Infinitely divisible metrics and curvature inequalities for operators in the Cowen-Douglas class

The curvature (T)(w) of a contraction T in the Cowen-Douglas class B-1() is bounded above by the curvature (S*)(w) of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. In this paper, we characterize a slightly smaller class of contractions using a stronger form of the curvature inequality. Along the way, we find conditions on the metric of the holomorphic Hermitian vector bundle E-T corresponding to the operator T in the Cowen-Douglas class B-1() which ensures negative definiteness of the curvature function. We obtain a generalization for commuting tuples of operators in the class B-1() for a bounded domain in C-m.

Frequency Domain Based Solution for Certain Class of Wave Equations: An exhaustive study of Numerical Solutions

The paper discusses the frequency domain based solution for a certain class of wave equations such as: a second order partial differential equation in one variable with constant and varying coefficients (Cantilever beam) and a coupled second order partial differential equation in two variables with constant and varying coefficients (Timoshenko beam). The exact solution of the Cantilever beam with uniform and varying cross-section and the Timoshenko beam with uniform cross-section is available. However, the exact solution for Timoshenko beam with varying cross-section is not available. Laplace spectral methods are used to solve these problems exactly in frequency domain. The numerical solution in frequency domain is done by discretisation in space by approximating the unknown function using spectral functions like Chebyshev polynomials, Legendre polynomials and also Normal polynomials. Different numerical methods such as Galerkin Method, Petrov- Galerkin method, Method of moments and Collocation method or the Pseudo-spectral method in frequency domain are studied and compared with the available exact solution. An approximate solution is also obtained for the Timoshenko beam with varying cross-section using Laplace Spectral Element Method (LSEM). The group speeds are computed exactly for the Cantilever beam and Timoshenko beam with uniform cross-section and is compared with the group speeds obtained numerically. The shear mode and the bending modes of the Timoshenko beam with uniform cross-section are separated numerically by applying a modulated pulse as the shear force and the corresponding group speeds for varying taper parameter in are obtained numerically by varying the frequency of the input pulse. An approximate expression for calculating group speeds corresponding to the shear mode and the bending mode, and also the cut-off frequency is obtained. Finally, we show that the cut-off frequency disappears for large in, for epsilon > 0 and increases for large in, for epsilon < 0.

Beadex Function in the Motor Neurons Is Essential for Female Reproduction in Drosophila melanogaster

Drosophila melanogaster has served as an excellent model system for understanding the neuronal circuits and molecular mechanisms regulating complex behaviors. The Drosophila female reproductive circuits, in particular, are well studied and can be used as a tool to understand the role of novel genes in neuronal function in general and female reproduction in particular. In the present study, the role of Beadex, a transcription co-activator, in Drosophila female reproduction was assessed by generation of mutant and knock down studies. Null allele of Beadex was generated by transposase induced excision of P-element present within an intron of Beadex gene. The mutant showed highly compromised reproductive abilities as evaluated by reduced fecundity and fertility, abnormal oviposition and more importantly, the failure of sperm release from storage organs. However, no defect was found in the overall ovariole development. Tissue specific, targeted knock down of Beadex indicated that its function in neurons is important for efficient female reproduction, since its neuronal knock down led to compromised female reproductive abilities, similar to Beadex null females. Further, different neuronal class specific knock down studies revealed that Beadex function is required in motor neurons for normal fecundity and fertility of females. Thus, the present study attributes a novel and essential role for Beadex in female reproduction through neurons.

Exact Phase Retrieval for a Class of 2-D Parametric Signals

We address the problem of two-dimensional (2-D) phase retrieval from magnitude of the Fourier spectrum. We consider 2-D signals that are characterized by first-order difference equations, which have a parametric representation in the Fourier domain. We show that, under appropriate stability conditions, such signals can be reconstructed uniquely from the Fourier transform magnitude. We formulate the phase retrieval problem as one of computing the parameters that uniquely determine the signal. We show that the problem can be solved by employing the annihilating filter method, particularly for the case when the parameters are distinct. For the more general case of the repeating parameters, the annihilating filter method is not applicable. We circumvent the problem by employing the algebraically coupled matrix pencil (ACMP) method. In the noiseless measurement setup, exact phase retrieval is possible. We also establish a link between the proposed analysis and 2-D cepstrum. In the noisy case, we derive Cramer-Rao lower bounds (CRLBs) on the estimates of the parameters and present Monte Carlo performance analysis as a function of the noise level. Comparisons with state-of-the-art techniques in terms of signal reconstruction accuracy show that the proposed technique outperforms the Fienup and relaxed averaged alternating reflections (RAAR) algorithms in the presence of noise.

