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Jib Huh - One of the best experts on this subject based on the ideXlab platform.

  • Estimation of a change Point in the variance function based on the χ2-distribution
    Communications in Statistics - Theory and Methods, 2016
    Co-Authors: Jib Huh
    Abstract:

    ABSTRACTLet us consider that the variance function or its νth derivative in a regression model has a change/Discontinuity Point at an unknown location. To use the local polynomial fits, the log-variance function which break the positivity is targeted. The location and the jump size of the change Point are estimated based on a one-sided kernel-weighted local-likelihood function which is provided by the χ2-distribution. The whole structure of the log-variance function is then estimated using the data sets split by the estimated location. Asymptotic results of the proposed estimators are described. Numerical works demonstrate the performances of the methods with simulated and real examples.

  • bandwidth selections based on cross validation for estimation of a Discontinuity Point in density
    Journal of the Korean Data and Information Science Society, 2012
    Co-Authors: Jib Huh
    Abstract:

    The cross-validation is a popular method to select bandwidth in all types of kernel estimation. The maximum likelihood cross-validation, the least squares cross-validation and biased cross-validation have been proposed for bandwidth selection in kernel density estimation. In the case that the probability density function has a Discontinuity Point, Huh (2012) proposed a method of bandwidth selection using the maximum likelihood cross-validation. In this paper, two forms of cross-validation with the one-sided kernel function are proposed for bandwidth selection to estimate the location and jump size of the Discontinuity Point of density. These methods are motivated by the least squares cross-validation and the biased cross-validation. By simulated examples, the finite sample performances of two proposed methods with the one of Huh (2012) are compared.

  • bandwidth selection for Discontinuity Point estimation in density
    Journal of the Korean Data and Information Science Society, 2012
    Co-Authors: Jib Huh
    Abstract:

    In the case that the probability density function has a Discontinuity Point, Huh (2002) estimated the location and jump size of the Discontinuity Point based on the difference between the right and left kernel density estimators using the one-sided kernel function. In this paper, we consider the cross-validation, made by the right and left maximum likelihood cross-validations, for the bandwidth selection in order to estimate the location and jump size of the Discontinuity Point. This method is motivated by the one-sided cross-validation of Hart and Yi (1998). The finite sample performance is illustrated by simulated example.

  • Detection of a change Point based on local-likelihood
    Journal of Multivariate Analysis, 2010
    Co-Authors: Jib Huh
    Abstract:

    In this paper, we consider the regression function or its @nth derivative in generalized linear models which may have a change/Discontinuity Point at an unknown location. The location and its jump size are estimated with the local polynomial fits based on one-sided kernel weighted local-likelihood functions. Asymptotic distributions of the proposed estimators of location and jump size are established. The finite-sample performances of the proposed estimators with practical aspects are illustrated by simulated and beetle mortality examples.

  • testing the existence of a Discontinuity Point in the variance function
    Journal of the Korean Data and Information Science Society, 2006
    Co-Authors: Jib Huh
    Abstract:

    When the regression function is discontinuous at a Point, the variance function is usually discontinuous at the Point. In this case, we had better propose a test for the existence of a Discontinuity Point with the regression function rather than the variance function. In this paper we consider that the variance function only has a Discontinuity Point. We propose a nonparametric test for the existence of a Discontinuity Point with the second moment function since the variance function and the second moment function have the same location and jump size of the Discontinuity Point. The proposed method is based on the asymptotic distribution of the estimated jump size.

Volodymyr Mykhaylyuk - One of the best experts on this subject based on the ideXlab platform.

  • A characterization of the Discontinuity Point set of strongly separately continuous functions on products
    Mathematica Slovaca, 2016
    Co-Authors: Olena Karlova, Volodymyr Mykhaylyuk
    Abstract:

    We study properties of strongly separately continuous mappings defined on products of topological spaces equipped with the topology of Pointwise convergence. In particular, we give a necessary and sufficient condition for a strongly separately continuous mapping to be continuous on a product of an arbitrary family of topological spaces. Moreover, we characterize the Discontinuity Point set of strongly separately continuous function defined on a subset of countable product of finite-dimensional normed spaces.

