Image reconstruction from scattered Radon data by weighted positive definite kernel functions

We propose a novel kernel-based method for image reconstruction from scattered Radon data. To this end, we employ generalized Hermite–Birkhoff interpolation by positive definite kernel functions. For radial kernels, however, a straightforward application of the generalized Hermite–Birkhoff interpolation method fails to work, as we prove in this paper. To obtain a well-posed reconstruction scheme for scattered Radon data, we introduce a new class of weighted positive definite kernels, which are symmetric but not radially symmetric. By our construction, the resulting weighted kernels are combinations of radial positive definite kernels and positive weight functions. This yields very flexible image reconstruction methods, which work for arbitrary distributions of Radon lines. We develop suitable representations for the weighted basis functions and the symmetric positive definite kernel matrices that are resulting from the proposed reconstruction scheme. For the relevant special case, where Gaussian radial kernels are combined with Gaussian weights, explicit formulae for the weighted Gaussian basis functions and the kernel matrices are given. Supporting numerical examples are finally presented

The global mass function of M15

Data obtained with the NICMOS instrument on board the Hubble Space Telescope (HST) have been used to determine the H-band luminosity function (LF) and mass function (MF) of three stellar fields in the globular cluster M15, located ~7' from the cluster centre. The data confirm that the cluster MF has a characteristic mass of ~0.3 Msolar, as obtained by Paresce & De Marchi (2000) for a stellar field at 4.6' from the centre. By combining the present data with those published by other authors for various radial distances (near the centre, at 20" and at 4.6'), we have studied the radial variation of the LF due to the effects of mass segregation and derived the global mass function (GMF) using the Michie-King approach. The model that simultaneously best fits the LF at various locations, the surface brightness profile and the velocity dispersion profile suggests that the GMF should resemble a segmented power-law with the following indices: x ~ 0.8 for stars more massive than 0.8 Msolar, x ~ 0.9 for 0.3 - 0.8 Msolar and x ~ -2.2 at smaller masses (Salpeter's IMF would have x=1.35). The best fitting model also suggests that the cluster mass is ~5.4 10^5 Msolar and that the mass-to-light ratio is on average M/L_V ~ 2.1, with M/L_V ~ 3.7 in the core. A large amount of mass (~ 44 %) is found in the cluster core in the form of stellar heavy remnants, which may be sufficient to explain the mass segregation in M15 without invoking the presence of an intermediate-mass black hole.Comment: 12 pages, 10 figures, accepted for publication in A&

Partition of unity interpolation using stable kernel-based techniques

In this paper we propose a new stable and accurate approximation technique which is extremely effective for interpolating large scattered data sets. The Partition of Unity (PU) method is performed considering Radial Basis Functions (RBFs) as local approximants and using locally supported weights. In particular, the approach consists in computing, for each PU subdomain, a stable basis. Such technique, taking advantage of the local scheme, leads to a significant benefit in terms of stability, especially for flat kernels. Furthermore, an optimized searching procedure is applied to build the local stable bases, thus rendering the method more efficient

RBF approximation of large datasets by partition of unity and local stabilization

We present an algorithm to approximate large dataset by Radial Basis Function (RBF) techniques. The method couples a fast domain decomposition procedure with a localized stabilization method. The resulting algorithm can efficiently deal with large problems and it is robust with respect to the typical instability of kernel methods

Heritability estimates of predicted blood β-hydroxybutyrate and nonesterified fatty acids and relationships with milk traits in early-lactation Holstein cows

At the beginning of lactation, high-producing cows commonly experience an unbalanced energy status that is often responsible for the onset of metabolic disorders and impaired health and performance. Blood β-hydroxybutyrate (BHB) and nonesterified fatty acids (NEFA) are indicators of excessive fat mobilization and circulating ketone bodies. Recently, prediction models based on mid-infrared (MIR) spectroscopy have been developed to assess blood BHB and NEFA from routinely collected individual milk samples. This study aimed to estimate genetic parameters of blood BHB and NEFA predicted from milk MIR spectra and to assess their phenotypic and genetic correlations with milk production and composition traits in early-lactation Holstein cows. The data set comprised the first test-day record within lactation and spectra of individual milk samples (n = 22,718) of 13,106 Holstein cows collected from 5 to 35 d in milk (DIM). Blood BHB and NEFA were predicted from milk MIR spectra using previously developed prediction models. Genetic parameters of blood metabolites and milk traits were estimated for the whole observational period (5–35 DIM) and within 6 classes of DIM. Blood BHB and NEFA showed similar genetic variation across DIM, with the highest heritability in the first 10 d after calving (0.31 ± 0.06 and 0.19 ± 0.05 for BHB and NEFA, respectively). The genetic correlation between BHB and NEFA was moderate (0.51 ± 0.05). Genetic correlations of BHB with milk yield, SCS, protein percentage, lactose percentage, and urea nitrogen content were similar to, or at least in the same direction as, the correlations of NEFA with the same traits, whereas opposite correlations were observed with fat percentage and fat-to-protein ratio. Results of the current study suggest that blood BHB and NEFA predicted from milk MIR spectra have genetic variation that is potentially exploitable for breeding purposes. Therefore, they could be used as indicator traits of hyperketonemia in a selection index aimed to reduce the susceptibility of dairy cows to metabolic disorders in early lactation