Re: [ccp4bb] visual mask editor - why

[Bernhard Rupp]

Another brilliant Super-Elf, with a blast from the past - Numerical Recipes FFT 
rules 

 

Many thanks for the excellent explanations,

 

Cheers, BR

 

From: James Holton  
Sent: Saturday, June 13, 2020 17:34
To: b...@hofkristallamt.org; CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] visual mask editor - why

 

Bernhard,

Sounds like you are plotting something similar to what I was tinkering with 
once.  A script you may find useful is this one:
https://bl831.als.lbl.gov/~jamesh/bin_stuff/map_func.com

I wrote this because although mapmask, maprot, etc have very useful 
functionalities I found I wanted additional features, such as dividing one map 
by another, or taking a square root.  These are important if you are trying to 
derive the "signal-to-noise ratio", for example.  

 Once you have a map of rho/sigma(rho) you can convert that into a "pobability" 
by passing it through the "erf()" and "pow()" functions.  This can be a good 
way of estimating the "probability something is there" or P(rho) for a given 
map voxel. Specifically: 

P(rho) = 1-pow(erf(abs(rho/sigma(rho))/sqrt(2)),V/2/d^3)

where:
rho is the electron density map value (preferably from a Fo-Fc map)
sigma(rho) is the error on that voxel
V is the unit cell volume (A^3)
d is the resolution in A
erf() is called the "error function"
pow(m,e) is the raise-to-a-power function: m^e

The erf() function by itself turns a rho/sigma(rho)=3 peak into 0.997, and a 
1-sigma peak into 0.683. What that means is: assuming the noise is Gaussian, 
you expect voxels in the range -1-sigma to +1-sigma to be ~68.3% of the total.  
The "probability it isn't noise" (sometimes called a "p-value") is then 1-0.683 
= 0.32.  Seems like a pretty high probability to give to a 1-sigma peak, but 
now remember that the map is not just a single observation but thousands.  So, 
the question you really want to ask is: if I generate 100x100x100 = 1e6 
Gaussian-random numbers, what are the odds that a 4-sigma peak occurred at 
random?  The answer is: pretty much garanteed.  In any collection of 1 million 
Gaussian-random numbers with rms=1 it is virtually impossible to not have at 
least one of them > 4. Trust me, I have tried. This is where the "pow()" 
function comes in.  You need to multiply all the individual voxel probabilities 
together to get the probability of at least one >4-sigma peak happening at 
random.

But, then again, map voxels are hardly independent observations.  Finite 
resolution means that neighboring pixels are highly correlated.  So, rather 
than map grid points, we should be considering "Shannon voxels".  All this is 
is the number of blobs of diameter d, where d is the resolution, that can fit 
into the volume of the map. For example, if we have a 100 A edge on a cubic 
cell and 3 A resolution, then we have about 3.7e4 independent "observations" of 
density, so the probability of a random 4-sigma peak is:
P(rho) = erf(4/sqrt(2))**(((100./3)**3)/2) = 0.31

That is, if you make a zillion maps of random data using different seeds each 
time, 3.7e4 voxels each, and draw from a Gaussian distribution with rms=1, you 
expect 31% of these maps to have a 4-sigma peak. Randomly. The other 69% will 
not have anything > 4.  So, if you see a 4-sigma peak in a map with 3.7e4 
Shannon voxels I'd say it is real about 69% of the time.  You might consider 
0.69 to be a decent "weight" you should give such a 4-sigma peak.  A 5-sigma 
peak under the same circumstances gets P(rho) = 0.989, and a 3-sigma peak gets 
P(rho) = 1e-22.  aka: probaby noise.  It is perhaps worth remembering that at a 
given resolution large-sigma noise peaks are more common in bigger cells than 
small ones.

So, how do you get sigma(rho)?  To be honest, the rms value of the mFo-DFc map 
is a pretty good estimate.  The rms value of the 2mFo-DFc map is not (Lang et 
al. PNAS 2013).  I usually get sigma(rho) empirically.  That is, by making a 
stack of maps: start with your favorite refined structure and introduce random 
noise from whatever source you want to test. I.E. Gaussian error proprotional 
to SigI is an obvious one.  A more realistic on is the Fo-Fc difference itself. 
 After adding this "extra" noise to the data, re-refine the structure and 
generate a 2mFo-DFc map.  Do this ~50 times with different random number seeds. 
Then take those 50 maps and compute the mean and standard deviation of "rho" at 
every voxel.  You can do this with mapmask's ADD, MULT and SCALE features, but 
you can't do the last step, which is taking the square root of the variance.  
Hence: map_func.com

There are lots of other functions supported, including random number genration, 
etc.  Run the script with no arguments to get a list.

