OpenRaiser/Intern-Atlas huggingface dataset:
Memory efficient scheduling of Strassen-Winograd's matrix multiplication algorithm
Venue: arXiv cs.MS 2009
Year: 2009

We propose several new schedules for Strassen-Winograd's matrix multiplication algorithm, they reduce the extra memory allocation requirements by three different means: by introducing a few pre-additions, by overwriting the input matrices, or by using a first recursive level of classical multiplication. In particular, we show two fully in-place schedules: one having the same number of operations, if the input matrices can be overwritten; the other one, slightly increasing the constant of the leading term of the complexity, if the input matrices are read-only. Many of these schedules have been found by an implementation of an exhaustive search algorithm based on a pebble game.
Star Unfolding Convex Polyhedra via Quasigeodesic Loops
Venue: arXiv cs.CG 2009
Year: 2009

We extend the notion of star unfolding to be based on a quasigeodesic loop Q rather than on a point. This gives a new general method to unfold the surface of any convex polyhedron P to a simple (non-overlapping), planar polygon: cut along one shortest path from each vertex of P to Q, and cut all but one segment of Q.
On sparse representations of linear operators and the approximation of matrix products
Venue: arXiv cs.DS 2009
Year: 2009

Thus far, sparse representations have been exploited largely in the context of robustly estimating functions in a noisy environment from a few measurements. In this context, the existence of a basis in which the signal class under consideration is sparse is used to decrease the number of necessary measurements while controlling the approximation error. In this paper, we instead focus on applications in numerical analysis, by way of sparse representations of linear operators with the objective of minimizing the number of operations needed to perform basic operations (here, multiplication) on these operators. We represent a linear operator by a sum of rank-one operators, and show how a sparse representation that guarantees a low approximation error for the product can be obtained from analyzing an induced quadratic form. This construction in turn yields new algorithms for computing approximate matrix products.
A variant of the Recoil Growth algorithm to generate multi-polymer systems
Venue: arXiv cs.CE 2009
Year: 2009

The Recoil Growth algorithm, proposed in 1999 by Consta et al., is one of the most efficient algorithm available in the literature to sample from a multi-polymer system. Such problems are closely related to the generation of self-avoiding paths. In this paper, we study a variant of the original Recoil Growth algorithm, where we constrain the generation of a new polymer to take place on a specific class of graphs. This makes it possible to make a fine trade-off between computational cost and success rate. We moreover give a simple proof for a lower bound on the irreducibility of this new algorithm, which applies to the original algorithm as well.
Fast minimum-weight double-tree shortcutting for Metric TSP: Is the best one good enough?
Venue: arXiv cs.DS 2009
Year: 2009

The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The double-tree shortcutting method for Metric TSP yields an exponentially-sized space of TSP tours, each of which approximates the optimal solution within at most a factor of 2. We consider the problem of finding among these tours the one that gives the closest approximation, i.e.\ the \emph{minimum-weight double-tree shortcutting}. Burkard et al. gave an algorithm for this problem, running in time $O(n^3+2^d n^2)$ and memory $O(2^d n^2)$, where $d$ is the maximum node degree in the rooted minimum spanning tree. We give an improved algorithm for the case of small $d$ (including planar Euclidean TSP, where $d \leq 4$), running in time $O(4^d n^2)$ and memory $O(4^d n)$. This improvement allows one to solve the problem on much larger instances than previously attempted. Our computational experiments suggest that in terms of the time-quality tradeoff, the minimum-weight double-tree shortcutting method provides one of the best known tour-constructing heuristics.
On the interaction between sharing and linearity
Venue: arXiv cs.PL 2009
Year: 2009

