OpenRaiser/Intern-Atlas huggingface dataset:
A Class of Parallel Tiled Linear Algebra Algorithms for Multicore Architectures
Venue: arXiv cs.MS 2008
Year: 2008

As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these new processors. Fine grain parallelism becomes a major requirement and introduces the necessity of loose synchronization in the parallel execution of an operation. This paper presents an algorithm for the Cholesky, LU and QR factorization where the operations can be represented as a sequence of small tasks that operate on square blocks of data. These tasks can be dynamically scheduled for execution based on the dependencies among them and on the availability of computational resources. This may result in an out of order execution of the tasks which will completely hide the presence of intrinsically sequential tasks in the factorization. Performance comparisons are presented with the LAPACK algorithms where parallelism can only be exploited at the level of the BLAS operations and vendor implementations.
Speeding up Simplification of Polygonal Curves using Nested Approximations
Venue: arXiv cs.CG 2008
Year: 2008

We develop a multiresolution approach to the problem of polygonal curve approximation. We show theoretically and experimentally that, if the simplification algorithm A used between any two successive levels of resolution satisfies some conditions, the multiresolution algorithm MR will have a complexity lower than the complexity of A. In particular, we show that if A has a O(N2/K) complexity (the complexity of a reduced search dynamic solution approach), where N and K are respectively the initial and the final number of segments, the complexity of MR is in O(N).We experimentally compare the outcomes of MR with those of the optimal "full search" dynamic programming solution and of classical merge and split approaches. The experimental evaluations confirm the theoretical derivations and show that the proposed approach evaluated on 2D coastal maps either shows a lower complexity or provides polygonal approximations closer to the initial curves.
The Importance and Criticality of Spreadsheets in the City of London
Venue: arXiv cs.CY 2008
Year: 2008

Spreadsheets have been with us in their present form for over a quarter of a century. We have become so used to them that we forget that we are using them at all. It may serve us well to stand back for a moment to review where, when and how we use spreadsheets in the financial markets and elsewhere in order to inform research that may guide their future development. In this article I bring together the experiences of a number of senior practitioners who have spent much of their careers working with large spreadsheets that have been and continue to be used to support major financial transactions and manage large institutions in the City of London. The author suggests that the City of London is presently exposed to significant reputational risk through the continued uncontrolled use of critical spreadsheets in the financial markets and elsewhere.
Scheduling and Pre-Conditioning in Multi-User MIMO TDD Systems
Venue: arXiv cs.IT 2008
Year: 2008

The downlink transmission in multi-user multiple-input multiple-output (MIMO) systems has been extensively studied from both communication-theoretic and information-theoretic perspectives. Most of these papers assume perfect/imperfect channel knowledge. In general, the problem of channel training and estimation is studied separately. However, in interference-limited communication systems with high mobility, this problem is tightly coupled with the problem of maximizing throughput of the system. In this paper, scheduling and pre-conditioning based schemes in the presence of reciprocal channel are considered to address this. In the case of homogeneous users, a scheduling scheme is proposed and an improved lower bound on the sum capacity is derived. The problem of choosing training sequence length to maximize net throughput of the system is studied. In the case of heterogeneous users, a modified pre-conditioning method is proposed and an optimized pre-conditioning matrix is derived. This method is combined with a scheduling scheme to further improve net achievable weighted-sum rate.
Cyclotomic FFTs with Reduced Additive Complexities Based on a Novel Common Subexpression Elimination Algorithm
Venue: arXiv cs.IT 2008
Year: 2008

In this paper, we first propose a novel common subexpression elimination (CSE) algorithm for matrix-vector multiplications over characteristic-2 fields. As opposed to previously proposed CSE algorithms, which usually focus on complexity savings due to recurrences of subexpressions, our CSE algorithm achieves two types of complexity reductions, differential savings and recurrence savings, by taking advantage of the cancelation property of characteristic-2 fields. Using our CSE algorithm, we reduce the additive complexities of cyclotomic fast Fourier transforms (CFFTs). Using a weighted sum of the numbers of multiplications and additions as a metric, our CFFTs achieve smaller total complexities than previously proposed CFFTs and other FFTs, requiring both fewer multiplications and fewer additions in many cases.
The Variable Hierarchy for the Games mu-Calculus
Venue: arXiv cs.LO 2008
Year: 2008