Oh, but don't try it on an mtz file!  mtz files are not maps.

-James Holton
MAD Scientist



On 5/28/2020 12:11 PM, Bernhard Rupp

Re: [ccp4bb] visual mask editor - why

[James Holton]

Bernhard,

Sounds like you are plotting something similar to what I was tinkering 
with once.  A script you may find useful is this one:

https://bl831.als.lbl.gov/~jamesh/bin_stuff/map_func.com

I wrote this because although mapmask, maprot, etc have very useful 
functionalities I found I wanted additional features, such as dividing 
one map by another, or taking a square root.  These are important if you 
are trying to derive the "signal-to-noise ratio", for example.


 Once you have a map of rho/sigma(rho) you can convert that into a 
"pobability" by passing it through the "erf()" and "pow()" functions.  
This can be a good way of estimating the "probability something is 
there" or P(rho) for a given map voxel. Specifically:


P(rho) = 1-pow(erf(abs(rho/sigma(rho))/sqrt(2)),V/2/d^3)

where:
rho is the electron density map value (preferably from a Fo-Fc map)
sigma(rho) is the error on that voxel
V is the unit cell volume (A^3)
d is the resolution in A
erf() is called the "error function"
pow(m,e) is the raise-to-a-power function: m^e

The erf() function by itself turns a rho/sigma(rho)=3 peak into 0.997, 
and a 1-sigma peak into 0.683. What that means is: assuming the noise is 
Gaussian, you expect voxels in the range -1-sigma to +1-sigma to be 
~68.3% of the total.  The "probability it isn't noise" (sometimes called 
a "p-value") is then 1-0.683 = 0.32.  Seems like a pretty high 
probability to give to a 1-sigma peak, but now remember that the map is 
not just a single observation but thousands.  So, the question you 
really want to ask is: if I generate 100x100x100 = 1e6 Gaussian-random 
numbers, what are the odds that a 4-sigma peak occurred at random?  The 
answer is: pretty much garanteed.  In any collection of 1 million 
Gaussian-random numbers with rms=1 it is virtually impossible to not 
have at least one of them > 4. Trust me, I have tried. This is where the 
"pow()" function comes in.  You need to multiply all the individual 
voxel probabilities together to get the probability of at least one 
>4-sigma peak happening at random.


But, then again, map voxels are hardly independent observations. Finite 
resolution means that neighboring pixels are highly correlated.  So, 
rather than map grid points, we should be considering "Shannon voxels".  
All this is is the number of blobs of diameter d, where d is the 
resolution, that can fit into the volume of the map. For example, if we 
have a 100 A edge on a cubic cell and 3 A resolution, then we have about 
3.7e4 independent "observations" of density, so the probability of a 
random 4-sigma peak is:

P(rho) = erf(4/sqrt(2))**(((100./3)**3)/2) = 0.31

That is, if you make a zillion maps of random data using different seeds 
each time, 3.7e4 voxels each, and draw from a Gaussian distribution with 
rms=1, you expect 31% of these maps to have a 4-sigma peak. Randomly. 
The other 69% will not have anything > 4.  So, if you see a 4-sigma peak 
in a map with 3.7e4 Shannon voxels I'd say it is real about 69% of the 
time.  You might consider 0.69 to be a decent "weight" you should give 
such a 4-sigma peak.  A 5-sigma peak under the same circumstances gets 
P(rho) = 0.989, and a 3-sigma peak gets P(rho) = 1e-22.  aka: probaby 
noise.  It is perhaps worth remembering that at a given resolution 
large-sigma noise peaks are more common in bigger cells than small ones.


