An Application of an Initialization Protocol to Permutation Routing in a Single-Hop Mobile Ad Hoc Networks

In 1999 Nakano, Olariu, and Schwing in [20], they showed that the permutation routing of n items pretitled on a mobile ad hoc network (MANET for short) of p stations (p known) and k channels (MANET{(n, p, k)) with k < p, can be carried out in broadcast rounds if k p and if each station has a -memory locations. And if k and if each station has a -memory locations, the permutations of these n pretitled items can be done also in broadcast rounds. They used two assumptions: first they suppose that each station of the mobile ad hoc network has an identifier beforehand. Secondly, the stations are partitioned into k groups such that each group has stations, but it was not shown how this partition can be obtained. In this paper, the stations have not identifiers beforehand and p is unknown. We develop a protocol which first names the stations, secondly gives the value of p, and partitions stations in groups of stations. Finally we show that the permutation routing problem can be solved on it in broadcast rounds in the worst case. It can be solved in broadcast rounds in the better case. Note that our approach does not impose any restriction on k.     

Quantum Orlicz Spaces in Information Geometry

Let H₀ be a selfadjoint operator such that Tr is of trace class for some , and let denote the set of ε-bounded forms, i.e., for some 0 $$" align="middle" border="0"> . Let χ := Span . Let denote the underlying set of the quantum information manifold of states of the form . We show that if Tr ,

Coupling and self-stabilization

A randomized self-stabilizing algorithm is an algorithm that, whatever the initial configuration is, reaches a set of М legal configurations} in finite time with probability 1. The proof of convergence towards is generally done by exhibiting a potential function , which measures the “vertical” distance of any configuration to , such that decreases with non-null probability at each step of . We propose here a method, based on the notion of coupling, which makes use of a “horizontal” distance between any pair of configurations, such that decreases in expectation at each step of . In contrast with classical methods, our coupling method does not require the knowledge of . In addition to the proof of convergence, the method allows us to assess the convergence rate according to two different measures. Proofs produced by the method are often simpler or give better upper bounds than their classical counterparts, as examplified here on Herman's mutual exclusion and Iterated Prisoner's Dilemma algorithms in the case of cyclic graphs.     

The complexity of constructing pseudorandom generators from hard functions

We study the complexity of constructing pseudorandom generators (PRGs) from hard functions, focussing on constant-depth circuits. We show that, starting from a function computable in alternating time O(l) with O(1) alternations that is hard on average (i.e. there is a constant such that every circuit of size fails to compute f on at least a 1/poly(l) fraction of inputs) we can construct a computable by DLOGTIME-uniform constant-depth circuits of size polynomial in n. Such a PRG implies under DLOGTIME-uniformity. On the negative side, we prove that starting from a worst-case hard function (i.e. there is a constant such that every circuit of size fails to compute f on some input) for every positive constant there is no black-box construction of a computable by constant-depth circuits of size polynomial in n. We also study worst-case hardness amplification, which is the related problem of producing an average-case hard function starting from a worst-case hard one. In particular, we deduce that there is no blackbox worst-case hardness amplification within the polynomial time hierarchy. These negative results are obtained by showing that polynomialsize constant-depth circuits cannot compute good extractors and listdecodable codes.     

Image Analysis and Reconstruction using a Wavelet Transform Constructed from a Reducible Representation of the Euclidean Motion Group

Inspired by the early visual system of many mammalians we consider the construction of-and reconstruction from- an orientation score as a local orientation representation of an image, . The mapping is a wavelet transform corresponding to a reducible representation of the Euclidean motion group onto and oriented wavelet . This wavelet transform is a special case of a recently developed generalization of the standard wavelet theory and has the practical advantage over the usual wavelet approaches in image analysis (constructed by irreducible representations of the similitude group) that it allows a stable reconstruction from one (single scale) orientation score. Since our wavelet transform is a unitary mapping with stable inverse, we directly relate operations on orientation scores to operations on images in a robust manner. Furthermore, by geometrical examination of the Euclidean motion group , which is the domain of our orientation scores, we deduce that an operator Φ on orientation scores must be left invariant to ensure that the corresponding operator on images is Euclidean invariant. As an example we consider all linear second order left invariant evolutions on orientation scores corresponding to stochastic processes on G. As an application we detect elongated structures in (medical) images and automatically close the gaps between them. Finally, we consider robust orientation estimates by means of channel representations, where we combine robust orientation estimation and learning of wavelets resulting in an auto-associative processing of orientation features. Here linear averaging of the channel representation is equivalent to robust orientation estimation and an adaptation of the wavelet to the statistics of the considered image class leads to an auto-associative behavior of the system. The Netherlands Organization for Scientific Research is gratefully acknowledged for financial support. This work has been supported by EC Grant IST-2003-004176 COSPAL.     

