On the completion of Latin rectangles to symmetric Latin squares

We find necessary and sufficient conditions for completing an arbitrary 2 by n latin rectangle to an n by n symmetric latin square, for completing an arbitrary 2 by n latin rectangle to an n by n unipotent symmetric latin square, and for completing an arbitrary 1 by n latin rectangle to an n by n idempotent symmetric latin square. Equivalently, we prove necessary and sufficient conditions for the existence of an (n - 1)-edge colouring of K-n (n even), and for an n-edge colouring of K-n (n odd) in which the colours assigned to the edges incident with two vertices are specified in advance.

Non-positivity of Groenewold operators

A central feature in the Hilbert space formulation of classical mechanics is the quantisation of classical Lionville densities, leading to what may be termed Groenewold operators. We investigate the spectra of the Groenewold operators that correspond to Gaussian and to certain uniform Lionville densities. We show that when the classical coordinate-momentum uncertainty product falls below Heisenberg's limit, the Groenewold operators in the Gaussian case develop negative eigenvalues and eigenvalues larger than 1. However, in the uniform case, negative eigenvalues are shown to persist for arbitrarily large values of the classical uncertainty product.

Full S matrix calculation via a single real-symmetric Lanczos recursion: The Lanczos artificial boundary inhomogeneity method

We present an efficient and robust method for the calculation of all S matrix elements (elastic, inelastic, and reactive) over an arbitrary energy range from a single real-symmetric Lanczos recursion. Our new method transforms the fundamental equations associated with Light's artificial boundary inhomogeneity approach [J. Chem. Phys. 102, 3262 (1995)] from the primary representation (original grid or basis representation of the Hamiltonian or its function) into a single tridiagonal Lanczos representation, thereby affording an iterative version of the original algorithm with greatly superior scaling properties. The method has important advantages over existing iterative quantum dynamical scattering methods: (a) the numerically intensive matrix propagation proceeds with real symmetric algebra, which is inherently more stable than its complex symmetric counterpart; (b) no complex absorbing potential or real damping operator is required, saving much of the exterior grid space which is commonly needed to support these operators and also removing the associated parameter dependence. Test calculations are presented for the collinear H+H-2 reaction, revealing excellent performance characteristics. (C) 2004 American Institute of Physics.

Recursive filtering of images with symmetric extension

Recursive filters are widely used in image analysis due to their efficiency and simple implementation. However these filters have an initialisation problem which either produces unusable results near the image boundaries or requires costly approximate solutions such as extending the boundary manually. In this paper, we describe a method for the recursive filtering of symmetrically extended images for filters with symmetric denominator. We begin with an analysis of symmetric extensions and their effect on non-recursive filtering operators. Based on the non-recursive case, we derive a formulation of recursive filtering on symmetric domains as a linear but spatially varying implicit operator. We then give an efficient method for decomposing and solving the linear implicit system, along with a proof that this decomposition always exists. This decomposition needs to be performed only once for each dimension of the image. This yields a filtering which is both stable and consistent with the ideal infinite extension. The filter is efficient, requiring less computation than the standard recursive filtering. We give experimental evidence to verify these claims. (c) 2005 Elsevier B.V. All rights reserved.

Dual-symmetric Lagrangians in quantum electrodynamics: I. Conservation laws and multi-polar coupling

By using a complex field with a symmetric combination of electric and magnetic fields, a first-order covariant Lagrangian for Maxwell's equations is obtained, similar to the Lagrangian for the Dirac equation. This leads to a dual-symmetric quantum electrodynamic theory with an infinite set of local conservation laws. The dual symmetry is shown to correspond to a helical phase, conjugate to the conserved helicity. There is also a scaling symmetry, conjugate to the conserved entanglement. The results include a novel form of the photonic wavefunction, with a well-defined helicity number operator conjugate to the chiral phase, related to the fundamental dual symmetry. Interactions with charged particles can also be included. Transformations from minimal coupling to multi-polar or more general forms of coupling are particularly straightforward using this technique. The dual-symmetric version of quantum electrodynamics derived here has potential applications to nonlinear quantum optics and cavity quantum electrodynamics.

On the construction of correlation functions for the integrable supersymmetric fermion models

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F-matrices (or the so-called F-basis) play an important role in the construction. In the F-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the U-q(gl(2 vertical bar 1)) (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analyzing physical properties of the integrable models in the thermodynamical limit.

Toy model for a relational formulation of quantum theory

In the absence of an external frame of reference-i.e., in background independent theories such as general relativity-physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is twofold. First, we demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental. Second, we describe how the original non-relational theory approximately emerges from the fully relational theory when reference systems become semi-classical. Our technique is motivated by a Bayesian approach to quantum mechanics, and relies on the noiseless subsystem method of quantum information science used to protect quantum states against undesired noise. The relational theory naturally predicts a fundamental decoherence mechanism, so an arrow of time emerges from a time-symmetric theory. Moreover, our model circumvents the problem of the collapse of the wave packet as the probability interpretation is only ever applied to diagonal density operators. Finally, the physical states of the relational theory can be described in terms of spin networks introduced by Penrose as a combinatorial description of geometry, and widely studied in the loop formulation of quantum gravity. Thus, our simple bottom-up approach (starting from the semiclassical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity.

Magnetization enumerator for real-valued symmetric channels in Gallager error-correcting codes

Using the magnetization enumerator method, we evaluate the practical and theoretical limitations of symmetric channels with real outputs. Results are presented for several regular Gallager code constructions.

