My understanding is that interferometers can detect distance changes on the order of the wavelength of light being used. LIGO uses 808 nm light but has a sensitivity of 10^-18 m. Where do those 11 orders of magnitude come from?
The currently proposed Gravitational wave detection apparatus consists of Michelson Interferometer which is supposed to measure distances of the order of $10^{-22}$m. But the wavelength of the light used is in the order of micrometers ($10^{-6}$m). How is this possible? The conventional way to measure distance is by counting the interference fringes. But for path difference smaller than wavelength of laser light this is not possible.
Detecting constexpr with SFINAE I'm level 10 on Pokemon Go. I've caught at least 150 Pokemon, and had no problems. Now, every time I try to catch a Pokemon, no matter the level, it just rolls twice in the pokeball, breaks free, then runs away. Can anyone provide some insight on how to fix this problem? Which past tense of "to light" should I use here? I know that there are two ways to form the past tense of to light (i.e. lit/lighted). Which one is appropriate for the sentence below?     His thoughts lighted our way.   or     His thoughts lit our way. Proper analyses for 2x2 contingency tables So I have multiple questions about the different types of analyses that can be used on a 2x2 contingency table and when different analyses should be used.   To open, I'll note that this stems from my efforts to find the appropriate analyses to run for research using categorical data in a 2x2 contingency table. In my case I have two conditions: control and experimental and within the experimental group there are two items of interest (say, Item A and Item B). In all cases I'm investigating whether an outcome occurs or not: How many experimental participants show the outcome on Item A? How many experimental participants show the outcome on Item B? How many control participants show the outcome? So in addition to comparing Item A with the Control group (A vs. C) and Item B with the Control group (B vs. C), I also want to compare Item A with Item B (A vs. B).   My understanding is that for between-subjects comparisons (e.g., A vs. C   &amp;   B vs. C) a  is traditionally used and that for within-subjects comparisons (e.g., A vs. B) that  is a common choice.   Question 1: is this an accurate understanding of the common choices for statistical tests using 2x2 contingency tables?    My follow-up questions, and where most of my confusion lies, are related to what to do when multiple observed cell counts are low (less than 10). I've explored numerous threads here, the Wikipedia pages for different topics (Yates's correction, Fisher's exact, etc.), a few journal articles, and descriptions in R-packages, but I have found conflicting views.   Some sources indicate that you should use , others say it's out-dated because, in addition to being overly conservative, it was only preferred because the other options were computationally intense.   Others say that you should use , but I've seen additional information suggesting that Fisher's exact test is only appropriate if you know both the row and column totals and that other options (Boschloo, Barnard, etc.) are generally more powerful. However, which of those to use is also not clear.  Finally, even others suggest that the Pearson's $\chi^{2}$ test is appropriate as long as the expected cell counts are not low.   I've seen some indication that these arguments occur for McNemar's test as well (e.g., continuity correction &amp; McNemar's exact test).  Question 2: Is the assumption regarding cell counts about expected cell counts or observed cell counts? If the observed cell counts are low, does that matter to the type of test that should be used?  Question 3: What is an exact test and when should exact tests be used?    In addition to answers to these questions, I would also greatly appreciate any suggestions as to books or articles I can read to learn more about this. Part of my struggle with all of this has been just general difficult finding clear information about these topics and how they relate to one another. When I boot my Windows 8 laptop (see details below), it displays this message:  Recovery  Your PC needs to be repaired  A required device isn't connected or can't be accessed.  Error code: 0xc0000225  [ A text saying I should use recovery tools on my installation media to fix the issue. ]  Press Enter to try again  Press F8 for Start-up Settings  Press Esc for UEFI Firmware Settings   If I press Enter or F8, the central part of the message changes to:  The application or operating system couldn't be loaded because a required file is missing or contains errors.  File: \Windows\system32\winload.efi  Error code: 0xc0000225   I don't have a recovery disk and I have owned this computer for a year with no problems. All I did prior to this error was unistall avast and restart. I can only access UEFI Firmware Settings and have no clue what to do from there. PLEASE HELP! Mysql: Select rows from a table that are not in another Understanding psql prompts How to access Winter 13's Push Major functionality We are ISV Partners and all of our packaging orgs have been upgraded to Winter 13. One of the features of Winter 13 was supposed to allow us to push major release versions to subscriber orgs. I would have expected it to be in the previously existing "Push Upgrade" section of our packaging orgs, but that still only allows pushing patch versions.  