OpenRaiser/Intern-Atlas huggingface dataset:
A direct formulation for sparse PCA using semidefinite programming
Venue: arXiv cs.CE 2006
Year: 2006

We examine the problem of approximating, in the Frobenius-norm sense, a positive, semidefinite symmetric matrix by a rank-one matrix, with an upper bound on the cardinality of its eigenvector. The problem arises in the decomposition of a covariance matrix into sparse factors, and has wide applications ranging from biology to finance. We use a modification of the classical variational representation of the largest eigenvalue of a symmetric matrix, where cardinality is constrained, and derive a semidefinite programming based relaxation for our problem. We also discuss Nesterov's smooth minimization technique applied to the SDP arising in the direct sparse PCA method.
Generalized Counters and Reversal Complexity
Venue: arXiv cs.CC 2006
Year: 2006

We generalize the definition of a counter and counter reversal complexity and investigate the power of generalized deterministic counter automata in terms of language recognition.
Intuitionistic computability logic
Venue: arXiv cs.LO 2006
Year: 2006

Computability logic (CL) is a systematic formal theory of computational tasks and resources, which, in a sense, can be seen as a semantics-based alternative to (the syntactically introduced) linear logic. With its expressive and flexible language, where formulas represent computational problems and "truth" is understood as algorithmic solvability, CL potentially offers a comprehensive logical basis for constructive applied theories and computing systems inherently requiring constructive and computationally meaningful underlying logics. Among the best known constructivistic logics is Heyting's intuitionistic calculus INT, whose language can be seen as a special fragment of that of CL. The constructivistic philosophy of INT, however, has never really found an intuitively convincing and mathematically strict semantical justification. CL has good claims to provide such a justification and hence a materialization of Kolmogorov's known thesis "INT = logic of problems". The present paper contains a soundness proof for INT with respect to the CL semantics. A comprehensive online source on CL is available at http://www.cis.upenn.edu/~giorgi/cl.html
Shortened Array Codes of Large Girth
Venue: arXiv cs.DM 2006
Year: 2006

One approach to designing structured low-density parity-check (LDPC) codes with large girth is to shorten codes with small girth in such a manner that the deleted columns of the parity-check matrix contain all the variables involved in short cycles. This approach is especially effective if the parity-check matrix of a code is a matrix composed of blocks of circulant permutation matrices, as is the case for the class of codes known as array codes. We show how to shorten array codes by deleting certain columns of their parity-check matrices so as to increase their girth. The shortening approach is based on the observation that for array codes, and in fact for a slightly more general class of LDPC codes, the cycles in the corresponding Tanner graph are governed by certain homogeneous linear equations with integer coefficients. Consequently, we can selectively eliminate cycles from an array code by only retaining those columns from the parity-check matrix of the original code that are indexed by integer sequences that do not contain solutions to the equations governing those cycles. We provide Ramsey-theoretic estimates for the maximum number of columns that can be retained from the original parity-check matrix with the property that the sequence of their indices avoid solutions to various types of cycle-governing equations. This translates to estimates of the rate penalty incurred in shortening a code to eliminate cycles. Simulation results show that for the codes considered, shortening them to increase the girth can lead to significant gains in signal-to-noise ratio in the case of communication over an additive white Gaussian noise channel.
On the Entropy Rate of Pattern Processes
Venue: arXiv cs.IT 2006
Year: 2006

We study the entropy rate of pattern sequences of stochastic processes, and its relationship to the entropy rate of the original process. We give a complete characterization of this relationship for i.i.d. processes over arbitrary alphabets, stationary ergodic processes over discrete alphabets, and a broad family of stationary ergodic processes over uncountable alphabets. For cases where the entropy rate of the pattern process is infinite, we characterize the possible growth rate of the block entropy.
Mapping Fusion and Synchronized Hyperedge Replacement into Logic Programming
Venue: arXiv cs.LO 2006
Year: 2006

