20,323 research outputs found

    Normal Factor Graphs and Holographic Transformations

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    This paper stands at the intersection of two distinct lines of research. One line is "holographic algorithms," a powerful approach introduced by Valiant for solving various counting problems in computer science; the other is "normal factor graphs," an elegant framework proposed by Forney for representing codes defined on graphs. We introduce the notion of holographic transformations for normal factor graphs, and establish a very general theorem, called the generalized Holant theorem, which relates a normal factor graph to its holographic transformation. We show that the generalized Holant theorem on the one hand underlies the principle of holographic algorithms, and on the other hand reduces to a general duality theorem for normal factor graphs, a special case of which was first proved by Forney. In the course of our development, we formalize a new semantics for normal factor graphs, which highlights various linear algebraic properties that potentially enable the use of normal factor graphs as a linear algebraic tool.Comment: To appear IEEE Trans. Inform. Theor

    Basic Singular Spectrum Analysis and Forecasting with R

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    Singular Spectrum Analysis (SSA) as a tool for analysis and forecasting of time series is considered. The main features of the Rssa package, which implements the SSA algorithms and methodology in R, are described and examples of its use are presented. Analysis, forecasting and parameter estimation are demonstrated by means of case study with an accompanying code in R

    The role of diffusion in the transport of energetic electrons during solar flares

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    The transport of the energy contained in suprathermal electrons in solar flares plays a key role in our understanding of many aspects of flare physics, from the spatial distributions of hard X-ray emission and energy deposition in the ambient atmosphere to global energetics. Historically the transport of these particles has been largely treated through a deterministic approach, in which first-order secular energy loss to electrons in the ambient target is treated as the dominant effect, with second-order diffusive terms (in both energy and angle) being generally either treated as a small correction or even neglected. We here critically analyze this approach, and we show that spatial diffusion through pitch-angle scattering necessarily plays a very significant role in the transport of electrons. We further show that a satisfactory treatment of the diffusion process requires consideration of non-local effects, so that the electron flux depends not just on the local gradient of the electron distribution function but on the value of this gradient within an extended region encompassing a significant fraction of a mean free path. Our analysis applies generally to pitch-angle scattering by a variety of mechanisms, from Coulomb collisions to turbulent scattering. We further show that the spatial transport of electrons along the magnetic field of a flaring loop can be modeled rather effectively as a Continuous Time Random Walk with velocity-dependent probability distribution functions of jump sizes and occurrences, both of which can be expressed in terms of the scattering mean free path.Comment: 11 pages, to be published in Astrophysical Journa

    Computation- and Space-Efficient Implementation of SSA

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    The computational complexity of different steps of the basic SSA is discussed. It is shown that the use of the general-purpose "blackbox" routines (e.g. found in packages like LAPACK) leads to huge waste of time resources since the special Hankel structure of the trajectory matrix is not taken into account. We outline several state-of-the-art algorithms (for example, Lanczos-based truncated SVD) which can be modified to exploit the structure of the trajectory matrix. The key components here are hankel matrix-vector multiplication and hankelization operator. We show that both can be computed efficiently by the means of Fast Fourier Transform. The use of these methods yields the reduction of the worst-case computational complexity from O(N^3) to O(k N log(N)), where N is series length and k is the number of eigentriples desired.Comment: 27 pages, 8 figure

    Generation of folk song melodies using Bayes transforms

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    The paper introduces the `Bayes transform', a mathematical procedure for putting data into a hierarchical representation. Applicable to any type of data, the procedure yields interesting results when applied to sequences. In this case, the representation obtained implicitly models the repetition hierarchy of the source. There are then natural applications to music. Derivation of Bayes transforms can be the means of determining the repetition hierarchy of note sequences (melodies) in an empirical and domain-general way. The paper investigates application of this approach to Folk Song, examining the results that can be obtained by treating such transforms as generative models

    An analysis of the fish pool market in the context of seasonality and stochastic convenience yield

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    On the basis of a popular two-factor approach applied in commodity markets, we develop a model featuring seasonality and study futures contracts written on fresh farmed salmon, which have been actively traded at the Fish Pool market in Norway since 2006. The model is estimated by means of Kalman filtering, using a rich data set of contracts with different maturities traded at Fish Pool between 01/01/2010 and 24/04/2014. The results are then discussed in the context of other commodity markets, specifically live cattle, which is a substitute. We show that the seasonally adjusted model proposed in this article describes the behavior of salmon price very well. More importantly we show that seasonality exists in the salmon futures market. This is highly important in pricing of contingent claims, designing hedging strategies, and making real investment decisions in marine resources
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