International Journal of Modern Physics C

In this paper a simple two-layer neural network's model, similar to that studied by D. Amit and N. Brunel,¹¹ is investigated in the frames of the mean-field approximation. The distributions of the local fields are analytically derived and compared to those obtained in Ref. 11. The dynamic properties are discussed and the basin of attraction in some parametric space is found. A procedure for driving the system into a basin of attraction by using a regulation imposed on the network is proposed. The effect of outer stimulus is shown to have a destructive influence on the attractor, forcing the latter to disappear if the distribution of the stimulus has high enough variance or if the stimulus has a spatial structure with sufficient contrast.

The techniques, used in this paper, for obtaining the analytical results can be applied to more complex topologies of linked recurrent neural networks.

We investigate the performance gains from hyper-systolic implementations of n²-loop problems on the massively parallel computer Quadrics, exploiting its three-dimensional interprocessor connectivity. For illustration we study the communication aspects of an exact molecular dynamics simulation of n particles with Coulomb (or gravitational) interactions.

We compare the interprocessor communication costs of the standard-systolic and the hyper-systolic approaches for various granularities. We predict gain factors as large as three on the Q4 and eight on the QH4 and measure actual performances on these machine configurations. We conclude that it appears feasible to investigate the thermodynamics of a full gravitating n-body problem with O(16.000) particles using the new method on a QH4 system.

The principle of indirect elimination states that an algorithm for solving discretized differential equations can be used to identify its own bad-converging modes. When the number of bad-converging modes of the algorithm is not too large, the modes thus identified can be used to strongly improve the convergence. The method presented here is applicable to any linear algorithm like relaxation or multigrid. An example from theoretical physics, the Dirac equation in the presence of almost-zero-modes arising from instantons, is studied. Using the principle, bad-converging modes are removed efficiently. It is sketched how the method can be used for a Conjugate Gradient algorithm. Applied locally, the principle is one of the main ingredients of the Iteratively Smoothing Unigrid algorithm.

After a review of widely used pattern recognition methods we present the Kalman filter and the associated smoother as a recursive variant of conventional least squares estimators. We first discuss its application to the reconstruction of charged tracks, including simultaneous track finding and track fitting and a robustification of the filter. This section is concluded by a case study of track reconstruction strategy in the DELPHI experiment. The second part deals with vertex reconstruction, including the detection of outlying tracks. It is shown that the detection of secondary vertices can be further improved by a robustification of the vertex fit via the M-estimator.

We present a numerical method to deal efficiently with large numbers of particles in incompressible fluids. The interactions between particles and fluid are taken into account by a physically motivated ansatz based on locally defined drag forces. We demonstrate the validity of our approach by performing numerical simulations of sedimenting non-Brownian spheres in two spatial dimensions and compare our results with experiments. Our method reproduces qualitatively important aspects of the experimental findings, in particular the strong anisotropy of the hydrodynamic bulk self-diffusivities.

In this paper the small relativistic correction for the energy eigenvalues of the two- and three-dimensional anisotropic quantum harmonic oscillator are calculated, using as eigenstates , for different values of the relativistic parameters β_i ≡ ħw_i / m₀c² with i = 1, 2 and 3.

By studying correlation functions of two replicas with the damage spreading method, the spin glass transition temperature of the 3D ±J EA model is evaluated by using Campbell's criterion D (T_g, t → ∞) = 1/2 or , where D and are the Hamming distance and the overlap of the two replicas, respectively. The two replicas evolve with the same series of the random numbers and with initial spin-configurations related to each other by (for all i). From our simulational data for system sizes up to L = 64, the spin glass transition temperature is estimated as T_g = 1.18 ± 0.06. The replica simulational method and the damage spreading method are compared with each other. The relaxation exponents of the magnetization and the correlation functions are also estimated in the vicinity of T_g on a large lattice and the dynamical critical exponent z is estimated as z ≃ 6.0.

Multiplicative random processes in (not necessarily equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the elementary variables. In terms of the original variables this gives a power-law distribution. This mechanism implies certain relations between the constraints of the system, the power of the distribution and the dispersion law of the fluctuations. These predictions are validated by Monte Carlo simulations and experimental data. We speculate that stochastic multiplicative dynamics might be the natural origin for the emergence of criticality and scale hierarchies without fine-tuning.

We study the probability of getting more than one spanning cluster at p_c for site percolation in dimensions of two to five. The probability increases from ~0.003 in two dimensions to ~0.16 in five. This shows that although there can be only one infinite cluster of finite density, there can be several spanning clusters at the same time.

In this article we will expose a connection between critical values of percolation and Ising model, i.e., the percolation threshold p_c, and the critical temperature T_c and energy E_c, respectively, by the approximation . For the two-dimensional square lattice even the identity holds. For higher dimensions — up to d = 7 — and other lattice types we find remarkably small differences from one to five percent.