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  • reservoir sampling problem

    - by eSKay
    This MSDN article proves the correctness of Reservoir Sampling algorithm as follows: Base case is trivial. For the k+1st case, the probability a given element i with position <= k is in R is s/k. The probability i is replaced is the probability k+1st element is chosen multiplied by i being chosen to be replaced, which is: s/(k+1) * 1/s = 1/(k+1), and prob that i is not replaced is k/k+1. So any given element's probability of lasting after k+1 rounds is: (chosen in k steps, and not removed in k steps) = s/k * k/(k+1), which is s/(k+1). So, when k+1 = n, any element is present with probability s/n. about step 3: What are the k+1 rounds mentioned? What is chosen in k steps, and not removed in k steps? Why are we only calculating this probability for elements that were already in R after the first s steps?

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  • Prove that the set of regular languages is a proper subset of the set of the context-free languages

    - by David Relihan
    I was brushing up (not homework)on some computation-theory and came accross this problem: How can you prove that the set of regular languages is a proper subset of the set of the context-free languages. Now I know a language is regular iff it is accepted by a finite automaton. And I know a language is context-free iff it is accepted by a pushdown automaton. But I'm not sure of what solution is.

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  • Sets, Surrogates, Normalisation, Referential Integrity - the Theory with example Scaling considerati

    - by tonyrogerson
    The Slides and Demo's for the SQLBits session I did today at SQL Bits in London are attached. The Agenda was... Thinking in Sets Surrogate Keys ú What they are ú Comparison NEWID, NEWSEQUENTIALID, IDENTITY ú Fragmenation Normalisation ú An introduction – what is it? Why use it? ú Joins – Pre-filter problems, index intersection ú Fragmentation again Referential Integrity ú Optimiser -> Query rewrite ú Locking considerations around Foreign Keys and Declarative RI (using Triggers)...(read more)

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  • The Grand Unified Framework Theory

    Tom Janssens left a comment: What still bugs me is that we do not have a unified pattern for all .net dev (using modelbinders and icommand for example...) But, Tom we are pretty close. At least as close as we should be, I think. With .NET there are plenty of low level patterns we can reuse regardless of the application platform or architecture. Stuff like: Asynchronous programming with events or the TPL. Object queries with LINQ. Resource management with IDispose. At a higher...Did you know that DotNetSlackers also publishes .net articles written by top known .net Authors? We already have over 80 articles in several categories including Silverlight. Take a look: here.

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  • PageRank is the Best Indicator of Competition Strength For a Keyword in SEO - New Verifiable Theory

    The major argument against PageRank in SEO is that pages with zero PageRank can be in the top positions even for highly competitive keywords. However, we are left with requiring an explanation as to why "PageRank is Google's view of the importance of this page." It becomes apparent that either Google is misleading us or we have all been misinterpreting Google's statement. From extensive evaluation of the top Google search engine results pages for hundreds of keywords, the author observed that those high positioned web pages with PageRanks of zero have a home page with higher PageRanks, usually three or more.

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  • 2-D Lighting Theory

    - by Richard
    I am writing a rogue-like 'zombie' management game. The game map will be similar to Prison Architect. A top-down 50 X 50 grid. I want to implemented a day night cycle and during the night I would like the player to be able to position lights. I would like to be able to lighten and dark to whole map to display the day and night cycle. Then lights would be a circle of light blocked by game entities such as walls, players, trees etc. How would I achieve and what is the standard way of achieving this?

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  • Context Free Language Question (Pumping Lemma)

    - by Maixy
    I know this isn't directly related to programming, but I was wondering if anyone know how to apply the pumping lemma to the following proof: Show that L={(a^n)(b^n)(c^m) : n!=m} is not a context free language I'm pretty confident with applying pumping lemmas, but this one is really irking me. What do you think?

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  • Convert a post-order binary tree traversal index to an level-order (breadth-first) index

    - by strfry
    Assuming a complete binary tree, each node can be adressed with the position it appears in a given tree traversal algorithm. For example, the node indices of a simple complete tree with height 3 would look like this: breadth first (aka level-order): 0 / \ 1 2 / \ / \ 3 4 5 6 post-order dept first: 6 / \ 2 5 / \ / \ 0 1 3 4 The height of the tree and an index in the post-order traversal is given. How can i calculate the breadth first index from this information?

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  • Graph Theory: How to compute closeness centrality for each node in a set of data?

    - by Jordan
    I'd like to learn how to apply network theory to my own cache of relational data. I'm trying to build a demo of a new way of browsing a music library, using network theory, that I think would make for a very intuitive and useful way of finding the right song at any given time. I have all the data (artists as nodes, similarity from 0 to 1 between each artist and those it is related to) and I can already program, but I don't know how to actually calculate the centrality of a node from that. I've spent a while trying to email different professors at my school but no one seems to know where I can learn this. I hope someone's done something similar. Thanks in advance you guys! ~Jordan

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  • Probability of failure with larger number of network elements

    - by MikeKulls
    I'm having a discussion with a work colleague. I'm saying that a network with 100 elements will have pretty much 10 times as many failures as a network with 10 elements, ie a tech will need to replace faulty hardware 10 times more often. He suggests that the failure rate doesn't go up in a linear fashion and the failure rate will be significantly less than 10x, in fact only slightly more failures. This is not the probability of an outage etc, we are just talking in relation to the amount of parts that a tech would need to swap out in a given time frame.

