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• Computation geometry: find where's the triangle after rotation, tranlastion or reflection in a mirro

  - by newba

  Hi, I have a small contest problem in which is given a set of points, in 2D, that form a triangle. This triangle may be subject to an arbitrary rotation, may be subject to an arbitrary translation (both in the 2D plane) and may be subject to a reflection on a mirror, but its dimensions were kept unchanged. Then, they give me a set of points in the plane, and I have to find 3 points that form my triangle after one or more of those geometric operations. Example: 5 15 8 5 20 10 6 5 17 5 20 20 5 10 5 15 20 15 10 I bet that have to apply some known algorithm, but I don't know which. The most common are: convex hull, sweep plane, triangulation, etc. Can someone give a tip? I don't need the code, only a push, please!

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• multidimensional vector rotation and angle computation -- how?

  - by macias

  Input: two multidimensional (for example dim=8) vectors a and b. I need to find out the "directed" angle (0-2*Pi, not 0-Pi) between those vectors a and b. And if they are not parallel I need to rotate vector b in plane a,b by "directed" angle L. If they are parallel, plane does not matter, but angle of rotation is still the same L. For 2d and 3d this is quite easy, but for more dimensions I am lost, I didn't find anything on google, and I prefer using some already proved&tested equations (avoiding errors introduced by my calculations :-D). Thank you in advance for tips, links, etc. Edit: dimension of the space is the same as dimension of the vectors.

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• Flag bit computation and detection

  - by Majid

  Hi all, In some code I'm working on I should take care of ten independent parameters which can take one of two values (0 or 1). This creates 2^10 distinct conditions. Some of the conditions never occur and can be left out, but those which do occur are still A LOT and making a switch to handle all cases is insane. I want to use 10 if statements instead of a huge switch. For this I know I should use flag bits, or rather flag bytes as the language is javascript and its easier to work with a 10 byte string with to represent a 10-bit binary. Now, my problem is, I don't know how to implement this. I have seen this used in APIs where multiple-selectable options are exposed with numbers 1, 2, 4, 8, ... , n^(n-1) which are decimal equivalents of 1, 10, 100, 1000, etc. in binary. So if we make call like bar = foo(7), bar will be an object with whatever options the three rightmost flags enable. I can convert the decimal number into binary and in each if statement check to see if the corresponding digit is set or not. But I wonder, is there a way to determine the n-th digit of a decimal number is zero or one in binary form, without actually doing the conversion?

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• Optimal Sharing of heavy computation job using Snow and/or multicore

  - by James

  Hi, I have the following problem. First my environment, I have two 24-CPU servers to work with and one big job (resampling a large dataset) to share among them. I've setup multicore and (a socket) Snow cluster on each. As a high-level interface I'm using foreach. What is the optimal sharing of the job? Should I setup a Snow cluster using CPUs from both machines and split the job that way (i.e. use doSNOW for the foreach loop). Or should I use the two servers separately and use multicore on each server (i.e. split the job in two chunks, run them on each server and then stich it back together). Basically what is an easy way to: 1. Keep communication between servers down (since this is probably the slowest bit). 2. Ensure that the random numbers generated in the servers are not highly correlated.

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• HOw to Extract image pixels and perform computation on it

  - by gavishna

  What i want to do is extract the pixels into array A(i,j).Let A(i,j) represent the pixel in the ith row & jth colm of the image. Let B(i,j) be the transformed array containing bits such that B(i,j) = 1 if (A(i,j)/2^t) mod 2 =1, where t=0,1,2,3,4,5,6,7 = 0 otherwise Then the array B(i,j) will be mutliplied by another array say C(i,j) representing another image. Then i want to plot the result of B*C as an image. How do i take in the pixels for the above conditions for both gray and RGB color format.Also how do i solve the above problem.Any helo will be usefull because i am not an expert in image processing.

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• numerical computation locks up ruby

  - by kolosy

  i'm trying to implement an id obfuscation scheme, with a simple hash borrowed elsewhere. i've added a method on the application helper: @@M_ID = 2**31-1 @@PRIME = 1580030173 @@PRIME_INVERSE = 59260789 # (calculated from MAXID and PRIME offline) def obfuscate_id(x) if x return ((x * @@PRIME) & @@M_ID) else x end end for some reason, whenever this is called, ruby locks up, and starts eating up disk space on my mac... like - gigs of it. any ideas?