In the analysis of logic programs, abstract domains for detecting sharing and linearity information are widely used. Devising abstract unification algorithms for such domains has proved to be rather hard. At the moment, the available algorithms are correct but not optimal, i.e., they cannot fully exploit the information conveyed by the abstract domains. In this paper, we define a new (infinite) domain ShLin-w which can be thought of as a general framework from which other domains can be easily derived by abstraction. ShLin-w makes the interaction between sharing and linearity explicit. We provide a constructive characterization of the optimal abstract unification operator on ShLin-w and we lift it to two well-known abstractions of ShLin-w. Namely, to the classical Sharing X Lin abstract domain and to the more precise ShLin-2 abstract domain by Andy King. In the case of single binding substitutions, we obtain optimal abstract unification algorithms for such domains. To appear in Theory and Practice of Logic Programming (TPLP).
Diagrammatic Inference
Venue: arXiv cs.LO 2009
Year: 2009

Diagrammatic logics were introduced in 2002, with emphasis on the notions of specifications and models. In this paper we improve the description of the inference process, which is seen as a Yoneda functor on a bicategory of fractions. A diagrammatic logic is defined from a morphism of limit sketches (called a propagator) which gives rise to an adjunction, which in turn determines a bicategory of fractions. The propagator, the adjunction and the bicategory provide respectively the syntax, the models and the inference process for the logic. Then diagrammatic logics and their morphisms are applied to the semantics of side effects in computer languages.
Multiuser MIMO Achievable Rates with Downlink Training and Channel State Feedback
Venue: arXiv cs.IT 2009
Year: 2009

We consider a MIMO fading broadcast channel and compute achievable ergodic rates when channel state information is acquired at the receivers via downlink training and it is provided to the transmitter by channel state feedback. Unquantized (analog) and quantized (digital) channel state feedback schemes are analyzed and compared under various assumptions. Digital feedback is shown to be potentially superior when the feedback channel uses per channel state coefficient is larger than 1. Also, we show that by proper design of the digital feedback link, errors in the feedback have a minor effect even if simple uncoded modulation is used on the feedback channel. We discuss first the case of an unfaded AWGN feedback channel with orthogonal access and then the case of fading MIMO multi-access (MIMO-MAC). We show that by exploiting the MIMO-MAC nature of the uplink channel, a much better scaling of the feedback channel resource with the number of base station antennas can be achieved. Finally, for the case of delayed feedback, we show that in the realistic case where the fading process has (normalized) maximum Doppler frequency shift 0 < F < 1/2, a fraction 1 - 2F of the optimal multiplexing gain is achievable. The general conclusion of this work is that very significant downlink throughput is achievable with simple and efficient channel state feedback, provided that the feedback link is properly designed.
New Construction of A Family of Quasi-Twisted Two-Weight Codes
Venue: arXiv cs.IT 2009
Year: 2009

Based on cyclic and consta-cyclic simplex codes, a new explicit construction of a family of two-weight codes is presented. These two-weight codes obtained are in the form of 2-generator quasi-cyclic, or quasi-twisted structure. Based on this construction, new optimal binary quasi-cyclic [195, 8, 96], [210, 8, 104] and [240, 8, 120] codes, and good QC ternary [208, 6, 135] and [221, 6, 144] codes are thus obtained. It is also shown that many codes among the family meet the Griesmer bound and thereful are optimal.
Equations of States in Singular Statistical Estimation
Venue: arXiv cs.LG 2009
Year: 2009

Learning machines which have hierarchical structures or hidden variables are singular statistical models because they are nonidentifiable and their Fisher information matrices are singular. In singular statistical models, neither the Bayes a posteriori distribution converges to the normal distribution nor the maximum likelihood estimator satisfies asymptotic normality. This is the main reason why it has been difficult to predict their generalization performances from trained states. In this paper, we study four errors, (1) Bayes generalization error, (2) Bayes training error, (3) Gibbs generalization error, and (4) Gibbs training error, and prove that there are mathematical relations among these errors. The formulas proved in this paper are equations of states in statistical estimation because they hold for any true distribution, any parametric model, and any a priori distribution. Also we show that Bayes and Gibbs generalization errors are estimated by Bayes and Gibbs training errors, and propose widely applicable information criteria which can be applied to both regular and singular statistical models.
Digital Ecosystems: Optimisation by a Distributed Intelligence
Venue: arXiv cs.NE 2009
Year: 2009

