OpenRaiser/Intern-Atlas huggingface dataset:
A Unified Approach to Ranking in Probabilistic Databases
Venue: arXiv cs.DB 2010
Year: 2010

The dramatic growth in the number of application domains that naturally generate probabilistic, uncertain data has resulted in a need for efficiently supporting complex querying and decision-making over such data. In this paper, we present a unified approach to ranking and top-k query processing in probabilistic databases by viewing it as a multi-criteria optimization problem, and by deriving a set of features that capture the key properties of a probabilistic dataset that dictate the ranked result. We contend that a single, specific ranking function may not suffice for probabilistic databases, and we instead propose two parameterized ranking functions, called PRF-w and PRF-e, that generalize or can approximate many of the previously proposed ranking functions. We present novel generating functions-based algorithms for efficiently ranking large datasets according to these ranking functions, even if the datasets exhibit complex correlations modeled using probabilistic and/xor trees or Markov networks. We further propose that the parameters of the ranking function be learned from user preferences, and we develop an approach to learn those parameters. Finally, we present a comprehensive experimental study that illustrates the effectiveness of our parameterized ranking functions, especially PRF-e, at approximating other ranking functions and the scalability of our proposed algorithms for exact or approximate ranking.
Error Bounds for Repeat-Accumulate Codes Decoded via Linear Programming
Venue: arXiv cs.IT 2010
Year: 2010

We examine regular and irregular repeat-accumulate (RA) codes with repetition degrees which are all even. For these codes and with a particular choice of an interleaver, we give an upper bound on the decoding error probability of a linear-programming based decoder which is an inverse polynomial in the block length. Our bound is valid for any memoryless, binary-input, output-symmetric (MBIOS) channel. This result generalizes the bound derived by Feldman et al., which was for regular RA(2) codes.
Successive Difference Substitution Based on Column Stochastic Matrix and Mechanical Decision for Positive Semi-definite Forms
Venue: arXiv cs.SC 2010
Year: 2010

The theory part of this paper is sketched as follows. Based on column stochastic average matrix $T_n$ selected as a basic substitution matrix, the method of advanced successive difference substitution is established. Then, a set of necessary and sufficient conditions for deciding positive semi-definite form on $\R^n_+$ is derived from this method. And furthermore, it is proved that the sequence of SDS sets of a positive definite form is positively terminating. Worked out according to these results, the Maple program TSDS3 not only automatically proves the polynomial inequalities, but also outputs counter examples for the false. Sometimes TSDS3 does not halt, but it is very useful by experimenting on so many examples.
Unsatisfiable Linear CNF Formulas Are Large and Complex
Venue: arXiv cs.DM 2010
Year: 2010

We call a CNF formula linear if any two clauses have at most one variable in common. We show that there exist unsatisfiable linear k-CNF formulas with at most 4k^2 4^k clauses, and on the other hand, any linear k-CNF formula with at most 4^k/(8e^2k^2) clauses is satisfiable. The upper bound uses probabilistic means, and we have no explicit construction coming even close to it. One reason for this is that unsatisfiable linear formulas exhibit a more complex structure than general (non-linear) formulas: First, any treelike resolution refutation of any unsatisfiable linear k-CNF formula has size at least 2^(2^(k/2-1))$. This implies that small unsatisfiable linear k-CNF formulas are hard instances for Davis-Putnam style splitting algorithms. Second, if we require that the formula F have a strict resolution tree, i.e. every clause of F is used only once in the resolution tree, then we need at least a^a^...^a clauses, where a is approximately 2 and the height of this tower is roughly k.
Interference Channels with Source Cooperation
Venue: arXiv cs.IT 2010
Year: 2010

