This paper presents an analysis of target localization accuracy, attainable by the use of multiple-input multiple-output (MIMO) radar systems, configured with multiple transmit and receive sensors, widely distributed over an area. The Cramer-Rao lower bound (CRLB) for target localization accuracy is developed for both coherent and noncoherent processing. Coherent processing requires a common phase reference for all transmit and receive sensors. The CRLB is shown to be inversely proportional to the signal effective bandwidth in the noncoherent case, but is approximately inversely proportional to the carrier frequency in the coherent case. We further prove that optimization over the sensors' positions lowers the CRLB by a factor equal to the product of the number of transmitting and receiving sensors. The best linear unbiased estimator (BLUE) is derived for the MIMO target localization problem. The BLUE's utility is in providing a closed-form localization estimate that facilitates the analysis of the relations between sensors locations, target location, and localization accuracy. Geometric dilution of precision (GDOP) contours are used to map the relative performance accuracy for a given layout of radars over a given geographic area.

Target Localization Accuracy Gain in MIMO Radar-Based Systems

Quantifying coherence is an essential endeavour for both quantum foundations and quantum technologies. Here the robustness of coherence is defined and proven a full monotone in the context of the recently introduced resource theories of quantum coherence. The measure is shown to be observable, as it can be recast as the expectation value of a coherence witness operator for any quantum state. The robustness of coherence is evaluated analytically on relevant classes of states, and an efficient semidefinite program that computes it on general states is given. An operational interpretation is finally provided: the robustness of coherence quantifies the advantage enabled by a quantum state in a phase discrimination task.

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Robustness of Coherence: An Operational and Observable Measure of Quantum Coherence.

In this paper, we study the link between a Chance-Constrained optimization Problem (CCP) and its sample counterpart (SP). SP has a finite number, say N, of sampled constraints. Further, some of these sampled constraints, say k, are discarded, and the final solution is indicated by $x^{\ast}_{N,k}$
 . Extending previous results on the feasibility of sample convex optimization programs, we establish the feasibility of $x^{\ast}_{N,k}$
 for the initial CCP problem. Constraints removal allows one to improve the cost function at the price of a decreased feasibility. The cost improvement can be inspected directly from the optimization result, while the theory here developed permits to keep control on the other side of the coin, the feasibility of the obtained solution. In this way, trading feasibility for performance is put on solid mathematical grounds in this paper. The feasibility result here obtained applies to a vast class of chance-constrained optimization problems, and has the distinctive feature that it holds true irrespective of the algorithm used to discard k constraints in the SP problem. For constraints discarding, one can thus, e.g., resort to one of the many methods introduced in the literature to solve chance-constrained problems with discrete distribution, or even use a greedy algorithm, which is computationally very low-demanding, and the feasibility result remains intact. We further prove that, if constraints in the SP problem are optimally removed—i.e., one deletes those constraints leading to the largest possible cost improvement—, then a precise optimality link to the original chance-constrained problem CCP in addition holds.

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A Sampling-and-Discarding Approach to Chance-Constrained Optimization: Feasibility and Optimality

Motivation: Classification and feature selection of genomics or transcriptomics data is often hampered by the large number of features as compared with the small number of samples available. Moreover, features represented by probes that either have similar molecular functions (gene expression analysis) or genomic locations (DNA copy number analysis) are highly correlated. Classical model selection methods such as penalized logistic regression or random forest become unstable in the presence of high feature correlations. Sophisticated penalties such as group Lasso or fused Lasso can force the models to assign similar weights to correlated features and thus improve model stability and interpretability. In this article, we show that the measures of feature relevance corresponding to the above-mentioned methods are biased such that the weights of the features belonging to groups of correlated features decrease as the sizes of the groups increase, which leads to incorrect model interpretation and misleading feature ranking.

Results: With simulation experiments, we demonstrate that Lasso logistic regression, fused support vector machine, group Lasso and random forest models suffer from correlation bias. Using simulations, we show that two related methods for group selection based on feature clustering can be used for correcting the correlation bias. These techniques also improve the stability and the accuracy of the baseline models. We apply all methods investigated to a breast cancer and a bladder cancer arrayCGH dataset and in order to identify copy number aberrations predictive of tumor phenotype.

Availability: R code can be found at: http://www.mpi-inf.mpg.de/~laura/Clustering.r.

Contact: laura.tolosi@mpi-inf.mpg.de

Supplementary information:Supplementary data are available at Bioinformatics online.

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Classification with correlated features

Quantum steering refers to the non-classical correlations that can be observed between the outcomes of measurements applied on half of an entangled state and the resulting post-measured states that are left with the other party. From an operational point of view, a steering test can be seen as an entanglement test where one of the parties performs uncharacterised measurements. Thus, quantum steering is a form of quantum inseparability that lies in between the well-known notions of Bell nonlocality and entanglement. Moreover, quantum steering is also related to several asymmetric quantum information protocols where some of the parties are considered untrusted. Because of these facts, quantum steering has received a lot of attention both theoretically and experimentally. The main goal of this review is to give an overview of how to characterise quantum steering through semidefinite programming. This characterisation provides efficient numerical methods to address a number of problems, including steering detection, quantification, and applications. We also give a brief overview of some important results that are not directly related to semidefinite programming. Finally, we make available a collection of semidefinite programming codes that can be used to study the topics discussed in this article.

/pdf/quantum-steering-a-review-with-focus-on-semidefinite-2jqjk2a1dw.pdf

Quantum steering: A review with focus on semidefinite programming

Statistical Learning Theory: A Pack-based Strategy for Uncertain Feasibility and Optimization Problems.- UAV Formation Control: Theory and Application.- Electrical and Mechanical Passive Network Synthesis.- Output Synchronization of Nonlinear Systems with Relative Degree One.- On the Computation of Optimal Transport Maps Using Gradient Flows and Multiresolution Analysis.- Realistic Anchor Positioning for Sensor Localization.- Graph Implementations for Nonsmooth Convex Programs.- When Is a Linear Continuous-time System Easy or Hard to Control in Practice?.- Metrics and Morphing of Power Spectra.- A New Type of Neural Computation.- Getting Mobile Autonomous Robots to Form a Prescribed Geometric Arrangement.- Convex Optimization in Infinite Dimensional Spaces.- The Servomechanism Problem for SISO Positive LTI Systems.- Passivity-based Stability of Interconnection Structures.- Identification of Linear Continuous-time Systems Based on Iterative Learning Control.- A Pontryagin Maximum Principle for Systems of Flows.- Safe Operation and Control of Diesel Particulate Filters Using Level Set Methods.- Robust Control of Smart Material-based Actuators.- Behaviors Described by Rational Symbols and the Parametrization of the Stabilizing Controllers.

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Hidenori Kimura

Papers

Recent Advances in Learning and Control