Separation of variables for a lattice integrable system and the inverse problem

We investigate the relation between the local variables of a discrete integrable lattice system and the corresponding separation variables, derived from the associated spectral curve. In particular, we have shown how the inverse transformation from the separation variables to the discrete lattice variables may be factorised as a sequence of canonical transformations, following the procedure outlined by Kuznetsov.Comment: 14 pages. submitted for publicatio

Spatial heterogeneity in the radiogenic activity of the lunar interior: Inferences from CHACE and LLRI on Chandrayaan-1

In the past, clues on the potential radiogenic activity of the lunar interior have been obtained from the isotopic composition of noble gases like Argon. Excess Argon (40) relative to Argon (36), as compared to the solar wind composition, is generally ascribed to the radiogenic activity of the lunar interior. Almost all the previous estimates were based on, 'on-the-spot' measurements from the landing sites. Relative concentration of the isotopes of 40Ar and 36Ar along a meridian by the Chandra's Altitudinal Composition Explorer (CHACE) experiment, on the Moon Impact Probe (MIP) of India's first mission to Moon, has independently yielded clues on the possible spatial heterogeneity in the radiogenic activity of the lunar interior in addition to providing indicative 'antiquity' of the lunar surface along the ground track over the near side of the moon. These results are shown to broadly corroborate the independent topography measurements by the Lunar Laser Ranging Instrument (LLRI) in the main orbiter Chandrayaan-1. The unique combination of these experiments provided high spatial resolution data while indicating the possible close linkages between the lunar interior and the lunar ambience

Symbiotic Human Gut Bacteria with Variable Metabolic Priorities for Host Mucosal Glycans.

UnlabelledMany symbiotic gut bacteria possess the ability to degrade multiple polysaccharides, thereby providing nutritional advantages to their hosts. Like microorganisms adapted to other complex nutrient environments, gut symbionts give different metabolic priorities to substrates present in mixtures. We investigated the responses of Bacteroides thetaiotaomicron, a common human intestinal bacterium that metabolizes more than a dozen different polysaccharides, including the O-linked glycans that are abundant in secreted mucin. Experiments in which mucin glycans were presented simultaneously with other carbohydrates show that degradation of these host carbohydrates is consistently repressed in the presence of alternative substrates, even by B. thetaiotaomicron previously acclimated to growth in pure mucin glycans. Experiments with media containing systematically varied carbohydrate cues and genetic mutants reveal that transcriptional repression of genes involved in mucin glycan metabolism is imposed by simple sugars and, in one example that was tested, is mediated through a small intergenic region in a transcript-autonomous fashion. Repression of mucin glycan-responsive gene clusters in two other human gut bacteria, Bacteroides massiliensis and Bacteroides fragilis, exhibited variable and sometimes reciprocal responses compared to those of B. thetaiotaomicron, revealing that these symbionts vary in their preference for mucin glycans and that these differences occur at the level of controlling individual gene clusters. Our results reveal that sensing and metabolic triaging of glycans are complex processes that vary among species, underscoring the idea that these phenomena are likely to be hidden drivers of microbiota community dynamics and may dictate which microorganisms preferentially commit to various niches in a constantly changing nutritional environment.ImportanceHuman intestinal microorganisms impact many aspects of health and disease, including digestion and the propensity to develop disorders such as inflammation and colon cancer. Complex carbohydrates are a major component of the intestinal habitat, and numerous species have evolved and refined strategies to compete for these coveted nutrients. Our findings reveal that individual bacteria exhibit different preferences for carbohydrates emanating from host diet and mucosal secretions and that some of these prioritization strategies are opposite to one another. Thus, we reveal new aspects of how individual bacteria, some with otherwise similar metabolic potential, partition to "preferred niches" in the complex gut ecosystem, which has important and immediate implications for understanding and predicting the behavioral dynamics of this community

Do you receive a lighter prison sentence because you are a woman? An economic analysis of federal criminal sentencing guidelines

The Federal criminal sentencing guidelines struck down by the U.S. Supreme Court in 2005 required that males and females who commit the same crime and have the same prior criminal record be sentenced equally. Using data obtained from the United States Sentencing Commission's records, we examine whether there exists any gender-based bias in criminal sentencing decisions. We treat months in prison as a censored variable in order to account for the frequent outcome of no prison time. Additionally, we control for the self-selection of the defendant into guilty pleas through use of an endogenous switching regression model. A new decomposition methodology is employed. Our results indicate that women receive more lenient sentences even after controlling for circumstances such as the severity of the offense and past criminal history

Eulerian Walkers as a model of Self-Organised Criticality

We propose a new model of self-organized criticality. A particle is dropped at random on a lattice and moves along directions specified by arrows at each site. As it moves, it changes the direction of the arrows according to fixed rules. On closed graphs these walks generate Euler circuits. On open graphs, the particle eventually leaves the system, and a new particle is then added. The operators corresponding to particle addition generate an abelian group, same as the group for the Abelian Sandpile model on the graph. We determine the critical steady state and some critical exponents exactly, using this equivalence.Comment: 4 pages, RevTex, 4 figure