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• Parallel computation of the median of a large array

  - by recipriversexclusion

  I got asked this question once and still haven't been able to figure it out: You have an array of N integers, where N is large, say, a billion. You want to calculate the median value of this array. Assume you have m+1 machines (m workers, one master) to distribute the job to. How would you go about doing this? Since the median is a nonlinear operator, you can't just find the median in each machine and then take the median of those values.

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• optimization math computation (multiplication and summing)

  - by wiso

  Suppose you want to compute the sum of the square of the differences of items: $\sum_{i=1}^{N-1} (x_i - x_{i+1})^2$, the simplest code (the input is std::vector<double> xs, the ouput sum2) is: double sum2 = 0.; double prev = xs[0]; for (vector::const_iterator i = xs.begin() + 1; i != xs.end(); ++i) { sum2 += (prev - (*i)) * (prev - (*i)); // only 1 - with compiler optimization prev = (*i); } I hope that the compiler do the optimization in the comment above. If N is the length of xs you have N-1 multiplications and 2N-3 sums (sums means + or -). Now suppose you know this variable: sum = $x_1^2 + x_N^2 + 2 sum_{i=2}^{N-1} x_i^2$ Expanding the binomial square: $sum_i^{N-1} (x_i-x_{i+1})^2 = sum - 2\sum_{i=1}^{N-1} x_i x_{i+1}$ so the code becomes: double sum2 = 0.; double prev = xs[0]; for (vector::const_iterator i = xs.begin() + 1; i != xs.end(); ++i) { sum2 += (*i) * prev; prev = (*i); } sum2 = -sum2 * 2. + sum; Here I have N multiplications and N-1 additions. In my case N is about 100. Well, compiling with g++ -O2 I got no speed up (I try calling the inlined function 2M times), why?

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• aov define F values computation

  - by essopapas

  Greetings to all This is my model: aov.fit<-aov(Y~A+B+C+D+E+A:C+A:E, data=dat) In summary(aov.fit) all F values are comptuted by eg MS(A)/MS(Residuals). This is not correct (or what I want), except for F(B) and F(A:E). I suppose P values are not correct either. Can I specify how the F computations will be done? I 'd like them to be like this: F(A)=MS(A)/MS(E), F(C)=MS(C)/MS(E), F(D)=MS(D)/MS(E), F(E)=MS(E)/MS(A:E), F(A:C)=MS(A:C)/MS(A:E) thanks

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• Array Multiplication and Division

  - by Narfanator

  I came across a question that (eventually) landed me wondering about array arithmetic. I'm thinking specifically in Ruby, but I think the concepts are language independent. So, addition and subtraction are defined, in Ruby, as such: [1,6,8,3,6] + [5,6,7] == [1,6,8,3,6,5,6,7] # All the elements of the first, then all the elements of the second [1,6,8,3,6] - [5,6,7] == [1,8,3] # From the first, remove anything found in the second and array * scalar is defined: [1,2,3] * 2 == [1,2,3,1,2,3] But What, conceptually, should the following be? None of these are (as far as I can find) defined: Array x Array: [1,2,3] * [1,2,3] #=> ? Array / Scalar: [1,2,3,4,5] / 2 #=> ? Array / Scalar: [1,2,3,4,5] % 2 #=> ? Array / Array: [1,2,3,4,5] / [1,2] #=> ? Array / Array: [1,2,3,4,5] % [1,2] #=> ? I've found some mathematical descriptions of these operations for set theory, but I couldn't really follow them, and sets don't have duplicates (arrays do). Edit: Note, I do not mean vector (matrix) arithmetic, which is completely defined. Edit2: If this is the wrong stack exchange, tell me which is the right one and I'll move it. Edit 3: Add mod operators to the list. Edit 4: I figure array / scalar is derivable from array * scalar: a * b = c => a = b / c [1,2,3] * 3 = [1,2,3]+[1,2,3]+[1,2,3] = [1,2,3,1,2,3,1,2,3] => [1,2,3] = [1,2,3,1,2,3,1,2,3] / 3 Which, given that programmer's division ignore the remained and has modulus: [1,2,3,4,5] / 2 = [[1,2], [3,4]] [1,2,3,4,5] % 2 = [5] Except that these are pretty clearly non-reversible operations (not that modulus ever is), which is non-ideal. Edit: I asked a question over on Math that led me to Multisets. I think maybe extensible arrays are "multisets", but I'm not sure yet.

