Barzilai–Borwein method with variable sample size for stochastic linear complementarity problems

A smoothing method for solving stochastic linear complementarity problems is proposed. The expected residual minimization reformulation of the problem is considered, and it is approximated by the sample average approximation (SAA). The proposed method is based on sequential solving of a sequence of smoothing problems where each of the smoothing problems is defined with its own sample average approximation. A nonmonotone line search with a variant of the Barzilai–Borwein (BB) gradient direction is used for solving each of the smoothing problems. The BB search direction is efficient and low cost, particularly suitable for nonmonotone line search procedure. The variable sample size scheme allows the sample size to vary across the iterations and the method tends to use smaller sample size far away from the solution. The key point of this strategy is a good balance between the variable sample size strategy, the smoothing sequence and nonmonotonicity. Eventually, the maximal sample size is used and the SAA problem is solved. Presented numerical results indicate that the proposed strategy reduces the overall computational cost.     

一种修正的CD共轭梯度法及其全局收敛性

求解无约束优化问题的共轭梯度法,其搜索方向的下降性往往依赖于所采用的线性搜索.将提出一种修正的CD算法,其搜索方向d_k始终满足1-1/u≤(-g_k~Td_k)/(‖g_k‖~2)≤1+1/u(u1),即算法在不依赖任何线性搜索的情况下能始终产生充分下降方向.同时,当采用精确线性搜索时,该修正的CD算法就是标准的CD共轭梯度法.在适当条件下,还证明了修正的CD算法在强Wolfe线性搜索下具有全局收敛性.最后,我们给出了相应的数值结果,说明了算法是一种有效的算法.     

肺部超声B线数目与血管外肺水的相关性分析

目的探讨肺部超声监测B线数目在老年脓毒症患者液体复苏过程中评估血管外肺水的价值。方法在老年脓毒症患者液体复苏过程中应用肺部超声动态监测患者双侧胸骨旁、锁骨中线、腋前线及腋中线B线数目,同时应用脉波指示剂连续心排血量法（pulseindicatorcontinuouscardiacoutput,PiCCO）监测血管外肺水指数（extravascularlungwaterindex,EVLWI）对比,对B线数目与EVLWI进行Pearson相关性分析。结果共纳入28例患者,采集95组数据,B线数目和EVLWI呈正相关（r=0.92,P＜0.01）,同时发现B线数目与肺血管通透性指数（pulmonaryvascularpenetrationindex,PVPI）呈正相关（r=0.80,P＜0.01）。结论B线数目与EVLWI相关性良好,在老年脓毒症液体复苏过程中应用无创肺部超声可实时、动态地进行肺水监测,以早期发现肺水肿。     

A product formula for the TASEP on a ring

For a random permutation sampled from the stationary distribution of the TASEP on a ring, we show that, conditioned on the event that the first entries are strictly larger than the last entries, the order of the first entries is independent of the order of the last entries. The proof uses multi‐line queues as defined by Ferrari and Martin, and the theorem has an enumerative combinatorial interpretation in that setting. Finally, we present a conjecture for the case where the small and large entries are not separated. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 247–259, 2016     

On Weak and Strong Convergence of the Projected Gradient Method for Convex Optimization in Real Hilbert Spaces

This work focuses on convergence analysis of the projected gradient method for solving constrained convex minimization problems in Hilbert spaces. We show that the sequence of points generated by the method employing the Armijo line search converges weakly to a solution of the considered convex optimization problem. Weak convergence is established by assuming convexity and Gateaux differentiability of the objective function, whose Gateaux derivative is supposed to be uniformly continuous on bounded sets. Furthermore, we propose some modifications in the classical projected gradient method in order to obtain strong convergence. The new variant has the following desirable properties: the sequence of generated points is entirely contained in a ball with diameter equal to the distance between the initial point and the solution set, and the whole sequence converges strongly to the solution of the problem that lies closest to the initial iterate. Convergence analysis of both methods is presented without Lipschitz continuity assumption.     

Heat kernel estimates for the Bessel differential operator in half‐line

In the paper we consider the Bessel differential operator in half‐line , , and its Dirichlet heat kernel . For , by combining analytical and probabilistic methods, we provide sharp two‐sided estimates of the heat kernel for the whole range of the space parameters and every , which complements the recent results given in 1 , where the case was considered.     

