414 research outputs found
Gaussian cubature arising from hybrid characters of simple Lie groups
Lie groups with two different root lengths allow two mixed sign homomorphisms
on their corresponding Weyl groups, which in turn give rise to two families of
hybrid Weyl group orbit functions and characters. In this paper we extend the
ideas leading to the Gaussian cubature formulas for families of polynomials
arising from the characters of irreducible representations of any simple Lie
group, to new cubature formulas based on the corresponding hybrid characters.
These formulas are new forms of Gaussian cubature in the short root length case
and new forms of Radau cubature in the long root case. The nodes for the
cubature arise quite naturally from the (computationally efficient) elements of
finite order of the Lie group.Comment: 23 pages, 3 figure
Sampling constrained probability distributions using Spherical Augmentation
Statistical models with constrained probability distributions are abundant in
machine learning. Some examples include regression models with norm constraints
(e.g., Lasso), probit, many copula models, and latent Dirichlet allocation
(LDA). Bayesian inference involving probability distributions confined to
constrained domains could be quite challenging for commonly used sampling
algorithms. In this paper, we propose a novel augmentation technique that
handles a wide range of constraints by mapping the constrained domain to a
sphere in the augmented space. By moving freely on the surface of this sphere,
sampling algorithms handle constraints implicitly and generate proposals that
remain within boundaries when mapped back to the original space. Our proposed
method, called {Spherical Augmentation}, provides a mathematically natural and
computationally efficient framework for sampling from constrained probability
distributions. We show the advantages of our method over state-of-the-art
sampling algorithms, such as exact Hamiltonian Monte Carlo, using several
examples including truncated Gaussian distributions, Bayesian Lasso, Bayesian
bridge regression, reconstruction of quantized stationary Gaussian process, and
LDA for topic modeling.Comment: 41 pages, 13 figure
Telepresence and the Role of the Senses
The telepresence experience can be evoked in a number of ways. A well-known example is a player of videogames who reports about a telepresence experience, a subjective experience of being in one place or environment, even when physically situated in another place. In this paper we set the phenomenon of telepresence into a theoretical framework. As people react subjectively to stimuli from telepresence, empirical studies can give more evidence about the phenomenon. Thus, our contribution is to bridge the theoretical with the empirical. We discuss theories of perception with an emphasis on Heidegger, Merleau-Ponty and Gibson, the role of the senses and the Spinozian belief procedure. The aim is to contribute to our understanding of this phenomenon. A telepresence-study that included the affordance concept is used to empirically study how players report sense-reactions to virtual sightseeing in two cities. We investigate and explore the interplay of the philosophical and the empirical. The findings indicate that it is not only the visual sense that plays a role in this experience, but all senses
Response operators for Markov processes in a finite state space: radius of convergence and link to the response theory for Axiom A systems
Using straightforward linear algebra we derive response operators describing the impact of small perturbations to finite state Markov processes. The results can be used for studying empirically constructed—e.g. from observations or through coarse graining of model simulations—finite state approximation of statistical mechanical systems. Recent results concerning the convergence of the statistical properties of finite state Markov approximation of the full asymptotic dynamics on the SRB measure in the limit of finer and finer partitions of the phase space are suggestive of some degree of robustness of the obtained results in the case of Axiom A system. Our findings give closed formulas for the linear and nonlinear response theory at all orders of perturbation and provide matrix expressions that can be directly implemented in any coding language, plus providing bounds on the radius of convergence of the perturbative theory. In particular, we relate the convergence of the response theory to the rate of mixing of the unperturbed system. One can use the formulas derived for finite state Markov processes to recover previous findings obtained on the response of continuous time Axiom A dynamical systems to perturbations, by considering the generator of time evolution for the measure and for the observables. A very basic, low-tech, and computationally cheap analysis of the response of the Lorenz ’63 model to perturbations provides rather encouraging results regarding the possibility of using the approximate representation given by finite state Markov processes to compute the system’s response
Carbon isotope fluctuations in Precambrian carbonate sequences of several localities in Brazil
The Formation of the First Massive Black Holes
Supermassive black holes (SMBHs) are common in local galactic nuclei, and
SMBHs as massive as several billion solar masses already exist at redshift z=6.
These earliest SMBHs may grow by the combination of radiation-pressure-limited
accretion and mergers of stellar-mass seed BHs, left behind by the first
generation of metal-free stars, or may be formed by more rapid direct collapse
of gas in rare special environments where dense gas can accumulate without
first fragmenting into stars. This chapter offers a review of these two
competing scenarios, as well as some more exotic alternative ideas. It also
briefly discusses how the different models may be distinguished in the future
by observations with JWST, (e)LISA and other instruments.Comment: 47 pages with 306 references; this review is a chapter in "The First
Galaxies - Theoretical Predictions and Observational Clues", Springer
Astrophysics and Space Science Library, Eds. T. Wiklind, V. Bromm & B.
