基于随机模型的艾滋病预防与控制策略研究

建立了艾滋病传播过程中感染者人数占总人口比例所满足的随机模型,分析了环境因素对艾滋病传播过程的影响,利用数值解方法对模型进行分析,结合我国数十年间艾滋病病毒感染者实际数据进行仿真,验证模型的有效性;并对未来我国艾滋病病毒感染者人数占总人口比例进行预测,通过对其中的传染率控制指标β进行分析,得出这一指标的波动对艾滋病流行趋势的影响.通过分析其均值与方差,提出对β的调整策略以达到一定的控制目标,从而为艾滋病的预防和控制提供一定程度上的决策支持.     

On minimum cost isolated failure immune networks

A telecommunications network is isolated failure immune (IFI) if and only if communication between operative sites can be completed as long as network failures are isolated. It is known that the class of minimal IFI networks is equivalent to the class of spanning 2-trees. To the best of our knowledge, this work is the first computational study dealing with the construction of a minimum cost IFI network. The problem is known to be NP-complete. We develop a tabu search based heuristic for solving the minimum cost spanning 2-tree (MCS2T) problem. The complex structure of 2-trees makes the tabu search heuristic highly dependent on the starting solution. We develop four heuristic algorithms to obtain diversified good starting solutions. They are: completion of a 2-tree from a spanning tree, two greedy approaches, and a method based on the recursive definition of a 2-tree. We also formulate an integer programming problem (IP) whose objective function value is a lower bound to the MCS2T problem. We solve the IP by developing a constraint generation scheme. The algorithms were tested on complete random graphs with Euclidean distances and on two real data sets (Civil Aeronautics Board) with instances of 10, 15, 20 and 25 nodes. As a result of this research for small problems (10 and 15 nodes), the heuristic solutions are on average within 0.8% from the optimal solution and for large problems (20 and 25 nodes), the average error is less than 2.8%.     

Scatter search and star-paths: beyond the genetic metaphor

Scatter search and genetic algorithms have originated from somewhat different traditions and perspectives, yet exhibit features that are strongly complementary. Links between the approaches have increased in recent years as variants of genetic algorithms have been introduced that embody themes in closer harmony with those of scatter search. Some researchers are now beginning to take advantage of these connections by identifying additional ways to incorporate elements of scatter search into genetic algorithm approaches. There remain aspects of the scatter approach that have not been exploited in conjunction with genetic algorithms, yet that provide ways to achieve goals that are basic to the genetic algorithm design. Part of the gap in implementing hybrids of these procedures may derive from relying too literally on the genetic metaphor, which in its narrower interpretation does not readily accommodate the strategic elements underlying scatter search. The theme of this paper is to show there are benefits to be gained by going beyond a perspective constrained too tightly by the connotations of the term genetic. We show that the scatter search framework directly leads to processes for combining solutions that exhibit special properties for exploiting combinatorial optimization problems. In the setting of zero-one integer programming, we identify a mapping that gives new ways to create combined solutions, producing constructions calledstar-paths for exploring the zero-one solution space. Star-path trajectories have the special property of lying within regions assured to include optimal solutions. They also can be exploited in association with both cutting plane and extreme point solution approaches. These outcomes motivate a deeper look into current conceptions of appropriate ways to combine solutions, and disclose there are more powerful methods to derive information from these combinations than those traditionally applied.This research is supported in part by the Joint Air Force Office of Scientific Research and Office of Naval Research Contract No. F49620-90-C-0033 at the University of Colorado     

Toward Flexible Embodied Energy: Scale-Inspired Overlapping Lithium-Ion Batteries with High-Energy-Density and Variable Stiffness

High performance flexible batteries are essential ingredients for flexible devices. However, general isolated flexible batteries face critical challenges in developing multifunctional embodied energy systems, owing to the lack of integrative design. Herein, inspired by scales in creatures, overlapping flexible lithium-ion batteries (FLIBs) consisting of energy storage scales and connections using LiNi_0.5Co_0.2Mn_0.3O₂ (NCM523) and graphite electrodes are presented. The scale-dermis structure ensures a high energy density of 374.4 Wh L⁻¹ as well as a high capacity retention of 93.2% after 200 charge/discharge cycles and 40 000 bending times. A variable stiffness property is revealed that can be controlled by battery configurations and deformation modes. Furthermore, the overlapping FLIBs can be housed directly into the architecture of several flexible devices, such as robots and grippers, allowing to create multifunctionalities that go far beyond energy storage and include load-bearing and variable flexibility. This study broadens the versatility of FLIBs toward energy storage structure engineering of flexible devices.     