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• Java NIO (Netty): How does Encryption or GZIPping work in theory (with filters)

  - by Tom

  Hello Experts, i would be very thankfull if you can explain to me, how in theory the "Interceptor/Filter" Pattern in ByteStreams (over Sockets/Channels) work (in Asynchronous IO with netty) in regard to encryption or compression of data. Given I have a Filter that does GZIPPING. How is this internally implemented? Does the Filter "collect" so many bytes form the channel, that this is a usefull number of bytes that can then be en/decoded? What is in general the minimal "blocksize(data to encode/decode in a chunk)" of socket based gzipping? Does this "blocksize" have to be negotiated in advance between server and client? What happens if the client does not send enough data to "fill" the blocksize (due to a network conquestion) but does not close the connection. Does this mean the other side will simply wait until it gets enough bytes to decode or until a timeout occoures...How is the Filter pattern the applied? The compression filter will de/compress the blocksize of bytes and then store them again in the same buffer would (in the case of netty) i normally be using the ChannelHanlderContext to pass the de/encoded data to the next filter?... Any explanations/links/tutorials (for beginners;-) will be very much appreciated to help me understand how for example encryption/compressing are implemented in socket based communication with filters/interceptor pattern. thank you very much tom

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• Ray-box Intersection Theory

  - by Myx

  Hello: I wish to determine the intersection point between a ray and a box. The box is defined by its min 3D coordinate and max 3D coordinate and the ray is defined by its origin and the direction to which it points. Currently, I am forming a plane for each face of the box and I'm intersecting the ray with the plane. If the ray intersects the plane, then I check whether or not the intersection point is actually on the surface of the box. If so, I check whether it is the closest intersection for this ray and I return the closest intersection. The way I check whether the plane-intersection point is on the box surface itself is through a function bool PointOnBoxFace(R3Point point, R3Point corner1, R3Point corner2) { double min_x = min(corner1.X(), corner2.X()); double max_x = max(corner1.X(), corner2.X()); double min_y = min(corner1.Y(), corner2.Y()); double max_y = max(corner1.Y(), corner2.Y()); double min_z = min(corner1.Z(), corner2.Z()); double max_z = max(corner1.Z(), corner2.Z()); if(point.X() >= min_x && point.X() <= max_x && point.Y() >= min_y && point.Y() <= max_y && point.Z() >= min_z && point.Z() <= max_z) return true; return false; } where corner1 is one corner of the rectangle for that box face and corner2 is the opposite corner. My implementation works most of the time but sometimes it gives me the wrong intersection. I was wondering if the way I'm checking whether the intersection point is on the box is correct or if I should use some other algorithm. Thanks.

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• Database theory - relationship between two tables

  - by iansinke

  I have a database with two tables - let's call them Foo and Bar. Each foo may be related to any number of bars, and each bar may be related to any number of foos. I want to be able to retrieve, with one query, the foos that are associated with a certain bar, and the bars that are associated with a certain foo. My question is, what is the best way of recording these relationships? Should I have a separate table with records of each relationship (e.g. two columns, foo and bar)? Should the foo table have a column for a list of bars, and vice versa? Is there another option that I'm overlooking? I'm using SQL Server, if that makes a difference.

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• Traceroute Theory

  - by Hamza Yerlikaya

  I am toying with trace route, my application send a ICMP echo request with a ttl of 0 every time i receive a time exceeded message i increment the ttl by one and resent the package, but what happens is I have 2 routers on my network i can trace the route through these router but third hop always ends up being one of the open dns servers same ip every time no matter where i traceroute to. AFAIK this is the correct traceroute implementation, can anyone tell me what i am doing wrong?

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• Discrete mathematics problem - Probability theory and counting

  - by Mohammad

  Hello All, I'm taking a discrete mathematics course, and I encountered a question and I need your help. I don't know if this is the right place for that though :) It says: Each user on a computer system has a password, which is six to eight characters long, where each character is an uppercase letter or a digit. Each password must contain at least one digit. How many possible passwords are there? The book solves this by adding the probabilities of having six,seven and eight characters long password. However, when he solves for probability of six characters he does this P6 = 36^6 - 26^6 and does P7 = 36^7 - 26^7 and P8 = 36^8 - 26^8 and then add them all I understand the solution, but my question is why doesn't calculating, P6 = 10*36^5 and the same for P7 and P8, work? 10 for the digit and 36 for the alphanumeric? Also, if anyone could give me another solution, other than the one in the book. Thank you very much :)

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• Theory of Game Interface Design

  - by anon

  Anyone know of a good book on Game Interface Design (not game play mechanics; the actual UI). I'm particular interested in theories of cognition, and how game interfaces are designed to allow the enduser efficient communication with the game (whether it in FPS, RTS, or so on). In a modern game, the amount of information conveyed to the user, the amount of choices the user can make; and the support for the user to make said decisions is simply astounding (think UIs for Starcraft II / WoW). Any insights into this would be greatly appreciated.

