Fault-Tolerant Load Management for Real-Time Distributed Computer Systems

This paper presents a fault-tolerant scheme applicable to any decentralized load balancing algorithms used in soft real-time distributed systems. Using the theory of distance-transitive graphs for representing topologies of these systems, the proposed strategy partitions these systems into independent symmetric regions (spheres) centered at some control points. These central points, called fault-control points, provide a two-level task redundancy and efficiently re-distribute the load of failed nodes within their spheres. Using the algebraic characteristics of these topologies, it is shown that the identification of spheres and fault-control points is, in general, is an NP-complete problem. An efficient solution for this problem is presented by making an exclusive use of a combinatorial structure known as the Hadamard matrix. Assuming a realistic failure-repair system environment, the performance of the proposed strategy has been evaluated and compared with no fault environment, through an extensive and detailed simulation. For our fault-tolerant strategy, we propose two measures of goodness, namely, the percentage of re-scheduled tasks which meet their deadlines and the overhead incurred for fault management. It is shown that using the proposed strategy, up to 80% of the tasks can still meet their deadlines. The proposed strategy is general enough to be applicable to many networks, belonging to a number of families of distance transitive graphs. Through simulation, we have analyzed the sensitivity of this strategy to various system parameters and have shown that the performance degradation due to failures does not depend on these parameter. Also, the probability of a task being lost altogether due to multiple failures has been shown to be extremely low

Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependence

Data in the form of pairwise comparisons arises in many domains, including preference elicitation, sporting competitions, and peer grading among others. We consider parametric ordinal models for such pairwise comparison data involving a latent vector $w^* \in \mathbb{R}^d$ that represents the "qualities" of the $d$ items being compared; this class of models includes the two most widely used parametric models--the Bradley-Terry-Luce (BTL) and the Thurstone models. Working within a standard minimax framework, we provide tight upper and lower bounds on the optimal error in estimating the quality score vector $w^*$ under this class of models. The bounds depend on the topology of the comparison graph induced by the subset of pairs being compared via its Laplacian spectrum. Thus, in settings where the subset of pairs may be chosen, our results provide principled guidelines for making this choice. Finally, we compare these error rates to those under cardinal measurement models and show that the error rates in the ordinal and cardinal settings have identical scalings apart from constant pre-factors.Comment: 39 pages, 5 figures. Significant extension of arXiv:1406.661

Efficient and Flexible Search in Large Scale Distributed Systems

Peer-to-peer (P2P) technology has triggered a wide range of distributed systems beyond simple file-sharing. Distributed XML databases, distributed computing, server-less web publishing and networked resource/service sharing are only a few to name. Despite of the diversity in applications, these systems share a common problem regarding searching and discovery of information. This commonality stems from the transitory nodes population and volatile information content in the participating nodes. In such dynamic environment, users are not expected to have the exact information about the available objects in the system. Rather queries are based on partial information, which requires the search mechanism to be flexible. On the other hand, to scale with network size the search mechanism is required to be bandwidth efficient. Since the advent of P2P technology experts from industry and academia have proposed a number of search techniques - none of which is able to provide satisfactory solution to the conflicting requirements of search efficiency and flexibility. Structured search techniques, mostly Distributed Hash Table (DHT)-based, are bandwidth efficient while semi(un)-structured techniques are flexible. But, neither achieves both ends. This thesis defines the Distributed Pattern Matching (DPM) problem. The DPM problem is to discover a pattern (\ie bit-vector) using any subset of its 1-bits, under the assumption that the patterns are distributed across a large population of networked nodes. Search problem in many distributed systems can be reduced to the DPM problem. This thesis also presents two distinct search mechanisms, named Distributed Pattern Matching System (DPMS) and Plexus, for solving the DPM problem. DPMS is a semi-structured, hierarchical architecture aiming to discover a predefined number of matches by visiting a small number of nodes. Plexus, on the other hand, is a structured search mechanism based on the theory of Error Correcting Code (ECC). The design goal behind Plexus is to discover all the matches by visiting a reasonable number of nodes

