Piecemeal Learning of an Unknown Environment

We introduce a new learning problem: learning a graph by piecemeal search, in which the learner must return every so often to its starting point (for refueling, say). We present two linear-time piecemeal-search algorithms for learning city-block graphs: grid graphs with rectangular obstacles.

Summarizing Qualitative Behavior from Measurements of NonlinearsCircuits

This report describes a program which automatically characterizes the behavior of any driven, nonlinear, electrical circuit. To do this, the program autonomously selects interesting input parameters, drives the circuit, measures its response, performs a set of numeric computations on the measured data, interprets the results, and decomposes the circuit's parameter space into regions of qualitatively distinct behavior. The output is a two-dimensional portrait summarizing the high-level, qualitative behavior of the circuit for every point in the graph, an accompanying textual explanation describing any interesting patterns observed in the diagram, and a symbolic description of the circuit's behavior which can be passed on to other programs for further analysis.

On the use of qualitative reasoning to simulate and identify metabolic pathways

King, R.D., Garrett, S.M., Coghill, G.M. (2005). On the use of qualitative reasoning to simulate and identify metabolic pathways. Bioinformatics 21(9):2017-2026 RAE2008

On the Emergence of Highly Variable Distributions in the Autonomous System Topology

Recent studies have noted that vertex degree in the autonomous system (AS) graph exhibits a highly variable distribution [15, 22]. The most prominent explanatory model for this phenomenon is the Barabási-Albert (B-A) model [5, 2]. A central feature of the B-A model is preferential connectivity—meaning that the likelihood a new node in a growing graph will connect to an existing node is proportional to the existing node’s degree. In this paper we ask whether a more general explanation than the B-A model, and absent the assumption of preferential connectivity, is consistent with empirical data. We are motivated by two observations: first, AS degree and AS size are highly correlated [11]; and second, highly variable AS size can arise simply through exponential growth. We construct a model incorporating exponential growth in the size of the Internet, and in the number of ASes. We then show via analysis that such a model yields a size distribution exhibiting a power-law tail. In such a model, if an AS’s link formation is roughly proportional to its size, then AS degree will also show high variability. We instantiate such a model with empirically derived estimates of growth rates and show that the resulting degree distribution is in good agreement with that of real AS graphs.

Graph Wavelets for Spatial Traffic Analysis

A number of problems in network operations and engineering call for new methods of traffic analysis. While most existing traffic analysis methods are fundamentally temporal, there is a clear need for the analysis of traffic across multiple network links — that is, for spatial traffic analysis. In this paper we give examples of problems that can be addressed via spatial traffic analysis. We then propose a formal approach to spatial traffic analysis based on the wavelet transform. Our approach (graph wavelets) generalizes the traditional wavelet transform so that it can be applied to data elements connected via an arbitrary graph topology. We explore the necessary and desirable properties of this approach and consider some of its possible realizations. We then apply graph wavelets to measurements from an operating network. Our results show that graph wavelets are very useful for our motivating problems; for example, they can be used to form highly summarized views of an entire network's traffic load, to gain insight into a network's global traffic response to a link failure, and to localize the extent of a failure event within the network.

Face Identification by a Cascade of Rejection Classifiers

Nearest neighbor search is commonly employed in face recognition but it does not scale well to large dataset sizes. A strategy to combine rejection classifiers into a cascade for face identification is proposed in this paper. A rejection classifier for a pair of classes is defined to reject at least one of the classes with high confidence. These rejection classifiers are able to share discriminants in feature space and at the same time have high confidence in the rejection decision. In the face identification problem, it is possible that a pair of known individual faces are very dissimilar. It is very unlikely that both of them are close to an unknown face in the feature space. Hence, only one of them needs to be considered. Using a cascade structure of rejection classifiers, the scope of nearest neighbor search can be reduced significantly. Experiments on Face Recognition Grand Challenge (FRGC) version 1 data demonstrate that the proposed method achieves significant speed up and an accuracy comparable with the brute force Nearest Neighbor method. In addition, a graph cut based clustering technique is employed to demonstrate that the pairwise separability of these rejection classifiers is capable of semantic grouping.

Isoperimetric Graph Partitioning for Data Clustering and Image Segmentation

Spectral methods of graph partitioning have been shown to provide a powerful approach to the image segmentation problem. In this paper, we adopt a different approach, based on estimating the isoperimetric constant of an image graph. Our algorithm produces the high quality segmentations and data clustering of spectral methods, but with improved speed and stability.

