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# Poisson Distribution Excel

The Poisson percent point function does not exist in simple closed form. Normal Approximation of the Binomial Distribution in Excel 2010 and Excel 2013. Some notations used in Poisson distribution are: λ is the rate at which an event occurs, t is the length of a time interval, And X is the number of events in that time interval. Suppose some event occurs times in some time interval. Jo, Erlang seems to work best at 1/4 or 1/2 hr intervals for forecasting accuracy. 13 POISSON DISTRIBUTION Examples 1. POISSON PROCESSES have an exponential distribution function; i. The variance of a distribution of a random variable is an important feature. Thus our mean of interest is (28. txt, or in excel. You cannot specify n 1 000 for the binomial distribution in Crystal Ball. INV function? I've been doing quite a bit of simulation recently, and I've been quite hampered by the fact that I'm not easily able to generate Poisson distributed numbers. The model obviously is not ideal: the data are clearly over-dispersed. , occurences) has no such limitation. It is a valid statistical model if all the following conditions exist:. The cumulative distribution function for a Poisson random variable is where lambda is the mean parameter. Poisson Distribution Number of vehicles passing a specified point on a highway, number of arrivals of customers per hour, or number of flaws in a glass sheet is often described by a Poisson distribution. l 1 M04_LEVI5199_06_OM_POIS. It's extremely important to note that this distribution model isn't appropriate for pricing most prop bets. In terms of the Poisson distribution, this condition can be expressed as. If you are, then great, let’s continue!What we now need to do is use the Poisson Distribution in Excel to calculate the probability of all possible scorelines for the hypothetical Arsenal vs Aston Villa game. Unlike the Binomial Distribution that has only two possible outcomes as a success or fail, this distribution focuses on the number of discrete occurrences over a defined interval. It can also be used for the number of events in other specified intervals such as distance, area or volume. In other words, when you are aware of how often the event happened, Poisson Distribution can be used to predict how often that event will occur. For each number of passengers, use POISSON(x, 0. Returns the Poisson distribution. View Notes - POISSON DISTRIBUTION EXCEL from STATISTICS 361 at California State University, Monterey Bay. Acceptance-Rejection Technique to Generate Random Variate. LOL! Rand is a built in FUNCTION in Excel. Computing Confidence Interval for Poisson Mean For Poisson distribution, there are many different ways for calculating the confidence interval. For example, the functions for the normal (Gaussian) distribution are NORMDIST and NORMINV. Generate an array of random numbers from one Poisson distribution. The actuary considers again the collective risk model where the number of claims is described by the Poisson distribution with parameter , i. The probability distribution that has the greatest chance of applying to this situation is the Poisson distribution When using Excel's POISSON function, one should choose TRUE for the third input if. The approximation is valid because the Binomial Distribution converges to the Poisson Distribution and n (the number of trials) approaches infinity and np remains fixed. Garwood, F. Simtools adds statistical functions and procedures for doing Monte Carlo simulation and risk analysis in spreadsheets. In addition, poisson is French for ﬁsh. This distribution can model batch arrivals (such as in a bulk queue). Inverse Poisson in Excel Software & Technology. Now, you must learn about Normal Distribution in R Programming. The step by step work help beginners or grade school students to learn how the input parameters are being used in the Poisson formula to find the probability of success in very large trials. customers entering the shop, defectives in a box of parts or in a fabric roll, cars arriving at a tollgate, calls arriving at the switchboard) over a continuum (e. Poisson Distribution Formula in Excel. Normal distribution, student-distribution, chi-square distribution, and F-distribution are the types of continuous random variable. Poisson vs Binomial Betting Strategy Thanks to late French Mathematician Simon Denis Poisson , we're able to calculate the probability of sports betting wagers using Poisson distribution. So the Excel command includes "INV" e. The POISSON. ) Let’s consider the following example. This problem can be solved using the following formula based on the Poisson distribution: where. The intensity values should follow a Poisson distribution around the expectation value (especially in the case of low intensity, above that it is OK approximated with Gaussian). In other words, if an event occurs, it does not affect the probability of another event occurring in the same time period. Count variables tend to follow distributions like the Poisson or negative binomial, which can be derived as an extension of the Poisson. It is what you use in the spreadsheet to generate random numbers there. Algorithm AS 243 — Cumulative distribution function of the non-central t distribution, Applied Statistics 38, 185–189. The binomial distribution model is an important probability model that is used when there are two possible outcomes (hence "binomial"). Thus the probability of exactly one aw in the rst 50m and exactly one aw in the. A couple of them, though — the ZTEST and the POISSON functions, in particular — are actually pretty useful. Using this cumulative distribution function calculator is as easy as 1,2,3: 1. The Poisson distribution may be useful to model events such as The number of meteorites greater than 1 meter diameter that strike Earth in a year; The number of patients arriving in an emergency room