arXiv subjects

Taishin Nomura

Publications and source records attributed to Taishin Nomura.

5 recordsLinked to original sources

arXiv2022

A Markov chain approximation of switched Fokker-Planck equations for a model of on-off intermittency in the postural control during quiet standing

The intermittent on-off switching of feedback control is considered as a major mechanism of postural stabilization during human quiet standing, which can be modeled by switched-type hybrid stochastic delay differential equations with unstable subsystems. Dynamics of the model can also be described by the corresponding switched-type Fokker-Planck (FP) equations. Here, we develop a comprehensive numerical recipe to simulate switched-type FP equations in the case that the probability current is conserved at the switching boundary, as is the case for noise-free models exhibiting C^0-continuity for solutions at the boundary, but in a way extendable to cases with discontinuous jump. Specifically, the FP equations are approximated by a finite state Markov chain model using the finite element method. Then, dynamics of the Markov chain model, including time evolution of probability density function (PDF), stationary PDF, and power spectrum of postural sway are analyzed. We further investigate how the stationary PDF alters as values of important parameters of the model change. Dynamics of the Markov chain model are compared with Monte Carlo-based dynamics of the model, by which the developed numerical recipe is validated. The obtained Markov chain model forms a basis of our future investigations of the intermittent postural control as a Markov decision process.

eess.SY↗

arXiv2018

Phase resetting and intermittent control at critical edge of stability as major mechanisms of fractality in human gait cycle variability

The fractality of human gait, namely, the long-range correlation that characterizes scale-free fluctuations of gait descriptors, such as the stride intervals during steady-state walking, depends on the well-tuned organization of the sensorimotor controller. Gait fractality is apparent in healthy young adults but tends to disappear in elderly individuals and neurological patients. Therefore, its partial loss may be indicative of pathological conditions. Despite its potential to be used as a dynamical biomarker for fall risk assessment, the mechanistic origin of gait fractality has been investigated by only a few studies, and even less attention has been devoted to the link between gait fractality and gait stability. Here, we propose a novel computational model of gait by addressing the flexibility-stability trade-off first, and then by showing that gait fractality is a natural consequence of the developed control mechanisms, including phase resetting and intermittent control, which supplement instability in a linear feedback controller operated at stability's edge. The results suggest that pathological gait, characterized by joint-rigidity and/or loss of fractality, may be caused by dysfunction in some of these mechanisms.

nlin.AO↗

arXiv2011

Gelfond-Bezier Curves

We show that the generalized Bernstein bases in Muntz spaces defined by Hirschman and Widder [7] and extended by Gelfond [6] can be obtained as limits of the Chebyshev-Bernstein bases in Muntz spaces with respect to an interval [a,1] as the real number, a, converges to zero. Such a realization allows for concepts of curve design such as de Casteljau algorithm, blossom, dimension elevation to be translated from the general theory of Chebyshev blossom in Muntz spaces to these generalized Bernstein bases that we termed here as Gelfond-Bernstein bases. The advantage of working with Gelfond-Bernstein bases lies in the simplicity of the obtained concepts and algorithms as compared to their Chebyshev-Bernstein bases counterparts.

math.NA↗

arXiv2011

A Muntz Type Theorem for a Family of Corner Cutting Schemes

By identifying a family of corner cutting schemes as a dimension elevation process of Gelfond-Bezier curves, we give a Muntz type condition for the convergence of the generated control polygons to the underlying curve. The surprising emergence of the Muntz condition in the problem raises the question of a possible connection between the density questions of nested Chebyshev spaces and the convergence of the corresponding dimension elevation algorithms.

math.NA↗

arXiv2011

Chebyshev Blossom in Muntz Spaces: Toward Shaping with Young Diagrams

The notion of blossom in extended Chebyshev spaces offers adequate generalizations and extra-utilities to the tools for free-form design schemes. Unfortunately, such advantages are often overshadowed by the complexity of the resulting algorithms. In this work, we show that for the case of Muntz spaces with integer exponents, the notion of Chebyshev blossom leads to elegant algorithms whose complexities are embedded in the combinatorics of Schur functions. We express the blossom and the pseudo-affinity property in Muntz spaces in term of Schur functions. We derive an explicit expression of the Chebyshev-Bernstein basis via an inductive argument on nested Muntz spaces. We also reveal a simple algorithm for the dimension elevation process. Free-form design schemes in Muntz spaces with Young diagrams as shape parameter will be discussed.

math.NA↗