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Academic Papers

2013

  1. Ryo Takahashi and Ken Umeno, "Performance Evaluation of CDMA Using Chaotic Spreading Sequence with Constant Power in Indoor Power Line Fading Channels", IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences. (2014, in press).　NEW
  2. K. Umeno and M. H. Kao, "Chaos Theory as the answer to limited spectrum?", ITU News, No.10, 2013.　　ItuNews_LOGO.jpg
  3. 201311-IEEE-Cover.jpgChen-An Yang, Kung Yao, Ken Umeno and Ezio Biglieri, "Using Deterministic Chaos for Superefficient Monte Carlo Simulations", IEEE Circuits and Systems Magazine, 13 (2013), pp.26 - 35.
  4. Shun Ogawa, Spectral and formal stability criteria of spatially inhomogeneous solutions to the Vlasov equation for the Hamiltonian mean-field model, Phys. Rev. E 87, 062107 (2013), arXiv:1301.1130
  5. Ken Umeno, Statistical Mechanics of Information, Mathematical sciences (in Japanese) No. 600 (2013), pp. 35-41
  6. K. Umeno and A.-H. Sato, "Chaotic Method for Generating q-Gaussian Random Variables", IEEE Transactions on Information Theory, 59 (2013), pp.3199 - 3209.

Master Theses

＊Master course students write Master Theses obligatorily.
We show the titles and abstracts of master course students belonging to our laboratory during the last few years.

March 2014
Tomoki ARII／Satoshi IRIE／Tomohiro KUSE
March 2013
Masato IWATA／Ryosuke OZAKI／Hiroshi KAJIKAWA／Yuzo MORITA／Genta YOSHIMURA
March 2012
Kazuo IKEDA／Minoru NODA／Atsushi MORIOKA
March 2011
Keigo NAGATA／Takeshi NAKAMOTO／Kenta NISHIOKA
March 2010
Takuya OHTANI／Atsushi SUNAGAWA
March 2009
Makoto KIMIZUKA／Takeo KONDO／Maiko NISHIMURA／Takashi MARUYAMA
March 2008
Shinpei IWAMA／Taiki KAWAMOTO／Hiroshi SAKAI／Mitsuki TARAO
March 2007
Motoya KOZAKI／Kohei SHINTANI／Boyong Joe／Yuki NAGANUMA／Yuma MATSUDA


March 2014

Tomoki ARII

Study on CDMA Systems with Primitive Root Codes

Abstract :
In this thesis, we study on CDMA systems with primitive root codes. First, we explain primitive roots modulo a prime number $p$, and introduce the concept of safe prime numbers. Second, using the properties of primitive roots, we construct synchronous CDMA systems with primitive root codes which are complex number sequences. In this paper, we construct the system with the following situations: (1) The same primitive root $q_1$ is assigned to every user. (2) Different primitive roots are assigned to each user. (3) Some users are assigned by the same primitive root $q_1$, and other users are assigned by another primitive root $q_2$. Third, we analyse theoretically Bit Error Rate (BER) of the systems and effects of a safe prime number. Fourth, we simulate numerically BER of the systems. Finally, we compare the theoretical and numerical analysis of BER and evaluate the performance of the systems.

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Satoshi IRIE

Study on the high-precision Monte-Carlo computation using random numbers with nonuniform density

Abstract :
In this paper, a generalized method and several practical methods of the high-precision Monte-Carlo computation using random numbers with nonuniform density which decrease are proposed. Also the results of comparison between the proposed methods and previous methods, which use random or quasi-random number sequences with uniform density, are shown for applications to several multidimensional integral computation. As a result, the superiority of this methods is demonstrated.

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Tomohiro KUSE

Robustness of interdependent networks with degree-correlated inter-connections

Abstract :
Modern systems are constructed with multiple networks that are connected to each other. For example, electrical systems are constructed with the power grids and their communication support systems. In such a interdependent network, failure of nodes in one constituent network leads nodes in the other network to fail. This happens recursively and leads to a cascade of failures. It is known that the interdependent networks with random inter-connections have weaker robustness, tolerance to failures, than the individual networks. However, if the interdependent networks have degree correlations between the networks constructing them, the robustness of the interdependent networks may be changed. Since actual interdependent networks have some correlations, we investigate the effects of the correlations on the networks.
A group that nodes connected with several links is called a cluster and if the number of nodes in the cluster is large, the network is robust. We perform simulations for various ratios of the initial failure of nodes and evaluate the cluster sizes after the cascade of failures. We show that when a interdependent network has a positive degree correlation between two networks that construct it, it has the stronger robustness than that for the networks with no degree correlation. Moreover, as the result of the numerical simulation this system shows a percolation phase transition and the threshold is approximately a linear function of the correlation coefficient. Then, we show not only the numerical simulation results but theoretical ones for the robustness of the interdependent networks. The theory can be applied to the interdependent networks with any degree distributions and any inter-correlations. The theoretical results correspond to the numerical simulation results mainly at any case.

