DESIGNING VLSI SIGNAL PROCESSING CHIPS USING DATA DEPENDENCE GRAPHS.

The highly structured nature of many digital signal processing operations allows these to be directly implemented as regular VLSI circuits. This feature has been successfully exploited in the design of a number of commercial chips, some examples of which are described. While many of the architectures on which such chips are based were originally derived on heuristic basis, there is an increasing interest in the development of systematic design techniques for the direct mapping of computations onto regular VLSI arrays. The purpose of this paper is to show how the the technique proposed by Kung can be readily extended to the design of VLSI signal processing chips where the organisation of computations at the level of individual data bits is of paramount importance. The technique in question allows architectures to be derived using the projection and retiming of data dependence graphs.

Implementation and testing of Lanczos-based algorithms for Random-Phase Approximation eigenproblems

The treatment of the Random-Phase Approximation Hamiltonians, encountered in different frameworks, like time-dependent density functional theory or Bethe-Salpeter equation, is complicated by their non-Hermicity. Compared to their Hermitian Hamiltonian counterparts, computational methods for the treatment of non-Hermitian Hamiltonians are often less efficient and less stable, sometimes leading to the breakdown of the method. Recently [Gruning et al. Nano Lett. 8 (2009) 28201, we have identified that such Hamiltonians are usually pseudo-Hermitian. Exploiting this property, we have implemented an algorithm of the Lanczos type for Random-Phase Approximation Hamiltonians that benefits from the same stability and computational load as its Hermitian counterpart, and applied it to the study of the optical response of carbon nanotubes. We present here the related theoretical grounds and technical details, and study the performance of the algorithm for the calculation of the optical absorption of a molecule within the Bethe-Salpeter equation framework. (C) 2011 Elsevier B.V. All rights reserved.

Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials

A numerical method is developed to simulate complex two-dimensional crack propagation in quasi-brittle materials considering random heterogeneous fracture properties. Potential cracks are represented by pre-inserted cohesive elements with tension and shear softening constitutive laws modelled by spatially varying Weibull random fields. Monte Carlo simulations of a concrete specimen under uni-axial tension were carried out with extensive investigation of the effects of important numerical algorithms and material properties on numerical efficiency and stability, crack propagation processes and load-carrying capacities. It was found that the homogeneous model led to incorrect crack patterns and load–displacement curves with strong mesh-dependence, whereas the heterogeneous model predicted realistic, complicated fracture processes and load-carrying capacity of little mesh-dependence. Increasing the variance of the tensile strength random fields with increased heterogeneity led to reduction in the mean peak load and increase in the standard deviation. The developed method provides a simple but effective tool for assessment of structural reliability and calculation of characteristic material strength for structural design.

Implementing efficient graphs in connection networks

We consider the problem of sharing the cost of a network that meets the connection demands of a set of agents. The agents simultaneously choose paths in the network connecting their demand nodes. A mechanism splits the total cost of the network formed among the participants. We introduce two new properties of implementation. The first property, Pareto Nash implementation (PNI), requires that the efficient outcome always be implemented in a Nash equilibrium and that the efficient outcome Pareto dominates any other Nash equilibrium. The average cost mechanism and other asymmetric variations are the only mechanisms that meet PNI. These mechanisms are also characterized under strong Nash implementation. The second property, weakly Pareto Nash implementation (WPNI), requires that the least inefficient equilibrium Pareto dominates any other equilibrium. The egalitarian mechanism (EG) and other asymmetric variations are the only mechanisms that meet WPNI and individual
rationality. EG minimizes the price of stability across all individually rational mechanisms. © Springer-Verlag Berlin Heidelberg 2012

Making heads or tails of probability:an experiment with random generators

The equiprobability bias is a tendency for individuals to think of probabilistic events as 'equiprobable' by nature, and to judge outcomes that occur with different probabilities as equally likely. The equiprobability bias has been repeatedly found to be related to formal education in statistics, and it is claimed to be based on a misunderstanding of the concept of randomness.

