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The reproducing kernel Hilbert space (RKHS) methodology has shown to be a suitable tool for the resolution of a wide range of problems in statistical signal processing both in the real and complex domains. It relies on the idea of transforming the original functional data into an infinite series representation by projection onto an specific RKHS, which usually simplifies the statistical treatment without any loss of efficiency. Moreover, the advantages of quaternion algebra over real-valued three and four-dimensional vector algebra in the modelling of multidimensional data have been proven useful in much relatively recent research. This paper accordingly proposes a generic RKHS framework for the statistical analysis of augmented quaternion random vectors, which provide a complete description of their second order characteristics. It will allow us to exploit the full advantages of the RKHS theory in widely linear processing applications, such as signal detection. In particular, we address the detection of a quaternion signal disturbed by additive Gaussian noise and the discrimination between two quaternion Gaussian signals in continuous time. [ABSTRACT FROM AUTHOR]

The article reports that Upper canines do not usually appear in the roe deer (Capreolus capreolus (Linnaeus, 1758)) and their occasional appearance represents the expression of a tooth, as a rudimentary canine, which has been suppressed in the evolution of the group. These dental anomalies could be potentially useful for tracing ancestral genes in local ecotypes and populations.

We investigated the occurrence of congenital dental abnormalities in 94 wild boars Sus scrofa scrofa, and 20 Iberian pigs Sus scrofa domesticus from Doñana (DNP) and Sierra de Andújar Natural Park (ANP) southern Spain. The only dental variation found was agenesis of the lower first premolar, either deciduous (Dp1) or permanent (P1). We analyzed prevalence variations using: odds ratios, Fisher's exact test and logistic-regression models. The lower first premolar has often been reported to be absent in modern domestic breeds of pigs, but it is usually reported as present in wild boar. However, we found a similar occurrence of agenesis in wild boar as in Iberian pigs. A common genotypic background between wild boar and Iberian pig populations of ANP sharing the same ecosystems may explain this result. When considering only wild boar, unexpected differences between populations were detected. The wild boar from ANP showed higher estimated probabilities of agenesis than those from DNP. Environmental conditions can also represent influencing factors for changes within subspecies. Our findings reinforce the idea that in suids the congenital absence of premolars probably has an evolutionary relevance, which could represent a generalized trend towards the reduction of the dental formula from the plesiomorphic placental dentition. [ABSTRACT FROM AUTHOR]

A numerical approach to the vector signal detection problem is proposed by using an approximate series representation for vector complex-valued random processes. This technique allows us to provide computationally feasible suboptimum receivers for the problem of detecting an improper or proper complex signal in additive white noise. Its implementation requires the knowledge of the correlation matrix of the vector process involved. The performance of the technique devised is assessed by some communication examples. [ABSTRACT FROM AUTHOR]

A new approach to numerically evaluate an inner product or a norm in an arbitrary reproducing kernel Hubert space (RKHS) is considered. The proposed methodology enables us to approximate the RKHS inner product with the desired accuracy avoiding analytical expressions. Furthermore, its implementation is illustrated by means of some classic examples and compared with the standard iterative method provided by Weiner for this purpose. Finally, applications in both the problem of representing approximately second-order stochastic processes by means of series expansions and in the problem of signal detection are studied. [ABSTRACT FROM AUTHOR]

• Modeling changes of Ca, P and Mg throughout life in hard tissues of two deer species. • Using scanning-electron-microscope with energy-dispersive X-ray simplified methods. • Detecting calcium deficiencies that coincide with period of environmental constraints. • Mineralization state changes with age differently according to species, sex and tissue. • Models allowing mineralization state inferences at different deer life history stages. In this paper we aim to provide baseline data and model the changes of Ca, P and Mg throughout life in the mandibular bone, enamel and dentin of red (Cervus elaphus) and fallow deer (Dama dama) in Mediterranean ecosystems. Through a cross-sectional study of cervids from 1.5 to 20 yrs old, hunted between 1990 and 1997, we apply generalized additive models (GAMs) with data from scanning-electron-microscope with energy-dispersive X-ray (FESEM-EDX) and inductively coupled plasma-mass spectrometry (ICP-MS) analyses. The mineral content varied in a similar range to that reported for other ruminants. However, we detected lower Ca content values, while more similar results were obtained for P and Mg contents, which led to relatively lower Ca/P ratios and higher Ca/Mg in our deer at that time. A significantly lesser pattern of decreasing mineral content with aging was detected in the fallow deer males, similarities were found between the sexes, and significantly less resistance to demineralization was observed in dentin compared to bone. We discuss how the basic macromineral elements involved in the biomineralization process vary with age throughout life depending on deer species, sex and hard tissues. Allowing for possible inferences of differential changes in the mineralization state at the main stages in life history, our methodological approach opens up new possibilities in zooarchaeological, paleontological, and wildlife research. [ABSTRACT FROM AUTHOR]

Presents a study which defined the approximate simultaneous orthogonal expansions of two-second order stochastic processes from the Rayleigh-Ritz eigenfunctions and prove its convergence. Mean-square estimation of Gaussian signals in noise; Detection of Gaussian signals.

Focuses on a study which examined an approach to the signal detection problem in continuous time on the basis of approximate Karhunen-Loeve expansions. Approximate series expansions; Detection of deterministic signals; Random signal detection.

The problem of estimating the intensity process of a doubly stochastic Poisson process is analyzed. Using the knowledge of the first and second-order moments of the intensity process, a recursive linear minimum mean-square error estimate is designed. Moreover, an efficient procedure for the computation of its associated error covariance is shown. The proposed solution becomes an alternative approach to the Kalman filter which is applicable under the only structural assumption that the intensity process to be estimated has a finite-dimensional covariance function. [ABSTRACT FROM AUTHOR]