A Multichannel Spatial Compressed Sensing Approach for Direction of Arrival Estimation

The final publication is available at http://link.springer.com/chapter/10.1007%2F978-3-642-15995-4_57ESPRC Leadership Fellowship EP/G007144/1EPSRC Platform Grant EP/045235/1EU FET-Open Project FP7-ICT-225913\"SMALL

Federal Forum Provisions and the Internal Affairs Doctrine

A key question at the intersection of state and federal law is whether corporations can use their charters or bylaws to restrict securities litigation to federal court. In December 2018, the Delaware Chancery Court answered this question in the negative in the landmark decision Sciabacucchi v. Salzberg. The court invalidated “federal forum provisions” (“FFPs”) that allow companies to select federal district courts as the exclusive venue for claims brought under the Securities Act of 1933 (“1933 Act”). The decision held that the internal affairs doctrine, which is the bedrock of U.S. corporate law, does not permit charter and bylaw provisions that restrict rights under federal law. In March 2020, the Delaware Supreme Court overturned the Chancery’s decision in Salzberg v. Sciabacucchi, holding, among others, that in addition to “internal” affairs, charters and bylaws can regulate “intra-corporate” affairs, including choosing the forum for Securities Act claims. This Article presents the first empirical analysis of federal forum provisions. Using a hand-collected data set, we examine the patterns of adoption of such provisions and the characteristics of adopting firms. We show that adoption rates are higher for firms with characteristics, such as belonging to a particular industry, that make them more vulnerable to claims under the 1933 Act. We also show that adoption rates substantially increased after the Supreme Court case Cyan Inc. v. Beaver County Employees Retirement Fund, which validated concurrent jurisdiction for both federal and state courts for 1933 Act claims. We also find that the firms that adopt FFPs at the initial public offering (“IPO”) stage tend to share characteristics that have been associated with relatively good corporate governance. To assess the impact of the Sciabacucchi decision, we also conduct an event study. We find that the decision is associated with a large negative stock price effect for companies that had FFPs in their charters or bylaws. The effect is robust even for firms that had better governance features, that underpriced their stock at the IPOs, and whose stock price traded at or above the IPO price prior to the Sciabacucchi decision. In light of the empirical findings suggesting that federal forum provisions may serve shareholders’ interests by mitigating excessive 1933 Act litigation, we consider alternative legal theories for validating federal forum provisions in corporate charters and bylaws. We suggest two possible approaches: (1) allowing corporate charters and bylaws to address matters that are technically external but deal with the “affairs” of the corporation; and (2) adopting a more “flexible” internal affairs doctrine that could view 1933 Act claims as being “internal” to a corporation’s affairs. The Delaware Supreme Court’s decision can be viewed as being more consistent with the first, rather than the second, approach. We examine the possible implications of adopting either approach, particularly with respect to the existing Delaware statute on exclusive forum provisions and to mandatory arbitration provisions

Quantum Detection with Unknown States

We address the problem of distinguishing among a finite collection of quantum states, when the states are not entirely known. For completely specified states, necessary and sufficient conditions on a quantum measurement minimizing the probability of a detection error have been derived. In this work, we assume that each of the states in our collection is a mixture of a known state and an unknown state. We investigate two criteria for optimality. The first is minimization of the worst-case probability of a detection error. For the second we assume a probability distribution on the unknown states, and minimize of the expected probability of a detection error. We find that under both criteria, the optimal detectors are equivalent to the optimal detectors of an ``effective ensemble''. In the worst-case, the effective ensemble is comprised of the known states with altered prior probabilities, and in the average case it is made up of altered states with the original prior probabilities.Comment: Refereed version. Improved numerical examples and figures. A few typos fixe

On the distinguishability of random quantum states

We develop two analytic lower bounds on the probability of success p of identifying a state picked from a known ensemble of pure states: a bound based on the pairwise inner products of the states, and a bound based on the eigenvalues of their Gram matrix. We use the latter to lower bound the asymptotic distinguishability of ensembles of n random quantum states in d dimensions, where n/d approaches a constant. In particular, for almost all ensembles of n states in n dimensions, p>0.72. An application to distinguishing Boolean functions (the "oracle identification problem") in quantum computation is given.Comment: 20 pages, 2 figures; v2 fixes typos and an error in an appendi

Finding the center reliably: robust patterns of developmental gene expression

We investigate a mechanism for the robust identification of the center of a developing biological system. We assume the existence of two morphogen gradients, an activator emanating from the anterior, and a co-repressor from the posterior. The co-repressor inhibits the action of the activator in switching on target genes. We apply this system to Drosophila embryos, where we predict the existence of a hitherto undetected posterior co-repressor. Using mathematical modelling, we show that a symmetric activator-co-repressor model can quantitatively explain the precise mid-embryo expression boundary of the hunchback gene, and the scaling of this pattern with embryo size.Comment: 4 pages, 3 figure

UVeQFed: Universal Vector Quantization for Federated Learning

Traditional deep learning models are trained at a centralized server using labeled data samples collected from end devices or users. Such data samples often include private information, which the users may not be willing to share. Federated learning (FL) is an emerging approach to train such learning models without requiring the users to share their possibly private labeled data. In FL, each user trains its copy of the learning model locally. The server then collects the individual updates and aggregates them into a global model. A major challenge that arises in this method is the need of each user to efficiently transmit its learned model over the throughput limited uplink channel. In this work, we tackle this challenge using tools from quantization theory. In particular, we identify the unique characteristics associated with conveying trained models over rate-constrained channels, and propose a suitable quantization scheme for such settings, referred to as universal vector quantization for FL (UVeQFed). We show that combining universal vector quantization methods with FL yields a decentralized training system in which the compression of the trained models induces only a minimum distortion. We then theoretically analyze the distortion, showing that it vanishes as the number of users grows. We also characterize the convergence of models trained with the traditional federated averaging method combined with UVeQFed to the model which minimizes the loss function. Our numerical results demonstrate the gains of UVeQFed over previously proposed methods in terms of both distortion induced in quantization and accuracy of the resulting aggregated model

Graph Signal Restoration Using Nested Deep Algorithm Unrolling

Graph signal processing is a ubiquitous task in many applications such as sensor, social, transportation and brain networks, point cloud processing, and graph neural networks. Graph signals are often corrupted through sensing processes, and need to be restored for the above applications. In this paper, we propose two graph signal restoration methods based on deep algorithm unrolling (DAU). First, we present a graph signal denoiser by unrolling iterations of the alternating direction method of multiplier (ADMM). We then propose a general restoration method for linear degradation by unrolling iterations of Plug-and-Play ADMM (PnP-ADMM). In the second method, the unrolled ADMM-based denoiser is incorporated as a submodule. Therefore, our restoration method has a nested DAU structure. Thanks to DAU, parameters in the proposed denoising/restoration methods are trainable in an end-to-end manner. Since the proposed restoration methods are based on iterations of a (convex) optimization algorithm, the method is interpretable and keeps the number of parameters small because we only need to tune graph-independent regularization parameters. We solve two main problems in existing graph signal restoration methods: 1) limited performance of convex optimization algorithms due to fixed parameters which are often determined manually. 2) large number of parameters of graph neural networks that result in difficulty of training. Several experiments for graph signal denoising and interpolation are performed on synthetic and real-world data. The proposed methods show performance improvements to several existing methods in terms of root mean squared error in both tasks