A Feynman integral via higher normal functions

We study the Feynman integral for the three-banana graph defined as the scalar two-point self-energy at three-loop order. The Feynman integral is evaluated for all identical internal masses in two space-time dimensions. Two calculations are given for the Feynman integral; one based on an interpretation of the integral as an inhomogeneous solution of a classical Picard-Fuchs differential equation, and the other using arithmetic algebraic geometry, motivic cohomology, and Eisenstein series. Both methods use the rather special fact that the Feynman integral is a family of regulator periods associated to a family of K3 surfaces. We show that the integral is given by a sum of elliptic trilogarithms evaluated at sixth roots of unity. This elliptic trilogarithm value is related to the regulator of a class in the motivic cohomology of the K3 family. We prove a conjecture by David Broadhurst that at a special kinematical point the Feynman integral is given by a critical value of the Hasse-Weil L-function of the K3 surface. This result is shown to be a particular case of Deligne's conjectures relating values of L-functions inside the critical strip to periods.Comment: Latex. 70 pages. 3 figures. v3: minor changes and clarifications. Version to appear in Compositio Mathematic

A biologically inspired spiking model of visual processing for image feature detection

To enable fast reliable feature matching or tracking in scenes, features need to be discrete and meaningful, and hence edge or corner features, commonly called interest points are often used for this purpose. Experimental research has illustrated that biological vision systems use neuronal circuits to extract particular features such as edges or corners from visual scenes. Inspired by this biological behaviour, this paper proposes a biologically inspired spiking neural network for the purpose of image feature extraction. Standard digital images are processed and converted to spikes in a manner similar to the processing that transforms light into spikes in the retina. Using a hierarchical spiking network, various types of biologically inspired receptive fields are used to extract progressively complex image features. The performance of the network is assessed by examining the repeatability of extracted features with visual results presented using both synthetic and real images

A genetic assessment of parentage in the blackspot sergeant damselfish, Abudefduf sordidus (Pisces: Pomacentridae)

Microsatellite markers were used to investigate the reproductive behavior of the damselfish Abudefduf sordidus at Johnston Atoll, Central Pacific Ocean. Genetic results indicated that ten males maintained guardianship over their nest territories for up to nine nest cycles during a 3.5 month period. Genotypes of 1025 offspring sampled from 68 nests (composed of 129 clutches) were consistent with 95% of the offspring being sired by the guardian male. Offspring lacking paternal alleles at two or more loci were found in 19 clutches, indicating that reproductive parasitism and subsequent alloparental care occurred. Reconstructed maternal genotypes allowed the identification of a minimum of 74 different females that spawned with these ten territorial males. Males were polygynous, mating with multiple females within and between cycles. Genetic data from nests, which consisted of up to four clutches during a reproductive cycle, indicated that each clutch usually had only one maternal contributor and that different clutches each had different dams. Females displayed sequential polyandry spawning with one male within a cycle but switched males in subsequent spawning cycles. These results highlight new findings regarding male parasitic spawning, polygyny, and sequential polyandry in a marine fish with exclusive male paternal care.Published versio

Prospects for India's cereal supply and demand to 2020:

The possibility of an emerging cereal gap of serious proportions by the year 2020, is a useful illustration of the kind of constructive dialogue IFPRI hopes to encourage. It responds to several quite recent developments, notably the rapid expansion of India's industrial and service sectors since the 1991 structural reforms, the improved prospects for continued growth over the next few decades, and the likelihood of rising per capita incomes that could generate substantially increased demand for livestock products. As demand for livestock products grows, livestock production could increasingly depend on cereals for feed — perhaps as much as 50 million tons by 2020, according to G.S. Bhalla, Peter Hazell, and John Kerr, authors of this 2020 discussion paper on Prospects for Balancing Cereal Needs in India to 2020. These conclusions differ somewhat from other IFPRI studies, which have generally found that growth in demand for livestock products will be lower than the current study. This divergence of views is a useful signal to policymakers to pay careful attention to trends in demand for livestock products in India in the coming years. This study and the rest of IFPRI's 2020 research have consistently pointed to the vital link between agricultural policies and prospects for production growth in the next two decades. (from Forward by Per Pinstrup-Andersen)South Asia, South Asia and Central Asia, Grain Yields India., Food supply India Forecasting., Grain as feed India Forecasting., Consumption (Economics) India., Livestock India.,

