Search results for "statistical"
showing 10 items of 4960 documents
The discretized harmonic oscillator: Mathieu functions and a new class of generalized Hermite polynomials
2003
We present a general, asymptotical solution for the discretised harmonic oscillator. The corresponding Schr\"odinger equation is canonically conjugate to the Mathieu differential equation, the Schr\"odinger equation of the quantum pendulum. Thus, in addition to giving an explicit solution for the Hamiltonian of an isolated Josephon junction or a superconducting single-electron transistor (SSET), we obtain an asymptotical representation of Mathieu functions. We solve the discretised harmonic oscillator by transforming the infinite-dimensional matrix-eigenvalue problem into an infinite set of algebraic equations which are later shown to be satisfied by the obtained solution. The proposed ansa…
Are most of the stationary points in a molecular association minima? Application of Fraga's potential to benzene-benzene
1993
The importance of characterizing the stationary points of the intermolecular potential by means of Hessian eigenvalues is illustrated for the calculation of the benzene–benzene interaction using an atom-to-atom pair potential proposed by Fraga (FAAP). Two models, the standard one-center-per atom and another using three-centers-per atom due to Hunter and Sanders, are used to evaluate the electrostatic contributions and the results are compared. It is found in both cases that although using low-gradient thresholds allows optimization procedures to avoid many stationary points that are not true minima computing time considerations makes the usual procedure of using high-gradient thresholds [sa…
Computer-aided detection of cerebral microbleeds in susceptibility-weighted imaging.
2014
Susceptibility-weighted imaging (SWI) is recognized as the preferred MRI technique for visualizing cerebral vasculature and related pathologies such as cerebral microbleeds (CMBs). Manual identification of CMBs is time-consuming, has limited reliability and reproducibility, and is prone to misinterpretation. In this paper, a novel computer-aided microbleed detection technique based on machine learning is presented: First, spherical-like objects (potential CMB candidates) with their corresponding bounding boxes were detected using a novel multi-scale Laplacian of Gaussian technique. A set of robust 3-dimensional Radon- and Hessian-based shape descriptors within each bounding box were then ex…
On the Symmetry of Solutions to a k-Hessian Type Equation
2013
Abstract In this note we prove that if u is a negative solution to a nonlinear elliptic equation involving a Hessian operator, and u is zero on the boundary of a ball, then u is radially symmetric and increasing along the radii.
PDF reweighting in the Hessian matrix approach
2014
We introduce the Hessian reweighting of parton distribution functions (PDFs). Similarly to the better-known Bayesian methods, its purpose is to address the compatibility of new data and the quantitative modifications they induce within an existing set of PDFs. By construction, the method discussed here applies to the PDF fits that carried out a Hessian error analysis using a non-zero tolerance $\Delta\chi^2$. The principle is validated by considering a simple, transparent example. We are also able to establish an agreement with the Bayesian technique provided that the tolerance criterion is appropriately accounted for and that a purely exponential Bayesian likelihood is assumed. As a practi…
Apertureless scanning near-field optical microscopy: a comparison between homodyne and heterodyne approaches
2006
International audience; In coherent homodyne apertureless scanning near-field optical microscopy (ASNOM) the background field cannot be fully suppressed because of the interference between the different collected fields, making the images difficult to interpret. We show that implementing the heterodyne version of ASNOM allows one to overcome this issue. We present a comparison between homodyne and heterodyne ASNOM through near-field analysis of gold nanowells, integrated waveguides, and a single evanescent wave generated by total internal reflection. The heterodyne approach allows for the control of the interferometric effect with the background light. In particular, the undesirable backgro…
Avoiding Boundary Effects in Wang-Landau Sampling
2003
A simple modification of the ``Wang-Landau sampling'' algorithm removes the systematic error that occurs at the boundary of the range of energy over which the random walk takes place in the original algorithm.
A heuristic model-based approach for compensating wind effects in ski jumping.
2021
Wind influences the jump length in ski jumping, which raises questions about the fairness. To counteract the wind problem, the International Ski Federation has introduced a wind compensation system in 2009: time-averaged wind velocity components tangential to the landing slope are obtained from several sites along the landing slope, and these data are used in a linear statistical model for estimating the jump length effect of wind. This is considered in the total score of the ski jump. However, it has been shown that the jump length effect estimates can be inaccurate and misleading. The present manuscript introduces an alternative mathematical wind compensation approach that is based on an …
Gravitational Test beyond the First Post-Newtonian Order with the Shadow of the M87 Black Hole
2020
All authors: Psaltis, Dimitrios; Medeiros, Lia; Christian, Pierre; Özel, Feryal; Akiyama, Kazunori; Alberdi, Antxon; Alef, Walter; Asada, Keiichi; Azulay, Rebecca; Ball, David; Baloković, Mislav; Barrett, John; Bintley, Dan; Blackburn, Lindy; Boland, Wilfred; Bower, Geoffrey C.; Bremer, Michael; Brinkerink, Christiaan D.; Brissenden, Roger; Britzen, Silke Broguiere, Dominique; Bronzwaer, Thomas; Byun, Do-Young; Carlstrom, John E.; Chael, Andrew; Chan, Chi-kwan; Chatterjee, Shami; Chatterjee, Koushik; Chen, Ming-Tang; Chen, Yongjun; Cho, Ilje; Conway, John E.; Cordes, James M.; Crew, Geoffrey B.; Cui, Yuzhu; Davelaar, Jordy; De Laurentis, Mariafelicia; Deane, Roger; Dempsey, Jessica; Desvign…
Cancelling out systematic uncertainties
2011
We present a method to minimize, or even cancel out, the nuisance parameters affecting a measurement. Our approach is general and can be applied to any experiment or observation. We compare it with the bayesian technique used to deal with nuisance parameters: marginalization, and show how the method compares and improves by avoiding biases. We illustrate the method with several examples taken from the astrophysics and cosmology world: baryonic acoustic oscillations, cosmic clocks, Supernova Type Ia luminosity distance, neutrino oscillations and dark matter detection. By applying the method we recover some known results but also find some interesting new ones. For baryonic acoustic oscillati…