## What is/are Fractional Abundances?

Fractional Abundances - Fractional abundances of methylated GSTP1 DNA fragments were significantly increased in subgroup III of metastatic PCa patients (p < 0.^{[1]}Initially hyperspectral (HS) data exploitation model on identification of pure spectral signatures (endmembers) and their corresponding fractional abundances in each pixel of the HS data cube has been proposed.

^{[2]}In addition, we identified several cell subsets whose fractional abundances associated with histological determined EE severity, small intestinal region, and HIV infection.

^{[3]}Hyperspectral unmixing is the procedure by which the end component elements are calculated and their fractional abundances are found in each pixel in hyperspectral images.

^{[4]}Blind hyperspectral unmixing is an important technique in hyperspectral image analysis, aiming at estimating endmembers and their respective fractional abundances.

^{[5]}Fractional abundances of bauxite were derived by using a matched-filtering method.

^{[6]}While gas-phase astrochemical reaction networks nicely replicate the abundance of hydrogen-deficient organics like linear cyanopolyynes, pathways to complex organic molecules (COMs)—organic molecules with six or more atoms—have not been completely understood, with gas-phase models often significantly underestimating fractional abundances of the astronomically observed organics by orders of magnitude.

^{[7]}We use the compiled dataset and new fractional abundances to generate brGDGT calibrations for warm-season air temperatures and lake water conductivity and pH for use in lake sediments globally.

^{[8]}The fractional abundances of HCNH+ with respect to H2, [HCNH+], are in the range 0.

^{[9]}The 13C- and 12C-isotopologues of the amino acid phenylalanine (Phe) proved to be a quantitatively accurate reporter molecules of cellular isotopic fractional abundances (fcell).

^{[10]}Spectral unmixing is an important technique for hyperspectral image application, which aims to estimate the pure spectral signatures in each mixed pixel and their corresponding fractional abundances.

^{[11]}In all cases we evaluate the fractional abundances of PBHs by comparing Press–Schechter approach and peak theory, while focusing on explaining the dark matter in the Universe.

^{[12]}It amounts at estimating the spectral signatures of the pure spectral constituents in the scene (endmembers) and their corresponding subpixel fractional abundances.

^{[13]}This indicates that the mechanism behind the changed fractional abundances is a pH-modulated bacterial community shift.

^{[14]}Due to the complex interaction of light with mixed materials, reflectance spectra are highly nonlinearly related to the pure material endmember spectra, making it hard to estimate the fractional abundances of the materials.

^{[15]}KRAS mutant droplets were detected in three out of nine platelet RNA samples with fractional abundances of 0.

^{[16]}Recent water line observations toward several low-mass protostars suggest low water gas fractional abundances (< 10−6 with respect total hydrogen density) in the inner warm envelopes (r < 102 au).

^{[17]}Meanwhile, the spectral-spatial weighted sparse regularization term is introduced to promote the sparsity of fractional abundances in the spectral and spatial domains.

^{[18]}These candidates present small velocity dispersions, high fractional abundances of NH2D, high NH3 deuterium fractionations, and are completely dark in the infrared wavelengths from 3.

^{[19]}We also adopt a double reweighted $\ell_{1}$ norm minimization scheme to promote the sparsity of fractional abundances.

^{[20]}The proposed deep image prior uses a convolutional neural network to estimate the fractional abundances, relying on the extracted endmembers and the observed hyperspectral dataset.

^{[21]}Second, we introduce a new approach for analyzing brGDGT data in which compound fractional abundances (FAs) are calculated within structural groups based on methylation number, methylation position, and cyclization number.

^{[22]}The proposed deep image prior uses a convolutional neural network to estimate the fractional abundances, relying on the extracted endmembers and the observed hyperspectral data set.

^{[23]}, endmembers and their associated fractional abundances, to retrieve hyperspectral scenes.

^{[24]}ABSTRACT Blind hyperspectral unmixing is a key technique for mixing spectral analysis, which separate the endmember spectra from hyperspectral image and evaluate their fractional abundances.

^{[25]}We also adopt a double reweighted $\ell_{1}$ norm minimization scheme to promote the sparsity of fractional abundances.

^{[26]}Their fractional abundances exhibited differences beyond the sample temperature.

^{[27]}We have obtained molecular fractional abundances with respect to H$_{2}$ from 10$^{-7}$ down to a few 10$^{-9}$ and with respect to CH$_{3}$OH from 10$^{-3}$ to $\sim$4$\times$10$^{-2}$.

^{[28]}ABSTRACT Nonnegative matrix factorization (NMF) has been one of the most widely used techniques for hyperspectral unmixing (HU), which aims at decomposing each mixed pixel into a set of endmembers and their corresponding fractional abundances.

^{[29]}Second, we introduce a new approach for analyzing brGDGT data in which compound fractional abundances (FAs) are calculated within structural groups based on methylation number, methylation position, and cyclization number.

^{[30]}In this work, we present a nonlinear spectral mixing model that, apart from the fractional abundances, contains two additional parameters, one accounting for multiple reflections and another accounting for shadow.