Formal Methods in Quantum Circuit Design

The design and compilation of correct, efficient quantum circuits is integral to the future operation of quantum computers. This thesis makes contributions to the problems of optimizing and verifying quantum circuits, with an emphasis on the development of formal models for such purposes. We also present software implementations of these methods, which together form a full stack of tools for the design of optimized, formally verified quantum oracles. On the optimization side, we study methods for the optimization of Rz and CNOT gates in Clifford+Rz circuits. We develop a general, efficient optimization algorithm called phase folding, which reduces the number of Rz gates without increasing any metrics by computing its phase polynomial. This algorithm can further be combined with synthesis techniques for CNOT-dihedral operators to optimize circuits with respect to particular costs. We then study the optimal synthesis problem for CNOT-dihedral operators from the perspectives of Rz and CNOT gate optimization. In the case of Rz gate optimization, we show that the optimal synthesis problem is polynomial-time equivalent to minimum-distance decoding in certain Reed-Muller codes. For the CNOT optimization problem, we show that the optimal synthesis problem is at least as hard as a combinatorial problem related to Gray codes. In both cases, we develop heuristics for the optimal synthesis problem, which together with phase folding reduces T counts by 42% and CNOT counts by 22% across a suite of real-world benchmarks. From the perspective of formal verification, we make two contributions. The first is the development of a formal model of quantum circuits with ancillary bits based on the Feynman path integral, along with a concrete verification algorithm. The path integral model, with some syntactic sugar, further doubles as a natural specification language for quantum computations. Our experiments show some practical circuits with up to hundreds of qubits can be efficiently verified. Our second contribution is a formally verified, optimizing compiler for reversible circuits. The compiler compiles a classical, irreversible language to reversible circuits, with a formal, machine-checked proof of correctness written in the proof assistant F*. The compiler is structured as a partial evaluator, allowing verification to be carried out significantly faster than previous results

Topology of Reticulate Evolution

The standard representation of evolutionary relationships is a bifurcating tree. However, many types of genetic exchange, collectively referred to as reticulate evolution, involve processes that cannot be modeled as trees. Increasing genomic data has pointed to the prevalence of reticulate processes, particularly in microorganisms, and underscored the need for new approaches to capture and represent the scale and frequency of these events. This thesis contains results from applying new techniques from applied and computational topology, under the heading topological data analysis, to the problem of characterizing reticulate evolution in molecular sequence data. First, we develop approaches for analyzing sequence data using topology. We propose new topological constructions specific to molecular sequence data that generalize standard constructions such as Vietoris-Rips. We draw on previous work in phylogenetic networks and use homology to provide a quantitative measure of reticulate events. We develop methods for performing statistical inference using topological summary statistics. Next, we apply our approach to several types of molecular sequence data. First, we examine the mosaic genome structure in phages. We recover inconsistencies in existing morphology-based taxonomies, use a network approach to construct a genome-based representation of phage relationships, and identify conserved gene families within phage populations. Second, we study influenza, a common human pathogen. We capture widespread patterns of reassortment, including nonrandom cosegregation of segments and barriers to subtype mixing. In contrast to traditional influenza studies, which focus on the phylogenetic branching patterns of only the two surface-marker proteins, we use whole-genome data to represent influenza molecular relationships. Using this representation, we identify unexpected relationships between divergent influenza subtypes. Finally, we examine a set of pathogenic bacteria. We use two sources of data to measure rates of reticulation in both the core genome and the mobile genome across a range of species. Network approaches are used to represent the population of S. aureus and analyze the spread of antibiotic resistance genes. The presence of antibiotic resistance genes in the human microbiome is investigated

NASA SERC 1990 Symposium on VLSI Design

This document contains papers presented at the first annual NASA Symposium on VLSI Design. NASA's involvement in this event demonstrates a need for research and development in high performance computing. High performance computing addresses problems faced by the scientific and industrial communities. High performance computing is needed in: (1) real-time manipulation of large data sets; (2) advanced systems control of spacecraft; (3) digital data transmission, error correction, and image compression; and (4) expert system control of spacecraft. Clearly, a valuable technology in meeting these needs is Very Large Scale Integration (VLSI). This conference addresses the following issues in VLSI design: (1) system architectures; (2) electronics; (3) algorithms; and (4) CAD tools

Geometric, Feature-based and Graph-based Approaches for the Structural Analysis of Protein Binding Sites : Novel Methods and Computational Analysis

In this thesis, protein binding sites are considered. To enable the extraction of information from the space of protein binding sites, these binding sites must be mapped onto a mathematical space. This can be done by mapping binding sites onto vectors, graphs or point clouds. To finally enable a structure on the mathematical space, a distance measure is required, which is introduced in this thesis. This distance measure eventually can be used to extract information by means of data mining techniques