"non grid based", "non-grid based", "non grid-based" or "non-grid-based"
Non in front of hyphenated adjective
What kind of behaviour causes an interrupted exception? I'm relatively new to Threading in Java and I've noticed that everytime I use Thread.sleep() I have to catch InterrupetdException.  What kind of behaviour causes this, and in simple applications where I have a monitor thread can I just Ignore the exception? Can I open Microsoft Word and Excel files with Ubuntu? Drive from US to Canada with a dog What is this story about 20 y.o. inexperienced "kids" fighting against a stronger foe in space? Years ago (mid 90's) I saw a show on network TV, and I'm trying to figure out what the name of it was. The parts of the plot I remember are:   The crew consisted of 20-year-olds (half were women). They were on some mission when they lose their commander. They must then try to get back home, while being tracked down by a foe in a faster, more powerful ship. One of the main characters turns traitor. He's locked up in the brig pending a decision on his fate. He hangs himself, and his body is incinerated by the crew. One of the main characters plays a video game that basically looks like a visor over his face. While playing the game, he's given an idea on how to outwit their foe by using the laser cannon on their ship to create a holographic projection of a larger ship. In the end, they are about to be destroyed by a torpedo launched from the enemy ship.  The torpedo is destroyed by a laser beam from a friendly capital ship that arrives at the last moment.  I remember there being some sort of romance sub-plot to the show as well between two crew members.    Other non-plot details:   This was live action, not animated. I remember the special effects being quite high-end.   The guns on the ships were manipulated by a person sitting in a gunnery chair. This chair projected a holographic view of the fight in front of him/her. From there the gunner used a joystick and a keypad to control the weapons on the ship.  All the crew wore simple Star-Trek style uniforms throughout the entire program, so no jumpsuits or helmets.    I don't know if this was a movie or a TV show, because I never actually saw the beginning of it. I think I saw at least 45 minutes worth, so it could be either as far as I know.   That's all I remember, other than I think the name of the show was fairly generic (something like "Star Command"). I loved the show as a kid even though I only saw it once. I would like to watch it again and see how lame it really was. I attempted a proof of mathematical induction using an arbitrary base case, but was unsuccessful (and hence this question). Below is what I was trying to do and along with my thinking; if anyone can point me in the right direction I'd appreciate it.  The induction I am using: Let $P$ be a property about the natural numbers $\mathbb{N}$ with $0\in\mathbb{N}$, and let $P(n)$ denote the statement that the property $P$ holds for $n\in\mathbb{N}$. Suppose $P(0)$. Furthermore suppose that for each natural number $k$, $P(k)$ implies $P(k+1)$. Then $\forall nP(n)$.  What I am trying to prove: Let $P$ be a property about the natural numbers $\mathbb{N}$ with $0\in\mathbb{N}$, and let $P(n)$ denote the statement that the property $P$ holds for $n\in\mathbb{N}$. Suppose for $n_0\in\mathbb{N}$, $P(n_0)$. Furthermore suppose that for each natural number $k\geq n_0$, $P(k)$ implies $P(k+1)$. Then $\forall n\geq n_0 P(n)$.  My attempted proof: define $Q(n)$ to be $n\geq n_0 \to P(n)$. Then we wish to prove $\forall nQ(n)$. We induct on $n$.  Base case (for ordinary induction): $Q(0)$ is $0\geq n_0\to P(0)$. Since $n_0\in\mathbb{N}$, $0\geq n_0$ implies that $n_0=0$. Since $P(n_0)$, $P(0)$, which proves the base case.  Inductive step: we want to show $\forall n(Q(n)\to Q(n+1))$. To do this, we assume $k\geq n_0 \to P(k)$ and try to show $k+1\geq n_0 \to P(k+1)$.  Since $k\geq n_0 \to P(k)$, we first prove the case where $k\geq n_0$ and $P(k)$. By the hypothesis of the proof, we see that $P(k+1)$, which proves the case for $k+1$.  This is where I am having trouble: For $k&lt;n_0$, I am unable to show the implication for $k+1$.  So my questions would be: (1) is the overall approach for the proof correct? (2) If so, how might I go on to prove the case when $k&lt;n_0$?  