Efficiency of informational transfer in regular and complex networks

We analyze the process of informational exchange through complex networks by measuring network efficiencies. Aiming to study nonclustered systems, we propose a modification of this measure on the local level. We apply this method to an extension of the class of small worlds that includes declustered networks and show that they are locally quite efficient, although their clustering coefficient is practically zero. Unweighted systems with small-world and scale-free topologies are shown to be both globally and locally efficient. Our method is also applied to characterize weighted networks. In particular we examine the properties of underground transportation systems of Madrid and Barcelona and reinterpret the results obtained for the Boston subway network.

Reconstruction of networks from their betweenness centrality

In this paper we study the reconstruction of a network topology from the values of its betweenness centrality, a measure of the influence of each of its nodes in the dissemination of information over the network. We consider a simple metaheuristic, simulated annealing, as the combinatorial optimization method to generate the network from the values of the betweenness centrality. We compare the performance of this technique when reconstructing different categories of networks –random, regular, small-world, scale-free and clustered–. We show that the method allows an exact reconstruction of small networks and leads to good topological approximations in the case of networks with larger orders. The method can be used to generate a quasi-optimal topology fora communication network from a list with the values of the maximum allowable traffic for each node.

Using Pareto optimality to explore the topology and dynamics of the human connectome.

Graph theory has provided a key mathematical framework to analyse the architecture of human brain networks. This architecture embodies an inherently complex relationship between connection topology, the spatial arrangement of network elements, and the resulting network cost and functional performance. An exploration of these interacting factors and driving forces may reveal salient network features that are critically important for shaping and constraining the brain's topological organization and its evolvability. Several studies have pointed to an economic balance between network cost and network efficiency with networks organized in an 'economical' small-world favouring high communication efficiency at a low wiring cost. In this study, we define and explore a network morphospace in order to characterize different aspects of communication efficiency in human brain networks. Using a multi-objective evolutionary approach that approximates a Pareto-optimal set within the morphospace, we investigate the capacity of anatomical brain networks to evolve towards topologies that exhibit optimal information processing features while preserving network cost. This approach allows us to investigate network topologies that emerge under specific selection pressures, thus providing some insight into the selectional forces that may have shaped the network architecture of existing human brains.

Nature of the Epidemic Threshold for the Susceptible-Infected-Susceptible Dynamics in Networks

We develop an analytical approach to the susceptible-infected-susceptible epidemic model that allows us to unravel the true origin of the absence of an epidemic threshold in heterogeneous networks. We find that a delicate balance between the number of high degree nodes in the network and the topological distance between them dictates the existence or absence of such a threshold. In particular, small-world random networks with a degree distribution decaying slower than an exponential have a vanishing epidemic threshold in the thermodynamic limit.

The von Neumann Minimax Theorem and its relatives and a study of externality in on-line auctions

This work consists of a theoretical part and an experimental one. The first part provides a simple treatment of the celebrated von Neumann minimax theorem as formulated by Nikaid6 and Sion. It also discusses its relationships with fundamental theorems of convex analysis. The second part is about externality in sponsored search auctions. It shows that in these auctions, advertisers have externality effects on each other which influence their bidding behavior. It proposes Hal R.Varian model and shows how adding externality to this model will affect its properties. In order to have a better understanding of the interaction among advertisers in on-line auctions, it studies the structure of the Google advertisements networ.k and shows that it is a small-world scale-free network.

Network Similarity Measures and Automatic Construction of Graph Models using Genetic Programming

A complex network is an abstract representation of an intricate system of interrelated elements where the patterns of connection hold significant meaning. One particular complex network is a social network whereby the vertices represent people and edges denote their daily interactions. Understanding social network dynamics can be vital to the mitigation of disease spread as these networks model the interactions, and thus avenues of spread, between individuals. To better understand complex networks, algorithms which generate graphs exhibiting observed properties of real-world networks, known as graph models, are often constructed. While various efforts to aid with the construction of graph models have been proposed using statistical and probabilistic methods, genetic programming (GP) has only recently been considered. However, determining that a graph model of a complex network accurately describes the target network(s) is not a trivial task as the graph models are often stochastic in nature and the notion of similarity is dependent upon the expected behavior of the network. This thesis examines a number of well-known network properties to determine which measures best allowed networks generated by different graph models, and thus the models themselves, to be distinguished. A proposed meta-analysis procedure was used to demonstrate how these network measures interact when used together as classifiers to determine network, and thus model, (dis)similarity. The analytical results form the basis of the fitness evaluation for a GP system used to automatically construct graph models for complex networks. The GP-based automatic inference system was used to reproduce existing, well-known graph models as well as a real-world network. Results indicated that the automatically inferred models exemplified functional similarity when compared to their respective target networks. This approach also showed promise when used to infer a model for a mammalian brain network.

