OpenRaiser/Intern-Atlas huggingface dataset:
Energy stable and momentum conserving hybrid finite element method for the incompressible Navier-Stokes equations
Venue: arXiv cs.CE 2012
Year: 2012

A hybrid method for the incompressible Navier--Stokes equations is presented. The method inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order interpolations can be used for the velocity and pressure fields, and mass can be conserved locally. Using continuous Lagrange multiplier spaces to enforce flux continuity across cell facets, the number of global degrees of freedom is the same as for a continuous Galerkin method on the same mesh. Different from our earlier investigations on the approach for the Navier--Stokes equations, the pressure field in this work is discontinuous across cell boundaries. It is shown that this leads to very good local mass conservation and, for an appropriate choice of finite element spaces, momentum conservation. Also, a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed, even in the absence of a point-wise solenoidal velocity field. Mass conservation, momentum conservation and global energy stability are proved for the time-continuous case, and for a fully discrete scheme. The presented analysis results are supported by a range of numerical simulations.
Unsolved Problems in Visibility Graphs of Points, Segments and Polygons
Venue: arXiv cs.CG 2012
Year: 2012

In this survey paper, we present open problems and conjectures on visibility graphs of points, segments and polygons along with necessary backgrounds for understanding them.
On Approximating the Riemannian 1-Center
Venue: arXiv cs.CG 2012
Year: 2012

In this paper, we generalize the simple Euclidean 1-center approximation algorithm of Badoiu and Clarkson (2003) to Riemannian geometries and study accordingly the convergence rate. We then show how to instantiate this generic algorithm to two particular cases: (1) hyperbolic geometry, and (2) Riemannian manifold of symmetric positive definite matrices.
Geometric representations for minimalist grammars
Venue: arXiv cs.CL 2012
Year: 2012

We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector spaces. We prove that the structure-building functions as well as simple processors for minimalist languages can be realized by piecewise linear operators in representation space. We also propose harmony, i.e. the distance of an intermediate processing step from the final well-formed state in representation space, as a measure of processing complexity. Finally, we illustrate our findings by means of two particular arithmetic and fractal representations.
On Communication Protocols that Compute Almost Privately
Venue: arXiv cs.CR 2012
Year: 2012

A traditionally desired goal when designing auction mechanisms is incentive compatibility, i.e., ensuring that bidders fare best by truthfully reporting their preferences. A complementary goal, which has, thus far, received significantly less attention, is to preserve privacy, i.e., to ensure that bidders reveal no more information than necessary. We further investigate and generalize the approximate privacy model for two-party communication recently introduced by Feigenbaum et al.[8]. We explore the privacy properties of a natural class of communication protocols that we refer to as "dissection protocols". Dissection protocols include, among others, the bisection auction in [9,10] and the bisection protocol for the millionaires problem in [8]. Informally, in a dissection protocol the communicating parties are restricted to answering simple questions of the form "Is your input between the values αand β(under a predefined order over the possible inputs)?". We prove that for a large class of functions, called tiling functions, which include the 2nd-price Vickrey auction, there always exists a dissection protocol that provides a constant average-case privacy approximation ratio for uniform or "almost uniform" probability distributions over inputs. To establish this result we present an interesting connection between the approximate privacy framework and basic concepts in computational geometry. We show that such a good privacy approximation ratio for tiling functions does not, in general, exist in the worst case. We also discuss extensions of the basic setup to more than two parties and to non-tiling functions, and provide calculations of privacy approximation ratios for two functions of interest.
Redesigning the Open Mobile Alliance License Choice Algorithm
Venue: arXiv cs.CR 2012
Year: 2012

We claim that the Open Mobile Alliance (OMA) License Choice Algorithm, implemented in mobile DRM agents as specified by OMA suffers from a bug. More precisely there exist some cases that the user, may end up losing some rights without even to exercise them. We redesign this algorithm and claim that our approach eliminates this bug.
Quasi-Optimal Network Utility Maximization for Scalable Video Streaming
Venue: arXiv cs.MM 2012
Year: 2012

