Can someone explain the concept of 'Negative Probabilities' in an intuitive manner?
Negative probabilities in quantum physics
Incorrectly answered 'No' to "Any previous visa refusals..." on a UK Standard Visitor visa application. How can I fix my mistake? I'm from Lebanon and I've been working in Saudi Arabia for nine years. In 2012, I put the money that I collected from my job as a teacher in my father's Lebanese account since I didn't have one in Lebanon. During the interview, my interviewer told me that my application will be rejected because I don't have proof that this money is mine and clearance officer will think someone else gave me the money. I didn't know that I had to bring with me from Saudi Arabia an employment letter and bank statements to prove that this money is mine and I earned it by working in Saudi Arabia. Anyways, my visa did get refused as my interviewer had told me it would be.    Last May, I was granted a US visitor visa Multi Entry for 5 years. I wanted to visit the US in August for 10 days but my mom entered the hospital so I had to postpone it. Now I'm applying for a teacher training program in the UK. I received an invitation letter from Brighton University and so I applied for a UK Standard Visitor visa. After I paid and printed the application, I realized that I answered the question Any previous visa rejections ... with "NO" and I don't know how should I fix this.  Please note that I still didn't give my biometrics, I still didn't use my US visa which I received on May 2016, I paid for my application so I can't amend it online. I'm supposed to give my biometrics and submit my documents this Monday.  If I don't say anything will they check it and refuse me?    Will my US visa be an advantage and they will disregard the previous rejection or should I correct it when I submit my documents this Monday? How does one use circular polarizers? Why is James Bond less tech savvy in the Daniel Craig movies? The most recent installments of  (ones featuring Daniel Craig) have fewer gadgets but more raw action (like the chase sequences in Casino Royale and Quantum of Solace). Is it because of plot related changes to the MI:6 or have the movies been altered to suit the audiences? Can I travel after visa's intended travel date? I just finished applying for my visa and had originally planned to travel on the 30th of September, so I put that as my intended date of travel. But now I will not be leaving until close to the second week of October.  How does this work, will I still be able to travel with this visa even though it says I intended to arrive on September 30th? find the value of limit Find the value of $$ \lim_{n\to\infty} \sum_{k=n+1}^{2n} \frac{1}{k} $$ I think it become a series with each denominator approach infinity. so the value of the limit is 0. am i true ? Are logs kept for past at jobs? Does the use of words such as 'fail', 'wrong', 'incorrect' and 'invalid' have a sufficiently negative impact on a users frame of mind to warrant the prohibition of their inclusion in the error messages generated by typical web forms?  i.e. Should we rephrase examples like these to just use positive words?  'date entered incorrectly'  or  'failed to complete registration, please see below for invalid field entries'  (PS, the examples are there to show use of the words in an error message, not to serve as examples of error messages I would use or things that need correcting in answers, I'm not looking for advice on how to write form error messages, but for information about the effect of certain words on a users frame of mind) Was the Wookiee language fully designed or is it just random emotionally-relevant sounds? We know that some of the other Star Wars languages were fairly well developed by the movie's creators, in terms of vocabulary, grammar, etc.  Was the Wookiee language designed in this level of detail or did they just try to put together sounds that made sense emotionally? What is this strange function definition syntax in C? Disabling Google Chrome Download auto numbering for existing files Find the determinant of the following matrix Run multiple instance of a program in parallel Center a column in align I have the following type of code in my document:  \begin{align*}        (-m)+m &amp; \stackrel{\mathrm{Ax 1.1 (i)}}{=}  m+(-m)\\   &amp;\stackrel{\mathrm{Ax 1.4}}{=}  0 \   I want to align on the = but that is complicated by the fact that there is something hovering over it.  It would seem to be easier to align their centers (no matter what, that is where the = will be).  How can I center a column in align (or align* to be honest, I am not that clear on the difference) Selecting through one-to-many relationship I'm trying to make a species distribution project where I can select a species from a non-spatial list of species and the selection would highlight (select) all the counties to which the species has been attributed.  Simplified example data: species, a non-spatial table of species (CSV with header): "species" "Mus borealis" "Mus australis"  species_distributions, a non-spatial relation table (csv with header): "species","county" "Mus borealis","North" "Mus borealis","Central" "Mus australis","South" "Mus australis","Central"  counties, a spatial feature class representing county boundaries (first row = field name): "county" "North" "South" "Central" "West"  So if I select "Mus borealis" from the species table, the "North" and "Central" counties would be highlighted in the map. Seems like a simple scenario, but I have been unable to uncover a solution on my own. The closest I've found is a plugin "Select by relationship" but it doesn't appear to be available for QGIS 3 (I'm using QGIS 3.4.3). I have a PostGIS server available. What are good books for graduates/undergraduates in Astrophysics? There are no book recommendations for Astrophysics here. I will write my own answer, but I am also interested in what are others' views on the question (I will NOT mark my own answer as the best one). How does SO's (or other SE sites) versioning work of questions and answers? Do they use some standard piece of code or is it something homebrew?  With versioning I meant if for example a question is edited you'll see all the changes (a diff). biblatex: Full Citations in Footnotes on Every Page How can I create this sort of bibliography using biblatex, ie, bibliography at the footer of every page? Is there a simple way to convert a string to Title Case? E.g. john smith becomes John Smith. I'm not looking for something complicated like , just (hopefully) some kind of one- or two-liner. Energy conservation and interference I have a problem with energy conservation in case of interfering waves.  Imagine two harmonic waves with amplitudes $A$. They both carry energy that is proportional to $A^2$, so the total energy is proportional to $2A^2$. When they interfere, the amplitude raises to $2A$, so energy is now proportional to $4A^2$ and bigger than before.  The equivalent question is what happens to the energy with the superposition of two waves that interfere destructively.  Also, if someone could comment on the statement about this problem in my physics book (Bykow, Butikow, Kondratiew):      The sources of the waves work with increased power during the interference because they feel the wave from the other source. How do I assign a value to a whole array of integers?