Utilidad de las relaciones estratégicas comunitarias y el marketing en la administración de negocios con clientes corporativos

Este trabajo de grado propone identificar la utilidad de las relaciones estratégicas comunitarias y el marketing en la administración de negocios con clientes corporativos, también se toman en cuenta conceptos como el marketing organizacional y relacional, estos conceptos ayudan en la investigación a determinar relaciones estratégicas entre las empresas, y el beneficio que estas le generan a las corporaciones; para así fomentar la implementación de estas estrategias en a las empresas a nivel nacional e internacional, así mismo, identificar el concepto de comunidad que tienen los clientes corporativos y como este concepto se puede adaptar al entorno que los rodea. Con el fin de entender las funciones y características de un cliente corporativo, así como su comportamiento, los objetivos específicos de la investigación son describir las estrategias de marketing en la administración de negocios con clientes corporativos, determinar si existe el concepto de comunidad en la administración de negocios con clientes corporativos y determinar si se utilizan relaciones estratégicas comunitarias en la administración de negocios con clientes corporativos. La metodología que se planteó usar fue teórica-conceptual, teniendo en cuenta el marketing y las relaciones estratégicas comunitarias de los clientes corporativos. Llevando la investigación al ámbito de la gerencia y dirección, los resultados que se obtuvieron gracias a la investigación, ayudaran a potenciar la dirección de las empresas, donde se evalué la verdadera utilidad de las estrategias basadas en las relaciones comunitarias y marketing en los negocios con clientes corporativos. Las estrategias comunitarias y el marketing influencian de manera directa las relaciones de las compañias con sus clientes corporativos, debido a que marketing nos permite extender la relación y generar una utilidad a futuro entre ambas partes. De la investigación se concluye que las empresas que logran crear estrategias comunitarias y relaciones estrechas entre ellas, tienden a tener mejores utilidades en el largo plazo y ser empresas más sostenibles.

Periodic Reordering

For many networks in nature, science and technology, it is possible to order the nodes so that most links are short-range, connecting near-neighbours, and relatively few long-range links, or shortcuts, are present. Given a network as a set of observed links (interactions), the task of finding an ordering of the nodes that reveals such a range-dependent structure is closely related to some sparse matrix reordering problems arising in scientific computation. The spectral, or Fiedler vector, approach for sparse matrix reordering has successfully been applied to biological data sets, revealing useful structures and subpatterns. In this work we argue that a periodic analogue of the standard reordering task is also highly relevant. Here, rather than encouraging nonzeros only to lie close to the diagonal of a suitably ordered adjacency matrix, we also allow them to inhabit the off-diagonal corners. Indeed, for the classic small-world model of Watts & Strogatz (1998, Collective dynamics of ‘small-world’ networks. Nature, 393, 440–442) this type of periodic structure is inherent. We therefore devise and test a new spectral algorithm for periodic reordering. By generalizing the range-dependent random graph class of Grindrod (2002, Range-dependent random graphs and their application to modeling large small-world proteome datasets. Phys. Rev. E, 66, 066702-1–066702-7) to the periodic case, we can also construct a computable likelihood ratio that suggests whether a given network is inherently linear or periodic. Tests on synthetic data show that the new algorithm can detect periodic structure, even in the presence of noise. Further experiments on real biological data sets then show that some networks are better regarded as periodic than linear. Hence, we find both qualitative (reordered networks plots) and quantitative (likelihood ratios) evidence of periodicity in biological networks.

A matter of choice: strategy and discretion in the shadow of World War Two

American policy-makers are predisposed towards the idea of a necessary war of survival, fought with little room for choice. This reflects a dominant memory of World War II that teaches Americans that they live in a dangerously small world that imposes conflict. Critics argue that the ‘choice versus necessity’ schema is ahistorical and mischievous. This article offers supporting fire to those critiques. America’s war against the Axis (1941–45) is a crucial case through which to test the ‘small world’ view. Arguments for war in 1941 pose overblown scenarios of the rise of a Eurasian super-threat. In 1941 conflict was discretionary and not strictly necessary in the interests of national security. The argument for intervention is a closer call that often assumed. This has implications for America’s choices today.

Sensitivity of complex networks measurements

Complex networks obtained from real-world networks are often characterized by incompleteness and noise, consequences of imperfect sampling as well as artifacts in the acquisition process. Because the characterization, analysis and modeling of complex systems underlain by complex networks are critically affected by the quality and completeness of the respective initial structures, it becomes imperative to devise methodologies for identifying and quantifying the effects of the sampling on the network structure. One way to evaluate these effects is through an analysis of the sensitivity of complex network measurements to perturbations in the topology of the network. In this paper, measurement sensibility is quantified in terms of the relative entropy of the respective distributions. Three particularly important kinds of progressive perturbations to the network are considered, namely, edge suppression, addition and rewiring. The measurements allowing the best balance of stability (smaller sensitivity to perturbations) and discriminability (separation between different network topologies) are identified with respect to each type of perturbation. Such an analysis includes eight different measurements applied on six different complex networks models and three real-world networks. This approach allows one to choose the appropriate measurements in order to obtain accurate results for networks where sampling bias cannot be avoided-a very frequent situation in research on complex networks.