The role of cooperation in managing interference - a fundamental feature of the wireless channel - is investigated by studying the two-user Gaussian interference channel where the source nodes can both transmit and receive in full-duplex. The sum-capacity of this channel is obtained within a gap of a constant number of bits. The coding scheme used builds up on the superposition scheme of Han and Kobayashi (1981) for the two-user interference channel without cooperation. New upperbounds on the sum-capacity are also derived. The same coding scheme is shown to obtain the sum-capacity of the symmetric two-user Gaussian interference channel with noiseless feedback within a constant gap.
Continued Fraction Expansion of Real Roots of Polynomial Systems
Venue: arXiv cs.SC 2010
Year: 2010

We present a new algorithm for isolating the real roots of a system of multivariate polynomials, given in the monomial basis. It is inspired by existing subdivision methods in the Bernstein basis; it can be seen as generalization of the univariate continued fraction algorithm or alternatively as a fully analog of Bernstein subdivision in the monomial basis. The representation of the subdivided domains is done through homographies, which allows us to use only integer arithmetic and to treat efficiently unbounded regions. We use univariate bounding functions, projection and preconditionning techniques to reduce the domain of search. The resulting boxes have optimized rational coordinates, corresponding to the first terms of the continued fraction expansion of the real roots. An extension of Vincent's theorem to multivariate polynomials is proved and used for the termination of the algorithm. New complexity bounds are provided for a simplified version of the algorithm. Examples computed with a preliminary C++ implementation illustrate the approach.
Variational structure of the optimal artificial diffusion method for the advection-diffusion equation
Venue: arXiv cs.CE 2010
Year: 2010

In this research note we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions when applied to one-dimensional problems with constant coefficients and forcing function. We first present a variational principle for a multi-dimensional advective-diffusive system, and then derive a new stable weak formulation. When applied to one-dimensional problems with constant coefficients and forcing function, this resulting weak formulation will be equivalent to the optimal artificial diffusion method. We present representative numerical results to corroborate our theoretical findings.
On Fulkerson conjecture
Venue: arXiv cs.DM 2010
Year: 2010

If $G$ is a bridgeless cubic graph, Fulkerson conjectured that we can find 6 perfect matchings (a{\em Fulkerson covering}) with the property that every edge of $G$ is contained in exactly two of them. A consequence of the Fulkerson conjecture would be that every bridgeless cubic graph has 3 perfect matchings with empty intersection (this problem is known as the Fan Raspaud Conjecture). A {\em FR-triple} is a set of 3 such perfect matchings. We show here how to derive a Fulkerson covering from two FR-triples. Moreover, we give a simple proof that the Fulkerson conjecture holds true for some classes of well known snarks.
On Quantum-Classical Equivalence for Composed Communication Problems
Venue: arXiv cs.CC 2010
Year: 2010

An open problem in communication complexity proposed by several authors is to prove that for every Boolean function f, the task of computing f(x AND y) has polynomially related classical and quantum bounded-error complexities. We solve a variant of this question. For every f, we prove that the task of computing, on input x and y, both of the quantities f(x AND y) and f(x OR y) has polynomially related classical and quantum bounded-error complexities. We further show that the quantum bounded-error complexity is polynomially related to the classical deterministic complexity and the block sensitivity of f. This result holds regardless of prior entanglement.
Learning with Spectral Kernels and Heavy-Tailed Data
Venue: arXiv cs.LG 2010
Year: 2010

Two ubiquitous aspects of large-scale data analysis are that the data often have heavy-tailed properties and that diffusion-based or spectral-based methods are often used to identify and extract structure of interest. Perhaps surprisingly, popular distribution-independent methods such as those based on the VC dimension fail to provide nontrivial results for even simple learning problems such as binary classification in these two settings. In this paper, we develop distribution-dependent learning methods that can be used to provide dimension-independent sample complexity bounds for the binary classification problem in these two popular settings. In particular, we provide bounds on the sample complexity of maximum margin classifiers when the magnitude of the entries in the feature vector decays according to a power law and also when learning is performed with the so-called Diffusion Maps kernel. Both of these results rely on bounding the annealed entropy of gap-tolerant classifiers in a Hilbert space. We provide such a bound, and we demonstrate that our proof technique generalizes to the case when the margin is measured with respect to more general Banach space norms. The latter result is of potential interest in cases where modeling the relationship between data elements as a dot product in a Hilbert space is too restrictive.
Coordinated Weighted Sampling for Estimating Aggregates Over Multiple Weight Assignments
Venue: arXiv cs.DB 2010
Year: 2010

