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  • 3d symmetry search algorithm

    - by aaa
    this may be more appropriate for math overflow, but nevertheless: Given 3d structure (for example molecule), what is a good approach/algorithm to find symmetry (rotational/reflection/inversion/etc.)? I came up with brute force naive algorithm, but it seems there should be better approach. I am not so much interested in genetic algorithms as I would like best symmetry rather then almost the best symmetry link to website/paper would be great. thanks

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  • Complex behavior generated by simple computation

    - by Yuval A
    Stephen Wolfram gave a fascinating talk at TED about his work with Mathematica and Wolfram Alpha. Amongst other things, he pointed out how very simple computations can yield extremely complex behaviors. (He goes on to discuss his ambition for computing the entire physical universe. Say what you will, you gotta give the guy some credit for his wild ideas...) As an example he showed several cellular automata. What other examples of simple computations do you know of that yield fascinating results?

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  • How to minimize total cost of shortest path tree

    - by Michael
    I have a directed acyclic graph with positive edge-weights. It has a single source and a set of targets (vertices furthest from the source). I find the shortest paths from the source to each target. Some of these paths overlap. What I want is a shortest path tree which minimizes the total sum of weights over all edges. For example, consider two of the targets. Given all edge weights equal, if they share a single shortest path for most of their length, then that is preferable to two mostly non-overlapping shortest paths (fewer edges in the tree equals lower overall cost). Another example: two paths are non-overlapping for a small part of their length, with high cost for the non-overlapping paths, but low cost for the long shared path (low combined cost). On the other hand, two paths are non-overlapping for most of their length, with low costs for the non-overlapping paths, but high cost for the short shared path (also, low combined cost). There are many combinations. I want to find solutions with the lowest overall cost, given all the shortest paths from source to target. Does this ring any bells with anyone? Can anyone point me to relevant algorithms or analogous applications? Cheers!

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  • How to draw a graph in LaTeX?

    - by Amir Rachum
    First of all, let me say I'm using LyX, though I have no problem using ERT. Secondly, what is the most simplest way to draw a simple graph like this in Latex? I've seen some documents with graphs and I've seen some examples, but I couldn't figure out how to just draw a simple graph - what packages do I need, etc?

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  • Provable planarity of flowcharts

    - by Nikolaos Kavvadias
    Hi all I have a question: is there any reference (e.g. paper) with a proof of the planarity of flowchart layouts? Can anyone suggest an algorithm for generating flowchart (planar) layouts? I know that there are some code-to-flowchart tools out there, but i'm unaware of their internals. Thanks in advance -kavi

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  • Can Haskell's Parsec library be used to implement a recursive descent parser with backup?

    - by Thor Thurn
    I've been considering using Haskell's Parsec parsing library to parse a subset of Java as a recursive descent parser as an alternative to more traditional parser-generator solutions like Happy. Parsec seems very easy to use, and parse speed is definitely not a factor for me. I'm wondering, though, if it's possible to implement "backup" with Parsec, a technique which finds the correct production to use by trying each one in turn. For a simple example, consider the very start of the JLS Java grammar: Literal: IntegerLiteral FloatingPointLiteral I'd like a way to not have to figure out how I should order these two rules to get the parse to succeed. As it stands, a naive implementation like this: literal = do { x <- try (do { v <- integer; return (IntLiteral v)}) <|> (do { v <- float; return (FPLiteral v)}); return(Literal x) } Will not work... inputs like "15.2" will cause the integer parser to succeed first, and then the whole thing will choke on the "." symbol. In this case, of course, it's obvious that you can solve the problem by re-ordering the two productions. In the general case, though, finding things like this is going to be a nightmare, and it's very likely that I'll miss some cases. Ideally, I'd like a way to have Parsec figure out stuff like this for me. Is this possible, or am I simply trying to do too much with the library? The Parsec documentation claims that it can "parse context-sensitive, infinite look-ahead grammars", so it seems like something like I should be able to do something here.

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  • Number of ways to place kings on chess board

    - by Rakesh
    You have an N x N chessboard and you wish to place N kings on it. Each row and column should contain exactly one king, and no two kings should attack each other (two kings attack each other if they are present in squares which share a corner). The kings in the first K rows of the board have already been placed. You are given the positions of these kings as an array pos[ ]. pos[i] is the column in which the king in the ith row has already been placed. All indices are 0-indexed. In how many ways can the remaining kings be placed? Input: The first line contains the number of test cases T. T test cases follow. Each test case contains N and K on the first line, followed by a line having K integers, denoting the array pos[ ] as described above. Output: Output the number of ways to place kings in the remaining rows satisfying the above conditions. Output all numbers modulo 1000000007. Constraints: 1 <= T <= 20 1 <= N <= 16 0 <= K <= N 0 <= pos_i < N The kings specified in the input will be in different columns and not attack each other. Sample Input: 5 4 1 2 3 0 5 2 1 3 4 4 1 3 0 2 6 1 2 Sample Output: 1 0 2 1 18 Explanation: For the first example, there is a king already placed at row 0 and column 2. The king in the second row must belong to column 0. The king in the third row must belong to column 3, and the last king must beong to column 1. Thus there is only 1 valid placement. For the second example, there is no valid placement. How should i approach this problem

