Alternating groups and moduli space lifting Invariants

Main Theorem: Spaces of r-branch point 3-cycle covers, degree n or Galois of degree n!/2 have one (resp. two) component(s) if r=n-1 (resp. r\ge n). Improves Fried-Serre on deciding when sphere covers with odd-order branching lift to unramified Spin covers. We produce Hurwitz-Torelli automorphic functions on Hurwitz spaces, and draw Inverse Galois conclusions. Example: Absolute spaces of 3-cycle covers with +1 (resp. -1) lift invariant carry canonical even (resp. odd) theta functions when r is even (resp. odd). For inner spaces the result is independent of r. Another use appears in, http://www.math.uci.edu/~mfried/paplist-mt/twoorbit.html, "Connectedness of families of sphere covers of A_n-Type." This shows the M(odular) T(ower)s for the prime p=2 lying over Hurwitz spaces first studied by, http://www.math.uci.edu/~mfried/othlist-cov/hurwitzLiu-Oss.pdf, Liu and Osserman have 2-cusps. That is sufficient to establish the Main Conjecture: (*) High tower levels are general-type varieties and have no rational points.For infinitely many of those MTs, the tree of cusps contains a subtree -- a spire -- isomorphic to the tree of cusps on a modular curve tower. This makes plausible a version of Serre's O(pen) I(mage) T(heorem) on such MTs. Establishing these modular curve-like properties opens, to MTs, modular curve-like thinking where modular curves have never gone before. A fuller html description of this paper is at http://www.math.uci.edu/~mfried/paplist-cov/hf-can0611591.html .Comment: To appear in the Israel Journal as of 1/5/09; v4 is corrected from proof sheets, but does include some proof simplification in \S

Ensembles of Human MTL Neurons Jump Back in Time in Response to a Repeated Stimulus

Episodic memory, which depends critically on the integrity of the medial temporal lobe (MTL), has been described as ‘‘mental time travel’’ in which the rememberer ‘‘jumps back in time.’’ The neural mechanism underlying this ability remains elusive. Mathematical and computational models of performance in episodic memory tasks provide a specific hypothesis regarding the computation that supports such a jump back in time. The models suggest that a representation of temporal context, a representation that changes gradually over macroscopic periods of time, is the cue for episodic recall. According to these models, a jump back in time corresponds to a stimulus recovering a prior state of temporal context. In vivo single-neuron recordings were taken from the human MTL while epilepsy patients distinguished novel from repeated images in a continuous recognition memory task. The firing pattern of the ensemble of MTL neurons showed robust temporal autocorrelation over macroscopic periods of time during performance of the memory task. The gradually-changing part of the ensemble state was causally affected by the visual stimulus being presented. Critically, repetition of a stimulus caused the ensemble to elicit a pattern of activity that resembled the pattern of activity present before the initial presentation of the stimulus. These findings confirm a direct prediction of this class of temporal context models and may be a signature of the mechanism that underlies the experience of episodic memory as mental time travel

A new simulation algorithm for lattice QCD with dynamical quarks

A previously introduced multi-boson technique for the simulation of QCD with dynamical quarks is described and some results of first test runs on a $6^3\times12$ lattice with Wilson quarks and gauge group SU(2) are reported.Comment: 7 pages, postscript file (166 KB

Ionization Potential of the Helium Atom

Ground state ionization potential of the He^4 atom is evaluated to be 5 945 204 221 (42) MHz. Along with lower order contributions, this result includes all effects of the relative orders alpha^4, alpha^3*m_e/m_alpha and alpha^5*ln^2(alpha).Comment: 4 page

Quantum Gauge Equivalence in QED

We discuss gauge transformations in QED coupled to a charged spinor field, and examine whether we can gauge-transform the entire formulation of the theory from one gauge to another, so that not only the gauge and spinor fields, but also the forms of the operator-valued Hamiltonians are transformed. The discussion includes the covariant gauge, in which the gauge condition and Gauss's law are not primary constraints on operator-valued quantities; it also includes the Coulomb gauge, and the spatial axial gauge, in which the constraints are imposed on operator-valued fields by applying the Dirac-Bergmann procedure. We show how to transform the covariant, Coulomb and spatial axial gauges to what we call ``common form,'' in which all particle excitation modes have identical properties. We also show that, once that common form has been reached, QED in different gauges has a common time-evolution operator that defines time-translation for states that represent systems of electrons and photons. By combining gauge transformations with changes of representation from standard to common form, the entire apparatus of a gauge theory can be transformed from one gauge to another.Comment: Contribution for a special issue of Foundations of Physics honoring Fritz Rohrlich; edited by Larry P. Horwitz, Tel-Aviv University, and Alwyn van der Merwe, University of Denver (Plenum Publishing, New York); 40 pages, REVTEX, Preprint UCONN-93-3, 1 figure available upon request from author