Many data sources are naturally modeled by multiple weight assignments over a set of keys: snapshots of an evolving database at multiple points in time, measurements collected over multiple time periods, requests for resources served at multiple locations, and records with multiple numeric attributes. Over such vector-weighted data we are interested in aggregates with respect to one set of weights, such as weighted sums, and aggregates over multiple sets of weights such as the $L_1$ difference. Sample-based summarization is highly effective for data sets that are too large to be stored or manipulated. The summary facilitates approximate processing queries that may be specified after the summary was generated. Current designs, however, are geared for data sets where a single {\em scalar} weight is associated with each key. We develop a sampling framework based on {\em coordinated weighted samples} that is suited for multiple weight assignments and obtain estimators that are {\em orders of magnitude tighter} than previously possible. We demonstrate the power of our methods through an extensive empirical evaluation on diverse data sets ranging from IP network to stock quotes data.
Distributed Sensor Selection using a Truncated Newton Method
Venue: arXiv cs.IT 2010
Year: 2010

We propose a new distributed algorithm for computing a truncated Newton method, where the main diagonal of the Hessian is computed using belief propagation. As a case study for this approach, we examine the sensor selection problem, a Boolean convex optimization problem. We form two distributed algorithms. The first algorithm is a distributed version of the interior point method by Joshi and Boyd, and the second algorithm is an order of magnitude faster approximation. As an example application we discuss distributed anomaly detection in networks. We demonstrate the applicability of our solution using both synthetic data and real traffic logs collected from the Abilene Internet backbone.
Evaluating Methods to Rediscover Missing Web Pages from the Web Infrastructure
Venue: arXiv cs.IR 2010
Year: 2010

Missing web pages (pages that return the 404 "Page Not Found" error) are part of the browsing experience. The manual use of search engines to rediscover missing pages can be frustrating and unsuccessful. We compare four automated methods for rediscovering web pages. We extract the page's title, generate the page's lexical signature (LS), obtain the page's tags from the bookmarking website delicious.com and generate a LS from the page's link neighborhood. We use the output of all methods to query Internet search engines and analyze their retrieval performance. Our results show that both LSs and titles perform fairly well with over 60% URIs returned top ranked from Yahoo!. However, the combination of methods improves the retrieval performance. Considering the complexity of the LS generation, querying the title first and in case of insufficient results querying the LSs second is the preferable setup. This combination accounts for more than 75% top ranked URIs.
The Semigroup of Combinatorial Configurations
Venue: arXiv cs.DM 2010
Year: 2010

A (v,b,r,k) combinatorial configuration is a (r,k)-biregular bipartite graph with v vertices on the left and b vertices on the right and with no cycle of length 4. Combinatorial configurations have become very important for some cryptographic applications to sensor networks and to peer-to-peer communities. Configurable tuples are those tuples (v,b,r,k) for which a (v,b,r,k) combinatorial configuration exists. It is proved in this work that the set of configurable tuples with fixed r and k has the structure of a numerical semigroup. The numerical semigroup is completely described for r=2 and r=3.
On Algebraic Traceback in Dynamic Networks
Venue: arXiv cs.IT 2010
Year: 2010

