Mesh-free approximations via the error reproducing kernel method and applications to nonlinear systems developing shocks

Error estimates for the error reproducing kernel method (ERKM) are provided. The ERKM is a mesh-free functional approximation scheme [A. Shaw, D. Roy, A NURBS-based error reproducing kernel method with applications in solid mechanics, Computational Mechanics (2006), to appear (available online)], wherein a targeted function and its derivatives are first approximated via non-uniform rational B-splines (NURBS) basis function. Errors in the NURBS approximation are then reproduced via a family of non-NURBS basis functions, constructed using a polynomial reproduction condition, and added to the NURBS approximation of the function obtained in the first step. In addition to the derivation of error estimates, convergence studies are undertaken for a couple of test boundary value problems with known exact solutions. The ERKM is next applied to a one-dimensional Burgers equation where, time evolution leads to a breakdown of the continuous solution and the appearance of a shock. Many available mesh-free schemes appear to be unable to capture this shock without numerical instability. However, given that any desired order of continuity is achievable through NURBS approximations, the ERKM can even accurately approximate functions with discontinuous derivatives. Moreover, due to the variation diminishing property of NURBS, it has advantages in representing sharp changes in gradients. This paper is focused on demonstrating this ability of ERKM via some numerical examples. Comparisons of some of the results with those via the standard form of the reproducing kernel particle method (RKPM) demonstrate the relative numerical advantages and accuracy of the ERKM.

On the growth of the Bergman kernel near an infinite-type point

We study diagonal estimates for the Bergman kernels of certain model domains in C-2 near boundary points that are of infinite type. To do so, we need a mild structural condition on the defining functions of interest that facilitates optimal upper and lower bounds. This is a mild condition; unlike earlier studies of this sort, we are able to make estimates for non-convex pseudoconvex domains as well. Thisn condition quantifies, in some sense, how flat a domain is at an infinite-type boundary point. In this scheme of quantification, the model domains considered below range-roughly speaking-from being mildly infinite-type'' to very flat at the infinite-type points.

Kernel-based spatial-color modeling for fast moving object tracking

Visual tracking has been a challenging problem in computer vision over the decades. The applications of Visual Tracking are far-reaching, ranging from surveillance and monitoring to smart rooms. Mean-shift (MS) tracker, which gained more attention recently, is known for tracking objects in a cluttered environment and its low computational complexity. The major problem encountered in histogram-based MS is its inability to track rapidly moving objects. In order to track fast moving objects, we propose a new robust mean-shift tracker that uses both spatial similarity measure and color histogram-based similarity measure. The inability of MS tracker to handle large displacements is circumvented by the spatial similarity-based tracking module, which lacks robustness to object's appearance change. The performance of the proposed tracker is better than the individual trackers for tracking fast-moving objects with better accuracy.

THE BERGMAN KERNEL FUNCTION

In this note, we point out that a large family of n x n matrix valued kernel functions defined on the unit disc D subset of C, which were constructed recently in [9], behave like the familiar Bergman kernel function on ID in several different ways. We show that a number of questions involving the multiplication operator on the corresponding Hilbert space of holomorphic functions on D can be answered using this likeness.

A fast dual algorithm for kernel logistic regression

This paper gives a new iterative algorithm for kernel logistic regression. It is based on the solution of a dual problem using ideas similar to those of the Sequential Minimal Optimization algorithm for Support Vector Machines. Asymptotic convergence of the algorithm is proved. Computational experiments show that the algorithm is robust and fast. The algorithmic ideas can also be used to give a fast dual algorithm for solving the optimization problem arising in the inner loop of Gaussian Process classifiers.

Observation of a power-law memory kernel for fluctuations within a single protein molecule

The fluctuation of the distance between a fluorescein-tyrosine pair within a single protein complex was directly monitored in real time by photoinduced electron transfer and found to be a stationary, time-reversible, and non-Markovian Gaussian process. Within the generalized Langevin equation formalism, we experimentally determine the memory kernel K(t), which is proportional to the autocorrelation function of the random fluctuating force. K(t) is a power-law decay, t(-0.51 +/- 0.07) in a broad range of time scales (10(-3)-10 s). Such a long-time memory effect could have implications for protein functions.

