Theory of Non-linear Waves in Multi-dimensions: with Special Reference to Surface Water Waves

The surface water waves are "modal" waves in which the "physical space" (t, x, y, z) is the product of a propagation space (t, x, y) and a cross space, the z-axis in the vertical direction. We have derived a new set of equations for the long waves in shallow water in the propagation space. When the ratio of the amplitude of the disturbance to the depth of the water is small, these equations reduce to the equations derived by Whitham (1967) by the variational principle. Then we have derived a single equation in (t, x, y)-space which is a generalization of the fourth order Boussinesq equation for one-dimensional waves. In the neighbourhood of a wave froat, this equation reduces to the multidimensional generalization of the KdV equation derived by Shen & Keller (1973). We have also included a systematic discussion of the orders of the various non-dimensional parameters. This is followed by a presentation of a general theory of approximating a system of quasi-linear equations following one of the modes. When we apply this general method to the surface water wave equations in the propagation space, we get the Shen-Keller equation.

Increased Efficacies of an Individual Catalytic Site in Clustered Multivalent Dendritic Catalysts

In the studies reported so far on dendrimer-mediated catalysis, the efficacies of the catalytic units were studied and compared primarily across the generations. In order to identify the efficacy of an individual catalytic unit with respect to the number of such units present within a given generation, a series of catalysts were prepared within a generation. Dendrimers incorporated with phosphinemetal complexes were chosen for the study and as many as 11 catalysts within three generations were synthesized. The C-C bond-forming reactions, namely, the Heck and the Suzuki coupling reactions, were then selected to study the catalytic efficiencies of the series of partially and fully phosphine-metal complex functionalized dendrimers. The efficacies of the formation of cinnamate and biphenyl. catalyzed by the dendritic catalysts, were compared. The comparative analyses show that an individual catalytic site is far more effective in its catalytic activity when presented in multiple numbers, i.e., in a multivalent dendritic system, than as a single unit within the same generation, i.e., in a monovalent dendritic system. The study identifies the beneficial effects of the multivalent presentation of the catalytic moieties, both within and across the dendrimer generations.

The C-Terminal Domain of the MutL Homolog from Neisseria gonorrhoeae Forms an Inverted Homodimer

The mismatch repair (MMR) pathway serves to maintain the integrity of the genome by removing mispaired bases from the newly synthesized strand. In E. coli, MutS, MutL and MutH coordinate to discriminate the daughter strand through a mechanism involving lack of methylation on the new strand. This facilitates the creation of a nick by MutH in the daughter strand to initiate mismatch repair. Many bacteria and eukaryotes, including humans, do not possess a homolog of MutH. Although the exact strategy for strand discrimination in these organisms is yet to be ascertained, the required nicking endonuclease activity is resident in the C-terminal domain of MutL. This activity is dependent on the integrity of a conserved metal binding motif. Unlike their eukaryotic counterparts, MutL in bacteria like Neisseria exist in the form of a homodimer. Even though this homodimer would possess two active sites, it still acts a nicking endonuclease. Here, we present the crystal structure of the C-terminal domain (CTD) of the MutL homolog of Neisseria gonorrhoeae (NgoL) determined to a resolution of 2.4 A. The structure shows that the metal binding motif exists in a helical configuration and that four of the six conserved motifs in the MutL family, including the metal binding site, localize together to form a composite active site. NgoL-CTD exists in the form of an elongated inverted homodimer stabilized by a hydrophobic interface rich in leucines. The inverted arrangement places the two composite active sites in each subunit on opposite lateral sides of the homodimer. Such an arrangement raises the possibility that one of the active sites is occluded due to interaction of NgoL with other protein factors involved in MMR. The presentation of only one active site to substrate DNA will ensure that nicking of only one strand occurs to prevent inadvertent and deleterious double stranded cleavage.

