This paper presents a new stochastic algorithm for box constrained global optimization problem. Bacause the level set of objective function is always not known, the authors designed a region containing the current mi...This paper presents a new stochastic algorithm for box constrained global optimization problem. Bacause the level set of objective function is always not known, the authors designed a region containing the current minimum point to replace it, and in order to fit the level set well, this region would be walking and contracting in the running process. Thus, the new algorithm is named as region's walk and contraction(RWC). Some numerical experiments for the RWC were conducted, which indicate good property of the algorithm.展开更多
The stochastic simulation algorithm (SSA) accurately depicts spatially homogeneous wellstirred chemically reacting systems with small populations of chemical species and properly represents noise, but it is often ab...The stochastic simulation algorithm (SSA) accurately depicts spatially homogeneous wellstirred chemically reacting systems with small populations of chemical species and properly represents noise, but it is often abandoned when modeling larger systems because of its computational complexity. In this work, a twin support vector regression based stochastic simulations algorithm (TS^3A) is proposed by combining the twin support vector regression and SSA, the former is a well-known robust regression method in machine learning. Numerical results indicate that this proposed algorithm can be applied to a wide range of chemically reacting systems and obtain significant improvements on efficiency and accuracy with fewer simulating runs over the existing methods.展开更多
In this paper, we develop a new theoretical framework by means of the absorbing Markov process theory for analyzing some stochastic global optimization algorithms. Applying the framework to the pure random search, we ...In this paper, we develop a new theoretical framework by means of the absorbing Markov process theory for analyzing some stochastic global optimization algorithms. Applying the framework to the pure random search, we prove that the pure random search converges to the global minimum in probability and its time has geometry distribution. We also analyze the pure adaptive search by this framework and turn out that the pure adaptive search converges to the global minimum in probability and its time has Poisson distribution.展开更多
The present study proposes a stochastic simulation scheme to model reactive boundaries through a position jump process which can be readily implemented into the Inhomogeneous Stochastic Simulation Algorithm by modifyi...The present study proposes a stochastic simulation scheme to model reactive boundaries through a position jump process which can be readily implemented into the Inhomogeneous Stochastic Simulation Algorithm by modifying the propensity of the diffusive jump over the reactive boundary. As compared to the literature, the present approach does not require any correction factors for the propensity. Also, the current expression relaxes the constraint on the compartment size allowing the problem to be solved with a coarser grid and therefore saves considerable computational cost. The modified algorithm is then applied to simulate three reaction-diffusion systems with reactive boundaries.展开更多
We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (...We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.展开更多
There are many population-based stochastic search algorithms for solving optimization problems. However, the universality and robustness of these algorithms are still unsatisfactory. This paper proposes an enhanced se...There are many population-based stochastic search algorithms for solving optimization problems. However, the universality and robustness of these algorithms are still unsatisfactory. This paper proposes an enhanced self-adaptiveevolutionary algorithm (ESEA) to overcome the demerits above. In the ESEA, four evolutionary operators are designed to enhance the evolutionary structure. Besides, the ESEA employs four effective search strategies under the framework of the self-adaptive learning. Four groups of the experiments are done to find out the most suitable parameter values for the ESEA. In order to verify the performance of the proposed algorithm, 26 state-of-the-art test functions are solved by the ESEA and its competitors. The experimental results demonstrate that the universality and robustness of the ESEA out-perform its competitors.展开更多
Presented here is an L-leap method for accelerating stochastic simulation of well-stirred chemically reacting systems, in which the number of reactions occurring in a reaction channel with the largest propensity funct...Presented here is an L-leap method for accelerating stochastic simulation of well-stirred chemically reacting systems, in which the number of reactions occurring in a reaction channel with the largest propensity function is calculated from the leap condition and the number of reactions occurring in the other reaction channels are generated by using binomial random variables during a leap. The L-leap method can better satisfy the leap condition. Numerical simulation results indicate that the L-leap method can obtain better performance than established methods.展开更多
In this paper, we develop a modified accelerated stochastic simulation method for chemically reacting systems, called the "final all possible steps" (FAPS) method, which obtains the reliable statistics of all spec...In this paper, we develop a modified accelerated stochastic simulation method for chemically reacting systems, called the "final all possible steps" (FAPS) method, which obtains the reliable statistics of all species in any time during the time course with fewer simulation times. Moreover, the FAPS method can be incorporated into the leap methods, which makes the simulation of larger systems more efficient. Numerical results indicate that the proposed methods can be applied to a wide range of chemically reacting systems with a high-precision level and obtain a significant improvement on efficiency over the existing methods.展开更多