So, how do you get sigma(rho)?  To be honest, the rms value of the 
mFo-DFc map is a pretty good estimate.  The rms value of the 2mFo-DFc 
map is not (Lang et al. PNAS 2013).  I usually get sigma(rho) 
empirically.  That is, by making a stack of maps: start with your 
favorite refined structure and introduce random noise from whatever 
source you want to test. I.E. Gaussian error proprotional to SigI is an 
obvious one.  A more realistic on is the Fo-Fc difference itself.  After 
adding this "extra" noise to the data, re-refine the structure and 
generate a 2mFo-DFc map.  Do this ~50 times with different random number 
seeds. Then take those 50 maps and compute the mean and standard 
deviation of "rho" at every voxel.  You can do this with mapmask's ADD, 
MULT and SCALE features, but you can't do the last step, which is taking 
the square root of the variance.  Hence: map_func.com


There are lots of other functions supported, including random number 
genration, etc.  Run the script with no arguments to get a list.


Oh, but don't try it on an mtz file!  mtz files are not maps.

-James Holton
MAD Scientist


On 5/28/2020 12:11 PM, Bernhard Rupp wrote:


Yes I have already pilfered useful parts of it in the scripts…

Thx, BR

*From:* Boaz Shaanan 
*Sent:* Thursday, May 28, 2020 11:59
*To:* b...@hofkristallamt.org
*Cc:* CCP4BB@JISCMAIL.AC.UK
*Subject:* Re: [ccp4bb] visual mask editor - why

Hi Bernhard,

Did you consider trying 'polder' in t

Re: [ccp4bb] visual mask editor - why

[dusan turk]

Dear Bernand,

In MAIN embedded map algebra can probably vover all what you need. If you want 
to go along this path, please, let me know and I will help you.

best,
dusan


> On 30 May 2020, at 01:00, CCP4BB automatic digest system 
>  wrote:
> 
> 
> Date:Fri, 29 May 2020 00:02:11 -0700
> From:Pavel Afonine 
> Subject: Re: visual mask editor - why
> 
> Hi Bernhard,
> 
> "Like comparing these map regions, excluding
> 
> intrusion of a solvent mask, etc.":
> 
> You didn't say much about the context.. So I'd say Polder map approach
> comes to mind first based on these keywords. Next is "map comparison" (
> https://doi.org/10.1107/S1399004714016289).
> 
> If none of the above: what we (or you) are missing?
> 
> Pavel
> 
> On Thu, May 28, 2020 at 11:17 AM Bernhard Rupp 
> wrote:
> 
>> Maybe I should explain an example: Say coot detects an unmodelled blob
>> (maybe a ligand). Now, I would like to do
>> 
>> a number of things without biasing towards a model. Like comparing these
>> map regions, excluding
>> 
>> intrusion of a solvent mask, etc.
>> 
>> 
>> 
>> Now could coot for example just generate a mask around what it already
>> knows are blobs?
>> 
>> Possible useful items could be a solvent mask not including that regions,
>> or a density map
>> 
>> that includes only features with a certain boundary around that blob.
>> 
>> 
>> 
>> I pilfered some kludges together from different sources, but let’s just
>> say inelegant would be a compliment.
>> 
>> 
>> 
>> Best, BR
>> 
>> 
>> 
>> Brief question: Does something like a visual density mask editor exist?
>> 
>> Thx, BR
>> 
>> --
>> 
>> Bernhard Rupp
>> 
>> http://www.hofkristallamt.org/
>> 
>> b...@hofkristallamt.org
>> 
>> +1 925 209 7429
>> 
>> +43 676 571 0536
>> 
>> --
>> 
>> Many plausible ideas vanish
>> 
>> at the presence of thought
>> 
>> --
>> 
>> 
>> 
>> --
>> 
>> To unsubscribe from the CCP4BB list, click the following link:
>> https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCP4BB=1
>> 
> 
> 
> 
> To unsubscribe from the CCP4BB list, click the following link:
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> 
> --
> 
> Date:Fri, 29 May 2020 09:34:23 +0100
> From:Harry Powell - CCP4BB 
> Subject: Re: Strange Pseudosymmetry Effects
> 
> Hi Tim
> 
> You could send out an SOS to some of the other authors in the same issue, who 
> might have kept a copy - several are “regular" posters on this forum, e.g.  
> 
>   Sacha Urzhumtsev
>   Gerard Kleywegt
>   Eleanor Dodson
> 
> There’s a good chance they’ll be stuck at home at the moment with plenty of 
> time to search through old boxes…
> 
> Harry
> 
>> On 28 May 2020, at 21:04, Tim Gruene  wrote:
>> Dear Eddie, dear all
>> 
>> According to ftp://ftp.ccp4.ac.uk/ccp4/newsletter/jun_95/, this article
>> appeare in Newsletter June 95. It is mentioned in the table of contents,
>> "Correction on perfection: primary extinction correction in protein
>> crystallography" by Polykarpov and Sawyer.
>> Unfortunately, the article itself is not there
>> 
>> Extinction is not the same as the dynamic effects that James mentioned,
>> but this seems the closest match.
>> 
>> Would anyone have a copy they can share with me?
>> 
>> Thanks a lot!
>> 
>> Best,
>> 
>> Tim 
> 
> 
> 
> To unsubscribe from the CCP4BB list, click the following link:
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> 
> This message was issued to members of www.jiscmail.ac.uk/CCP4BB, a mailing 
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> 
> --
> 
> Date:Fri, 29 May 2020 10:49:03 +0100
> From:Eleanor Dodson 
> Subject: Re: visual mask editor - why
> 
> Wont mapmask do that?  Find the fraction coordinate of the blob extent then
> carve that section out of the map?
> Eleanor
> From documentation:
> 
> *XYZLIM [ASU] [CELL] [MATCH]  **Set the output
> map extent as `extend'. - are given in grid units or in fractional
> coordinates. It is possible to automatically extend to the CCP4 default
> asymmetric unit, or a whole unit cell, by specifying `XYZLIM ASU' or
> `XYZLIM CELL'. It is also possible to extend the map to match another map
> (given as MAPLIM) by specifiying `XYZLIM MATCH'. The default is to keep the
> extent of the input map.*
> 
> On Fri, 29 May 2020 at 08:03, Pavel Afonine  wrote:
> 
>> Hi 

