The sodium-potassium pump controls the intrinsic firing of the cerebellar Purkinje neuron

In vitro, cerebellar Purkinje cells can intrinsically fire action potentials in a repeating trimodal or bimodal pattern. The trimodal pattern consists of tonic spiking, bursting, and quiescence. The bimodal pattern consists of tonic spiking and quiescence. It is unclear how these firing patterns are generated and what determines which firing pattern is selected. We have constructed a realistic biophysical Purkinje cell model that can replicate these patterns. In this model, Na+/K+ pump activity sets the Purkinje cell's operating mode. From rat cerebellar slices we present Purkinje whole cell recordings in the presence of ouabain, which irreversibly blocks the Na+/K+ pump. The model can replicate these recordings. We propose that Na+/K+ pump activity controls the intrinsic firing mode of cerbellar Purkinje cells

Finite-Size-Scaling at the Jamming Transition: Corrections to Scaling and the Correlation Length Critical Exponent

We carry out a finite size scaling analysis of the jamming transition in frictionless bi-disperse soft core disks in two dimensions. We consider two different jamming protocols: (i) quench from random initial positions, and (ii) quasistatic shearing. By considering the fraction of jammed states as a function of packing fraction for systems with different numbers of particles, we determine the spatial correlation length critical exponent $\nu\approx 1$, and show that corrections to scaling are crucial for analyzing the data. We show that earlier numerical results yielding $\nu<1$ are due to the improper neglect of these corrections.Comment: 5 pages, 4 figures -- slightly revised version as accepted for Phys. Rev. E Rapid Communication

Nonlinear Scattering of a Bose-Einstein Condensate on a Rectangular Barrier

We consider the nonlinear scattering and transmission of an atom laser, or Bose-Einstein condensate (BEC) on a finite rectangular potential barrier. The nonlinearity inherent in this problem leads to several new physical features beyond the well-known picture from single-particle quantum mechanics. We find numerical evidence for a denumerably infinite string of bifurcations in the transmission resonances as a function of nonlinearity and chemical potential, when the potential barrier is wide compared to the wavelength of oscillations in the condensate. Near the bifurcations, we observe extended regions of near-perfect resonance, in which the barrier is effectively invisible to the BEC. Unlike in the linear case, it is mainly the barrier width, not the height, that controls the transmission behavior. We show that the potential barrier can be used to create and localize a dark soliton or dark soliton train from a phonon-like standing wave.Comment: 15 pages, 15 figures, new version includes clarification of definition of transmission coefficient in general nonlinear vs. linear cas

Numerical propagation of high energy cosmic rays in the Galaxy I: technical issues

We present the results of a numerical simulation of propagation of cosmic rays with energy above $10^{15}$ eV in a complex magnetic field, made in general of a large scale component and a turbulent component. Several configurations are investigated that may represent specific aspects of a realistic magnetic field of the Galaxy, though the main purpose of this investigation is not to achieve a realistic description of the propagation in the Galaxy, but rather to assess the role of several effects that define the complex problem of propagation. Our simulations of Cosmic Rays in the Galaxy will be presented in Paper II. We identified several effects that are difficult to interpret in a purely diffusive approach and that play a crucial role in the propagation of cosmic rays in the complex magnetic field of the Galaxy. We discuss at length the problem of the extrapolation of our results to much lower energies where data are available on the confinement time of cosmic rays in the Galaxy. The confinement time and its dependence on particles' rigidity are crucial ingredients for 1) relating the source spectrum to the observed cosmic ray spectrum; 2) quantifying the production of light elements by spallation; 3) predicting the anisotropy as a function of energy.Comment: 29 pages, 12 figures, submitted to JCA

Generalized Simulated Annealing

We propose a new stochastic algorithm (generalized simulated annealing) for computationally finding the global minimum of a given (not necessarily convex) energy/cost function defined in a continuous D-dimensional space. This algorithm recovers, as particular cases, the so called classical ("Boltzmann machine") and fast ("Cauchy machine") simulated annealings, and can be quicker than both. Key-words: simulated annealing; nonconvex optimization; gradient descent; generalized statistical mechanics.Comment: 13 pages, latex, 4 figures available upon request with the authors

Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation

We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Levy alpha-stable distribution of jumps in space and a Mittag-Leffler distribution of waiting times, and apply it to the stochastic solution of the Cauchy problem for a partial differential equation with fractional derivatives both in space and in time. The one-parameter Mittag-Leffler function is the natural survival probability leading to time-fractional diffusion equations. Transformation methods for Mittag-Leffler random variables were found later than the well-known transformation method by Chambers, Mallows, and Stuck for Levy alpha-stable random variables and so far have not received as much attention; nor have they been used together with the latter in spite of their mathematical relationship due to the geometric stability of the Mittag-Leffler distribution. Combining the two methods, we obtain an accurate approximation of space- and time-fractional diffusion processes almost as easy and fast to compute as for standard diffusion processes.Comment: 7 pages, 5 figures, 1 table. Presented at the Conference on Computing in Economics and Finance in Montreal, 14-16 June 2007; at the conference "Modelling anomalous diffusion and relaxation" in Jerusalem, 23-28 March 2008; et

Identifying a Two-State Hamiltonian in the Presence of Decoherence

Mapping the system evolution of a two-state system allows the determination of the effective system Hamiltonian directly. We show how this can be achieved even if the system is decohering appreciably over the observation time. A method to include various decoherence models is given and the limits of this technique are explored. This technique is applicable both to the problem of calibrating a control Hamiltonian for quantum computing applications and for precision experiments in two-state quantum systems. For simple models of decoherence, this method can be applied even when the decoherence time is comparable to the oscillation period of the system.Comment: 8 pages, 6 figures. Minor corrections, published versio

Spin Dynamics of the LAGEOS Satellite in Support of a Measurement of the Earth's Gravitomagnetism

LAGEOS is an accurately-tracked, dense spherical satellite covered with 426 retroreflectors. The tracking accuracy is such as to yield a medium term (years to decades) inertial reference frame determined via relatively inexpensive observations. This frame is used as an adjunct to the more difficult and data intensive VLBI absolute frame measurements. There is a substantial secular precession of the satellite's line of nodes consistent with the classical, Newtonian precession due to the non-sphericity of the earth. Ciufolini has suggested the launch of an identical satellite (LAGEOS-3) into an orbit supplementary to that of LAGEOS-1: LAGEOS-3 would then experience an equal and opposite classical precession to that of LAGEOS-1. Besides providing a more accurate real-time measurement of the earth's length of day and polar wobble, this paired-satellite experiment would provide the first direct measurement of the general relativistic frame-dragging effect. Of the five dominant error sources in this experiment, the largest one involves surface forces on the satellite, and their consequent impact on the orbital nodal precession. The surface forces are a function of the spin dynamics of the satellite. Consequently, we undertake here a theoretical effort to model the spin ndynamics of LAGEOS. In this paper we present our preliminary results.Comment: 16 pages, RevTeX, LA-UR-94-1289. (Part I of II, postscript figures in Part II

Gravitational waves from inspiraling compact binaries: Validity of the stationary-phase approximation to the Fourier transform

We prove that the oft-used stationary-phase method gives a very accurate expression for the Fourier transform of the gravitational-wave signal produced by an inspiraling compact binary. We give three arguments. First, we analytically calculate the next-order correction to the stationary-phase approximation, and show that it is small. This calculation is essentially an application of the steepest-descent method to evaluate integrals. Second, we numerically compare the stationary-phase expression to the results obtained by Fast Fourier Transform. We show that the differences can be fully attributed to the windowing of the time series, and that they have nothing to do with an intrinsic failure of the stationary-phase method. And third, we show that these differences are negligible for the practical application of matched filtering.Comment: 8 pages, ReVTeX, 4 figure

Muon-spin spectroscopy of the organometallic spin-1/2 kagome-lattice compound Cu(1,3-benzenedicarboxylate)

Using muon-spin resonance, we examine the organometallic hybrid compound Cu(1,3-benzenedicarboxylate) [Cu(1,3-bdc)], which has structurally perfect spin-1/2 copper kagome planes separated by pure organic linkers. This compound has antiferromagnetic interactions with Curie-Weiss temperature of −33 K. We found slowing down of spin fluctuations starting at T=1.8 K and that the state at T→0 is quasistatic with no long-range order and extremely slow spin fluctuations at a rate of 3.6 μs[superscript −1]. This indicates that Cu(1,3-bdc) behaves as expected from a kagome magnet and could serve as a model kagome compound.European Commission (under the Sixth Framework Program through the Key Action: Strengthening the European Research Area, Research Infrastructures, Contract No. RII3-CT-2004-506008)European Science FoundationIsrael U.S.A. Binational Science Foundatio