OpenRaiser/Intern-Atlas huggingface dataset:
Fibonacci Index and Stability Number of Graphs: a Polyhedral Study
Venue: arXiv cs.DM 2008
Year: 2008

The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight upper bounds for the Fibonacci index in terms of the stability number and the order of general graphs and connected graphs. Turán graphs frequently appear in extremal graph theory. We show that Turán graphs and a connected variant of them are also extremal for these particular problems. We also make a polyhedral study by establishing all the optimal linear inequalities for the stability number and the Fibonacci index, inside the classes of general and connected graphs of order $n$.
Stability Bound for Stationary Phi-mixing and Beta-mixing Processes
Venue: arXiv cs.LG 2008
Year: 2008

Most generalization bounds in learning theory are based on some measure of the complexity of the hypothesis class used, independently of any algorithm. In contrast, the notion of algorithmic stability can be used to derive tight generalization bounds that are tailored to specific learning algorithms by exploiting their particular properties. However, as in much of learning theory, existing stability analyses and bounds apply only in the scenario where the samples are independently and identically distributed. In many machine learning applications, however, this assumption does not hold. The observations received by the learning algorithm often have some inherent temporal dependence. This paper studies the scenario where the observations are drawn from a stationary phi-mixing or beta-mixing sequence, a widely adopted assumption in the study of non-i.i.d. processes that implies a dependence between observations weakening over time. We prove novel and distinct stability-based generalization bounds for stationary phi-mixing and beta-mixing sequences. These bounds strictly generalize the bounds given in the i.i.d. case and apply to all stable learning algorithms, thereby extending the use of stability-bounds to non-i.i.d. scenarios. We also illustrate the application of our phi-mixing generalization bounds to general classes of learning algorithms, including Support Vector Regression, Kernel Ridge Regression, and Support Vector Machines, and many other kernel regularization-based and relative entropy-based regularization algorithms. These novel bounds can thus be viewed as the first theoretical basis for the use of these algorithms in non-i.i.d. scenarios.
Artificial Intelligence Techniques for Steam Generator Modelling
Venue: arXiv cs.AI 2008
Year: 2008

This paper investigates the use of different Artificial Intelligence methods to predict the values of several continuous variables from a Steam Generator. The objective was to determine how the different artificial intelligence methods performed in making predictions on the given dataset. The artificial intelligence methods evaluated were Neural Networks, Support Vector Machines, and Adaptive Neuro-Fuzzy Inference Systems. The types of neural networks investigated were Multi-Layer Perceptions, and Radial Basis Function. Bayesian and committee techniques were applied to these neural networks. Each of the AI methods considered was simulated in Matlab. The results of the simulations showed that all the AI methods were capable of predicting the Steam Generator data reasonably accurately. However, the Adaptive Neuro-Fuzzy Inference system out performed the other methods in terms of accuracy and ease of implementation, while still achieving a fast execution time as well as a reasonable training time.
A Class of Transformations that Polarize Symmetric Binary-Input Memoryless Channels
Venue: arXiv cs.IT 2008
Year: 2008

A generalization of Arıkan's polar code construction using transformations of the form $G^{\otimes n}$ where $G$ is an $\ell \times \ell$ matrix is considered. Necessary and sufficient conditions are given for these transformations to ensure channel polarization. It is shown that a large class of such transformations polarize symmetric binary-input memoryless channels.
Perfect Matchings via Uniform Sampling in Regular Bipartite Graphs
Venue: arXiv cs.DS 2008
Year: 2008

