OpenRaiser/Intern-Atlas huggingface dataset:
Non-negative mixed finite element formulations for a tensorial diffusion equation
Venue: arXiv cs.NA 2009
Year: 2009

We consider the tensorial diffusion equation, and address the discrete maximum-minimum principle of mixed finite element formulations. In particular, we address non-negative solutions (which is a special case of the maximum-minimum principle) of mixed finite element formulations. The discrete maximum-minimum principle is the discrete version of the maximum-minimum principle. In this paper we present two non-negative mixed finite element formulations for tensorial diffusion equations based on constrained optimization techniques (in particular, quadratic programming). These proposed mixed formulations produce non-negative numerical solutions on arbitrary meshes for low-order (i.e., linear, bilinear and trilinear) finite elements. The first formulation is based on the Raviart-Thomas spaces, and is obtained by adding a non-negative constraint to the variational statement of the Raviart-Thomas formulation. The second non-negative formulation based on the variational multiscale formulation. For the former formulation we comment on the affect of adding the non-negative constraint on the local mass balance property of the Raviart-Thomas formulation. We also study the performance of the active set strategy for solving the resulting constrained optimization problems. The overall performance of the proposed formulation is illustrated on three canonical test problems.
A New Method for Constructing Large Size WBE Codes with Low Complexity ML Decoder
Venue: arXiv cs.IT 2009
Year: 2009

In this paper we wish to introduce a method to reconstruct large size Welch Bound Equality (WBE) codes from small size WBE codes. The advantage of these codes is that the implementation of ML decoder for the large size codes is reduced to implementation of ML decoder for the core codes. This leads to a drastic reduction of the computational cost of ML decoder. Our method can also be used for constructing large Binary WBE (BWBE) codes from smaller ones. Additionally, we explain that although WBE codes are maximizing the sum channel capacity when the inputs are real valued, they are not necessarily appropriate when the input alphabet is binary. The discussion shows that when the input alphabet is binary, the Total Squared Correlation (TSC) of codes is not a proper figure of merit.
Non-Negative Matrix Factorization, Convexity and Isometry
Venue: arXiv cs.AI 2009
Year: 2009

In this paper we explore avenues for improving the reliability of dimensionality reduction methods such as Non-Negative Matrix Factorization (NMF) as interpretive exploratory data analysis tools. We first explore the difficulties of the optimization problem underlying NMF, showing for the first time that non-trivial NMF solutions always exist and that the optimization problem is actually convex, by using the theory of Completely Positive Factorization. We subsequently explore four novel approaches to finding globally-optimal NMF solutions using various ideas from convex optimization. We then develop a new method, isometric NMF (isoNMF), which preserves non-negativity while also providing an isometric embedding, simultaneously achieving two properties which are helpful for interpretation. Though it results in a more difficult optimization problem, we show experimentally that the resulting method is scalable and even achieves more compact spectra than standard NMF.
Camera distortion self-calibration using the plumb-line constraint and minimal Hough entropy
Venue: arXiv cs.CV 2009
Year: 2009

In this paper we present a simple and robust method for self-correction of camera distortion using single images of scenes which contain straight lines. Since the most common distortion can be modelled as radial distortion, we illustrate the method using the Harris radial distortion model, but the method is applicable to any distortion model. The method is based on transforming the edgels of the distorted image to a 1-D angular Hough space, and optimizing the distortion correction parameters which minimize the entropy of the corresponding normalized histogram. Properly corrected imagery will have fewer curved lines, and therefore less spread in Hough space. Since the method does not rely on any image structure beyond the existence of edgels sharing some common orientations and does not use edge fitting, it is applicable to a wide variety of image types. For instance, it can be applied equally well to images of texture with weak but dominant orientations, or images with strong vanishing points. Finally, the method is performed on both synthetic and real data revealing that it is particularly robust to noise.
Monotonic Convergence in an Information-Theoretic Law of Small Numbers
Venue: arXiv cs.IT 2009
Year: 2009

An "entropy increasing to the maximum" result analogous to the entropic central limit theorem (Barron 1986; Artstein et al. 2004) is obtained in the discrete setting. This involves the thinning operation and a Poisson limit. Monotonic convergence in relative entropy is established for general discrete distributions, while monotonic increase of Shannon entropy is proved for the special class of ultra-log-concave distributions. Overall we extend the parallel between the information-theoretic central limit theorem and law of small numbers explored by Kontoyiannis et al. (2005) and Harremoës et al.\ (2007, 2008). Ingredients in the proofs include convexity, majorization, and stochastic orders.
The Church Problem for Countable Ordinals
Venue: arXiv cs.LO 2009
Year: 2009

