Search results for "square"
showing 10 items of 1317 documents
Extrapolation of water and formaldehyde harmonic and anharmonic frequencies to the B3LYP/CBS limit using polarization consistent basis sets
2010
The harmonic and anharmonic frequencies of fundamental vibrations in formaldehyde and water were successfully estimated using the B3LYP Kohn-Sham limit. The results obtained with polarization- and correlation-consistent basis sets were fitted with a two-parameter formula. Anharmonic corrections were obtained by a second order perturbation treatment (PT2). We compared the performance of the PT2 scheme on the two title molecules using SCF, MP2 and DFT (BLYP, B3LYP, PBE and B3PW91 functionals) methods combined with polarization consistent pc-n (n = 0, 1, 2, 3, 4) basis sets, Dunning’s basis sets (aug)-cc-pVXZ where X = D, T, Q, 5, 6 and Pople’s basis sets up to 6-311++G(3df,2pd). The influence…
RootsGLOH2: embedding RootSIFT 'square rooting' in sGLOH2
2020
This study introduces an extension of the shifting gradient local orientation histogram doubled (sGLOH2) local image descriptor inspired by RootSIFT ‘square rooting’ as a way to indirectly alter the matching distance used to compare the descriptor vectors. The extended descriptor, named RootsGLOH2, achieved the best results in terms of matching accuracy and robustness among the latest state-of-the-art non-deep descriptors in recent evaluation contests dealing with both planar and non-planar scenes. RootsGLOH2 also achieves a matching accuracy very close to that obtained by the best deep descriptors to date. Beside confirming that ‘square rooting’ has beneficial effects on sGLOH2 as it happe…
Accuracy assessment of fraction of vegetation cover and leaf area index estimates from pragmatic methods in a cropland area
2009
The fraction of vegetation cover (FVC) and the leaf area index (LAI) are important parameters for many agronomic, ecological and meteorological applications. Several in-situ and remote sensing techniques for estimating FVC and LAI have been developed in recent years. In this paper, the uncertainty of in-situ FVC and LAI measurements was evaluated by comparing estimates from LAI-2000 and digital hemispherical photography (DHP). The accuracy achieved with a spectral mixture analysis algorithm and two vegetation indices-based methods was assessed using atmospherically corrected Landsat Thematic Mapper (TM) data over the Barrax cropland area where the European Space Agency (ESA) SENtinel-2 and …
Retrieval of aboveground crop nitrogen content with a hybrid machine learning method
2020
Abstract Hyperspectral acquisitions have proven to be the most informative Earth observation data source for the estimation of nitrogen (N) content, which is the main limiting nutrient for plant growth and thus agricultural production. In the past, empirical algorithms have been widely employed to retrieve information on this biochemical plant component from canopy reflectance. However, these approaches do not seek for a cause-effect relationship based on physical laws. Moreover, most studies solely relied on the correlation of chlorophyll content with nitrogen, and thus neglected the fact that most N is bound in proteins. Our study presents a hybrid retrieval method using a physically-base…
RationalizeRoots: Software Package for the Rationalization of Square Roots
2019
The computation of Feynman integrals often involves square roots. One way to obtain a solution in terms of multiple polylogarithms is to rationalize these square roots by a suitable variable change. We present a program that can be used to find such transformations. After an introduction to the theoretical background, we explain in detail how to use the program in practice.
Subdivision into i-packings and S-packing chromatic number of some lattices
2015
An ?$i$?-packing in a graph ?$G$? is a set of vertices at pairwise distance greater than ?$i$?. For a nondecreasing sequence of integers ?$S=(s_1,s_2,\ldots)$?, the?$S$?-packing chromatic number of a graph ?$G$? is the least integer ?$k$? such that there exists a coloring of ?$G$? into ?$k$? colors where each set of vertices colored ?$i$?, ?$i=1,\ldots,k$?, is an ?$s_i$?-packing. This paper describes various subdivisions of an ?$i$?-packing into ?$j$?-packings ?$(j>i)$? for the hexagonal, square and triangular lattices. These results allow us to bound the ?$S$?-packing chromatic number for these graphs, with more precise bounds and exact values for sequences ?$S=(s_i,i \in \mathbb{N}^*)$?, …
Abelian-Square-Rich Words
2017
An abelian square is the concatenation of two words that are anagrams of one another. A word of length $n$ can contain at most $\Theta(n^2)$ distinct factors, and there exist words of length $n$ containing $\Theta(n^2)$ distinct abelian-square factors, that is, distinct factors that are abelian squares. This motivates us to study infinite words such that the number of distinct abelian-square factors of length $n$ grows quadratically with $n$. More precisely, we say that an infinite word $w$ is {\it abelian-square-rich} if, for every $n$, every factor of $w$ of length $n$ contains, on average, a number of distinct abelian-square factors that is quadratic in $n$; and {\it uniformly abelian-sq…
A Bayesian Multilevel Random-Effects Model for Estimating Noise in Image Sensors
2020
Sensor noise sources cause differences in the signal recorded across pixels in a single image and across multiple images. This paper presents a Bayesian approach to decomposing and characterizing the sensor noise sources involved in imaging with digital cameras. A Bayesian probabilistic model based on the (theoretical) model for noise sources in image sensing is fitted to a set of a time-series of images with different reflectance and wavelengths under controlled lighting conditions. The image sensing model is a complex model, with several interacting components dependent on reflectance and wavelength. The properties of the Bayesian approach of defining conditional dependencies among parame…
Heretical Mutiple Importance Sampling
2016
Multiple Importance Sampling (MIS) methods approximate moments of complicated distributions by drawing samples from a set of proposal distributions. Several ways to compute the importance weights assigned to each sample have been recently proposed, with the so-called deterministic mixture (DM) weights providing the best performance in terms of variance, at the expense of an increase in the computational cost. A recent work has shown that it is possible to achieve a trade-off between variance reduction and computational effort by performing an a priori random clustering of the proposals (partial DM algorithm). In this paper, we propose a novel "heretical" MIS framework, where the clustering …
Unbiased Estimators and Multilevel Monte Carlo
2018
Multilevel Monte Carlo (MLMC) and unbiased estimators recently proposed by McLeish (Monte Carlo Methods Appl., 2011) and Rhee and Glynn (Oper. Res., 2015) are closely related. This connection is elaborated by presenting a new general class of unbiased estimators, which admits previous debiasing schemes as special cases. New lower variance estimators are proposed, which are stratified versions of earlier unbiased schemes. Under general conditions, essentially when MLMC admits the canonical square root Monte Carlo error rate, the proposed new schemes are shown to be asymptotically as efficient as MLMC, both in terms of variance and cost. The experiments demonstrate that the variance reduction…