Generalized decision rule approximations for stochastic programming via liftings

Stochastic programming provides a versatile framework for decision-making under uncertainty, but the resulting optimization problems can be computationally demanding. It has recently been shown that, primal and dual linear decision rule approximations can yield tractable upper and lower bounds on the optimal value of a stochastic program. Unfortunately, linear decision rules often provide crude approximations that result in loose bounds. To address this problem, we propose a lifting technique that maps a given stochastic program to an equivalent problem on a higher-dimensional probability space. We prove that solving the lifted problem in primal and dual linear decision rules provides tighter bounds than those obtained from applying linear decision rules to the original problem. We also show that there is a one-to-one correspondence between linear decision rules in the lifted problem and families of non-linear decision rules in the original problem. Finally, we identify structured liftings that give rise to highly flexible piecewise linear decision rules and assess their performance in the context of a stylized investment planning problem

Проблема достоверности научного знания

Знание в самом общем виде можно определить как верное отражение в сознании человека явлений материального и духовного мира и, в частности, многообразных явлений общественной жизни

Highly Specific, Bi-substrate-Competitive Src Inhibitors from DNA-Templated Macrocycles

Protein kinases are attractive therapeutic targets, but their high sequence and structural conservation complicates the development of specific inhibitors. We recently discovered from a DNA-templated macrocycle library inhibitors with unusually high selectivity among Src-family kinases. Starting from these compounds, we developed and characterized in molecular detail potent macrocyclic inhibitors of Src kinase and its cancer-associated gatekeeper mutant. We solved two co-crystal structures of macrocycles bound to Src kinase. These structures reveal the molecular basis of the combined ATP- and substrate peptide-competitive inhibitory mechanism and the remarkable kinase specificity of the compounds. The most potent compounds inhibit Src activity in cultured mammalian cells. Our work establishes that macrocycles can inhibit protein kinases through a bi-substrate competitive mechanism with high potency and exceptional specificity, reveals the precise molecular basis for their desirable properties, and provides new insights into the development of Src-specific inhibitors with potential therapeutic relevance.Chemistry and Chemical Biolog

World citation and collaboration networks: uncovering the role of geography in science

Modern information and communication technologies, especially the Internet, have diminished the role of spatial distances and territorial boundaries on the access and transmissibility of information. This has enabled scientists for closer collaboration and internationalization. Nevertheless, geography remains an important factor affecting the dynamics of science. Here we present a systematic analysis of citation and collaboration networks between cities and countries, by assigning papers to the geographic locations of their authors' affiliations. The citation flows as well as the collaboration strengths between cities decrease with the distance between them and follow gravity laws. In addition, the total research impact of a country grows linearly with the amount of national funding for research & development. However, the average impact reveals a peculiar threshold effect: the scientific output of a country may reach an impact larger than the world average only if the country invests more than about 100,000 USD per researcher annually.Comment: Published version. 9 pages, 5 figures + Appendix, The world citation and collaboration networks at both city and country level are available at http://becs.aalto.fi/~rajkp/datasets.htm

Thirty-two Goldbach Variations

We give thirty-two diverse proofs of a small mathematical gem--the fundamental Euler sum identity zeta(2,1)=zeta(3) =8zeta(\bar 2,1). We also discuss various generalizations for multiple harmonic (Euler) sums and some of their many connections, thereby illustrating both the wide variety of techniques fruitfully used to study such sums and the attraction of their study.Comment: v1: 34 pages AMSLaTeX. v2: 41 pages AMSLaTeX. New introductory material added and material on inequalities, Hilbert matrix and Witten zeta functions. Errors in the second section on Complex Line Integrals are corrected. To appear in International Journal of Number Theory. Title change

Shedding light on the performance of a pyrosequencing assay for drug-resistant tuberculosis diagnosis

BACKGROUND: Rapid molecular diagnostics, with their ability to quickly identify genetic mutations associated with drug resistance in Mycobacterium tuberculosis clinical specimens, have great potential as tools to control multi- and extensively drug-resistant tuberculosis (M/XDR-TB). The Qiagen PyroMark Q96 ID system is a commercially available pyrosequencing (PSQ) platform that has been validated for rapid M/XDR-TB diagnosis. However, the details of the assay’s diagnostic and technical performance have yet to be thoroughly investigated in diverse clinical environments. METHODS: This study evaluates the diagnostic performance of the PSQ assay for 1128 clinical specimens from patients from three areas of high TB burden. We report on the diagnostic performance of the PSQ assay between the three sites and identify variables associated with poor PSQ technical performance. RESULTS: In India, the sensitivity of the PSQ assay ranged from 89 to 98 % for the detection of phenotypic resistance to isoniazid, rifampicin, fluoroquinolones, and the injectables. In Moldova, assay sensitivity ranged from 7 to 94 %, and in South Africa, assay sensitivity ranged from 71 to 92 %. Specificity was high (94–100 %) across all sites. The addition of eis promoter sequencing information greatly improved the sensitivity of kanamycin resistance detection in Moldova (7 % to 79 %). Nearly all (89.4 %) sequencing reactions conducted on smear-positive, culture-positive specimens and most (70.8 %) reactions conducted on smear-negative, culture-positive specimens yielded valid PSQ reads. An investigation into the variables influencing sequencing failures indicated smear negativity, culture negativity, site (Moldova), and sequencing of the rpoB, gyrA, and rrs genes were highly associated with poor PSQ technical performance (adj. OR > 2.0). CONCLUSIONS: This study has important implications for the global implementation of PSQ as a molecular TB diagnostic, as it demonstrates how regional factors may impact PSQ diagnostic performance, while underscoring potential gene targets for optimization to improve overall PSQ assay technical performance. TRIAL REGISTRATION: ClinicalTrials.gov (#NCT02170441). Registered 12 June 2014. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12879-016-1781-y) contains supplementary material, which is available to authorized users