Biochemical systems have numerous practical applications, in particular to the study of critical intracellular processes. Frequently, biochemical kinetic models depict cellular processes as systems of chemical reactio...Biochemical systems have numerous practical applications, in particular to the study of critical intracellular processes. Frequently, biochemical kinetic models depict cellular processes as systems of chemical reactions. Many biological processes in a cell are inherently stochastic, due to the existence of some low molecular amounts. These stochastic fluctuations may have a great effect on the biochemical system’s behaviour. In such cases, stochastic models are necessary to accurately describe the system’s dynamics. Biochemical systems at the cellular level may entail many species or reactions and their mathematical models may be non-linear and with multiple scales in time. In this work, we provide a numerical technique for simplifying stochastic discrete models of well-stirred biochemical systems, which ensures that the main properties of the original system are preserved. The proposed technique employs sensitivity analysis and requires solving an optimization problem. The numerical tests on several models of practical interest show that our model reduction strategy performs very well.展开更多
Direct sequence spread spectrum transmission can be realized at low SNR, and has low probabilityof detection. It is aly problem how to obtain the original users' signal in a non-cooperative context. In practicality, ...Direct sequence spread spectrum transmission can be realized at low SNR, and has low probabilityof detection. It is aly problem how to obtain the original users' signal in a non-cooperative context. In practicality, the DS/CDMA sources received are linear convolute mixing. A more complex multichannel blind deconvolution MBD algorithm is required to achieve better source separation. An improved MBD algorithm for separating linear convolved mixtures of signals in CDMA system is proposed. This algorithm is based on minimizing the average squared cross-output-channel-correlation. The mixture coefficients are totally unknown, while some knowledge about temporal model exists. Results show that the proposed algorithm can bring about the exactness and low computational complexity.展开更多
Special input signals identification method based on the auxiliary model based multi-innovation stochastic gradient algorithm for Hammerstein output-error system was proposed.The special input signals were used to rea...Special input signals identification method based on the auxiliary model based multi-innovation stochastic gradient algorithm for Hammerstein output-error system was proposed.The special input signals were used to realize the identification and separation of the Hammerstein model.As a result,the identification of the dynamic linear part can be separated from the static nonlinear elements without any redundant adjustable parameters.The auxiliary model based multi-innovation stochastic gradient algorithm was applied to identifying the serial link parameters of the Hammerstein model.The auxiliary model based multi-innovation stochastic gradient algorithm can avoid the influence of noise and improve the identification accuracy by changing the innovation length.The simulation results show the efficiency of the proposed method.展开更多
Cellular environments are in essence stochastic, owing to the random character of the biochemical reaction events in a single cell. Stochastic fluctuations may substantially contribute to the dynamics of systems with ...Cellular environments are in essence stochastic, owing to the random character of the biochemical reaction events in a single cell. Stochastic fluctuations may substantially contribute to the dynamics of systems with small copy numbers of some biochemical species. Then, stochastic models are indispensable for properly portraying the behaviour of the system. Sensitivity analysis is one of the central tools for studying stochastic models of cellular dynamics. Here, we propose some finite-difference strategies for estimating parametric sensitivities of higher-order moments of the system state for stochastic discrete biochemical kinetic models. To reduce the variance of the sensitivity estimator, we employ various coupling techniques. The advantages of the proposed methods are illustrated in several models of biochemical systems of practical relevance.展开更多
This paper proposes the cooperative position estimation of a group of mobile robots, which pertbrms disaster relief tasks in a wide area. When searching the wide area, it becomes important to know a robot's position ...This paper proposes the cooperative position estimation of a group of mobile robots, which pertbrms disaster relief tasks in a wide area. When searching the wide area, it becomes important to know a robot's position correctly. However, for each mobile robot, it is impossible to know its own position correctly. Therefore, each mobile robot estimates its position from the data of sensor equipped on it. Generally, the sensor data is incorrect since there is sensor noise, etc. This research considers two types of the sensor data errors from omnidirectional camera. One is the error of white noise of the image captured by omnidirectional camera and so on. Another is the error of position and posture between two omnidirectional cameras. To solve the error of latter case, we proposed a self-position estimation algorithm for multiple mobile robots using two omnidirectional cameras and an accelerometer. On the other hand, to solve the error of the former case, this paper proposed an algorithm of cooperative position estimation for multiple mobile robots. In this algorithm, each mobile robot uses two omnidirectional cameras to observe the surrounding mobile robot and get the relative position between mobile robots. Each mobile robot estimates its position with only measurement data of each other mobile robots. The algorithm is based on a Bayesian filtering. Simulations of the proposed cooperative position estimation algorithm for multiple mobile robots are performed. The results show that position estimation is possible by only using measurement value from each other robot.展开更多