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March 2013

Masato IWATA

Title

Abstract :

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Ryosuke OZAKI

Title

Abstract :

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Hiroshi KAJIKAWA

Linear Regression Analysis of Foreign Exchanges with a Method of Segmenting Time Series Based on the Likelihood-Ratio Test

Abstract :
There has been a lot of researches to analyze time series data. On the other hand, a variation of information which we can obtain is getting wider and wider these days because of the development of information technology. Therefore, it is important to deal with various information for a purpose to analyze financial time series data more accurately.
In this paper, we conduct a linear regression analysis and set Google search queries as explanatory variables of the model in order to analyze financial time series data with taking various information into consideration. Additionally, we also set the interbank exchange frequencies and the volatility calculated by GARCH(1,1) model as explanatory variables.
Since financial time series are not generally modeled as a stationary process, but modeled as a non-stationary process, we assume that the non-stationary time series consists of several stationary segments with different properties. In order to discriminate the joint of these distributions, we conduct a likelihood- ratio test. According to this test, the point which maximizes the likelihood- ratio between the null model (homogeneous disturbance distribution) and the alternative model (a mixture of two different normal distributions) is regarded as the most possible combination point. Since likelihood usually includes sample errors, we evaluate the significance level of it by using the bootstrap method. We employ the bootstrap distribution as a discriminant measure to divide the time series into two segments at an adequate point, recursively.
We apply this method to the data of foreign exchange market and make an analysis of them in terms of segmenting points and regression coefficients. We compare our proposed method with the ordinary linear regression method visually and numerically. We conclude that Google search term which segments the time series at a point different from other search term has an additional relation with the explained variable. Our proposed method can detect the data point at which the tendency of the time series changes and can analyze the time series better than the ordinary method.

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Yuzo MORITA

Analysis of Foreign Exchange Rates Based on Parametric Risk Assessment Procedures with q-Gaussian and Pearson type IV Distributions

Abstract :
Recently, it has been much easier for individuals to buy and sell foreign currencies in the market and it is becoming more important to understand the foreign currency risks to hold foreign currencies safely. Exchange rates sometimes fluctuate unpredictably and it could cause loss of the deposit. Especially, it is well-known that the volatilities of the price fluctuate de- pending on the time period, which seems to cause fat-tailedness observed in actual data. Therefore, it is important to regard its fat-tailedness when we estimate the risk from historical data.
In this paper, we introduce parametric risk assessment procedures in the foreign exchange market. In order to consider the ruin probability when we have some deposit, we assume two types of distributions, the q-Gaussian and the Pearson type IV distributions that log-returns in foreign exchange rates obey.
We perform parameter estimation of q-Gaussian distribution for 30 currency pairs with a maximum likelihood method. The parameter q is estimated in the range of from 1.3 to 1.7, and we confirm that the empirical distributions of the market data have fat-tails. To check whether the estimated parameters are statistically significant, we calculate p-values of two types of statistical test, Kolmogorov-Smirnov (KS) test and Anderson-Darling (AD) test. We reveal that all p-values in KS test are larger than 0.1, although p-values of 9 currency pairs are less than 0.1. This means that the log-returns obey the q-Gaussian as a whole, but do not when we focus on tails of the distributions.
We also perform parameter estimation of the Pearson type IV distribution, which has skewness, for 30 currency pairs. In this case, the average p-values in both KS and AD test are better than those of the q-Gaussian and the p-values in AD test for only 5 pairs are less than 0.1. This means that the Pearson type IV is better-fitted to the market data. Therefore, we reveal that the model with skewness is preferred for risk estimation. We calculate 1% Value-at-Risk (VaR) in both cases. The difference of the VaR between the q-Gaussian and the Pearson type IV is about 10%. This indicates that VaR with the q-Gaussian could cause underestimation of the risk.

