Parametric Level Set Methods for Inverse Problems

In this paper, a parametric level set method for reconstruction of obstacles in general inverse problems is considered. General evolution equations for the reconstruction of unknown obstacles are derived in terms of the underlying level set parameters. We show that using the appropriate form of parameterizing the level set function results a significantly lower dimensional problem, which bypasses many difficulties with traditional level set methods, such as regularization, re-initialization and use of signed distance function. Moreover, we show that from a computational point of view, low order representation of the problem paves the path for easier use of Newton and quasi-Newton methods. Specifically for the purposes of this paper, we parameterize the level set function in terms of adaptive compactly supported radial basis functions, which used in the proposed manner provides flexibility in presenting a larger class of shapes with fewer terms. Also they provide a "narrow-banding" advantage which can further reduce the number of active unknowns at each step of the evolution. The performance of the proposed approach is examined in three examples of inverse problems, i.e., electrical resistance tomography, X-ray computed tomography and diffuse optical tomography

Measuring entanglement entropy through the interference of quantum many-body twins

Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is rapidly gaining prominence in diverse fields ranging from condensed matter to quantum gravity. Despite this generality, measuring entanglement remains challenging. This is especially true in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Leveraging our single-site resolved control of ultra-cold bosonic atoms in optical lattices, we prepare and interfere two identical copies of a many-body state. This enables us to directly measure quantum purity, Renyi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly-correlated many-body systems.Comment: 14 pages, 12 figures (6 in the main text, 6 in supplementary material

Probing the Superfluid to Mott Insulator Transition at the Single Atom Level

Quantum gases in optical lattices offer an opportunity to experimentally realize and explore condensed matter models in a clean, tunable system. We investigate the Bose-Hubbard model on a microscopic level using single atom-single lattice site imaging; our technique enables space- and time-resolved characterization of the number statistics across the superfluid-Mott insulator quantum phase transition. Site-resolved probing of fluctuations provides us with a sensitive local thermometer, allows us to identify microscopic heterostructures of low entropy Mott domains, and enables us to measure local quantum dynamics, revealing surprisingly fast transition timescales. Our results may serve as a benchmark for theoretical studies of quantum dynamics, and may guide the engineering of low entropy phases in a lattice

A rare case of isolated duodenal metastases from hepatocellular carcinoma associated with p53 and ki-67 expression: a case report

Hepatocellular carcinoma (HCC) is the most common primary tumor of the liver worldwide. The incidence of HCC is increasing in North America secondary to rises in chronic liver disease from alcohol abuse and viral hepatitis. HCC most commonly metastasizes hematogenously or through lymphatics to the lungs and regional lymph nodes. Involvement of small bowel is rare and typically results from direct invasion and extension. We examined the molecular features related to this extremely rare case of isolated duodenal metastasis of HCC and noted p53 and Ki-67 positive staining. Here, we review the possible molecular and immunohistochemical studies that may aid definitive diagnosis and the evidence for the management of metastatic hepatocellular carcinoma

Collaborative Pharmacy Practice: An Update

Collaborative practice among health professionals is slowly coming of age, given the global focus on efficiency and effectiveness of care to achieve positive patient outcomes and to reduce the economic burden of fragmented care. Collaborative pharmacy practice (CPP) is accordingly evolving within different models including: disease management, medication therapy management, patient centered medical home, and accountable care organizations. Pharmacist roles in these models relate to drug therapy management and include therapy introduction, adjustment, or discontinuation, patient counseling and education, and identification, resolution, and prevention of problems leading to drug interactions and adverse reactions. Most forms of CPP occur with physicians in various settings. Collaborative practice agreements exist in many states in the US and are mentioned in the International Pharmaceutical Federation policy statement. Impetus for CPP comes from health system and economic concerns, as well as from a regulatory push. There are positive examples in community, ambulatory care, and inpatient settings that have well documented protocols, indicators of care, and measurement and reporting of clinical, economic, and patient reported outcomes; however, implementation of the practice is still not widespread. Conceptual and implementation challenges include health professional training, attitudes, confidence and comfort levels, power and communication issues, logistic barriers of time, workload, proximity, resistance to establish and adopt regulations, and importantly, payment models. Some of the attitudinal and perceptual challenges can be mitigated by incorporation of interprofessional concepts and practice in health profession education. Other challenges need to be addressed across health systems, given the inefficiencies and problems that arise from lack of communication and coordination of patient care including medication nonadherence, errors and patient safety, complexity of compounded health problems, and potential liability. The existing evidence needs to be examined to address some challenges and improve infrastructure for CPP

Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice

Understanding exotic forms of magnetism in quantum mechanical systems is a central goal of modern condensed matter physics, with implications from high temperature superconductors to spintronic devices. Simulating magnetic materials in the vicinity of a quantum phase transition is computationally intractable on classical computers due to the extreme complexity arising from quantum entanglement between the constituent magnetic spins. Here we employ a degenerate Bose gas confined in an optical lattice to simulate a chain of interacting quantum Ising spins as they undergo a phase transition. Strong spin interactions are achieved through a site-occupation to pseudo-spin mapping. As we vary an applied field, quantum fluctuations drive a phase transition from a paramagnetic phase into an antiferromagnetic phase. In the paramagnetic phase the interaction between the spins is overwhelmed by the applied field which aligns the spins. In the antiferromagnetic phase the interaction dominates and produces staggered magnetic ordering. Magnetic domain formation is observed through both in-situ site-resolved imaging and noise correlation measurements. By demonstrating a route to quantum magnetism in an optical lattice, this work should facilitate further investigations of magnetic models using ultracold atoms, improving our understanding of real magnetic materials.Comment: 12 pages, 9 figure