• Journal of the Korean Data and Information Science Society
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• v.22 no.2
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• pp.353-360
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• 2011

We consider an asymmetric power transformed threshold GARCH(1.1) process and find sufficient conditions for the existence of a strictly stationary solution, geometric ergodicity and ${\beta}$-mixing property. Moments conditions are given. Box-Cox transformed threshold GARCH(1.1) is also considered as a special case.

• Proceedings of the Korea Society for Simulation Conference
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• 2001.05a
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• pp.169-169
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• 2001

With the aid of fast computing power, resampling techniques are being introduced for simulation output analysis (SOA). Autocorrelation among the output from discrete-event simulation prohibit the direct application of resampling schemes (Threshold bootstrap, Binary bootstrap, Stationary bootstrap, etc) extend its usage to time-series data such as simulation output. We present a new method for inference from a regenerative process, regenerative bootstrap, that equals or exceeds the performance of classical regenerative method and approximation regeneration techniques. Regenerative bootstrap saves computation time and overcomes the problem of scarce regeneration cycles. Computational results are provided using M/M/1 model.

• Communications for Statistical Applications and Methods
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• v.13 no.2
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• pp.343-358
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• 2006

The distributional properties of forecasts in an integer-valued time series model have not been discovered yet mainly because of the complexity arising from the binomial thinning operator. We propose two bootstrap methods to obtain nonparametric prediction intervals for an integer-valued autoregressive model : one accommodates the variation of estimating parameters and the other does not. Contrary to the results of the continuous ARMA model, we show that the latter is better than the former in forecasting the future values of the integer-valued autoregressive model.

• Journal of Communications and Networks
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• v.11 no.2
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• pp.134-147
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• 2009

Tracking and exploiting instantaneous spectrum opportunities are fundamental challenges in opportunistic spectrum access (OSA) in presence of the bursty traffic of primary users and the limited spectrum sensing capability of secondary users. In order to take advantage of the history of spectrum sensing and access decisions, a sequential decision framework is widely used to design optimal policies. However, many existing schemes, based on a partially observed Markov decision process (POMDP) framework, reveal that optimal policies are non-stationary in nature which renders them difficult to calculate and implement. Therefore, this work pursues stationary OSA policies, which are thereby efficient yet low-complexity, while still incorporating many practical factors, such as spectrum sensing errors and a priori unknown statistical spectrum knowledge. First, with an approximation on channel evolution, OSA is formulated in a multi-armed bandit (MAB) framework. As a result, the optimal policy is specified by the wellknown Gittins index rule, where the channel with the largest Gittins index is always selected. Then, closed-form formulas are derived for the Gittins indices with tunable approximation, and the design of a reinforcement learning algorithm is presented for calculating the Gittins indices, depending on whether the Markovian channel parameters are available a priori or not. Finally, the superiority of the scheme is presented via extensive experiments compared to other existing schemes in terms of the quality of policies and optimality.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.11a
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• pp.173-179
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• 2006

In order to explain a U-shape pattern of stock returns, Fama and French(1988) suggested the state-space model consisting of I(1) permanent component and AR(1) stationary component. They concluded the autoregression coefficient induced from the state-space model follow the U-shape pattern and the U-shape pattern of stock returns was due to both negative autocorrelation in returns beyond a year and substantial mean-reversion in stock market prices. However, we found negative autocorrelation is induced under the assumption that permanent and stationary noise component are independent in the state-space model. In this paper, we derive the autoregression coefficient based on ARIMA process equivalent to the state-space model without the assumption of independency. Based on the estimated parameters, we investigate the pattern of the time-varying autoregression coefficient and conclude the autoregression coefficient from the state-space model of ARIMA(1,1,1) process does not follow a U-shape pattern, but has always positive sign. We applied this result on the data of 1 month retums for all NYSE stocks for the 1926-85 period from the Center for Research in Security Prices.

• Journal of the Korean Operations Research and Management Science Society
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• v.36 no.1
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• pp.13-26
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• 2011

In order to explain the U-shaped pattern of autocorrelations of stock returns i.e., autocorrelations starting around 0 for short-term horizons and becoming negative and then moving toward 0 for long-term horizons, researchers suggested the use of a state-space model consisting of an I(1) permanent component and an AR(1) stationary component, where the two components are assumed to be independent. They concluded that auto-regression coefficients derived from the state-space model follow a U-shape pattern and thus there is mean-reversion in stock prices. In this paper, we show that only negative autocorrelations are feasible under the assumption that the permanent component and the stationary component are independent in the state-space model. When the two components are allowed to be correlated in the state-space model, we show that the sign of the auto-regression coefficients is not restricted as negative. Monthly return data for all NYSE stocks for the period from 1926 to 2007 support the state-space model with correlated noise processes. However, the auto-regression coefficients of the ARIMA process, equivalent to the state-space model with correlated noise processes, do not follow a U-shaped pattern, but are always positive.

