Statistical correlation analysis for comparing vibration data from test and analysis

A theory was developed to compare vibration modes obtained by NASTRAN analysis with those obtained experimentally. Because many more analytical modes can be obtained than experimental modes, the analytical set was treated as expansion functions for putting both sources in comparative form. The dimensional symmetry was developed for three general cases: nonsymmetric whole model compared with a nonsymmetric whole structural test, symmetric analytical portion compared with a symmetric experimental portion, and analytical symmetric portion with a whole experimental test. The theory was coded and a statistical correlation program was installed as a utility. The theory is established with small classical structures

Any-order propagation of the nonlinear Schroedinger equation

We derive an exact propagation scheme for nonlinear Schroedinger equations. This scheme is entirely analogous to the propagation of linear Schroedinger equations. We accomplish this by defining a special operator whose algebraic properties ensure the correct propagation. As applications, we provide a simple proof of a recent conjecture regarding higher-order integrators for the Gross-Pitaevskii equation, extend it to multi-component equations, and to a new class of integrators.Comment: 10 pages, no figures, submitted to Phys. Rev.

The Dynamics of Viral Marketing

We present an analysis of a person-to-person recommendation network, consisting of 4 million people who made 16 million recommendations on half a million products. We observe the propagation of recommendations and the cascade sizes, which we explain by a simple stochastic model. We analyze how user behavior varies within user communities defined by a recommendation network. Product purchases follow a 'long tail' where a significant share of purchases belongs to rarely sold items. We establish how the recommendation network grows over time and how effective it is from the viewpoint of the sender and receiver of the recommendations. While on average recommendations are not very effective at inducing purchases and do not spread very far, we present a model that successfully identifies communities, product and pricing categories for which viral marketing seems to be very effective

Homeless drug users' awareness and risk perception of peer "Take Home Naloxone" use – a qualitative study

BACKGROUND Peer use of take home naloxone has the potential to reduce drug related deaths. There appears to be a paucity of research amongst homeless drug users on the topic. This study explores the acceptability and potential risk of peer use of naloxone amongst homeless drug users. From the findings the most feasible model for future treatment provision is suggested. METHODS In depth face-to-face interviews conducted in one primary care centre and two voluntary organisation centres providing services to homeless drug users in a large UK cosmopolitan city. Interviews recorded, transcribed and analysed thematically by framework techniques. RESULTS Homeless people recognise signs of a heroin overdose and many are prepared to take responsibility to give naloxone, providing prior training and support is provided. Previous reports of the theoretical potential for abuse and malicious use may have been overplayed. CONCLUSION There is insufficient evidence to recommend providing "over the counter" take home naloxone" to UK homeless injecting drug users. However a programme of peer use of take home naloxone amongst homeless drug users could be feasible providing prior training is provided. Peer education within a health promotion framework will optimise success as current professionally led health promotion initiatives are failing to have a positive impact amongst homeless drug users

Analytic, Group-Theoretic Density Profiles for Confined, Correlated N-Body Systems

Confined quantum systems involving $N$ identical interacting particles are to be found in many areas of physics, including condensed matter, atomic and chemical physics. A beyond-mean-field perturbation method that is applicable, in principle, to weakly, intermediate, and strongly-interacting systems has been set forth by the authors in a previous series of papers. Dimensional perturbation theory was used, and in conjunction with group theory, an analytic beyond-mean-field correlated wave function at lowest order for a system under spherical confinement with a general two-body interaction was derived. In the present paper, we use this analytic wave function to derive the corresponding lowest-order, analytic density profile and apply it to the example of a Bose-Einstein condensate.Comment: 15 pages, 2 figures, accepted by Physics Review A. This document was submitted after responding to a reviewer's comment

Methadone and buprenorphine-related deaths among people prescribed and not prescribed Opioid Agonist Therapy during the COVID-19 pandemic in England

