Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

Cosmic shear requirements on the wavelength dependence of telescope point spread functions

Cosmic shear requires high precision measurement of galaxy shapes in the presence of the observational point spread function (PSF) that smears out the image. The PSF must therefore be known for each galaxy to a high accuracy. However, for several reasons, the PSF is usually wavelength dependent; therefore, the differences between the spectral energy distribution of the observed objects introduce further complexity. In this paper, we investigate the effect of the wavelength dependence of the PSF, focusing on instruments in which the PSF size is dominated by the diffraction limit of the telescope and which use broad-band filters for shape measurement. We first calculate biases on cosmological parameter estimation from cosmic shear when the stellar PSF is used uncorrected. Using realistic galaxy and star spectral energy distributions and populations and a simple three-component circular PSF, we find that the colour dependence must be taken into account for the next generation of telescopes. We then consider two different methods for removing the effect: (i) the use of stars of the same colour as the galaxies and (ii) estimation of the galaxy spectral energy distribution using multiple colours and using a telescope model for the PSF. We find that both of these methods correct the effect to levels below the tolerances required for per cent level measurements of dark energy parameters. Comparison of the two methods favours the template-fitting method because its efficiency is less dependent on galaxy redshift than the broad-band colour method and takes full advantage of deeper photometry.

Moho map of South America from receiver functions and surface waves

We estimate crustal structure and thickness of South America north of roughly 40 degrees S. To this end, we analyzed receiver functions from 20 relatively new temporary broadband seismic stations deployed across eastern Brazil. In the analysis we include teleseismic and some regional events, particularly for stations that recorded few suitable earthquakes. We first estimate crustal thickness and average Poisson`s ratio using two different stacking methods. We then combine the new crustal constraints with results from previous receiver function studies. To interpolate the crustal thickness between the station locations, we jointly invert these Moho point constraints, Rayleigh wave group velocities, and regional S and Rayleigh waveforms for a continuous map of Moho depth. The new tomographic Moho map suggests that Moho depth and Moho relief vary slightly with age within the Precambrian crust. Whether or not a positive correlation between crustal thickness and geologic age is derived from the pre-interpolation point constraints depends strongly on the selected subset of receiver functions. This implies that using only pre-interpolation point constraints (receiver functions) inadequately samples the spatial variation in geologic age. The new Moho map also reveals an anomalously deep Moho beneath the oldest core of the Amazonian Craton.

Deep crustal structure of the Parana Basin from receiver functions and Rayleigh-wave dispersion: Evidence for a fragmented cratonic root

The deep crustal structure of the Parana Basin of southern Brazil is investigated by analyzing P- and PP-wave receiver functions at 17 Brazilian Lithosphere Seismic Project stations within the basin. The study area can be described as a typical Paleozoic intracratonic basin that hosts one of the largest Large Igneous Province of the world and makes a unique setting for investigating models of basin subsidence and their interaction with mantle plumes. Our study consists of (1) an analysis of the Moho interaction phases in the receiver functions to obtain the thickness and bulk Vp/Vs ratio of the basin`s underlying crust and (2) a joint inversion with Rayleigh-wave dispersion velocities from an independent tomographic study to delineate the detailed S-wave velocity variation with depth. The results of our analysis reveal that Moho depths and bulk Vp/Vs ratios (including sediments) vary between 41 and 48 km and between 1.70 and 1.76, respectively, with the largest values roughly coinciding with the basin`s axis, and that S-wave velocities in the lower crust are generally below 3.8 km/s. Select sites within the basin, however, show lower crustal S-wave velocities slightly above 3.9 km/s suggestive of underplated mafic material. We show that these observations are consistent with a fragmented cratonic root under the Parana basin that defined a zone of weakness for the initial Paleozoic subsidence of the basin and which allowed localized mafic underplating of the crust along the suture zones by Cenozoic magmatism.