Parity games are combinatorial representations of closed Boolean mu-terms. By adding to them draw positions, they have been organized by Arnold and one of the authors into a mu-calculus. As done by Berwanger et al. for the propositional modal mu-calculus, it is possible to classify parity games into levels of a hierarchy according to the number of fixed-point variables. We ask whether this hierarchy collapses w.r.t. the standard interpretation of the games mu-calculus into the class of all complete lattices. We answer this question negatively by providing, for each n >= 1, a parity game Gn with these properties: it unravels to a mu-term built up with n fixed-point variables, it is semantically equivalent to no game with strictly less than n-2 fixed-point variables.
JANUS: an FPGA-based System for High Performance Scientific Computing
Venue: arXiv cs.AR 2008
Year: 2008

This paper describes JANUS, a modular massively parallel and reconfigurable FPGA-based computing system. Each JANUS module has a computational core and a host. The computational core is a 4x4 array of FPGA-based processing elements with nearest-neighbor data links. Processors are also directly connected to an I/O node attached to the JANUS host, a conventional PC. JANUS is tailored for, but not limited to, the requirements of a class of hard scientific applications characterized by regular code structure, unconventional data manipulation instructions and not too large data-base size. We discuss the architecture of this configurable machine, and focus on its use on Monte Carlo simulations of statistical mechanics. On this class of application JANUS achieves impressive performances: in some cases one JANUS processing element outperfoms high-end PCs by a factor ~ 1000. We also discuss the role of JANUS on other classes of scientific applications.
A Numerical Algorithm for Zero Counting. I: Complexity and Accuracy
Venue: arXiv cs.CC 2008
Year: 2008

We describe an algorithm to count the number of distinct real zeros of a polynomial (square) system f. The algorithm performs O(n D kappa(f)) iterations where n is the number of polynomials (as well as the dimension of the ambient space), D is a bound on the polynomials' degree, and kappa(f) is a condition number for the system. Each iteration uses an exponential number of operations. The algorithm uses finite-precision arithmetic and a polynomial bound for the precision required to ensure the returned output is correct is exhibited. This bound is a major feature of our algorithm since it is in contrast with the exponential precision required by the existing (symbolic) algorithms for counting real zeros. The algorithm parallelizes well in the sense that each iteration can be computed in parallel polynomial time with an exponential number of processors.
Computing the Tutte polynomial in vertex-exponential time
Venue: arXiv cs.DS 2008
Year: 2008

The deletion--contraction algorithm is perhaps the most popular method for computing a host of fundamental graph invariants such as the chromatic, flow, and reliability polynomials in graph theory, the Jones polynomial of an alternating link in knot theory, and the partition functions of the models of Ising, Potts, and Fortuin--Kasteleyn in statistical physics. Prior to this work, deletion--contraction was also the fastest known general-purpose algorithm for these invariants, running in time roughly proportional to the number of spanning trees in the input graph. Here, we give a substantially faster algorithm that computes the Tutte polynomial--and hence, all the aforementioned invariants and more--of an arbitrary graph in time within a polynomial factor of the number of connected vertex sets. The algorithm actually evaluates a multivariate generalization of the Tutte polynomial by making use of an identity due to Fortuin and Kasteleyn. We also provide a polynomial-space variant of the algorithm and give an analogous result for Chung and Graham's cover polynomial. An implementation of the algorithm outperforms deletion--contraction also in practice.
Faster Algorithms for Rigidity in the Plane
Venue: arXiv cs.CG 2008
Year: 2008

