DRUM Collection: Mathematics Theses and Dissertations
http://hdl.handle.net/1903/2793
Sat, 19 Apr 2014 06:53:00 GMT2014-04-19T06:53:00ZRegulation of Systemic Risk Through Contributory Endogenous Agent-Based Modeling
http://hdl.handle.net/1903/14956
Title: Regulation of Systemic Risk Through Contributory Endogenous Agent-Based Modeling
Authors: Bristor, Aurora
Abstract: The Financial Stability Oversight Council (FSOC) was created to identify and respond to emerging threats to the stability of the United States financial system. The research arm of the FSOC, the Office of Financial Research (OFR), has begun to explore agent-based models (ABMs) for measuring the emergent threat of systemic risk. We propose an ABM-based regulatory structure that incentivizes the honest participation and data contribution of regulated firms while providing clarity into the actions of the firms as endogenous to the market and driving emergent behavior. We build this scheme onto an existing ABM of a single-asset market to examine whether the structure of the scheme could provide its own benefits to market stabilization. We find that without regulatory intervention, markets acting within this proposed structure experience fewer bankruptcies and lower leverage buildup while returning larger profits for the same amount of risk.Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/1903/149562013-01-01T00:00:00ZERGODIC PROPERTIES OF GIBBS MEASURES FOR EXPANDING MAPS
http://hdl.handle.net/1903/14920
Title: ERGODIC PROPERTIES OF GIBBS MEASURES FOR EXPANDING MAPS
Authors: Tapia, Adriana Maria
Abstract: Gibbs measure which are also called Sinai-Ruelle-Bowen Measure describe asymptotic behavior and statistical properties of typical trajectories in many physical systems. In this work we review several methods of studying Gibbs measures by Ya.G. Sinai, D. Ruelle, R. Bowen, and P. Walters. First, using symbolic dynamics we show for subshifts of finite type that the invariant measure obtained in the Ruelle-Perron-Frobenius (R-P-F)Theorem is an ergodic Gibbs measure. Second, the proof of the R-P-F theorem is given following Walters approach, where he considers maps with infinitely many branches. In both cases, the idea is to find a fixed point of the transfer operator which will allow us to define the measure μ . Ergodic properties of μ are studied. In particular results are valid for expanding maps. These ideas are illustrated in the example of an expanding map with two branches where we show explicitly the existence of an invariant measure as well as we prove ergodicity, exactness, and the Rochlin Entropy formula.Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/1903/149202013-01-01T00:00:00ZAn efficient method for radiation hydrodynamics in models of feedback-regulated star formation
http://hdl.handle.net/1903/14883
Title: An efficient method for radiation hydrodynamics in models of feedback-regulated star formation
Authors: Skinner, Michael Aaron Reed
Abstract: We describe a module for the <italic>Athena</italic> code that solves the gray equations of radiation hydrodynamics (RHD), based on the first two moments of the radiative transfer equation. We combine explicit Godunov methods to advance the gas and radiation variables including non-stiff source terms with a local implicit method to integrate stiff source terms. We adopt the M<sub>1</sub> closure relation, including leading source terms to $mathcal{O}(betatau)$ and employ the reduced speed of light approximation (RSLA) with subcycling of the radiation variables to reduce computational costs. We consider self-gravitating fragmentation and evolution of turbulent gaseous clouds, modeling the propagation and interaction of radiation from embedded star clusters that form with the surrounding gas. To model the luminosity sources, we use the star particle algorithm of Gong & Ostriker (2013) based on the particle mesh method combined with an efficient open boundary condition Poisson solver for the self-gravitational potential. Our code is dimensionally unsplit in one, two, and three space dimensions and is parallelized using MPI. The streaming and diffusion limits are well-described by the M<sub>1</sub> closure model, and our implementation shows excellent behavior for a problem with a concentrated radiation source containing both regimes simultaneously. Our operator-split method is ideally suited for problems with a slowly-varying radiation field and dynamical gas flows in which the effect of the RSLA is minimal. We present an analysis of the dispersion relation of RHD linear waves highlighting the conditions of applicability for the RSLA. To demonstrate the accuracy of our method, we utilize a suite of radiation and RHD tests covering a broad range of regimes, including RHD waves, shocks, and equilibria, showing second-order convergence in most cases, and a test to demonstrate the accuracy of particle orbits obtained using our method. Applying our method to the study of feedback-regulated star formation in models of giant molecular clouds, we conclude that the radiation force on dust from reprocessed radiation is an efficient mechanism for cloud disruption, which may be particularly important in super star clusters with deep gravitational potential wells.Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/1903/148832013-01-01T00:00:00ZOutlier Modeling for Spatial Gaussian Random Fields
http://hdl.handle.net/1903/14877
Title: Outlier Modeling for Spatial Gaussian Random Fields
Authors: Sotiris, Ekaterina
Abstract: In this dissertation, we worked on extending time series outlier detection methodology to spatial data. An integral part of the outlier detection algorithm is a hypothesis test for the presence of at least one outlier in the data. The distribution of the corresponding test statistic is not known and as a result the critical value corresponding to a size α test is estimated by approximating the tail probability for the test statistic. We identified and studied two methods of approximating the tail probability for the test statistic in the case when the parameters of the underlying spatial process are known. These approximations are based on bounds on the tail probability of the maxima of a discretely sampled Gaussian random field. We also study the distribution of the test statistic in the case when the parameters of the underlying spatial process are unknown and are estimated using maximum likelihood.Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/1903/148772013-01-01T00:00:00Z