Constrained Approximation of Effective Generators for Multiscale Stochastic Reaction Networks and Application to Conditioned Path Sampling

Efficient analysis and simulation of multiscale stochastic systems of chemical kinetics is an ongoing area for research, and is the source of many theoretical and computational challenges. In this paper, we present a significant improvement to the constrained approach, which is a method for computing effective dynamics of slowly changing quantities in these systems, but which does not rely on the quasi-steady-state assumption (QSSA). The QSSA can cause errors in the estimation of effective dynamics for systems where the difference in timescales between the "fast" and "slow" variables is not so pronounced. This new application of the constrained approach allows us to compute the effective generator of the slow variables, without the need for expensive stochastic simulations. This is achieved by finding the null space of the generator of the constrained system. For complex systems where this is not possible, or where the constrained subsystem is itself multiscale, the constrained approach can then be applied iteratively. This results in breaking the problem down into finding the solutions to many small eigenvalue problems, which can be efficiently solved using standard methods. Since this methodology does not rely on the quasi steady-state assumption, the effective dynamics that are approximated are highly accurate, and in the case of systems with only monomolecular reactions, are exact. We will demonstrate this with some numerics, and also use the effective generators to sample paths of the slow variables which are conditioned on their endpoints, a task which would be computationally intractable for the generator of the full system.Comment: 31 pages, 7 figure

Improving product availability in hospitals : the role of inventory inaccuracies

Thesis (Ph. D.)--Massachusetts Institute of Technology, Engineering Systems Division, 2010.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. [184]-193).All players in the healthcare industry face increasing public and political pressure to improve quality of care and control costs. Hospitals, on the frontline of this challenge, face nursing shortages and financial constraints. Survey data indicate that missing medication and supplies interrupt nurses more than twice per shift, increasing costs and putting patients at risk. These challenges persist even though over 72% of U.S. hospitals have deployed Automated Dispensing Machines (ADMs), electronic cabinets that automate inventory management processes and improve product availability. This research investigates the role of inventory inaccuracies, i.e., mismatches between book inventory and physical inventory on hand, as drivers of product availability in hospitals. The research objectives are three-fold: (1) characterize the sources of inventory inaccuracies prevalent in a hospital context; (2) quantify the impact of inventory inaccuracies on product availability and performance metrics; and (3) identify and evaluate practical strategies that hospitals can use to improve product availability by reducing and mitigating inventory inaccuracies. This thesis views the hospital supply chain as a socio-technical system and addresses the research questions using a multilevel, multi-method approach. The research is empirically grounded by the case study of Lambda, a New England area hospital that provided qualitative and high-frequency transactional data from its network of 108 ADMs that stock over 21,000 product-location combinations. First, by classifying sources of inventory inaccuracies this thesis identifies Imperfect Demand Recording as a hospital-specific source of such inaccuracies. Recording Accuracy is proposed as a metric of user behavior at product and location levels, and reveals that between five and thirty percent of product usage is not recorded. Then, a single-product Discrete-Event Simulation (DES) model shows that Imperfect Demand Recording causes large reductions in availability unless mitigated by frequent and consistent (i.e., equally-spaced) inventory counts, and that service level estimates provided by ADMs can have a large, optimistic bias. Assuming that count timing is independent of inventory state, an analytical model provides a closed-form generalization of the simulation results and shows that variability in cycle count has a nonlinear and substantial effect, causing 35% of counts performed at Lambda to be ineffective. Finally, a sequential and iterative framework integrating the managerial implications of these contributions is proposed.by David C. Opolon.Ph.D

On inter-satellite laser ranging, clock synchronization and gravitational wave data analysis

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Safety and Reliability - Safe Societies in a Changing World

The contributions cover a wide range of methodologies and application areas for safety and reliability that contribute to safe societies in a changing world. These methodologies and applications include: - foundations of risk and reliability assessment and management - mathematical methods in reliability and safety - risk assessment - risk management - system reliability - uncertainty analysis - digitalization and big data - prognostics and system health management - occupational safety - accident and incident modeling - maintenance modeling and applications - simulation for safety and reliability analysis - dynamic risk and barrier management - organizational factors and safety culture - human factors and human reliability - resilience engineering - structural reliability - natural hazards - security - economic analysis in risk managemen

ADM-CLE approach for detecting slow variables in continuous time Markov chains and dynamic data

A method for detecting intrinsic slow variables in high-dimensional stochastic chemical reaction networks is developed and analyzed. It combines anisotropic diffusion maps (ADM) with approximations based on the chemical Langevin equation (CLE). The resulting approach, called ADM-CLE, has the potential of being more efficient than the ADM method for a large class of chemical reaction systems, because it replaces the computationally most expensive step of ADM (running local short bursts of simulations) by using an approximation based on the CLE. The ADM-CLE approach can be used to estimate the stationary distribution of the detected slow variable, without any a-priori knowledge of it. If the conditional distribution of the fast variables can be obtained analytically, then the resulting ADM-CLE approach does not make any use of Monte Carlo simulations to estimate the distributions of both slow and fast variables