Global anomalies on orbifolds

Communicated by A. Jaffe     

Final state interactions in nuclear pion photoproduction over the (3, 3) resonance

An impulse approximation calculation is made on the reaction ⁵¹V(γ, π⁺)⁵¹Ti from the region just above photopion threshold to the tail of the (3, 3) resonance. Pion final state distortions are taken into account through realistic optical potentials. Results are compared to those for plane-wave and surface-produced pions and to recent experiment. Comparison is made between surface-produced pions and pions distorted by the s-wave component of the optical potential.     

A variable temperature EPR study of Mn-doped NH4Cl0.9I0.1 single crystal at 170 GHz: Zero-field splitting parameter and its absolute sign

EPR measurements have been carried out on a single crystal of Mn(2+)-doped NH(4)Cl(0.9)I(0.1) at 170-GHz in the temperature range of 312-4.2K. The spectra have been analyzed (i) to estimate the spin-Hamiltonian parameters; (ii) to study the temperature variation of the zero-field splitting (ZFS) parameter; (iii) to confirm the negative absolute sign of the ZFS parameter unequivocally from the temperature-dependent relative intensities of hyperfine sextets at temperatures below 10K; and (iv) to detect the occurrence of a structural phase transition at 4.35K from the change in the structure of the EPR lines with temperature below 10K.     

Theoretical Foundations Of Purely Semi-Empirical Quantum Chemistry. III. Repulsion Integrals

Results of ab initio calculations of correlation energies are used to estimate the correlation contribution to true repulsion integrals γpq. The one-center true γpp and the distance dependence of the true γpq are shown to be in semi-quantitative agreement with the empirical resonance integrals used in pi-electron theories. The relationship between the true γpp and the difference between true molecular ionization potentials and electron affinities is also discussed.     

A derivation of the exact pi-electron hamiltonian

The exact pi-electron hamiltonian is derived from the full many-electron Schrödinger equation. The derivation employs techniques which also enable the development of open shell generalized perturbation theory. The parameters occurring in the pi-hamiltonian are therefore amenable to calculation using the approximate theories and methods of Sinano?lu, Nesbet, Kelly, etc. To a good approximation, the pi-hamiltonian is found to be generally consistent with its customarily assumed form.     

Coherence transfer processes in vibrational relaxation of polyatomic molecules in condensed media

The vibrational relaxation of a polyatomic molecule in a condensed host is studied by a consideration of two molecular vibrations. Relaxation processes, intermode coupling terms and vibrational frequency fluctuation contributions are retained. Population decay (T₁), dephasing (T₂), and coherence transfer rates are evaluated through second order in the limit where the host bath dynamics are rapid compared to these molecular timescales. The rates are expressed in terms of temperature and frequency dependent bath correlation functions. For the special case of a three level system (the ground state and ones where one of the two vibrational modes is excited) the important effects of anharmonicity are incorporated. It is shown that certain coherence transfer terms involve zero frequency bath correlation functions, so they should be larger than the high frequency ones which obey modified energy gap laws. A discussion is presented of the types of interactions which may contribute to these coherence transfer processes.     

A correlation between the order parameters of rigid solutes dissolved in two nematic solvents and in a mixture of them

The orientational data of four rigid solutes dissolved in the nematic solvents ZLI1132, EBBA and in a 55wt% ZLI1132 + EBBA mixture have been obtained from proton NMR spectra at different temperatures and used to find a relationship between the solute order in the two nematics and in their mixture. A crossed comparison of the data shows that a simple linear relation, where the normalized weights of the combination are coincident with the molar fractions of ZLI1132 and EBBA in the mixture, gives excellent agreement independently of the solutes and temperatures. Consideration is given to the possibility of a generalization of the results to any mixture of two nematics.     