In this paper we further investigate the well-studied problem of finding a perfect matching in a regular bipartite graph. The first non-trivial algorithm, with running time $O(mn)$, dates back to König's work in 1916 (here $m=nd$ is the number of edges in the graph, $2n$ is the number of vertices, and $d$ is the degree of each node). The currently most efficient algorithm takes time $O(m)$, and is due to Cole, Ost, and Schirra. We improve this running time to $O(\min\{m, \frac{n^{2.5}\ln n}{d}\})$; this minimum can never be larger than $O(n^{1.75}\sqrt{\ln n})$. We obtain this improvement by proving a uniform sampling theorem: if we sample each edge in a $d$-regular bipartite graph independently with a probability $p = O(\frac{n\ln n}{d^2})$ then the resulting graph has a perfect matching with high probability. The proof involves a decomposition of the graph into pieces which are guaranteed to have many perfect matchings but do not have any small cuts. We then establish a correspondence between potential witnesses to non-existence of a matching (after sampling) in any piece and cuts of comparable size in that same piece. Karger's sampling theorem for preserving cuts in a graph can now be adapted to prove our uniform sampling theorem for preserving perfect matchings. Using the $O(m\sqrt{n})$ algorithm (due to Hopcroft and Karp) for finding maximum matchings in bipartite graphs on the sampled graph then yields the stated running time. We also provide an infinite family of instances to show that our uniform sampling result is tight up to poly-logarithmic factors (in fact, up to $\ln^2 n$).
Origins of Modern Data Analysis Linked to the Beginnings and Early Development of Computer Science and Information Engineering
Venue: arXiv cs.CY 2008
Year: 2008

The history of data analysis that is addressed here is underpinned by two themes, -- those of tabular data analysis, and the analysis of collected heterogeneous data. "Exploratory data analysis" is taken as the heuristic approach that begins with data and information and seeks underlying explanation for what is observed or measured. I also cover some of the evolving context of research and applications, including scholarly publishing, technology transfer and the economic relationship of the university to society.
Amendment to "Performance Analysis of the V-BLAST Algorithm: An Analytical Approach." [1]
Venue: arXiv cs.IT 2008
Year: 2008

An analytical technique for the outage and BER analysis of the nx2 V-BLAST algorithm with the optimal ordering has been presented in [1], including closed-form exact expressions for average BER and outage probabilities, and simple high-SNR approximations. The analysis in [1] is based on the following essential approximations: 1. The SNR was defined in terms of total after-projection signal and noise powers, and the BER was analyzed based on their ratio. This corresponds to a non-coherent (power-wise) equal-gain combining of both the signal and the noise, and it is not optimum since it does not provide the maximum output SNR. 2. The definition of the total after-projection noise power at each step ignored the fact that the after-projection noise vector had correlated components. 3. The after-combining noises at different steps (and hence the errors) were implicitly assumed to be independent of each other. Under non-coherent equal-gain combining, that is not the case. It turns out that the results in [1] hold also true without these approximations, subject to minor modifications only. The purpose of this note is to show this and also to extend the average BER results in [1] to the case of BPSK-modulated V-BLAST with more than two Rx antennas (eq. 18-20). Additionally, we emphasize that the block error rate is dominated by the first step BER at the high-SNR mode (eq. 14 and 21).
Encapsulation theory: the configuration efficiency limit
Venue: arXiv cs.SE 2008
Year: 2008

This paper shows how maximum possible configuration efficiency of an indefinitely large software system is constrained by chosing a fixed upper limit to the number of program units per subsystem. It is then shown how the configuration efficiency of an indefinitely large software system depends on the ratio of the total number of informaiton hiding violational software units divided by the total number of program units.
On models of a nondeterministic computation
Venue: arXiv cs.CC 2008
Year: 2008

In this paper we consider a nondeterministic computation by deterministic multi-head 2-way automata having a read-only access to an auxiliary memory. The memory contains additional data (a guess) and computation is successful iff it is successful for some memory content. Also we consider the case of restricted guesses in which a guess should satisfy some constraint. We show that the standard complexity classes such as L, NL, P, NP, PSPACE can be characterized in terms of these models of nondeterministic computation. These characterizations differ from the well-known ones by absence of alternation.
Codes against Online Adversaries
Venue: arXiv cs.IT 2008
Year: 2008

