Suppose in the 2D space we have an array of points, and each point has a weighting factor, which is a float value ranging from 0 to 1. Each point also has a coordinate in the 2D grid. The following pseduo-codes show the property of the point:  class Point {  public:     float weightingFactor_; // [0,1].     float x_;     float y_;  }   Now my question is: given an array of points, how can we select the best point pair? The criterion for best point pair is: (1) both points should have large weighting factors; (2) the two points should be as far as possible spatially based on the Euclidean distance. For the time being, my solution is for each point pair calculate the following criterion:  Point1.weightingFactor_*Point2.weightingFactor*Distance(Point1, Point2)   Among all the point pair, then select the pair whose criterion value is the largest. I am not sure whether this is the best solution. Any ideas? Thanks.
I have four numeric variables. All of them are measures of soil quality. Higher the variable, higher the quality. The range for all of them is different:  Var1 from 1 to 10  Var2 from 1000 to 2000  Var3 from 150 to 300  Var4 from 0 to 5  I need to combine four variables into single soil quality score which will successfully rank order.  My idea is very simple. Standardize all four variables, sum them up and whatever you get is the score which should rank-order. Do you see any problem with applying this approach. Is there any other (better) approach that you would recommend?  Thanks  Edit:  Thanks guys. A lot of discussion went into "domain expertise"... Agriculture stuff... Whereas I expected more stats-talk. In terms of technique that I will be using... It will probably be simple z-score summation + logistic regression as an experiment. Because vast majority of samples has poor quality 90% I'm going to combine 3 quality categories into one and basically have binary problem (somequality vs no-quality). I kill two birds with one stone. I increase my sample in terms of event rate and I make a use of experts by getting them to clasify my samples. Expert classified samples will then be used to fit log-reg model to maximize level of concordance / discordance with the experts.... How does that sound to you?
Several files in my home directory have been disappearing. E.g. .bashrc, .bash_profile, authorized_keys and now .profile.  Regardless of how this happened, I would like to restore the original pristine .profile file. If I create a new user on my system one is created. Where can I find this .profile contents from a fresh, untouched install? Given any uncountable subset $S$ of the unit interval. Then $S$ clearly has an accumulation point and indeed uncountably many (which might also be a nice exercise). So my question is: Is there an accumulation point, that again lies in $S$? Can “zealot” have a positive connotation? A zealot is a person who is fanatical and uncompromising in pursuit of their religious, political, or other ideals.  I have never seen this word used with positive connotation, but could it (without causing raised eyebrows)? For example, “Gandhi was a zealot and should be admired by all who believe in non-violence.”  Also, do “zealous” and “zeal” carry the same connotation as “zealot”? Difference between "I have got" and "I have gotten" I was looking for a derivation of the expression for the energy density at any point in a static magnetic field. I do know that it is  $$u_B=\dfrac {1}{2 \mu_0}\left|\mathbf{B}\right|^2,$$ I was just wondering if there was a derivation that could be built up the way one derives the energy density, $$u_E=\dfrac {\epsilon_0}{2}\left|\mathbf{E}\right|^2$$ at any point in an electric field, by considering the energy needed to build up a 'source' charge bit by infinitesimal bit.  Whatever proof I have come across seems to bring inductance into the picture -- is there a way of doing it without that? I ask because the corresponding proof for the electric field does not seem to need the definition of capacitance anywhere. Alternate moves, first one to roll a 6 wins: what's the probability of winning? Question: Players A and B play a sequence of independent games. Player A starts and throws a fair die and wins on a "six". If she fails then player B throws the same die and wins on a "six" or fails otherwise. If she fails then player A gets the die and throws again, and so on. The first player to throw a "six" wins. Find the probability that player A wins.  Here is what I have done:  A wins right away: $\dfrac{1}{6}$  A fails B wins: $\dfrac{5}{6}\times \dfrac{1}{6}$  A fails B fails A wins: $\dfrac{5}{6}\times \dfrac{5}{6}\times \dfrac{1}{6}$  Unlike another similar question which the player B can win on "five" and "six" after player A fails on the first throw, in this case, the games do not seem to have an endpoint. How should I calculate the probability that player A wins then? Solving the complex equation $\sin(z) = \cos(z)$ To find the complex numbers z satisfying $\sin(z) = \cos(z)$, can I say: $$\sin(z) = \frac{(e^{iz}-e^{-iz})}{2i}=\frac{(e^{iz}+e^{-iz})}{2}$$   and solve for z? So we then reduce this to $$-e^{-iz} = e^{-iz}$$ but this doesn't look right jQuery 1.9 checkbox not checked second time after once it unchecked I was writing a toString() for a class in Java the other day by manually writing out each element of the class to a String and it occurred to me that using reflection it might be possible to create a generic toString() method that could work on ALL classes. I.E. it would figure out the field names and values and send them out to a String.  