Density classification on infinite lattices and trees

Consider an infinite graph with nodes initially labeled by independent Bernoulli random variables of parameter p. We address the density classification problem, that is, we want to design a (probabilistic or deterministic) cellular automaton or a finite-range interacting particle system that evolves on this graph and decides whether p is smaller or larger than 1/2. Precisely, the trajectories should converge to the uniform configuration with only 0's if p1/2. We present solutions to that problem on the d-dimensional lattice, for any d>1, and on the regular infinite trees. For Z, we propose some candidates that we back up with numerical simulations

Alternative Fourier Expansions for Inverse Square Law Forces

Few-body problems involving Coulomb or gravitational interactions between pairs of particles, whether in classical or quantum physics, are generally handled through a standard multipole expansion of the two-body potentials. We discuss an alternative based on a compact, cylindrical Green's function expansion that should have wide applicability throughout physics. Two-electron "direct" and "exchange" integrals in many-electron quantum systems are evaluated to illustrate the procedure which is more compact than the standard one using Wigner coefficients and Slater integrals.Comment: 10 pages, latex/Revtex4, 1 figure

Measurements of Scintillation Efficiency and Pulse-Shape for Low Energy Recoils in Liquid Xenon

Results of observations of low energy nuclear and electron recoil events in liquid xenon scintillator detectors are given. The relative scintillation efficiency for nuclear recoils is 0.22 +/- 0.01 in the recoil energy range 40 keV - 70 keV. Under the assumption of a single dominant decay component to the scintillation pulse-shape the log-normal mean parameter T0 of the maximum likelihood estimator of the decay time constant for 6 keV < Eee < 30 keV nuclear recoil events is equal to 21.0 ns +/- 0.5 ns. It is observed that for electron recoils T0 rises slowly with energy, having a value ~ 30 ns at Eee ~ 15 keV. Electron and nuclear recoil pulse-shapes are found to be well fitted by single exponential functions although some evidence is found for a double exponential form for the nuclear recoil pulse-shape.Comment: 11 pages, including 5 encapsulated postscript figure

Generalizations of entanglement based on coherent states and convex sets

Unentangled pure states on a bipartite system are exactly the coherent states with respect to the group of local transformations. What aspects of the study of entanglement are applicable to generalized coherent states? Conversely, what can be learned about entanglement from the well-studied theory of coherent states? With these questions in mind, we characterize unentangled pure states as extremal states when considered as linear functionals on the local Lie algebra. As a result, a relativized notion of purity emerges, showing that there is a close relationship between purity, coherence and (non-)entanglement. To a large extent, these concepts can be defined and studied in the even more general setting of convex cones of states. Based on the idea that entanglement is relative, we suggest considering these notions in the context of partially ordered families of Lie algebras or convex cones, such as those that arise naturally for multipartite systems. The study of entanglement includes notions of local operations and, for information-theoretic purposes, entanglement measures and ways of scaling systems to enable asymptotic developments. We propose ways in which these may be generalized to the Lie-algebraic setting, and to a lesser extent to the convex-cones setting. One of our original motivations for this program is to understand the role of entanglement-like concepts in condensed matter. We discuss how our work provides tools for analyzing the correlations involved in quantum phase transitions and other aspects of condensed-matter systems.Comment: 37 page

Recent developments in planet migration theory

Planetary migration is the process by which a forming planet undergoes a drift of its semi-major axis caused by the tidal interaction with its parent protoplanetary disc. One of the key quantities to assess the migration of embedded planets is the tidal torque between the disc and planet, which has two components: the Lindblad torque and the corotation torque. We review the latest results on both torque components for planets on circular orbits, with a special emphasis on the various processes that give rise to additional, large components of the corotation torque, and those contributing to the saturation of this torque. These additional components of the corotation torque could help address the shortcomings that have recently been exposed by models of planet population syntheses. We also review recent results concerning the migration of giant planets that carve gaps in the disc (type II migration) and the migration of sub-giant planets that open partial gaps in massive discs (type III migration).Comment: 52 pages, 18 figures. Review article to be published in "Tidal effects in Astronomy and Astrophysics", Lecture Notes in Physic

