Wikipedia:Reference desk/Archives/Science/2015 January 25

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January 25

In which cases can we find infection or inflammation without Leukocytosis or non-normal CRP?

213.57.12.140 (talk) 08:58, 25 January 2015 (UTC)

You are presuming that we can find such cases. Perhaps they do not exist. 50.43.56.168 (talk) 14:22, 25 January 2015 (UTC)

For an infection without an immune response, you'd either need someone who lacks a functional immune system (say due to AIDS) or a type of infection that manages to bypass the immune system. You could also get inflammation for reasons other than infection. Some foods cause inflammation, as can a physical injury. Presumably there is no immune response when there is no infection. StuRat (talk) 16:10, 27 January 2015 (UTC)

Removing instability in a linear system

I have a somewhat poorly conditioned linear system, $A\mathbf {x} =\mathbf {b}$. The right hand side, b, contains physical data which has some associated (though poorly characterized) uncertainty. The matrix is exact, rectangular (more rows than columns), but near singular for some variables, so small errors in b can result in large errors in some of the x's. I'd like to identify the most uncertain x's and exclude them (fix them to zero). Is there a typical process for picking which and how many x's to exclude? Dragons flight (talk) 10:37, 25 January 2015 (UTC)

I don't know this topic, and don't have ready access to some of the best-looking results, but Google delivers many hits for "Monte Carlo" "linear system" "exclude" that look promising... Wnt (talk) 13:47, 25 January 2015 (UTC)

Perhaps you are looking for a preconditioning method. This stage usually precedes inversion in an iterative solution.

Image Estimation by Example, chapter 5, covers this approach with practical examples. "This book is not a statistics book. Never-the-less, many of you have some statistical knowledge that allows you a statistical interpretation of these views of preconditioning."

If you'd like a more formal math book, the standard reference is Golub's constrained optimization book, Matrix Computations, which is not an easy read, and it's also not free.

Nimur (talk) 14:45, 25 January 2015 (UTC)

I'm not sure if preconditioning is the right thing. The preconditioning that I am aware of (and what seems to appear on the wiki page) is generally about reducing roundoff error and improving computation speed without changing the value of the solution (the x's). In my case, it's not roundoff error in A that is the problem, but actual error in the b's. The manifestation of that is that sometimes you get things like x₁ = -1000 when we know for physical reasons that the plausible values are +/- 3. However, because it is a large linear system, any instability at one point leads to instability elsewhere, e.g. x₁ = -1000 is met with a partially compensating swing x₂ = +1001. I'm trying to figure out which parts of the system are most sensitive to the noise in b and cut them out. Is there a variant of preconditioning that does things like that? Dragons flight (talk) 17:31, 25 January 2015 (UTC)

Yes, exactly! Outlier rejection is exactly the point! Half of GEE (the book I linked above) is about examples of that problem: physically, we know that a large outlier value is implausible; so we use a preconditioner or a regularization method to automatically determine where the outlier data is - and to avoid using it in the optimized solution. You can apply any precondition you like - for example, you can discard values above some threshold, or throw out any jump discontinuities, and so forth. If you already know that ±1000 is the outlier threshold, your job is very easy. If you aren't sure where the outliers are, you need an algorithm that can estimate a threshold (or otherwise generate a precondition) from the data itself. This can be automated, with a little bit of skill. Nimur (talk) 23:06, 25 January 2015 (UTC)

I think the basic thing you have to do is compute the singular value decomposition of your matrix. But where you go from there is more than I can say. Looie496 (talk) 16:54, 25 January 2015 (UTC)

You know, I had the exact same impulse that SVD ought to be useful, but I also am unsure of what to do with the SVD result after I get it. My current thought process is to use the pseudoinverse ($P_{i,j}$) along with some crude assumption for the error in b to estimate the errors in the inverse: $\delta x_{i}^{2}\approx \sum _{j}P_{i,j}^{2}*\delta b_{j}^{2}$. That assumes uncorrelated errors, which is probably false, and that I can usefully estimate the errors in the b's. My plan is then to find the x with the largest implied uncertainty, remove that term, and then iterate until the implied uncertainty on the remaining terms is within some tolerable threshold. It feels like this will work, but I'm also wondering if there are better ways to go about it. Dragons flight (talk) 18:40, 25 January 2015 (UTC)

This is a basic model in factor analysis. Let the covariance structure of your observables guide you. --Mark viking (talk) 20:01, 25 January 2015 (UTC)

Care to elaborate? I could use the generic covariance estimate $Q\approx {1 \over n}A^{T}A$. Then apply principal component decomposition to Q, and what? Presumably retain only some of the components, but how many, which ones, and why? Dragons flight (talk) 21:07, 25 January 2015 (UTC)

What is the nature of the noise in b? Sometimes there are errors not only in the numerical value, but also at what time (or at what position or whatever, you get the point) the samples were taken. YohanN7 (talk) 20:18, 25 January 2015 (UTC)

How does the electric current of a Taser (or a similar electroshock weapon) spread?

If someone is holding you with a headlock and you apply an electrical shock on your attacker, wouldn't you get a shock too? And if the shock is only local to the touching point, wouldn't that be ineffective? It would certainly hurt, but not making him release you or stop attacking through other means.--Noopolo (talk) 23:29, 25 January 2015 (UTC)

It sends two wires and the current mainly travels between the electrodes on the contacts, so there is not much outside the contact area. The idea is to hurt but not be lethal. Graeme Bartlett (talk) 07:44, 26 January 2015 (UTC)

And why does it disrupt the body to a point that people fall down, although they were hit on the shoulder? I get that an electrical shock to my right arm will make the muscles of my right arm contract, which is also consistent with your explanation (electricity traveling between the electrodes). But why does the whole body collapse? See a youtube video about some tests on people. --Noopolo (talk) 13:06, 26 January 2015 (UTC)

While electricity mostly follows the path of least resistance (which is the shortest path in the case of a material of uniform resistance), some takes the longer path. You can see this in a spark, which jumps around a bit, rather than just forming a straight line. And it doesn't take much electricity to disrupt nerves, since they use only a tiny amount of electricity to communicate. StuRat (talk) 15:31, 26 January 2015 (UTC)

@Noopolo: According to this study [1] over whether a TASER could affect the human heart adversely,

".. causes involuntary muscle contraction and intense pain in the unfortunate target".

Note this was done on a guinea-pig heart in a laboratory setting (petri dish?), not a 'whole body' subject! The heart is, presumably, not the 'target' for a taser in any case.

From what I have seen on-line, the 'trunk' of the body would be the target (similar to pistols, the main mass of the body). If hit only on the same shoulder, it might not have the 'desired effect', disabling you, as it might indeed only affect the muscles on the one limb, though the pain could be disabling, if not the muscle contractions.

• "How Stun Guns Work" at howstuffworks.com may have some useful info, but doesn't seem to be very certain about its statements regarding the science behind it effects on the body.
• This BBCstory [2] makes fairly definitive statements about the 'process':

"Electrical signals - taser waves or T-Waves -overpower the body's normal electrical signals, temporarily confusing the nervous system."

And here is a (not particularly informative) explanation at taser.com [3]

• "The TASER CEW (Conducted Electrical Weapon) simulates the pulsed communications used within the nerves, and interferes with communication – like static on the telephone lines within the body."

220 of ^Borg 06:21, 27 January 2015 (UTC)

This sourced "How Stuff Works" may explain better. How the Taser Shotgun Shell Works. --220 of ^Borg 07:29, 27 January 2015 (UTC)