ABSTRACT&CV

　

Introduction to the Session "Simulation of Complex Systems -- Realism and Simple Modeling"

Kohji Hirata
CCRE SOKEN-DAI & Research Organization for High Energy Accelerators

http://koryu.soken.ac.jp/home/kokusai/simulation/hirata.html

　

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Embodiment and Abstraction of Dynamo Simulation

Tetsuya Sato
National Institute for Fusion Science

Notwithstanding its 80 years long history, the dynamo problem had remained unsolved until very recently. This obstinate problem has finally come to a clue to its essential resolution. The advancement of simulation techniques along with the supercomputer and periphery technologies has made it possible to resolve highly tangled complex intertwinements.
　　As this example of dynamo problem indicates, an individual physical phenomenon, no matter how complex it looks, can be solved as far as its first principles are known. This may give an evidence that supercomputer simulation will be a scientific tool superior to the conventional mathematical tool to comprehend an embodiment of an individual complex phenomenon. As far as one is kept captured with standpoint that one wants to find a solution for a given problem, however, simulation stays a passive tool to gather ears of corn after the reapers in Modern Science. Simulation has a great potentiality to cultivate a new field in science to abstract universal laws from complex phenomena in various different fields.
　　In this talk, embodiment and abstraction will be addressed through the simulation of the dynamo problem.　

Tetsuya Sato (Doctor of　Engineering , Kyoto University)
Professor, National Institute for Fusion Science
1967 Research Associate, Kyoto university
1974 Lecturer, University of Tokyo
1976 Associate Professor, University of Tokyo
1980 Professor, Hiroshima University
1989 Professor, National Institute for Fusion Science
Theoretical and simulation researches on nonlinear phenomena in space plasmas such as aurora and magnetosphric substorms. Simulation research on nonlinear dynamics of fusion plasmas. Currently, he is devoted himself on promoting Simulation Science as cultivating a new paradigm of science.

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Abstract Simulation

Tatsuo Yanagita
Hokkaido University

http://aurora.es.hokudai.ac.jp/yanagita/job/cloud/html/souken.html

　

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Rugged energy landscape of a protein in the native state

Nobuhiro Go
Graduate School of Science, Kyoto University

Life on the earth is the result of evolution of self-reproductive chemical systems. Such systems have in general made themselves more and more complex during the history of evolution in order to increase the stability against environmental fluctuations, and also have developed so that they transfer the information about their own complex system to their offspring in the form of genetic information. Genetic information is expressed as base sequences of DNA or RNA, and a whole set of genetic information of a single living organism is called genome. Genome consists of a unit called gene, and in a living cell molecular machinery made of protein and/or RNA is produced based on information carried by each gene. Each molecular machinery carries an elementary function　which is a constituent of a set of various functions necessary for each individual organism to maintain its life and to reproduce its offspring. Here we can see a one to one to one correspondence between genetic information, molecular machinery and elementary function.
　　Protein is a polymer, in which 20 types of amino acids are　polymerized linearly in a specific sequence determined by genetic information. After polymerized in a cell, a polymer chain is folded autonomously into a specific three-dimensional structure determined by the amino acid sequence without using any additional pieces of information. When folded into the specific structure, a protein molecule is said to be in the native state. The molecule can carry out its function in this native state. When a protein molecule is taken out of a cell and the environmental condition is changed beyond a certain extent, the folded specific structure is destroyed and goes over to a state in which the molecule takes random structures. This is a phenomenon similar to the order-disorder phase transitions like solid-liquid transitions. Therefore the native state must be characterized by a distinctively low energy which can cope with the large entropy gain associated with the transition into the random unfolded state. The molecule searches out the point with the distinctively low energy in a very large conformational space with a very complex rugged energy surface during the autonomous folding process. Currently this folding process is being studied actively both experimentally and theoretically. In theoretical studies, simulation studies in terms of simplified theoretical models of proteins are actively carried out to extract the essential aspects of the folding phenomenon.
　　One of the ultimate goals of the studies of proteins is to understand the mechanism of biological functions based on the molecular structure in terms of the language of such material science as physics. The three-dimensional structures of proteins are known to be thermally fluctuating to quite a significant extent around the average structure elucidated by e.g. the X-ray crystallography. It is also known that such fluctuation is necessary for the molecule to carry out its function. From the point of view of the study of protein folding,　the native state is represented by a single point in the conformational space. However, from the point of view of the study of the molecular mechanism of functions, the native state corresponds to a certain range in the conformational space, and conformational fluctuation in such a space must be considered. The conformational dynamics necessary for carrying out the function is determined by the landscape of the energy surface in this space. The landscape is known both experimentally and theoretically to be very complex and rugged. For simulation studies, detailed theoretical models of proteins are necessary. In the lecture I will present our　such recent study, and will also describe how the energy landscape is related to various functions of proteins.

Nobuhiro Go
Professor, Graduate School of Science, Kyoto University
1961, Graduated from Department of Physics, Faculty of Science, Tokyo University
1964-1971, Research Assistant, Department of Physics, Faculty of Science, Tokyo University
1971-1987, Associate Professor, Department of Physics, Faculty of Science, Kyushu Univrsity
1987-, Professor, Department of Chemistry, Graduate School of Science, Kyoto University

Member of Science Council of Japan, Chairman of Commission on Biological
Physics of IUPAP, Council Member of IUPAB
Theoretical studies of structure and function of biopolymers.

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Protein Folding: From Lattice Models to Real Proteins

Eugene Shakhnovich
Harvard University

Protein folding is a field where theoretical physics, chemistry, molecular and evolutionary biology meet. A theoretical study of statistical mechanics of heteropolymers provides fundamental insights into protein folding, evolution and design. We show that there exist deep analogies between protein design/evolution and well-known statistical-mechanical models which make it possible to address, from a fundamental perspective such questions as degeneracy of protein code (i.e. how many sequences can fold to a given structure). Further we present the results of simulation of ''Darwinian'' evolution towards fast folding sequences which provide valuable hints in a quest for evolutionary messages about protein folding encoded in protein sequences. In particular, using the lessons from model protein evolution we were able to decipher evolutionary ''signals'' that call for fast folding in the superfamilies of structurally related nonhomologous proteins

Eugene Shakhnovich
Professor of Chemistry and Chemical Biology Harvard University

1984 PhD Theoretical Physics and Biophysics Moscow University
1984-1986 Research Associate Academy of Sciences USSR
1986-1990 Senior Fellow Academy of Sciences USSR
1990-1991 Research Associate Harvard University
1991-1995 Assistant Professor Harvard University
1995-1997 Associate Professor Harvard University
1997-Present Full Professor Harvard University

Theoretical and experimental studies of protein folding. evolution and design, bioinformatics, rational drug/ligand design, theory of soft-condensed complex systems including complex polymer gels, polyelectropytes/ampholytes, polymer dynamics, polymer adsorption/recognition, liquid crystals, hydrodynamics and spin glasses.