Prospects for India's cereal supply and demand to 2020:

The possibility of an emerging cereal gap of serious proportions by the year 2020, is a useful illustration of the kind of constructive dialogue IFPRI hopes to encourage. It responds to several quite recent developments, notably the rapid expansion of India's industrial and service sectors since the 1991 structural reforms, the improved prospects for continued growth over the next few decades, and the likelihood of rising per capita incomes that could generate substantially increased demand for livestock products. As demand for livestock products grows, livestock production could increasingly depend on cereals for feed — perhaps as much as 50 million tons by 2020, according to G.S. Bhalla, Peter Hazell, and John Kerr, authors of this 2020 discussion paper on Prospects for Balancing Cereal Needs in India to 2020. These conclusions differ somewhat from other IFPRI studies, which have generally found that growth in demand for livestock products will be lower than the current study. This divergence of views is a useful signal to policymakers to pay careful attention to trends in demand for livestock products in India in the coming years. This study and the rest of IFPRI's 2020 research have consistently pointed to the vital link between agricultural policies and prospects for production growth in the next two decades. (from Forward by Per Pinstrup-Andersen)Grain Yields India., Food supply India Forecasting., Grain as feed India Forecasting., Consumption (Economics) India., Livestock India.,

Magneto-optics in pure and defective Ga_{1-x}Mn_xAs from first-principles

The magneto-optical properties of Ga$_{1-x}$Mn$_{x}$As including their most common defects were investigated with precise first--principles density-functional FLAPW calculations in order to: {\em i}) elucidate the origin of the features in the Kerr spectra in terms of the underlying electronic structure; {\em ii}) perform an accurate comparison with experiments; and {\em iii}) understand the role of the Mn concentration and occupied sites in shaping the spectra. In the substitutional case, our results show that most of the features have an interband origin and are only slightly affected by Drude--like contributions, even at low photon energies. While not strongly affected by the Mn concentration for the intermediately diluted range ($x\sim$ 10%), the Kerr factor shows a marked minimum (up to 1.5$^o$) occurring at a photon energy of $\sim$ 0.5 eV. For interstitial Mn, the calculated results bear a striking resemblance to the experimental spectra, pointing to the comparison between simulated and experimental Kerr angles as a valid tool to distinguish different defects in the diluted magnetic semiconductors framework.Comment: 10 pages including 2 figures, submitted to Phys. Rev.

X-Ray Observations of Black Widow Pulsars

We describe the first X-ray observations of five short orbital period ($P_B < 1$ day), $\gamma$-ray emitting, binary millisecond pulsars. Four of these, PSRs J0023+0923, J1124$-$3653, J1810+1744, and J2256$-$1024 are `black-widow' pulsars, with degenerate companions of mass $\ll0.1 M_{\odot}$, three of which exhibit radio eclipses. The fifth source, PSR J2215+5135, is an eclipsing `redback' with a near Roche-lobe filling $\sim$0.2 solar mass non-degenerate companion. Data were taken using the \textit{Chandra X-Ray Observatory} and covered a full binary orbit for each pulsar. Two pulsars, PSRs J2215+5135 and J2256$-$1024, show significant orbital variability while PSR J1124$-$3653 shows marginal orbital variability. The lightcurves for these three pulsars have X-ray flux minima coinciding with the phases of the radio eclipses. This phenomenon is consistent with an intrabinary shock emission interpretation for the X-rays. The other two pulsars, PSRs J0023+0923 and J1810+1744, are fainter and do not demonstrate variability at a level we can detect in these data. All five spectra are fit with three separate models: a power-law model, a blackbody model, and a combined model with both power-law and blackbody components. The preferred spectral fits yield power-law indices that range from 1.3 to 3.2 and blackbody temperatures in the hundreds of eV. The spectrum for PSR J2215+5135 shows a significant hard X-ray component, with a large number of counts above 2 keV, which is additional evidence for the presence of intrabinary shock emission and is similar to what has been detected in the low-mass X-ray binary to millisecond pulsar transition object PSR J1023+0038.Comment: 8 pages, 6 figures, 2 tables, submitted to Ap