Re: [ccp4bb] visual mask editor - why

[Eleanor Dodson]

Wont mapmask do that?  Find the fraction coordinate of the blob extent then
carve that section out of the map?
Eleanor
>From documentation:

*XYZLIM [ASU] [CELL] [MATCH]  **Set the output
map extent as `extend'. - are given in grid units or in fractional
coordinates. It is possible to automatically extend to the CCP4 default
asymmetric unit, or a whole unit cell, by specifying `XYZLIM ASU' or
`XYZLIM CELL'. It is also possible to extend the map to match another map
(given as MAPLIM) by specifiying `XYZLIM MATCH'. The default is to keep the
extent of the input map.*

On Fri, 29 May 2020 at 08:03, Pavel Afonine  wrote:

> Hi Bernhard,
>
> "Like comparing these map regions, excluding
>
> intrusion of a solvent mask, etc.":
>
> You didn't say much about the context.. So I'd say Polder map approach
> comes to mind first based on these keywords. Next is "map comparison" (
> https://doi.org/10.1107/S1399004714016289).
>
> If none of the above: what we (or you) are missing?
>
> Pavel
>
> On Thu, May 28, 2020 at 11:17 AM Bernhard Rupp 
> wrote:
>
>> Maybe I should explain an example: Say coot detects an unmodelled blob
>> (maybe a ligand). Now, I would like to do
>>
>> a number of things without biasing towards a model. Like comparing these
>> map regions, excluding
>>
>> intrusion of a solvent mask, etc.
>>
>>
>>
>> Now could coot for example just generate a mask around what it already
>> knows are blobs?
>>
>> Possible useful items could be a solvent mask not including that regions,
>> or a density map
>>
>> that includes only features with a certain boundary around that blob.
>>
>>
>>
>> I pilfered some kludges together from different sources, but let’s just
>> say inelegant would be a compliment.
>>
>>
>>
>> Best, BR
>>
>> 
>>
>> Brief question: Does something like a visual density mask editor exist?
>>
>> Thx, BR
>>
>> --
>>
>> Bernhard Rupp
>>
>> http://www.hofkristallamt.org/
>>
>> b...@hofkristallamt.org
>>
>> +1 925 209 7429
>>
>> +43 676 571 0536
>>
>> --
>>
>> Many plausible ideas vanish
>>
>> at the presence of thought
>>
>> --
>>
>>
>>
>> --
>>
>> To unsubscribe from the CCP4BB list, click the following link:
>> https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCP4BB=1
>>
>
> --
>
> To unsubscribe from the CCP4BB list, click the following link:
> https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCP4BB=1
>



