b929a5b9-4497-4a1a-9079-230f686232cd 52 4 5 decimal
&[DATE] &[TIME] - &[FILENAME]
&[PAGENUM] / &[COUNT]

Part 1: Inspect raw data ... collect for next fitting

 <p> ANALYSIS UTILITIES </p> <p> Data: XY from Smath Forum </p> 1184

Division by zero indicates duplicates or multiplicates to be stripped. Once stripped, isolate for next anlysis

Division by zero

XY Deriv #

Once stripped isolate

Strip XY Strip_X : <p> XY stripped from repeated X's </p> 1080

First points negative derivative ... next points ondulate ... start sub-collection at point 4.

 D pts 2 1 sys

Collect wisely

XY XY 4 XY rows 32 - ( range 1 2 range el : 0.0048 0.1486 1 2 mat 2.8008 94.4881 1 2 mat 2 1 mat 1045

Next ondulation ... NOISY

 D

Trend suite ... NOISY

 D

Tail end ... safely zap 32 pts

 D pts 2 1 sys

Part 2: Explore fitting

 <p> Collected data for fitting session </p> 1045 94.4881 <p> Minimize Conjugate-Gradient </p>

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 : 2 1 line ct ct 1 + : 4 1 line for V 3 1 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 0 2 2 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + ( 1 el 1 el 0 1 2 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 : 7 1 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 + 0 4 2 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 1 1 line for B 4 1 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 2 1 line :

SSD = "Sum Square Differences"

SSD Y i el X i el β f - ( 2 ^ ( i 1 XY rows sum :

Otherwise Pearson independent of f(x,ParameterName)

x y corr n x length : xy x y * vectorize : x2 x x * vectorize : y2 y y * vectorize : n xy sum ( * x sum ( y sum ( * - n x2 sum ( * x sum ( 2 ^ - ( n y2 sum ( * y sum ( 2 ^ - ( * ( sqrt / 5 1 line :

<= Gradient Vector Function

x β φ x β f 2 φ :

algo solving for β

β init iter Minimize :

assign/isolate ..

β β :

NO meaning vis the noisy data

SSD 671 1.0084 XY x β f x λ * 2 1 sys 0.739053 1.067052 2 1 mat <p> Minimize Conjugate-Gradient </p>

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 : 2 1 line ct ct 1 + : 4 1 line for V 3 1 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 0 2 2 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + ( 1 el 1 el 0 1 2 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 : 7 1 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 + 0 4 2 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 1 1 line for B 4 1 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 2 1 line :

SSD = "Sum Square Differences"

SSD Y i el X i el β f - ( 2 ^ ( i 1 XY rows sum : <p> Collected data for fitting session </p> 1045 141.7322

Ligand system

M 141.7322 : m 0 : 2 1 sys

Shifted bindingLigand Sigmoidal...

Model function

x β f m M m - ( 1 10 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 :

Experimetal initials. Convenient iterative CG

0.0006 3.586 0.8125 46.3 4 1 mat 0.0048 0.1486 1 2 mat 0.024 2.087 1 2 mat 0.0936 7.3908 1 2 mat 2.8008 94.4881 1 2 mat 4 1 mat

algo solving for β

β init iter Minimize :

assign/isolate ..

β β :

saturates wrt to data ondulation

corr 1.002086 0.000513 3.631779 0.813717 46.390684 4 1 mat 2.8264 3.9884 8.2981 93.9416 4 1 mat

bindingLigand is largely used in Pharmacokinetics. Recognized as a good fit to systems of 2 DE ... Here, the data set suffers multiple ondulations. ~ 5% of the variate, data set and bindingLigand don't cry to murder mutually. Better data set will probably confirm bindingLigand..