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• How to put theory into practise

  - by Dave greg

  I like to read alot of IT books e.g programming / functional. But the problem is that after reading I cannot find reasons to put it into practise and I soon forget what I read. Any advise?

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• Permutations distinct under given symmetry (Mathematica 8 group theory)

  - by Yaroslav Bulatov

  Given a list of integers like {2,1,1,0} I'd like to list all permutations of that list that are not equivalent under given group. For instance, using symmetry of the square, the result would be {{2, 1, 1, 0}, {2, 1, 0, 1}}. Approach below (Mathematica 8) generates all permutations, then weeds out the equivalent ones. I can't use it because I can't afford to generate all permutations, is there a more efficient way? Update: actually, the bottleneck is in DeleteCases. The following list {2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 0, 0, 0} has about a million permutations and takes 0.1 seconds to compute. Apparently there are supposed to be 1292 orderings after removing symmetries, but my approach doesn't finish in 10 minutes removeEquivalent[{}] := {}; removeEquivalent[list_] := ( Sow[First[list]]; equivalents = Permute[First[list], #] & /@ GroupElements[group]; DeleteCases[list, Alternatives @@ equivalents] ); nonequivalentPermutations[list_] := ( reaped = Reap@FixedPoint[removeEquivalent, Permutations@list]; reaped[[2, 1]] ); group = DihedralGroup[4]; nonequivalentPermutations[{2, 1, 1, 0}]

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• Goldbach theory in C

  - by nofe

  I want to write some code which takes any positive, even number (greater than 2) and gives me the smallest pair of primes that sum up to this number. I need this program to handle any integer up to 9 digits long. My aim is to make something that looks like this: Please enter a positive even integer ( greater than 2 ) : 10 The first primes adding : 3+7=10. Please enter a positive even integer ( greater than 2 ) : 160 The first primes adding : 3+157=160. Please enter a positive even integer ( greater than 2 ) : 18456 The first primes adding : 5+18451=18456. I don't want to use any library besides stdio.h. I don't want to use arrays, strings, or anything besides for the most basic toolbox: scanf, printf, for, while, do-while, if, else if, break, continue, and the basic operators (<,, ==, =+, !=, %, *, /, etc...). Please no other functions especially is_prime. I know how to limit the input to my needs so that it loops until given a valid entry. So now I'm trying to figure out the algorithm. I thought of starting a while loop like something like this: #include <stdio.h> long first, second, sum, goldbach, min; long a,b,i,k; //indices int main (){ while (1){ printf("Please enter a positive integer :\n"); scanf("%ld",&goldbach); if ((goldbach>2)&&((goldbach%2)==0)) break; else printf("Wrong input, "); } while (sum!=goldbach){ for (a=3;a<goldbach;a=(a+2)) for (i=2;(goldbach-a)%i;i++) first = a; for (b=5;b<goldbach;b=(b+2)) for (k=2;(goldbach-b)%k;k++) sum = first + second; } }

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• SQL Query Theory Question...

  - by Keng

  I have a large historical transaction table (15-20 million rows MANY columns) and a table with one row one column. The table with one row contains a date (last processing date) which will be used to pull the data in the trasaction table ('process_date'). Question: Should I inner join the 'process_date' table to the transaction table or the transaction table to the 'process_date' table?

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• C: theory on how to extract files from an archived file

  - by donok

  In C I have created a program which can archive multiple files into an archive file via the command line. e.g. $echo 'file1/2' > file1/2.txt $./archive file1.txt file2.txt arhivedfile $cat archivedfile file1 file2 How do I create a process so that in my archivedfile I have: header file1 end header file2 end They are all stored in the archive file one after another after another. I know that perhaps a header file is needed(containing filename, size of filename, start and end of file) for extracting these files back out into their original form, but how would I go about doing this. I am stuck on where and how to start. Please could someone help me on some logic as to how to approach extracting files back out of an archived file.

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• Very basic database theory.