In this paper we compare three different formalisms that can be used in the area of models for distributed, concurrent and mobile systems. In particular we analyze the relationships between a process calculus, the Fusion Calculus, graph transformations in the Synchronized Hyperedge Replacement with Hoare synchronization (HSHR) approach and logic programming. We present a translation from Fusion Calculus into HSHR (whereas Fusion Calculus uses Milner synchronization) and prove a correspondence between the reduction semantics of Fusion Calculus and HSHR transitions. We also present a mapping from HSHR into a transactional version of logic programming and prove that there is a full correspondence between the two formalisms. The resulting mapping from Fusion Calculus to logic programming is interesting since it shows the tight analogies between the two formalisms, in particular for handling name generation and mobility. The intermediate step in terms of HSHR is convenient since graph transformations allow for multiple, remote synchronizations, as required by Fusion Calculus semantics.
Reasoning about transfinite sequences
Venue: arXiv cs.LO 2006
Year: 2006

We introduce a family of temporal logics to specify the behavior of systems with Zeno behaviors. We extend linear-time temporal logic LTL to authorize models admitting Zeno sequences of actions and quantitative temporal operators indexed by ordinals replace the standard next-time and until future-time operators. Our aim is to control such systems by designing controllers that safely work on $ω$-sequences but interact synchronously with the system in order to restrict their behaviors. We show that the satisfiability problem for the logics working on $ω^k$-sequences is EXPSPACE-complete when the integers are represented in binary, and PSPACE-complete with a unary representation. To do so, we substantially extend standard results about LTL by introducing a new class of succinct ordinal automata that can encode the interaction between the different quantitative temporal operators.
Large Alphabets and Incompressibility
Venue: arXiv cs.IT 2006
Year: 2006

We briefly survey some concepts related to empirical entropy -- normal numbers, de Bruijn sequences and Markov processes -- and investigate how well it approximates Kolmogorov complexity. Our results suggest $\ell$th-order empirical entropy stops being a reasonable complexity metric for almost all strings of length $m$ over alphabets of size $n$ about when $n^\ell$ surpasses $m$.
Strictly convex drawings of planar graphs
Venue: arXiv cs.CG 2006
Year: 2006

Every three-connected planar graph with n vertices has a drawing on an O(n^2) x O(n^2) grid in which all faces are strictly convex polygons. These drawings are obtained by perturbing (not strictly) convex drawings on O(n) x O(n) grids. More generally, a strictly convex drawing exists on a grid of size O(W) x O(n^4/W), for any choice of a parameter W in the range n<W<n^2. Tighter bounds are obtained when the faces have fewer sides. In the proof, we derive an explicit lower bound on the number of primitive vectors in a triangle.
Well-founded and Stable Semantics of Logic Programs with Aggregates
Venue: arXiv cs.LO 2006
Year: 2006

In this paper, we present a framework for the semantics and the computation of aggregates in the context of logic programming. In our study, an aggregate can be an arbitrary interpreted second order predicate or function. We define extensions of the Kripke-Kleene, the well-founded and the stable semantics for aggregate programs. The semantics is based on the concept of a three-valued immediate consequence operator of an aggregate program. Such an operator approximates the standard two-valued immediate consequence operator of the program, and induces a unique Kripke-Kleene model, a unique well-founded model and a collection of stable models. We study different ways of defining such operators and thus obtain a framework of semantics, offering different trade-offs between precision and tractability. In particular, we investigate conditions on the operator that guarantee that the computation of the three types of semantics remains on the same level as for logic programs without aggregates. Other results show that, in practice, even efficient three-valued immediate consequence operators which are very low in the precision hierarchy, still provide optimal precision.
Security Problems with Improper Implementations of Improved FEA-M
Venue: arXiv cs.CR 2006
Year: 2006

