Integrable nonlinear evolution equations and dynamical systems in multidimensions

The investigation of nonlinear evolution equations and dynamical systems integrable in multidimensions constitutes at present our main research interest. Here we survey findings obtained recently as well as over time: solvable equations (both PDEs and ODEs) are reported, philosophical motivations and methodological approaches are outlined. For more detailed treatments, including the display and analysis of solutions, the interested reader is referred to the original papers.On leave while serving as Secretary General, Pugwash Conferences on Science and World Affairs, Geneva, London, Rome.     

Simulation based analysis of patient arrival to health care systems and evaluation of an operations improvement scheme

Various demands of different patients over both medical resource and time domains in health care systems raise requests of strategies for balanced system capacity from an operations perspective. In this paper, a quantitative modeling technique with both patient arrival and associated treatment process integrated are used to characterize health care system performance and evaluate system efficiency. The patient arrival process is described as a dynamic random Poisson process and patient treatments are characterized as consumption processes of various health care resources over time with a view of the “product line” used. The waiting time of patients and usage of health care resources are proposed as system performance measures based on their means, variances, and confidence intervals. A simulation considering patients with several various diseases is given to find a mechanism of conflicting factors in decisions of balanced system capacity, and an operation scheme of “evenly balanced load for bottlenecks” is obtained based on analysis of simulation outputs. Simul8 provides the software environment for the simulation.     

ON THE BREAKDOWNS OF THE GALERKIN AND LEAST-SQUARES METHODS

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Behavioral modeling in weight loss interventions

Designing systems with human agents is difficult because it often requires models that characterize agents’ responses to changes in the system’s states and inputs. An example of this scenario occurs when designing treatments for obesity. While weight loss interventions through increasing physical activity and modifying diet have found success in reducing individuals’ weight, such programs are difficult to maintain over long periods of time due to lack of patient adherence. A promising approach to increase adherence is through the personalization of treatments to each patient. In this paper, we make a contribution toward treatment personalization by developing a framework for predictive modeling using utility functions that depend upon both time-varying system states and motivational states evolving according to some modeled process corresponding to qualitative social science models of behavior change. Computing the predictive model requires solving a bilevel program, which we reformulate as a mixed-integer linear program (MILP). This reformulation provides the first (to our knowledge) formulation for Bayesian inference that uses empirical histograms as prior distributions. We study the predictive ability of our framework using a data set from a weight loss intervention, and our predictive model is validated by comparison to standard machine learning approaches. We conclude by describing how our predictive model could be used for optimization, unlike standard machine learning approaches that cannot.     

Switching dynamics of multiple linear oscillators

In this paper, the switching dynamics of linear oscillators with arbitrary discontinuous forcing are investigated through the concept of switching systems, and such switching systems consist of countable prescribed linear oscillators with different external excitations. The traditional treatments are to smoothen the discontinuity at switching points of two subsystems in a switching system, which can provide an approximate solution only. Therefore, an alternative method is presented to obtain an exact solution of the resultant switching linear system. Under periodic piecewise forcing and random forcing, the corresponding exact solutions and stochastic responses of switching linear systems are developed. For any periodic forcing, the periodic responses and stability of the resultant system composed of multiple linear oscillators in different time intervals are presented. In addition, the resultant switching system consisting of two oscillators are discussed, and the corresponding stability analysis is carried out.     

The limits of phenomenology: From behaviorism to drug testing and engineering design

It is widely believed that theory is useful in physics because it describes simple systems and that strictly empirical phenomenological approaches are necessary for complex biological and social systems. Here, we prove based on an analysis of the information that can be obtained from experimental observations that theory is even more essential in the understanding of complex systems. Implications of this proof revise the general understanding of how we can understand complex systems including the behaviorist approach to human behavior, problems with testing engineered systems, and medical experimentation for evaluating treatments and the Food and Drug Administration approval of medications. Each of these approaches are inherently limited in their ability to characterize real world systems due to the large number of conditions that can affect their behavior. Models are necessary as they can help to characterize behavior without requiring observations for all possible conditions. The testing of models by empirical observations enhances the utility of those observations. For systems for which adequate models have not been developed, or are not practical, the limitations of empirical testing lead to uncertainty in our knowledge and risks in individual, organizational, and social policy decisions. These risks should be recognized and inform our decisions. © 2015 Wiley Periodicals, Inc. Complexity 21: 181–189, 2016     

三重积分计算浅析

本文首先讨论了不同坐标系中一例三重积分的计算,然后研究了变量置换在三重积分计算中的应用,指出它是三重积分在柱(球)坐标系中计算的本质,最后讨论了例题若干变形的处理,这些都有助于丰富和完善相关的教学内容与细节.     

