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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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• Reinforcement learning And POMDP

  - by Betamoo

  I am trying to use Multi-Layer NN to implement probability function in Partially Observable Markov Process.. I thought inputs to the NN would be: current state, selected action, result state; The output is a probability in [0,1] (prob. that performing selected action on current state will lead to result state) In training, I fed the inputs stated before, into the NN, and I taught it the output=1.0 for each case that already occurred. The problem : For nearly all test case the output probability is near 0.95.. no output was under 0.9 ! Even for nearly impossible results, it gave that high prob. PS:I think this is because I taught it happened cases only, but not un-happened ones.. But I can not at each step in the episode teach it the output=0.0 for every un-happened action! Any suggestions how to over come this problem? Or may be another way to use NN or to implement prob function? Thanks

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• Relational Database pioneer Chris Date is giving a seminar 13th/14th May Edinburgh on "SQL and Relat

  - by tonyrogerson

  One of the pioneers of the Relational Database, Chris Date is giving a 2 day seminar in Edinburgh (13th and 14th May 2010) based around his new book "SQL and Relational Theory - How to Write Accurate SQL Code" which if you don't already have I'd say is a must buy. When I first saw this and what he will cover I thought, oh yer - this is going to cost the earth, well it doesn't - its £750 for the two days and there are discounts available for multiple bookings, being a member...(read more)

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• solve TOR edge node problem by using .onion proxy?

  - by rd.

  I would like to improve the TOR network, where the exit nodes are a vulnerability to concealing traffic. From my understanding, traffic to .onion sites are not decrypted by exit nodes, so therefore - in theory - a .onion site web proxy could be used to further anonymize traffic. Yes/no? perhaps you have insight into the coding and routing behind these concepts to elaborate on why this is a good/not good idea.

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• Emulating old-school sprite flickering (theory and concept)

  - by Jeffrey Kern

  I'm trying to develop an oldschool NES-style video game, with sprite flickering and graphical slowdown. I've been thinking of what type of logic I should use to enable such effects. I have to consider the following restrictions if I want to go old-school NES style: No more than 64 sprites on the screen at a time No more than 8 sprites per scanline, or for each line on the Y axis If there is too much action going on the screen, the system freezes the image for a frame to let the processor catch up with the action From what I've read up, if there were more than 64 sprites on the screen, the developer would only draw high-priority sprites while ignoring low-priority ones. They could also alternate, drawing each even numbered sprite on opposite frames from odd numbered ones. The scanline issue is interesting. From my testing, it is impossible to get good speed on the XBOX 360 XNA framework by drawing sprites pixel-by-pixel, like the NES did. This is why in old-school games, if there were too many sprites on a single line, some would appear if they were cut in half. For all purposes for this project, I'm making scanlines be 8 pixels tall, and grouping the sprites together per scanline by their Y positioning. So, dumbed down I need to come up with a solution that.... 64 sprites on screen at once 8 sprites per 'scanline' Can draw sprites based on priority Can alternate between sprites per frame Emulate slowdown Here is my current theory First and foremost, a fundamental idea I came up with is addressing sprite priority. Assuming values between 0-255 (0 being low), I can assign sprites priority levels, for instance: 0 to 63 being low 63 to 127 being medium 128 to 191 being high 192 to 255 being maximum Within my data files, I can assign each sprite to be a certain priority. When the parent object is created, the sprite would randomly get assigned a number between its designated range. I would then draw sprites in order from high to low, with the end goal of drawing every sprite. Now, when a sprite gets drawn in a frame, I would then randomly generate it a new priority value within its initial priority level. However, if a sprite doesn't get drawn in a frame, I could add 32 to its current priority. For example, if the system can only draw sprites down to a priority level of 135, a sprite with an initial priority of 45 could then be drawn after 3 frames of not being drawn (45+32+32+32=141) This would, in theory, allow sprites to alternate frames, allow priority levels, and limit sprites to 64 per screen. Now, the interesting question is how do I limit sprites to only 8 per scanline? I'm thinking that if I'm sorting the sprites high-priority to low-priority, iterate through the loop until I've hit 64 sprites drawn. However, I shouldn't just take the first 64 sprites in the list. Before drawing each sprite, I could check to see how many sprites were drawn in it's respective scanline via counter variables . For example: Y-values between 0 to 7 belong to Scanline 0, scanlineCount[0] = 0 Y-values between 8 to 15 belong to Scanline 1, scanlineCount[1] = 0 etc. I could reset the values per scanline for every frame drawn. While going down the sprite list, add 1 to the scanline's respective counter if a sprite gets drawn in that scanline. If it equals 8, don't draw that sprite and go to the sprite with the next lowest priority. SLOWDOWN The last thing I need to do is emulate slowdown. My initial idea was that if I'm drawing 64 sprites per frame and there's still more sprites that need to be drawn, I could pause the rendering by 16ms or so. However, in the NES games I've played, sometimes there's slowdown if there's not any sprite flickering going on whereas the game moves beautifully even if there is some sprite flickering. Perhaps give a value to each object that uses sprites on the screen (like the priority values above), and if the combined values of all objects w/ sprites surpass a threshold, introduce the sprite flickering? IN CONCLUSION... Does everything I wrote actually sound legitimate and could work, or is it a pipe dream? What improvements can you all possibly think with this game programming theory of mine?