Depth propagation and surface construction in 3-D vision

Motion discontinuities can signal object boundaries where few or no other cues, such as luminance, colour, or texture, are available. Hence, motion-defined contours are an ecologically important counterpart to luminance contours. We developed a novel motion-defined Gabor stimulus to investigate the nature of neural operators analysing visual motion fields in order to draw parallels with known luminance operators. Luminance-defined Gabors have been successfully used to discern the spatial-extent and spatial-frequency specificity of possible visual contour detectors. We now extend these studies into the motion domain. We define a stimulus using limited-lifetime moving dots whose velocity is described over 2-D space by a Gabor pattern surrounded by randomly moving dots. Participants were asked to determine whether the orientation of the Gabor pattern (and hence of the motion contours) was vertical or horizontal in a 2AFC task, and the proportion of correct responses was recorded. We found that with practice participants became highly proficient at this task, able in certain cases to reach 90% accuracy with only 12 limited-lifetime dots. However, for both practised and novice participants we found that the ability to detect a single boundary saturates with the size of the Gaussian envelope of the Gabor at approximately 5 deg full-width at half-height. At this optimal size we then varied spatial frequency and found the optimum was at the lowest measured spatial frequency (0.1 cycle deg-1 ) and then steadily decreased with higher spatial frequencies, suggesting that motion contour detectors may be specifically tuned to a single, isolated edge.

Symbol synchronization exploiting the symmetric property in optical fast OFDM

We propose a new simple method to achieve precise symbol synchronization using one start-of-frame (SOF) symbol in optical fast orthogonal frequency-division multiplexing (FOFDM) with subchannel spacing equal to half of the symbol rate per sub-carrier. The proposed method first identifies the SOF symbol, then exploits the evenly symmetric property of the discrete cosine transform in FOFDM, which is also valid in the presence of chromatic dispersion, to achieve precise symbol synchronization. We demonstrate its use in a 16.88-Gb/s phase-shifted-keying-based FOFDM system over a 124-km field-installed single-mode fiber link and show that this technique operates well in automatic precise symbol synchronization at an optical signal-to-noise ratio as low as 3 dB and after transmission.

Mach bands and multiscale models of spatial vision:the role of first, second, and third derivative operators in encoding bars and edges

Ernst Mach observed that light or dark bands could be seen at abrupt changes of luminance gradient in the absence of peaks or troughs in luminance. Many models of feature detection share the idea that bars, lines, and Mach bands are found at peaks and troughs in the output of even-symmetric spatial filters. Our experiments assessed the appearance of Mach bands (position and width) and the probability of seeing them on a novel set of generalized Gaussian edges. Mach band probability was mainly determined by the shape of the luminance profile and increased with the sharpness of its corners, controlled by a single parameter (n). Doubling or halving the size of the images had no significant effect. Variations in contrast (20%-80%) and duration (50-300 ms) had relatively minor effects. These results rule out the idea that Mach bands depend simply on the amplitude of the second derivative, but a multiscale model, based on Gaussian-smoothed first- and second-derivative filtering, can account accurately for the probability and perceived spatial layout of the bands. A key idea is that Mach band visibility depends on the ratio of second- to first-derivative responses at peaks in the second-derivative scale-space map. This ratio is approximately scale-invariant and increases with the sharpness of the corners of the luminance ramp, as observed. The edges of Mach bands pose a surprisingly difficult challenge for models of edge detection, but a nonlinear third-derivative operation is shown to predict the locations of Mach band edges strikingly well. Mach bands thus shed new light on the role of multiscale filtering systems in feature coding. © 2012 ARVO.

Comparison of frequency symmetric signal generation from a BPSK input using fiber and semiconductor-based nonlinear elements

This letter compares two nonlinear media for simultaneous carrier recovery and generation of frequency symmetric signals from a 42.7-Gb/s nonreturn-to-zero binary phase-shift-keyed input by exploiting four-wave mixing in a semiconductor optical amplifier and a highly nonlinear optical fiber for use in a phase-sensitive amplifier.

Simultaneous strain and temperature measurement of advanced 3-D braided composite materials using an improved EFPI/FBG system

Simultaneous strain and temperature measurement for advanced 3-D braided composite materials using fibre-optic sensor technology is demonstrated, for the first time. These advanced 3-D braided composites can virtually eliminate the most serious problem of delamination for conventional composites. A tandem in-fibre Bragg-grating (FBG)/extrinsic Fabry-Perot interferometric sensor (EFPI) system with improved accuracy has been used to facilitate simultaneous temperature and strain measurement in this work. The non-symmetric distortion of the optical spectrum of the FBG, due to the combination of the FBG and the EFPI, is observed for the first time. Experimental and theoretical studies indicate that this type of distortion can affect the measurement accuracy seriously and it is mainly caused by the modulation of the periodic output of the EFPI. A simple method has been demonstrated to improve the accuracy for detection of the wavelength-shift of the FBG induced by temperature change. A strain accuracy of ∼ ±20 με and a temperature accuracy of ∼ ±1 °C have been achieved, which can meet the requirements for practical applications of 3-D braided composites. © 2002 Elsevier Science Ltd. All rights reserved.

Somme Ponctuelle D'operateurs Maximaux Monotones

∗ Cette recherche a été partiellement subventionnée, en ce qui concerne le premier et le dernier auteur, par la bourse OTAN CRG 960360 et pour le second auteur par l’Action Intégrée 95/0849 entre les universités de Marrakech, Rabat et Montpellier.

On Multi-Dimensional Random Walk Models Approximating Symmetric Space-Fractional Diffusion Processes

Mathematics Subject Classification: 26A33, 47B06, 47G30, 60G50, 60G52, 60G60.