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  • Code bacteria: evolving mathematical behavior

    - by Stefano Borini
    It would not be my intention to put a link on my blog, but I don't have any other method to clarify what I really mean. The article is quite long, and it's in three parts (1,2,3), but if you are curious, it's worth the reading. A long time ago (5 years, at least) I programmed a python program which generated "mathematical bacteria". These bacteria are python objects with a simple opcode-based genetic code. You can feed them with a number and they return a number, according to the execution of their code. I generate their genetic codes at random, and apply an environmental selection to those objects producing a result similar to a predefined expected value. Then I let them duplicate, introduce mutations, and evolve them. The result is quite interesting, as their genetic code basically learns how to solve simple equations, even for values different for the training dataset. Now, this thing is just a toy. I had time to waste and I wanted to satisfy my curiosity. however, I assume that something, in terms of research, has been made... I am reinventing the wheel here, I hope. Are you aware of more serious attempts at creating in-silico bacteria like the one I programmed? Please note that this is not really "genetic algorithms". Genetic algorithms is when you use evolution/selection to improve a vector of parameters against a given scoring function. This is kind of different. I optimize the code, not the parameters, against a given scoring function.

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  • suggestions on syntax to express mathematical formula concisely

    - by aaa
    hello. I am developing functional domain specific embedded language within C++ to translate formulas into working code as concisely and accurately as possible. I post prototype in the comment, it is about 2 hundred lines long. Right now my language looks something like this (well, actually is going to look like): // implies two nested loops j=0:N, i=0,j (range(i) < j < N)[T(i,j) = (T(i,j) - T(j,i))/e(i+j)]; // implies summation over above expression sum(range(i) < j < N))[(T(i,j) - T(j,i))/e(i+j)]; I am looking for possible syntax improvements/extensions or just different ideas about expressing mathematical formulas as clearly and precisely as possible (in any language, not just C++). Can you give me some syntax examples relating to my question which can be accomplished in your language of choice which consider useful. In particular, if you have some ideas about how to translate the above code segments, I would be happy to hear them. Thank you just to clarify and give actual formula, my short-term goal is to express the following expression concisely where values in <> are already computed as 4-dimensional array

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  • How to parse mathematical expressions involving parentheses

    - by Rob P.
    Please forgive my title, I really don't know how to phrase it better. This isn't a school assignment or anything, but I realize it's a mostly academic question. But, what I've been struggling to do is parse 'math' text and come up with an answer. For Example - I can figure out how to parse '5 + 5' or '3 * 5' - but I fail when I try to correctly chain operations together. (5 + 5) * 3 It's mostly just bugging me that I can't figure it out. If anyone can point me in a direction, I'd really appreciate it. EDIT Thanks for all of the quick responses. I'm sorry I didn't do a better job of explaining. First - I'm not using regular expressions. I also know there are already libraries available that will take, as a string, a mathematical expression and return the correct value. So, I'm mostly looking at this because, sadly, I don't "get it". Second - What I've tried doing (is probably misguided) but I was counting '(' and ')' and evaluating the deepest items first. In simple examples, this worked; but my code is not pretty and more complicated stuff crashes. When I 'calculated' the lowest level, I was modifying the string. So... (5 + 5) * 3 Would turn into 10 * 3 Which would then evaluate to 30 But it just felt 'wrong'. I hope that helps clarify things. I'll certainly check out the links provided.

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  • Code Golf: Evaluating Mathematical Expressions

