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 $N\times n$ random matrix $Y_n=(Y_{ij}^{n})$ where the entries are given by $Y_{ij}^{n}=\frac{\sigma(i/N,j/n)}{\sqrt{n}} X_{ij}^{n}$, the $X_{ij}^{n}$ being centered i.i.d. and $\sigma:[0,1]^2 \to (0,\infty)$ being a continuous function called a variance profile. Consider now a deterministic $N\times n$ matrix $\Lambda_n=(\Lambda_{ij}^{n})$ whose non diagonal elements are zero. Denote by $\Sigma_n$ the non-centered matrix $Y_n + \Lambda_n$. Then under the assumption that $\lim_{n\to \infty} \frac Nn =c>0$ and $$\frac{1}{N} \sum_{i=1}^{N} \delta_{(\frac{i}{N}, (\Lambda_{ii}^n)^2)} \xrightarrow[n\to \infty]{} H(dx,d\lambda),$$ where $H$ is a probability measure, it is proven that the empirical distribution of the eigenvalues of $\Sigma_n \Sigma_n^T$ 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 $N\times n$ random matrix $Z_n=(Z^n_{j_1 j_2})$ 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 $Z_n Z_n ^*$ and $(Z_n +A_n)(Z_n +A_n)^*$ where $A_n$ is a deterministic matrix with appropriate assumptions in the case where $n\to \infty$ and $\frac Nn \to c \in (0,\infty)$. 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 $n \times n$ matrix from the Gaussian Unitary Ensemble (GUE). Given a finite collection of bounded disjoint real Borel sets $(\Delta_{i,n},\ 1\leq i\leq p)$, properly rescaled, and eventually included in any neighbourhood of the support of Wigner's semi-circle law, we prove that the related counting measures$({\mathcal N}_n(\Delta_{i,n}), 1\leq i\leq p)$, where${\mathcal N}_n(\Delta)$represents the number of eigenvalues within$\Delta$, are asymptotically independent as the size$n$goes to infinity,$p$ 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 “V” Corrugated Absorber Plate

In This paper, an experimental study was carried out on a dual channel with perforating “V” 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 “V” 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 “V” 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 “V” 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 “V” corrugated absorber plate of solar collector is having a greatest exergetic efficiency. Keywords:Solar air collector; Dual channel; Double flow; Exergy analysis; perforating “V” corrugated; Heat removal facto

The Effect of Twisted Wire Configuration on the Stability of External Fixator: A Biomechanical Study

The Ilizarov fixator is a type of external fixator that is used to treat patients who have suffered injuries from accidents, bone shortening, or nonunion of the bone. The principle behind the Ilizarov fixator is that thin wires (called Kirschner wires) are used to support the bones and connect them to framed rings. Before being fastened to the rings, the wires are tensioned and drilled through the bones. This study suggests using a new parallel wires configuration at the same level on the same ring and two revised versions, which are divergent and convergent models, and compare them with standard wires, 60 angle wires model. All models were designed using SolidWorks, a computer-aided design (CAD) software, and then analyzed in four conditions (axial compression, medial bending, posterior bending, and torsion) with Finite Element Analysis (FEA) using Ansys Workbench 2020 R2. Mechanical testing was conducted to validate the FEA results, A simple model consisting of a single ring, two K-wires, and polylactic acid (PLA) cylinders was utilized in a tensile test. It has been concluded from the results that the parallel model and its improvement have higher stiffness to axial compression, medial bending, and torsion, but a lower posterior bending stiffness, except the divergent model with 8-hole separation which has a relatively acceptable stiffness for posterior bending

Determination of Cadmium and Lead in Sewage Sludge from the Middle Region (Misrata, Msallata and Tarhünah 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 Tarhünah 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 (275–613) ppm

The Role of Social Media Advertisement and Physical Activity on Eating Behaviors among the General Population in Saudi Arabia

Abstract: Over the past few decades, people in Saudi Arabia have become less inclined to adopt active lifestyles and healthy eating habits due to the increasing use of digital technologies such as social media. The objective of this online-based cross-sectional study was to assess the role of social media food advertisements and physical activity on eating behaviors among the general population in Saudi Arabia (n = 471). Data were collected through a structured questionnaire, which consisted of four parts: (i) sociodemographic information, (ii) attitude towards social media, (iii) eating behaviorsrelated information, and (iv) exposure to and engagement with social media advertisements. The study’s outcome variable, eating behaviors (healthy vs. unhealthy), was assessed using the following question: “Are you on a healthy diet (such as a balanced diet, keto, or low carb)?” A multiple binary logistic regression analysis was performed to investigate the factors that influence unhealthy eating behaviors. Approximately 79.6% of the participants had unhealthy eating behaviors. Participants who were not involved in daily physical activity were more likely to have unhealthy eating behaviors compared to their counterparts (adjusted odds ratio, AOR = 4.86). Participants who watched food ads on social media channels 1–3 times a week (AOR = 2.58) or daily (AOR = 3.49) were more likely to have unhealthy eating behaviors than their counterparts. Participants whose appetite to try foods increases always (AOR = 1.42) or usually (AOR = 2.88) after viewing ads on social media were more likely to have unhealthy eating behaviors. These findings suggest that policymakers should take immediate action to regulate food advertising policy to promote a healthy food environment across the country. Saudis should be encouraged to engage in more physical activity, which could support the maintenance of healthy eating patterns and lifestyles.info:eu-repo/semantics/publishedVersio