Orthogonality Relations and Supercharacter Formulas of U(m|n) Representations

In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of complex conjugated and mixed representations. Our results are expressed in terms of the Young tableaux notation for irreducible representations. We use the supersymmetric Harish-Chandra-Itzykson-Zuber integral and the character expansion technique as mathematical tools for deriving these relations. As a byproduct we also obtain closed expressions for the supercharacters and dimensions of some particular irreducible U(m|n) representations. A new way of labeling the U(m|n) irreducible representations in terms of m + n numbers is proposed. Finally, as a corollary of our results, new identities among the dimensions of the irreducible representations of the unitary group U(N) are presented.Comment: 56 pages, LaTeX, changes only in the writing of the titl

Detection of equine atypical myopathy-associated hypoglycin A in plant material: Optimisation and validation of a novel LC-MS based method without derivatisation

Hypoglycin A (HGA) toxicity, following ingestion of material from certain plants, is linked to an acquired multiple acyl-CoA dehydrogenase deficiency known as atypical myopathy, a commonly fatal form of equine rhabdomyolysis seen worldwide. Whilst some plants are known to contain this toxin, little is known about its function or the mechanisms that lead to varied HGA concentrations between plants. Consequently, reliable tools to detect this amino acid in plant samples are needed. Analytical methods for HGA detection have previously been validated for the food industry, however, these techniques rely on chemical derivatisation to obtain accurate results at low HGA concentrations. In this work, we describe and validate a novel method, without need for chemical derivatisation (accuracy = 84–94%; precision = 3–16%; reproducibility = 3–6%; mean linear range R2 = 0.999). The current limit of quantitation for HGA in plant material was halved (from 1μg/g in previous studies) to 0.5μg/g. The method was tested in Acer pseudoplatanus material and other tree and plant species. We confirm that A. pseudoplatanus is most likely the only source of HGA in trees found within European pastures

Pyramidal Fisher Motion for Multiview Gait Recognition

The goal of this paper is to identify individuals by analyzing their gait. Instead of using binary silhouettes as input data (as done in many previous works) we propose and evaluate the use of motion descriptors based on densely sampled short-term trajectories. We take advantage of state-of-the-art people detectors to define custom spatial configurations of the descriptors around the target person. Thus, obtaining a pyramidal representation of the gait motion. The local motion features (described by the Divergence-Curl-Shear descriptor) extracted on the different spatial areas of the person are combined into a single high-level gait descriptor by using the Fisher Vector encoding. The proposed approach, coined Pyramidal Fisher Motion, is experimentally validated on the recent `AVA Multiview Gait' dataset. The results show that this new approach achieves promising results in the problem of gait recognition.Comment: Submitted to International Conference on Pattern Recognition, ICPR, 201

Full transmission through perfect-conductor subwavelength hole arrays

Light transmission through 2D subwavelength hole arrays in perfect-conductor films is shown to be complete (100%) at some resonant wavelengths even for arbitrarily narrow holes. Conversely, the reflection on a 2D planar array of non-absorbing scatterers is shown to be complete at some wavelengths regardless how weak the scatterers are. These results are proven analytically and corroborated by rigorous numerical solution of Maxwell's equations. This work supports the central role played by dynamical diffraction during light transmission through subwavelength hole arrays and it provides a systematics to analyze more complex geometries and many of the features observed in connection with transmission through hole arrays.Comment: 5 pages, 4 figure

Stripe to spot transition in a plant root hair initiation model

A generalised Schnakenberg reaction-diffusion system with source and loss terms and a spatially dependent coefficient of the nonlinear term is studied both numerically and analytically in two spatial dimensions. The system has been proposed as a model of hair initiation in the epidermal cells of plant roots. Specifically the model captures the kinetics of a small G-protein ROP, which can occur in active and inactive forms, and whose activation is believed to be mediated by a gradient of the plant hormone auxin. Here the model is made more realistic with the inclusion of a transverse co-ordinate. Localised stripe-like solutions of active ROP occur for high enough total auxin concentration and lie on a complex bifurcation diagram of single and multi-pulse solutions. Transverse stability computations, confirmed by numerical simulation show that, apart from a boundary stripe, these 1D solutions typically undergo a transverse instability into spots. The spots so formed typically drift and undergo secondary instabilities such as spot replication. A novel 2D numerical continuation analysis is performed that shows the various stable hybrid spot-like states can coexist. The parameter values studied lead to a natural singularly perturbed, so-called semi-strong interaction regime. This scaling enables an analytical explanation of the initial instability, by describing the dispersion relation of a certain non-local eigenvalue problem. The analytical results are found to agree favourably with the numerics. Possible biological implications of the results are discussed.Comment: 28 pages, 44 figure