    - by Noldorin
    Challenge Here is the challenge (of my own invention, though I wouldn't be surprised if it has previously appeared elsewhere on the web). Write a function that takes a single argument that is a string representation of a simple mathematical expression and evaluates it as a floating point value. A "simple expression" may include any of the following: positive or negative decimal numbers, +, -, *, /, (, ). Expressions use (normal) infix notation. Operators should be evaluated in the order they appear, i.e. not as in BODMAS, though brackets should be correctly observed, of course. The function should return the correct result for any possible expression of this form. However, the function does not have to handle malformed expressions (i.e. ones with bad syntax). Examples of expressions: 1 + 3 / -8 = -0.5 (No BODMAS) 2*3*4*5+99 = 219 4 * (9 - 4) / (2 * 6 - 2) + 8 = 10 1 + ((123 * 3 - 69) / 100) = 4 2.45/8.5*9.27+(5*0.0023) = 2.68... Rules I anticipate some form of "cheating"/craftiness here, so please let me forewarn against it! By cheating, I refer to the use of the eval or equivalent function in dynamic languages such as JavaScript or PHP, or equally compiling and executing code on the fly. (I think my specification of "no BODMAS" has pretty much guaranteed this however.) Apart from that, there are no restrictions. I anticipate a few Regex solutions here, but it would be nice to see more than just that. Now, I'm mainly interested in a C#/.NET solution here, but any other language would be perfectly acceptable too (in particular, F# and Python for the functional/mixed approaches). I haven't yet decided whether I'm going to accept the shortest or most ingenious solution (at least for the language) as the answer, but I would welcome any form of solution in any language, except what I've just prohibited above! My Solution I've now posted my C# solution here (403 chars). Update: My new solution has beaten the old one significantly at 294 chars, with the help of a bit of lovely regex! I suspected that this will get easily beaten by some of the languages out there with lighter syntax (particularly the funcional/dynamic ones), and have been proved right, but I'd be curious if someone could beat this in C# still. Update I've seen some very crafty solutions already. Thanks to everyone who has posted one. Although I haven't tested any of them yet, I'm going to trust people and assume they at least work with all of the given examples. Just for the note, re-entrancy (i.e. thread-safety) is not a requirement for the function, though it is a bonus. Format Please post all answers in the following format for the purpose of easy comparison: Language Number of characters: ??? Fully obfuscated function: (code here) Clear/semi-obfuscated function: (code here) Any notes on the algorithm/clever shortcuts it takes.

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  • Random Complete System Unresponsiveness Running Mathematical Functions

    - by Computer Guru
    I have a program that loads a file (anywhere from 10MB to 5GB) a chunk at a time (ReadFile), and for each chunk performs a set of mathematical operations (basically calculates the hash). After calculating the hash, it stores info about the chunk in an STL map (basically <chunkID, hash>) and then writes the chunk itself to another file (WriteFile). That's all it does. This program will cause certain PCs to choke and die. The mouse begins to stutter, the task manager takes 2 min to show, ctrl+alt+del is unresponsive, running programs are slow.... the works. I've done literally everything I can think of to optimize the program, and have triple-checked all objects. What I've done: Tried different (less intensive) hashing algorithms. Switched all allocations to nedmalloc instead of the default new operator Switched from stl::map to unordered_set, found the performance to still be abysmal, so I switched again to Google's dense_hash_map. Converted all objects to store pointers to objects instead of the objects themselves. Caching all Read and Write operations. Instead of reading a 16k chunk of the file and performing the math on it, I read 4MB into a buffer and read 16k chunks from there instead. Same for all write operations - they are coalesced into 4MB blocks before being written to disk. Run extensive profiling with Visual Studio 2010, AMD Code Analyst, and perfmon. Set the thread priority to THREAD_MODE_BACKGROUND_BEGIN Set the thread priority to THREAD_PRIORITY_IDLE Added a Sleep(100) call after every loop. Even after all this, the application still results in a system-wide hang on certain machines under certain circumstances. Perfmon and Process Explorer show minimal CPU usage (with the sleep), no constant reads/writes from disk, few hard pagefaults (and only ~30k pagefaults in the lifetime of the application on a 5GB input file), little virtual memory (never more than 150MB), no leaked handles, no memory leaks. The machines I've tested it on run Windows XP - Windows 7, x86 and x64 versions included. None have less than 2GB RAM, though the problem is always exacerbated under lower memory conditions. I'm at a loss as to what to do next. I don't know what's causing it - I'm torn between CPU or Memory as the culprit. CPU because without the sleep and under different thread priorities the system performances changes noticeably. Memory because there's a huge difference in how often the issue occurs when using unordered_set vs Google's dense_hash_map. What's really weird? Obviously, the NT kernel design is supposed to prevent this sort of behavior from ever occurring (a user-mode application driving the system to this sort of extreme poor performance!?)..... but when I compile the code and run it on OS X or Linux (it's fairly standard C++ throughout) it performs excellently even on poor machines with little RAM and weaker CPUs. What am I supposed to do next? How do I know what the hell it is that Windows is doing behind the scenes that's killing system performance, when all the indicators are that the application itself isn't doing anything extreme? Any advice would be most welcome.

