Mathematical Formulation of Multi-Layer Networks

A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems is very rich. Achieving a deep understanding of such systems necessitates generalizing "traditional" network theory, and the newfound deluge of data now makes it possible to test increasingly general frameworks for the study of networks. In particular, although adjacency matrices are useful to describe traditional single-layer networks, such a representation is insufficient for the analysis and description of multiplex and time-dependent networks. One must therefore develop a more general mathematical framework to cope with the challenges posed by multi-layer complex systems. In this paper, we introduce a tensorial framework to study multi-layer networks, and we discuss the generalization of several important network descriptors and dynamical processes --including degree centrality, clustering coefficients, eigenvector centrality, modularity, Von Neumann entropy, and diffusion-- for this framework. We examine the impact of different choices in constructing these generalizations, and we illustrate how to obtain known results for the special cases of single-layer and multiplex networks. Our tensorial approach will be helpful for tackling pressing problems in multi-layer complex systems, such as inferring who is influencing whom (and by which media) in multichannel social networks and developing routing techniques for multimodal transportation systems.Comment: 15 pages, 5 figure

Clustering data by inhomogeneous chaotic map lattices

A new approach to clustering, based on the physical properties of inhomogeneous coupled chaotic maps, is presented. A chaotic map is assigned to each data-point and short range couplings are introduced. The stationary regime of the system corresponds to a macroscopic attractor independent of the initial conditions. The mutual information between couples of maps serves to partition the data set in clusters, without prior assumptions about the structure of the underlying distribution of the data. Experiments on simulated and real data sets show the effectiveness of the proposed algorithm.Comment: 8 pages, 6 figures. Revised version accepted for publication on Physical Review Letter

Scale-Free model for governing universe dynamics

We investigate the effects of scale-free model on cosmology, providing, in this way, a statistical background in the framework of general relativity. In order to discuss properties and time evolution of some relevant universe dynamical parameters (cosmographic parameters), such as $H(t)$ (Hubble parameter), $q(t)$ (deceleration parameter), $j(t)$ (jerk parameter) and $s(t)$ (snap parameter), which are well re-defined in the framework of scale-free model, we analyze a comparison between WMAP data. Hence the basic purpose of the work is to consider this statistical interpretation of mass distribution of universe, in order to have a mass density $\rho$ dynamics, not inferred from Friedmann equations, via scale factor $a(t)$. This model, indeed, has been used also to explain a possible origin and a viable explanation of cosmological constant, which assumes a statistical interpretation without the presence of extended theories of gravity; hence the problem of dark energy could be revisited in the context of a classical probability distribution of mass, which is, in particular, for the scale-free model, $P(k)\sim k^{-\gamma}$, with $2<\gamma<3$. The $\Lambda$CDM model becomes, with these considerations, a consequence of the particular statistics together with the use of general relativity.Comment: 7 pages, 4 figure

Spatial organization in cyclic Lotka-Volterra systems

We study the evolution of a system of $N$ interacting species which mimics the dynamics of a cyclic food chain. On a one-dimensional lattice with N<5 species, spatial inhomogeneities develop spontaneously in initially homogeneous systems. The arising spatial patterns form a mosaic of single-species domains with algebraically growing size, $\ell(t)\sim t^\alpha$, where $\alpha=3/4$ (1/2) and 1/3 for N=3 with sequential (parallel) dynamics and N=4, respectively. The domain distribution also exhibits a self-similar spatial structure which is characterized by an additional length scale, ${\cal L}(t)\sim t^\beta$, with $\beta=1$ and 2/3 for N=3 and 4, respectively. For $N\geq 5$, the system quickly reaches a frozen state with non interacting neighboring species. We investigate the time distribution of the number of mutations of a site using scaling arguments as well as an exact solution for N=3. Some possible extensions of the system are analyzed.Comment: 18 pages, 10 figures, revtex, also available from http://arnold.uchicago.edu/~ebn

NMR-based metabolomics to evaluate the milk composition from Friesian and autochthonous cows of Northern Italy at different lactation times

<p>It is well established that different factors affect milk composition in cows and that milk composition, in turn, affect both technological and nutritional qualities. In this respect the comprehension of the metabolic variability of milk composition in relation to the lactation time as well as to the genetic background may be of paramount importance for the agri-food industries. In the present study we investigated the variations of the metabolic profiles during lactation in milks obtained from Friesian and autochthonous races from Northern Italy by ¹H NMR metabolomics. Furthermore, the external factors influencing the milk composition were minimized: the cows were breeded in the same farm, were fed with the same diet and were paired for the lactation interval and lactation stage. Our results showed a difference in milk composition between races and in relation to late lactation. The PLS-DA analysis permitted to distinguish the Friesian and autochthonous cow milks at the investigated different lactation times. Interestingly, the metabolites significantly involved into the discrimination between races appeared to be also technological property parameters, highlighting the importance of maintaining the biodiversity of cow breeds. Therefore, NMR-based metabolomics of milk could represent an informative tool to identify metabolites involved in milk quality both from a nutritional and industrial perspective.</p

Demographic characteristics of the subjects studied (n = 52).

<p>Demographic characteristics of the subjects studied (n = 52).</p

Solid-phase synthesis of peptides containing the spin-labeled 2,2,6,6,-tetramethylpiperidine-1-oxyl-4-amino-4-carboxylic acid (TOAC)

2,2,6,6-Tetramethylpiperidine-1-oxyl-4-amino-4-carboxylic acid (TOAC) is a nitroxide spin-labeled, achiral C-alpha-tetrasubstituted amino acid recently shown to be not only an effective beta -turn and 3(10)/alpha -helix promoter in peptides, but also an excellent rigid electron paramagnetic resonance probe and fluorescence quencher. Here, we demonstrate that TOAC can be effectively incorporated into internal positions of peptide sequences using Fmoc chemistry and solid-phase synthesis in an automated apparatus