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Genta YOSHIMURA

Capacity-Approaching LDPC Codes Constructed from Extended Protographs

Abstract :
Low-density parity-check (LDPC) codes are in a class of the most powerful error correcting codes available today. In this paper, to improve the decoding performance we introduce a new class of LDPC codes con- structed from a template called an extended protograph, which belongs to the superset of the popular protographs. We exploit the extrinsic informa- tion transfer (EXIT) chart and asymptotic ensemble weight enumerator techniques to predict the capacity-approaching performance of extended protograph code ensembles. EXIT charts compute the iterative decoding threshold of a code ensemble, which contributes to the waterfall region performance for the decoding error rate. Asymptotic ensemble weight enumerators estimate whether or not the minimum distance of code en- semble increases linearly with code length, which affects the error floor performance for the decoding error rate. Taking account of these conflict- ing performance indices, we apply the simulated annealing (SA) algorithm to find extended protograph based codes which have low iterative decod- ing threshold and the linear minimum distance growth property. Finally, the performance of optimized extended protograph based codes over the binary-input additive white Gaussian noise (BIAWGN) channel are com- pared with that of existing protograph based codes and the quasi-cyclic (QC) code adopted by IEEE 802.16e (WiMAX) standard.

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March 2012

Kazuo IKEDA

Opinion propagation using partisan voter　models on several networks

Abstract :
The partisan voter model is the one of　models which treat the social opinion dynamics. We use them in order to treat opinion dynamics on　several networks. This model is a modified version of the voter model which describes the evolution to consensus in the networks of nodes, voters, that possess respective opinions within a discrete set. In the partisan voter model, each node has also an innate and fixed liking for one opinion. This liking determines the probability that each node changes its opinion. We calculate the convergence time toward consensus of opinions in several networks by using the partisan voter model. The convergence time in the scale-free networks, the BA model, is smaller than that in the complete graph. With the modified BA model we investigate the dependence on the exponent of the degree distribution, that is, on the number and size of hubs on the network. If the exponent is small, the number of hubs is small and the size of hubs is large. From our simulation, for the small exponent, the convergence time is shorter than that for the large exponent. The correlation of degrees is controlled by rewires of the links in the network initially created by the BA model. For assortative networks, we confirm with our simulation that convergence time is, in general, longer than that for uncorrelated networks. On the other hand, for disassortative networks, it is shorter than that for uncorrelated one in general.

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Minoru NODA

Japanese hotel statistics in terms of regional room capacities

Abstract :
In this paper, in order to understand the dependence of stay capacity on regionality, we propose a method to determine districts depending on the number of rooms and to classify its districts. We empirically analyze the geographical positions and the number of rooms about 2,881 Japanese hotels which have 582,898 rooms in total. Firstly, we conduct a clustering analysis of the regional stay capacity by centroid method. Secondly, we introduce the maximum entropy principle in order to divide regional areas into some levels. It may be concluded that the rank size distribution for the number of rooms in the cluster is fitted with a power-law function and that the scaling exponent is dependent on the number of clusters.

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Atsushi MORIOKA

Optimization of routing strategies for data transfer in peer-to-peer networks

Abstract :
Recently, peer-to-peer file-sharing systems have become familiar and the information traffic in the networks is increasing. Therefore it causes various traffic problems in peer-to-peer networks. In this paper, we model some features of the peer-to-peer networks, and investigate the traffic problems. Peer-to-peer networks have two notable characters. One is that each peer frequently searches for a file and download it from a peer who has the requested file. To decide whether a peer has the requested file or not in modeling of the search and download process, we introduce a file-parameter Pj , which expresses the normalized amount of files stored in peer j. It is assumed that if Pj is large, peer j has many files and can meet other peers' requests with high probability. The other character is that peers leave and join into the network repeatedly. Many researchers address traffic problems of data transfer in computer communication networks. To our knowledge, however, no reports focus on those in peer-to-peer networks whose topology changes with time. For routing paths of data transfer, generally, the shortest paths are used in usual computer networks. In this paper, we introduce a new optimal routing strategy which uses weights of peers to avoid traffic congestion. We find that the new routing strategy is superior to the shortest path strategy in terms of data traveling time when many peers join in the data transfer.

