We consider the problem of spatiotemporal sampling in which an initial state of an evolution process is to be recovered from a set of samples at different time levels. We are particularly interested in lossless trade-...
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We consider the problem of spatiotemporal sampling in which an initial state of an evolution process is to be recovered from a set of samples at different time levels. We are particularly interested in lossless trade-off between spatial and temporal samples. We show. that for a special class of signals it is possible to recover the initial state using a reduced number of measuring devices activated more frequently. We present several algorithms for this kind of recovery and describe their robustness to noise. (C) 2012 Elsevier Inc. All rights reserved.
In this paper, we study the problem of dynamical sampling in multiply generated shift-invariant spaces. We give a necessary and sufficient condition for stable reconstruction of signals in multiply generated shiftinva...
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In this paper, we study the problem of dynamical sampling in multiply generated shift-invariant spaces. We give a necessary and sufficient condition for stable reconstruction of signals in multiply generated shiftinvariant spaces. Moreover, we show the condition which can make the dynamic sampling problem in multiply generated shift-invariant spaces into the dynamic sampling problem in l2(Z). At last, we give a concrete example to show how to transform the dynamic sampling problem in shiftinvariant space into the dynamic sampling problem in l2(Z). Our results generalize similar ones for the principal shift-invariant spaces.
We consider the problem of spatiotemporal sampling in a discrete infinite dimensional spatially invariant evolutionary process x ((n)) = A (n) x to recover an unknown convolution operator A given by a filter and an un...
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We consider the problem of spatiotemporal sampling in a discrete infinite dimensional spatially invariant evolutionary process x ((n)) = A (n) x to recover an unknown convolution operator A given by a filter and an unknown initial state x modeled as a vector in . Traditionally, under appropriate hypotheses, any x can be recovered from its samples on and A can be recovered by the classical techniques of deconvolution. In this paper, we will exploit the spatiotemporal correlation and propose a new sampling scheme to recover A and x that allows us to sample the evolving states x,A x,ai ,A (N-1) x on a sub-lattice of , and thus achieve a spatiotemporal trade off. The spatiotemporal trade off is motivated by several industrial applications (Lu and Vetterli, 2249-2252, 2009). Specifically, we show that contains enough information to recover a typical "low pass filter" a and x almost surely, thus generalizing the idea of the finite dimensional case in Aldroubi and Krishtal, arXiv:1412.1538"http://***/abs/1412.1538" TargetType="URL" (2014). In particular, we provide an algorithm based on a generalized Prony method for the case when both a and x are of finite impulse response and an upper bound of their support is known. We also perform a perturbation analysis based on the spectral properties of the operator A and initial state x, and verify the results by several numerical experiments. Finally, we provide several other numerical techniques to stabilize the proposed method, with some examples to demonstrate the improvement.
We consider the problem of spatiotemporal sampling in which an initial state of an evolution process is to be recovered from a combined set of coarse spatial samples from varying time levels . This new way of sampling...
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We consider the problem of spatiotemporal sampling in which an initial state of an evolution process is to be recovered from a combined set of coarse spatial samples from varying time levels . This new way of sampling, which we call dynamical sampling, differs from standard sampling since at any fixed time there are not enough samples to recover the function or the state . Although dynamical sampling is an inverse problem, it differs from the typical inverse problems in which is to be recovered from for a single time . In this paper, we consider signals that are modeled by or a shift invariant space , and are evolving under the action of a spatial convolution operator , so that . We provide sufficient conditions for the spatiotemporal sampling problem to be solvable. In special cases, we provide error analysis based on the spectral properties of the operator A.
We address the issue of measuring distribution fairness in Internet-scale networks. This problem has several interesting instances encountered in different applications, ranging from assessing the distribution of load...
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We address the issue of measuring distribution fairness in Internet-scale networks. This problem has several interesting instances encountered in different applications, ranging from assessing the distribution of load between network nodes for load balancing purposes, to measuring node utilization for optimal resource exploitation, and to guiding autonomous decisions of nodes in networks built with market-based economic principles. Although some metrics have been proposed, particularly for assessing load balancing algorithms, they fall short. We first study the appropriateness of various known and previously proposed statistical metrics for measuring distribution fairness. We put forward a number of required characteristics for appropriate metrics. We propose and comparatively study the appropriateness of the Gini coefficient (G) for this task. Our study reveals as most appropriate the metrics of G, the fairness index (FI), and the coefficient of variation (CV) in this order. Second, we develop six distributed sampling algorithms to estimate metrics online efficiently, accurately, and scalably. One of these algorithms (2-PRWS) is based on two effective optimizations of a basic algorithm, and the other two (the sequential sampling algorithm, LBS-HL, and the clustered sampling one, EBSS) are novel, developed especially to estimate G. Third, we show how these metrics, and especially G, can be readily utilized online by higher-level algorithms, which can now know when to best intervene to correct unfair distributions (in particular, load imbalances). We conclude with a comprehensive experimentation which comparatively evaluates both the various proposed estimation algorithms and the three most appropriate metrics (G, CV, and FI). Specifically, the evaluation quantifies the efficiency (in terms of number of the messages and a latency indicator), precision, and accuracy achieved by the proposed algorithms when estimating the competing fairness metrics. The central conclus
To maintain the accuracy of supervised learning models in the presence of evolving data streams, we provide temporally biased sampling schemes that weight recent data most heavily, with inclusion probabilities for a g...
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To maintain the accuracy of supervised learning models in the presence of evolving data streams, we provide temporally biased sampling schemes that weight recent data most heavily, with inclusion probabilities for a given data item decaying over time according to a specified "decay function." We then periodically retrain the models on the current sample. This approach speeds up the training process relative to training on all of the data. Moreover, time-biasing lets the models adapt to recent changes in the data while-unlike in a sliding-window approach-still keeping some old data to ensure robustness in the face of temporary fluctuations and periodicities in the data values. In addition, the sampling-based approach allows existing analytic algorithms for static data to be applied to dynamic streaming data essentially without change. We provide and analyze both a simple sampling scheme (Targeted-Size Time-Biased sampling (T-TBS)) that probabilistically maintains a target sample size and a novel reservoir-based scheme (Reservoir-Based Time-Biased sampling (R-TBS)) that is the first to provide both control over the decay rate and a guaranteed upper bound on the sample size. If the decay function is exponential. then control over the decay rate is complete, and R-TBS maximizes both expected sample size and sample-size stability. For general decay functions, the actual item inclusion probabilities can be made arbitrarily close to the nominal probabilities, and we provide a scheme that allows a tradeoff between sample footprint and sample-size stability. R-TBS rests on the notion of a "fractional sample" and allows for data arrival rates that are unknown and time varying (unlike T-TBS). The R-TBS and T-TBS schemes are of independent interest, extending the known set of unequal-probability sampling schemes. We discuss distributed implementation strategies;experiments in Spark illuminate the performance and scalability of the algorithms, and show that our approach can incr
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