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  • Fixing VBSCRIPT inaccurate mathematical results due to rounding

    - by jay
    Try running this in a .VBS file MsgBox(545.14-544.94) You get a neat little answer of 0.199999999999932! This rounding issue also occurs unfortunately in Sin(2 * pi) since VB can only ever see the (user defined) variable pi as accurate as 3.14159265358979. Is rounding it manually (and loosing accuracy) the only way to improve the result? What is the most effective way of dealing with this kind of problem?

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  • Array: mathematical sequence

    - by VaioIsBorn
    An array of integers A[i] (i 1) is defined in the following way: an element A[k] ( k 1) is the smallest number greater than A[k-1] such that the sum of its digits is equal to the sum of the digits of the number 4* A[k-1] . You need to write a program that calculates the N th number in this array based on the given first element A[1] . INPUT: In one line of standard input there are two numbers seperated with a single space: A[1] (1 <= A[1] <= 100) and N (1 <= N <= 10000). OUTPUT: The standard output should only contain a single integer A[N] , the Nth number of the defined sequence. Input: 7 4 Output: 79 Explanation: Elements of the array are as follows: 7, 19, 49, 79... and the 4th element is solution. I tried solving this by coding a separate function that for a given number A[k] calculates the sum of it's digits and finds the smallest number greater than A[k-1] as it says in the problem, but with no success. The first testing failed because of a memory limit, the second testing failed because of a time limit, and now i don't have any possible idea how to solve this. One friend suggested recursion, but i don't know how to set that. Anyone who can help me in any way please write, also suggest some ideas about using recursion/DP for solving this problem. Thanks.

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  • Mathematical attack on the Digital Signature Algorithm

    - by drelihan
    Does anybody know the mathematics behind an attack on DSA where modulus p has p-1 made up of only small factors. In reality, this would not happen as the key generator would guarantee that this is not so. There is much information on the web on generating good input paramters for DSA so that it is hard to crack but no information on how you find X if modulus p has p-1 made up of only small factors.

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  • Are mathematical Algorithms protected by copyright?

    - by analogy
    I wish to implement an algorithm which i read in a journal paper in my software (commercial). I want to know if this is allowed or not. The algorithm in question is described in http://arxiv.org/abs/0709.2938 It is a very simple algorithm and a number of implementations exist in python (http://igraph.sourceforge.net/) and java. One of them is in gpl another which i got from a different researcher and had no license attached. There are significant differences in two implementations, e.g. second one uses threads and multiple cores. It is possible to rewrite/ (not translate) the algorithm. So can I use it in my software or on a server for commercial purpose. Thanks UPDATE: I am completely aware of copyright on the text of paper, it was published in phys rev E. I am concerned with use of the algorithm, in commercial software. Also the publication means that unless the patent has been already filed. The method has been disclosed publicly hence barring patent in future. Also the GPL implementation is not by authors themselves but comes from a third party. Finally i am not using the GPL implementation but creating my own using C++.

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  • Mysql - Grouping the result based on a mathematical operation and SUM() function

    - by SpikETidE
    Hi all... I'm having the following two tables... Table : room_type type_id type_name no_of_rooms max_guests rate 1 Type 1 15 2 1254 2 Type 2 10 1 3025 Table : reservation reservation_id start_date end_date room_type booked_rooms 1 2010-04-12 2010-04-15 1 8 2 2010-04-12 2010-04-15 1 2 Now... I have this query SELECT type_id, type_name FROM room_type WHERE id NOT IN (SELECT room_type FROM reservation WHERE start_date >= '$start_date' AND end_date <= '$end_date') What the query does is it selects the rooms that are not booked between the start date and end date. Also, as you can see from the reservation table, we also have 'number of rooms booked between the two dates' factor also... I need to add this 'no.of booked rooms between the two dates' factor also in to the query... The query should return the type of rooms for which at least one room is free between the two dates. I worked out the logic but just can't represent it as a query....! How will you do this...? Thanks for your suggestions..!

