An efficient basis update for asymptotic linear programming

AbstractFor a linear program in which the constraint coefficients vary linearly with the time parameter, we showed in a previous paper that a basic feasible solution can be evaluated using O((k + 1)m3) arithmetic operations, where m is the number of constraints and k is the index of the basis matrix pair. Here we show, in the special case when k = 1 for all basis matrix pairs, and when one of the matrices in each pair has nearly full rank, how the (possibly singular) matrix factorization can be updated with only O(m2) operations, using rank-one update techniques. This makes the arithmetic complexity of updating the basis in asymptotic linear programming comparable to that of updating the inverse in ordinary linear programming, in this case. Moreover, we show that the result holds, in particular, when computing a Blackwell optimal policy for Markov decision chains in the unichain case or when all policies have only a small number of recurrent subchains

Note on “Parameters estimators of irregular right-angled triangular distribution”

Simple estimators were given in [3] for the lower and upper limits of an irregular right-angled triangular distribution together with convenient formulas for removing their bias. We argue here that the smallest observation is not a maximum likelihood estimator (MLE) of the lower limit and we present a procedure for computing an MLE of this parameter. We show that the MLE is strictly smaller than the smallest observation and we give some bounds that are useful in a numerical solution procedure. We also present simulation results to assess the bias and variance of the ML

Controlled approximation of the value function in stochastic dynamic programming for multi-reservoir systems

We present a new approach for adaptive approximation of the value function in stochastic dynamic programming. Under convexity assumptions, our method is based on a simplicial partition of the state space. Bounds on the value function provide guidance as to where refinement should be done, if at all. Thus, the method allows for a trade-off between solution time and accuracy. The proposed scheme is experimented in the particular context of hydroelectric production across multiple reservoirs

Approximate stochastic dynamic programming for hydroelectric production planning

This paper presents a novel approach for approximate stochastic dynamic programming (ASDP) over a continuous state space when the optimization phase has a near-convex structure. The approach entails a simplicial partitioning of the state space. Bounds on the true value function are used to refine the partition. We also provide analytic formulae for the computation of the expectation of the value function in the “uni-basin” case where natural inflows are strongly correlated. The approach is experimented on several configurations of hydro-energy systems. It is also tested against actual industrial data

Flood risk perceptions and the UK media: Moving beyond “once in a lifetime” to “Be Prepared” reporting

In the winter 2015/2016 a series of storms resulted in widespread flooding in northern England, damaging hundreds of properties, disrupting transport and causing public disdain. The flooding was widely covered in the media. This article develops a methodological framework to conceptualise factors influencing risk perception related to flood events, discusses the media’s role as amplifier or attenuator of risks, and demonstrates how understanding risk perception can influence the deployment of effective policies to modify and reinforce more accurate risk perception to increase individual and community resilience and create a two-way dialogue between those risk and authorities. Given that climate change induced increased flood risk is a reality and the evidence that this is not yet understood by the public, nor addressed by the media, we suggest an urgent shift from the status quo media coverage based on blame to one of “Be Prepared”. Furthermore, we suggest risk communication be based on better understanding of how at-risk communities perceive risk

Long non-coding RNAs: spatial amplifiers that control nuclear structure and gene expression

Over the past decade, it has become clear that mammalian genomes encode thousands of long non-coding RNAs (lncRNAs), many of which are now implicated in diverse biological processes. Recent work studying the molecular mechanisms of several key examples — including Xist, which orchestrates X chromosome inactivation — has provided new insights into how lncRNAs can control cellular functions by acting in the nucleus. Here we discuss emerging mechanistic insights into how lncRNAs can regulate gene expression by coordinating regulatory proteins, localizing to target loci and shaping three-dimensional (3D) nuclear organization. We explore these principles to highlight biological challenges in gene regulation, in which lncRNAs are well-suited to perform roles that cannot be carried out by DNA elements or protein regulators alone, such as acting as spatial amplifiers of regulatory signals in the nucleus

Matrix methods in queueing and dynamic programming

We investigate some modern matrix methods for the solution of finite state stochastic models with an infinite time horizon. Markov and semi-Markov decision processes and finite queues in tandem with exponential service times are considered. The methods are based on the Drazin generalized inverse and use matrix decomposition. Unlike the related Jordan canonical form, the decompositions considered are numerically tractable and use real arithmetic when the original matrix has real entries. The spectral structure of the transition matrix of a Markov chain, deduced from non-negative matrix theory, provides a decomposition from which the limiting and deviation matrices are directly obtained. The matrix decomposition approach to the solution of Markov reward processes provides a new, simple derivation of the Laurent expansion of the resolvent. Many other basic results of dynamic programming are easily derived in a similar fashion and the extension to semi-Markov decision processes is straightforward. Further, numerical algorithms for matrix decomposition can be used efficiently in the policy iteration method, for evaluating the terms of the Laurent series. The problem of finding the stationary distribution of a system with two finite queues in tandem, when the service times have an exponential distribution, can also be expressed in matrix form. Two numerical methods, one iterative and one using matrix decomposition, are reviewed for computing the stationary probabilities. Job-local-balance is used to derive some bounds on the call congestion. A numerical investigation of the bounds is included. It suggests that the bounds are insensitive to the distribution of the service times.Business, Sauder School ofGraduat

Minimizing the expected processing time on a flexible machine with random tool lives

We present a stochastic version of economic tool life models for machines with finite capacity tool magazines and a variable processing speed capability, where the tool life is a random variable. Using renewal theory to express the expected number of tool setups as a function of cutting speed and magazine capacity, we extend previously published deterministic mathematical programming models to the case of minimizing the expected total processing time. A numerical illustration with typical cutting tool data shows the deterministic model underestimates the optimal expected processing time by more than 8% when the coefficient of variation equals 0.3 (typical for carbide tools), and the difference exceeds 15% for single-injury tools having an exponentially distributed economic life (worst case). Copyright © IIE