Spectral statistics of random geometric graphs

We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the spectrum via the nearest neighbour and next nearest neighbour spacing distribution and long range correlations via the spectral rigidity Delta_3 statistic. These correlations in the level spacings give information about localisation of eigenvectors, level of community structure and the level of randomness within the networks. We find a parameter dependent transition between Poisson and Gaussian orthogonal ensemble statistics. That is the spectral statistics of spatial random geometric graphs fits the universality of random matrix theory found in other models such as Erdos-Renyi, Barabasi-Albert and Watts-Strogatz random graph.Comment: 19 pages, 6 figures. Substantially updated from previous versio

Trial of Remote Continuous versus Intermittent NEWS monitoring after major surgery (TRaCINg): protocol for a feasibility randomised controlled trial

Background: Despite medical advances, major surgery remains high risk. Up to 44% of patients experience postoperative complications, which can have huge impacts for patients and the healthcare system. Early recognition of postoperative complications is crucial in reducing morbidity and preventing long-term disability. The current standard of care is intermittent manual vital signs monitoring, but new wearable remote monitors offer the benefits of continuous vital signs monitoring without limiting the patient’s mobility. The aim of this study is to evaluate the feasibility, acceptability and clinical impacts of continuous remote monitoring after major surgery. Methods: The study is a randomised, controlled, unblinded, parallel group, feasibility trial. Adult patients undergoing elective major surgery will be invited to participate if they have the capacity to provided informed, written consent and do not have a cardiac pacemaker or an allergy to adhesives. Participants will be randomly assigned to receive continuous remote monitoring and normal National Early Warning Score (NEWS) monitoring (intervention group) or normal NEWS monitoring alone (control group). Continuous remote monitoring will be achieved using the SensiumVitals® wireless patch which is worn on the patient’s chest and monitors heart rate, respiratory rate and temperature continuously and alerts the nurse when there is deviation from pre-set physiological norms. Participants will be followed up throughout their hospital admission and for 30 days after discharge. Feasibility will be assessed by evaluating recruitment rate, adherence to protocol and randomisation, and the amount of missing data. The acceptability of the patch to nursing staff and patients will be assessed using questionnaires and interviews. Clinical outcomes will include time to antibiotics in cases of sepsis, length of hospital stay, number of critical care admissions and rate of readmission within 30 days of discharge. Discussion: Early detection and treatment of complications minimises the need for critical care, improves patient outcomes, and produces significant cost savings for the healthcare system. Remote continuous monitoring systems have the potential to allow earlier detection of complications, but evidence from the literature is mixed. Demonstrating significant benefit over intermittent monitoring to offset the practical and economic implications of continuous monitoring requires well-controlled studies in high-risk populations to demonstrate significant differences in clinical outcomes; this feasibility trial seeks to provide evidence of how best to conduct such a confirmatory trial. Trial registration: This study is listed on the ISRCTN registry with study ID ISRCTN16601772

On the rate of quantum ergodicity in Euclidean billiards

For a large class of quantized ergodic flows the quantum ergodicity theorem due to Shnirelman, Zelditch, Colin de Verdi\`ere and others states that almost all eigenfunctions become equidistributed in the semiclassical limit. In this work we first give a short introduction to the formulation of the quantum ergodicity theorem for general observables in terms of pseudodifferential operators and show that it is equivalent to the semiclassical eigenfunction hypothesis for the Wigner function in the case of ergodic systems. Of great importance is the rate by which the quantum mechanical expectation values of an observable tend to their mean value. This is studied numerically for three Euclidean billiards (stadium, cosine and cardioid billiard) using up to 6000 eigenfunctions. We find that in configuration space the rate of quantum ergodicity is strongly influenced by localized eigenfunctions like bouncing ball modes or scarred eigenfunctions. We give a detailed discussion and explanation of these effects using a simple but powerful model. For the rate of quantum ergodicity in momentum space we observe a slower decay. We also study the suitably normalized fluctuations of the expectation values around their mean, and find good agreement with a Gaussian distribution.Comment: 40 pages, LaTeX2e. This version does not contain any figures. A version with all figures can be obtained from http://www.physik.uni-ulm.de/theo/qc/ (File: http://www.physik.uni-ulm.de/theo/qc/ulm-tp/tp97-8.ps.gz) In case of any problems contact Arnd B\"acker (e-mail: [email protected]) or Roman Schubert (e-mail: [email protected]