Can intelligence optimise Digital Ecosystems? How could a distributed intelligence interact with the ecosystem dynamics? Can the software components that are part of genetic selection be intelligent in themselves, as in an adaptive technology? We consider the effect of a distributed intelligence mechanism on the evolutionary and ecological dynamics of our Digital Ecosystem, which is the digital counterpart of a biological ecosystem for evolving software services in a distributed network. We investigate Neural Networks and Support Vector Machine for the learning based pattern recognition functionality of our distributed intelligence. Simulation results imply that the Digital Ecosystem performs better with the application of a distributed intelligence, marginally more effectively when powered by Support Vector Machine than Neural Networks, and suggest that it can contribute to optimising the operation of our Digital Ecosystem.
Digital Ecosystems: Evolving Service-Oriented Architectures
Venue: arXiv cs.NE 2009
Year: 2009

We view Digital Ecosystems to be the digital counterparts of biological ecosystems, exploiting the self-organising properties of biological ecosystems, which are considered to be robust, self-organising and scalable architectures that can automatically solve complex, dynamic problems. Digital Ecosystems are a novel optimisation technique where the optimisation works at two levels: a first optimisation, migration of agents (representing services) which are distributed in a decentralised peer-to-peer network, operating continuously in time; this process feeds a second optimisation based on evolutionary computing that operates locally on single peers and is aimed at finding solutions to satisfy locally relevant constraints. We created an Ecosystem-Oriented Architecture of Digital Ecosystems by extending Service-Oriented Architectures with distributed evolutionary computing, allowing services to recombine and evolve over time, constantly seeking to improve their effectiveness for the user base. Individuals within our Digital Ecosystem will be applications (groups of services), created in response to user requests by using evolutionary optimisation to aggregate the services. These individuals will migrate through the Digital Ecosystem and adapt to find niches where they are useful in fulfilling other user requests for applications. Simulation results imply that the Digital Ecosystem performs better at large scales than a comparable Service-Oriented Architecture, suggesting that incorporating ideas from theoretical ecology can contribute to useful self-organising properties in digital ecosystems.
Matrix Graph Grammars
Venue: arXiv cs.DM 2009
Year: 2009

This book objective is to develop an algebraization of graph grammars. Equivalently, we study graph dynamics. From the point of view of a computer scientist, graph grammars are a natural generalization of Chomsky grammars for which a purely algebraic approach does not exist up to now. A Chomsky (or string) grammar is, roughly speaking, a precise description of a formal language (which in essence is a set of strings). On a more discrete mathematical style, it can be said that graph grammars -- Matrix Graph Grammars in particular -- study dynamics of graphs. Ideally, this algebraization would enforce our understanding of grammars in general, providing new analysis techniques and generalizations of concepts, problems and results known so far.
Well-Centered Triangulation
Venue: arXiv cs.CG 2009
Year: 2009

Meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primal-dual mesh pairs. We prove that well-centered meshes also have optimality properties and relationships to Delaunay and minmax angle triangulations. We present an iterative algorithm that seeks to transform a given triangulation in two or three dimensions into a well-centered one by minimizing a cost function and moving the interior vertices while keeping the mesh connectivity and boundary vertices fixed. The cost function is a direct result of a new characterization of well-centeredness in arbitrary dimensions that we present. Ours is the first optimization-based heuristic for well-centeredness, and the first one that applies in both two and three dimensions. We show the results of applying our algorithm to small and large two-dimensional meshes, some with a complex boundary, and obtain a well-centered tetrahedralization of the cube. We also show numerical evidence that our algorithm preserves gradation and that it improves the maximum and minimum angles of acute triangulations created by the best known previous method.
Characterization of the convergence of stationary Fokker-Planck learning
Venue: arXiv cs.NE 2009
Year: 2009

