Statistical significance of episodes with general partial orders

Frequent episode discovery is one of the methods used for temporal pattern discovery in sequential data. An episode is a partially ordered set of nodes with each node associated with an event type. For more than a decade, algorithms existed for episode discovery only when the associated partial order is total (serial episode) or trivial (parallel episode). Recently, the literature has seen algorithms for discovering episodes with general partial orders. In frequent pattern mining, the threshold beyond which a pattern is inferred to be interesting is typically user-defined and arbitrary. One way of addressing this issue in the pattern mining literature has been based on the framework of statistical hypothesis testing. This paper presents a method of assessing statistical significance of episode patterns with general partial orders. A method is proposed to calculate thresholds, on the non-overlapped frequency, beyond which an episode pattern would be inferred to be statistically significant. The method is first explained for the case of injective episodes with general partial orders. An injective episode is one where event-types are not allowed to repeat. Later it is pointed out how the method can be extended to the class of all episodes. The significance threshold calculations for general partial order episodes proposed here also generalize the existing significance results for serial episodes. Through simulations studies, the usefulness of these statistical thresholds in pruning uninteresting patterns is illustrated. (C) 2014 Elsevier Inc. All rights reserved.

A Statistical Model of Current Loops and Magnetic Monopoles

We formulate a natural model of loops and isolated vertices for arbitrary planar graphs, which we call the monopole-dimer model. We show that the partition function of this model can be expressed as a determinant. We then extend the method of Kasteleyn and Temperley-Fisher to calculate the partition function exactly in the case of rectangular grids. This partition function turns out to be a square of a polynomial with positive integer coefficients when the grid lengths are even. Finally, we analyse this formula in the infinite volume limit and show that the local monopole density, free energy and entropy can be expressed in terms of well-known elliptic functions. Our technique is a novel determinantal formula for the partition function of a model of isolated vertices and loops for arbitrary graphs.

Estimation of nonlinearities from pseudodynamic and dynamic responses of bridge structures using the Delay Vector Variance method

Analysis of the variability in the responses of large structural systems and quantification of their linearity or nonlinearity as a potential non-invasive means of structural system assessment from output-only condition remains a challenging problem. In this study, the Delay Vector Variance (DVV) method is used for full scale testing of both pseudo-dynamic and dynamic responses of two bridges, in order to study the degree of nonlinearity of their measured response signals. The DVV detects the presence of determinism and nonlinearity in a time series and is based upon the examination of local predictability of a signal. The pseudo-dynamic data is obtained from a concrete bridge during repair while the dynamic data is obtained from a steel railway bridge traversed by a train. We show that DVV is promising as a marker in establishing the degree to which a change in the signal nonlinearity reflects the change in the real behaviour of a structure. It is also useful in establishing the sensitivity of instruments or sensors deployed to monitor such changes. (C) 2015 Elsevier B.V. All rights reserved.