In this paper,we present a stochastic adaptive algorithm using radial basis function models for global optimization of costly black-box functions.The exploration radii in local searches are generated adaptively.Each i...In this paper,we present a stochastic adaptive algorithm using radial basis function models for global optimization of costly black-box functions.The exploration radii in local searches are generated adaptively.Each iteration point is selected from some randomly generated trial points according to certain criteria.A restarting strategy is adopted to build the restarting version of the algorithm.The performance of the presented algorithm and its restarting version are tested on 13 standard numerical examples.The numerical results suggest that the algorithm and its restarting version are very effective.展开更多
Adaptive digital filtering has traditionally been developed based on the minimum mean square error (MMSE) criterion and has found ever-increasing applications in communications. This paper presents an alternative ad...Adaptive digital filtering has traditionally been developed based on the minimum mean square error (MMSE) criterion and has found ever-increasing applications in communications. This paper presents an alternative adaptive filtering design based on the minimum symbol error rate (MSER) criterion for communication applications. It is shown that the MSER filtering is smarter, as it exploits the non-Gaussian distribution of filter output effectively. Consequently, it provides significant performance gain in terms of smaller symbol error over the MMSE approach. Adopting Parzen window or kernel density estimation for a probability density function, a block-data gradient adaptive MSER algorithm is derived. A stochastic gradient adaptive MSER algorithm, referred to as the least symbol error rate, is further developed for sample-by-sample adaptive implementation of the MSER filtering. Two applications, involving single-user channel equalization and beamforming assisted receiver, are included to demonstrate the effectiveness and generality of the proposed adaptive MSER filtering approach.展开更多
This paper introduces a post-iteration averaging algorithm to achieve asymptotic optimality in convergence rates of stochastic approximation algorithms for consensus control with structural constraints. The algorithm ...This paper introduces a post-iteration averaging algorithm to achieve asymptotic optimality in convergence rates of stochastic approximation algorithms for consensus control with structural constraints. The algorithm involves two stages. The first stage is a coarse approximation obtained using a sequence of large stepsizes. Then, the second stage provides a refinement by averaging the iterates from the first stage. We show that the new algorithm is asymptotically efficient and gives the optimal convergence rates in the sense of the best scaling factor and 'smallest' possible asymptotic variance.展开更多
In this paper, the improvement of pure random search is studied. By taking some information of the function to be minimized into consideration, the authors propose two stochastic global optimization algorithms. Some n...In this paper, the improvement of pure random search is studied. By taking some information of the function to be minimized into consideration, the authors propose two stochastic global optimization algorithms. Some numerical experiments for the new stochastic global optimization algorithms are presented for a class of test problems.展开更多
This paper is a continuation of the research carried out in [1]-[2], where the robustnessanalysis for stochastic approximation algorithms is given for two cases: 1. The regression functionand the Liapunov function are...This paper is a continuation of the research carried out in [1]-[2], where the robustnessanalysis for stochastic approximation algorithms is given for two cases: 1. The regression functionand the Liapunov function are not zero at the sought-for x^0, 2. lim supnot zero, here {ξ_i} are the measurement errors and {a_n} are the weighting coefficients in thealgorithm. Allowing these deviations from zero to occur simultaneously but to remain small, thispaper shows that the estimation error is still small even for a class fo measurement errors moregeneral than that considered in [2].展开更多
We present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics.The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a cons...We present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics.The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte Carlo method to simulate time-dependent statistical characteristics of growing cell populations.To benchmark performance,we compare simulation results with steadystate and time-dependent analytical solutions for several scenarios,including steadystate and time-dependent gene expression,and the effects on population heterogeneity of cell growth,division,and DNA replication.This comparison demonstrates that the algorithm provides an efficient and accurate approach to simulate how complex biological features influence gene expression.We also use the algorithm to model gene expression dynamics within"bet-hedging"cell populations during their adaption to environmental stress.These simulations indicate that the algorithm provides a framework suitable for simulating and analyzing realistic models of heterogeneous population dynamics combining molecular-level stochastic reaction kinetics,relevant physiological details and phenotypic variability.展开更多
In this paper,we revisit the Nested Stochastic Simulation Algorithm(NSSA)for stochastic chemical reacting networks by first proving its strong convergence.We then study a speed up of the algorithm by using the explici...In this paper,we revisit the Nested Stochastic Simulation Algorithm(NSSA)for stochastic chemical reacting networks by first proving its strong convergence.We then study a speed up of the algorithm by using the explicit Tau-Leaping method as the Inner solver to approximate invariant measures of fast processes,for which strong error estimates can also be obtained.Numerical experiments are presented to demonstrate the validity of our analysis.展开更多
文摘This paper presents a new stochastic algorithm for box constrained global optimization problem. Bacause the level set of objective function is always not known, the authors designed a region containing the current minimum point to replace it, and in order to fit the level set well, this region would be walking and contracting in the running process. Thus, the new algorithm is named as region's walk and contraction(RWC). Some numerical experiments for the RWC were conducted, which indicate good property of the algorithm.