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Social Complexity and Socio-Politics of Information

Tadashi Yamamoto
National Museum of Ethnology

Chaotic social phenomena will generate new social systems under the circumstance that the existing social value systems are abandoned around the world and whole world system is transformed as a nation states are collapsing and the boundaries disappear.
　　It is very clear that the formation of societies is caused by imperfect information which is symbolized by "uncertainty to the future". Human beings might form the societies in order to overcome not "primitive violent state" but such imperfect information. For example, the power of prediction has been a strong ability, as it were a centripetal force, to form the societies. From the prediction to "the rule of law", from the uncontrollable market to the plan, human beings pursued regularized societies and (linear) ordered and operational social systems.
　　Today, the world society aims to introduce "transparency" and "legal stability of market" to all countries from the end of the cold war. The global communities are artificially constructed with the intension of ordering the world. Back of the tendency, this world ordering is dual to the trend to develop the operation and realization of information and risk supported by advanced computer network. The social transformation normally works from the chaotic and disordered world structure to the ordered world structure. At the same time, the disordered wordl is ready to be covered by the plural global communities which strengthen the network containing the non-linear interactions and oppose to the ordering of social systems.
　　In this research, assuming the basic structure which is composed of distributed and autonomous, and heterogeneous agents and their interactions, the nested and stratificated society which is generated from the dynamics of such structure is regarded as a model of the virtual society on the computer network. The purpose of building the model is to investigate the possibility to design the new social systems as the model of liberal society, based on the autonomous distributed societies which are established by the freedom and autonomy of the components, which enable us not only to exclude the real power of nation and society but also to enjoy the emergent productions of the complex societies. On such social composition, it should be discussed how the social value making process behaves and what social values are yielded.
　　Societies and virtual societies are generated from frequent transformations which are based on the linkage of interaction caused by heterogeneous or asymmetric imperfect information among agents. The plural heterogeneous communities are intermediary and locally generated bodies. As the community based society is considered, it is a very typical trial to investigate the scale, incidence and height of hierarchy about the formed communities, characteristics and its changing of the boundary, and non-linear interaction.
　　On the other hand, homogeneous system structure and transformation are nested and stratificated through every step of generating societies from the individual level to the global society. Thus, the nested and stratificated structure, and the traversing loops through hierarchy yield the characteristics of virtual societies. It is very crucial to clear the characteristics of political decision making process on the complex society which is so stratificated and nested that it contains complex or non-linear interaction. Moreover, ripple process of the political symbolic operation should be characterized. In particular, when each local society changes autonomously, there occcurs the political behavior dilemma under the asymmetric imperfect information.
　　Social complexity is the base which can provide emergence and development of human societies and can be considered to yield new societies against the ordering of social systems.　

Tadashi Yamamoto
Assistant Professor, National Museum of Ethnology
1994 Ph.D., Tokyo Institute of Technology (Systems Science)
1994-97 Research Associate, University of Erectro-Communications
1997 Assistant Professor, National Museum of Ethnology

His academic concerns are across the area of politics, sociology, systems science, and computer science. In more detail, he is deeply interested in generating conceptual and mathmatical modeling of societies, simulating societies and in visibly presenting social characters. Also, he is concerned with development of new social/political systems based on information systems.
(a) Mathematical modeling of social systems and computer simulation.
(b) Design of new social systems and advanced political systems.
(c) Liberalism and democracy realized by computer technology on information networks.

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The emergence and collapse of money

YASUTOMI Ayumu
Nagoya University

Money is　a structure which emerges amongst people who are trying to exchange their commodities. Its elements are the behaviour of exchange conducted by such people. As Karl Marx indicated, once this structure emerges, people mistake the function of this structure for the function of　the commodity which becomes money. This mistake supports the reproduction of this structure's elements.
　　In this presentation I will explain a computer simulation model based on this concept of money. We have N numbers of agents whose characters are the same in the long run apart from what they can produce. I assume that each agent produces a different commodity, namely the perfect division of labour. The agents repeat production, exchange and consumption in the course of time.
　　If we assume that each agent wants only one kind of commodity at once, we are able to observe that it is very difficult for agents to exchange their commodities, if N is sufficiently large. This kind of difficulty is generally referred to as the double coincidence of wants'. The powerful method agents can use in order to avoid the difficulty encountered in exchange is to obey the strategy accept that which everyone else accepts''. Money is the structure which emerges when agents obey this strategy, and its emergence drastically simplifies exchange.
　　The problem is to define how many people constitute everyone''? If we define this as value X, if X is too large, there is little exchange. However, if X becomes sufficiently small, we can observe the emergence of money in my computer simulation.
　　Next, I allow each person to choose their own value of X and to observe the population dynamics of X under the pressure of natural selection'. Namely, we shall revise the model and let those agents whose performance is bad follow the way of agents who are doing well. This kind of selfish effort of each agent, the invisible hand', lets emerge the structure of money. However, the emergence of money discontinuously changes the environment of the economy. The efforts by selfish agents in the new environment lets money　be instable and it collapses. The collapse of money brings the situation back to the initial state without Money, and the invisible hand' starts again to guide agents to select a strategy which lets Money emerge. After the second emergence of Money, the same invisible hand' again guides agents to select a strategy which forces Money to collapse. This process is repeated through computer simulation.

YASUTOMI Ayumu
Associate-Professor, School of Information and Science, Nagoya University,
1991-97 Research Assistant, Kyoto University
1997 Ph.D., Kyoto University (Economics)
1997 Associate Professor, Nagoya University.

The　research of Economic History in Manchuria by the method of financial analysis and of Complex Systems by the method of computer simulation. Recently he is active in observing the formation process of soybean and cotton products markets in Manchuria and in computational analysis of dynamical systems whose dimension is variable.

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Dynamics - Nonlinear Phenomena and Time Series Analysis

Tohru Ozaki
SOKEN-DAI & Inst. Stats. Math.

The behavior of chaotic processes generated by relatively simple dynamical systems is the subject of ongoing research in complex systems. Many researchers in these fields are scientists with backgrounds in physical sciences and engineering interested in constructing simple non-linear models to simulate complex phenomena in natural and social sciences.

On the other hand, a major concern of traditional statistical time series analysis has been the model estimation, prediction and control of inear and nonlinear time series generated from stochastic processes. Models for prediction and control of multivariate systems often involve complex feed-backs among the variables. Linear models have been useful in producing good results in real applications such as control of power plant boilers or cement rotary kilns. With the development of Akaike's Information Criterion, the linear time series approach has made remarkable progress in the last few decades.

Since the late 1970's, however, new types of time series data, often with very nonlinear and complex patterns of oscillation, for example limit cyclic nonlinear vibrations in mechanical engineering, EEG data taken from epileptic subjects or ECG data in biomedical sciences, have lead statistical time series analysts to the development of non-linear and non-stationary time series models. Here, although their main concern is still model estimation, prediction and control, checking whether an "estimated" model generates time series "similar" to the real data is also an important issue.

It is easy to contrast statistical time series analysis and chaos time series analysis born from physics. However, it is more productive to find similarities in the two approaches which will help to solve many difficult problems arising from science. Although there has not been much communication between the two schools of thought, they have not be in complete ignorance of each otherユs work. It is well known that Akaike's Information Criterion is closely connected with the work of Boltzmann at the end of last century. Also at the beginning of this century, a long time before some of the recent chaos physicists paid attention to the similarity of their work to statistical time series analysis, the Ehrenfests(1912) pointed out the importance of Einstein's inductive use of Boltzmann's entropy in his work on Brownian motion. They also highlighted the close relationship of Einstein's idea of the inductive method to the statistics beeing developed at that time by Pearson and others. They even wrote "the extension of the statistical treatment to a steadily increasing range of physical phenomena gives the "statistical experiment" an increasing methodological significance in the whole of physical research."

At the end of the twentieth century, we should not lose any opportunity for discussion between different schools with common interests. At this symposium and in this particular session, we are especially interested in the characterization(both quantitative and qualitative) of time series. It may be interesting to discuss how we can use knowledge from nonlinear science to improve the prediction and control of series in the real world taken from a wide range of fields such as neuroscience, astronomy, economics and finance etc.

