44,639 research outputs found
On homogeneous skewness of unimodal distributions
We introduce a new concept of skewness for unimodal continuous distributions which is built on the asymmetry of the density function around its mode. The asymmetry is captured through a skewness function. We call a distribution homogeneously skewed if this skewness function is consistently positive or negative throughout its domain, and partially homogeneously skewed if the skewness function changes its sign at most once. This type of skewness is shown to exist in many popular continuous distributions such as Triangular, Gamma, Beta, Lognormal and Weibull. Two alternative ways of partial ordering among the partially homogeneously skewed distributions are described. Extensions of the notion to broader classes of distributions including discrete distributions have also been discussed
Ordered Products, -Algebra, and Two-Variable, Definite-Parity, Orthogonal Polynomials
It has been shown that the Cartan subalgebra of - algebra is the
space of the two-variable, definite-parity polynomials. Explicit expressions of
these polynomials, and their basic properties are presented. Also has been
shown that they carry the infinite dimensional irreducible representation of
the algebra having the spectrum bounded from below. A realization of
this algebra in terms of difference operators is also obtained. For particular
values of the ordering parameter they are identified with the classical
orthogonal polynomials of a discrete variable, such as the Meixner,
Meixner-Pollaczek, and Askey-Wilson polynomials. With respect to variable
they satisfy a second order eigenvalue equation of hypergeometric type. Exact
scattering states with zero energy for a family of potentials are expressed in
terms of these polynomials. It has been put forward that it is the
\.{I}n\"{o}n\"{u}-Wigner contraction and its inverse that form bridge between
the difference and differential calculus.Comment: 17 pages,no figure. to appear in J. Math.Phy
Discrete Signal Processing on Graphs: Frequency Analysis
Signals and datasets that arise in physical and engineering applications, as
well as social, genetics, biomolecular, and many other domains, are becoming
increasingly larger and more complex. In contrast to traditional time and image
signals, data in these domains are supported by arbitrary graphs. Signal
processing on graphs extends concepts and techniques from traditional signal
processing to data indexed by generic graphs. This paper studies the concepts
of low and high frequencies on graphs, and low-, high-, and band-pass graph
filters. In traditional signal processing, there concepts are easily defined
because of a natural frequency ordering that has a physical interpretation. For
signals residing on graphs, in general, there is no obvious frequency ordering.
We propose a definition of total variation for graph signals that naturally
leads to a frequency ordering on graphs and defines low-, high-, and band-pass
graph signals and filters. We study the design of graph filters with specified
frequency response, and illustrate our approach with applications to sensor
malfunction detection and data classification
Functional renormalization group for commensurate antiferromagnets: Beyond the mean-field picture
We present a functional renormalization group (fRG) formalism for interacting
fermions on lattices that captures the flow into states with commensurate
spin-density wave order. During the flow, the growth of the order parameter is
fed back into the flow of the interactions and all modes can be integrated out.
This extends previous fRG flows in the symmetric phase that run into a
divergence at a nonzero RG scale, i.e., that have to be stopped at the ordering
scale. We use the corresponding Ward identity to check the accuracy of the
results. We apply our new method to a model with two Fermi pockets that have
perfect particle-hole nesting. The results obtained from the fRG are compared
with those in random phase approximation.Comment: revised version; 24 pages, 12 figure
Queues and risk processes with dependencies
We study the generalization of the G/G/1 queue obtained by relaxing the
assumption of independence between inter-arrival times and service
requirements. The analysis is carried out for the class of multivariate matrix
exponential distributions introduced in [12]. In this setting, we obtain the
steady state waiting time distribution and we show that the classical relation
between the steady state waiting time and the workload distributions re- mains
valid when the independence assumption is relaxed. We also prove duality
results with the ruin functions in an ordinary and a delayed ruin process.
These extend several known dualities between queueing and risk models in the
independent case. Finally we show that there exist stochastic order relations
between the waiting times under various instances of correlation
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