Optimal prediction and the Klein-Gordon equation

The method of optimal prediction is applied to calculate the future means of solutions to the Klein-Gordon equation. It is shown that in an appropriate probability space, the difference between the average of all solutions that satisfy certain constraints at time t=0, and the average computed by an approximate method, is small with high probability.Comment: 18 page

Inverse spectral problems for Sturm-Liouville operators with singular potentials

The inverse spectral problem is solved for the class of Sturm-Liouville operators with singular real-valued potentials from the space $W^{-1}_2(0,1)$. The potential is recovered via the eigenvalues and the corresponding norming constants. The reconstruction algorithm is presented and its stability proved. Also, the set of all possible spectral data is explicitly described and the isospectral sets are characterized.Comment: Submitted to Inverse Problem

Time-Local Quantum-State-Diffusion Equation for Multilevel Quantum Dynamics

An open quantum system with multiple levels coupled to a bosonic environment at zero temperature is investigated systematically using the non-Markovian quantum-state-diffusion (QSD) method [W. T. Strunz, L. Di\'osi, and N. Gisin, Phys. Rev. Lett. 82, 1801 (1999)]. We have established exact time-local QSD equations for a set of interesting multilevel open systems, including high-spin systems, multiple-transition atomic models, and multilevel atomic models driven by time-dependent external fields. These exact QSD equations have paved the way to evaluate the dynamics of open multilevel atomic systems in the general non-Markovian regimes without any approximation.Comment: 7 pages, 3 figures, 1 tabl

Review of biorthogonal coupled cluster representations for electronic excitation

Single reference coupled-cluster (CC) methods for electronic excitation are based on a biorthogonal representation (bCC) of the (shifted) Hamiltonian in terms of excited CC states, also referred to as correlated excited (CE) states, and an associated set of states biorthogonal to the CE states, the latter being essentially configuration interaction (CI) configurations. The bCC representation generates a non-hermitian secular matrix, the eigenvalues representing excitation energies, while the corresponding spectral intensities are to be derived from both the left and right eigenvectors. Using the perspective of the bCC representation, a systematic and comprehensive analysis of the excited-state CC methods is given, extending and generalizing previous such studies. Here, the essential topics are the truncation error characteristics and the separability properties, the latter being crucial for designing size-consistent approximation schemes. Based on the general order relations for the bCC secular matrix and the (left and right) eigenvector matrices, formulas for the perturbation-theoretical (PT) order of the truncation errors (TEO) are derived for energies, transition moments, and property matrix elements of arbitrary excitation classes and truncation levels. In the analysis of the separability properties of the transition moments, the decisive role of the so-called dual ground state is revealed. Due to the use of CE states the bCC approach can be compared to so-called intermediate state representation (ISR) methods based exclusively on suitably orthonormalized CE states. As the present analysis shows, the bCC approach has decisive advantages over the conventional CI treatment, but also distinctly weaker TEO and separability properties in comparison with a full (and hermitian) ISR method

A stationary source of non-classical or entangled atoms

A scheme for generating continuous beams of atoms in non-classical or entangled quantum states is proposed and analyzed. For this the recently suggested transfer technique of quantum states from light fields to collective atomic excitation by Stimulated Raman adiabatic passage [M.Fleischhauer and M.D. Lukin, Phys.Rev.Lett. 84, 5094 (2000)] is employed and extended to matter waves

Phase Coherence and Control of Stored Photonic Information

We report the demonstration of phase coherence and control for the recently developed "light storage" technique. Specifically, we use a pulsed magnetic field to vary the phase of atomic spin excitations which result from the deceleration and storing of a light pulse in warm Rb vapor. We then convert the spin excitations back into light and detect the resultant phase shift in an optical interferometric measurement. The coherent storage of photon states in matter is essential for the practical realization of many basic concepts in quantum information processing.Comment: 5 pages, 3 figures. Submitted to Phys. Rev. Let

Storage of light in atomic vapor

We report an experiment in which a light pulse is decelerated and trapped in a vapor of Rb atoms, stored for a controlled period of time, and then released on demand. We accomplish this storage of light by dynamically reducing the group velocity of the light pulse to zero, so that the coherent excitation of the light is reversibly mapped into a collective Zeeman (spin) coherence of the Rb vapor

Deep Learning Analysis of Cardiac MRI in Legacy Datasets:Multi-Ethnic Study of Atherosclerosis

The shape and motion of the heart provide essential clues to understanding the mechanisms of cardiovascular disease. With the advent of large-scale cardiac imaging data, statistical atlases become a powerful tool to provide automated and precise quantification of the status of patient-specific heart geometry with respect to reference populations. The Multi-Ethnic Study of Atherosclerosis (MESA), begun in 2000, was the first large cohort study to incorporate cardiovascular MRI in over 5000 participants, and there is now a wealth of follow-up data over 20 years. Building a machine learning based automated analysis is necessary to extract the additional imaging information necessary for expanding original manual analyses. However, machine learning tools trained on MRI datasets with different pulse sequences fail on such legacy datasets. Here, we describe an automated atlas construction pipeline using deep learning methods applied to the legacy cardiac MRI data in MESA. For detection of anatomical cardiac landmark points, a modified VGGNet convolutional neural network architecture was used in conjunction with a transfer learning sequence between two-chamber, four-chamber, and short-axis MRI views. A U-Net architecture was used for detection of the endocardial and epicardial boundaries in short axis images. Both network architectures resulted in good segmentation and landmark detection accuracies compared with inter-observer variations. Statistical relationships with common risk factors were similar between atlases derived from automated vs manual annotations. The automated atlas can be employed in future studies to examine the relationships between cardiac morphology and future events

Quantum memory for photons: I. Dark state polaritons

An ideal and reversible transfer technique for the quantum state between light and metastable collective states of matter is presented and analyzed in detail. The method is based on the control of photon propagation in coherently driven 3-level atomic media, in which the group velocity is adiabatically reduced to zero. Form-stable coupled excitations of light and matter (``dark-state polaritons'') associated with the propagation of quantum fields in Electromagnetically Induced Transparency are identified, their basic properties discussed and their application for quantum memories for light analyzed.Comment: 13 pages, 6 figures, paragraph on photon echo adde

Social prescribing in cardiology : rediscovering the nature of and within us

Personalised care is integral to the delivery of the NHSE Long Term Plan. Enabling choice and supporting patients to make decisions predicated on what matters to them, rather than what is the matter with them, is a fundamental part of the NHS vision. Social prescribing uses nonmedical, asset based, salutogenic approaches to promote this personalised paradigm, and places the patient central to decision making. We discuss how Personalised care can be used to help people with Cardiovascular Disease (CVD) using socially prescribed ‘nature-based’ interventions to support the prehabilitation and rehabilitation of patients with CVD. The concept of Personalised care outlined and the significance of salutogenic principles as complementary approach to the pathogenic model is discussed. We argue that this seemingly novel approach to using nature-based interventions can help promote wellbeing for people with CVD as part of the wider personalised agenda