Crash failure detection in asynchronous agent communication languages

Agent Communication Languages (ACLs) have been developed to provide a way for agents to communicate with each other supporting cooperation in Multi-Agent Systems (MAS). In the past few years many ACLs have been proposed for MAS and new standards are emerging such as the ACL developed by the Foundation for Intelligent Physical Agents (FIPA). Despite these efforts, an important issue in the research on ACLs is still open and concerns how these languages should deal with failures of agents in asynchronous MAS. The Fault Tolerant Agent Communication Language ( - ) presented in this paper addresses this issue dealing with crash failures of agents. - provides high-level communication primitives which support a fault-tolerant anonymous interaction protocol designed for open MAS. We present a formal semantics for - and a formal specification of the underlying agent architecture. This formal framework allows us to prove that the ACL satisfies a set of well defined knowledge-level programming requirements. To illustrate the language features we show how - can be effectively used to write high-level executable specifications of fault tolerant protocols, such as the Contract Net one.     

Deriving escape analysis by abstract interpretation

Escape analysis of object-oriented languages approximates the set of objects which do not escape from a given context. If we take a method as context, the non-escaping objects can be allocated on its activation stack; if we take a thread, Java synchronisation locks on such objects are not needed. In this paper, we formalise a basic escape domain as an abstract interpretation of concrete states, which we then refine into an abstract domain which is more concrete than and, hence, leads to a more precise escape analysis than . We provide optimality results for both and , in the form of Galois insertions from the concrete to the abstract domains and of optimal abstract operations. The Galois insertion property is obtained by restricting the abstract domains to those elements which do not contain garbage, by using an abstract garbage collector. Our implementation of is hence an implementation of a formally correct escape analyser, able to detect the stack allocatable creation points of Java (bytecode) applications.     

Some Remarks on the Role of Minimal Length of Positive Maps in Constructing Entanglement Witnesses

The main objective of this paper is to discuss correspondence between the concept of entanglement witnesses (self-adjoint operators on a composite Hilbert space that are, in general, not positive, but are positive on separable states) and positive maps which are not completely positive. The notion of minimal length of linear positive map is introduced and the role of this quantity in the constructing of entanglement witnesses is explained.Presented at the 36th Symposium on Mathematical Physics, ‘Open Systems & Quantum Information’, Toruń, Poland, June 9-12, 2004.Supported by the Grant PBZ-MIN-008/P03/2003.     

Combining the Perceptron Algorithm with Logarithmic Simulated Annealing

We present results of computational experiments with an extension of the Perceptron algorithm by a special type of simulated annealing. The simulated annealing procedure employs a logarithmic cooling schedule , where is a parameter that depends on the underlying configuration space. For sample sets S of n-dimensional vectors generated by randomly chosen polynomials , we try to approximate the positive and negative examples by linear threshold functions. The approximations are computed by both the classical Perceptron algorithm and our extension with logarithmic cooling schedules. For and , the extension outperforms the classical Perceptron algorithm by about 15% when the sample size is sufficiently large. The parameter was chosen according to estimations of the maximum escape depth from local minima of the associated energy landscape.      

Stability of Linear Difference and Differential Inclusions

Any given n×n matrix A is shown to be a restriction, to the A-invariant subspace, of a nonnegative N×N matrix B of spectral radius (B) arbitrarily close to (A). A difference inclusion , where is a compact set of matrices, is asymptotically stable if and only if can be extended to a set of nonnegative matrices B with or . Similar results are derived for differential inclusions.     

Complexity of some arithmetic problems for binary polynomials

We study various combinatorial complexity measures of Boolean functions related to some natural arithmetic problems about binary polynomials, that is, polynomials over . In particular, we consider the Boolean function deciding whether a given polynomial over is squarefree. We obtain an exponential lower bound on the size of a decision tree for this function, and derive an asymptotic formula, having a linear main term, for its average sensitivity. This allows us to estimate other complexity characteristics such as the formula size, the average decision tree depth and the degrees of exact and approximative polynomial representations of this function. Finally, using a different method, we show that testing squarefreeness and irreducibility of polynomials over cannot be done in for any odd prime p. Similar results are obtained for deciding coprimality of two polynomials over as well.     

Free binary decision diagrams for the computation of EAR n

Free binary decision diagrams (FBDDs) are graph-based data structures representing Boolean functions with the constraint (additional to binary decision diagram) that each variable is tested at most once during the computation. The function EAR_n is the following Boolean function defined for n × n Boolean matrices: EAR_n(M) = 1 iff the matrix M contains two equal adjacent rows. We prove that each FBDD computing EAR_n has size at least and we present a construction of such diagrams of size approximately .