Group 1 and group 2 metal complexes supported by a bidentate bulky iminopyrrolyl ligand: synthesis, structural diversity, and ε-caprolactone polymerization study

We report here a series of alkali and alkaline earth metal complexes, each with a bulky iminopyrrolyl ligand [2-(Ph3CN[double bond, length as m-dash]CH)C4H3NH] (1-H) moiety in their coordination sphere, synthesized using either alkane elimination or silylamine elimination methods or the salt metathesis route. The lithium salt of molecular composition [Li(2-(Ph3CN[double bond, length as m-dash]CH)C4H3N)(THF)2] (2) was prepared using the alkane elimination method, and the silylamine elimination method was used to synthesize the dimeric sodium and tetra-nuclear potassium salts of composition [(2-(Ph3CN[double bond, length as m-dash]CH)C4H3N)Na(THF)]2 (3) and [(2-(Ph3CN[double bond, length as m-dash]CH)C4H3N)K(THF)0.5]4 (4) respectively. The magnesium complex of composition [(THF)2Mg(CH2Ph){2-(Ph3CN[double bond, length as m-dash]CH)C4H3N}] (5) was synthesized through the alkane elimination method, in which [Mg(CH2Ph)2(OEt2)2] was treated with the bulky iminopyrrole ligand 1-H in 1 : 1 molar ratio, whereas the bis(iminopyrrolyl)magnesium complex [(THF)2Mg{2-(Ph3CN[double bond, length as m-dash]CH)C4H3N}2] (6) was isolated using the salt metathesis route. The heavier alkaline earth metal complexes of the general formula {(THF)nM(2-(Ph3CN[double bond, length as m-dash]CH)C4H3N)2} [M = Ca (7), Sr (8), and n = 2; M = Ba (9), n = 3] were prepared in pure form using two synthetic methods: in the first method, the bulky iminopyrrole ligand 1-H was directly treated with the alkaline earth metal precursor [M{N(SiMe3)2}2(THF)n] (where M = Ca, Sr and Ba) in 2 : 1 molar ratio in THF solvent at ambient temperature. The complexes 7–9 were also obtained using the salt metathesis reaction, which involves the treatment of the potassium salt (4) with the corresponding metal diiodides MI2 (M = Ca, Sr and Ba) in 2 : 1 molar ratio in THF solvent. The molecular structures of all the metal complexes (1-H, 2–9) in the solid state were established through single-crystal X-ray diffraction analysis. The complexes 5–9 were tested as catalysts for the ring-opening polymerization of ε-caprolactone. High activity was observed in the heavier alkaline earth metal complexes 7–9, with a very narrow polydispersity index in comparison to that of magnesium complexes 5 and 6

Non-equilibrium phase transitions in biomolecular signal transduction

We study a mechanism for reliable switching in biomolecular signal-transduction cascades. Steady bistable states are created by system-size cooperative effects in populations of proteins, in spite of the fact that the phosphorylation-state transitions of any molecule, by means of which the switch is implemented, are highly stochastic. The emergence of switching is a nonequilibrium phase transition in an energetically driven, dissipative system described by a master equation. We use operator and functional integral methods from reaction-diffusion theory to solve for the phase structure, noise spectrum, and escape trajectories and first-passage times of a class of minimal models of switches, showing how all critical properties for switch behavior can be computed within a unified framework

Investigation of the crystal structures of n-(4-fluorobenzoyl) benzenesulfonamide and n-(4-fluoro-benzoyl)-4-methylbenzenesulfonamide

The title compound, C26H26N2O7, is a thia­midine derivative. Geometric parameters are in the usual ranges. The crystal packing is stabilized by a classical N—H⋯O hydrogen bond, several weak C—H⋯O hydrogen bonds and a π–π stacking inter­action

Noncommutative brane-world, (Anti) de Sitter vacua and extra dimensions

We investigate a curved brane-world, inspired by a noncommutative D3-brane, in a type IIB string theory. We obtain, an axially symmetric and a spherically symmetric, (anti) de Sitter black holes in 4D. The event horizons of these black holes possess a constant curvature and may be seen to be governed by different topologies. The extremal geometries are explored, using the noncommutative scaling in the theory, to reassure the attractor behavior at the black hole event horizon. The emerging two dimensional, semi-classical, black hole is analyzed to provide evidence for the extra dimensions in a curved brane-world. It is argued that the gauge nonlinearity in the theory may be redefined by a potential in a moduli space. As a result, D=11 and D=12 dimensional geometries may be obtained at the stable extrema of the potential.Comment: 17 pages, 1 figur