Testing threshold functions using implied minterm structure

A geometrical structure called the implied minterm structure (IMS) has been developed from the properties of minterms of a threshold function. The IMS is useful for the manual testing of linear separability of switching functions of up to six variables. This testing is done just by inspection of the plot of the function on the IMS.

Purification and functional characterization of type II DNA topoisomerase from rat testis and comparison with topoisomerase II from liver

A number of studies in yeast have shown that DNA topoisomerase TI is essential for chromosome condensation and disjunction during mitosis at the metaphase/anaphase transition and meiosis I. Accordingly, kinetic and mechanistic studies have implied a role for topoisomerase rr in chromosome disjunction. As a step toward understanding the nature and role of topoisomerase II in a mammalian germline in vivo, we have purified topoisomerase II from rat testis to homogeneity and ascertained several of its catalytic activities in conjunction with that of the purified enzyme from liver. The purified enzymes appeared to be monomers under denaturing conditions; however, they differed in their relative molecular mass. Topoisomerase II from testis and liver have apparent molecular masses of 150 +/- 10 kDa and 160 +/- 10 kDa, respectively. The native molecular mass of testis topoisomerase II as assayed by immunoblot analysis of cell-foe extracts, prepared in the presence of SDS and a number of protease inhibitors, corroborated with the size of the purified enzyme. Both enzymes are able to promote decatenation and relax supercoiled DNA substrates in an ATP and Mg2+-dependent manner. However, quantitative comparison of catalytic properties of topoisomerase II from testis with that of the enzyme from liver displayed significant differences in their efficiencies. Optimal pH values for testis enzyme are 6.5 to 8.5 while they are 6 to 7.5 for the liver enzyme. Intriguingly, the relaxation activity of liver topoisomerase II was inhibited by potassium glutamate at 1 M, whereas testis enzyme required about half its concentration. These findings argue that topoisomerase II from rat testis is structurally distinct from that of its somatic form and the functional differences between the two enzymes parallels with the physiological environment that is unique to these two tissues.

Risk Minimizing Option Pricing in a Semi-Markov Modulated Market

We address risk minimizing option pricing in a semi-Markov modulated market where the floating interest rate depends on a finite state semi-Markov process. The growth rate and the volatility of the stock also depend on the semi-Markov process. Using the Föllmer–Schweizer decomposition we find the locally risk minimizing price for European options and the corresponding hedging strategy. We develop suitable numerical methods for computing option prices.

An uncommon nucleotide conformation shown by molecular structure of deoxyuridine-5-phosphate and nucleic acid stereochemistry

CRYSTAL structure determinations of nucleic acid fragments have shown that several of the conformational features found in the monomeric building blocks are also manifested at the nucleic acid level. Stereochemical variations between thymine and uracil nucleotides are therefore of interest as they can provide a structural basis for some of the differences between the conformations of DNA and RNA. X-ray studies have so far not shown any major dissimilarities between these two nucleotide species although the sugar ring of deoxyribonucleotides is found to possess greater flexibility than that in ribonucleotides. We report here the molecular structure of deoxyuridine-5'-phosphate (dUMP-5') which is not a common monomer unit of DNAs as it is replaced by its 5-methyl analogue deoxythymidine-5'-phosphate (dTMP-5'). The investigation was undertaken to help determine whether or not this implied a fundamental difference between the geometries of these two molecules.

A playful side to twelfth-century mathematics

As editors of the book Lilavati's Daughters: The Women Scientists of India, reviewed by Asha Gopinathan (Nature 460, 1082; 2009), we would like to elaborate on the background to its title. Lilavati was a mathematical treatise of the twelfth century, composed by the mathematician and astronomer Bhaskaracharya (1114–85) — also known as Bhaskara II — who was a teacher of repute and author of several other texts. The name Lilavati, which literally means 'playful', is a surprising title for an early scientific book. Some of the mathematical problems posed in the book are in verse form, and are addressed to a girl, the eponymous Lilavati. However, there is little real evidence concerning Lilavati's historicity. Tradition holds that she was Bhaskaracharya's daughter and that he wrote the treatise to console her after an accident that left her unable to marry. But this could be a later interpolation, as the idea was first mentioned in a Persian commentary. An alternative view has it that Lilavati was married at an inauspicious time and was widowed shortly afterwards. Other sources have implied that Lilavati was Bhaskaracharya's wife, or even one of his students — raising the possibility that women in parts of the Indian subcontinent could have participated in higher education as early as eight centuries ago. However, given that Bhaskara was a poet and pedagogue, it is also possible that he chose to address his mathematical problems to a doe-eyed girl simply as a whimsical and charming literary device.