This paper reports security problems with improper implementations of an improved version of FEA-M (fast encryption algorithm for multimedia). It is found that an implementation-dependent differential chosen-plaintext attack or its chosen-ciphertext counterpart can reveal the secret key of the cryptosystem, if the involved (pseudo-)random process can be tampered (for example, through a public time service). The implementation-dependent differential attack is very efficient in complexity and needs only $O(n^2)$ chosen plaintext or ciphertext bits. In addition, this paper also points out a minor security problem with the selection of the session key. In real implementations of the cryptosystem, these security problems should be carefully avoided, or the cryptosystem has to be further enhanced to work under such weak implementations.
Tree-Based Construction of LDPC Codes Having Good Pseudocodeword Weights
Venue: arXiv cs.IT 2006
Year: 2006

We present a tree-based construction of LDPC codes that have minimum pseudocodeword weight equal to or almost equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a $d$-regular tree for a fixed number of layers and employing a connection algorithm based on permutations or mutually orthogonal Latin squares to close the tree. Methods are presented for degrees $d=p^s$ and $d = p^s+1$, for $p$ a prime. One class corresponds to the well-known finite-geometry and finite generalized quadrangle LDPC codes; the other codes presented are new. We also present some bounds on pseudocodeword weight for $p$-ary LDPC codes. Treating these codes as $p$-ary LDPC codes rather than binary LDPC codes improves their rates, minimum distances, and pseudocodeword weights, thereby giving a new importance to the finite geometry LDPC codes where $p > 2$.
Computing the Kalman form
Venue: arXiv cs.SC 2006
Year: 2006

We present two algorithms for the computation of the Kalman form of a linear control system. The first one is based on the technique developed by Keller-Gehrig for the computation of the characteristic polynomial. The cost is a logarithmic number of matrix multiplications. To our knowledge, this improves the best previously known algebraic complexity by an order of magnitude. Then we also present a cubic algorithm proven to more efficient in practice.
The egalitarian effect of search engines
Venue: arXiv cs.CY 2006
Year: 2006

Search engines have become key media for our scientific, economic, and social activities by enabling people to access information on the Web in spite of its size and complexity. On the down side, search engines bias the traffic of users according to their page-ranking strategies, and some have argued that they create a vicious cycle that amplifies the dominance of established and already popular sites. We show that, contrary to these prior claims and our own intuition, the use of search engines actually has an egalitarian effect. We reconcile theoretical arguments with empirical evidence showing that the combination of retrieval by search engines and search behavior by users mitigates the attraction of popular pages, directing more traffic toward less popular sites, even in comparison to what would be expected from users randomly surfing the Web.
Pbit and other list sorting algorithms
Venue: arXiv cs.DS 2006
Year: 2006

Pbit, besides its simplicity, is definitely the fastest list sorting algorithm. It considerably surpasses all already known methods. Among many advantages, it is stable, linear and be made to run in place. I will compare Pbit with algorithm described by Donald E. Knuth in the third volume of ''The Art of Computer Programming'' and other (QuickerSort, MergeSort) list sorting algorithms.
Decoding the structure of the WWW: facts versus sampling biases
Venue: arXiv cs.NI 2006
Year: 2006

The understanding of the immense and intricate topological structure of the World Wide Web (WWW) is a major scientific and technological challenge. This has been tackled recently by characterizing the properties of its representative graphs in which vertices and directed edges are identified with web-pages and hyperlinks, respectively. Data gathered in large scale crawls have been analyzed by several groups resulting in a general picture of the WWW that encompasses many of the complex properties typical of rapidly evolving networks. In this paper, we report a detailed statistical analysis of the topological properties of four different WWW graphs obtained with different crawlers. We find that, despite the very large size of the samples, the statistical measures characterizing these graphs differ quantitatively, and in some cases qualitatively, depending on the domain analyzed and the crawl used for gathering the data. This spurs the issue of the presence of sampling biases and structural differences of Web crawls that might induce properties not representative of the actual global underlying graph. In order to provide a more accurate characterization of the Web graph and identify observables which are clearly discriminating with respect to the sampling process, we study the behavior of degree-degree correlation functions and the statistics of reciprocal connections. The latter appears to enclose the relevant correlations of the WWW graph and carry most of the topological information of theWeb. The analysis of this quantity is also of major interest in relation to the navigability and searchability of the Web.
Poseidon: a 2-tier Anomaly-based Intrusion Detection System
Venue: arXiv cs.CR 2006
Year: 2006

