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This paper studies closed 3-manifolds which are the attractors of a system of finitely many affine contractions that tile R 3 . Such attractors are called self-affine tiles. Effective characterization and recognition theorems for these 3-manifolds as well as theoretical generalizations of these results to higher dimensions are established. The methods developed build a bridge linking geometric topology with iterated function systems and their attractors. A method to model self-affine tiles by simple iterative systems is developed in order to study their topology. The model is functorial in the sense that there is an easily computable map that induces isomorphisms between the natural subdivisions of the attractor of the model and the self-affine tile. It has many beneficial qualities including ease of computation allowing one to determine topological properties of the attractor of the model such as connectedness and whether it is a manifold. The induced map between the attractor of the model and the self-affine tile is a quotient map and can be checked in certain cases to be monotone or cell-like. Deep theorems from geometric topology are applied to characterize and develop algorithms to recognize when a self-affine tile is a topological or generalized manifold in all dimensions. These new tools are used to check that several self-affine tiles in the literature are 3-balls. An example of a wild 3-dimensional self-affine tile is given whose boundary is a topological 2-sphere but which is not itself a 3-ball. The paper describes how any 3-dimensional handlebody can be given the structure of a self-affine 3-manifold. It is conjectured that every self-affine tile which is a manifold is a handlebody. [ABSTRACT FROM AUTHOR]

Abstract: The notion of irreducible forms of systems of linear differential equations with formal power series coefficients as defined by Moser [Moser, J., 1960. The order of a singularity in Fuchs’ theory. Math. Z. 379–398] and its generalisation, the super-irreducible forms introduced in Hilali and Wazner [Hilali, A., Wazner, A., 1987. Formes super-irréductibles des systèmes différentiels linéaires. Numer. Math. 50, 429–449], are important concepts in the context of the symbolic resolution of systems of linear differential equations [Barkatou, M., 1997. An algorithm to compute the exponential part of a formal fundamental matrix solution of a linear differential system. Journal of App. Alg. in Eng. Comm. and Comp. 8 (1), 1–23; Pflügel, E., 1998. Résolution symbolique des systèmes différentiels linéaires. Ph.D. Thesis, LMC-IMAG; Pflügel, E., 2000. Effective formal reduction of linear differential systems. Appl. Alg. Eng. Comm. Comp., 10 (2) 153–187]. In this paper, we reduce the task of computing a super-irreducible form to that of computing one or several Moser-irreducible forms, using a block-reduction algorithm. This algorithm works on the system directly without converting it to more general types of systems as needed in our previous paper [Barkatou, M., Pflügel, E., 2007. Computing super-irreducible forms of systems of linear differential equations via Moser-reduction: A new approach. In: Proceedings of ISSAC’07. ACM Press, Waterloo, Canada, pp. 1–8]. We perform a cost analysis of our algorithm in order to give the complexity of the super-reduction in terms of the dimension and the Poincaré-rank of the input system. We compare our method with previous algorithms and show that, for systems of big size, the direct block-reduction method is more efficient. [Copyright &y& Elsevier]

Abstract: Most of the existing search algorithms for unstructured peer-to-peer (P2P) systems share one common approach: the requesting node sends out a keyword search query and the query message is repeatedly routed and forwarded to other peers in the overlay network. Due to multiple hops involved in query forwarding, the search may result in a long delay before it is answered. Furthermore, some incapable nodes may be overloaded when the query traffic becomes intensive or bursty. In this paper, we present a novel content-pushing, Advertisement-based Search Algorithm for unstructured Peer-to-peer systems (ASAP). An advertisement (ad) is a synopsis of contents a peer tends to share, and appropriately distributed and selectively cached by other peers in the system. In ASAP, nodes proactively advertise their contents by delivering ads, and selectively storing interesting ads received from other peers. Upon a request, a node can locate the destination nodes by looking up its local ads repository, and thus obtain a one-hop search latency with modest search cost. Comprehensive experimental results show that, compared with traditional query-based search algorithms, ASAP achieves much better search efficiency, and maintains system load at a low level with small variations. In addition, ASAP works well under node churn. [Copyright &y& Elsevier]

Abstract: In this paper, we consider how to optimize I/O server placement in order to improve parallel I/O performance in switch-based clusters. The significant advances in cluster networks in recent years have made it practical to connect tens of thousands of hosts via networks that have enormous and scalable total capacity, and in which communications between a host and any other host incur the same cost. The same cost property frees users from consideration of network contention and allows them to concentrate on load-balancing issues. We formulate the server placement problem on a cluster that has the same cost property as a weighted bipartite matching with the goal of balancing the workload on the I/O nodes. To find an optimal solution to this problem, we propose an algorithm, called Load Balance Matching (LBM), where is the number of compute nodes and is the number of I/O servers. We also investigate server placement for general clusters in which multiple same-cost subclusters are interconnected to form a large cluster. This class of clusters typically adopt irregular topologies that allow the construction of scalable systems with an incremental expansion capability. Also, due to the limited bandwidth on network links between subclusters, network link contention is a major concern when distributing servers over the entire network. We show that finding an optimal placement strategy for general clusters with the goal of minimizing link contention is computationally intractable. To resolve this problem, we propose a hierarchical strategy that places servers in two steps. First, to minimize link contention, we decide which subcluster each server should be assigned to. We propose a tree-based heuristic algorithm, called Load Balance Traversing (LBT), to solve this problem. In the second step, the LBM algorithm decides the location of each server within a subcluster. Our simulation results demonstrate that LBT achieves a significant improvement in parallel I/O performance over four other algorithms, and is near-optimal in some cases. [Copyright &y& Elsevier]

