Financial Time Series Forecasting is an important tool to support both individual and organizational decisions. Periodic phenomena are very popular in econometrics. Many models have been built aiding capture of these ...Financial Time Series Forecasting is an important tool to support both individual and organizational decisions. Periodic phenomena are very popular in econometrics. Many models have been built aiding capture of these periodic trends as a way of enhancing forecasting of future events as well as guiding business and social activities. The nature of real-world systems </span><span style="font-family:Verdana;">is</span><span style="font-family:Verdana;"> characterized by many uncertain fluctuations which makes prediction difficult. In situations when randomness is mixed with periodicity, prediction is even much harder. We therefore constructed an ANN Time Varying Garch model with both linear and non-linear attributes and specific for processes with fixed and random periodicity. To eliminate the need for time series linear component filtering</span><span style="font-family:Verdana;">,</span><span style="font-family:Verdana;"> we incorporated the use of Artificial Neural Networks (ANN) and constructed Time Varying GARCH model on its disturbances. We developed the estimation procedure of the ANN time varying GARCH model parameters using non parametric techniques.展开更多
This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the n...This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.展开更多
Current hyperelastic constitutive models of hydrogels face difficulties in capturing the stress-strain behaviors of hydrogels under extremely large deformation because the effect of non-affine deformation of the polym...Current hyperelastic constitutive models of hydrogels face difficulties in capturing the stress-strain behaviors of hydrogels under extremely large deformation because the effect of non-affine deformation of the polymer network inside is ambiguous.In this work,we construct periodic random network(PRN)models for the effective polymer network in hydrogels and investigate the non-affine deformation of polymer chains intrinsically originates from the structural randomness from bottom up.The non-affine deformation in PRN models is manifested as the actual stretch of polymer chains randomly deviated from the chain stretch predicted by affine assumption,and quantified by a non-affine ratio of each polymer chain.It is found that the non-affine ratios of polymer chains are closely related to bulk deformation state,chain orientation,and initial chain elongation.By fitting the non-affine ratio of polymer chains in all PRN models,we propose a non-affine constitutive model for the hydrogel polymer network based on micro-sphere model.The stress-strain curves of the proposed constitutive models under uniaxial tension condition agree with the simulation results of different PRN models of hydrogels very well.展开更多
In this paper, we present a basic theory of mean-square almost periodicity, apply the theory in random differential equation, and obtain mean-square almost periodic solution of some types stochastic differential equat...In this paper, we present a basic theory of mean-square almost periodicity, apply the theory in random differential equation, and obtain mean-square almost periodic solution of some types stochastic differential equation.展开更多
Consider C^(2)Anosov systems on a compact manifold driven by a quasi-periodic force.We study their dynamical complexity on various levels from the perspectives of both path-wise dynamics and stochastic processes.Assum...Consider C^(2)Anosov systems on a compact manifold driven by a quasi-periodic force.We study their dynamical complexity on various levels from the perspectives of both path-wise dynamics and stochastic processes.Assuming that these systems are non-wandering(i.e.,every point in the phase space is nonwandering),we prove a set of results:(1)the existence of abundance of random periodic points;(2)a random Livsic theorem;(3)a random Mañé-Bousch-Conze-Guivarc'h lemma;(4)the existence of strong random horseshoes.Additionally,a concrete example constructed on a 2-dimensional torus is also given to uncover some interesting phenomena of the systems.展开更多
In this paper,we make use of stochastic theta method to study the existence of the numerical approximation of random periodic solution.We prove that the error between the exact random periodic solution and the approxi...In this paper,we make use of stochastic theta method to study the existence of the numerical approximation of random periodic solution.We prove that the error between the exact random periodic solution and the approximated one is at the 1/4 order time step in mean sense when the initial time tends to∞.展开更多
Consider an inverse problem that aims to identify key statistical pro-perties of the profile for the unknown random perfectly conducting grating structure by boundary measurements of the diffracted fields in transvers...Consider an inverse problem that aims to identify key statistical pro-perties of the profile for the unknown random perfectly conducting grating structure by boundary measurements of the diffracted fields in transverse mag-netic polarization.The method proposed in this paper is based on a novel combination of the Monte Carlo technique,a continuation method and the Karhunen-Loève expansion for the uncertainty quantification of the random structure.Numerical results are presented to demonstrate the effectiveness of the proposed method.展开更多
This paper presents the design and implementation of a 14-bit, 100 MS/s CMOS digital-to-analog converter （DAC）. Analog background self-calibration based on the concept of analog current trimming is introduced. A con...This paper presents the design and implementation of a 14-bit, 100 MS/s CMOS digital-to-analog converter （DAC）. Analog background self-calibration based on the concept of analog current trimming is introduced. A constant clock load switch driver, a calibration period randomization circuit and a return-to-zero output stage have been adopted to improve the dynamic performance. The chip has been manufactured in a SMIC 0.13-μm process and occupies 1.33 × 0.97 mm2 of the core area. The current consumption is 50 mA under 1.2/3.3 V dual power supplies for digital and analog, respectively. The measured differential and integral nonlinearity is 3.1 LSB and 4.3 LSB, respectively. The SFDR is 72.8 dB at a 1 MHz signal and a 100 MHz sampling frequency.展开更多
文摘Financial Time Series Forecasting is an important tool to support both individual and organizational decisions. Periodic phenomena are very popular in econometrics. Many models have been built aiding capture of these periodic trends as a way of enhancing forecasting of future events as well as guiding business and social activities. The nature of real-world systems </span><span style="font-family:Verdana;">is</span><span style="font-family:Verdana;"> characterized by many uncertain fluctuations which makes prediction difficult. In situations when randomness is mixed with periodicity, prediction is even much harder. We therefore constructed an ANN Time Varying Garch model with both linear and non-linear attributes and specific for processes with fixed and random periodicity. To eliminate the need for time series linear component filtering</span><span style="font-family:Verdana;">,</span><span style="font-family:Verdana;"> we incorporated the use of Artificial Neural Networks (ANN) and constructed Time Varying GARCH model on its disturbances. We developed the estimation procedure of the ANN time varying GARCH model parameters using non parametric techniques.
