We propose a new method of nonparametric estimation which is based on locally constant smoothing with an adaptive choice of weights for every pair of data points. Some theoretical properties of the procedure are investigated. Then we demonstrate the performance of the method on some simulated univariate and bivariate examples and compare it with other nonparametric methods. Finally we discuss applications of this procedure to magnetic resonance and satellite imaging.

The paper presents a unified approach to local likelihood estimation for a broad class of nonparametric models, including e.g. the regression, This includes the "propagation" property which particularly yields the root-n consistency of the resulting estimate in the homogeneous case.We also state an "oracle" result which implies rate optimality of the estimate under usual smoothness conditions and a "separation" result which explains the sensitivity of the method to structural changes.

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We introduce an algorithm for diffusion weighted magnetic resonance imaging data enhancement based on structural adaptive smoothing in both voxel space and diffusion-gradient space. The method, called POAS, does not refer to a specific model for the data, like the diffusion tensor or higher order models. It works by embedding the measurement space into a space with defined metric, in this case the Lie group of three-dimensional Euclidean motion SE(3). Subsequently, pairwise comparisons of the values of the diffusion weighted signal are used for adaptation. POAS preserves the edges of the observed fine and anisotropic structures. It is designed to reduce noise directly in the diffusion weighted images and consequently also to reduce bias and variability of quantities derived from the data for specific models. We evaluate the algorithm on simulated and experimental data and demonstrate that it can be used to reduce the number of applied diffusion gradients and hence acquisition time while achieving a similar quality of data, or to improve the quality of data acquired in a clinically feasible scan time setting.

Electrophysiological and activity-dependent gene expression studies of birdsong have contributed to the understanding of the neural representation of natural sounds. However, we have limited knowledge about the overall spatial topography of song representation in the avian brain. Here, we adapt the noninvasive functional MRI method in mildly sedated zebra finches (Taeniopygia guttata) to localize and characterize song driven brain activation. Based on the blood oxygenation level-dependent signal, we observed a differential topographic responsiveness to playback of bird's own song, tutor song, conspecific song, and a pure tone as a nonsong stimulus. The bird's own song caused a stronger response than the tutor song or tone in higher auditory areas. This effect was more pronounced in the medial parts of the forebrain. We found left-right hemispheric asymmetry in sensory responses to songs, with significant discrimination between stimuli observed only in the right hemisphere. This finding suggests that perceptual responses might be lateralized in zebra finches. In addition to establishing the feasibility of functional MRI in sedated songbirds, our results demonstrate spatial coding of song in the zebra finch forebrain, based on developmental familiarity and experience.imaging ͉ learning ͉ memory B irdsong is studied as a model of vocal learning, perception, production, and motor abnormalities of speech (1, 2). There are interesting parallels between song development and speech development (3) and between auditory and vocal pathways in the songbird and human brain (4). Therefore, insights from experiments on songbirds may contribute to the understanding of auditory and vocal function in humans. For example, minimal models of speech dyspraxia (5) and dysfluencies such as stuttering are being developed in zebra finches (6). Zebra finches are capable of learning, producing, perceiving, and discriminating complex sound patterns. Birdsong in zebra finches consists of a sequence of distinctive sounds produced by males and is characterized by a consistent and reproducible acoustic profile. Song is learned by imitating the song of an adult conspecific tutor during a sensitive period of development (7-10). Recently, it has been shown that songbirds are able to learn recursive syntactic patterns, presumably a simple form of grammar (11), thus extending the potential applicability of the birdsong model to our understanding of the biological basis of languages. Several brain structures are required for learning, production, and perception of birdsong. It is known from electrophysiological studies that song learning nuclei, such as the lateral magnocellular nucleus of the anterior nidopallium (LMAN) and X (12), play an important role in song development. In parallel with song motor learning, auditory song selectivity gradually emerges during development (13-17). Robust sensory responses to auditory stimuli have been recorded in the primary auditory area in the caudal telencephalic region (field L), the caudomedial nidopallium (N...

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