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## Correlação in vitro in vivo para formas farmacêuticas sólidas de liberação modificada contendo diclofenaco de sódio; In vitro-in vivo correlation for sodium diclofenac modified release tablet formulations

Mourão, Samanta Cardozo
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
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A correlação in vitro-in vivo (CIVIV) refere-se ao estabelecimento de uma relação racional entre as propriedades biológicas, ou parâmetros derivados destas, produzidos por uma forma farmacêutica e suas propriedades ou características físico-químicas. O estabelecimento desse tipo de correlação de dados pode possibilitar a substituição dos estudos in vivo, necessários à demonstração da bioequivalência, pelos estudos in vitro, no caso de alterações no processo de fabricação pós-registro. Os sistemas matriciais apresentam, como principal exemplo de material controlador da liberação, substâncias poliméricas formadoras de matrizes hidrofílicas. Hidroxipropilmetilcelulose (HPMC) é um excipiente de escolha para o preparo de matrizes hidrofílicas, devido à capacidade de formação de gel e controle da liberação. O diclofenaco de sódio (DCL) é um antiinflamatório não esteroidal com ação analgésica e antipirética. Considerando suas características físico-químicas e farmacológicas, é objetivo deste trabalho o estabelecimento de uma CIVIV para DCL incorporado em sistemas matriciais. Os comprimidos de DCL com HPMC foram desenvolvidos e submetidos aos ensaios de dissolução utilizando os aparatos 1...

## Avaliação das variáveis que influenciaram no uso da terra como material construtivo para habitação social rural no Assentamento Rural Sepé Tiaraju - Serra Azul - SP; Evaluation of variables which influenced the adoption of the earth as a building material for social housing in rural areas of Sepé Tiaraju Rural Settlement - Serra Azul - SP

Maia, Rafael Torres
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
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## Characteristic Analysis on UAV-MIMO Channel Based on Normalized Correlation Matrix

Xi jun, Gao; Zi li, Chen; Yong Jiang, Hu
Fonte: Hindawi Publishing Corporation Publicador: Hindawi Publishing Corporation
Tipo: Artigo de Revista Científica
EN
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Based on the three-dimensional GBSBCM (geometrically based double bounce cylinder model) channel model of MIMO for unmanned aerial vehicle (UAV), the simple form of UAV space-time-frequency channel correlation function which includes the LOS, SPE, and DIF components is presented. By the methods of channel matrix decomposition and coefficient normalization, the analytic formula of UAV-MIMO normalized correlation matrix is deduced. This formula can be used directly to analyze the condition number of UAV-MIMO channel matrix, the channel capacity, and other characteristic parameters. The simulation results show that this channel correlation matrix can be applied to describe the changes of UAV-MIMO channel characteristics under different parameter settings comprehensively. This analysis method provides a theoretical basis for improving the transmission performance of UAV-MIMO channel. The development of MIMO technology shows practical application value in the field of UAV communication.

## Patterns in correlation matrices arising in wine-tasting and other experiments.

Brien, Christopher James
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There are two distinct areas of research on which the work in this thesis impinges. They are methods for the analysis of patterns in correlation matrices and the analysis of taster performance in wine-tasting experiments in which the wines are scored. For the analysis patterns in correlation matrices, least squares procedures are developed to examine patterns under certain equal correlation hypotheses. The procedures are applied to the z-transforms of the elements of correlation matrices that can be based on either a single group of variables, or variables that can be cross-indexed by two factors such as the multitrait-multimethod matrices given by Campbell and Fiske (1959). The procedures are of the analysis of variance type, being investigative in the sense that, in the event that the correlation matrix is judged to depart from the hypothesised pattern, alternative models to be pursued further are indicated. The associated statistics are calculated directly from closed-form expressions, rather that requiring the iterative solution of some estimation function as is the case with some alternative methods. The procedures are used to analyse the data from a number of wine-tasting and other experiments. The results obtained are shown to be similar...

## Proximal methods for structured group features and correlation matrix nearness

Alaíz Gudín, Carlos María
SPA; ENG
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Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Escuela Politécnica Superior, Departamento de Ingeniería Informática. Fecha de lectura: junio de 2014; Optimization is ubiquitous in real life as many of the strategies followed both by nature and by humans aim to minimize a certain cost, or maximize a certain benefit. More specifically, numerous strategies in engineering are designed according to a minimization problem, although usually the problems tackled are convex with a di erentiable objective function, since these problems have no local minima and they can be solved with gradient-based techniques. Nevertheless, many interesting problems are not di erentiable, such as, for instance, projection problems or problems based on non-smooth norms. An approach to deal with them can be found in the theory of Proximal Methods (PMs), which are based on iterative local minimizations using the Proximity Operator (ProxOp) of the terms that compose the objective function. This thesis begins with a general introduction and a brief motivation of the work done. The state of the art in PMs is thoroughly reviewed, defining the basic concepts from the very beginning and describing the main algorithms, as far as possible...

