122 research outputs found
A strong pair correlation bound implies the CLT for Sinai Billiards
For Dynamical Systems, a strong bound on multiple correlations implies the
Central Limit Theorem (CLT) [ChMa]. In Chernov's paper [Ch2], such a bound is
derived for dynamically Holder continuous observables of dispersing Billiards.
Here we weaken the regularity assumption and subsequently show that the bound
on multiple correlations follows directly from the bound on pair correlations.
Thus, a strong bound on pair correlations alone implies the CLT, for a wider
class of observables. The result is extended to Anosov diffeomorphisms in any
dimension.Comment: 13 page
A Spectral Bernstein Theorem
We study the spectrum of the Laplace operator of a complete minimal properly
immersed hypersurface in . (1) Under a volume growth condition on
extrinsic balls and a condition on the unit normal at infinity, we prove that
has only essential spectrum consisting of the half line .
This is the case when , where
is the extrinsic distance to a point of and are the
principal curvatures. (2) If the satisfy the decay conditions
, and strict inequality is achieved at some point
, then there are no eigenvalues. We apply these results to minimal
graphic and multigraphic hypersurfaces.Comment: 16 pages. v2. Final version: minor revisions, we add Proposition 3.2.
Accepted for publication in the Annali di Matematica Pura ed Applicata, on
the 05/03/201
The road to deterministic matrices with the restricted isometry property
The restricted isometry property (RIP) is a well-known matrix condition that
provides state-of-the-art reconstruction guarantees for compressed sensing.
While random matrices are known to satisfy this property with high probability,
deterministic constructions have found less success. In this paper, we consider
various techniques for demonstrating RIP deterministically, some popular and
some novel, and we evaluate their performance. In evaluating some techniques,
we apply random matrix theory and inadvertently find a simple alternative proof
that certain random matrices are RIP. Later, we propose a particular class of
matrices as candidates for being RIP, namely, equiangular tight frames (ETFs).
Using the known correspondence between real ETFs and strongly regular graphs,
we investigate certain combinatorial implications of a real ETF being RIP.
Specifically, we give probabilistic intuition for a new bound on the clique
number of Paley graphs of prime order, and we conjecture that the corresponding
ETFs are RIP in a manner similar to random matrices.Comment: 24 page
Effective Lagrangian Approach to the Theory of Eta Photoproduction in the Region
We investigate eta photoproduction in the resonance region
within the effective Lagrangian approach (ELA), wherein leading contributions
to the amplitude at the tree level are taken into account. These include the
nucleon Born terms and the leading -channel vector meson exchanges as the
non-resonant pieces. In addition, we consider five resonance contributions in
the - and - channel; besides the dominant , these are:
and . The amplitudes for the
and the photoproduction near threshold have significant
differences, even as they share common contributions, such as those of the
nucleon Born terms. Among these differences, the contribution to the
photoproduction of the -channel excitation of the is the most
significant. We find the off-shell properties of the spin-3/2 resonances to be
important in determining the background contributions. Fitting our effective
amplitude to the available data base allows us to extract the quantity
, characteristic of the
photoexcitation of the resonance and its decay into the
-nucleon channel, of interest to precise tests of hadron models. At the
photon point, we determine it to be from
the old data base, and from a
combination of old data base and new Bates data. We obtain the helicity
amplitude for to be from the old data base, and from the combination of the old data base and new Bates
data, compared with the results of the analysis of pion photoproduction
yielding , in the same units.Comment: 43 pages, RevTeX, 9 figures available upon request, to appear in
Phys. Rev.
