I will be looking to create a Logo very shortly.  I am not formally educated in this principle, where I am self learning through a variety of online resources.  Through my learning, I have come across the term 'Golden Ratio' and the 'Golden Spiral'.  I have read and watched countless resources but my only taking is that the ratio is set at 1:1.618 and its purpose is to help inform the creation of something that is visually pleasing.  I understand how ratios and proportionality works.  Where I am at a loss, is on where and how these ratios and spirals are integrated into the design process.  Due to not actually getting anywhere with my understanding, I thought I would look at some images that claim to abide by these ratios and spirals.  Using Photoshop, I then placed the Spiral on top of the images as an overlay as follows ...       I understand the ratio of 1:1.618.  When it comes to the Grid approach, would I be right in saying that each Box is simply in proportion of its adjacent Boxes by a ratio of 1.618?  Does it matter where the Grids are and how many Boxes the image includes?  For example, I could place many more Boxes within the Grid approach, as long as they follow the 1.618 ratio?  Obviously, the more Boxes being added, the smaller they would have to be.    Assuming I have understood the Mathematics/Technicalities of the Golden Ratio Grid, I am still at a loss of its implementation.  What exactly should I look out for and what would I need to ensure was in each Box for example.  That still leaves the question ... How does the Spiral work?       Maybe its just the frustrations within but it often seems to be that many resources try and make the Spiral fit an image rather than the Spiral informing the ideation and creative process.   Any clarification, on this, would be greatly appreciated since I am at a loss at its usage.
The  is the stuff of legend () and is . My question is two-fold, really: Is the Golden Ratio really a good tool used in modern design (defined here as 20th century on forward), and if so, how often is it used outside of the aforementioned known uses?  EDIT: To @e100's first comment, examples of modern use of the Golden Ratio would be a great thing to add here if there any documented or arguably conclusive uses of it.
While executing a C program, a.out, using the Ubuntu terminal, why do I always need to type ./ before a.out, instead of just writing a.out? Is there solution for this? Is it standard to say $-i \log(-1)$ is $\pi$? I typed $\pi$ into Wolfram Alpha and in the short list of definitions there appeared  $$ \pi = -i \log(-1)$$  which really bothered me. Multiplying on both sides by $2i$:  $$ 2\pi i = 2 \log(-1) = \log(-1)^2 = \log 1= 0$$  which is clearly false.  I guess my error is $\log 1 = 0$ when $\log$ is complex-valued.  I need to use $1 = e^{2 \pi i}$ instead.  So my question: is it correct for WA to say $\pi = -i \log(-1)$?  Or should be they specifying "which" $-1$ they mean?  Clearly $ -1 = e^{i \pi}$ is the "correct" value of $-1$ here. biblatex: Tighter integration of \textcite "in the flow of text" This question led to a new feature in a package:      Many biblatex citation styles feature the \textcite command which is "intended for use in the flow of text, replacing the subject of a sentence" (manual, section 3.6.2). At the moment, this works well for citations of single works -- e.g. (assuming the authoryear style), one may write in the source  The reference work is \textcite{knuth:ct:a}.   which will be typeset as     The reference work is Knuth (1984).   Citing multiple works, on the other hand, is somewhat tedious. If one simply writes (1):  Important works are \textcite{knuth:ct:a,knuth:ct:b,markey}.   the output is rather a list than a correct sentence (2):     Important works are Knuth (1984); Knuth (1986); Markey (2005).   One has to write (3):  Important works are \textcite{knuth:ct:a}, \textcite{knuth:ct:b}, and \textcite{markey}.   to get (4):     Important works are Knuth (1984), Knuth (1986), and Markey (2005).   Can \textcite be modified so that input (1) will yield output (4), hereby achieving a tighter integration "in the flow of text"?  \documentclass{article}  \usepackage[style=authoryear]{biblatex}  \addbibresource{biblatex-examples.bib}  \begin{document}  This is how \texttt{\textbackslash textcite} currently works:\\ Important works are \textcite{knuth:ct:a,knuth:ct:b,markey}.  \bigskip  But I'd like \texttt{\textbackslash textcite} to output the following:\\ Important works are \textcite{knuth:ct:a}, \textcite{knuth:ct:b}, and \textcite{markey}.  \printbibliography  \end{document} Integral vanishes on all intervals implies the function is a.e. zero I am having trouble with the following problem:      $f:\mathbb{R}\to \mathbb{R}$ is a measurable function such that for all $a$:   $$\int_{[0,a]}f\,dm=0.$$   Prove that $f=0$ for $m$ almost every $x$ (here $m$ is the Lebesgue measure).    I have no problem proving this for $f$ non-negative, or under the assumption that $f$ is integrable. But the question only assumes that $f$ is measurable and no more.  My idea was the usual thing; we look at the set of points where $f$ is positive and negative and assume one of these has measure greater than zero. Then I wanted to estimate one of these by an open set, look at the integral on the open set and show that it had to be greater than zero, a contradiction. But a key part of this attack is the assumption of the absolute continuity of the integral, which only holds in the case where $f$ is integrable.  Alternatively, if it were integrable one could simply estimate $f$ by a continuous function, where the result is quite obvious.  Ultimately we are going to show that $f$ is integrable, but it is not clear to me how to show this before showing it is zero a.e. So there must be a simpler way. Does anyone have suggestions? How to divide an image into blocks in MATLAB? Sort arrays of primitive types in descending order I've got a large array of primitive types (double). How do I sort the elements in descending order?  Unfortunately the Java API doesn't support sorting of primitive types with a Comparator.  The first approach that probably comes to mind is to convert it to a list of objects (boxing):  double[] array = new double[1048576];     Arrays.stream(array).boxed().sorted(Collections.reverseOrder())…   However, boxing each primitive in the array is too slow and causes a lot of GC pressure!  Another approach would be to sort and then reverse:  double[] array = new double[1048576]; ... Arrays.sort(array); // reverse the array for (int i = 0; i &lt; array.length / 2; i++) {      // swap the elements      double temp = array[i];      array[i] = array[array.length - (i + 1)];      array[array.length - (i + 1)] = temp; }   This approach is also slow - particularly if the array is already sorted quite well.  What's a better alternative? How were the number of rounds for different key sizes of AES selected? The number of AES rounds increases with the key length. Why increase the number of rounds at all, and how were these round counts chosen? Right identity and Right inverse implies a group Let $(G, *)$ be a semi-group. Suppose   $ \exists e \in G$ such that $\forall a \in G,\  ae = a$;  $\forall a \in G, \exists a^{-1} \in G$ such that $aa^{-1} = e$.    How can we prove that $(G,*)$ is a group? Loading a package conditionally Should training data in each batch size be resample only one time or at each epoch when using mini-batch I saw some related question regarding to the fact is one should use sampling with resampling or without when using minibatch.  However my question is different.  Let's assume that I use sampling witouth replacement. Meaning that for each epoch one training example can only belong one 'batch size' group.  I want to know if one should only resample the training data (into the different batch size) only 1 time or before to start to update the parameters before each epoch.  For instance suppose I have 20 'batch size' group. Suppose at the first iteration I have sampled picture A in group 2 and picture B in group 4.  If so should picture A always stay in group 2 and picture B in group 4. Or should I resample it before to start a new epoch (e.g. at epoch 2 put picture B in group 6 and picture B in group 20). Must present perfect tense be used if the action takes place more than once? I was told that if an action is completed once in the past, the simple past is used. Ex:  I saw that movie.  If the action is completed more than once, the present perfect tense must be used. Ex:  I have seen that movie twelve times.    So, "I have seen that movie twelve times on Tuesday." is correct and "I saw that movie twelve times on Tuesday." is incorrect? When two objects -one of them transparent- intersects it creates some artifacts visible even in the alpha channel. Even with 1024 transparent bounces the artifacts remain.    In the example file there are two cubes in the same position, one transparent and one emission.    