Optimal healthcare decisions: Comparing medical treatments on a cost-effectiveness basis

This paper deals with medical treatments comparison from the cost-effectiveness viewpoint. A decision theory scheme is considered, where the decision space is the set of treatments involved, the space of states of nature consists of the respective net benefits of the treatments, and the utility function is one of two possible candidates. A first candidate is the one typically used in the literature on cost-effectiveness analysis, for which the utility of a decision is proportional to the net benefit gain, and a second one is of the type 0–1, which penalizes the wrong decisions with a fixed quantity. Their associated optimal decision rules, both frequentist and Bayesian, are analyzed and compared via frequentist evaluation of their performance, and the conclusion is that the latter beats the former in the sense of choosing the optimal treatment more often than any other, thus minimizing the proportion of wrong decisions. Illustrations with simulated and real data are provided.     

Preservation of reliability classes under the formation of coherent systems

The preservation of reliability aging classes under the formation of coherent systems is a relevant topic in reliability theory. Thus, it is well known that the new better than used class is preserved under the formation of coherent systems with independent components. However, surprisingly, the increasing failure rate class is not preserved in the independent and identically distributed case, that is, the components may have the (negative) aging increasing failure rate property, but the system does not have this property. In this paper, we study conditions for the preservation of the main reliability classes under the formation of general coherent systems. These results can be applied both for systems with independent or dependent components. We consider both the case of systems with identically distributed components and the case of systems with components having different distributions. Copyright © 2013 John Wiley & Sons, Ltd.     

On the efficiency of some supplemented (α1,α2,…,αR)-resolvable block designs

Statistical properties of designs with two kinds of treatments: basic and supplementary, are examined. The basic treatments are arranged randomly in an (α₁,α₂,…,α_R)-resolvable block design. This basic design is orthogonally supplemented by some orthogonal addition of the supplementary treatments.Mixed linear models of observations following two- or three-step randomizations are considered. The final design under these models is generally balanced and that allows obtaining its stratum efficiency factors for both cases.     

Quantum Backreaction (Casimir) Effect I. What are Admissible Idealizations?

Casimir effect, in a broad interpretation which we adopt here, consists in a backreaction of a quantum system to adiabatically changing external conditions. Although the system is usually taken to be a quantum field, we show that this restriction rather blurs than helps to clarify the statement of the problem. We discuss the problem from the point of view of algebraic structure of quantum theory, which is most appropriate in this context. The system in question may be any quantum system, among others both finite- as infinite-dimensional canonical systems are allowed. A simple finite-dimensional model is discussed. We identify precisely the source of difficulties and infinities in most of traditional treatments of the problem for infinite-dimensional systems (such as quantum fields), which is incompatibility of algebras of observables or their representations. We formulate conditions on model idealizations which are acceptable for the discussion of the adiabatic backreaction problem. In the case of quantum field models in that class we find that the normal ordered energy density is a well-defined distribution, yielding global energy in the limit of a unit test function. Although we see the “zero point” expressions as inappropriate, we show how they can arise in the quantum field theory context as a result of uncontrollable manipulations.Communicated by Klaus Fredenhagensubmitted 13/04/04, accepted 24/11/04     

On the use of two QMR algorithms for solving singular systems and applications in Markov chain modeling

Recently, Freund and Nachtigal proposed the quasi-minimal residual algorithm (QMR) for solving general nonsingular non-Hermitian linear systems. The method is based on the Lanczos process, and thus it involves matrix—vector products with both the coefficient matrix of the linear system and its transpose. Freund developed a variant of QMR, the transpose-free QMR algorithm (TFQMR), that only requires products with the coefficient matrix. In this paper, the use of QMR and TFQMR for solving singular systems is explored. First, a convergence result for the general class of Krylov-subspace methods applied to singular systems is presented. Then, it is shown that QMR and TFQMR both converge for consistent singular linear systems with coefficient matrices of index 1. Singular systems of this type arise in Markov chain modeling. For this particular application, numerical experiments are reported.     

