Meta-control of an interacting-particle algorithm for global optimization

A common issue for stochastic global optimization algorithms is how to set the parameters of the sampling distribution (e.g. temperature, mutation/cross-over rates, selection rate, etc.) so that the samplings converge to the optimum effectively and efficiently. We consider an interacting-particle algorithm and develop a meta-control methodology which analytically guides the inverse temperature parameter of the algorithm to achieve desired performance characteristics (e.g. quality of the final outcome, algorithm running time, etc.). The main aspect of our meta-control methodology is to formulate an optimal control problem where the fractional change in the inverse temperature parameter is the control variable. The objectives of the optimal control problem are set according to the desired behavior of the interacting-particle algorithm. The control problem considers particles’ average behavior, rather than treating the behavior of individual particles. The solution to the control problem provides feedback on the inverse temperature parameter of the algorithm.     

三率调控宏观经济的数学模型

本文利用中国宏观经济发展状况，建立三率调控宏观经济的数学模型，利用宏观经济指标与三率间的回归分析考证它们的相关程度，并根据实际经验建立收益矩阵，根据经济指标对宏观经济贡献的大小建立权重系数，最后建立目标函数并求组合最优化的解。由于数据不足，而且没有考虑 风险的最小化，我们获得的决策并非一定最优，只是在某些特定的条件下最优，因此决策仅供参考。此外，随着宏观经济状况的不断变化，收益矩阵和加权系数必须随时修正，以便形成动态决策。     

基于时滞效应的随机微分投资与比例再保险博弈

金融市场不断发展,激烈的市场竞争使得相对绩效比较在保险机构的业绩评估中占据越来越重要的地位。考虑历史业绩对公司决策的影响,引入时滞效应,研究时滞效应对具有竞争关系公司之间最优投资策略和最优再保险策略的影响。运用随机最优控制和微分博弈理论,针对Cramér-Lundberg模型,得到了均衡投资和再保险策略,给出了值函数的显式解;然后进一步针对近似扩散过程,求得指数效用下均衡投资策略和比例再保险策略的显式表达。通过数值算例,分析了最优均衡策略随模型各重要参数的动态变化。结论显示:保险公司在决策时是否将时滞信息纳入考虑之中将大大影响其投资和再保险行为。保险公司考虑较早时间财富值越多,其投资再保险行为就表现得越趋向于保守和谨慎;与之相反,如果保险公司对行业间的竞争越看重,其投资再保险策略就越倾向于冒险和激进。     

FUZZY聚类在植物辐射育种上的应用——普通小麦品种辐射敏感性的FUZZY聚类分析(英文)

本研究将FUZZY聚类分析方法首次应用于辐射生物学和植物辐射育种,对普通小麦品种辐射敏感性作了FUZZY聚类分析.供试的小麦品种,按其对γ-射线的辐射敏感性强弱分为极敏感型、敏感型、中间型、迟钝型和极迟钝型五类.这一结果对小麦辐射育种工作中选择适宜的辐照材料、确定最佳的辐照剂量,从而提高辐射诱变效率具有重要的指导意义.研究还表明,采用FUZZY聚类分析对植物的品种辐射敏感性进行分类较其他方法具有更强的可靠性.     

Mutation rates and equilibrium selection under stochastic evolutionary dynamics

We examine an evolutionary model in which the mutation rate varies with the strategy. Bergin and Lipman (Econometrica 64:943–956, 1996) show that equilibrium selection using stochastic evolutionary processes depends on the specification of mutation rates. We offer a characterization of how mutation rates determine the selection of Nash equilibria in 2 × 2 symmetric coordination games for single and double limits of the small mutation rate and the large population size. We prove that the restrictions on mutation rates which ensure that the risk-dominated equilibrium is selected are the same for both orders of limits.     