Shear wave propagation in vertically heterogeneous viscoelastic layer over a micropolar elastic half-space

This article deals with the propagation of SH-wave in a vertically heterogeneous viscoelastic layer lying over a micropolar elastic half-space. Dispersion and damping equations are obtained analytically in closed form. Phase and damped velocities are computed numerically and depicted by means of a graph to exhibit the substantial effect of heterogeneity, viscoelasticity (internal friction), and micropolar parameter. As a special case of the problem, it is found that deduced dispersion relation is well in agreement to the classical-Love wave equation and damping equation vanishes identically for the isotropic case. Influence of micropolarity present in the medium of half-space is highlighted through comparative study.     

Effect of undulation on SH-wave propagation in corrugated magneto-elastic transversely isotropic layer

This article delves to study the effect of corrugated boundary surfaces on the propagation of horizontally-polarized shear waves (SH-waves) in a magnetoelastic transversely isotropic layer under a hydrostatic state of stress lying over an elastic half-space under gravity. A dispersion equation has been derived in closed-form and is found to be in good agreement to the classical Love-wave equation. The effect of magnetoelasticity, hydrostatic state of stress, gravity, corrugation, position parameter, and undulation on the phase velocity of the SH-wave has been identified. Numerical computation along with graphical demonstration has been carried out for cadmium, magnesium, and zinc materials of hexagonal symmetry to highlight some significant facts.     

Generation of SH-type waves in a poroelastic layer sandwiched between prestressed orthotropic and nonhomogeneous mantles

The present work is concerned with a detailed illustration on the study of horizontally polarized shear waves (SH-type) propagation in a prestressed fluid saturated anisotropic porous layer sandwiched by prestressed orthotropic medium and nonhomogeneous mantles. The frequency equation for the assumed model is derived and their medium characteristics, such as porosity, prestress, anisotropy, and nonhomogeneity, are discussed. Numerical treatment is given to analyze these effects on phase velocities of SH-type waves and is plotted in various graphs. The parametric study divulges that the magnitude of wave velocities increases with the increase of nonhomogeneity parameter and prestress parameter.     

不完全观测数据下混合效应模型的正交投影估计

基于矩阵的QR分解技术,对一类含有不完全观测数据的线性混合效应模型提出了一种基于正交投影的估计方法。在一些正则条件下,证明了固定效应参数的估计渐近服从标准正态分布,得到了固定效应参数的置信区间。另外,所提出的固定效应参数的估计过程不受随机效应的任何影响,具有较好的有效性和稳健性。最后,通过一些数值模拟和一个实例分析研究了所提出估计方法的有限样本性质。     

A subexponential bound for linear programming

We present a simple randomized algorithm which solves linear programs withn constraints andd variables in expected $$\min \{ O(d^2 2^d n),e^{2\sqrt {dIn({n \mathord{\left/ {\vphantom {n {\sqrt d }}} \right. \kern-\nulldelimiterspace} {\sqrt d }})} + O(\sqrt d + Inn)} \}$$ time in the unit cost model (where we count the number of arithmetic operations on the numbers in the input); to be precise, the algorithm computes the lexicographically smallest nonnegative point satisfyingn given linear inequalities ind variables. The expectation is over the internal randomizations performed by the algorithm, and holds for any input. In conjunction with Clarkson's linear programming algorithm, this gives an expected bound of $$O(d^2 n + e^{O(\sqrt {dInd} )} ).$$ The algorithm is presented in an abstract framework, which facilitates its application to several other related problems like computing the smallest enclosing ball (smallest volume enclosing ellipsoid) ofn points ind-space, computing the distance of twon-vertex (orn-facet) polytopes ind-space, and others. The subexponential running time can also be established for some of these problems (this relies on some recent results due to Gärtner).     

Arbitrary decay rate for two connected strings with joint anti-damping by boundary output feedback

In this paper, we are concerned with the boundary stabilization of two connected strings with middle joint anti-damping for which all eigenvalues of the (control) free system are located on the right complex plane. We first design an explicit state feedback controller to achieve exponential stability for the closed-loop system. Consequently, we design the output feedback by using infinite-dimensional observer. The backstepping approach is adopted in investigation. It is shown that by using one boundary stabilizer only, the output feedback can make the closed-loop system exponentially stable with arbitrary decay rate.