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https://www.ncbi.nlm.nih.gov/pmc/articles/PMC395890/
Apr 20, 2004 · We say that a real function on the real line has a spectral gap if its Fourier transform is zero in a neighborhood of the origin. In communication engineering, such functions are called high-pass signals. It is known that functions with a spectral gap oscillate.Cited by: 7
https://www.jstor.org/stable/24491536
the support of functions and distributions with a spectral gap created date: 20160730064411z ...
https://www.math.purdue.edu/~eremenko/dvi/pnas.pdf
stationary process whose correlation function has a spectral gap ( −a;a) (this implies that almost all trajectories have this spectral gap as well). Our main result con rms Logan’s conjecture for a wide class of distributions which contains S 0. A smooth positive even function on the real line, concave1 on some ray [t 0;+1), will be called ...
https://www.math.purdue.edu/~eremenko/dvi/novik999.pdf
Statement 1 Suppose that a real function f has a spectral gap, that is its Fourier transform is zero on an interval (−a;a). Then the number of sign changes s(r;f) of fon the interval [0;r] satis es liminf r!1 s(r;f) r a ˇ: (2) Supported by NSF grant DMS 0100512 and by the Humboldt Foundation.
http://www.math.uni.wroc.pl/~lorek/papers/LorekSzekli_spectral_gap_JAP_PRINTED.pdf
Spectral gap for network processes 405 stronglight-tailnessofthestationarydistribution. Itisworthmentioningthatadmittingservice rates which are state dependent in the model implies that each discrete distribution with the support{0,1,2,...}canappearasthestationarydistributionforanodeinthenetwork. Wewill
https://www.stat.berkeley.edu/~pitman/s205s03/lecture28.pdf
Lecture 28: The Spectral Gap 28-4 The expression above exhibits the fact that for reversible Markov chains the spectral gap controls the rate of exponential decay to the stationary distribution. Lemma 28.4 Let K be a Markov kernel with spectral gap λ= λ(K).
https://core.ac.uk/download/pdf/81137638.pdf
In engineering literature, functions with a spectral gap are called high-pass signals. Condition (3) is too weak to develop a proper extension of Harmonic Analysis [5]. For example, it may happen for a locally integrable functionf =0thatF+ and F− are restrictions of a single entire function, so according to our Definition 1, the spectrum of f
https://projecteuclid.org/euclid.acta/1485892605
— On the transfer function of a one-dimensional boundary problem of the second order. Dokl. Akad.Nauk SSSR, 88 (1953), 405–408 (Russian). — On a basic approximation problem of the theory of extrapolation and filtration of stationary random processes. Dokl. Akad.Nauk SSSR, 94 (1954), 13–16 (Russian). L evinson, N., Gap andDensity Theorems. American Mathematical Society Colloquium …Cited by: 20
https://www.sciencedirect.com/science/article/pii/S1631073X03000360
It is known that if a real finite Borel measure has a spectral gap at the origin then either it must have many sign changes or it is zero identically. Assume the Fourier transform of a real temperate distribution agrees in a neighborhood of the origin with the sum of an analytic function and a …Cited by: 5
https://www.researchgate.net/publication/251701212_On_sign_changes_of_tempered_distributions_having_a_spectral_gap_at_the_origin
On sign changes of tempered distributions having a spectral gap at the origin Article in Comptes Rendus Mathematique 336(4):325-330 · February 2003 with 9 Reads How we measure 'reads'
https://arxiv.org/abs/1101.0332v3
Next, utilizing some results on birth and death processes, we find bounds on the spectral gap for network processes in terms of the hazard and equilibrium functions of the one dimensional marginal distributions of the stationary distribution of the network.
https://link.springer.com/article/10.1007%2FBF02649110
We survey various mathematical aspects of the uncertainty principle, including Heisenberg’s inequality and its variants, local uncertainty inequalities, logarithmic uncertainty inequalities, results relating to Wigner distributions, qualitative uncertainty principles, theorems on approximate concentration, and decompositions of phase space.
http://europepmc.org/articles/PMC395890
We prove an old conjecture on oscillation of functions that have a spectral gap at the origin. Suppose that the Fourier transform of a real measure f on the real line satisfies (x) = 0 for x (–a, a).Then, when r → ∞, the asymptotic lower density of the sequence of sign changes of f on the intervals [0, r) is at least a/π.This still holds for some wider classes of measures characterized ...