Isoperimetric Partitioning: A New Algorithm for Graph Partitioning

Temporal structure is skilled, fluent action exists at several nested levels. At the largest scale considered here, short sequences of actions that are planned collectively in prefronatal cortex appear to be queued for performance by a cyclic competitive process that operates in concert with a parallel analog representation that implicitly specifies the relative priority of elements of the sequence. At an intermediate scale, single acts, like reaching to grasp, depend on coordinated scaling of the rates at which many muscles shorten or lengthen in parallel. To ensure success of acts such as catching an approaching ball, such parallel rate scaling, which appears to be one function of the basal ganglia, must be coupled to perceptual variables such as time-to-contact. At a finer scale, within each act, desired rate scaling can be realized only if precisely timed muscle activations first accelerate and then decelerate the limbs, to ensure that muscle length changes do not under- or over- shoot the amounts needed for precise acts. Each context of action may require a different timed muscle activation pattern than similar contexts. Because context differences that require different treatment cannot be known in advance, a formidable adaptive engine-the cerebellum-is needed to amplify differences within, and continuosly search, a vast parallel signal flow, in order to discover contextual "leading indicators" of when to generate distinctive patterns of analog signals. From some parts of the cerebellum, such signals control muscles. But a recent model shows how the lateral cerebellum may serve the competitive queuing system (frontal cortex) as a repository of quickly accessed long-term sequence memories. Thus different parts of the cerebellum may use the same adaptive engine design to serve the lowest and highest of the three levels of temporal structure treated. If so, no one-to-one mapping exists between leveels of temporal structure and major parts of the brain. Finally, recent data cast doubt on network-delay models of cerebellar adaptive timing.

The Graph Analysis Toolbox: Image Processing on Arbitrary Graphs

Office of Naval Research (N00014-01-1-0624)

Systematic delay-driven power optimisation and power-driven delay optimisation of combinational circuits

With the proliferation of mobile wireless communication and embedded systems, the energy efficiency becomes a major design constraint. The dissipated energy is often referred as the product of power dissipation and the input-output delay. Most of electronic design automation techniques focus on optimising only one of these parameters either power or delay. Industry standard design flows integrate systematic methods of optimising either area or timing while for power consumption optimisation one often employs heuristics which are characteristic to a specific design. In this work we answer three questions in our quest to provide a systematic approach to joint power and delay Optimisation. The first question of our research is: How to build a design flow which incorporates academic and industry standard design flows for power optimisation? To address this question, we use a reference design flow provided by Synopsys and integrate in this flow academic tools and methodologies. The proposed design flow is used as a platform for analysing some novel algorithms and methodologies for optimisation in the context of digital circuits. The second question we answer is: Is possible to apply a systematic approach for power optimisation in the context of combinational digital circuits? The starting point is a selection of a suitable data structure which can easily incorporate information about delay, power, area and which then allows optimisation algorithms to be applied. In particular we address the implications of a systematic power optimisation methodologies and the potential degradation of other (often conflicting) parameters such as area or the delay of implementation. Finally, the third question which this thesis attempts to answer is: Is there a systematic approach for multi-objective optimisation of delay and power? A delay-driven power and power-driven delay optimisation is proposed in order to have balanced delay and power values. This implies that each power optimisation step is not only constrained by the decrease in power but also the increase in delay. Similarly, each delay optimisation step is not only governed with the decrease in delay but also the increase in power. The goal is to obtain multi-objective optimisation of digital circuits where the two conflicting objectives are power and delay. The logic synthesis and optimisation methodology is based on AND-Inverter Graphs (AIGs) which represent the functionality of the circuit. The switching activities and arrival times of circuit nodes are annotated onto an AND-Inverter Graph under the zero and a non-zero-delay model. We introduce then several reordering rules which are applied on the AIG nodes to minimise switching power or longest path delay of the circuit at the pre-technology mapping level. The academic Electronic Design Automation (EDA) tool ABC is used for the manipulation of AND-Inverter Graphs. We have implemented various combinatorial optimisation algorithms often used in Electronic Design Automation such as Simulated Annealing and Uniform Cost Search Algorithm. Simulated Annealing (SMA) is a probabilistic meta heuristic for the global optimization problem of locating a good approximation to the global optimum of a given function in a large search space. We used SMA to probabilistically decide between moving from one optimised solution to another such that the dynamic power is optimised under given delay constraints and the delay is optimised under given power constraints. A good approximation to the global optimum solution of energy constraint is obtained. Uniform Cost Search (UCS) is a tree search algorithm used for traversing or searching a weighted tree, tree structure, or graph. We have used Uniform Cost Search Algorithm to search within the AIG network, a specific AIG node order for the reordering rules application. After the reordering rules application, the AIG network is mapped to an AIG netlist using specific library cells. Our approach combines network re-structuring, AIG nodes reordering, dynamic power and longest path delay estimation and optimisation and finally technology mapping to an AIG netlist. A set of MCNC Benchmark circuits and large combinational circuits up to 100,000 gates have been used to validate our methodology. Comparisons for power and delay optimisation are made with the best synthesis scripts used in ABC. Reduction of 23% in power and 15% in delay with minimal overhead is achieved, compared to the best known ABC results. Also, our approach is also implemented on a number of processors with combinational and sequential components and significant savings are achieved.

