Schur functions and their realizations in the slice hyperholomorphic setting

we start the study of Schur analysis in the quaternionic setting using the theory of slice hyperholomorphic functions. The novelty of our approach is that slice hyperholomorphic functions allows to write realizations in terms of a suitable resolvent, the so called S-resolvent operator and to extend several results that hold in the complex case to the quaternionic case. We discuss reproducing kernels, positive definite functions in this setting and we show how they can be obtained in our setting using the extension operator and the slice regular product. We define Schur multipliers, and find their co-isometric realization in terms of the associated de Branges-Rovnyak space

Counterexamples in multimarginal optimal transport with Coulomb cost and spherically symmetric data

We disprove a conjecture in Density Functional Theory, relative to multimarginal optimal transport maps with Coulomb cost. In the case of spherically symmetric data, which model for instance Lithium and Beryllium atoms, we show that some special maps, introduced by Seidl, Gori-Giorgi and Savin are not always optimal in the corresponding transport problem. We also provide examples of maps satisfying optimality conditions for special classes of data

Thermodynamics of beta-amyloid fibril formation

Amyloid fibers are aggregates of proteins. They are built out of a peptide called $\beta$--amyloid (A$\beta$) containing between 41 and 43 residues, produced by the action of an enzyme which cleaves a much larger protein known as the Amyloid Precursor Protein (APP). X-ray diffraction experiments have shown that these fibrils are rich in $\beta$--structures, whereas the shape of the peptide displays an $\alpha$--helix structure within the APP in its biologically active conformation. A realistic model of fibril formation is developed based on the seventeen residues A$\beta$12--28 amyloid peptide, which has been shown to form fibrils structurally similar to those of the whole A$\beta$ peptide. With the help of physical arguments and in keeping with experimental findings, the A$\beta$12--28 monomer is assumed to be in four possible states (i.e., native helix conformation, $\beta$--hairpin, globular low--energy state and unfolded state). Making use of these monomeric states, oligomers (dimers, tertramers and octamers) were constructed. With the help of short, detailed Molecular Dynamics (MD) calculations of the three monomers and of a variety of oligomers, energies for these structures were obtained. Making use of these results within the framework of a simple yet realistic model to describe the entropic terms associated with the variety of amyloid conformations, a phase diagram can be calculated of the whole many--body system, leading to a thermodynamical picture in overall agreement with the experimental findings. In particular, the existence of micellar metastable states seem to be a key issue to determine the thermodynamical properties of the system

Understanding the determinants of stability and folding of small globular proteins from their energetics

The results of minimal model calculations suggest that the stability and the kinetic accessibility of the native state of small globular proteins are controlled by few "hot" sites. By mean of molecular dynamics simulations around the native conformation, which simulate the protein and the surrounding solvent at full--atom level, we generate an energetic map of the equilibrium state of the protein and simplify it with an Eigenvalue decomposition. The components of the Eigenvector associated with the lowest Eigenvalue indicate which are the "hot" sites responsible for the stability and for the fast folding of the protein. Comparison of these predictions with the results of mutatgenesis experiments, performed for five small proteins, provide an excellent agreement

Restoration and enhancement of historical stereo photos

Restoration of digital visual media acquired from repositories of historical photographic and cinematographic material is of key importance for the preservation, study and transmission of the legacy of past cultures to the coming generations. In this paper, a fully automatic approach to the digital restoration of historical stereo photographs is proposed, referred to as Stacked Median Restoration plus (SMR+). The approach exploits the content redundancy in stereo pairs for detecting and fixing scratches, dust, dirt spots and many other defects in the original images, as well as improving contrast and illumination. This is done by estimating the optical flow between the images, and using it to register one view onto the other both geometrically and photometrically. Restoration is then accomplished in three steps: (1) image fusion according to the stacked median operator, (2) low-resolution detail enhancement by guided supersampling, and (3) iterative visual consistency checking and refinement. Each step implements an original algorithm specifically designed for this work. The restored image is fully consistent with the original content, thus improving over the methods based on image hallucination. Comparative results on three different datasets of historical stereograms show the effectiveness of the proposed approach, and its superiority over single-image denoising and super-resolution methods. Results also show that the performance of the state-of-the-art single-image deep restoration network Bringing Old Photo Back to Life (BOPBtL) can be strongly improved when the input image is pre-processed by SMR+

Selective visual odometry for accurate AUV localization

In this paper we present a stereo visual odometry system developed for autonomous underwater vehicle localization tasks. The main idea is to make use of only highly reliable data in the estimation process, employing a robust keypoint tracking approach and an effective keyframe selection strategy, so that camera movements are estimated with high accuracy even for long paths. Furthermore, in order to limit the drift error, camera pose estimation is referred to the last keyframe, selected by analyzing the feature temporal flow. The proposed system was tested on the KITTI evaluation framework and on the New Tsukuba stereo dataset to assess its effectiveness on long tracks and different illumination conditions. Results of a live archaeological campaign in the Mediterranean Sea, on an AUV equipped with a stereo camera pair, show that our solution can effectively work in underwater environments

Fast adaptive frame preprocessing for 3D reconstruction

This paper presents a new online preprocessing strategy to detect and discard ongoing bad frames in video sequences. These include frames where an accurate localization between corresponding points is difficult, such as for blurred frames, or which do not provide relevant information with respect to the previous frames in terms of texture, image contrast and non-flat areas. Unlike keyframe selectors and deblurring methods, the proposed approach is a fast preprocessing working on a simple gradient statistic, that does not require to compute complex time-consuming image processing, such as the computation of image feature keypoints, previous poses and 3D structure, or to know a priori the input sequence. The presented method provides a fast and useful frame pre-analysis which can be used to improve further image analysis tasks, including also the keyframe selection or the blur detection, or to directly filter the video sequence as shown in the paper, improving the final 3D reconstruction by discarding noisy frames and decreasing the final computation time by removing some redundant frames. This scheme is adaptive, fast and works at runtime by exploiting the image gradient statistic of the last few frames of the video sequence. Experimental results show that the proposed frame selection strategy is robust and improves the final 3D reconstruction both in terms of number of obtained 3D points and reprojection error, also reducing the computational time

Accurate keyframe selection and keypoint tracking for robust visual odometry

This paper presents a novel stereo visual odometry (VO) framework based on structure from motion, where a robust keypoint tracking and matching is combined with an effective keyframe selection strategy. In order to track and find correct feature correspondences a robust loop chain matching scheme on two consecutive stereo pairs is introduced. Keyframe selection is based on the proportion of features with high temporal disparity. This criterion relies on the observation that the error in the pose estimation propagates from the uncertainty of 3D points—higher for distant points, that have low 2D motion. Comparative results based on three VO datasets show that the proposed solution is remarkably effective and robust even for very long path lengths

Preface: Bioplasmas and plasmas with liquids

The Bioplasma and Plasmas with Liquids joint conference of the COST Actions TD1208 Electrical discharges with liquids for future applications and MP1101 Biomedical applications of atmospheric pressure plasma technology was held in Bertinoro (Italy) on September 13-16, 2015. The purpose of the Bioplasma and Plasmas with Liquids joint conference was to bring together researchers of different fields, and to establish an open forum for presentation and discussion of the latest advances in the fields of electrical discharges with liquids and plasma medicine, by bridging the scientific communities associated with the COST Actions TD1208 Electrical discharges with liquids for future applications and MP1101 Biomedical applications of atmospheric pressure plasma technology