Current fluctuations in stochastic systems with long-range memory

We propose a method to calculate the large deviations of current fluctuations in a class of stochastic particle systems with history-dependent rates. Long-range temporal correlations are seen to alter the speed of the large deviation function in analogy with long-range spatial correlations in equilibrium systems. We give some illuminating examples and discuss the applicability of the Gallavotti-Cohen fluctuation theorem.Comment: 10 pages, 1 figure. v2: Minor alterations. v3: Very minor alterations for consistency with published version appearing at http://stacks.iop.org/1751-8121/42/34200

Spatial and spatio-temporal patterns in a cell-haptotaxis model

We investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyse the steady state problem for specific boundary conditions and show the existence of spatially hetero-geneous steady states. A linear analysis shows that stability is lost through a Hopf bifurcation. We carry out a nonlinear multi-time scale perturbation procedure to study the evolution of the resulting spatio-temporal patterns. We also analyse the model in a parameter domain wherein it exhibits a singular dispersion relation

A COMPARISON OF RESISTED AND ASSISTED SPRINT TRAINING IN COLLEGIATE SPRINTERS

Sprint time (ST) is the product of stride length (SL) and stride rate (SR). Increases in either of these variables results in speed improvement. Purpose:  To compare resisted (RST) and assisted sprint training (AST) on sprint performance. Methods:  Twenty (10 male, 10 female) collegiate sprinters and hurdlers were randomly divided into two training groups: RST (age: 21.8±1.8yrs, height: 1.73±0.10m, mass: 69.5±12.8kg) and AST (age: 22.2±2.4yrs, height: 1.76±0.10m, mass: 69.1±9.9kg). Each group trained 3 days/week for 6 weeks. The RST group used a combination of weighted sled pulls, uphill sprinting and depth jumps. The AST group combined downhill running, towing, sprint ladders and single leg bounds. Prior to and following the training interventions SL and ST (10 meter sprint time) were recorded at sprint distances of 30m, 60m, and 120m during the last 10 meters of each sprint distance. Pre-post training ST and SL were compared within training groups at each sprint distance using paired t-tests. Additionally, a gain score was calculated by taking the difference between the post and pre test scores. The gain scores for SL and ST were compared between training groups via independent t-tests at each sprint distance. Results: For the RST 30m, ST (1.18±0.08s vs 1.14±0.08s, p<0.01) and SL (2.06±0.08m vs. 2.09±1.14m, p<0.01) were significantly improved. For the AST, 30m ST (1.19±0.08s vs. 1.18±0.08s, p<0.01) and SL (2.10±0.13m vs. 2.11±0.13, p=0.04) were significantly improved. No improvements in ST or SL were detected for either the RST or AST groups at the 60m sprint distance. For the RST 120m, ST (1.13±0.07s vs. 1.12±0.08s, p<0.01) was significantly improved. For the AST 120m, ST (1.12±0.07s vs. 1.11±0.07s, p<0.01) and SL (2.30±0.08 vs. 2.33±0.08, p<0.01) were significantly improved. At the 30M interval, the RST demonstrated significant improvements in SL and ST as compared to the AST (p<0.01). However, at the 120M interval, the AST demonstrated a significant improvement in SL as compared to the RST (p<0.01). Conclusion: Within the parameters of this study, RST and AST methods have proven effective at improving sprint performance. It appears that RST protocols may be of greatest benefit for improving sprint performance at shorter distances, while AST protocols may be of greater benefit at longer sprinting distances.  Article visualizations

A modified Oster-Murray-Harris mechanical model of morphogenesis

There are two main modeling paradigms for biological pattern formation in developmental biology: chemical prepattern models and cell aggregation models. This paper focuses on an example of a cell aggregation model, the mechanical model developed by Oster, Murray, and Harris [Development, 78 (1983), pp. 83--125]. We revisit the Oster--Murray--Harris model and find that, due to the infinitesimal displacement assumption made in the original version of this model, there is a restriction on the types of boundary conditions that can be prescribed. We derive a modified form of the model which relaxes the infinitesimal displacement assumption. We analyze the dynamics of this model using linear and multiscale nonlinear analysis and show that it has the same linear behavior as the original Oster--Murray--Harris model. Nonlinear analysis, however, predicts that the modified model will allow for a wider range of parameters where the solution evolves to a bounded steady state. The results from both analyses are verified through numerical simulations of the full nonlinear model in one and two dimensions. The increased range of boundary conditions that are well-posed, as well as a wider range of parameters that yield bounded steady states, renders the modified model more applicable to, and more robust for, comparisons with experiments

Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis

We present an in-depth study of spatio-temporal patterns in a simplified version of a mechanical model for pattern formation in mesenchymal morphogenesis. We briefly motivate the derivation of the model and show how to choose realistic boundary conditions to make the system well-posed. We firstly consider one-dimensional patterns and carry out a nonlinear perturbation analysis for the case where the uniform steady state is linearly unstable to a single mode. In two-dimensions, we show that if the displacement field in the model is represented as a sum of orthogonal parts, then the model can be decomposed into two sub-models, only one of which is capable of generating pattern. We thus focus on this particular sub-model. We present a nonlinear analysis of spatio-temporal patterns exhibited by the sub-model on a square domain and discuss mode interaction. Our analysis shows that when a two-dimensional mode number admits two or more degenerate mode pairs, the solution of the full nonlinear system of partial differential equations is a mixed mode solution in which all the degenerate mode pairs are represented in a frequency locked oscillation

