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least-squares algorithm  (MathWorks Inc)


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    Structured Review

    MathWorks Inc least-squares algorithm
    Least Squares Algorithm, supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/product/least-squares+algorithm/pmc12267651-385-30-36
    Average 90 stars, based on 1 article reviews
    least-squares algorithm - by Bioz Stars, 2026-10
    90/100 stars

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    Related Articles

    Expressing:

    Article Title: Deep learning-based high-resolution time inference for deciphering dynamic gene regulation from fixed embryos
    Article Snippet: Within position ranges 0.10−0.75 EL (for Bcd), 0.15−0.85 EL (for Hb), 0.20−0.85 EL (for Kr in OreR ), and 0.10−0.80 EL (for Kr in 1× bcd ), we used a least-squares algorithm (the “fit” function in MATLAB) to fit the binned data from each species to the following functions: 5 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[{{{\rm{Bcd}}}}]={c}_{1,{{{\rm{Bcd}}}}}{e}^{-x/\lambda }+{c}_{0,{{{\rm{Bcd}}}}},$$\end{document} [ Bcd ] = c 1 , Bcd e − x / λ + c 0 , Bcd , 6 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[{{{\rm{Hb}}}}]={c}_{1,{{{\rm{Hb}}}}}\frac{{e}^{-(x-{x}_{0})/d}}{{e}^{-(x-{x}_{0})/d}+1}+{c}_{0,{{{\rm{Hb}}}}},$$\end{document} [ Hb ] = c 1 , Hb e − ( x − x 0 ) / d e − ( x − x 0 ) / d + 1 + c 0 , Hb , 7 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R={r}_{1}\frac{{e}^{(x-{x}_{{{{\rm{A}}}}})/{d}_{{{{\rm{A}}}}}}}{{e}^{(x-{x}_{{{{\rm{A}}}}})/{d}_{{{{\rm{A}}}}}}+1}\cdot \frac{{e}^{-(x-{x}_{{{{\rm{P}}}}})/{d}_{{{{\rm{P}}}}}}}{{e}^{-(x-{x}_{{{{\rm{P}}}}})/{d}_{{{{\rm{P}}}}}}+1}+{r}_{0},$$\end{document} R = r 1 e ( x − x A ) / d A e ( x − x A ) / d A + 1 ⋅ e − ( x − x P ) / d P e − ( x − x P ) / d P + 1 + r 0 , where c 1,· , c 0,· , r 1 , and r 0 denote the peak and background levels of the corresponding species, respectively; λ , d , d A , and d P indicate the decay lengths of Bcd, Hb, and Kr patterns, respectively; x 0 represents the boundary position of Hb expression pattern; x A and x P denote the anterior and posterior boundary positions of Kr expression domain, respectively.

    Article Title: Differential regulation of alternative promoters emerges from unified kinetics of enhancer-promoter interaction.
    Article Snippet: To extract the GRF, we binned individual data points by Bcd concentration and fitted them to a Hill function using a least-squares algorithm (the “nlinfit” function in MATLAB): y 1⁄4 a 1⁄2Bcd h 1⁄2Bcd h þ Ch0 þ d ð10Þ where h is the Hill coefficient, C0 is the concentration threshold for promoter activation, a indicates the maximal level of Bcd-dependent activity, and d denotes the basal activity.

    Article Title: Change detection in the primate auditory cortex through feedback of prediction error signals
    Article Snippet: Using all the timepoints except for those where F roi exceeded the time-averaged mean plus 1 SD, F roi values were regressed against F neuropil using an iteratively re-weighted least-squares algorithm (robustfit in MATLAB), and the slope of the regression line was defined as a contamination factor for the ROI , .

    Article Title: Deep learning-based high-resolution time inference for deciphering dynamic gene regulation from fixed embryos
    Article Snippet: Experimental data from different positions and time points were fitted altogether to theoretical results using a least-squares algorithm (the “lsqcurvefit” function in MATLAB) to extract kinetic parameters.

