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Ken Umeno

Publications and source records attributed to Ken Umeno.

At least 37 records · Page 2Linked to original sources

Universality of the Route to Chaos -- Exact Analysis

The universality of the route to chaos is analytically proven for countably infinite number of maps by proposing the Super Generalized Boole (SGB) transformations. As one of the route to chaos, intermittency route was studied by Pomeau and Manneville numerically. They conjectured the universality in Type 1 intermittency, that the critical exponent of the Lyapunov exponent is $1/2$ in Type 1 intermittency. In order to prove their conjecture, we showed that for certain parameter ranges, the SGB transformations are exact and preserve the Cauchy distribution. Using the property of exactness, we proved that the critical exponent is $1/2$ for countably infinite number of maps where Type 1 intermittency occurs.

nlin.CD↗

Pre-seismic ionospheric anomalies detected before the 2016 Kumamoto earthquake

On April 15, 2016, the Kumamoto earthquake (Mw 7.3) occurred in Japan with no warning signals. Global Navigation Satellite System (GNSS) receivers provide useful information on disturbances in ionosphere by calculating the changes in Total Electron Content (TEC), which is the number of electrons in ionosphere. Here we show our recently proposed correlation analysis of TEC data which can detect the pre-seismic ionospheric anomalies from the public GNSS data. Our method detected the ionospheric anomaly several tens of minutes before the 2016 Kumamoto earthquake near its epicenter. Furthermore, we gave an indicator to distinguish between the pre-seismic TEC anomalies and the medium scale traveling ionospheric disturbances (MSTIDs) by calculating the anomalous area rates. These results support the hypothesis for existence of the preceding phenomena before large earthquakes.

physics.geo-ph↗

Randomness Evaluation with the Discrete Fourier Transform Test Based on Exact Analysis of the Reference Distribution

In this paper, we study the problems in the discrete Fourier transform (DFT) test included in NIST SP 800-22 released by the National Institute of Standards and Technology (NIST), which is a collection of tests for evaluating both physical and pseudo-random number generators for cryptographic applications. The most crucial problem in the DFT test is that its reference distribution of the test statistic is not derived mathematically but rather numerically estimated, the DFT test for randomness is based on a pseudo-random number generator (PRNG). Therefore, the present DFT test should not be used unless the reference distribution is mathematically derived. Here, we prove that a power spectrum, which is a component of the test statistic, follows a chi-squared distribution with 2 degrees of freedom. Based on this fact, we propose a test whose reference distribution of the test statistic is mathematically derived. Furthermore, the results of testing non-random sequences and several PRNGs showed that the proposed test is more reliable and definitely more sensitive than the present DFT test.

cs.CR↗

Non-Linear Programming: Maximize SNR for Designing Spreading Sequence - Part II: Conditions for Optimal Spreading Sequences

Signal to Noise Ratio (SNR) is an important index for wireless communications. In CDMA systems, spreading sequences are utilized. This series of papers show the method to derive spreading sequences as the solutions of non-linear programming: maximize SNR. In this paper, we derive the optimization problems with the expression SNR derived in Part I and the necessary conditions for the global solutions. We numerically solve the problems and evaluate the solutions with two factors, mean-square correlations and maximum mean-square correlations.

cs.IT↗

Non-Linear Programming: Maximize SNR for Designing Spreading Sequence - Part I: SNR versus Mean-Square Correlation

Signal to Noise Ratio (SNR) is an important index for wireless communications. In CDMA systems, spreading sequences are utilized. This series of papers show the method to derive spreading sequences as the solutions of the non-linear programming: maximize SNR. In this paper, we consider a frequency-selective wide-sense-stationary uncorrelated-scattering (WSSUS) channel and evaluate the worst case of SNR. Then, we derive the new expression of SNR whose main term consists of the periodic correlation terms and the aperiodic correlation terms. In general, there is a relation between SNR and mean-square correlations, which are indices for performance of spreading sequences. Then, we show the relation between our expression and them. With this expression, we can maximize SNR with the Lagrange multiplier method. In Part II, with this expression, we construct two types optimization problems and evaluate them.

