How the Weak Variance of Momentum Can Turn Out to be Negative

Weak values are average quantities,therefore investigating their associated variance is crucial in understanding their place in quantum mechanics. We develop the concept of a position-postselected weak variance of momentum as cohesively as possible, building primarily on material from Moyal (Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press, Cambridge, 1949) and Sonego (Found Phys 21(10):1135, 1991) . The weak variance is defined in terms of the Wigner function, using a standard construction from probability theory. We show this corresponds to a measurable quantity, which is not itself a weak value. It also leads naturally to a connection between the imaginary part of the weak value of momentum and the quantum potential. We study how the negativity of the Wigner function causes negative weak variances, and the implications this has on a class of `subquantum' theories. We also discuss the role of weak variances in studying determinism, deriving the classical limit from a variational principle.Comment: 22 page

One-point fluctuation analysis of IceCube neutrino events outlines a significant unassociated isotropic component and constrains the Galactic contribution

The origins of the extraterrestrial neutrinos observed in IceCube have yet to be determined. In this study we perform a one-point fluctuation analysis of the six-year high-energy starting event (HESE) shower data, with fixed non-Poissonian contributions from atmospheric, Galactic and some extragalactic components, as well as an isotropic (and weakly non-Poissonian) template. In addition to the star-forming galaxies and blazars, our analysis suggests the presence of an additional isotropic component, not associated with any known class of sources, with best-fit intensity of $(2.8\pm0.2)\times 10^{-18}\,(E/100~{\rm TeV})^{-2.7\pm 0.5}$ ${\mathrm{cm}^{-2}\, \mathrm{s}^{-1}\,\mathrm{sr}^{-1}\,\mathrm{GeV}^{-1}}$. For the first time, we also consider high-energy extrapolations of several phenomenological models for the diffuse Galactic emission (tuned to both local cosmic-ray data and diffuse gamma-ray emission in the GeV-TeV domain). We demonstrate the potential of our framework in discriminating between different scenarios, with possible implications on the physics of cosmic ray transport in the TeV-PeV range.Comment: 10 pages, 3 figures, accepted for publication in PR

How bright can the brightest neutrino source be?

After the discovery of extraterrestrial high-energy neutrinos, the next major goal of neutrino telescopes will be identifying astrophysical objects that produce them. The flux of the brightest source $F_{\rm max}$, however, cannot be probed by studying the diffuse neutrino intensity. We aim at constraining $F_{\rm max}$ by adopting a broken power-law flux distribution, a hypothesis supported by observed properties of any generic astrophysical sources. The first estimate of $F_{\rm max}$ comes from the fact that we can only observe one universe, and hence, the expected number of sources above $F_{\rm max}$ cannot be too small compared with one. For abundant source classes such as starburst galaxies, this one-source constraint yields a value of $F_{\rm max}$ that is an order of magnitude lower than the current upper limits from point-source searches. Then we derive upper limits on $F_{\rm max}$ assuming that the angular power spectrum is consistent with neutrino shot noise yet. We find that the limits obtained with upgoing muon neutrinos in IceCube can already be quite competitive, especially for rare but bright source populations such as blazars. The limits will improve nearly quadratically with exposure, and therefore be even more powerful for the next generation of neutrino telescopes.Comment: 13 pages, 10 figures, accepted by Phys.Rev.

One-point fluctuation analysis of the high-energy neutrino sky

We perform the first one-point fluctuation analysis of the high-energy neutrino sky. This method reveals itself to be especially suited to contemporary neutrino data, as it allows to study the properties of the astrophysical components of the high-energy flux detected by the IceCube telescope, even with low statistics and in the absence of point source detection. Besides the veto-passing atmospheric foregrounds, we adopt a simple model of the high-energy neutrino background by assuming two main extra-galactic components: star-forming galaxies and blazars. By leveraging multi-wavelength data from Herschel and Fermi, we predict the spectral and anisotropic probability distributions for their expected neutrino counts in IceCube. We find that star-forming galaxies are likely to remain a diffuse background due to the poor angular resolution of IceCube, and we determine an upper limit on the number of shower events that can reasonably be associated to blazars. We also find that upper limits on the contribution of blazars to the measured flux are unfavourably affected by the skewness of the blazar flux distribution. One-point event clustering and likelihood analyses of the IceCube HESE data suggest that this method has the potential to dramatically improve over more conventional model-based analyses, especially for the next generation of neutrino telescopes.Comment: 41 pages, 6 figures, 2 tables; different blazar model than v1 but same result

Deterministic optical rogue waves

Experimental observations of rare giant pulses or rogue waves were done in the output intensity of an optically injected semiconductor laser. The long-tailed probability distribution function of the pulse amplitude displays clear non-Gaussian features that confirm the rogue wave character of the intensity pulsations. Simulations of a simple rate equation model show good qualitative agreement with the experiments and provide a framework for understanding the observed extreme amplitude events as the result of a deterministic nonlinear process.Peer ReviewedPostprint (published version

Analysis and preliminary characterisation of the cytochrome P450 monooxygenases from Frankia sp. EuI1c (Frankia inefficax sp.)

