scholarly journals Cover-based bounds on the numerical rank of Gaussian kernels

2014 ◽  
Vol 36 (2) ◽  
pp. 302-315 ◽  
Author(s):  
Amit Bermanis ◽  
Guy Wolf ◽  
Amir Averbuch
Keyword(s):  
Numerical Rank ◽  
Gaussian Kernels

scholarly journals Superpixel Segmentation Based on Anisotropic Edge Strength

2019 ◽  
Vol 5 (6) ◽  
pp. 57 ◽  
Author(s):  
Gang Wang ◽  
Bernard De Baets
Keyword(s):  
Distance Measure ◽  
Saliency Detection ◽  
Experimental Results ◽  
Segmentation Method ◽  
Superpixel Segmentation ◽  
Gaussian Kernels ◽  
First Derivative ◽  
Edge Strength

Superpixel segmentation can benefit from the use of an appropriate method to measure edge strength. In this paper, we present such a method based on the first derivative of anisotropic Gaussian kernels. The kernels can capture the position, direction, prominence, and scale of the edge to be detected. We incorporate the anisotropic edge strength into the distance measure between neighboring superpixels, thereby improving the performance of an existing graph-based superpixel segmentation method. Experimental results validate the superiority of our method in generating superpixels over the competing methods. It is also illustrated that the proposed superpixel segmentation method can facilitate subsequent saliency detection.

scholarly journals Multi-omics-based prediction of hybrid performance in canola

2021 ◽  
Author(s):  
Dominic Knoch ◽  
Christian R. Werner ◽  
Rhonda C. Meyer ◽  
David Riewe ◽  
Amine Abbadi ◽  
...  
Keyword(s):  
Hilbert Space ◽  
Genetic Markers ◽  
Reproducing Kernel ◽  
Prediction Models ◽  
Agronomic Traits ◽  
Reproducing Kernel Hilbert Space ◽  
Hybrid Performance ◽  
Hybrid Prediction ◽  
Gaussian Kernels ◽  
Breeding Programmes

Abstract Key message Complementing or replacing genetic markers with transcriptomic data and use of reproducing kernel Hilbert space regression based on Gaussian kernels increases hybrid prediction accuracies for complex agronomic traits in canola. In plant breeding, hybrids gained particular importance due to heterosis, the superior performance of offspring compared to their inbred parents. Since the development of new top performing hybrids requires labour-intensive and costly breeding programmes, including testing of large numbers of experimental hybrids, the prediction of hybrid performance is of utmost interest to plant breeders. In this study, we tested the effectiveness of hybrid prediction models in spring-type oilseed rape (Brassica napus L./canola) employing different omics profiles, individually and in combination. To this end, a population of 950 F1 hybrids was evaluated for seed yield and six other agronomically relevant traits in commercial field trials at several locations throughout Europe. A subset of these hybrids was also evaluated in a climatized glasshouse regarding early biomass production. For each of the 477 parental rapeseed lines, 13,201 single nucleotide polymorphisms (SNPs), 154 primary metabolites, and 19,479 transcripts were determined and used as predictive variables. Both, SNP markers and transcripts, effectively predict hybrid performance using (genomic) best linear unbiased prediction models (gBLUP). Compared to models using pure genetic markers, models incorporating transcriptome data resulted in significantly higher prediction accuracies for five out of seven agronomic traits, indicating that transcripts carry important information beyond genomic data. Notably, reproducing kernel Hilbert space regression based on Gaussian kernels significantly exceeded the predictive abilities of gBLUP models for six of the seven agronomic traits, demonstrating its potential for implementation in future canola breeding programmes.

scholarly journals Learning Theory Estimates with Observations from General Stationary Stochastic Processes

2016 ◽  
Vol 28 (12) ◽  
pp. 2853-2889 ◽  
Author(s):  
Hanyuan Hang ◽  
Yunlong Feng ◽  
Ingo Steinwart ◽  
Johan A. K. Suykens
Keyword(s):  
Stochastic Processes ◽  
Type Inequality ◽  
Empirical Risk Minimization ◽  
Risk Minimization ◽  
Mixing Processes ◽  
Gaussian Kernels ◽  
Empirical Risk ◽  
Learning Rates ◽  
Stationary Stochastic Processes ◽  
Learning Schemes

This letter investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by general, we mean that many stationary stochastic processes can be included. We show that when the stochastic processes satisfy a generalized Bernstein-type inequality, a unified treatment on analyzing the learning schemes with various mixing processes can be conducted and a sharp oracle inequality for generic regularized empirical risk minimization schemes can be established. The obtained oracle inequality is then applied to derive convergence rates for several learning schemes such as empirical risk minimization (ERM), least squares support vector machines (LS-SVMs) using given generic kernels, and SVMs using gaussian kernels for both least squares and quantile regression. It turns out that for independent and identically distributed (i.i.d.) processes, our learning rates for ERM recover the optimal rates. For non-i.i.d. processes, including geometrically [Formula: see text]-mixing Markov processes, geometrically [Formula: see text]-mixing processes with restricted decay, [Formula: see text]-mixing processes, and (time-reversed) geometrically [Formula: see text]-mixing processes, our learning rates for SVMs with gaussian kernels match, up to some arbitrarily small extra term in the exponent, the optimal rates. For the remaining cases, our rates are at least close to the optimal rates. As a by-product, the assumed generalized Bernstein-type inequality also provides an interpretation of the so-called effective number of observations for various mixing processes.