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  • Probability of Blade Chassis Failure

    - by ChrisZZ
    In my organisation we are thinking about buying blade servers - instead of rack servers. Of course technology vendors also make them sound very nice. A concern, that I read very often in different forums, is, that there is a theoretical possibility of the server chassis going down - which would in consequence take all the blades down. That is due to shared infrastructure. My reaction on this probability would be to have redundancy and by two chassis instead of one (very costly of course). Some people (including e.g. HP Vendors) try to convince us, that the chassis is very very unlikely to fail, due to many redundancies (redundant power supply, etc.). Another concern on my side is, that if something goes down, spare parts might be required - which is difficult in our location (Ethiopia). So I would ask to experienced administrators, that have managed blade server: What is your experience? Do they go down as a whole - and what is the sensible shared infrastructure, that might fail? That question could be extended to shared storage. Again I would say, that we need two storage units instead of only one - and again the vendors say, that this things are so rock solid, that no failure is expected. Well - I can hardly believe, that such a critical infrastructure can be very reliable without redundancy - but maybe you can tell me, whether you have successfull blade-based projects, that work without redundancy in its core parts (chassis, storage...) At the moment, we look at HP - as IBM looks much to expensive... thanks a lot best regards Christian

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  • What is the most easy way to get in advanced Type Theory.

    - by Bubba88
    Of course, by 'advanced' I mean here just something beyond what every programmer does know. I'm currently more-or-less comfortable with the basics and want to understand the most important, most elegant and most practically applicable achievements of modern type theory. I just do not have much time, desire and mental powers to study all the formalistics more thoroughly and that may change in the future. But there is something really attractive for me in that branch, that just forces to ask silly questions like this :) Thank you very much!

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  • Theory: Can JIT Compiler be used to parse the whole program first, then execute later?

    - by unknownthreat
    Normally, JIT Compiler works by reads the byte code, translate it into machine code, and execute it. This is what I understand, but in theory, is it possible to make the JIT Compiler parses the whole program first, then execute the program later as machine code? I do not know how JIT Compiler works technically and exactly, so I don't know any feasibility in this case. But theoretically, is it possible? Or am I doing it wrong?

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  • Choose between multiple options with defined probability

    - by Sijin
    I have a scenario where I need to show a different page to a user for the same url based on a probability distribution, so for e.g. for 3 pages the distribution might be page 1 - 30% of all users page 2 - 50% of all users page 3 - 20% of all users When deciding what page to load for a given user, what technique can I use to ensure that the overall distribution matches the above? I am thinking I need a way to choose an object at "random" from a set X { x1, x2....xn } except that instead of all objects being equally likely the probability of an object being selected is defined beforehand.

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  • MySQL create stored procedure fails but all internal queries succeed alone?

    - by Mark
    Hi all, I just created a simple database in MySQL, and I am learning how to write stored proc's. I'm familiar with M$SQL and as far as I can see the following should work: use mydb; -- -------------------------------------------------------------------------------- -- Routine DDL -- -------------------------------------------------------------------------------- DELIMITER // CREATE PROCEDURE mydb.doStats () BEGIN CREATE TABLE IF NOT EXISTS resultprobability ( ballNumber INT NOT NULL , probability FLOAT NULL, PRIMARY KEY (ballNumber) ); CREATE TABLE IF NOT EXISTS drawProbability ( drawDate DATE NOT NULL , ball1 INT NULL , ball2 INT NULL , ball3 INT NULL , ball4 INT NULL , ball5 INT NULL , ball6 INT NULL , ball7 INT NULL , score FLOAT NULL , PRIMARY KEY (drawDate) ); TRUNCATE TABLE resultprobability; TRUNCATE TABLE drawprobability; INSERT INTO resultprobability (ballNumber, probability) (select resultset.ballNumber ballNumber,(count(0)/(select count(0) from resultset)) probability from resultset group by resultset.ballNumber); INSERT INTO drawProbability (drawDate, ball1, ball2, ball3, ball4, ball5, ball6, ball7, score) (select distinct r.drawDate, a.ballnumber ball1, b.ballnumber ball2, c.ballnumber ball3, d.ballnumber ball4, e.ballnumber ball5, f.ballnumber ball6,g.ballnumber ball7, ((a.probability + b.probability + c.probability + d.probability + e.probability + f.probability + g.probability)/7) score from resultset r inner join (select r.drawDate, r.ballNumber, p.probability from resultset r inner join resultprobability p on p.ballNumber = r.ballNumber where r.appearence = 1) a on a.drawdate = r.drawDate inner join (select r.drawDate, r.ballNumber, p.probability from resultset r inner join resultprobability p on p.ballNumber = r.ballNumber where r.appearence = 2) b on b.drawdate = r.drawDate inner join (select r.drawDate, r.ballNumber, p.probability from resultset r inner join resultprobability p on p.ballNumber = r.ballNumber where r.appearence = 3) c on c.drawdate = r.drawDate inner join (select r.drawDate, r.ballNumber, p.probability from resultset r inner join resultprobability p on p.ballNumber = r.ballNumber where r.appearence = 4) d on d.drawdate = r.drawDate inner join (select r.drawDate, r.ballNumber, p.probability from resultset r inner join resultprobability p on p.ballNumber = r.ballNumber where r.appearence = 5) e on e.drawdate = r.drawDate inner join (select r.drawDate, r.ballNumber, p.probability from resultset r inner join resultprobability p on p.ballNumber = r.ballNumber where r.appearence = 6) f on f.drawdate = r.drawDate inner join (select r.drawDate, r.ballNumber, p.probability from resultset r inner join resultprobability p on p.ballNumber = r.ballNumber where r.appearence = 7) g on g.drawdate = r.drawDate order by score desc); END // DELIMITER ; instead i get the following Executed successfully in 0.002 s, 0 rows affected. Line 1, column 1 Error code 1064, SQL state 42000: You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near '' at line 26 Line 6, column 1 Error code 1064, SQL state 42000: You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near ')) probability from resultset group by resultset.ballNumber); INSERT INTO d' at line 1 Line 31, column 51 Error code 1064, SQL state 42000: You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near ') score from resultset r inner join (select r.drawDate, r.ballNumber, p.probabi' at line 1 Line 39, column 114 Execution finished after 0.002 s, 3 error(s) occurred. What am I doing wrong? I seem to have exhausted my limited mental abilities!