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  • parsing of mathematical expressions

    - by gcc
    (in c90) (linux) input: sqrt(2 - sin(3*A/B)^2.5) + 0.5*(C*~(D) + 3.11 +B) a b /*there are values for a,b,c,d */ c d input: cos(2 - asin(3*A/B)^2.5) +cos(0.5*(C*~(D)) + 3.11 +B) a b /*there are values for a,b,c,d */ c d input: sqrt(2 - sin(3*A/B)^2.5)/(0.5*(C*~(D)) + sin(3.11) +ln(B)) /*max lenght of formula is 250 characters*/ a b /*there are values for a,b,c,d */ c /*each variable with set of floating numbers*/ d As you can see infix formula in the input depends on user. My program will take a formula and n-tuples value. Then it calculate the results for each value of a,b,c and d. If you wonder I am saying ;outcome of program is graph. /sometimes,I think i will take input and store in string. then another idea is arise " I should store formula in the struct" but i don't know how I can construct the code on the base of structure./ really, I don't know way how to store the formula in program code so that I can do my job. can you show me? /* a,b,c,d is letters cos,sin,sqrt,ln is function*/

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  • How to make simple mathematical operations and displaying the result in a textbox

    - by Audel
    Hi, I know is a rather simple question but I just can't find an appropriate example in google or anywhere. I've got this piece int numberOfPlays = int.Parse(textBox2.Text); numberOfPlays = (numberOfPlays++); textBox2.Text = (numberOfPlays.ToString()); MessageBox.Show(numberOfPlays.ToString()); So basically what I want to do is to get the value of the textBox2, make it an integer and then add 1 to it. I can't think of any more details right now, so if i'm not clear enough please ask Thanks in advance

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  • Less Mathematical Approaches to Machine Learning?

    - by Ed
    Out of curiosity, I've been reading up a bit on the field of Machine Learning, and I'm surprised at the amount of computation and mathematics involved. One book I'm reading through uses advanced concepts such as Ring Theory and PDEs (note: the only thing I know about PDEs is that they use that funny looking character). This strikes me as odd considering that mathematics itself is a hard thing to "learn." Are there any branches of Machine Learning that use different approaches? I would think that a approaches relying more on logic, memory, construction of unfounded assumptions, and over-generalizations would be a better way to go, since that seems more like the way animals think. Animals don't (explicitly) calculate probabilities and statistics; at least as far as I know.

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  • How would someone implement mathematical formulae in java?

    - by Mohit Deshpande
    What I mean is like have to user input a string with multiple variables and get the value of those variable. Like a simple quadratic formula: x^2 + 5x + 10. Or in java: (Math.pow(x,2)) + (x * 5) + 10The user would then enter that and then the program would solve for x. I will be using the BeanShell Interpreter class to interpret the string as an equation. But how would I solve for x?

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  • Why can't c# calculate exact values of mathematical functions

    - by Timo Willemsen
    Hey everyone, Why can't c# do any exact operations. Math.Pow(Math.Sqrt(2.0),2) == 2.0000000000000004 I know how doubles work, I know where the rounding error is from, I know that it's almost the correct value, and I know that you can't store infinite numbers in a finite double. But why isn't there a way that c# can calculate it exactly, while my calculator can do it. Edit It's not about my calculator, I was just giving an example: http://www.wolframalpha.com/input/?i=Sqrt%282.000000000000000000000000000000000000000000000000000000000000000000000000000000001%29%5E2 Cheers

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  • a mathematical problem

    - by Max
    Hi i need a function that should give me a 10th or 100th array, for example if i pass 5, it should return 1 to 10 if i pass 67, it should return 1 to 100 if i pass 126, it should return 101 to 200 if i pass 2524, it should return 2001 to 3000 Any guidance?