A Safe Vaccine (DV-STM-07) against Salmonella Infection Prevents Abortion and Confers Protective Immunity to the Pregnant and New Born Mice

Pregnancy is a transient immuno-compromised condition which has evolved to avoid the immune rejection of the fetus by the maternal immune system. The altered immune response of the pregnant female leads to increased susceptibility to invading pathogens, resulting in abortion and congenital defects of the fetus and a subnormal response to vaccination. Active vaccination during pregnancy may lead to abortion induced by heightened cell mediated immune response. In this study, we have administered the highly attenuated vaccine strain delta pmrG-HM-D (DV-STM-07) in female mice before the onset of pregnancy and followed the immune reaction against challenge with virulent S. Typhimurium in pregnant mice. Here we demonstrate that DV-STM-07 vaccine gives protection against Salmonella in pregnant mice and also prevents Salmonella induced abortion. This protection is conferred by directing the immune response towards Th2 activation and Th1 suppression. The low Th1 response prevents abortion. The use of live attenuated vaccine just before pregnancy carries the risk of transmission to the fetus. We have shown that this vaccine is safe as the vaccine strain is quickly eliminated from the mother and is not transmitted to the fetus. This vaccine also confers immunity to the new born mice of vaccinated mothers. Since there is no evidence of the vaccine candidate reaching the new born mice, we hypothesize that it may be due to trans-colostral transfer of protective anti-Salmonella antibodies. These results suggest that our vaccine DV-STM-07 can be very useful in preventing abortion in the pregnant individuals and confer immunity to the new born. Since there are no such vaccine candidates which can be given to the new born and to the pregnant women, this vaccine holds a very bright future to combat Salmonella induced pregnancy loss.

Proteomics of Trypanosoma evansi Infection in Rodents

Background: Trypanosoma evansi infections, commonly called 'surra', cause significant economic losses to livestock industry. While this infection is mainly restricted to large animals such as camels, donkeys and equines, recent reports indicate their ability to infect humans. There are no World Animal Health Organization (WAHO) prescribed diagnostic tests or vaccines available against this disease and the available drugs show significant toxicity. There is an urgent need to develop improved methods of diagnosis and control measures for this disease. Unlike its related human parasites T. brucei and T. cruzi whose genomes have been fully sequenced T. evansi genome sequence remains unavailable and very little efforts are being made to develop improved methods of prevention, diagnosis and treatment. With a view to identify potential diagnostic markers and drug targets we have studied the clinical proteome of T. evansi infection using mass spectrometry (MS).Methodology/Principal Findings: Using shot-gun proteomic approach involving nano-lc Quadrupole Time Of Flight (QTOF) mass spectrometry we have identified over 160 proteins expressed by T. evansi in mice infected with camel isolate. Homology driven searches for protein identification from MS/MS data led to most of the matches arising from related Trypanosoma species. Proteins identified belonged to various functional categories including metabolic enzymes; DNA metabolism; transcription; translation as well as cell-cell communication and signal transduction. TCA cycle enzymes were strikingly missing, possibly suggesting their low abundances. The clinical proteome revealed the presence of known and potential drug targets such as oligopeptidases, kinases, cysteine proteases and more.Conclusions/Significance: Previous proteomic studies on Trypanosomal infections, including human parasites T. brucei and T. cruzi, have been carried out from lab grown cultures. For T. evansi infection this is indeed the first ever proteomic study reported thus far. In addition to providing a glimpse into the biology of this neglected disease, our study is the first step towards identification of diagnostic biomarkers, novel drug targets as well as potential vaccine candidates to fight against T. evansi infections.

The heat kernel on AdS(3) and its applications

We derive the heat kernel for arbitrary tensor fields on S-3 and (Euclidean) AdS(3) using a group theoretic approach. We use these results to also obtain the heat kernel on certain quotients of these spaces. In particular, we give a simple, explicit expression for the one loop determinant for a field of arbitrary spin s in thermal AdS(3). We apply this to the calculation of the one loop partition function of N = 1 supergravity on AdS(3). We find that the answer factorizes into left- and right-moving super Virasoro characters built on the SL(2, C) invariant vacuum, as argued by Maloney and Witten on general grounds.

Change in spectrum of Brownian fluctuations of optically trapped red blood cells due to malarial infection

We study the properties of single red blood cells (RBCs) held in an optical-tweezers trap. We observe a change in the spectrum of Brownian fluctuations between RBCs from normal and malaria-infected samples. The change, caused by infection-induced structural changes in the cell, appears as a statistical increase in the mean (by 25%) and standard deviation (by 200%) of the corner frequency measured over similar to 100 cells. The increase is observed even though the ensemble of cells being measured consists mostly of cells that do not actually host the parasite, but are from an infected pool. This bystander effect appears to vindicate other observations that infected cells can affect the biomechanical properties of uninfected cells. The change is also observed to be independent of the stage of infection and its duration, highlighting its potential for disease detection. (C) 2010 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.3427142].