Here, we would like to bring together statistical time series analysts, neural network, chaos chaos researchers neuroscientists and others working in related fields. I look forward to hearing stimulating ideas and views on nonlinear dynamics in the talks and discussions in this session. Further I hope that we could see, beyond the difference of the approaches and schools, in this session the future direction of the study of complex systems in the next century.

References

[1] Ehrenfest, T. and P.(1912) The Conceptual Foundation of the Statistical Approach in Mechanics. Published in German Encyclopedia of Mathematical Sciences. English translation (by M.J. Moravcsik) published by Dover Publishing Co., New York.　

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The Statistical Analysis of Nonlinear Brain Dynamics

Pedro Valdes-Sosa
Cuban Neuroscience Center

Elucidating the complex nonlinear dynamics of the brain is a formidable task. This work presents some initial tools developed for the analysis of complex neural systems by the Cuban Neuroscience Center and the Institute of Statistical Mathematics of Japan. The approach involves combining convergent data driven and model driven techniques to the same set of data. The data driven approach fits nonlinear nonparametric Autoregressive time series models in order to evaluate the dynamical behavior of the non stochastic "skeleton" of EEG data in order to empirically identify bifurcations of brain activity. Included is a new technique for the empirical estimation of the differential equations of the observed system. The model driven approach then explores the capacity of continuos time neural mass models to explain the empirically estimated dynamics. The continuos time neural mass models are formulated as stochastic differential equations. The Local linearization approach of T. Ozaki is then applied to discretize these equations, construct the corresponding Kalman filter, and carry out Maximum Likelihood estimation of model parameters. The use of this methodology is illustrated by an analysis of the human alpha rhythm. Both data driven and model driven approaches support the existence, in this type of EEG activity, of a Hopf bifurcation. The procedures developed are an instance of solving a dynamical inverse problem. The evaluation of neural dynamics in intact human subjects by noninvasive imaging methods further complicates the issue by embedding the dynamical inverse problem within another inverse problem, the spatial inverse problem of constructing functional tomographic images. A hierarchical Bayesian approach to the solution of this problem will be presented and directions of future work sketched out.

Pedro A. Valdes-Sosa
Senior Researcher, Acting Director, and Co-founder of Cuban Neuroscience Center (CNC)

1973 MD. University of Havana, 1978 Ph.D. CNIC (National Center for Scientific Research, With training in Mathematical statistics and Computer Science University of Havana).
1979 Postdoc New York University Brain Research Laboratories

Past work: 1969 computer programming of EEG brain signals and time series analysis with Laboratory of Neurophysiology of CNIC (predecessor of CNC).
Co-author of Neurometrics methodology (1977). Present work: Development of computerized systems for EEG analysis; use of multivariate statistics and time series analysis in Neurophysiology; nonlinear dynamical systems theory applied to brain function; theory and development of EEG/MEG Tomographic imaging systems; Multimodal Brain Image Fusion and statistical problems of Brain Images.

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Chaotic Features of Rhythmic Brain Activity

Hatsuo Hayashi
Kyushu Institute of Technology

Hippocampal and thalamic neurons cause spontaneous firing. Such spontaneous firing is one of the major causes of rhythmic brain activity. However, neuronal networks cause complex spatiotemporal activity which is different from the activity of single neurons, because the activity of neuronal networks depends not only on intrinsic properties of individual neurons but also on the network structure, balance of excitatory and inhibitory connections, and properties of synapses.
　　In general, the dynamical degrees of freedom of rhythmic brain activity is high, so that it is difficult to investigate geometrical structure of their phase portraits and represent chaotic features by means of one-dimensional maps. Actually, evidence for chaotic brain activity was not provided for ten years in spite of a huge number of publications after Babloyantz and her colleagues successfully demonstrated relatively law and non-integer correlation dimensions of human sleep EEGs in 1985. During the period, statistical measures, such as correlation dimensions and Lyapunov exponents, were entirely used to explore dynamical features of brain activity, and those were inconclusive debates about the determinism of brain activity. In other words, such statistical measures were not certain evidence for chaos.
　　Brain activity can be often observed as rhythmic EEGs. This fact indicates that neurons fire in synchrony. Larger brain waves reflect better synchronization, and epileptic EEGs are in the case of excessive synchronization. Although the synchronization of neuronal activity is consistent with low and non-integer correlation dimensions of brain waves, synchronization of neuronal activity of most spontaneous brain waves appears to be insufficient for analysis to gain insight into their dynamical features in phase spaces less than three dimensions. This is, probably, one of the reasons why it is generally difficult to investigate geometrical structure of attractors and features of Poinc*re maps obtained from "spontaneous" brain waves.
　　If chaotic features of rhythmic brain activity appear due to synchronization of neuronal activity, we can consider several cases where we may observe chaotic brain activity: (1) short-lasting facilitation of the synchronization due to afferent input, (2) long-term facilitation of the synchronization due to long-term potentiation (LTP) of post-synaptic potential, and (3) facilitated synchronization in pathological activity, such as spontaneous seizure.
　　In this lecture, first of all, we will show that a neural network model of the hippocampal CA3 spontaneously causes field current rhythms, which resemble epileptic, delta, theta and beta waves, depending on the strength of excitatory and inhibitory connections. These irregular rhythmic waves reflect complex spatiotemporal activity of the network and have not been characterized as low-dimensional chaos. However, synchronization of such neuronal activity is facilitated by afferent input, and field current of the network causes phase-lockings and chaotic responses depending on the stimulus parameters. The chaotic responses are well characterized by means of one-dimensional maps.
　　Second, phase-locked and chaotic field potential responses of the rat hippocampal CA3 in vitro and the rat somatosensory cortex in vivo to afferent input will be demonstrated. These responses are also characterized by means of attractors reconstructed in phase-spaces and one-dimensional strobomaps.
　　Third, it will be shown that rat hippocampal CA3 slices spontaneously cause synchronized bursting discharges due to LTP of excitatory synapses between pyramidal cells. The cross-correlation functions of spontaneous field potentials simultaneously recorded at two sites indicate that synchronization of neuronal activity in CA3 is highly facilitated due to LTP.
　　Finally, we will show an example of human seizure activity intracranially recorded at the hippocampus. The time series of the seizure was divided into 10 s epochs, and correlation dimensions were estimated in those epochs. The correlation dimension at the initial stage is quite high and reduces with time. This suggests that synchronization of neuronal activity is facilitated with time. Attractors in phase-spaces and one-dimensional return maps at earlier stages are just messy, and the structure of the attractor changes with time. At an intermediate stage where correlation dimension is quite low, the one-dimensional map clearly shows chaotic features. When the synchronization is extremely facilitated at the final stage, chaotic activity bifurcates to a limit cycle and the seizure stops.
　　Spatial complexity reduces when synchronization of neuronal activity in the brain is facilitated by afferent input or in some pathological cases. However, temporal complexity of rhythmic brain activity remains and the survived temporal complexity shows chaotic features.

Hatsuo Hayashi
Associate Professor,
1983 Dr. Eng., Kyushu University (Electronics)
1976 Assistant Professor, Kyushu University
1987 Associate Professor, Kyushu Institute of Technology

I am recently interested in nonlinear dynamical features of the brain activity which are related to brain functions.

