The Noether-Lefschetz theorem for the divisor class group

Let X be a normal projective threefold over a field of characteristic zero and vertical bar L vertical bar be a base-point free, ample linear system on X. Under suitable hypotheses on (X, vertical bar L vertical bar), we prove that for a very general member Y is an element of vertical bar L vertical bar, the restriction map on divisor class groups Cl(X) -> Cl(Y) is an isomorphism. In particular, we are able to recover the classical Noether-Lefschetz theorem, that a very general hypersurface X subset of P-C(3) of degree >= 4 has Pic(X) congruent to Z.

Synthesis of new 4-isopropylthiazole hydrazide analogs and some derived clubbed triazole, oxadiazole ring systems - A novel class of potential antibacterial, antifungal and antitubercular agents

In the present study a series of 4-isopropylthiazole-2-carbohydrazide analogs, derived clubbed oxadiazole-thiazole and triazole-thiazole derivatives have been synthesized and characterized by IR, H-1 NMR, C-13 NMR, elemental and mass spectral analyses. The synthesized compounds were evaluated for their preliminary in vitro antibacterial, antifungal and antitubercular activity against Mycobacterium tuberculosis H(37)Rv strain by broth dilution assay method. The synthesized compounds 7a, 7b, 7d and 4 showed an antitubercular efficacy considerably greater than that of the parent 4-isopropyl-1,3-thiazole-2-carbohydrazide 1, suggesting that the substituted 4-isopropylthiazole-2-carbohydrazide moiety plays an important role in enhancing the antitubercular properties of this class of compounds. Compounds 2c, 3, 4, 6d, 7a and 7b exhibited good or moderate antibacterial and antifungal activity. Compounds 4 and 7b showed appreciable cytotoxicity at a concentration of 250 mu M.

Synthesis and Evaluation of a Novel Class of G-Quadruplex-Stabilizing Small Molecules Based on the 1,3-Phenylene-Bis(piperazinyl benzimidazole) System

Achieving stabilization of telomeric DNA in G-quadruplex conformation by Various organic compounds has been an important goal for the medicinal chemists seeking to develop new anticancer agents. Several compounds are known to stabilize G-quadruplexes. However, relatively few are known to induce their formation and/or alter the topology, of the preformed quadruplex DNA. Herein, four compounds having the 1,3-phenylene-bis(piperazinyl benzimidazole) unit as a basic skeleton have been synthesized, and their interactions with the 24-mer telomeric DNA sequences from Tetrahymena thermophilia d(T(2)G(4))(4) have been investigated using high-resolution techniques Such as circular dichroism (CD) spectropolarimetry, CD melting, emission spectroscopy, and polyacrylamide gel electrophoresis. The data obtained, in the presence of one of three ions (Li+, Na+, or K+), indicate that all the new compounds have a high affinity for G-quadruplex DNA, and the strength of the binding with G-quadruplex depends on (1) phenyl ring substitution, (ii) the piperazinyl side chain, and (iii) the type of monovalent cation present in the buffer. Results further Suggest that these compounds are able to abet the conversion of the Intramolecular quadruplex into parallel stranded intermolecular G-quadruplex DNA. Notably, these compounds are also capable of inducing and stabilizing the parallel stranded quadruplex from randomly structured DNA in the absence of any stabilizing cation. The kinetics of the structural changes Induced by these compounds could be followed by recording the changes in the CD signal as a function of time. The implications of the findings mentioned above are discussed in this paper.

Adiabatic quantum computation with a one-dimensional projector Hamiltonian

Adiabatic quantum computation is based on the adiabatic evolution of quantum systems. We analyze a particular class of quantum adiabatic evolutions where either the initial or final Hamiltonian is a one-dimensional projector Hamiltonian on the corresponding ground state. The minimum-energy gap, which governs the time required for a successful evolution, is shown to be proportional to the overlap of the ground states of the initial and final Hamiltonians. We show that such evolutions exhibit a rapid crossover as the ground state changes abruptly near the transition point where the energy gap is minimum. Furthermore, a faster evolution can be obtained by performing a partial adiabatic evolution within a narrow interval around the transition point. These results generalize and quantify earlier works.

Shortcomings of discontinuous-pressure finite element methods on a class of transient problems

Past studies that have compared LBB stable discontinuous- and continuous-pressure finite element formulations on a variety of problems have concluded that both methods yield Solutions of comparable accuracy, and that the choice of interpolation is dictated by which of the two is more efficient. In this work, we show that using discontinuous-pressure interpolations can yield inaccurate solutions at large times on a class of transient problems, while the continuous-pressure formulation yields solutions that are in good agreement with the analytical Solution.

