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

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

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

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

Intrinsic switching field distribution of arrays of Ni80Fe20 nanowires probed by in situ\mathit{in\, situ} magnetic force microscopy

The progress of magnetization reversal of weakly packed ferromagnetic Ni80Fe20 nanowire arrays of different diameters (40, 50, 70 and 100 nm) electrodeposited in polycarbonate membranes was studied by magnetic force microscopy (MFM). For such a low packing density of nanomagnets, the dipolar interactions between neighbouring wires can be neglected. The intrinsic switching field distribution has been extracted from in situ MFM images and its width was found to be considerably smaller than for densely packed nanowire arrays.Comment: 4 pages, 5 figures. To appear in Journal of Superconductivity and Novel Magnetis

Two-sided asymmetric subduction; implications for tectonomagmatic and metallogenic evolution of the Lut Block, Eastern Iran

West directed subduction zones show common characteristics, such as low structural elevation, deep trench, steep slab and a conjugate back-arc basin that are opposite to those of the east directed subduction zones. The tectonomagmatic and metallogenic setting of the Lut Block is still a matter of debate and several hypotheses have been put forward. Despite some authors denying the influence of the operation of Benioff planes, the majority propose that it occurred beneath the Afghan Block, while others consider that oceanic lithosphere was dragged under the Lut Block. Cu-Au porphyry deposits seem to occur in an island arc geotectonic setting during the middle Eocene while Mo-bearing deposits are coincident with the crustal thickening during Oligocene. We introduce new trace element and isotope geochemical data for granitoids and structural evidences testifying the two-sided asymmetric subduction beneath both Afghan and Lut Blocks, with different rates of consumption of oceanic lithosphere

Capillary rise of a liquid between two vertical plates making a small angle.

The penetration of a wetting liquid in the narrow gap between two vertical plates making a small angle is analyzed in the framework of the lubrication approximation. At the beginning of the process, the liquid rises independently at different distances from the line of intersection of the plates except in a small region around this line where the effect of the gravity is negligible. The maximum height of the liquid initially increases as the cubic root of time and is attained at a point that reaches the line of intersection only after a certain time. At later times, the motion of the liquid is confined to a thin layer around the line of intersection whose height increases as the cubic root of time and whose thickness decreases as the inverse of the cubic root of time. The evolution of the liquid surface is computed numerically and compared with the results of a simple experiment

Magnetic force microscopy investigation of arrays of nickel nanowires and nanotubes

The magnetic properties of arrays of nanowires (NWs) and nanotubes (NTs), 150 nm in diameter, electrodeposited inside nanoporous polycarbonate membranes are investigated. The comparison of the nanoscopic magnetic force microscopy (MFM) imaging and the macroscopic behavior as measured by alternating gradient force magnetometry (AGFM) is made. It is shown that MFM is a complementary technique that provides an understanding of the magnetization reversal characteristics at the microscopic scale of individual nanostructures. The local hysteresis loops have been extracted by MFM measurements. The influence of the shape of such elongated nanostructures on the dipolar coupling and consequently on the squareness of the hysteresis curves is demonstrated. It is shown that the nanowires exhibit stronger magnetic interactions than nanotubes. The non-uniformity of the magnetization states is also revealed by combining the MFM and AGFM measurements.Comment: 7 pages, 5 figure