cs.IT↗

Orthogonal Basis Spreading Sequence for Optimal CDMA

Recently, new spreading sequences have been proposed to increase the capacity of users. In particular, the Weyl spreading sequences have the larger capacity of users than the Gold codes. This paper shows that the Weyl spreading sequences appear in a bit recovering model and they are orthogonal basis vectors. This result shows the reason why they have the large capacity and that any spreading sequence is expressed as the sum of the Weyl spreading sequences.

cs.IT↗

Canonical superdiffusion and energy fluctuation divergence

We propose a noble physical model obtained from a Hamiltonian with periodic potential. This model is canonical, reversible and brings about chaotic superdiffusion with energy fluctuation divergence. The analytical formula of invariant density can be obtained in some parameter range. In the range it is proved that the map is Anosov diffeomorphism and the invariant measure is a SRB measure. We calculate the analytical formula of Lyapunov exponent.

nlin.CD↗

Numerical Approach to Maximize SNR for CDMA Systems

Signal to Noise Ratio (SNR) is an important index for wireless communications. There are many methods for increasing SNR. In CDMA systems, spreading sequences are used. To increase SNR, we have to improve spreading sequences. In classical approaches, the expression of SNR is not differentiable in terms of the parameter of the spreading sequences even in no fading situations. Thus, we express it as the differentiable form and construct the non-linear programing for maximizing SNR. In particular, we solve the problem of maximizing SNR numerically by obtaining spreading sequences whose SNR is guaranteed to be high.

cs.IT↗

Further improving security of Vector Stream Cipher

Vector Stream Cipher (VSC) is a stream cipher which consists of permutation polynomial over a ring of modulo $2^w$. The algorithm for generating key stream is very simple and the encryption is very fast. Some theoretical attacks for VSC have been reported so far since the invention of VSC in 2004. Then, the authors proposed some improvements and developed "Vector Stream Cipher 2.0 (VSC 2.0)" to be immune against the theoretical attacks. In this paper, we propose further improvement of VSC 2.0 to publish as a new chaos cipher "Vector Stream Cipher 2.1 (VSC2.1)". VSC 2.1 is faster and more secure than VSC 2.0. Our result suggests that permutation polynomials over a ring of modulo $2^w$ are useful for cryptography.

cs.IT↗

SNR Maximization as a Non-Linear Programming -Towards Optimal Spreading Sequence-

Signal to Noise Ratio (SNR) is an important index for wireless communications. There are many methods for increasing SNR. In CDMA systems, spreading sequences are used. We consider the frequency-selective wide-sense-stationary uncorrelated-scattering (WSSUS) channel and evaluate the worst case of SNR. We construct the non-linear programing for maximizing the lower bound of the average of SNR. This problem becomes the convex programming if we did not take into account the norm constraint. We derive necessary conditions for optimal spreading sequences for the problem.

cs.IT↗

One-stroke polynomials over a ring of modulo $2^w$

Permutation polynomials over a ring of modulo $2^w$ are compatible with digital computers and digital signal processors, and so they are in particular expected to be useful for cryptography and pseudo random number generator. In general, the period of the polynomial should be long in such fields. In this paper, we derive the necessary and sufficient condition which specify one-stroke polynomials which are permutation polynomials whose periods are maximized.

cs.IT↗

Solvable Chaotic Synchronization -A New Interpretation of Common Noise-induced Synchronization with Conditional Lyapunov Exponents-

We show the first solvable chaotic synchronization model of unidirectionally coupled dynamical systems. We establish a new interpretation of the conditional Lyapunov exponent that characterizes chaotic synchronization completely. Moreover, we newly show how the conditional Lyapunov exponent relates to common noise-induced synchronization phenomena by the new interpretation.

