Francesc Comellas

Distributed loop computer networks: a survey

Abstract Distributed loop computer networks are extensions of the ring networks and are widely used in the design and implementation of local area networks and parallel processing architectures. We give a survey of recent results on this class of interconnection networks. We pay special attention to the actual computation of the minimum diameter and the construction of loop networks which can achieve this optimal number. Some open problems are offered for further investigation.

Deterministic small-world communication networks

Abstract Many real life networks, including the World Wide Web, electric power grids, and social networks, are small-world networks . The two distinguishing characteristics of small-world networks are strong local clustering (nodes have many mutual neighbors), and small average distance between two nodes. Small-world networks are promising candidates for communication networks since typical data-flow patterns in communication networks show a large amount of clustering with a small number of “long-distance” communications that need to be completed quickly. Most previous research on small-world networks has used simulations, probabilistic techniques, and random replacements of edges to study the limiting behaviour of these networks. In this paper, we initiate the study of small-world networks as communication networks using graph-theoretic methods to obtain exact results. We construct networks with strong local clustering and small diameter (instead of average distance). Our networks have the additional property that they are regular .

Recursive graphs with small-world scale-free properties.

We discuss a category of graphs, recursive clique trees, which have small-world and scale-free properties and allow a fine tuning of the clustering and the power-law exponent of their discrete degree distribution. We determine relevant characteristics of those graphs: the diameter, degree distribution, and clustering parameter. The graphs have also an interesting recursive property, and generalize recent constructions with fixed degree distributions.

Deterministic small-world networks

Many real-life networks, such as the World Wide Web, transportation systems, biological or social networks, achieve both a strong local clustering (nodes have many mutual neighbors) and a small diameter (maximum distance between any two nodes). These networks have been characterized as small-world networks and modeled by the addition of randomness to regular structures. We show that small-world networks can be constructed in a deterministic way. This exact approach permits a direct calculation of relevant network parameters allowing their immediate contrast with real-world networks and avoiding complex computer simulations.

High-dimensional random Apollonian networks

We propose a simple algorithm which produces a new category of networks, high-dimensional random Apollonian networks, with small-world and scale-free characteristics. We derive analytical expressions for their degree distributions and clustering coefficients which are determined by the dimension of the network. The values obtained for these parameters are in good agreement with simulation results and comparable to those coming from real networks. We estimate also analytically that the average path length of the networks increases at most logarithmically with the number of vertices.

High-dimensional Apollonian networks

We propose a simple algorithm which produces high-dimensional Apollonian networks with both small-world and scale-free characteristics. We derive analytical expressions for the degree distribution, the clustering coefficient and the diameter of the networks, which are determined by their dimension.

Evolving small-world networks with geographical attachment preference

We introduce a minimal extended evolving model for small-world networks which is controlled by a parameter. In this model, the network growth is determined by the attachment of new nodes to already existing nodes that are geographically close. We analyse several topological properties for our model both analytically and by numerical simulations. The resulting network shows some important characteristics of real-life networks such as small-world effect and high clustering.

Oxidative Stress Is a Central Target for Physical Exercise Neuroprotection Against Pathological Brain Aging

Physical exercise is suggested for preventing or delaying senescence and Alzheimers disease (AD). We have examined its therapeutic value in the advanced stage of AD-like pathology in 3xTg-AD female mice through voluntary wheel running from 12 to 15 months of age. Mice submitted to exercise showed improved body fitness, immunorejuvenation, improvement of behavior and cognition, and reduced amyloid and tau pathology. Brain tissue analysis of aged 3xTg-AD mice showed high levels of oxidative damage. However, this damage was decreased by physical exercise through regulation of redox homeostasis. Network analyses showed that oxidative stress was a central event, which correlated with AD-like pathology and the AD-related behaviors of anxiety, apathy, and cognitive loss. This study corroborates the importance of redox mechanisms in the neuroprotective effect of physical exercise, and supports the theory of the crucial role of oxidative stress in the switch from normal brain aging to pathological aging and AD.

Synchronizability of complex networks

Recent interest in the study of networks associated with complex systems has led to a better understanding of the factors and parameters relating the topology of the associated networks with the dynamics of the systems, and in particular their synchronization. In this paper, by using known and new results from spectral graph theory, we characterize relevant factors which affect the synchronization of complex networks.

Quantum Google in a Complex Network

We investigate the behaviour of the recently proposed Quantum PageRank algorithm, in large complex networks. We find that the algorithm is able to univocally reveal the underlying topology of the network and to identify and order the most relevant nodes. Furthermore, it is capable to clearly highlight the structure of secondary hubs and to resolve the degeneracy in importance of the low lying part of the list of rankings. The quantum algorithm displays an increased stability with respect to a variation of the damping parameter, present in the Google algorithm, and a more clearly pronounced power-law behaviour in the distribution of importance, as compared to the classical algorithm. We test the performance and confirm the listed features by applying it to real world examples from the WWW. Finally, we raise and partially address whether the increased sensitivity of the quantum algorithm persists under coordinated attacks in scale-free and random networks.