Computation of optimal radiation treatment plans

The goal of radiotherapy is to destroy a tumour in the patient's body by means of radiation. At the same time, healthy tissue is to be damaged as little as possible. In mathematical terms this means: in certain parts of the body minimal doses - necessary to destroy the cancerous tissue - must be achieved; in other parts maximum doses should not be exceeded to preserve organs like liver, spinal cord, etc. If we minimize the total time of irradiation, taking into account these constraints, we find an optimal solution to the treatment problem. The dose depends on a number of parameters. By fixing some of them and determining the remaining ones so as to satisfy constraints given in advance, a model for radiation-treatment planning is obtained. It is discretized and so reduced to a practical form. The result of this discretization process is a mixed-integer problem or a problem with a nonlinear constraint. The implementation of the model as optimizing system for radiation-treatment planning is described. An example demonstrates the application of the system to a kidney tumour.     

Evolving phylogenies of trait-dependent branching with mutation and competition,Part I: Existence

We propose a type-dependent branching model with mutation and competition for modelling phylogenies of a virus population. The competition kernel depends on the total mass, the types of the virus particles, and the genetic information available through the number of nucleotide substitutions separating the virus particles. We consider evolving phylogenies in the huge population, short reproduction time and frequent mutation regime, show tightness in the space of marked metric measure spaces and characterize the limit through a martingale problem. Due to heterogeneity in the branching rates, the phylogenies are not ultra-metric. We therefore develop new techniques for verifying compact containment.     

On nonlinear dynamics of interacting populations: Coupled kink waves in a system of two populations

We discuss a nonlinear model of the spatial–time interaction among populations which reproduction and intensity of interaction depend on their spatial density. For the particular case of two populations with constant growth rates and competition coefficients we obtain analytical nonlinear waves of kink kind. The kinks are connected to propagation of the deviations from the stationary densities corresponding to fixed points in the phase space of the population densities. The kinks are coupled, i.e. the changes of the densities of the two populations are synchronous. Coupled kink solutions are obtained also for the general case of variable growth rates and variable coefficients of interactions.     

Dynamical behaviors of a classical Lotka–Volterra competition–diffusion–advection system

This paper deals with a two-species competition model in a homogeneous advective environment, where two species are subjected to a net loss of individuals at the downstream end. Under the assumption that the advection and diffusion rates of two species are proportional, we give a basic classification on the global dynamics by employing the theory of monotone dynamical system. It turns out that bistability does not happen, but coexistence and competitive exclusion may occur. Furthermore, we present a complete classification on the global dynamics in terms of the growth rates of two species. However, once the above assumption does not hold, bistability may occur. In detail, there exists a tradeoff between growth rates of two species such that competition outcomes can shift between three possible scenarios, including competitive exclusion, bistability and coexistence. These results show that growth competence is important to determine dynamical behaviors.     

A cellular automata model of chemotherapy effects on tumour growth: targeting cancer and immune cells

The effects of therapy on avascular cancer development based on a stochastic cellular automata model are considered. Making the model more compatible with the biology of cancer, the following features are implemented: intrinsic resistance of cancerous cells along with drug-induced resistance, drug-sensitive cells, immune system. Results are reported for no treatment, discontinued treatment after only one cycle of chemotherapy, and periodic drug administration therapy modes. Growth fraction, necrotic fraction, and tumour volume are used as output parameters beside a 2-D graphical growth presentation. Periodic drug administration is more effective to inhibit the growth of tumours. The model has been validated by the verification of the simulation results using in vivo literature data. Considering immune cells makes the model more compatible with the biological realities. Beside targeting cancer cells, the model can also simulate the activation of the immune system to fight against cancer.

Abbreviations CA: cellular automata; DSC: drug sensitive cell; DRC: drug resistant cell; GF: growth fraction; NF: necrotic fraction; ODE: ordinary differential equation; PDE: partial differential equation; SCAM: The proposed stochastic cellular automata model     

