Integral Representations of Functional Series with Members Containing Jacobi Polynomials

MSC 2010: Primary 33C45, 40A30; Secondary 26D07, 40C10

Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space

2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.

Spatial modeling of data with excessive zeros applied to reindeer pellet-group counts

We analyze a real data set pertaining to reindeer fecal pellet-group counts obtained from a survey conducted in a forest area in northern Sweden. In the data set, over 70% of counts are zeros, and there is high spatial correlation. We use conditionally autoregressive random effects for modeling of spatial correlation in a Poisson generalized linear mixed model (GLMM), quasi-Poisson hierarchical generalized linear model (HGLM), zero-inflated Poisson (ZIP), and hurdle models. The quasi-Poisson HGLM allows for both under- and overdispersion with excessive zeros, while the ZIP and hurdle models allow only for overdispersion. In analyzing the real data set, we see that the quasi-Poisson HGLMs can perform better than the other commonly used models, for example, ordinary Poisson HGLMs, spatial ZIP, and spatial hurdle models, and that the underdispersed Poisson HGLMs with spatial correlation fit the reindeer data best. We develop R codes for fitting these models using a unified algorithm for the HGLMs. Spatial count response with an extremely high proportion of zeros, and underdispersion can be successfully modeled using the quasi-Poisson HGLM with spatial random effects.

Methods for objective and interpretative evaluation of function and motor control: gait in perturbed condition and in the aquatic therapy

Gait analysis allows to characterize motor function, highlighting deviations from normal motor behavior related to an underlying pathology. The widespread use of wearable inertial sensors has opened the way to the evaluation of ecological gait, and a variety of methodological approaches and algorithms have been proposed for the characterization of gait from inertial measures (e.g. for temporal parameters, motor stability and variability, specific pathological alterations). However, no comparative analysis of their performance (i.e. accuracy, repeatability) was available yet, in particular, analysing how this performance is affected by extrinsic (i.e. sensor location, computational approach, analysed variable, testing environmental constraints) and intrinsic (i.e. functional alterations resulting from pathology) factors. The aim of the present project was to comparatively analyze the influence of intrinsic and extrinsic factors on the performance of the numerous algorithms proposed in the literature for the quantification of specific characteristics (i.e. timing, variability/stability) and alterations (i.e. freezing) of gait. Considering extrinsic factors, the influence of sensor location, analyzed variable, and computational approach on the performance of a selection of gait segmentation algorithms from a literature review was analysed in different environmental conditions (e.g. solid ground, sand, in water). Moreover, the influence of altered environmental conditions (i.e. in water) was analyzed as referred to the minimum number of stride necessary to obtain reliable estimates of gait variability and stability metrics, integrating what already available in the literature for over ground gait in healthy subjects. Considering intrinsic factors, the influence of specific pathological conditions (i.e. Parkinson’s Disease) was analyzed as affecting the performance of segmentation algorithms, with and without freezing. Finally, the analysis of the performance of algorithms for the detection of gait freezing showed how results depend on the domain of implementation and IMU position.

Transmission Of Intra-cellular Genetic Information: A System Proposal.

One of the great challenges of the scientific community on theories of genetic information, genetic communication and genetic coding is to determine a mathematical structure related to DNA sequences. In this paper we propose a model of an intra-cellular transmission system of genetic information similar to a model of a power and bandwidth efficient digital communication system in order to identify a mathematical structure in DNA sequences where such sequences are biologically relevant. The model of a transmission system of genetic information is concerned with the identification, reproduction and mathematical classification of the nucleotide sequence of single stranded DNA by the genetic encoder. Hence, a genetic encoder is devised where labelings and cyclic codes are established. The establishment of the algebraic structure of the corresponding codes alphabets, mappings, labelings, primitive polynomials (p(x)) and code generator polynomials (g(x)) are quite important in characterizing error-correcting codes subclasses of G-linear codes. These latter codes are useful for the identification, reproduction and mathematical classification of DNA sequences. The characterization of this model may contribute to the development of a methodology that can be applied in mutational analysis and polymorphisms, production of new drugs and genetic improvement, among other things, resulting in the reduction of time and laboratory costs.

Neural networks and statistical analysis for classification of corneal videokeratography maps based on Zernike coefficients: a quantitative comparison

PURPOSE: The main goal of this study was to develop and compare two different techniques for classification of specific types of corneal shapes when Zernike coefficients are used as inputs. A feed-forward artificial Neural Network (NN) and discriminant analysis (DA) techniques were used. METHODS: The inputs both for the NN and DA were the first 15 standard Zernike coefficients for 80 previously classified corneal elevation data files from an Eyesys System 2000 Videokeratograph (VK), installed at the Departamento de Oftalmologia of the Escola Paulista de Medicina, São Paulo. The NN had 5 output neurons which were associated with 5 typical corneal shapes: keratoconus, with-the-rule astigmatism, against-the-rule astigmatism, "regular" or "normal" shape and post-PRK. RESULTS: The NN and DA responses were statistically analyzed in terms of precision ([true positive+true negative]/total number of cases). Mean overall results for all cases for the NN and DA techniques were, respectively, 94% and 84.8%. CONCLUSION: Although we used a relatively small database, results obtained in the present study indicate that Zernike polynomials as descriptors of corneal shape may be a reliable parameter as input data for diagnostic automation of VK maps, using either NN or DA.