A structure-dynamic approach to cortical organization: Number of paths and accessibility

A structure-dynamic approach to cortical systems is reported which is based on the number of paths and the accessibility of each node. The latter measurement is obtained by performing self-avoiding random walks in the respective networks, so as to simulate dynamics, and then calculating the entropies of the transition probabilities for walks starting from each node. Cortical networks of three species, namely cat, macaque and humans, are studied considering structural and dynamical aspects. It is verified that the human cortical network presents the highest accessibility and number of paths (in terms of z-scores). The correlation between the number of paths and accessibility is also investigated as a mean to quantify the level of independence between paths connecting pairs of nodes in cortical networks. By comparing the cortical networks of cat, macaque and humans, it is verified that the human cortical network tends to present the largest number of independent paths of length larger than four. These results suggest that the human cortical network is potentially the most resilient to brain injures. (C) 2009 Elsevier B.V. All rights reserved.

Border trees of complex networks

The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small-world properties of real networks were fundamental to stimulate more realistic models and to understand important dynamical processes related to network growth. However, the properties of the network borders (nodes with degree equal to 1), one of its most fragile parts, remained little investigated and understood. The border nodes may be involved in the evolution of structures such as geographical networks. Here we analyze the border trees of complex networks, which are defined as the subgraphs without cycles connected to the remainder of the network (containing cycles) and terminating into border nodes. In addition to describing an algorithm for identification of such tree subgraphs, we also consider how their topological properties can be quantified in terms of their depth and number of leaves. We investigate the properties of border trees for several theoretical models as well as real-world networks. Among the obtained results, we found that more than half of the nodes of some real-world networks belong to the border trees. A power-law with cut-off was observed for the distribution of the depth and number of leaves of the border trees. An analysis of the local role of the nodes in the border trees was also performed.

Fast long-range connections in transportation networks

Multidimensional scaling is applied in order to visualize an analogue of the small-world effect implied by edges having different displacement velocities in transportation networks. Our findings are illustrated for two real-world systems, namely the London urban network (streets and underground) and the US highway network enhanced by some of the main US airlines routes. We also show that the travel time in these two networks is drastically changed by attacks targeting the edges with large displacement velocities. (C) 2011 Elsevier By. All rights reserved.

Multiple Pathways Analysis of Brain Functional Networks from EEG Signals: An Application to Real Data

In the present study, we propose a theoretical graph procedure to investigate multiple pathways in brain functional networks. By taking into account all the possible paths consisting of h links between the nodes pairs of the network, we measured the global network redundancy R (h) as the number of parallel paths and the global network permeability P (h) as the probability to get connected. We used this procedure to investigate the structural and dynamical changes in the cortical networks estimated from a dataset of high-resolution EEG signals in a group of spinal cord injured (SCI) patients during the attempt of foot movement. In the light of a statistical contrast with a healthy population, the permeability index P (h) of the SCI networks increased significantly (P < 0.01) in the Theta frequency band (3-6 Hz) for distances h ranging from 2 to 4. On the contrary, no significant differences were found between the two populations for the redundancy index R (h) . The most significant changes in the brain functional network of SCI patients occurred mainly in the lower spectral contents. These changes were related to an improved propagation of communication between the closest cortical areas rather than to a different level of redundancy. This evidence strengthens the hypothesis of the need for a higher functional interaction among the closest ROIs as a mechanism to compensate the lack of feedback from the peripheral nerves to the sensomotor areas.

Estimating complex cortical networks via surface recordings-A critical note

We discuss potential caveats when estimating topologies of 3D brain networks from surface recordings. It is virtually impossible to record activity from all single neurons in the brain and one has to rely on techniques that measure average activity at sparsely located (non-invasive) recording sites Effects of this spatial sampling in relation to structural network measures like centrality and assortativity were analyzed using multivariate classifiers A simplified model of 3D brain connectivity incorporating both short- and long-range connections served for testing. To mimic M/EEG recordings we sampled this model via non-overlapping regions and weighted nodes and connections according to their proximity to the recording sites We used various complex network models for reference and tried to classify sampled versions of the ""brain-like"" network as one of these archetypes It was found that sampled networks may substantially deviate in topology from the respective original networks for small sample sizes For experimental studies this may imply that surface recordings can yield network structures that might not agree with its generating 3D network. (C) 2010 Elsevier Inc All rights reserved