The convergence properties of the stationary Fokker-Planck algorithm for the estimation of the asymptotic density of stochastic search processes is studied. Theoretical and empirical arguments for the characterization of convergence of the estimation in the case of separable and nonseparable nonlinear optimization problems are given. Some implications of the convergence of stationary Fokker-Planck learning for the inference of parameters in artificial neural network models are outlined.
Gaussian Interference Networks: Sum Capacity in the Low Interference Regime and New Outer Bounds on the Capacity Region
Venue: arXiv cs.IT 2009
Year: 2009

Establishing the capacity region of a Gaussian interference network is an open problem in information theory. Recent progress on this problem has led to the characterization of the capacity region of a general two user Gaussian interference channel within one bit. In this paper, we develop new, improved outer bounds on the capacity region. Using these bounds, we show that treating interference as noise achieves the sum capacity of the two user Gaussian interference channel in a low interference regime, where the interference parameters are below certain thresholds. We then generalize our techniques and results to Gaussian interference networks with more than two users. In particular, we demonstrate that the total interference threshold, below which treating interference as noise achieves the sum capacity, increases with the number of users.
Data Traffic Dynamics and Saturation on a Single Link
Venue: arXiv cs.NI 2009
Year: 2009

The dynamics of User Datagram Protocol (UDP) traffic over Ethernet between two computers are analyzed using nonlinear dynamics which shows that there are two clear regimes in the data flow: free flow and saturated. The two most important variables affecting this are the packet size and packet flow rate. However, this transition is due to a transcritical bifurcation rather than phase transition in models such as in vehicle traffic or theorized large-scale computer network congestion. It is hoped this model will help lay the groundwork for further research on the dynamics of networks, especially computer networks.
Curves That Must Be Retraced
Venue: arXiv cs.CC 2009
Year: 2009

We exhibit a polynomial time computable plane curve GAMMA that has finite length, does not intersect itself, and is smooth except at one endpoint, but has the following property. For every computable parametrization f of GAMMA and every positive integer n, there is some positive-length subcurve of GAMMA that f retraces at least n times. In contrast, every computable curve of finite length that does not intersect itself has a constant-speed (hence non-retracing) parametrization that is computable relative to the halting problem.
Graph Sparsification by Effective Resistances
Venue: arXiv cs.DS 2009
Year: 2009

We present a nearly-linear time algorithm that produces high-quality sparsifiers of weighted graphs. Given as input a weighted graph $G=(V,E,w)$ and a parameter $ε>0$, we produce a weighted subgraph $H=(V,\tilde{E},\tilde{w})$ of $G$ such that $|\tilde{E}|=O(n\log n/ε^2)$ and for all vectors $x\in\R^V$ $(1-ε)\sum_{uv\in E}(x(u)-x(v))^2w_{uv}\le \sum_{uv\in\tilde{E}}(x(u)-x(v))^2\tilde{w}_{uv} \le (1+ε)\sum_{uv\in E}(x(u)-x(v))^2w_{uv}. (*)$ This improves upon the sparsifiers constructed by Spielman and Teng, which had $O(n\log^c n)$ edges for some large constant $c$, and upon those of Benczúr and Karger, which only satisfied (*) for $x\in\{0,1\}^V$. A key ingredient in our algorithm is a subroutine of independent interest: a nearly-linear time algorithm that builds a data structure from which we can query the approximate effective resistance between any two vertices in a graph in $O(\log n)$ time.
Lexical growth, entropy and the benefits of networking
Venue: arXiv cs.IT 2009
Year: 2009