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  • Find all cycles in graph, redux

    - by Shadow
    Hi, I know there are a quite some answers existing on this question. However, I found none of them really bringing it to the point. Some argue that a cycle is (almost) the same as a strongly connected components (s. http://stackoverflow.com/questions/546655/finding-all-cycles-in-graph/549402#549402) , so one could use algorithms designed for that goal. Some argue that finding a cycle can be done via DFS and checking for back-edges (s. boost graph documentation on file dependencies). I now would like to have some suggestions on whether all cycles in a graph can be detected via DFS and checking for back-edges? My opinion is that it indeed could work that way as DFS-VISIT (s. pseudocode of DFS) freshly enters each node that was not yet visited. In that sense, each vertex exhibits a potential start of a cycle. Additionally, as DFS visits each edge once, each edge leading to the starting point of a cycle is also covered. Thus, by using DFS and back-edge checking it should indeed be possible to detect all cycles in a graph. Note that, if cycles with different numbers of participant nodes exist (e.g. triangles, rectangles etc.), additional work has to be done to discriminate the acutal "shape" of each cycle.

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  • Is information a subset of data?

    - by Jason Baker
    I apologize as I don't know whether this is more of a math question that belongs on mathoverflow or if it's a computer science question that belongs here. That said, I believe I understand the fundamental difference between data, information, and knowledge. My understanding is that information carries both data and meaning. One thing that I'm not clear on is whether information is data. Is information considered a special kind of data, or is it something completely different?

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  • Windows Batch file to echo a specific line number

    - by Lee
    So for the second part of my current dilemma, I have a list of folders in c:\file_list.txt. I need to be able to extract them (well, echo them with some mods) based on the line number because this batch script is being called by an iterative macro process. I'm passing the line number as a parameter. @echo off setlocal enabledelayedexpansion set /a counter=0 set /a %%a = "" for /f "usebackq delims=" %%a in (c:\file_list.txt) do ( if "!counter!"=="%1" goto :printme & set /a counter+=1 ) :printme echo %%a which gives me an output of %a. Doh! So, I've tried echoing !a! (result: ECHO is off.); I've tried echoing %a (result: a) I figured the easy thing to do would be to modify the head.bat code found here: http://stackoverflow.com/questions/130116/dos-batch-commands-to-read-first-line-from-text-file except rather than echoing every line - I'd just echo the last line found. Not as simple as one might think. I've noticed that my counter is staying at zero for some reason; I'm wondering if the set /a counter+=1 is doing what I think it's doing.

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  • Find all complete sub-graphs within a graph

    - by mvid
    Is there a known algorithm or method to find all complete sub-graphs within a graph? I have an undirected, unweighted graph and I need to find all subgraphs within it where each node in the subgraph is connected to each other node in the subgraph. Is there an existing algorithm for this?

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  • What are logical and path queries

    - by NomeN
    I'm reading a paper which mentions that a language for refactoring has three specific requirements. functional features (like ML) logical queries (like Datalog) path queries (like Datalog) I know what they mean by functional features, but I'm not totally clear on the latter two and can't find a clear explanation either. Although I have a good idea after what I could find on the subjects, I need to be sure so here goes: Could the SO-community please clearly explain to me what logical queries and path queries are? Or at the very least what the people from the paper meant?

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  • Java: Match tokens between two strings and return the number of matched tokens

    - by Cryssie
    Need some help to find the number of matched tokens between two strings. I have a list of string stored in ArrayList (example given below): Line 0 : WRB VBD NN VB IN CC RB VBP NNP Line 1 : WDT NNS VBD DT NN NNP NNP Line 2 : WRB MD PRP VB DT NN IN NNS POS JJ NNS Line 3 : WDT NN VBZ DT NN IN DT JJ NN IN DT NNP Line 4 : WP VBZ DT JJ NN IN NN Here, you can see each string consists of a bunch of tokens separated by spaces. So, there's three things I need to work with.. Compare the first token (WRB) in Line 0 to the tokens in Line 1 to see if they match. Move on to the next tokens in Line 0 until a match is found. If there's a match, mark the matched tokens in Line 1 so that it will not be matched again. Return the number of matched tokens between Line 0 and Line 1. Return the distance of the matched tokens. Example: token NN is found on position 3 on line 0 and position 5 on Line 1. Distance = |3-5| = 2 I've tried using split string and store it to String[] but String[] is fixed and doesn't allow shrinking or adding of new elements. Tried Pattern Matcher but with disasterous results. Tried a few other methods but there's some problems with my nested for loops..(will post part of my coding if it will help). Any advice or pointers on how to solve this problem this would be very much appreciated. Thank you very much.