This paper addresses rate control for transmission of scalable video streams via Network Utility Maximization (NUM) formulation. Due to stringent QoS requirements of video streams and specific characterization of utility experienced by end-users, one has to solve nonconvex and even nonsmooth NUM formulation for such streams, where dual methods often prove incompetent. Convexification plays an important role in this work as it permits the use of existing dual methods to solve an approximate to the NUM problem iteratively and distributively. Hence, to tackle the nonsmoothness and nonconvexity, we aim at reformulating the NUM problem through approximation and transformation of the ideal discretely adaptive utility function for scalable video streams. The reformulated problem is shown to be a D.C. (Difference of Convex) problem. We leveraged Sequential Convex Programming (SCP) approach to replace the nonconvex D.C. problem by a sequence of convex problems that aim to approximate the original D.C. problem. We then solve each convex problem produced by SCP approach using existing dual methods. This procedure is the essence of two distributed iterative rate control algorithms proposed in this paper, for which one can show the convergence to a locally optimal point of the nonconvex D.C. problem and equivalently to a locally optimal point of an approximate to the original nonconvex problem. Our experimental results show that the proposed rate control algorithms converge with tractable convergence behavior.
Higher-Order Symbolic Execution via Contracts
Venue: arXiv cs.PL 2012
Year: 2012

We present a new approach to automated reasoning about higher-order programs by extending symbolic execution to use behavioral contracts as symbolic values, enabling symbolic approximation of higher-order behavior. Our approach is based on the idea of an abstract reduction semantics that gives an operational semantics to programs with both concrete and symbolic components. Symbolic components are approximated by their contract and our semantics gives an operational interpretation of contracts-as-values. The result is a executable semantics that soundly predicts program behavior, including contract failures, for all possible instantiations of symbolic components. We show that our approach scales to an expressive language of contracts including arbitrary programs embedded as predicates, dependent function contracts, and recursive contracts. Supporting this feature-rich language of specifications leads to powerful symbolic reasoning using existing program assertions. We then apply our approach to produce a verifier for contract correctness of components, including a sound and computable approximation to our semantics that facilitates fully automated contract verification. Our implementation is capable of verifying contracts expressed in existing programs, and of justifying valuable contract-elimination optimizations.
Trust beyond reputation: A computational trust model based on stereotypes
Venue: arXiv cs.CR 2012
Year: 2012

Models of computational trust support users in taking decisions. They are commonly used to guide users' judgements in online auction sites; or to determine quality of contributions in Web 2.0 sites. However, most existing systems require historical information about the past behavior of the specific agent being judged. In contrast, in real life, to anticipate and to predict a stranger's actions in absence of the knowledge of such behavioral history, we often use our "instinct"- essentially stereotypes developed from our past interactions with other "similar" persons. In this paper, we propose StereoTrust, a computational trust model inspired by stereotypes as used in real-life. A stereotype contains certain features of agents and an expected outcome of the transaction. When facing a stranger, an agent derives its trust by aggregating stereotypes matching the stranger's profile. Since stereotypes are formed locally, recommendations stem from the trustor's own personal experiences and perspective. Historical behavioral information, when available, can be used to refine the analysis. According to our experiments using Epinions.com dataset, StereoTrust compares favorably with existing trust models that use different kinds of information and more complete historical information.
Coevolution of trustful buyers and cooperative sellers in the trust game
Venue: arXiv cs.GT 2012
Year: 2012

