Adaptive Testing for Cointegration with Nonstationary Volatility

This paper generalises Boswijk and Zu (2018)'s adaptive unit root test for time series with nonstationary volatility to a multivariate context. Persistent changes in the innovation variance matrix of a vector autoregressive model lead to size distortions in conventional cointegration tests, which may be resolved using the wild bootstrap, as shown by Cavaliere et al. (2010, 2014). We show that it also leads to the possibility of constructing tests with higher power, by taking the time-varying volatilities and correlations into account in the formulation of the likelihood function and the resulting likelihood ratio test statistic. We find that under suitable conditions, adaptation with respect to the volatility process is possible, in the sense that nonparametric volatility matrix estimation does not lead to a loss of asymptotic local power relative to the case where the volatilities are observed. The asymptotic null distribution of the test is nonstandard and depends on the volatility process; we show that various bootstrap implementations may be used to conduct asymptotically valid inference. Monte Carlo simulations show that the resulting test has good size properties, and higher power than existing tests. Two empirical examples illustrate the applicability of the tests

High performance Beowulf computer for lattice QCD

We describe the construction of a high performance parallel computer composed of PC components, as well as the performance test in lattice QCD.Comment: Lattice 2001 (Algorithms and Machines) 3 page

Non-Markovian dynamics in a spin star system: The failure of thermalization

In most cases, a small system weakly interacting with a thermal bath will finally reach the thermal state with the temperature of the bath. We show that this intuitive picture is not always true by a spin star model where non-Markov effect predominates in the whole dynamical process. The spin star system consists a central spin homogeneously interacting with an ensemble of identical noninteracting spins. We find that the correlation time of the bath is infinite, which implies that the bath has a perfect memory, and that the dynamical evolution of the central spin must be non- Markovian. A direct consequence is that the final state of the central spin is not the thermal state equilibrium with the bath, but a steady state which depends on its initial state.Comment: 8 page

Liouvillian Approach to the Integer Quantum Hall Effect Transition

We present a novel approach to the localization-delocalization transition in the integer quantum Hall effect. The Hamiltonian projected onto the lowest Landau level can be written in terms of the projected density operators alone. This and the closed set of commutation relations between the projected densities leads to simple equations for the time evolution of the density operators. These equations can be used to map the problem of calculating the disorder averaged and energetically unconstrained density-density correlation function to the problem of calculating the one-particle density of states of a dynamical system with a novel action. At the self-consistent mean-field level, this approach yields normal diffusion and a finite longitudinal conductivity. While we have not been able to go beyond the saddle point approximation analytically, we show numerically that the critical localization exponent can be extracted from the energetically integrated correlation function yielding $\nu=2.33 \pm 0.05$ in excellent agreement with previous finite-size scaling studies.Comment: 9 pages, submitted to PR

First-passage and extreme-value statistics of a particle subject to a constant force plus a random force

We consider a particle which moves on the x axis and is subject to a constant force, such as gravity, plus a random force in the form of Gaussian white noise. We analyze the statistics of first arrival at point $x_1$ of a particle which starts at $x_0$ with velocity $v_0$. The probability that the particle has not yet arrived at $x_1$ after a time $t$, the mean time of first arrival, and the velocity distribution at first arrival are all considered. We also study the statistics of the first return of the particle to its starting point. Finally, we point out that the extreme-value statistics of the particle and the first-passage statistics are closely related, and we derive the distribution of the maximum displacement $m={\rm max}_t[x(t)]$.Comment: Contains an analysis of the extreme-value statistics not included in first versio

Demographic noise slows down cycles of dominance

We study the phenomenon of cyclic dominance in the paradigmatic Rock--Paper--Scissors model, as occurring in both stochastic individual-based models of finite populations and in the deterministic replicator equations. The mean-field replicator equations are valid in the limit of large populations and, in the presence of mutation and unbalanced payoffs, they exhibit an attracting limit cycle. The period of this cycle depends on the rate of mutation; specifically, the period grows logarithmically as the mutation rate tends to zero. We find that this behaviour is not reproduced in stochastic simulations with a fixed finite population size. Instead, demographic noise present in the individual-based model dramatically slows down the progress of the limit cycle, with the typical period growing as the reciprocal of the mutation rate. Here we develop a theory that explains these scaling regimes and delineates them in terms of population size and mutation rate. We identify a further intermediate regime in which we construct a stochastic differential equation model describing the transition between stochastically-dominated and mean-field behaviour.Comment: 25 pages, 11 figure

Common and specific downstream signaling targets controlled by Tlr2 and Tlr5 innate immune signaling in zebrafish

Animal science

CP violation in chargino decays in the MSSM

In the minimal supersymmetric standard model (MSSM) with complex parameters, supersymmetric loop effects can lead to \emph{CP} violation. We calculate the rate asymmetries of decays of charginos into the lightest neutralino and a $W$ boson on the basis of the most important loop contributions in the third generation squark sectors. It turns out that the \emph{CP} violating asymmetries can be a few per cent in typical regions of the parameter space of the MSSM. These processes would provide very promising channels for probing \emph{CP} violation in the MSSM at future high-energy colliders.Comment: 15 pages, 5 figures, LaTeX2