Synthesis and bioassay of a new class of heterocycles pyrrolyl oxadiazoles/thiadiazoles/triazoles

A new class of heterocycles pyrrolyl thiadiazoles, pyrrolyl oxadiazoles and pyrrolyl triazoles were prepared from arylsulfonylethenesulfonylacetic acid methyl ester and tested for their antimicrobial and cytotoxic activities. (C) 2008 Elsevier Masson SAS. All rights reserved.

Facile one-pot synthesis of thio and selenourea derivatives: A new class of potent urease inhibitors

A facile, one-pot synthesis of thio and selenourea derivatives from amines using tetrathiomolybdate 1 and tetraseleno-tungstate 2 as sulfur and selenium transfer reagents, respectively, is reported. The compounds were tested for their activity as urease inhibitors and some of the compounds showed potent activity in the nanomolar range towards jack bean urease. (C) 2007 Elsevier Ltd. All rights reserved.

Time and Energy Complexity of Distributed Computation of a Class of Functions in Wireless Sensor Networks

We consider a scenario in which a wireless sensor network is formed by randomly deploying n sensors to measure some spatial function over a field, with the objective of computing a function of the measurements and communicating it to an operator station. We restrict ourselves to the class of type-threshold functions (as defined in the work of Giridhar and Kumar, 2005), of which max, min, and indicator functions are important examples: our discussions are couched in terms of the max function. We view the problem as one of message-passing distributed computation over a geometric random graph. The network is assumed to be synchronous, and the sensors synchronously measure values and then collaborate to compute and deliver the function computed with these values to the operator station. Computation algorithms differ in (1) the communication topology assumed and (2) the messages that the nodes need to exchange in order to carry out the computation. The focus of our paper is to establish (in probability) scaling laws for the time and energy complexity of the distributed function computation over random wireless networks, under the assumption of centralized contention-free scheduling of packet transmissions. First, without any constraint on the computation algorithm, we establish scaling laws for the computation time and energy expenditure for one-time maximum computation. We show that for an optimal algorithm, the computation time and energy expenditure scale, respectively, as Theta(radicn/log n) and Theta(n) asymptotically as the number of sensors n rarr infin. Second, we analyze the performance of three specific computation algorithms that may be used in specific practical situations, namely, the tree algorithm, multihop transmission, and the Ripple algorithm (a type of gossip algorithm), and obtain scaling laws for the computation time and energy expenditure as n rarr infin. In particular, we show that the computation time for these algorithms scales as Theta(radicn/lo- g n), Theta(n), and Theta(radicn log n), respectively, whereas the energy expended scales as , Theta(n), Theta(radicn/log n), and Theta(radicn log n), respectively. Finally, simulation results are provided to show that our analysis indeed captures the correct scaling. The simulations also yield estimates of the constant multipliers in the scaling laws. Our analyses throughout assume a centralized optimal scheduler, and hence, our results can be viewed as providing bounds for the performance with practical distributed schedulers.

Synthesis and Characterization of a Class of Donor-Acceptor Conjugated Molecules: Experiments and Theoretical Calculations

A class of conjugated molecules containing donor (thiophene) and acceptor (malononitrile) is synthesized by Knoevenagel condensation reaction between 2-(2,6-dimethy1-4H-pyran-4-ylidene) malononitrile and thiophene carbaldehyde containing two and three thiophene units. The resulting molecules are characterized by H-1 and C-13 NMR. We have performed UV-vis absorption, fluorescence, and cyclic voltammetry measurements on these materials. The spectroscopic and electrochemical measurements proved beyond doubt that these materials possess lowexcitation gap and are suitable for being an active material in various electronic devices. We have also performed electronic structure calculations using density functional theory (DFT) and INDO/SCI methods to characterize the ground and excited states of this class of molecules. These donor-acceptor molecules show a strong charge transfercharacter that increases with the increase in the number of thiophene rings coupled to the malononitrile acceptor moiety. We have also calculated the pi-coherence length, Stoke's shift, and effect of solvents on excited states for this class of molecules, Our theoretical values agree well with experimental results.

A unified construction of space-time codes with optimal rate-diversity tradeoff

The problem of constructing space-time (ST) block codes over a fixed, desired signal constellation is considered. In this situation, there is a tradeoff between the transmission rate as measured in constellation symbols per channel use and the transmit diversity gain achieved by the code. The transmit diversity is a measure of the rate of polynomial decay of pairwise error probability of the code with increase in the signal-to-noise ratio (SNR). In the setting of a quasi-static channel model, let n(t) denote the number of transmit antennas and T the block interval. For any n(t) <= T, a unified construction of (n(t) x T) ST codes is provided here, for a class of signal constellations that includes the familiar pulse-amplitude (PAM), quadrature-amplitude (QAM), and 2(K)-ary phase-shift-keying (PSK) modulations as special cases. The construction is optimal as measured by the rate-diversity tradeoff and can achieve any given integer point on the rate-diversity tradeoff curve. An estimate of the coding gain realized is given. Other results presented here include i) an extension of the optimal unified construction to the multiple fading block case, ii) a version of the optimal unified construction in which the underlying binary block codes are replaced by trellis codes, iii) the providing of a linear dispersion form for the underlying binary block codes, iv) a Gray-mapped version of the unified construction, and v) a generalization of construction of the S-ary case corresponding to constellations of size S-K. Items ii) and iii) are aimed at simplifying the decoding of this class of ST codes.