Data compression by linear prediction for storage and transmission of EEG signals

The EEG time series has been subjected to various formalisms of analysis to extract meaningful information regarding the underlying neural events. In this paper the linear prediction (LP) method has been used for analysis and presentation of spectral array data for the better visualisation of background EEG activity. It has also been used for signal generation, efficient data storage and transmission of EEG. The LP method is compared with the standard Fourier method of compressed spectral array (CSA) of the multichannel EEG data. The autocorrelation autoregressive (AR) technique is used for obtaining the LP coefficients with a model order of 15. While the Fourier method reduces the data only by half, the LP method just requires the storage of signal variance and LP coefficients. The signal generated using white Gaussian noise as the input to the LP filter has a high correlation coefficient of 0.97 with that of original signal, thus making LP as a useful tool for storage and transmission of EEG. The biological significance of Fourier method and the LP method in respect to the microstructure of neuronal events in the generation of EEG is discussed.

Output-Sensitive Construction of Reeb Graphs

The Reeb graph of a scalar function represents the evolution of the topology of its level sets. This paper describes a near-optimal output-sensitive algorithm for computing the Reeb graph of scalar functions defined over manifolds or non-manifolds in any dimension. Key to the simplicity and efficiency of the algorithm is an alternate definition of the Reeb graph that considers equivalence classes of level sets instead of individual level sets. The algorithm works in two steps. The first step locates all critical points of the function in the domain. Critical points correspond to nodes in the Reeb graph. Arcs connecting the nodes are computed in the second step by a simple search procedure that works on a small subset of the domain that corresponds to a pair of critical points. The paper also describes a scheme for controlled simplification of the Reeb graph and two different graph layout schemes that help in the effective presentation of Reeb graphs for visual analysis of scalar fields. Finally, the Reeb graph is employed in four different applications-surface segmentation, spatially-aware transfer function design, visualization of interval volumes, and interactive exploration of time-varying data.

On the zeta function of a periodic-finite-type shift

Periodic-finite-type shifts (PFT's) are sofic shifts which forbid the appearance of finitely many pre-specified words in a periodic manner. The class of PFT's strictly includes the class of shifts of finite type (SFT's). The zeta function of a PET is a generating function for the number of periodic sequences in the shift. For a general sofic shift, there exists a formula, attributed to Manning and Bowen, which computes the zeta function of the shift from certain auxiliary graphs constructed from a presentation of the shift. In this paper, we derive an interesting alternative formula computable from certain ``word-based graphs'' constructed from the periodically-forbidden word description of the PET. The advantages of our formula over the Manning-Bowen formula are discussed.

Minimal crystallizations of 3-manifolds

We have introduced the weight of a group which has a presentation with number of relations is at most the number of generators. We have shown that the number of facets of any contracted pseudotriangulation of a connected closed 3-manifold M is at least the weight of the fundamental group of M. This lower bound is sharp for the 3-manifolds RP3, L(3, 1), L(5, 2), S-1 x S-1 x S-1, S-2 x S-1, S-2 (x) under bar S-1 and S-3/Q(8), where Q(8) is the quaternion group. Moreover, there is a unique such facet minimal pseudotriangulation in each of these seven cases. We have also constructed contracted pseudotriangulations of L(kq - 1, q) with 4(q + k - 1) facets for q >= 3, k >= 2 and L(kq + 1, q) with 4(q + k) facets for q >= 4, k >= 1. By a recent result of Swartz, our pseudotriangulations of L(kg + 1, q) are facet minimal when kg + 1 are even. In 1979, Gagliardi found presentations of the fundamental group of a manifold M in terms of a contracted pseudotriangulation of M. Our construction is the converse of this, namely, given a presentation of the fundamental group of a 3-manifold M, we construct a contracted pseudotriangulation of M. So, our construction of a contracted pseudotriangulation of a 3-manifold M is based on a presentation of the fundamental group of M and it is computer-free.