Integration of micro- and macroscopic models for pedestrian evacuation simulation

Simulation of pedestrian evacuations of smart buildings in emergency is a powerful tool for building analysis, dynamic evacuation planning and real-time response to the evolving state of evacuations. Macroscopic pedestrian models are low-complexity models that are and well suited to algorithmic analysis and planning, but are quite abstract. Microscopic simulation models allow for a high level of simulation detail but can be computationally intensive. By combining micro- and macro- models we can use each to overcome the shortcomings of the other and enable new capability and applications for pedestrian evacuation simulation that would not be possible with either alone. We develop the EvacSim multi-agent pedestrian simulator and procedurally generate macroscopic flow graph models of building space, integrating micro- and macroscopic approaches to simulation of the same emergency space. By “coupling” flow graph parameters to microscopic simulation results, the graph model captures some of the higher detail and fidelity of the complex microscopic simulation model. The coupled flow graph is used for analysis and prediction of the movement of pedestrians in the microscopic simulation, and investigate the performance of dynamic evacuation planning in simulated emergencies using a variety of strategies for allocation of macroscopic evacuation routes to microscopic pedestrian agents. The predictive capability of the coupled flow graph is exploited for the decomposition of microscopic simulation space into multiple future states in a scalable manner. By simulating multiple future states of the emergency in short time frames, this enables sensing strategy based on simulation scenario pattern matching which we show to achieve fast scenario matching, enabling rich, real-time feedback in emergencies in buildings with meagre sensing capabilities.

Automatic segmentation of seven retinal layers in SDOCT images congruent with expert manual segmentation.

Segmentation of anatomical and pathological structures in ophthalmic images is crucial for the diagnosis and study of ocular diseases. However, manual segmentation is often a time-consuming and subjective process. This paper presents an automatic approach for segmenting retinal layers in Spectral Domain Optical Coherence Tomography images using graph theory and dynamic programming. Results show that this method accurately segments eight retinal layer boundaries in normal adult eyes more closely to an expert grader as compared to a second expert grader.

Adaptive Mixture Modelling Metropolis Methods for Bayesian Analysis of Non-linear State-Space Models.

We describe a strategy for Markov chain Monte Carlo analysis of non-linear, non-Gaussian state-space models involving batch analysis for inference on dynamic, latent state variables and fixed model parameters. The key innovation is a Metropolis-Hastings method for the time series of state variables based on sequential approximation of filtering and smoothing densities using normal mixtures. These mixtures are propagated through the non-linearities using an accurate, local mixture approximation method, and we use a regenerating procedure to deal with potential degeneracy of mixture components. This provides accurate, direct approximations to sequential filtering and retrospective smoothing distributions, and hence a useful construction of global Metropolis proposal distributions for simulation of posteriors for the set of states. This analysis is embedded within a Gibbs sampler to include uncertain fixed parameters. We give an example motivated by an application in systems biology. Supplemental materials provide an example based on a stochastic volatility model as well as MATLAB code.

PenPC: A two-step approach to estimate the skeletons of high-dimensional directed acyclic graphs.

Estimation of the skeleton of a directed acyclic graph (DAG) is of great importance for understanding the underlying DAG and causal effects can be assessed from the skeleton when the DAG is not identifiable. We propose a novel method named PenPC to estimate the skeleton of a high-dimensional DAG by a two-step approach. We first estimate the nonzero entries of a concentration matrix using penalized regression, and then fix the difference between the concentration matrix and the skeleton by evaluating a set of conditional independence hypotheses. For high-dimensional problems where the number of vertices p is in polynomial or exponential scale of sample size n, we study the asymptotic property of PenPC on two types of graphs: traditional random graphs where all the vertices have the same expected number of neighbors, and scale-free graphs where a few vertices may have a large number of neighbors. As illustrated by extensive simulations and applications on gene expression data of cancer patients, PenPC has higher sensitivity and specificity than the state-of-the-art method, the PC-stable algorithm.

Computer aided parallelisation tools (CAPTools) — conceptual overview and performance on the parallelisation of structured mesh codes

Computer Aided Parallelisation Tools (CAPTools) is a toolkit designed to automate as much as possible of the process of parallelising scalar FORTRAN 77 codes. The toolkit combines a very powerful dependence analysis together with user supplied knowledge to build an extremely comprehensive and accurate dependence graph. The initial version has been targeted at structured mesh computational mechanics codes (eg. heat transfer, Computational Fluid Dynamics (CFD)) and the associated simple mesh decomposition paradigm is utilised in the automatic code partition, execution control mask generation and communication call insertion. In this, the first of a series of papers [1–3] the authors discuss the parallelisations of a number of case study codes showing how the various component tools may be used to develop a highly efficient parallel implementation in a few hours or days. The details of the parallelisation of the TEAMKE1 CFD code are described together with the results of three other numerical codes. The resulting parallel implementations are then tested on workstation clusters using PVM and an i860-based parallel system showing efficiencies well over 80%.