In this work we consider the communication of information in the presence of an online adversarial jammer. In the setting under study, a sender wishes to communicate a message to a receiver by transmitting a codeword x=x_1,...,x_n symbol-by-symbol over a communication channel. The adversarial jammer can view the transmitted symbols x_i one at a time, and can change up to a p-fraction of them. However, the decisions of the jammer must be made in an online or causal manner. More generally, for a delay parameter 0<d<1, we study the scenario in which the jammer's decision on the corruption of x_i must depend solely on x_j for j < i - dn. In this work, we initiate the study of codes for online adversaries, and present a tight characterization of the amount of information one can transmit in both the 0-delay and, more generally, the d-delay online setting. We prove tight results for both additive and overwrite jammers when the transmitted symbols are assumed to be over a sufficiently large field F. Finally, we extend our results to a jam-or-listen online model, where the online adversary can either jam a symbol or eavesdrop on it. We again provide a tight characterization of the achievable rate for several variants of this model. The rate-regions we prove for each model are informational-theoretic in nature and hold for computationally unbounded adversaries. The rate regions are characterized by "simple" piecewise linear functions of p and d. The codes we construct to attain the optimal rate for each scenario are computationally efficient.
Approximate Sparse Decomposition Based on Smoothed L0-Norm
Venue: arXiv cs.MM 2008
Year: 2008

In this paper, we propose a method to address the problem of source estimation for Sparse Component Analysis (SCA) in the presence of additive noise. Our method is a generalization of a recently proposed method (SL0), which has the advantage of directly minimizing the L0-norm instead of L1-norm, while being very fast. SL0 is based on minimization of the smoothed L0-norm subject to As=x. In order to better estimate the source vector for noisy mixtures, we suggest then to remove the constraint As=x, by relaxing exact equality to an approximation (we call our method Smoothed L0-norm Denoising or SL0DN). The final result can then be obtained by minimization of a proper linear combination of the smoothed L0-norm and a cost function for the approximation. Experimental results emphasize on the significant enhancement of the modified method in noisy cases.
Secondary Indexing in One Dimension: Beyond B-trees and Bitmap Indexes
Venue: arXiv cs.DB 2008
Year: 2008

Let S be a finite, ordered alphabet, and let x = x_1 x_2 ... x_n be a string over S. A "secondary index" for x answers alphabet range queries of the form: Given a range [a_l,a_r] over S, return the set I_{[a_l;a_r]} = {i |x_i \in [a_l; a_r]}. Secondary indexes are heavily used in relational databases and scientific data analysis. It is well-known that the obvious solution, storing a dictionary for the position set associated with each character, does not always give optimal query time. In this paper we give the first theoretically optimal data structure for the secondary indexing problem. In the I/O model, the amount of data read when answering a query is within a constant factor of the minimum space needed to represent I_{[a_l;a_r]}, assuming that the size of internal memory is (|S| log n)^{delta} blocks, for some constant delta > 0. The space usage of the data structure is O(n log |S|) bits in the worst case, and we further show how to bound the size of the data structure in terms of the 0-th order entropy of x. We show how to support updates achieving various time-space trade-offs. We also consider an approximate version of the basic secondary indexing problem where a query reports a superset of I_{[a_l;a_r]} containing each element not in I_{[a_l;a_r]} with probability at most epsilon, where epsilon > 0 is the false positive probability. For this problem the amount of data that needs to be read by the query algorithm is reduced to O(|I_{[a_l;a_r]}| log(1/epsilon)) bits.
Collecting and Preserving Videogames and Their Related Materials: A Review of Current Practice, Game-Related Archives and Research Projects
Venue: arXiv cs.DL 2008
Year: 2008

This paper reviews the major methods and theories regarding the preservation of new media artifacts such as videogames, and argues for the importance of collecting and coming to a better understanding of videogame artifacts of creation, which will help build a more detailed understanding of the essential qualities of these culturally significant artifacts. We will also review the major videogame collections in the United States, Europe and Japan to give an idea of the current state of videogame archives, and argue for a fuller, more comprehensive coverage of these materials in institutional repositories.
Self-stabilizing Numerical Iterative Computation
Venue: arXiv cs.DC 2008
Year: 2008