Basement depths in the Parecis Basin (Amazon) with receiver functions from small local earthquakes in the Porto dos Gauchos seismic zone

Receiver functions from small local earthquakes were used to determine sediment thicknesses in Porto dos Gauchos seismic zone (PGSZ), Parecis basin, Amazonian craton, Brazil. The high velocity contrast between basement and sediments (P-wave velocities of 6.1 and 3.0 km/s, respectively) favors the generation of clear P-to-S converted phases (Ps) seen in the radial component, and also S-to-P conversions (Sp) seen in the vertical component. A reference 10 velocity model determined with shallow refraction experiment in PGSZ helped to convert Ps P time differences to basement depths at 15 stations deployed for aftershocks studies. The results of receiver function integrated with the shallow refraction reveal that the basement depths in the PGSZ increases from the basin border in the north up to about 600 m depth in the south. The basement topography, however, does not vary smoothly and a basement high with a steep topography was detected near the epicentral area. A 400 m elevation difference within 1.7 km distance suggests a possible border fault of a buried graben. This feature seems to be oriented roughly WSW-ENE and could indicate basement structures related to the seismicity of the Porto dos Gauchos Seismic Zone. (C) 2011 Elsevier Ltd. All rights reserved.

Specific leaf areas of the tank bromeliad Guzmania monostachia perform distinct functions in response to water shortage

Leaves comprise most of the vegetative body of tank bromeliads and are usually subjected to strong longitudinal gradients. For instance, while the leaf base is in contact with the water accumulated in the tank, the more light-exposed middle and upper leaf sections have no direct access to this water reservoir. Therefore, the present study attempted to investigate whether different leaf portions of Guzmania monostachia, a tank-forming C(3)-CAM bromeliad, play distinct physiological roles in response to water shortage, which is a major abiotic constraint in the epiphytic habitat. Internal and external morphological features, relative water content, pigment composition and the degree of CAM expression were evaluated in basal, middle and apical leaf portions in order to allow the establishment of correlations between the structure and the functional importance of each leaf region. Results indicated that besides marked structural differences, a high level of functional specialization is also present along the leaves of this bromeliad. When the tank water was depleted, the abundant hydrenchyma of basal leaf portions was the main reservoir for maintaining a stable water status in the photosynthetic tissues of the apical region. In contrast, the CAM pathway was intensified specifically in the upper leaf section, which is in agreement with the presence of features more suitable for the occurrence of photosynthesis at this portion. Gas exchange data indicated that internal recycling of respiratory CO(2) accounted for virtually all nighttime acid accumulation, characterizing a typical CAM-idling pathway in the drought-exposed plants. Altogether, these data reveal a remarkable physiological complexity along the leaves of G. monostachia, which might be a key adaptation to the intermittent water supply of the epiphytic niche. (C) 2009 Elsevier GmbH. All rights reserved.

CCP1/Nna1 functions in protein turnover in mouse brain: Implications for cell death in Purkinje cell degeneration mice

Purkinje cell degeneration (pcd) mice have a mutation within the gene encoding cytosolic carboxypeptidase 1 (CCP1/Nna1), which has homology to metallocarboxypeptidases. To assess the function of CCP1/Nna1, quantitative proteomics and peptidomics approaches were used to compare proteins and peptides in mutant and wild-type mice. Hundreds of peptides derived from cytosolic and mitochondrial proteins are greatly elevated in pcd mouse hypothalamus, amygdala, cortex, prefrontal cortex, and striatum. However, the major proteins detected on 2-D gel electrophoresis were present in mutant and wild-type mouse cortex and hypothalamus at comparable levels, and proteasome activity is normal in these brain regions of pcd mice, suggesting that the increase in cellular peptide levels in the pcd mice is due to reduced degradation of the peptides downstream of the proteasome. Both nondegenerating and degenerating regions of pcd mouse brain, but not wild-type mouse brain, show elevated autophagy, which can be triggered by a decrease in amino acid levels. Taken together with previous studies on CCP1/Nna1, these data suggest that CCP1/Nna1 plays a role in protein turnover by cleaving proteasome-generated peptides into amino acids and that decreased peptide turnover in the pcd mice leads to cell death.-Berezniuk, I., Sironi, J., Callaway, M. B., Castro, L. M., Hirata, I. Y., Ferro, E. S., Fricker, L. D. CCP1/Nna1 functions in protein turnover in mouse brain: Implications for cell death in Purkinje cell degeneration mice. FASEB J. 24, 1813-1823 (2010). www.fasebj.org

On the Barnes double zeta and Gamma functions

We present a complete description of the analytic properties of the Barnes double zeta and Gamma functions. (C) 2009 Elsevier Inc. All rights reserved.