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March 2011

Keigo NAGATA

Analysis of image encryption schemes using chaotic maps

Abstract :
Along with the development of the information and telecommunications networks, various kinds of encryption schemes have been developed by many researchers. Some of them pay attention to chaotic encryption. They utilize chaotic properties such as initial sensitivity, synchronization, and so on, for enhancing security and effect of encryption. In this paper, we consider image encryption schemes using baker's map, which is one of chaotic maps. Image encryption scheme is divided into two phases, "permutation" and "diffusion". Permutation is encryption on positions of pixels, and diffusion is that on gray values. Both of them are necessary for secure encryption. In some previous studies, baker's map is used for permutation. With repeated application of this map, the pixels are permutated, and the original image comes to look featureless and random like noise. We can decrypt it easily if and only if the widths of the rectangles, called keys, are known because baker's map is reversible. First, we analyze the properties of baker's map and improve it to surmount the weakness. Secondly, we apply baker's map to diffusion. Finally, we evaluate the security of the proposed encryption scheme, and prove the usefulness of it.

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Takeshi NAKAMOTO

Estimating the tail index of distributions: Case study on the foreign exchange market

Abstract :
We study an unconditional distribution derived from Alfarano-Lux model which has the two parameters: the herding propensity and the autonomous switching tendency. One of the parameters, the herding propensity characterizes the tail shape of its distribution, but does not accord with the well-known Hill's estimator in case of foreign exchange market data. In this paper, we transform the probability density function of Alfarano-Lux model to the expanded form and obtain the analytical form of its cumulative distribution function. Additionally, we explain the reason why the difference between the estimates of Alfarano-Lux model and Hill's estimator is generated, and conduct Kolmogorov-Smirnov test to measure the goodness-of-fit. As an application of Alfarano-Lux model to the foreign exchange market data, we measure the fluctuation risk for some currency pairs.

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Kenta NISHIOKA

Log returns of stock values and q-Gaussian distributions: Application to the risk-assessment

Abstract :
We assess a risk of financial time series with the distribution estimated from them. Because it is not easy to infer its tail shape due to a lack of data in a practical manner.(1) We introduce Value at Risk(VaR) to a risk measure and compare it with variance under the q-Gaussian assumption.(2) We examine performance of the maximum likelihood estimator with the q-Gaussian log-likelihood function.(3) By using the distribution estimates, we verify errors of the VaR to estimated one. Finally we conduct an empirical analysis on log-returns of a stock traded in the Tokyo Stock Exchange.

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March 2010

Takuya OHTANI

Sequential associative memories on complex networks

Abstract :
The models of associative memories in neural networks, such as Hopfield model, are quite tractable mathematically, and applied to many areas. One of them is a model of sequential associative memories. Most of the models, however, including sequential associative memories, are usually applied to all-to-all networks. Since the studies of neural networks originate in brain science, it is natural to apply them to more realistic networks. Many researchers have been interested in complex networks, which is said to describe properties of real networks in society, computers, and neurons, that is, the small-world and scale-free properties. For example, random graph, the Watts-Strogatz model, the Barabási-Albert model, are the most famous complex networks which have some interesting properties. These days, the studies of complex networks are developed drastically. In this paper, the model of sequential associative memories is applied to these complex networks. The main subject is how the network topology affects the temperature dependence of the retrieval performance. Computer simulation reveals that the temperature dependence varies with the network topology, and it also comes out that the local performance on each node is increasing monotonically with its degree. Modifying the existing theory to be suitable for complex networks, we have been obtained a new approximated equation for overlap using a mean-field approximation and the the central limit theorem. This approximated equation can describe the temperature dependence of performance with any networks whose degree distributions are known. Numerical solution of the equation on the Barabási-Albert model is compatible with simulation results. On the other networks, the numerical solutions do not agree well with the results. Loops of networks are considered as one of the possible causes for the inagreement because the loops could disturb the independence of node states which is essential to apply the central limit theorem. As the Barabási-Albert model is known to have a very small number of loops than the other complex networks, the above compatibility between simulation and theoretical results is consistent with the loop effects. In order to determine whether the loops are the cause of the error, in the last of this paper, we present new approximated simultaneous equations which evaluate the effects of loops. As far as the numerical solution on random graph, it is likely that the loops have little effect on the performance of sequential associative memories on complex networks.