  • A characterization of the Discontinuity Point set of strongly separately continuous functions on products
    arXiv: General Topology, 2014
    Co-Authors: Olena Karlova, Volodymyr Mykhaylyuk
    Abstract:

    We study properties of strongly separately continuous mappings defined on subsets of products of topological spaces equipped with the topology of Pointwise convergence. In particular, we give a necessary and sufficient condition for a strongly separately continuous mapping to be continuous on a product of an arbitrary family of topological spaces. Moreover, we charac\-terize the Discontinuity Point set of strongly separately continuous function defined on a subset of countable product of finite-dimensional normed spaces.

M. F. Dimentberg - One of the best experts on this subject based on the ideXlab platform.

  • Random vibrations of an isochronous SDOF bilinear system
    Nonlinear Dynamics, 1996
    Co-Authors: M. F. Dimentberg
    Abstract:

    A single-degree-of-freedom (SDOF) system with bilinear restoring force and damping characteristics is excited by a white-noise force. For the case of small damping the asymptotic method of quasi-conservative stochastic averaging is applied, which reduces the problem to that of a single Ito stochastic differential equation (SDE) for total energy of the response. A special case of the isochronous system is considered, where the static equilibrium position coincides with the slope Discontinuity Point of the system's characteristics, such as that of a moored body without slack and pretension in the mooring cable. For this case an analytical solution is obtained for autocorrelation function of the response energy. For the limiting case of a vibroimpact system the results are shown to agree with the exact solution.

S. A. Van Gils - One of the best experts on this subject based on the ideXlab platform.

  • Stability analysis of $\pi$-kinks in a 0-$\pi$ Josephson junction
    arXiv: Pattern Formation and Solitons, 2008
    Co-Authors: Gianne Derks, S. A. Van Gils, Arjen Doelman, Hadi Susanto
    Abstract:

    We consider a spatially non-autonomous discrete sine-Gordon equation with constant forcing and its continuum limit(s) to model a 0-$\pi$ Josephson junction with an applied bias current. The continuum limits correspond to the strong coupling limit of the discrete system. The non-autonomous character is due to the presence of a Discontinuity Point, namely a jump of $\pi$ in the sine-Gordon phase. The continuum models admits static solitary waves which are called $\pi$-kinks and are attached to the Discontinuity Point. For small forcing, there are three types of $\pi$-kinks. We show that one of the kinks is stable and the others are unstable. There is a critical value of the forcing beyond all static $\pi$-kinks fail to exist. Up to this value, the (in)stability of the $\pi$-kinks can be established analytically in the strong coupling limits. Applying a forcing above the critical value causes the nucleation of $2\pi$-kinks and -antikinks. Besides a $\pi$-kink, the unforced system also admits a static $3\pi$-kink. This state is unstable in the continuum models. By combining analytical and numerical methods in the discrete model, it is shown that the stable $\pi$-kink remains stable, and that the unstable $\pi$-kinks cannot be stabilized by decreasing the coupling. The $3\pi$-kink does become stable in the discrete model when the coupling is sufficiently weak.

  • Stability analysis of p-kinks in a 0-p Josephson junction
    2007
    Co-Authors: Gianne Derks, S. A. Van Gils, Arjen Doelman, Hadi Susanto
    Abstract:

    We consider a spatially nonautonomous discrete sine-Gordon equation with constant forcing and its continuum limit(s) to model a 0-pi Josephson junction with an applied bias current. The continuum limits correspond to the strong coupling limit of the discrete system. The nonautonomous character is due to the presence of a Discontinuity Point, namely, a jump of pi in the sine- Gordon phase. The continuum model admits static solitary waves which are called pi-kinks and are attached to the Discontinuity Point. For small forcing, there are three types of pi-kinks. We show that one of the kinks is stable and the others are unstable. There is a critical value of the forcing beyond which all static pi-kinks fail to exist. Up to this value, the (in)stability of the pi-kinks can be established analytically in the strong coupling limits. Applying a forcing above the critical value causes the nucleation of 2pi-kinks and -antikinks. Besides a pi-kink, the unforced system also admits a static 3pi-kink. This state is unstable in the continuum models. By combining analytical and numerical methods in the discrete model, it is shown that the stable pi-kink remains stable and that the unstable pi-kinks cannot be stabilized by decreasing the coupling. The 3pi-kink does become stable in the discrete model when the coupling is sufficiently weak.