Abstract: This paper presents two new randomized distributed algorithms for the generation of acyclic orientations upon anonymous distributed systems of arbitrary topology. Both algorithms, called Alg-Neighbors and Alg-Edges, make use of biased and unbiased dice having faces, and are analyzed in terms of correctness, expected time complexity and rate of convergence. First, the Alg-Neighbors algorithm is presented as a generalization of the Calabrese/França algorithm for dice (or coins) with 2 faces. It is proved that a convenient biasing function applied to all dice changes the expected time complexity from sub-exponential, i.e., (for unbiased dice with faces), to , where is the number of the system’s nodes. Next, it is shown that the Alg-Edges algorithm is able to produce acyclic orientations in steps with high probability, where denotes the total number of edges. Finally, a speed of convergence versus quality of acyclic orientation generation (associated number of colors) tradeoff is identified between Alg-Neighbors and Alg-Edges algorithms. Computational experiments were carried out in order to provide a more accurate description of the behavior of both algorithms. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to study multidimensional continued fraction algorithm over the field of formal power series. In the case of the Brun algorithm by using its homogenous version, we prove that it converges. [Copyright &y& Elsevier]

Abstract: This paper investigates both the precision and the model checking efficiency of abstract models designed to preserve branching time logics w.r.t. a 3-valued semantics. Current abstract models use ordinary transitions to over approximate the concrete transitions, while they use hyper transitions to under approximate the concrete transitions. In this work, we refer to precision measured w.r.t. the choice of abstract states, independently of the formalism used to describe abstract models. We show that current abstract models do not allow maximal precision. We suggest a new class of models and a construction of an abstract model which is most precise w.r.t. any choice of abstract states. As before, the construction of such models might involve an exponential blowup, which is inherent by the use of hyper transitions. We therefore suggest an efficient algorithm in which the abstract model is constructed during model checking, by need. Our algorithm achieves maximal precision w.r.t. the given property while remaining quadratic in the number of abstract states. To complete the picture, we incorporate it into an abstraction-refinement framework. [Copyright &y& Elsevier]

Abstract: This paper presents an algorithm for fast sorting of large lists using modern GPUs. The method achieves high speed by efficiently utilizing the parallelism of the GPU throughout the whole algorithm. Initially, GPU-based bucketsort or quicksort splits the list into enough sublists then to be sorted in parallel using merge-sort. The algorithm is of complexity , and for lists of 8 M elements and using a single Geforce 8800 GTS-512, it is 2.5 times as fast as the bitonic sort algorithms, with standard complexity of , which for a long time was considered to be the fastest for GPU sorting. It is 6 times faster than single CPU quicksort, and 10% faster than the recent GPU-based radix sort. Finally, the algorithm is further parallelized to utilize two graphics cards, resulting in yet another 1.8 times speedup. [Copyright &y& Elsevier]

Abstract: The Singular Value Decomposition (SVD) is a vital problem that finds a place in numerous application domains in science and engineering. As an example, SVDs are used in processing voluminous datasets. Many sequential and parallel algorithms have been proposed to compute SVDs. The best known sequential algorithms take cubic time. This amount of time may not be acceptable especially when the data size is large. Thus parallel algorithms are desirable. In this paper, we present a novel technique for the parallel computation of SVDs. This technique yields impressive speedups. We discuss implementation of our technique on parallel models of computing such as the mesh and the PRAM. We also present an experimental evaluation of our technique. [Copyright &y& Elsevier]

Abstract: Boosting algorithms are procedures that “boost” low-accuracy weak learning algorithms to achieve arbitrarily high accuracy. Over the past decade boosting has been widely used in practice and has become a major research topic in computational learning theory. In this paper we study boosting in the presence of random classification noise, giving both positive and negative results. We show that a modified version of a boosting algorithm due to Mansour and McAllester (J. Comput. System Sci. 64(1) (2002) 103) can achieve accuracy arbitrarily close to the noise rate. We also give a matching lower bound by showing that no efficient black-box boosting algorithm can boost accuracy beyond the noise rate (assuming that one-way functions exist). Finally, we consider a variant of the standard scenario for boosting in which the “weak learner” satisfies a slightly stronger condition than the usual weak learning guarantee. We give an efficient algorithm in this framework which can boost to arbitrarily high accuracy in the presence of classification noise. [Copyright &y& Elsevier]

Abstract: In this paper we present a generic algorithm for factoring polynomials over global fields . As efficient implementations of that algorithm for number fields and function fields differ substantially, these cases will be treated separately. Complexity issues and implementations will be discussed in part II which also contains illustrative examples. [Copyright &y& Elsevier]

Abstract: The expressions and are unusual among linear combinations of arithmetic functions in that they each vanish on a nonempty set of composite numbers. In 1966, Nicol proved that the set contains if and only if is prime and conjectured that contains no odd integers. A 2008 paper by Luca and Sandor completely classifies the elements of that have three distinct prime factors and observes that Nicol''s conjecture holds for numbers with fewer than six distinct prime factors. In this paper we let denote the set of with exactly K distinct prime factors and present a computer-implementable algorithm that decides whether Nicol''s conjecture holds for a given . Using this algorithm, we verify Nicol''s conjecture for and completely classify the elements of . We prove that all but finitely many have the form , and that all but finitely many are divisible by 6 and not 9. In addition, we prove that every is contained in a finite union of sequences that each have the form , where , are distinct primes, and each as well as the least prime factor of go to infinity as i does. [Copyright &y& Elsevier]