An elementary approach to gap theorems

Using elementary comparison geometry, we prove: Let (M, g) be a simply-connected complete Riemannian manifold of dimension >= 3. Suppose that the sectional curvature K satisfies -1-s(r) <= K <= -1, where r denotes distance to a fixed point in M. If lim(r ->infinity) e(2r) s(r) = 0, then (M, g) has to be isometric to H-n.The same proof also yields that if K satisfies -s(r) <= K <= 0 where lim(r ->infinity) r(2) s(r) = 0, then (M, g) is isometric to R-n, a result due to Greene and Wu.Our second result is a local one: Let (M, g) be any Riemannian manifold. For a E R, if K < a on a geodesic ball Bp (R) in M and K = a on partial derivative B-p (R), then K = a on B-p (R).

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.

On the generalized continuum model of dipolar solvation dynamics

The continuum model of dipolar solvation dynamics is reviewed. The effects of non-spherical molecular shapes, of non-Debye dielectric relaxation of the polar solvent and of dielectric inhomogeneity of the solvent around the solute dipole are investigated. Several new theoretical results are presented. It is found that our generalized continuum model, which takes into account the dielectric inhomogeneity of the surrounding solvent, provides a description of solvation dynamics consistent with recent experimental results.

Reproductive behavior and health in consanguineous marriages

In many regions of Asia and Africa, consanguineous marriages currently account for approximately 20 to 50% of all unions, and preliminary observations indicate that migrants from these areas continue to contract marriages with close relatives when resident in North America and Western Europe. Consanguinity is associated with increased gross fertility, due at least in part to younger maternal age at first livebirth. Morbidity and mortality also may be elevated, resulting in comparable numbers of surviving offspring in consanguineous and nonconsanguineous families. With advances in medicine and public health, genetic disorders will account for an increased proportion of disease worldwide. Predictably, this burden will fall more heavily on countries and communities in which consanguinity is strongly favored, as the result of the expression of deleterious recessive genes. However, studies conducted in such populations indicate that the adverse effects associated with inbreeding are experienced by a minority of families.

Roofed polyquinanes: synthesis and electronic structure

Starting from readily available norbornenobenzoquinone 7 and employing a photothermal metathesis reaction as the main strategy, novel "roofed" polyquinane bisenones 3 and 13 have been synthesized. Among these, the former is potentially serviceable for further elaboration to dodecahedrane 1. Catalytic hydrogenation of 3 provided the dione 12, which fully inscribes the circumference of dodecahedrane sphere. The "roofed" C-16-bisenone 3 has been successfully annulated to C19-bisenone 24 and C19-trisenone 26 by employing the Greene methodology and Pauson-Khand reaction, respectively. The molecular structures of 3 and 13 were computed using molecular mechanics and semiempirical MO methods. The nonbonded distances between the double bonds vary strongly with the method employed. The interactions between the pi-MO's were, therefore, probed by means of photoelectron (PE) spectroscopy. Comparison with the PE spectra of a series of model systems with increasing complexity enabled an unambiguous assignment of the observed peaks. The symmetric and antisymmetric combinations of the pi-MO's of the enone moieties of 3 and 13 show large splittings, characteristic of propano-bridged systems in which through-space and through-bond effects act in concert.

Dynamics of activationless reactions in solution

Recent picosecond and subpicosecond laser spectroscopy experiments have revealed several chemically and biologically important reactions in solution in which the reaction potential surface does not present a barrier to the motion along the reaction coordinate.The dynamics of these reactions display diverse and interesting behavior. They include the dependence of relaxation rate on the solvent viscosity, the solvent polarity, the temperature, and the wavelength of the exciting light. In this article we review the recent developments in the theoretical description of activationless processes in solution and compare them with the available experimental results

Dependence of giant magnetoresistance on oxygen stoichiometry and magnetization in polycrystalline La0.67Ba0.33MnOz

We have studied resistivity, magnetization, and magnetoresistance in polycrystalline La0.67Ba0.33MnOz by reducing the oxygen stoichiometry from z=2.99 to 2.80. As the oxygen content decreases, the resistivity of La0.67Ba0.33 MnOz increases and the magnetic transition temperature shifts to lower temperature. A large magnetoresistance effect was observed over a wide temperature range for all samples except the insulating z=2.80 sample. The similarity between our results on oxygen-deficient polycrystalline La0.67 Ba0.33MnOz and films previously reported to have a very large intrinsic magnetoresistance is discussed. At low temperature the magnetoresistance was observed to be strongly dependent on the magnetization. A possible mechanism for this effect is discussed.

Electronic conduction in LaNiO3-delta: the dependence on the oxygen stoichiometry delta

We report a systematic study of the electronic transport properties of the metallic perovskite oxide LaNiO3-delta as a function of the oxygen stoichiometry delta (delta less than or equal to 0.14). The electrical resistivity, magnetoresistance, susceptibility, Hall effect and thermopower have been studied, All of the transport coefficients are dependent on the value of delta. The resistivity increases almost exponentially as delta increases. We relate this increase in rho to the creation of Ni2+ with square-planar coordination. We find that there is a distinct T-1.5-contribution to the resistivity over the whole temperature range. The thermopower is negative, as expected for systems with electrons as the carrier, but the Hall coefficient is positive. We have given a qualitative and quantitative explanation for the different quantities observed and their systematic variation with the stoichiometry delta.

Proof of a conjecture of Frankl and Furedi

We give a simple linear algebraic proof of the following conjecture of Frankl and Furedi [7, 9, 13]. (Frankl-Furedi Conjecture) if F is a hypergraph on X = {1, 2, 3,..., n} such that 1 less than or equal to /E boolean AND F/ less than or equal to k For All E, F is an element of F, E not equal F, then /F/ less than or equal to (i=0)Sigma(k) ((i) (n-1)). We generalise a method of Palisse and our proof-technique can be viewed as a variant of the technique used by Tverberg to prove a result of Graham and Pollak [10, 11, 14]. Our proof-technique is easily described. First, we derive an identity satisfied by a hypergraph F using its intersection properties. From this identity, we obtain a set of homogeneous linear equations. We then show that this defines the zero subspace of R-/F/. Finally, the desired bound on /F/ is obtained from the bound on the number of linearly independent equations. This proof-technique can also be used to prove a more general theorem (Theorem 2). We conclude by indicating how this technique can be generalised to uniform hypergraphs by proving the uniform Ray-Chaudhuri-Wilson theorem. (C) 1997 Academic Press.

Magnetoresistance of the metallic perovskite oxide LaNiO3-delta

We report a study of the magnetoresistance (MR) of the metallic perovskite oxide LaNiO3-delta as a function of the oxygen stoichiometry delta (delta less than or equal to 0.14), magnetic field (H less than or equal to 6 T) and temperature (1.5 K less than or equal to T less than or equal to 25 K). We find a strong dependence of the nature of the MR on the oxygen stoichiometry. The MR at low temperatures changes from positive to negative as the sample becomes more oxygen deficient (i.e. delta increases). Some of the samples, which are more resistive, show resistivity minima at T-min approximate to 20 K. We find that in these samples the MR is positive for T > T-min and negative for T < T-min. We conclude that in the absence of strong magnetic interaction, the negative MR in these oxides can arise from weak-localization effects.

Spin-orbital ordering and mesoscopic phase separation in the double perovskite Ca2FeReO6

Neutron powder diffraction measurements on Ca2FeReO6 reveal that this double perovskite orders ferrimagnetically and shows anomalous lattice parameter behavior below T-C=521 K. Below similar to300 K and similar to160 K we observe that the high-T monoclinic crystal structure separates into two and three monoclinic phases, respectively. A magnetic field suppresses the additional phases at low T in favor of the highest-T phase. These manifestations of the orbital degree of freedom of Re 5d electrons indicate that these electrons are strongly correlated and the title compound is a Mott insulator, with competing spin-orbitally ordered states.

Synthesis and structure of La14V6CuO36.5: a transparent Cu(I) vanadate containing [OCuO](3-) sticks

The title compound, La14V6CuO36.5, was prepared from a stoichiometric mixture of La2O3,V2O5, and CuO at 1050-1080 degreesC. The compound forms transparent, pale green crystals and was characterized by wavelength dispersive spectroscopy and single crystal X-ray diffraction. The structure contains isolated VO43- tetrahedra and [OCuO](3-) sticks dispersed in a lanthanum oxide network. Films of La14V6CuO36.5 were grown on R-plane sapphire by using pulsed laser deposition. Rutherford backscattering spectroscopic and X-ray diffraction analyses of the films showed oriented growth of the title phase, a similar to5 eV optical band gap and n-type conductivity. The compound is an example of a transparent copper(I) oxide.

Novel ABO(3) oxides related to perovskite and YAlO3 structure types in the La-B-V-O (B = Ni, Cu) systems

The synthesis, structure and magnetic properties of mixed-metal oxides of ABO(3) composition in the La-B-V-O (B = Ni, Cu) systems are described in the present paper. While the B = Ni oxides adopt GdFeO3-like perovskite structure containing disordered nickel and vanadium at the octahedral B site, La3Cu2VO9 crystallizes in a YAlO3-type structure. A detailed investigation of the superstructure of nominal La3Cu2VO9 by WDS analysis and Rietveld refinement of powder XRD data reveal that the likely composition of the phase is La13Cu9V4O38.5, where the Cu and V atoms are ordered in a root13a(h) (a(h) = hexagonal a parameter of YAlO3-like subcell) superstructure. Magnetic susceptibility data support the proposed superstructure consisting of triangular Cu-3 clusters. At low temperatures, the magnetic moment corresponds to S = 1/2 per Cu-3 cluster, while at high temperatures the behavior is Curie-Weiss like, showing S = 1/2 per copper. The present work reveals the contrasting behavior of La-Cu-V-O and La-Ni-V-O systems: while a unique line-phase related to YAlO3 structure is formed around La3Cu2VO9 Composition in the copper system, a continuous series of perovskite-GdFeO3 solid solutions, LaNi1-xVxO3 for 0 less than or equal to x less than or equal to 1/3 seems to be obtained in the nickel system, where the oxidation state of nickel varies from 3+ to 2+.

Properties of the Ferrimagnetic Double-Perovskites A2FeReO6 (A=Ba and Ca)

We have synthesized ceramics of A2FeReO6 double-perovskites A2FeReO6 (A=Ba, Ca). Structural characterizations indicate a cubic structure with a=8.0854(1) Å for Ba2FeReO6 and a distorted monoclinic symmetry with a=5.396(1) Å, b=5.522(1) Å, c=7.688(2) Å and β=90.4° for Ca2FeReO6. The barium compound is metallic from 5K to 385K, i.e. no metal-insulator transition has been seen up to 385K, and the calcium compound is semiconducting from 5K to 385K. Magnetization measurements show a ferrimagnetic behavior for both materials, with Tc =315 K for Ba2FeReO6 and above 385K for Ca2FeReO6. At 5K we observed, only for Ba2FeReO6, a negative magnetoresistance of 10% in a magnetic field of 5T. Electrical, magnetic and thermal properties are discussed and compared to those of the analogous compounds Sr2Fe(Mo,Re)O6 recently studied.