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  • How would you solve this graph theory handshake problem in python?

    - by Zachary Burt
    I graduated college last year with a degree in Psychology, but I also took a lot of math for fun. I recently got the book "Introductory Graph Theory" by Gary Chartrand to brush up on my math and have some fun. Here is an exercise from the book that I'm finding particularly befuddling: Suppose you and your husband attended a party with three other married couples. Several handshakes took place. No one shook hands with himself (or herself) or with his (or her) spouse, and no one shook hands with the same person more than once. After all the handshaking was completed, suppose you asked each person, including your husband, how many hands he or she had shaken. Each person gave a different answer. a) How many hands did you shake? b) How many hands did your husband shake? Now, I've been reasoning about this for a while, and trying to draw sample graphs that could illustrate a solution, but I'm coming up empty-handed. My logic is this: there are 8 different vertices in the graph, and 7 of them have different degrees. The values for the degrees must therefore be 0, 1, 2, 3, 4, 5, 6, and x. The # of degrees for one married couple is (0, 6). Since all graphs have an even number of odd vertices, x must be either 5, 3, or 1. What's your solution to this problem? And, if you could solve it in python, how would you do it? (python is fun.) Cheers.

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  • How would you solve this graph theory handshake problem in python?

    - by Zachary Burt
    I graduated college last year with a degree in Psychology, but I also took a lot of math for fun. I recently got the book "Introductory Graph Theory" by Gary Chartrand to brush up on my math and have some fun. Here is an exercise from the book that I'm finding particularly befuddling: Suppose you and your husband attended a party with three other married couples. Several handshakes took place. No one shook hands with himself (or herself) or with his (or her) spouse, and no one shook hands with the same person more than once. After all the handshaking was completed, suppose you asked each person, including your husband, how many hands he or she had shaken. Each person gave a different answer. a) How many hands did you shake? b) How many hands did your husband shake? Now, I've been reasoning about this for a while, and trying to draw sample graphs that could illustrate a solution, but I'm coming up empty-handed. My logic is this: there are 8 different vertices in the graph, and 7 of them have different degrees. The values for the degrees must therefore be 0, 1, 2, 3, 4, 5, 6, and x. The # of degrees for one married couple is (0, 6). Since all graphs have an even number of odd vertices, x must be either 5, 3, or 1. What's your solution to this problem? And, if you could solve it in python, how would you do it? (python is fun.) Cheers.

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  • banner rotator advertising with probability

    - by cosy
    I have banners advertising with number of views, like CPM system. And for example : i have 3 banner: banner1 with 20.000 nr of views banner2 with 10.000 nr of views banner3 with 5.000 nr of views and on my website the banner must to appear in this position (when the page is reloaded) : banner1 banner2 banner1 banner2 banner3 if the number of views is higher then the probability of apparition is higher how can i do this in php? Thanks a lot for helping :)

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  • Probability algorithm: Finding probable correct item in a list (e.g John, John, Jon)

    - by Andrew White
    Hi, Take for example the list (L): John, John, John, John, Jon We are to presume one item is to be correct (e.g. John in this case), and give a probability it is correct. First (and good!) attempt: MostFrequentItem(L).Count / L.Count (e.g. 4/5 or 80% likelihood) But consider the cases: John, John, Jon, Jonny John, John, Jon, Jon I want to consider the likelihood of the correct item being John to be higher in the first list! I know I have to count the SecondMostFrequent Item and compare them. Any ideas? This is really busting my brain! Thx, Andrew

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