Towards Machine Wald
The past century has seen a steady increase in the need of estimating and
predicting complex systems and making (possibly critical) decisions with
limited information. Although computers have made possible the numerical
evaluation of sophisticated statistical models, these models are still designed
\emph{by humans} because there is currently no known recipe or algorithm for
dividing the design of a statistical model into a sequence of arithmetic
operations. Indeed enabling computers to \emph{think} as \emph{humans} have the
ability to do when faced with uncertainty is challenging in several major ways:
(1) Finding optimal statistical models remains to be formulated as a well posed
problem when information on the system of interest is incomplete and comes in
the form of a complex combination of sample data, partial knowledge of
constitutive relations and a limited description of the distribution of input
random variables. (2) The space of admissible scenarios along with the space of
relevant information, assumptions, and/or beliefs, tend to be infinite
dimensional, whereas calculus on a computer is necessarily discrete and finite.
With this purpose, this paper explores the foundations of a rigorous framework
for the scientific computation of optimal statistical estimators/models and
reviews their connections with Decision Theory, Machine Learning, Bayesian
Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty
Quantification and Information Based Complexity.Comment: 37 page
Metal enrichment processes
There are many processes that can transport gas from the galaxies to their
environment and enrich the environment in this way with metals. These metal
enrichment processes have a large influence on the evolution of both the
galaxies and their environment. Various processes can contribute to the gas
transfer: ram-pressure stripping, galactic winds, AGN outflows, galaxy-galaxy
interactions and others. We review their observational evidence, corresponding
simulations, their efficiencies, and their time scales as far as they are known
to date. It seems that all processes can contribute to the enrichment. There is
not a single process that always dominates the enrichment, because the
efficiencies of the processes vary strongly with galaxy and environmental
properties.Comment: 18 pages, 8 figures, accepted for publication in Space Science
Reviews, special issue "Clusters of galaxies: beyond the thermal view",
Editor J.S. Kaastra, Chapter 17; work done by an international team at the
International Space Science Institute (ISSI), Bern, organised by J.S.
Kaastra, A.M. Bykov, S. Schindler & J.A.M. Bleeke
National identity predicts public health support during a global pandemic
Changing collective behaviour and supporting non-pharmaceutical interventions is an important component in mitigating virus transmission during a pandemic. In a large international collaboration (Study 1, Nâ=â49,968 across 67 countries), we investigated self-reported factors associated with public health behaviours (e.g., spatial distancing and stricter hygiene) and endorsed public policy interventions (e.g., closing bars and restaurants) during the early stage of the COVID-19 pandemic (April-May 2020). Respondents who reported identifying more strongly with their nation consistently reported greater engagement in public health behaviours and support for public health policies. Results were similar for representative and non-representative national samples. Study 2 (Nâ=â42 countries) conceptually replicated the central finding using aggregate indices of national identity (obtained using the World Values Survey) and a measure of actual behaviour change during the pandemic (obtained from Google mobility reports). Higher levels of national identification prior to the pandemic predicted lower mobility during the early stage of the pandemic (râ=ââ0.40). We discuss the potential implications of links between national identity, leadership, and public health for managing COVID-19 and future pandemics.publishedVersio
Measurement of the cross section of high transverse momentum ZâbbÌ production in protonâproton collisions at âs = 8 TeV with the ATLAS detector
This Letter reports the observation of a high transverse momentum ZâbbÌ signal in protonâproton collisions at âs=8 TeV and the measurement of its production cross section. The data analysed were collected in 2012 with the ATLAS detector at the LHC and correspond to an integrated luminosity of 19.5 fbâÂč. The ZâbbÌ decay is reconstructed from a pair of b -tagged jets, clustered with the anti-ktkt jet algorithm with R=0.4R=0.4, that have low angular separation and form a dijet with pT>200 GeVpT>200 GeV. The signal yield is extracted from a fit to the dijet invariant mass distribution, with the dominant, multi-jet background mass shape estimated by employing a fully data-driven technique that reduces the dependence of the analysis on simulation. The fiducial cross section is determined to be
ÏZâbbÂŻfid=2.02±0.20 (stat.) ±0.25 (syst.)±0.06 (lumi.) pb=2.02±0.33 pb,
in good agreement with next-to-leading-order theoretical predictions
- âŠ