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  • How do I compute the approximate entropy of a bit string?

    - by dreeves
    Is there a standard way to do this? Googling -- "approximate entropy" bits -- uncovers multiple academic papers but I'd like to just find a chunk of pseudocode defining the approximate entropy for a given bit string of arbitrary length. (In case this is easier said than done and it depends on the application, my application involves 16,320 bits of encrypted data (cyphertext). But encrypted as a puzzle and not meant to be impossible to crack. I thought I'd first check the entropy but couldn't easily find a good definition of such. So it seemed like a question that ought to be on StackOverflow! Ideas for where to begin with de-cyphering 16k random-seeming bits are also welcome...) See also this related question: http://stackoverflow.com/questions/510412/what-is-the-computer-science-definition-of-entropy

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  • Gaining information from nodes of tree

    - by jainp
    I am working with the tree data structure and trying to come up with a way to calculate information I can gain from the nodes of the tree. I am wondering if there are any existing techniques which can assign higher numerical importance to a node which appears less frequently at lower level (Distance from the root of the tree) than the same nodes appearance at higher level and high frequency. To give an example, I want to give more significance to node Book, at level 2 appearing once, then at level 3 appearing thrice. Will appreciate any suggestions/pointers to techniques which achieve something similar. Thanks, Prateek

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  • Examples of useful or non-trival dual interfaces

    - by Scott Weinstein
    Recently Erik Meijer and others have show how IObservable/IObserver is the dual of IEnumerable/IEnumerator. The fact that they are dual means that any operation on one interface is valid on the other, thus providing a theoretical foundation for the Reactive Extentions for .Net Do other dual interfaces exist? I'm interested in any example, not just .Net based.

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  • [UNIX] Sort lines of massive file by number of words on line (ideally in parallel)

    - by conradlee
    I am working on a community detection algorithm for analyzing social network data from Facebook. The first task, detecting all cliques in the graph, can be done efficiently in parallel, and leaves me with an output like this: 17118 17136 17392 17064 17093 17376 17118 17136 17356 17318 12345 17118 17136 17356 17283 17007 17059 17116 Each of these lines represents a unique clique (a collection of node ids), and I want to sort these lines in descending order by the number of ids per line. In the case of the example above, here's what the output should look like: 17118 17136 17356 17318 12345 17118 17136 17356 17283 17118 17136 17392 17064 17093 17376 17007 17059 17116 (Ties---i.e., lines with the same number of ids---can be sorted arbitrarily.) What is the most efficient way of sorting these lines. Keep the following points in mind: The file I want to sort could be larger than the physical memory of the machine Most of the machines that I'm running this on have several processors, so a parallel solution would be ideal An ideal solution would just be a shell script (probably using sort), but I'm open to simple solutions in python or perl (or any language, as long as it makes the task simple) This task is in some sense very easy---I'm not just looking for any old solution, but rather for a simple and above all efficient solution

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  • What is an XYZ-complete problem?

    - by TheMachineCharmer
    EDIT: Diagram: http://www.cs.umass.edu/~immerman/complexity_theory.html There must be some meaning to the word "complete" its used every now and then. Look at the diagram. I tried reading previous posts about NP- My question is what does the word "COMPLETE" mean? Why is it there? What is its significance? N- Non-deterministic - makes sense' P- Polynomial - makes sense but the "COMPLETE" is still a mystery for me.

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  • curious ill conditioned numerical problem

    - by aaa
    hello. somebody today showed me this curious ill conditioned problem (apparently pretty famous), which looks relatively simple ƒ = (333.75 - a^2)b^6 + a^2 (11a^2 b^2 - 121b^4 - 2) + 5.5b^8 + a/(2^b) where a = 77617 and b = 33096 can you determine correct answer?

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  • Create My own language with "Functional Programming Language"

    - by esehara
    I prefer Haskell. I already know How to create my own language with Procedural Language (for example: C, Java, Python, etc). But, I know How to create my own language with Functional Language (for example Haskell, Clojure and Scala). I've already read: Internet Resources Write Yourself a Scheme in 48 Hours Real World Haskell - Chapter 16.Using Persec Writing A Lisp Interpreter In Haskell Parsec, a fast combinator parser Implementing functional languages: a tutorial Books Introduction Functional Programming Using Haskell 2nd Edition -- Haskell StackOverflow (but with procedural language) Learning to write a compiler create my own programming language Source Libraries and tools/HJS -- Haskell Are there any other good sources? I wants to get more links,or sources.

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  • What exactly are administrative redexes after CPS conversion?

    - by eljenso
    In the context of Scheme and CPS conversion, I'm having a little trouble deciding what administrative redexes (lambdas) exactly are: all the lambda expressions that are introduced by the CPS conversion only the lambda expressions that are introduced by the CPS conversion but you wouldn't have written if you did the conversion "by hand" or through a smarter CPS-converter If possible, a good reference would be welcome.

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