276 research outputs found
Moderate deviations for particle filtering
Consider the state space model (X_t,Y_t), where (X_t) is a Markov chain, and
(Y_t) are the observations. In order to solve the so-called filtering problem,
one has to compute L(X_t|Y_1,...,Y_t), the law of X_t given the observations
(Y_1,...,Y_t). The particle filtering method gives an approximation of the law
L(X_t|Y_1,...,Y_t) by an empirical measure \frac{1}{n}\sum_1^n\delta_{x_{i,t}}.
In this paper we establish the moderate deviation principle for the empirical
mean \frac{1}{n}\sum_1^n\psi(x_{i,t}) (centered and properly rescaled) when the
number of particles grows to infinity, enhancing the central limit theorem.
Several extensions and examples are also studied.Comment: Published at http://dx.doi.org/10.1214/105051604000000657 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
The empirical distribution of the eigenvalues of a Gram matrix with a given variance profile
Consider a random matrix where the entries are
given by , the
being centered i.i.d. and being a
continuous function called a variance profile. Consider now a deterministic
matrix whose non diagonal elements
are zero. Denote by the non-centered matrix . Then
under the assumption that and where is a probability measure, it is proven
that the empirical distribution of the eigenvalues of
converges almost surely in distribution to a non random probability measure.
This measure is characterized in terms of its Stieltjes transform, which is
obtained with the help of an auxiliary system of equations. This kind of
results is of interest in the field of wireless communication.Comment: 25 pages, revised version. Assumption (A2) has been relaxe
The empirical eigenvalue distribution of a Gram matrix: From independence to stationarity
Consider a random matrix where the
individual entries are a realization of a properly rescaled stationary gaussian
random field.
The purpose of this article is to study the limiting empirical distribution
of the eigenvalues of Gram random matrices such as and where is a deterministic matrix with appropriate
assumptions in the case where and .
The proof relies on related results for matrices with independent but not
identically distributed entries and substantially differs from related works in
the literature (Boutet de Monvel et al., Girko, etc.).Comment: 15 page
Cooperative Spectrum Sensing Using Random Matrix Theory
In this paper, using tools from asymptotic random matrix theory, a new
cooperative scheme for frequency band sensing is introduced for both AWGN and
fading channels. Unlike previous works in the field, the new scheme does not
require the knowledge of the noise statistics or its variance and is related to
the behavior of the largest and smallest eigenvalue of random matrices.
Remarkably, simulations show that the asymptotic claims hold even for a small
number of observations (which makes it convenient for time-varying topologies),
outperforming classical energy detection techniques.Comment: Submitted to International Symposium on Wireless Pervasive Computing
200
Asymptotic Independence in the Spectrum of the Gaussian Unitary Ensemble
Consider a matrix from the Gaussian Unitary Ensemble (GUE).
Given a finite collection of bounded disjoint real Borel sets $(\Delta_{i,n},\
1\leq i\leq p)({\mathcal N}_n(\Delta_{i,n}), 1\leq i\leq p){\mathcal N}_n(\Delta)\Deltanp$
being fixed.
As a consequence, we prove that the largest and smallest eigenvalues,
properly centered and rescaled, are asymptotically independent; we finally
describe the fluctuations of the condition number of a matrix from the GUE.Comment: 15 page
Energy and Exergy Analysis of Dual Channel Solar Air Collector with Perforating âVâ Corrugated Absorber Plate
In This paper, an experimental study was carried out on a dual channel with perforating âVâ corrugated absorber plate of solar air collector which the air flows both in upper channel and lower channel of the absorber plate for increasing heat transfer coefficient and improving thermal performance. The results of experimental procedures for dual channel with perforating âVâ corrugated absorber plate of solar collector were compared with the flat plate dual channel of solar collector. Experimental calculations had been performed under Baghdad (33.34° North latitude, 44.4° East longitude) climatic conditions at different values of mass flow rates 0.021 kg/s, 0.027 kg/s and 0.032 kg/s. The results showed that the dual channel with perforating âVâ corrugated absorber plate of solar collector is found to perform more efficiently than the flat plate dual channel of solar collector with increased 39% in thermal efficiency. Then, it showed that the efficiency increases with increasing mass flow rates. Also, it showed that the heat removal factor of the dual channel with perforating âVâ corrugated absorber plate of solar collector is 36% more than the flat plate dual channel of solar collector. At the last part of the study, the exergy relations were derived for both collectors. The results of this part showed that the flat plate dual channel of solar collector is having largest irreversibility (exergy loss) and the dual channel with perforating âVâ corrugated absorber plate of solar collector is having a greatest exergetic efficiency. Keywords:Solar air collector; Dual channel; Double flow; Exergy analysis; perforating âVâ corrugated; Heat removal facto
Determination of Cadmium and Lead in Sewage Sludge from the Middle Region (Misrata, Msallata and TarhĂŒnah Cities) of Libya
The concentrations of cadmium and lead in sewage sludge samples were determined by Atomic Absorption Spectrometric Method. Samples of sewage sludge were obtained from three sewage treatment plants localised in Middle Region of Libya (Misrata, Msallata and TarhĂŒnah cities). The results shows that, the mean levels of Cadmium for all regions are ranges from 81 to 123.4 ppm and these values are higher than the limitations for the international standard which are not registered more than 50 ppm (dry weight) in USA, Egypt and the EU countries. While, the lead concentrations are ranged from 8.0 to 189.2 ppm and all values are within the standard limits which graduated between (275â613) ppm
Thermophysical optimization of specialized concrete pavement materials for collection of surface heat energy and applications for shallow heat storage
There is great potential to use pavement structures to collect and/or store solar energy for the heating and cooling of adjacent buildings, e.g. airport terminals, shopping malls, etc. Therefore, pavement materials comprising both conventional and unconventional concrete mixtures with a wide range of densities, thermal conductivities, specific heat capacities, and thermal diffusivities were investigated. Their thermo-physical properties were then used as inputs to a one dimensional transient heat transport model in order to evaluate the temperature changes at the various depths at which heat might be abstracted or stored. The results indicated that a high diffusivity pavement, e.g. incorporating high conductive aggregates and/or metallic fibres, can significantly enhance heat transfer as well as reduction of thermal stresses across the concrete slab. On the other hand a low diffusivity concrete can induce a more stable temperature at shallower depth enabling easier heat storage in the pavement as well as helping to reduce the risk of damage due to freeze-thaw cycling in cold regions
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