## Estimación del espectro de potencias del fondo cósmico de microondas con el método QML; Cosmic microwave background power spectrum estimation using QML method

Bilbao Ahedo, Juan Daniel
SPA
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RESUMEN: El espectro de potencias de la radiación del Fondo Cósmico de Microondas (FCM) viene determinado por los parámetros del modelo cosmológico que describe nuestro universo. Por tanto, una estimación óptima del mismo es un paso fundamental para extraer toda la valiosa información contenida en dicha radiación. En este proyecto se implementa una aproximación cuadrática al estimador de máxima verosimilitud, QML, del espectro de potencias del FCM, se analizan las condiciones en las que la matriz de correlación de los mapas de temperatura del FCM resulta óptima para los cálculos, la carga computacional y velocidad a la que se realizan, y se testa el método con simulaciones realistas del FCM, incluyendo máscara y ruido, y con productos de la colaboración Planck. Para que el método funcione, la matriz de correlación debe ser regular, y se ha encontrado que esta propiedad depende en el plano teórico del número de armónicos esféricos que se incluyan en su desarrollo y de la simetría de los puntos con los que se trabaje, pero en la práctica los errores numéricos hacen que el rango sea menor de lo esperado. En este trabajo se proporcionan técnicas para analizar y controlar este fenómeno. Se ha comprobado que el método produce buenas estimaciones del espectro de potencias en condiciones diversas...

## Some remarks on estimating a covariance structure model from a sample correlation matrix

Tipo: Trabalho em Andamento Formato: application/octet-stream; application/octet-stream; application/pdf
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A popular model in structural equation modeling involves a multivariate normal density with a structured covariance matrix that has been categorized according to a set of thresholds. In this setup one may estimate the covariance structure parameters from the sample tetrachoricl polychoric correlations but only if the covariance structure is scale invariant. Doing so when the covariance structure is not scale invariant results in estimating a more restricted covariance structure than the one intended. When the covariance structure is not scale invariant, then the model parameters must be estimated jointly from the sample thresholds and tetrachoricl polychoric correlations. In general, when fitting a covariance structure from a sample correlation matrix one should consider the population correlation structure under the null hypothesis. This is obtained by pre and post-multiplying the covariance structure by a diagonal matrix consisting of the inverse of the square root of the diagonal of the covariance structure under consideration. We provide computer algebra code for assessing whether a covariance structure is scale invariant and for assessing the identification of threshold and correlation structures.

## A Non-simulation Based Method for Inducing Pearson's Correlation between Input Random Variables

Eric R. Druker; Richard L. Coleman; Peter J. Braxton
Tipo: Relatório
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Proceedings Paper (for Acquisition Research Program); Several previously published papers have cited the need to include correlation in risk-analysis models. In particular, a landmark paper published by Philip Lurie and Matthew Goldberg presented a methodology for inducing Pearson''s correlation between input/independent random variables. The one subject, absent from the paper, was a methodology for finding the optimal applied correlation matrix given a desired outcome correlation. Since the publishing of the Lurie-Goldberg paper, there has been continuing discussion on its implementation; however, there has not been any presentation of an optimization algorithm that does not involve the use of computing-heavy simulations. This paper reviews the general methodology used by Lurie and Goldberg (along with its predecessor papers) and presents a non-simulation approach to finding the optimal input correlation matrix, given a set of marginal distributions and a desired correlation matrix.; Acquisition Research Program

## Consequences of omitting relevant inputs on the quality of the data envelopment analysis under different input correlation structures

Ramírez Hassan, Andrés
Tipo: workingPaper; Documento de trabajo de investigación; draf
ENG
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This paper establishes the consequences of a wrong specification on the quality of the data envelopment analysis. Specifically, the case of omitting a relevant variable in the input oriented problem is analyzed when there are different correlation structures between the inputs. It is established that the correlation matrix gives relevant information about the homogeneity of the decision making units and the intensity of inputs used in the production process. The methodology is based on a series of Monte Carlo simulations and the quality of the data envelopment analysis is measured as the difference between the true efficiency and the efficiency calculated. It is found that omitting relevant inputs causes inconsistency, and this problem is worse when there is a negative correlation structure.; This paper establishes the consequences of a wrong specification on the quality of the data envelopment analysis. Specifically, the case of omitting a relevant variable in the input oriented problem is analyzed when there are different correlation structures between the inputs. It is established that the correlation matrix gives relevant information about the homogeneity of the decision making units and the intensity of inputs used in the production process. The methodology is based on a series of Monte Carlo simulations and the quality of the data envelopment analysis is measured as the difference between the true efficiency and the efficiency calculated. It is found that omitting relevant inputs causes inconsistency...

