[SciPy-User] technical question: normed exponential fit for data?

Daniel Mader danielstefanmader@googlemail....
Thu Mar 24 15:14:29 CDT 2011

```Hi David,

no, x is °C, but I use to specify temperature differences in K sind I
find °C only useful as an absolute value.

Maybe you are right about the intercept, but you need to keep in mind
that this is a complicated chemical assay. I wouldn't make any
assumption for temperatures lower than 15°C and higner than 35°C. In
my experiment, temperatures are typically between 20 and 25°C...

Judging from the data, I would say that an exponential behavior is
justified, i.e. the light emission increases with some percent per
delta T. To my understanding, that is the exact description for an
exponential curve, or am I mistaken?

Thanks in advance, I really enjoy the discussion here,
Daniel

2011/3/24 David Baddeley <david_baddeley@yahoo.com.au>:
> A really silly question - you are using temperature values in Kelvin (rather
> than centigrade) aren't you? The chemical/physical assumption is probably that
> rates are an exponential function of the temperature in Kelvin, not in C. Your
> high concentration curve is looking awfully like it's heading for an intercept
> at 0C.
>
> cheers,
> David
>
> ----- Original Message ----
> From: Robert Kern <robert.kern@gmail.com>
> To: SciPy Users List <scipy-user@scipy.org>
> Sent: Fri, 25 March, 2011 5:09:33 AM
> Subject: Re: [SciPy-User] technical question: normed exponential fit for data?
>
> On Thu, Mar 24, 2011 at 10:33, Daniel Mader
> <danielstefanmader@googlemail.com> wrote:
>> Hi,
>>
>> this is not a software question or scipy problem but rather I have no
>> clue how to tackle this on a mathematical level.
>>
>> I'd like to create a unique fit function for data. Attached is a file
>> which holds three measurements for three different known
>> concentrations, i.e. my "calibration" measurement at low, medium and
>> high concentration.
>>
>> Apparently, the temperature behavior of the chemical reaction is
>> exponential, i.e. the photon yield increases with about 10%/K for the
>> examined range for a given concentration.
>
> Hmm. I certainly wouldn't have come to that conclusion looking at the
> data. At least for #0 (high concentration?), the linear fit is
> substantially better.
>
>> Now comes the tricky part: I'd like to use this knowledge for a
>> temperature compensation because I only need to determine the
>> concentration. The temperature of the reaction is measured
>> simultaneously but might vary in the range of +-3K. In terms of assay
>> performance, that makes a huge difference due to the 10%/K so that I'd
>> need to compensate for it.
>>
>> How can I use my calibration measurement to find a function which I
>> could use to compensate for varying temperatures?
>
> Can you do more calibrations with different concentrations? For any
> given temperature, you essentially only have three data points with
> which to determine the relationship between concentration and photon
> count. That's pretty difficult without any theory to help you fill in
> the gaps.
```

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