between 10 and 11 pm. First, you have to have an average of the past n matches of the teams and in my case I used the last 22 matches dating back to 2013 in all competitions (may it be friendlies, WC qualifiers, etc. Excel was asked to generate 50 Poisson random numbers with mean λ = 5. The normal distribution is the most important distribution in statistics because it fits many natural phenomena. For example, the functions for the normal (Gaussian) distribution are NORMDIST and NORMINV. and corresponding intervals for the parameter pof the binomial distribution. QXD 2/4/10 10:52 AM Page 1. n;p/can be thought of as the distribution of a sum of independent indicator random variables X1 C:::CXn, with fXi D1gdenoting a head on the ith toss of a coin. The Poisson Distribution is only a valid probability analysis tool under certain conditions. Generate random numbers according to a given distribution A commonly used technique is called the Inverse transform technique. Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale. For large means, the Poisson distribution is well approximated by the normal distribution. The Poisson probability mass function calculates the probability that there will be exactly x occurrences and is given by the formula:. Of course, we can use the formula to calculate MLE of the parameter λ in the Poisson model as: λˆ =X (please check this yourselves. Below is the syntax of the function-. In a Poisson probability distribution,. TINV for the T distribution. So, here we go to discuss the difference between Binomial and Poisson distribution. What is the probability of x worms being in a particular quadrat? Use a Poisson distribution Probability of finding X worms in a quadrat # of worms – A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow. Our model was founded on the belief that the number goals can be accurately expressed as a Poisson distribution. In our problem, we want to suppose that we have a consulting business that receives an average of 30 phone calls per hour, and during a two-hour period, we want to determine:. The following is the plot of the Poisson probability. The most common log-linear regression is the Poisson regression. Poisson Distribution Example (iii) Now let X denote the number of aws in a 50m section of cable. Of course, we can use the formula to calculate MLE of the parameter λ in the Poisson model as: λˆ =X (please check this yourselves. Poisson distribution Where do you meet this distribution? Accident : The number of soldiers killed by horse-kicks each year in each corps; Queuing Theory: Number of phone calls per minute, number of access to web sever per minute. Today we will learn how you can make a statistical distribution of test scores using excel. Poisson Distribution. A common application of the Poisson distribution is predicting the number of events over a specific time. Internal Report SUF–PFY/96–01 Stockholm, 11 December 1996 1st revision, 31 October 1998 last modiﬁcation 10 September 2007 Hand-book on STATISTICAL. Suppose that if case 1 occurs, the count is zero. INV function? I've been doing quite a bit of simulation recently, and I've been quite hampered by the fact that I'm not easily able to generate Poisson distributed numbers. If a mean or average probability of an event happening per unit time/per page/per mile cycled etc. Estimate if given problem is indeed approximately Poisson-distributed. The Poisson distribution played a key role in experiments that had a historic role in the development of molecular biology. It is what you use in the spreadsheet to generate random numbers there. Poisson regression is similar to regular multiple regression except that the dependent (Y) variable is an observed count that follows the Poisson distribution. ©2016 Matt Bognar Department of Statistics and Actuarial Science University of Iowa. These are: • The number of events that occur in any time interval is independent of the number of events in any other disjoint interval. Binomial, Geometric and Poisson Distributions with Excel The question was to find the probability that 7 rabbits would be found (based on a Poisson distribution with an average of 3. Using Excel, R & Python for checking Binomial Distribution. This is evidenced by the stepwise shape of the above graph of a Poisson distribution's PDF (Probability Density Function) curve. These distributions differ in their location and scale parameters: the mean ("average") of the distribution defines its location, and the standard deviation ("variability") defines the scale. A convenient approach to the calculation is to calculate the mean value "a" of the observation for which the observation of value x=0 is 10% probable. Software Add-ins About SIMTOOLS and FORMLIST. Poisson_Dist method (Excel) 05/24/2019; 2 minutes to read +1; In this article. Normal distribution means that most of the numbers are close to average while relatively few examples to the one extreme or the other. They are data that come from a Poisson distribution. This kind of projection is well suited to Poisson statistics. Excel's new and improved random number generator, at default, is supposed to produce uniform numbers on the interval (0,1); but it also produces negative numbers. If the random variable, x, has an Exponential distribution then the reciprocal (1/x) has a Poisson Distribution. A common application of the Poisson distribution is predicting the number of events over a specific time, such as the number of cars arriving at a toll plaza in 1 minute. Hopefully you are still with me…if not, go back and read again. Just like the binomial distribution, the Poisson is a discrete probability distribution. 