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Re: [ccp4bb] visual mask editor - why

[Pavel Afonine]

Hi Bernhard,

"Like comparing these map regions, excluding

intrusion of a solvent mask, etc.":

You didn't say much about the context.. So I'd say Polder map approach
comes to mind first based on these keywords. Next is "map comparison" (
https://doi.org/10.1107/S1399004714016289).

If none of the above: what we (or you) are missing?

Pavel

On Thu, May 28, 2020 at 11:17 AM Bernhard Rupp 
wrote:

> Maybe I should explain an example: Say coot detects an unmodelled blob
> (maybe a ligand). Now, I would like to do
>
> a number of things without biasing towards a model. Like comparing these
> map regions, excluding
>
> intrusion of a solvent mask, etc.
>
>
>
> Now could coot for example just generate a mask around what it already
> knows are blobs?
>
> Possible useful items could be a solvent mask not including that regions,
> or a density map
>
> that includes only features with a certain boundary around that blob.
>
>
>
> I pilfered some kludges together from different sources, but let’s just
> say inelegant would be a compliment.
>
>
>
> Best, BR
>
> 
>
> Brief question: Does something like a visual density mask editor exist?
>
> Thx, BR
>
> --
>
> Bernhard Rupp
>
> http://www.hofkristallamt.org/
>
> b...@hofkristallamt.org
>
> +1 925 209 7429
>
> +43 676 571 0536
>
> --
>
> Many plausible ideas vanish
>
> at the presence of thought
>
> --
>
>
>
> --
>
> To unsubscribe from the CCP4BB list, click the following link:
> https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCP4BB=1
>



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Re: [ccp4bb] visual mask editor - why

[Bernhard Rupp]

Yes I have already pilfered useful parts of it in the scripts.

Thx, BR

 

From: Boaz Shaanan  
Sent: Thursday, May 28, 2020 11:59
To: b...@hofkristallamt.org
Cc: CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] visual mask editor - why

 

Hi Bernhard,

Did you consider trying 'polder' in the phenix package? 

Boaz

Boaz Shaanan, Ph.D.
Department of Life Sciences
Ben Gurion University of the Negev
Beer Sheva
Israel

 

On May 28, 2020 21:17, Bernhard Rupp mailto:hofkristall...@gmail.com> > wrote:

Maybe I should explain an example: Say coot detects an unmodelled blob
(maybe a ligand). Now, I would like to do

a number of things without biasing towards a model. Like comparing these map
regions, excluding

intrusion of a solvent mask, etc.

 

Now could coot for example just generate a mask around what it already knows
are blobs?  

Possible useful items could be a solvent mask not including that regions, or
a density map

that includes only features with a certain boundary around that blob.

 

I pilfered some kludges together from different sources, but let's just say
inelegant would be a compliment.

 

Best, BR



Brief question: Does something like a visual density mask editor exist?

Thx, BR

--

Bernhard Rupp

http://www.hofkristallamt.org/

b...@hofkristallamt.org <mailto:b...@hofkristallamt.org> 

+1 925 209 7429

+43 676 571 0536

--

Many plausible ideas vanish 

at the presence of thought

--

 

 

  _  

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Re: [ccp4bb] visual mask editor - why

[Boaz Shaanan]

Hi Bernhard,
Did you consider trying 'polder' in the phenix package?
Boaz

Boaz Shaanan, Ph.D.
Department of Life Sciences
Ben Gurion University of the Negev
Beer Sheva
Israel



On May 28, 2020 21:17, Bernhard Rupp  wrote:




Maybe I should explain an example: Say coot detects an unmodelled blob (maybe a ligand). Now, I would like to do
a number of things without biasing towards a model. Like comparing these map regions, excluding
intrusion of a solvent mask, etc.
 
Now could coot for example just generate a mask around what it already knows are blobs?  
Possible useful items could be a solvent mask not including that regions, or a density map
that includes only features with a certain boundary around that blob.
 