We present Poseidon, a new anomaly based intrusion detection system. Poseidon is payload-based, and presents a two-tier architecture: the first stage consists of a Self-Organizing Map, while the second one is a modified PAYL system. Our benchmarks on the 1999 DARPA data set show a higher detection rate and lower number of false positives than PAYL and PHAD.
Modularizing the Elimination of r=0 in Kleene Algebra
Venue: arXiv cs.LO 2006
Year: 2006

Given a universal Horn formula of Kleene algebra with hypotheses of the form r = 0, it is already known that we can efficiently construct an equation which is valid if and only if the Horn formula is valid. This is an example of <i>elimination of hypotheses</i>, which is useful because the equational theory of Kleene algebra is decidable while the universal Horn theory is not. We show that hypotheses of the form r = 0 can still be eliminated in the presence of other hypotheses. This lets us extend any technique for eliminating hypotheses to include hypotheses of the form r = 0.
Understanding the internet topology evolution dynamics
Venue: arXiv cs.NI 2006
Year: 2006

The internet structure is extremely complex. The Positive-Feedback Preference (PFP) model is a recently introduced internet topology generator. The model uses two generic algorithms to replicate the evolution dynamics observed on the internet historic data. The phenomenological model was originally designed to match only two topology properties of the internet, i.e. the rich-club connectivity and the exact form of degree distribution. Whereas numerical evaluation has shown that the PFP model accurately reproduces a large set of other nontrivial characteristics as well. This paper aims to investigate why and how this generative model captures so many diverse properties of the internet. Based on comprehensive simulation results, the paper presents a detailed analysis on the exact origin of each of the topology properties produced by the model. This work reveals how network evolution mechanisms control the obtained topology properties and it also provides insights on correlations between various structural characteristics of complex networks.
Incremental copying garbage collection for WAM-based Prolog systems
Venue: arXiv cs.PL 2006
Year: 2006

The design and implementation of an incremental copying heap garbage collector for WAM-based Prolog systems is presented. Its heap layout consists of a number of equal-sized blocks. Other changes to the standard WAM allow these blocks to be garbage collected independently. The independent collection of heap blocks forms the basis of an incremental collecting algorithm which employs copying without marking (contrary to the more frequently used mark© or mark&slide algorithms in the context of Prolog). Compared to standard semi-space copying collectors, this approach to heap garbage collection lowers in many cases the memory usage and reduces pause times. The algorithm also allows for a wide variety of garbage collection policies including generational ones. The algorithm is implemented and evaluated in the context of hProlog.
Perturbation Analysis of a Variable M/M/1 Queue: A Probabilistic Approach
Venue: arXiv cs.NI 2006
Year: 2006

Motivated by the problem of the coexistence on transmission links of telecommunication networks of elastic and unresponsive traffic, we study in this paper the impact on the busy period of an M/M/1 queue of a small perturbation in the server rate. The perturbation depends upon an independent stationary process (X(t)) and is quantified by means of a parameter \eps \ll 1. We specifically compute the two first terms of the power series expansion in \eps of the mean value of the busy period duration. This allows us to study the validity of the Reduced Service Rate (RSR) approximation, which consists in comparing the perturbed M/M/1 queue with the M/M/1 queue where the service rate is constant and equal to the mean value of the perturbation. For the first term of the expansion, the two systems are equivalent. For the second term, the situation is more complex and it is shown that the correlations of the environment process (X(t)) play a key role.
Canonical Abstract Syntax Trees
Venue: arXiv cs.PL 2006
Year: 2006

