We investigate some aspects of the self-consistency in the Dyson-Schwinger approach to both the QED and the self-interacting scalar field theories. We prove that the set of the Dyson-Schwinger equations, together with the Green-Ward-Takahashi identity, is equivalent to the analogous set of integral equations studied in condensed matter, namely, many-body perturbation theory, where it is solved self-consistently and iteratively. In this framework, we compute the nonperturbative solution of the gap equation for the self-interacting scalar field theory.

In this article a nonnegative blind source separation technique, known as nonnegative matrix factorization, is applied to microdiffraction data in order to extract characteristic patterns and to determine their spatial distribution in tissue typing problems occurring in bone-tissue engineering. In contrast to other blind source separation methods, nonnegative matrix factorization only requires nonnegative constraints on the extracted sources and corresponding weights, which makes it suitable for the analysis of data occurring in a variety of applications. In particular, here nonnegative matrix factorization is hierarchically applied to two-dimensional meshes of X-ray diffraction data measured in bone samples with implanted tissue. Such data are characterized by nonnegative profiles and their analysis provides significant information about the structure of possibly new deposited bone tissue. A simulation and real data studies show that the proposed method is able to retrieve the patterns of interest and to provide a reliable and accurate segmentation of the given X-ray diffraction data.

Scanning small and wide angle X-ray scattering (scanning SWAXS) experiments were performed on healthy and pathologic human bone sections. Via crystallographic tools the data were transformed into quantitative images and as such compared with circularly polarized light (CPL) microscopy images. SWAXS and CPL images allowed extracting information of the mineral nanocrystalline phase embedded, with and without preferred orientation, in the collagen fibrils, mapping local changes at sub-osteon resolution. This favorable combination has been applied for the first time to biopsies of dwarfism syndrome and Paget's disease to shed light onto the cortical structure of natural bone in healthy and pathologic sections.

The Debye Function Analysis of diffraction patterns from nanosized mineral crystals showing different average degrees of maturity was carried out on engineered bone samples. The analysis relied on a bivariate family of atomistic hydroxyapatite nanocrystal models and provided information about crystal structure, size and shape distributions of the mineral component of the newly formed bone. An average rod-like shape of nanocrystals was found in all samples, with average sizes well matching the collagen I gap region. The diffraction patterns investigated through the Debye Function Analysis were used as signal models to perform the Canonical Correlation Analysis of high resolution X-ray micro-diffraction patterns collected on porous and resorbable hydroxyapatite/silicon-stabilized tricalcium phosphate (Si-TCP) implants. The nosologic maps clearly showed a size gradient in the new formed bone that validates the mechanism (mimicking the bone remodelling in orthotopic bones) of a continuous deposition of bone by osteoblasts, an increasing mineralization of the newly deposited bone, a growth of the new crystals, at the same time that osteoclasts adhere to the scaffold surface and resorb the bioceramic. The comparison of samples at different implantation times proved that the selective resorption of Si-TCP component from the scaffold was already evident after two and almost complete after six months.

Bovine cornea was studied with scanning small-angle X-ray scattering (SAXS) microscopy, by using both synchrotron radiation and a microfocus laboratory source. A combination of statistical (adaptive binning and canonical correlation analysis) and crystallographic (pair distribution function analysis) approaches allowed inspection of the collagen lateral packing of the supramolecular structure. Results reveal (i) a decrease of the interfibrillar distance and of the shell thickness around the fibrils from the periphery to the center of the cornea, (ii) a uniform fibril diameter across the explored area, and (iii) a distorted quasi-hexagonal arrangement of the collagen fibrils. The results are in agreement with existing literature. The overlap between laboratory and synchrotron-radiation data opens new perspectives for further studies on collagen-based/engineered tissues by the SAXS microscopy technique at laboratory-scale facilities.Bovine cornea was studied with scanning small-angle X-ray scattering microscopy, by using both synchrotron radiation and a microfocus laboratory source. The supramolecular structure of the collagen fibers is explored thanks to the combination of statistical (adaptive binning and canonical correlation analysis) and crystallographic (pair distribution function analysis) approaches.

Electronic poster ("Graphene Factory" CNR project)

We present two possible approaches to calculate the momentum distribution n(p) and the Compton profile within the framework of the ab initio GW approximation on the self-energy. The approaches are based on integration of the Green's function along either the real or the imaginary axes. Examples will be presented on the jellium model and on real bulk sodium. Advantages and drawbacks of both methods are discussed in comparison with accurate quantum Monte Carlo calculations and x-ray Compton scattering experiments. We illustrate the effect of many-body correlations and disentangle them from band-structure and anisotropy effects by a comparison with density functional theory in the local density approximation. Our results suggest the use of G0W0 momentum distributions as reference for future experiments and theory developments.