Structure-function studies of serine hydrolases: synthesis of a gene for ∝-lytic protease and the purification and characterization of a mutant β-lactamase

The author has constructed a synthetic gene for ∝-lytic protease. Since the DNA sequence of the protein is not known, the gene was designed by using the reverse translation of ∝-lytic protease's amino acid sequence. Unique restriction sites are carefully sought in the degenerate DNA sequence to aid in future mutagenesis studies. The unique restriction sites are designed approximately 50 base pairs apart and their appropriate codons used in the DNA sequence. The codons used to construct the DNA sequence of ∝-lytic protease are preferred codons in E-coli or used in the production of β-lactamase. Codon usage is also distributed evenly to ensure that one particular codon is not heavily used. The gene is essentially constructed from the outside in. The gene is built in a stepwise fashion using plasmids as the vehicles for the ∝-lytic oligomers. The use of plasmids allows the replication and isolation of large quantities of the intermediates during gene synthesis. The ∝-lytic DNA is a double-stranded oligomer that has sufficient overhang and sticky ends to anneal correctly in the vector. After six steps of incorporating ∝-lytic DNA, the gene is completed and sequenced to ensure that the correct DNA sequence is present and that no mutations occurred in the structural gene.

β-lactamase is the other serine hydrolase studied in this thesis. The author used the class A RTEM-1 β- lactamase encoded on the plasmid pBR322 to investigate the roll of the conserved threonine residue at position 71. Cassette mutagenesis was previously used to generate all possible amino acid substitutions at position 71. The work presented here describes the purification and kinetic characterization of a T71H mutant previously constructed by S. Schultz. The mutated gene was transferred into plasmid pJN for expression and induced with IPTG. The enzyme is purified by column chromatography and FPLC to homogeneity. Kinetic studies reveal that the mutant has lower k_(cat) values on benzylpenicillin, cephalothin and 6-aminopenicillanic acid but no changes in k_m except for cephalothin which is approximately 4 times higher. The mutant did not change siginificantly in its pH profile compared to the wild-type enzyme. Also, the mutant is more sensitive to thermal denaturation as compared to the wild-type enzyme. However, experimental evidence indicates that the probable generation of a positive charge at position 71 thermally stabilized the mutant.

Edge function method applied to thin plates resting on Winkler foundation

The Edge Function method formerly developed by Quinlan⁽²⁵⁾ is applied to solve the problem of thin elastic plates resting on spring supported foundations subjected to lateral loads the method can be applied to plates of any convex polygonal shapes, however, since most plates are rectangular in shape, this specific class is investigated in this thesis. The method discussed can also be applied easily to other kinds of foundation models (e.g. springs connected to each other by a membrane) as long as the resulting differential equation is linear. In chapter VII, solution of a specific problem is compared with a known solution from literature. In chapter VIII, further comparisons are given. The problems of concentrated load on an edge and later on a corner of a plate as long as they are far away from other boundaries are also given in the chapter and generalized to other loading intensities and/or plates springs constants for Poisson's ratio equal to 0.2

MicroRNA-132 is a physiological regulator of hematopoietic stem cell function and B-cell development

