Excitations of a Bose-condensed gas in anisotropic traps

We investigate the zero-temperature collective excitations of a Bose-condensed atomic gas in anisotropic parabolic traps. The condensate density is determined by solving the Gross-Pitaevskii (GP) equation using a spherical harmonic expansion. The GP eigenfunctions are then used to solve the Bogoliubov equations to obtain the collective excitation frequencies and mode densities. The frequencies of the various modes, classified by their parity and the axial angular momentum quantum number, m, are mapped out as a function of the axial anisotropy. Specific emphasis is placed upon the evolution of these modes from the modes in the limit of an isotropic trap.Comment: 7 pages Revtex, 9 Postscript figure

Finite temperature theory of the trapped two dimensional Bose gas

We present a Hartree-Fock-Bogoliubov (HFB) theoretical treatment of the two-dimensional trapped Bose gas and indicate how semiclassical approximations to this and other formalisms have lead to confusion. We numerically obtain results for the fully quantum mechanical HFB theory within the Popov approximation and show that the presence of the trap stabilizes the condensate against long wavelength fluctuations. These results are used to show where phase fluctuations lead to the formation of a quasicondensate.Comment: 4 pages, 3 figure

Patterns in rational base number systems

Number systems with a rational number $a/b > 1$ as base have gained interest in recent years. In particular, relations to Mahler's 3/2-problem as well as the Josephus problem have been established. In the present paper we show that the patterns of digits in the representations of positive integers in such a number system are uniformly distributed. We study the sum-of-digits function of number systems with rational base $a/b$ and use representations w.r.t. this base to construct normal numbers in base $a$ in the spirit of Champernowne. The main challenge in our proofs comes from the fact that the language of the representations of integers in these number systems is not context-free. The intricacy of this language makes it impossible to prove our results along classical lines. In particular, we use self-affine tiles that are defined in certain subrings of the ad\'ele ring $\mathbb{A}_\mathbb{Q}$ and Fourier analysis in $\mathbb{A}_\mathbb{Q}$. With help of these tools we are able to reformulate our results as estimation problems for character sums

Thomae type formulae for singular Z_N curves

We give an elementary and rigorous proof of the Thomae type formula for singular $Z_N$ curves. To derive the Thomae formula we use the traditional variational method which goes back to Riemann, Thomae and Fuchs.Comment: 22 page

Paleobiology of titanosaurs: reproduction, development, histology, pneumaticity, locomotion and neuroanatomy from the South American fossil record

Fil: García, Rodolfo A.. Instituto de Investigación en Paleobiología y Geología. Museo Provincial Carlos Ameghino. Cipolletti; ArgentinaFil: Salgado, Leonardo. Instituto de Investigación en Paleobiología y Geología. General Roca. Río Negro; ArgentinaFil: Fernández, Mariela. Inibioma-Centro Regional Universitario Bariloche. Bariloche. Río Negro; ArgentinaFil: Cerda, Ignacio A.. Instituto de Investigación en Paleobiología y Geología. Museo Provincial Carlos Ameghino. Cipolletti; ArgentinaFil: Carabajal, Ariana Paulina. Museo Carmen Funes. Plaza Huincul. Neuquén; ArgentinaFil: Otero, Alejandro. Museo de La Plata. Universidad Nacional de La Plata; ArgentinaFil: Coria, Rodolfo A.. Instituto de Paleobiología y Geología. Universidad Nacional de Río Negro. Neuquén; ArgentinaFil: Fiorelli, Lucas E.. Centro Regional de Investigaciones Científicas y Transferencia Tecnológica. Anillaco. La Rioja; Argentin

Diving into the vertical dimension of elasmobranch movement ecology

Knowledge of the three-dimensional movement patterns of elasmobranchs is vital to understand their ecological roles and exposure to anthropogenic pressures. To date, comparative studies among species at global scales have mostly focused on horizontal movements. Our study addresses the knowledge gap of vertical movements by compiling the first global synthesis of vertical habitat use by elasmobranchs from data obtained by deployment of 989 biotelemetry tags on 38 elasmobranch species. Elasmobranchs displayed high intra- and interspecific variability in vertical movement patterns. Substantial vertical overlap was observed for many epipelagic elasmobranchs, indicating an increased likelihood to display spatial overlap, biologically interact, and share similar risk to anthropogenic threats that vary on a vertical gradient. We highlight the critical next steps toward incorporating vertical movement into global management and monitoring strategies for elasmobranchs, emphasizing the need to address geographic and taxonomic biases in deployments and to concurrently consider both horizontal and vertical movements

Collaborative European NeuroTrauma Effectiveness Research in Traumatic Brain Injury (CENTER-TBI): A Prospective Longitudinal Observational Study

BACKGROUND: Current classification of traumatic brain injury (TBI) is suboptimal, and management is based on weak evidence, with little attempt to personalize treatment. A need exists for new precision medicine and stratified management approaches that incorporate emerging technologies. OBJECTIVE: To improve characterization and classification of TBI and to identify best clinical care, using comparative effectiveness research approaches. METHODS: This multicenter, longitudinal, prospective, observational study in 22 countries across Europe and Israel will collect detailed data from 5400 consenting patients, presenting within 24 hours of injury, with a clinical diagnosis of TBI and an indication for computed tomography. Broader registry-level data collection in approximately 20 000 patients will assess generalizability. Cross sectional comprehensive outcome assessments, including quality of life and neuropsychological testing, will be performed at 6 months. Longitudinal assessments will continue up to 24 months post TBI in patient subsets. Advanced neuroimaging and genomic and biomarker data will be used to improve characterization, and analyses will include neuroinformatics approaches to address variations in process and clinical care. Results will be integrated with living systematic reviews in a process of knowledge transfer. The study initiation was from October to December 2014, and the recruitment period was for 18 to 24 months. EXPECTED OUTCOMES: Collaborative European NeuroTrauma Effectiveness Research in TBI should provide novel multidimensional approaches to TBI characterization and classification, evidence to support treatment recommendations, and benchmarks for quality of care. Data and sample repositories will ensure opportunities for legacy research. DISCUSSION: Comparative effectiveness research provides an alternative to reductionistic clinical trials in restricted patient populations by exploiting differences in biology, care, and outcome to support optimal personalized patient management

Uses and management of saltmarshes: A global survey

Saltmarshes are important coastal fringe ecosystems supporting a myriad of coastal uses and users. However, saltmarshes have undergone a significant period of global decline, losing 25%–50% of their coverage due to a range of drivers, but mainly as a result of anthropogenic pressures and land-use change. While the value of these coastal systems to society is recognised, global data are fragmented, patchy, and often restricted to local case studies. There is currently no comprehensive understanding of the global variation of ecosystem services, benefits and management practices available. This pioneering study addresses this by investigating the socio-ecological dimension of global variation in ecosystem service provision, and how this is being managed by and for different saltmarsh users. Through a global online questionnaire survey (n = 438) targeting professional saltmarsh researchers and practitioners representing 40 countries across 5 continents, this paper presents an overview of saltmarsh ecosystem services, key drivers influencing management and the variation in factors that influence them. Analysis indicates considerable variation, with geographical location (‘continent’) being the most common moderator, influencing perceptions of saltmarshes, the prioritisation of ecosystem services and management perceptions. Finally, the paper presents a series of recommendations, including the development of an interdisciplinary, international research programme to support restoration and conservation of saltmarshes worldwide