^{[31]}In a first step, we propose to use sparse fractional abundances as decision source, complementary to class probabilities obtained from a supervised classifier.

^{[32]}Hyperspectral unmixing is the process of finding the fractional abundances and corresponding spectral signatures of a mixed pixel in a hyperspectral image.

^{[33]}Finally, from our application to L1157, we find that the fractional abundances within the B2 region are consistent with both C-type and J-type shock emission.

^{[34]}The physical and chemical conditions, such as density, temperature, and fractional abundances are calculated.

^{[35]}It is the process of estimating constituent endmembers and their fractional abundances present at each pixel in a hyperspectral image.

^{[36]}We update the calibration of [NeII] and [NeIII] strength as a SFR indicator, explicitly considering the effects of metallicity, finding very good relations between Ne fractional abundances and the [NeIII]/[NeII] ratio for different metallicities, ionization parameters, and starburst ages.

^{[37]}Linear Spectral Unmixing (LSU) is a widely used technique in the field of Remote Sensing (RS) for the estimation of fractional abundances of endmembers and their spectral signatures.

^{[38]}It aims at estimating the fractional abundances of pure spectral signatures in mixed pixels in hyperspectral images.

^{[39]}However, small fractional abundances were observed below 3000 m a.

^{[40]}The C-S bearing species C2S and o-H2CS present fractional abundances a factor of > two higher in the core than in the PDR.

^{[41]}We performed excitation and radiative transfer calculations based on the large velocity gradient (LVG) method to model the observed lines of the molecules and to derive their fractional abundances in the observed envelopes.

^{[42]}The column densities and fractional abundances of these species are measured and together these species account for 10\% of the cosmic sulfur abundance in the region.

^{[43]}It comprises the identification of pure spectral signatures (endmembers) and their corresponding fractional abundances in each pixel of the HS data cube.

^{[44]}The mechanical and chemical properties of a compound material are determined by the fractional abundances of its components.

^{[45]}The fragment ion fractional abundances, plotted in the breakdown diagram, along with the time-of-flight mass spectra for the first three metastable CO-loss channels were modeled using a statistical approach.

^{[46]}The importance of the Hall effect varies with the Hall coefficient, and this coefficient is determined by the fractional abundances of charged species.

^{[47]}Production of simple and complex molecules to depth on the order of 10 m or more is achieved, with local fractional abundances comparable to observed values in many cases.

^{[48]}The linear mixture model has been widely utilized to unmix hyperspectral images by extracting a set of pure spectral signatures, called endmembers in hyperspectral jargon, and estimating their respective fractional abundances in each pixel of the scene.

^{[49]}This method factorizes a hyperspectral cube into constituent endmembers and their fractional abundances.

^{[50]}

## Corresponding Fractional Abundances

Initially hyperspectral (HS) data exploitation model on identification of pure spectral signatures (endmembers) and their corresponding fractional abundances in each pixel of the HS data cube has been proposed.^{[1]}Spectral unmixing is an important technique for hyperspectral image application, which aims to estimate the pure spectral signatures in each mixed pixel and their corresponding fractional abundances.

^{[2]}ABSTRACT Nonnegative matrix factorization (NMF) has been one of the most widely used techniques for hyperspectral unmixing (HU), which aims at decomposing each mixed pixel into a set of endmembers and their corresponding fractional abundances.

^{[3]}It comprises the identification of pure spectral signatures (endmembers) and their corresponding fractional abundances in each pixel of the HS data cube.

^{[4]}Blind hyperspectral unmixing (HU), as a crucial technique for hyperspectral data exploitation, aims to decompose mixed pixels into a collection of constituent materials weighted by the corresponding fractional abundances.

^{[5]}Hyperspectral unmixing has been widely used to decompose a mixed pixel into a collection of endmembers weighted by their corresponding fractional abundances, in which endmember extraction step is of crucial importance.

^{[6]}

## Respective Fractional Abundances

Blind hyperspectral unmixing is an important technique in hyperspectral image analysis, aiming at estimating endmembers and their respective fractional abundances.^{[1]}The linear mixture model has been widely utilized to unmix hyperspectral images by extracting a set of pure spectral signatures, called endmembers in hyperspectral jargon, and estimating their respective fractional abundances in each pixel of the scene.

^{[2]}

## Estimated Fractional Abundances

Furthermore, a reweighted^{[1]}Then noise-adjusted principal component analysis (NAPCA) is taken to transform the original datasets into PCA domain and maintain only the most significant principal component as well as wipe off the inaccurate estimated fractional abundances.

^{[2]}

## Compound Fractional Abundances

Second, we introduce a new approach for analyzing brGDGT data in which compound fractional abundances (FAs) are calculated within structural groups based on methylation number, methylation position, and cyclization number.^{[1]}Second, we introduce a new approach for analyzing brGDGT data in which compound fractional abundances (FAs) are calculated within structural groups based on methylation number, methylation position, and cyclization number.

^{[2]}