基金supported by the National Natural Science Foundation of China(Nos.12471394,12371417)Natural Science Foundation of Changsha(No.kq2502101)。
文摘This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.
基金supported by the National Natural Science Foundation of China(Grant Nos.12202339 and 12172273)Xi’an Jiaotong University Tang Scholar.
文摘Current hyperelastic constitutive models of hydrogels face difficulties in capturing the stress-strain behaviors of hydrogels under extremely large deformation because the effect of non-affine deformation of the polymer network inside is ambiguous.In this work,we construct periodic random network(PRN)models for the effective polymer network in hydrogels and investigate the non-affine deformation of polymer chains intrinsically originates from the structural randomness from bottom up.The non-affine deformation in PRN models is manifested as the actual stretch of polymer chains randomly deviated from the chain stretch predicted by affine assumption,and quantified by a non-affine ratio of each polymer chain.It is found that the non-affine ratios of polymer chains are closely related to bulk deformation state,chain orientation,and initial chain elongation.By fitting the non-affine ratio of polymer chains in all PRN models,we propose a non-affine constitutive model for the hydrogel polymer network based on micro-sphere model.The stress-strain curves of the proposed constitutive models under uniaxial tension condition agree with the simulation results of different PRN models of hydrogels very well.
文摘In this paper, we present a basic theory of mean-square almost periodicity, apply the theory in random differential equation, and obtain mean-square almost periodic solution of some types stochastic differential equation.
基金supported by National Natural Science Foundation of China(Grant Nos.12090010,12090013,11971330,12090012,12031019,11725105,and 12226102).
文摘Consider C^(2)Anosov systems on a compact manifold driven by a quasi-periodic force.We study their dynamical complexity on various levels from the perspectives of both path-wise dynamics and stochastic processes.Assuming that these systems are non-wandering(i.e.,every point in the phase space is nonwandering),we prove a set of results:(1)the existence of abundance of random periodic points;(2)a random Livsic theorem;(3)a random Mañé-Bousch-Conze-Guivarc'h lemma;(4)the existence of strong random horseshoes.Additionally,a concrete example constructed on a 2-dimensional torus is also given to uncover some interesting phenomena of the systems.
基金supported by the National Natural Science Foundation of China (No.11871184,11701127)by the Natural Science Foundation of Hainan Province(Grant No.117096)
文摘In this paper,we make use of stochastic theta method to study the existence of the numerical approximation of random periodic solution.We prove that the error between the exact random periodic solution and the approximated one is at the 1/4 order time step in mean sense when the initial time tends to∞.
基金supported in part by National Natural Science Foundation of China Innovative Group Fund(Grant No.11621101)
文摘Consider an inverse problem that aims to identify key statistical pro-perties of the profile for the unknown random perfectly conducting grating structure by boundary measurements of the diffracted fields in transverse mag-netic polarization.The method proposed in this paper is based on a novel combination of the Monte Carlo technique,a continuation method and the Karhunen-Loève expansion for the uncertainty quantification of the random structure.Numerical results are presented to demonstrate the effectiveness of the proposed method.
基金Project supported by the National High Technology Research and Development Program of China(No.2009AA011605)
文摘This paper presents the design and implementation of a 14-bit, 100 MS/s CMOS digital-to-analog converter （DAC）. Analog background self-calibration based on the concept of analog current trimming is introduced. A constant clock load switch driver, a calibration period randomization circuit and a return-to-zero output stage have been adopted to improve the dynamic performance. The chip has been manufactured in a SMIC 0.13-μm process and occupies 1.33 × 0.97 mm2 of the core area. The current consumption is 50 mA under 1.2/3.3 V dual power supplies for digital and analog, respectively. The measured differential and integral nonlinearity is 3.1 LSB and 4.3 LSB, respectively. The SFDR is 72.8 dB at a 1 MHz signal and a 100 MHz sampling frequency.
