We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in that it involves the properties of two-and not just one-vertices. The formalism is completed with the definition of a three-vertex correlation function, whi...

Description The genes of the Human Leukocyte Antigen (HLA) system reside on chromosome 6, and code for cellsurface proteins that play a crucial role in the presentation of endogenic peptides to effector cells of the immune system. The HLA Class I protein molecule is a heterodimer, made up of two chains; a heavy one and a light one (beta 2 microglobulin). The HLA-B gene is one of the three HLA C...

Respiratory chain complex I is a complicated enzyme of mitochondria, that couples electron transfer from NADH to ubiquinone to the proton translocation across the inner membrane of the organelle. The fungus Neurospora crassa has been used as one of the main model organisms to study this enzyme. Complex I is composed of multiple polypeptide subunits of dual genetic origin and contains several pr...

Complex I has a unique structure in plants and includes extra subunits. Here, we present a novel study to define its protein constituents. Mitochondria were isolated from Arabidopsis thaliana cell cultures, leaves, and roots. Subunits of complex I were resolved by 3D blue-native (BN)/SDS/SDS-PAGE and identified by mass spectrometry. Overall, 55 distinct proteins were found, seven of which occur...

A complex hyperbolic triangle group is the group of complex hyperbolic isometries generated by complex involutions fixing three complex lines in complex hyperbolic space. Such a group is called equilateral if there is an isometry of order three that cyclically permutes the three complex lines. We consider equilateral triangle groups for which the product of each pair of involutions and the prod...

In this first chapter, we give an introduction to random graphs and complex networks. We discuss examples of realworld networks and their empirical properties, and give a brief introduction to the kinds of models that we investigate in this book. Further, we introduce the notation used throughout the book.

a normed space $mathfrak{x}$ is said to have the fixed point property, if for each nonexpansive mapping $t : e longrightarrow e $ on a nonempty bounded closed convex subset $ e $ of $ mathfrak{x} $ has a fixed point. in this paper, we first show that if $ x $ is a locally compact hausdorff space then the following are equivalent: (i) $x$ is infinite set, (ii) $c_0(x)$ is infinite dimensional, (...

Heuristic techniques for recognizing PL spheres using the topological software polymake are presented. These methods have been successful very often despite sphere recognition being known to be hard (for dimensions d ≥ 3) or even undecidable (for d ≥ 5). A deeper look into the simplicial complexes for which the heuristics failed uncovered a trove of examples having interesting topological and c...

We investigate the problem of removing singularities from a non-manifold tetrahedral mesh so as to convert it to a more exploitable manifold representation. Given the twofold combinatorial and geometrical nature of a 3D simplicial complex, we propose two conversion algorithms that, depending on the targeted application, modify either its connectivity only or both its connectivity and its geomet...

Mitochondrial complex I has a molecular mass of almost 1 MDa and comprises more than 40 polypeptides. Fourteen central subunits harbour the bioenergetic core functions. We are only beginning to understand the significance of the numerous accessory subunits. The present review addresses the role of accessory subunits for assembly, stability and regulation of complex I and for cellular functions ...