Sublinear Bounds for Randomized Leader Election

This paper concerns randomized leader election in synchronous distributed networks. A distributed leader election algorithm is presented for complete n-node networks that runs in O(1) rounds and (with high probability) takes only O(n-vlog3/2n) messages to elect a unique leader (with high probability). This algorithm is then extended to solve leader election on any connected non-bipartiten-node graph G in O(t(G)) time and O(t(G)n-vlog3/2n) messages, where t(G) is the mixing time of a random walk on G. The above result implies highly efficient (sublinear running time and messages) leader election algorithms for networks with small mixing times, such as expanders and hypercubes. In contrast, previous leader election algorithms had at least linear message complexity even in complete graphs. Moreover, super-linear message lower bounds are known for time-efficientdeterministic leader election algorithms. Finally, an almost-tight lower bound is presented for randomized leader election, showing that O(n-v) messages are needed for any O(1) time leader election algorithm which succeeds with high probability. It is also shown that O(n 1/3) messages are needed by any leader election algorithm that succeeds with high probability, regardless of the number of the rounds. We view our results as a step towards understanding the randomized complexity of leader election in distributed networks.

Using Graphs to Visualise and Detect Anomalies in Access Control System Transactions

Physical Access Control Systems are commonly used to secure doors in buildings such as airports, hospitals, government buildings and offices. These systems are designed primarily to provide an authentication mechanism, but they also log each door access as a transaction in a database. Unsupervised learning techniques can be used to detect inconsistencies or anomalies in the mobility data, such as a cloned or forged Access Badge, or unusual behaviour by staff members. In this paper, we present an overview of our method of inferring directed graphs to represent a physical building network and the flows of mobility within it. We demonstrate how the graphs can be used for Visual Data Exploration, and outline how to apply algorithms based on Information Theory to the graph data in order to detect inconsistent or abnormal behaviour.

Sublinear bounds for randomized leader election

This paper concerns randomized leader election in synchronous distributed networks. A distributed leader election algorithm is presented for complete n-node networks that runs in O(1) rounds and (with high probability) uses only O(√ √nlog^3/2n) messages to elect a unique leader (with high probability). When considering the "explicit" variant of leader election where eventually every node knows the identity of the leader, our algorithm yields the asymptotically optimal bounds of O(1) rounds and O(. n) messages. This algorithm is then extended to one solving leader election on any connected non-bipartite n-node graph G in O(τ(. G)) time and O(τ(G)n√log^3/2n) messages, where τ(. G) is the mixing time of a random walk on G. The above result implies highly efficient (sublinear running time and messages) leader election algorithms for networks with small mixing times, such as expanders and hypercubes. In contrast, previous leader election algorithms had at least linear message complexity even in complete graphs. Moreover, super-linear message lower bounds are known for time-efficient deterministic leader election algorithms. Finally, we present an almost matching lower bound for randomized leader election, showing that Ω(n) messages are needed for any leader election algorithm that succeeds with probability at least 1/. e+. ε, for any small constant ε. >. 0. We view our results as a step towards understanding the randomized complexity of leader election in distributed networks.

Finding the Most Descriptive Substructures in Graphs with Discrete and Numeric Labels

Many graph datasets are labelled with discrete and numeric attributes. Most frequent substructure discovery algorithms ignore numeric attributes; in this paper we show how they can be used to improve search performance and discrimination. Our thesis is that the most descriptive substructures are those which are normative both in terms of their structure and in terms of their numeric values. We explore the relationship between graph structure and the distribution of attribute values and propose an outlier-detection step, which is used as a constraint during substructure discovery. By pruning anomalous vertices and edges, more weight is given to the most descriptive substructures. Our method is applicable to multi-dimensional numeric attributes; we outline how it can be extended for high-dimensional data. We support our findings with experiments on transaction graphs and single large graphs from the domains of physical building security and digital forensics, measuring the effect on runtime, memory requirements and coverage of discovered patterns, relative to the unconstrained approach.