Orbits of operators commuting with the Volterra operator

Asymptotic estimates of the norms of orbits of certain operators that commute with the classical Volterra operator V acting on L-P[0,1], with 1 0, but also to operators of the form phi (V), where phi is a holomorphic function at zero. The method to obtain the estimates is based on the fact that the Riemann-Liouville operator as well as the Volterra operator can be related to the Levin-Pfluger theory of holomorphic functions of completely regular growth. Different methods, such as the Denjoy-Carleman theorem, are needed to analyze the behavior of the orbits of I - cV, where c > 0. The results are applied to the study of cyclic properties of phi (V), where phi is a holomorphic function at 0.

Integral completeness of locally convex spaces

A locally convex space X is said to be integrally complete if each continuous mapping f: [0, 1] --> X is Riemann integrable. A criterion for integral completeness is established. Readily verifiable sufficient conditions of integral completeness are proved.

Optic variables used to judge future ball arrival position in expert and novice soccer players

Although many studies have looked at the perceptual-cognitive strategies used to make anticipatory judgments in sport, few have examined the informational invariants that our visual system may be attuned to. Using immersive interactive virtual reality to simulate the aerodynamics of the trajectory of a ball with and without sidespin, the present study examined the ability of expert and novice soccer players to make judgments about the ball's future arrival position. An analysis of their judgment responses showed how participants were strongly influenced by the ball's trajectory. The changes in trajectory caused by sidespin led to erroneous predictions about the ball's future arrival position. An analysis of potential informational variables that could explain these results points to the use of a first-order compound variable combining optical expansion and optical displacement.

Infinite Dimensional Banach spaces of functions with nonlinear properties

The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on Rn failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function.

Detecting Deception in Movement: The Case of the Side-Step in Rugby

Although coordinated patterns of body movement can be used to communicate action intention, they can also be used to deceive. Often known as deceptive movements, these unpredictable patterns of body movement can give a competitive advantage to an attacker when trying to outwit a defender. In this particular study, we immersed novice and expert rugby players in an interactive virtual rugby environment to understand how the dynamics of deceptive body movement influence a defending player’s decisions about how and when to act. When asked to judge final running direction, expert players who were found to tune into prospective tau-based information specified in the dynamics of ‘honest’ movement signals (Centre of Mass), performed significantly better than novices who tuned into the dynamics of ‘deceptive’ movement signals (upper trunk yaw and out-foot placement) (p<.001). These findings were further corroborated in a second experiment where players were able to move as if to intercept or ‘tackle’ the virtual attacker. An analysis of action responses showed that experts waited significantly longer before initiating movement (p<.001). By waiting longer and picking up more information that would inform about future running direction these experts made significantly fewer errors (p<.05). In this paper we not only present a mathematical model that describes how deception in body-based movement is detected, but we also show how perceptual expertise is manifested in action expertise. We conclude that being able to tune into the ‘honest’ information specifying true running action intention gives a strong competitive advantage.

Modelling road traffic accidents using macroscopic second-order models of traffic flow

In this paper, we introduce a macroscopic model for road traffic accidents along highway sections. We discuss the motivation and the derivation of such a model, and we present its mathematical properties. The results are presented by means of examples where a section of a crowded one-way highway contains in the middle a cluster of drivers whose dynamics are prone to road traffic accidents. We discuss the coupling conditions and present some existence results of weak solutions to the associated Riemann Problems. Furthermore, we illustrate some features of the proposed model through some numerical simulations. © The authors 2012.

Algorithms for Self-Healing Networks

Many modern networks are \emph{reconfigurable}, in the sense that the topology of the network can be changed by the nodes in the network. For example, peer-to-peer, wireless and ad-hoc networks are reconfigurable. More generally, many social networks, such as a company's organizational chart; infrastructure networks, such as an airline's transportation network; and biological networks, such as the human brain, are also reconfigurable. Modern reconfigurable networks have a complexity unprecedented in the history of engineering, resembling more a dynamic and evolving living animal rather than a structure of steel designed from a blueprint. Unfortunately, our mathematical and algorithmic tools have not yet developed enough to handle this complexity and fully exploit the flexibility of these networks. We believe that it is no longer possible to build networks that are scalable and never have node failures. Instead, these networks should be able to admit small, and maybe, periodic failures and still recover like skin heals from a cut. This process, where the network can recover itself by maintaining key invariants in response to attack by a powerful adversary is what we call \emph{self-healing}. Here, we present several fast and provably good distributed algorithms for self-healing in reconfigurable dynamic networks. Each of these algorithms have different properties, a different set of gaurantees and limitations. We also discuss future directions and theoretical questions we would like to answer. %in the final dissertation that this document is proposed to lead to.

Self-healing systems and virtual structures

Modern networks are large, highly complex and dynamic. Add to that the mobility of the agents comprising many of these networks. It is difficult or even impossible for such systems to be managed centrally in an efficient manner. It is imperative for such systems to attain a degree of self-management. Self-healing i.e. the capability of a system in a good state to recover to another good state in face of an attack, is desirable for such systems. In this paper, we discuss the self-healing model for dynamic reconfigurable systems. In this model, an omniscient adversary inserts or deletes nodes from a network and the algorithm responds by adding a limited number of edges in order to maintain invariants of the network. We look at some of the results in this model and argue for their applicability and further extensions of the results and the model. We also look at some of the techniques we have used in our earlier work, in particular, we look at the idea of maintaining virtual graphs mapped over the existing network and assert that this may be a useful technique to use in many problem domains.