Getting the field names is fairly simple, here is what a co-worker came up with:  public static List initFieldArray(String className) throws ClassNotFoundException {      Class c = Class.forName(className);     Field field[] = c.getFields();     List&lt;String&gt; classFields = new ArrayList(field.length);      for (int i = 0; i &lt; field.length; i++) {         String cf = field[i].toString();         classFields.add(cf.substring(cf.lastIndexOf(".") + 1));     }      return classFields; }   Using a factory I could reduce the performance overhead by storing the fields once, the first time the toString() is called. However finding the values could be a lot more expensive.  Due to the performance of reflection this may be more hypothetical then practical. But I am interested in the idea of reflection and how I can use it to improve my everyday programming. Show that any bounded linear functional on a normed linear space is continuous.   Can we say that it is uniformly continuous ?   Also, is it true, if we reverse the statement    any continuous  linear functional on a normed linear space is bounded ?? Proof of property of abelian group I'd like to provide template implementation in my module and allow themes to override it. Basically, I add a suggestion by this simplified code:  function attach_preprocess_node(&amp;$vars) {   $vars['theme_hook_suggestions'][] = 'node__test'; }   (I don't want to use hook_theme to add a new theme because I want to reuse preprocess node functions. The theme name are awkward but I don't want to write node_attach_% to avoid confusion with node type.)  Then I use hook_theme_registry_alter() to add module path:  function attach_theme_registry_alter(&amp;$theme_registry) {   $path = drupal_get_path('module', 'attach') . '/themes';   $theme_registry_copy = $theme_registry;   _theme_process_registry($theme_registry_copy, 'phptemplate', 'theme_engine', 'node', drupal_get_path('module', 'node'));   $theme_registry += array_diff_key($theme_registry_copy, $theme_registry);   if (!isset($theme_registry['node']['theme paths'])) {     $theme_registry['node']['theme paths'] = array();   }   if (!isset($theme_registry['node']['theme paths'])) {     $first_element = array_shift($theme_registry['node']['theme paths']);     if ($first_element) {       array_unshift($theme_registry['node']['theme paths'], $first_element, $path);     }     else {       array_unshift($theme_registry['node']['theme paths'], $path);     }   } }   However it does not work. That means: the file themes/node--super.tpl.php is not used. It is used only if I copied it to the theme folder. How could I get the terminal to be launched once I have logged in, so that typing commands is much simpler? How to read a text file reversely with iterator in C# I need to process a large file, around 400K lines and 200 M. But sometimes I have to process from bottom up. How can I use iterator (yield return) here? Basically I don't like to load everything in memory. I know it is more efficient to use iterator in .NET. Image looks embossed when converted to SVG What are the possible values of the Hibernate hbm2ddl.auto configuration and what do they do I really want to know more about the update, export and the values that could be given to hibernate.hbm2ddl.auto I need to know when to use the update and when not? And what is the alternative?  These are changes that could happen over DB:   new tables new columns in old tables columns deleted data type of a column changed a type of a column changed its attributes tables dropped values of a column changed    In each case what is the best solution? Bonferroni adjustment in SPSS - what does it do? I'm probably being a bit simplistic here, but from what I understand the Bonferroni post hoc test is simply when we adjust the alpha to account for inflated error when several post hoc tests are conducted. You divide the alpha by number of tests. So what exactly does SPSS do when we click the button for Bonferroni?   Shouldn't the dividing of alpha be done by us in interpreting the result, e.g. if we do 10 post hoc tests our alpha criterion should be .005 so if the p value is .012 then it is not significant, but SPSS hasn't done anything there, we have just changed our interpretation. So what exactly is it adjusting? Test whether string is a valid integer Proof of linear independence of $e^{at}$ Find the almost sure limit of $X_n/n$, where each random variable $X_n$ has a Poisson distribution with parameter $n$ $X_{n}$ independent and $X_n \sim \mathcal{P}(n) $  meaning that $X_{n}$ has Poisson distributions with parameter $n$. What is the $\lim\limits_{n\to \infty} \frac{X_{n}}{n}$ almost surely ?    I think we can write $X(n) \sim X(1)+X(1)+\cdots+X(1)$ where the sum is taken on independent identical distribution then use the law of large number. But I am not sure that is it correct or not. Can anyone give me some hints? Thank you in advance!