An Algebraic Implicitization and Specialization of Minimum KL-Divergence Models

In this paper we study representation of KL-divergence minimization, in the cases where integer sufficient statistics exists, using tools from polynomial algebra. We show that the estimation of parametric statistical models in this case can be transformed to solving a system of polynomial equations. In particular, we also study the case of Kullback-Csiszar iteration scheme. We present implicit descriptions of these models and show that implicitization preserves specialization of prior distribution. This result leads us to a Grobner bases method to compute an implicit representation of minimum KL-divergence models.

Salmonella enterica Serovar Typhimurium Lacking hfq Gene Confers Protective Immunity against Murine Typhoid

Salmonella enterica is an important enteric pathogen and its various serovars are involved in causing both systemic and intestinal diseases in humans and domestic animals. The emergence of multidrug-resistant strains of Salmonella leading to increased morbidity and mortality has further complicated its management. Live attenuated vaccines have been proven superior over killed or subunit vaccines due to their ability to induce protective immunity. Of the various strategies used for the generation of live attenuated vaccine strains, focus has gradually shifted towards manipulation of virulence regulator genes. Hfq is a RNA chaperon which mediates the binding of small RNAs to the mRNA and assists in post-transcriptional gene regulation in bacteria. In this study, we evaluated the efficacy of the Salmonella Typhimurium Dhfq strain as a candidate for live oral vaccine in murine model of typhoid fever. Salmonella hfq deletion mutant is highly attenuated in cell culture and animal model implying a significant role of Hfq in bacterial virulence. Oral immunization with the Salmonella hfq deletion mutant efficiently protects mice against subsequent oral challenge with virulent strain of Salmonella Typhimurium. Moreover, protection was induced upon both multiple as well as single dose of immunizations. The vaccine strain appears to be safe for use in pregnant mice and the protection is mediated by the increase in the number of CD4(+) T lymphocytes upon vaccination. The levels of serum IgG and secretory-IgA in intestinal washes specific to lipopolysaccharide and outer membrane protein were significantly increased upon vaccination. Furthermore, hfq deletion mutant showed enhanced antigen presentation by dendritic cells compared to the wild type strain. Taken together, the studies in murine immunization model suggest that the Salmonella hfq deletion mutant can be a novel live oral vaccine candidate.

Spherical aberration and its correction using Lie algebraic methods

We discuss three methods to correct spherical aberration for a point to point imaging system. First, results obtained using Fermat's principle and the ray tracing method are described briefly. Next, we obtain solutions using Lie algebraic techniques. Even though one cannot always obtain analytical results using this method, it is often more powerful than the first method. The result obtained with this approach is compared and found to agree with the exact result of the first method.

An algebraic formulation of exact force-, moment-isotropy in spatial parallel manipulators

In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions.We use the force and moment transformation matrices separately,and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation has been applied to a class of Stewart platform manipulators. We obtain multi-parameter families of isotropic manipulator analytically. In addition to computing the isotropic configurations of an existing manipulator,we demonstrate a procedure for designing the manipulator for isotropy at a given configuration.

Algebraic Approaches to Space-Time Code Construction for Multiple-Antenna Communication

A major challenge in wireless communications is overcoming the deleterious effects of fading, a phenomenon largely responsible for the seemingly inevitable dropped call. Multiple-antennas communication systems, commonly referred to as MIMO systems, employ multiple antennas at both transmitter and receiver, thereby creating a multitude of signalling pathways between transmitter and receiver. These multiple pathways give the signal a diversity advantage with which to combat fading. Apart from helping overcome the effects of fading, MIMO systems can also be shown to provide a manyfold increase in the amount of information that can be transmitted from transmitter to receiver. Not surprisingly,MIMO has played, and continues to play, a key role in the advancement of wireless communication.Space-time codes are a reference to a signalling format in which information about the message is dispersed across both the spatial (or antenna) and time dimension. Algebraic techniques drawing from algebraic structures such as rings, fields and algebras, have been extensively employed in the construction of optimal space-time codes that enable the potential of MIMO communication to be realized, some of which have found their way into the IEEE wireless communication standards. In this tutorial article, reflecting the authors’interests in this area, we survey some of these techniques.

Algebraic characterization of rainbow connectivity

The use of algebraic techniques to solve combinatorial problems is studied in this paper. We formulate the rainbow connectivity problem as a system of polynomial equations. We first consider the case of two colors for which the problem is known to be hard and we then extend the approach to the general case. We also present a formulation of the rainbow connectivity problem as an ideal membership problem.

The Glycosylated Rv1860 Protein of Mycobacterium tuberculosis Inhibits Dendritic Cell Mediated TH1 and TH17 Polarization of T Cells and Abrogates Protective Immunity Conferred by BCG

We previously reported interferon gamma secretion by human CD4(+) and CD8(+) T cells in response to recombinant E. coli-expressed Rv1860 protein of Mycobacterium tuberculosis (MTB) as well as protection of guinea pigs against a challenge with virulent MTB following prime-boost immunization with DNA vaccine and poxvirus expressing Rv1860. In contrast, a Statens Serum Institute Mycobacterium bovis BCG (BCG-SSI) recombinant expressing MTB Rv1860 (BCG-TB1860) showed loss of protective ability compared to the parent BCG strain expressing the control GFP protein (BCG-GFP). Since Rv1860 is a secreted mannosylated protein of MTB and BCG, we investigated the effect of BCG-TB1860 on innate immunity. Relative to BCG-GFP, BCG-TB1860 effected a significant near total reduction both in secretion of cytokines IL-2, IL-12p40, IL-12p70, TNF-alpha, IL-6 and IL-10, and up regulation of co-stimulatory molecules MHC-II, CD40, CD54, CD80 and CD86 by infected bone marrow derived dendritic cells (BMDC), while leaving secreted levels of TGF-beta unchanged. These effects were mimicked by BCG-TB1860His which carried a 6-Histidine tag at the C-terminus of Rv1860, killed sonicated preparations of BCG-TB1860 and purified H37Rv-derived Rv1860 glycoprotein added to BCG-GFP, but not by E. coli-expressed recombinant Rv1860. Most importantly, BMDC exposed to BCG-TB1860 failed to polarize allogeneic as well as syngeneic T cells to secrete IFN-gamma and IL-17 relative to BCG-GFP. Splenocytes from mice infected with BCG-SSI showed significantly less proliferation and secretion of IL-2, IFN-gamma and IL-17, but secreted higher levels of IL-10 in response to in vitro restimulation with BCG-TB1860 compared to BCG-GFP. Spleens from mice infected with BCG-TB1860 also harboured significantly fewer DC expressing MHC-II, IL-12, IL-2 and TNF-alpha compared to mice infected with BCG-GFP. Glycoproteins of MTB, through their deleterious effects on DC may thus contribute to suppress the generation of a TH1- and TH17-dominated adaptive immune response that is vital for protection against tuberculosis.

An Algebraic Preservation Theorem for Aleph-Zero Categorical Quantified Constraint Satisfaction

23 p. -- An extended abstract of this work appears in the proceedings of the 2012 ACM/IEEE Symposium on Logic in Computer Science