Sub-Riemannian heat kernels and mean curvature flow of graphs

We introduce a sub-Riemannian analogue of the Bence-Merriman-Osher diffusion driven algorithm and show that it leads to weak solutions of the horizontal mean curvature flow of graphs over sub-Riemannian Carnot groups. The proof follows the nonlinear semi-group theory approach originally introduced by L. C. Evans in the Euclidean setting and is based on new results on the relation between sub-Riemannian heat flows of characteristic functions of subgraphs and the horizontal mean curvature of the corresponding graphs.Comment: 24 page

An Analysis of the Consequences of the General Data Protection Regulation on Social Network Research

This article examines the principles outlined in the General Data Protection Regulation in the context of social network data. We provide both a practical guide to General Data Protection Regulation--compliant social network data processing, covering aspects such as data collection, consent, anonymization, and data analysis, and a broader discussion of the problems emerging when the general principles on which the regulation is based are instantiated for this research area

Analysis of Multiplex Social Networks with R

Multiplex social networks are characterized by a common set of actors connected through multiple types of relations. The multinet package provides a set of R functions to analyze multiplex social networks within the more general framework of multilayer networks, where each type of relation is represented as a layer in the network. The package contains functions to import/export, create and manipulate multilayer networks, implementations of several state-of-the-art multiplex network analysis algorithms, e.g., for centrality measures, layer comparison, community detection and visualization. Internally, the package is mainly written in native C++ and integrated with R using the Rcpp package

Towards effective visual analytics on multiplex and multilayer networks

In this article we discuss visualisation strategies for multiplex networks. Since Moreno's early works on network analysis, visualisation has been one of the main ways to understand networks thanks to its ability to summarise a complex structure into a single representation highlighting multiple properties of the data. However, despite the large renewed interest in the analysis of multiplex networks, no study has proposed specialised visualisation approaches for this context and traditional methods are typically applied instead. In this paper we initiate a critical and structured discussion of this topic, and claim that the development of specific visualisation methods for multiplex networks will be one of the main drivers pushing current research results into daily practice

ddit4 gene expression is switched on by a new hdac4 function in ataxia telangiectasia

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Identification of the main ubiquitination site in human erythroid α-spectrin

AbstractErythroid spectrin is the main component of the red cell membrane skeleton, which is very important in determining the shape, resistance to mechanical stresses and deformability of red cells. Previously we demonstrated that human erythroid α-spectrin is ubiquitinated in vitro and in vivo, and using recombinant peptides we identified on repeat 17 the main ubiquitination site of α-spectrin. In order to identify the lysine(s) involved in the ubiquitination process, in the present study we mutated the lysines by site-directed mutagenesis. We found that ubiquitination was dramatically inhibited in peptides carrying the mutation of lysine 27 on repeat 17 (mutants K25,27R and K27R). We also demonstrated that the correct folding of this protein is fundamental for its recognition by the ubiquitin conjugating system. Furthermore, the region flanking lysine 27 showed a 75% similarity with the leucine zipper pattern present in many regulatory proteins. Thus, a new potential ubiquitin recognition motif was identified in α-spectrin and may be present in several other proteins

Identification of ä-Spectrin Domains Susceptible to Ubiquitination

Previously, we demonstrated that alpha-spectrin is a substrate for the ubiquitin system and that this conjugation is a dynamic process (Corsi, D., Galluzzi, L., Crinelli, R., and Magnani, M. (1995) J. Biol. Chem. 270, 8928-8935). In this study, we mapped the sites of ubiquitination on erythrocyte alpha-spectrin. A peptide map of digested alpha-spectrin, previously submitted to in vitro 125I-ubiquitin conjugation, revealed the presence of four distinct labeled bands with Mr 40,000, 36,000, 29,000, and 25,500. Western blotting experiments using antibodies against each alpha-spectrin domain revealed that only IgG anti-alphaIII domain recognized the 125I-labeled ubiquitin peptide of 29 kDa, whereas the IgG anti-alphaV domain recognized the Mr 40,000 125I-ubiquitin-labeled peptide. The other two labeled bands of Mr 36,000 and Mr 25,500 were identified as tetra and tri multiubiquitin chains. Ubiquitination of the alphaIII and alphaV domains was further confirmed by anti-alpha-spectrin domain immunoaffinity chromatography. Endoprotease Lys C-digested spectrin conjugated previously to 125I-ubiquitin was incubated with antibodies against each trypsin-resistant domain of alpha-spectrin. Gamma counting of the radiolabeled antigen-antibody complexes purified by protein A chromatography showed labeling in the IgG anti-alphaIII and anti-alphaV complexes alone. Domain alphaIII is not associated with any known function, whereas domain alphaV contains the nucleation site for the association of the alpha and beta chains. Ubiquitination of the latter domain suggests a role for ubiquitin in the modulation of the stability, deformability, and viscoelastic properties of the erythrocyte membrane