Nonconforming mixed finite element methods for linear elasticity using rectangular elements in two and three dimensions

Abstract We present nonconforming, rectangular mixed finite element methods based on the Hellinger-Reissner variational principle in both two and three dimensions and show stability and convergence. An optimal error estimate of is obtained for the displacement, along with a suboptimal, , error estimate for the stress, in both dimensions.     

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.     

Computational challenges in bounded model checking

We describe several observations regarding the completeness and the complexity of bounded model checking and propose techniques to solve some of the associated computational challenges. We begin by defining the completeness threshold ( ) problem: for every finite model M and an LTL property , there exists a number such that if there is no counterexample to in M of length or less, then M . Finding this number, if it is sufficiently small, offers a practical method for making bounded model checking complete. We describe how to compute an overapproximation to for a general LTL property using Büchi automata, following the Vardi–Wolper LTL model checking framework. This computation is based on finding the initialized diameter and initialized recurrence-diameter (the longest loop-free path from an initial state) of the product automaton. We show a method for finding a recurrence diameter with a formula of size O(klogk) (or O(k(logk)²) in practice), where k is the attempted depth, which is an improvement compared to the previously known method that requires a formula of size in O(k²). Based on the value of , we prove that the complexity of standard SAT-based BMC is doubly exponential and that, consequently, there is a complexity gap of an exponent between this procedure and standard LTL model checking. We discuss ways to bridge this gap.     

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 ,

The Expected Size of the Rule k Dominating Set

Dai, Li, and Wu proposed Rule k, a localized approximation algorithm that attempts to find a small connected dominating set in a graph. In this paper we consider the "average-case" performance of two closely related versions of Rule k for the model of random unit disk graphs constructed from n random points in an square. We show that if and then for both versions of Rule k, the expected size of the Rule k dominating set is as It follows that, for in a suitable range, the expected size of the Rule k dominating sets are within a constant factor of the optimum.     

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.     

Efficient Algorithms for k Maximum Sums

We study the problem of computing the k maximum sum subsequences. Given a sequence of real numbers and an integer parameter k, the problem involves finding the k largest values of for The problem for fixed k = 1, also known as the maximum sum subsequence problem, has received much attention in the literature and is linear-time solvable. Recently, Bae and Takaoka presented a -time algorithm for the k maximum sum subsequences problem. In this paper we design an efficient algorithm that solves the above problem in time in the worst case. Our algorithm is optimal for and improves over the previously best known result for any value of the user-defined parameter k < 1. Moreover, our results are also extended to the multi-dimensional versions of the k maximum sum subsequences problem; resulting in fast algorithms as well.     

On the Power of Unambiguity in Alternating Machines

Unambiguity in alternating Turing machines has received considerable attention in the context of analyzing globally unique games by Aida et al. [ACRW] and in the design of efficient protocols involving globally unique games by Crasmaru et al. [CGRS]. This paper explores the power of unambiguity in alternating Turing machines in the following settings: 1. We show that unambiguity-based hierarchies-AUPH, UPH, and UPH-are infinite in some relativized world. For each , we construct another relativized world where the unambiguity-based hierarchies collapse so that they have exactly k distinct levels and their k-th levels coincide with PSPACE. These results shed light on the relativized power of the unambiguity-based hierarchies, and parallel the results known for the case of the polynomial hierarchy. 2. For every , we define the bounded-level unambiguous alternating solution class UAS(k) as the class of all sets L for which there exists a polynomial-time alternating Turing machine N, which need not be unambiguous on every input, with at most k alternations such that if and only if x is accepted unambiguously by N. We construct a relativized world where, for all and . 3. Finally, we show that robustly k-level unambiguous alternating polynomial-time Turing machines, i.e., polynomial-time alternating Turing machines that for every oracle have k alternating levels and are unambiguous, accept languages that are computable in , for every oracle A. This generalizes a result of Hartmanis and Hemachandra [HH].     

Convex Drawings of 3-Connected Plane Graphs

We use Schnyder woods of 3-connected planar graphs to produce convex straight-line drawings on a grid of size The parameter depends on the Schnyder wood used for the drawing. This parameter is in the range The algorithm is a refinement of the face-counting algorithm; thus, in particular, the size of the grid is at most The above bound on the grid size simultaneously matches or improves all previously known bounds for convex drawings, in particular Schnyder's and the recent Zhang and He bound for triangulations and the Chrobak and Kant bound for 3-connected planar graphs. The algorithm takes linear time. The drawing algorithm has been implemented and tested. The expected grid size for the drawing of a random triangulation is close to For a random 3-connected plane graph, tests show that the expected size of the drawing is      

An algebraic approach for $${\mathcal{H}}$$-matrix preconditioners

Hierarchical matrices ( -matrices) approximate matrices in a data-sparse way, and the approximate arithmetic for -matrices is almost optimal. In this paper we present an algebraic approach for constructing -matrices which combines multilevel clustering methods with -matrix arithmetic to compute the -inverse, -LU, and the -Cholesky factors of a matrix. Then the -inverse, -LU or -Cholesky factors can be used as preconditioners in iterative methods to solve systems of linear equations. The numerical results show that this method is efficient and greatly speeds up convergence compared to other approaches, such as JOR or AMG, for solving some large, sparse linear systems, and is comparable to other -matrix constructions based on Nested Dissection.     

A Time-Splitting Spectral Method for the Generalized Zakharov System in Multi-Dimensions

The generalized Zakharov system (ZS) couples a dispersive field E (scalar or vectorial) and nondispersive fields with a propagating speed of . In this paper, we extend our one-dimensional time-splitting spectral method (TSSP) for the generalized ZS into higher dimension. A main new idea is to reformulate the multi-dimensional wave equations for the nondispersive fields into a first-order system using a change of variable defined in the Fourier space. The proposed scheme TSSP is unconditionally stable, second-order in time and spectrally accurate in space. Moreover, in the subsonic regime, it allows numerical capturing of the subsonic limit without resolving the small parameters . Numerical examples confirm these properties of this method     

Polynomial-Time Algorithms for the Ordered Maximum Agreement Subtree Problem

For a set of rooted, unordered, distinctly leaf-labeled trees, the NP-hard maximum agreement subtree problem (MAST) asks for a tree contained (up to isomorphism or homeomorphism) in all of the input trees with as many labeled leaves as possible. We study the ordered variants of MAST where the trees are uniformly or non-uniformly ordered. We provide the first known polynomial-time algorithms for the uniformly and non-uniformly ordered homeomorphic variants as well as the uniformly and non-uniformly ordered isomorphic variants of MAST. Our algorithms run in time , , , and , respectively, where n is the number of leaf labels and k is the number of input trees.