Overlap of task/WU contents

Artonibus Rex
Artonibus Rex
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Topic 195359

For my own interest, how match overlap is there in the content of the WUs. Presumably the Arecibo data is continuous stream and we receive a 'square' victual for CPU consumption. (I guess my second question is whether certain tiling methods that would minimize the total number of WUs).

If a pulsar signal exists on a boundary of the WU is it guaranteed to be detected by some other adjacent WU processing? I guess its something like the old centrefold staple problem where manufacturing process interefered with the viewing.

So if there is no overlap, how are boundaries examined...? What if a pulsar sat at a four corner? Would it be presented as a 4+ WU detection?

If there is overlap, does the project repackage the WU data to exclude areas already scanned by the other adjacent blocks...as an optimization?

Mike Hewson
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Overlap of task/WU contents

Quote:

For my own interest, how match overlap is there in the content of the WUs. Presumably the Arecibo data is continuous stream and we receive a 'square' victual for CPU consumption. (I guess my second question is whether certain tiling methods that would minimize the total number of WUs).

If a pulsar signal exists on a boundary of the WU is it guaranteed to be detected by some other adjacent WU processing? I guess its something like the old centrefold staple problem where manufacturing process interefered with the viewing.

So if there is no overlap, how are boundaries examined...? What if a pulsar sat at a four corner? Would it be presented as a 4+ WU detection?

If there is overlap, does the project repackage the WU data to exclude areas already scanned by the other adjacent blocks...as an optimization?


Alas I haven't yet seen the specifics on the Aricebo based search, but I'm pretty sure of the detail for LIGO GW work units. I can talk of that if it helps, as the task is going to possess certain similiarities. [ But beware I last properly read up on this a couple or three years ago. So I may slip on some soap, and of course things change too ... ]

There is certainly attempted overlap in all selected 'volumes' of the problem space - the totality of sky positions and putative signal characteristics/parameters. Viewed as a phase space ( in the classical mechanics sense ) the trick is to select a metric or transform that takes subsets of it, while assessing the coverage for a given probability of detection ( or threshold of non-detection ). These would be ( hyper ) cubes if there were all simple/linear relationships within the problem at hand.

One obvious exception to linearity is the right ascension and declination of sky position, as across the domain equal increments in the arguments don't give equal solid angle or sky area on projection out to the celestial sphere. You can't properly flatten an orange peel to the table without splitting it. For some reason related to the search algorithm applied to each area, you wind up with ellipsoidal shaped probability density 'hills' that overlap. Thus there is not equal probability of detection over the landscape. I think it behaves roughly like the 'circular error probability' quoted with military ordinance accuracy. From memory, some related topological theorem says you can't do this perfectly using a finite number of cuts. So you run a risk of missing signals no matter how granular you get, as absolutely complete coverage is only achieved in the limit of some infinite number of divisions - with 'slow' asymptotic approach. Rapidly diminishing returns. Thus one chooses/accepts some level of possible failure ie. missing a signal, and offset that against computing resources available. You pays your money and you takes your choice ....

The frequency intervals/cuts have 'wings' which overlap with adjacent ones, I think in all about 12 - 15 % of the frequency band is doubled covered in this way.

For frequency derivative ( spin-up or spin down ) the work unit signal templates look at a number of discrete guesses in this parameter - I think about six - with most on the spin down side ( negative frequency derivative ). This is an astrophysical expectation.

Actually the potentially hardest estimates are the signal templates - what GW waveforms should we be expecting? This is a relatively tame issue for E@H, as we only do GW data analysis for the Continuous Wave Group ( that's Bruce Allen's purview ) within LIGO. So you'd expect quasi-monochromatic waves, essentially sinusoidal profiles with a slowly changing intrinsic frequency ( spin-ups and spin-downs ). For the other LIGO groups, not related to E@H, their task is steeper in this respect - transients, rapid inspirals, stochastic background, Kleine-Welle or little wavelets etc.

But now that you've raised this, I'll see if I can ferret about and find something more specific for ABP's .... I too find this aspect quite fascinating. :-) :-)

Cheers, Mike.