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• ICMP Redirect Theory VS. Application

  - by joeqwerty

  I'm trying to watch ICMP redirects in a lab using Cisco Packet Tracer (version 5.3.2) and I'm not seeing them, which leads me to believe that either my lab configuration isn't correct or my understanding of ICMP redirects isn't correct or that Packet Tracer doesn't support/use ICMP redirects. Here's what I believe to be true regarding ICMP redirects: Routers send ICMP redirects when all of these conditions are met: The interface on which the packet comes into the router is the same interface on which the packet gets routed out. The subnet or network of the source IP address is on the same subnet or network of the next-hop IP address of the routed packet. The datagram is not source-routed. The router kernel is configured to send redirects. I have the lab set up in Cisco Packet Tracer as displayed in the image and would expect to see an ICMP redirect from Router1 when pinging from PC1 to PC3. I'm not seeing the ICMP redirect and it looks like Router1 is actually routing all of the packets via Router2. I have IP ICMP debugging enabled on Router1 (and Router2) and I'm not seeing any ICMP redirect activity in either console. I'm also not seeing a route to the PC3 network in the routing table on PC1, which I think confirms that the ICMP redirect is not occurring. I'm using only static routing on Routers 1 and 2. Is my understanding of ICMP redirects incorrect, or is there a problem with my lab configuration or does Packet Tracer not support/use ICMP redirects?

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• Determining the chances of an event occurring when it hasn't occurred yet

  - by sanity

  A user visits my website at time t, and they may or may not click on a particular link I care about, if they do I record the fact that they clicked the link, and also the duration since t that they clicked it, call this d. I need an algorithm that allows me to create a class like this: class ClickProbabilityEstimate { public void reportImpression(long id); public void reportClick(long id); public double estimateClickProbability(long id); } Every impression gets a unique id, and this is used when reporting a click to indicate which impression the click belongs to. I need an algorithm that will return a probability, based on how much time has past since an impression was reported, that the impression will receive a click, based on how long previous clicks required. Clearly one would expect that this probability will decrease over time if there is still no click. If necessary, we can set an upper-bound, beyond which we consider the click probability to be 0 (eg. if its been an hour since the impression occurred, we can be pretty sure there won't be a click). The algorithm should be both space and time efficient, and hopefully make as few assumptions as possible, while being elegant. Ease of implementation would also be nice. Any ideas?

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• Recommended book about parallel programming - theory & best practice?

  - by Klesk

  I'm looking for a book or books about multicore, multithreaded programming. The perfect book should focus on best practices and maybe include a bit of theory background. I'm not interested in a book which only describes a single library and focuses on its API. OS actually doesn't matter.

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• What will we use Theory Attribute for ?

  - by Sandbox

  I discovered [Theory] and [Datapoint] attributes in NUnit. I am not very sure about how should I use these. I think they can be used for data-driven testing and this has got me interested. There aren't many resources available on the same. Can someone explain to me how to use them or point me to resources? Thanks.

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• Point me to info about constructing filters (of lists)

  - by jah

  I would like some pointers to information which would help me understand how to go about providing the ability to filter a list of entities by their attributes as well as by attributes of related entities. As an example, imagine a web app which provides order management of some kind. Orders and related entities are stored in a relational database. And imagine that the app has an interface which lists the orders. The problem is: how does one allow the list to be filtered by, for example:- order number (an attribute) line item name (an attribute of a n-n related entity) some text in an administrative note related to the order (text found in an attribute of a 1-1 related entity) I'm trying to discover whether there is something like a standard, efficient way to construct the queries and the filtering form; or some possible strategies; or any theory on the topic; or some example code. My google foo fails me.

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• Studying Quantum Computing?