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Detecting a Driven Nonlinear Oscillator Underlying Experimental Time Series: The Sunspot Cycle

Milan Palus
Institute of Computer Science AS CR, Czech

The historical data of the sunspot index have been attracting researchers for more than a century. In 1852 Wolf reported the now well-know 11-year cycle. Of course, the sunspot cycle is not strictly periodic, but fluctuations in its amplitude as well as in its frequency occur. Therefore researchers have turned towards stochastic models in order to make predictions of the future behavior of the sunspot cycle. On the other hand, development in nonlinear dynamics and theory of deterministic chaos, namely methods and algorithms for analysis and prediction of (potentially) nonlinear and chaotic time series have naturally found their way into the analyses of the sunspot series. Several authors have claimed an evidence for the deterministic chaotic origin of the sunspot cycle, based on estimations of correlation dimension, Lyapunov exponents and an increase of a prediction error with a prediction horizon. The dimensional algorithms, however, have been found unreliable when applied to relatively short experimental data, and properties consistent with stochastic processes (colored noises) such as autocorrelations can lead to spurious convergence of dimensional estimates. Similar behavior has been observed also for Lyapunov exponent estimators. And the increase of a prediction error with an increasing prediction horizon is not a property exclusive for chaos, but it can also be observed in systems with a deterministic skeleton and an intrinsic stochastic component (``dynamical noise'').
　　Looking for deterministic chaos in experimental time series, a statistical technique of surrogate data based on rejection by a statistical test of an appropriate null hypothesis has become a standard in nonlinear time series analysis. Applying this approach, the deterministic chaotic origin of the sunspot cycle has not been confirmed, just some (unspecified) nonlinearity has been found in this data. It is also questionable whether the hypothesis of a closed stationary autonomous system possessing a strange attractor is a reasonable explanation of the dynamics underlying the solar cycle. It might be reasonable, on the other hand, to search for a weaker hypothesis than a chaotic attractor, which, however, would provide a physical meaning to the previously confirmed (unspecified) nonlinearity in the sunspot cycle dynamics. In particular, a property of nonlinear oscillators -- mutual dependence between their instantaneous amplitude and frequency is tested in the yearly and monthly records of the sunspot numbers using the histogram-adjusted isospectral surrogate data and the Barnes model as the ARMA surrogates. The instantaneous amplitudes and frequencies are obtained by means of the analytic signal approach using the discrete Hilbert transform. In several tests the amplitude-frequency correlation has been found significant on levels ranging from p<0.03 to p<0.07, which supports the hypothesis of a driven nonlinear oscillator as a mechanism underlying the sunspot cycle, unless the amplitude-frequency relation is explained by a different mechanism.
　　The presented approach can be applied also in analysis of different potentially nonlinear and non-stationary time series in order to assess their nonlinear dynamical origin.

Milan Palus
1963 Born in Bojnice, Slovakia
1986 RNDr (MSc equivalent) Charles University Prague (Mathematical Physics)
1992 CSc (PhD equivalent) Czechoslovak Academy of Sciences, Prague (Computer Science)
1992 Visiting Fellow, Center for Complex System Research, Beckman Institute, University of Illinois at Urbana-Champaigne
1992 - 1994 Postdoctoral Fellow, Santa Fe Institute (Fogarty International Research Fellowship, National Institutes of Health)
1996 Visiting Scholar, School of Mathematics, Queensland University of Technology, Brisbane, Australia
1994 - present Researcher, Department of Nonlinear Modelling, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague

Detection and characterization of nonlinear phenomena in experimental time series. Applications in physics, meteorology, climatology, physiology, engineering, economy and finance.

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Reconstruction and Prediction of Nonlinear Dynamical Systems: Neural Net Approach

Takashi Matsumoto
Waseda University

When nonlinearity is involved, time series prediction becomes a rather difficult task where the conventional linear methods have limited successes for various reasons.
　　One of the greatest challenges stems from the fact that typical observation data is a scalar time series so that dimension of the nonlinear dynamical system (embedding dimension) is unknown.
　　This paper proposes a Hierarchical Bayesian approach to nonlinear time series prediction ploblems with neural net. This class of schemes considers a family of prior distributions parameterized by hyperparameters instead of a single prior so that it enables algorithms less dependent on a particular prior. One can estimate posterior of parameters, hyperparameters and embedding dimension by marginalization with respect to the parameters and hyperparameters.

Takashi Matsumoto
Professor, Department of Electrical, Electronics and Computer Engineering, Waseda University

1973 Ph.D., Waseda University (Electrical Engineering)
1973 Associate Professor, Waseda University
1977-79 Visting Research Scientist, U.C.Berkeley
1980 Professor, Waseda University

Field of Interests: Nonlinear time series prediction problems, Bifurcation/Chaos, On-line signature verification via HMM, IC design/implementation

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Modelling Finanfial Time Series With Continuous-Time Non-Linear Autoregressions

Peter Brockwell
Colorado State University

Continuous-time autoregressive (CAR) processes have been of interest to physicists and engineers for many years (see e.g. Fowler (1936)). Early papers dealing with the properties and statistical analysis of such processes, and of the more general continuous-time autoregressive moving average (CARMA) processes, include those of Doob (1944), Bartlett (1946), Phillips (1959) and Durbin (1961). In the last ten years there has been a resurgence of interest in continuous-time processes partly as a result of the very successful application of stochastic differential equation models to problems in finance, exemplified by the derivation of the Black-Scholes option-pricing formula and its generalizations (Hull and White (1987)). Numerous examples of econometric applications of continuous-time models are contained in the book of Bergstrom (1990). Continuous-time models have also been utilized very successfully for the modelling of irregularly-spaced data (Jones (1981)). At the same time there has been an increasing realization that non-linear time series models provide much better representations of many empirically observed time series than linear models. The threshold ARMA models of Tong (1983) have been particularly successful in representing a wide variety of data sets, and the ARCH and GARCH models of Engle (1982) and Bollerslev (1986) respectively have had great success in the modelling of financial data. Continuous-time versions of ARCHand GARCH models have been developed by Nelson (1990). In this paper we discuss continuous-time ARMA models, their basic properties, their relationship with discrete-time ARMA models, inference based on observations made at discrete times and non-linear processes which include continuous-time analogues of Tong's threshold ARMA models.
　　A general class of non-linear continuous-time autoregressive processes is defined, which includes continuous-time analogues of the threshold models of Tong. Questions of existence and uniqueness of solutions of the defining stochastic differential equations are considered as well as methods for numerical approximation. The question of fitting such models to data observed at discrete times is considered together with the use of such models for forecasting future values of the series.
　　The use of such models is illustrated by fitting them to Australian financial time series. It is found that the non-linear models provide a very good representation of the changing volatility of the series.

References:
Bartlett, M.S. (1946). On the theoretical specification and sampling properties of autocorrelated time series. J. Royal Statistical Soc. (Supplement)} 7, 27--41.
Bergstrom, A.R. (1990). Continuous Time Econometric Modelling. Oxford University Press, Oxford.
Bollerslev, T. (1986). Generalised autoregressive conditional heteroscedasticity. J. of Econometrics 51, 307--327.
Doob, J.L. (1944). The elementary Gaussian processes. Ann. Math. Statist. 25, 229--282.
Durbin, J. (1961). Efficient fitting of linear models for continuous stationary time series from discrete data. Bull. Int. Statist. Inst. 38, 273--281.
Fowler, R.H. (1936). Statistical Mechanics. Cambridge University Press, Cambridge.
Hull, J. and A. White (1987). The pricing of assets on options with stochastic volatilities. J. of Finance 42, 281--300.
Jones, R.H. (1981). Fitting a continuous time autoregression to discrete data. Applied Time Series Analysis II ed. D.F. Findley. Academic Press, New York, 651--682.
Nelson, D. (1990). ARCH models as diffusion approximations. J. of Econometrics 45, 7-38.
Tong, H. (1983). Threshold Models in Non-linear Time Series Analysis, Springer Lecture Notes in Statistics 21. Springer-Verlag, New York.