On the performance analysis of a class of neuron circuits

A new performance metric, Peak-Error Ratio (PER) has been presented to benchmark the performance of a class of neuron circuits to realize neuron activation function (NAF) and its derivative (DNAF). Neuron circuits, biased in subthreshold region, based on the asymmetric cross-coupled differential pair configuration and conventional configuration of applying small external offset voltage at the input have been compared on the basis of PER. It is shown that the technique of using transistor asymmetry in a cross-coupled differential pair performs on-par with that of applying external offset voltage. The neuron circuits have been experimentally prototyped and characterized as a proof of concept on the 1.5 mu m AMI technology.

On the performance analysis of a class of neuron circuits

A new performance metric, Peak-Error Ratio (PER) has been presented to benchmark the performance of a class of neuron circuits to realize neuron activation function (NAF) and its derivative (DNAF). Neuron circuits, biased in subthreshold region, based on the asymmetric cross-coupled differential pair configuration and conventional configuration of applying small external offset voltage at the input have been compared on the basis of PER. It is shown that the technique of using transistor asymmetry in a cross-coupled differential pair performs on-par with that of applying external offset voltage. The neuron circuits have been experimentally prototyped and characterized as a proof of concept on the 1.5 mu m AMI technology.

Study of a class of non-linear systems reducible to equivalent linear systems

In this paper, a method of arriving at transformations which convert a class of non-linear systems into equivalent linear systems, has been presented along with suitable examples, which illustrate its application.

An automated framework for understanding structural variations in the binding grooves of MHC class II molecules

Background: MHC/HLA class II molecules are important components of the immune system and play a critical role in processes such as phagocytosis. Understanding peptide recognition properties of the hundreds of MHC class II alleles is essential to appreciate determinants of antigenicity and ultimately to predict epitopes. While there are several methods for epitope prediction, each differing in their success rates, there are no reports so far in the literature to systematically characterize the binding sites at the structural level and infer recognition profiles from them. Results: Here we report a new approach to compare the binding sites of MHC class II molecules using their three dimensional structures. We use a specifically tuned version of our recent algorithm, PocketMatch. We show that our methodology is useful for classification of MHC class II molecules based on similarities or differences among their binding sites. A new module has been used to define binding sites in MHC molecules. Comparison of binding sites of 103 MHC molecules, both at the whole groove and individual sub-pocket levels has been carried out, and their clustering patterns analyzed. While clusters largely agree with serotypic classification, deviations from it and several new insights are obtained from our study. We also present how differences in sub-pockets of molecules associated with a pair of autoimmune diseases, narcolepsy and rheumatoid arthritis, were captured by PocketMatch(13). Conclusion: The systematic framework for understanding structuralvariations in MHC class II molecules enables large scale comparison of binding grooves and sub-pockets, which is likely to have direct implications towards predicting epitopes and understanding peptide binding preferences.

An automated framework for understanding structural variations in the binding grooves of MHC class II molecules

Background: MHC/HLA class II molecules are important components of the immune system and play a critical role in processes such as phagocytosis. Understanding peptide recognition properties of the hundreds of MHC class II alleles is essential to appreciate determinants of antigenicity and ultimately to predict epitopes. While there are several methods for epitope prediction, each differing in their success rates, there are no reports so far in the literature to systematically characterize the binding sites at the structural level and infer recognition profiles from them. Results: Here we report a new approach to compare the binding sites of MHC class II molecules using their three dimensional structures. We use a specifically tuned version of our recent algorithm, PocketMatch. We show that our methodology is useful for classification of MHC class II molecules based on similarities or differences among their binding sites. A new module has been used to define binding sites in MHC molecules. Comparison of binding sites of 103 MHC molecules, both at the whole groove and individual sub-pocket levels has been carried out, and their clustering patterns analyzed. While clusters largely agree with serotypic classification, deviations from it and several new insights are obtained from our study. We also present how differences in sub-pockets of molecules associated with a pair of autoimmune diseases, narcolepsy and rheumatoid arthritis, were captured by PocketMatch(13). Conclusion: The systematic framework for understanding structural variations in MHC class II molecules enables large scale comparison of binding grooves and sub-pockets, which is likely to have direct implications towards predicting epitopes and understanding peptide binding preferences.