Adiabatic theorem for non-hermitian time-dependent open systems

In the conventional quantum mechanics (i.e., hermitian QM) the adia- batic theorem for systems subjected to time periodic fields holds only for bound systems and not for open ones (where ionization and dissociation take place) [D. W. Hone, R. Ketzmerik, and W. Kohn, Phys. Rev. A 56, 4045 (1997)]. Here with the help of the (t,t') formalism combined with the complex scaling method we derive an adiabatic theorem for open systems and provide an analytical criteria for the validity of the adiabatic limit. The use of the complex scaling transformation plays a key role in our derivation. As a numerical example we apply the adiabatic theorem we derived to a 1D model Hamiltonian of Xe atom which interacts with strong, monochromatic sine-square laser pulses. We show that the gener- ation of odd-order harmonics and the absence of hyper-Raman lines, even when the pulses are extremely short, can be explained with the help of the adiabatic theorem we derived

From Health Decisions to Performance: The Network Effect

This study uses a simulation as a vehicle for social networks research application. Eighty five companies were created as partof a simulated healthcare industry. Our results suggest that companies positioning themselves at pivotal points within thenetwork outperform companies that do not. The findings show the applicability of network theory and the use of simulationsin applied research on healthcare decision-making

On Interactive Proofs of Proximity with Proof-Oblivious Queries

Interactive proofs of proximity (IPPs) offer ultra-fast approximate verification of assertions regarding their input, where ultra-fast means that only a small portion of the input is read and approximate verification is analogous to the notion of approximate decision that underlies property testing. Specifically, in an IPP, the prover can make the verifier accept each input in the property, but cannot fool the verifier into accepting an input that is far from the property (except for with small probability). The verifier in an IPP system engages in two very different types of activities: interacting with an untrusted prover, and querying its input. The definition allows for arbitrary coordination between these two activities, but keeping them separate is both conceptually interesting and necessary for important applications such as addressing temporal considerations (i.e., at what time is each of the services available) and facilitating the construction of zero-knowledge schemes. In this work we embark on a systematic study of IPPs with proof-oblivious queries, where the queries should not be affected by the interaction with the prover. We assign the query and interaction activities to separate modules, and consider different limitations on their coordination. The most strict limitation requires these activities to be totally isolated from one another; they just feed their views to a separate deciding module. We show that such systems can be efficiently emulated by standard testers. Going to the other extreme, we only disallow information to flow from the interacting module to the querying module, but allow free information flow in the other direction. We show that extremely efficient one-round (i.e., two-message) systems of such type can be used to verify properties that are extremely hard to test (without the help of a prover). That is, the complexity of verifying can be polylogarithmic in the complexity of testing. This stands in contrast the MAPs (viewed as 1/2-round systems) in which proof-oblivious queries are as limited as our isolated model. Our focus is on an intermediate model that allows shared randomness between the querying and interacting modules but no information flow between them. In this case we show that 1-round systems are efficiently emulated by standard testers but 3/2-round systems of extremely low complexity exist for properties that are extremely hard to test. One additional result about this model is that it can efficiently emulate any IPP for any property of low-degree polynomials