Peter Brockwell
Professor of Statistics, Colorado State University
1967 Ph.D. Australian National University (Stochastic Processes in Transport Theory)
1965-1970 Assistant Mathematician, Argonne National Laboratory
1970-1973 Associate Professor of Statistics, Michigan State University
1974-1976 Professor of Statistics, La Trobe University
1976-1988 Professor of Statistics, Colorado State University
1982-1984 Visiting Professor of Mathematics, Kuwait University
1988-1989 Professor of Statistics, Melbourne University
1993-1997 Foundation Professor of Mathematics, Royal Melbourne Institute of Technology

Stochastic processes and their applications in physics, biology and economics. Time series and their applications. Coauthor with Richard Davis of Time Series: Theory and Methods, Introduction to Time Series and Forecasting, and ITSM for Windows.

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Yukito IBA
The institute of Statistical Mathematics and SOKEN-DAI

We can find various kinds of symbolical structures behind the activities of our daily life. Natural languages that we speak and write are the most remarkable, but not the only example of the representations with symbolical structures. How we code the landscape around us as a cognitive map? How we can identify an object in complex scenes? These questions naturally lead to the quests for the symbolical structures in our mind, which will be essential for understanding the cognitive behavior of us. Such a study is also relevant for automatic analysis of complex data from the real world.
　　In the history of cognitive sciences, many efforts are devoted for the investigation of the symbolical structures embedded in our mind. Now we know that the scope of our explorations should not be restricted to the special types of symbols such as the ones in logical formulas. We need more flexible notions of symbols and they should be understood in connection with other structures, e.g., geometrical representations. Another important issue in this field is that our quest for the symbolical mind should be extended beyond that of human beings. Other primates, birds, and even animals very different from us, may have symbolical representations in their minds and communicate with them.
　　Statistical scientists also have much interest in symbolical structures. In the studies of the statistical information processing, major success was obtained with geometrical representations (e.g., multidimensional scaling) and the use of geometrical constraints (e.g., smoothness prior). Recent developments of artificial neural network models may change the situation, but it is still not accomplished yet. Now, many researchers in this field consider that innovative use of the models with symbolical structures, or, the models that create the symbols by themselves, is essential in the analysis of complex patterns in data.
　　In the "complex system" paradigm, researchers mainly concerned with the emergence of symbols in artificial worlds. Such a "constructive" approach can be a powerful way to understand the nature of symbolical structures. They are, however, not independent of traditional studies: (1) It is important to study the cognitive symbols in the real animals or human beings with the reference to the simulations. (2) Studies on the statistical models that generate the symbols in the learning process are closely related to the study of emergence of the symbols. (3) When we simulate an artificial world, we need good representation as a tool for the analysis of the simulations --- That is, constructive and traditional (or "descriptive") approaches are closely related in several different ways.
　　In this session of the symposium, we will discuss the cognitive science of symbols in human beings and animals. We also discuss the emergence of symbolical structures in robots and agents in computer worlds. With these examples, we explore flexible notions of the symbols and the emergence and embedding of symbols in other representations.

In Tani's talk, autonomous robots are constructed and used as a tool for exploration of the emergence of symbols. These robots develop symbolical structures in their "mind" through the interaction with an environment and use them for a given task. On the other hand, in a computer world constructed by Hashimoto, agents developed a system of language through mutual communications. The studies of Tani and Hashimoto are regarded as typical examples of the "complex system" approach to symbols.
　　The other speakers, Inoue, Edelman, and Okanoya give lectures on different examples of symbolical structures in real worlds. Inoue discuss the relevance of culture and sociological factors in the study of natural languages. Edelman's talk treats the higher vision problem, i.e., how we recognize or categorize objects in a scene. It is relevant for the understanding of pre-language symbolical structures in our mind. Okanoya gives a survey of his study on bird's song, which is an interesting example of "language" of animals that are far from human beings. These lectures will be useful to understand the perspective of the problem that we treat in this session.
　　It is interesting to compare the works of Inoue, Edelman and Tani, because they treat related topics with very different methodologies and backgrounds. How "complex system" paradigm can contribute to the problems arising from the studies of Inoue, Edelman, and Okanoya? We leave this interesting and difficult question for the discussion in the symposium. On the other hand, statistical methods are conveniently used in many of these works: For example, in Tani's work, recurrent neural networks are used as a "brain" of the robots. Multidimensional scaling is used in Hashimoto'work (and, perhaps, in Edelman's work) for the analysis of data. We are interested in the interaction of both directions; how statistical methods can contribute their studies and how their works can contribute statistical sciences.
　　And, etc. etc.--- I hope that interactions among people working in different fields and policies give fruitful results !

Yukito IBA
Yukito Iba is an assistant professor of the Graduate University for Advanced Studies and the Institute of Statistical Mathematics.

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A Dynamical Systems Approach to Represent Cognition of Robots

Jun Tani
Sony Computer Science Laboratory

We speculate that the problems of cognitions commence when the robots attempt to acquire certain form of representation of the world so that they can mentally simulate or plan their own behavior sequences. In considering representation, it is important to consider how the representation can be grounded to the physical environments and how the mental processes manipulating them can be situated in the behavioral contexts. We study these problems with focusing on tasks of the robot navigation learning.
　　In the conventional approach of the robot navigation problems,　a robot collects the sequences of the landmark-types and try to build the chain representation of them in the form of finite state machines (FSM) as the topological map of the environment. Although it is true that this approach could provide an adequate representation of a given environment in ideal situations, the symbolic representation of the FSM can cause the symbol grounding problems in real physical situations. The symbol grounding problem is a general problem, as discussed by Steven Harnad, that discrepancies which occur between the objects in the physical environment and their symbolic representations in the system cannot be resolved autonomously through the system's own operations.
　　We have investigated this problem from the dynamical systems perspectives. We speculate that real number systems best represent the mental activities of robots. We expect that the chaotic dynamics may serve as a basis for the mental activities of robots, as the theories of symbolic dynamics \cite{Crutchfield89,Pollack91,Tani95b} have shown that chaos exhibits a certain linguistic complexity. When the internal dynamics, which describe the mental processes of the robot, and the environment dynamics are coupled together through the sensory-motor loop, those two dynamics would share the same metric space. We consider that the mental processes of the robots can be naturally situated to the environments as the coherence is achieved between those two dynamics interacting each other in the same phase space. An important objective here is to unify the two separate entities for ``descriptions'' and their ``manipulations'' in the systems into one entity within the framework of the time-development of dynamical systems. Since it is highly speculated that all there exist in the cognitive processes are the time development of the dynamical systems, there might be no symbols whcih cause the symbol grounding problems in our proposed systems.

Jun Tani
Jun Tani is a senior researcher at. He started his professional career as a piping engineer for chemical plants. Later he became interested in researches in complex systems, robotics, neural modeling, cognition and consciousness problems. He received PhD in electrical engineering from Sophia University in 1994. Currently, he is jointly appointed to a visiting associate professor in graduate school of arts and sciences in University of Tokyo.

