Minimize Conjugate-Gradient

e64e5b18-cb5c-4c5d-bf3d-d9fd1eec106e 16 4 5 decimal

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Export publish Ligand binding

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

init iter Minimize XY f φ β LS X XY 1 col : Y XY 2 col : n XY rows : k x β φ length 1 - : vx-> raw initial vector fit i 1 X length range vx i el X i el β f eval : for M-> Cholesky GradientMatrix j 1 k range i 1 n range M i j el X i el β φ j 1 + el eval : for for CholeskySolver LeastSquares Φ M transpose M * : d M transpose Y vx - (* : Δβ Φ 1 -^eval d * : b β Δβ + : 131 line : β 1 el init : i 1 : i iter ≤ β i 1 + el XY f φ β i el LS : i i 1 + : 21 line while β β iter el : 41 line β 31 line :

Vector Gradient ... Optimiz Symbolic
seemingly a scalar kernel  not 
recognized in program loop x β f n φ ct 1 : i 1 n range PD ct el x β f (β ct el diff : stack f(x,β) & PD V 1 el x β f : V i 1 + el PD i el : 21 line ct ct 1 + : 41 line for V 31 line :

Error stem plot for QuickPlot unicolor data Error stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line :

L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 41 line :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

corr Pearson correlation χ X Mean : μ Y Mean : n XY rows : 13 mat X i el χ - (Y i el μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum Y i el μ - (2^(i 1 n sum * sqrt / X i el χ - (X i el β f eval μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum X i el β f eval μ - (2^(i 1 n sum * sqrt / / 31 line :

correlation between [X,Y data]

correlation ... [X,fitted model]

Absolute  residuals observer
fetches β from calculated δ j 1 XY rows range Δ j el Y j el X j el β f - eval : for X Δ augment 21 line :

SSD = "Sum Square Differences" SSD Y i el X i el β f - (2^(i 1 XY rows sum :

Clean data set ... Decimate

XY 0 0.4462 0.05 4.0862 0.1 7.7306 0.15 11.368 0.2 14.9869 0.25 18.5763 0.3 22.1253 0.35 25.6237 0.4 29.0618 0.45 32.4307 0.5 35.7221 0.55 38.9287 0.6 42.0441 0.65 45.0626 0.7 47.9798 0.75 50.7919 0.8 53.4962 0.85 56.0906 0.9 58.5742 0.95 60.9465 1 63.2078 1.05 65.3593 1.1 67.4023 1.15 69.339 1.2 71.1718 1.25 72.9036 1.3 74.5374 1.35 76.0767 1.4 77.525 1.45 78.8859 1.5 80.1632 1.55 81.3608 1.6 82.4824 1.65 83.5319 1.7 84.5129 1.75 85.4293 1.8 86.2845 1.85 87.0821 1.9 87.8255 1.95 88.5178 2 89.1622 2.05 89.7617 2.1 90.3191 2.15 90.8371 2.2 91.3183 2.25 91.7652 2.3 92.1799 2.35 92.5648 2.4 92.9217 2.45 93.2527 2.5 93.5596 2.55 93.844 2.6 94.1074 2.65 94.3515 2.7 94.5775 2.75 94.7868 2.8 94.9806 2.85 95.1599 2.9 95.3259 2.95 95.4795 3 95.6216 3.05 95.7531 3.1 95.8747 3.15 95.9872 3.2 96.0912 3.25 96.1874 3.3 96.2763 3.35 96.3585 3.4 96.4346 3.45 96.5049 3.5 96.5698 3.55 96.6299 3.6 96.6854 3.65 96.7367 3.7 96.7841 3.75 96.8279 3.8 96.8684 3.85 96.9059 3.9 96.9404 3.95 96.9724 4 97.0019 4.05 97.0292 4.1 97.0544 4.15 97.0777 4.2 97.0992 4.25 97.1191 4.3 97.1375 4.35 97.1545 4.4 97.1702 4.45 97.1846 4.5 97.198 4.55 97.2104 4.6 97.2218 4.65 97.2324 4.7 97.2421 4.75 97.2511 4.8 97.2595 4.85 97.2671 4.9 97.2742 4.95 97.2808 1002 mat :

data n Decimate collect every 'n' pairs range 1 data rows n range : k 1 : i range u k el data i 1 el : v k el data i 2 el : k k 1 + : 31 line for u v augment 31 line 31 line :

X XY 1 col : Y XY 2 col : 12 mat x λ 1 0.5 - x ≤ (x 10 ≤ (& cases : 21 mat

xy XY 10 Decimate : sparse xy . 14 black plot : 21 sys

XY rows 100

Ligand system M 183.75 : m 0 : 12 mat

Model function x β f m M m - (110 β 1 el log10 x β 2 el - (- (β 3 el *^+ / + β 4 el - :

ConjugateGradient Vector Fnct x β φ x β f 4 φ :

critical wrt β2 0.001 3.5 140 0.000693 3.22843 0.68919 86.389726 41 mat 15 mat

init 0.001 3.5 14014 mat transpose :

iter 7 :

algo solving for β β init iter Minimize :

assign/isolate .. β β :

Pearson correlation corr 0.999999

fit to noisy 
original data β 0.000178 3.818773 0.68919 86.389722 41 mat ≡

β 0.000693 3.22843 0.68919 86.389726 41 mat

u 5 :

U u β f :

track 1032232 u U 32 mat :

plot XY x β f x λ * sparse track 61 sys :

NOT sanity checked x β f x 05 int 400

Proposed fit to the unknown/clean data set XY

plot

Recast project, publish ...

β 0.000693 3.22843 0.68919 86.389726 183.75 51 mat :

u U 12 mat 5 97.29 12 mat

Ligand x f β 5 el 110 β 1 el log10 x β 2 el - (- (β 3 el *^+ / β 4 el - :

Ligand binding to a receptor protein alters the conformation by affecting the three-dimensional shape orientation. The conformation of a receptor protein composes the functional state. Ligands include substrates... inhibitors, activators, signaling lipids, and neurotransmitters.