Size of Outbreaks Near the Epidemic Threshold

The spread of infectious diseases near the epidemic threshold is investigated. Scaling laws for the size and the duration of outbreaks originating from a single infected individual in a large susceptible population are obtained. The maximal size of an outbreak n_* scales as N^{2/3} with N the population size. This scaling law implies that the average outbreak size scales as N^{1/3}. Moreover, the maximal and the average duration of an outbreak grow as t_* ~ N^{1/3} and ~ ln N, respectively.Comment: 4 pages, 5 figure

Structure of the X-ray Emission from the Jet of 3C 273

We present images from five observations of the quasar 3C 273 with the Chandra X-ray Observatory. The jet has at least four distinct features which are not resolved in previous observations. The first knot in the jet (A1) is very bright in X-rays. Its X-ray spectrum is well fitted with a power law with alpha = 0.60 +/- 0.05. Combining this measurement with lower frequency data shows that a pure synchrotron model can fit the spectrum of this knot from 1.647 GHz to 5 keV (over nine decades in energy) with alpha = 0.76 +/- 0.02, similar to the X-ray spectral slope. Thus, we place a lower limit on the total power radiated by this knot of 1.5e43 erg/s; substantially more power may be emitted in the hard X-ray and gamma-ray bands. Knot A2 is also detected and is somewhat blended with knot B1. Synchrotron emission may also explain the X-ray emission but a spectral bend is required near the optical band. For knots A1 and B1, the X-ray flux dominates the emitted energy. For the remaining optical knots (C through H), localized X-ray enhancements that might correspond to the optical features are not clearly resolved. The position angle of the jet ridge line follows the optical shape with distinct, aperiodic excursions of +/-1 deg from a median value of -138.0deg. Finally, we find X-ray emission from the ``inner jet'' between 5 and 10" from the core.Comment: 10 pages, 5 figures; accepted for publication in the Astrophysical Journal Letters. For the color image, see fig1.ps or http://space.mit.edu/~hermanm/papers/3c273/fig1.jp

Assessment of soil water, carbon and nitrogen cycling in reseeded grassland on the North Wyke Farm Platform using a process-based model

The North Wyke Farm Platform (NWFP) generates large volumes of temporally-indexed data that provides a valuable test-bed for agricultural mathematical models in temperate grasslands. In our study, we used the primary datasets generated from the NWFP (https://nwfp.rothamsted.ac.uk/) to validate the SPACSYS model in terms of the dynamics of water loss and forage dry matter yield estimated through cutting. The SPACSYS model is capable of simulating soil water, carbon (C) and nitrogen (N) balance in the soil-plant-atmosphere system. The validated model was then used to simulate the responses of soil water, C and N to reseeding grass cultivars with either high sugar (Lolium perenne L cv. AberMagic) or deep rooting (Festulotium cv. Prior) traits. Simulation results demonstrated that the SPACSYS model could predict reliably soil water, C and N cycling in reseeded grassland. Compared to AberMagic, the Nor grass could fix more C in the second year following reseeding, whereas less C was lost through soil respiration in the first transition year. In comparison to the grass cifitivar of the permanent pasture that existed before reseeding, both grasses reduced N losses through runoff and conhibuted to reducing water loss, especially Prior in relation to the latter. The SPACSYS model could predict these differences as supported by the rich dataset from the NWFP, providing a tool for future predictions on less characterized pasture. (C) 2017 The Authors. Published by Elsevier B.V. This is an open access articleRN the CC BY licens

Globular Clusters and X-ray Point Sources in Centaurus A (NGC 5128)

We detect 353 X-ray point sources, mostly low-mass X-ray binaries (LMXBs), in four Chandra observations of Centaurus A (NGC 5128), the nearest giant early-type galaxy, and correlate this point source population with the largest available ensemble of confirmed and likely globular clusters associated with this galaxy. Of the X-ray sources, 31 are coincident with 30 globular clusters that are confirmed members of the galaxy by radial velocity measurement (2 X-ray sources match one globular cluster within our search radius), while 1 X-ray source coincides with a globular cluster resolved by HST images. Another 36 X-ray point sources match probable, but spectroscopically unconfirmed, globular cluster candidates. The color distribution of globular clusters and cluster candidates in Cen A is bimodal, and the probability that a red, metal rich GC candidate contains an LMXB is at least 1.7 times that of a blue, metal poor one. If we consider only spectroscopically confirmed GCs, this ratio increases to ~3. We find that LMXBs appear preferentially in more luminous (massive) GCs. These two effects are independent, and the latter is likely a consequence of enhanced dynamical encounter rates in more massive clusters which have on average denser cores. The X-ray luminosity functions of the LMXBs found in GCs and of those that are unmatched with GCs reveal similar underlying populations, though there is some indication that fewer X-ray faint LMXBs are found in globular clusters than X-ray bright ones. Our results agree with previous observations of the connection of GCs and LMXBs in early-type galaxies and extend previous work on Centaurus A.Comment: 34 pages, 10 figures, 2 tables, Accepted for Publication in The Astrophysical Journa

Propagation and Extinction in Branching Annihilating Random Walks

We investigate the temporal evolution and spatial propagation of branching annihilating random walks in one dimension. Depending on the branching and annihilation rates, a few-particle initial state can evolve to a propagating finite density wave, or extinction may occur, in which the number of particles vanishes in the long-time limit. The number parity conserving case where 2-offspring are produced in each branching event can be solved exactly for unit reaction probability, from which qualitative features of the transition between propagation and extinction, as well as intriguing parity-specific effects are elucidated. An approximate analysis is developed to treat this transition for general BAW processes. A scaling description suggests that the critical exponents which describe the vanishing of the particle density at the transition are unrelated to those of conventional models, such as Reggeon Field Theory. P. A. C. S. Numbers: 02.50.+s, 05.40.+j, 82.20.-wComment: 12 pages, plain Te