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Communication and Emergence of Languages in Toy Worlds

Takashi Hashimoto
RIKEN

Our cognitive activities are based on articulating the world and symbolizing the articulated entities. We group the symbols and recognized them as unite objects. The system how we articulate and recognize the world and how they group entities in the world is called a categorical structure. To know how the categorical structure is established and develops is a key to study emergence of symbols.
　　We study dynamical changes of categorical structures in language users via communication by constructing artificial toy worlds using computer simulations. We study development of categorical structure based on the dynamical view of language. The dynamical view is that meanings of words are dynamically created through activities of sense-making by individual language users. In this view, we do not think that words are statically linked with their indicating objects a priori. Words are situated in a web of relationships among words according to the usage of the word in each use. The whole web of relation among words is a kind of representation of meaning. The relationships are derived from the usage of words in language.
　　We model development of categorical structure in language users by a constructive approach. The constructive approach is to build models with elements having internal dynamics that interact with each other, and then to observe the emergence of global behavior of the system. The elements in our model are language-using individuals having word relation matrices as their internal structure. They communicate by uttering and accepting sentences. Words in sentences are situated in relation with other words by each individual and word relationship dynamically changes with communication. They do not share any grammatical or semantic structure at first but an inference algorithm to calculate relationship among words from the usage of words in sentences and in a chain of conversations.
　　How words are organized in word relationship and how the relationship dynamically changes with conversation are observed by simulating "conversation" in which individuals speak and listen sentences. Words make clusters in the word relationship matrix according to the mutual relationship among words. This clustering is through of as categorization by each individual, since words in a cluster have strong relation and have weak relation with ones outside of the cluster. The cluster has a structure like prototype category. Relation between words gradually changes from strong to weak and boundaries of clusters are fuzzy. The large changes in the cluster structure are induced by appearing new words or new usage of words. A shared part to individuals in word relationship develops with conversation. However whole of relationship does not become to be the same among individuals. Since each individual has its own experience of communication by conversing with various individuals, interrelation among individuals ever changes. As the result of ever-changing relation, coexisting commonality and individuality of categorical structure is observed in an ensemble of individuals.

Takashi Hashimoto
1996 Ph. D. University of Tokyo 1996-1999 Special Postdoctoral Resercher at The Institute of Physical and Chemical Research (RIKEN) 1996　

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Spatial Cognition and Relativity

Kyoko Inoue
Keio University

Recently in the field of linguistics, human cognitive ability is discussed in conjunction with their ability to categorize. Accordingly, stronger interests have been drawn on the fact that people process information based on their habitual experience in everyday life. This is one approach toward answering to our year-long question, "which comes first, reality or language?"
　　In this paper, I will present a model of conceptual constraints in spatial conception and language in reference to the previous studies conducted by Cognitive Anthropology Research Group (CARG) at Max Planck Institute for Psycholinguistics. The "Space Project" of CARG, which was a cross-linguistic study in more than 15 field sites where languages other than Indo-European were spoken, revealed two distinct spatial frames of reference: the egocentric (RELATIVE) and the environmental (ABSOLUTE). A case study in a Japanese community will be examined here in order to search for the possible conceptual constraints. More concretely, field results will be discussed in terms of (1) linguistic frames of spatial reference, (2) socio-cultural extension of space, and (3) communication disorder.
　　Japanese, like many Indo-European languages, possesses both RELATIVE and ABSOLUTE frames of reference, although its present linguistic system is overwhelmingly RELATIVE. A close comparison of the usage of RELATIVE and ABSOLUTE spatial lexemes in communication will illustrate the effect on how the human relationship has come to be recognized differently over the century, in the course of which the Japanese has switched from ABSOLUTE to RELATIVE linguistic system.

Kyoko Inoue
Assistant Professor, Keio University
1993 Ph.D., University of Illinois at Urbana-Champaign (Anthropology)
1993-95 Post Doctoral Researcher, Max Planck Institute for Psycholinguistics
1995 Assistant Professor, Faculty of Science and Technology, Keio University

The research of linguistic anthropology with a focus on the relationship between grammatical categories and conceptualization of environmental information. Her special interests rest on the system of nominal classification as well as human spatial cognition.

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Core Problems in High-Level Vision

Shimon Edelman
University of Sussex, UK

I shall discuss the following three core problems of high-level vision: (1) generalization of object recognition across changes in viewpoint, (2) recognition of novel instances of familiar categories of objects, and (3) representation and processing of structural information. The approach taken by the human visual system vis a vis these problems, as characterized by psychophysical, electrophysiological and imaging studies, will be examined and compared with expectations stemming from theories collectively labeled as ``classical'' symbolic AI.
　　At present, both the emergence of a comprehensive theory of object recognition in the brain and the development of better computer vision algorithms for recognition are impeded by our lack of understanding of the nature of the memory trace left by perceived objects in the visual system. From a computational standpoint, this Problem of Representation of object shapes has several aspects, paralleling the list of core recognition tasks mentioned above. First, to achieve generalization across viewpoints, any computational model of recognition must explain how to represent objects internally in such a manner that the variability of their appearance caused by changing viewing conditions will not disrupt recognition. Thus, on the face of it, representing each object by a few of its ``snapshots'' will not do, because different views of the same object may appear quite dissimilar. Second, any model of recognition must be open-ended, that is, able of accommodating a potentially infinite variety of novel instances of objects. As before, template-like representations seem to be incapable of meeting this challenge, because different instances of the same category may differ in various unexpected ways. Third, a comprehensive model must also provide a mechanism for making sense of completely new shapes, which are not members of any of the familiar categories; by extension, such a mechanism would automatically support the processing of scenes (that is, arbitrary compositions of objects).
　　Until recently, the only theoretical approach to representation capable of satisfying these computational requirements was structural decomposition. In structural models, object shapes are described in terms of relatively few generic components, joined by spatial relationships chosen from an equally small fixed set. The discrete, symbolic nature of the resulting representation can, in principle, achieve invariance with respect to viewpoint by abstracting away the unnecessary details of the shape. Likewise, the representation of novel instances of familiar categories may be possible through the standardization of the primitives (components and their relationships). Finally, if these primitives are sufficiently varied, a great many arbitrary shapes and scenes can be described, just as tens of thousands of spoken words can be generated using a small number of phonemes as components.
　　This symbolic/compositional approach to representation is now being challenged both as a model of human performance (which falls short of viewpoint invariance, and is limited in various ways insofar as the processing of novel objects is concerned), and as a blueprint for computer vision (where no full-fledged system based on structural representations was ever implemented). The analysis of data from biological vision, accompanied by computational experiments, suggests an alternative approach, centered on graded similarity computation instead of logical manipulation of symbols. If this idea proves to lead to a viable theory of object representation, the symbolic paradigm that currently dominates other branches of cognitive science, such as linguistics, would require a revision.

　

　

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A GENERATIVE GRAMMAR FOR THE BIRDSONG AND ITS BRAIN REPRESENTATION

Kazuo OKANOYA
Department of Cognitive and Information Sciences, Faculty of Letters, Chiba University and PRESTO, Japan Science and Technology Corporation.