( edit ) One other aspect is the amplitude of the signal. This is more related to the quality of data acquisition at the detectors, especially the 'coherence time' for good quality data stretches. The blocks of data are selected for later analysis based upon ongoing detector performance ( locking, simultaneity of collection at multiple sites, "Crab integration time" and inspiral range etc ) and known outages. The S6 run ( the data from which we haven't yet touched upon at E@H ) I believe was fairly messy in this regard compared to prior runs. In any case if you chop the sky up with a finer grid of those ellipsoidal hills mentioned above, you have less chance of missing something in the valleys between them. So there will be some lowest possible points on the probability density terrain and that represents the lowest limit for signal strength that you have probed. Or an upper bound on the weakest signal missed, depending on how you want to phrase it.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

Artonibus Rex
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Is it not possible to test

Message 99910 in response to message 99909

Is it not possible to test families of detection input frequency domain structure signals and then make sensor robust across the family of wave forms? How close to the boundary of background noise do the detected frequencies lie? Are they very specific frequencies so that data is prefiltered with specific notch devices etc.?

I have a thought experiment. If I fire a green photon and a blue photon at a perfect mirror target moving towards me at a some significant fraction of the speed of light would you expect the same frequency shift for each photon detected on the measuring device? Can a red shift be detected on single photons or is this only a phenomenon which manifests due to sample size of multiple and/or continuous signals?

With respect to the GW experiments, are the detections based on a continuous feedback signal? Is the duration of the feedback signal a component in manifesting the detection of the GW (that is can I measure the red shift on a single photon by the analogy which is stuck in my head)

Perhaps I need to read more to gain a greater appreciation of the certainty of the GW pursuit. Some book recommendations for the layman level and then maybe some more intermediate stuff beyond that would be appreciated.

Holy Hilbert space, batman, those grad skule days are coming to life.

Mike Hewson
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Again I reply with respect to

Message 99911 in response to message 99910

Again I reply with respect to GW efforts especially.

Quote:
Is it not possible to test families of detection input frequency domain structure signals and then make sensor robust across the family of wave forms? How close to the boundary of background noise do the detected frequencies lie? Are they very specific frequencies so that data is prefiltered with specific notch devices etc.?


The base problem is that no-one has yet confidently detected a GW signal to date. Excellent guesses abound however. The LIGO interferometers, with limitations, are broad band and omni-directional antennae. Thus the urge is to not pre-filter at the device level.

For Aricebo the burden is lower in this regard, so I'm sure your suggestions would apply to some degree. Having said that, the recent new pulsar discovery ( via E@H ABP efforts ) was of an unusual type - pulsar population wise.

Quote:
I have a thought experiment. If I fire a green photon and a blue photon at a perfect mirror target moving towards me at a some significant fraction of the speed of light would you expect the same frequency shift for each photon detected on the measuring device? Can a red shift be detected on single photons or is this only a phenomenon which manifests due to sample size of multiple and/or continuous signals?


You get Dopplering of any photon, grouped or single. It's a shift of a frequency fraction, say 10% or somesuch, not an absolute number of Hertz. Depending on whether you use particle or wave language, a frequency shift morphs to an energy shift ( one is proportional to the other ). Quantum mechanics then talks of single photon detection being probability based. So if one uses the model of electric fields, a higher electric field value equates to increased chance/rate/probability of single photon detections.

Quote:
With respect to the GW experiments, are the detections based on a continuous feedback signal? Is the duration of the feedback signal a component in manifesting the detection of the GW (that is can I measure the red shift on a single photon by the analogy which is stuck in my head)


Sort of but not quite. The LIGO/Michelson/Fabry-Perot type interferometers are maintained in a 'locked' resonant state, by rapid actuators linked to short feedback loops on photodetectors. Thus if a gravity wave passes by, altering the 4km length to the other mirror then a constant phase difference between arms is held. We deduce the passing of the wave by examining the feedback corrections that occurred to achieve this. My analogy is holding a truck on a dead straight course on a roadway, in a blustering crosswind, by altering steering inputs. You use the steering data to measure the variation in crosswind strength.

Quote:

Perhaps I need to read more to gain a greater appreciation of the certainty of the GW pursuit. Some book recommendations for the layman level and then maybe some more intermediate stuff beyond that would be appreciated.

Holy Hilbert space, batman, those grad skule days are coming to life.


I don't honestly know of a layman level GW book, but if you've done grad school it won't be too long a shot to grab a copy of this book by one of the LIGO interferometer designers. I'll admit to not yet successfully swallowing it whole, but I keep coming back to it. I think Mr Saulson has a great writing style and he doesn't hide the necessities, so there's no Mickey-Mouse hand waving. I play around with the maths alot.

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

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