Case Presentation for Suprascapular Neuropathy

CASE HISTORY: The patient is an 18-year-old female collegiate volleyball player who has suffered progressive shoulder pain in her right shoulder. She states that the pain has progressively gotten worse over the past 3-4 years. The sharp pain began when she would raise her right arm above 90 degrees when hitting an overhand serve. Over time, the pain progressed and became noticeable in additional movements. The patient had noted significant weakness in both her right arm and right shoulder. The patient states when she sleeps on her right arm/shoulder she wakes up in severe pain. She has tried sleeping with the right elbow in extension which has helped in alleviating the pain. PHYSICAL EXAM: The patient’s vital signs were all within normal ranges. A physical exam was performed and identified pain with Hawkins-Kennedy and empty can. Manual muscle testing demonstrated infraspinatus (2/5) and supraspinatus (3/5) weakness. Upper Quarter Y Balance Test revealed right and left composite scores of 85.7 and 96.1, respectively. DIFFERENTIAL DIAGNOSES: Suprascapular nerve palsy; Ulnar nerve palsy; Infraspinatus atrophy; Subacromial impingement syndrome; and rotator cuff injury. TESTS & RESULTS: An X-ray for the right arm and shoulder was also preformed which did not show any pathologies. The patient had a magnetic resonance imaging (MRI) of the right arm and shoulder revealing two lesions in the head of the humerus. An MRI of the cervical spine without contrast was preformed and revealed a mild disk bulge at C5 and C6 with no significant Neural Foraminal Stenosis (NF) narrowing. There was straightening and very slight reversal of the normal cervical lordosis. A nerve conduction study was performed and identified a right sided suprascapular neuropathy at the spinoglenoid notch with significant motor axon loss. Lastly, electrophysiologic testing was done which identified right sided ulnar neuropathy. FINAL DIAGNOSIS: Right sided suprascapular neuropathy at the spinoglenoid notch. Right sided ulnar neuropathy. DISCUSSION: Suprascapular neuropathy is a very uncommon cause for shoulder pain and is often times misdiagnosed. Frequently the diagnosis of suprascapular neuropathy is mistaken for subacromial impingement syndrome, rotator cuff injuries, etc. Common signs and symptoms of suprascapular neuropathy are pain and weakness in the shoulder, atrophy, and often burning and aching. Suprascapular neuropathy is reported to only be found in 0.4% of patients with shoulder pain. The compression of the suprascapular nerve at the spinoglenoid notch is often due to repetitive use and space-occupying lesions. Athletes that perform sports like tennis, weight-lifting, and volleyball are more likely to experience a suprascapular neuropathy injury. OUTCOME OF THE CASE: The patient has been diagnosed with suprascapular neuropathy caused by compression of the suprascapular nerve at the spinoglenoid notch. This patient has been prescribed a rehabilitation program involving the throwers ten to strengthen her rotator cuff muscles along with improving her scapular and glenohumeral stabilization and proprioception. The athlete is participating in normal practice and play and has been told to take over the counter anti-inflammatory medications such as ibuprofen, as needed. RETURN TO ACTIVITY AND FURTHER FOLLOW-UP: The patient is to remain in normal practice and play and continue her basic rehabilitation program. She has been referred to a surgical doctor and has been asked to seek a surgical consultation in the future

Efficient Quantum Polar Coding

Polar coding, introduced 2008 by Arikan, is the first (very) efficiently encodable and decodable coding scheme whose information transmission rate provably achieves the Shannon bound for classical discrete memoryless channels in the asymptotic limit of large block sizes. Here we study the use of polar codes for the transmission of quantum information. Focusing on the case of qubit Pauli channels and qubit erasure channels, we use classical polar codes to construct a coding scheme which, using some pre-shared entanglement, asymptotically achieves a net transmission rate equal to the coherent information using efficient encoding and decoding operations and code construction. Furthermore, for channels with sufficiently low noise level, we demonstrate that the rate of preshared entanglement required is zero.Comment: v1: 15 pages, 4 figures. v2: 5+3 pages, 3 figures; argumentation simplified and improve

Entropy, Optimization and Counting

In this paper we study the problem of computing max-entropy distributions over a discrete set of objects subject to observed marginals. Interest in such distributions arises due to their applicability in areas such as statistical physics, economics, biology, information theory, machine learning, combinatorics and, more recently, approximation algorithms. A key difficulty in computing max-entropy distributions has been to show that they have polynomially-sized descriptions. We show that such descriptions exist under general conditions. Subsequently, we show how algorithms for (approximately) counting the underlying discrete set can be translated into efficient algorithms to (approximately) compute max-entropy distributions. In the reverse direction, we show how access to algorithms that compute max-entropy distributions can be used to count, which establishes an equivalence between counting and computing max-entropy distributions

Multi-Modal Motion Planning Using Composite Pose Graph Optimization

In this paper, we present a motion planning framework for multi-modal vehicle dynamics. Our proposed algorithm employs transcription of the optimization objective function, vehicle dynamics, and state and control constraints into sparse factor graphs, which -- combined with mode transition constraints -- constitute a composite pose graph. By formulating the multi-modal motion planning problem in composite pose graph form, we enable utilization of efficient techniques for optimization on sparse graphs, such as those widely applied in dual estimation problems, e.g., simultaneous localization and mapping (SLAM). The resulting motion planning algorithm optimizes the multi-modal trajectory, including the location of mode transitions, and is guided by the pose graph optimization process to eliminate unnecessary transitions, enabling efficient discovery of optimized mode sequences from rough initial guesses. We demonstrate multi-modal trajectory optimization in both simulation and real-world experiments for vehicles with various dynamics models, such as an airplane with taxi and flight modes, and a vertical take-off and landing (VTOL) fixed-wing aircraft that transitions between hover and horizontal flight modes.Comment: 7 pages, 6 figures, to be included in proceedings of IEEE International Conference on Robotics and Automation 202

Conformal Risk Control

We extend conformal prediction to control the expected value of any monotone loss function. The algorithm generalizes split conformal prediction together with its coverage guarantee. Like conformal prediction, the conformal risk control procedure is tight up to an $\mathcal{O}(1/n)$ factor. Worked examples from computer vision and natural language processing demonstrate the usage of our algorithm to bound the false negative rate, graph distance, and token-level F1-score.Comment: Code available at https://github.com/aangelopoulos/conformal-ris