基金This work was supported by the National Natural Science Foundation of China (No.30871341), the National High-Tech Research and Development Program of China (No.2006AA02-Z190), the Shanghai Leading Academic Discipline Project (No.S30405), and the Natural Science Foundation of Shanghai Normal University (No.SK200937).
文摘The stochastic simulation algorithm (SSA) accurately depicts spatially homogeneous wellstirred chemically reacting systems with small populations of chemical species and properly represents noise, but it is often abandoned when modeling larger systems because of its computational complexity. In this work, a twin support vector regression based stochastic simulations algorithm (TS^3A) is proposed by combining the twin support vector regression and SSA, the former is a well-known robust regression method in machine learning. Numerical results indicate that this proposed algorithm can be applied to a wide range of chemically reacting systems and obtain significant improvements on efficiency and accuracy with fewer simulating runs over the existing methods.
文摘In this paper, we develop a new theoretical framework by means of the absorbing Markov process theory for analyzing some stochastic global optimization algorithms. Applying the framework to the pure random search, we prove that the pure random search converges to the global minimum in probability and its time has geometry distribution. We also analyze the pure adaptive search by this framework and turn out that the pure adaptive search converges to the global minimum in probability and its time has Poisson distribution.
文摘The present study proposes a stochastic simulation scheme to model reactive boundaries through a position jump process which can be readily implemented into the Inhomogeneous Stochastic Simulation Algorithm by modifying the propensity of the diffusive jump over the reactive boundary. As compared to the literature, the present approach does not require any correction factors for the propensity. Also, the current expression relaxes the constraint on the compartment size allowing the problem to be solved with a coarser grid and therefore saves considerable computational cost. The modified algorithm is then applied to simulate three reaction-diffusion systems with reactive boundaries.
文摘We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.
基金supported by the Aviation Science Funds of China(2010ZC13012)the Fund of Jiangsu Innovation Program for Graduate Education (CXLX11 0203)
文摘There are many population-based stochastic search algorithms for solving optimization problems. However, the universality and robustness of these algorithms are still unsatisfactory. This paper proposes an enhanced self-adaptiveevolutionary algorithm (ESEA) to overcome the demerits above. In the ESEA, four evolutionary operators are designed to enhance the evolutionary structure. Besides, the ESEA employs four effective search strategies under the framework of the self-adaptive learning. Four groups of the experiments are done to find out the most suitable parameter values for the ESEA. In order to verify the performance of the proposed algorithm, 26 state-of-the-art test functions are solved by the ESEA and its competitors. The experimental results demonstrate that the universality and robustness of the ESEA out-perform its competitors.
基金Project supported by the National Natural Science Foundation of China (No.30571059)the National High-Tech Research and Development Program of China(No.2006AA02Z190).
文摘Presented here is an L-leap method for accelerating stochastic simulation of well-stirred chemically reacting systems, in which the number of reactions occurring in a reaction channel with the largest propensity function is calculated from the leap condition and the number of reactions occurring in the other reaction channels are generated by using binomial random variables during a leap. The L-leap method can better satisfy the leap condition. Numerical simulation results indicate that the L-leap method can obtain better performance than established methods.