Many online marketplaces enjoy great success. Buyers and sellers in successful markets carry out cooperative transactions even if they do not know each other in advance and a moral hazard exists. An indispensable component that enables cooperation in such social dilemma situations is the reputation system. Under the reputation system, a buyer can avoid transacting with a seller with a bad reputation. A transaction in online marketplaces is better modeled by the trust game than other social dilemma games, including the donation game and the prisoner's dilemma. In addition, most individuals participate mostly as buyers or sellers; each individual does not play the two roles with equal probability. Although the reputation mechanism is known to be able to remove the moral hazard in games with asymmetric roles, competition between different strategies and population dynamics of such a game are not sufficiently understood. On the other hand, existing models of reputation-based cooperation, also known as indirect reciprocity, are based on the symmetric donation game. We analyze the trust game with two fixed roles, where trustees (i.e., sellers) but not investors (i.e., buyers) possess reputation scores. We study the equilibria and the replicator dynamics of the game. We show that the reputation mechanism enables cooperation between unacquainted buyers and sellers under fairly generous conditions, even when such a cooperative equilibrium coexists with an asocial equilibrium in which buyers do not buy and sellers cheat. In addition, we show that not many buyers may care about the seller's reputation under cooperative equilibrium. Buyers' trusting behavior and sellers' reputation-driven cooperative behavior coevolve to alleviate the social dilemma.
A Transform Approach to Linear Network Coding for Acyclic Networks with Delay
Venue: arXiv cs.IT 2012
Year: 2012

The algebraic formulation for linear network coding in acyclic networks with the links having integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary acyclic network with integer delay assumed for the links, the output symbols at the sink nodes, at any given time instant, is a \mathbb{F}_{q}$-linear combination of the input symbols across different generations, where $\mathbb{F}_{q}$ denotes the field over which the network operates. We use finite-field discrete fourier transform (DFT) to convert the output symbols at the sink nodes, at any given time instant, into a $\mathbb{F}_{q}$-linear combination of the input symbols generated during the same generation. We call this as transforming the acyclic network with delay into {\em $n$-instantaneous networks} ($n$ is sufficiently large). We show that under certain conditions, there exists a network code satisfying sink demands in the usual (non-transform) approach if and only if there exists a network code satisfying sink demands in the transform approach. Furthermore, we show that the transform method (along with the use of alignment strategies) can be employed to achieve half the rate corresponding to the individual source-destination min-cut (which are assumed to be equal to 1) for some classes of three-source three-destination unicast network with delays, when the zero-interference conditions are not satisfied.
A Goal-Directed Implementation of Query Answering for Hybrid MKNF Knowledge Bases
Venue: arXiv cs.AI 2012
Year: 2012

Ontologies and rules are usually loosely coupled in knowledge representation formalisms. In fact, ontologies use open-world reasoning while the leading semantics for rules use non-monotonic, closed-world reasoning. One exception is the tightly-coupled framework of Minimal Knowledge and Negation as Failure (MKNF), which allows statements about individuals to be jointly derived via entailment from an ontology and inferences from rules. Nonetheless, the practical usefulness of MKNF has not always been clear, although recent work has formalized a general resolution-based method for querying MKNF when rules are taken to have the well-founded semantics, and the ontology is modeled by a general oracle. That work leaves open what algorithms should be used to relate the entailments of the ontology and the inferences of rules. In this paper we provide such algorithms, and describe the implementation of a query-driven system, CDF-Rules, for hybrid knowledge bases combining both (non-monotonic) rules under the well-founded semantics and a (monotonic) ontology, represented by a CDF Type-1 (ALQ) theory. To appear in Theory and Practice of Logic Programming (TPLP)
Formalizing Randomized Matching Algorithms
Venue: arXiv cs.LO 2012
Year: 2012

Using Jeřábek 's framework for probabilistic reasoning, we formalize the correctness of two fundamental RNC^2 algorithms for bipartite perfect matching within the theory VPV for polytime reasoning. The first algorithm is for testing if a bipartite graph has a perfect matching, and is based on the Schwartz-Zippel Lemma for polynomial identity testing applied to the Edmonds polynomial of the graph. The second algorithm, due to Mulmuley, Vazirani and Vazirani, is for finding a perfect matching, where the key ingredient of this algorithm is the Isolating Lemma.
Reconstruction of Binary Functions and Shapes from Incomplete Frequency Information
Venue: arXiv cs.IT 2012
Year: 2012

