Periodic and almost periodic flows of periodic Ito equations

summary:Under the uniform asymptotic stability of a finite dimensional Ito equation with periodic coefficients, the asymptotically almost periodicity of the $l^p$-bounded solution and the existence of a trajectory of an almost periodic flow defined on the space of all probability measures are established

Steps to Better Cardiovascular Health: How Many Steps Does It Take to Achieve Good Health and How Confident Are We in This Number?

Pedometers and other types of step-counting devices are growing in popularity with both researchers and practitioners. The focus of this article is on describing the most recent pedometer-related advances in terms of cardiovascular health. The emergent body of evidence suggests that pedometer-determined physical activity is related to a number of cardiovascular health outcomes and that intervention participants can realize modest changes in body mass index and blood pressure. Taking into consideration individual baseline values, tailored messages congruent with public health recommendations should promote incremental increases in steps/day on the order of an extra 3,000 to 4,000 (approximately 30 min) of at least moderate intensity and taken in at least 10-minute bouts. Additional health benefits accrue with greater increases. Of course, even more benefits are possible from engaging in vigorous physical activity, but this seems less appealing for most people. Pedometer-based guidelines are not intended to supplant existing public health recommendations, but rather supplement them

Optimization of an Electromagnetic Energy Harvesting Device

This paper presents the modeling and optimization of an electromagnetic-based generator for generating power from ambient vibrations. Basic equations describing such generators are presented and the conditions for maximum power generation are described. Two-centimeter scale prototype generators, which consist of magnets suspended on a beam vibrating relative to a coil, have been built and tested. The measured power and modeled results are compared. It is shown that the experimental results confirm the optimization theory

Classical Optimizers for Noisy Intermediate-Scale Quantum Devices

We present a collection of optimizers tuned for usage on Noisy Intermediate-Scale Quantum (NISQ) devices. Optimizers have a range of applications in quantum computing, including the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization (QAOA) algorithms. They are also used for calibration tasks, hyperparameter tuning, in machine learning, etc. We analyze the efficiency and effectiveness of different optimizers in a VQE case study. VQE is a hybrid algorithm, with a classical minimizer step driving the next evaluation on the quantum processor. While most results to date concentrated on tuning the quantum VQE circuit, we show that, in the presence of quantum noise, the classical minimizer step needs to be carefully chosen to obtain correct results. We explore state-of-the-art gradient-free optimizers capable of handling noisy, black-box, cost functions and stress-test them using a quantum circuit simulation environment with noise injection capabilities on individual gates. Our results indicate that specifically tuned optimizers are crucial to obtaining valid science results on NISQ hardware, and will likely remain necessary even for future fault tolerant circuits

Training health visitors in cognitive behavioural and person-centred approaches for depression in postnatal women as part of a cluster randomised trial and economic evaluation in primary care: the PoNDER trial

Aim: This paper aims to describe the training preparation for health visitors who took part in the intervention arm of a cluster randomised controlled trial and economic evaluation of training for health visitors – the POstNatal Depression Economic evaluation and Randomised (the PoNDER) trial. A secondary aim is to make available, by electronic links, the training manuals developed for and used for the cognitive behavioural approach (CBA) and the person-centred approach (PCA) training for the health visitors. The paper is of relevance to health visitors, general practitioners, nurse practitioners, midwives, clinical psychologists, mental health nurses, community psychiatric nurses, counsellors, and service commissioners. Background: The trial clinical outcomes have been published, indicating the pragmatic effectiveness of the package of training for health visitors to identify depressive symptoms and provide a psychologically informed intervention. The training was associated with a reduction in depressive symptoms at six months postnatally among intervention group women and some evidence of a benefit for the intervention group for some of the secondary outcomes at 18 months follow-up. Methods: The two experimental interventions examined in the PoNDER trial built upon promising work on the potential for psychological interventions to help women recover from postnatal depression as an alternative to pharmaceutical interventions and to address the limitations of previous research in the area. Findings: The package of health visitor training comprised the development of clinical skills in assessing postnatal women and identifying depressive symptoms, and the delivery of a CBA or a PCA for eligible women. This was the largest trial a health visitor intervention and of postnatal depression ever conducted. We are aware of no other rigorously performed trial that has published details of an extensively tested training programme for the benefit of health-care professionals and clients

Lagrange-Poincare field equations

The Lagrange-Poincare equations of classical mechanics are cast into a field theoretic context together with their associated constrained variational principle. An integrability/reconstruction condition is established that relates solutions of the original problem with those of the reduced problem. The Kelvin-Noether theorem is formulated in this context. Applications to the isoperimetric problem, the Skyrme model for meson interaction, metamorphosis image dynamics, and molecular strands illustrate various aspects of the theory.Comment: Submitted to Journal of Geometry and Physics, 45 pages, 1 figur

Families of moment matching based, structure preserving approximations for linear port Hamiltonian systems

In this paper we propose a solution to the problem of moment matching with preservation of the port Hamiltonian structure, in the framework of time-domain moment matching. We characterize several families of parameterized port Hamiltonian models that match the moments of a given port Hamiltonian system, at a set of finite interpolation points. We also discuss the problem of Markov parameters matching for linear systems as a moment matching problem for descriptor representations associated to the given system, at zero interpolation points. Solving this problem yields families of parameterized reduced order models that achieve Markov parameter matching. Finally, we apply these results to the port Hamiltonian case, resulting in families of parameterized reduced order port Hamiltonian approximations.Comment: 27 pages, 8 figures, Automatica journa