基金the National Natural Science Foundation of China(No.30571059)the National High-Tech Research and Development Program of China(No.2006AA02Z190)
文摘In this paper, we develop a modified accelerated stochastic simulation method for chemically reacting systems, called the "final all possible steps" (FAPS) method, which obtains the reliable statistics of all species in any time during the time course with fewer simulation times. Moreover, the FAPS method can be incorporated into the leap methods, which makes the simulation of larger systems more efficient. Numerical results indicate that the proposed methods can be applied to a wide range of chemically reacting systems with a high-precision level and obtain a significant improvement on efficiency over the existing methods.
文摘Biochemical systems have numerous practical applications, in particular to the study of critical intracellular processes. Frequently, biochemical kinetic models depict cellular processes as systems of chemical reactions. Many biological processes in a cell are inherently stochastic, due to the existence of some low molecular amounts. These stochastic fluctuations may have a great effect on the biochemical system’s behaviour. In such cases, stochastic models are necessary to accurately describe the system’s dynamics. Biochemical systems at the cellular level may entail many species or reactions and their mathematical models may be non-linear and with multiple scales in time. In this work, we provide a numerical technique for simplifying stochastic discrete models of well-stirred biochemical systems, which ensures that the main properties of the original system are preserved. The proposed technique employs sensitivity analysis and requires solving an optimization problem. The numerical tests on several models of practical interest show that our model reduction strategy performs very well.
基金the National Natural Science Foundation of China (60472052,10577007)the Specialized Research Fund for National Key Lab of Communication (51434020105ZS04).
文摘Direct sequence spread spectrum transmission can be realized at low SNR, and has low probabilityof detection. It is aly problem how to obtain the original users' signal in a non-cooperative context. In practicality, the DS/CDMA sources received are linear convolute mixing. A more complex multichannel blind deconvolution MBD algorithm is required to achieve better source separation. An improved MBD algorithm for separating linear convolved mixtures of signals in CDMA system is proposed. This algorithm is based on minimizing the average squared cross-output-channel-correlation. The mixture coefficients are totally unknown, while some knowledge about temporal model exists. Results show that the proposed algorithm can bring about the exactness and low computational complexity.
基金National Natural Science Foundation of China(No.61374044)Shanghai Science Technology Commission,China(Nos.15510722100,16111106300)
文摘Special input signals identification method based on the auxiliary model based multi-innovation stochastic gradient algorithm for Hammerstein output-error system was proposed.The special input signals were used to realize the identification and separation of the Hammerstein model.As a result,the identification of the dynamic linear part can be separated from the static nonlinear elements without any redundant adjustable parameters.The auxiliary model based multi-innovation stochastic gradient algorithm was applied to identifying the serial link parameters of the Hammerstein model.The auxiliary model based multi-innovation stochastic gradient algorithm can avoid the influence of noise and improve the identification accuracy by changing the innovation length.The simulation results show the efficiency of the proposed method.
文摘Cellular environments are in essence stochastic, owing to the random character of the biochemical reaction events in a single cell. Stochastic fluctuations may substantially contribute to the dynamics of systems with small copy numbers of some biochemical species. Then, stochastic models are indispensable for properly portraying the behaviour of the system. Sensitivity analysis is one of the central tools for studying stochastic models of cellular dynamics. Here, we propose some finite-difference strategies for estimating parametric sensitivities of higher-order moments of the system state for stochastic discrete biochemical kinetic models. To reduce the variance of the sensitivity estimator, we employ various coupling techniques. The advantages of the proposed methods are illustrated in several models of biochemical systems of practical relevance.
文摘This paper proposes the cooperative position estimation of a group of mobile robots, which pertbrms disaster relief tasks in a wide area. When searching the wide area, it becomes important to know a robot's position correctly. However, for each mobile robot, it is impossible to know its own position correctly. Therefore, each mobile robot estimates its position from the data of sensor equipped on it. Generally, the sensor data is incorrect since there is sensor noise, etc. This research considers two types of the sensor data errors from omnidirectional camera. One is the error of white noise of the image captured by omnidirectional camera and so on. Another is the error of position and posture between two omnidirectional cameras. To solve the error of latter case, we proposed a self-position estimation algorithm for multiple mobile robots using two omnidirectional cameras and an accelerometer. On the other hand, to solve the error of the former case, this paper proposed an algorithm of cooperative position estimation for multiple mobile robots. In this algorithm, each mobile robot uses two omnidirectional cameras to observe the surrounding mobile robot and get the relative position between mobile robots. Each mobile robot estimates its position with only measurement data of each other mobile robots. The algorithm is based on a Bayesian filtering. Simulations of the proposed cooperative position estimation algorithm for multiple mobile robots are performed. The results show that position estimation is possible by only using measurement value from each other robot.
