ON THE WEIGHTED INEQUALITY BETWEEN THE GAGLIARDO AND SOBOLEV SEMINORMS

We prove weighted inequalities between the Gagliardo and Sobolev seminorms. With A1 weights we improve earlier results of Bourgain, Brezis, and Mironescu

Statistical models of images and early vision

A fundamental question in visual neuroscience is: Why are the receptive fields and response properties of visual neurons as they are? A modern approach to this problem emphasizes the importance of adaptation to ecologically valid input. In this paper, we will review work on modelling statistical regularities in ecologically valid visual input (“natural images”) and the obtained functional explanation of the properties of visual neurons. A seminal statistical model for natural images was linear sparse coding which is equivalent to the model called independent component analysis (ICA). Linear features estimated by ICA resemble wavelets or Gabor functions, and provide a very good description of the properties of simple cells in the primary visual cortex. We have introduced extensions of ICA that are based on modelling dependencies of the ”independent ” components estimated by basic ICA. The dependencies of the components are used to define either a grouping or a topographic order between the components. With natural image data, these models lead to emergence of further properties of visual neurons: the topographic organization and complex cell receptive fields. We have also modelled the temporal structure of natural image sequences, which provides an alternative approach to the sparseness used in most models. These models can be combined in a unifying framework that we call bubble coding. Finally, we will discuss a promising new direction of research: predictive visual neuroscience. There, the goal is to try to predict response properties of neurons in areas that are poorly understood, still based on statistical modelling of natural input. 1

Independent Component Analysis-motivated Approach to Classificatory Decomposition of Cortical Evoked Potentials

BACKGROUND: Independent Component Analysis (ICA) proves to be useful in the analysis of neural activity, as it allows for identification of distinct sources of activity. Applied to measurements registered in a controlled setting and under exposure to an external stimulus, it can facilitate analysis of the impact of the stimulus on those sources. The link between the stimulus and a given source can be verified by a classifier that is able to "predict" the condition a given signal was registered under, solely based on the components. However, the ICA's assumption about statistical independence of sources is often unrealistic and turns out to be insufficient to build an accurate classifier. Therefore, we propose to utilize a novel method, based on hybridization of ICA, multi-objective evolutionary algorithms (MOEA), and rough sets (RS), that attempts to improve the effectiveness of signal decomposition techniques by providing them with "classification-awareness." RESULTS: The preliminary results described here are very promising and further investigation of other MOEAs and/or RS-based classification accuracy measures should be pursued. Even a quick visual analysis of those results can provide an interesting insight into the problem of neural activity analysis. CONCLUSION: We present a methodology of classificatory decomposition of signals. One of the main advantages of our approach is the fact that rather than solely relying on often unrealistic assumptions about statistical independence of sources, components are generated in the light of a underlying classification problem itself

Pregnancy related back pain, is it related to aerobic fitness? A longitudinal cohort study

<p>Abstract</p> <p>Background</p> <p>Low back pain with onset during pregnancy is common and approximately one out of three women have disabling pain. The pathogenesis of the pain condition is uncertain and there is no information on the role of physical fitness. Whether poorer physical conditioning is a cause or effect of back pain is also disputed and information from prospective studies needed.</p> <p>Methods</p> <p>A cohort of pregnant women, recruited from maternal health care centers in central Sweden, were examined regarding estimated peak oxygen uptake by cycle ergometer test in early pregnancy, reported physical activity prior to pregnancy, basic characteristics, back pain during pregnancy and back pain postpartum.</p> <p>Results</p> <p>Back pain during the current pregnancy was reported by nearly 80% of the women. At the postpartum appointment this prevalence was 40%. No association was displayed between estimated peak oxygen uptake and incidence of back pain during and after pregnancy, adjusted for physical activity, back pain before present pregnancy, previous deliveries, age and weight. A significant inverse association was found between estimated peak oxygen uptake and back pain intensity during pregnancy and a direct association post partum, in a fully adjusted multiple linear regression analysis.</p> <p>Conclusions</p> <p>Estimated peak oxygen uptake and reported physical activity in early pregnancy displayed no influence on the onset of subsequent back pain during or after pregnancy, where the time sequence support the hypothesis that poorer physical deconditioning is not a cause but a consequence of the back pain condition. The mechanism for the attenuating effect of increased oxygen uptake on back pain intensity is uncertain.</p

Pointwise estimates to the modified Riesz potential

In a smooth domain a function can be estimated pointwise by the classical Riesz potential of its gradient. Combining this estimate with the boundedness of the classical Riesz potential yields the optimal Sobolev-Poincar, inequality. We show that this method gives a Sobolev-Poincar, inequality also for irregular domains whenever we use the modified Riesz potential which arise naturally from the geometry of the domain. The exponent of the Sobolev-Poincar, inequality depends on the domain. The Sobolev-Poincar, inequality given by this approach is not sharp for irregular domains, although the embedding for the modified Riesz potential is optimal. In order to obtain the results we prove a new pointwise estimate for the Hardy-Littlewood maximal operator.Peer reviewe

Defect detection in textile fabric images using subband domain subspace analysis

In this work, a new model that combines the concepts of wavelet transformation and subspace analysis tools, like Independent Component Analysis, Topographic Independent Component Analysis, and Independent Subspace Analysis, is developed for the purpose of defect detection in textile images. In previous works, it has been shown that reduction of the textural components of the textile image by preprocessing has increased the performance of the system. Based on this observation, in present work, the aforementioned subspace analysis tools are aimed to be applied on the sub-band images. The feature vector of a sub-window of a test image is compared with that of the defect-free image in order to make a decision. This decision is based on a Euclidean distance classifier. The performance increase that results using wavelet transformation prior to subspace analysis has been discussed in detail. While all the subspace analysis methods has been found to lead to the same detection performances, as a further step, independent subspace analysis is used to classify the detected defects according to their directionalities