Flatness and null controllability of 1-D parabolic equations

We present a recent result on null controllability of one-dimensional linear parabolic equations with boundary control. The space-varying coefficients in the equation can be fairly irregular, in particular they can present discontinuities, degeneracies or singularities at some isolated points; the boundary conditions at both ends are of generalized Robin-Neumann type. Given any (fairly irregular) initial condition θ₀ and any final time T, we explicitly construct an open-loop control which steers the system from θ₀ at time 0 to the final state 0 at time T. This control is very regular (namely Gevrey of order s with 1 < s < 2); it is simply zero till some (arbitrary) intermediate time τ, so as to take advantage of the smoothing effect due to diffusion, and then given by a series from τ to the final time T. We illustrate the effectiveness of the approach on a nontrivial numerical example, namely a degenerate heat equation with control at the degenerate side. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A boundary layer problem in nonflat domains with measurable viscous coefficients

We study the convergence of weak solutions of the Navier–Stokes equations with vanishing measurable viscous coefficients in domains with nonflat boundaries. Sufficient anisotropic conditions on the vanishing rates of the viscous coefficients are found to prove the convergence of Leray–Hopf weak solutions of the Navier–Stokes equations to solutions of the corresponding Euler equations. As the domains are not flat, we apply a change of variables to flatten the domains. We then construct explicit boundary layers for the system of Navier–Stokes equations in the upper-half space with measurable viscous coefficients. The result is new even when the viscous coefficients are constant, and it recovers the classical results when domains are flat and with constant viscous coefficients.     

On the power and limitations of affine policies in two-stage adaptive optimization

We consider a two-stage adaptive linear optimization problem under right hand side uncertainty with a min–max objective and give a sharp characterization of the power and limitations of affine policies (where the second stage solution is an affine function of the right hand side uncertainty). In particular, we show that the worst-case cost of an optimal affine policy can be times the worst-case cost of an optimal fully-adaptable solution for any δ > 0, where m is the number of linear constraints. We also show that the worst-case cost of the best affine policy is times the optimal cost when the first-stage constraint matrix has non-negative coefficients. Moreover, if there are only k ≤ m uncertain parameters, we generalize the performance bound for affine policies to , which is particularly useful if only a few parameters are uncertain. We also provide an -approximation algorithm for the general case without any restriction on the constraint matrix but the solution is not an affine function of the uncertain parameters. We also give a tight characterization of the conditions under which an affine policy is optimal for the above model. In particular, we show that if the uncertainty set, is a simplex, then an affine policy is optimal. However, an affine policy is suboptimal even if is a convex combination of only (m + 3) extreme points (only two more extreme points than a simplex) and the worst-case cost of an optimal affine policy can be a factor (2 − δ) worse than the worst-case cost of an optimal fully-adaptable solution for any δ > 0.     

Biologically guided intensity modulated radiation therapy planning optimization with fraction-size dose constraints

Although intensity modulated radiation therapy plans are optimized as a single overall treatment plan, they are delivered over 30–50 treatment sessions (fractions) and both cumulative and per-fraction dose constraints apply. Recent advances in imaging technology provide more insight on tumour biology that has been traditionally disregarded in planning. The current practice of delivering physical dose distributions across the tumour may potentially be improved by dose distributions guided by the biological responses of the tumour points. The biological optimization models developed and tested in this paper generate treatment plans reacting to the tumour biology prior to the treatment as well as the changing tumour biology throughout the treatment while satisfying both cumulative and fraction-size dose limits. Complete computational testing of the proposed methods would require an array of clinical data sets with tumour biology information. Finding no open source ones in the literature, the authors sought proof of concept by testing on a simulated head-and-neck case adapted from a more standard one in the CERR library by blending it with available tumour biology data from a published study. The results show computed biologically optimized plans improve on tumour control obtained by traditional plans ignoring biology, and that such improvements persist under likely uncertainty in sensitivity values. Furthermore, adaptive plans using biological information improve on non-adaptive methods.     

时间序列中方差的结构变点的小波识别(英文)

本文给出了时间序列中方差的小波系数的两种估计:连续估计和离散估计.这两种估计可以用来检测时间序列中方差的结构变点.利用这两种估计我们给出了方差变点的位置和跳跃幅度的估计,并且显示出这些估计可达到最佳收敛速度.同时,我们还给出了这些估计的收敛速度以及检验统计量的渐进分布!     

