The median procedure in cluster analysis and social choice theory

Classical approachs for fitting and aggregation problems, specially in cluster analysis, social choice theory and paired comparisons methods, consist in the minimization of a remoteness function between relational data and a relational model. The notion of median, with its algebraic, metric, geometrical and statistical aspects, allow a unified treatment of many of base problems. Properties of median procedures are organized according to four directions: stabilities and axiomatic characterizations; Arrow-like properties; combinatorial properties; effective computational possibilities. Finally, interesting mathematical problems, related to the notion of median are surveyed.     

High resolution electron backscatter diffraction (EBSD) data from calcite biominerals in recent gastropod shells

Electron backscatter diffraction (EBSD) is a microscopy technique that reveals in situ crystallographic information. Currently, it is widely used for the characterization of geological materials and in studies of biomineralization. Here, we analyze high resolution EBSD data from biogenic calcite in two mollusk taxa, Concholepas and Haliotis, previously used in the understanding of complex biomineralization and paleoenvironmental studies. Results indicate that Concholepas has less ordered prisms than in Haliotis, and that in Concholepas the level of order is not homogenous in different areas of the shell. Overall, the usefulness of data integration obtained from diffraction intensity and crystallographic orientation maps, and corresponding pole figures, is discussed as well as its application to similar studies.     

Dirac particles in a gravitational field

The semiclassical approximation for the Hamiltonian of Dirac particles interacting with an arbitrary gravitational field is investigated. The time dependence of the metric leads to new contributions to the in-band energy operator in comparison to previous works in the static case. In particular we find a new coupling term between the linear momentum and the spin, as well as couplings that contribute to the breaking of the particle–antiparticle symmetry.     

Parameterized reduced order modeling of misaligned stacked disks rotor assemblies

Light and flexible rotating parts of modern turbine engines operating at supercritical speeds necessitate application of more accurate but rather computationally expensive 3D FE modeling techniques. Stacked disks misalignment due to manufacturing variability in the geometry of individual components constitutes a particularly important aspect to be included in the analysis because of its impact on system dynamics. A new parametric model order reduction algorithm is presented to achieve this goal at affordable computational costs. It is shown that the disks misalignment leads to significant changes in nominal system properties that manifest themselves as additional blocks coupling neighboring spatial harmonics in Fourier space. Consequently, the misalignment effects can no longer be accurately modeled as equivalent forces applied to a nominal unperturbed system. The fact that the mode shapes become heavily distorted by extra harmonic content renders the nominal modal projection-based methods inaccurate and thus numerically ineffective in the context of repeated analysis of multiple misalignment realizations. The significant numerical bottleneck is removed by employing an orthogonal projection onto the subspace spanned by first few Fourier harmonic basis vectors. The projected highly sparse systems are shown to accurately approximate the specific misalignment effects, to be inexpensive to solve using direct sparse methods and easy to parameterize with a small set of measurable eccentricity and tilt angle parameters. Selected numerical examples on an industrial scale model are presented to illustrate the accuracy and efficiency of the algorithm implementation.     

Early visual evoked potentials are modulated by eye position in humans induced by whole body rotations

Background  

To reach and grasp an object in space on the basis of its image cast on the retina requires different coordinate transformations that take into account gaze and limb positioning. Eye position in the orbit influences the image's conversion from retinotopic (eye-centered) coordinates to an egocentric frame necessary for guiding action. Neuroimaging studies have revealed eye position-dependent activity in extrastriate visual, parietal and frontal areas that is along the visuo-motor pathway. At the earliest vision stage, the role of the primary visual area (V1) in this process remains unclear. We used an experimental design based on pattern-onset visual evoked potentials (VEP) recordings to study the effect of eye position on V1 activity in humans.     

Influence of light polarization on dynamics of all-fiber Raman lasers: theoretical analysis

Using Stokes-vectors formalism, we present a simple model describing steady and dynamic characteristics of all-fiber Raman lasers. This model allows us to describe experimental behaviors that are not yet understood in Raman lasers. In lasers made with standard fibers we show theoretically that weak birefringence and the optical Kerr effect lead to the emergence of unstable regimes similar to those recently observed in experiments [Opt. Lett. 28, 2464 (2003)]. However, the model shows that lasers made with polarization-maintaining fibers are always stable, as evidenced in experiments.     

Time-Reversed Dynamical Entropy and Irreversibility in Markovian Random Processes

A concept of time-reversed entropy per unit time is introduced in analogy with the entropy per unit time by Shannon, Kolmogorov, and Sinai. This time-reversed entropy per unit time characterizes the dynamical randomness of a stochastic process backward in time, while the standard entropy per unit time characterizes the dynamical randomness forward in time. The difference between the time-reversed and standard entropies per unit time is shown to give the entropy production of Markovian processes in nonequilibrium steady states.     

Ultrabroadband conical emission generated from the ultraviolet up to the far-infrared during the optical filamentation in air

Ultraviolet and infrared conical emissions were observed during the filamentation in air of powerful femtosecond laser pulses produced by a portable terawatt laser system. The broadband spectrum was measured from 200 nm up to 14 microm and covered the complete optical transmission window of the atmosphere. The angularly resolved spectrum showed some X-wave structure across the frequency range analyzed. However, we demonstrated that the strong conical emission observed in the mid- and far-infrared is mainly owing to the four-wave mixing between the pump pulse and its blueshifted conical emission.