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

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

Scanning tunneling microscopy simulations of poly(3-dodecylthiophene) chains adsorbed on highly oriented pyrolytic graphite

We report on a novel scheme to perform efficient simulations of Scanning Tunneling Microscopy (STM) of molecules weakly bonded to surfaces. Calculations are based on a tight binding (TB) technique including self-consistency for the molecule to predict STM imaging and spectroscopy. To palliate the lack of self-consistency in the tunneling current calculation, we performed first principles density-functional calculations to extract the geometrical and electronic properties of the system. In this way, we can include, in the TB scheme, the effects of structural relaxation upon adsorption on the electronic structure of the molecule. This approach is applied to the study of regioregular poly(3-dodecylthiophene) (P3DDT) polymer chains adsorbed on highly oriented pyrolytic graphite (HOPG). Results of spectroscopic calculations are discussed and compared with recently obtained experimental datComment: 15 pages plus 5 figures in a tar fil

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

Current-voltage characteristics of quasi-one-dimensional superconductors: An S-curve in the constant voltage regime

Applying a constant voltage to superconducting nanowires we find that its IV-characteristic exhibits an unusual S-behavior. This behavior is the direct consequence of the dynamics of the superconducting condensate and of the existence of two different critical currents: j_{c2} at which the pure superconducting state becomes unstable and j_{c1}<j_{c2} at which the phase slip state is realized in the system.Comment: 4 pages, 5 figures, replaced with minor change

Algebraic structure of gravity in Ashtekar variables

The BRST transformations for gravity in Ashtekar variables are obtained by using the Maurer-Cartan horizontality conditions. The BRST cohomology in Ashtekar variables is calculated with the help of an operator $\delta$ introduced by S.P. Sorella, which allows to decompose the exterior derivative as a BRST commutator. This BRST cohomology leads to the differential invariants for four-dimensional manifolds.Comment: 19 pages, report REF. TUW 94-1

Susceptibility of the Endangered Karner Blue Butterfly (Lepidoptera: Lycaenidae) to \u3ci\u3eBacillus Thuringiensis\u3c/i\u3e Var. \u3ci\u3eKurstaki\u3c/i\u3e Used for Gypsy Moth Suppression in Michigan

We investigated the phenological and physiological susceptibility of the endangered Karner blue butterfly (Lycaeides melissa samuelis) to Bacillus thuringiensis var. kurstaki (Bt), a product widely used for gypsy moth (Lymantria dispar) suppression in Michigan and other infested states. We monitored phenology of the bivoltine Karner blue in two regions of Michigan from 1993 to 1995 to determine if larval stages overlapped temporally with the period of Bt application for gypsy moth suppression. Karner blue larvae of the spring generation were found during the period that Bt was applied in nearby areas in 1993 only. However, spring-generation adults or newly laid eggs were observed up to 11 days before applications in 1994 and 1995. Since Karner blue eggs develop within one week, summer-generation larvae were most likely present during or shortly after 1994 and 1995 Bt application periods. These larvae would have been at risk, assuming Bt persistence of 4 to 6 days. Physiological susceptibility of Karner blue larvae to Bt was determined in a laboratory bioassay. Larvae were reared on wild lupine (Lupinus perennis) foliage that was untreated, or sprayed with Bt formulations at rates of 30-37 or 90 BIU/ha. A similar bioassay with second instar gypsy moth larvae on similarly treated white oak (Quercus alba) foliage was conducted concurrently. Karner blue survival was 100%, 27% and 14% on control, low and high Bt treatments, respectively. Early and late Karner blue instars were equally susceptible to Bt. Survival of gypsy moth was 80%, 33% and 5% on control, low and high Bt treatments, respectively, and did not differ significantly from Karner blue survival. We conclude that Karner blue is both phenologically and physiologically susceptible to Bt used for gypsy moth suppression, although the larval generation at risk and extent of phenological overlap may vary from year to year