Time Blocks Decomposition of Multistage Stochastic Optimization Problems

Multistage stochastic optimization problems are, by essence, complex because their solutions are indexed both by stages (time) and by uncertainties (scenarios). Their large scale nature makes decomposition methods appealing.The most common approaches are time decomposition --- and state-based resolution methods, like stochastic dynamic programming, in stochastic optimal control --- and scenario decomposition --- like progressive hedging in stochastic programming. We present a method to decompose multistage stochastic optimization problems by time blocks, which covers both stochastic programming and stochastic dynamic programming. Once established a dynamic programming equation with value functions defined on the history space (a history is a sequence of uncertainties and controls), we provide conditions to reduce the history using a compressed "state" variable. This reduction is done by time blocks, that is, at stages that are not necessarily all the original unit stages, and we prove areduced dynamic programming equation. Then, we apply the reduction method by time blocks to \emph{two time-scales} stochastic optimization problems and to a novel class of so-called \emph{decision-hazard-decision} problems, arising in many practical situations, like in stock management. The \emph{time blocks decomposition} scheme is as follows: we use dynamic programming at slow time scale where the slow time scale noises are supposed to be stagewise independent, and we produce slow time scale Bellman functions; then, we use stochastic programming at short time scale, within two consecutive slow time steps, with the final short time scale cost given by the slow time scale Bellman functions, and without assuming stagewise independence for the short time scale noises

Squarefree polynomials and Mobius values in short intervals and arithmetic progressions

We calculate the mean and variance of sums of the M\"obius function and the indicator function of the squarefrees, in both short intervals and arithmetic progressions, in the context of the ring of polynomials over a finite field of $q$ elements, in the limit $q\to \infty$. We do this by relating the sums in question to certain matrix integrals over the unitary group, using recent equidistribution results due to N. Katz, and then by evaluating these integrals. In many cases our results mirror what is either known or conjectured for the corresponding problems involving sums over the integers, which have a long history. In some cases there are subtle and surprising differences. The ranges over which our results hold is significantly greater than those established for the corresponding problems in the number field setting.Comment: Added references and corrected misprint

Bibliographic Control of Serial Publications

An important problem with serials is bibliographic control. What good does it do for libraries to select, acquire, record, catalog, and bind large holdings of serial publications if the contents of those serials remain a mystery to all except the few who have the opportunity to examine selected journals of continuing personal interest and have discovered some magic way of retaining the gist of the contents? Bibliographic control is the indexing and abstracting of the contents or guts of what is included in the serials. It is this control, provided by secondary publishing services, which this article will discuss. Just as there are problems with serials in general, there are some easily identifiable problems connected with their bibliographic control including: volume, overlap, costs, elements and methods, and a few other miscellaneous considerations. Some history of bibliographic control will also put the current problems in a helpful perspective. Hereafter "bibliographic control" will be designated by the term "abstracting and indexing," one of these alone, or the shorter "a & i." (I do distinguish between abstracting and indexing and believe that they are not in order of importance and difficulty.) Although a & i do provide bibliographic control, this paper will not discuss cataloging, tables of contents, back-of-the-book indexes, year-end indexes, cumulative indexes, lists of advertisers, or bibliographies. If there is to be control, there must always be indexing. Abstracting is a short cut, a convenience, and perhaps a bibliographic luxury which may be now, or is fast becoming, too rich, in light of other factors to be discussed, for library blood and for the users of libraries especially for the users of indexes who may not depend upon the library interface. Abstracting, though, provides a desirable control, and one which will continue to be advocated.published or submitted for publicatio

Dificultades de aprendizaje de los conceptos de carga y de campo eléctrico en estudiantes de bachillerato y universidad

This article tries to analyse what the students' principal learning difficulties on the concept of charge and electric field are. In this way, we have supposed certain parallels between learning difficulties in these concepts and the problems in their formation throughout history. We have carried out a short description of principal epistemological problems, and a design based on a questionnaire containing open questions and personal interviews of secondary and University students. The results obtained seem to indicate that the students have problems to interpret electrification phenomena, which are not easy to explain by a hydrostatic model of electric charge. Likewise, we have verified that few students significantly use the concept of electric field

Montenegro’s decade of independence: tracing a state back to its origins

May 2016 marked ten years since Montenegro achieved its independence from Serbia, the final act in the demise of Yugoslavia. Petar Marković traces the country’s short history and analyses the celebrations from a political theory perspective. His analysis highlights that, in spite of projecting an image of multi-ethnic cohesion and political stability, problems affecting Montenegro’s economy and society remain considerable and deeply rooted