Semiclassical measures and the Schroedinger flow on Riemannian manifolds

In this article we study limits of Wigner distributions (the so-called semiclassical measures) corresponding to sequences of solutions to the semiclassical Schroedinger equation at times scales $\alpha_{h}$ tending to infinity as the semiclassical parameter $h$ tends to zero (when $\alpha _{h}=1/h$ this is equivalent to consider solutions to the non-semiclassical Schreodinger equation). Some general results are presented, among which a weak version of Egorov's theorem that holds in this setting. A complete characterization is given for the Euclidean space and Zoll manifolds (that is, manifolds with periodic geodesic flow) via averaging formulae relating the semiclassical measures corresponding to the evolution to those of the initial states. The case of the flat torus is also addressed; it is shown that non-classical behavior may occur when energy concentrates on resonant frequencies. Moreover, we present an example showing that the semiclassical measures associated to a sequence of states no longer determines those of their evolutions. Finally, some results concerning the equation with a potential are presented.Comment: 18 pages; Theorems 1,2 extendend to deal with arbitrary time-scales; references adde

Large deviations for non-uniformly expanding maps

We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space average with respect to a physical measure and compare this with the time averages along orbits of the map, showing that the Lebesgue measure of the set of points whose time averages stay away from the space average decays to zero exponentially fast with the number of iterates involved. As easy by-products we deduce escape rates from subsets of the basins of physical measures for these types of maps. The rates of decay are naturally related to the metric entropy and pressure function of the system with respect to a family of equilibrium states. The corrections added to the published version of this text appear in bold; see last section for a list of changesComment: 36 pages, 1 figure. After many PhD students and colleagues having pointed several errors in the statements and proofs, this is a correction to published article answering those comments. List of main changes in a new last sectio

The acquisition of Sign Language: The impact of phonetic complexity on phonology

Research into the effect of phonetic complexity on phonological acquisition has a long history in spoken languages. This paper considers the effect of phonetics on phonological development in a signed language. We report on an experiment in which nonword-repetition methodology was adapted so as to examine in a systematic way how phonetic complexity in two phonological parameters of signed languages — handshape and movement — affects the perception and articulation of signs. Ninety-one Deaf children aged 3–11 acquiring British Sign Language (BSL) and 46 hearing nonsigners aged 6–11 repeated a set of 40 nonsense signs. For Deaf children, repetition accuracy improved with age, correlated with wider BSL abilities, and was lowest for signs that were phonetically complex. Repetition accuracy was correlated with fine motor skills for the youngest children. Despite their lower repetition accuracy, the hearing group were similarly affected by phonetic complexity, suggesting that common visual and motoric factors are at play when processing linguistic information in the visuo-gestural modality

Atmospheric teleconnections between the Arctic and the Baltic Sea region as simulated by CESM1-LE

This paper examines teleconnections between the Arctic and the Baltic Sea region and is based on two cases of Community Earth System Model version 1 large ensemble (CESM-LE) climate model simulations: the stationary case with pre-industrial radiative forcing and the climate change case with RCP8.5 radiative forcing. The stationary control simulation's 1800-year long time series were used for stationary teleconnection and a 40-member ensemble from the period 1920–2100 is used for teleconnections during ongoing climate change. We analyzed seasonal temperature at a 2 m level, sea-level pressure, sea ice concentration, precipitation, geopotential height, and 10 m level wind speed. The Arctic was divided into seven areas. The Baltic Sea region climate has strong teleconnections with the Arctic climate; the strongest connections are with Svalbard and Greenland region. There is high seasonality in the teleconnections, with the strongest correlations in winter and the lowest correlations in summer, when the local meteorological factors are stronger. North Atlantic Oscillation (NAO) and Arctic Oscillation (AO) climate indices can explain most teleconnections in winter and spring. During ongoing climate change, the teleconnection patterns did not show remarkable changes by the end of the 21st century. Minor pattern changes are between the Baltic Sea region temperature and the sea ice concentration. We calculated the correlation between the parameter and its ridge regression estimation to estimate different Arctic regions' collective statistical connections with the Baltic Sea region. The seasonal coefficient of determination, R2, was highest for winter: for T2 m, R2=0.64; for sea level pressure (SLP), R2=0.44; and for precipitation (PREC), R2=0.35. When doing the same for the seasons' previous month values in the Arctic, the relations are considerably weaker, with the highest R2=0.09 being for temperature in the spring. Hence, Arctic climate data forecasting capacity for the Baltic Sea region is weak. Although there are statistically significant teleconnections between the Arctic and Baltic Sea region, the Arctic impacts are regional and mostly connected with climate indexes. There are no simple cause-and-effect pathways. By the end of the 21st century, the Arctic ice concentration has significantly decreased. Still, the general teleconnection patterns between the Arctic and the Baltic Sea region will not change considerably by the end of the 21st century.</p

Natural equilibrium states for multimodal maps

This paper is devoted to the study of the thermodynamic formalism for a class of real multimodal maps. This class contains, but it is larger than, Collet-Eckmann. For a map in this class, we prove existence and uniqueness of equilibrium states for the geometric potentials $-t \log|Df|$, for the largest possible interval of parameters $t$. We also study the regularity and convexity properties of the pressure function, completely characterising the first order phase transitions. Results concerning the existence of absolutely continuous invariant measures with respect to the Lebesgue measure are also obtained