Analytic results for Gaussian wave packets in four model systems: II. Autocorrelation functions

The autocorrelation function, A(t), measures the overlap (in Hilbert space) of a time-dependent quantum mechanical wave function, psi(x,t), with its initial value, psi(x,0). It finds extensive use in the theoretical analysis and experimental measurement of such phenomena as quantum wave packet revivals. We evaluate explicit expressions for the autocorrelation function for time-dependent Gaussian solutions of the Schrodinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a particle in a harmonic oscillator potential, and a system corresponding to an unstable equilibrium (the so-called `inverted' oscillator.) We emphasize the importance of momentum-space methods where such calculations are often more straightforwardly realized, as well as stressing their role in providing complementary information to results obtained using position-space wavefunctions.Comment: 18 pages, RevTeX, to appear in Found. Phys. Lett, Vol. 17, Dec. 200

Estimating Nuisance Parameters in Inverse Problems

Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is variable projection, where nonlinear least squares problems which are linear in some parameters can be very efficiently optimized. In this paper, we extend the idea of projecting out a subset over the variables to a broad class of maximum likelihood (ML) and maximum a posteriori likelihood (MAP) problems with nuisance parameters, such as variance or degrees of freedom. As a result, we are able to incorporate nuisance parameter estimation into large-scale constrained and unconstrained inverse problem formulations. We apply the approach to a variety of problems, including estimation of unknown variance parameters in the Gaussian model, degree of freedom (d.o.f.) parameter estimation in the context of robust inverse problems, automatic calibration, and optimal experimental design. Using numerical examples, we demonstrate improvement in recovery of primary parameters for several large- scale inverse problems. The proposed approach is compatible with a wide variety of algorithms and formulations, and its implementation requires only minor modifications to existing algorithms.Comment: 16 pages, 5 figure

The anomaly line bundle of the self-dual field theory

In this work, we determine explicitly the anomaly line bundle of the abelian self-dual field theory over the space of metrics modulo diffeomorphisms, including its torsion part. Inspired by the work of Belov and Moore, we propose a non-covariant action principle for a pair of Euclidean self-dual fields on a generic oriented Riemannian manifold. The corresponding path integral allows to study the global properties of the partition function over the space of metrics modulo diffeomorphisms. We show that the anomaly bundle for a pair of self-dual fields differs from the determinant bundle of the Dirac operator coupled to chiral spinors by a flat bundle that is not trivial if the underlying manifold has middle-degree cohomology, and whose holonomies are determined explicitly. We briefly sketch the relevance of this result for the computation of the global gravitational anomaly of the self-dual field theory, that will appear in another paper.Comment: 41 pages. v2: A few typos corrected. Version accepted for publication in CM

Analytic results for Gaussian wave packets in four model systems: I. Visualization of the kinetic energy

Using Gaussian wave packet solutions, we examine how the kinetic energy is distributed in time-dependent solutions of the Schrodinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a particle in a harmonic oscillator potential, and a system corresponding to an unstable equilibrium. We find, for specific choices of initial parameters, that as much as 90% of the kinetic energy can be localized (at least conceptually) in the `front half' of such Gaussian wave packets, and we visualize these effects.Comment: 22 pages, RevTeX, four .eps figures, to appear in Found. Phys. Lett. Vol. 17, Dec. 200

Quantum mechanics: Myths and facts

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.Comment: 51 pages, pedagogic review, revised, new references, to appear in Found. Phy

Spin Glass and Antiferromagnetic Behaviour in a Diluted fcc Antiferromagnet

We report on a Monte Carlo study of a diluted Ising antiferromagnet on a fcc lattice. This is a typical model example of a highly frustrated antiferromagnet, and we ask, whether sufficient random dilution of spins does produce a spin glass phase. Our data strongly indicate the existence of a spin glass transition for spin--concentration $p<0.75$: We find a divergent spin glass susceptibility and a divergent spin glass correlation length, whereas the antiferromagnetic correlation length saturates in this regime. Furthermore, we find a first order phase transition to an antiferromagnet for $1\ge p>0.85$, which becomes continuous in the range $0.85>p>0.75$. Finite size scaling is employed to obtain critical exponents. We compare our results with experimental systems as diluted frustrated antiferromagnets as ${\rm Zn_{1-p}Mn_{p}Te}$.Comment: 29 pages (revtex) and 10 figures uuencoded and Z-compresse

Aging partially restores the efficacy of malaria vector control in insecticide-resistant populations of Anopheles gambiae s.l. from Burkina Faso