Centrality dependence of charged hadron and strange hadron elliptic flow from root s(NN)=200 GeVAu+Au collisions

We present STAR results on the elliptic flow upsilon(2) Of charged hadrons, strange and multistrange particles from,root s(NN) = 200 GeV Au+Au collisions at the BNL Relativistic Heavy Ion Collider (RHIC). The detailed study of the centrality dependence of upsilon(2) over a broad transverse momentum range is presented. Comparisons of different analysis methods are made in order to estimate systematic uncertainties. To discuss the nonflow effect, we have performed the first analysis Of upsilon(2) with the Lee-Yang zero method for K(S)(0) and A. In the relatively low PT region, P(T) <= 2 GeV/c, a scaling with m(T) - m is observed for identified hadrons in each centrality bin studied. However, we do not observe nu 2(p(T))) scaled by the participant eccentricity to be independent of centrality. At higher PT, 2 1 <= PT <= 6 GeV/c, V2 scales with quark number for all hadrons studied. For the multistrange hadron Omega, which does not suffer appreciable hadronic interactions, the values of upsilon(2) are consistent with both m(T) - m scaling at low p(T) and number-of-quark scaling at intermediate p(T). As a function ofcollision centrality, an increase of p(T)-integrated upsilon(2) scaled by the participant eccentricity has been observed, indicating a stronger collective flow in more central Au+Au collisions.

On the determination of the rotational oblateness of Achernar

The recent interferometric study of Achernar, leading to the conclusion that its geometrical oblateness cannot be explained by the Roche approximation, has stirred substantial interest in the community, in view of its potential impact on many fields of stellar astrophysics. It is the purpose of this Letter to reinterpret the interferometric observations with a fast-rotating, gravity-darkened central star surrounded by a small equatorial disk, whose presence is consistent with contemporaneous spectroscopic data. We find that we can fit the available data only assuming a critically rotating central star. We identified two different disk models that simultaneously fit the spectroscopic, polarimetric, and interferometric observational constraints: a tenuous disk in hydrostatic equilibrium (i.e., with small scale height) and a smaller, scale height enhanced disk. We believe that these relatively small disks correspond to the transition region between the photosphere and the circumstellar environment and that they are probably perturbed by some photospheric mechanism. The study of this interface between photosphere and circumstellar disk for near-critical rotators is crucial to our understanding of the Be phenomenon and the mass and angular momentum loss of stars in general. This work shows that it is nowadays possible to directly study this transition region from simultaneous multitechnique observations.

Escape patterns of chaotic magnetic field lines in a tokamak with reversed magnetic shear and an ergodic limiter

The existence of a reversed magnetic shear in tokamaks improves the plasma confinement through the formation of internal transport barriers that reduce radial particle and heat transport. However, the transport poloidal profile is much influenced by the presence of chaotic magnetic field lines at the plasma edge caused by external perturbations. Contrary to many expectations, it has been observed that such a chaotic region does not uniformize heat and particle deposition on the inner tokamak wall. The deposition is characterized instead by structured patterns called magnetic footprints, here investigated for a nonmonotonic analytical plasma equilibrium perturbed by an ergodic limiter. The magnetic footprints appear due to the underlying mathematical skeleton of chaotic magnetic field lines determined by the manifold tangles. For the investigated edge safety factor ranges, these effects on the wall are associated with the field line stickiness and escape channels due to internal island chains near the flux surfaces. Comparisons between magnetic footprints and escape basins from different equilibrium and ergodic limiter characteristic parameters show that highly concentrated magnetic footprints can be avoided by properly choosing these parameters. (c) 2008 American Institute of Physics.

g factors of coexisting isomeric states in (188)Pb

The g factors of the 12(+), 11(-), and 8(-) isomeric states in (188)Pb were measured using the time-differential perturbed angular distribution method as g(12(+)) = -0.179(6), g(11(-)) = +1.03(3), and g(8(-)) = -0.037(7). The g factor of the 12(+) state follows the observed slight down-sloping evolution of the g factors of the i(13/2)(2) neutron spherical states with decreasing N. The g factors of the 11(-) and 8(-) isomers proposed as oblate and prolate deformed states, respectively, were interpreted within the rotational model, using calculated and empirical g factor values for the involved single-particle orbitals.

Instability of Higher-Dimensional Charged Black Holes in the de Sitter World

We have shown that higher-dimensional Reissner-Nordstrom-de Sitter black holes are gravitationally unstable for large values of the electric charge and cosmological constant in D >= 7 space-time dimensions. We have found the shape of the slightly perturbed black hole at the threshold point of instability.

Random perturbations of stochastic processes with unbounded variable length memory

We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the transition probabilities of the perturbed chain are uniformly close to the corresponding transition probabilities of the original chain. As a consequence, in the case of stochastic chains with unbounded but otherwise finite variable length memory, we show that it is possible to recover the context tree of the original chain, using a suitable version of the algorithm Context, provided that the noise is small enough.

Effects of joint immobilization on standing balance

We investigated the effect of joint immobilization on the postural sway during quiet standing. We hypothesized that the center of pressure (COP), rambling, and trembling trajectories would be affected by joint immobilization. Ten young adults stood on a force plate during 60 s without and with immobilized joints (only knees constrained, CK; knees and hips, CH; and knees, hips, and trunk, CT). with their eyes open (OE) or closed (CE). The root mean square deviation (RMS, the standard deviation from the mean) and mean speed of COP, rambling, and trembling trajectories in the anterior-posterior and medial-lateral directions were analyzed. Similar effects of vision were observed for both directions: larger amplitudes for all variables were observed in the CE condition. In the anterior-posterior direction, postural sway increased only when the knees, hips, and trunk were immobilized. For the medial-lateral direction, the RMS and the mean speed of the COP, rambling, and trembling displacements decreased after immobilization of knees and hips and knees, hips, and trunk. These findings indicate that the single inverted pendulum model is unable to completely explain the processes involved in the control of the quiet upright stance in the anterior-posterior and medial-lateral directions. (C) 2009 Elsevier B.V. All rights reserved.