Let Iν and Kν denote the modified Bessel functions of the first and second kinds of order ν. In this note we prove that the monotonicity of u → Iν(u)Kν(u) on (0,∞) for all ν ≥ −1/2 is an almost immediate consequence of the corresponding Turán type inequalities for the modified Bessel functions of the first and second kinds of order ν. Moreover, we show that the function u → Iν(u)Kν(u) is strict...

Prostate cancer (PCa) is the second leading cause of cancer death in men worldwide. Most PCa deaths are due to osteoblastic bone metastases. What triggers PCa metastasis to the bone and what causes osteoblastic lesions remain unanswered. A major contributor to PCa metastasis is the host microenvironment. Here, we address how the primary tumor microenvironment influences PCa metastasis via integ...

The selection of appropriate wavelets is an important target for any application. In this paper Face recognition has been performed using Principal component analysis (PCA), Gaussian based PCA and Gabor based PCA. PCA extracts the relevant information from complex data sets and provides a solution to reduce dimensionality. PCA is based on Euclidean distance calculation which is minimized by app...

In analysis of bioinformatics data, a unique challenge arises from the high dimensionality of measurements. Without loss of generality, we use genomic study with gene expression measurements as a representative example but note that analysis techniques discussed in this article are also applicable to other types of bioinformatics studies. Principal component analysis (PCA) is a classic dimensio...

Recently, many l1-norm based PCA methods have been developed for dimensionality reduction, but they do not explicitly consider the reconstruction error. Moreover, they do not take into account the relationship between reconstruction error and variance of projected data. This reduces the robustness of algorithms. To handle this problem, a novel formulation for PCA, namely angle PCA, is proposed....