Foliations and polynomial diffeomorphisms of R(3)

Let Y = (f, g, h): R(3) -> R(3) be a C(2) map and let Spec(Y) denote the set of eigenvalues of the derivative DY(p), when p varies in R(3). We begin proving that if, for some epsilon > 0, Spec(Y) boolean AND (-epsilon, epsilon) = empty set, then the foliation F(k), with k is an element of {f, g, h}, made up by the level surfaces {k = constant}, consists just of planes. As a consequence, we prove a bijectivity result related to the three-dimensional case of Jelonek`s Jacobian Conjecture for polynomial maps of R(n).

Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3

In this paper, we classify all the global phase portraits of the quadratic polynomial vector fields having a rational first integral of degree 3. (C) 2008 Elsevier Ltd. All rights reserved.

Invariant theory and reversible-equivariant vector fields

In this paper we present results for the systematic study of reversible-equivariant vector fields - namely, in the simultaneous presence of symmetries and reversing symmetries - by employing algebraic techniques from invariant theory for compact Lie groups. The Hilbert-Poincare series and their associated Molien formulae are introduced,and we prove the character formulae for the computation of dimensions of spaces of homogeneous anti-invariant polynomial functions and reversible-equivariant polynomial mappings. A symbolic algorithm is obtained for the computation of generators for the module of reversible-equivariant polynomial mappings over the ring of invariant polynomials. We show that this computation can be obtained directly from a well-known situation, namely from the generators of the ring of invariants and the module of the equivariants. (C) 2008 Elsevier B.V, All rights reserved.

THE IMPLICIT FUNCTION THEOREM FOR CONTINUOUS FUNCTIONS

In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence. some versions of these classic theorems are proved when we consider differenciable (not necessarily C-1) maps.

The univalent polynomial of Suffridge as a summability kernel

A positive summability trigonometric kernel {K(n)(theta)}(infinity)(n=1) is generated through a sequence of univalent polynomials constructed by Suffridge. We prove that the convolution {K(n) * f} approximates every continuous 2 pi-periodic function f with the rate omega(f, 1/n), where omega(f, delta) denotes the modulus of continuity, and this provides a new proof of the classical Jackson`s theorem. Despite that it turns out that K(n)(theta) coincide with positive cosine polynomials generated by Fejer, our proof differs from others known in the literature.

Twofold adaptive partition of unity implicits

Partition of Unity Implicits (PUI) has been recently introduced for surface reconstruction from point clouds. In this work, we propose a PUI method that employs a set of well-observed solutions in order to produce geometrically pleasant results without requiring time consuming or mathematically overloaded computations. One feature of our technique is the use of multivariate orthogonal polynomials in the least-squares approximation, which allows the recursive refinement of the local fittings in terms of the degree of the polynomial. However, since the use of high-order approximations based only on the number of available points is not reliable, we introduce the concept of coverage domain. In addition, the method relies on the use of an algebraically defined triangulation to handle two important tasks in PUI: the spatial decomposition and an adaptive polygonization. As the spatial subdivision is based on tetrahedra, the generated mesh may present poorly-shaped triangles that are improved in this work by means a specific vertex displacement technique. Furthermore, we also address sharp features and raw data treatment. A further contribution is based on the PUI locality property that leads to an intuitive scheme for improving or repairing the surface by means of editing local functions.

Reaction functions for weakly bound systems

We propose a new technique to analyze total reaction cross sections. In this technique, which has been previously applied to fusion reactions, the experimental data are used to build a dimensionless reaction function, which does not depend oil the system size or details of the optical potential. In this way, total reaction cross sections for different systems can be directly compared. We employ this technique to perform a systematic study of reaction cross sections of weakly bound systems in different mass ranges, and compare their reaction functions with the ones of tightly bound systems with similar masses. We show that breakup reactions and neutron transfers in halo systems lead to large reaction functions, well above the ones of typical tightly or weakly bound stable systems. (C) 2009 Elsevier B.V. All rights reserved.