The analysis of cross-Correlations is extensively applied for understanding of interconnections in stock markets. Variety of methods are used in order to search stock cross- Correlations including the Random Matrix Theory (RMT), the Principal Component Analysis (PCA) and the Hierachical Structures. In this work, we analyze cross-crrelations between price uctuations of 20 company stocks of Iran by using RMT. We find the eigenvalues and eigenvectors of the matrices of the cross-Correlations related to these stocks. The results show some eigenvalues do not fall within the bounds of RMT eigenvalues, that indicate the Correlations of stocks in usual and critical ucatutions.

One of the fundamental methods used in collaborative filtering systems is Correlation based on K-nearest neighborhood. These systems rely on historical rating data and preferences of users and items in order to propose appropriate recommendations for active users. These systems do not often have a complete Matrix of input data. This challenge leads to a decrease in the accuracy level of recommendations for new users. The exact Matrix completion technique tries to predict unknown values in data matrices. This study is to show how the exact Matrix completion can be used as a preprocessing step to tackle the sparseness problem. Compared to application of the sparse data Matrix, selection of neighborhood set for active user based on the completed data Matrix leads to achieving more similar users. The main advantages of the proposed method are higher prediction accuracy and an explicit model representation. The experiments show significant improvement in prediction accuracy in comparison with other substantial methods.

There are emerging data on novel tumor markers such as Matrix metalloproteinase-2 (MMP-2 or gelatinase-A), which play a key role in tissue invasion and metastasis. We designed an investigation to assess the usefulness of MMP-2 activity as compared to prostate specific antigen (PSA) in cancer staging process. We have analyzed the circulating form of MMP-2 in serum samples of patients suffering from either benign prostate hyperplasia (BPH, n = 54) or prostate cancer (PC, n = 26), and prostatitis (n = 4) as compared to control normal individual (n = 26), respectively. Protein-content adjusted samples were separated by gelatin-embedded polyacrylamide gel electrophoresis then were subjected to densitometric analysis. Total PSA (tPSA) and free PSA (fPSA) were quantified using a standard ELISA technique. Correlation coefficient (r) between tPSA and MMP-2 activity in patient group was +0.938 and in controls group was 0.799 (P<0.01). In addition, (r) between tPSA and MMP-2 activity in PC patients was 0.940 and in BPH patients was 0.962 (P<0.01). (r) between fPSA and MMP- 2 activity in PC patients was 0.913, in BPH patients was 0.644, and in prostatitis patients was -0.994 (P<0.01). These results demonstrate that MMP-2, compared to PSA, might be considered as a better tumor marker in monitoring and screening patients with PC.