The characterization of a binary function by partial frequency information is considered. We show that it is possible to reconstruct binary signals from incomplete frequency measurements via the solution of a simple linear optimization problem. We further prove that if a binary function is spatially structured (e.g. a general black-white image or an indicator function of a shape), then it can be recovered from very few low frequency measurements in general. These results would lead to efficient methods of sensing, characterizing and recovering a binary signal or a shape as well as other applications like deconvolution of binary functions blurred by a low-pass filter. Numerical results are provided to demonstrate the theoretical arguments.
Compressed Sensing and Matrix Completion with Constant Proportion of Corruptions
Venue: arXiv cs.IT 2012
Year: 2012

We improve existing results in the field of compressed sensing and matrix completion when sampled data may be grossly corrupted. We introduce three new theorems. 1) In compressed sensing, we show that if the m \times n sensing matrix has independent Gaussian entries, then one can recover a sparse signal x exactly by tractable \ell1 minimimization even if a positive fraction of the measurements are arbitrarily corrupted, provided the number of nonzero entries in x is O(m/(log(n/m) + 1)). 2) In the very general sensing model introduced in "A probabilistic and RIPless theory of compressed sensing" by Candes and Plan, and assuming a positive fraction of corrupted measurements, exact recovery still holds if the signal now has O(m/(log^2 n)) nonzero entries. 3) Finally, we prove that one can recover an n \times n low-rank matrix from m corrupted sampled entries by tractable optimization provided the rank is on the order of O(m/(n log^2 n)); again, this holds when there is a positive fraction of corrupted samples.
Tractable Set Constraints
Venue: arXiv cs.AI 2012
Year: 2012

Many fundamental problems in artificial intelligence, knowledge representation, and verification involve reasoning about sets and relations between sets and can be modeled as set constraint satisfaction problems (set CSPs). Such problems are frequently intractable, but there are several important set CSPs that are known to be polynomial-time tractable. We introduce a large class of set CSPs that can be solved in quadratic time. Our class, which we call EI, contains all previously known tractable set CSPs, but also some new ones that are of crucial importance for example in description logics. The class of EI set constraints has an elegant universal-algebraic characterization, which we use to show that every set constraint language that properly contains all EI set constraints already has a finite sublanguage with an NP-hard constraint satisfaction problem.
New Techniques for Upper-Bounding the ML Decoding Performance of Binary Linear Codes
Venue: arXiv cs.IT 2012
Year: 2012

In this paper, new techniques are presented to either simplify or improve most existing upper bounds on the maximum-likelihood (ML) decoding performance of the binary linear codes over additive white Gaussian noise (AWGN) channels. Firstly, the recently proposed union bound using truncated weight spectrums by Ma {\em et al} is re-derived in a detailed way based on Gallager's first bounding technique (GFBT), where the "good region" is specified by a sub-optimal list decoding algorithm. The error probability caused by the bad region can be upper-bounded by the tail-probability of a binomial distribution, while the error probability caused by the good region can be upper-bounded by most existing techniques. Secondly, we propose two techniques to tighten the union bound on the error probability caused by the good region. The first technique is based on pair-wise error probabilities, which can be further tightened by employing the independence between the error events and certain components of the received random vectors. The second technique is based on triplet-wise error probabilities, which can be upper-bounded by proving that any three bipolar vectors form a non-obtuse triangle. The proposed bounds improve the conventional union bounds but have a similar complexity since they involve only the $Q$-function. The proposed bounds can also be adapted to bit-error probabilities.
On-line construction of position heaps
Venue: arXiv cs.DS 2012
Year: 2012

