Ken Umeno

Design of spread-spectrum sequences using chaotic dynamical systems and ergodic theory

A new design methodology for the design of optimal spread-spectrum sequences for asynchronous code-division multiple access (A-CDMA) and chip-synchronous CDMA (CS-CDMA) systems is proposed. We derive general results on the partial auto-correlation function of the optimal spreading sequences for CS-CDMA and A-CDMA systems with respect to the minimization of the average bit error rate under the standard-Gaussian-approximation condition without assuming the spreading sequences as independent stationary random processes. Based on the ergodic theory, a practical implementation of the optimal spreading sequence by using chaotic dynamical systems with Lebesgue spectrum is provided and the corresponding system performance is analyzed.

Chaotic Monte Carlo Computation: A Dynamical Effect of Random-Number Generations

Chaotic maps with absolutely continuous invariant probability measures are implemented as random-number generators for Monte Carlo computation. We observe that such Monte Carlo computation based on chaotic random-number generators yields sometimes unexpected dynamical dependency behavior which cannot be explained by usual statistical arguments. Furthermore, we find that superefficient Monte Carlo computation with O(1/N2) mean square error can be carried out as an extreme case of such dynamical dependency behavior. Here, such superefficiency sharply contrasts with the conventional Monte Carlo simulation with O(1/N) mean square error. By deriving a necessary and sufficient condition for the superefficiency, it is shown that such high-performance Monte Carlo simulations can be carried out only if there exists a strong correlation with chaotic dynamical variables. Numerical calculation illustrates this dynamics dependency and the superefficiency of various chaotic Monte Carlo computations.

SUPERPOSITION OF CHAOTIC PROCESSES WITH CONVERGENCE TO LEVY'S STABLE LAW

We construct a family of chaotic dynamical systems with explicit broad distributions, which always violate the central limit theorem. In particular, we show that the superposition of many statistically independent, identically distributed random variables obeying such chaotic process converge in density �

Improvement of SNR with chaotic spreading sequences for CDMA

We show that chaotic spreading sequences generated by ergodic mappings of Chebyshev orthogonal polynomials have better correlation properties for CDMA than the optimal binary sequences (Gold sequences) in the sense of ensemble average.

Higher-Order Decomposition Theory of Exponential Operators and Its Applications to QMC and Nonlinear Dynamics

A general theory of higher-order decomposition of exponential operators and symplectic integrators is reviewed briefly. Some explicit formulas are given up to the tenth order. An application of these higher-order decompositions to Hamiltonian dynamics is also presented to confirm their usefulness.

Blind source separation of chaotic laser signals by independent component analysis

We experimentally demonstrate blind source separation of chaos generated in Nd:YVO(4) microchip solid-state lasers by using independent component analysis. Two chaotic source signals are linearly mixed with randomly selected mixing ratio and independent component analysis is applied for the mixed signals to extract the source signals. We investigate blind source separation of many chaotic laser signals and succeed 100-signal separation of chaotic temporal waveforms. Longer temporal waveforms are required with increase of the number of mixed signals.

Non-integrable character of Hamiltonian systems with global and symmetric coupling

Abstract A new sufficient condition to prove non-integrability of Hamiltonian systems with symmetric variational equations is proposed. Though the present condition is taken as an extension of Ziglin and Yoshidas “non-resonant condition”, the algorithmic bottle-neck proving non-integrability in high dimensional cases can be removed here. As a result, the non-existence of additional integrals of various symmetric Hamiltonian systems with an arbitrary number of degrees of freedom is proven.

Solvable Performances of Optimization Neural Networks with Chaotic Noise and Stochastic Noise with Negative Autocorrelation

By adding chaotic sequences to a neural network that solves combinatorial optimization problems, its performance improves much better than the case that random number sequences are added. It was already shown in a previous study that a specific autocorrelation of the chaotic noise makes a positive effect on its high performance. Autocorrelation of such an effective chaotic noise takes a negative value at lag 1, and decreases with dumped oscillation as the lag increases. In this paper, we generate a stochastic noise whose autocorrelation is C(i¾?) ≈ C×( i¾? r)i¾?, similar to effective chaotic noise, and evaluate the performance of the neural network with such stochastic noise. First, we show that an appropriate amplitude value of the additive noise changes depending on the negative autocorrelation parameter r. We also show that the performance with negative autocorrelation noise is better than those with the white Gaussian noise and positive autocorrelation noise, and almost the same as that of the chaotic noise. Based on such results, it can be considered that high solvable performance of the additive chaotic noise is due to its negative autocorrelation.

Galois extensions in Kowalevski exponents and nonintegrability of nonlinear lattices

Abstract Nonintegrability of some one-dimensional nonlinear lattices with many degrees of freedom is proved by using the Ziglin-Yoshida test for integrability. The key of the present proof is to consider the degree of algebraic extensions with respect to Kowalevski exponents over Q .

Chaotic Method for Generating q-Gaussian Random Variables

This study proposes a pseudorandom number generator of q -Gaussian random variables for a range of q values, -∞ <; q <; 3, based on deterministic chaotic map dynamics. Our method consists of chaotic maps on the unit circle and map dynamics based on the piecewise linear map. We perform the q-Gaussian random number generator for several values of q and conduct both Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) tests. The q-Gaussian samples generated by our proposed method pass the KS test at more than 5% significance level for values of q ranging from -1.0 to 2.7, while they pass the AD test at more than 5% significance level for q ranging from -1 to 2.4.