What is causing this? Any way to get rid of this artifacts? Package Listings Warning: Text dropped after begin of listing when calling function I'm trying to this:  \newcommand{\code}[1] {\begin{lstlisting} {#1} \end{lstlisting} }   But I keep getting this error:  Package Listings Warning: Text dropped after begin of listing   I'm calling \usepackage and all so, do any of you knows how to solve this? How Do I improve the performance of my Drupal7 Site? For somebody who is new to Drupal,  I see that there are many resources available on Drupal Caching but I am not sure which of them to use. Compare two files with first column and remove duplicate row from 2nd file in shell script I will ask my question with an example. I have 2 files:  File #1:  118D FC300_R5_TP  FX.B      32775       2112   6       2038   6       2112   0 118E FC300_R5_TP  FX.B      32775       2136   7       2065   6       2136   0 118F FC300_R5_TP  FX.B      32775       2124   6       2064   6       2124   0 1190 FC300_R5_TP  FX.B     819210     814632  99     814609  99     814632   0 1191 FC300_R5_TP  FX.B     819210     104100  13     103714  13     104100   0 1192 FC300_R5_TP  FX.B    1638420    1609476  98    1609402  98    1609476   0 1196 FC300_R5_TP  FX.B    1638420    1638432 100    1638379 100    1638432   0 119A FC300_R5_TP  FX.B    3276840    3271776 100    3271698 100    3271776   0 119E FC300_R5_TP  FX.B    3276840    3264120 100    3264034 100    3264120   0 11A2 FC300_R5_TP  FX.B    3276840    2328648  71    2328546  71    2328648   0 11A6 FC300_R5_TP  FX.B    3276840    2328444  71    2328355  71    2328444   0 11AA FC300_R5_TP  FX.B    3276840    2328528  71    2328403  71    2328528   0 11AE FC300_R5_TP  FX.B    3276840    2328648  71    2328468  71    2328648   0 11B2 FC300_R5_TP  FX.B    3276840    2130000  65    2129766  65    2130000   0 173A FC300_R5_TP  FX.B    6553680    6478572  99    6477747  99    6478572   0   File #2:  11AA FC300_R5_TP  FX.B    3276840    2328528  71    2328403  71    2328528   0 11AE FC300_R5_TP  FX.B    3276840    2328648  71    2328468  71    2328648   0 11B2 FC300_R5_TP  FX.B    3276840    2130000  65    2129766  65    2130000   0 173A FC300_R5_TP  FX.B    6553680    6478572  99    6477747  99    6478572   0 0BDB FC600_R5_TP  FX.B   33554640    6044364  18    6033105  18    6044364   0 0BDC FC600_R5_TP  FX.B   33554640    6613536  20    6481974  19    6613536   0 0BDD FC600_R5_TP  FX.B   33554640    4435848  13    4057170  12    4435848   0 0BDE FC600_R5_TP  FX.B   33554640    6620868  20    6249518  19    6620868   0   Desired Output  File #3:  0BDB FC600_R5_TP  FX.B   33554640    6044364  18    6033105  18    6044364   0 0BDC FC600_R5_TP  FX.B   33554640    6613536  20    6481974  19    6613536   0 0BDD FC600_R5_TP  FX.B   33554640    4435848  13    4057170  12    4435848   0 0BDE FC600_R5_TP  FX.B   33554640    6620868  20    6249518  19    6620868   0   I'd like to compare file 1 and file 2 using their first columns and remove the entire line or row from file 2 where they match in file 1. I'd also like to save the results to a 3rd file, file #3. What are these notices above my post? My post has been marked with an informational notice in a box above it.   What should I do about this? Who attaches notices to posts? What kinds of notices are available? What should I do if I think a notice should be added to a post? What should I do if I think a notice should be removed from a post? I am using Ubuntu 11.10 (64 bits) and I do not want to mount automatically USB thumb drives in my system. I tried the command dconf-editor and gconf-editor but there isn't the icon to disable it in nautilus preferences (apps|nautilus|preferences|media_automount).  Thanks. How can I know when my computer running Windows 7 was last restarted?   I prefer a solution that doesn't involve searching the event log, but something like wmic or maybe cmd commands. How can I fix a 404 Error when using a PPA or updating my package lists? PPA seems to be constantly offline. Whenever I use sudo apt-get update, this error is shown:  W: Failed to fetch http://ppa.launchpad.net/ 404  Not Found   How do I fix these errors? Can I get notification when event occur? SQL Servers has Traces and XEvents. These are used to capture and analyze what is going on with our SQL Server Instances. Events are stored in the stack for later analysis. For example,  If I decide to monitor any dead lock in the database, I just query the trace file to see the history of deadlock for a period of time. Here is my question:  While events occur, in our example deadlock event, is there a way to get an email notification using msdb.dbo.xp_send_dbmail?