Ethnic Preferences and Residential Segregation: Theoretical Explorations Beyond Detroit

We are strongly supportive of Fossett's theoretical approach and modeling methodology, which uses computational methods to perform thought experiments that generate compelling insights into the enigma of persistent residential segregation in the U.S. We also agree with his theoretical results, which challenge the prevailing view among demographers that institutional discrimination is the essential cause. However, we think he did not go far enough. Fossett limited his analysis to a narrow region of the parameter space that corresponded to conditions observed in one city at one time. This precludes generalization to other times and places and exploration of theoretically motivated “what if” scenarios that trespass beyond the Detroit city limits. When we extended the parameter space, we noticed two interesting results. First, Fossett's “paradox of weak minority preferences” requires qualification. Disproportionate in-group preferences among minorities are indeed segregation-promoting, not integration-promoting, but they generally have less impact on segregation than the in-group preferences of the majority. Second, not only are exclusionary practices and institutional discrimination not necessary for segregation (as Fossett demonstrates), we show that in certain regions of the parameter space they are not even sufficient.     

Benchmarking implicit solvent folding simulations of the amyloid beta(10-35) fragment

A pathogenetic feature of Alzhemier disease is the aggregation of monomeric beta-amyloid proteins (Abeta) to form oligomers. Usually these oligomers of long peptides aggregate on time scales of microseconds or longer, making computational studies using atomistic molecular dynamics models prohibitively expensive and making it essential to develop computational models that are cheaper and at the same time faithful to physical features of the process. We benchmark the ability of our implicit solvent model to describe equilibrium and dynamic properties of monomeric Abeta(10-35) using all-atom Langevin dynamics (LD) simulations, since Alphabeta(10-35) is the only fragment whose monomeric properties have been measured. The accuracy of the implicit solvent model is tested by comparing its predictions with experiment and with those from a new explicit water MD simulation, (performed using CHARMM and the TIP3P water model) which is approximately 200 times slower than the implicit water simulations. The dependence on force field is investigated by running multiple trajectories for Alphabeta(10-35) using the CHARMM, OPLS-aal, and GS-AMBER94 force fields, whereas the convergence to equilibrium is tested for each force field by beginning separate trajectories from the native NMR structure, a completely stretched structure, and from unfolded initial structures. The NMR order parameter, S2, is computed for each trajectory and is compared with experimental data to assess the best choice for treating aggregates of Alphabeta. The computed order parameters vary significantly with force field. Explicit and implicit solvent simulations using the CHARMM force fields display excellent agreement with each other and once again support the accuracy of the implicit solvent model. Alphabeta(10-35) exhibits great flexibility, consistent with experiment data for the monomer in solution, while maintaining a general strand-loop-strand motif with a solvent-exposed hydrophobic patch that is believed to be important for aggregation. Finally, equilibration of the peptide structure requires an implicit solvent LD simulation as long as 30 ns.     

Membrane-bound alpha-synuclein forms an extended helix: long-distance pulsed ESR measurements using vesicles, bicelles, and rodlike micelles

We apply pulsed dipolar ESR spectroscopy (Ku-band DEER) to elucidate the global conformation of the Parkinson's disease-associated protein, alpha-synuclein (alphaS) bound to small unilamellar phospholipid vesicles, rodlike SDS micelles, or lipid bicelles. By measuring distances as long as approximately 7 nm between introduced pairs of nitroxide spin labels, we show that distances are close to the expectations for a single continuous helix in all cases studied. In particular, we find distances of 7.5 nm between sites 24 and 72; 5.5 nm between sites 24 and 61; and 2 nm between sites 35 and 50. We conclude that alphaS does not retain a "hairpin" structure with two antiparallel helices, as is known to occur with spheroidal micelles, in agreement with our earlier finding that the protein's geometry is determined by the surface topology rather than being constrained by the interhelix linker. While the possibility of local helix discontinuities in the structure of membrane-bound alphaS remains, our data are more consistent with one intact helix. Importantly, we demonstrate that bicelles produce very similar results to liposomes, while offering a major improvement in experimentally accessible distance range and resolution, and thus are an excellent lipid membrane mimetic for the purpose of pulse dipolar ESR spectroscopy.