12,653 research outputs found
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 . A special
role is played by the extension to the framework of non-commutative geometry of
the permutation of two copies of . 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 . These constructions are illustrated with the example of the
algebra of matrices.Comment: 15 pages, LMPM ../94 (uses phyzzx
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 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
Local methylthiolate adsorption geometry on Au(111) from photoemission core-level shifts
The local adsorption structure of methylthiolate in the ordered Au(111)-(â3Ăâ3)R30° phase has been investigated using core-level-shift measurements of the surface and bulk components of the Au 4f7/2 photoelectron binding energy. The amplitude ratio of the core-level-shift components associated with surface Au atoms that are, and are not, bonded to the thiolate is found to be compatible only with the previously proposed Au-adatom-monothiolate moiety in which the thiolate is bonded atop Au adatoms in hollow sites, and not on an unreconstructed surface, or in Au-adatom-dithiolate species
On the Informational Comparison of Qualitative Fuzzy Measures
International audienceFuzzy measures or capacities are the most general representation of uncertainty functions. However, this general class has been little explored from the point of view of its information content, when degrees of uncertainty are not supposed to be numerical, and belong to a finite qualitative scale, except in the case of possibility or necessity measures. The thrust of the paper is to define an ordering relation on the set of qualitative capacities expressing the idea that one is more informative than another, in agreement with the possibilistic notion of relative specificity. To this aim, we show that the class of qualitative capacities can be partitioned into equivalence classes of functions containing the same amount of information. They only differ by the underlying epistemic attitude such as pessimism or optimism. A meaningful information ordering between capacities can be defined on the basis of the most pessimistic (resp. optimistic) representatives of their equivalence classes. It is shown that, while qualitative capacities bear strong similarities to belief functions, such an analogy can be misleading when it comes to information content
Thiol density dependent classical potential for methyl-thiol on a Au(111) surface
A new classical potential for methyl-thiol on a Au(111) surface has been
developed using density functional theory electronic structure calculations.
Energy surfaces between methyl-thiol and a gold surface were investigated in
terms of symmetry sites and thiol density. Geometrical optimization was
employed over all the configurations while minimum energy and thiol height were
determined. Finally, a new interatomic potential has been generated as a
function of thiol density, and applications to coarse-grained simulations are
presented
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