Abstracts of Invited Lectures

2012 Asia-Pacific Psychiatry  
Various kinds of scaling laws are often observed in complex dynamical systems; for instance, SOC and punctuated equilibrium near the edge of chaos, 1/f spectrum, long time tails and anomalous diffusion in non-hyperbolic systems, where the self-similarity structures play essential roles in dynamical space and induce the breaking of central limit theorem for gaussian regime. In the present paper we discuss three complex dynamical systems with non-gaussian scaling regime described by the Weibull
more » ... stribution. Though the universality of Weibull distribution functions has not yet been made clear, but it is surmised that the Weibull regime is omnipresent in the systems under consideration. In this work we study second and third order approximations of water wave equations of the KdV type. First we derive analytical expressions for solitary wave solutions for some special sets of parameters of the equations. Remarkably enough, in all these approximations, the form of the solitary wave and its amplitude-velocity dependence are identical to the sech 2 -formula of the one-soliton solution of the KdV. Next we carry out a detailed numerical study of these solutions using a Fourier pseudospectral method combined with a finite-difference scheme, in parameter regions where soliton-like behavior is observed. In these regions, we find solitary waves which are stable and behave like solitons in the sense that they remain virtually unchanged under time evolution and mutual interaction. In general, these solutions sustain small oscillations in the form of radiation waves (trailing the solitary wave) and may still be regarded as stable, provided these radiation waves do not exceed a numerical stability threshold. Instability occurs at high enough wave speeds, when these oscillations exceed the stability threshold already at the outset, and manifests itself as a sudden increase of these oscillations followed by a blowup of the wave after relatively short time intervals. In interacting many body systems such as nuclei, complex atoms, quantum dots, and quantum spin glasses, the interaction leads to quantum chaos characterized by ergodicity of eigenstates and level spacing statistics as in Random Matrix Theory. In this regime, a quantum computer eigenstate is composed by an exponentially large number of quantum register states and the computer operability is destroyed. Here we model an isolated quantum computer as a twodimensional lattice of qubits (spin halves) with fluctuations in individual qubit energies and residual short-range inter-qubit couplings. We show that above a critical inter-qubit coupling strength, quantum chaos sets in and this results in the interaction induced dynamical thermalization and the occupation numbers well described by the Fermi-Dirac distribution. This thermalization destroys the noninteracting qubit structure and sets serious requirements for the quantum computer operability. We then construct a quantum algorithm which uses the number of qubits in an optimal way and efficiently simulates a physical model with rich and complex dynamics. The numerical study of the effect of static imperfections in the quantum computer hardware shows that the main elements of the phase space structures are accurately reproduced up to a time scale which is polynomial in the number of qubits. The errors generated by these imperfections are more significant than the errors of random noise in gate operations. Recent developments in string and M-theory are reviewed with an emphasis on particle physics implications. Aspects of non-perturbative extended objects -branes are introduced. The focus is on the role these objects play in the construction of new four-dimensional solutions of string theory with the structure of the standard model and three families of quarks and leptons. A beautiful relationship of these constructions to purely geometric one, as an Mtheory compactified on special holonomy spaces is highlighted. The pressure and flow regulation in the individual functional unit of the kidney (the nephron) tends to operate in an unstable regime. For normal rats, the regulation displays regular selfsustained oscillations, but for rats with high blood pressure the oscillations become chaotic. The lecture explains the mechanisms responsible for this behavior and discusses the involved bifurcations. Experimental data show that neighboring nephrons adjust their pressure and flow regulation in accordance with one another. For rats with normal blood pressure, in-phase as well as anti-phase synchronization can be observed. For spontaneously hypertensive rats, indications of chaotic phase synchronization are found. Accounting for a hermodynamics as well as for a vascular coupling between nephrons that share a common interlobular artery, the lecture presents a model of the interaction of the pressure and flow regulation between adjacent nephrons. It is shown that this model, with physiologically realistic parameter values, can reproduce the different types of experimentally observed synchronization. Signals derived from the human cardiovascular system are well known to exhibit highly complex, nearly periodic, oscillatory behaviour whose nature is something of an enigma and still the subject of vigorous debate. The variation of cardiac frequency with time, known as heart rate variability (HRV), has been intensively investigated using both deterministic and stochastic methods. It has, for example, been variously described as chaotic, fractal, stochastic, and subject to 1/f fluctuations and it was proposed that the state of the system can be classified by the slope of its power spectrum on a log-log plot. tomography: Three-dimensional anatomical localization of spontaneous and stimulus-locked synchronization in the human brain Cerebral synchronization processes play an essential role under both physiological (Freeman 1975) and pathological (Llinás and Jahnsen 1982, Bergman et al. 1994) conditions. To detect and localize phase synchronization and stochastic phase resetting dynamics in the human brain non-invasively with magnetoencephalography novel methods have been developed:
doi:10.1111/appy.12002 fatcat:snd6hn73bvh5liawo4pkmxirue