    Article Title: Cerebrovascular integrity affects gradients of aging-related dopamine D1 differences in the striatum
    Article Snippet: Linear age-models were fit using a piecewise-linear least-squares algorithm ( https://www.mathworks.com/matlabcentral/fileexchange/40913-piecewise-linear-least-square-fit ).

    Article Title: Network-level encoding of local neurotransmitters in cortical astrocytes.
    Article Snippet: To identify this point, traces were fitted using a modified Boltzmann’s sigmoidal equation: f x a c( ) = 1 + e +b x d( − ) / in which a is the difference between the minimum and the maximum fluorescence, b is the inflection point, c is the baseline fluorescence and d is the slope, using a nonlinear least-squares algorithm (Levenberg– Marquardt) in MATLAB (Mathworks).

    Article Title: Biphasic patterns of age-related differences in dopamine D1 receptors across the adult lifespan.
    Article Snippet: Bilinear age-models were fit using a piecewise-linear least-squares algorithm (https://www.mathworks.com/matlabcentral/fileexchange/40913-piecewise-linear-leastsquare-fit).

    Article Title: Objective monitoring of laser tattoo removal in human volunteers using an innovative optical technique: A proof of principle.
    Article Snippet: In doing so, we account also for the finite sample opening of our IS (see Section 2.1).27 Assessment of skin properties (inverse Monte Carlo) Matching of the measured PPTR signals and DRS spectra with predictions of our numerical model is performed iteratively using a nonlinear least‐squares algorithm (lsqnonlin by Mathworks).

    Modification:

    Article Title: Deep learning-based high-resolution time inference for deciphering dynamic gene regulation from fixed embryos
    Article Snippet: Within position ranges 0.10−0.75 EL (for Bcd), 0.15−0.85 EL (for Hb), 0.20−0.85 EL (for Kr in OreR ), and 0.10−0.80 EL (for Kr in 1× bcd ), we used a least-squares algorithm (the “fit” function in MATLAB) to fit the binned data from each species to the following functions: 5 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[{{{\rm{Bcd}}}}]={c}_{1,{{{\rm{Bcd}}}}}{e}^{-x/\lambda }+{c}_{0,{{{\rm{Bcd}}}}},$$\end{document} [ Bcd ] = c 1 , Bcd e − x / λ + c 0 , Bcd , 6 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[{{{\rm{Hb}}}}]={c}_{1,{{{\rm{Hb}}}}}\frac{{e}^{-(x-{x}_{0})/d}}{{e}^{-(x-{x}_{0})/d}+1}+{c}_{0,{{{\rm{Hb}}}}},$$\end{document} [ Hb ] = c 1 , Hb e − ( x − x 0 ) / d e − ( x − x 0 ) / d + 1 + c 0 , Hb , 7 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R={r}_{1}\frac{{e}^{(x-{x}_{{{{\rm{A}}}}})/{d}_{{{{\rm{A}}}}}}}{{e}^{(x-{x}_{{{{\rm{A}}}}})/{d}_{{{{\rm{A}}}}}}+1}\cdot \frac{{e}^{-(x-{x}_{{{{\rm{P}}}}})/{d}_{{{{\rm{P}}}}}}}{{e}^{-(x-{x}_{{{{\rm{P}}}}})/{d}_{{{{\rm{P}}}}}}+1}+{r}_{0},$$\end{document} R = r 1 e ( x − x A ) / d A e ( x − x A ) / d A + 1 ⋅ e − ( x − x P ) / d P e − ( x − x P ) / d P + 1 + r 0 , where c 1,· , c 0,· , r 1 , and r 0 denote the peak and background levels of the corresponding species, respectively; λ , d , d A , and d P indicate the decay lengths of Bcd, Hb, and Kr patterns, respectively; x 0 represents the boundary position of Hb expression pattern; x A and x P denote the anterior and posterior boundary positions of Kr expression domain, respectively.