Osteoarthritis (OA), among other bone pathologies, is expected to determine supramolecular changes at the level of the mineralized collagen fiber. In a proof-of-principle study, bone biopsies were collected from six coxarthritis-affected patients, aged 62-87 years, during hip prosthesis implant surgery, sliced down to 100 mm-thick tissues, and investigated using scanning small-angle and wide-angle X-ray scattering (SAXS and WAXS) transmission microscopy. A multimodal imaging evaluation of the SAXS and WAXS data, combined with principal component and canonical correlation analyses, allowed the transformation of the raw data into microscopy images and inspection of the nanoscale structure of the mineralized collagen fibers across mm 2 tissue areas. The combined scanning SAXS and WAXS microscopy is shown to be a suitable choice for characterizing and quantifying the nanostructural properties of collagen over extended areas. The results suggest the existence of a correlation between age and cross-linking-induced rigidity of collagen fibers.

SUNBIM (Supramolecular & SUbmolecular Nano & Bio Materials X-ray IMaging Project) is a suite of integrated programs developed, in collaboration with Rigaku Innovative Technologies, to treat Small and Wide Angle X-ray Scattering data, collected either in transmission geometry (SAXS/WAXS) or in reflection geometry (GISAXS/GIWAXS). In addition, a specific routine to collect and analyze data in SAXS scanning transmission microscopy has been developed as additional tool to investigate tissues or material science samples through a focused X-ray beam which is used to raster scan a specimen while acquiring SAXS scattering patterns with a 2D detector. Indeed, a first-generation-synchrotron-class FrE+ SuperBright Rigaku microsource, coupled to a three pinhole S-MAX3000 camera, was recently installed at the X-ray MicroImaging Laboratory (XMI-L@b) and used with success in SAXS/WAXS/GISAXS/GIWAXS experiments (De Caro et al, 2012; 2013)and for SAXS scanning microscopy (Altamura et al, 2012; Giannini et al, 2013).

SUNBIM (supramolecular and submolecular nano- and biomaterials X-rayimaging) is a suite of integrated programs which, through a user-friendlygraphical user interface, are optimized to perform the following: (i) q-scalecalibration and two-dimensional ! one-dimensional folding on small- andwide-angle X-ray scattering (SAXS/WAXS) and grazing-incidence SAXS/WAXS (GISAXS/GIWAXS) data, also including possible eccentricity correctionsfor WAXS/GIWAXS data; (ii) background evaluation and subtraction,denoising, and deconvolution of the primary beam angular divergence onSAXS/GISAXS profiles; (iii) indexing of two-dimensional GISAXS frames andextraction of one-dimensional GISAXS profiles along specific cuts; (iv) scanningmicroscopy in absorption and SAXS contrast. The latter includes collection oftransmission and SAXS data, respectively, in a mesh across a mm2 area,organization of the as-collected data into a single composite image oftransmission values or two-dimensional SAXS frames, analysis of the composeddata to derive the absorption map and/or the spatial distribution, andorientation of nanoscale structures over the scanned area.

During recent decades innovative nanomaterials have been extensively studied, aiming at both investigating the structure-property relationship and discovering new properties, in order to achieve relevant improvements in current state-of-the art materials. Lately, controlled growth and/or assembly of nanostructures into hierarchical and complex architectures have played a key role in engineering novel functionalized materials. Since the structural characterization of such materials is a fundamental step, here we discuss X-ray scattering/diffraction techniques to analyze inorganic nanomaterials under different conditions: dispersed in solutions, dried in powders, embedded in matrix, and deposited onto surfaces or underneath them.

A first-generation-synchrotron-class X-ray laboratory microsource, coupled to a three-pinhole camera, is presented. It allows (i) small- and wide-angle X-ray scattering images to be acquired simultaneously, and (ii) scanning small- and wide-angle X-ray scattering microscopy to be carried out. As representative applications, the structural complexity of a biological natural material (human bone biopsy) and of a metamaterial (colloidal nanocrystal assembly) are inspected at different length scales, studying the atomic/molecular ordering by (grazing-incidence) wide-angle X-ray scattering and the morphological/structural conformation by (grazing-incidence) small-angle X-ray scattering. In particular, the grazing-incidence measurement geometries are needed for inspecting materials lying on top of surfaces or buried underneath surfaces.