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

Detection of amblyopia utilizing generated retinal reflexes

Investigation confirmed that GRR images can be consistently obtained and that these images contain information required to detect the optical inequality of one eye compared to the fellow eye. Digital analyses, electro-optical analyses, and trained observers were used to evaluate the GRR images. Two and three dimensional plots were made from the digital analyses results. These plotted data greatly enhanced the GRR image content, and it was possible for nontrained observers to correctly identify normal vs abnormal ocular status by viewing the plots. Based upon the criteria of detecting equality or inequality of ocular status of a person's eyes, the trained observer correctly identified the ocular status of 90% of the 232 persons who participated in this program

Embedding impedance approximations in the analysis of SIS mixers

Future millimeter-wave radio astronomy instruments will use arrays of many SIS receivers, either as focal plane arrays on individual radio telescopes, or as individual receivers on the many antennas of radio interferometers. Such applications will require broadband integrated mixers without mechanical tuners. To produce such mixers, it will be necessary to improve present mixer design techniques, most of which use the three-frequency approximation to Tucker's quantum mixer theory. This paper examines the adequacy of three approximations to Tucker's theory: (1) the usual three-frequency approximation which assumes a sinusoidal LO voltage at the junction, and a short-circuit at all frequencies above the upper sideband; (2) a five-frequency approximation which allows two LO voltage harmonics and five small-signal sidebands; and (3) a quasi five-frequency approximation in which five small-signal sidebands are allowed, but the LO voltage is assumed sinusoidal. These are compared with a full harmonic-Newton solution of Tucker's equations, including eight LO harmonics and their corresponding sidebands, for realistic SIS mixer circuits. It is shown that the accuracy of the three approximations depends strongly on the value of omega R(sub N)C for the SIS junctions used. For large omega R(sub N)C, all three approximations approach the eight-harmonic solution. For omega R(sub N)C values in the range 0.5 to 10, the range of most practical interest, the quasi five-frequency approximation is a considerable improvement over the three-frequency approximation, and should be suitable for much design work. For the realistic SIS mixers considered here, the five-frequency approximation gives results very close to those of the eight-harmonic solution. Use of these approximations, where appropriate, considerably reduces the computational effort needed to analyze an SIS mixer, and allows the design and optimization of mixers using a personal computer

Pulsar Timing with the Fermi LAT

We present an overview of precise pulsar timing using data from the Large Area Telescope (LAT) on Fermi. We describe the analysis techniques including a maximum likelihood method for determining pulse times of arrival from unbinned photon data. In addition to determining the spindown behavior of the pulsars and detecting glitches and timing noise, such timing analyses allow the precise determination of the pulsar position, thus enabling detailed multiwavelength follow up.Comment: 6 page, 3 figures, to appear in AIP Conference Proceedings of Pulsar Conference 2010 "Radio Pulsars: a key to unlock the secrets of the Universe", Sardinia, October 201

Local form interference in biological motion perception

Peer reviewedPublisher PD