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The spectral data matrix X can be assumed to be linearly and additively related to the concentrations of chemical components according to Beer Lambert's law: begin{aligned} X = YA end{aligned} (3)where Y is the matrix of concentrations of the chemical components and A is the matrix of standardised diffraction contributions to each energy channel from each chemical component.
The use of a matrix of concentrations of signals in both the wild type Arabidopsis and in G protein mutants provides information about signal interactions in complex biological responses and the ability to assign branches of the signaling pathway to possible roles for signaling elements.
Cells were treated simultaneously with FRAX1036 (dose range = 0 to 5 μM) or docetaxel (dose range = 0 to 0.4 nM) in an 8 × 10 matrix of concentrations.
This leads to where S is the matrix of spectral components, c is the matrix of concentrations to be predicted and X is the measured spectra.
Consider analysis of a mixture containing K pure components, whose mass spectra are δ1, δ2,..., δ K : (1) The above equations can be written more concisely by introducing the matrix Δ, (2) Let C be the matrix of concentrations of K pure components over the time of the GC-MS experiment, sampled at points t1, t2,..., t R.
MCF-7 cells (1.7×10/cm) were treated simultaneously with YM155 (0.0004 to 0.1 μmol/L) and either doxorubicin, taxol, camptothecin, or etoposide (dose range for each agent 0.004 to 1 μmol/L) in a 7 × 7 matrix of concentrations for 48 h.
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where the matrix A represents the absorbance matrix, C is the concentration matrix, P is the calibration coefficients and E is a matrix of concentration prediction error.
Images were processed and evaluated by a custom MATLAB script with Equation 2 at its core: (2) C = 1 ε 365nm · L A 365nm - A 436nm where C is the matrix of concentration values across the image (i.e. pixels), the absorbance matrices A λ are described by Equation 1, and ε365nm and L are scalar values as in Equation 1 as well.
For analysis of the bi bi substrate kinetic mechanism of GmATPS1, initial velocity rates were measured under standard assay conditions with a matrix of substrate concentrations.
A secondary screen to further narrow mutant selection employed a quantitative assessment of the growth of the original 48 colonies on 1 mM Ome using a matrix of chloramphenicol concentrations.
Following the initial dilution period, we transferred cells to 96 well microplates (round bottom, polystyrene, Corning) and set up a two-dimensional matrix of drug concentrations in each 96-well microplate (165 μl media per well).
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