Proper motions of ROSAT discovered isolated neutron stars measured with Chandra: First X-ray measurement of the large proper motion of RX J1308.6+2127/RBS 1223

The unprecedented spatial resolution of the Chandra observatory opens the possibility to detect with relatively high accuracy proper motions at X-ray wavelengths. We have conducted an astrometric study of three of the "Magnificent Seven", the thermally emitting radio quiet isolated neutron stars (INSs) discovered by ROSAT. These three INSs (RX J0420.0-5022, RX J0806.4-4123 and RX J1308.6+2127/RBS 1223) either lack an optical counterpart or have one too faint to be used for astrometric purposes. We obtained ACIS observations 3 to 5 years apart to constrain or measure the displacement of the sources on the X-ray sky using as reference the background of extragalactic or remote galactic X-ray sources. Upper limits of 138 mas/yr and 76 mas/yr on the proper motion of RX J0420.0-5022 and RX J0806.4-4123, respectively, have already been presented in Motch et al. (2007). Here we report the very significant measurement (~ 10 sigma) of the proper motion of the third INS of our program, RX J1308.6+2127/RBS1223. Comparing observations obtained in 2002 and 2007 reveals a displacement of 1.1 arcsec implying a yearly proper motion of 223 mas, the second fastest measured for the ROSAT discovered INSs. The source is rapidly moving away from the galactic plane at a speed which precludes any significant accretion of matter from the interstellar medium. Its transverse velocity of ~ 740 (d/700pc) km/s might be the largest of the "Magnificent Seven" and among the fastest recorded for neutron stars. RX J1308.6+2127/RBS1223 is thus a young high velocity cooling neutron star. The source may have its origin in the closest part of the Scutum OB2 association about 0.8 Myr ago, an age consistent with that expected from cooling curves, but significantly younger than inferred from pulse timing measurements (1.5 Myr).Comment: 3 pages, 2 figures, proceedings of the conference "40 Years of Pulsars", 12-17 August 2007, Montreal, Canad

Multi-stage Antenna Selection for Adaptive Beamforming in MIMO Arrays

Increasing the number of transmit and receive elements in multiple-input-multiple-output (MIMO) antenna arrays imposes a substantial increase in hardware and computational costs. We mitigate this problem by employing a reconfigurable MIMO array where large transmit and receive arrays are multiplexed in a smaller set of k baseband signals. We consider four stages for the MIMO array configuration and propose four different selection strategies to offer dimensionality reduction in post-processing and achieve hardware cost reduction in digital signal processing (DSP) and radio-frequency (RF) stages. We define the problem as a determinant maximization and develop a unified formulation to decouple the joint problem and select antennas/elements in various stages in one integrated problem. We then analyze the performance of the proposed selection approaches and prove that, in terms of the output SINR, a joint transmit-receive selection method performs best followed by matched-filter, hybrid and factored selection methods. The theoretical results are validated numerically, demonstrating that all methods allow an excellent trade-off between performance and cost.Comment: Submitted for publicatio

A Tractable Fault Detection and Isolation Approach for Nonlinear Systems with Probabilistic Performance

This article presents a novel perspective along with a scalable methodology to design a fault detection and isolation (FDI) filter for high dimensional nonlinear systems. Previous approaches on FDI problems are either confined to linear systems or they are only applicable to low dimensional dynamics with specific structures. In contrast, shifting attention from the system dynamics to the disturbance inputs, we propose a relaxed design perspective to train a linear residual generator given some statistical information about the disturbance patterns. That is, we propose an optimization-based approach to robustify the filter with respect to finitely many signatures of the nonlinearity. We then invoke recent results in randomized optimization to provide theoretical guarantees for the performance of the proposed filer. Finally, motivated by a cyber-physical attack emanating from the vulnerabilities introduced by the interaction between IT infrastructure and power system, we deploy the developed theoretical results to detect such an intrusion before the functionality of the power system is disrupted

Improved Generalization Bounds for Robust Learning

We consider a model of robust learning in an adversarial environment. The learner gets uncorrupted training data with access to possible corruptions that may be affected by the adversary during testing. The learner's goal is to build a robust classifier that would be tested on future adversarial examples. We use a zero-sum game between the learner and the adversary as our game theoretic framework. The adversary is limited to $k$ possible corruptions for each input. Our model is closely related to the adversarial examples model of Schmidt et al. (2018); Madry et al. (2017). Our main results consist of generalization bounds for the binary and multi-class classification, as well as the real-valued case (regression). For the binary classification setting, we both tighten the generalization bound of Feige, Mansour, and Schapire (2015), and also are able to handle an infinite hypothesis class $H$. The sample complexity is improved from $O(\frac{1}{\epsilon^4}\log(\frac{|H|}{\delta}))$ to $O(\frac{1}{\epsilon^2}(k\log(k)VC(H)+\log\frac{1}{\delta}))$. Additionally, we extend the algorithm and generalization bound from the binary to the multiclass and real-valued cases. Along the way, we obtain results on fat-shattering dimension and Rademacher complexity of $k$-fold maxima over function classes; these may be of independent interest. For binary classification, the algorithm of Feige et al. (2015) uses a regret minimization algorithm and an ERM oracle as a blackbox; we adapt it for the multi-class and regression settings. The algorithm provides us with near-optimal policies for the players on a given training sample.Comment: Appearing at the 30th International Conference on Algorithmic Learning Theory (ALT 2019