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Atsushi SUNAGAWA

Active random walkers: a simple model fro catalyst dynamics

Abstract :
Some problems related to active random walkers are studied with use of a model for a chemical system which consists of catalysts(C), products(P) and reactants(R). For numerical experiments we use a Monte Carlo method to follow motion of C- and P-particles. For analytical considerations a Langevin model for particle dynamics is introduced, which is converted to a coupled diffusion equation, whose linear stability is studied in relation to numerical experiments. We assume either attractive or repulsive interactions between C-particles and P-particles and the catalysts C are able to change environment locally by producing P-particles from R-particles. P-particles and C-particles can diffuse in the system and P-particles are characterized by a decay constant, which prevents the number of P-particles from increasing indefinitely. Our main results include

◦1) In case of attractive interaction between C- and P-particles, the density fields of C-particles and P-particles tend to a stationary bound state, which consists of a bump of C-particles and a bump of P-particles occupying the same small region (in a long time limit).
◦2) In case of repulsive interaction between C- and P-particles, we observe (irregular) density waves for both C-particles and P-particles, in which a region of high P-particles density corresponds to a region of low C-particles density, and vice versa.
◦3) When the amount of R-particles, available for the chemical reaction, is finite we observe that a ring, inside of which R-particles are consumed completely, expands outward.
◦4) Linear stability analyses give us information on the characteristic length of the stationary state and this turned out to be consistent with our findings (1) and (2) above.

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March 2009

Makoto KIMIZUKA

Properties of coupled double well systems with delay and noise

Abstract :
The interplay between noise and delay in physical as well as biological systems gives rise to a lot of interesting phenomena and is gathering interest of many researchers. An especially hot area in this connection is the semiconductor laser emitter (VCSEL in short), which is modeled by a Brownian particle in a double-well potential under delayed force. If there were no delayed force, the system would show a simple barrier-crossing or hopping, which means for VCSEL the transition from the vertically polarized state of light to the horizontally polarized one and vice versa. In the presence of delay, which represents the delayed feedback for VCSEL, this hopping is modified due to strong correlation between (x(t)) and (x(t-τ)) , with (x(t)) and (τ) denoting position of the Brownian particle at time t and the delay time, respectively. In this work we consider a model which consists of (N)-Brownian particles put in a double-well potential and investigate some theoretical problems such as the positional stationary state distribution function (Pss) and the time correlation function(TCF). This model may be considered as a model for VCSEL in which (N) laser emitters are connected in cascade. At the moment we have no experimental results available for comparison with our theory. Thus we performed ourselves computer experiments to obtain some physical quantities of interest. For theoretical analysis of Brownian dynamics in a double well potential, we employ a two-state approximation, which replaces the continuous position x(t) with s(t), which takes only two values +1 ( if (x(t)>0) ) and -1 ( if (x(t)<0) ). This greatly simplifies our problem and at the same time gives much insight into our problem. Some results obtained in this work include, 1) the positional stationary state distribution function (Pss) for the Brownian particle model is calculated (computer) experimentally and its (τ) and feedback strength ε dependences are clarified. These dependences are theoretically studied for the case (N=2) based on the two-state approximation, which results in (Pss) well correlated with our experiments. It is remarked that this (τ) dependence is absent for the case (N=1, 2) the time correlation function is also calculated numerically by solving the Langevin equation and theoretically based on the two-state approximation.

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Takeo KONDO

Signal response in scale-free network of bistable units

Abstract :
Information processing in biological systems, such as brains or cell membranes, has several features in common: (i) it is an analog information processing; (ii) scale-free networks play an important role; and (iii) each information processing unit possesses strong nonlinearity. We studied the efficiency of information processing in a scale-free network, consisting of many interacting nonlinear units with double-well potential, both theoretically and (computer) experimentally. We introduced the gain (G) to quantify the efficiency, which is defined as the ratio of the output strength aL of the maximum response unit L to the periodic input signal strength (A), i.e. (G≡aL/A) . In the previous work, Acebron et al. calculated (G) as a function of coupling (or interaction) strength (λ) i.e. &math (G(λ)) , by simulations and they found that (G(λ)) showed plateau behavior in some range of (λ) They tried to understand their numerical results with emphasis put on a hub, which is a typical feature of the scale-free network. That is, they analyzed dynamics based on a simplified model (starlike network). However, the analysis contains some problems: (i) it is limited to a very small (λ) region; and (ii) the overall role of the scale-free network for information processing is not touched upon. In this study, we develop a formalism, in which the gain (G) is studied based on a one-body problem, which turns out to be a good approximation to replace the dynamics of the complex network. We analyzed this model, and obtained four theoretical predictions: (i) the value (Gplateau) of the plateau height of (G(λ)) (ii) the initial transient behavior of (G(λ)) in a small (λ) region, (Gtrans(λ)) with finiteness of the system taken into account, (iii) the asymptotic (G) value, (Gsync) after full synchronization is achieved for large (λ) and (iv) the critical value (λsync) , beyond which all units are fully synchronized and the gain (G); becomes (Gsync) We compared these theoretical predictions with computer experiments and confirmed that our theory reproduces experimental results at least semi-quantitatively. From this we may say that we could understand (G(λ)) in the whole coupling strength range by revealing the role of the complex network in information processing.