Invariance principles for hybrid systems with memory

Hybrid systems with memory are dynamical systems exhibiting both delayed and hybrid dynamics. Such systems can be described by hybrid functional inclusions. Classical invariance principles play an instrumental role in proving stability and convergence of dynamical systems. Invariance principles for general hybrid systems with delays, however, remain an open topic. In this paper, we prove invariance principles for hybrid systems with memory, using both Lyapunov–Razumikhin function and Lyapunov–Krasovskii functional methods. These invariance principles are then applied to derive two stability results as corollaries.     

自主研发与技术引进对企业绩效影响差异分析

以上海工业企业为研究样本分析了企业自主研发和技术引进对企业绩效的不同贡献.文中将两种不同的促进技术进步策略作异质性的分析处理,同时考虑模型的选择偏差,再通过计量方法的匹配,做基于倾向得分的平均处理效应估计.研究结果显示,同不做任何技术创新与引进的企业相比,试图通过技术进步寻求发展的企业均对企业绩效产生了积极效应.其中技术引进方式对企业的当期利润和企业劳动生产率的提高更优于自主研发方式,而自主研发对于企业TFP的贡献却是大于技术引进的.研究还显示这两种技术进步方式对于不同所有制结构的企业作用不同.     

Simple adaptive variable structure control for unknown chaotic systems

This paper proposes two novel adaptive variable structure tracking controllers for a large class of chaotic systems with unknown dynamics in presence of both external disturbances and input nonlinearities. The pros and cons of each proposed methodology is also represented. In order to eliminate the chattering effect in the former controlled system, two corresponding fuzzy adaptive controllers are presented. Besides, synchronization of two non-identical uncertain chaotic systems is investigated using our proposed methods in both full and reduced-order forms. It can be seen that not only our proposed control schemes can be applied to a wide class of uncertain chaotic systems but also it is simple to implement in practical application. Finally, the proposed methods are applied to some famous chaotic systems to verify the effectiveness of the proposed methods.     

Dynamics of an HIV Infection Model with Two Infection Routes and Evolutionary Competition between Two Viral Strains

The existing combination therapy of HIV antiretroviral drugs can lead to the emergence of drug-resistant viruses, and cannot effectively block direct cell-to-cell infections, these factors results in incomplete virus suppression and increased risk of disease progression. In this paper, we formulate an HIV model with two strains representing a drug-sensitive virus and a drug-resistant virus to study the joint mechanism of drug resistance. We first reduce the infection-age model to a system of integro-differential equations with infinite delays. Then the stability of the equilibria and the dynamics of competition between two viruses are studied to illuminate the joint effects of infection-age and two infection routes on the evolution of both drug-sensitive and drug-resistant strains before and during drug treatment. Applying a persistence theorem for infinite dimensional systems, we obtain that the disease is always present when the basic reproduction number is larger than unity. Numerical simulations confirm that the basic reproduction numbers and mutation coefficient are the key threshold parameters for determining the competition results of the two viral strains and indicate the cell-to-cell transmission increases the likelihood that HIV breaks out within the host. Finally, sensitivity analyses suggest that the available combination therapy should be taken once symptoms of resistance appear during drug treatment, and demonstrate that the presence of cell-to-cell transmission attenuates the efficacy of the existing antiretroviral drug treatments.     

Order restricted randomized designs for control versus treatment comparison

We develop a method of randomizing units to treatments that relies on subjective judgement or on possible coarse modeling to produce restrictions on the randomization. The procedure thus fits within the general framework of ranked set sampling. However, instead of selecting a single unit from each set for full measurement, all units within a set are used. The units within a set are assigned to different treatments. Such an assignment translates the positive dependence among units within a set into a reduction in variation of contrasting features of the treatments. A test for treatment versus control comparison, with controlled familywise error rate, is developed along with the associated confidence intervals. The new procedure is shown to be superior to corresponding procedures based on completely randomized or ranked set sample designs. The superiority appears both in asymptotic relative efficiency and in power for finite sample sizes. Importantly, this test does not rely on perfect rankings; rather, the information in the data on the quality of rankings is exploited to maintain the level of the test when rankings are imperfect. The asymptotic relative efficiency of the test is not affected by estimation of the quality of rankings, and the finite sample performance is only mildly affected.     

一类线性系统的数值控制设计

主要讨论了具有不稳定切换子模型的切换线性系统的稳定性问题.首先考虑了通过设计切换律来达到切换线性系统的稳定性问题.然后研究了切换线性控制系统可镇定性问题,通过设计控制律和切换律得到系统可镇定的判据.