Thanks in advance. (This is not homework, by the way.) Why KL divergence is non-negative? Why is KL divergence non-negative?  From the perspective of information theory, I have such an intuitive understanding:  Say there are two ensembles $A$ and $B$ which are composed of the same set of elements labeled by $x$. $p(x)$ and $q(x)$ are different probability distributions over ensemble $A$ and $B$ respectively.   From the perspective of information theory, $\log_{2}(P(x))$ is the least amount of bits that required for recording an element $x$ for ensemble $A$. So that the expectation $$\sum_{x \in  ensemble}-p(x)\ln(p(x))$$ can be interpreted as at least how many bits that we need for recording an element in $A$ on average.   Since this formula puts a lower bound on the bits that we need on average, so that for a different ensemble $B$ which brings about a different probability distribution $q(x)$, the bound that it gives for each element $x$ will surely not bit that is given by $p(x)$, which means taking the expectation, $$\sum_{x\in ensemble}-p(x)\ln(q(x))$$ this average length will surely be greater than the former one, which leads to $$\sum_{x\in ensemble }p(x)\frac{\ln(p(x))}{\ln(q(x))} &gt; 0$$  I don't put $\ge$ here since $p(x)$ and $q(x)$ are different.  This is my intuitive understanding, is there a purely mathematical way of proving KL divergence is non-negative? The problem can be stated as:  Given $p(x)$ and $q(x)$ are both positive over real line, and $\int_{-\infty}^{+\infty}p(x)dx = 1$, $\int_{-\infty}^{+\infty}q(x)dx = 1$.  Prove $$\int_{-\infty}^{+\infty}p(x)\ln\frac{p(x)}{q(x)}$$ is non-negative.  How can this be proved? Or can this be proved without extra conditions? Computing second partial derivative with polar coordinates Consider the polar coordinates with $x=r\cos\theta$ and $y=r\sin\theta$.  I can show using the chain rule that $$\frac{\partial}{\partial x} = \frac{x}{r} \frac{\partial}{\partial r} -\frac{y}{r^2} \frac{\partial}{\partial \theta}$$   What is the method to compute $\dfrac{\partial^2}{\partial x^2}$? I don't know how to do it. A rubber viewfinder cover is connected to my camera strap.  What's it for, and when do I use it?  What happens to a photo if I don't use it? Is there any work-around if you are somewhere where images are blocked? I'm currently working in a bank, and while about 99.7% of the internet is blocked, Stack Exchange thankfully isn't (yet) however imgur is.  It means I can't view images posted alongside questions. The only workaround I have found is to search Google images for the URL, but you get a  which is a bit useless.  Does anybody know any clever tricks for viewing the images accompanying questions when you are somewhere where imgur is blocked?  Are there any plans to route the images stored on imgur through a Stack Exchange URL? Automatically login and lock In which cases should I use the subjunctive mood?     I suggest that every applicant fill out the form carefully.        If she were rich, she would live on Long Island. fp - How to keep running sum in variable? I have this code in my LaTeX:   \FPset{totalHours}{0}  \newcommand{\entry}[5]{     \FPeval{totalHours}{(totalHours)+#5}     #1 &amp; #2 &amp; #3 &amp; #4 &amp; #5 \\ }   Where \entry is meant to be an entry in a time log. The 5th argument is a number representing the number of hours in that entry. I want to keep a running total of the hours in a variable I can print later on, totalHours.   This seems to do the \FPeval but then totalHours gets reset to 0 by the next time I write \entry. What is the correct way to keep a running total? Thanks. Moving SQL Server to different domain How to load Windows 7 from GRUB rescue Is it true that $(R\times S)[G]\cong R[G]\times S[G]$? Suppose Player 1 has a Dragon on the table and  in hand, while Player 2 has two Spiders on the table.  Player 1 chooses to attack with the Dragon and Player 2 chooses to block with one of the Spiders.  Before combat damage is to be dealt, Player 1 uses Unsummon on the blocking Spider.    