This paper introduces the concept of incremental traceback for determining changes in the trace of a network as it evolves with time. A distributed algorithm, based on the methodology of algebraic traceback developed by Dean et al, is proposed which can completely determine a path of d nodes/routers using O(d) marked packets, and subsequently determine the changes in its topology using O(log d) marked packets with high probability. The algorithm is established to be order-wise optimal i.e., no other distributed algorithm can determine changes in the path topology using lesser order of bits (i.e., marked packets). The algorithm is shown to have a computational complexity of O(d log d), which is significantly less than that of any existing non-incremental algorithm of algebraic traceback. Extensions of this algorithm to settings with node identity spoofing and network coding are also presented.
Passive network tomography for erroneous networks: A network coding approach
Venue: arXiv cs.NI 2010
Year: 2010

Passive network tomography uses end-to-end observations of network communication to characterize the network, for instance to estimate the network topology and to localize random or adversarial glitches. Under the setting of linear network coding this work provides a comprehensive study of passive network tomography in the presence of network (random or adversarial) glitches. To be concrete, this work is developed along two directions: 1. Tomographic upper and lower bounds (i.e., the most adverse conditions in each problem setting under which network tomography is possible, and corresponding schemes (computationally efficient, if possible) that achieve this performance) are presented for random linear network coding (RLNC). We consider RLNC designed with common randomness, i.e., the receiver knows the random code-books all nodes. (To justify this, we show an upper bound for the problem of topology estimation in networks using RLNC without common randomness.) In this setting we present the first set of algorithms that characterize the network topology exactly. Our algorithm for topology estimation with random network errors has time complexity that is polynomial in network parameters. For the problem of network error localization given the topology information, we present the first computationally tractable algorithm to localize random errors, and prove it is computationally intractable to localize adversarial errors. 2. New network coding schemes are designed that improve the tomographic performance of RLNC while maintaining the desirable low-complexity, throughput-optimal, distributed linear network coding properties of RLNC. In particular, we design network codes based on Reed-Solomon codes so that a maximal number of adversarial errors can be localized in a computationally efficient manner even without the information of network topology.
Nominal Abstraction
Venue: arXiv cs.LO 2010
Year: 2010

Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such descriptions: the interpretation of atomic judgments through recursive definitions and an encoding of binding constructs via generic judgments. However, logics encompassing these two features do not currently allow for the definition of relations that embody dynamic aspects related to binding, a capability needed in many reasoning tasks. We propose a new relation between terms called nominal abstraction as a means for overcoming this deficiency. We incorporate nominal abstraction into a rich logic also including definitions, generic quantification, induction, and co-induction that we then prove to be consistent. We present examples to show that this logic can provide elegant treatments of binding contexts that appear in many proofs, such as those establishing properties of typing calculi and of arbitrarily cascading substitutions that play a role in reducibility arguments.
Monotonicity, thinning and discrete versions of the Entropy Power Inequality
Venue: arXiv cs.IT 2010
Year: 2010

We consider the entropy of sums of independent discrete random variables, in analogy with Shannon's Entropy Power Inequality, where equality holds for normals. In our case, infinite divisibility suggests that equality should hold for Poisson variables. We show that some natural analogues of the Entropy Power Inequality do not in fact hold, but propose an alternative formulation which does always hold. The key to many proofs of Shannon's Entropy Power Inequality is the behaviour of entropy on scaling of continuous random variables. We believe that Rényi's operation of thinning discrete random variables plays a similar role to scaling, and give a sharp bound on how the entropy of ultra log-concave random variables behaves on thinning. In the spirit of the monotonicity results established by Artstein, Ball, Barthe and Naor, we prove a stronger version of concavity of entropy, which implies a strengthened form of our discrete Entropy Power Inequality.
Inferring Loop Invariants using Postconditions
Venue: arXiv cs.SE 2010
Year: 2010

One of the obstacles in automatic program proving is to obtain suitable loop invariants. The invariant of a loop is a weakened form of its postcondition (the loop's goal, also known as its contract); the present work takes advantage of this observation by using the postcondition as the basis for invariant inference, using various heuristics such as "uncoupling" which prove useful in many important algorithms. Thanks to these heuristics, the technique is able to infer invariants for a large variety of loop examples. We present the theory behind the technique, its implementation (freely available for download and currently relying on Microsoft Research's Boogie tool), and the results obtained.
Randomized Shellsort: A Simple Oblivious Sorting Algorithm
Venue: arXiv cs.DS 2010
Year: 2010