Asymptotic analysis of option pricing in a Markov modulated market

We address asymptotic analysis of option pricing in a regime switching market where the risk free interest rate, growth rate and the volatility of the stocks depend on a finite state Markov chain. We study two variations of the chain namely, when the chain is moving very fast compared to the underlying asset price and when it is moving very slow. Using quadratic hedging and asymptotic expansion, we derive corrections on the locally risk minimizing option price.

Manifolds with nonnegative isotropic curvature

We prove that if (M-n, g), n >= 4, is a compact, orientable, locally irreducible Riemannian manifold with nonnegative isotropic curvature,then one of the following possibilities hold: (i) M admits a metric with positive isotropic curvature. (ii) (M, g) is isometric to a locally symmetric space. (iii) (M, g) is Kahler and biholomorphic to CPn/2. (iv) (M, g) is quaternionic-Kahler. This is implied by the following result: Let (M-2n, g) be a compact, locally irreducible Kahler manifold with nonnegative isotropic curvature. Then either M is biholomorphic to CPn or isometric to a compact Hermitian symmetric space. This answers a question of Micallef and Wang in the affirmative. The proof is based on the recent work of Brendle and Schoen on the Ricci flow.

Studies on a chitooligosaccharide-specific lectin from Coccinia indica. Thermodynamics and kinetics of umbelliferyl glycoside binding.

Coccinia indica agglutinin (CIA) is a chitooligosaccharide-specific lectin with two binding sites/homodimer of M(r) 32,000. Quenching studies implied tryptophan involvement in binding activity, which was confirmed by chemical modification experiments (A. R. Sanadi and A. Surolia, submitted for publication). Binding of 4-methylumbelliferyl chitooligosaccharides has been carried out to study their binding by CIA. Reversal experiments confirm the validity of the data previously obtained (A. R. Sanadi and A. Surolia, submitted for publication) from intrinsic fluorescence studies. Surprisingly, unlike wheat germ agglutinin, there is no consistent thermodynamic effect of the chromophoric label on binding activities as compared with the native sugars. From the changes in the optical properties of the chromophoric group upon binding to CIA, it has been possible to confirm that the tryptophan located in the binding site is closest to the fourth subsite. Thermodynamic analysis shows that the binding of the labeled tetrasaccharide is very strongly entropically driven, with the terminal, nonreducing sugar residue protruding from the binding pocket. The results of stopped-flow kinetic studies on the binding of the chromophoric trisaccharide by CIA show that the mechanism of binding is a one-step process.

Evaluation of noise attenuation due to exhaust mufflers

This paper deals with the evaluation of noise attenuation due to exhaust mufflers fitted to the conventional piston engines. A discussion of the existing methods for the purpose, reveals the undesirability of the assumptions and simplifications implied therein. An expression for the attenuation of a general muffler has been derived. The classical theory of "sound transmission in pipes" [1] has been exploited to evaluate this "expression" for mufflers of different geometry. The quantitative effects of atmospheric impedance, and the engine exhaust impedance on the attenuation curves of a specific muffler have been found for an automotive engine. Finally, attenuation curves of a number of mufflers have been drawn and compared to suggest certain design criteria.