  - by The_Neo

  Hi I am a computer science student currently on an internship and I have been thinking more and more about looking into working for a company / places that is developing quantum computers/ing when I graduate. Here is my problem, I have a pretty solid grasp of mathematics involved in Comp Sci and enjoy learning about more Comp Sci theory but in doing some minor research about Quantum Computing it seems to me to be more about hardware and I have always leant more to the software side of things. I haven't studied any physics since high school so I am wondering if I would be suitable to work in such a field with a Comp Sci degree, is it a field more aimed at physicists?

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• Translation of clustering problem to graph theory language

  - by honk

  I have a rectangular planar grid, with each cell assigned some integer weight. I am looking for an algorithm to identify clusters of 3 to 6 adjacent cells with higher-than-average weight. These blobs should have approximately circular shape. For my case the average weight of the cells not containing a cluster is around 6, and that for cells containing a cluster is around 6+4, i.e. there is a "background weight" somewhere around 6. The weights fluctuate with a Poisson statistic. For small background greedy or seeded algorithms perform pretty well, but this breaks down if my cluster cells have weights close to fluctuations in the background. Also, I cannot do a brute-force search looping through all possible setups because my grid is large (something like 1000x1000). I have the impression there might exist ways to tackle this in graph theory. I heard of vertex-covers and cliques, but am not sure how to best translate my problem into their language.

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• box stacking in graph theory

  - by mozhdeh

  Please help me find a good solution for this problem. We have n boxes with 3 dimensions. We can orient them and we want to put them on top of another to have a maximun height. We can put a box on top of an other box, if 2 dimensions (width and lenght) are lower than the dimensions of the box below. For exapmle we have 3 dimensions w*D*h, we can show it in to (h*d,d*h,w*d,d*W,h*w,w*h) please help me to solve it in graph theory.

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• Theory of computation - Using the pumping lemma for context free languages

  - by Tony

  I'm reviewing my notes for my course on theory of computation and I'm having trouble understanding how to complete a certain proof. Here is the question: A = {0^n 1^m 0^n | n>=1, m>=1} Prove that A is not regular. It's pretty obvious that the pumping lemma has to be used for this. So, we have |vy| = 1 |vxy| <= p (p being the pumping length, = 1) uv^ixy^iz exists in A for all i = 0 Trying to think of the correct string to choose seems a bit iffy for this. I was thinking 0^p 1^q 0^p, but I don't know if I can obscurely make a q, and since there is no bound on u, this could make things unruly.. So, how would one go about this?

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• Theory of computation - Using the pumping lemma for CFLs

  - by Tony

  I'm reviewing my notes for my course on theory of computation and I'm having trouble understanding how to complete a certain proof. Here is the question: A = {0^n 1^m 0^n | n>=1, m>=1} Prove that A is not regular. It's pretty obvious that the pumping lemma has to be used for this. So, we have |vy| = 1 |vxy| <= p (p being the pumping length, = 1) uv^ixy^iz exists in A for all i = 0 Trying to think of the correct string to choose seems a bit iffy for this. I was thinking 0^p 1^q 0^p, but I don't know if I can obscurely make a q, and since there is no bound on u, this could make things unruly.. So, how would one go about this?

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• Real life usage of the projective plane theory

  - by Elazar Leibovich

  I'm learning about the theory of the projective plane. Very generally speaking, it is an extension of the plane, which includes additional points which are defined as the intersection points of two parallel lines. In the projective plane, every two lines have an interesection point. Whether they're parallel or not. Every point in the projective plane can be represented by three numbers (you actually need less than that, but nevemind now). Is there any real life application which uses the projective plane? I can think that, for instance, a software which needs to find the intersections of a line, can benefit from always having an intersection point which might lead to simpler code, but is it really used?

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• A compiler for automata theory

  - by saadtaame

  I'm designing a programming language for automata theory. My goal is to allow programmers to use machines (DFA, NFA, etc...) as units in expressions. I'm confused whether the language should be compiled, interpreted, or jit-compiled! My intuition is that compilation is a good choice, for some operations might take too much time (converting NFA's to equivalent DFA's can be expensive). Translating to x86 seems good. There is one issue however: I want the user to be able to plot machines. Any ideas?

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• How can I make sense of the word "Functor" from a semantic standpoint?