 XY x β f x λ * 2 1 sys

1. The data set is RAW by inspection of the noisy derivative. 2. at this point, take it as given stripped/sub-collected. 3. Over population is generally not profitable for a fitting session. 4. Once wisely collected/decimated, isolate [X,Y] for Thiele. 5. By inspection, the XY phenomenon evoluates as convolution. 6. If good enough from Originators ... the Thiele suite follows. 7. New similar system will result from simply giving original XY ...as long as wisely stripped/collected/decimated. 8. You could spline "ainterp" the collected, but you don't have ...an exportable function. Model function will need be re-fitted. 9. From whatever technique to produce original XY, it is the guilty ...that generates the "observable wiggling". This wiggling may result ...from the range switching of the measuring sytem. 10. As well, Thiele wiggles impercible between support points.

1045 15 0.0048 0.1486 1 2 mat 0.1392 10.6466 1 2 mat 2.7648 94.4626 1 2 mat 3 1 mat 2.7648 94.4626 2 1 mat <p> Thiele Mathcd style </p> 0.14857 0.012803 219.126577 0.002133 223.415816 0.002412 - 2126.420111 - 0.000118 1801.927221 0.147847 0.871475 - 0.215109 - 430.314772 - 0.000449 484.016787 15 1 mat

PROJECT OBSERVER ... as given, Thiele works fine and generally. However, in this project, it is victim of the noise and 3 ondulations. Consequently, the Thiele will suffer 3 glitches, exposed from the FD derivative analysis. The 1045 collected data might support smoothing. Savitsky_Golay may be candidate ... not offered. A normalized rational fraction will clean as well. Thiele suite follows as such as an exportable interpolation function. From adequately strip/collect/decimate, Thiele will collect similar projects for comparing/export.

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Recast the Project

Thiele on length of support points 'j'

K X x Cfr j K rows 1 - : N j 1 + el K j 1 + el : c j el N j el : a j el K j el : jj j 1 - ( 1 range c jj el a jj 1 + el : a jj el K jj el x X jj el - c jj el / + : 2 1 line for a 1 el 6 1 line :

Recast inclusive of parameters K's , X's

x Cf K X x Cfr :

NUMERIC

SYMBOLIC

 Analyse XY . 12 black plot x Cf x λ * 2 1 sys 72.24 72.26 2 1 mat

SYMBOLIC ▼ optimiz NONE

 14857 100000 / x 4795611 1000000000 / - 12803 1000000 / x 139199987 1000000000 / - 219126577 1000000 / x 139199987 500000000 / - 2133 1000000 / x 424799979 1000000000 / - 27926977 125000 / x 290397793 500000000 / - 603 250000 / - x 184799999 250000000 / - 2126420111 1000000 / - x 907199979 1000000000 / - 59 500000 / x 136500001 125000000 / - 1801927221 1000000 / x 1293599963 1000000000 / - 147847 1000000 / x 1502399921 1000000000 / - 34859 40000 / - x 431400001 250000000 / - 215109 1000000 / - x 490199983 250000000 / - 107578693 250000 / - x 441599989 200000000 / - 449 1000000 / / + / + / + / + / + / + / + / + / + / + / + / + / +
About the Project . . .
This project like most physical experiments runs on long range of measued variate X.
Forcibly, it is not governed by a single DE . . . Example: Atmospheric properties.
Consequently: it can't be represented by a single model function. It could be recasted
by joining two of the best segments. Thiele, is compliant wrt this project.
The binding Ligand is the best choice for a single model segment fit .
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Unexplored model

Inverse/Exponential brute force ...

 1

A pretty attractive 7 parameters model Remember: data set ondulates. Automated fit NOT attempted.

x G datum s m el 1 x XY 15 1 el + ( 1.0375 ^ / ( m ^ * m 1 4 sum + : x G XY . 12 black plot datum + 50 red plot 3 1 sys 0.03 2.23 - 8.96 9.34 17.65 20.37 26.29 30 35.14 39.06 43.91 47.19 52.55 55.02 61.11 62.28 69.45 69.57 76.55 75.89 82.33 81.18 86.98 85.7 90.52 89.45 93.01 92.5 94.37 95.05 15 2 mat