&lt;br&gt;Background: The operational impact of insecticide resistance on the effectiveness of long-lasting insecticide nets (LLINs) and indoor residual spraying (IRS) is poorly understood. One factor which may prolong the effectiveness of these tools in the field is the increase in insecticide susceptibility with mosquito age. In this study, LLINs and IRS were tested against young (three to five days) and old (17-19 days) pyrethroid resistant Anopheles gambiae s.l. from Burkina Faso.&lt;/br&gt; &lt;br&gt;Methods: Blood-fed adult Anopheles gambiae s.l. were collected from south-west Burkina Faso and identified to species/form level. Cohorts of the F1 progeny of An. gambiae s.s. S-forms were exposed to deltamethrin (0.05%) at three to five or 17-19 days post-emergence and tested for the frequency of the resistance allele 1014F. Isofemale lines of the M, S- form of An. gambiae s.s. and Anopheles arabiensis were exposed in WHO cone tests to either a) LLINs deployed in households for two years or (b) bendiocarb sprayed walls.&lt;/br&gt; &lt;br&gt;Results: Mortality rates in response to deltamethrin (0.05%) increased from levels indicative of strong resistance in three to five day old F1 mosquitoes, to near full susceptibility in the 17-19 day old cohort. On exposure to LLINs sampled from the field, the mortality rate in isofemale lines was higher in older mosquitoes than young (OR = 5.28, CI 95% = 2.81-9.92), although the mortality estimates were affected by the LLIN tested. In general, the LLINs sampled from the field performed poorly in WHO cone bioassays using either laboratory susceptible or field caught mosquito populations. Finally, there was a clear relationship between mortality and age on exposure to bendiocarb-sprayed walls, with older mosquitoes again proving more susceptible (OR = 3.39, CI 95% = 2.35-4.90).&lt;/br&gt; &lt;br&gt;Conclusions: Age is a key factor determining the susceptibility of mosquitoes to insecticides, not only in laboratory studies, but in response to field-based vector control interventions. This has important implications for understanding the epidemiological impact of resistance. If mosquitoes old enough to transmit malaria are still being suppressed with available insecticides, is resistance potentially having less of an impact than often assumed? However, the poor performance of LLINs used in this study in Burkina Faso, is a cause for concern and requires urgent investigation.&lt;/br&gt

C. elegans Germline-Deficient Mutants Respond to Pathogen Infection Using Shared and Distinct Mechanisms

Reproduction extracts a cost in resources that organisms are then unable to utilize to deal with a multitude of environmental stressors. In the nematode C. elegans, development of the germline shortens the lifespan of the animal and increases its susceptibility to microbial pathogens. Prior studies have demonstrated germline-deficient nematodes to have increased resistance to Gram negative bacteria. We show that germline-deficient strains display increased resistance across a broad range of pathogens including Gram positive and Gram negative bacteria, and the fungal pathogen Cryptococcus neoformans. Furthermore, we show that the FOXO transcription factor DAF-16, which regulates longevity and immunity in C. elegans, appears to be crucial for maintaining longevity in both wild-type and germline-deficient backgrounds. Our studies indicate that germline-deficient mutants glp-1 and glp-4 respond to pathogen infection using common and different mechanisms that involve the activation of DAF-16

Xer Recombinase and Genome Integrity in Helicobacter pylori, a Pathogen without Topoisomerase IV

In the model organism E. coli, recombination mediated by the related XerC and XerD recombinases complexed with the FtsK translocase at specialized dif sites, resolves dimeric chromosomes into free monomers to allow efficient chromosome segregation at cell division. Computational genome analysis of Helicobacter pylori, a slow growing gastric pathogen, identified just one chromosomal xer gene (xerH) and its cognate dif site (difH). Here we show that recombination between directly repeated difH sites requires XerH, FtsK but not XerT, the TnPZ transposon associated recombinase. xerH inactivation was not lethal, but resulted in increased DNA per cell, suggesting defective chromosome segregation. The xerH mutant also failed to colonize mice, and was more susceptible to UV and ciprofloxacin, which induce DNA breakage, and thereby recombination and chromosome dimer formation. xerH inactivation and overexpression each led to a DNA segregation defect, suggesting a role for Xer recombination in regulation of replication. In addition to chromosome dimer resolution and based on the absence of genes for topoisomerase IV (parC, parE) in H. pylori, we speculate that XerH may contribute to chromosome decatenation, although possible involvement of H. pylori's DNA gyrase and topoisomerase III homologue are also considered. Further analyses of this system should contribute to general understanding of and possibly therapy development for H. pylori, which causes peptic ulcers and gastric cancer; for the closely related, diarrheagenic Campylobacter species; and for unrelated slow growing pathogens that lack topoisomerase IV, such as Mycobacterium tuberculosis