• The Bulletin of The Korean Astronomical Society
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• v.42 no.2
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• pp.37.1-37.1
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• 2017

Since the seminal work of Perrin, physicists have understood in the context of kinetic theory how ink slowly diffuses in a glass of water. The fluctuations of the stochastic forces acting on water molecules drive the diffusion of the ink in the fluid. This is the archetype of a process described by the so-called fluctuation-dissipation theorem, which universally relates the rate of diffusion to the power spectrum of the fluctuating forces. For stars in galaxies, a similar process occurs but with two significant differences, due to the long-range nature of the gravitational interaction: (i) for the diffusion to be effective, stars need to resonate, i.e. present commensurable frequencies, otherwise they only follow the orbit imposed by their mean field; (ii) the amplitudes of the induced fluctuating forces are significantly boosted by collective effects, i.e. by the fact that, because of self-gravity, each star generates a wake in its neighbours. In the expanding universe, an overdense perturbation passing a critical threshold will collapse onto itself and, through violent relaxation and mergers, rapidly converge towards a stationary, phase-mixed and highly symmetric state, with a partially frozen orbital structure. The object is then locked in a quasi-stationary state imposed by its mean gravitational field. Of particular interests are strongly responsive colder systems which, given time and kicks, find the opportunity to significantly reshuffle their orbital structure towards more likely configurations. This presentation aims to explain this long-term reshuffling called gravity-driven secular evolution on cosmic timescales, described by extended kinetic theory. I will illustrate this with radial migration, disc thickening and the stellar cluster in the galactic centre.

• Progress in Superconductivity
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• v.6 no.1
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• pp.74-78
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• 2004

YBCO coated conductor is one of the most promising materials as a new generations wire especially for practical power applications. In this work, $YBa_2$$Cu_3$$O_{7}$ -$\delta$/(YBCO) coated conductors (CC) were deposited by pulsed laser deposition (PLD) from buffer layers to superconducting layer on hi-axially textured metal tape. The oxide multilayer buffered substrate of architectures of $CeO_2$/$YSZ/Y_2$$O_3$ was fabricated by PLD at steady status. Then YBCO layer was deposited on RABiTS substrate by stationary and reel-to-reel (R2R) continuous process and we compared with deposition conditions of both processes. The degree of texture of each layer was investigated using X-ray diffraction including $\theta$-2$\theta$ scans, $\omega$-scans and $\Phi$-scans analysis. Their surface morphology was observed by scanning electron microscopy (SEM). The FWHM of the X-ray $\Phi$-scans and $\Phi$-scans indicated that YBCO and buffer layers closely replicate the in-plane and out-of-plane texture of metal tape. Critical current (Ic) at 77 K, self-field of 75.8 A/cm-width, critical temperature (Tc) of 85 K, and critical current density (Ic) of 3.7 MA/$\textrm{cm}^2$ were measured from coated conductor deposited by stationary process. And coated conductor deposited by R2R continuous process had Ic of 57.5 A/cm-width, Tc of 86.5 K and Jc of 2.0 MA/$\textrm{cm}^2$. The film also exhibits a homogeneous and dense surface morphology.

• Journal of Information Processing Systems
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• v.14 no.2
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• pp.455-468
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• 2018

The concepts of graph theory are applied to model and analyze dynamics of computer networks, biochemical networks and, semantics of social networks. The analysis of dynamics of complex networks is important in order to determine the stability and performance of networked systems. The analysis of non-stationary and nonlinear complex networks requires the applications of ordinary differential equations (ODE). However, the process of resolving input excitation to the dynamic non-stationary networks is difficult without involving external functions. This paper proposes an analytical formulation for generating solutions of nonlinear network ODE systems with functional decomposition. Furthermore, the input excitations are analytically resolved in linearized dynamic networks. The stability condition of dynamic networks is determined. The proposed analytical framework is generalized in nature and does not require any domain or range constraints.

• Structural Engineering and Mechanics
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• v.32 no.1
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• pp.179-191
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• 2009

A stochastic response spectrum method is proposed for simple evaluation of the structural response of an actively controlled aseismic structure. The response spectrum is constructed assuming a linear structure with an active mass damper (AMD) system, and an earthquake wave model given by the product of a non-stationary envelope function and a stationary Gaussian random process with Kanai-Tajimi power spectral density. The control design is executed using a linear quadratic Gaussian control strategy for an enlarged state space system, and the response amplification factor is given by the combination of the obtained statistical response values and extreme value theory. The response spectrum thus produced can be used for simple dynamical analyses. The response factors obtained by this method for a multi-degree-of-freedom structure are shown to be comparable with those determined by numerical simulations, demonstrating the validity and utility of the proposed technique as a simple design tool. This method is expected to be useful for engineers in the initial design stage for structures with active aseismic control.