If each node of an idealized network has an equal capacity to efficiently exchange benefits, then the network's capacity to use energy is scaled by the average amount of energy required to connect any two of its nodes. The scaling factor equals \textit{e}, and the network's entropy is $\ln(n)$. Networking emerges in consequence of nodes minimizing the ratio of their energy use to the benefits obtained for such use, and their connectability. Networking leads to nested hierarchical clustering, which multiplies a network's capacity to use its energy to benefit its nodes. Network entropy multiplies a node's capacity. For a real network in which the nodes have the capacity to exchange benefits, network entropy may be estimated as $C \log_L(n)$, where the base of the log is the path length $L$, and $C$ is the clustering coefficient. Since $n$, $L$ and $C$ can be calculated for real networks, network entropy for real networks can be calculated and can reveal aspects of emergence and also of economic, biological, conceptual and other networks, such as the relationship between rates of lexical growth and divergence, and the economic benefit of adding customers to a commercial communications network. \textit{Entropy dating} can help estimate the age of network processes, such as the growth of hierarchical society and of language.
Some results on $\mathbb{R}$-computable structures
Venue: arXiv cs.DB 2009
Year: 2009

This survey paper examines the effective model theory obtained with the BSS model of real number computation. It treats the following topics: computable ordinals, satisfaction of computable infinitary formulas, forcing as a construction technique, effective categoricity, effective topology, and relations with other models for the effective theory of uncountable structures.
Recorded Step Directional Mutation for Faster Convergence
Venue: arXiv cs.NE 2009
Year: 2009

Two meta-evolutionary optimization strategies described in this paper accelerate the convergence of evolutionary programming algorithms while still retaining much of their ability to deal with multi-modal problems. The strategies, called directional mutation and recorded step in this paper, can operate independently but together they greatly enhance the ability of evolutionary programming algorithms to deal with fitness landscapes characterized by long narrow valleys. The directional mutation aspect of this combined method uses correlated meta-mutation but does not introduce a full covariance matrix. These new methods are thus much more economical in terms of storage for problems with high dimensionality. Additionally, directional mutation is rotationally invariant which is a substantial advantage over self-adaptive methods which use a single variance per coordinate for problems where the natural orientation of the problem is not oriented along the axes.
Asymptotic behavior of growth functions of D0L-systems
Venue: arXiv cs.DM 2009
Year: 2009

A D0L-system is a triple (A, f, w) where A is a finite alphabet, f is an endomorphism of the free monoid over A, and w is a word over A. The D0L-sequence generated by (A, f, w) is the sequence of words (w, f(w), f(f(w)), f(f(f(w))), ...). The corresponding sequence of lengths, that is the function mapping each non-negative integer n to |f^n(w)|, is called the growth function of (A, f, w). In 1978, Salomaa and Soittola deduced the following result from their thorough study of the theory of rational power series: if the D0L-sequence generated by (A, f, w) is not eventually the empty word then there exist a non-negative integer d and a real number b greater than or equal to one such that |f^n(w)| behaves like n^d b^n as n tends to infinity. The aim of the present paper is to present a short, direct, elementary proof of this theorem.
Linear-Programming Decoding of Nonbinary Linear Codes
Venue: arXiv cs.IT 2009
Year: 2009

A framework for linear-programming (LP) decoding of nonbinary linear codes over rings is developed. This framework facilitates linear-programming based reception for coded modulation systems which use direct modulation mapping of coded symbols. It is proved that the resulting LP decoder has the 'maximum-likelihood certificate' property. It is also shown that the decoder output is the lowest cost pseudocodeword. Equivalence between pseudocodewords of the linear program and pseudocodewords of graph covers is proved. It is also proved that if the modulator-channel combination satisfies a particular symmetry condition, the codeword error rate performance is independent of the transmitted codeword. Two alternative polytopes for use with linear-programming decoding are studied, and it is shown that for many classes of codes these polytopes yield a complexity advantage for decoding. These polytope representations lead to polynomial-time decoders for a wide variety of classical nonbinary linear codes. LP decoding performance is illustrated for the [11,6] ternary Golay code with ternary PSK modulation over AWGN, and in this case it is shown that the performance of the LP decoder is comparable to codeword-error-rate-optimum hard-decision based decoding. LP decoding is also simulated for medium-length ternary and quaternary LDPC codes with corresponding PSK modulations over AWGN.