A fundamental theorem of Buchi and Landweber shows that the Church synthesis problem is computable. Buchi and Landweber reduced the Church Problem to problems about ω-games and used the determinacy of such games as one of the main tools to show its computability. We consider a natural generalization of the Church problem to countable ordinals and investigate games of arbitrary countable length. We prove that determinacy and decidability parts of the Bu}chi and Landweber theorem hold for all countable ordinals and that its full extension holds for all ordinals < ω\^ω.
An Efficient Algorithm for Partial Order Production
Venue: arXiv cs.DS 2009
Year: 2009

We consider the problem of partial order production: arrange the elements of an unknown totally ordered set T into a target partially ordered set S, by comparing a minimum number of pairs in T. Special cases include sorting by comparisons, selection, multiple selection, and heap construction. We give an algorithm performing ITLB + o(ITLB) + O(n) comparisons in the worst case. Here, n denotes the size of the ground sets, and ITLB denotes a natural information-theoretic lower bound on the number of comparisons needed to produce the target partial order. Our approach is to replace the target partial order by a weak order (that is, a partial order with a layered structure) extending it, without increasing the information theoretic lower bound too much. We then solve the problem by applying an efficient multiple selection algorithm. The overall complexity of our algorithm is polynomial. This answers a question of Yao (SIAM J. Comput. 18, 1989). We base our analysis on the entropy of the target partial order, a quantity that can be efficiently computed and provides a good estimate of the information-theoretic lower bound.
Automatic Generation of the Axial Lines of Urban Environments to Capture What We Perceive
Venue: arXiv cs.CG 2009
Year: 2009

Based on the concepts of isovists and medial axes, we developed a set of algorithms that can automatically generate axial lines for representing individual linearly stretched parts of open space of an urban environment. Open space is the space between buildings, where people can freely move around. The generation of the axial lines has been a key aspect of space syntax research, conventionally relying on hand-drawn axial lines of an urban environment, often called axial map, for urban morphological analysis. Although various attempts have been made towards an automatic solution, few of them can produce the axial map that consists of the least number of longest visibility lines, and none of them really works for different urban environments. Our algorithms provide a better solution than existing ones. Throughout this paper, we have also argued and demonstrated that the axial lines constitute a true skeleton, superior to medial axes, in capturing what we perceive about the urban environment. Keywords: Visibility, space syntax, topological analysis, medial axes, axial lines, isovists
Linear-Time Algorithms for Geometric Graphs with Sublinearly Many Edge Crossings
Venue: arXiv cs.CG 2009
Year: 2009

We provide linear-time algorithms for geometric graphs with sublinearly many crossings. That is, we provide algorithms running in O(n) time on connected geometric graphs having n vertices and k crossings, where k is smaller than n by an iterated logarithmic factor. Specific problems we study include Voronoi diagrams and single-source shortest paths. Our algorithms all run in linear time in the standard comparison-based computational model; hence, we make no assumptions about the distribution or bit complexities of edge weights, nor do we utilize unusual bit-level operations on memory words. Instead, our algorithms are based on a planarization method that "zeroes in" on edge crossings, together with methods for extending planar separator decompositions to geometric graphs with sublinearly many crossings. Incidentally, our planarization algorithm also solves an open computational geometry problem of Chazelle for triangulating a self-intersecting polygonal chain having n segments and k crossings in linear time, for the case when k is sublinear in n by an iterated logarithmic factor.
Emerge-Sort: Converging to Ordered Sequences by Simple Local Operators
Venue: arXiv cs.AI 2009
Year: 2009

In this paper we examine sorting on the assumption that we do not know in advance which way to sort a sequence of numbers and we set at work simple local comparison and swap operators whose repeating application ends up in sorted sequences. These are the basic elements of Emerge-Sort, our approach to self-organizing sorting, which we then validate experimentally across a range of samples. Observing an O(n2) run-time behaviour, we note that the n/logn delay coefficient that differentiates Emerge-Sort from the classical comparison based algorithms is an instantiation of the price of anarchy we pay for not imposing a sorting order and for letting that order emerge through the local interactions.
Equivalence of SQL Queries in Presence of Embedded Dependencies
Venue: arXiv cs.DB 2009
Year: 2009

We consider the problem of finding equivalent minimal-size reformulations of SQL queries in presence of embedded dependencies [1]. Our focus is on select-project-join (SPJ) queries with equality comparisons, also known as safe conjunctive (CQ) queries, possibly with grouping and aggregation. For SPJ queries, the semantics of the SQL standard treat query answers as multisets (a.k.a. bags), whereas the stored relations may be treated either as sets, which is called bag-set semantics for query evaluation, or as bags, which is called bag semantics. (Under set semantics, both query answers and stored relations are treated as sets.) In the context of the above Query-Reformulation Problem, we develop a comprehensive framework for equivalence of CQ queries under bag and bag-set semantics in presence of embedded dependencies, and make a number of conceptual and technical contributions. Specifically, we develop equivalence tests for CQ queries in presence of arbitrary sets of embedded dependencies under bag and bag-set semantics, under the condition that chase [9] under set semantics (set-chase) on the inputs terminates. We also present equivalence tests for aggregate CQ queries in presence of embedded dependencies. We use our equivalence tests to develop sound and complete (whenever set-chase on the inputs terminates) algorithms for solving instances of the Query-Reformulation Problem with CQ queries under each of bag and bag-set semantics, as well as for instances of the problem with aggregate queries.
Optimal Succinctness for Range Minimum Queries
Venue: arXiv cs.DS 2009
Year: 2009

