Transverse and longitudinal components of the propagating and evanescent waves associated to radially-polarized nonparaxial fields

A comparison is established between the contributions of transverse and longitudinal components of both the propagating and the evanescent waves associated to freely propagating radially polarized nonparaxial beams. Attention is focused on those fields that remain radially polarized upon propagation. In terms of the plane-wave angular spectrum of these fields, analytical expressions are given for determining both the spatial shape of the above components and their relative weight integrated over the whole transverse plane. The results are applied to two kinds of doughnut-like beams with radial polarization, and we compare the behavior of such fields at two transverse planes.

Question Waves: A multicast query routing algorithm for social search

This paper describes Question Waves, an algorithm that can be applied to social search protocols, such as Asknext or Sixearch. In this model, the queries are propagated through the social network, with faster propagation through more trustable acquaintances. Question Waves uses local information to make decisions and obtain an answer ranking. With Question Waves, the answers that arrive first are the most likely to be relevant, and we computed the correlation of answer relevance with the order of arrival to demonstrate this result. We obtained correlations equivalent to the heuristics that use global knowledge, such as profile similarity among users or the expertise value of an agent. Because Question Waves is compatible with the social search protocol Asknext, it is possible to stop a search when enough relevant answers have been found; additionally, stopping the search early only introduces a minimal risk of not obtaining the best possible answer. Furthermore, Question Waves does not require a re-ranking algorithm because the results arrive sorted

The seasonal evolution of high vertical–mode internal waves in a deep reservoir

The causal mechanism and seasonal evolution of the internal wave field in a deep, warm, monomictic reservoirare examined through the analysis of field observations and numerical techniques. The study period extends fromthe onset of thermal stratification in the spring until midsummer in 2005. During this time, wind forcing wasperiodic, with a period of 24 h (typical of land–sea breezes), and the thermal structure in the lake wascharacterized by the presence of a shallow surface layer overlying a thick metalimnion, typical of small to mediumsized reservoirs with deep outtakes. Basin-scale internal seiches of high vertical mode (ranging from mode V3 toV5) were observed in the metalimnion. The structure of the dominant modes of oscillation changed asstratification evolved on seasonal timescales, but in all cases, their periods were close to that of the local windforcing (i.e., 24 h), suggesting a resonant response. Nonresonant oscillatory modes of type V1 and V2 becamedominant after large frontal events, which disrupted the diurnal periodicity of the wind forcing

Feature selection for automatic analysis of emotional response based on nonlinear speech modeling suitable for diagnosis of Alzheimer׳s disease

Alzheimer׳s disease (AD) is the most common type of dementia among the elderly. This work is part of a larger study that aims to identify novel technologies and biomarkers or features for the early detection of AD and its degree of severity. The diagnosis is made by analyzing several biomarkers and conducting a variety of tests (although only a post-mortem examination of the patients’ brain tissue is considered to provide definitive confirmation). Non-invasive intelligent diagnosis techniques would be a very valuable diagnostic aid. This paper concerns the Automatic Analysis of Emotional Response (AAER) in spontaneous speech based on classical and new emotional speech features: Emotional Temperature (ET) and fractal dimension (FD). This is a pre-clinical study aiming to validate tests and biomarkers for future diagnostic use. The method has the great advantage of being non-invasive, low cost, and without any side effects. The AAER shows very promising results for the definition of features useful in the early diagnosis of AD.

Equivalent representation form of oscillators with elastic and damping nonlinear terms

In this work we consider the nonlinear equivalent representation form of oscillators that exhibit nonlinearities in both the elastic and the damping terms. The nonlinear damping effects are considered to be described by fractional power velocity terms which provide better predictions of the dissipative effects observed in some physical systems. It is shown that their effects on the system dynamics response are equivalent to a shift in the coefficient of the linear damping term of a Duffing oscillator. Then, its numerical integration predictions, based on its equivalent representation form given by the well-known forced, damped Duffing equation, are compared to the numerical integration values of its original equations of motion. The applicability of the proposed procedure is evaluated by studying the dynamics response of four nonlinear oscillators that arise in some engineering applications such as nanoresonators, microresonators, human wrist movements, structural engineering design, and chain dynamics of polymeric materials at high extensibility, among others

Coherent patterns and self-induced diffraction of electrons on a thin nonlinear layer

Electron scattering on a thin layer where the potential depends self-consistently on the wave function has been studied. When the amplitude of the incident wave exceeds a certain threshold, a soliton-shaped brightening (darkening) appears on the layer causing diffraction of the wave. Thus the spontaneously formed transverse pattern can be viewed as a self-induced nonlinear quantum screen. Attractive or repulsive nonlinearities result in different phase shifts of the wave function on the screen, which give rise to quite different diffraction patterns. Among others, the nonlinearity can cause self-focusing of the incident wave into a beam, splitting in two "beams," single or double traces with suppressed reflection or transmission, etc.

Nonlinear principal and canonical directions from continuous extensions of multidimensional scaling

A continuous random variable is expanded as a sum of a sequence of uncorrelated random variables. These variables are principal dimensions in continuous scaling on a distance function, as an extension of classic scaling on a distance matrix. For a particular distance, these dimensions are principal components. Then some properties are studied and an inequality is obtained. Diagonal expansions are considered from the same continuous scaling point of view, by means of the chi-square distance. The geometric dimension of a bivariate distribution is defined and illustrated with copulas. It is shown that the dimension can have the power of continuum.

Full instability behavior of N-dimensional dynamical systems with a one-directional nonlinear vector field

We show how certain N-dimensional dynamical systems are able to exploit the full instability capabilities of their fixed points to do Hopf bifurcations and how such a behavior produces complex time evolutions based on the nonlinear combination of the oscillation modes that emerged from these bifurcations. For really different oscillation frequencies, the evolutions describe robust wave form structures, usually periodic, in which selfsimilarity with respect to both the time scale and system dimension is clearly appreciated. For closer frequencies, the evolution signals usually appear irregular but are still based on the repetition of complex wave form structures. The study is developed by considering vector fields with a scalar-valued nonlinear function of a single variable that is a linear combination of the N dynamical variables. In this case, the linear stability analysis can be used to design N-dimensional systems in which the fixed points of a saddle-node pair experience up to N21 Hopf bifurcations with preselected oscillation frequencies. The secondary processes occurring in the phase region where the variety of limit cycles appear may be rather complex and difficult to characterize, but they produce the nonlinear mixing of oscillation modes with relatively generic features

Palaeolithic Populations and Waves of Advance

The wave-of-advance model has been previously applied to Neolithic human range expansions, yielding good agreement to the speeds inferred from archaeological data. Here, we apply it for the first time to Palaeolithic human expansions by using reproduction and mobility parameters appropriate to hunter-gatherers (instead of the corresponding values for preindustrial farmers). The order of magnitude of the predicted speed is in agreement with that implied by the AMS radiocarbon dating of the lateglacial human recolonization of northern Europe (14.2–12.5 kyr BP). We argue that this makes it implausible for climate change to have limited the speed of the recolonization front. It is pointed out that a similar value for the speed can be tentatively inferred from the archaeological data on the expansion of modern humans into the Levant and Europe (42–36 kyr BP)