In [1], a new construction called red-black hierarchy characterizing Laman graphs and an algorithm for computing it were presented. For a Laman graph G=(V,E) with n vertices it runs in O(n^2) time assuming that a partition of (V,E+e) into two spanning trees is given. We show that a simple modification reduces the running time to O(n\log n). The total running time can be reduced O(n\sqrt{n\log n}) using the algorithm by Gabow and Westermann [2] for partitioning a graph into two forests. The existence of a red-black hierarchy is a necessary and sufficient condition for a graph to be a Laman graph. The algorithm for constructing a red-black hierarchy can be then modified to recognize Laman graphs in the same time.
Multipath Channels of Bounded Capacity
Venue: arXiv cs.IT 2008
Year: 2008

The capacity of discrete-time, non-coherent, multipath fading channels is considered. It is shown that if the delay spread is large in the sense that the variances of the path gains do not decay faster than geometrically, then capacity is bounded in the signal-to-noise ratio.
A Distributed Dynamic Frequency Allocation Algorithm
Venue: arXiv cs.NI 2008
Year: 2008

We consider a network model where the nodes are grouped into a number of clusters and propose a distributed dynamic frequency allocation algorithm that achieves performance close to that of a centralized optimal algorithm. Each cluster chooses its transmission frequency band based on its knowledge of the interference that it experiences. The convergence of the proposed distributed algorithm to a sub-optimal frequency allocation pattern is proved. For some specific cases of spatial distributions of the clusters in the network, asymptotic bounds on the performance of the algorithm are derived and comparisons to the performance of optimal centralized solutions are made. These analytic results and additional simulation studies verify performance close to that of an optimum centralized frequency allocation algorithm. It is demonstrated that the algorithm achieves about 90% of the Shannon capacities corresponding to the optimum/near-optimum centralized frequency band assignments. Furthermore, we consider the scenario where each cluster can be in active or inactive mode according to a two-state Markov model. We derive conditions to guarantee finite steady state variance for the output of the algorithm using stochastic analysis. Further simulation studies confirm the results of stochastic modeling and the performance of the algorithm in the time-varying setup.
An Estimation of Distribution Algorithm with Intelligent Local Search for Rule-based Nurse Rostering
Venue: arXiv cs.NE 2008
Year: 2008

This paper proposes a new memetic evolutionary algorithm to achieve explicit learning in rule-based nurse rostering, which involves applying a set of heuristic rules for each nurse's assignment. The main framework of the algorithm is an estimation of distribution algorithm, in which an ant-miner methodology improves the individual solutions produced in each generation. Unlike our previous work (where learning is implicit), the learning in the memetic estimation of distribution algorithm is explicit, i.e. we are able to identify building blocks directly. The overall approach learns by building a probabilistic model, i.e. an estimation of the probability distribution of individual nurse-rule pairs that are used to construct schedules. The local search processor (i.e. the ant-miner) reinforces nurse-rule pairs that receive higher rewards. A challenging real world nurse rostering problem is used as the test problem. Computational results show that the proposed approach outperforms most existing approaches. It is suggested that the learning methodologies suggested in this paper may be applied to other scheduling problems where schedules are built systematically according to specific rules
Distributed Consensus Algorithms in Sensor Networks: Link Failures and Channel Noise
Venue: arXiv cs.IT 2008
Year: 2008

The paper studies average consensus with random topologies (intermittent links) \emph{and} noisy channels. Consensus with noise in the network links leads to the bias-variance dilemma--running consensus for long reduces the bias of the final average estimate but increases its variance. We present two different compromises to this tradeoff: the $\mathcal{A-ND}$ algorithm modifies conventional consensus by forcing the weights to satisfy a \emph{persistence} condition (slowly decaying to zero); and the $\mathcal{A-NC}$ algorithm where the weights are constant but consensus is run for a fixed number of iterations $\hat{\imath}$, then it is restarted and rerun for a total of $\hat{p}$ runs, and at the end averages the final states of the $\hat{p}$ runs (Monte Carlo averaging). We use controlled Markov processes and stochastic approximation arguments to prove almost sure convergence of $\mathcal{A-ND}$ to the desired average (asymptotic unbiasedness) and compute explicitly the m.s.e. (variance) of the consensus limit. We show that $\mathcal{A-ND}$ represents the best of both worlds--low bias and low variance--at the cost of a slow convergence rate; rescaling the weights...
On Myopic Sensing for Multi-Channel Opportunistic Access: Structure, Optimality, and Performance
Venue: arXiv cs.NI 2008
Year: 2008