A Nonmoving-Part Fluidic Display Using Photoelastic Effect

Digital fluidic and pneumatic systems incorporate displays for the presentation of information to the operator. Displays reported so far for such systems use moving pistons, tapes, and other mechanisms leading to lower reliability. This paper describes a nonmoving part fluidic display employing the photoelastic effect. The display is pressure actuated and has a long life. When fabricated from compatible materials, this device can withstand hostile environments like nuclear radiation, vibrations, etc. The display is compact, economical and is virtually maintenance free. The display unit has been tested in the laboratory for reliability and speed of response.

A CD8(+) T cell clone specific for antigen also recognizes peptidomimics present in anti-idiotypic antibody: Implications for T cell memory

The relay hypothesis [R. Nayak, S. Mitra-Kaushik, M.S. Shaila, Perpetuation of immunological memory: a relay hypothesis, Immunology 102 (2001) 387-395] was earlier proposed to explain perpetuation of immunological memory without requiring long lived memory cells or persisting antigen. This hypothesis envisaged cycles of interaction and proliferation of complementary idiotypic B cells (Burnet cells) and anti-idiotypic B cells (Jerne cells) as the primary reason for perpetuation of immunological memory. The presence of pepti-domimics of antigen in anti-idiotypic antibody and their presentation to antigen specific T cells was postulated to be primary reason for perpetuation of T cell memory. Using a viral hemagglutinin as a model, in this work, we demonstrate the presence of peptidomimics in the variable region of ail anti-idiotypic antibody capable of functionally mimicking the antigen derived peptides. A CD8(+) CTL clone was generated against the hemagglutinin protein which specifically responds to either peptidomimic synthesizing cells or peptidomimic pulsed antigen presenting cells. Thus, it appears reasonable that a population of activated antigen specific T cells is maintained in the body by presentation of peptidomimic through Jerne cells and other antigen presenting cells long after immunization. (C) 2007 Elsevier Inc. All rights reserved.

Nitride synthesis using ammonia and hydrazine - a thermodynamic panorama

Because of the wide variety of projected applications of ultrapure nitrides in advanced technologies, there is interest in developing new cost-effective methods of synthesis. Explored in this study is the use of ammonia and hydrazine for the synthesis of nitrides from oxides, sulfides and chlorides. Even when the standard Gibbs energy change for the nitridation reactions involved are moderately positive, the reaction can be made to proceed by lowering the partial pressure of the product gas below its equilibrium value. Use of a metastable form of precursor in the nanometric size range is an alternative method to facilitate nitridation. Ellingham-Richardson-Jeffes diagrams are used for a panoramic presentation of the driving force for each set of reactions as a function of temperature. Oxides are the least promising precursors for nitride synthesis; sulfides offer a larger synthetic window for many useful nitrides such as BN, AlN, InN, VN, TiN, ThN and Si3N4. The standard Gibbs free energy changes for reactions involving chlorides with either ammonia or hydrazine are much more negative. Hydrazine is a more powerful nitriding agent than ammonia. The metastability of hydrazine requires that it be introduced into a reactor through a water-cooled lance. The use of volatile halides with ammonia or hydrazine offers the potential for synthesis of pure and doped nanocrystalline nitrides. Nitride thin films can also be prepared by suitable adaptations of the chloride route. (C) 2002 Kluwer Academic Publishers.

Nitric oxide and KLF4 protein epigenetically modify class II transactivator to repress Major histocompatibility complex II expression during Mycobacterium bovis Bacillus Calmette-Guerin infection

Pathogenic mycobacteria employ several immune evasion strategies such as inhibition of class II transactivator (CIITA) and MHC-II expression, to survive and persist in host macrophages. However, precise roles for specific signaling components executing down-regulation of CIITA/MHC-II have not been adequately addressed. Here, we demonstrate that Mycobacterium bovis bacillus Calmette-Guerin (BCG)-mediated TLR2 signaling-induced iNOS/NO expression is obligatory for the suppression of IFN-gamma-induced CIITA/MHC-II functions. Significantly, NOTCH/PKC/MAPK-triggered signaling cross-talk was found critical for iNOS/NO production. NO responsive recruitment of a bifunctional transcription factor, KLF4, to the promoter of CIITA during M. bovis BCG infection of macrophages was essential to orchestrate the epigenetic modifications mediated by histone methyltransferase EZH2 or miR-150 and thus calibrate CIITA/MHC-II expression. NO-dependent KLF4 regulated the processing and presentation of ovalbumin by infected macrophages to reactive T cells. Altogether, our study delineates a novel role for iNOS/NO/KLF4 in dictating the mycobacterial capacity to inhibit CIITA/MHC-II-mediated antigen presentation by infected macrophages and thereby elude immune surveillance.

