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One of the most notable features in repulsive particle based active matter systems is motility-induced-phase separation (MIPS) where a dense, often crystalline phase coexists with a low density fluid. In most active matter studies, the activity is kept constant as a function of time; however, there are many examples of active systems in which individual particles transition from living or moving to dead or nonmotile due to lack of fuel, infection, or poisoning. Here we consider an active matter particle system at densities where MIPS does not occur. When we add a small number of infected particles that can effectively poison other particles, rendering them nonmotile, we find a rich variety of time dependent pattern formation, including MIPS, a wetting phase, and a fragmented state formed when mobile particles plow through an nonmotile packing. We map out the patterns as a function of time scaled by the duration of the epidemic, and show that the pattern formation is robust for a wide range of poisoning rates and activity levels. We also show that pattern formation does not occur in a random death model, but requires the promotion of nucleation by contact poisoning. Our results should be relevant to biological and active matter systems where there is some form of poisoning, death, or transition to nonmotility., Comment: 7 pages, 6 figures

The Susceptible-Infected (SI) and Susceptible-Infected-Recovered (SIR) models provide two distinct representations of epidemic evolution, distinguished by the lack of spontaneous recovery in the SI model. Here we introduce a new active matter epidemic model, the ``Susceptible-Cleric-Zombie-Recovered'' (SCZR) model, in which spontaneous recovery is absent but zombies can recover with probability $\gamma$ via interaction with a cleric. Upon interacting with a zombie, both susceptibles and clerics can enter the zombie state with probability $\beta$ and $\alpha$, respectively. By changing the intial fraction of clerics or their healing ability rate $\gamma$, we can tune the SCZR model between SI dynamics, in which no susceptibles or clerics remain at long times, and SIR dynamics, in which no zombies remain at long times. The model is relevant to certain real world diseases such as HIV where spontaneous recovery is impossible but where medical interventions by a limited number of caregivers can reduce or eliminate the spread of infection., Comment: 10 pages, 7 figures

The widely used susceptible-infected-recovered (S-I-R) epidemic model assumes a uniform, well-mixed population, and incorporation of spatial heterogeneities remains a major challenge. Understanding failures of the mixing assumption is important for designing effective disease mitigation approaches. We combine a run-and-tumble self-propelled active matter system with an S-I-R model to capture the effects of spatial disorder. Working in the motility-induced phase separation regime both with and without quenched disorder, we find two epidemic regimes. For low transmissibility, quenched disorder lowers the frequency of epidemics and increases their average duration. For high transmissibility, the epidemic spreads as a front and the epidemic curves are less sensitive to quenched disorder; however, within this regime it is possible for quenched disorder to enhance the contagion by creating regions of higher particle densities. We discuss how this system could be realized using artificial swimmers with mobile optical traps operated on a feedback loop., Comment: 9 pages, 8 figures

We analyze the noise in macro-particle methods used in plasma physics and fluid dynamics, leading to approaches for minimizing the total error, focusing on electrostatic models in one dimension. We describe kernel density estimation for continuous values of the spatial variable, $x$, and compute the covariance matrix for uniform true density. The band width of the covariance matrix is related to the width of the kernel. We find the presence of constant negative terms in the elements of the covariance matrix both on and off-diagonal. These negative correlations are related to the fact that the total number of particles is fixed at each time step. The effect of these negative correlations on the electric field, computed by Gauss's law, is that the noise in the electric field is related to a process called the Ornstein-Uhlenbeck bridge. For non-constant density still with continuous $x$, we analyze the total error in the density estimation and discuss it in terms of bias-variance optimization (BVO). For some characteristic length $l$ and kernel width $h$, having too few particles within $h$ leads to too much variance; for $h$ large relative to $l$, there is too much smoothing of the density. The optimum between these two limits is found by BVO. We repeat the analysis for $x$ discretized on a grid, connecting particle shapes and estimation kernels. If the particle shape satisfies a sum rule, the charge deposited on the grid is conserved exactly. Particle shapes expressed as the convolution of a kernel with another kernel that satisfies the sum rule also obey the sum rule. This property holds for kernels of arbitrary width, including widths that are not integer multiples of the grid spacing. We show good agreement with numerical computations.

This article presents a Bayesian inferential method where the likelihood for a model is unknown but where data can easily be simulated from the model. We discretize simulated (continuous) data to estimate the implicit likelihood in a Bayesian analysis employing a Markov chain Monte Carlo algorithm. Three examples are presented as well as a small study on some of the method's properties.

