Hokkaido University Collection of Scholarly and Academic Papers
(65.354 recursos)
HUSCAP (Hokkaido University Collection of Scholarly and Academic Papers) contains peer-reviewed journal articles, proceedings, educational resources and any kind of scholarly works of Hokkaido University.
Mostrando recursos 1 - 20 de 228
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Markov property and strong additivity of von Neumann entropy for graded quantum systems - Moriya, Hajime
The quantum Markov property is equivalent to the strong additivity of von Neumann
entropy for graded quantum systems. The additivity of von Neumann entropy
for bipartite graded systems implies the statistical independence of states. However,
the structure of Markov states for graded systems is different from that for tensorproduct
systems which have trivial grading. For three-composed graded systems we
have U(1)-gauge invariant Markov states whose restriction to the marginal pair of
subsystems is nonseparable.
4.
Neocortical gap junction-coupled interneuron systems may induce chaotic behavior itinerant among quasi-attractors exhibiting transient synchrony - Fujii, Hiroshi; Tsuda, Ichiro
Recent discovery of the massive presence of gap junction couplings among neocortical FS
(and LTS) interneurons poses serious questions about their collective dynamical behavior, and
their possible cognitive roles. We present here the theoretical possibility that a class of
neurons coupled by gap junctions may emerge spatio-temporal chaos itinerant among
attractors in Milnor’s sense, which in turn organizes synchronous cell groups transiently.
Some physiological observations from the neocortex, e.g., local field potential (LFP) data
exhibiting transient synchrony may provide evidence. We suggest also possible role in the
so-called binding problem.
5.
Chaotic itinerancy generated by coupling of Milnor attractors - Tsuda, Ichiro; Umemura, Toshiya
We report the existence of chaotic itinerancy in a coupled Milnor attractor system. The
attractor ruins consist of tori or local chaos generated from the original Milnor attractors.
The chaotic behavior exhibited by a single orbit can be considered a \non-stationary"
state, due to the extremely slow convergence of the Lyapunov exponents, but the behavior
averaged over randomly chosen initial conditions is consistent with the limit theorem. We
present as a possibly new indication of chaotic itinerancy the presence of slow decay of
large
uctuations of the largest Lyapunov exponent.
6.
Chaotic Itinerancy - Kaneko, Kunihiko; Tsuda, Ichiro
Chaotic itinerancy is universal dynamics in high-dimensional dy-
namical systems, showing itinerant motion among varieties of low-
dimensional ordered states through high-dimensional chaos. Discov-
ery, basic features, characterization, examples, and significance of
chaotic itinerancy are surveyed
7.
Fractal encoding in a chaotic neural network - Ryeu, J. K.; Aihara, K.; Tsuda, I.
We analyze a model of a chaotic neural network consisting of three neurons, namely a chaotically forcing
neuron and two neurons comprizing a stable response system with a contraction mapping property, for digital
encoding with chaotic dynamics. We show that dynamics of the chaotically forcing neuron is embedded in the
form of a code sequence on a fractal attractor of the two-neuron response system. We consider the relation
between the state transition of the chaotically forcing neuron and the hierarchical fractal structure on the
attractor in the state space of the contracting system. We also report hardware implementation of the presented
model with an analog electronic...
11.
Singularities of improper affine spheres and surfaces of constant Gaussian curvature - Ishikawa, Go-o; Machida, Yoshinori
We study the equation for improper (parabolic) affine spheres from the view point of contact geometry and provide the generic classification of singularities appearing in geometric solutions to the equation as well as their duals. We also show the results for surfaces of constant Gaussian curvature and for developable surfaces. In particular we confirm that generic singularities appearing in such a surface are just cuspidal edges and swallowtails
12.
Sharp-interface limit of the Allen-Cahn action functional in one space dimension - Kohn, Robert V.; Reznikoff, Maria G.; Tonegawa, Yoshihiro
We analyze the sharp-interface limit of the action minimization problem for the stochastically perturbed Allen-Cahn equation in one space dimension. The action is a deterministic functional which is linked to the behavior of the stochastic process in the small noise limit. Previously, heuristic arguments and numerical results have suggested that the limiting action should “count” two competing costs: the cost to nucleate interfaces and the cost to propagate them. In addition, constructions have been used to derive an upper bound for the minimal action which was proved optimal on the level of scaling. In this paper, we prove that for...
14.
Transition of global dynamics of a polygonal vortex ring on a sphere with pole vortices - SAKAJO, Takashi
We study the motion of a polygonal ring consists of identical vortex points
that are equally spaced at a line of latitude on a sphere with vortex points fixed
at the both poles. First, we calculate explicitly all the eigenvalues and the
eigenvectors corresponding to them for the linearized problem, from which we
consider the stability of the polygonal vortex ring in the presence of the pole
vortices. Next, when the number of the vortex points is even in particular,
the equations of the vortex points are reduced to those for a pair of two
vortex points by assuming a special symmetry. Studying the reduced system
mathematically and...
16.
Chaotic itinerancy is a key to mental diversity - Tsuda, Ichiro
Kampis proposes the study of chaotic itinerancy, pointing out its significance in domains of cognitive science and philosophy.
He has discovered in the concept of chaotic itinerancy the possibility for a new dynamical approach that elucidates mental states with a physical basis. This approach may therefore provide the means to go beyond the connectionist approach. In accordance
with his theory, I here highlight three issues regarding chaotic itinerancy: transitory dynamics, diversity, and self-modifying system.
19.
Functional relevance of 'excitatory' GABA actions in cortical interneurons : a dynamical systems approach - Fujii, Hiroshi; Aihara, Kazuyuki; Tsuda, Ichito
The non-classical, but frequently reported behavior of GABA[A] receptor-mediated excitation in mature CNS has long been regarded as a puzzle. We theorize that the function of cortical GABAergic interneurons, which might constitute a subsystem of brain's GABA interneurons, is their ability of switching from inhibitory action to excitatory action depending on the level of spatio-temporal activity in progress. From the perspective of a dynamical systems approach, such "excitatory" GABAergic responses may serve to temporarily invoke attractor-like memories when extensively activated by, for example, top-down signals as category information or attention, while an ongoing background state of GABA changes its action...
20.
Chaotic itinerancy as a mechanism of irregular changes between synchronization and desynchronization in a neural network - Tsuda, Ichiro; Fujii, Hiroshi; Tadokoro, Satoru; Yasuoka, Takui; Yamaguti, Yutaka
We investigate the dynamic character of a network of electrotonically coupled cells consisting of class I point neurons, in terms of a finite dimensional dynamical system. We classify a subclass of class I point neurons, called class I* point neurons. Based on this classification, we use a reduced Hindmarsh-Rose (H-R) model, which consists of two dynamical variables, to construct a network model consisting of electrotonically coupled H-R neurons. Although biologically simple, the system is sufficient to extract the essence of the complex dynamics, which the system may yield under certain physiological conditions. The network model produces a transitory behavior as...
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