## Covariance, correlation matrix and the multi-scale community structure of networks

Shen, Hua-Wei; Cheng, Xue-Qi; Fang, Bin-Xing
Tipo: Artigo de Revista Científica
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Empirical studies show that real world networks often exhibit multiple scales of topological descriptions. However, it is still an open problem how to identify the intrinsic multiple scales of networks. In this article, we consider detecting the multi-scale community structure of network from the perspective of dimension reduction. According to this perspective, a covariance matrix of network is defined to uncover the multi-scale community structure through the translation and rotation transformations. It is proved that the covariance matrix is the unbiased version of the well-known modularity matrix. We then point out that the translation and rotation transformations fail to deal with the heterogeneous network, which is very common in nature and society. To address this problem, a correlation matrix is proposed through introducing the rescaling transformation into the covariance matrix. Extensive tests on real world and artificial networks demonstrate that the correlation matrix significantly outperforms the covariance matrix, identically the modularity matrix, as regards identifying the multi-scale community structure of network. This work provides a novel perspective to the identification of community structure and thus various dimension reduction methods might be used for the identification of community structure. Through introducing the correlation matrix...

## Random, but not so much: A parameterization for the returns and correlation matrix of financial time series

Martins, Andre C. R.
Tipo: Artigo de Revista Científica
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A parameterization that is a modified version of a previous work is proposed for the returns and correlation matrix of financial time series and its properties are studied. This parameterization allows easy introduction of non-stationarity and it shows several of the characteristics of the true, observed realizations, such as fat tails, volatility clustering, and a spectrum of eigenvalues of the correlation matrix that can be understood as an extension of Random Matrix Theory results. The predicted behavior of this parameterization for the eigenvalues is compared with the eigenvalues of Brazilian assets and it is shown that those predictions fit the data better than Random Matrix Theory.; Comment: 4 pages, 3 figures

## The bulk of the stock market correlation matrix is not pure noise

Kwapien, J.; Oswiecimka, P.; Drozdz, S.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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We analyse the structure of the distribution of eigenvalues of the stock market correlation matrix with increasing length of the time series representing the price changes. We use 100 highly-capitalized stocks from the American market and relate result to the corresponding ensemble of Wishart random matrices. It turns out that systematically more eigenvalues stay beyond the borders prescribed by this variant of the Random Matrix Theory (RMT). This may indicate that even the bulk of the spectrum of the stock market correlation matrix carries some sort of correlations that are masked by a measurement noise when the time series used to construct the matrix are short. We also study some other characteristics of the "noisy" eigensignals, like their return distributions, temporal correlations or their multifractal spectra and the results support the above conclusions.; Comment: updated version to appear in Physica A

## Efficient Algorithms for Positive Semi-Definite Total Least Squares Problems, Minimum Rank Problem and Correlation Matrix Computation

Bagherpour, Negin; Mahdavi-Amiri, Nezam
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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We have recently presented a method to solve an overdetermined linear system of equations with multiple right hand side vectors, where the unknown matrix is to be symmetric and positive definite. The coefficient and the right hand side matrices are respectively named data and target matrices. A more complicated problem is encountered when the unknown matrix is to be positive semi-definite. The problem arises in estimating the compliance matrix to model deformable structures and approximating correlation and covariance matrices in financial modeling. Several methods have been proposed for solving such problems assuming that the data matrix is unrealistically error free. Here, considering error in measured data and target matrices, we propose a new approach to solve a positive semi-definite constrained total least squares problem. We first consider solving the problem when the rank of the unknown matrix is known, by defining a new error formulation for the positive semi-definite total least squares problem and use of optimization methods on Stiefel manifolds. We prove quadratic convergence of our proposed approach. We then describe how to generalize our proposed method to solve the general positive semi-definite total least squares problem. We further apply the proposed approach to solve the minimum rank problem and the problem of computing correlation matrix. Comparative numerical results show the efficiency of our proposed algorithms. Finally...