文摘In this paper,we present a stochastic adaptive algorithm using radial basis function models for global optimization of costly black-box functions.The exploration radii in local searches are generated adaptively.Each iteration point is selected from some randomly generated trial points according to certain criteria.A restarting strategy is adopted to build the restarting version of the algorithm.The performance of the presented algorithm and its restarting version are tested on 13 standard numerical examples.The numerical results suggest that the algorithm and its restarting version are very effective.
文摘Adaptive digital filtering has traditionally been developed based on the minimum mean square error (MMSE) criterion and has found ever-increasing applications in communications. This paper presents an alternative adaptive filtering design based on the minimum symbol error rate (MSER) criterion for communication applications. It is shown that the MSER filtering is smarter, as it exploits the non-Gaussian distribution of filter output effectively. Consequently, it provides significant performance gain in terms of smaller symbol error over the MMSE approach. Adopting Parzen window or kernel density estimation for a probability density function, a block-data gradient adaptive MSER algorithm is derived. A stochastic gradient adaptive MSER algorithm, referred to as the least symbol error rate, is further developed for sample-by-sample adaptive implementation of the MSER filtering. Two applications, involving single-user channel equalization and beamforming assisted receiver, are included to demonstrate the effectiveness and generality of the proposed adaptive MSER filtering approach.
基金supported by the U.S. Army Research Office (No. W911NF-12-1-0223)
文摘This paper introduces a post-iteration averaging algorithm to achieve asymptotic optimality in convergence rates of stochastic approximation algorithms for consensus control with structural constraints. The algorithm involves two stages. The first stage is a coarse approximation obtained using a sequence of large stepsizes. Then, the second stage provides a refinement by averaging the iterates from the first stage. We show that the new algorithm is asymptotically efficient and gives the optimal convergence rates in the sense of the best scaling factor and 'smallest' possible asymptotic variance.
文摘In this paper, the improvement of pure random search is studied. By taking some information of the function to be minimized into consideration, the authors propose two stochastic global optimization algorithms. Some numerical experiments for the new stochastic global optimization algorithms are presented for a class of test problems.
基金This project is supported by the National Natural Science Foundation of China
文摘This paper is a continuation of the research carried out in [1]-[2], where the robustnessanalysis for stochastic approximation algorithms is given for two cases: 1. The regression functionand the Liapunov function are not zero at the sought-for x^0, 2. lim supnot zero, here {ξ_i} are the measurement errors and {a_n} are the weighting coefficients in thealgorithm. Allowing these deviations from zero to occur simultaneously but to remain small, thispaper shows that the estimation error is still small even for a class fo measurement errors moregeneral than that considered in [2].
基金the National Science and Engineering Research Council of Canada(NSERC)the Canadian Institutes of Health Research(CIHR)+1 种基金the Academy of Finland(Application Number 129657,Finnish Programme for Centres of Excellence in Research 2006-2011,and 124615)the Tampere Graduate School in Information Science and Engineering(TISE).
文摘We present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics.The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte Carlo method to simulate time-dependent statistical characteristics of growing cell populations.To benchmark performance,we compare simulation results with steadystate and time-dependent analytical solutions for several scenarios,including steadystate and time-dependent gene expression,and the effects on population heterogeneity of cell growth,division,and DNA replication.This comparison demonstrates that the algorithm provides an efficient and accurate approach to simulate how complex biological features influence gene expression.We also use the algorithm to model gene expression dynamics within"bet-hedging"cell populations during their adaption to environmental stress.These simulations indicate that the algorithm provides a framework suitable for simulating and analyzing realistic models of heterogeneous population dynamics combining molecular-level stochastic reaction kinetics,relevant physiological details and phenotypic variability.
基金The research of D.Liu and C.Huang is supported by National Science Foundation DMS0845061.
文摘In this paper,we revisit the Nested Stochastic Simulation Algorithm(NSSA)for stochastic chemical reacting networks by first proving its strong convergence.We then study a speed up of the algorithm by using the explicit Tau-Leaping method as the Inner solver to approximate invariant measures of fast processes,for which strong error estimates can also be obtained.Numerical experiments are presented to demonstrate the validity of our analysis.