nlin.CD↗

Correlation Analysis for Total Electron Content Anomalies on 11th March, 2011

We can observe the changes of Total Electron Content, TEC, in ionosphere by analyzing the data from GNSS satellites. There are many reports about TEC anomalies after earthquakes, i.e. large earthquakes often disturb the ionosphere. Up to now, preseismic TEC anomalies have been reported in several papers. However, they are not so clear as coseismic TEC anomalies, and their analysis methods have some problems for practical earthquake prediction. One factor making it difficult to detect TEC anomalies is large noises in TEC data. Non-negligible TEC disturbances are caused by many natural mechanisms. To overcome this difficulty, we propose correlation analyses between one GNSS station and GNSS stations surrounding it. First, we model TEC time series over a few hours using polynomial functions of time. Second, we calculate prediction errors as the departure of the TEC time series from the models over time scale of a few minutes, and define it as the TEC anomaly. Third, we calculate the correlation between anomaly of one GNSS station and those at the surrounding stations. Although such a correlation method has long been used for radio communications, in particular for spread spectrum communications and very long baseline interferometry (VLBI) to increase SNR (signal to noise ratio), it has not been widely applied for TEC analyses. As a result of our method, we demonstrate that the correlation analysis let us detect TEC anomaly one hour before 2011 Tohoku-oki earthquake. In this paper, we examined the 2011 Tohoku-oki case extensively.

physics.geo-ph↗

Three Theorems on odd degree Chebyshev polynomials and more generalized permutation polynomials over a ring of module $2^w$

Odd degree Chebyshev polynomials over a ring of modulo $2^w$ have two kinds of period. One is an "orbital period". Odd degree Chebyshev polynomials are bijection over the ring. Therefore, when an odd degree Chebyshev polynomial iterate affecting a factor of the ring, we can observe an orbit over the ring. The "orbital period" is a period of the orbit. The other is a "degree period". It is observed when changing the degree of Chebyshev polynomials with a fixed argument of polynomials. Both kinds of period have not been completely studied. In this paper, we clarify completely both of them. The knowledge about them enables us to efficiently solve degree decision problem of Chebyshev polynomial over the ring, and so a key-exchange protocol with Chebyshev polynomial over the ring is not secure. In addition, we generalize the discussion and show that a key-exchange protocol with more generalized permutation polynomials which belong to a certain class is not secure.

cs.IT↗

Exact Lyapunov exponents of the generalized Boole transformations

The generalized Boole transformations have rich behavior ranging from the \textit{mixing} phase with the Cauchy invariant measure to the \textit{dissipative} phase through the \textit{infinite ergodic} phase with the Lebesgue measure. In this Letter, by giving the proof of mixing property for $0<α<1$ we show an \textit{analytic} formula of the Lyapunov exponents $λ$ which are explicitly parameterized in terms of the parameter $α$ of the generalized Boole transformations for the whole region $α>0$ and bridge those three phase \textit{continuously}. We found the different scale behavior of the Lyapunov exponent near $α=1$ using analytic formula with the parameter $α$. In particular, for $0<α<1$, we then prove an existence of extremely sensitive dependency of Lyapunov exponents, where the absolute values of the derivative of Lyapunov exponents with respect to the parameter $α$ diverge to infinity in the limit of $α\to 0$, and $α\to 1$. This result shows the computational complexity on the numerical simulations of the Lyapunov exponents near $α\simeq$ 0, 1.

nlin.CD↗

New chaos indicators for systems with extremely small Lyapunov exponents

We propose new chaos indicators for systems with extremely small positive Lyapunov exponents. These chaos indicators can firstly detect a sharp transition between the Arnold diffusion regime and the Chirikov diffusion regime of the Froeschlé map and secondly detect chaoticity in systems with zero Lyapunov exponent such as the Boole transformation and the $S$-unimodal function to characterize sub-exponential diffusions.

nlin.CD↗

Chaotic Method for Generating q-Gaussian Random Variables

This study proposes a pseudo random number generator of q-Gaussian random variables for a range of q values, -infinity < 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.

cs.IT↗

Towards international E-stat for monitoring the socio-economic activities across the globe

We investigate relationship between annual electric power consumption per capita and gross domestic production (GDP) per capita for 131 countries. We found that the relationship can be fitted with a power-law function. We examine the relationship for 47 prefectures in Japan. Furthermore, we investigate values of annual electric power production reported by four international organizations. We collected the data from U.S. Energy Information Administration (EIA), Statistics by International Energy Agency (IEA), OECD Factbook (Economic, Environmental and Social Statistics), and United Nations (UN) Energy Statistics Yearbook. We found that the data structure, values, and unit depend on the organizations. This implies that it is further necessary to establish data standards and an organization to collect, store, and distribute the data on socio-economic systems.

q-fin.GN↗