## Optimal Rates of Convergence for Latent Generalized Correlation Matrix Estimation in Transelliptical Distribution

Han, Fang; Liu, Han
Tipo: Artigo de Revista Científica
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Correlation matrix plays a key role in many multivariate methods (e.g., graphical model estimation and factor analysis). The current state-of-the-art in estimating large correlation matrices focuses on the use of Pearson's sample correlation matrix. Although Pearson's sample correlation matrix enjoys various good properties under Gaussian models, its not an effective estimator when facing heavy-tail distributions with possible outliers. As a robust alternative, \cite{han2012transelliptical} advocated the use of a transformed version of the Kendall's tau sample correlation matrix in estimating high dimensional latent generalized correlation matrix under the transelliptical distribution family (or elliptical copula). The transelliptical family assumes that after unspecified marginal monotone transformations, the data follow an elliptical distribution. In this paper, we study the theoretical properties of the Kendall's tau sample correlation matrix and its transformed version proposed in \cite{han2012transelliptical} for estimating the population Kendall's tau correlation matrix and the latent Pearson's correlation matrix under both spectral and restricted spectral norms. With regard to the spectral norm, we highlight the role of "effective rank" in quantifying the rate of convergence. With regard to the restricted spectral norm...

## On Jiang's asymptotic distribution of the largest entry of a sample correlation matrix

Li, Deli; Qi, Yongcheng; Rosalsky, Andrew
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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Let $\{X, X_{k,i}; i \geq 1, k \geq 1 \}$ be a double array of nondegenerate i.i.d. random variables and let $\{p_{n}; n \geq 1 \}$ be a sequence of positive integers such that $n/p_{n}$ is bounded away from $0$ and $\infty$. This paper is devoted to the solution to an open problem posed in Li, Liu, and Rosalsky (2010) on the asymptotic distribution of the largest entry $L_{n} = \max_{1 \leq i < j \leq p_{n}} \left | \hat{\rho}^{(n)}_{i,j} \right |$ of the sample correlation matrix ${\bf \Gamma}_{n} = \left ( \hat{\rho}_{i,j}^{(n)} \right )_{1 \leq i, j \leq p_{n}}$ where $\hat{\rho}^{(n)}_{i,j}$ denotes the Pearson correlation coefficient between $(X_{1, i},..., X_{n,i})'$ and $(X_{1, j},..., X_{n,j})'$. We show under the assumption $\mathbb{E}X^{2} < \infty$ that the following three statements are equivalent: \begin{align*} & {\bf (1)} \quad \lim_{n \to \infty} n^{2} \int_{(n \log n)^{1/4}}^{\infty} \left( F^{n-1}(x) - F^{n-1}\left(\frac{\sqrt{n \log n}}{x} \right) \right) dF(x) = 0, \\ & {\bf (2)} \quad \left ( \frac{n}{\log n} \right )^{1/2} L_{n} \stackrel{\mathbb{P}}{\rightarrow} 2, \\ & {\bf (3)} \quad \lim_{n \rightarrow \infty} \mathbb{P} \left (n L_{n}^{2} - a_{n} \leq t \right ) = \exp \left \{ - \frac{1}{\sqrt{8 \pi}} e^{-t/2} \right \}...

## Spectral statistics of large dimensional Spearman's rank correlation matrix and its application

Bao, Zhigang; Lin, Liang-Ching; Pan, Guangming; Zhou, Wang
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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Let $\mathbf{Q}=(Q_1,\ldots,Q_n)$ be a random vector drawn from the uniform distribution on the set of all $n!$ permutations of $\{1,2,\ldots,n\}$. Let $\mathbf{Z}=(Z_1,\ldots,Z_n)$, where $Z_j$ is the mean zero variance one random variable obtained by centralizing and normalizing $Q_j$, $j=1,\ldots,n$. Assume that $\mathbf {X}_i,i=1,\ldots ,p$ are i.i.d. copies of $\frac{1}{\sqrt{p}}\mathbf{Z}$ and $X=X_{p,n}$ is the $p\times n$ random matrix with $\mathbf{X}_i$ as its $i$th row. Then $S_n=XX^*$ is called the $p\times n$ Spearman's rank correlation matrix which can be regarded as a high dimensional extension of the classical nonparametric statistic Spearman's rank correlation coefficient between two independent random variables. In this paper, we establish a CLT for the linear spectral statistics of this nonparametric random matrix model in the scenario of high dimension, namely, $p=p(n)$ and $p/n\to c\in(0,\infty)$ as $n\to\infty$. We propose a novel evaluation scheme to estimate the core quantity in Anderson and Zeitouni's cumulant method in [Ann. Statist. 36 (2008) 2553-2576] to bypass the so-called joint cumulant summability. In addition, we raise a two-step comparison approach to obtain the explicit formulae for the mean and covariance functions in the CLT. Relying on this CLT...