Does Player 2 take any life damage from the attacking Dragon? Stripping seasoning from cast iron After reading , I want to try to re-season a skillet with flaxseed oil; I'm fairly certain I did a terrible job when I seasoned the skillet several years ago. Is it possible to do this with steel wool or vinegar? (I don't have a self-cleaning oven, so that method is out.) How to avoid noisy renders in Cycles? When does a reaction happen if the trigger is movement? I'm a beginner in Leaflet and I need help to deal with GeoJSON files.  I succeeded in creating a Leaflet basemap. I can add markers without troubles but I cannot manage to show a GeoJSON layer.  Here is the code I picked up from Leaflet Tutorials website  :  var geojsonFeature = {     "type": "Feature",     "properties": {         "name": "Coors Field",         "amenity": "Baseball Stadium",         "popupContent": "This is where the Rockies play!"     },     "geometry": {         "type": "Point",         "coordinates": [-104.99404, 39.75621]     } }; L.geoJSON(geojsonFeature).addTo(map);   Unfortunatly, the GeoJSON does not appear in my map.   Can you tell me where I missed something ?    Alright, you're fine Francisco, this part was OK. I changed the whole script and it works !  However, would you know how to load a GeoJSON from an external source ?  I tried this :   var geojsonLayer = new L.GeoJSON.AJAX("foo.geojson");        geojsonLayer.addTo(map);   from   but this definitely does not work.  Any ideas ?    I am not skilled enough to understand your advice.  Here is the whole code I am using to create my map :  &lt;!DOCTYPE html&gt; &lt;html&gt; &lt;head&gt; &lt;title&gt;data&lt;/title&gt; &lt;meta charset="UTF-8"&gt; &lt;link rel="stylesheet" href="https://unpkg.com/leaflet@1.0.3/dist/leaflet.css" /&gt; &lt;script src="https://unpkg.com/leaflet@1.0.3/dist/leaflet.js"&gt;&lt;/script&gt; &lt;script src="https://code.jquery.com/jquery-3.1.1.min.js"&gt;&lt;/script&gt;   &lt;script type="text/javascript" src="http://maps.stamen.com/js/tile.stamen.js?v1.3.0"&gt;&lt;/script&gt; &lt;script src="/js/leaflet-0.7.2/leaflet.ajax.min.js"&gt;&lt;/script&gt; &lt;script src="htdocs/webmap101/leaflet.ajax.min.js" type="text/javascript" &gt;&lt;/script&gt; &lt;style&gt;    #map {width: 960px; height:700px;} &lt;/style&gt; &lt;/head&gt; &lt;body&gt;   &lt;div id="map"&gt;&lt;/div&gt; &lt;script&gt;   // create map var lat = 44.933331; var lon = 4.9;  var map = L.map('map',{center: [lat,lon],zoom: 6});   // basemaps var base = L.tileLayer('http://{s}.tile.osm.org/{z}/{x}/{y}.png',   {attribution: '© &lt;a href="http://osm.org/copyright"&gt;OpenStreetMap&lt;/a&gt; contributors'  }); var toner = new L.StamenTileLayer("toner"); var watercolor = new L.StamenTileLayer("watercolor"); var landscape = L.tileLayer('https://tile.thunderforest.com/landscape/{z}/{x}/{y}.png'); base.addTo(map);   // markers  var mark1=L.marker([lat,lon]) mark1.addTo(map)    // layers panel  L.control.layers({"base": base, "water": watercolor, "toner": toner , "landscape" : landscape}).addTo(map);    // geojson files var geojsonFeature = {     "type": "Feature",     "properties": {         "name": "Coors Field",         "amenity": "Baseball Stadium",         "popupContent": "This is where the Rockies play!"     },     "geometry": {         "type": "Point",         "coordinates": [-104.99404, 39.75621]     } }; L.geoJSON(geojsonFeature).addTo(map);    //ajax  var geojsonLayer = new L.GeoJSON.AJAX("foo.geojson");        geojsonLayer.addTo(map);  &lt;/script&gt; &lt;/body&gt; &lt;/html&gt;   I know it's a bit messy but this is actually my very first HTML script... I guess I did not include in a proper way the AJAX library.    Actually, I just want a solution to replace the lines where I create the GeoJSON by something that tells javascript to load the GeoJSON stored locally in my folder. This :  var geojsonFeature = {     "type": "Feature",     "properties": {         "name": "Coors Field",         "amenity": "Baseball Stadium",         "popupContent": "This is where the Rockies play!"     },     "geometry": {         "type": "Point",         "coordinates": [-104.99404, 39.75621]     } };   should be transformed into something like (I don't know if it exists) :  var geojsonFeature = [foo.geosjon]   where "foo.geosjson" is a file like :  { "type": "FeatureCollection", "name": "abies", "crs": { "type": "name", "properties": { "name": "urn:ogc:def:crs:OGC:1.3:CRS84" } }, "features": [ { "type": "Feature"