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Maiko NISHIMURA

Scaling analysis on quotation activities in the foreign exchange market: Empirical investigation and stochastic modeling

Abstract :
We investigate quotation activities in the foreign exchange market both empirically and theoretically. We found the scaling relationship between means of the number of quotations during window lengths and their standard deviations. We confirm that the scaling exponent temporally changes from 0.8 to 0.9 depending on observation days and that it tends to be unity as the time window length increases. We also estimate a cross-correlation coefficients and relative frequencies of the quotation activities. As a result, it is found that the scaling exponent and the cross-correlation coefficients show a significant correspondence relationship. Therefore, it is concluded that scaling analysis would be one of adequate ways to grasp the total market state. Besides, we propose a stochastic model to understand the market participants' activities and conduct a theoretical analysis for the proposed model with parameter fitting by empirical data. Comparing empirical results with theoretical ones, we examine the adequency of the model. Consequently, we found that the fluctuation of the probability with which market participants decide their attitudes and the weight of each currency pair have an important role to determine the value of a scaling exponent under the condition that the probability is homogeneous for every market participant.

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Takashi MARUYAMA

Virus Spreading Models on Peer-to-Peer Network

Abstract :
Recently peer-to-peer (p2p) file-sharing systems have become a new communication paradigm. In this paper, we model virus spreading on Gnutella Network, which is one of p2p networks. P2p networks have two notable aspects. One is that a peer searches for a file and downloads it from a "host peer", which has the requested file. To determine whether a peer has the requested file or not in modeling of search and download process, we introduce a parameter Pj , which expresses the normalized amount of files stored in the peer j. It is assumed that the more a peer has files, the more possibly it becomes a host peer, that is, if Pj is large, the peer j has many files and can meet other peers' requests with high probability. The other aspect is that peers leave and join the network repeatedly. The topology of the network, therefore, changes gradually with time and the behaviour of ρ (the density of infected peers) becomes complicated. To our knowledge, several researchers address modeling of virus spreading on p2p networks. However, no reports have done in adequate consideration of the effect of peers' leave and join. We appropriately simulate virus spreading on the networks under the change of its topology by the effect of leave and join. Since peers empirically seem not to leave the network randomly, this work examines the two cases of directions of separation from the networks. One is that peers randomly leave (called "RA-separation") and the other is that the peer j leaves at the rate which is proportional to 1-Pj (called "F2-separation"). Moreover, using mean-field approximation, we obtain an analytical formulations and emulate virus spreading on the network and compare the results with those of simulation. We attain the fact that viruses spread on the network independently of infection rate when peers leave in accordance with F2-separation. In other words, the network is more vulnerable to virus in case of F2-separation.

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March 2008

Shinpei IWAMA

Effects of time delay on nonlinear stochastic systems

Abstract :
Considerable attention is paid to some stochastic systems, whose dynamics is determined by the present state x(t) and the state x(t-T) in the past with r(> 0) denoting the delay time. Usually this delay is ascribed to the finite speed of information transmission and it is rather natural that effects of delay are intensively studied mainly for biological systems, e.g. as models to describe postural sway, visual feedback, and brain activity, to mention a few. Effects of delay are also studied for chemical, physical, and engineering systems. So long as we know, there have been no systematic studies on nonlinear systems where effects of delay play essential roles to determine system properties. Also from the viewpoint of methodology we have no reliable method, which can be applied for large delay time and strong nonlinearity. From these points stochastic systems with delay are offering many problems, interesting both from mathematical and physical viewpoints. Recent progress in understanding the delayed system may be partly due to the advent of the Fokker-Planck equation for the (one-body) distribution function p(x, t). However this equation is not a closed one for the distribution function p(x, t) in the sense that it contains additional 'collision' term, expressed in terms of two-body conditional distribution function p(y, t-T | x, t) for x(t-T) = y when x(t) = x. Developing some approximation schemes to make it a closed one, we give detailed discussions on the range of validity of each approximation scheme for the delay Fokker-Planck equation. Our strategy is as follows: First we note that the delay Fokker-Planck equation has two important parameters, the delay time T and the strength E of a delay term. We propose three approximation schemes, namely, which are supposed to be applicable for (i) small T, (ii) small E and (iii) large T regions. By applying these schemes to a double-well potential system and comparing theoretical predictions with (numerical) experiments, we estimate how our proposed schemes work to this problem.

