Importance sampling for stochastic programming

Stochastic programming models are large-scale optimization problems that are used to facilitate decision-making under uncertainty. Optimization algorithms for such problems need to evaluate the exptected future costs of current decisions, often referred to as the recourse function. In practice, this calculation is computationally difficult as it requires the evaluation of a multidimensional integral whose integrand is an optimization problem. In turn, the recourse function has to be estimated using techniques such as scenario trees or Monte Carlo methods, both of which require numerous function evaluations to produce accurate results for large-scale problems with multiple periods and high-dimensional uncertainty. In this thesis, we introduce an Importance Sampling framework for stochastic programming that can produce accurate estimates of the recourse function using a small number of samples. Previous approaches for importance sampling in stochastic programming were limited to problems where the uncertainty was modelled using discrete random variables, and the recourse function was additively separable in the uncertain dimensions. Our framework avoids these restrictions by pairing Markov Chain Monte Carlo methods with Kernel Density Estimation algorithms to build a non-parametric Importance Sampling distribution, which can then be used to produce a low-variance estimate of the recourse function. We demonstrate the increased accuracy and efficiency of our approach using variants of well-known multistage stochastic programming problems. Our numerical results show that our framework produces more accurate estimates of the optimal value of stochastic programming models, especially for problems with moderate-to-high variance distributions or rare-event distributions. For example, in some applications, we found that if the random variables are drawn from a rare-event distribution, our proposed algorithm can achieve four times reduction in the mean square error and variance given by other existing methods (e.g.: SDDP with Crude Monte Carlo or SDDP with Quasi Monte Carlo method) for the same number of samples. Or when the random variables are drawn from the high variance distribution, our proposed algorithm can reduce the variance averagely by two times compared to the results obtained by other methods for approximately the same level of mean square error and a fixed number of samples. We use our proposed algorithm to solve a capacity expansion planning problem in the electric power industry. The model includes the unit commitment problem and maintenance scheduling. It allows the investors to make optimal decisions on the capacity and the type of generators to build in order to minimize the capital cost and operating cost over a long period of time. Our model computes the optimal schedule for each of the generators while meeting the demand and respecting the engineering constraints of each generator. We use an aggregation method to group generators of similar features, in order to reduce the problem size. The numerical experiment shows that by clustering the generators of the same technology with similar size together and apply the SDDP algorithm with our proposed sampling framework on this simplified formulation, we are able to solve the problem using only one fourth the amount of time to solve the original problem by conventional algorithms. The speed-up is achieved without a significant reduction in the quality of the solution.Open Acces

Organ Transplantation Eligibility: Discrimination on the Basis of Cognitive Disability

Congress passed the Rehabilitation Act of 1973 and the Americans with Disabilities Act of 1990 in response to the extensive history of discrimination Americans with disabilities have faced. These federal statutes provide that no individual is to be precluded from enjoying the programs provided by certain entities solely on the basis of their disability. However, this is difficult in regards to organ transplantation and individuals with cognitive disabilities. The issue lies where a physician is faced with the difficult decision in pursuing their moral and ethical obligations to preserve life while determining whether a specific cognitive disability is a contraindication for organ transplantation. This Note advocates for federally implemented guidelines, supplementing current federal antidiscrimination statutes, which would be more stringent on healthcare providers and provide clarity to physicians to prevent discrimination in determining whether an individual with a cognitive disability should receive an organ transplant. This Note provides the background of the applicable federal antidiscrimination statutes and judicial interpretation of the applicable statutes as well as the difficulties in procuring an organ transplant and the risks subsequent to an organ transplant procedure. Additionally, this Note discusses public policies and how some states have taken steps to deter discrimination. This Note will also provide an analysis of physician discretion in evaluating organ transplant eligibility and how absolute discretion presents the opportunity for discrimination. Lastly, this Note provides solutions, including judicial intervention and policy reform implementing a spectrum of risk classification, and mandatory disclosure of the reasons for transplantation refusal

Determining the Mechanical Properties of the E. coli Methionine Transporter

Adenosine Triphosphate Binding Cassette (ABC) transporters constitute a superfamily of active transporters embedded in the cellular membrane. They consist of two highly conserved nucleotide-binding subunits which bind and hydrolyze ATP, and two diverse transmembrane subunits which provide a pathway for the substrate to pass through the membrane. ABC transporters serve a broad range of vital functions. Various conditions like cystic fibrosis and Stargardt disease are caused by defunct ABC transporters, and certain medical complications like antibiotic drug resistance are linked to promiscuous ABC transporters. Despite the importance of these transporters in crucial biological processes, the mechanisms of many transporters are yet to be solved. While many universal features of ABC transporters have been identified, the step-by-step process by which individual transporters move the substrate are a mystery. / To further understand the mechanism of ABC transporters, we are studying the E. coli methionine ABC importer MetNI. Because the bacterium needs to vary methionine import based on cellular needs, MetNI ATPase activity and coupled substrate transport must be properly regulated. Our current goal is to understand the mechanistic details of MetNI ATP binding and hydrolysis using a real-time ATPase assay. Here we present our preliminary work on analyzing the kinetics of MetNI ATP usage under varying conditions and with different mutations. This detailed study of MetNI kinetics will ultimately provide insight into the mechanism of methionine import, which may be more broadly applicable to the ABC transporter superfamily

Family of Circulant Graphs and Its Expander Properties

In this thesis, we apply spectral graph theory to show the non-existence of an expander family within the class of circulant graphs. Using the adjacency matrix and its properties, we prove Cheeger\u27s inequalities and determine when the equalities hold. In order to apply Cheeger\u27s inequalities, we compute the spectrum of a general circulant graph and approximate its second largest eigenvalue. Finally, we show that circulant graphs do not contain an expander family

Indoor location prediction using multiple wireless received signal strengths

This paper presents a framework for indoor location prediction system using multiple wireless signals available freely in public or office spaces. We first propose an abstract architectural design for the system, outlining its key components and their functionalities. Different from existing works, such as robot indoor localization which requires as precise localization as possible, our work focuses on a higher grain: location prediction. Such a problem has a great implication in context-aware systems such as indoor navigation or smart self-managed mobile devices (e.g., battery management). Central to these systems is an effective method to perform location prediction under different constraints such as dealing with multiple wireless sources, effects of human body heats or mobility of the users. To this end, the second part of this pa- per presents a comparative and comprehensive study on different choices for modeling signals strengths and prediction methods under different condition settings. The results show that with simple, but effective modeling method, almost perfect prediction accuracy can be achieved in the static environment, and up to 85% in the presence of human movements. Finally, adopting the proposed framework we outline a fully developed system, named Marauder, that support user interface interaction and real-time voice-enabled location prediction.<br /

High accuracy context recovery using clustering mechanisms

This paper examines the recovery of user context in indoor environmnents with existing wireless infrastructures to enable assistive systems. We present a novel approach to the extraction of user context, casting the problem of context recovery as an unsupervised, clustering problem. A well known density-based clustering technique, DBSCAN, is adapted to recover user context that includes user motion state, and significant places the user visits from WiFi observations consisting of access point id and signal strength. Furthermore, user rhythms or sequences of places the user visits periodically are derived from the above low level contexts by employing state-of-the-art probabilistic clustering technique, the Latent Dirichiet Allocation (LDA), to enable a variety of application services. Experimental results with real data are presented to validate the proposed unsupervised learning approach and demonstrate its applicability.<br /