Mobasher, in pres
Measurement of the B+ and B-0 lifetimes and search for CP(T) violation using reconstructed secondary vertices
The lifetimes of the B+ and B-0 mesons, and their ratio, have been measured in the OPAL experiment using 2.4 million hadronic Z(0) decays recorded at LEP. Z(0) --> b (b) over bar decays were tagged using displaced secondary vertices and high momentum electrons and muons. The lifetimes were then measured using well-reconstructed charged and neutral secondary vertices selected in this tagged data sample. The results aretau(B+) = 1.643 +/- 0.037 +/- 0.025 pstau(Bo) = 1.523 +/- 0.057 +/- 0.053 pstau(B+)/tau(Bo) = 1.079 +/- 0.064 +/- 0.041,where in each case the first error is statistical and the second systematic.A larger data sample of 3.1 million hadronic Z(o) decays has been used to search for CP and CPT violating effects by comparison of inclusive b and (b) over bar hadron decays, No evidence fur such effects is seen. The CP violation parameter Re(epsilon(B)) is measured to be Re(epsilon(B)) = 0.001 +/- 0.014 +/- 0.003and the fractional difference between b and (b) over bar hadron lifetimes is measured to(Delta tau/tau)(b) = tau(b hadron) - tau((b) over bar hadron)/tau(average) = -0.001 +/- 0.012 +/- 0.008
Global, regional, and national comparative risk assessment of 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks, 1990-2015: a systematic analysis for the Global Burden of Disease Study 2015
SummaryBackground The Global Burden of Diseases, Injuries, and Risk Factors Study 2015 provides an up-to-date synthesis of the evidence for risk factor exposure and the attributable burden of disease. By providing national and subnational assessments spanning the past 25 years, this study can inform debates on the importance of addressing risks in context. Methods We used the comparative risk assessment framework developed for previous iterations of the Global Burden of Disease Study to estimate attributable deaths, disability-adjusted life-years (DALYs), and trends in exposure by age group, sex, year, and geography for 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks from 1990 to 2015. This study included 388 risk-outcome pairs that met World Cancer Research Fund-defined criteria for convincing or probable evidence. We extracted relative risk and exposure estimates from randomised controlled trials, cohorts, pooled cohorts, household surveys, census data, satellite data, and other sources. We used statistical models to pool data, adjust for bias, and incorporate covariates. We developed a metric that allows comparisons of exposure across risk factors—the summary exposure value. Using the counterfactual scenario of theoretical minimum risk level, we estimated the portion of deaths and DALYs that could be attributed to a given risk. We decomposed trends in attributable burden into contributions from population growth, population age structure, risk exposure, and risk-deleted cause-specific DALY rates. We characterised risk exposure in relation to a Socio-demographic Index (SDI). Findings Between 1990 and 2015, global exposure to unsafe sanitation, household air pollution, childhood underweight, childhood stunting, and smoking each decreased by more than 25%. Global exposure for several occupational risks, high body-mass index (BMI), and drug use increased by more than 25% over the same period. All risks jointly evaluated in 2015 accounted for 57·8% (95% CI 56·6–58·8) of global deaths and 41·2% (39·8–42·8) of DALYs. In 2015, the ten largest contributors to global DALYs among Level 3 risks were high systolic blood pressure (211·8 million [192·7 million to 231·1 million] global DALYs), smoking (148·6 million [134·2 million to 163·1 million]), high fasting plasma glucose (143·1 million [125·1 million to 163·5 million]), high BMI (120·1 million [83·8 million to 158·4 million]), childhood undernutrition (113·3 million [103·9 million to 123·4 million]), ambient particulate matter (103·1 million [90·8 million to 115·1 million]), high total cholesterol (88·7 million [74·6 million to 105·7 million]), household air pollution (85·6 million [66·7 million to 106·1 million]), alcohol use (85·0 million [77·2 million to 93·0 million]), and diets high in sodium (83·0 million [49·3 million to 127·5 million]). From 1990 to 2015, attributable DALYs declined for micronutrient deficiencies, childhood undernutrition, unsafe sanitation and water, and household air pollution; reductions in risk-deleted DALY rates rather than reductions in exposure drove these declines. Rising exposure contributed to notable increases in attributable DALYs from high BMI, high fasting plasma glucose, occupational carcinogens, and drug use. Environmental risks and childhood undernutrition declined steadily with SDI; low physical activity, high BMI, and high fasting plasma glucose increased with SDI. In 119 countries, metabolic risks, such as high BMI and fasting plasma glucose, contributed the most attributable DALYs in 2015. Regionally, smoking still ranked among the leading five risk factors for attributable DALYs in 109 countries; childhood underweight and unsafe sex remained primary drivers of early death and disability in much of sub-Saharan Africa. Interpretation Declines in some key environmental risks have contributed to declines in critical infectious diseases. Some risks appear to be invariant to SDI. Increasing risks, including high BMI, high fasting plasma glucose, drug use, and some occupational exposures, contribute to rising burden from some conditions, but also provide opportunities for intervention. Some highly preventable risks, such as smoking, remain major causes of attributable DALYs, even as exposure is declining. Public policy makers need to pay attention to the risks that are increasingly major contributors to global burden. Funding Bill & Melinda Gates Foundation
Appearance of fluctuating stripes at the onset of the pseudogap in the high-Tc Superconductor Bi2Sr2CaCu2O8+x
Doped Mott insulators have been shown to have a strong propensity to form
patterns of holes and spins often referred to as stripes. In copper-oxides,
doping also gives rise to the pseudogap state, which transforms into a high
temperature superconductor with sufficient doping or by reducing the
temperature. A long standing question has been the interplay between pseudogap,
which is generic to all hole-doped cuprates, and stripes, whose static form
occurs in only one family of cuprates over a narrow range of the phase diagram.
Here we examine the spatial reorganization of electronic states with the onset
of the pseudogap state at T* in the high-temperature superconductor
Bi2Sr2CaCu2O8+x using spectroscopic mapping with the scanning tunneling
microscope (STM). We find that the onset of the pseudogap phase coincides with
the appearance of electronic patterns that have the predicted characteristics
of fluctuating stripes. As expected, the stripe patterns are strongest when the
hole concentration in the CuO2 planes is close to 1/8 (per Cu). While
demonstrating that the fluctuating stripes emerge with the onset of the
pseudogap state and occur over a large part of the cuprate phase diagram, our
experiments indicate that they are a consequence of pseudogap behavior rather
than its cause.Comment: preprint version, 25 pages including supplementary informatio
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