For a static array A of n ordered objects, a range minimum query asks for the position of the minimum between two specified array indices. We show how to preprocess A into a scheme of size 2n+o(n) bits that allows to answer range minimum queries on A in constant time. This space is asymptotically optimal in the important setting where access to A is not permitted after the preprocessing step. Our scheme can be computed in linear time, using only n + o(n) additional bits at construction time. In interesting by-product is that we also improve on LCA-computation in BPS- or DFUDS-encoded trees.
Minimax Trees in Linear Time
Venue: arXiv cs.DS 2009
Year: 2009

A minimax tree is similar to a Huffman tree except that, instead of minimizing the weighted average of the leaves' depths, it minimizes the maximum of any leaf's weight plus its depth. Golumbic (1976) introduced minimax trees and gave a Huffman-like, $\Oh{n \log n}$-time algorithm for building them. Drmota and Szpankowski (2002) gave another $\Oh{n \log n}$-time algorithm, which checks the Kraft Inequality in each step of a binary search. In this paper we show how Drmota and Szpankowski's algorithm can be made to run in linear time on a word RAM with (Ω(\log n))-bit words. We also discuss how our solution applies to problems in data compression, group testing and circuit design.
Foundations of SPARQL Query Optimization
Venue: arXiv cs.DB 2009
Year: 2009

The SPARQL query language is a recent W3C standard for processing RDF data, a format that has been developed to encode information in a machine-readable way. We investigate the foundations of SPARQL query optimization and (a) provide novel complexity results for the SPARQL evaluation problem, showing that the main source of complexity is operator OPTIONAL alone; (b) propose a comprehensive set of algebraic query rewriting rules; (c) present a framework for constraint-based SPARQL optimization based upon the well-known chase procedure for Conjunctive Query minimization. In this line, we develop two novel termination conditions for the chase. They subsume the strongest conditions known so far and do not increase the complexity of the recognition problem, thus making a larger class of both Conjunctive and SPARQL queries amenable to constraint-based optimization. Our results are of immediate practical interest and might empower any SPARQL query optimizer.
The Complexity of Weighted Boolean #CSP with Mixed Signs
Venue: arXiv cs.CC 2009
Year: 2009

We give a complexity dichotomy for the problem of computing the partition function of a weighted Boolean constraint satisfaction problem. Such a problem is parameterized by a set of rational-valued functions, which generalize constraints. Each function assigns a weight to every assignment to a set of Boolean variables. Our dichotomy extends previous work in which the weight functions were restricted to being non-negative. We represent a weight function as a product of the form (-1)^s g, where the polynomial s determines the sign of the weight and the non-negative function g determines its magnitude. We show that the problem of computing the partition function (the sum of the weights of all possible variable assignments) is in polynomial time if either every weight function can be defined by a "pure affine" magnitude with a quadratic sign polynomial or every function can be defined by a magnitude of "product type" with a linear sign polynomial. In all other cases, computing the partition function is FP^#P-complete.
Induction and Co-induction in Sequent Calculus
Venue: arXiv cs.LO 2009
Year: 2009

Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles are based on a proof theoretic (rather than set-theoretic) notion of definition. Definitions are akin to (stratified) logic programs, where the left and right rules for defined atoms allow one to view theories as "closed" or defining fixed points. The use of definitions makes it possible to reason intensionally about syntax, in particular enforcing free equality via unification. We add in a consistent way rules for pre and post fixed points, thus allowing the user to reason inductively and co-inductively about properties of computational system making full use of higher-order abstract syntax. Consistency is guaranteed via cut-elimination, where we give the first, to our knowledge, cut-elimination procedure in the presence of general inductive and co-inductive definitions.
The Complexity of Generalized Satisfiability for Linear Temporal Logic
Venue: arXiv cs.LO 2009
Year: 2009

In a seminal paper from 1985, Sistla and Clarke showed that satisfiability for Linear Temporal Logic (LTL) is either NP-complete or PSPACE-complete, depending on the set of temporal operators used. If, in contrast, the set of propositional operators is restricted, the complexity may decrease. This paper undertakes a systematic study of satisfiability for LTL formulae over restricted sets of propositional and temporal operators. Since every propositional operator corresponds to a Boolean function, there exist infinitely many propositional operators. In order to systematically cover all possible sets of them, we use Post's lattice. With its help, we determine the computational complexity of LTL satisfiability for all combinations of temporal operators and all but two classes of propositional functions. Each of these infinitely many problems is shown to be either PSPACE-complete, NP-complete, or in P.
Limited-Rate Channel State Feedback for Multicarrier Block Fading Channels
Venue: arXiv cs.IT 2009
Year: 2009