基于嵌入式系统的搬运机器人设计与路径规划研究

为了解决目前工业搬运机器人发展的需求问题,设计了一款基于嵌入式系统的搬运机器人。该型搬运机器人的循线采用的是一种七路灰度传感器,并通过设计的一种蓝牙模块将灰度信息发送到手机端,从而简化了循线时的调试,具有创新性。搬运机器人前端安装有颜色传感器用以区分不同种类的物料。电机控制部分设计了一个PID闭环控制系统,通过PWM脉冲宽度调节来控制电机的转速。然后,针对模拟场地提出了一种路径规划算法,并通过设计的搬运机器人进行了实验测试与分析,验证了该方法的准确性和有效性。     

On-line preparation of microsamples prior to CE

An experimental setup is presented here for the automated analysis of microsamples, based on the on-line coupling of a capillary SPE module and a CE unit using a two-position six-port valve, an open-closed valve to isolate electrically the sample preparation from the CE unit and a "T" interface. A C18 trapping microcolumn (dimensions 2.5 cm x 100 microm id x 360 microm od) was used for the SPE step. The utility of the proposed experimental setup was demonstrated by applying it to the determination of quinolone antibiotics in serum microsamples, which was efficiently carried out in less than 20 min (4 min for protein denaturation and 15 min for analytes preconcentration and CE-UV separation-determination). A complete optimization study was performed for preconcentration and cleanup of quinolones, the coupling of sample preparation module to the CE unit and electrophoretic separation of quinolones. A preconcentration factor of 10.4 was achieved. The volume injected with the proposed method was 125 nL versus 160 nL introduced by hydrodynamic injection. The volume required for the analysis was 2 microL, which makes the proposed experimental setup very useful for the analysis of microsamples in fields of current interest such as metabolomics or proteomics.     

Silver(I) bromide complexes of the rigid diphosphanes 1,2-bis(diphenylphosphano)benzene (dppbz) and 4,5-bis(diphenylphosphano)-9,9-dimethyl-xanthene (xantphos): Crystal structures of [Ag(μ2-Br)(dppbz)]2, [AgBr(xantphos)] and [AgBr(xantphos)(py2SH)]

Reaction of silver(I) bromide with equimolar amounts of the rigid diphos ligands 1,2-bis(diphenylphosphano)benzene (dppbz) and 4,5-bis(diphenylphosphano)-9,9-dimethyl-xanthene (xantphos) in acetone and acetonitrile led to the corresponding chelates [Ag(μ₂-Br)(dppbz)]₂ (1) and [AgBr(xantphos)] (2). Treatment of 1 and 2 with pyridine-2-thione (py2SH) in ethanol gave the mixed-ligand complexes [AgBr(dppbz)(py2SH)] (3) and [AgBr(xantphos)(py2SH)] (4), respectively. Compounds 1, 2 and 4 have been characterized by X-ray diffraction, establishing distorted tetrahedral or trigonal planar coordination geometries of the silver atoms.     

On the crystalline cohomology of Deligne–Lusztig varieties

Let $X\to Y^0$ be an abelian prime-to-p Galois covering of smooth schemes over a perfect field k of characteristic $p>0$. Let Y be a smooth compactification of $Y^0$ such that $Y-Y^0$ is a normal crossings divisor on Y. We describe a logarithmic F-crystal on Y whose rational crystalline cohomology is the rigid cohomology of X, in particular provides a natural $W[F]$-lattice inside the latter; here W is the Witt vector ring of k. If a finite group G acts compatibly on X, $Y^0$ and Y then our construction is G-equivariant. As an example we apply it to Deligne–Lusztig varieties. For a finite field k, if $\mathbb{G}$ is a connected reductive algebraic group defined over k and $\mathbb{L}$ a k-rational torus satisfying a certain standard condition, we obtain a meaningful equivariant $W[F]$-lattice in the cohomology (ℓ-adic or rigid) of the corresponding Deligne–Lusztig variety and an expression of its reduction modulo p in terms of equivariant Hodge cohomology groups.