Symbol correspondences for spin systems

The present monograph explores the correspondence between quantum and classical mechanics in the particular context of spin systems, that is, SU(2)-symmetric mechanical systems. Here, a detailed presentation of quantum spin-j systems, with emphasis on the SO(3)-invariant decomposition of their operator algebras, is followed by an introduction to the Poisson algebra of the classical spin system and a similarly detailed presentation of its SO(3)-invariant decomposition. Subsequently, this monograph proceeds with a detailed and systematic study of general quantum-classical symbol correspondences for spin-j systems and their induced twisted products of functions on the 2-sphere. This original systematic presentation culminates with the study of twisted products in the asymptotic limit of high spin numbers. In the context of spin systems, it shows how classical mechanics may or may not emerge as an asymptotic limit of quantum mechanics.Comment: Research Monograph, 171 pages (book format, preliminary version

DOLPHIn - Dictionary Learning for Phase Retrieval

We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements of a complex-valued linear transformation of the original image. Several recent phase retrieval algorithms exploit underlying sparsity of the unknown signal in order to improve recovery performance. In this work, we consider such a sparse signal prior in the context of phase retrieval, when the sparsifying dictionary is not known in advance. Our algorithm jointly reconstructs the unknown signal - possibly corrupted by noise - and learns a dictionary such that each patch of the estimated image can be sparsely represented. Numerical experiments demonstrate that our approach can obtain significantly better reconstructions for phase retrieval problems with noise than methods that cannot exploit such "hidden" sparsity. Moreover, on the theoretical side, we provide a convergence result for our method

Spatial Compressive Sensing for MIMO Radar

We study compressive sensing in the spatial domain to achieve target localization, specifically direction of arrival (DOA), using multiple-input multiple-output (MIMO) radar. A sparse localization framework is proposed for a MIMO array in which transmit and receive elements are placed at random. This allows for a dramatic reduction in the number of elements needed, while still attaining performance comparable to that of a filled (Nyquist) array. By leveraging properties of structured random matrices, we develop a bound on the coherence of the resulting measurement matrix, and obtain conditions under which the measurement matrix satisfies the so-called isotropy property. The coherence and isotropy concepts are used to establish uniform and non-uniform recovery guarantees within the proposed spatial compressive sensing framework. In particular, we show that non-uniform recovery is guaranteed if the product of the number of transmit and receive elements, MN (which is also the number of degrees of freedom), scales with K(log(G))^2, where K is the number of targets and G is proportional to the array aperture and determines the angle resolution. In contrast with a filled virtual MIMO array where the product MN scales linearly with G, the logarithmic dependence on G in the proposed framework supports the high-resolution provided by the virtual array aperture while using a small number of MIMO radar elements. In the numerical results we show that, in the proposed framework, compressive sensing recovery algorithms are capable of better performance than classical methods, such as beamforming and MUSIC.Comment: To appear in IEEE Transactions on Signal Processin

Optimal quantum detectors for unambiguous detection of mixed states

We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space optimization, we derive necessary and sufficient conditions for an optimal measurement that maximizes the probability of correct detection. We show that the previous optimal measurements that were derived for certain special cases satisfy these optimality conditions. We then consider state sets with strong symmetry properties, and show that the optimal measurement operators for distinguishing between these states share the same symmetries, and can be computed very efficiently by solving a reduced size semidefinite program.Comment: Submitted to Phys. Rev.

Group polytope faces pursuit for recovery of block-sparse signals

This is the accepted version of the article. The final publication is available at link.springer.com. http://www.springerlink.com/content/e0r61416446277w0

Building Reference Architectures for the Industrial IoT

The Internet of Things (IoT) comprises many emerging technologies that enable wireless interconnections among “things” (usually objects such as personal devices, appliances, cars, or industrial equipment, but also living things such as animals and people) equipped with data-gathering sensors. Early predictions indicate that the number of IoT devices could reach 26 billion worldwide by 2020 (Lee and Lee, 2015), but this estimate is likely to increase as more companies are jumping on the IoT bandwagon. One of the greatest predicted impacts of IoT is in industrial settings – where it will help transform entire industries by creating new opportunities for companies to manage their internal processes and interact with customers (Iansiti and Lakhani, 2014). These industrial IoT technologies and applications are denoted by the term Industry 4.0. Accenture predicts that collecting data from sensors placed on products, equipment, and even users, and using this data to improve processes inside and outside organizations “can add trillions of dollars to the global economy by 2030.” (Purdy and Davarzan, 2015). As IoT technologies proliferate, it will become increasingly important for companies to understand the existing opportunities for Industry 4.0 and effectively adopt and deploy the technologies both internally and in inter-organizational relationships. Architectures are models that can help guide companies in their Industrial IoT journey. For example, understanding the layered architecture of digital technologies can help companies innovate by developing appropriate digital product platforms (Yoo et al., 2010). Companies can use architectural frameworks to make sense of strategic recommendations emerging from current research studies – such as the need to build adequate operational and digital services infrastructures to support a company’s digital strategy (Ross et al., 2016). Architectures can be built at the company level, such as in the case of enterprise architectures (EA) that describe a company’s “business and operating model, organizational structure, business processes, data, applications and technology” (Ahlemann et al., 2012), or at the industry level, such as in the case of reference architectures (RA) that present a high-level, organizing view for an industry, including its processes, stakeholders, organizational, informational and technology structure (Czarnecki and Dietze, 2017). EAs and especially RAs are essential for developing interconnected business platforms that enable companies and their customers, vendors and business partners to orchestrate the delivery of internal and external services in effective and efficient ways (Stettiner and Fienhold, 2012). At present, the work on Industrial IoT architectures is just starting, and few models exist. In this paper, we report on our experience working with academic and industry partners to select architectural frameworks and build reference architectures for several industries. We also discuss the challenges for the adoption and use of Industrial IoT reference architectures