Many challenging tasks in sensor networks, including sensor calibration, ranking of nodes, monitoring, event region detection, collaborative filtering, collaborative signal processing, {\em etc.}, can be formulated as a problem of solving a linear system of equations. Several recent works propose different distributed algorithms for solving these problems, usually by using linear iterative numerical methods. In this work, we extend the settings of the above approaches, by adding another dimension to the problem. Specifically, we are interested in {\em self-stabilizing} algorithms, that continuously run and converge to a solution from any initial state. This aspect of the problem is highly important due to the dynamic nature of the network and the frequent changes in the measured environment. In this paper, we link together algorithms from two different domains. On the one hand, we use the rich linear algebra literature of linear iterative methods for solving systems of linear equations, which are naturally distributed with rapid convergence properties. On the other hand, we are interested in self-stabilizing algorithms, where the input to the computation is constantly changing, and we would like the algorithms to converge from any initial state. We propose a simple novel method called \syncAlg as a self-stabilizing variant of the linear iterative methods. We prove that under mild conditions the self-stabilizing algorithm converges to a desired result. We further extend these results to handle the asynchronous case. As a case study, we discuss the sensor calibration problem and provide simulation results to support the applicability of our approach.
Craig Interpolation for Quantifier-Free Presburger Arithmetic
Venue: arXiv cs.LO 2008
Year: 2008

Craig interpolation has become a versatile algorithmic tool for improving software verification. Interpolants can, for instance, accelerate the convergence of fixpoint computations for infinite-state systems. They also help improve the refinement of iteratively computed lazy abstractions. Efficient interpolation procedures have been presented only for a few theories. In this paper, we introduce a complete interpolation method for the full range of quantifier-free Presburger arithmetic formulas. We propose a novel convex variable projection for integer inequalities and a technique to combine them with equalities. The derivation of the interpolant has complexity low-degree polynomial in the size of the refutation proof and is typically fast in practice.
Temporal Support of Regular Expressions in Sequential Pattern Mining
Venue: arXiv cs.DB 2008
Year: 2008

Classic algorithms for sequential pattern discovery, return all frequent sequences present in a database, but, in general, only a few ones are interesting for the user. Languages based on regular expressions (RE) have been proposed to restrict frequent sequences to the ones that satisfy user-specified constraints. Although the support of a sequence is computed as the number of data-sequences satisfying a pattern with respect to the total number of data-sequences in the database, once regular expressions come into play, new approaches to the concept of support are needed. For example, users may be interested in computing the support of the RE as a whole, in addition to the one of a particular pattern. Also, when the items are frequently updated, the traditional way of counting support in sequential pattern mining may lead to incorrect (or, at least incomplete), conclusions. The problem gets more involved if we are interested in categorical sequential patterns. In light of the above, in this paper we propose to revise the classic notion of support in sequential pattern mining, introducing the concept of temporal support of regular expressions, intuitively defined as the number of sequences satisfying a target pattern, out of the total number of sequences that could have possibly matched such pattern, where the pattern is defined as a RE over complex items (i.e., not only item identifiers, but also attributes and functions).
Communication Efficiency in Self-stabilizing Silent Protocols
Venue: arXiv cs.DS 2008
Year: 2008

Self-stabilization is a general paradigm to provide forward recovery capabilities to distributed systems and networks. Intuitively, a protocol is self-stabilizing if it is able to recover without external intervention from any catastrophic transient failure. In this paper, our focus is to lower the communication complexity of self-stabilizing protocols \emph{below} the need of checking every neighbor forever. In more details, the contribution of the paper is threefold: (i) We provide new complexity measures for communication efficiency of self-stabilizing protocols, especially in the stabilized phase or when there are no faults, (ii) On the negative side, we show that for non-trivial problems such as coloring, maximal matching, and maximal independent set, it is impossible to get (deterministic or probabilistic) self-stabilizing solutions where every participant communicates with less than every neighbor in the stabilized phase, and (iii) On the positive side, we present protocols for coloring, maximal matching, and maximal independent set such that a fraction of the participants communicates with exactly one neighbor in the stabilized phase.
The Relationship between Tsallis Statistics, the Fourier Transform, and Nonlinear Coupling
Venue: arXiv cs.IT 2008
Year: 2008