E-供应链竞争下自营品牌商的第三方零售渠道引入与定价策略

基于电商平台销售渠道的多样性,决策是否引入第三方零售渠道是自营品牌商在现实的E-供应链竞争中常常面临的重要难题。在多渠道竞争环境下,构建由两个自营品牌商和一个电商平台组成的E-供应链系统。考虑品牌商不引入、单一品牌商引入与两个品牌商均引入第三方零售渠道三种情形,分别建立Stackelberg博弈模型并求解,分析了平台佣金、消费者的自营零售渠道偏好和交叉价格弹性系数等因素对第三方零售渠道引入及E-供应链各成员最优策略的影响。研究表明:不同的交叉价格弹性系数和消费者自营渠道偏好对第三方零售渠道引入策略具有差异性,且两个品牌商均引入第三方零售渠道对电商平台最有利。此外,平台佣金、消费者自营渠道偏好和交叉价格弹性系数对自营、第三方商品的定价以及电商平台、品牌商的利润具有重要影响。     

Large Deviation Principle for Optimal Filtering

   Abstract. We derive a large deviation principle for the optimal filter where the signal and the observation processes take values in conuclear spaces. The approach follows from the framework established by the author in an earlier paper. The key is the verification of the exponential tightness for the optimal filtering process and the exponential continuity of the coefficients in the Zakai equation.     

Circadian rhythm and tumour growth

We address the following question: can one sustain, on the basis of mathematical models, that for cancer cells, the loss of control by circadian rhythm favours a faster growth? This question, which comes from the observation that tumour growth in mice is enhanced by experimental disruption of the circadian rhythm, may be tackled by mathematical modelling of the cell cycle. For this purpose we consider an age-structured population model with control of death (apoptosis) rates and phase transitions, and two eigenvalues: one for periodic control coefficients (via a variant of Floquet theory in infinite dimension) and one for constant coefficients (taken as the time average of the periodic case). We show by a direct proof that, surprisingly enough considering the above-mentioned observation, the periodic eigenvalue is always greater than the steady state eigenvalue when the sole apoptosis rate is concerned. We also show by numerical simulations when transition rates between the phases of the cell cycle are concerned, that, without further hypotheses, no natural hierarchy between the two eigenvalues exists. This at least shows that, if such models are to take account of the above-mentioned observation, control of death rates inside phases is not sufficient, and that transition rates between phases are a key target in proliferation control. To cite this article: J. Clairambault et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Orlicz regularity for higher order parabolic equations in divergence form with coefficients in weak BMO

We consider higher order parabolic equations in divergence form with measurable coefficients to find optimal regularity in Orlicz spaces of the maximum order derivatives of the weak solutions. The relevant minimal regularity requirement on the tensor matrix coefficients is of small BMO in the spatial variable and is measurable in the time variable. As a consequence we prove the classical W ^m,p regularity, m = 1, 2, . . . , 1 < p < ∞, for such higher order equations. In the same spirit the results easily extend to higher order parabolic systems as well as up to the boundary.     

基于时间敏感需求及随机完工期的承诺交货期决策

在新的经济形势和高新技术指引下,产品更新换代的速度加快,基于时间的竞争成为供应链竞争的焦点.在制造商为核心的供应链中,产品需求除了与价格有关外,与承诺交货期也有一定关联,且部分客户愿意为快速交货而支付更高价格.当需求与时间及价格具有敏感性且实际完工期服从一定的随机分布时,建立利润最大化及服务水平约束的承诺交货期决策模型,并对模型进行讨论及优化分析.通过算例验证了模型的有效性,通过参数敏感性分析得出的结论是:当客户服务水平达到一定阈值时,最优承诺交货期将发生改变;价格及交货期敏感系数不影响承诺交货期,但影响产品需求及最终利润;最优承诺交货期与单位提早完工成本是反向变动的关系而与单位延迟完工成本是正向变动的关系;随着完工期均值及标准差的不断增大,最优承诺交货期呈上升趋势,利润、市场需求及价格不断下降.