Optimality of Treating Interference as Noise: A Combinatorial Perspective

For single-antenna Gaussian interference channels, we re-formulate the problem of determining the Generalized Degrees of Freedom (GDoF) region achievable by treating interference as Gaussian noise (TIN) derived in [3] from a combinatorial perspective. We show that the TIN power control problem can be cast into an assignment problem, such that the globally optimal power allocation variables can be obtained by well-known polynomial time algorithms. Furthermore, the expression of the TIN-Achievable GDoF region (TINA region) can be substantially simplified with the aid of maximum weighted matchings. We also provide conditions under which the TINA region is a convex polytope that relax those in [3]. For these new conditions, together with a channel connectivity (i.e., interference topology) condition, we show TIN optimality for a new class of interference networks that is not included, nor includes, the class found in [3]. Building on the above insights, we consider the problem of joint link scheduling and power control in wireless networks, which has been widely studied as a basic physical layer mechanism for device-to-device (D2D) communications. Inspired by the relaxed TIN channel strength condition as well as the assignment-based power allocation, we propose a low-complexity GDoF-based distributed link scheduling and power control mechanism (ITLinQ+) that improves upon the ITLinQ scheme proposed in [4] and further improves over the heuristic approach known as FlashLinQ. It is demonstrated by simulation that ITLinQ+ provides significant average network throughput gains over both ITLinQ and FlashLinQ, and yet still maintains the same level of implementation complexity. More notably, the energy efficiency of the newly proposed ITLinQ+ is substantially larger than that of ITLinQ and FlashLinQ, which is desirable for D2D networks formed by battery-powered devices.Comment: A short version has been presented at IEEE International Symposium on Information Theory (ISIT 2015), Hong Kon

Foundations of the Geometric Mechanics Udwadia-Kalaba Framework for Rigid Body Constrained Motion Analysis

Presented herein are multiple tools for constrained motion analysis extended to different dynamical frameworks. The Udwadia-Kalaba (UK) formalism for the constrained motion analysis of a point mass is a well-documented and applied methodology. Here, UK formulation is generalized to the dynamics of rigid bodies on nonlinear manifolds in the geometric mechanics framework. This approach simultaneously treats rotational and translational motion in a unified method without encountering singularites or non-uniqueness, issues that would arise were attitude parameterization sets used. The viability of this geometric mechanics UK formalism is demonstrated for the cases of fully and underconstrained systems. The nominal UK formalism requires the complete knowledge of the system dynamics. In the presence of unmodeled dynamics or uncertainties in the system, the stability of the system cannot be assessed using the nominal UK formulation. Therefore, a controller is presented that stabilizes the system under unmodeled dynamics and external perturbations. In addition, the UK formulation has been historically applied to systems with equality constraints. However, it has not been formulated for usage with inequality constraints. Here, the implementation of slack and excess variables to treat this class of constraints is presented for usage within the UK formulation for the point mass constrained motion with inequality constraints. Also contained within is an extension of pre-existing work which models the gravitational force acting on a rigid body from a nonuniform gravitational field that holds for any degree and order of spherical harmonics

Efficient and Reasonable Object-Oriented Concurrency

Making threaded programs safe and easy to reason about is one of the chief difficulties in modern programming. This work provides an efficient execution model for SCOOP, a concurrency approach that provides not only data race freedom but also pre/postcondition reasoning guarantees between threads. The extensions we propose influence both the underlying semantics to increase the amount of concurrent execution that is possible, exclude certain classes of deadlocks, and enable greater performance. These extensions are used as the basis an efficient runtime and optimization pass that improve performance 15x over a baseline implementation. This new implementation of SCOOP is also 2x faster than other well-known safe concurrent languages. The measurements are based on both coordination-intensive and data-manipulation-intensive benchmarks designed to offer a mixture of workloads.Comment: Proceedings of the 10th Joint Meeting of the European Software Engineering Conference and the ACM SIGSOFT Symposium on the Foundations of Software Engineering (ESEC/FSE '15). ACM, 201

Mathematical Methods for Network Analysis, Proteomics and Disease Prevention

This dissertation aims at analyzing complex problems arising in the context of dynamical networks, proteomics, and disease prevention. First, a new graph-based method for proving global stability of synchronization in directed dynamical networks is developed. This method utilizes stability and graph theories to clarify the interplay between individual oscillator dynamics and network topology. Secondly, a graph-theoretical algorithm is proposed to predict Ca2+-binding site in proteins. The new algorithm enables us to identify previously-unknown Ca2+-binding sites, and deepens our understanding towards disease-related Ca2+-binding proteins at a molecular level. Finally, an optimization model and algorithm to solve a disease prevention problem are described at the population level. The new resource allocation model is designed to assist clinical managers to make decisions on identifying at-risk population groups, as well as selecting a screening and treatment strategy for chlamydia and gonorrhea patients under a fixed budget. The resource allocation model and algorithm can have a significant impact on real treatment strategy issues