Neurophysical data analysis using a remote console computing system

Neurophysiological data analysis using time shared remote console computer syste

Lyapunov vs. Geometrical Stability Analysis of the Kepler and the Restricted Three Body Problem

In this letter we show that although the application of standard Lyapunov analysis predicts that completely integrable Kepler motion is unstable, the geometrical analysis of Horwitz et al [1] predicts the observed stability. This seems to us to provide evidence for both the incompleteness of the standard Lyapunov analysis and the strength of the geometrical analysis. Moreover, we apply this approach to the three body problem in which the third body is restricted to move on a circle of large radius which induces an adiabatic time dependent potential on the second body. This causes the second body to move in a very interesting and intricate but periodic trajectory; however, the standard Lyapunov analysis, as well as methods based on the parametric variation of curvature associated with the Jacobi metric, incorrectly predict chaotic behavior. The geometric approach predicts the correct stable motion in this case as well.Comment: 9 pages, 14 figure

Effects of Noise in a Cortical Neural Model

Recently Segev et al. (Phys. Rev. E 64,2001, Phys.Rev.Let. 88, 2002) made long-term observations of spontaneous activity of in-vitro cortical networks, which differ from predictions of current models in many features. In this paper we generalize the EI cortical model introduced in a previous paper (S.Scarpetta et al. Neural Comput. 14, 2002), including intrinsic white noise and analyzing effects of noise on the spontaneous activity of the nonlinear system, in order to account for the experimental results of Segev et al.. Analytically we can distinguish different regimes of activity, depending from the model parameters. Using analytical results as a guide line, we perform simulations of the nonlinear stochastic model in two different regimes, B and C. The Power Spectrum Density (PSD) of the activity and the Inter-Event-Interval (IEI) distributions are computed, and compared with experimental results. In regime B the network shows stochastic resonance phenomena and noise induces aperiodic collective synchronous oscillations that mimic experimental observations at 0.5 mM Ca concentration. In regime C the model shows spontaneous synchronous periodic activity that mimic activity observed at 1 mM Ca concentration and the PSD shows two peaks at the 1st and 2nd harmonics in agreement with experiments at 1 mM Ca. Moreover (due to intrinsic noise and nonlinear activation function effects) the PSD shows a broad band peak at low frequency. This feature, observed experimentally, does not find explanation in the previous models. Besides we identify parametric changes (namely increase of noise or decreasing of excitatory connections) that reproduces the fading of periodicity found experimentally at long times, and we identify a way to discriminate between those two possible effects measuring experimentally the low frequency PSD.Comment: 25 pages, 10 figures, to appear in Phys. Rev.

Nature-Inspired Interconnects for Self-Assembled Large-Scale Network-on-Chip Designs

Future nano-scale electronics built up from an Avogadro number of components needs efficient, highly scalable, and robust means of communication in order to be competitive with traditional silicon approaches. In recent years, the Networks-on-Chip (NoC) paradigm emerged as a promising solution to interconnect challenges in silicon-based electronics. Current NoC architectures are either highly regular or fully customized, both of which represent implausible assumptions for emerging bottom-up self-assembled molecular electronics that are generally assumed to have a high degree of irregularity and imperfection. Here, we pragmatically and experimentally investigate important design trade-offs and properties of an irregular, abstract, yet physically plausible 3D small-world interconnect fabric that is inspired by modern network-on-chip paradigms. We vary the framework's key parameters, such as the connectivity, the number of switch nodes, the distribution of long- versus short-range connections, and measure the network's relevant communication characteristics. We further explore the robustness against link failures and the ability and efficiency to solve a simple toy problem, the synchronization task. The results confirm that (1) computation in irregular assemblies is a promising and disruptive computing paradigm for self-assembled nano-scale electronics and (2) that 3D small-world interconnect fabrics with a power-law decaying distribution of shortcut lengths are physically plausible and have major advantages over local 2D and 3D regular topologies

Photometric variability of candidate white dwarf binary systems from Palomar Transient Factory archival data

We present a sample of 59 periodic variables from the Palomar Transient Factory, selected from published catalogues of white dwarf (WD) candidates. The variability can likely be attributed to ellipsoidal variation of the tidally distorted companion induced by the gravity of the primary (WD or hot subdwarf) or to the reflection of hot emission by a cooler companion. We searched 11311 spectroscopically or photometrically selected WD candidates from three hot star/WD catalogues, using the Lomb-Scargle periodogram to single out promising sources. We present period estimates for the candidates, 45 of which were not previously identified as periodic variables, and find that most have a period shorter than a few days. Additionally, we discuss the eclipsing systems in our sample and present spectroscopic data on selected sources

Inverse eigenvalue problem for discrete three-diagonal Sturm-Liouville operator and the continuum limit

In present article the self-contained derivation of eigenvalue inverse problem results is given by using a discrete approximation of the Schroedinger operator on a bounded interval as a finite three-diagonal symmetric Jacobi matrix. This derivation is more correct in comparison with previous works which used only single-diagonal matrix. It is demonstrated that inverse problem procedure is nothing else than well known Gram-Schmidt orthonormalization in Euclidean space for special vectors numbered by the space coordinate index. All the results of usual inverse problem with continuous coordinate are reobtained by employing a limiting procedure, including the Goursat problem -- equation in partial derivatives for the solutions of the inversion integral equation.Comment: 19 pages There were made some additions (and reformulations) to the text making the derivation of the results more precise and understandabl

Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum

Motivated by a problem in climate dynamics, we investigate the solution of a Bessel-like process with negative constant drift, described by a Fokker-Planck equation with a potential V(x) = - [b \ln(x) + a\, x], for b>0 and a<0. The problem belongs to a family of Fokker-Planck equations with logarithmic potentials closely related to the Bessel process, that has been extensively studied for its applications in physics, biology and finance. The Bessel-like process we consider can be solved by seeking solutions through an expansion into a complete set of eigenfunctions. The associated imaginary-time Schroedinger equation exhibits a mix of discrete and continuous eigenvalue spectra, corresponding to the quantum Coulomb potential describing the bound states of the hydrogen atom. We present a technique to evaluate the normalization factor of the continuous spectrum of eigenfunctions that relies solely upon their asymptotic behavior. We demonstrate the technique by solving the Brownian motion problem and the Bessel process both with a negative constant drift. We conclude with a comparison with other analytical methods and with numerical solutions.Comment: 21 pages, 8 figure

Inverse Spectral-Scattering Problem with Two Sets of Discrete Spectra for the Radial Schroedinger Equation

The Schroedinger equation on the half line is considered with a real-valued, integrable potential having a finite first moment. It is shown that the potential and the boundary conditions are uniquely determined by the data containing the discrete eigenvalues for a boundary condition at the origin, the continuous part of the spectral measure for that boundary condition, and a subset of the discrete eigenvalues for a different boundary condition. This result extends the celebrated two-spectrum uniqueness theorem of Borg and Marchenko to the case where there is also a continuous spectru