The Milky Way Bulge: Observed properties and a comparison to external galaxies

The Milky Way bulge offers a unique opportunity to investigate in detail the role that different processes such as dynamical instabilities, hierarchical merging, and dissipational collapse may have played in the history of the Galaxy formation and evolution based on its resolved stellar population properties. Large observation programmes and surveys of the bulge are providing for the first time a look into the global view of the Milky Way bulge that can be compared with the bulges of other galaxies, and be used as a template for detailed comparison with models. The Milky Way has been shown to have a box/peanut (B/P) bulge and recent evidence seems to suggest the presence of an additional spheroidal component. In this review we summarise the global chemical abundances, kinematics and structural properties that allow us to disentangle these multiple components and provide constraints to understand their origin. The investigation of both detailed and global properties of the bulge now provide us with the opportunity to characterise the bulge as observed in models, and to place the mixed component bulge scenario in the general context of external galaxies. When writing this review, we considered the perspectives of researchers working with the Milky Way and researchers working with external galaxies. It is an attempt to approach both communities for a fruitful exchange of ideas.Comment: Review article to appear in "Galactic Bulges", Editors: Laurikainen E., Peletier R., Gadotti D., Springer Publishing. 36 pages, 10 figure

The Science of Sungrazers, Sunskirters, and Other Near-Sun Comets

This review addresses our current understanding of comets that venture close to the Sun, and are hence exposed to much more extreme conditions than comets that are typically studied from Earth. The extreme solar heating and plasma environments that these objects encounter change many aspects of their behaviour, thus yielding valuable information on both the comets themselves that complements other data we have on primitive solar system bodies, as well as on the near-solar environment which they traverse. We propose clear definitions for these comets: We use the term near-Sun comets to encompass all objects that pass sunward of the perihelion distance of planet Mercury (0.307 AU). Sunskirters are defined as objects that pass within 33 solar radii of the Sun’s centre, equal to half of Mercury’s perihelion distance, and the commonly-used phrase sungrazers to be objects that reach perihelion within 3.45 solar radii, i.e. the fluid Roche limit. Finally, comets with orbits that intersect the solar photosphere are termed sundivers. We summarize past studies of these objects, as well as the instruments and facilities used to study them, including space-based platforms that have led to a recent revolution in the quantity and quality of relevant observations. Relevant comet populations are described, including the Kreutz, Marsden, Kracht, and Meyer groups, near-Sun asteroids, and a brief discussion of their origins. The importance of light curves and the clues they provide on cometary composition are emphasized, together with what information has been gleaned about nucleus parameters, including the sizes and masses of objects and their families, and their tensile strengths. The physical processes occurring at these objects are considered in some detail, including the disruption of nuclei, sublimation, and ionisation, and we consider the mass, momentum, and energy loss of comets in the corona and those that venture to lower altitudes. The different components of comae and tails are described, including dust, neutral and ionised gases, their chemical reactions, and their contributions to the near-Sun environment. Comet-solar wind interactions are discussed, including the use of comets as probes of solar wind and coronal conditions in their vicinities. We address the relevance of work on comets near the Sun to similar objects orbiting other stars, and conclude with a discussion of future directions for the field and the planned ground- and space-based facilities that will allow us to address those science topics

Acceptance and commitment therapy for late-life treatment-resistant generalised anxiety disorder: a feasibility study.

