Quick & Dirty Update

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A Snapshot Of My Day

Selected random lyrics I've written:

To form a chronology of Grande E, you must traverse the breeze, start in the Sin City;
Las Vegas gave birth to me, but the Mormon mecca took the role of raising me, SLC!
Sugarhood be the last remaining levy versus developments, the change is heavy.
Spent some time around, Ft. Collins, start the bud, had the Cough, I found;
Met some colored contacts, spent some time in Cincy, hooked me up, thought it looked kinda chintzy;
That's OK, ended up delayed in faux Jewel, Joya, jolly neighbor air destroyer;
Coronado, low hum constant, interfere with, environs were heaven sent.

I heard you had beef with your external disguise, with these guys on all sides, unzippin' they flies;
tried to take care of it with yay-yea, you only made yourself sick, life felt like shit, yea.
You've got to believe that desire and relief are just chains on you and me, please don't bleed,
satisfyin' serotonin needs. Lettin' lifes abstract greeds get underneath your sheets.
Compassion is the fashion, send a polyphonic lashin', that gold shimmers n' fades, bling disappeared in the shade.
Aqua regia took it completely away.
Gotta open up your third eyes, believe, get high, get by, pay attention, got mine. Gonna get yours? For you kid, I'll teach a course.

Morality Play At The Delta Center

At the Jazz game last night they had a little 'contest' during one of the breaks. Three guys had a chance to win a basketball, they just had to make a slam dunk off the trampoline like they do during the halftime show.

The MC asks the first guy why he entered the contest: "Because it looks easy!" so the guy jumps on the trampoline and falls woefully short of the basket. The second guy's answer is: "So I can sell the ball on eBay and make some money!", prompting the crowd to boo. He goes up in the air and at the last moment loses his grip on the ball, causing him to miss his dunk too.

Finally, the MC asks the third man why he's entered the contest: "So that I can win that basketball for the biggest Jazz fan in the world, my DAUGHTER!". The crowd cheers and the man runs up to the trampoline, his two year old daughters' hopes and dreams resting on his shoulders. He jumps off the trampoline and delivers a ferocious two-handed jam.


No. Seriously. That is exactly how it went down in real life. This is not a parable or a fable, this was the real, off-action, entertainment at the game.

Increasing 'N' For Improved CRQL Recovery

To start off, there is a great book on error analysis called "An Introduction To Error Analysis" by John R. Taylor. This book has very succinct and easy to use explanations of least squares analysis, linear regression, and propagation of errors.

On the back cover are the expressions we will need to examine how the choice of 'N' in constructing a calibration curve will effect the slope and intercept of a linear regression line.

If (x₁,y₁),...,(x_N,y_N) are data points then the best fit straight line A=mc+b is given by:
m = [(sum(x²)*(sum(y)) - (sum(x)*sum(x*y))]/D
b = [(sum(x*y) - (sum(x)*sum(y))]/D
D = N*(sum(x²) - (sum(x))²)

We can see that N appears in the expression for both m and b in the denominator. Since sum(x²) >= (sum(x))² for any x we can see that increasing N will increase the value of D.

Examining the expressions for 'm' and 'b' we see that the concentration of the calibration standard added will have some effect on whether m or b are increasing or decreasing.

For now, let us focus on a calibration standard with a concentration of less than 1.0 in whatever units you are working in. Now, x² will be less than x. The value of y will depend on the choice for the value of x. For the CETAC M-7500, out of the box, the absorbance in µAbs units is approximately 10,000 times the concentration in ppb or µg/L. This means that in this specific case the values of 'y' will be very large.

The overall effect, when the additional calibration standards have a concentration of 0.5 or less, is to increase the slope as well as decrease the intercept.

Practically, this means that if your CRQL is coming in too low you may be able to make additional calibration standards at concentrations near the CRQL. Their inclusion should increase your overall recovery for low standards while not affecting the recovery very much for your high standards.

Below is an example demonstrating how adding low standards increases the slope gradually while decreasing the intercept more rapidly.

Click image for larger version. Data and graphs showing the effect of increasing N.

In this example computing percent recoveries reveals that including two standards near 0.5x the CRQL increases the percent recovery of the CRQL itself by around 2.5%.