Siegert pseudostates: completeness and time evolution

Within the theory of Siegert pseudostates, it is possible to accurately calculate bound states and resonances. The energy continuum is replaced by a discrete set of states. Many questions of interest in scattering theory can be addressed within the framework of this formalism, thereby avoiding the need to treat the energy continuum. For practical calculations it is important to know whether a certain subset of Siegert pseudostates comprises a basis. This is a nontrivial issue, because of the unusual orthogonality and overcompleteness properties of Siegert pseudostates. Using analytical and numerical arguments, it is shown that the subset of bound states and outgoing Siegert pseudostates forms a basis. Time evolution in the context of Siegert pseudostates is also investigated. From the Mittag-Leffler expansion of the outgoing-wave Green's function, the time-dependent expansion of a wave packet in terms of Siegert pseudostates is derived. In this expression, all Siegert pseudostates--bound, antibound, outgoing, and incoming--are employed. Each of these evolves in time in a nonexponential fashion. Numerical tests underline the accuracy of the method

Haptoglobin frequencies in Jewish communities *

Haptoglobin and transferrin types have been determined by starch gel electrophoresis on blood from 929 subjects belonging to various Jewish communities. The frequency of the Hp 1 gene in 499 Ashkenazic Jews is 0.29 and does not differ significantly from the value of 0–26 found in 345 Jews of Oriental origin. The Hp 1 frequency of Ashkenazic Jews is significantly lower than that reported for the autochthonous populations of Central and Western Europe. Two small samples collected among Sephardic Jews and among the offspring of intercommunity marriages exhibit somewhat higher frequencies of the Hp 1 gene. The modified 2-1 phenotype was found in a single subject from Baghdad. There were three cases of ahaptoglobinaemia among Ashkenazic Jews and three among the Oriental groups. No ahaptoglobinaemia was discovered in a family sample of ninety-two Jews from Kurdistan among whom thalassaemia minor was common and the majority of whom were affeeted with G-6-P-D deficiency. All transferrins were of type C.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66130/1/j.1469-1809.1962.tb01307.x.pd

Radiative Corrections to W and Quark Propagators in the Resonance Region

We discuss radiative corrections to W and quark propagators in the resonance region, |s-M^2| \lsim M*Gamma. We show that conventional mass renormalization, when applied to photonic or gluonic corrections, leads in next to leading order (NLO) to contributions proportional to [M*Gamma/(s-M^2)]^n, (n=1,2...), i.e. to a non-convergent series in the resonance region, a difficulty that affects all unstable particles coupled to massless quanta. A solution of this problem, based on the concepts of pole mass and width, is presented. It elucidates the issue of renormalization of amplitudes involving unstable particles and automatically circumvents the problem of apparent on-shell singularities. The roles of the Fried-Yennie gauge and the Pinch Technique prescription are discussed. Because of special properties of the photonic and gluonic contributions, and in contrast with the Z case, the gauge dependence of the conventional on-shell definition of mass is unbounded in NLO. The evaluations of the width in the conventional and pole formulations are compared and shown to agree in NLO but not beyond.Comment: 19 pages, 7 figures, LaTeX (uses epsfig). Slight rewording of the abstract and one of the sentences of the text. Minor misprints corrected. To appear in Phys. Rev.

Loop-after-loop contribution to the second-order Lamb shift in hydrogenlike low-Z atoms

We present a numerical evaluation of the loop-after-loop contribution to the second-order self-energy for the ground state of hydrogenlike atoms with low nuclear charge numbers Z. The calculation is carried out in the Fried-Yennie gauge and without an expansion in Z \alpha. Our calculation confirms the results of Mallampalli and Sapirstein and disagrees with the calculation by Goidenko and coworkers. A discrepancy between different calculations is investigated. An accurate fitting of the numerical results provides a detailed comparison with analytic calculations based on an expansion in the parameter Z \alpha. We confirm the analytic results of order \alpha^2 (Z\alpha)^5 but disagree with Karshenboim's calculation of the \alpha^2 (Z \alpha)^6 \ln^3(Z \alpha)^{-2} contribution.Comment: RevTex, 19 pages, 4 figure