The capacity of a fading channel can be substantially increased by feeding back channel state information from the receiver to the transmitter. With limited-rate feedback what state information to feed back and how to encode it are important open questions. This paper studies power loading in a multicarrier system using no more than one bit of feedback per sub-channel. The sub-channels can be correlated and full channel state information is assumed at the receiver.
Filtering Microarray Correlations by Statistical Literature Analysis Yields Potential Hypotheses for Lactation Research
Venue: arXiv cs.DL 2009
Year: 2009

Our results demonstrated that a previously reported protein name co-occurrence method (5-mention PubGene) which was not based on a hypothesis testing framework, it is generally statistically more significant than the 99th percentile of Poisson distribution-based method of calculating co-occurrence. It agrees with previous methods using natural language processing to extract protein-protein interaction from text as more than 96% of the interactions found by natural language processing methods to overlap with the results from 5-mention PubGene method. However, less than 2% of the gene co-expressions analyzed by microarray were found from direct co-occurrence or interaction information extraction from the literature. At the same time, combining microarray and literature analyses, we derive a novel set of 7 potential functional protein-protein interactions that had not been previously described in the literature.
Random Linear Network Coding For Time Division Duplexing: Energy Analysis
Venue: arXiv cs.IT 2009
Year: 2009

We study the energy performance of random linear network coding for time division duplexing channels. We assume a packet erasure channel with nodes that cannot transmit and receive information simultaneously. The sender transmits coded data packets back-to-back before stopping to wait for the receiver to acknowledge the number of degrees of freedom, if any, that are required to decode correctly the information. Our analysis shows that, in terms of mean energy consumed, there is an optimal number of coded data packets to send before stopping to listen. This number depends on the energy needed to transmit each coded packet and the acknowledgment (ACK), probabilities of packet and ACK erasure, and the number of degrees of freedom that the receiver requires to decode the data. We show that its energy performance is superior to that of a full-duplex system. We also study the performance of our scheme when the number of coded packets is chosen to minimize the mean time to complete transmission as in [1]. Energy performance under this optimization criterion is found to be close to optimal, thus providing a good trade-off between energy and time required to complete transmissions.
Thoughts on an Unified Framework for Artificial Chemistries
Venue: arXiv cs.AI 2009
Year: 2009

Artificial Chemistries (ACs) are symbolic chemical metaphors for the exploration of Artificial Life, with specific focus on the problem of biogenesis or the origin of life. This paper presents authors thoughts towards defining a unified framework to characterize and classify symbolic artificial chemistries by devising appropriate formalism to capture semantic and organizational information. We identify three basic high level abstractions in initial proposal for this framework viz., information, computation, and communication. We present an analysis of two important notions of information, namely, Shannon's Entropy and Algorithmic Information, and discuss inductive and deductive approaches for defining the framework.
Measures for classification and detection in steganalysis
Venue: arXiv cs.OH 2009
Year: 2009

Still and multi-media images are subject to transformations for compression, steganographic embedding and digital watermarking. In a major program of activities we are engaged in the modeling, design and analysis of digital content. Statistical and pattern classification techniques should be combined with understanding of run length, transform coding techniques, and also encryption techniques.
Polar Codes: Characterization of Exponent, Bounds, and Constructions
Venue: arXiv cs.IT 2009
Year: 2009

Polar codes were recently introduced by Arıkan. They achieve the capacity of arbitrary symmetric binary-input discrete memoryless channels under a low complexity successive cancellation decoding strategy. The original polar code construction is closely related to the recursive construction of Reed-Muller codes and is based on the $2 \times 2$ matrix $\bigl[ 1 &0 1& 1 \bigr]$. It was shown by Arıkan and Telatar that this construction achieves an error exponent of $\frac12$, i.e., that for sufficiently large blocklengths the error probability decays exponentially in the square root of the length. It was already mentioned by Arıkan that in principle larger matrices can be used to construct polar codes. A fundamental question then is to see whether there exist matrices with exponent exceeding $\frac12$. We first show that any $\ell \times \ell$ matrix none of whose column permutations is upper triangular polarizes symmetric channels. We then characterize the exponent of a given square matrix and derive upper and lower bounds on achievable exponents. Using these bounds we show that there are no matrices of size less than 15 with exponents exceeding $\frac12$. Further, we give a general construction based on BCH codes which for large $n$ achieves exponents arbitrarily close to 1 and which exceeds $\frac12$ for size 16.