Javier Pello

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.

A NODE-BASED MULTISCALE VULNERABILITY OF COMPLEX NETWORKS

A novel node-based approach to quantify the vulnerability of a complex network is presented. The proposed measure represents a multiscale evaluation of vulnerability closely related to the edge multiscale vulnerability. In fact, a linear relationship between the edge multiscale vulnerability and the node multiscale vulnerability is stated for p = 1. Upper and lower bounds are established for other values of p. This mathematical framework is subsequently used to obtain some interesting results about the Madrid underground network.

VULNERABILITY AND FALL OF EFFICIENCY IN COMPLEX NETWORKS: A NEW APPROACH WITH COMPUTATIONAL ADVANTAGES

An efficient and computationally advantageous definition of vulnerability of a complex network is introduced, through which one is able to overcome a series of practical difficulties encountered by the measurements used so far to quantify a networks security and stability under the effects of failures, attacks or disfunctions. By means of this approach, we prove a series of theorems that allow to gather information on the ranking of the nodes of a network with respect to their strategic importance in order to preserve the functioning and performance of the network as a whole.

Improvements in performance and security for complex networks

It is important to know how to improve a network when dealing with performance and security. We characterize the optimal design of a network for efficiency or vulnerability giving the extreme networks for those parameters. Moreover, we give an algorithm to improve the vulnerability of a given network when adding a new link. For efficiency, we present two facts that have to be considered in order to improve it when adding a new link, and we calculate bounds for the increment.

(ψ,p,q)-vulnerabilities : A unified approach to network robustness

We define a new general framework, the family of (psi,p,q)-vulnerabilities, as a tool that produces many new vulnerability functions that measure the capacity of a network to maintain its functional performance under random damages or malicious attacks. This new framework comprises most of the vulnerability definitions appearing in the literature and allows to calculate some relationships between the different (psi,p,q)-vulnerabilities in terms of their function psi or their parameters p, q that improve several known results for the vulnerability functions. Some graphics of simulations are provided in order to show the sharpness of these relationships.

Finite representability of operators

Abstract We introduce operator local supportability as a new type of operator finite representability that generalizes Bellenot finite representability. We prove that local supportability and local representability are mutually independent. New examples of both types of finite representability are given. For instance, for every operator T, we prove that (T U ) ∗ is locally supportable in (T ∗ ) U . We also prove that, given an operator T with range in C [0,1] , T ∗ is locally representable in T ∗ | L 1 .

Quantities Characterizing Lower Semi-Fredholm Linear Relations

Certain operational quantities derived from the norm and from the injection modulus in the context of multivalued linear operators are considered in order to obtain characterizations of lower semi-Fredholm multivalued linear operators.

On Subprojectivity and Superprojectivity of Banach Spaces

We obtain some results for and further examples of subprojective and superprojective Banach spaces. We also give several conditions providing examples of non-reflexive superprojective spaces; one of these conditions is stable under c0-sums and projective tensor products.