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The data of interest are assumed to be represented as N-dimensional real vectors, and these vectors are compressible in some linear basis B, implying that the signal can be reconstructed accurately using only a small number M ≪ N of basis-function coefficients associated with B. Compressive sensing is a framework whereby one does not measure one of the aforementioned N-dimensional signals directly, but rather a set of related measurements, with the new measurements a linear combination of the original underlying N-dimensional signal. The number of required compressive-sensing measurements is typically much smaller than N, offering the potential to simplify the sensing system. Let f denote the unknown underlying N-dimensional signal, and g a vector of compressive-sensing measurements, then one may approximate f accurately by utilizing knowledge of the (under-determined) linear relationship between f and g, in addition to knowledge of the fact that f is compressible in B. In this paper we employ a Bayesian formalism for estimating the underlying signal f based on compressive-sensing measurements g. The proposed framework has the following properties: (i) in addition to estimating the underlying signal f, “error bars ” are also estimated, these giving a measure of confidence in the inverted signal; (ii) using knowledge of the error bars, a principled means is provided for determining when a sufficient

. This paper discusses the mathematical formulation of and solution attempts for the so-called protein folding problem. The static aspect is concerned with how to predict the folded (native, tertiary) structure of a protein, given its sequence of amino acids. The dynamic aspect asks about the possible pathways to folding and unfolding, including the stability of the folded protein. From a mathematical point of view, there are several main sides to the static problem: -- the selection of an appropriate potential energy function; -- the parameter identification by fitting to experimental data; and -- the global optimization of the potential. The dynamic problem entails, in addition, the solution of (because of multiple time scales very stiff) ordinary or stochastic differential equations (molecular dynamics simulation), or (in case of constrained molecular dynamics) of differential-algebraic equations. A theme connecting the static and dynamic aspect is the determination and formation of...

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Abstract—This paper presents a methodology for optimal allocation of sensors in a multistation assembly process for the purpose of diagnosing in a timely manner variation sources that are responsible for product quality defects. A sensor system distributed in such a way can help manufacturers improve product quality while, at the same time, reducing process downtime. Traditional approaches in sensor optimization fall into two categories: multistation sensor allocation for the purpose of product inspection (rather than diagnosis); and allocation of sensors for the purpose of variation diagnosis but at a single measurement station. In our approach, sensing information from different measurement stations is integrated into a state-space model and the effectiveness of a distributed sensor system is quantified by a diagnosability index. This index is further studied in terms of variation transmissibility between stations as well as variation detectability at individual stations. Based on an understanding of the mechanism of variation propagation, we develop a backward-propagation strategy to determine the locations of measurement stations and the minimum number of sensors needed to achieve full diagnosability. An assembly example illustrates the methodology. Index Terms—Diagnosability, diagnosis of variation sources, multistation assembly process, sensor distribution.

Active-Sampling-at-the-Boundary method is applied using orthogonal decision support vectors to facilitate pattern classification in identifying optimal decision boundary for a stochastic oracle. The result of the active sampling near the boundary using these vectors is shown in comparison with Active Learning using random selection in the multi-dimensional decision hyperplane. This shows the optimality of boundary active sampling using decision support vectors in the case of non-separable linear decision hyperplanes in multi-dimensional space.

We present a new approach for site survey by autonomous surface robots. In our method the agent constructs an intelligent map, a multi-scale model of the explored environment incorporating in situ and remote sensing data. The agent learns the model’s parameters on the fly and exploits its predictions to guide adaptive navigation and sampling. In this manner the agent can respond appropriately to novel correlations, resource constraints and execution errors. Rover tests at Amboy Crater, California demonstrate improved performance over non-adaptive strategies for a geologic survey task.

Abstract—This paper investigates the advantages of adaptive waveform amplitude design for estimating parameters of an unknown channel/medium under average energy constraints. We present a statistical framework for sequential design (e.g., design of waveforms in adaptive sensing) of experiments that improves parameter estimation (e.g., unknown channel parameters) performance in terms of reduction in mean-squared error (MSE). We treat an time step design problem for a linear Gaussian model where the shape of the input design vectors (one per time step) remains constant and their amplitudes are chosen as a function of past measurements to minimize MSE. For aP, we derive the optimal energy allocation at the second step as a function of the first measurement. Our adaptive two-step strategy yields an MSE improvement of at least 1.65 dB relative to the optimal nonadaptive strategy, but is not implementable since it requires knowledge of the noise amplitude. We then present an implementable design for the two-step strategy which asymptotically achieves optimal performance. Motivated by the optimal two-step strategy, we propose a suboptimal adaptive-step energy allocation strategy that can achieve an MSE improvement of more than 5 dB for aSH. We demonstrate our general approach in the context of MIMO channel estimation and inverse scattering problems. Index Terms—Channel estimation, energy management, inverse scattering, maximum likelihood, parameter estimation, sequential design. I.

Abstract — We recast the problem of unconstrained continuous evolutionary optimization as inference in a fixed graphical model. This approach allows us to address several pervasive issues in optimization, including the traditionally difficult problem of selecting an algorithm that is most appropriate for a given task. This is accomplished by placing a prior distribution over the expected class of functions, then employing inference and intuitively defined utilities and costs to transform the evolutionary optimization problem into one of active sampling. This allows us to pose an approach to optimization that is optimal for each expressly stated function class. The resulting solution methodology can optimally navigate exploration-exploitation tradeoffs using well-motivated decision theory, while providing the process with a natural stopping criterion. Finally, the model naturally accommodates the expression of dynamic and noisy functions, setting it apart from most existing algorithms that address these issues as an afterthought. We demonstrate the characteristics and advantages of this algorithm formally and with examples. I.

The kernel matching pursuit (KMP) algorithm is re-formulated in the framework of the theory of optimal experiments, using a weighted sum of squared errors as the loss function, and it is extended to the case of M-ary target classification and kernel optimization. The M-ary KMP classifier is applied to multiaspect classification of moving targets based on high-range resolution (HRR) radar signatures, for which the target-sensor orientations are assumed approximately known. A multi-aspect processing method is presented based on the use of the estimates of target-sensor orientation angles. The KMP classification results for ten MSTAR targets are presented, with a comparison to corresponding results using the relevance vector machine (RVM).