We consider a multi-channel opportunistic communication system where the states of these channels evolve as independent and statistically identical Markov chains (the Gilbert-Elliot channel model). A user chooses one channel to sense and access in each slot and collects a reward determined by the state of the chosen channel. The problem is to design a sensing policy for channel selection to maximize the average reward, which can be formulated as a multi-arm restless bandit process. In this paper, we study the structure, optimality, and performance of the myopic sensing policy. We show that the myopic sensing policy has a simple robust structure that reduces channel selection to a round-robin procedure and obviates the need for knowing the channel transition probabilities. The optimality of this simple policy is established for the two-channel case and conjectured for the general case based on numerical results. The performance of the myopic sensing policy is analyzed, which, based on the optimality of myopic sensing, characterizes the maximum throughput of a multi-channel opportunistic communication system and its scaling behavior with respect to the number of channels. These results apply to cognitive radio networks, opportunistic transmission in fading environments, and resource-constrained jamming and anti-jamming.
Axiomatizing rational power series
Venue: arXiv cs.LO 2008
Year: 2008

Iteration semirings are Conway semirings satisfying Conway's group identities. We show that the semirings $\N^{\rat}\llangle Σ^* \rrangle$ of rational power series with coefficients in the semiring $\N$ of natural numbers are the free partial iteration semirings. Moreover, we characterize the semirings $\N_\infty^{\rat}\llangle Σ^* \rrangle$ as the free semirings in the variety of iteration semirings defined by three additional simple identities, where $\N_\infty$ is the completion of $\N$ obtained by adding a point of infinity. We also show that this latter variety coincides with the variety generated by the complete, or continuous semirings. As a consequence of these results, we obtain that the semirings $\N_\infty^{\rat}\llangle Σ^* \rrangle$, equipped with the sum order, are free in the class of symmetric inductive $^*$-semirings. This characterization corresponds to Kozen's axiomatization of regular languages.
Common knowledge logic in a higher order proof assistant?
Venue: arXiv cs.AI 2008
Year: 2008

This paper presents experiments on common knowledge logic, conducted with the help of the proof assistant Coq. The main feature of common knowledge logic is the eponymous modality that says that a group of agents shares a knowledge about a certain proposition in a inductive way. This modality is specified by using a fixpoint approach. Furthermore, from these experiments, we discuss and compare the structure of theorems that can be proved in specific theories that use common knowledge logic. Those structures manifests the interplay between the theory (as implemented in the proof assistant Coq) and the metatheory.
Does intelligence imply contradiction?
Venue: arXiv cs.AI 2008
Year: 2008

Contradiction is often seen as a defect of intelligent systems and a dangerous limitation on efficiency. In this paper we raise the question of whether, on the contrary, it could be considered a key tool in increasing intelligence in biological structures. A possible way of answering this question in a mathematical context is shown, formulating a proposition that suggests a link between intelligence and contradiction. A concrete approach is presented in the well-defined setting of cellular automata. Here we define the models of ``observer'', ``entity'', ``environment'', ``intelligence'' and ``contradiction''. These definitions, which roughly correspond to the common meaning of these words, allow us to deduce a simple but strong result about these concepts in an unbiased, mathematical manner. Evidence for a real-world counterpart to the demonstrated formal link between intelligence and contradiction is provided by three computational experiments.
New results on Noncommutative and Commutative Polynomial Identity Testing
Venue: arXiv cs.CC 2008
Year: 2008

