Topology of multiple log transforms of 4-manifolds

Given a 4-manifold X and an imbedding of T^{2} x B^2 into X, we describe an algorithm X --> X_{p,q} for drawing the handlebody of the 4-manifold obtained from X by (p,q)-logarithmic transforms along the parallel tori. By using this algorithm, we obtain a simple handle picture of the Dolgachev surface E(1)_{p,q}, from that we deduce that the exotic copy E(1)_{p,q} # 5(-CP^2) of E(1) # 5(-CP^2) differs from the original one by a codimension zero simply connected Stein submanifold M_{p,q}, which are therefore examples of infinitely many Stein manifolds that are exotic copies of each other (rel boundaries). Furthermore, by a similar method we produce infinitely many simply connected Stein submanifolds Z_{p} of E(1)_{p,2} # 2(-CP^2)$ with the same boundary and the second Betti number 2, which are (absolutely) exotic copies of each other; this provides an alternative proof of a recent theorem of the author and Yasui [AY4]. Also, by using the description of S^2 x S^2 as a union of two cusps glued along their boundaries, and by using this algorithm, we show that multiple log transforms along the tori in these cusps do not change smooth structure of S^2 x S^2.Comment: Updated, with 17 pages 21 figure

The Paradoxical Forces for the Classical Electromagnetic Lag Associated with the Aharonov-Bohm Phase Shift

The classical electromagnetic lag assocated with the Aharonov-Bohm phase shift is obtained by using a Darwin-Lagrangian analysis similar to that given by Coleman and Van Vleck to identify the puzzling forces of the Shockley-James paradox. The classical forces cause changes in particle velocities and so produce a relative lag leading to the same phase shift as predicted by Aharonov and Bohm and observed in experiments. An experiment is proposed to test for this lag aspect implied by the classical analysis but not present in the currently-accepted quantum topological description of the phase shift.Comment: 8 pages, 3 figure

Optical properties of potential-inserted quantum wells in the near infrared and Terahertz ranges

We propose an engineering of the optical properties of GaAs/AlGaAs quantum wells using AlAs and InAs monolayer insertions. A quantitative study of the effects of the monolayer position and the well thickness on the interband and intersubband transitions, based on the extended-basis sp3d5s* tight-binding model, is presented. The effect of insertion on the interband transitions is compared with existing experimental data. As for intersubband transitions, we show that in a GaAs/AlGaAs quantum well including two AlAs and one InAs insertions, a three level {e1 , e2 , e3 } system where the transition energy e3-e2 is lower and the transition energy e2-e1 larger than the longitudinal optical phonon energy (36 meV) can be engineered together with a e3-e2 transition energy widely tunable through the TeraHertz range

Derivation of the Blackbody Radiation Spectrum from a Natural Maximum-Entropy Principle Involving Casimir Energies and Zero-Point Radiation

By numerical calculation, the Planck spectrum with zero-point radiation is shown to satisfy a natural maximum-entropy principle whereas alternative choices of spectra do not. Specifically, if we consider a set of conducting-walled boxes, each with a partition placed at a different location in the box, so that across the collection of boxes the partitions are uniformly spaced across the volume, then the Planck spectrum correspond to that spectrum of random radiation (having constant energy kT per normal mode at low frequencies and zero-point energy (1/2)hw per normal mode at high frequencies) which gives maximum uniformity across the collection of boxes for the radiation energy per box. The analysis involves Casimir energies and zero-point radiation which do not usually appear in thermodynamic analyses. For simplicity, the analysis is presented for waves in one space dimension.Comment: 11 page

Structures of fibrils formed by α-synuclein hereditary disease mutant H50Q reveal new polymorphs.

