Analysis of path integrals at low temperature : Box formula, occupation time and ergodic approximation

We study the low temperature behaviour of path integrals for a simple one-dimensional model. Starting from the Feynman-Kac formula, we derive a new functional representation of the density matrix at finite temperature, in terms of the occupation times of Brownian motions constrained to stay within boxes with finite sizes. From that representation, we infer a kind of ergodic approximation, which only involves double ordinary integrals. As shown by its applications to different confining potentials, the ergodic approximation turns out to be quite efficient, especially in the low-temperature regime where other usual approximations fail

Informed design of educational technology for teaching and learning? Towards an evidence-informed model of good practice

The aim of this paper is to model evidence-informed design based on a selective critical analysis of research articles. We draw upon findings from an investigation into practitioners’ use of educational technologies to synthesise and model what informs their designs. We found that practitioners’ designs were often driven by implicit assumptions about learning. These shaped both the design of interventions and the methods sought to derive evaluations and interpret the findings. We argue that interventions need to be grounded in better and explicit conceptualisations of what constitutes learning in order to have well-informed designs that focus on improving the quality of student learning

Remarks on Shannon's Statistical Inference and the Second Law in Quantum Statistical Mechanics

We comment on a formulation of quantum statistical mechanics, which incorporates the statistical inference of Shannon. Our basic idea is to distinguish the dynamical entropy of von Neumann, $H = -k Tr \hat{\rho}\ln\hat{\rho}$, in terms of the density matrix $\hat{\rho}(t)$, and the statistical amount of uncertainty of Shannon, $S= -k \sum_{n}p_{n}\ln p_{n}$, with $p_{n}=$ in the representation where the total energy and particle numbers are diagonal. These quantities satisfy the inequality $S\geq H$. We propose to interprete Shannon's statistical inference as specifying the {\em initial conditions} of the system in terms of $p_{n}$. A definition of macroscopic observables which are characterized by intrinsic time scales is given, and a quantum mechanical condition on the system, which ensures equilibrium, is discussed on the basis of time averaging. An interesting analogy of the change of entroy with the running coupling in renormalization group is noted. A salient feature of our approach is that the distinction between statistical aspects and dynamical aspects of quantum statistical mechanics is very transparent.Comment: 16 pages. Minor refinement in the statements in the previous version. This version has been published in Journal of Phys. Soc. Jpn. 71 (2002) 6

4 Gy versus 24 Gy radiotherapy for follicular and marginal zone lymphoma (FoRT): long-term follow-up of a multicentre, randomised, phase 3, non-inferiority trial

BACKGROUND: The optimal radiotherapy dose for indolent non-Hodgkin lymphoma is uncertain. We aimed to compare 24 Gy in 12 fractions (representing the standard of care) with 4 Gy in two fractions (low-dose radiation). METHODS: FoRT (Follicular Radiotherapy Trial) is a randomised, multicentre, phase 3, non-inferiority trial at 43 study centres in the UK. We enrolled patients (aged >18 years) with indolent non-Hodgkin lymphoma who had histological confirmation of follicular lymphoma or marginal zone lymphoma requiring radical or palliative radiotherapy. No limit on performance status was stipulated, and previous chemotherapy or radiotherapy to another site was permitted. Radiotherapy target sites were randomly allocated (1:1) either 24 Gy in 12 fractions or 4 Gy in two fractions using minimisation and stratified by histology, treatment intent, and study centre. Randomisation was centralised through the Cancer Research UK and University College London Cancer Trials Centre. Patients, treating clinicians, and investigators were not masked to random assignments. The primary endpoint was time to local progression in the irradiated volume based on clinical and radiological evaluation and analysed on an intention-to-treat basis. The non-inferiority threshold aimed to exclude the chance that 4 Gy was more than 10% inferior to 24 Gy in terms of local control at 2 years (HR 1·37). Safety (in terms of adverse events) was analysed in patients who received any radiotherapy and who returned an adverse event form. FoRT is registered with ClinicalTrials.gov, NCT00310167, and the ISRCTN Registry, ISRCTN65687530, and this report represents the long-term follow-up. FINDINGS: Between April 7, 2006, and June 8, 2011, 614 target sites in 548 patients were randomly assigned either 24 Gy in 12 fractions (n=299) or 4 Gy in two fractions (n=315). At a median follow-up of 73·8 months (IQR 61·9-88·0), 117 local progression events were recorded, 27 in the 24 Gy group and 90 in the 4 Gy group. The 2-year local progression-free rate was 94·1% (95% CI 90·6-96·4) after 24 Gy and 79·8% (74·8-83·9) after 4 Gy; corresponding rates at 5 years were 89·9% (85·5-93·1) after 24 Gy and 70·4% (64·7-75·4) after 4 Gy (hazard ratio 3·46, 95% CI 2·25-5·33; p<0·0001). The difference at 2 years remains outside the non-inferiority margin of 10% at -13·0% (95% CI -21·7 to -6·9). The most common events at week 12 were alopecia (19 [7%] of 287 sites with 24 Gy vs six [2%] of 301 sites with 4 Gy), dry mouth (11 [4%] vs five [2%]), fatigue (seven [2%] vs five [2%]), mucositis (seven [2%] vs three [1%]), and pain (seven [2%] vs two [1%]). No treatment-related deaths were reported. INTERPRETATION: Our findings at 5 years show that the optimal radiotherapy dose for indolent lymphoma is 24 Gy in 12 fractions when durable local control is the aim of treatment. FUNDING: Cancer Research UK