https://core.ac.uk/download/pdf/81137638.pdf
Oscillation of Fourier integrals with a spectral gap A. Eremenko∗,1,D.Novikov2 Purdue University, West Lafayette, IN 47907, USA Received 4 May 2003 Abstract Suppose that for a real function f on the real line, the support of its Fourier transform is disjoint from an interval (−a,a). We prove the conjecture of B. Logan that under these ...
https://openreview.net/pdf?id=HJlQfnCqKX
Published as a conference paper at ICLR 2019 PREDICTING THE GENERALIZATION GAP IN DEEP NETWORKS WITH MARGIN DISTRIBUTIONS Yiding Jiang , Dilip Krishnan, Hossein Mobahi, Samy Bengio Google AI fydjiang, dilipkay, hmobahi, [email protected]
https://hal.archives-ouvertes.fr/hal-01756961
Nonlocal Coulomb correlations in pure and electron-doped Sr2IrO4: Spectral functions, Fermi surface, and pseudo-gap-like spectral weight distributions from …
https://en.wikipedia.org/wiki/Distribution_(mathematics)
Distributions are a class of linear functionals that map a set of test functions (conventional and well-behaved functions) into the set of real numbers. In the simplest case, the set of test functions considered is D(R), which is the set of functions : R → R having two properties: is smooth (infinitely differentiable);; has compact support (is identically zero outside some bounded interval).
http://www.arxiv-vanity.com/papers/1712.02429/
Motivated by the intriguing behavior displayed in a dynamic network that models a population of extreme introverts and extroverts (XIE), we consider the spectral properties of ensembles of random split graph adjacency matrices. We discover that, in general, a gap emerges in the bulk spectrum between −1 and 0 that contains a single eigenvalue. An analytic expression for the bulk distribution ...
https://core.ac.uk/download/pdf/50534026.pdf
SPECTRAL GAP FOR SPHERICALLY SYMMETRIC LOG-CONCAVE PROBABILITY MEASURES, AND BEYOND MICHEL BONNEFONT, ALDERIC JOULIN, AND YUTAO MA´ Abstract. Let µ be a probability measure on Rn (n ≥ 2) with Lebesgue density proportional to e−V( kx ), where V : R + → R is a smooth convex potential. We
https://stat.duke.edu/~dawn/torpidMixConditions.pdf
Conditions for Torpid Mixing of Parallel and Simulated Tempering on Multimodal Distributions Dawn B. Woodardy, Scott C. Schmidlery, and Mark Huberz yDepartment of Statistical Science Box 90251 Duke University Durham, NC 27708-0251
https://aip.scitation.org/doi/full/10.1063/1.4919931
Because Planck’s blackbody spectral distribution of thermal radiation does not take the contribution of evanescent waves into account, it is not valid anymore in the near-field, where radiative transfer via tunneling of evanescent waves is dominant. In the case of two planar parallel bodies separated by a subwavelength distance, this leads to a large increase of the radiative heat flux 1,2 1.
https://stat.duke.edu/~dawn/rapidMixTemper.pdf
mixing on two speci c nite state space distributions, the \exponential val-ley density" and the mean- eld Ising model, where the standard (untempered) Metropolis-Hastings chain is torpidly mixing. Zheng (30) bounds the spectral gap of simulated tempering below by a multiple of the spectral gap of parallel
http://www2.stat.duke.edu/%7Escs/Papers/TorpidMixingTemperEJP.pdf
Sufficient Conditions for Torpid Mixing of Parallel and Simulated Tempering Dawn B. Woodard⋆, Scott C. Schmidler†, and Mark Huber‡ We obtain upper bounds on the spectral gap of Markov chains constructed by parallel and simulated tempering, and provide a set of sufficient conditions for torpid mixing of both techniques.
http://rem-main.rem.sfu.ca/forestry/downloads/Files/GLAV2UsersManual.pdf
functions to register and manipulate these imported images. Image processing functions — such as, image threshold, brightness, and contrast — can be used to affect the entire image or only a select portion of it. Results from the GLA calculations are displayed on a separate form with an option to append these data to a spreadsheet.
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