    Article Title: Differential regulation of alternative promoters emerges from unified kinetics of enhancer-promoter interaction.
    Article Snippet: To extract the GRF, we binned individual data points by Bcd concentration and fitted them to a Hill function using a least-squares algorithm (the “nlinfit” function in MATLAB): y 1⁄4 a 1⁄2Bcd h 1⁄2Bcd h þ Ch0 þ d ð10Þ where h is the Hill coefficient, C0 is the concentration threshold for promoter activation, a indicates the maximal level of Bcd-dependent activity, and d denotes the basal activity.

    Article Title: Change detection in the primate auditory cortex through feedback of prediction error signals
    Article Snippet: Using all the timepoints except for those where F roi exceeded the time-averaged mean plus 1 SD, F roi values were regressed against F neuropil using an iteratively re-weighted least-squares algorithm (robustfit in MATLAB), and the slope of the regression line was defined as a contamination factor for the ROI , .

    Article Title: Deep learning-based high-resolution time inference for deciphering dynamic gene regulation from fixed embryos
    Article Snippet: Experimental data from different positions and time points were fitted altogether to theoretical results using a least-squares algorithm (the “lsqcurvefit” function in MATLAB) to extract kinetic parameters.

    Article Title: Cerebrovascular integrity affects gradients of aging-related dopamine D1 differences in the striatum
    Article Snippet: Linear age-models were fit using a piecewise-linear least-squares algorithm ( https://www.mathworks.com/matlabcentral/fileexchange/40913-piecewise-linear-least-square-fit ).

    Article Title: Network-level encoding of local neurotransmitters in cortical astrocytes.
    Article Snippet: To identify this point, traces were fitted using a modified Boltzmann’s sigmoidal equation: f x a c( ) = 1 + e +b x d( − ) / in which a is the difference between the minimum and the maximum fluorescence, b is the inflection point, c is the baseline fluorescence and d is the slope, using a nonlinear least-squares algorithm (Levenberg– Marquardt) in MATLAB (Mathworks).

    Article Title: Biphasic patterns of age-related differences in dopamine D1 receptors across the adult lifespan.
    Article Snippet: Bilinear age-models were fit using a piecewise-linear least-squares algorithm (https://www.mathworks.com/matlabcentral/fileexchange/40913-piecewise-linear-leastsquare-fit).

    Article Title: Objective monitoring of laser tattoo removal in human volunteers using an innovative optical technique: A proof of principle.
    Article Snippet: In doing so, we account also for the finite sample opening of our IS (see Section 2.1).27 Assessment of skin properties (inverse Monte Carlo) Matching of the measured PPTR signals and DRS spectra with predictions of our numerical model is performed iteratively using a nonlinear least‐squares algorithm (lsqnonlin by Mathworks).

    Fluorescence:

    Article Title: Deep learning-based high-resolution time inference for deciphering dynamic gene regulation from fixed embryos
    Article Snippet: Within position ranges 0.10−0.75 EL (for Bcd), 0.15−0.85 EL (for Hb), 0.20−0.85 EL (for Kr in OreR ), and 0.10−0.80 EL (for Kr in 1× bcd ), we used a least-squares algorithm (the “fit” function in MATLAB) to fit the binned data from each species to the following functions: 5 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[{{{\rm{Bcd}}}}]={c}_{1,{{{\rm{Bcd}}}}}{e}^{-x/\lambda }+{c}_{0,{{{\rm{Bcd}}}}},$$\end{document} [ Bcd ] = c 1 , Bcd e − x / λ + c 0 , Bcd , 6 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[{{{\rm{Hb}}}}]={c}_{1,{{{\rm{Hb}}}}}\frac{{e}^{-(x-{x}_{0})/d}}{{e}^{-(x-{x}_{0})/d}+1}+{c}_{0,{{{\rm{Hb}}}}},$$\end{document} [ Hb ] = c 1 , Hb e − ( x − x 0 ) / d e − ( x − x 0 ) / d + 1 + c 0 , Hb , 7 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R={r}_{1}\frac{{e}^{(x-{x}_{{{{\rm{A}}}}})/{d}_{{{{\rm{A}}}}}}}{{e}^{(x-{x}_{{{{\rm{A}}}}})/{d}_{{{{\rm{A}}}}}}+1}\cdot \frac{{e}^{-(x-{x}_{{{{\rm{P}}}}})/{d}_{{{{\rm{P}}}}}}}{{e}^{-(x-{x}_{{{{\rm{P}}}}})/{d}_{{{{\rm{P}}}}}}+1}+{r}_{0},$$\end{document} R = r 1 e ( x − x A ) / d A e ( x − x A ) / d A + 1 ⋅ e − ( x − x P ) / d P e − ( x − x P ) / d P + 1 + r 0 , where c 1,· , c 0,· , r 1 , and r 0 denote the peak and background levels of the corresponding species, respectively; λ , d , d A , and d P indicate the decay lengths of Bcd, Hb, and Kr patterns, respectively; x 0 represents the boundary position of Hb expression pattern; x A and x P denote the anterior and posterior boundary positions of Kr expression domain, respectively.

    Article Title: Differential regulation of alternative promoters emerges from unified kinetics of enhancer-promoter interaction.
    Article Snippet: To extract the GRF, we binned individual data points by Bcd concentration and fitted them to a Hill function using a least-squares algorithm (the “nlinfit” function in MATLAB): y 1⁄4 a 1⁄2Bcd h 1⁄2Bcd h þ Ch0 þ d ð10Þ where h is the Hill coefficient, C0 is the concentration threshold for promoter activation, a indicates the maximal level of Bcd-dependent activity, and d denotes the basal activity.

    Article Title: Change detection in the primate auditory cortex through feedback of prediction error signals
    Article Snippet: Using all the timepoints except for those where F roi exceeded the time-averaged mean plus 1 SD, F roi values were regressed against F neuropil using an iteratively re-weighted least-squares algorithm (robustfit in MATLAB), and the slope of the regression line was defined as a contamination factor for the ROI , .

    Article Title: Deep learning-based high-resolution time inference for deciphering dynamic gene regulation from fixed embryos
    Article Snippet: Experimental data from different positions and time points were fitted altogether to theoretical results using a least-squares algorithm (the “lsqcurvefit” function in MATLAB) to extract kinetic parameters.

    Article Title: Cerebrovascular integrity affects gradients of aging-related dopamine D1 differences in the striatum
    Article Snippet: Linear age-models were fit using a piecewise-linear least-squares algorithm ( https://www.mathworks.com/matlabcentral/fileexchange/40913-piecewise-linear-least-square-fit ).

    Article Title: Network-level encoding of local neurotransmitters in cortical astrocytes.
    Article Snippet: To identify this point, traces were fitted using a modified Boltzmann’s sigmoidal equation: f x a c( ) = 1 + e +b x d( − ) / in which a is the difference between the minimum and the maximum fluorescence, b is the inflection point, c is the baseline fluorescence and d is the slope, using a nonlinear least-squares algorithm (Levenberg– Marquardt) in MATLAB (Mathworks).

    Article Title: Biphasic patterns of age-related differences in dopamine D1 receptors across the adult lifespan.
    Article Snippet: Bilinear age-models were fit using a piecewise-linear least-squares algorithm (https://www.mathworks.com/matlabcentral/fileexchange/40913-piecewise-linear-leastsquare-fit).

    Article Title: Objective monitoring of laser tattoo removal in human volunteers using an innovative optical technique: A proof of principle.
    Article Snippet: In doing so, we account also for the finite sample opening of our IS (see Section 2.1).27 Assessment of skin properties (inverse Monte Carlo) Matching of the measured PPTR signals and DRS spectra with predictions of our numerical model is performed iteratively using a nonlinear least‐squares algorithm (lsqnonlin by Mathworks).

    Concentration Assay:

    Article Title: Deep learning-based high-resolution time inference for deciphering dynamic gene regulation from fixed embryos
    Article Snippet: Within position ranges 0.10−0.75 EL (for Bcd), 0.15−0.85 EL (for Hb), 0.20−0.85 EL (for Kr in OreR ), and 0.10−0.80 EL (for Kr in 1× bcd ), we used a least-squares algorithm (the “fit” function in MATLAB) to fit the binned data from each species to the following functions: 5 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[{{{\rm{Bcd}}}}]={c}_{1,{{{\rm{Bcd}}}}}{e}^{-x/\lambda }+{c}_{0,{{{\rm{Bcd}}}}},$$\end{document} [ Bcd ] = c 1 , Bcd e − x / λ + c 0 , Bcd , 6 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[{{{\rm{Hb}}}}]={c}_{1,{{{\rm{Hb}}}}}\frac{{e}^{-(x-{x}_{0})/d}}{{e}^{-(x-{x}_{0})/d}+1}+{c}_{0,{{{\rm{Hb}}}}},$$\end{document} [ Hb ] = c 1 , Hb e − ( x − x 0 ) / d e − ( x − x 0 ) / d + 1 + c 0 , Hb , 7 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R={r}_{1}\frac{{e}^{(x-{x}_{{{{\rm{A}}}}})/{d}_{{{{\rm{A}}}}}}}{{e}^{(x-{x}_{{{{\rm{A}}}}})/{d}_{{{{\rm{A}}}}}}+1}\cdot \frac{{e}^{-(x-{x}_{{{{\rm{P}}}}})/{d}_{{{{\rm{P}}}}}}}{{e}^{-(x-{x}_{{{{\rm{P}}}}})/{d}_{{{{\rm{P}}}}}}+1}+{r}_{0},$$\end{document} R = r 1 e ( x − x A ) / d A e ( x − x A ) / d A + 1 ⋅ e − ( x − x P ) / d P e − ( x − x P ) / d P + 1 + r 0 , where c 1,· , c 0,· , r 1 , and r 0 denote the peak and background levels of the corresponding species, respectively; λ , d , d A , and d P indicate the decay lengths of Bcd, Hb, and Kr patterns, respectively; x 0 represents the boundary position of Hb expression pattern; x A and x P denote the anterior and posterior boundary positions of Kr expression domain, respectively.

    Article Title: Differential regulation of alternative promoters emerges from unified kinetics of enhancer-promoter interaction.
    Article Snippet: To extract the GRF, we binned individual data points by Bcd concentration and fitted them to a Hill function using a least-squares algorithm (the “nlinfit” function in MATLAB): y 1⁄4 a 1⁄2Bcd h 1⁄2Bcd h þ Ch0 þ d ð10Þ where h is the Hill coefficient, C0 is the concentration threshold for promoter activation, a indicates the maximal level of Bcd-dependent activity, and d denotes the basal activity.

    Article Title: Change detection in the primate auditory cortex through feedback of prediction error signals
    Article Snippet: Using all the timepoints except for those where F roi exceeded the time-averaged mean plus 1 SD, F roi values were regressed against F neuropil using an iteratively re-weighted least-squares algorithm (robustfit in MATLAB), and the slope of the regression line was defined as a contamination factor for the ROI , .

    Article Title: Deep learning-based high-resolution time inference for deciphering dynamic gene regulation from fixed embryos
    Article Snippet: Experimental data from different positions and time points were fitted altogether to theoretical results using a least-squares algorithm (the “lsqcurvefit” function in MATLAB) to extract kinetic parameters.

    Article Title: Cerebrovascular integrity affects gradients of aging-related dopamine D1 differences in the striatum
    Article Snippet: Linear age-models were fit using a piecewise-linear least-squares algorithm ( https://www.mathworks.com/matlabcentral/fileexchange/40913-piecewise-linear-least-square-fit ).

    Article Title: Network-level encoding of local neurotransmitters in cortical astrocytes.
    Article Snippet: To identify this point, traces were fitted using a modified Boltzmann’s sigmoidal equation: f x a c( ) = 1 + e +b x d( − ) / in which a is the difference between the minimum and the maximum fluorescence, b is the inflection point, c is the baseline fluorescence and d is the slope, using a nonlinear least-squares algorithm (Levenberg– Marquardt) in MATLAB (Mathworks).

    Article Title: Biphasic patterns of age-related differences in dopamine D1 receptors across the adult lifespan.
    Article Snippet: Bilinear age-models were fit using a piecewise-linear least-squares algorithm (https://www.mathworks.com/matlabcentral/fileexchange/40913-piecewise-linear-leastsquare-fit).

    Article Title: Objective monitoring of laser tattoo removal in human volunteers using an innovative optical technique: A proof of principle.
    Article Snippet: In doing so, we account also for the finite sample opening of our IS (see Section 2.1).27 Assessment of skin properties (inverse Monte Carlo) Matching of the measured PPTR signals and DRS spectra with predictions of our numerical model is performed iteratively using a nonlinear least‐squares algorithm (lsqnonlin by Mathworks).

    Activation Assay:

    Article Title: Deep learning-based high-resolution time inference for deciphering dynamic gene regulation from fixed embryos
    Article Snippet: Within position ranges 0.10−0.75 EL (for Bcd), 0.15−0.85 EL (for Hb), 0.20−0.85 EL (for Kr in OreR ), and 0.10−0.80 EL (for Kr in 1× bcd ), we used a least-squares algorithm (the “fit” function in MATLAB) to fit the binned data from each species to the following functions: 5 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[{{{\rm{Bcd}}}}]={c}_{1,{{{\rm{Bcd}}}}}{e}^{-x/\lambda }+{c}_{0,{{{\rm{Bcd}}}}},$$\end{document} [ Bcd ] = c 1 , Bcd e − x / λ + c 0 , Bcd , 6 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[{{{\rm{Hb}}}}]={c}_{1,{{{\rm{Hb}}}}}\frac{{e}^{-(x-{x}_{0})/d}}{{e}^{-(x-{x}_{0})/d}+1}+{c}_{0,{{{\rm{Hb}}}}},$$\end{document} [ Hb ] = c 1 , Hb e − ( x − x 0 ) / d e − ( x − x 0 ) / d + 1 + c 0 , Hb , 7 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R={r}_{1}\frac{{e}^{(x-{x}_{{{{\rm{A}}}}})/{d}_{{{{\rm{A}}}}}}}{{e}^{(x-{x}_{{{{\rm{A}}}}})/{d}_{{{{\rm{A}}}}}}+1}\cdot \frac{{e}^{-(x-{x}_{{{{\rm{P}}}}})/{d}_{{{{\rm{P}}}}}}}{{e}^{-(x-{x}_{{{{\rm{P}}}}})/{d}_{{{{\rm{P}}}}}}+1}+{r}_{0},$$\end{document} R = r 1 e ( x − x A ) / d A e ( x − x A ) / d A + 1 ⋅ e − ( x − x P ) / d P e − ( x − x P ) / d P + 1 + r 0 , where c 1,· , c 0,· , r 1 , and r 0 denote the peak and background levels of the corresponding species, respectively; λ , d , d A , and d P indicate the decay lengths of Bcd, Hb, and Kr patterns, respectively; x 0 represents the boundary position of Hb expression pattern; x A and x P denote the anterior and posterior boundary positions of Kr expression domain, respectively.

    Article Title: Differential regulation of alternative promoters emerges from unified kinetics of enhancer-promoter interaction.
    Article Snippet: To extract the GRF, we binned individual data points by Bcd concentration and fitted them to a Hill function using a least-squares algorithm (the “nlinfit” function in MATLAB): y 1⁄4 a 1⁄2Bcd h 1⁄2Bcd h þ Ch0 þ d ð10Þ where h is the Hill coefficient, C0 is the concentration threshold for promoter activation, a indicates the maximal level of Bcd-dependent activity, and d denotes the basal activity.

    Article Title: Change detection in the primate auditory cortex through feedback of prediction error signals
    Article Snippet: Using all the timepoints except for those where F roi exceeded the time-averaged mean plus 1 SD, F roi values were regressed against F neuropil using an iteratively re-weighted least-squares algorithm (robustfit in MATLAB), and the slope of the regression line was defined as a contamination factor for the ROI , .

    Article Title: Deep learning-based high-resolution time inference for deciphering dynamic gene regulation from fixed embryos
    Article Snippet: Experimental data from different positions and time points were fitted altogether to theoretical results using a least-squares algorithm (the “lsqcurvefit” function in MATLAB) to extract kinetic parameters.

    Article Title: Cerebrovascular integrity affects gradients of aging-related dopamine D1 differences in the striatum
    Article Snippet: Linear age-models were fit using a piecewise-linear least-squares algorithm ( https://www.mathworks.com/matlabcentral/fileexchange/40913-piecewise-linear-least-square-fit ).

    Article Title: Network-level encoding of local neurotransmitters in cortical astrocytes.
    Article Snippet: To identify this point, traces were fitted using a modified Boltzmann’s sigmoidal equation: f x a c( ) = 1 + e +b x d( − ) / in which a is the difference between the minimum and the maximum fluorescence, b is the inflection point, c is the baseline fluorescence and d is the slope, using a nonlinear least-squares algorithm (Levenberg– Marquardt) in MATLAB (Mathworks).

    Article Title: Biphasic patterns of age-related differences in dopamine D1 receptors across the adult lifespan.
    Article Snippet: Bilinear age-models were fit using a piecewise-linear least-squares algorithm (https://www.mathworks.com/matlabcentral/fileexchange/40913-piecewise-linear-leastsquare-fit).

    Article Title: Objective monitoring of laser tattoo removal in human volunteers using an innovative optical technique: A proof of principle.
    Article Snippet: In doing so, we account also for the finite sample opening of our IS (see Section 2.1).27 Assessment of skin properties (inverse Monte Carlo) Matching of the measured PPTR signals and DRS spectra with predictions of our numerical model is performed iteratively using a nonlinear least‐squares algorithm (lsqnonlin by Mathworks).

    Activity Assay:

    Article Title: Deep learning-based high-resolution time inference for deciphering dynamic gene regulation from fixed embryos
    Article Snippet: Within position ranges 0.10−0.75 EL (for Bcd), 0.15−0.85 EL (for Hb), 0.20−0.85 EL (for Kr in OreR ), and 0.10−0.80 EL (for Kr in 1× bcd ), we used a least-squares algorithm (the “fit” function in MATLAB) to fit the binned data from each species to the following functions: 5 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[{{{\rm{Bcd}}}}]={c}_{1,{{{\rm{Bcd}}}}}{e}^{-x/\lambda }+{c}_{0,{{{\rm{Bcd}}}}},$$\end{document} [ Bcd ] = c 1 , Bcd e − x / λ + c 0 , Bcd , 6 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[{{{\rm{Hb}}}}]={c}_{1,{{{\rm{Hb}}}}}\frac{{e}^{-(x-{x}_{0})/d}}{{e}^{-(x-{x}_{0})/d}+1}+{c}_{0,{{{\rm{Hb}}}}},$$\end{document} [ Hb ] = c 1 , Hb e − ( x − x 0 ) / d e − ( x − x 0 ) / d + 1 + c 0 , Hb , 7 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R={r}_{1}\frac{{e}^{(x-{x}_{{{{\rm{A}}}}})/{d}_{{{{\rm{A}}}}}}}{{e}^{(x-{x}_{{{{\rm{A}}}}})/{d}_{{{{\rm{A}}}}}}+1}\cdot \frac{{e}^{-(x-{x}_{{{{\rm{P}}}}})/{d}_{{{{\rm{P}}}}}}}{{e}^{-(x-{x}_{{{{\rm{P}}}}})/{d}_{{{{\rm{P}}}}}}+1}+{r}_{0},$$\end{document} R = r 1 e ( x − x A ) / d A e ( x − x A ) / d A + 1 ⋅ e − ( x − x P ) / d P e − ( x − x P ) / d P + 1 + r 0 , where c 1,· , c 0,· , r 1 , and r 0 denote the peak and background levels of the corresponding species, respectively; λ , d , d A , and d P indicate the decay lengths of Bcd, Hb, and Kr patterns, respectively; x 0 represents the boundary position of Hb expression pattern; x A and x P denote the anterior and posterior boundary positions of Kr expression domain, respectively.

    Article Title: Differential regulation of alternative promoters emerges from unified kinetics of enhancer-promoter interaction.
    Article Snippet: To extract the GRF, we binned individual data points by Bcd concentration and fitted them to a Hill function using a least-squares algorithm (the “nlinfit” function in MATLAB): y 1⁄4 a 1⁄2Bcd h 1⁄2Bcd h þ Ch0 þ d ð10Þ where h is the Hill coefficient, C0 is the concentration threshold for promoter activation, a indicates the maximal level of Bcd-dependent activity, and d denotes the basal activity.

    Article Title: Change detection in the primate auditory cortex through feedback of prediction error signals
    Article Snippet: Using all the timepoints except for those where F roi exceeded the time-averaged mean plus 1 SD, F roi values were regressed against F neuropil using an iteratively re-weighted least-squares algorithm (robustfit in MATLAB), and the slope of the regression line was defined as a contamination factor for the ROI , .

    Article Title: Deep learning-based high-resolution time inference for deciphering dynamic gene regulation from fixed embryos
    Article Snippet: Experimental data from different positions and time points were fitted altogether to theoretical results using a least-squares algorithm (the “lsqcurvefit” function in MATLAB) to extract kinetic parameters.

    Article Title: Cerebrovascular integrity affects gradients of aging-related dopamine D1 differences in the striatum
    Article Snippet: Linear age-models were fit using a piecewise-linear least-squares algorithm ( https://www.mathworks.com/matlabcentral/fileexchange/40913-piecewise-linear-least-square-fit ).

    Article Title: Network-level encoding of local neurotransmitters in cortical astrocytes.
    Article Snippet: To identify this point, traces were fitted using a modified Boltzmann’s sigmoidal equation: f x a c( ) = 1 + e +b x d( − ) / in which a is the difference between the minimum and the maximum fluorescence, b is the inflection point, c is the baseline fluorescence and d is the slope, using a nonlinear least-squares algorithm (Levenberg– Marquardt) in MATLAB (Mathworks).

    Article Title: Biphasic patterns of age-related differences in dopamine D1 receptors across the adult lifespan.
    Article Snippet: Bilinear age-models were fit using a piecewise-linear least-squares algorithm (https://www.mathworks.com/matlabcentral/fileexchange/40913-piecewise-linear-leastsquare-fit).

    Article Title: Objective monitoring of laser tattoo removal in human volunteers using an innovative optical technique: A proof of principle.
    Article Snippet: In doing so, we account also for the finite sample opening of our IS (see Section 2.1).27 Assessment of skin properties (inverse Monte Carlo) Matching of the measured PPTR signals and DRS spectra with predictions of our numerical model is performed iteratively using a nonlinear least‐squares algorithm (lsqnonlin by Mathworks).



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