scholarly journals Multiscale Modeling of Electronic Spectra Including Nuclear Quantum Effects

2021 ◽  
Author(s):  
Peter Feher ◽  
Ádám Madarász ◽  
András Stirling
Keyword(s):  
Electronic Absorption Spectra ◽  
Quantum Effects ◽  
Experimental Spectrum ◽  
Redox States ◽  
Line Shapes ◽  
Gaussian Kernels ◽  
The Individual ◽  
The Impact ◽  
Nuclear Quantum Effects ◽  
Vertical Transitions

<div>Theoretical prediction of electronic absorption spectra without input from experiment is no easy feat as it requires addressing all the factors that affect line shapes. In practice, however, the methodologies are limited to treat these ingredients only to a certain extent. Here we present a multiscale protocol that addresses the temperature, solvent and nuclear quantum effects, anharmonicity and reconstruction of the final spectra from the individual transitions. First, QM/MM molecular dynamics is conducted to obtain trajectories of solute-solvent configurations, from which the corresponding quantum corrected ensembles are generated through the Generalized Smoothed Trajectory Analysis (GSTA). The optical spectra of the ensembles are then produced by calculating vertical transitions using TDDFT with implicit solvation. To obtain the final spectral shapes, the stick spectra from TDDFT are convoluted with Gaussian kernels where the half-widths are determined by a statistically motivated strategy. We have tested our method by calculating the UV-vis spectra of a recently discovered acridine photocatalyst in two redox states and evaluated the impact of each step. Nuclear quantization affects the relative peak intensities and widths, which is necessary to reproduce the experimental spectrum. We have also found that using only the optimized geometry of each molecule works surprisingly well if a proper empirical broadening factor is applied. This is explained by the rigidity of the conjugated chromophore moieties of the selected molecules which are mainly responsible for the excitations in the spectra. In contrast, we have also shown that the molecules are flexible enough to feature anharmonicities that impair the Wigner sampling. </div>

scholarly journals An Overview of Various Importance Measures of Reliability System

2017 ◽  
Vol 2 (3) ◽  
pp. 150-171 ◽  
Author(s):  
Kalpesh P. Amrutkar ◽  
Kirtee K. Kamalja
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
System Failure ◽  
Numerical Rank ◽  
Reliability Improvement ◽  
System Reliability Analysis ◽  
Component Importance ◽  
Critical Components ◽  
The Impact ◽  
Reliability Systems

One of the purposes of system reliability analysis is to identify the weaknesses or the critical components in a system and to quantify the impact of component’s failures. Various importance measures are being introduced by many researchers since 1969. These component importance measures provide a numerical rank to determine which components are more important to system reliability improvement or more critical to system failure. In this paper, we overview various components importance measures and briefly discuss them with examples. We also discuss some other extended importance measures and review the developments in study of various importance measures with respect to some of the popular reliability systems.

Effect of medical school attended on the chances of successfully embarking on a clinical-academic career in the UK

2020 ◽  
pp. postgradmedj-2020-139001
Author(s):  
Callum John Donaldson ◽  
Miguel Sequeira Campos ◽  
Joanne Ridgley ◽  
Alexander Light
Keyword(s):  
Academic Performance ◽  
Medical School ◽  
Medical Curriculum ◽  
Academic Career ◽  
Research Focus ◽  
Numerical Rank ◽  
Application Rates ◽  
Equal Chance ◽  
Intercalated Degree ◽  
The Uk

Purpose of the studyThis study aimed to investigate whether, in the UK, medical school attended influences the propensity to apply to and be successful in obtaining an offer from the Academic Foundation Programme (AFP), thus taking the first step to embarking on a clinical-academic career.Study designA retrospective observational study was performed. Using the UK Foundation Programme’s yearly statistical report data, mean application rates to, and mean offer rates from the AFP were calculated by medical school, between the years 2017–2019. Mean application and mean offer rates were subsequently correlated with metrics of medical school academic performance and research focus.ResultsMean application rates to the AFP were higher in medical schools that had a mandatory intercalated degree as part of the undergraduate medical curriculum (mean=33.99%, SD=13.93 vs mean=19.44%, SD=6.88, p<0.001), lower numerical rank in the Times Higher Education 2019 World Rankings (correlation with higher numerical rank, r=−0.50, p=0.004), and lower numerical rank in the Research Excellence Framework 2014 UK rankings (correlation with higher numerical rank, r=−0.37, p=0.004). Mean offer rates from the AFP were not correlated with any metric of medical school academic performance or research focus.ConclusionsStudents attending a medical school with greater academic performance and research focus are more likely to apply and subsequently embark on a clinical-academic career. However, students wishing to embark a clinical-academic career from any medical school have an equal chance of success.

scholarly journals Bump hunting with non-Gaussian kernels

2004 ◽  
Vol 32 (5) ◽  
pp. 2124-2141 ◽  
Author(s):  
Chunming Zhang ◽  
Michael C. Minnotte ◽  
Peter Hall
Keyword(s):  
Gaussian Kernels ◽  
Bump Hunting ◽  
Non Gaussian
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