  - by John R

  I have a set of tables to show the relationship between organziations and supporters below. Although I have done some basic mySQL querries, I know very little about database 'design'. I plan to querry the database for: -a list of contributors to a specific organization... or, -a list of organizations that a specific suporter supports. The database tables for organiations and contributors may have other columns in the future and recieve a lesser amount of querries based on that information. A | X A | Y A | Z B | X B | Y C | X C | Z How should the tables be set up? I assume that there should be a third table, but there is still redundent information in the third table. Is there a better way of setting up the tables? +----+-------+ +-------------+----------+ +----+-------+ | id | org | | org | contr | | id | contr.| +----+-------+ +-------------+----------+ +----+-------+ | 1 | A | | 1 | 1 | | 1 | X | | 2 | B | | 1 | 2 | | 2 | Y | | 3 | C | | 1 | 3 | | 3 | Z | +----+-------+ | 2 | 1 | +----+-------+ | 2 | 2 | | 3 | 1 | | 3 | 3 | +-------------+----------+

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• Do game-theoretic considerations stand in the way of this market-based game-mechanic achieving its goals?

  - by BerndBrot

  Mechanic The mechanic is called "market manipulation" and is supposed to work like this: Players can enter the London Stock Exchange (LSE) LSE displays the stock prices of 8 to 10 companies and derivatives. This number is relatively small to ensure that players will collide in their efforts to manipulate the market in their favor. The prices are calculated based on real world prices of these companies and derivatives (in real time) any market manipulations that were conducted by the players any market corrections of the system Players can buy and sell shares with cash, a resource in the game, at current in-game market value Players can manipulate the market, i.e. let the price of a share either rise or fall, by some amount, over a certain period of time. Manipulating the market requires spending certain in-game resources and is therefore limited. The system continuously corrects market manipulations by letting the in-game prices converge towards their real world counterparts at a rate of 2% of the difference between the two per hour. Because of this market correction mechanism, pushing up prices (and screwing down prices) becomes increasingly difficult the higher (lower) the price already is. Goals Players are supposed to collide (and have incentives to collide) in their efforts to manipulate the market in their favor, especially when it comes to manipulation efforts by different groups. Prices should not resolve around any equilibrium points. The more variance the better. Band-wagoning should always involve risk (recognizing that prices start rising should not be a sure sign that they will keep rising so that everybody can make easy profits even when they don't manipulate the market themselves) Question Are there any game-theoretic considerations that prevent the mechanic from achieving these goals?

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• Cuppa Corner talk "A trip to First Normal Form" available - Domains, Functional Dependencies, Repeat

  - by tonyrogerson

  It's 15 minutes, I talk about Domains, Functional Dependencies, Repeating Groups, Relational Valued Attributes and of course First Normal Form. http://sqlcontent.sqlblogcasts.com/video/cctr20100507dbdesign1nf/cctr20100507dbdesign1nf.html For questions just ask on the http://sqlserverfaq.com chat control or Twitter using #sqlfaq tag. Slides are also availble here: http://sqlcontent.sqlblogcasts.com/video/cctr20100507dbdesign1nf/cc_tr20100507_dbdesign1nf.pptx...(read more)

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• Data validation best practices: how can I better construct user feedback?

  - by Cory Larson

  Data validation, whether it be domain object, form, or any other type of input validation, could theoretically be part of any development effort, no matter its size or complexity. I sometimes find myself writing informational or error messages that might seem harsh or demanding to unsuspecting users, and frankly I feel like there must be a better way to describe the validation problem to the user. I know that this topic is subjective and argumentative. I've migrated this question from StackOverflow where I originally asked it with little response. Basically, I'm looking for good resources on data validation and user feedback that results from it at a theoretical level. Topics and questions I'm interested in are: Content Should I be describing what the user did correctly or incorrectly, or simply what was expected? How much detail can the user read before they get annoyed? (e.g. Is "Username cannot exceed 20 characters." enough, or should it be described more fully, such as "The username cannot be empty, and must be at least 6 characters but cannot exceed 30 characters."?) Grammar How do I decide between phrases like "must not," "may not," or "cannot"? Delivery This can depend on the project, but how should the information be delivered to the user? Should it be obtrusive (e.g. JavaScript alerts) or friendly? Should they be displayed prominently? Immediately (i.e. without confirmation steps, etc.)? Logging Do you bother logging validation errors? Internationalization Some cultures prefer or better understand directness over subtlety and vice-versa (e.g. "Don't do that!" vs. "Please check what you've done."). How do I cater to the majority of users? I may edit this list as I think more about the topic, but I'm genuinely interested in proper user feedback techniques. I'm looking for things like research results, poll results, etc. I've developed and refined my own techniques over the years that users seem to be okay with, but I work in an environment where the users prefer to adapt to what you give them over speaking up about things they don't like. I'm interested in hearing your experiences in addition to any resources to which you may be able to point me.

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