Tsallis statistics (or q-statistics) in nonextensive statistical mechanics is a one-parameter description of correlated states. In this paper we use a translated entropic index: $1 - q \to q$ . The essence of this translation is to improve the mathematical symmetry of the q-algebra and make q directly proportional to the nonlinear coupling. A conjugate transformation is defined $\hat q \equiv \frac{- 2q}{2 + q}$ which provides a dual mapping between the heavy-tail q-Gaussian distributions, whose translated q parameter is between $ - 2 < q < 0$, and the compact-support q-Gaussians, between $0 < q < \infty $ . This conjugate transformation is used to extend the definition of the q-Fourier transform to the domain of compact support. A conjugate q-Fourier transform is proposed which transforms a q-Gaussian into a conjugate $\hat q$ -Gaussian, which has the same exponential decay as the Fourier transform of a power-law function. The nonlinear statistical coupling is defined such that the conjugate pair of q-Gaussians have equal strength but either couple (compact-support) or decouple (heavy-tail) the statistical states. Many of the nonextensive entropy applications can be shown to have physical parameters proportional to the nonlinear statistical coupling.
Analytical Framework for Optimizing Weighted Average Download Time in Peer-to-Peer Networks
Venue: arXiv cs.NI 2008
Year: 2008

This paper proposes an analytical framework for peer-to-peer (P2P) networks and introduces schemes for building P2P networks to approach the minimum weighted average download time (WADT). In the considered P2P framework, the server, which has the information of all the download bandwidths and upload bandwidths of the peers, minimizes the weighted average download time by determining the optimal transmission rate from the server to the peers and from the peers to the other peers. This paper first defines the static P2P network, the hierarchical P2P network and the strictly hierarchical P2P network. Any static P2P network can be decomposed into an equivalent network of sub-peers that is strictly hierarchical. This paper shows that convex optimization can minimize the WADT for P2P networks by equivalently minimizing the WADT for strictly hierarchical networks of sub-peers. This paper then gives an upper bound for minimizing WADT by constructing a hierarchical P2P network, and lower bound by weakening the constraints of the convex problem. Both the upper bound and the lower bound are very tight. This paper also provides several suboptimal solutions for minimizing the WADT for strictly hierarchical networks, in which peer selection algorithms and chunk selection algorithm can be locally designed.
Computation of Grobner basis for systematic encoding of generalized quasi-cyclic codes
Venue: arXiv cs.IT 2008
Year: 2008

Generalized quasi-cyclic (GQC) codes form a wide and useful class of linear codes that includes thoroughly quasi-cyclic codes, finite geometry (FG) low density parity check (LDPC) codes, and Hermitian codes. Although it is known that the systematic encoding of GQC codes is equivalent to the division algorithm in the theory of Grobner basis of modules, there has been no algorithm that computes Grobner basis for all types of GQC codes. In this paper, we propose two algorithms to compute Grobner basis for GQC codes from their parity check matrices: echelon canonical form algorithm and transpose algorithm. Both algorithms require sufficiently small number of finite-field operations with the order of the third power of code-length. Each algorithm has its own characteristic; the first algorithm is composed of elementary methods, and the second algorithm is based on a novel formula and is faster than the first one for high-rate codes. Moreover, we show that a serial-in serial-out encoder architecture for FG LDPC codes is composed of linear feedback shift registers with the size of the linear order of code-length; to encode a binary codeword of length n, it takes less than 2n adder and 2n memory elements. Keywords: automorphism group, Buchberger's algorithm, division algorithm, circulant matrix, finite geometry low density parity check (LDPC) codes.