This paper presents Gom, a language for describing abstract syntax trees and generating a Java implementation for those trees. Gom includes features allowing the user to specify and modify the interface of the data structure. These features provide in particular the capability to maintain the internal representation of data in canonical form with respect to a rewrite system. This explicitly guarantees that the client program only manipulates normal forms for this rewrite system, a feature which is only implicitly used in many implementations.
Quasiperiodic Sturmian words and morphisms
Venue: arXiv cs.DM 2006
Year: 2006

We characterize all quasiperiodic Sturmian words: a Sturmian word is not quasiperiodic if and only if it is a Lyndon word. Moreover, we study links between Sturmian morphisms and quasiperiodicity.
Journal Status
Venue: arXiv cs.DL 2006
Year: 2006

The status of an actor in a social context is commonly defined in terms of two factors: the total number of endorsements the actor receives from other actors and the prestige of the endorsing actors. These two factors indicate the distinction between popularity and expert appreciation of the actor, respectively. We refer to the former as popularity and to the latter as prestige. These notions of popularity and prestige also apply to the domain of scholarly assessment. The ISI Impact Factor (ISI IF) is defined as the mean number of citations a journal receives over a 2 year period. By merely counting the amount of citations and disregarding the prestige of the citing journals, the ISI IF is a metric of popularity, not of prestige. We demonstrate how a weighted version of the popular PageRank algorithm can be used to obtain a metric that reflects prestige. We contrast the rankings of journals according to their ISI IF and their weighted PageRank, and we provide an analysis that reveals both significant overlaps and differences. Furthermore, we introduce the Y-factor which is a simple combination of both the ISI IF and the weighted PageRank, and find that the resulting journal rankings correspond well to a general understanding of journal status.
Genetic Programming, Validation Sets, and Parsimony Pressure
Venue: arXiv cs.LG 2006
Year: 2006

Fitness functions based on test cases are very common in Genetic Programming (GP). This process can be assimilated to a learning task, with the inference of models from a limited number of samples. This paper is an investigation on two methods to improve generalization in GP-based learning: 1) the selection of the best-of-run individuals using a three data sets methodology, and 2) the application of parsimony pressure in order to reduce the complexity of the solutions. Results using GP in a binary classification setup show that while the accuracy on the test sets is preserved, with less variances compared to baseline results, the mean tree size obtained with the tested methods is significantly reduced.
Computing Fibonacci numbers on a Turing Machine
Venue: arXiv cs.DM 2006
Year: 2006

A Turing machine that computes Fibonacci numbers is described.
A Constructive Semantic Characterization of Aggregates in ASP
Venue: arXiv cs.AI 2006
Year: 2006

This technical note describes a monotone and continuous fixpoint operator to compute the answer sets of programs with aggregates. The fixpoint operator relies on the notion of aggregate solution. Under certain conditions, this operator behaves identically to the three-valued immediate consequence operator $Φ^{aggr}_P$ for aggregate programs, independently proposed Pelov et al. This operator allows us to closely tie the computational complexity of the answer set checking and answer sets existence problems to the cost of checking a solution of the aggregates in the program. Finally, we relate the semantics described by the operator to other proposals for logic programming with aggregates. To appear in Theory and Practice of Logic Programming (TPLP).
CAGD - Computer Aided Gripper Design for a Flexible Gripping System
Venue: arXiv cs.RO 2006
Year: 2006

This paper is a summary of the recently accomplished research work on flexible gripping systems. The goal is to develop a gripper which can be used for a great amount of geometrically variant workpieces. The economic aspect is of particular importance during the whole development. The high flexibility of the gripper is obtained by three parallel used principles. These are human and computer based analysis of the gripping object as well as mechanical adaptation of the gripper to the object with the help of servo motors. The focus is on the gripping of free-form surfaces with suction cup.