Importance sampling large deviations in nonequilibrium steady states. I

Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states, and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies, evaluating large deviation functions numerically for all but the simplest systems is difficult, because by construction they depend on exponentially rare events. In this first paper of a series, we evaluate different trajectory-based sampling methods capable of computing large deviation functions of time integrated observables within nonequilibrium steady states. We illustrate some convergence criteria and best practices using a number of different models, including a biased Brownian walker, a driven lattice gas, and a model of self-assembly. We show how two popular methods for sampling trajectory ensembles, transition path sampling and diffusion Monte Carlo, suffer from exponentially diverging correlations in trajectory space as a function of the bias parameter when estimating large deviation functions. Improving the efficiencies of these algorithms requires introducing guiding functions for the trajectories.Comment: Published in JC

A Unified Perspective on Sampling Algorithms for Rare Trajectories of Discrete Markov Processes

This article analyzes and compares two general techniques of rare event simulation for generating paths of Markov processes over fixed time horizons: backtracking and exponential tilting. These two methods allow to compute the probability that the process ends within a rare region, which is unlikely to be attained. Backtracking consists in reversing the time of the process: the path is obtained backwards, from the terminal point until the initial one. The terminal point is generated from an appropriately chosen distribution that covers well the arrival region. Exponential tilting is a general technique for obtaining an alternative sampling probability measure, under which the process is likely to hit the rare region at terminal time. We show that both methods belong to the same class of importance sampling procedures, by providing the common mathematical framework of these two conceptually different methods of sampling rare trajectories. Besides this analytical comparison, we compare the two methods numerically, by means of a simple random walk and a process with meta-stable states. The numerical analysis shows that both methods possess distinct areas of application where they exhibit greater efficiency. Detailed algorithms of the proposed simulation methods are provided

Population-based algorithms for improved history matching and uncertainty quantification of Petroleum reservoirs

In modern field management practices, there are two important steps that shed light on a multimillion dollar investment. The first step is history matching where the simulation model is calibrated to reproduce the historical observations from the field. In this inverse problem, different geological and petrophysical properties may provide equally good history matches. Such diverse models are likely to show different production behaviors in future. This ties the history matching with the second step, uncertainty quantification of predictions. Multiple history matched models are essential for a realistic uncertainty estimate of the future field behavior. These two steps facilitate decision making and have a direct impact on technical and financial performance of oil and gas companies. Population-based optimization algorithms have been recently enjoyed growing popularity for solving engineering problems. Population-based systems work with a group of individuals that cooperate and communicate to accomplish a task that is normally beyond the capabilities of each individual. These individuals are deployed with the aim to solve the problem with maximum efficiency. This thesis introduces the application of two novel population-based algorithms for history matching and uncertainty quantification of petroleum reservoir models. Ant colony optimization and differential evolution algorithms are used to search the space of parameters to find multiple history matched models and, using a Bayesian framework, the posterior probability of the models are evaluated for prediction of reservoir performance. It is demonstrated that by bringing latest developments in computer science such as ant colony, differential evolution and multiobjective optimization, we can improve the history matching and uncertainty quantification frameworks. This thesis provides insights into performance of these algorithms in history matching and prediction and develops an understanding of their tuning parameters. The research also brings a comparative study of these methods with a benchmark technique called Neighbourhood Algorithms. This comparison reveals the superiority of the proposed methodologies in various areas such as computational efficiency and match quality

Multi-level characterization and information extraction in directed and node-labeled functional brain networks

Current research in computational neuroscience puts great emphasis on the computation and analysis of the functional connectivity of the brain. The methodological developments presented in this work are concerned with a group-specific comprehensive analysis of networks that represent functional interaction patterns. Four application studies are presented, in which functional brain network samples of different clinical background were analyzed in different ways, using combinations of established approaches and own methodological developments. Study I is concerned with a sample-specific decomposition of the functional brain networks of depressed subjects and healthy controls into small functionally important and recurring subnetworks (motifs) using own developments. Study II investigates whether lithium treatment effects are reflected in the functional brain networks of HIV-positive subjects with diagnosed cognitive impairment. For it, microscopic and macroscopic structural properties were analyzed. Study III explores spatially highly resolved functional brain networks with regard to a functional segmentation given by identified module (community) structure. Also, ground truth networks with known module structure were generated using own methodological developments. They formed the basis of a comprehensive simulation study that quantified module structure quality and preservation in order to evaluate the effects of a novel approach for the identification of connectivity (lsGCI). Study IV tracks the time-evolution of module structure and introduces a newly developed own approach for the determination of edge weight thresholds based on multicriteria optimization. The methodological challenges that underly these different topological analyses, but also the various opportunities to gain an improved understanding of neural information processing among brain areas were highlighted by this work and the presented results

Random sampling and generation over data streams and graphs

Ph.DDOCTOR OF PHILOSOPH

Debating Termination: Rhetoric and Responses to U.S. American Indian Policy, 1947-1970

This thesis examines discussions surrounding U.S. American Indian policy from 1947 to 1970, a period in which Congress aimed to “terminate” the federal trust status of Native individuals and groups. Federal rhetoric promised that Termination would lead to “equality” for Native Americans, allowing them to become “full citizens” and gain “freedom” from government paternalism. In practice terminated tribes, like the Klamath, lost both Bureau of Indian Affairs health and educational services and protections on their land holdings, and were consequently subjected to land tax. These changes led to a loss of lands, as well as increasing rates of unemployment, alcoholism and ill-health among members of terminated tribes. This thesis argues that public and tribal acceptance of Termination was secured by the vague nature of policy rhetoric, obscuring the gravity of federal aims, as well as the persistence of assimilationist social evolutionary ideology in the U.S. throughout the twentieth century. Scholarship agrees that Termination was destructive, but generally presents the policy as short-lived, beginning in 1953 and running out of political steam by 1958. However, it was not actually repudiated until 1970. Drawing on discussions in the national press and the councils of both terminated tribes (Klamath) and groups that retained their trust status (Navajo, Mississippi Choctaw, Five Tribes), this thesis argues that eventual Termination remained the aim of federal Indian policy until President Nixon’s 1970 Special Message on Indian Affairs. It also demonstrates that the rhetoric of “freedom” and “citizenship” was interpreted in multiple ways, playing both to the mainstream belief in the inevitability of Indian assimilation, and tribal governments’ hopes to gain further self-determination. This thesis thus highlights the power and significance of language, demonstrating that understanding the development of U.S. Indian policy demands that more attention be paid to its role