Sensitivity of the Optimum to Perturbations of the Profit or Weight of an Item in the Binary Knapsack Problem

In the binary single constraint Knapsack Problem, denoted KP, we are given a knapsack of fixed capacity c and a set of n items. Each item j, j = 1,...,n, has an associated size or weight w_j and a profit p_j. The goal is to determine whether or not item j, j = 1,...,n, should be included in the knapsack. The objective is to maximize the total profit without exceeding the capacity c of the knapsack. In this paper, we study the sensitivity of the optimum of the KP to perturbations of either the profit or the weight of an item. We give approximate and exact interval limits for both cases (profit and weight) and propose several polynomial time algorithms able to reach these interval limits. The performance of the proposed algorithms are evaluated on a large number of problem instances.     

开放的圆环：从《蚌壳》的叙事结构看格非小说对反映论的颠覆

对于传统小说首尾呼应、线性发展的叙事规律，《蚌壳》无疑打破了故事在时空界面上的有序性。文章认为先锋小说的艺术品性在于文本的充分自足，它给创作主体带来了自由创造的愉悦，给读者则提供了消费性的满足。     

On wavelet analysis of the nth order fractional Brownian motion

In this paper, we investigate the use of wavelet techniques in the study of the nth order fractional Brownian motion (n-fBm). First, we exploit the continuous wavelet transform??s capabilities in derivative calculation to construct a two-step estimator of the scaling exponent of the n-fBm process. We show, via simulation, that the proposed method improves the estimation performance of the n-fBm signals contaminated by large-scale noise. Second, we analyze the statistical properties of the n-fBm process in the time-scale plan. We demonstrate that, for a convenient choice of the wavelet basis, the discrete wavelet detail coefficients of the n-fBm process are stationary at each resolution level whereas their variance exhibits a power-law behavior. Using the latter property, we discuss a weighted least squares regression based-estimator for this class of stochastic process. Experiments carried out on simulated and real-world datasets prove the relevance of the proposed method.     

Non-Statutory Mental Health Social Work in Primary Care: A Chance for Renewal?

Correspondence to Malcolm T. Firth, Honorary Research Fellow & Senior Psychiatric Social Worker, 'DEAL', Department of Psychiatric Social Work, 12th Floor, Mathematics Building, University of Manchester, Oxford Road, Manchester M13 9PL, UK. E-mail: malcolm.firth{at}mhsc.manchester.nhs.uk Summary The current status of evidence-based practice in the field ofmental health has led some to question the potential for innovationif social work practice is organizationally proscribed or reducedto a dogged adherence to methodological orthodoxy. Conversely,social work's value base is esteemed disproportionately to itsevidence base. Changing service contexts in the UK, particularlythe emergence of Primary Care Trusts as gatekeepers and commissionersof health and social care services, are providing opportunitiesfor social work to develop a new presence and purpose. The authorsdescribe their work in a small-scale service based in primarycare that anticipated these opportunities, by a retrospectivestudy of 120 cases. A new evidence base that derives directlyfrom practice is suggested as a way forward for social workeducation and training, as well as for service and professionaldevelopment.