  • Stability Analysis of π‐Kinks in a 0‐π Josephson Junction
    SIAM Journal on Applied Dynamical Systems, 2007
    Co-Authors: Gianne Derks, S. A. Van Gils, Arjen Doelman, Hadi Susanto
    Abstract:

    We consider a spatially nonautonomous discrete sine-Gordon equation with constant forcing and its continuum limit(s) to model a 0-$\pi$ Josephson junction with an applied bias current. The continuum limits correspond to the strong coupling limit of the discrete system. The nonautonomous character is due to the presence of a Discontinuity Point, namely, a jump of $\pi$ in the sine-Gordon phase. The continuum model admits static solitary waves which are called $\pi$-kinks and are attached to the Discontinuity Point. For small forcing, there are three types of $\pi$-kinks. We show that one of the kinks is stable and the others are unstable. There is a critical value of the forcing beyond which all static $\pi$-kinks fail to exist. Up to this value, the (in)stability of the $\pi$-kinks can be established analytically in the strong coupling limits. Applying a forcing above the critical value causes the nucleation of 2$\pi$-kinks and -antikinks. Besides a $\pi$-kink, the unforced system also admits a static 3$\pi$-kink. This state is unstable in the continuum models. By combining analytical and numerical methods in the discrete model, it is shown that the stable $\pi$-kink remains stable and that the unstable $\pi$-kinks cannot be stabilized by decreasing the coupling. The 3$\pi$-kink does become stable in the discrete model when the coupling is sufficiently weak.

  • Instability of a lattice semifluxon in a current-biased 0-π array of Josephson junctions
    Physical Review B, 2004
    Co-Authors: Hadi Susanto, S. A. Van Gils
    Abstract:

    We consider a one-dimensional parallel biased array of small Josephson junctions with a Discontinuity Point characterized by a phase jump of π in the phase difference. The system is described by a spatially nonautonomous discrete sine-Gordon equation. It is shown that in the infinitely long case there is a semifluxon spontaneously generated attached to the Discontinuity Point. Comparing the configurations of the semifluxon, we find an energy barrier similar to the Peierls-Nabarro barrier. We calculate numerically the minimum bias current density to overcome this barrier which is a function of the lattice spacing. It is found that the minimum bias current is the critical current for the existence of static lattice semifluxons. For bias current density above the minimum value, the semifluxon changes the polarity and releases 2π fluxons. An analytical approximation to the critical current as a function of the lattice spacing is presented.

Hadi Susanto - One of the best experts on this subject based on the ideXlab platform.

  • Fluxons interactions in a Josephson junction with a phase-shift
    Physics Letters A, 2009
    Co-Authors: Hadi Susanto, Ja Espinola-rocha
    Abstract:

    We consider a long Josephson junction with a Discontinuity Point characterized by a gauge phase-shift. The system is described by a modified sine-Gordon equation. We study, in particular, the interactions between a fluxon and a fractional fluxon. A perturbation theory is developed in the small phase-shift limit to understand the characteristics of the interaction. Finally, numerical computations of the threshold bias current and the threshold velocity for a fluxon running over a fractional fluxon are presented.

  • Stability analysis of $\pi$-kinks in a 0-$\pi$ Josephson junction
    arXiv: Pattern Formation and Solitons, 2008
    Co-Authors: Gianne Derks, S. A. Van Gils, Arjen Doelman, Hadi Susanto
    Abstract:

    We consider a spatially non-autonomous discrete sine-Gordon equation with constant forcing and its continuum limit(s) to model a 0-$\pi$ Josephson junction with an applied bias current. The continuum limits correspond to the strong coupling limit of the discrete system. The non-autonomous character is due to the presence of a Discontinuity Point, namely a jump of $\pi$ in the sine-Gordon phase. The continuum models admits static solitary waves which are called $\pi$-kinks and are attached to the Discontinuity Point. For small forcing, there are three types of $\pi$-kinks. We show that one of the kinks is stable and the others are unstable. There is a critical value of the forcing beyond all static $\pi$-kinks fail to exist. Up to this value, the (in)stability of the $\pi$-kinks can be established analytically in the strong coupling limits. Applying a forcing above the critical value causes the nucleation of $2\pi$-kinks and -antikinks. Besides a $\pi$-kink, the unforced system also admits a static $3\pi$-kink. This state is unstable in the continuum models. By combining analytical and numerical methods in the discrete model, it is shown that the stable $\pi$-kink remains stable, and that the unstable $\pi$-kinks cannot be stabilized by decreasing the coupling. The $3\pi$-kink does become stable in the discrete model when the coupling is sufficiently weak.

