Achievable Angles Between two Compressed Sparse Vectors Under Norm/Distance Constraints Imposed by the Restricted Isometry Property: A Plane Geometry Approach

The angle between two compressed sparse vectors subject to the norm/distance constraints imposed by the restricted isometry property (RIP) of the sensing matrix plays a crucial role in the studies of many compressive sensing (CS) problems. Assuming that (i) u and v are two sparse vectors separated by an angle thetha, and (ii) the sensing matrix Phi satisfies RIP, this paper is aimed at analytically characterizing the achievable angles between Phi*u and Phi*v. Motivated by geometric interpretations of RIP and with the aid of the well-known law of cosines, we propose a plane geometry based formulation for the study of the considered problem. It is shown that all the RIP-induced norm/distance constraints on Phi*u and Phi*v can be jointly depicted via a simple geometric diagram in the two-dimensional plane. This allows for a joint analysis of all the considered algebraic constraints from a geometric perspective. By conducting plane geometry analyses based on the constructed diagram, closed-form formulae for the maximal and minimal achievable angles are derived. Computer simulations confirm that the proposed solution is tighter than an existing algebraic-based estimate derived using the polarization identity. The obtained results are used to derive a tighter restricted isometry constant of structured sensing matrices of a certain kind, to wit, those in the form of a product of an orthogonal projection matrix and a random sensing matrix. Follow-up applications to three CS problems, namely, compressed-domain interference cancellation, RIP-based analysis of the orthogonal matching pursuit algorithm, and the study of democratic nature of random sensing matrices are investigated.Comment: submitted to IEEE Trans. Information Theor

TYPE VI COLLAGEN STIMULATES MACROPHAGES TO PROMOTE INFLAMMATION

poster abstractCollagen VI (COL6), an extracellular matrix protein (ECM), is important in maintaining the integrity of the tissue. Our recent findings have demonstrat-ed that excess COL6 is present in the lungs of comorbid patients with em-physema and adenocarcinoma. COL6 localized in the pulmonary interstitium is likely to interact with endothelial, epithelial and infiltrated pulmonary mac-rophages. The hypothesis is that excessive COL6 activates macrophages to promote inflammation, which may exacerbate pulmonary diseases. To test our hypothesis, bone marrow derived macrophages or macrophage cell lines were stimulated with soluble COL6 followed by analysis of activation markers and pro inflammatory cytokines. And results showed an increase in the number of CD86 positive cells and the levels of IL-12 and IFNγ production following stimulation. Taken together, our data have provided a link between increased amounts of COL6 and subsequent immune responses, which may play a role in the pathogenesis of pulmonary inflammatory diseases

ENHANCING THE TUMOR FIGHTING CAPACITY OF NK CELLS THROUGH THE USE OF SOYPEPTIDE

poster abstractNatural killer or (NK) cells are important components of the innate immune system, which play a major role in the rejection of tumors, and virally in-fected cells. By producing pro-inflammatory cytokines such as IFN-gamma, NK cells are able to exert immunoregulatory functions that influence the adaptive immunity of other immune cells. Due to its critical role in tumor inhibition, researchers, utilizing various cytokines, including IL-12 and IL-2, have fervently pursued the manipulation of NK activity. NK cells respond to cytokines in a dose-dependent manner; however, the toxicity of certain cy-tokines (like IL-2) in high doses prohibits their widespread clinical use. Therefore, efforts to activate NK cells without requiring high doses of cyto-kines is warranted. We recently exploited a soy derived dietary peptide called lunasin to improve the immune functions. The hypothesis was that the lunasin peptide has stimulatory effects on immune cells. To test this hy-pothesis, human peripheral blood mononuclear cells (PBMCs) of healthy do-nors were stimulated with and without lunasin in combination with cytokines IL-12 or IL-2. Our results showed that the lunasin peptide exerts a robust synergistic effect when combined with the selected cytokines. This effect ap-pears to regulate the expression of a number of genes that are important for NK activity. Our findings support the potential clinical use of lunasin in com-bination with cytokine to enhance the tumor fighting capacity of NK cells