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Taiki KAWAMOTO

Efficient packet routing strategy in complex networks

Abstract :
We investigate new packet routing strategies which mitigate traffic congestion on complex networks. Instead of using shortest paths, we propose efficient paths which avoid hubs on scale-free networks with a weight of each node. Firstly, we compare the routing strategy using degree-based weights with that using betweenness-based weights on two types of scale-free networks. The strategy using degree-based weights is more efficient than that using betweenness-based weights on scale-free networks generated by a preferential attachment. On the other hand, the ascendancy of the strategy using degree-based weights over that using betweenness-based weights is reversed on scale-free networks composed by taking into account the distance between nodes. Next, we consider the heuristic algorithm which improves step by step routing properties on congestion by using the information of betweenness of each node in every step. We propose new heuristic algorithm which balances traffic on networks by achieving minimization of the maximum betweenness in the much smaller number of iteration steps.

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Hiroshi SAKAI

Discrimination and Cluster methods for multi-dimensional time series of the Foreign Exchange Market based on Spectral Distances

Abstract :
In this thesis, the similarities between multi-dimensional time series extracted from high frequency financial data of the foreign exchange market are measured and the hierarchical clustering is performed based on them. We introduce two methods to calculate their similarities based on spectral distances. One is the sum of the Kullback-Leibler divergence between two normalized power spectra of time series of each elements for different observations, and the other is that between two largest eigenvalues of cross spectral matrix computed from multiple time series. In order to verify adequateness of these methods, we introduce the agent-based model of the foreign exchange market in which N market participants exchange M currency pairs, and perform numerical simulation and the hierarchical clustering with pseudo price movements obtained from it. As the results, it is found that the tendency that time series are unified sequentially as the difference of parameters became large, and that results obtained by means of two methods are almost similar. Finally applying this procedure to actual tick data we confirm that this can extract meaningful information from a large amount of data. The day when the rate movements of several currency pairs are greatly abnormal has a tendency that that on the day belongs to a separated cluster from those on other days. Therefore, it is concluded that this procedure is applicable to automatic extraction of meaningful information about markets from enomarous amounts of financial data.

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Mitsuki TARAO

Information Flow and Causality in Coupled Systems

Abstract :
In studies of a complex system, one of the major concerns is the detection and quantification of "causal interdependencies" among many dynamical subsystem, which constitute the complex system. For systems studied via physics or chemistry, this interdependency may be called "coupling" or "interaction". The purpose of this thesis is to study both physical and man-made systems on equal footing, using the concept of entropy transfer (or information flow) between subsystems. From physics we know that heat flows from a high to a low temperature region and sound wave propagates through a system with a constant velocity. These may be regarded as a kind of information transfer and there have been many works to understand these phenomena from the viewpoint of information flow. Based on the recent advance in methodology to quantify entropy transfer, as developed by Schreiber, we consider three systems, (1) a linearly coupled Langevin system, (2) FitzHugh?-Nagumo neural networks and (3) foreign exchange market. For each system we quantitatively analyze the system dynamics, especially the interrelation among subsystems, based on entropy transfer. The characteristics of these systems is that they have many units that are coupled with each other, unidirectionally or bidirectionally. In the linear system composed of two Brownian particles, we derive the transfer entropy rate in a theoretical way by taking the limit dt→0 where dt represents the sampling time. And we compare it with the entropy production rate. In the non-linear system that consists of many neurons, the information flow in three types of network, (i) linear array type, (ii) triangular type and (iii) a star-like one is analyzed. For a foreign exchange market, we treat the thirteen currency pairs. By calculating the entropy transfer among currency pairs, we observed some rules, which are rather vague but suggestive and seem to be consistent with our intuition.

