577 research outputs found

    Phase transitions in Restricted Boltzmann Machines with generic priors

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    We study Generalised Restricted Boltzmann Machines with generic priors for units and weights, interpolating between Boolean and Gaussian variables. We present a complete analysis of the replica symmetric phase diagram of these systems, which can be regarded as Generalised Hopfield models. We underline the role of the retrieval phase for both inference and learning processes and we show that retrieval is robust for a large class of weight and unit priors, beyond the standard Hopfield scenario. Furthermore we show how the paramagnetic phase boundary is directly related to the optimal size of the training set necessary for good generalisation in a teacher-student scenario of unsupervised learning.Comment: 5 pages, 4 figures; extensive simulations and 2 new figures added; corrected typos; added reference

    Spectral Detection on Sparse Hypergraphs

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    We consider the problem of the assignment of nodes into communities from a set of hyperedges, where every hyperedge is a noisy observation of the community assignment of the adjacent nodes. We focus in particular on the sparse regime where the number of edges is of the same order as the number of vertices. We propose a spectral method based on a generalization of the non-backtracking Hashimoto matrix into hypergraphs. We analyze its performance on a planted generative model and compare it with other spectral methods and with Bayesian belief propagation (which was conjectured to be asymptotically optimal for this model). We conclude that the proposed spectral method detects communities whenever belief propagation does, while having the important advantages to be simpler, entirely nonparametric, and to be able to learn the rule according to which the hyperedges were generated without prior information.Comment: 8 pages, 5 figure

    LOT: Logic Optimization with Testability - new transformations for logic synthesis

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    A new approach to optimize multilevel logic circuits is introduced. Given a multilevel circuit, the synthesis method optimizes its area while simultaneously enhancing its random pattern testability. The method is based on structural transformations at the gate level. New transformations involving EX-OR gates as well as Reed–Muller expansions have been introduced in the synthesis of multilevel circuits. This method is augmented with transformations that specifically enhance random-pattern testability while reducing the area. Testability enhancement is an integral part of our synthesis methodology. Experimental results show that the proposed methodology not only can achieve lower area than other similar tools, but that it achieves better testability compared to available testability enhancement tools such as tstfx. Specifically for ISCAS-85 benchmark circuits, it was observed that EX-OR gate-based transformations successfully contributed toward generating smaller circuits compared to other state-of-the-art logic optimization tools

    Integrated application of compositional and behavioural safety analysis

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    To address challenges arising in the safety assessment of critical engineering systems, research has recently focused on automating the synthesis of predictive models of system failure from design representations. In one approach, known as compositional safety analysis, system failure models such as fault trees and Failure Modes and Effects Analyses (FMEAs) are constructed from component failure models using a process of composition. Another approach has looked into automating system safety analysis via application of formal verification techniques such as model checking on behavioural models of the system represented as state automata. So far, compositional safety analysis and formal verification have been developed separately and seen as two competing paradigms to the problem of model-based safety analysis. This thesis shows that it is possible to move forward the terms of this debate and use the two paradigms synergistically in the context of an advanced safety assessment process. The thesis develops a systematic approach in which compositional safety analysis provides the basis for the systematic construction and refinement of state-automata that record the transition of a system from normal to degraded and failed states. These state automata can be further enhanced and then be model-checked to verify the satisfaction of safety properties. Note that the development of such models in current practice is ad hoc and relies only on expert knowledge, but it being rationalised and systematised in the proposed approach – a key contribution of this thesis. Overall the approach combines the advantages of compositional safety analysis such as simplicity, efficiency and scalability, with the benefits of formal verification such as the ability for automated verification of safety requirements on dynamic models of the system, and leads to an improved model-based safety analysis process. In the context of this process, a novel generic mechanism is also proposed for modelling the detectability of errors which typically arise as a result of component faults and then propagate through the architecture. This mechanism is used to derive analyses that can aid decisions on appropriate detection and recovery mechanisms in the system model. The thesis starts with an investigation of the potential for useful integration of compositional and formal safety analysis techniques. The approach is then developed in detail and guidelines for analysis and refinement of system models are given. Finally, the process is evaluated in three cases studies that were iteratively performed on increasingly refined and improved models of aircraft and automotive braking and cruise control systems. In the light of the results of these studies, the thesis concludes that integration of compositional and formal safety analysis techniques is feasible and potentially useful in the design of safety critical systems

    Data Minimisation in Communication Protocols: A Formal Analysis Framework and Application to Identity Management

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    With the growing amount of personal information exchanged over the Internet, privacy is becoming more and more a concern for users. One of the key principles in protecting privacy is data minimisation. This principle requires that only the minimum amount of information necessary to accomplish a certain goal is collected and processed. "Privacy-enhancing" communication protocols have been proposed to guarantee data minimisation in a wide range of applications. However, currently there is no satisfactory way to assess and compare the privacy they offer in a precise way: existing analyses are either too informal and high-level, or specific for one particular system. In this work, we propose a general formal framework to analyse and compare communication protocols with respect to privacy by data minimisation. Privacy requirements are formalised independent of a particular protocol in terms of the knowledge of (coalitions of) actors in a three-layer model of personal information. These requirements are then verified automatically for particular protocols by computing this knowledge from a description of their communication. We validate our framework in an identity management (IdM) case study. As IdM systems are used more and more to satisfy the increasing need for reliable on-line identification and authentication, privacy is becoming an increasingly critical issue. We use our framework to analyse and compare four identity management systems. Finally, we discuss the completeness and (re)usability of the proposed framework

    Data based identification and prediction of nonlinear and complex dynamical systems

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    We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin
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