If it didn't make the final Winter 13 release, I would have expected Salesforce to take it off the release page. Is this something we have to ask to be enabled? Rules for the usage of "me" VS. "myself"? What are general guidelines for the use of "me" and "myself"?     Did I describe me or did I describe Maria?   OR     Did I describe myself or did I describe Maria? Is it possible to detect a player consuming food items? I am looking for shapefiles or a list of suburb names for Melbourne and Canberra. I have ABS shapefiles, but I need to filter that to end up with only metropolitan suburbs.  My shapefile has codes in it for  - I just need to know which suburbs belong to the metros. How to terminate a script? Let $G$ be abelian, $H$ and $K$ subgroups of orders $n$, $m$. Then G has subgroup of order $\operatorname{lcm}(n,m)$. Let $G$ be abelian, $H$ and $K$ subgroups of orders $n$, $m$. Then G   has subgroup of order $\operatorname{lcm}(n,m)$.   This is a statement that my lecturer mentioned in my (beginners') Abstract Algebra class. I'm not sure I understand why it's true.  What I have so far: Use the abelian group structure theorem on $\langle H, K\rangle$ (finite group generated by $H$ and $K$). Then $\langle H,K\rangle=C_{a_1}C_{a_2}\dotsm$ and $n, m |\langle H,K\rangle$. Which means it's also true that $\operatorname{lcm}(n,m)|\langle H,K\rangle$. Can I leverage this to say there's a subgroup of order $\operatorname{lcm}(n,m)$? Algorithms for Time Series Anomaly Detection I'm currently using Twitter's AnomalyDetection in R: .  This algorithm provides time series anomaly detection for data with seasonality.  Question: are there any other algorithms similar to this (controlling for seasonality doesn't matter)?  I'm trying to score as many time series algorithms as possible on my data so that I can pick the best one / ensemble. Distance between surfaces Particles rotation not working correct Why is the change in Hamiltonian for an active infinitesimal canonical transformation defined the way it is? I'm trying to understand infinitesimal canonical transformations and conservation theorems (section 9.6 Goldstein ed3). My specific problem is with understanding eq 9.104,         $\partial H = H(B) - K(A^{'}) $, where $\partial H$ represents the change in the hamiltonian under an infinitesimal canonical transformation (from the active view point ofc). The issue only arises for generating functions that explicitly depend on time.  Here's what I've thought of so far. I understand what $K$ is from the passive viewpoint (or so I think), its the hamiltonian that would furnish Hamilton's equations for the transformed variables $Q=q+ \delta q$ and $P = p + \delta p$. In the specific case of the generating function being a time dependent hamiltonian, $K = H + \delta t \frac{\partial H}{\partial t} = H + \delta t\dot H$, which makes sense because once you transform the variables to what they'll be in time $\delta t$, you'll also need to add on a term that comes from the Hamiltonian being at a later time $t+ \delta t$.   In the book, this is explained as a transformation depending on time changes the hamiltonian, so $H(A) \rightarrow K(A^{'}) $. Which I sorta get. But why not for $H(B)$? And what about the case when the Hamiltonian is time dependent and it is the generating function? Is $H(B)$ at a later time then?   Note: $A$ represents the original variables, $B$ is the transformed variables in the active sense, so in the same phase space as $A$, and $A^{'}$ is the same point as A but in the transformed phase space (passive). Theorem environment with hanging indentation I would like to define a theorem environment with custom layout. In particular, I want the body of the theorem to be indented, like this  Text body. Text body. Text body.  Theorem 1 (Pythagoras).     Let a,b,c the sides of a rectangular triangle.     Without loss of generality, we assume that  a&lt;b&lt;c .     Then, the following equality holds:            a^2 + b^2 = c^2  More text. And even more text.   This is similar to the quote environment, I believe.  How can I do this?  Preferably, I would like to use the existing \newtheorem command, but that's not mandatory. How to explain in layman’s terms the significance of the difference of qubits of the D-Wave and IBM QX? So, @AndrewO mentioned recently that he has had 'encounters' with people wondering why D-Wave has a lot more qubits than IBM. Of course, this comparison is faulty, since the IBM and D-Wave's machine may both exploit quantum effects to a certain degree, IBM's machine matches the thing the TCS people call a 'Quantum computer' a bit more than D-Waves's alleged quantum annealer.   How do you explain to a novice why IBM is still reaching important milesstones, even though the D-Wave has a lot more 'qubits'. I understand that an easy answer is, 'well, you're comparing apples and pears', but that is merely relying on your possible authority and simply doesn't explain anything!   How can you explain that those devices are different, how can you dispell the myth that the number of qubits is not the only metric to judge quantum devices? (preferably to a layman, but assuming basic (undergrad?) physics knowledge is ok, if needed) How to print only defined variables (shell and/or environment variables) in bash The bash builtin command set, if invoked without arguments, will print all shell and environment variables, but also all defined functions. This makes the output unusable for humans and difficult to grep.  How can I make the bash builtin command set print only the variables and not the functions?  Are there other commands which prints only the shell variables, without the functions?  Note: bash differentiates between shell variables and environment variables. see here