MicroRNAs are a class of small non-coding RNAs that negatively regulate gene expression. Several microRNAs have been implicated in altering hematopoietic cell fate decisions. Importantly, deregulation of many microRNAs can lead to deleterious consequences in the hematopoietic system, including the onset of cancer, autoimmunity, or a failure to respond effectively to infection. As such, microRNAs fine-tune the balance between normal hematopoietic output and pathologic consequences. In this work, we explore the role of two microRNAs, miR-132 and miR-125b, in regulating hematopoietic stem cell (HSC) function and B cell development. In particular, we uncover the role of miR-132 in maintaining the appropriate balance between self-renewal, differentiation, and survival in aging HSCs by buffering the expression of a critical transcription factor, FOXO3. By maintain this balance, miR-132 may play a critical role in preventing aging-associated hematopoietic conditions such as autoimmune disease and cancer. We also find that miR-132 plays a critical role in B cell development by targeting a key transcription factor, Sox4, that is responsible for the differentiation of pro-B cells into pre-B cells. We find that miR-132 regulates B cell apoptosis, and by delivering miR-132 to mice that are predisposed to developing B cell cancers, we can inhibit the formation of these cancers and improve the survival of these mice. In addition to miR-132, we uncovered the role of another critical microRNA, miR-125b, that potentiates hematopoietic stem cell function. We found that enforced expression of miR-125b causes an aggressive myeloid leukemia by downregulation of its target Lin28a. Importantly, miR-125b also plays a critical role in inhibiting the formation of pro-B cells. Thus, we have discovered two microRNAs with important roles in regulating normal hematopoiesis, and whose dregulation can lead to deleterious consequences such as cancer in the aging hematopoietic system. Both miR-132 and miR-125b may therefore be targeted for therapeutics to inhibit age-related immune diseases associated with the loss of HSC function and cancer progression.

Major histocompatibility complex class I involvement in the rejection of allogeneic erythrocytes in rainbow trout (Oncorhynchus mykiss)

Major histocompatibility complex genes are thought to be involved in allogeneic graft rejection but not many reports are available on their functional analysis in fish. Analysis of available sequences of MHC genes suggests functions in antigen presentation similar to those found in higher vertebrates. In mammals, the MHC class I and class II molecules are major determinants of allogeneic graft rejection due to their polymorphism in conjunction with their antigen presenting function. In fish, MHC class H molecules are found to be involved in rejection of allogeneic scale grafts. The present study was designed to investigate the involvement of MHC class I molecules in allograft rejection. Erythrocytes were collected from donors of rainbow trout expressed different class MHC class I alleles, stained with two dyes, mixed and grafted to the recipients that were of the same sibling group as the donors. The grafts were rejected by allogeneic recipients and the MHC class I linkage group was the major determinant for the rejection.

Confirmation of Data Mining Based Predictions of Protein Function

King, R. D. and Wise, P. H. and Clare, A. (2004) Confirmation of Data Mining Based Predictions of Protein Function. Bioinformatics 20(7), 1110-1118

Machine learning of functional class from phenotype data

Clare, A. and King R.D. (2002) Machine learning of functional class from phenotype data. Bioinformatics 18(1) 160-166

A fast, streaming SIMD extensions 2, logistic squashing function

Schraudolph proposed an excellent exponential approximation providing increased performance particularly suited to the logistic squashing function used within many neural networking applications. This note applies Intel's streaming SIMD Extensions 2 (SSE2), where SIMD is single instruction multiple data, of the Pentum IV class processor to Schraudolph's technique, further increasing the performance of the logistic squashing function. It was found that the calculation of the new 32-bit SSE2 logistic squashing function described here was up to 38 times faster than the conventional exponential function and up to 16 times faster than a Schraudolph-style 32-bit method on an Intel Pentum D 3.6 GHz CPU.

The Impact of Polystyrene Microplastics on Feeding, Function and Fecundity in the Marine CopepodCalanus helgolandicus

Microscopic plastic debris, termed “microplastics”, are of increasing environmental concern. Recent studies have demonstrated that a range of zooplankton, including copepods, can ingest microplastics. Copepods are a globally abundant class of zooplankton that form a key trophic link between primary producers and higher trophic marine organisms. Here we demonstrate that ingestion of microplastics can significantly alter the feeding capacity of the pelagic copepod Calanus helgolandicus. Exposed to 20 μm polystyrene beads (75 microplastics mL–1) and cultured algae ([250 μg C L–1) for 24 h, C. helgolandicus ingested 11% fewer algal cells (P = 0.33) and 40% less carbon biomass (P < 0.01). There was a net downward shift in the mean size of algal prey consumed (P < 0.001), with a 3.6 fold increase in ingestion rate for the smallest size class of algal prey (11.6–12.6 μm), suggestive of postcapture or postingestion rejection. Prolonged exposure to polystyrene microplastics significantly decreased reproductive output, but there were no significant differences in egg production rates, respiration or survival. We constructed a conceptual energetic (carbon) budget showing that microplastic-exposed copepods suffer energetic depletion over time. We conclude that microplastics impede feeding in copepods, which over time could lead to sustained reductions in ingested carbon biomass.