  • Stability analysis of p-kinks in a 0-p Josephson junction
    2007
    Co-Authors: Gianne Derks, S. A. Van Gils, Arjen Doelman, Hadi Susanto
    Abstract:

    We consider a spatially nonautonomous discrete sine-Gordon equation with constant forcing and its continuum limit(s) to model a 0-pi Josephson junction with an applied bias current. The continuum limits correspond to the strong coupling limit of the discrete system. The nonautonomous character is due to the presence of a Discontinuity Point, namely, a jump of pi in the sine- Gordon phase. The continuum model admits static solitary waves which are called pi-kinks and are attached to the Discontinuity Point. For small forcing, there are three types of pi-kinks. We show that one of the kinks is stable and the others are unstable. There is a critical value of the forcing beyond which all static pi-kinks fail to exist. Up to this value, the (in)stability of the pi-kinks can be established analytically in the strong coupling limits. Applying a forcing above the critical value causes the nucleation of 2pi-kinks and -antikinks. Besides a pi-kink, the unforced system also admits a static 3pi-kink. This state is unstable in the continuum models. By combining analytical and numerical methods in the discrete model, it is shown that the stable pi-kink remains stable and that the unstable pi-kinks cannot be stabilized by decreasing the coupling. The 3pi-kink does become stable in the discrete model when the coupling is sufficiently weak.

  • Stability Analysis of π‐Kinks in a 0‐π Josephson Junction
    SIAM Journal on Applied Dynamical Systems, 2007
    Co-Authors: Gianne Derks, S. A. Van Gils, Arjen Doelman, Hadi Susanto
    Abstract:

    We consider a spatially nonautonomous discrete sine-Gordon equation with constant forcing and its continuum limit(s) to model a 0-$\pi$ Josephson junction with an applied bias current. The continuum limits correspond to the strong coupling limit of the discrete system. The nonautonomous character is due to the presence of a Discontinuity Point, namely, a jump of $\pi$ in the sine-Gordon phase. The continuum model admits static solitary waves which are called $\pi$-kinks and are attached to the Discontinuity Point. For small forcing, there are three types of $\pi$-kinks. We show that one of the kinks is stable and the others are unstable. There is a critical value of the forcing beyond which all static $\pi$-kinks fail to exist. Up to this value, the (in)stability of the $\pi$-kinks can be established analytically in the strong coupling limits. Applying a forcing above the critical value causes the nucleation of 2$\pi$-kinks and -antikinks. Besides a $\pi$-kink, the unforced system also admits a static 3$\pi$-kink. This state is unstable in the continuum models. By combining analytical and numerical methods in the discrete model, it is shown that the stable $\pi$-kink remains stable and that the unstable $\pi$-kinks cannot be stabilized by decreasing the coupling. The 3$\pi$-kink does become stable in the discrete model when the coupling is sufficiently weak.

  • Stability analysis of pi-kinks in a 0-pi Josephson junction
    2006
    Co-Authors: Gianne Derks, Arjen Doelman, S.a. Vangils, Hadi Susanto
    Abstract:

    We consider a spatially non-autonomous discrete sine-Gordon equation with constant forcing and its continuum limit(s) to model a 0-pi Josephson junction with an applied bias current. The continuum limits correspond to the strong coupling limit of the discrete system. The non-autonomous character is due to the presence of a Discontinuity Point, namely a jump of pi in the sine-Gordon phase. The continuum models admits static solitary waves which are called pi-kinks and are attached to the Discontinuity Point. For small forcing, there are three types of pi-kinks. We show that one of the solitary waves is stable and the others are unstable. There is a critical value of the forcing beyond all static pi-kinks fail to exist. Up to this value, the (in)stability of the pi-kinks can be established analytically in the strong coupling limits. Applying a forcing above the critical value causes the nucleation of 2pi-kinks and -antikinks. Besides a pi-kink, the unforced system also admits a static 3pi-kink. This state is unstable in the continuum models. By combining analytical and numerical methods in the discrete model, it is shown that the stable pi-kink remains stable, and that the unstable pi-kinks cannot be stabilized. The 3pi-kink does become stable in the discrete model when the coupling is sufficiently weak