15,470 research outputs found
Some Useful Integral Representations for Information-Theoretic Analyses
This work is an extension of our earlier article, where a well-known integral
representation of the logarithmic function was explored, and was accompanied
with demonstrations of its usefulness in obtaining compact, easily-calculable,
exact formulas for quantities that involve expectations of the logarithm of a
positive random variable. Here, in the same spirit, we derive an exact integral
representation (in one or two dimensions) of the moment of a nonnegative random
variable, or the sum of such independent random variables, where the moment
order is a general positive noninteger real (also known as fractional moments).
The proposed formula is applied to a variety of examples with an
information-theoretic motivation, and it is shown how it facilitates their
numerical evaluations. In particular, when applied to the calculation of a
moment of the sum of a large number, , of nonnegative random variables, it
is clear that integration over one or two dimensions, as suggested by our
proposed integral representation, is significantly easier than the alternative
of integrating over dimensions, as needed in the direct calculation of the
desired moment.Comment: Published in Entropy, vol. 22, no. 6, paper 707, pages 1-29, June
2020. Available at: https://www.mdpi.com/1099-4300/22/6/70
Tullio Regge's legacy: Regge calculus and discrete gravity
The review paper "Discrete Structures in Physics", written in 2000, describes
how Regge's discretization of Einstein's theory has been applied in classical
relativity and quantum gravity. Here, developments since 2000 are reviewed
briefly, with particular emphasis on progress in quantum gravity through spin
foam models and group field theories.Comment: 15 pages; a contribution to the forthcoming volume "Tullio Regge: an
eclectic genius, from quantum gravity to computer play", Eds. L Castellani,
A. Ceresole, R. D'Auria and P. Fr\`e (World Scientific); v2: added references
to more relevant work, minor changes to the tex
Detailed black hole state counting in loop quantum gravity
We give a complete and detailed description of the computation of black hole
entropy in loop quantum gravity by employing the most recently introduced
number-theoretic and combinatorial methods. The use of these techniques allows
us to perform a detailed analysis of the precise structure of the entropy
spectrum for small black holes, showing some relevant features that were not
discernible in previous computations. The ability to manipulate and understand
the spectrum up to the level of detail that we describe in the paper is a
crucial step towards obtaining the behavior of entropy in the asymptotic (large
horizon area) regime
A Deflationary Account of Mental Representation
Among the cognitive capacities of evolved creatures is the capacity to represent. Theories in cognitive neuroscience typically explain our manifest representational capacities by positing internal representations, but there is little agreement about how these representations function, especially with the relatively recent proliferation of connectionist, dynamical, embodied, and enactive approaches to cognition. In this talk I sketch an account of the nature and function of representation in cognitive neuroscience that couples a realist construal of representational vehicles with a pragmatic account of mental content. I call the resulting package a deflationary account of mental representation and I argue that it avoids the problems that afflict competing accounts
A New Framework for the Performance Analysis of Wireless Communications under Hoyt (Nakagami-q) Fading
(c) 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. DOI:10.1109/TIT.2017.2655342We present a novel relationship between the distribution of circular and non-circular complex Gaussian random variables. Specifically, we show that the distribution of the squared norm of a non-circular complex Gaussian random variable, usually referred to as the squared Hoyt distribution, can be constructed from a conditional exponential distribution. From this fundamental connection we introduce a new approach, the Hoyt transform method, that allows to analyze the performance of a wireless link under Hoyt (Nakagami-q) fading in a very simple way. We illustrate that many performance metrics for Hoyt fading can be calculated by leveraging well-known results for Rayleigh fading and only performing a finite-range integral. We use this technique to obtain novel results for some information and communication-theoretic metrics in Hoyt fading channels.Universidad de Málaga. Campus de Execelencia Internacional. AndalucĂa Tech
Localization and diffusion in polymer quantum field theory
Polymer quantization is a non-standard approach to quantizing a classical
system inspired by background independent approaches to quantum gravity such as
loop quantum gravity. When applied to field theory it introduces a
characteristic polymer scale at the level of the fields classical configuration
space. Compared with models with space-time discreteness or non-commutativity
this is an alternative way in which a characteristic scale can be introduced in
a field theoretic context. Motivated by this comparison we study here
localization and diffusion properties associated with polymer field observables
and dispersion relation in order to shed some light on the novel physical
features introduced by polymer quantization. While localization processes seems
to be only mildly affected by polymer effects, we find that polymer diffusion
differs significantly from the "dimensional reduction" picture emerging in
other Planck-scale models beyond local quantum field theory.Comment: 16 pages, 5 figure
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