Limits of life in hostile environments: no barriers to biosphere function?

Environments that are hostile to life are characterized by reduced microbial activity which results in poor soil- and plant-health, low biomass and biodiversity, and feeble ecosystem development. Whereas the functional biosphere may primarily be constrained by water activity (a w) the mechanism(s) by which this occurs have not been fully elucidated. Remarkably we found that, for diverse species of xerophilic fungi at a w values of = 0.72, water activity per se did not limit cellular function. We provide evidence that chaotropic activity determined their biotic window, and obtained mycelial growth at water activities as low as 0.647 (below that recorded for any microbial species) by addition of compounds that reduced the net chaotropicity. Unexpectedly we found that some fungi grew optimally under chaotropic conditions, providing evidence for a previously uncharacterized class of extremophilic microbes. Further studies to elucidate the way in which solute activities interact to determine the limits of life may lead to enhanced biotechnological processes, and increased productivity of agricultural and natural ecosystems in arid and semiarid regions.

Divergence of chemical function in the alkaline phosphatase superfamily: Structure and mechanism of the P-C bond cleaving enzyme phosphonoacetate hydrolase

Phosphonates constitute a class of natural products that mimic the properties of the more common organophosphate ester metabolite yet are not readily degraded owing to the direct linkage of the phosphorus atom to the carbon atom. Phosphonate hydrolases have evolved to allow bacteria to utilize environmental phosphonates as a source of carbon and phosphorus. The work reported in this paper examines one such enzyme, phosphonoacetate hydrolase. By using a bioinformatic approach, we circumscribed the biological range of phosphonoacetate hydrolase to a select group of bacterial species from different classes of Proteobacteria. In addition, using gene context, we identified a novel 2-aminoethylphosphonate degradation pathway in which phosphonoacetate hydrolase is a participant. The X-ray structure of phosphonoformate-bound phosphonoacetate hydrolase was determined to reveal that this enzyme is most closely related to nucleotide pyrophosphatase/diesterase, a promiscuous two-zinc ion metalloenzyme of the alkaline phosphatase enzyme superfamily. The X-ray structure and metal ion specificity tests showed that phosphonoacetate hydrolase is also a two-zinc ion metalloenzyme. By using site-directed mutagenesis and P-32-labeling strategies, the catalytic nucleophile was shown to be Thr64. A structure-guided, site-directed mutation-based inquiry of the catalytic contributions of active site residues identified Lys126 and Lys128 as the most likely candidates for stabilization of the aci-carboxylate dianion leaving group. A catalytic mechanism is proposed which combines Lys12/Lys128 leaving group stabilization with zinc ion activation of the Thr64 nucleophile and the substrate phosphoryl group.

Observations of enhanced extreme ultraviolet continua during an X-class solar flare using SDO/EVE.

Observations of extreme ultraviolet (EUV) emission from an X-class solar flare that occurred on 2011 February 15 at 01: 44 UT are presented, obtained using the EUV Variability Experiment (EVE) on board the Solar Dynamics Observatory. The complete EVE spectral range covers the free-bound continua of H I (Lyman continuum), He I, and He II, with recombination edges at 91.2, 50.4, and 22.8 nm, respectively. By fitting the wavelength ranges blueward of each recombination edge with an exponential function, light curves of each of the integrated continua were generated over the course of the flare, as was emission from the free-free continuum (6.5-37 nm). The He II 30.4 nm and Ly alpha 121.6 nm lines, and soft X-ray (SXR; 0.1-0.8 nm) emission from GOES are also included for comparison. Each free-bound continuum was found to have a rapid rise phase at the flare onset similar to that seen in the 25-50 keV light curves from RHESSI, suggesting that they were formed by recombination with free electrons in the chromosphere. However, the free-free emission exhibited a slower rise phase seen also in the SXR emission from GOES, implying a predominantly coronal origin. By integrating over the entire flare the total energy emitted via each process was determined. We find that the flare energy in the EVE spectral range amounts to at most a few percent of the total flare energy, but EVE gives us a first comprehensive look at these diagnostically important continuum components.