Attentional selection of noncontiguous locations: The spotlight is only transiently “split"

It is still a matter of debate whether observers can attend simultaneously to more than one location. Using essentially the same paradigm as was used previously by N. P. Bichot, K. R. Cave, and H. Pashler (1999), we demonstrate that their finding of an attentional “split” between separate target locations only reflects the early phase of attentional selection. Our subjects were asked to compare the shapes (circle or square) of 2 oddly colored targets within an array of 8 stimuli. After a varying stimulus onset asynchrony (SOA), 8 letters were flashed at the previous stimulus locations, followed by a mask. For a given SOA, the performance of subjects at reporting letters in each location was taken to reflect the distribution of spatial attention. In particular, by considering the proportion of trials in which none or both of the target letters were reported, we were able to infer the respective amount of attention allocated to each target without knowing, on a trial-by-trial basis which location (if any) was receiving the most attentional resources. Our results show that for SOAs under 100–150 ms, attention can be equally split between the two targets, a conclusion compatible with previous reports. However, with longer SOAs, this attentional division can no longer be sustained and attention ultimately settles at the location of one single stimulus

Linear Connections on Fuzzy Manifolds

Linear connections are introduced on a series of noncommutative geometries which have commutative limits. Quasicommutative corrections are calculated.Comment: 10 pages PlainTex; LPTHE Orsay 95/42; ESI Vienna 23

Linear Connections in Non-Commutative Geometry

A construction is proposed for linear connections on non-commutative algebras. The construction relies on a generalisation of the Leibnitz rules of commutative geometry and uses the bimodule structure of $\Omega^1$. A special role is played by the extension to the framework of non-commutative geometry of the permutation of two copies of $\Omega^1$. The construction of the linear connection as well as the definition of torsion and curvature is first proposed in the setting of the derivations based differential calculus of Dubois- Violette and then a generalisation to the framework proposed by Connes as well as other non-commutative differential calculi is suggested. The covariant derivative obtained admits an extension to the tensor product of several copies of $\Omega^1$. These constructions are illustrated with the example of the algebra of $n \times n$ matrices.Comment: 15 pages, LMPM ../94 (uses phyzzx

Linear connections on matrix geometries

A general definition of a linear connection in noncommutative geometry has been recently proposed. Two examples are given of linear connections in noncommutative geometries which are based on matrix algebras. They both possess a unique metric connection.Comment: 14p, LPTHE-ORSAY 94/9

On Byzantine Broadcast in Loosely Connected Networks

We consider the problem of reliably broadcasting information in a multihop asynchronous network that is subject to Byzantine failures. Most existing approaches give conditions for perfect reliable broadcast (all correct nodes deliver the authentic message and nothing else), but they require a highly connected network. An approach giving only probabilistic guarantees (correct nodes deliver the authentic message with high probability) was recently proposed for loosely connected networks, such as grids and tori. Yet, the proposed solution requires a specific initialization (that includes global knowledge) of each node, which may be difficult or impossible to guarantee in self-organizing networks - for instance, a wireless sensor network, especially if they are prone to Byzantine failures. In this paper, we propose a new protocol offering guarantees for loosely connected networks that does not require such global knowledge dependent initialization. In more details, we give a methodology to determine whether a set of nodes will always deliver the authentic message, in any execution. Then, we give conditions for perfect reliable broadcast in a torus network. Finally, we provide experimental evaluation for our solution, and determine the number of randomly distributed Byzantine failures than can be tolerated, for a given correct broadcast probability.Comment: 1

A Scalable Byzantine Grid

Modern networks assemble an ever growing number of nodes. However, it remains difficult to increase the number of channels per node, thus the maximal degree of the network may be bounded. This is typically the case in grid topology networks, where each node has at most four neighbors. In this paper, we address the following issue: if each node is likely to fail in an unpredictable manner, how can we preserve some global reliability guarantees when the number of nodes keeps increasing unboundedly ? To be more specific, we consider the problem or reliably broadcasting information on an asynchronous grid in the presence of Byzantine failures -- that is, some nodes may have an arbitrary and potentially malicious behavior. Our requirement is that a constant fraction of correct nodes remain able to achieve reliable communication. Existing solutions can only tolerate a fixed number of Byzantine failures if they adopt a worst-case placement scheme. Besides, if we assume a constant Byzantine ratio (each node has the same probability to be Byzantine), the probability to have a fatal placement approaches 1 when the number of nodes increases, and reliability guarantees collapse. In this paper, we propose the first broadcast protocol that overcomes these difficulties. First, the number of Byzantine failures that can be tolerated (if they adopt the worst-case placement) now increases with the number of nodes. Second, we are able to tolerate a constant Byzantine ratio, however large the grid may be. In other words, the grid becomes scalable. This result has important security applications in ultra-large networks, where each node has a given probability to misbehave.Comment: 17 page

Mentoring to reduce antisocial behaviour in childhood

The effects of social interventions need to be examined in real life situations as well as studie

Chirality and Dirac Operator on Noncommutative Sphere

We give a derivation of the Dirac operator on the noncommutative $2$-sphere within the framework of the bosonic fuzzy sphere and define Connes' triple. It turns out that there are two different types of spectra of the Dirac operator and correspondingly there are two classes of quantized algebras. As a result we obtain a new restriction on the Planck constant in Berezin's quantization. The map to the local frame in noncommutative geometry is also discussed.Comment: 24 pages, latex, no figure