Pharmacokinetics and chemotherapeutic efficacy of adriamycin encapsulated in immunoliposomes against avian myeloblastosis virus infection

Immunoliposomes were prepared using rabbit anti-AMV gp80 IgG for the targeted chemotherapy of avian myeloblastosis virus infection. Adriamycin was encapsulated into immunoliposomes and used for in vivo studies. Comparative pharmacokinetics of free drug, drug encapsulated in free liposomes and of drug encapsulated in immunoliposomes in the virus-infected cells revealed that (i) the drug encapsulated in liposomes was cleared from the plasma slowly, and (ii) the drug encapsulated in immunoliposomes accumulated in the target tissue, the bone marrow, 5- and 8.5-fold more than the drug encapsulated in free liposomes and free drug, respectively. The drug encapsulated in immunoliposomes inactivated the virus and exhibited more chemotherapeutic efficacy as compared to controls when injected up to 24 h post-infection. However, when injected 48 h post-infection the drug encapsulated in immunoliposomes did not offer any protection against the virus infection. There is no detectable antibody response against immunoliposomes in the infected animals.

Confirmation of pauling's theory that vitamin C improves immunity to infection

It is pointed out that the complement Clq, associated with the immune response system, has a part containing about 80 residues with a collagen-like sequence, with Gly at every third location and having also a number of Hyp and Hyl residues in locations before Gly, and that it takes the triple-helical conformation characteristic of collagen. As with collagen biosynthesis, ascorbic acid is therefore expected to be required for its production. Also, collagen itself, in the extracellular matrix, is connected with the fibroblast surface protein (FSP), whose absence leads to cell proliferation, and whose addition leads to suppression of malignancy in tissue culture. All these show the great importance of vitamin C for resistance to diseases, and even to cancer, as has been widely advocated by Pauling.

Visiting the cell biology of Salmonella infection

Salmonella, a Gram-negative facultative intracellular pathogen is capable of infecting vast array of hosts. The striking ability of Salmonella to overcome every hurdle encountered in the host proves that they are true survivors. In the host, Salmonella infects various cell types and needs to survive and replicate by countering the defense mechanism of the specific cell. In this review, we will summarize the recent insights into the cell biology of Salmonella infection. Here, we will focus on the findings that deal with the specific mechanism of various cell types to control Salmonella infection. Further, the survival strategies of the pathogen in response to the host immunity will also be discussed in detail. Better understanding of the mechanisms by which Salmonella evade the host defense system and establish pathogenesis will be critical in disease management. (C) 2010 Institut Pasteur. Published by Elsevier Masson SAS. All rights reserved.

Solution concepts in continuous-kernel multicriteria games

This paper considers nonzero-sum multicriteria games with continuous kernels. Solution concepts based on the notions of Pareto optimality, equilibrium, and security are extended to these games. Separate necessary and sufficient conditions and existence results are presented for equilibrium, Pareto-optimal response, and Pareto-optimal security strategies of the players.

A Smooth Finite Element Method Based on Reproducing Kernel DMS-Splines

The element-based piecewise smooth functional approximation in the conventional finite element method (FEM) results in discontinuous first and higher order derivatives across element boundaries Despite the significant advantages of the FEM in modelling complicated geometries, a motivation in developing mesh-free methods has been the ease with which higher order globally smooth shape functions can be derived via the reproduction of polynomials There is thus a case for combining these advantages in a so-called hybrid scheme or a `smooth FEM' that, whilst retaining the popular mesh-based discretization, obtains shape functions with uniform C-p (p >= 1) continuity One such recent attempt, a NURBS based parametric bridging method (Shaw et al 2008b), uses polynomial reproducing, tensor-product non-uniform rational B-splines (NURBS) over a typical FE mesh and relies upon a (possibly piecewise) bijective geometric map between the physical domain and a rectangular (cuboidal) parametric domain The present work aims at a significant extension and improvement of this concept by replacing NURBS with DMS-splines (say, of degree n > 0) that are defined over triangles and provide Cn-1 continuity across the triangle edges This relieves the need for a geometric map that could precipitate ill-conditioning of the discretized equations Delaunay triangulation is used to discretize the physical domain and shape functions are constructed via the polynomial reproduction condition, which quite remarkably relieves the solution of its sensitive dependence on the selected knotsets Derivatives of shape functions are also constructed based on the principle of reproduction of derivatives of polynomials (Shaw and Roy 2008a) Within the present scheme, the triangles also serve as background integration cells in weak formulations thereby overcoming non-conformability issues Numerical examples involving the evaluation of derivatives of targeted functions up to the fourth order and applications of the method to a few boundary value problems of general interest in solid mechanics over (non-simply connected) bounded domains in 2D are presented towards the end of the paper