Deposits of amyloid fibrils of α-synuclein are the histological hallmarks of Parkinson's disease, dementia with Lewy bodies and multiple system atrophy, with hereditary mutations in α-synuclein linked to the first two of these conditions. Seeing the changes to the structures of amyloid fibrils bearing these mutations may help to understand these diseases. To this end, we determined the cryo-EM structures of α-synuclein fibrils containing the H50Q hereditary mutation. We find that the H50Q mutation results in two previously unobserved polymorphs of α-synuclein: narrow and wide fibrils, formed from either one or two protofilaments, respectively. These structures recapitulate conserved features of the wild-type fold but reveal new structural elements, including a previously unobserved hydrogen-bond network and surprising new protofilament arrangements. The structures of the H50Q polymorphs help to rationalize the faster aggregation kinetics, higher seeding capacity in biosensor cells and greater cytotoxicity that we observe for H50Q compared to wild-type α-synuclein

The Development of the Neoclassical Tradition in Labor Economics

This essay on labor economics examines neoclassical theory\u27s rise to ascendancy following the second World War, with a secondary focus on the relative decline but continued influence of institutionalist economic theory. The authors describe the evolution of institutional and neoclassical theory from the late nineteenth to mid-twentieth centuries, examine some early intellectual debates between the two camps, briefly describe the work of neoclassical labor economics pioneers, and look at major developments over the past 30 years. They argue that neoclassical economists\u27 increasing intellectual breadth and influence in public policy have led them to pay closer attention to issues that have long been of concern to institutionalists and neoinstitutionalists

On the distribution of estimators of diffusion constants for Brownian motion

We discuss the distribution of various estimators for extracting the diffusion constant of single Brownian trajectories obtained by fitting the squared displacement of the trajectory. The analysis of the problem can be framed in terms of quadratic functionals of Brownian motion that correspond to the Euclidean path integral for simple Harmonic oscillators with time dependent frequencies. Explicit analytical results are given for the distribution of the diffusion constant estimator in a number of cases and our results are confirmed by numerical simulations.Comment: 14 pages, 5 figure

Randomizing world trade. II. A weighted network analysis

Based on the misleading expectation that weighted network properties always offer a more complete description than purely topological ones, current economic models of the International Trade Network (ITN) generally aim at explaining local weighted properties, not local binary ones. Here we complement our analysis of the binary projections of the ITN by considering its weighted representations. We show that, unlike the binary case, all possible weighted representations of the ITN (directed/undirected, aggregated/disaggregated) cannot be traced back to local country-specific properties, which are therefore of limited informativeness. Our two papers show that traditional macroeconomic approaches systematically fail to capture the key properties of the ITN. In the binary case, they do not focus on the degree sequence and hence cannot characterize or replicate higher-order properties. In the weighted case, they generally focus on the strength sequence, but the knowledge of the latter is not enough in order to understand or reproduce indirect effects.Comment: See also the companion paper (Part I): arXiv:1103.1243 [physics.soc-ph], published as Phys. Rev. E 84, 046117 (2011

Structure of amyloid-β (20-34) with Alzheimer's-associated isomerization at Asp23 reveals a distinct protofilament interface.

Amyloid-β (Aβ) harbors numerous posttranslational modifications (PTMs) that may affect Alzheimer's disease (AD) pathogenesis. Here we present the 1.1 Å resolution MicroED structure of an Aβ 20-34 fibril with and without the disease-associated PTM, L-isoaspartate, at position 23 (L-isoAsp23). Both wild-type and L-isoAsp23 protofilaments adopt β-helix-like folds with tightly packed cores, resembling the cores of full-length fibrillar Aβ structures, and both self-associate through two distinct interfaces. One of these is a unique Aβ interface strengthened by the isoaspartyl modification. Powder diffraction patterns suggest a similar structure may be adopted by protofilaments of an analogous segment containing the heritable Iowa mutation, Asp23Asn. Consistent with its early onset phenotype in patients, Asp23Asn accelerates aggregation of Aβ 20-34, as does the L-isoAsp23 modification. These structures suggest that the enhanced amyloidogenicity of the modified Aβ segments may also reduce the concentration required to achieve nucleation and therefore help spur the pathogenesis of AD