## Direct formulation to Cholesky decomposition of a general nonsingular correlation matrix

Tipo: Artigo de Revista Científica
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We present two novel, explicit representations of Cholesky factor of a nonsingular correlation matrix. The first representation uses semi-partial correlation coefficients as its entries. The second, uses an equivalent form of the square roots of the differences between two ratios of successive determinants. Each of the two new forms enjoys parsimony of notations and offers a simpler alternative to both spherical factorization and the multiplicative partial correlation Cholesky matrix (Cooke et al 2011). Two relevant applications are offered for each form: a simple $t$-test for assessing the independence of a single variable in a multivariate normal structure, and a straightforward algorithm for generating random positive-definite correlation matrix. The second representation is also extended to any nonsingular hermitian matrix.; Comment: Accepted to Statistics and Probability Letters, March 2015

## Controlling the N - and S -representability of the second-order reduced density matrix: The doublet-state case

Alcoba, Diego Ricardo; Valdemoro, Carmela; Tel, Luis María; Pérez-Romero, Encarnación
Fonte: American Physical Society Publicador: American Physical Society
Tipo: Artículo Formato: 203581 bytes; application/pdf
ENG
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12 pages, 6 figures, 3 tables.-- PACS nrs.: 31.10.+z; 31.15.vj; 31.15.xh.; A purification procedure that simultaneously corrects the N- and S-representability main defects of a second-order reduced density matrix (2RDM), second-order hole reduced density matrix (2HRDM), and second-order G matrix is presented here. In this purifying procedure, the generalized unitarily invariant second-order matrix decomposition [D. R. Alcoba, Int. J. Quantum Chem. 97, 776 (2004)] for the 2RDM and the 2HRDM as well as for the G matrix is combined with the S-representability conditions. In particular, here we will focus our attention on the RDMs corresponding to doublet states. We will thus explicitly give the S-representability conditions that a two-body correlation matrix has to satisfy when an N-electron system is in a doublet spin-state in the spin-component of maximum projection. Furthermore, as a consequence of the G-matrix spin properties (which directly affect the S-representability of the 2RDM), we show that a different contracting form for the 2RDM is possible. The numerical results presented in this work confirm the efficiency of our purifying procedure.; The authors acknowledge the financial support granted to this work by the Ministerio de Ciencia y Tecnología of Spain...

## Four new forms of the contracted Schrödinger equation and their connection with the second-order hypervirial condition

Valdemoro, Carmela; Tel, Luis María; Pérez-Romero, Encarnación; Alcoba, Diego Ricardo
Fonte: John Wiley & Sons Publicador: John Wiley & Sons
Tipo: Artículo Formato: 102798 bytes; application/pdf
ENG
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7 pages.-- Printed version published May 2008.; Through the use of an important property of a fourth-order correlation matrix previously reported (Valdemoro, C.; Tel, L. M.; Alcoba, D. R.; Perez-Romero, E.; Casquero, F. J. Int J Quantum Chem 2002, 90, 1555; Alcoba, D. R.; Valdemoro, C. Phys Rev A 2001, 64, 062105) four new equivalent forms of the second-order contracted Schrödinger equation (2-CSE) are obtained. The role played by the energy terms involving these correlation matrices is crucial in the solution of these equations. The relations linking the Hermitian (Yasuda, K. Phys Rev A 1999, 59, 4133) and antiHermitian parts (Mazziotti, D. A. Phys Rev Lett 2006, 97, 142002) of the 2-CSE with these correlation energy terms are analyzed in detail. A discussion of the second-order hypervirial condition is also given here.; This work was supported by the Spanish Ministerio de Educación y Ciencia, Contract Grant no. BFM2003-05133, by Universidad de Buenos Aires, Contract Grant no. X-024 and by Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), República Argentina, Contract Grant no. 5098/05.; Peer reviewed

## Channel Capacity Estimation for MIMO Systems with Correlated Noise

Krusevac, Snezana; Rapajic, Predrag; Kennedy, Rodney
Fonte: Institute of Electrical and Electronics Engineers (IEEE Inc) Publicador: Institute of Electrical and Electronics Engineers (IEEE Inc)
Tipo: Conference paper
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In this paper we determine the MIMO channel capacity in the presence of correlated noise. We employ a normalized noise correlation matrix in the channel capacity formula, in order to identify the noise correlation contribution to the MIMO subchannel decorrelation. Then, we analyze the thermal noise correlation due to mutual coupling. We calculate thermal noise correlation matrix in the multi-antenna system with closely spaced antennae by applying the Nyquist's thermal noise theorem. Simulation results shows that mean and outage MIMO channel capacity is underestimated if the noise correlation due to mutual coupling is not accounted for. We present results for cases when the transmitter does and does not know the channel realization.