Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form

In this paper we consider minimizers of the functional$\min \{{\lambda }_1(\mathrm{\Omega })+\cdots +{\lambda }_k(\mathrm{\Omega })+\mathrm{\Lambda }|\mathrm{\Omega }|,:\mathrm{\Omega }\subset D\text{ open}\}$ where $D\subset {\mathbb{R}}^d$ is a bounded open set and where $0<{\lambda }_1(\mathrm{\Omega })\le \cdots \le {\lambda }_k(\mathrm{\Omega })$ are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets ${\mathrm{\Omega }}^{⁎}$ have finite perimeter and that their free boundary $\partial {\mathrm{\Omega }}^{⁎}\cap D$ is composed of a regular part, which is locally the graph of a $C^{1,\alpha }$-regular function, and a singular part, which is empty if $d<d^{⁎}$, discrete if $d=d^{⁎}$ and of Hausdorff dimension at most $d-d^{⁎}$ if $d>d^{⁎}$, for some $d^{⁎}\in \{5,6,7\}$.     

Looking ahead: Joint small group detection and tracking in crowd scenes

Small group detection and tracking in crowd scenes are basis for high level crowd analysis tasks. However, it suffers from the ambiguities in generating proper groups and in handling dynamic changes of group configurations. In this paper, we propose a novel delay decision-making based method for addressing the above problems, motivated by the idea that these ambiguities can be solved using rich temporal context. Specifically, given individual detections, small group hypotheses are generated. Then candidate group hypotheses across consecutive frames and their potential associations are built in a tree. By seeking for the best non-conflicting subset from the hypothesis tree, small groups are determined and simultaneously their trajectories are got. So this framework is called joint detection and tracking. This joint framework reduces the ambiguities in small group decision and tracking by looking ahead for several frames. However, it results in the unmanageable solution space because the number of track hypotheses grows exponentially over time. To solve this problem, effective pruning strategies are developed, which can keep the solution space manageable and also improve the credibility of small groups. Experiments on public datasets demonstrate the effectiveness of our method. The method achieves the state-of-the-art performance even in noisy crowd scenes.     

Off‐grid DoA estimation method of wideband signals

In this paper, an off‐grid direction of arrival (DoA) estimation method is proposed for wideband signals. This method is based on the sparse representation (SR) of the array covariance matrix. Similar to the time domain DoA estimation methods, the correlation function of the sources was assumed to be the same and known. A new measurement vector is obtained using the lower‐left triangular elements of the covariance matrix. The DoAs are estimated by quantizing the entire range of continuous angle space into discrete grid points. However, the exact DoAs may be located between two grid points; therefore, this estimation has errors. The accuracy of DoA estimation is improved by the minimization of the difference between the new measurement vector and its estimated values. Simulation results revealed that the proposed method can enhance the DoA estimation accuracy of wideband signals.     

SDN中基于KMOBPSO的高可靠性控制器部署算法

针对SDN中控制器系统的单节点故障问题,兼顾系统成本和系统时延,应用N+1冗余备份模型来提高SDN控制器部署的可靠性,并将其抽象为多目标优化问题.同时,提出了一种融合K-means聚类算法和遗传算子的多目标二进制粒子群算法——KMOBPSO算法,以求解SDN控制器高可靠性部署问题的解.仿真结果表明,所提算法具有求解精度高、分布均匀、沿Pareto前沿面覆盖广的特点,能够显著提高SDN中控制器部署的可靠性.     

On the performance of improved quadrature spatial modulation

Quadrature spatial modulation (QSM) utilizes the in‐phase and quadrature spatial dimensions to transmit the real and imaginary parts of a single signal symbol, respectively. The improved QSM (IQSM) transmits two signal symbols per channel use through a combination of two antennas for each of the real and imaginary parts. The main contributions of this study can be summarized as follows. First, we derive an upper bound for the error performance of the IQSM. We then design constellation sets that minimize the error performance of the IQSM for several system configurations. Second, we propose a double QSM (DQSM) that transmits the real and imaginary parts of two signal symbols through any available transmit antennas. Finally, we propose a parallel IQSM (PIQSM) that splits the antenna set into equal subsets and performs IQSM within each subset using the same two signal symbols. Simulation results demonstrate that the proposed constellations significantly outperform conventional constellations. Additionally, DQSM and PIQSM provide a performance similar to that of IQSM while requiring a smaller number of transmit antennas and outperform IQSM with the same number of transmit antennas.     

Statistical Optimization of Flavonoid and Antioxidant Recovery from Macerated Chinese and Malaysian Lotus Root (Nelumbo nucifera) Using Response Surface Methodology

In this study, the combination of parameters required for optimal extraction of anti-oxidative components from the Chinese lotus (CLR) and Malaysian lotus (MLR) roots were carefully investigated. Box–Behnken design was employed to optimize the pH (X₁: 2–3), extraction time (X₂: 0.5–1.5 h) and solvent-to-sample ratio (X₃: 20–40 mL/g) to obtain a high flavonoid yield with high % DPPH_sc free radical scavenging and Ferric-reducing power assay (FRAP). The analysis of variance clearly showed the significant contribution of quadratic model for all responses. The optimal conditions for both Chinese lotus (CLR) and Malaysian lotus (MLR) roots were obtained as: CLR: X₁ = 2.5; X₂ = 0.5 h; X₃ = 40 mL/g; MLR: X₁ = 2.4; X₂ = 0.5 h; X₃ = 40 mL/g. These optimum conditions gave (a) Total flavonoid content (TFC) of 0.599 mg PCE/g sample and 0.549 mg PCE/g sample, respectively; (b) % DPPH_sc of 48.36% and 29.11%, respectively; (c) FRAP value of 2.07 mM FeSO₄ and 1.89 mM FeSO₄, respectively. A close agreement between predicted and experimental values was found. The result obtained succinctly revealed that the Chinese lotus exhibited higher antioxidant and total flavonoid content when compared with the Malaysia lotus root at optimum extraction condition.     

基于Kronecker型替换的黑盒多项式稀疏插值

本文基于新的Kronecker型替换,给出两个由黑盒表示的稀疏多项式的新确定性插值算法.令f∈R[x1,……,xn]是一个稀疏黑盒多项式,其次数上界为D.当R是C或者是有限域时,相对于已有算法,新算法具有更好的计算复杂度或者关于D的复杂度更低.特别地,对于一般黑盒模型,D是复杂度中的主要因素,而在所有的确定性算法中,本文的第二个算法的复杂度关于D是最低的.     

优化军工科研项目管理的具体策略

我国的军工科研所成立于上世纪，它以军工项目的科研、预研为主，为我国的国防军工提供研发产品。伴随着我国经济实力的增强和科技军事力量的增长，军工科研院所也转变了原有的工业专属性质，走上了军民两用、寓军于民的道路，并在时代的进步中成为了我国先进装备制造业的重要科研力量和科技创新支柱。凸现军事工业“高、精、尖”的特点，以项目管理的优化为具体策略进行军工科研开发工作。     

Spectral estimates for saddle point matrices arising in weak constraint four‐dimensional variational data assimilation

We consider the large sparse symmetric linear systems of equations that arise in the solution of weak constraint four‐dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can be written as saddle point systems with a 3 × 3 block structure but block eliminations can be performed to reduce them to saddle point systems with a 2 × 2 block structure, or further to symmetric positive definite systems. In this article, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds.