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    MathWorks Inc optimization toolbox software
    Optimization Toolbox Software, supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 96/100, based on 3261 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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    Average 96 stars, based on 3261 article reviews
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    Article Title: Refined modelling of hypervelocity impact crater size predictions
    Article Snippet: The parameters were identified through non-linear least-squares optimization using the MATLAB function lsqcurvefit.

    Article Title: Solid-state NMR dipolar recoupling in the presence of large chemical shielding anisotropies by quaternion-based effective Hamiltonian optimal control.
    Article Snippet: Dipolar recoupling is a key element in magic-angle-spinning (MAS) solid-state NMR spectroscopy with reintroduced dipole–dipole coupling interactions providing information about internuclear distances and enabling transfer of polarization between spins in resolution-enhancing multiple-dimensional experiments.. Such methods may be challenged in many important applications by the presence of large anisotropic nuclear spin interactions such as chemical shielding anisotropy.. In this paper, we address this challenge by presenting quaternion-based optimal control.

    Article Title: Sparse time-delay and amplitude estimation of multipath arrivals in ocean acoustics.
    Article Snippet: We estimate multipath arrival time delays and amplitudes with high resolution for accurate characterization of ocean acoustic channels.. Although matched filtering (MF) is robust and widely used, its output represents a superposition of contributions from multiple arrivals, which can bias delay and amplitude estimates.. More advanced high-resolution (HR) methods exist but are usually computationally expensive.

    Article Title: Resistance Profile of Listeria monocytogenes and Escherichia coli to High Power Ultrasound in Juice Matrices.
    Article Snippet: Regression analyses were performed to obtain the parameter estimation of the primary and secondary model using Matlab Version 6.1 (MathWorks, MA, USA) while the parameter optimization was performed with the optimization function of Isqnonlin of the Matlab Optimisation Toolbox.

    Article Title: Optimization of the Volumetric Overall Mass Transfer Coefficient in an L-Shaped Pulsed Sieve Plate Extraction Column
    Article Snippet: Nonlinear regression and optimization were performed in MATLAB R2022b using the Optimization Toolbox (Version 9.4) and the lsqnonlin solver.

    Article Title: Trade-off between flux efficiency and metabolic control shapes enzyme allocation.
    Article Snippet: As the whole procedure computes pathway flux J from kcat ;KS;KP;K;E; Sin1⁄2 ; 1⁄2Sout , the pathway flux J can also be written as a function of these parameters and concentrations: J 1⁄4 Jðkcat ;KS;KP;K ;E; Sin1⁄2 ; 1⁄2Sout Þ Optimal enzyme allocation profile maximizing flux efficiency under a given parameter set was computed using the MATLAB constrained optimization solver fmincon[] to maximize the pathway flux with the upper bound of total enzyme abundance set to 1: max E Jðkcat ;KS;KP;K ;E; Sin1⁄2 ; 1⁄2Sout Þ s:t: 0 1⁄2Ei 1Pn i1⁄41 Ei1⁄2 1

    Article Title: Network-Irreducible Multiparty Entanglement in Quantum Matter.
    Article Snippet: [27] MOSEK Optimization Toolbox for MATLAB 10.2.17, MOSEK ApS (2024), https://docs.mosek.com/10.2/toolbo x/index.html.

    Article Title: Protocol for thermodynamically optimal construction and analysis of metabolic networks using ThermOptCOBRA.
    Article Snippet: Other MATLAB toolboxes to be installed are Optimization Toolbox, Statistics and Machine Learning Toolbox, and Parallel Computing Toolbox.



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    ( a ) Droplet-like DPICs were initially formed by mixing 20 μM ATTO565-labeled p53 4M ΔTAD with 0.6 μM ATTO488-labeled Random DNA and incubating for 30 minutes at room temperature. Subsequently, Cy5-labeled p21 DNA was added at varying concentrations and incubated for an additional 120 minutes: (i) 0.15 μM; (ii) 0.225 μM; (iii) 0.3 μM; (iv) 0.45 μM; (v) 0.6 μM; (vi) 0.75 μM; (vii) 0.9 μM. Representative fluorescence images at incubation time t = 4-min and t = 120-min are shown. Independent in vitro droplet experiments were repeated three times (n = 3). ( b ) <t>Boxplot</t> of characteristic time constants τ 1 and τ 2 for p21 DNA concentrations ranging from 0.3 to 0.9 μM. N indicates the number of individual biomolecule-rich condensates analyzed under each condition. In box plots, the black line denotes the median, box edges represent the 25 th and 75 th percentiles, whiskers indicate the range excluding outliers, and outliers are shown as individual dots (•). ( c ) Phase diagram showing normalized fluorescence intensities of ATTO565-labeled p53 4M ΔTAD and ATTO488-labeled Random DNA at the center of condensates under increasing concentrations of p21 DNA (0.3, 0.45, 0.6, and 0.75 μM). Values are shown both before p21 DNA addition and at the end of Stage I. Control experiments in which Random DNA was used in place of p21 DNA are also included. Error bars indicate mean ± s.d. Green dashed lines mark the estimated binodal boundary, and purple dashed lines represent the spinodal boundary, as confirmed by our phase-field model (see – ).
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    ( a ) Droplet-like DPICs were initially formed by mixing 20 μM ATTO565-labeled p53 4M ΔTAD with 0.6 μM ATTO488-labeled Random DNA and incubating for 30 minutes at room temperature. Subsequently, Cy5-labeled p21 DNA was added at varying concentrations and incubated for an additional 120 minutes: (i) 0.15 μM; (ii) 0.225 μM; (iii) 0.3 μM; (iv) 0.45 μM; (v) 0.6 μM; (vi) 0.75 μM; (vii) 0.9 μM. Representative fluorescence images at incubation time t = 4-min and t = 120-min are shown. Independent in vitro droplet experiments were repeated three times (n = 3). ( b ) <t>Boxplot</t> of characteristic time constants τ 1 and τ 2 for p21 DNA concentrations ranging from 0.3 to 0.9 μM. N indicates the number of individual biomolecule-rich condensates analyzed under each condition. In box plots, the black line denotes the median, box edges represent the 25 th and 75 th percentiles, whiskers indicate the range excluding outliers, and outliers are shown as individual dots (•). ( c ) Phase diagram showing normalized fluorescence intensities of ATTO565-labeled p53 4M ΔTAD and ATTO488-labeled Random DNA at the center of condensates under increasing concentrations of p21 DNA (0.3, 0.45, 0.6, and 0.75 μM). Values are shown both before p21 DNA addition and at the end of Stage I. Control experiments in which Random DNA was used in place of p21 DNA are also included. Error bars indicate mean ± s.d. Green dashed lines mark the estimated binodal boundary, and purple dashed lines represent the spinodal boundary, as confirmed by our phase-field model (see – ).
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    ( a ) Droplet-like DPICs were initially formed by mixing 20 μM ATTO565-labeled p53 4M ΔTAD with 0.6 μM ATTO488-labeled Random DNA and incubating for 30 minutes at room temperature. Subsequently, Cy5-labeled p21 DNA was added at varying concentrations and incubated for an additional 120 minutes: (i) 0.15 μM; (ii) 0.225 μM; (iii) 0.3 μM; (iv) 0.45 μM; (v) 0.6 μM; (vi) 0.75 μM; (vii) 0.9 μM. Representative fluorescence images at incubation time t = 4-min and t = 120-min are shown. Independent in vitro droplet experiments were repeated three times (n = 3). ( b ) <t>Boxplot</t> of characteristic time constants τ 1 and τ 2 for p21 DNA concentrations ranging from 0.3 to 0.9 μM. N indicates the number of individual biomolecule-rich condensates analyzed under each condition. In box plots, the black line denotes the median, box edges represent the 25 th and 75 th percentiles, whiskers indicate the range excluding outliers, and outliers are shown as individual dots (•). ( c ) Phase diagram showing normalized fluorescence intensities of ATTO565-labeled p53 4M ΔTAD and ATTO488-labeled Random DNA at the center of condensates under increasing concentrations of p21 DNA (0.3, 0.45, 0.6, and 0.75 μM). Values are shown both before p21 DNA addition and at the end of Stage I. Control experiments in which Random DNA was used in place of p21 DNA are also included. Error bars indicate mean ± s.d. Green dashed lines mark the estimated binodal boundary, and purple dashed lines represent the spinodal boundary, as confirmed by our phase-field model (see – ).
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    ( a ) Droplet-like DPICs were initially formed by mixing 20 μM ATTO565-labeled p53 4M ΔTAD with 0.6 μM ATTO488-labeled Random DNA and incubating for 30 minutes at room temperature. Subsequently, Cy5-labeled p21 DNA was added at varying concentrations and incubated for an additional 120 minutes: (i) 0.15 μM; (ii) 0.225 μM; (iii) 0.3 μM; (iv) 0.45 μM; (v) 0.6 μM; (vi) 0.75 μM; (vii) 0.9 μM. Representative fluorescence images at incubation time t = 4-min and t = 120-min are shown. Independent in vitro droplet experiments were repeated three times (n = 3). ( b ) <t>Boxplot</t> of characteristic time constants τ 1 and τ 2 for p21 DNA concentrations ranging from 0.3 to 0.9 μM. N indicates the number of individual biomolecule-rich condensates analyzed under each condition. In box plots, the black line denotes the median, box edges represent the 25 th and 75 th percentiles, whiskers indicate the range excluding outliers, and outliers are shown as individual dots (•). ( c ) Phase diagram showing normalized fluorescence intensities of ATTO565-labeled p53 4M ΔTAD and ATTO488-labeled Random DNA at the center of condensates under increasing concentrations of p21 DNA (0.3, 0.45, 0.6, and 0.75 μM). Values are shown both before p21 DNA addition and at the end of Stage I. Control experiments in which Random DNA was used in place of p21 DNA are also included. Error bars indicate mean ± s.d. Green dashed lines mark the estimated binodal boundary, and purple dashed lines represent the spinodal boundary, as confirmed by our phase-field model (see – ).
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    ( a ) Droplet-like DPICs were initially formed by mixing 20 μM ATTO565-labeled p53 4M ΔTAD with 0.6 μM ATTO488-labeled Random DNA and incubating for 30 minutes at room temperature. Subsequently, Cy5-labeled p21 DNA was added at varying concentrations and incubated for an additional 120 minutes: (i) 0.15 μM; (ii) 0.225 μM; (iii) 0.3 μM; (iv) 0.45 μM; (v) 0.6 μM; (vi) 0.75 μM; (vii) 0.9 μM. Representative fluorescence images at incubation time t = 4-min and t = 120-min are shown. Independent in vitro droplet experiments were repeated three times (n = 3). ( b ) <t>Boxplot</t> of characteristic time constants τ 1 and τ 2 for p21 DNA concentrations ranging from 0.3 to 0.9 μM. N indicates the number of individual biomolecule-rich condensates analyzed under each condition. In box plots, the black line denotes the median, box edges represent the 25 th and 75 th percentiles, whiskers indicate the range excluding outliers, and outliers are shown as individual dots (•). ( c ) Phase diagram showing normalized fluorescence intensities of ATTO565-labeled p53 4M ΔTAD and ATTO488-labeled Random DNA at the center of condensates under increasing concentrations of p21 DNA (0.3, 0.45, 0.6, and 0.75 μM). Values are shown both before p21 DNA addition and at the end of Stage I. Control experiments in which Random DNA was used in place of p21 DNA are also included. Error bars indicate mean ± s.d. Green dashed lines mark the estimated binodal boundary, and purple dashed lines represent the spinodal boundary, as confirmed by our phase-field model (see – ).
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    ( a ) Droplet-like DPICs were initially formed by mixing 20 μM ATTO565-labeled p53 4M ΔTAD with 0.6 μM ATTO488-labeled Random DNA and incubating for 30 minutes at room temperature. Subsequently, Cy5-labeled p21 DNA was added at varying concentrations and incubated for an additional 120 minutes: (i) 0.15 μM; (ii) 0.225 μM; (iii) 0.3 μM; (iv) 0.45 μM; (v) 0.6 μM; (vi) 0.75 μM; (vii) 0.9 μM. Representative fluorescence images at incubation time t = 4-min and t = 120-min are shown. Independent in vitro droplet experiments were repeated three times (n = 3). ( b ) <t>Boxplot</t> of characteristic time constants τ 1 and τ 2 for p21 DNA concentrations ranging from 0.3 to 0.9 μM. N indicates the number of individual biomolecule-rich condensates analyzed under each condition. In box plots, the black line denotes the median, box edges represent the 25 th and 75 th percentiles, whiskers indicate the range excluding outliers, and outliers are shown as individual dots (•). ( c ) Phase diagram showing normalized fluorescence intensities of ATTO565-labeled p53 4M ΔTAD and ATTO488-labeled Random DNA at the center of condensates under increasing concentrations of p21 DNA (0.3, 0.45, 0.6, and 0.75 μM). Values are shown both before p21 DNA addition and at the end of Stage I. Control experiments in which Random DNA was used in place of p21 DNA are also included. Error bars indicate mean ± s.d. Green dashed lines mark the estimated binodal boundary, and purple dashed lines represent the spinodal boundary, as confirmed by our phase-field model (see – ).
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    ( a ) Droplet-like DPICs were initially formed by mixing 20 μM ATTO565-labeled p53 4M ΔTAD with 0.6 μM ATTO488-labeled Random DNA and incubating for 30 minutes at room temperature. Subsequently, Cy5-labeled p21 DNA was added at varying concentrations and incubated for an additional 120 minutes: (i) 0.15 μM; (ii) 0.225 μM; (iii) 0.3 μM; (iv) 0.45 μM; (v) 0.6 μM; (vi) 0.75 μM; (vii) 0.9 μM. Representative fluorescence images at incubation time t = 4-min and t = 120-min are shown. Independent in vitro droplet experiments were repeated three times (n = 3). ( b ) <t>Boxplot</t> of characteristic time constants τ 1 and τ 2 for p21 DNA concentrations ranging from 0.3 to 0.9 μM. N indicates the number of individual biomolecule-rich condensates analyzed under each condition. In box plots, the black line denotes the median, box edges represent the 25 th and 75 th percentiles, whiskers indicate the range excluding outliers, and outliers are shown as individual dots (•). ( c ) Phase diagram showing normalized fluorescence intensities of ATTO565-labeled p53 4M ΔTAD and ATTO488-labeled Random DNA at the center of condensates under increasing concentrations of p21 DNA (0.3, 0.45, 0.6, and 0.75 μM). Values are shown both before p21 DNA addition and at the end of Stage I. Control experiments in which Random DNA was used in place of p21 DNA are also included. Error bars indicate mean ± s.d. Green dashed lines mark the estimated binodal boundary, and purple dashed lines represent the spinodal boundary, as confirmed by our phase-field model (see – ).
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    ( a ) Droplet-like DPICs were initially formed by mixing 20 μM ATTO565-labeled p53 4M ΔTAD with 0.6 μM ATTO488-labeled Random DNA and incubating for 30 minutes at room temperature. Subsequently, Cy5-labeled p21 DNA was added at varying concentrations and incubated for an additional 120 minutes: (i) 0.15 μM; (ii) 0.225 μM; (iii) 0.3 μM; (iv) 0.45 μM; (v) 0.6 μM; (vi) 0.75 μM; (vii) 0.9 μM. Representative fluorescence images at incubation time t = 4-min and t = 120-min are shown. Independent in vitro droplet experiments were repeated three times (n = 3). ( b ) <t>Boxplot</t> of characteristic time constants τ 1 and τ 2 for p21 DNA concentrations ranging from 0.3 to 0.9 μM. N indicates the number of individual biomolecule-rich condensates analyzed under each condition. In box plots, the black line denotes the median, box edges represent the 25 th and 75 th percentiles, whiskers indicate the range excluding outliers, and outliers are shown as individual dots (•). ( c ) Phase diagram showing normalized fluorescence intensities of ATTO565-labeled p53 4M ΔTAD and ATTO488-labeled Random DNA at the center of condensates under increasing concentrations of p21 DNA (0.3, 0.45, 0.6, and 0.75 μM). Values are shown both before p21 DNA addition and at the end of Stage I. Control experiments in which Random DNA was used in place of p21 DNA are also included. Error bars indicate mean ± s.d. Green dashed lines mark the estimated binodal boundary, and purple dashed lines represent the spinodal boundary, as confirmed by our phase-field model (see – ).
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    ( a ) Droplet-like DPICs were initially formed by mixing 20 μM ATTO565-labeled p53 4M ΔTAD with 0.6 μM ATTO488-labeled Random DNA and incubating for 30 minutes at room temperature. Subsequently, Cy5-labeled p21 DNA was added at varying concentrations and incubated for an additional 120 minutes: (i) 0.15 μM; (ii) 0.225 μM; (iii) 0.3 μM; (iv) 0.45 μM; (v) 0.6 μM; (vi) 0.75 μM; (vii) 0.9 μM. Representative fluorescence images at incubation time t = 4-min and t = 120-min are shown. Independent in vitro droplet experiments were repeated three times (n = 3). ( b ) <t>Boxplot</t> of characteristic time constants τ 1 and τ 2 for p21 DNA concentrations ranging from 0.3 to 0.9 μM. N indicates the number of individual biomolecule-rich condensates analyzed under each condition. In box plots, the black line denotes the median, box edges represent the 25 th and 75 th percentiles, whiskers indicate the range excluding outliers, and outliers are shown as individual dots (•). ( c ) Phase diagram showing normalized fluorescence intensities of ATTO565-labeled p53 4M ΔTAD and ATTO488-labeled Random DNA at the center of condensates under increasing concentrations of p21 DNA (0.3, 0.45, 0.6, and 0.75 μM). Values are shown both before p21 DNA addition and at the end of Stage I. Control experiments in which Random DNA was used in place of p21 DNA are also included. Error bars indicate mean ± s.d. Green dashed lines mark the estimated binodal boundary, and purple dashed lines represent the spinodal boundary, as confirmed by our phase-field model (see – ).
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    ( a ) Droplet-like DPICs were initially formed by mixing 20 μM ATTO565-labeled p53 4M ΔTAD with 0.6 μM ATTO488-labeled Random DNA and incubating for 30 minutes at room temperature. Subsequently, Cy5-labeled p21 DNA was added at varying concentrations and incubated for an additional 120 minutes: (i) 0.15 μM; (ii) 0.225 μM; (iii) 0.3 μM; (iv) 0.45 μM; (v) 0.6 μM; (vi) 0.75 μM; (vii) 0.9 μM. Representative fluorescence images at incubation time t = 4-min and t = 120-min are shown. Independent in vitro droplet experiments were repeated three times (n = 3). ( b ) <t>Boxplot</t> of characteristic time constants τ 1 and τ 2 for p21 DNA concentrations ranging from 0.3 to 0.9 μM. N indicates the number of individual biomolecule-rich condensates analyzed under each condition. In box plots, the black line denotes the median, box edges represent the 25 th and 75 th percentiles, whiskers indicate the range excluding outliers, and outliers are shown as individual dots (•). ( c ) Phase diagram showing normalized fluorescence intensities of ATTO565-labeled p53 4M ΔTAD and ATTO488-labeled Random DNA at the center of condensates under increasing concentrations of p21 DNA (0.3, 0.45, 0.6, and 0.75 μM). Values are shown both before p21 DNA addition and at the end of Stage I. Control experiments in which Random DNA was used in place of p21 DNA are also included. Error bars indicate mean ± s.d. Green dashed lines mark the estimated binodal boundary, and purple dashed lines represent the spinodal boundary, as confirmed by our phase-field model (see – ).
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    ( a ) Droplet-like DPICs were initially formed by mixing 20 μM ATTO565-labeled p53 4M ΔTAD with 0.6 μM ATTO488-labeled Random DNA and incubating for 30 minutes at room temperature. Subsequently, Cy5-labeled p21 DNA was added at varying concentrations and incubated for an additional 120 minutes: (i) 0.15 μM; (ii) 0.225 μM; (iii) 0.3 μM; (iv) 0.45 μM; (v) 0.6 μM; (vi) 0.75 μM; (vii) 0.9 μM. Representative fluorescence images at incubation time t = 4-min and t = 120-min are shown. Independent in vitro droplet experiments were repeated three times (n = 3). ( b ) Boxplot of characteristic time constants τ 1 and τ 2 for p21 DNA concentrations ranging from 0.3 to 0.9 μM. N indicates the number of individual biomolecule-rich condensates analyzed under each condition. In box plots, the black line denotes the median, box edges represent the 25 th and 75 th percentiles, whiskers indicate the range excluding outliers, and outliers are shown as individual dots (•). ( c ) Phase diagram showing normalized fluorescence intensities of ATTO565-labeled p53 4M ΔTAD and ATTO488-labeled Random DNA at the center of condensates under increasing concentrations of p21 DNA (0.3, 0.45, 0.6, and 0.75 μM). Values are shown both before p21 DNA addition and at the end of Stage I. Control experiments in which Random DNA was used in place of p21 DNA are also included. Error bars indicate mean ± s.d. Green dashed lines mark the estimated binodal boundary, and purple dashed lines represent the spinodal boundary, as confirmed by our phase-field model (see – ).

    Journal: bioRxiv

    Article Title: Hollow condensates emerge from gelation-induced spinodal decomposition

    doi: 10.1101/2025.06.25.661497

    Figure Lengend Snippet: ( a ) Droplet-like DPICs were initially formed by mixing 20 μM ATTO565-labeled p53 4M ΔTAD with 0.6 μM ATTO488-labeled Random DNA and incubating for 30 minutes at room temperature. Subsequently, Cy5-labeled p21 DNA was added at varying concentrations and incubated for an additional 120 minutes: (i) 0.15 μM; (ii) 0.225 μM; (iii) 0.3 μM; (iv) 0.45 μM; (v) 0.6 μM; (vi) 0.75 μM; (vii) 0.9 μM. Representative fluorescence images at incubation time t = 4-min and t = 120-min are shown. Independent in vitro droplet experiments were repeated three times (n = 3). ( b ) Boxplot of characteristic time constants τ 1 and τ 2 for p21 DNA concentrations ranging from 0.3 to 0.9 μM. N indicates the number of individual biomolecule-rich condensates analyzed under each condition. In box plots, the black line denotes the median, box edges represent the 25 th and 75 th percentiles, whiskers indicate the range excluding outliers, and outliers are shown as individual dots (•). ( c ) Phase diagram showing normalized fluorescence intensities of ATTO565-labeled p53 4M ΔTAD and ATTO488-labeled Random DNA at the center of condensates under increasing concentrations of p21 DNA (0.3, 0.45, 0.6, and 0.75 μM). Values are shown both before p21 DNA addition and at the end of Stage I. Control experiments in which Random DNA was used in place of p21 DNA are also included. Error bars indicate mean ± s.d. Green dashed lines mark the estimated binodal boundary, and purple dashed lines represent the spinodal boundary, as confirmed by our phase-field model (see – ).

    Article Snippet: The function of “boxplot” in MATLAB software (R2015a, 64-bit, February 12, 2015) was used to plot the boxplots in , , and Supplementary Fig. 3.

    Techniques: Labeling, Incubation, Fluorescence, In Vitro, Control