Whole exome sequencing in an Indian family links Coats plus syndrome and dextrocardia with a homozygous novel CTC1 and a rare HES7 variation

Background: Coats plus syndrome is an autosomal recessive, pleiotropic, multisystem disorder characterized by retinal telangiectasia and exudates, intracranial calcification with leukoencephalopathy and brain cysts, osteopenia with predisposition to fractures, bone marrow suppression, gastrointestinal bleeding and portal hypertension. It is caused by compound heterozygous mutations in the CTC1 gene. Case presentation: We encountered a case of an eight-year old boy from an Indian family with manifestations of Coats plus syndrome along with an unusual occurrence of dextrocardia and situs inversus. Targeted resequencing of the CTC1 gene as well as whole exome sequencing (WES) were conducted in this family to identify the causal variations. The identified candidate variations were screened in ethnicity matched healthy controls. The effect of CTC1 variation on telomere length was assessed using Southern blot. A novel homozygous missense mutation c.1451A > C (p.H484P) in exon 9 of the CTC1 gene and a rare 3'UTR known dbSNP variation (c.*556 T > C) in HES7 were identified as the plausible candidates associated with this complex phenotype of Coats plus and dextrocardia. This CTC1 variation was absent in the controls and we also observed a reduced telomere length in the affected individual's DNA, suggesting its likely pathogenic nature. The reported p.H484P mutation is located in the N-terminal 700 amino acid regionthat is important for the binding of CTC1 to ssDNA through its two OB domains. WES data also showed a rare homozygous missense variation in the TEK gene in the affected individual. Both HES7 and TEK are targets of the Notch signaling pathway. Conclusions: This is the first report of a genetically confirmed case of Coats plus syndrome from India. By means of WES, the genetic variations in this family with unique and rare complex phenotype could be traced effectively. We speculate the important role of Notch signaling in this complex phenotypic presentation of Coats plus syndrome and dextrocardia. The present finding will be useful for genetic diagnosis and carrier detection in the family and for other patients with similar disease manifestations.

Do we see what we should see? Describing non-covalent interactions in protein structures including precision

The power of X-ray crystal structure analysis as a technique is to `see where the atoms are'. The results are extensively used by a wide variety of research communities. However, this `seeing where the atoms are' can give a false sense of security unless the precision of the placement of the atoms has been taken into account. Indeed, the presentation of bond distances and angles to a false precision (i.e. to too many decimal places) is commonplace. This article has three themes. Firstly, a basis for a proper representation of protein crystal structure results is detailed and demonstrated with respect to analyses of Protein Data Bank entries. The basis for establishing the precision of placement of each atom in a protein crystal structure is non-trivial. Secondly, a knowledge base harnessing such a descriptor of precision is presented. It is applied here to the case of salt bridges, i.e. ion pairs, in protein structures; this is the most fundamental place to start with such structure-precision representations since salt bridges are one of the tenets of protein structure stability. Ion pairs also play a central role in protein oligomerization, molecular recognition of ligands and substrates, allosteric regulation, domain motion and alpha-helix capping. A new knowledge base, SBPS (Salt Bridges in Protein Structures), takes these structural precisions into account and is the first of its kind. The third theme of the article is to indicate natural extensions of the need for such a description of precision, such as those involving metalloproteins and the determination of the protonation states of ionizable amino acids. Overall, it is also noted that this work and these examples are also relevant to protein three-dimensional structure molecular graphics software.