Correlation of Matrix Metalloproteinase-9 Level, Erythrocyte Sedimentation Rate, Rheumatoid Factor, and the Duration of Illness with Radiological Findings in Rheumatoid Arthritis Patients

Background: Rheumatoid arthritis (RA) is a common autoimmune disease of the joint indicated by chronic inflammation of synovium, cartilage destruction, and osteopenia. The end results of RA are joint deformity and disability that will decrease the quality of life ofthe patients. Until now there is not a specifi c marker to assess the process of joint and bone damage in RA. Available markers such as C-reactive protein and erythrocyte sedimentation rate (ESR) indicate more about the infl ammatory status of the patient. Thediscovery of matrix metalloproteinases (MMPs) enzyme overexpression in RA has brought a new hope for the discovery of more specifi c markers of joint damage.Objective: To study the correlation of MMP-9 level, ESR, rheumatoid factor (RF), and the duration of illness with joint damage in RA patients.Methods: A cross-sectional study was conducted on RA outpatients in rheumatology clinic at Cipto Mangunkusumo General Hospital, Jakarta from January to October 2009. From the patients who fulfilled the inclusion criteria and did not fulfi ll the exclusion criteria, blood sample was collected for MMP-9 level, RF, and ESR examinations; hand radiography (posterior-anterior view) was also taken. Results: From the study of 46 patients, we found a significant correlation between MMP-9 level and radiographic feature of bone erosion (r = 0.3, p = 0.02) and between the duration of illness and Sharp score (r = 0.36, p = 0.014). There was no correlation between ESR and radiological fi ndings nor between RF and radiological fi ndings. Linear regression analysis showed the duration of illness as the most infl uencing factor toradiological fi ndings in RA patients.Conclusion: We found a signifi cant correlation between MMP-9 level and radiographic feature of bone erosion, and between the duration of illness and radiological fi ndings in RA patients

Correlation, hierarchies, and networks in financial markets

We discuss some methods to quantitatively investigate the properties of correlation matrices. Correlation matrices play an important role in portfolio optimization and in several other quantitative descriptions of asset price dynamics in financial markets. Specifically, we discuss how to define and obtain hierarchical trees, correlation based trees and networks from a correlation matrix. The hierarchical clustering and other procedures performed on the correlation matrix to detect statistically reliable aspects of the correlation matrix are seen as filtering procedures of the correlation matrix. We also discuss a method to associate a hierarchically nested factor model to a hierarchical tree obtained from a correlation matrix. The information retained in filtering procedures and its stability with respect to statistical fluctuations is quantified by using the Kullback-Leibler distance.Comment: 37 pages, 9 figures, 3 table

Correlation Functions of Complex Matrix Models

For a restricted class of potentials (harmonic+Gaussian potentials), we express the resolvent integral for the correlation functions of simple traces of powers of complex matrices of size $N$, in term of a determinant; this determinant is function of four kernels constructed from the orthogonal polynomials corresponding to the potential and from their Cauchy transform. The correlation functions are a sum of expressions attached to a set of fully packed oriented loops configurations; for rotational invariant systems, explicit expressions can be written for each configuration and more specifically for the Gaussian potential, we obtain the large $N$ expansion ('t Hooft expansion) and the so-called BMN limit.Comment: latex BMN.tex, 7 files, 6 figures, 30 pages (v2 for spelling mistake and added reference) [http://www-spht.cea.fr/articles/T05/174

Signal and Noise in Correlation Matrix

Using random matrix technique we determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator. This relation can be used in practice to compute eigenvalue invariants of the covariance (correlation) matrix. Results can be applied in various problems where one experimentally estimates correlations in a system with many degrees of freedom, like in statistical physics, lattice measurements of field theory, genetics, quantitative finance and other applications of multivariate statistics.Comment: 17 pages, 3 figures, corrected typos, revtex style changed to elsar

Systematic analysis of group identification in stock markets

We propose improved methods to identify stock groups using the correlation matrix of stock price changes. By filtering out the marketwide effect and the random noise, we construct the correlation matrix of stock groups in which nontrivial high correlations between stocks are found. Using the filtered correlation matrix, we successfully identify the multiple stock groups without any extra knowledge of the stocks by the optimization of the matrix representation and the percolation approach to the correlation-based network of stocks. These methods drastically reduce the ambiguities while finding stock groups using the eigenvectors of the correlation matrix.Comment: 9 pages, 7 figure

Configuration model for correlation matrices preserving the node strength

Correlation matrices are a major type of multivariate data. To examine properties of a given correlation matrix, a common practice is to compare the same quantity between the original correlation matrix and reference correlation matrices, such as those derived from random matrix theory, that partially preserve properties of the original matrix. We propose a model to generate such reference correlation and covariance matrices for the given matrix. Correlation matrices are often analysed as networks, which are heterogeneous across nodes in terms of the total connectivity to other nodes for each node. Given this background, the present algorithm generates random networks that preserve the expectation of total connectivity of each node to other nodes, akin to configuration models for conventional networks. Our algorithm is derived from the maximum entropy principle. We will apply the proposed algorithm to measurement of clustering coefficients and community detection, both of which require a null model to assess the statistical significance of the obtained results.Comment: 8 figures, 4 table

Correlation density matrices for 1- dimensional quantum chains based on the density matrix renormalization group

A useful concept for finding numerically the dominant correlations of a given ground state in an interacting quantum lattice system in an unbiased way is the correlation density matrix. For two disjoint, separated clusters, it is defined to be the density matrix of their union minus the direct product of their individual density matrices and contains all correlations between the two clusters. We show how to extract from the correlation density matrix a general overview of the correlations as well as detailed information on the operators carrying long-range correlations and the spatial dependence of their correlation functions. To determine the correlation density matrix, we calculate the ground state for a class of spinless extended Hubbard models using the density matrix renormalization group. This numerical method is based on matrix product states for which the correlation density matrix can be obtained straightforwardly. In an appendix, we give a detailed tutorial introduction to our variational matrix product state approach for ground state calculations for 1- dimensional quantum chain models. We show in detail how matrix product states overcome the problem of large Hilbert space dimensions in these models and describe all techniques which are needed for handling them in practice.Comment: 50 pages, 34 figures, to be published in New Journal of Physic