Background Generalised anxiety disorder (GAD) is the most common anxiety disorder in older people. First-line management includes pharmacological and psychological therapies, but many do not find these effective or acceptable. Little is known about how to manage treatment-resistant generalised anxiety disorder (TR-GAD) in older people. Objectives To examine the acceptability, feasibility and preliminary estimates of the effectiveness of acceptance and commitment therapy (ACT) for older people with TR-GAD. Participants People aged ≥65 years with TR-GAD (defined as not responding to GAD treatment, tolerate it or refused treatment) recruited from primary and secondary care services and the community. Intervention Participants received up to 16 one-to-one sessions of ACT, developed specifically for older people with TR-GAD, in addition to usual care. Measurements Co-primary outcomes were feasibility (defined as recruitment of ≥32 participants and retention of ≥60% at follow-up) and acceptability (defined as participants attending ≥10 sessions and scoring ≥21/30 on the satisfaction with therapy subscale). Secondary outcomes included measures of anxiety, worry, depression and psychological flexibility (assessed at 0 and 20 weeks). Results Thirty-seven participants were recruited, 30 (81%) were retained and 26 (70%) attended ≥10 sessions. A total of 18/30 (60%) participants scored ≥21/30 on the satisfaction with therapy subscale. There was preliminary evidence suggesting that ACT may improve anxiety, depression and psychological flexibility. Conclusions There was evidence of good feasibility and acceptability, although satisfaction with therapy scores suggested that further refinement of the intervention may be necessary. Results indicate that a larger-scale randomised controlled trial of ACT for TR-GAD is feasible and warranted

Variational formulas and cocycle solutions for directed polymer and percolation models

We discuss variational formulas for the law of large numbers limits of certain models of motion in a random medium: namely, the limiting time constant for last-passage percolation and the limiting free energy for directed polymers. The results are valid for models in arbitrary dimension, steps of the admissible paths can be general, the environment process is ergodic under spatial translations, and the potential accumulated along a path can depend on the environment and the next step of the path. The variational formulas come in two types: one minimizes over gradient-like cocycles, and another one maximizes over invariant measures on the space of environments and paths. Minimizing cocycles can be obtained from Busemann functions when these can be proved to exist. The results are illustrated through 1+1 dimensional exactly solvable examples, periodic examples, and polymers in weak disorder

A randomised controlled trial of acceptance and commitment therapy plus usual care compared to usual care alone for improving psychological health in people with motor neuron disease (COMMEND): study protocol

Background Motor neuron disease (MND) is a rapidly progressive, fatal neurodegenerative disease that predominantly affects motor neurons from the motor cortex to the spinal cord and causes progressive wasting and weakening of bulbar, limb, abdominal and thoracic muscles. Prognosis is poor and median survival is 2–3 years following symptom onset. Psychological distress is relatively common in people living with MND. However, formal psychotherapy is not routinely part of standard care within MND Care Centres/clinics in the UK, and clear evidence-based guidance on improving the psychological health of people living with MND is lacking. Previous research suggests that Acceptance and Commitment Therapy (ACT) may be particularly suitable for people living with MND and may help improve their psychological health. Aims To assess the clinical and cost-effectiveness of ACT modified for MND plus usual multidisciplinary care (UC) in comparison to UC alone for improving psychological health in people living with MND. Methods The COMMEND trial is a multi-centre, assessor-blind, parallel, two-arm RCT with a 10-month internal pilot phase. 188 individuals aged ≥ 18 years with a diagnosis of definite, laboratory-supported probable, clinically probable, or possible familial or sporadic amyotrophic lateral sclerosis, and additionally the progressive muscular atrophy and primary lateral sclerosis variants, will be recruited from approximately 14 UK-based MND Care Centres/clinics and via self-referral. Participants will be randomly allocated to receive up to eight 1:1 sessions of ACT plus UC or UC alone by an online randomisation system. Participants will complete outcome measures at baseline and at 6- and 9-months post-randomisation. The primary outcome will be quality of life at six months. Secondary outcomes will include depression, anxiety, psychological flexibility, health-related quality of life, adverse events, ALS functioning, survival at nine months, satisfaction with therapy, resource use and quality-adjusted life years. Primary analyses will be by intention to treat and data will be analysed using multi-level modelling. Discussion This trial will provide definitive evidence on the clinical and cost-effectiveness of ACT plus UC in comparison to UC alone for improving psychological health in people living with MND