Positions of convex bodies associated to extremal problems and isotropic measures

We show that there are close relations between extremal problems in dual Brunn-Minkowski theory and isotropic-type properties for some Borel measures on the sphere. The methods we use allow us to obtain similar results in the context of Firey-Brunn-Minkowski theory. We also study reverse inequalities for dual mixed volumes which are related with classical positions, such as ?-position or isotropic position.     

Optimal communication schemes in a complex network: From trees to bottleneck networks

The robustness of a communication scheme in a complex network may depend on the location of distinguished nodes. We collect different approaches to the idea of vulnerability and we give methods that help us to decide the good spots for the leader nodes. More specifically, we present a constructive method that yields the best location in a communication scheme for a leader node in the case that the underlying network is tree-shaped and show how it can be used for more general networks. In order to do that we consider a local approach via the bottleneck tree associated to a given node, as well as a uniform a approach by means of the so-called bottleneck network for several communication topologies.     

Interest point detection in images using complex network analysis

This paper presents a new application of complex network theory and tools to digital image analysis and computer vision problems in order to detect interest points in digital images. We associate a weighted geometrical and fast computable complex network to each image and then we propose two different methods to locate these feature points based on both local and global (spectral) centrality measures of the corresponding network.     

Effective measurement of network vulnerability under random and intentional attacks

The study of the security and stability of complex networks plays a central role in reducing the risk and consequences of attacks or disfunctions of any type. The concept of vulnerability helps to measure the response of complex networks subjected to attacks on vertices and edges and it allows to spot the critical component of a network in order to improve its security. We introduce an accurate and computable definition of network vulnerability which is directly connected with its topology and we analyze its basic properties. We discuss the relationship of the vulnerability with other parameters of the network and we illustrate this with some examples.     

The structure and dynamics of multilayer networks

In the past years, network theory has successfully characterized the interaction among the constituents of a variety of complex systems, ranging from biological to technological, and social systems. However, up until recently, attention was almost exclusively given to networks in which all components were treated on equivalent footing, while neglecting all the extra information about the temporal- or context-related properties of the interactions under study. Only in the last years, taking advantage of the enhanced resolution in real data sets, network scientists have directed their interest to the multiplex character of real-world systems, and explicitly considered the time-varying and multilayer nature of networks. We offer here a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics.     

Evolutionary games defined at the network mesoscale: the Public Goods game

The evolutionary dynamics of the Public Goods game addresses the emergence of cooperation within groups of individuals. However, the Public Goods game on large populations of interconnected individuals has been usually modeled without any knowledge about their group structure. In this paper, by focusing on collaboration networks, we show that it is possible to include the mesoscopic information about the structure of the real groups by means of a bipartite graph. We compare the results with the projected (coauthor) and the original bipartite graphs and show that cooperation is enhanced by the mesoscopic structure contained. We conclude by analyzing the influence of the size of the groups in the evolutionary success of cooperation.     

On PageRank versatility for multiplex networks: properties and some useful bounds

In this paper, some results concerning the PageRank versatility measure for multiplex networks are given. This measure extends to the multiplex setting the well-known classic PageRank. Particularly, we focus on some spectral properties of the Laplacian matrix of the multiplex and on obtaining boundaries for the ranking value of a given node when some personalization vector is added, as in the classic setting.     

A characterization of the<Emphasis Type="Italic">MM</Emphasis>*-position of a convex body in terms of covariance matrices

We characterize the position of a convex bodyK such that it minimizesM(TK)M*(TK) (theMM*-position) in terms of properties of the measures ‖ · ‖ _K d σ(·) and ‖ · ‖ _K °d σ(·), answering a question posed by A. Giannopoulos and V. Milman. The techniques used allow us to study other extremal problems in the context of dual Brunn-Minkowski theory. Partially supported by MCYT Grant (Spain) BFM2001-1793 and FEDER funds from UE. Partially supported by MCYT Grant (Spain) BFM2001-1793 and FEDER funds from UE.     

Expanding the Role of K‐5 Science Instruction in Educational Reform: Implications of an Interdisciplinary Model for Integrating Science and Reading

Addressed is the current practice in educational reform of reducing time for science instruction in favor of traditional reading/language arts instruction. In contrast, presented is an evidence‐based rationale for increasing instructional time for K‐5 science instruction as an educational reform initiative. Overviewed are consensus interdisciplinary research and complementary multi‐year findings of the Science IDEAS model demonstrating the effectiveness of integrating conceptually‐relevant reading within science instruction in improving student achievement in both science and reading comprehension. Based on research summarized, increasing time for integrated K‐5 science is advocated as a meaningful reform‐based approach to science learning and reading comprehension proficiency that, in turn, better prepares students for subsequent success in science and content‐area reading comprehension across upper elementary and middle school grades (3–8).     

Inequalities for the Gamma function and estimates for the volume of sections of

Let and let be a -dimensional subspace of . We prove that , for and whenever . We also consider and other related cases. We obtain sharp inequalities involving Gamma function in order to get these results.