduced lever arm at strong coupling. In energy units, fluctuations are consistent with previous measurements.Comment: includes supplementary materia

Synchronization Landscapes in Small-World-Connected Computer Networks

Motivated by a synchronization problem in distributed computing we studied a simple growth model on regular and small-world networks, embedded in one and two-dimensions. We find that the synchronization landscape (corresponding to the progress of the individual processors) exhibits Kardar-Parisi-Zhang-like kinetic roughening on regular networks with short-range communication links. Although the processors, on average, progress at a nonzero rate, their spread (the width of the synchronization landscape) diverges with the number of nodes (desynchronized state) hindering efficient data management. When random communication links are added on top of the one and two-dimensional regular networks (resulting in a small-world network), large fluctuations in the synchronization landscape are suppressed and the width approaches a finite value in the large system-size limit (synchronized state). In the resulting synchronization scheme, the processors make close-to-uniform progress with a nonzero rate without global intervention. We obtain our results by ``simulating the simulations", based on the exact algorithmic rules, supported by coarse-grained arguments.Comment: 20 pages, 22 figure

Childhood motor performance is increased by participation in organized sport: the CHAMPS Study-DK

Evidence suggests that motor performance in children is declining globally. We tested whether participation in organized sport is associated with motor performance, and estimate the effect of 30 months participation in organized sport on motor performance. Study participants were 1067 primary school students, enrolled in the Danish Childhood Health, Activity, and Motor Performance School study. Participation in organized sport was reported via text messaging. Coordination-related motor performance composite, fitness-related motor performance composite, and total motor performance composite were calculated. Data were analyzed using Generalized Estimating Equations. Participation in organized sport was positively associated with motor performance (all composites) in models that did and did not control for baseline motor performance. For models that did not control for baseline motor performance, this equated to 2–6% increases in motor performance per weekly sport session; for models that did control for baseline motor performance, this equated to 1–5% increases in motor performance per weekly sport session. Positive associations between participation in organized sport and motor performance identify participation in organized sport as a way to improve motor performance in children. These results might provide the basis to determine whether participation in organized sport could be beneficial for children with developmental movement disorders

Fractional Kinetics for Relaxation and Superdiffusion in Magnetic Field

We propose fractional Fokker-Planck equation for the kinetic description of relaxation and superdiffusion processes in constant magnetic and random electric fields. We assume that the random electric field acting on a test charged particle is isotropic and possesses non-Gaussian Levy stable statistics. These assumptions provide us with a straightforward possibility to consider formation of anomalous stationary states and superdiffusion processes, both properties are inherent to strongly non-equilibrium plasmas of solar systems and thermonuclear devices. We solve fractional kinetic equations, study the properties of the solution, and compare analytical results with those of numerical simulation based on the solution of the Langevin equations with the noise source having Levy stable probability density. We found, in particular, that the stationary states are essentially non-Maxwellian ones and, at the diffusion stage of relaxation, the characteristic displacement of a particle grows superdiffusively with time and is inversely proportional to the magnetic field.Comment: 15 pages, LaTeX, 5 figures PostScrip

Characterizing the structure of small-world networks

We give exact relations which are valid for small-world networks (SWN's) with a general `degree distribution', i.e the distribution of nearest-neighbor connections. For the original SWN model, we illustrate how these exact relations can be used to obtain approximations for the corresponding basic probability distribution. In the limit of large system sizes and small disorder, we use numerical studies to obtain a functional fit for this distribution. Finally, we obtain the scaling properties for the mean-square displacement of a random walker, which are determined by the scaling behavior of the underlying SWN

The effect of color type on early wound healing in farmed mink (Neovison vison)

Abstract Background Individual differences of mink, including color type, are speculated to affect the course of wound healing, thereby impacting wound assessment and management on the farms, as well as the assessment of wounds in forensic cases. In this study, we examined the effect of color type on early wound healing in farmed mink. Full thickness excisional wounds (2 × 2 cm) were made on the back in 18 mink of the color types Brown, Silverblue and Blue Iris. Gross and microscopic pathology of the wounds was evaluated 2 days post-wounding together with degree of wound size reduction, presence of bacteria and blood analyses. Results Pathological examination on day 2 showed the greatest mean wound size reduction in Brown mink (11.0%) followed by Blue Iris (7.9%) and Silverblue (1.6%). Bacteria were cultured from all wounds, and predominantly Staphylococcus species were recovered in mixed or pure culture. Histopathology from day 2 wounds showed a scab overlying necrotic wound edges, which were separated from underlying vital tissue by a demarcation zone rich in polymorphonuclear leukocytes. Fibroblasts and plump endothelial cells were more numerous in the deeper tissues. Complete blood count parameters were within normal ranges in most cases, however, the mink showed mildly to markedly decreased hematocrit and six mink of the color types Silverblue and Blue Iris showed moderately elevated numbers of circulating segmented neutrophils on day 2. There was a marked increase in concentration of serum amyloid A from day 0 to day 2 in all color types. Conclusions We have described differences in early wound healing between mink of the color types Brown, Silverblue and Blue Iris by use of an experimental wound model in farmed mink. The most pronounced difference pertained to the degree of wound size reduction which was greatest in Brown mink, followed by Blue Iris and Silverblue, respectively

Fractional transport equations for Levy stable processes

The influence functional method of Feynman and Vernon is used to obtain a quantum master equation for a Brownian system subjected to a Levy stable random force. The corresponding classical transport equations for the Wigner function are then derived, both in the limit of weak and strong friction. These are fractional extensions of the Klein-Kramers and the Smoluchowski equations. It is shown that the fractional character acquired by the position in the Smoluchowski equation follows from the fractional character of the momentum in the Klein-Kramers equation. Connections among fractional transport equations recently proposed are clarified.Comment: 4 page