Analyticity of smooth eigenfunctions and spectral analysis of the Gauss map

We provide a sufficient condition of analyticity of infinitely differentiable eigenfunctions of operators of the form Uf(x) = integral a(x, y) f(b( x, y)) mu(dy) acting on functions f: [u, v] --> C ( evolution operators of one-dimensional dynamical systems and Markov processes have this form). We estimate from below the region of analyticity of the eigenfunctions and apply these results for studying the spectral properties of the Frobenius-Perron operator of the continuous fraction Gauss map. We prove that any infinitely differentiable eigenfunction f of this Frobenius-Perron operator, corresponding to a non-zero eigenvalue admits a (unique) analytic extension to the set C\(-infinity, 1]. Analyzing the spectrum of the Frobenius Perron operator in spaces of smooth functions, we extend significantly the domain of validity of the Mayer and Ropstorff asymptotic formula for the decay of correlations of the Gauss map.

MRI diffusion tractography study in individuals with schizotypal features: A pilot study

Diffusion tensor imaging (DTI) studies have identified changes in white matter tracts in schizophrenia patients and those at high risk of transition. Schizotypal samples represent a group on the schizophrenia continuum that share some aetiological risk factors but without the confounds of illness. The aim of the current study was to compare tract microstructural coherence as measured by
fractional anisotropy (FA) between 12 psychometrically defined schizotypes and controls. We investigated bilaterally the uncinate and arcuate fasciculi (UF and AF) via a probabilistic tractography algorithm (PICo), with FA values compared between groups. Partial correlations were also examined between measures of subclinical hallucinatory/delusional experiences and FA values. High schizotypes
were found to have significantly higher FA values in bilateral UF only, but failed to reach significance in each hemisphere. In the whole sample there was a positive correlation between increasing FA values and measures of hallucinatory experience in the right AF. These findings suggest subtle changes in microstructural coherence are present in schizotypes. Correlations between mild hallucinatory experience and increasing FA values could indicate increasing coherence could be associated with symptom formation.

Impact of prosthodontic rehabilitation on the chewing efficiency of partially dentate older patients

Objectives: This study compared two tooth replacement strategies for partially dentate older patients namely; removable partial dentures (RPDs) and functionally orientated treatment based on the shortened dental arch (SDA) concept. Patients were compared in terms of chewing efficiency after prosthodontic rehabilitation. Methods: Chewing efficiency was assessed electronically by a two-colour gum-mixing test. Specimens were assembled from two different colours of chewing gums with a size of 30 x 18 x 3 mm. After participants chewed for 20 cycles, the gum was retrieved, flattened to a 1-mm-thick wafer, and digitized with a flatbed image scanner. The pixels of unmixed colour in the specimen were counted by means of Adobe Photoshop 2.0R software (Adobe Systems, San Jose, CA, USA), and the ratio to the pixels of the entire frame was computed. This ratio is called the Unmixed Fraction (UF). The more efficiently the specimen is chewed, the less unmixed colour remains, and the smaller the gum becomes. Consequently, a low unmixed fraction corresponds to good chewing efficiency. Results: 32 patients completed the chewing efficiency test (17 RPDs and 15 SDA). The mean UF recorded for the SDA group was not significantly different to that recorded for the RPD group (p>0.05, unpaired t-test). Conclusion: These results indicate that prosthodontic rehabilitation according to the principles of the SDA is equivalent to RPDs in terms of restoration of chewing ability for partially dentate older patients.