Global Equation of State of two-dimensional hard sphere systems

Hard sphere systems in two dimensions are examined for arbitrary density. Simulation results are compared to the theoretical predictions for both the low and the high density limit, where the system is either disordered or ordered, respectively. The pressure in the system increases with the density, except for an intermediate range of volume fractions $0.65 \le \nu \le 0.75$, where a disorder-order phase transition occurs. The proposed {\em global equation of state} (which describes the pressure {\em for all densities}) is applied to the situation of an extremely dense hard sphere gas in a gravitational field and shows reasonable agreement with both experimental and numerical data.Comment: 4 pages, 2 figure

High real-space resolution measurement of the local structure of Ga_1-xIn_xAs using x-ray diffraction

High real-space resolution atomic pair distribution functions (PDF)s from the alloy series Ga_1-xIn_xAs have been obtained using high-energy x-ray diffraction. The first peak in the PDF is resolved as a doublet due to the presence of two nearest neighbor bond lengths, Ga-As and In-As, as previously observed using XAFS. The widths of nearest, and higher, neighbor pairs are analyzed by separating the strain broadening from the thermal motion. The strain broadening is five times larger for distant atomic neighbors as compared to nearest neighbors. The results are in agreement with model calculations.Comment: 4 pages, 5 figure

Beware of density dependent pair potentials

Density (or state) dependent pair potentials arise naturally from coarse-graining procedures in many areas of condensed matter science. However, correctly using them to calculate physical properties of interest is subtle and cannot be uncoupled from the route by which they were derived. Furthermore, there is usually no unique way to coarse-grain to an effective pair potential. Even for simple systems like liquid Argon, the pair potential that correctly reproduces the pair structure will not generate the right virial pressure. Ignoring these issues in naive applications of density dependent pair potentials can lead to an apparent dependence of thermodynamic properties on the ensemble within which they are calculated, as well as other inconsistencies. These concepts are illustrated by several pedagogical examples, including: effective pair potentials for systems with many-body interactions, and the mapping of charged (Debye-H\"{u}ckel) and uncharged (Asakura-Oosawa) two-component systems onto effective one-component ones.Comment: 22 pages, uses iopart.cls and iopart10.clo; submitted to Journal of Physics Condensed Matter, special issue in honour of professor Jean-Pierre Hanse

The Origin of Spatial Intermittency in the Galaxy Distribution

The dynamical equations describing the evolution of a self-gravitating fluid can be rewritten in the form of a Schrodinger equation coupled to a Poisson equation determining the gravitational potential. This approach has a number of interesting features, many of which were pointed out in a seminal paper by Widrow & Kaiser (1993). In particular we show that this approach yields an elegant reformulation of an idea due to Jones (1999) concerning the origin of lognormal intermittency in the galaxy distribution.Comment: 4 pages, to appear in MNRAS, no figure

Cytogerontology since 1881: A reappraisal of August Weismann and a review of modern progress

Cytogerontology, the science of cellular ageing, originated in 1881 with the prediction by August Weismann that the somatic cells of higher animals have limited division potential. Weismann's prediction was derived by considering the role of natural selection in regulating the duration of an organism's life. For various reasons, Weismann's ideas on ageing fell into neglect following his death in 1914, and cytogerontology has only reappeared as a major research area following the demonstration by Hayflick and Moorhead in the early 1960s that diploid human fibroblasts are restricted to a finite number of divisions in vitro. In this review we give a detailed account of Weismann's theory, and we reveal that his ideas were both more extensive in their scope and more pertinent to current research than is generally recognised. We also appraise the progress which has been made over the past hundred years in investigating the causes of ageing, with particular emphasis being given to (i) the evolution of ageing, and (ii) ageing at the cellular level. We critically assess the current state of knowledge in these areas and recommend a series of points as primary targets for future research