Intrinsic Electron localization in manganites

We mention here an unusual disorder effect in manganites, namely the ubiquitous hopping behavior for electron transport observed in them over a wide range of doping. We argue that the implied Anderson localization is intrinsic to manganites, because of the existence of polarons in them which are spatially localized, generally at random sites (unless there is polaron ordering). We have developed a microscopic two fluid lb model for manganites, where l denotes lattice site localized l polarons, and b denotes band electrons. Using this, and the self-consistent theory of localization, we show that the occupied b states are Anderson localized in a large range of doping due to the scattering of b electrons from l polarons. Numerical simulations which further include the effect of long range Coulomb interactions support this, as well the existence of a novel polaronic Coulomb glass. A consequence is the inevitable hopping behaviour for electron transport observed in doped insulating manganites.

Superconducting Y--Ba--Cu--O Thin Films by RF Sputtering

Thin films of Y--Ba--Cu--O have been prepared by conventional methods of RF sputtering. The films exhibit superconducting onset temperatures as high as 91K, midpoint at 80K and a zero resistance state at 35K. Critical current measurements implied critical current densities of the order of 31 A/cm exp 2 . An attempt has been made to establish the role of substrate and various deposition parameters. 7 ref.--AA.

Development stage-specific expression of fibroin in the silk worm Bombyx mori is regulated translationally

The contents of fibroin H RNA as a function of development have been quantitated in the posterior silk glands of Bombyx mori larvae on different days of 4th and 5th instars. The fibroin RNA levels increased during the feeding stages of larvae and the RNA got completely degraded during the interim moult. The patterns of accumulation of fibroin RNA were similar in both the instars. Although there was considerable increase in the fibroin RNA content during the 5th larval instar, the relative abundance of fibroin RNA in the total RNA was fairly constant during the 4th and 5th instars. The increased content of fibroin RNA in 5th instar was the consequence of an overall increase in transcription accompanying the development progress, rather than specific increase only in fibroin transcription. The contents of fibroin protein in the 4th and 5th instars of development have also been quantitated making use of a sensitive radioimmune assay with a purified, antifibroin antibody. There were substantial differences between 4th and 5th instars in the absolute fibroin contents as well as the relative proportion of fibroin in the total proteins. These results implied that although the fibroin gene was transcribed at the same efficiency during the 4th and 5th instars, the translational efficiency was much lower during the 4th instar. The extent of polyadenylation of fibroin RNA was similar in both instars. However, there was a two-fold increase in the polysome association of fibroin RNA in the 5th instar. Over and above this, there was substantial increase during the 5th instar in the contents of those tRNAs. (e.g. Gly, Ala and Ser) which are abundantly represented in fibroin and therefore directly related to the expression of fibroin. The increased polysome association of fibroin mRNA and the adequate supply of cognate tRNAs in the 5th instar, together contributes to the translational regulation of fibroin in a developmental stage-specific manner. Based on these observations, we propose that translational regulation plays a major role in the development stage-specific synthesis of fibroin in Bombyx mori.

S-matrix for magnons in the D1-D5 system

We show that integrability and symmetries of the near horizon geometry of the D1-D5 system determine the S-matrix for the scattering of magnons with polarizations in AdS(3) x S-3 completely up to a phase. Using semi-classical methods we evaluate the phase to the leading and to the one-loop approximation in the strong coupling expansion. We then show that the phase obeys the unitarity constraint implied by the crossing relations to the one-loop order. We also verify that the dispersion relation obeyed by these magnons is one-loop exact at strong coupling which is consistent with their BPS nature.

On reconfirming the evidence for pre-imaginal caste bias in a primitively eusocial wasp

Caste is usually thought to be determined entirely in the adult stage in most primitively eusocial wasps and bees. A pre-imaginal caste bias has however been recently discovered in the primitively eusocial waspRopalidia marginata. This study also suggested that reigning queens and possibly other adults may influence the production of new queens and implied at least partial support to the parental manipulation or sub-fertility hypothesis for the evolution of insect sociality. The interest of these results prompted an attempt at their reconfirmation. Complete reconfirmation has now been obtained using data from an independent experiment and two additional methods of data analysis. We therefore conclude that caste is at least partly determined prior to eclosion in the primitively eusocial waspRopalidia marginata which lacks morphological differentiation between egg-layers and non-egg-layers.