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  • The Numerical ‘Magic’ of Cyclic Numbers

    - by Akemi Iwaya
    If you love crunching numbers or are just a fan of awesome number ‘tricks’ to impress your friends with, then you will definitely want to have a look at cyclic numbers. Dr Tony Padilla from the University of Nottingham shows how these awesome numbers work in Numberphile’s latest video. Cyclic Numbers – Numberphile [YouTube] Want to learn more about cyclic numbers? Then make sure to visit the Wikipedia page linked below! Cyclic number [Wikipedia]     

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  • Variable font height via tables in LaTeX

    - by Hooked
    I've been looking for a more elegant solution to the following typesetting problem. Consider those banners found in print media where the text is aligned like: B I G T E X T small text small text small text m o r e m e d i u m t e x t The font sizes are adjusted so that the height is scaled down for longer lines of text such that each line has equal width. I've written a small script that runs each line separately, compiles, crops the resulting pdf and then \includegraphics each in a table. This gives the desired effect but requires an both an outside script and pdfcrop (which only crops to a white bounding box). Since much of LaTeX is self-aware, I imagine it would be possible to have it recognize the width of a box and scale it appropriately so that any text fits exactly into the desired width. Any thoughts or ideas on how a pure LaTeX implementation might work?

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  • "pdf_open: Not a PDF 1.[1-5] file." when typesetting TeX file in TextMate

    - by Manti
    I have a TeX file, which is typeset by XeLaTeX. The file has \includegraphics{coverimage.eps} on the first page, and coverimage.eps is located in the same directory as the TeX file. OS: MacOS 10.6.5, TextMate 1.5.10, xelatex 3.1415926-2.2-0.9997.4 (TeX Live 2010) If I run xelatex doc.tex in console, file compiles without errors, and eps file is included. If I typeset it in TextMate (xelatex engine is selected in preferences), I get the following error: ** WARNING ** pdf_open: Not a PDF 1.[1-5] file. ** WARNING ** Failed to include image file "./coverimage.eps" ** WARNING ** >> Please check if ** WARNING ** >> rungs -q -dNOPAUSE -dBATCH -sPAPERSIZE=a0 -sDEVICE=pdfwrite -dCompatibilityLevel=%v -dAutoFilterGrayImages=false -dGrayImageFilter=/FlateEncode -dAutoFilterColorImages=false -dColorImageFilter=/FlateEncode -sOutputFile=%o %i -c quit ** WARNING ** >> %o = output filename, %i = input filename, %b = input filename without suffix ** WARNING ** >> can really convert "./coverimage.eps" to PDF format image. ** WARNING ** pdf: image inclusion failed for "coverimage.eps". ** WARNING ** Failed to read image file: coverimage.eps ** WARNING ** Interpreting special command PSfile (ps:) failed. ** WARNING ** >> at page="1" position="(107.149, 124.566)" (in PDF) ** WARNING ** >> xxx "PSfile="coverimage.eps" llx=0 lly=0 urx=408 ury=526 rwi=3809 and there is no image included in the resulting file (but text looks ok). I am not sure whether it is the error of xelatex or TextMate LaTeX bundle. What I tried to do: As I said, xelatex doc.tex from console works. The exact command line that TextMate uses is: xelatex -interaction=nonstopmode -file-line-error-style -synctex=1 But it works from console too. If I convert the image to pdf (and fix the .tex file accordingly), typesetting from TextMate works too. I tried running rungs with parameters specified in the error message, and got valid .pdf file with image as a result. I compared .log files from typesetting in TextMate and in console, they are absolutely identical except for this error message (in particular, version of xelatex is the same). Does anyone know what can cause this? Please tell me if you need any additional information. Thank you in advance.

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  • Javascript points calculating system

    - by coolboycsaba
    I trying to create a points calculating system with javascript, but the problem is with the mathematical part. I have saved on the server the points number, and based on that number I want to decide the level. Sorry for my bad english, I cant explain very well :D. I want something like: level 1 need 0 points level 2 needs 100 points level 3 needs 240 points level 4 needs 420 points level 5 needs 640 points and so on.... I need a mathematical function to calculate each level with it. Something that if I know the level to calculate the points needed, and if I know only the points to calculate the level.

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