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March 2007

Motoya KOZAKI

Application of the Beck model to stock markets: Value-at-Risk and portfolio risk assessment

Abstract :
We have applied the Beck model, developed for mechanical systems that exhibit scaling properties, to stock markets. Our study revealed that the Beck model elucidates properties of stock market returns and is applicable to practical use such as the Value-at-Risk estimation and the portfolio analysis. We have performed empirical analysis with daily/intraday data of the S&P 500 index returns and found that the volatility fluctuation of real markets iw well consistent with the assumptions of the Beck model: the volatility fluctuates in much larger time scale than return itself and the inverse of variance, or "inverse temperature," beta obeys Gamma-distribution. As predicted by the Beck model. the method of Value-at-Risk (VaR), one of the most significant indicator in risk management, is studied for q-Gaussian distribution. Our proposed method enables the VaR estimation in consideration of tail risk, which is underestimated by the variance-covariance method. A framework of portfolio risk assessment under the existence of tail risk is considered. We have proposed a multi-asset model with a single volatility fluctuation shared by all assets, named the single beta model, and empirically examined the agreement between the model an and an imaginary portfolio with Dow Jones indices. It turns out that the single beta model gives good approximation to portfolios composed of the assets with non-Gaussian and correlated returns.

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Kohei SHINTANI

Empirical analysis and numerical simulation of foreign exchange market dynamics

Abstract :
In this thesis, the dynamics of the foreign currency markets is analyzed with the tick frequency, which is the trace of market participatnts' activities. With the double-threshold agent model, the relation between the tick frequency time series of two agent groups is discussed. Empirical analysis with actual tick data indicates that the similarity of the tick frequency time series is getting similar as time passes and the similarity network among currency pairs changes by the areas where the markets are active. It means that in the present financial markets, market participants become more homogeneous, and the risks in the financial markets must be calibrated depending on areas, respectively. Alternative analysis indicates that the similarity between the best ask price and the similarity between the tick frequency time series influence each other constantly and weakly, and that the co-movement of them quickly and largely changes. Finally, a way of constructing the real-time market monitoring system is discussed.

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Boyong Joe

Self-tuning of activation energy in a two-state system

Abstract :
Many researchers have observed, in various biological and physical systems, that noise can enhance responses(i.e. output signals) of nonlinear systems to a weak periodic driving force(i.e. input signals) in a positive way, thus transfering more information than a case without noise. The phenomenon is closely related to stochastic resonance(SR), which states that there exists optimal noise strength T* where best information transfer is achieved. However it seems that not much attention has been paid to a situation where noise is rather weak and information transfer is very limited. In order to solve this problem, we attempt to apply an idea of self-tuning (ST), first proposed to explain high sensitivity of auditory systems of animals. That is, we consider a simple adaptation process of an activation energy(to be regarded as a threshold), which turns out to work well for a two-state system (TSS) in a weak noise region. Improvement of information processing ability of the TSS in a strong noise region was made possible by analytically studying the adaptation equation. We apply our ST method to a double-well potential system (DWPS), showing that the ST method works well also for the DWPS. Some quantities, not directly obtainable theoretically such as the first-passage-time distribution function, are calculated based on Monte-Carlo simulations. Finally we consider ST and SR from the viewpoint of 'energy transfer' from input signals to reservoirs. It is shown from numerical experiments that this energy transfer shows similar behavior as the information transfer.

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Yuki NAGANUMA

Packet routing strategy using neural networks on complex networks

Abstract :
We investigate routing strategies on complex networks. Firstly, using neural networks, we introduce a routing strategy where path lengths and queue lenghts are taken into account within a framework of statistical physics. The performance in this strategy becomes more efficient from improvement of the distance term. At the same time, we analyze how the properties of networks influence the performance of this strategy. Secondly, we propose a routing strategy where connection weights in neural networks are adjusted by local information. We also confirm how the distance term and the properties of networks influence the performance of this adjustive strategy.

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Yuma MATSUDA

Synchronization of a randomly coupled map model for neural networks

Abstract :
Neurons are known to oscillate synchronously with each other to achieve various functions. Studies on randomly coupled Hodgkin-Huxley neuron models have show that neurons synchronize their activity even in noisy environments. Synchronization is reported to occur when the size of networks is large enough even for sparsely connected neurons. Because fluctuation is neglected in large size networks, synchronization is controlled only by average states of neurons. Although it is widely observed in nature, especially in nervous systems, most of the mechanism is still unknown. In this paper, the condition for synchronization on neural networks is investigated with numerical simulations of a one-dimensional map neuron model. Then, the synchronization in noisy fields is theoretically understood throughout the distribution of neuron states formulated by inductive statistics and Gaussian mixture models.

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