We study the long-term qualitative behavior of randomly perturbed dynamical systems. More specifi... more We study the long-term qualitative behavior of randomly perturbed dynamical systems. More specifically, we look at limit cycles of stochastic differential equations (SDE) with Markovian switching, in which the process switches at random times among different systems of SDEs, when the switching is fast and the diffusion (white noise) term is small. The system is modeled by $$ dX^{\epsilon,\delta}(t)=f(X^{\epsilon,\delta}(t), \alpha^\epsilon(t))dt+\sqrt{\delta}\sigma(X^{\epsilon,\delta}(t), \alpha^\epsilon(t))dW(t) , \ X^\epsilon(0)=x, $$ where $\alpha^\epsilon(t)$ is a finite state space Markov chain with irreducible generator $Q=(q_{ij})$. The relative changing rates of the switching and the diffusion are highlighted by the two small parameters $\epsilon$ and $\delta$. We associate to the system the averaged ODE \[ d\bar X(t)=\bar f(\bar X(t))dt, \ X(0)=x, \] where $\bar f(\cdot)=\sum_{i=1}^{m_0}f(\cdot, i)\nu_i$ and $(\nu_1,\dots,\nu_{m_0})$ is the unique invariant probability meas...
We investigate in this paper the effect of measurement errors on the performance of Run Rules con... more We investigate in this paper the effect of measurement errors on the performance of Run Rules control charts monitoring the coefficient of variation (CV) squared. The previous Run Rules - CV in literature is improved slightly by monitoring the CV squared instead of the CV itself. The numerical results show that this improvement gives better performance for Run Rules charts. Moreover, we will show through simulation that the precision and accuracy errors do have negative effect on the performance Run Rules charts. We also find out that multiple measurements per item does not high efficiency in reducing these negative effects.Peer reviewe
Recent years have witnessed the rapid development of human activity recognition (HAR) based on we... more Recent years have witnessed the rapid development of human activity recognition (HAR) based on wearable sensor data. One can find many practical applications in this area, especially in the field of health care. Many machine learning algorithms such as Decision Trees, Support Vector Machine, Naive Bayes, K-Nearest Neighbor, and Multilayer Perceptron are successfully used in HAR. Although these methods are fast and easy for implementation, they still have some limitations due to poor performance in a number of situations. In this chapter, we propose an improved machine learning method based on the ensemble algorithm to boost the performance of these machine learning methods for HAR.
This paper is concerned with a formula of stability radii for a linear implicit difference equati... more This paper is concerned with a formula of stability radii for a linear implicit difference equation (LIDEs for short) varying in time with index-1 under structured parameter perturbations. It is shown that the lp-real and complex stability radii of these systems coincide and they are given by a formula of input-output operators. The result is an extension of a previous result for time-varying ordinary differential equations [7].
The major methodologies of crowd simulation in dynamic environment are either based on micro and ... more The major methodologies of crowd simulation in dynamic environment are either based on micro and macro models. Each of the two types of model represent choices in the trade-off between level of details and efficiency. The domain of pedestrian flow simulation in road networks is no exception and theories rely either on equation based model (LWR) or agent based models. There is a growing interest for hybrid modeling that combines both models together. This paper addresses the problem of combining both micro and macro models of pedestrians to speedup identification of optimal evacuation plan. The goal is therefor to use efficient macro modeling in part of the road networks that do not require fine grained model and less efficient but more detailed micro modeling elsewhere. The key issue raised by such an approach is to demonstrate the consistency of the resulting hybrid model. Preliminary results presented in this article are a proof of concept of how important speed up may be obtained using hybrid model to simulate evacuation plan in road networks.
We study the long-term qualitative behavior of randomly perturbed dynamical systems. More specifi... more We study the long-term qualitative behavior of randomly perturbed dynamical systems. More specifically, we look at limit cycles of stochastic differential equations (SDE) with Markovian switching, in which the process switches at random times among different systems of SDEs, when the switching is fast and the diffusion (white noise) term is small. The system is modeled by $$ dX^{\epsilon,\delta}(t)=f(X^{\epsilon,\delta}(t), \alpha^\epsilon(t))dt+\sqrt{\delta}\sigma(X^{\epsilon,\delta}(t), \alpha^\epsilon(t))dW(t) , \ X^\epsilon(0)=x, $$ where $\alpha^\epsilon(t)$ is a finite state space Markov chain with irreducible generator $Q=(q_{ij})$. The relative changing rates of the switching and the diffusion are highlighted by the two small parameters $\epsilon$ and $\delta$. We associate to the system the averaged ODE \[ d\bar X(t)=\bar f(\bar X(t))dt, \ X(0)=x, \] where $\bar f(\cdot)=\sum_{i=1}^{m_0}f(\cdot, i)\nu_i$ and $(\nu_1,\dots,\nu_{m_0})$ is the unique invariant probability meas...
We investigate in this paper the effect of measurement errors on the performance of Run Rules con... more We investigate in this paper the effect of measurement errors on the performance of Run Rules control charts monitoring the coefficient of variation (CV) squared. The previous Run Rules - CV in literature is improved slightly by monitoring the CV squared instead of the CV itself. The numerical results show that this improvement gives better performance for Run Rules charts. Moreover, we will show through simulation that the precision and accuracy errors do have negative effect on the performance Run Rules charts. We also find out that multiple measurements per item does not high efficiency in reducing these negative effects.Peer reviewe
Recent years have witnessed the rapid development of human activity recognition (HAR) based on we... more Recent years have witnessed the rapid development of human activity recognition (HAR) based on wearable sensor data. One can find many practical applications in this area, especially in the field of health care. Many machine learning algorithms such as Decision Trees, Support Vector Machine, Naive Bayes, K-Nearest Neighbor, and Multilayer Perceptron are successfully used in HAR. Although these methods are fast and easy for implementation, they still have some limitations due to poor performance in a number of situations. In this chapter, we propose an improved machine learning method based on the ensemble algorithm to boost the performance of these machine learning methods for HAR.
This paper is concerned with a formula of stability radii for a linear implicit difference equati... more This paper is concerned with a formula of stability radii for a linear implicit difference equation (LIDEs for short) varying in time with index-1 under structured parameter perturbations. It is shown that the lp-real and complex stability radii of these systems coincide and they are given by a formula of input-output operators. The result is an extension of a previous result for time-varying ordinary differential equations [7].
The major methodologies of crowd simulation in dynamic environment are either based on micro and ... more The major methodologies of crowd simulation in dynamic environment are either based on micro and macro models. Each of the two types of model represent choices in the trade-off between level of details and efficiency. The domain of pedestrian flow simulation in road networks is no exception and theories rely either on equation based model (LWR) or agent based models. There is a growing interest for hybrid modeling that combines both models together. This paper addresses the problem of combining both micro and macro models of pedestrians to speedup identification of optimal evacuation plan. The goal is therefor to use efficient macro modeling in part of the road networks that do not require fine grained model and less efficient but more detailed micro modeling elsewhere. The key issue raised by such an approach is to demonstrate the consistency of the resulting hybrid model. Preliminary results presented in this article are a proof of concept of how important speed up may be obtained using hybrid model to simulate evacuation plan in road networks.
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