20,323 research outputs found
Normal Factor Graphs and Holographic Transformations
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
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
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
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
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
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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