Birdsong is a hierarchical behavior that is controlled by a set of discrete forebrain nuclei. Male Bengalese finches sing complex songs by arranging several discrete phonological elements into temporally dynamic sequences. Each song elements are organized into several *chunks,* and these chunks are arranged by a finite state grammar. Furthermore, adult birds rely on auditory feedback to produce normal songs and neural substrates for song production are lateralized into the left hemisphere.　These　characteristics makes Bengalese finch song much similar to the human language than any other birdsongs. Why is this so?　　　Song is a sexual behavior in oscine songbirds. In general, males sing and females assess the quality of the male based on the song. We first asked whether the song complexity affects reproductive behavior in female birds. Two groups of eight birds were each kept in a sound proof chamber. One group of birds　were stimulated by a complex song while the other heard a simple song. We counted numbers of the eggs laid and numbers of nesting strings carried into the nest by each bird for 4 weeks. In addition, we collected blood samples before and after the experiments and these samples were used to assay the blood content of Estradiol. Results turned out that in all indices　measured, the birds in the complex song group scored higher. Thus, complex songs are more effective in stimulating female reproductive behavior.
　　Within the song control system, it has been suggested that HVC　controls phrase-level structure of the song and RA controls phonology of each song element. There are several other nuclei in the song system whose functions are not known. Some of these include the Nif that is afferent to HVC, and the LMAN and area X, both are in the recurrent pathway connecting HVC and RA indirectly. We sought to examine the functions of these nuclei in Bengalese finches by anatomical and physiological techniques. When area X was destroyed, a symptom similar to *stuttering* was observed; the bird repeated a particular element many times before proceeding into the next element. By lesioning Nif, the complex syntax of the Bengalese finch song changed into simple one. When a part of HVC was destroyed, some chunks disappeared form the song. Based on these results, we are now ready to establish brain representation of the syntactical behavior.
　　In juvenile Bengalese finches, phonology of each song element is established first. Then, the ordering of these elements gradually changes and adult songs with complex syntax appear throughout development. This is reminiscent of the development of language in human infants. Although birdsong and human language might seem like quite apart in phylogeny and surely independently evolved, we may be able to establish the biology of language evolution based on analogical comparison between human languages and birdsongs. (Supported by PRESTO, JST).

Kazuo　Okanoya
Associate Professor, Chiba University
Researcher, Japan Science and Technology Corporation
1989 Ph.D.　in　Bioacoustics (University of Maryland, USA).
1989 Post Doctoral Fellow, Japan Society for the Promotion of Science
1993 Post Doctoral Fellow, Agency of Science and Technology
1994 Associate Professor, Chiba University
1996 Researcher, Japan Science and Technology Corporation

I am interested in functions and mechanisms of animal behavior. My ultimate goal is to understand evolution of language as a biological process. For this purpose, I am currently working of the birdsong system.

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Exploring Simulation Science for the 21st Century

Tetsuya Sato
National Institute for Fusion Science

It may be said that towards the dawning of 21st century Modern Science has reached to its completeness. The jigsaw puzzle of Modern Science framed by the Reductionism has yet unpaved parts left behind. However, they will be completed sooner or later. "Science of Complex Systems", which is spreading over the would around the Santa Fe Institute, aims at revealing laws that govern the behaviors of many-body systems (complex systems) whose first interacting principles are almost impossible to find. Towards that aim one assumes an artificial simple rule for the evolution of an element of a complex system and follows its evolution repeatedly by, say, using a personal computer. Then, one compares the obtained spacial or temporal pattern with a similar one that is observed in a real world and hypothesizes that the given rule must be the rule that governs the real world. In contract, we, the computer simulation group at NIFS, have been exploring for nearly 20 years the 21st Century's Science with a new conception. The methodology is based on the fundamental interaction forces, or, the fundamental　equations,　that Modern Science has been revealing for more than 300 years since Descartes and Newton. The essential tools for exploring this science, so-called "Simulation Science", are advanced supercomputers and visualization technologies.
The procedure of Simulation Science is as follows:
1.　To solve all kinds of phenomena of nonlinear, nonequilibrium, and open systems which occur in nature and laboratories.
2.　To extract common rules or characteristics by comparing the simulation results.
3.　To propose a working hypothesis that rules complex systems irrespectively of governing interaction forces.
4.　To upgrade the hypothesis by performing further simulations where the key agents of the complexity, such as the information (energy, entropy, etc) exchange between the complex system and the external world, are changed.
5. To systematize the upgraded hypothesis by applying it to other complex systems such as the social complexity, the economic complexity, and the biological complexity where interaction forces are unclear.
　　In this talk, an innovative research strategy called "MISSION" and the present status of research accomplished by the above-mentioned procedure will be described. More specifically, a self-organization hypothesis obtained by investigating macro and micro plasma complexities, polymer crystallization, generation and reversal of geodynamo, etc., will be presented.

Tetsuya Sato (Doctor of　Engineering , Kyoto University)
Professor, National Institute for Fusion Science
1967 Research Associate, Kyoto university
1974 Lecturer, University of Tokyo
1976 Associate Professor, University of Tokyo
1980 Professor, Hiroshima University
1989 Professor, National Institute for Fusion Science

Theoretical and simulation researches on nonlinear phenomena in space plasmas such as aurora and magnetosphric substorms. Simulation research on nonlinear dynamics of fusion plasmas. Currently, he is devoted himself on promoting Simulation Science as cultivating a new paradigm of science.

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Earthquake Scale-Invariance, Their Modelling and Prediction

Yan Kagan
UCLA

To study statistical properties of earthquake occurrence, we analyze several earthquake catalogs which include origin time, hypocenter, earthquake size (scalar seismic moment), and focal mechanism orientation for each earthquake. The seismicity is represented as a stochastic, tensor-valued, multidimensional, point process.
　　Earthquake process exhibits scale-invariant properties (Kagan, 1994): (1) Earthquake size distribution is a power-law (the Ishimoto-Iida or Gutenberg-Richter relation for magnitudes or the Pareto distribution for seismic moment). Conservation of energy requires that the size distribution should be limited on the high side; thus we use the gamma distribution with a maximum size for the largest earthquakes. Both the slope of the distribution and the maximum moment have universal values for shallow earthquakes (depth interval 0-70 km), occurring in continents and continental boundaries (Kagan, 1997a). (2) Shallow earthquakes have a power-law rate decay of the aftershock and foreshock occurrence (Omori's law), i.e., their temporal pattern is fractal. (3) Spatial distribution of earthquakes is also self-similar: as the time span of a catalog increases, the correlation dimension of earthquake hypocenters asymptotically reaches the value 2.2 for shallow earthquakes. (4) The three-dimensional disorientation of earthquake focal mechanisms is approximated by the rotational Cauchy distribution. (5) We investigate the statistical properties of incremental static stress caused by earthquakes. Theoretical calculations, simulations and measurements of the rotation of earthquake focal mechanisms suggest that the stress in the earthquake focal zones follows the Cauchy distribution which is one of the stable probability distributions.
　　We offer a model of random defect interaction in a critical stress environment which seems to explain most of the available empirical results. In the time domain, Omori's law of foreshock/aftershock occurrence and, in general, the temporal complexity of earthquake events and their temporal clustering, is a consequence of a Brownian motion-like behavior of random stress due to defect dynamics. Similarly, the presence, the evolution, and the self-organized aggregation of the defects in the rock medium are responsible for complex, fractal spatial patterns of earthquake faults. The Cauchy and other symmetric stable distributions govern the stress caused by these defects, as well as the random rotation of focal mechanisms. The stable distributions have a power-law tail (i.e., they are scale-invariant and should yield fractal fault patterns).
　　We discuss several definitions and possible classifications of earthquake prediction methods (Kagan, 1997b). An empirical search for earthquake precursors which forecast the size of an impending earthquake, has been fruitless. The most probable consequence of earthquake self-similarity is lack of earthquake predictability as a forecast of a specific individual earthquake. Many small earthquakes occur throughout seismic zone, demonstrating that the critical conditions for earthquake nucleation are satisfied almost everywhere; apparently, any small shock can grow into a large event. Thus, it is likely that an earthquake has no preparatory stage. Although earthquake prediction, as popularly defined, may well be impossible, the seismic moment conservation principle, combined with space geodetic data, offers a new way to evaluate the seismic hazard, not only for tectonic plate boundaries, but for areas of low seismicity, i.e., the interior of continents. Earthquake clustering with the power-law temporal decay (Omori's law) can be used to estimate the time-dependent rate of future earthquake occurrence.

