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A guide to stochastic Löwner evolution and its applications
 J. Statist. Phys
"... This article is meant to serve as a guide to recent developments in the study of the scaling limit of critical models. These new developments were made possible through the definition of the Stochastic Löwner Evolution (SLE) by Oded Schramm. This article opens with a discussion of Löwner’s method, e ..."
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This article is meant to serve as a guide to recent developments in the study of the scaling limit of critical models. These new developments were made possible through the definition of the Stochastic Löwner Evolution (SLE) by Oded Schramm. This article opens with a discussion of Löwner’s method, explaining how this method can be used to describe families of random curves. Then we define SLE and discuss some of its properties. We also explain how the connection can be made between SLE and the discrete models whose scaling limits it describes, or is believed to describe. Finally, we have included a discussion of results that were obtained from SLE computations. Some explicit proofs are presented as typical examples of such computations. To understand SLE sufficient knowledge of conformal mapping theory and stochastic calculus is required. This material is covered in the appendices. Key words: scaling limits, critical exponents, conformal invariance, conformal mappings, stochastic processes, Löwner’s equation. 1 1
Aggregate Queries for Discrete and Continuous Probabilistic XML
, 2010
"... Sources of data uncertainty and imprecision are numerous. A way to handle this uncertainty is to associate probabilistic annotations to data. Many such probabilistic database models have been proposed, both in the relational and in the semistructured setting. The latter is particularly well adapted ..."
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Cited by 21 (18 self)
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Sources of data uncertainty and imprecision are numerous. A way to handle this uncertainty is to associate probabilistic annotations to data. Many such probabilistic database models have been proposed, both in the relational and in the semistructured setting. The latter is particularly well adapted to the management of uncertain data coming from a variety of automatic processes. An important problem, in the context of probabilistic XML databases, is that of answering aggregate queries (count, sum, avg, etc.), which has received limited attention so far. In a model unifying the various (discrete) semistructured probabilistic models studied up to now, we present algorithms to compute the distribution of the aggregation values (exploiting some regularity properties of the aggregate functions) and probabilistic moments (especially, expectation and variance) of this distribution. We also prove the intractability of some of these problems and investigate approximation techniques. We finally extend the discrete model to a continuous one, in order to take into account continuous data values, such as measurements from sensor networks, and present algorithms to compute distribution functions and moments for various classes of continuous distributions of data values.
Learning from dependent observations
, 2006
"... In most papers establishing consistency for learning algorithms it is assumed that the observations used for training are realizations of an i.i.d. process. In this paper we go far beyond this classical framework by showing that support vector machines (SVMs) essentially only require that the datag ..."
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Cited by 19 (3 self)
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In most papers establishing consistency for learning algorithms it is assumed that the observations used for training are realizations of an i.i.d. process. In this paper we go far beyond this classical framework by showing that support vector machines (SVMs) essentially only require that the datagenerating process satisfies a certain law of large numbers. We then consider the learnability of SVMs for αmixing (not necessarily stationary) processes for both classification and regression, where for the latter we explicitly allow unbounded noise. Keywords: Support vector machine, Consistency, Nonstationary mixing process, Classification, Regression
Beyond random walk and metropolishastings samplers: Why you should not backtrack for unbiased graph sampling
, 2012
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Statistical Modeling of DiscreteTime Chaotic
 Processes  Advanced FiniteDimensional Tools and Applications,”, PROCEEDING OF THE IEEE
"... The application of chaotic dynamics to signal processing tasks stems from the realization that its complex behaviors become tractable when observed from a statistical perspective. Here we illustrate the validity of this statement by considering two noteworthy problems—namely, the synthesis of highe ..."
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Cited by 11 (3 self)
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The application of chaotic dynamics to signal processing tasks stems from the realization that its complex behaviors become tractable when observed from a statistical perspective. Here we illustrate the validity of this statement by considering two noteworthy problems—namely, the synthesis of highelectromagnetic compatibility clock signals and the generation of spreading sequences for directsequence codedivision comunication systems, and by showing how the statistical approach to discretetime chaotic systems can be applied to find their optimal solution. To this aim, we first review the basic mathematical tools both intuitively and formally; we consider the Perron–Frobenius operator, its spectral decomposition and its tie to the correlation properties of chaotic sequences. Then, by leveraging on the modeling/approximation of chaotic systems through Markov chains, we introduce a matrix/tensorbased framework where statistical indicators such as highorder correlations can be quantified. We underline how, for many particular cases, the proposed analysis tools can be reversed into synthesis methodologies and we use them to tackle the two above mentioned problems. In both cases, experimental evidence shows that the availability of statistical tools enables the design of chaosbased systems which favorably compare with analogous nonchaosbased counterparts. Keywords—Chaosbased CDMA, chaosbased EMC, chaotic systems, correlations, Markov processes, quantized processes,
Mobility increases the connectivity of Khop clustered wireless networks
 in ACM MobiCom
, 2009
"... In this paper we investigate the connectivity for largescale clustered wireless sensor and ad hoc networks. We study the effect of mobility on the critical transmission range for asymptotic connectivity in khop clustered networks, and compare to existing results on nonclustered stationary networ ..."
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Cited by 11 (2 self)
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In this paper we investigate the connectivity for largescale clustered wireless sensor and ad hoc networks. We study the effect of mobility on the critical transmission range for asymptotic connectivity in khop clustered networks, and compare to existing results on nonclustered stationary networks. By introducing khop clustering, any packet from a cluster member can reach a cluster head within k hops, and thus the transmission delay is bounded as Θ(1) for any finite k. We first characterize the critical transmission range for connectivity in mobile khop clustered networks where all nodes move under either the random walk mobility model with nontrivial velocity or the i.i.d. mobility model. By the term nontrivial velocity, we mean that the velocity of nodes v is Θ(1). We then compare with the critical transmission range for stationary khop clustered networks. We also study the transmission power versus delay tradeoff and the average energy consumption per flow among different types of networks. We show that random walk mobility with nontrivial velocity increases connectivity in khop clustered networks, and thus significantly decreases the energy consumption and improves the powerdelay tradeoff. The decrease of energy consumption per flow is shown to be Θ logn nd in clustered networks. These results provide insights on network design and fundamental guidelines on building a largescale wireless network.
Activized Learning: Transforming Passive to Active with Improved Label Complexity
"... Active learning methods often achieve improved performance using fewer labels compared to passive learning methods. A variety of practically successful active learning algorithms use a passive learning algorithm as a subroutine, and the essential role of the active component is to construct data set ..."
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Cited by 11 (4 self)
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Active learning methods often achieve improved performance using fewer labels compared to passive learning methods. A variety of practically successful active learning algorithms use a passive learning algorithm as a subroutine, and the essential role of the active component is to construct data sets to feed into the passive subroutine. This general idea is appealing for a variety of reasons, as it may be able
S.: Uniformity by construction in the analysis of nondeterministic stochastic systems
 In: Proceedings of the 37th Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN
, 2007
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