We study the effects of randomness on competitions based on an elementary random process in which there is a finite probability that a weaker team upsets a stronger team. We apply this model to sports leagues and sports tournaments, and compare the theoretical results with empirical data. Our model shows that single-elimination tournaments are efficient but unfair: the number of games is proportional to the number of teams N, but the probability that the weakest team wins decays only algebraically with N. In contrast, leagues, where every team plays every other team, are fair but inefficient: the top $\sqrt{N}$ of teams remain in contention for the championship, while the probability that the weakest team becomes champion is exponentially small. We also propose a gradual elimination schedule that consists of a preliminary round and a championship round. Initially, teams play a small number of preliminary games, and subsequently, a few teams qualify for the championship round. This algorithm is fair and efficient: the best team wins with a high probability and the number of games scales as $N^{9/5}$, whereas traditional leagues require N^3 games to fairly determine a champion., Comment: 10 pages, 8 figures, reviews arXiv:physics/0512144, arXiv:physics/0608007, arXiv:cond-mat/0607694, arXiv:physics/0612217

Using polarized neutron reflectometry (PNR) we measured the neutron spin dependent reflectivity from four LaAlO3/SrTiO3 superlattices. This experiment implies that the upper limit for the magnetization induced by an 11 T magnetic field at 1.7 K is 2 emu/cm3. SQUID magnetometry of the superlattices sporadically finds an enhanced moment, possibly due to experimental artifacts. These observations set important restrictions on theories which imply a strongly enhanced magnetism at the interface between LaAlO3 and SrTiO3.

In multivariate nonparametric analysis, sparseness of the covariates also called curse of dimensionality, forces one to use large smoothing parameters. This leads to a biased smoother. Instead of focusing on optimally selecting the smoothing parameter, we fix it to some reasonably large value to ensure an over-smoothing of the data. The resulting base smoother has a small variance but a substantial bias. In this paper, we propose an R package named ibr to iteratively correct the initial bias of the (base) estimator by an estimate of the bias obtained by smoothing the residuals. After a brief description of Iterated Bias Reduction smoothers, we examine the base smoothers implemented in the packages: Nadaraya-Watson kernel smoothers and thin plate splines smoothers. Then, we explain the stopping rules available in the package and their implementation. Finally we illustrate the package on two examples: a toy example in RxR and the original Los Angeles ozone dataset., Comment: 20 pages, 7 figures

This paper presents a practical and simple fully nonparametric multivariate smoothing procedure that adapts to the underlying smoothness of the true regression function. Our estimator is easily computed by successive application of existing base smoothers (without the need of selecting an optimal smoothing parameter), such as thin-plate spline or kernel smoothers. The resulting smoother has better out of sample predictive capabilities than the underlying base smoother, or competing structurally constrained models (GAM) for small dimension (3 < d < 8) and moderate sample size (n < 800). Moreover our estimator is still useful when (d> 10) and to our knowledge, no other adaptive fully nonparametric regression estimator is available without constrained assumption such as additivity for example. On a real example, the Boston Housing Data, our method reduces the out of sample prediction error by 20 %. An R package ibr, available at CRAN, implements the proposed multivariate nonparametric method in R., Comment: 26 pages, 6 figures

This paper discusses linear regression of strongly correlated data that arises, for example, in magnetohydrodynamic equilibrium reconstructions. We have proved that, generically, the covariance matrix of the estimated regression parameters for fixed sample size goes to zero as the correlations become unity. That is, in this limit the estimated parameters are known with perfect accuracy. Simple examples are shown to illustrate this effect and the nature of the exceptional cases in which the estimate covariance does not go to zero.

League competition is investigated using random processes and scaling techniques. In our model, a weak team can upset a strong team with a fixed probability. Teams play an equal number of head-to-head matches and the team with the largest number of wins is declared to be the champion. The total number of games needed for the best team to win the championship with high certainty, T, grows as the cube of the number of teams, N, i.e., T ~ N^3. This number can be substantially reduced using preliminary rounds where teams play a small number of games and subsequently, only the top teams advance to the next round. When there are k rounds, the total number of games needed for the best team to emerge as champion, T_k, scales as follows, T_k ~N^(\gamma_k) with gamma_k=1/[1-(2/3)^(k+1)]. For example, gamma_k=9/5,27/19,81/65 for k=1,2,3. These results suggest an algorithm for how to infer the best team using a schedule that is linear in N. We conclude that league format is an ineffective method of determining the best team, and that sequential elimination from the bottom up is fair and efficient., Comment: 6 pages, 3 figures

We define gradient networks as directed graphs formed by local gradients of a scalar field distributed on the nodes of a substrate network G. We derive an exact expression for the in-degree distribution of the gradient network when the substrate is a binomial (Erdos-Renyi) random graph, G(N,p). Using this expression we show that the in-degree distribution R(l) of gradient graphs on G(N,p) obeys the power law R(l)~1/l for arbitrary, i.i.d. random scalar fields. We then relate gradient graphs to congestion tendency in network flows and show that while random graphs become maximally congested in the large network size limit, scale-free networks are not, forming fairly efficient substrates for transport. Combining this with other constraints, such as uniform edge cost, we obtain a plausible argument in form of a selection principle, for why a number of spontaneously evolved massive networks are scale-free. This paper also presents detailed derivations of the results recently reported in Nature, vol. 428, pp. 716 (2004)., Comment: 20 pages, 8 postscript figures included, submitted for publication