We propose a simple linear-time on-line algorithm for constructing a position heap for a string [Ehrenfeucht et al, 2011]. Our definition of position heap differs slightly from the one proposed in [Ehrenfeucht et al, 2011] in that it considers the suffixes ordered from left to right. Our construction is based on classic suffix pointers and resembles the Ukkonen's algorithm for suffix trees [Ukkonen, 1995]. Using suffix pointers, the position heap can be extended into the augmented position heap that allows for a linear-time string matching algorithm [Ehrenfeucht et al, 2011].
Finite Satisfiability for Guarded Fixpoint Logic
Venue: arXiv cs.LO 2012
Year: 2012

The finite satisfiability problem for guarded fixpoint logic is decidable and complete for 2ExpTime (resp. ExpTime for formulas of bounded width).
The vertex leafage of chordal graphs
Venue: arXiv cs.DM 2012
Year: 2012

Every chordal graph $G$ can be represented as the intersection graph of a collection of subtrees of a host tree, a so-called {\em tree model} of $G$. The leafage $\ell(G)$ of a connected chordal graph $G$ is the minimum number of leaves of the host tree of a tree model of $G$. The vertex leafage $\vl(G)$ is the smallest number $k$ such that there exists a tree model of $G$ in which every subtree has at most $k$ leaves. The leafage is a polynomially computable parameter by the result of \cite{esa}. In this contribution, we study the vertex leafage. We prove for every fixed $k\geq 3$ that deciding whether the vertex leafage of a given chordal graph is at most $k$ is NP-complete by proving a stronger result, namely that the problem is NP-complete on split graphs with vertex leafage of at most $k+1$. On the other hand, for chordal graphs of leafage at most $\ell$, we show that the vertex leafage can be calculated in time $n^{O(\ell)}$. Finally, we prove that there exists a tree model that realizes both the leafage and the vertex leafage of $G$. Notably, for every path graph $G$, there exists a path model with $\ell(G)$ leaves in the host tree and it can be computed in $O(n^3)$ time.
Common information revisited
Venue: arXiv cs.IT 2012
Year: 2012

One of the main notions of information theory is the notion of mutual information in two messages (two random variables in Shannon information theory or two binary strings in algorithmic information theory). The mutual information in $x$ and $y$ measures how much the transmission of $x$ can be simplified if both the sender and the recipient know $y$ in advance. Gács and Körner gave an example where mutual information cannot be presented as common information (a third message easily extractable from both $x$ and $y$). Then this question was studied in the framework of algorithmic information theory by An. Muchnik and A. Romashchenko who found many other examples of this type. K. Makarychev and Yu. Makarychev found a new proof of Gács--Körner results by means of conditionally independent random variables. The question about the difference between mutual and common information can be studied quantitatively: for a given $x$ and $y$ we look for three messages $a$, $b$, $c$ such that $a$ and $c$ are enough to reconstruct $x$, while $b$ and $c$ are enough to reconstruct $y$. In this paper: We state and prove (using hypercontractivity of product spaces) a quantitative version of Gács--Körner theorem; We study the tradeoff between $\abs{a}, \abs{b}, \abs{c}$ for a random pair $(x, y)$ such that Hamming distance between $x$ and $y$ is $\eps n$ (our bounds are almost tight); We construct "the worst possible" distribution on $(x, y)$ in terms of the tradeoff between $\abs{a}, \abs{b}, \abs{c}$.
Practical and Efficient Circle Graph Recognition
Venue: arXiv cs.DS 2012
Year: 2012

Circle graphs are the intersection graphs of chords in a circle. This paper presents the first sub-quadratic recognition algorithm for the class of circle graphs. Our algorithm is O(n + m) times the inverse Ackermann function, α(n + m), whose value is smaller than 4 for any practical graph. The algorithm is based on a new incremental Lexicographic Breadth-First Search characterization of circle graphs, and a new efficient data-structure for circle graphs, both developed in the paper. The algorithm is an extension of a Split Decomposition algorithm with the same running time developed by the authors in a companion paper.