I pilfered some kludges together from different sources, but let’s just say inelegant would be a compliment.
 
Best, BR

Brief question: Does something like a visual density mask editor exist?
Thx, BR
--
Bernhard Rupp
http://www.hofkristallamt.org/
b...@hofkristallamt.org
+1 925 209 7429
+43 676 571 0536
--
Many plausible ideas vanish 
at the presence of thought
--
 



To unsubscribe from the CCP4BB list, click the following link:
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Re: [ccp4bb] visual mask editor - why

[Bernhard Rupp]

Looks like the density manipulation/carving tools might be useful.

Thx, BR

 

From: CCP4 bulletin board  On Behalf Of Jurgen Bosch
Sent: Thursday, May 28, 2020 11:29
To: CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] visual mask editor - why

 

Give this a shot: https://www.eyesopen.com/afitt

 

At least in Vida from the same suite of programs, you can select such a blob as 
you describe and export it in a useful way.

Jürgen 

___

Jürgen Bosch, Ph.D.

Division of Pediatric Pulmonology and Allergy/Immunology
Case Western Reserve University

2109 Adelbert Rd, BRB 835

Cleveland, OH 44106

Phone: 216.368.7565

Fax: 216.368.4223

https://www.linkedin.com/in/jubosch/





CEO & Co-Founder at InterRayBio, LLC

 

Johns Hopkins University
Bloomberg School of Public Health
Department of Biochemistry & Molecular Biology





On May 28, 2020, at 2:17 PM, Bernhard Rupp mailto:hofkristall...@gmail.com> > wrote:

 

Maybe I should explain an example: Say coot detects an unmodelled blob (maybe a 
ligand). Now, I would like to do

a number of things without biasing towards a model. Like comparing these map 
regions, excluding

intrusion of a solvent mask, etc.

 

Now could coot for example just generate a mask around what it already knows 
are blobs?  

Possible useful items could be a solvent mask not including that regions, or a 
density map

that includes only features with a certain boundary around that blob.

 

I pilfered some kludges together from different sources, but let’s just say 
inelegant would be a compliment.

 

Best, BR



Brief question: Does something like a visual density mask editor exist?

Thx, BR

--

Bernhard Rupp

 <http://www.hofkristallamt.org/> http://www.hofkristallamt.org/

 <mailto:b...@hofkristallamt.org> b...@hofkristallamt.org

+1 925 209 7429

+43 676 571 0536

--

Many plausible ideas vanish 

at the presence of thought

--

 

 

  _  

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Re: [ccp4bb] visual mask editor - why

[Jurgen Bosch]

Give this a shot: https://www.eyesopen.com/afitt 


At least in Vida from the same suite of programs, you can select such a blob as 
you describe and export it in a useful way.
Jürgen 
___
Jürgen Bosch, Ph.D.
Division of Pediatric Pulmonology and Allergy/Immunology
Case Western Reserve University
2109 Adelbert Rd, BRB 835
Cleveland, OH 44106
Phone: 216.368.7565
Fax: 216.368.4223
https://www.linkedin.com/in/jubosch/

CEO & Co-Founder at InterRayBio, LLC

Johns Hopkins University
Bloomberg School of Public Health
Department of Biochemistry & Molecular Biology

> On May 28, 2020, at 2:17 PM, Bernhard Rupp  wrote:
> 
> Maybe I should explain an example: Say coot detects an unmodelled blob (maybe 
> a ligand). Now, I would like to do
> a number of things without biasing towards a model. Like comparing these map 
> regions, excluding
> intrusion of a solvent mask, etc.
>  
> Now could coot for example just generate a mask around what it already knows 
> are blobs?  
> Possible useful items could be a solvent mask not including that regions, or 
> a density map
> that includes only features with a certain boundary around that blob.
>  
> I pilfered some kludges together from different sources, but let’s just say 
> inelegant would be a compliment.
>  
> Best, BR
> 
> Brief question: Does something like a visual density mask editor exist?
> Thx, BR
> --
> Bernhard Rupp
> http://www.hofkristallamt.org/ 
> b...@hofkristallamt.org 
> +1 925 209 7429
> +43 676 571 0536
> --
> Many plausible ideas vanish 
> at the presence of thought
> --
>  
> 
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