Frankia bacteria are nitrogen fixing species from the Actinobacterium phylum which live on the root nodules of plants. They have been hypothesised to have significant potential for natural product biosynthesis. The cytochrome P450 monooxygenase complement of Frankia sp. EuI1c (Frankia inefficax sp.), which comprises 68 members, was analysed. Several members belonged to previously uncharacterised bacterial P450 families. There was an unusually high number of CYP189 family members (21) suggesting that this family has undergone gene duplication events which are classified as "blooms". The likely electron transfer partners for the P450 enzymes were also identified and analysed. These consisted of predominantly [3Fe-4S] cluster containing ferredoxins (eight), a single [2Fe-2S] ferredoxin and a couple of ferredoxin reductases. Three of these CYP family members were produced and purified, using Escherichia coli as a host, and their substrate range was characterised. CYP1027H1 and CYP150A20 bound a broad range of norisoprenoids and terpenoids. CYP1074A2 was highly specific for certain steroids including testosterone, progesterone, stanolone and 4-androstene-3,17-dione. It is likely that steroids are the physiological substrates of CYP1074A2. These results also give an indication that terpenoids are the likely substrates of CYP1027H1 and CYP150A2. The large number of P450s belonging to distinct families as well as the associated electron transfer partners found in different Frankia strains highlights the importance of this family of enzymes has in the secondary metabolism of these bacteria.Ian C.K. Lau, René Feyereisen, David R. Nelson, Stephen G. Bel

Gene expression profiling of Spodoptera frugiperda hemocytes and fat body using cDNA microarray reveals polydnavirus-associated variations in lepidopteran host genes transcript levels

BACKGROUND: Genomic approaches provide unique opportunities to study interactions of insects with their pathogens. We developed a cDNA microarray to analyze the gene transcription profile of the lepidopteran pest Spodoptera frugiperda in response to injection of the polydnavirus HdIV associated with the ichneumonid wasp Hyposoter didymator. Polydnaviruses are associated with parasitic ichneumonoid wasps and are required for their development within the lepidopteran host, in which they act as potent immunosuppressive pathogens. In this study, we analyzed transcriptional variations in the two main effectors of the insect immune response, the hemocytes and the fat body, after injection of filter-purified HdIV. RESULTS: Results show that 24 hours post-injection, about 4% of the 1750 arrayed host genes display changes in their transcript levels with a large proportion (76%) showing a decrease. As a comparison, in S. frugiperda fat body, after injection of the pathogenic JcDNV densovirus, 8 genes display significant changes in their transcript level. They differ from the 7 affected by HdIV and, as opposed to HdIV injection, are all up-regulated. Interestingly, several of the genes that are modulated by HdIV injection have been shown to be involved in lepidopteran innate immunity. Levels of transcripts related to calreticulin, prophenoloxidase-activating enzyme, immulectin-2 and a novel lepidopteran scavenger receptor are decreased in hemocytes of HdIV-injected caterpillars. This was confirmed by quantitative RT-PCR analysis but not observed after injection of heat-inactivated HdIV. Conversely, an increased level of transcripts was found for a galactose-binding lectin and, surprisingly, for the prophenoloxidase subunits. The results obtained suggest that HdIV injection affects transcript levels of genes encoding different components of the host immune response (non-self recognition, humoral and cellular responses). CONCLUSION: This analysis of the host-polydnavirus interactions by a microarray approach indicates that the presence of HdIV induces, directly or indirectly, variations in transcript levels of specific host genes, changes that could be responsible in part for the alterations observed in the parasitized host physiology. Development of such global approaches will allow a better understanding of the strategies employed by parasites to manipulate their host physiology, and will permit the identification of potential targets of the immunosuppressive polydnaviruses

Application of time-dependent density functional theory to optical activity

As part of a general study of the time-dependent local density approximation (TDLDA), we here report calculations of optical activity of chiral molecules. The theory automatically satisfies sum rules and the Kramers-Kronig relation between circular dichroism and optical rotatory power. We find that the theory describes the measured circular dichroism of the lowest states in methyloxirane with an accuracy of about a factor of two. In the chiral fullerene C_76 the TDLDA provides a consistent description of the optical absorption spectrum, the circular dichroism spectrum, and the optical rotatory power, except for an overall shift of the theoretical spectrum.Comment: 17 pages and 13 PostScript figure

Optical response of small silver clusters

The time-dependent local density approximation is applied to the optical response of the silver clusters, Ag_2, Ag_3, Ag_8 and Ag_9^+. The calculation includes all the electrons beyond the closed-shell Ag^{+11} ionic core, thus including for the first time explicitly the filled d-shell in the response. The excitation energy of the strong surface plasmon near 4 eV agrees well with experiment. The theoretical transition strength is quenched by a factor of 4 with respect to the pure s-electron sum rule in Ag_8 due to the d-electrons. A comparable amount of strength lies in complex states below 6 eV excitation. The total below 6 eV, about 50% of the s sum rule, is consistent with published experiments.Comment: 13 pages RevTex and 9 Postscript figure