REFERENCES
Kagan, Y. Y., 1994. Observational evidence for earthquakes as a nonlinear dynamic process, Physica D, 77, 160-192.
Kagan, Y. Y., 1997a. Seismic moment-frequency relation for shallow earthquakes: Regional comparison, Journal of Geophysical Research, 102, 2835-2852.
Kagan, Y. Y., 1997b. Are earthquakes predictable?, Geophysical Journal International, 131, 505-525.

Yan Y. Kagan
Research Geophysicist, Institute of Geophysics and Planetary Physics, University of California, Los Angeles, USA
1968 Ph.D. in Physical and Mathematical Sciences, Institute of the Physics of the Earth, USSR Academy of Sciences,
1957-1960 Researcher, Geophysical Research Institute, Moscow
1960-1974 Research Geophysicist, Mining Institute, USSR Academy of Sciences, Moscow
1974-present Research Geophysicist, Institute of Geophysics and Planetary Physics, University of California, Los Angeles, USA

RESEARCH INTERESTS: Earthquake statistics, modeling of earthquake occurrence, earthquake prediction and hazard assessment

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Signal Extraction and Knowledge Discovery by Statistical Modeling

Genshiro Kitagawa
The　Institute of Statistical Mathematics

In statistical analysis, a model is built based on not only the current data but also prior knowledge on the object and the objective of the analysis. By the use of a proper model, it becomes possible to combine　various　knowledge on the object or the information from current and other data sets. This makes it possible to extract useful information　which cannot be obtained by simple manipulation of the current data　and may result in important knowledge or discovery in sciences.　On the other hand, there is a danger of extracting biased result　if an analysis is made by using improper model. Therefore, in the analysis based on statistical modeling,　use of proper model is crucial.
　　In statistical modeling, the development of proper model class,　model evaluation criterion and computationally efficient procedure　is necessary.　Akaike information criterion AIC is an objective criterion　to evaluate the goodness of fit of statistical models.　In time series modeling, the state space model is a unified platform for developing structural time series models.　The non-Gaussian filter and smoothing algorithms then provide　unified method for the prediction, signal extraction and　parameter estimation.　A proper use of these tools facilitates the development of semi-automatic statistical information　processing procedures.
　　In this talk, the process of signal extraction and knowledge discovery based on the modeling by structural time series models,　is exemplified by the signal extraction problems in seismology　and the financial and economic data.
The examples include
1)　Estimation of arrival times of seismic signals.
2)　Extraction of small seismic signal in noisy data.
3)　Detection of coseismic effect in ground water level data.
4)　Seasonal adjustment of economic time series.

Genshiro Kitagawa
Professor, The Institute of Statistical Mathematics,
1973 Graduated from Tokyo University, Graduate School of Science
1974 Researcher, The Institute of Statistical Mathematics
1985 Associate Professor, The Institute of Statistical Mathematics
1991 Professor, The Institute of Statistical Mathematics

His main research interests are the time series snalysis and　statistical modeling. His recent research area includes nonlinear non-Gaussian state space modeling and extendsion of the information criterion based on numerical method. He joins many cooperative reserch projects in earth science and　finance/economics.

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Object Recognition: More Than Remembrance of Things Past?

Shimon Edelman
University of Sussex, UK

To recognize a previously seen object, the visual system must overcome the variability in the object's appearance caused by illumination, pose, and, for articulated or flexible objects, by the effects of the additional degrees of freedom peculiar to such objects. Developments in computer vision suggest that it may be possible to achieve recognition invariant to these factors, by learning to interpolate between stored views of the target object, taken under representative combinations of viewing conditions. One may observe, however, that daily life situations typically require categorization, rather than recognition, of objects. Due to the open-ended character both of natural kinds and of artifical categories, categorization cannot rely on interpolation between stored examples. Nonetheless, knowledge of several representative members, or prototypes, of each of the categories of interest can still provide the necessary computational substrate for the categorization of new instances. The resulting representational scheme based on similarities to prototypes is readily mapped onto the mechanisms of biological vision revealed by recent psychophysical and physiological studies, and has intriguing implications for the understanding of the general issue of cognitive representation, and, in particular, of the manner in which representation can conform, or be faithful, to its object.

　

　

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Complex System Biology： An Introduction

Kunihiko KANEKO
Univ. of Tokyo

Basic problems for the construction of a scenario for the Life are discussed. Starting from the complementarity betwee syntax/rule/logic and semantics/behavior/image, the following problems are highlighted; intrinsic diversification, recursive type formation, rule generation, formation of internal representation, macroscopic robustness at an ensemble level, fixation of differentiation to symbols. To study these basic problems ``intra-inter dynamics" is introduced, which consists of internal dynamics of a unit, interaction among the units, and the replication (and death) of units according to their internal states.
　　Applying the above idea to cell differentiation, isologous diversification theory is proposed. According to it, orbital instability leads to diversified cell behaviors first. At the next stage, several cell types are formed, first triggered by clustering of oscillations, and then as attracting states of internal dynamics stabilized by the cell-cell interaction. At the third stage, the differentiation is determined as a recursive state by cell division. At the last stage, hierarchical differentiation proceeds, with the emergence of stochastic rule as is seen in the differentaition from a stem cell, where regulation of the differentiation emerges spontaneously. It is shown that `internal image' is formed in the internal dynamics that follows the interaction term. Relevance of our results to cell biology is discussed.
　　Next, a consequence of this theory to evolution is discussed. It is shown that the evolution (speciation) proceeds as genetic fixation of interaction-induced phenotypic diversification. Although the theory is consistent with the central dogma of molecular biology and Darwin's theory, the consequence is rather different from the conventional view on the evolution. Experimental verification is also discussed.
　　Then, problems of energy transdutcion in to molecular motor are discussed from our viewpoint, where a `toy protein' with coupled pendula show energy absorpotion and stroage, through dynamic differentiation mechanism.
　　Last, if I have time, I would like to mention few remarks for symbolization and rule generation in a language system, by extending dynamical systems to functional domain. In particular, possible relatioship with coginitive semantics will be discussed.

Kunihiko KANEKO
Born July 6, 1956 in Japan

Department of Pure and Applied Sciences,
College of Arts and Sciences, Univ. of Tokyo, 3-8-1, Komaba, Meguro, Tokyo 153, Japan
Ph. D. (1984, March) Univ. of Tokyo

Research and professional Experience
postdoctoral fellow, Japan Society for the Promotion of Science, Univ.　of　Tokyo, 1984 April-1984 October
postdoctoral fellow, Center for Nonlinear Sudies, Los Alamos National Laboratory, 1984 October-1985 March
Joshu (assistant professor), Institute of Physics, Univ. of Tokyo, 1985 March-1990 July
Visiting fellow by Japanese government program, Univ. of Illinois at Urbana-Champaign, 1987 October-1988 July
Stanislaw Ulam Visiting Scholar, Center for Nonlinear Studies, Los Alamos National Laboratory, 1988 September- 1989 September
Asscoiate Professor, Department of Pure and Applied Sciences, Univ. of Tokyo, 1990 July--- 1994 August
Professor, Department of Pure and Applied Sciences, Univ. of Tokyo, 1994 August --- Present

Research Field
Chaos,High-dimensional chaos, in particular coupled maps, and complex system biology.
By introcuing coupled map lattices and global coupled maps, he has been working on several aspects of high-dimensional chaos. Recently his main research interest is in the field of biology, where he is trying to establish a new field, `` complex system biology".

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