Conventional multivariate statistical methods for process monitoring may not be suitable for dynamic processes since they usually rely on assumptions such as time invariance or uncorrelation. We are therefore motivate...Conventional multivariate statistical methods for process monitoring may not be suitable for dynamic processes since they usually rely on assumptions such as time invariance or uncorrelation. We are therefore motivated to propose a new monitoring method by compensating the principal component analysis with a weight approach.The proposed monitor consists of two tiers. The first tier uses the principal component analysis method to extract cross-correlation structure among process data, expressed by independent components. The second tier estimates auto-correlation structure among the extracted components as auto-regressive models. It is therefore named a dynamic weighted principal component analysis with hybrid correlation structure. The essential of the proposed method is to incorporate a weight approach into principal component analysis to construct two new subspaces, namely the important component subspace and the residual subspace, and two new statistics are defined to monitor them respectively. Through computing the weight values upon a new observation, the proposed method increases the weights along directions of components that have large estimation errors while reduces the influences of other directions. The rationale behind comes from the observations that the fault information is associated with online estimation errors of auto-regressive models. The proposed monitoring method is exemplified by the Tennessee Eastman process. The monitoring results show that the proposed method outperforms conventional principal component analysis, dynamic principal component analysis and dynamic latent variable.展开更多
We provide a general dynamical approach for the quantum Zeno and anti-Zeno effects in an open quantum system under repeated non-demolition measurements. In our approach the repeated measurements are described by a gen...We provide a general dynamical approach for the quantum Zeno and anti-Zeno effects in an open quantum system under repeated non-demolition measurements. In our approach the repeated measurements are described by a general dynamical model without the wave function collapse postulation. Based on that model, we further study both the short-time and long-time evolutions of the open quantum system under repeated non-demolition measurements, and derive the measurement-modified decay rates of the excited state. In the cases with frequent ideal measurements at zero-temperature, we re-obtain the same decay rate as that from the wave function collapse postulation （Nature, 2000, 405： 546）. The correction to the ideal decay rate is also obtained under the non-ideal measurements. Especially, we find that the quantum Zeno and anti-Zeno effects are possibly enhanced by the non-ideal natures of measurements. For the open system under measurements with arbitrary period, we generally derive the rate equation for the long-time evolution for the cases with arbitrary temperature and noise spectrum, and show that in the long-time evolution the noise spectrum is effectively tuned by the repeated measurements. Our approach is also able to describe the quantum Zeno and anti-Zeno effects given by the phase modulation pulses, as well as the relevant quantum control schemes.展开更多
Surveillance to detect cancer recurrence is an important part of care for cancer survivors.In this paper we discuss the design of optimal strategies for early detection of disease recurrence based on each patient'...Surveillance to detect cancer recurrence is an important part of care for cancer survivors.In this paper we discuss the design of optimal strategies for early detection of disease recurrence based on each patient's distinct biomarker trajectory and periodically updated risk estimated in the setting of a prospective cohort study.We adopt a latent class joint model which considers a longitudinal biomarker process and an event process jointly,to address heterogeneity of patients and disease,to discover distinct biomarker trajectory patterns,to classify patients into different risk groups,and to predict the risk of disease recurrence.The model is used to develop a monitoring strategy that dynamically modifies the monitoring intervals according to patients' current risk derived from periodically updated biomarker measurements and other indicators of disease spread.The optimal biomarker assessment time is derived using a utility function.We develop an algorithm to apply the proposed strategy to monitoring of new patients after initial treatment.We illustrate the models and the derivation of the optimal strategy using simulated data from monitoring prostate cancer recurrence over a 5-year period.展开更多
基金Supported by the National Natural Science Foundation of China(61174114)the Research Fund for the Doctoral Program of Higher Education in China(20120101130016)+1 种基金the Natural Science Foundation of Zhejiang Province(LQ15F030006)and the Science and Technology Program Project of Zhejiang Province(2015C33033)
文摘Conventional multivariate statistical methods for process monitoring may not be suitable for dynamic processes since they usually rely on assumptions such as time invariance or uncorrelation. We are therefore motivated to propose a new monitoring method by compensating the principal component analysis with a weight approach.The proposed monitor consists of two tiers. The first tier uses the principal component analysis method to extract cross-correlation structure among process data, expressed by independent components. The second tier estimates auto-correlation structure among the extracted components as auto-regressive models. It is therefore named a dynamic weighted principal component analysis with hybrid correlation structure. The essential of the proposed method is to incorporate a weight approach into principal component analysis to construct two new subspaces, namely the important component subspace and the residual subspace, and two new statistics are defined to monitor them respectively. Through computing the weight values upon a new observation, the proposed method increases the weights along directions of components that have large estimation errors while reduces the influences of other directions. The rationale behind comes from the observations that the fault information is associated with online estimation errors of auto-regressive models. The proposed monitoring method is exemplified by the Tennessee Eastman process. The monitoring results show that the proposed method outperforms conventional principal component analysis, dynamic principal component analysis and dynamic latent variable.
基金supported by the National Natural Science Foundation of China(Grant Nos.11074305,10935010,11074261 and 11121403)the National Basic Research Program of China(Grant Nos.2012CB922104 and 2014CB921402)
文摘We provide a general dynamical approach for the quantum Zeno and anti-Zeno effects in an open quantum system under repeated non-demolition measurements. In our approach the repeated measurements are described by a general dynamical model without the wave function collapse postulation. Based on that model, we further study both the short-time and long-time evolutions of the open quantum system under repeated non-demolition measurements, and derive the measurement-modified decay rates of the excited state. In the cases with frequent ideal measurements at zero-temperature, we re-obtain the same decay rate as that from the wave function collapse postulation （Nature, 2000, 405： 546）. The correction to the ideal decay rate is also obtained under the non-ideal measurements. Especially, we find that the quantum Zeno and anti-Zeno effects are possibly enhanced by the non-ideal natures of measurements. For the open system under measurements with arbitrary period, we generally derive the rate equation for the long-time evolution for the cases with arbitrary temperature and noise spectrum, and show that in the long-time evolution the noise spectrum is effectively tuned by the repeated measurements. Our approach is also able to describe the quantum Zeno and anti-Zeno effects given by the phase modulation pulses, as well as the relevant quantum control schemes.
基金supported by National Cancer Institute(Grant No.U01CA079778)
文摘Surveillance to detect cancer recurrence is an important part of care for cancer survivors.In this paper we discuss the design of optimal strategies for early detection of disease recurrence based on each patient's distinct biomarker trajectory and periodically updated risk estimated in the setting of a prospective cohort study.We adopt a latent class joint model which considers a longitudinal biomarker process and an event process jointly,to address heterogeneity of patients and disease,to discover distinct biomarker trajectory patterns,to classify patients into different risk groups,and to predict the risk of disease recurrence.The model is used to develop a monitoring strategy that dynamically modifies the monitoring intervals according to patients' current risk derived from periodically updated biomarker measurements and other indicators of disease spread.The optimal biomarker assessment time is derived using a utility function.We develop an algorithm to apply the proposed strategy to monitoring of new patients after initial treatment.We illustrate the models and the derivation of the optimal strategy using simulated data from monitoring prostate cancer recurrence over a 5-year period.