Using ideas from automata theory we design a new efficient (deterministic) identity test for the \emph{noncommutative} polynomial identity testing problem (first introduced and studied in \cite{RS05,BW05}). We also apply this idea to the reconstruction of black-box noncommuting algebraic branching programs. Assuming the black-box model allows us to query the ABP for the output at any given gate, we can reconstruct an (equivalent) ABP in deterministic polynomial time. Finally, we explore commutative identity testing when the coefficients of the input polynomial come from an arbitrary finite commutative ring with unity.
On Infinite Real Trace Rational Languages of Maximum Topological Complexity
Venue: arXiv cs.LO 2008
Year: 2008

We consider the set of infinite real traces, over a dependence alphabet (Gamma, D) with no isolated letter, equipped with the topology induced by the prefix metric. We then prove that all rational languages of infinite real traces are analytic sets and that there exist some rational languages of infinite real traces which are analytic but non Borel sets, and even Sigma^1_1-complete, hence of maximum possible topological complexity.
Applying the CobiT Control Framework to Spreadsheet Developments
Venue: arXiv cs.SE 2008
Year: 2008

One of the problems reported by researchers and auditors in the field of spreadsheet risks is that of getting and keeping managements attention to the problem. Since 1996, the Information Systems Audit & Control Foundation and the IT Governance Institute have published CobiT which brings mainstream IT control issues into the corporate governance arena. This paper illustrates how spreadsheet risk and control issues can be mapped onto the CobiT framework and thus brought to managers attention in a familiar format.
Implementation of perception and action at nanoscale
Venue: arXiv cs.RO 2008
Year: 2008

Real time combination of nanosensors and nanoactuators with virtual reality environment and multisensorial interfaces enable us to efficiently act and perceive at nanoscale. Advanced manipulation of nanoobjects and new strategies for scientific education are the key motivations. We have no existing intuitive representation of the nanoworld ruled by laws foreign to our experience. A central challenge is then the construction of nanoworld simulacrum that we can start to visit and to explore. In this nanoworld simulacrum, object identifications will be based on probed entity physical and chemical intrinsic properties, on their interactions with sensors and on the final choices made in building a multisensorial interface so that these objects become coherent elements of the human sphere of action and perception. Here we describe a 1D virtual nanomanipulator, part of the Cité des Sciences EXPO NANO in Paris, that is the first realization based on this program.
Regular Expression Subtyping for XML Query and Update Languages
Venue: arXiv cs.PL 2008
Year: 2008

XML database query languages such as XQuery employ regular expression types with structural subtyping. Subtyping systems typically have two presentations, which should be equivalent: a declarative version in which the subsumption rule may be used anywhere, and an algorithmic version in which the use of subsumption is limited in order to make typechecking syntax-directed and decidable. However, the XQuery standard type system circumvents this issue by using imprecise typing rules for iteration constructs and defining only algorithmic typechecking, and another extant proposal provides more precise types for iteration constructs but ignores subtyping. In this paper, we consider a core XQuery-like language with a subsumption rule and prove the completeness of algorithmic typechecking; this is straightforward for XQuery proper but requires some care in the presence of more precise iteration typing disciplines. We extend this result to an XML update language we have introduced in earlier work.
Period-Different $m$-Sequences With At Most A Four-Valued Cross Correlation
Venue: arXiv cs.IT 2008
Year: 2008

In this paper, we follow the recent work of Helleseth, Kholosha, Johanssen and Ness to study the cross correlation between an $m$-sequence of period $2^m-1$ and the $d$-decimation of an $m$-sequence of shorter period $2^{n}-1$ for an even number $m=2n$. Assuming that $d$ satisfies $d(2^l+1)=2^i({\rm mod} 2^n-1)$ for some $l$ and $i$, we prove the cross correlation takes exactly either three or four values, depending on ${\rm gcd}(l,n)$ is equal to or larger than 1. The distribution of the correlation values is also completely determined. Our result confirms the numerical phenomenon Helleseth et al found. It is conjectured that there are no more other cases of $d$ that give at most a four-valued cross correlation apart from the ones proved here.