  - by guillaume31

  When facing new programming jargon words, I first try to reason about them from an semantic and etymological standpoint when possible (that is, when they aren't obscure acronyms). For instance, you can get the beginning of a hint of what things like Polymorphism or even Monad are about with the help of a little Greek/Latin. At the very least, once you've learned the concept, the word itself appears to go along with it well. I guess that's part of why we name things names, to make mental representations and associations more fluent. I found Functor to be a tougher nut to crack. Not so much the C++ meaning -- an object that acts (-or) as a function (funct-), but the various functional meanings (in ML, Haskell) definitely left me puzzled. From the (mathematics) Functor Wikipedia article, it seems the word was borrowed from linguistics. I think I get what a "function word" or "functor" means in that context - a word that "makes function" as opposed to a word that "makes sense". But I can't really relate that to the notion of Functor in category theory, let alone functional programming. I imagined a Functor to be something that creates functions, or behaves like a function, or short for "functional constructor", but none of those seems to fit... How do experienced functional programmers reason about this ? Do they just need any label to put in front of a concept and be fine with it ? Generally speaking, isn't it partly why advanced functional programming is hard to grasp for mere mortals compared to, say, OO -- very abstract in that you can't relate it to anything familiar ? Note that I don't need a definition of Functor, only an explanation that would allow me to relate it to something more tangible, if there is any.

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• Minimizing data sent over a webservice call on expensive connection

  - by aceinthehole

  I am working on a system that has many remote laptops all connected to the internet through cellular data connections. The application will synchronize periodically to a central database. The problem is, due to factors outside our control, the cost to move data across the cellular networks are spectacularly expensive. Currently the we are sending a compressed XML file across the wire where it is being processed and various things are done with (mainly stuffing it into a database). My first couple of thoughts were to convert that XML doc to json, just prior to transmission and convert back to XML just after receipt on the other end, and get some extra compression for free without changing much. Another thought was to test various other compression algorithms to determine the smallest one possible. Although, I am not entirely sure how much difference json vs xml would make once it is compressed. I thought that their must be resources available that address this problem from an information theory perspective. Does anyone know of any such resources or suggestions on what direction to go in. This developed on the MS .net stack on windows for reference.

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• Japanese Multiplication simulation - is a program actually capable of improving calculation speed?

  - by jt0dd

  On SuperUser, I asked a (possibly silly) question about processors using mathematical shortcuts and would like to have a look at the possibility at the software application of that concept. I'd like to write a simulation of Japanese Multiplication to get benchmarks on large calculations utilizing the shortcut vs traditional CPU multiplication. I'm curious as to whether it makes sense to try this. My Question: I'd like to know whether or not a software math shortcut, as described above is actually a shortcut at all. This is a question of programming concept. By utilizing the simulation of Japanese Multiplication, is a program actually capable of improving calculation speed? Or am I doomed from the start? The answer to this question isn't required to determine whether or not the experiment will succeed, but rather whether or not it's logically possible for such a thing to occur in any program, using this concept as an example. My theory is that since addition is computed faster than multiplication, a simulation of Japanese multiplication may actually allow a program to multiply (large) numbers faster than the CPU arithmetic unit can. I think this would be a very interesting finding, if it proves to be true. If, in the multiplication of numbers of any immense size, the shortcut were to calculate the result via less instructions (or faster) than traditional ALU multiplication, I would consider the experiment a success.

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• Probability Question

  - by Juddling

  if i pick 10 numbers from a possible 80. what is the probablity for someone else picking the same 10 numbers as me? or just 4 numbers? or no numbers? i think it's no matches: 10/80 one match: 10*9/80*79 so the formula would be (10!/matches!)/(80!/matches!) is this right? i've only just started doing this at A-level and i need it for a game script i'm making.

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• C++: Calculate probability percentage during each iteration

  - by Mur Quirk

  Can't seem to get this to work. The idea is to calculate the percentage of heads and tails after each count, accumulating after each iteration. Except I keep getting nan% for my calculations. Anybody see what I'm doing wrong? void flipCoin(time_t seconds, int flipCount){ vector<int> flips; float headCount = 0; float tailCount = 0; double headProbability = double((headCount/(headCount + tailCount))*100); double tailProbability = double((tailCount/(headCount + tailCount))*100); for (int i=0; i < flipCount; i++) { int flip = rand() % (HEADS - TAILS + 1) + TAILS; flips.push_back(flip); if (flips[i] == 1) { tailCount++; cout << "Tail Percent: " << tailProbability << "%" << endl; }else{ headCount++; cout << "Head Percent: " << headProbability << "%" << endl; } } }

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• Where to find viterbi algorithm transition values for natural language processing?

  - by Rodrigo Salazar

  I just watched a video where they used Viterbi algorithm to determine whether certain words in a sentence are intended to be nouns/verbs/adjs etc, they used transition and emission probabilities, for example the probability of the word 'Time' being used as a verb is known (emission) and the probability of a noun leading onto a verb (transition). http://www.youtube.com/watch?v=O_q82UMtjoM&feature=relmfu (The video) How can I find a good dataset of transition and emission probabilities for this use-case? Or EVEN just a single example with all the probabilities displayed, I want to use realistic numbers in a demonstration.

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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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