Global Properties of Locally Spatially Homogeneous Cosmological Models with Matter

The existence and nature of singularities in locally spatially homogeneous solutions of the Einstein equations coupled to various phenomenological matter models is investigated. It is shown that, under certain reasonable assumptions on the matter, there are no singularities in an expanding phase of the evolution and that unless the spacetime is empty a contracting phase always ends in a singularity where at least one scalar invariant of the curvature diverges uniformly. The class of matter models treated includes perfect fluids, mixtures of non-interacting perfect fluids and collisionless matter.Comment: 18 pages, MPA-AR-94-

A Product Line Systems Engineering Process for Variability Identification and Reduction

Software Product Line Engineering has attracted attention in the last two decades due to its promising capabilities to reduce costs and time to market through reuse of requirements and components. In practice, developing system level product lines in a large-scale company is not an easy task as there may be thousands of variants and multiple disciplines involved. The manual reuse of legacy system models at domain engineering to build reusable system libraries and configurations of variants to derive target products can be infeasible. To tackle this challenge, a Product Line Systems Engineering process is proposed. Specifically, the process extends research in the System Orthogonal Variability Model to support hierarchical variability modeling with formal definitions; utilizes Systems Engineering concepts and legacy system models to build the hierarchy for the variability model and to identify essential relations between variants; and finally, analyzes the identified relations to reduce the number of variation points. The process, which is automated by computational algorithms, is demonstrated through an illustrative example on generalized Rolls-Royce aircraft engine control systems. To evaluate the effectiveness of the process in the reduction of variation points, it is further applied to case studies in different engineering domains at different levels of complexity. Subject to system model availability, reduction of 14% to 40% in the number of variation points are demonstrated in the case studies.Comment: 12 pages, 6 figures, 2 tables; submitted to the IEEE Systems Journal on 3rd June 201

Robust Estimation of 3D Human Poses from a Single Image

Human pose estimation is a key step to action recognition. We propose a method of estimating 3D human poses from a single image, which works in conjunction with an existing 2D pose/joint detector. 3D pose estimation is challenging because multiple 3D poses may correspond to the same 2D pose after projection due to the lack of depth information. Moreover, current 2D pose estimators are usually inaccurate which may cause errors in the 3D estimation. We address the challenges in three ways: (i) We represent a 3D pose as a linear combination of a sparse set of bases learned from 3D human skeletons. (ii) We enforce limb length constraints to eliminate anthropomorphically implausible skeletons. (iii) We estimate a 3D pose by minimizing the $L_1$-norm error between the projection of the 3D pose and the corresponding 2D detection. The $L_1$-norm loss term is robust to inaccurate 2D joint estimations. We use the alternating direction method (ADM) to solve the optimization problem efficiently. Our approach outperforms the state-of-the-arts on three benchmark datasets

Software Obfuscation with Symmetric Cryptography

Software protection is of great interest to commercial industry. Millions of dollars and years of research are invested in the development of proprietary algorithms used in software programs. A reverse engineer that successfully reverses another company‘s proprietary algorithms can develop a competing product to market in less time and with less money. The threat is even greater in military applications where adversarial reversers can use reverse engineering on unprotected military software to compromise capabilities on the field or develop their own capabilities with significantly less resources. Thus, it is vital to protect software, especially the software’s sensitive internal algorithms, from adversarial analysis. Software protection through obfuscation is a relatively new research initiative. The mathematical and security community have yet to agree upon a model to describe the problem let alone the metrics used to evaluate the practical solutions proposed by computer scientists. We propose evaluating solutions to obfuscation under the intent protection model, a combination of white-box and black-box protection to reflect how reverse engineers analyze programs using a combination white-box and black-box attacks. In addition, we explore use of experimental methods and metrics in analogous and more mature fields of study such as hardware circuits and cryptography. Finally, we implement a solution under the intent protection model that demonstrates application of the methods and evaluation using the metrics adapted from the aforementioned fields of study to reflect the unique challenges in a software-only software protection technique

Network Analysis with Stochastic Grammars

Digital forensics requires significant manual effort to identify items of evidentiary interest from the ever-increasing volume of data in modern computing systems. One of the tasks digital forensic examiners conduct is mentally extracting and constructing insights from unstructured sequences of events. This research assists examiners with the association and individualization analysis processes that make up this task with the development of a Stochastic Context -Free Grammars (SCFG) knowledge representation for digital forensics analysis of computer network traffic. SCFG is leveraged to provide context to the low-level data collected as evidence and to build behavior profiles. Upon discovering patterns, the analyst can begin the association or individualization process to answer criminal investigative questions. Three contributions resulted from this research. First , domain characteristics suitable for SCFG representation were identified and a step -by- step approach to adapt SCFG to novel domains was developed. Second, a novel iterative graph-based method of identifying similarities in context-free grammars was developed to compare behavior patterns represented as grammars. Finally, the SCFG capabilities were demonstrated in performing association and individualization in reducing the suspect pool and reducing the volume of evidence to examine in a computer network traffic analysis use case

Intrinsic noise in systems with switching environments

We study individual-based dynamics in finite populations, subject to randomly switching environmental conditions. These are inspired by models in which genes transition between on and off states, regulating underlying protein dynamics. Similarly switches between environmental states are relevant in bacterial populations and in models of epidemic spread. Existing piecewise-deterministic Markov process (PDMP) approaches focus on the deterministic limit of the population dynamics while retaining the randomness of the switching. Here we go beyond this approximation and explicitly include effects of intrinsic stochasticity at the level of the linear-noise approximation. Specifically we derive the stationary distributions of a number of model systems, in good agreement with simulations. This improves existing approaches which are limited to the regimes of fast and slow switching.Comment: 15 pages, 11 figure