BACKGROUND: The coronavirus pandemic resulted in many changes which had the potential to impact mortality related to opioid agonist therapy (OAT; methadone, buprenorphine), including changes in the prescribing and dispensing of OAT and patterns of drug availability and use. We aimed to assess the impact of the first lockdown (initiated March 23rd 2020) on methadone- and buprenorphine-related deaths in England in people both prescribed and not prescribed OAT using data from the National Programme on Substance Abuse Deaths. METHODS: This was a retrospective post-mortem toxicology study of OAT-related deaths which occurred in the 3-month period March 23rd to June 22nd in the years 2016-2020. Provisional data regarding numbers accessing treatment for opioid use disorder was provided by the National Drug Treatment Monitoring System. RESULTS: We found a 64% increase in methadone-related deaths in March to June 2020 compared to March to June 2019 (2019 n = 96; 2020 projected n = 157). There were increases in the mortality rate of both in-treatment decedents (22% increase; 2019 n = 45; an exponential smoothing model of the 2016-19 trend [α=0.5] predicted 44 deaths in 2020, 55 were reported) and decedents not prescribed methadone (74% increase; 2019 n = 46; 2016-19 trend predicted 43 deaths in 2020, 80 were reported). There was no increase in buprenorphine-related deaths (2019 n = 9/529; 2020 n = 11/566). There were no changes in the numbers of deaths where other opioids or multiple substances were detected, or in methadone levels detected. Numbers of people accessing treatment for opioid use disorder in 2020 did not decrease relative to previous years (p >0.05). CONCLUSIONS: Methadone-related deaths in non-prescribed individuals, but not prescribed individuals, increased considerably above the annual trend forecast for 2020 during the first COVID-19 lockdown in England. Further studies are thus needed to understand this difference

Mirror formation control in the vicinity of an asteroid

Two strategies are presented for the positioning and control of a spacecraft formation designed to focus sunlight onto a point on the surface of asteroid, thereby sublimating the material and ejecting debris creating thrust. In the first approach, the formation is located at artficial equilibrium points around the asteroid and controlled using the force from the solar radiation pressure. The second approach determines the optimal periodic formation orbits, subject to the gravitational perturbations from the asteroid, the solar radiation pressure and the control acceleration derived from a control law

Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization

A versatile method is described for the practical computation of the discrete Fourier transforms (DFT) of a continuous function $g(t)$ given by its values $g_{j}$ at the points of a uniform grid $F_{N}$ generated by conjugacy classes of elements of finite adjoint order $N$ in the fundamental region $F$ of compact semisimple Lie groups. The present implementation of the method is for the groups SU(2), when $F$ is reduced to a one-dimensional segment, and for $SU(2)\times ... \times SU(2)$ in multidimensional cases. This simplest case turns out to result in a transform known as discrete cosine transform (DCT), which is often considered to be simply a specific type of the standard DFT. Here we show that the DCT is very different from the standard DFT when the properties of the continuous extensions of these two discrete transforms from the discrete grid points $t_j; j=0,1, ... N$ to all points $t \in F$ are considered. (A) Unlike the continuous extension of the DFT, the continuous extension of (the inverse) DCT, called CEDCT, closely approximates $g(t)$ between the grid points $t_j$. (B) For increasing $N$, the derivative of CEDCT converges to the derivative of $g(t)$. And (C), for CEDCT the principle of locality is valid. Finally, we use the continuous extension of 2-dimensional DCT to illustrate its potential for interpolation, as well as for the data compression of 2D images.Comment: submitted to JMP on April 3, 2003; still waiting for the referee's Repor

On Approximation of the Eigenvalues of Perturbed Periodic Schrodinger Operators

This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrodinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so called quadratic projection method, in order to achieve convergence free from spectral pollution. We describe the theoretical foundations of the method in detail, and illustrate its effectiveness by several examples.Comment: 17 pages, 2 tables and 2 figure

Dense Motion Estimation for Smoke

Motion estimation for highly dynamic phenomena such as smoke is an open challenge for Computer Vision. Traditional dense motion estimation algorithms have difficulties with non-rigid and large motions, both of which are frequently observed in smoke motion. We propose an algorithm for dense motion estimation of smoke. Our algorithm is robust, fast, and has better performance over different types of smoke compared to other dense motion estimation algorithms, including state of the art and neural network approaches. The key to our contribution is to use skeletal flow, without explicit point matching, to provide a sparse flow. This sparse flow is upgraded to a dense flow. In this paper we describe our algorithm in greater detail, and provide experimental evidence to support our claims.Comment: ACCV201