Image processing methods for human brain connectivity analysis from in-vivo diffusion MRI

The structural connectivity of the brain is considered to encode species-wise and subject-wise patterns that will unlock large areas of understanding of the human brain. Currently, diffusion MRI of the living brain enables to map the microstructure of tissue, allowing to track the pathways of fiber bundles connecting the cortical regions across the brain. These bundles are summarized in a network representation called connectome that is analyzed using graph theory. The extraction of the connectome from diffusion MRI requires a large processing flow including image enhancement, reconstruction, segmentation, registration, diffusion tracking, etc. Although a concerted effort has been devoted to the definition of standard pipelines for the connectome extraction, it is still crucial to define quality assessment protocols of these workflows. The definition of quality control protocols is hindered by the complexity of the pipelines under test and the absolute lack of gold-standards for diffusion MRI data. Here we characterize the impact on structural connectivity workflows of the geometrical deformation typically shown by diffusion MRI data due to the inhomogeneity of magnetic susceptibility across the imaged object. We propose an evaluation framework to compare the existing methodologies to correct for these artifacts including whole-brain realistic phantoms. Additionally, we design and implement an image segmentation and registration method to avoid performing the correction task and to enable processing in the native space of diffusion data. We release PySDCev, an evaluation framework for the quality control of connectivity pipelines, specialized in the study of susceptibility-derived distortions. In this context, we propose Diffantom, a whole-brain phantom that provides a solution to the lack of gold-standard data. The three correction methodologies under comparison performed reasonably, and it is difficult to determine which method is more advisable. We demonstrate that susceptibility-derived correction is necessary to increase the sensitivity of connectivity pipelines, at the cost of specificity. Finally, with the registration and segmentation tool called regseg we demonstrate how the problem of susceptibility-derived distortion can be overcome allowing data to be used in their original coordinates. This is crucial to increase the sensitivity of the whole pipeline without any loss in specificity.

Finite Element Model of the Innovation Diffusion: An Application to Photovoltaic Systems

This paper presents a Finite Element Model, which has been used for forecasting the diffusion of innovations in time and space. Unlike conventional models used in diffusion literature, the model considers the spatial heterogeneity. The implementation steps of the model are explained by applying it to the case of diffusion of photovoltaic systems in a local region in southern Germany. The applied model is based on a parabolic partial differential equation that describes the diffusion ratio of photovoltaic systems in a given region over time. The results of the application show that the Finite Element Model constitutes a powerful tool to better understand the diffusion of an innovation as a simultaneous space-time process. For future research, model limitations and possible extensions are also discussed.

A subgrid viscosity Lagrance-Galerkin method for convection-diffusion problems

We present and analyze a subgrid viscosity Lagrange-Galerk in method that combines the subgrid eddy viscosity method proposed in W. Layton, A connection between subgrid scale eddy viscosity and mixed methods. Appl. Math. Comp., 133: 14 7-157, 2002, and a conventional Lagrange-Galerkin method in the framework of P1��� cubic bubble finite elements. This results in an efficient and easy to implement stabilized method for convection dominated convection diffusion reaction problems. Numerical experiments support the numerical analysis results and show that the new method is more accurate than the conventional Lagrange-Galerkin one.

Classical solutions for a logarithmic fractional diffusion equation

We prove global existence and uniqueness of strong solutions to the logarithmic porous medium type equation with fractional diffusion ?tu + (?)1/2 log(1 + u) = 0, posed for x ? R, with nonnegative initial data in some function space of LlogL type. The solutions are shown to become bounded and C? smooth in (x, t) for all positive times. We also reformulate this equation as a transport equation with nonlocal velocity and critical viscosity, a topic of current relevance. Interesting functional inequalities are involved.

Rhizobium leguminosarum HupE is a highly-specific diffusion facilitator for nickel uptake

Bacteria require nickel transporters for the synthesis of Ni-containing metalloenzymes in natural, low nickel habitats. In this work we carry out functional and topological characterization of Rhizobium leguminosarum HupE, a nickel permease required for the provision of this element for [NiFe] hydrogenase synthesis. Expression studies in the Escherichia coli nikABCDE mutant strain HYD723 revealed that HupE is a medium-affinity permease (apparent Km 227 ! 21 nM; Vmax 49 ! 21 pmol Ni2+ min"1 mg"1 bacterial dry weight) that functions as an energy-independent diffusion facilitator for the uptake of Ni(II) ions. This Ni2+ transport is not inhibited by similar cations such as Mn2+, Zn2+, or Co2+, but is blocked by Cu2+. Analysis of site-directed HupE mutants allowed the identification of several residues (H36, D42, H43, F69, E90, H130, and E133) that are essential for HupE-mediated Ni uptake in E. coli cells. By using translational fusions to reporter genes we demonstrated the presence of five transmembrane domains with a periplasmic N-terminal domain and a C-terminal domain buried in the lipid bilayer. The periplasmic N-terminal domain contributes to stability and functionality of the protein

Optimizing phosphorus diffusion for photovoltaic applications: peak doping, inactive phosphorus,gettering, and contact formation

The phosphosilicate glass (PSG), fabricated by tube furnace diffusion using a POCl3 source, is widely used as a dopant source in the manufacturing of crystalline silicon solar cells. Although it has been a widely addressed research topic for a long time, there is still lack of a comprehensive understanding of aspects such as the growth, the chemical composition, possible phosphorus depletion, the resulting in-diffused phosphorus profiles, the gettering behavior in silicon, and finally the metal-contact formation. This paper addresses these different aspects simultaneously to further optimize process conditions for photovoltaic applications. To do so, a wide range of experimental data is used and combined with device and process simulations, leading to a more comprehensive interpretation. The results show that slight changes in the PSG process conditions can produce high-quality emitters. It is predicted that PSG processes at 860�����C for 60���min in combination with an etch-back and laser doping from PSG layer results in high-quality emitters with a peak dopant density Npeak���=���8.0��������1018���cm���3 and a junction depth dj���=���0.4�����m, resulting in a sheet resistivity��sh���=���380 ��/sq and a saturation current-density J0 below 10 fA/cm2. With these properties, the POCl3 process can compete with ion implantation or doped oxide approaches.