Checking robust nonsingularity of tridiagonal matrices in linear time

In this paper we present a linear time algorithm for checking whether a tridiagonal matrix will become singular under certain perturbations of its coefficients. The problem is known to be NP-hard for general matrices. Our algorithm can be used to get perturbation bounds on the solutions to tridiagonal systems.Research produced with the help of the Cooperation Agreement CNR-MOSA.     

Restricted Robust Uniform Matroid Maximization Under Interval Uncertainty

For the problem of selecting p items with interval objective function coefficients so as to maximize total profit, we introduce the r-restricted robust deviation criterion and seek solutions that minimize the r-restricted robust deviation. This new criterion increases the modeling power of the robust deviation (minmax regret) criterion by reducing the level of conservatism of the robust solution. It is shown that r-restricted robust deviation solutions can be computed efficiently. Results of experiments and comparisons with absolute robustness, robust deviation and restricted absolute robustness criteria are reported. This work is supported by a grant from Turkish Academy of Science(TUBA).     

Robust weighted vertex p-center model considering uncertain data: An application to emergency management

This paper presents a generalized weighted vertex p-center (WVPC) model that represents uncertain nodal weights and edge lengths using prescribed intervals or ranges. The objective of the robust WVPC (RWVPC) model is to locate p facilities on a given set of candidate sites so as to minimize worst-case deviation in maximum weighted distance from the optimal solution. The RWVPC model is well-suited for locating urgent relief distribution centers (URDCs) in an emergency logistics system responding to quick-onset natural disasters in which precise estimates of relief demands from affected areas and travel times between URDCs and affected areas are not available. To reduce the computational complexity of solving the model, this work proposes a theorem that facilitates identification of the worst-case scenario for a given set of facility locations. Since the problem is NP-hard, a heuristic framework is developed to efficiently obtain robust solutions. Then, a specific implementation of the framework, based on simulated annealing, is developed to conduct numerical experiments. Experimental results show that the proposed heuristic is effective and efficient in obtaining robust solutions. We also examine the impact of the degree of data uncertainty on the selected performance measures and the tradeoff between solution quality and robustness. Additionally, this work applies the proposed RWVPC model to a real-world instance based on a massive earthquake that hit central Taiwan on September 21, 1999.     

Alkyl-chain branched effect on the aggregation and photophysical behavior of polydiarylfluorenes toward stable deep-blue electroluminescence and efficient amplified spontaneous emission

The control of the condensed superstructure of light-emitting conjugated polymers(LCPs) is a crucial factor to obtain high performance and stable organic optoelectronic devices.Side-chain engineering strategy is an effective platform to tune inter chain aggregation and photophysical behaviour of LCPs.Herein,we systematically investigated the alkyl-chain branched effecton the conformational transition and photophysical behaviour of polydiarylfluorenes toward efficient blue optoelectronic devices.The branched side chain will improve materials solubility to inhibit interchain aggregation in solution according to DLS and optical analysis,which is useful to obtain high quality film.Therefore,our branched PEODPF,POYDPF pristine film present high luminance efficiency of 36.1% and 39.6%,enhanced about 20%relative to that of PODPF.Compared to the liner-type sides' chain,these branched chains also suppress chain planarization and improve film morphological stability effectively.Interestingly,the branched polymer also had excellent stable amplified spontaneous emission(ASE) behaviour with low threshold(4.72 μJ/cm~2) and a center peak of 465 nm,even thermal annealing at 220 C in the air atmosphere.Therefore,side-chain branched strategy for LCPs is an effective means to control interchain aggregation,film morphology and photophysical property of LCPs.     

Modelling and system identification of an experimental apparatus for anomaly detection in mechanical systems

This paper presents design, modelling and system identification of a laboratory test apparatus that has been constructed to experimentally validate the concepts of anomaly detection in complex mechanical systems. The test apparatus is designed to be complex in itself due to partially correlated interactions amongst its individual components and functional modules. The experiments are conducted on the test apparatus to represent operations of mechanical systems where both dynamic performance and structural durability are critical.     

Robust multiclass kernel-based classifiers

In this research, a robust optimization approach applied to multiclass support vector machines (SVMs) is investigated. Two new kernel based-methods are developed to address data with input uncertainty where each data point is inside a sphere of uncertainty. The models are called robust SVM and robust feasibility approach model (Robust-FA) respectively. The two models are compared in terms of robustness and generalization error. The models are compared to robust Minimax Probability Machine (MPM) in terms of generalization behavior for several data sets. It is shown that the Robust-SVM performs better than robust MPM.     

Minimization Algorithms Based on Supervisor and Searcher Cooperation

In the present work, we explore a general framework for the design of new minimization algorithms with desirable characteristics, namely, supervisor-searcher cooperation. We propose a class of algorithms within this framework and examine a gradient algorithm in the class. Global convergence is established for the deterministic case in the absence of noise and the convergence rate is studied. Both theoretical analysis and numerical tests show that the algorithm is efficient for the deterministic case. Furthermore, the fact that there is no line search procedure incorporated in the algorithm seems to strengthen its robustness so that it tackles effectively test problems with stronger stochastic noises. The numerical results for both deterministic and stochastic test problems illustrate the appealing attributes of the algorithm.     

Estimating sample mean under interval uncertainty and constraint on sample variance

Traditionally, practitioners start a statistical analysis of a given sample x₁, … , x_n by computing the sample mean E and the sample variance V. The sample values x_i usually come from measurements. Measurements are never absolutely accurate and often, the only information that we have about the corresponding measurement errors are the upper bounds Δ_i on these errors. In such situations, after obtaining the measurement result , the only information that we have about the actual (unknown) value x_i of the ith quantity is that x_i belongs to the interval . Different values x_i from the corresponding intervals lead, in general, to different values of the sample mean and sample variance. It is therefore desirable to find the range of possible values of these characteristics when x_i ∈ x_i.Often, we know that the values x_i cannot differ too much from each other, i.e., we know the upper bound V₀ on the sample variance V : V ? V₀. It is therefore desirable to find the range of E under this constraint. This is the main problem that we solve in this paper.     

具离散和分布时滞的不确定奇异系统的鲁棒H∞控制

本文讨论了具离散和分布时滞不确定奇异系统的鲁棒H∞控制问题.这里假定参数不确定性是模有界的和时变的,同时考虑的时滞也假定为时变的,得到了依赖于时滞的鲁棒稳定性准则和一个对于所有可容许的参数不确定性保证闭环系统正则,无脉冲和稳定并满足模有界条件的状态反馈控制律.