A \Gamma-structure on Lagrangian Grassmannians

For n odd the Lagrangian Grassmannian of \R^{2n} is a \Gamma-manifold.Comment: 6 pages; v2: new coauthor, nicer proo

Stability is not open

We give an example of a symplectic manifold with a stable hypersurface such that nearby hypersurfaces are typically unstable.Comment: 9 page

Floer homology for magnetic fields with at most linear growth on the universal cover

The Floer homology of a cotangent bundle is isomorphic to loop space homology of the underlying manifold, as proved by Abbondandolo-Schwarz, Salamon-Weber, and Viterbo. In this paper we show that in the presence of a Dirac magnetic monopole which admits a primitive with sublinear growth on the universal cover, the Floer homology in atoroidal free homotopy classes is again isomorphic to loop space homology. As a consequence we prove that for any atoroidal free homotopy class and any sufficiently small T>0, any magnetic flow associated to the Dirac magnetic monopole has a closed orbit of period T belonging to the given free homotopy class. In the case where the Dirac magnetic monopole admits a bounded primitive on the universal cover we also prove the Conley conjecture for Hamiltonians that are quadratic at infinity, i.e., we show that such Hamiltonians have infinitely many periodic orbits.Comment: 24 pages, V2 - minor corrections, final version to appear in JF

The contact geometry of the restricted 3-body problem

We show that the planar circular restricted three body problem is of restricted contact type for all energies below the first critical value (action of the first Lagrange point) and for energies slightly above it. This opens up the possibility of using the technology of Contact Topology to understand this particular dynamical system.Comment: 29 pages, 1 figur

Conformational Dependence of a Protein Kinase Phosphate Transfer Reaction

Atomic motions and energetics for a phosphate transfer reaction catalyzed by the cAMP-dependent protein kinase (PKA) are calculated by plane-wave density functional theory, starting from structures of proteins crystallized in both the reactant conformation (RC) and the transition-state conformation (TC). In the TC, we calculate that the reactants and products are nearly isoenergetic with a 0.2 eV barrier; while phosphate transfer is unfavorable by over 1.2 eV in the RC, with an even higher barrier. With the protein in the TC, the motions involved in reaction are small, with only P$_\gamma$ and the catalytic proton moving more than 0.5 \AA. Examination of the structures reveals that in the RC the active site cleft is not completely closed and there is insufficient space for the phosphorylated serine residue in the product state. Together, these observations imply that the phosphate transfer reaction occurs rapidly and reversibly in a particular conformation of the protein, and that the reaction can be gated by changes of a few tenths of an \AA in the catalytic site.Comment: revtex4, 7 pages, 4 figures, to be submitted to Scienc

Model Independent Form Factors for Spin Independent Neutralino-Nucleon Scattering from Elastic Electron Scattering Data

Theoretical calculations of neutralino-nucleon interaction rates with various nuclei are of great interest to direct dark matter searches such as CDMS, EDELWEISS, ZEPLIN, and other experiments since they are used to establish upper bounds on the WIMP-proton cross section. These interaction rates and cross sections are generally computed with standard, one or two parameter model-dependent nuclear form factors, which may not exactly mirror the actual form factor for the particular nucleus in question. As is well known, elastic electron scattering can allow for very precise determinations of nuclear form factors and hence nuclear charge densities for spherical or near-spherical nuclei. We use charge densities derived from elastic electron scattering data to calculate model independent, analytic form factors for various target nuclei important in dark matter searches, such as Si, Ge, S, Ca and others. We have found that for nuclear recoils in the range of 1-100 keV significant differences in cross sections and rates exist when the model independent form factors are used: at 30 keV nuclear recoil the form factors squared differ by a factor of 1.06 for $^{28}$Si, 1.11 for $^{40}$Ca, 1.27 for $^{70}$Ge, and 1.92 for $^{129}$Xe. We show the effect of different form factors on the upper limit on the WIMP-proton cross section obtained with a hypothetical $^{70}$Ge detector during a 100 kg-day effective exposure. Helm form factors with various parameter choices differ at most by 10--20% from the best (Fourier Bessel) form factor, and can approach it to better than 1% if the parameters are chosen to mimic the actual nuclear density.Comment: 20 pages, 8 figure

Analytic models for mechanotransduction: gating a mechanosensitive channel

Analytic estimates for the forces and free energy generated by bilayer deformation reveal a compelling and intuitive model for MscL channel gating analogous to the nucleation of a second phase. We argue that the competition between hydrophobic mismatch and tension results in a surprisingly rich story which can provide both a quantitative comparison to measurements of opening tension for MscL when reconstituted in bilayers of different thickness and qualitative insights into the function of the MscL channel and other transmembrane proteins

Hysteretic Optimization For Spin Glasses

The recently proposed Hysteretic Optimization (HO) procedure is applied to the 1D Ising spin chain with long range interactions. To study its effectiveness, the quality of ground state energies found as a function of the distance dependence exponent, $\sigma$, is assessed. It is found that the transition from an infinite-range to a long-range interaction at $\sigma=0.5$ is accompanied by a sharp decrease in the performance . The transition is signaled by a change in the scaling behavior of the average avalanche size observed during the hysteresis process. This indicates that HO requires the system to be infinite-range, with a high degree of interconnectivity between variables leading to large avalanches, in order to function properly. An analysis of the way auto-correlations evolve during the optimization procedure confirm that the search of phase space is less efficient, with the system becoming effectively stuck in suboptimal configurations much earlier. These observations explain the poor performance that HO obtained for the Edwards-Anderson spin glass on finite-dimensional lattices, and suggest that its usefulness might be limited in many combinatorial optimization problems.Comment: 6 pages, 9 figures. To appear in JSTAT. Author website: http://www.bgoncalves.co

p-Adic Models of Ultrametric Diffusion Constrained by Hierarchical Energy Landscapes

We demonstrate that p-adic analysis is a natural basis for the construction of a wide variety of the ultrametric diffusion models constrained by hierarchical energy landscapes. A general analytical description in terms of p-adic analysis is given for a class of models. Two exactly solvable examples, i.e. the ultrametric diffusion constraned by the linear energy landscape and the ultrametric diffusion with reaction sink, are considered. We show that such models can be applied to both the relaxation in complex systems and the rate processes coupled to rearrangenment of the complex surrounding.Comment: 14 pages, 6 eps figures, LaTeX 2.0

Thermodynamics of protein folding: a random matrix formulation

The process of protein folding from an unfolded state to a biologically active, folded conformation is governed by many parameters e.g the sequence of amino acids, intermolecular interactions, the solvent, temperature and chaperon molecules. Our study, based on random matrix modeling of the interactions, shows however that the evolution of the statistical measures e.g Gibbs free energy, heat capacity, entropy is single parametric. The information can explain the selection of specific folding pathways from an infinite number of possible ways as well as other folding characteristics observed in computer simulation studies.Comment: 21 Pages, no figure