Initial data to vacuum Einstein equations with asymptotic expansion

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1998.Includes bibliographical references (leaf 92).by Sang Hoon Chin.Ph.D

Detection of Early-Stage Enterprise Infection by Mining Large-Scale Log Data

Recent years have seen the rise of more sophisticated attacks including advanced persistent threats (APTs) which pose severe risks to organizations and governments by targeting confidential proprietary information. Additionally, new malware strains are appearing at a higher rate than ever before. Since many of these malware are designed to evade existing security products, traditional defenses deployed by most enterprises today, e.g., anti-virus, firewalls, intrusion detection systems, often fail at detecting infections at an early stage. We address the problem of detecting early-stage infection in an enterprise setting by proposing a new framework based on belief propagation inspired from graph theory. Belief propagation can be used either with "seeds" of compromised hosts or malicious domains (provided by the enterprise security operation center -- SOC) or without any seeds. In the latter case we develop a detector of C&C communication particularly tailored to enterprises which can detect a stealthy compromise of only a single host communicating with the C&C server. We demonstrate that our techniques perform well on detecting enterprise infections. We achieve high accuracy with low false detection and false negative rates on two months of anonymized DNS logs released by Los Alamos National Lab (LANL), which include APT infection attacks simulated by LANL domain experts. We also apply our algorithms to 38TB of real-world web proxy logs collected at the border of a large enterprise. Through careful manual investigation in collaboration with the enterprise SOC, we show that our techniques identified hundreds of malicious domains overlooked by state-of-the-art security products

Sparse Coding and Autoencoders

In "Dictionary Learning" one tries to recover incoherent matrices $A^* \in \mathbb{R}^{n \times h}$ (typically overcomplete and whose columns are assumed to be normalized) and sparse vectors $x^* \in \mathbb{R}^h$ with a small support of size $h^p$ for some $0 <p < 1$ while having access to observations $y \in \mathbb{R}^n$ where $y = A^*x^*$. In this work we undertake a rigorous analysis of whether gradient descent on the squared loss of an autoencoder can solve the dictionary learning problem. The "Autoencoder" architecture we consider is a $\mathbb{R}^n \rightarrow \mathbb{R}^n$ mapping with a single ReLU activation layer of size $h$. Under very mild distributional assumptions on $x^*$, we prove that the norm of the expected gradient of the standard squared loss function is asymptotically (in sparse code dimension) negligible for all points in a small neighborhood of $A^*$. This is supported with experimental evidence using synthetic data. We also conduct experiments to suggest that $A^*$ is a local minimum. Along the way we prove that a layer of ReLU gates can be set up to automatically recover the support of the sparse codes. This property holds independent of the loss function. We believe that it could be of independent interest.Comment: In this new version of the paper with a small change in the distributional assumptions we are actually able to prove the asymptotic criticality of a neighbourhood of the ground truth dictionary for even just the standard squared loss of the ReLU autoencoder (unlike the regularized loss in the older version

Discrete-Event Analytic Technique for Surface Growth Problems

We introduce an approach for calculating non-universal properties of rough surfaces. The technique uses concepts of distinct surface-configuration classes, defined by the surface growth rule. The key idea is a mapping between discrete events that take place on the interface and its elementary local-site configurations. We construct theoretical probability distributions of deposition events at saturation for surfaces generated by selected growth rules. These distributions are then used to compute measurable physical quantities. Despite the neglect of temporal correlations, our approximate analytical results are in very good agreement with numerical simulations. This discrete-event analytic technique can be particularly useful when applied to quantification problems, which are known to not be suited to continuum methods.Comment: 4 pages, 7 figures, published 17 Feb. 200

Gene Expression Correlates with Process Rates Quantified for Sulfate- and Fe(III)-Reducing Bacteria in U(VI)-Contaminated Sediments

Though iron- and sulfate-reducing bacteria are well known for mediating uranium(VI) reduction in contaminated subsurface environments, quantifying the in situ activity of the microbial groups responsible remains a challenge. The objective of this study was to demonstrate the use of quantitative molecular tools that target mRNA transcripts of key genes related to Fe(III) and sulfate reduction pathways in order to monitor these processes during in situ U(VI) remediation in the subsurface. Expression of the Geobacteraceae-specific citrate synthase gene (gltA) and the dissimilatory (bi)sulfite reductase gene (dsrA), were correlated with the activity of iron- or sulfate-reducing microorganisms, respectively, under stimulated bioremediation conditions in microcosms of sediments sampled from the U.S. Department of Energy’s Oak Ridge Integrated Field Research Challenge (OR-IFRC) site at Oak Ridge, TN, USA. In addition, Geobacteraceae-specific gltA and dsrA transcript levels were determined in parallel with the predominant electron acceptors present in moderately and highly contaminated subsurface sediments from the OR-IFRC. Phylogenetic analysis of the cDNA generated from dsrA mRNA, sulfate-reducing bacteria-specific 16S rRNA, and gltA mRNA identified activity of specific microbial groups. Active sulfate reducers were members of the Desulfovibrio, Desulfobacterium, and Desulfotomaculum genera. Members of the subsurface Geobacter clade, closely related to uranium-reducing Geobacter uraniireducens and Geobacter daltonii, were the metabolically active iron-reducers in biostimulated microcosms and in situ core samples. Direct correlation of transcripts and process rates demonstrated evidence of competition between the functional guilds in subsurface sediments. We further showed that active populations of Fe(III)-reducing bacteria and sulfate-reducing bacteria are present in OR-IFRC sediments and are good potential targets for in situ bioremediation