In this paper, we describe randomized Shellsort--a simple, randomized, data-oblivious version of the Shellsort algorithm that always runs in O(n log n) time and, as we show, succeeds in sorting any given input permutation with very high probability. Thus, randomized Shellsort is simultaneously simple, time-optimal, and data-oblivious. Taken together, these properties imply applications in the design of new efficient privacy-preserving computations based on the secure multi-party computation (SMC) paradigm. In addition, by a trivial conversion of this Monte Carlo algorithm to its Las Vegas equivalent, one gets the first version of Shellsort with a running time that is provably O(n log n) with very high probability.
Coordination Capacity
Venue: arXiv cs.IT 2010
Year: 2010

We develop elements of a theory of cooperation and coordination in networks. Rather than considering a communication network as a means of distributing information, or of reconstructing random processes at remote nodes, we ask what dependence can be established among the nodes given the communication constraints. Specifically, in a network with communication rates {R_{i,j}} between the nodes, we ask what is the set of all achievable joint distributions p(x1, ..., xm) of actions at the nodes of the network. Several networks are solved, including arbitrarily large cascade networks. Distributed cooperation can be the solution to many problems such as distributed games, distributed control, and establishing mutual information bounds on the influence of one part of a physical system on another.
On the communication complexity of XOR functions
Venue: arXiv cs.CC 2010
Year: 2010

An XOR function is a function of the form g(x,y) = f(x + y), for some boolean function f on n bits. We study the quantum and classical communication complexity of XOR functions. In the case of exact protocols, we completely characterise one-way communication complexity for all f. We also show that, when f is monotone, g's quantum and classical complexities are quadratically related, and that when f is a linear threshold function, g's quantum complexity is Theta(n). More generally, we make a structural conjecture about the Fourier spectra of boolean functions which, if true, would imply that the quantum and classical exact communication complexities of all XOR functions are asymptotically equivalent. We give two randomised classical protocols for general XOR functions which are efficient for certain functions, and a third protocol for linear threshold functions with high margin. These protocols operate in the symmetric message passing model with shared randomness.
Random scattering of bits by prediction
Venue: arXiv cs.AI 2010
Year: 2010

We investigate a population of binary mistake sequences that result from learning with parametric models of different order. We obtain estimates of their error, algorithmic complexity and divergence from a purely random Bernoulli sequence. We study the relationship of these variables to the learner's information density parameter which is defined as the ratio between the lengths of the compressed to uncompressed files that contain the learner's decision rule. The results indicate that good learners have a low information density$ρ$ while bad learners have a high $ρ$. Bad learners generate mistake sequences that are atypically complex or diverge stochastically from a purely random Bernoulli sequence. Good learners generate typically complex sequences with low divergence from Bernoulli sequences and they include mistake sequences generated by the Bayes optimal predictor. Based on the static algorithmic interference model of \cite{Ratsaby_entropy} the learner here acts as a static structure which "scatters" the bits of an input sequence (to be predicted) in proportion to its information density $ρ$ thereby deforming its randomness characteristics.
On Carpi and Alessandro conjecture
Venue: arXiv cs.FL 2010
Year: 2010

The well known open Černý conjecture states that each \san with $n$ states has a \sw of length at most $(n-1)^2$. On the other hand, the best known upper bound is cubic of $n$. Recently, in the paper \cite{CARPI1} of Alessandro and Carpi, the authors introduced the new notion of strongly transitivity for automata and conjectured that this property with a help of \emph{Extension} method allows to get a quadratic upper bound for the length of the shortest \sws. They also confirmed this conjecture for circular automata. We disprove this conjecture and the long-standing \emph{Extension} conjecture too. We also consider the widely used Extension method and its perspectives.