4, find PX()=6. poisson¶ scipy. The Poisson distribution may be useful to model events such as The number of meteorites greater than 1 meter diameter that strike Earth in a year; The number of patients arriving in an emergency room between 10 and 11 pm. In this case, the Poisson parameter Lambda should be less than 1, usually much less. What follows are step-by-step instructions for using various types of technology to evaluate statistical concepts. There is this formula parameter that follows a normal distribution ("K" in the safety stock wiki article). More about the Poisson distribution probability so you can better use the Poisson calculator above: The Poisson probability is a type of discrete probability distribution that can take random values on the range $$[0, +\infty)$$. Example of Binomial Distribution and Probability This Tutorial will explain the Binomial Distribution, Formula, and related Discrete Probabilities Suppose you toss a coin over and over again and each time you can count the number of “Heads” you get. This simple Poisson calculator tool takes the goal expectancy for the home and away teams in a particular match then using a Poisson function calculates the percentage chance and likely number of goals each team will score. Therefore, given a part population (n), the failure rate of the part (λ) and a time interval (t) during which no further spares will be available, the Poisson distribution can be used to predict the number of failures that will occur, with a certain probability, and thus the number of spares required for some time period of interest. In other words, if an event occurs, it does not affect the probability of another event occurring in the same time period. Before reading this lecture, you might want to revise the lectures about maximum likelihood estimation and about the Poisson distribution. Here, “time interval” is the standard. You can calculate Poisson distribution on the Excel using the following function. All we really need to know is that it can be used to calculate the probability of outcomes for a football match, which in turn can be turned into odds which we can use. A common application of the Poisson distribution is predicting the number of events over a specific time, such as the number of cars arriving at a toll plaza in 1 minute. The rate is notated with λ λ = 'lambda', Greek letter 'L' - There is only one parameter for the Poisson distribution. Poisson does come across as a bit of a mouthful, but the good thing is that you don't need to fully understand the formula to make it work. • The process of counted events is a non homogeneous Poisson process with rate λ(t)=λp(t). Generating Poisson random values Posted on 14 June 2010 by John The most direct way of generating random samples from a Poisson distribution is efficient for some parameters and inefficient for others. Poisson method (Excel) 05/24/2019; 2 minutes to read +1; In this article. Final revision April 2003] Summary. This tutorial explains how use the POISSON. The cumulative distribution function for a Poisson random variable is where lambda is the mean parameter. The probability of a chargeback is 50% for customers waiting for more than 20 minutes and the cost of each chargeback is multiplied by this number. For this example, you're looking for pr(1), so. Calculate the Poisson Distribution in Excel using function POISSON. Poisson Distribution will give you the probability of a number of independent events occurring in a fixed time frame. Normal distribution. If a mean or average probability of an event happening per unit time/per page/per mile cycled etc. It is a valid statistical model if all the following conditions exist:. Generate random numbers according to a given distribution A commonly used technique is called the Inverse transform technique. (a) Calculate the sample mean. Interpreting and Reporting the Output of Poisson Regression Analysis. In our case, these will be numbers between 10 and 40. A couple of them, though — the ZTEST and the POISSON functions, in particular — are actually pretty useful. SOLUTION: Given that X has a poisson distribution with u=9 what is the probability that x=5 Algebra -> Probability-and-statistics -> SOLUTION: Given that X has a poisson distribution with u=9 what is the probability that x=5 Log On. The Poisson distribution has density p(x) = λ^x exp(-λ)/x! for x = 0, 1, 2, …. Inverse Gamma Distribution. By definition, the x in our Poisson formula is discrete, since we need to count the number of flaws (or sickness cases, or whatever). TINV for the T distribution. I have an excel spreadsheet that uses poisson to figure out the probability of correct scores in soccer matches. So as of now I have poisson(x value, mean, true-cumulative) and that lets me get the probability for that occurence. Below is the syntax of the function-. In this recording, what I want to do is examine that question, show you how. Internal Report SUF–PFY/96–01 Stockholm, 11 December 1996 1st revision, 31 October 1998 last modiﬁcation 10 September 2007 Hand-book on STATISTICAL. Poisson distribution calculator, formulas, work with steps, real world and practice problems to learn how to find the probability of given number of events that occurred in a fixed interval of time with respect to the known average rate of events occurred. If , the rate of decay increases in a nonlinear fashion, thus shortening the tail of the distribution (underdispersed data). Poisson distribution with a mean of 1. 2 Comparing the Ability of MS Excel and R while Simulating from Poisson Distribution Tanushree Deb Roy 1, Dibyojyoti Bhattacharjee 2 and Kishore K. How to calculate frequency distribution in Excel? A frequency distribution is a summary of counting how often values occur within a range of values, take the following screenshot for example, column B contains the score numbers, D2:E6 is the score bands you specified by yourself, and the Frequency column get the value occurs based on the bands. probability and distributions formulas list online. Poisson Approximation for the Binomial Distribution • For Binomial Distribution with large n, calculating the mass function is pretty nasty • So for those nasty “large” Binomials (n ≥100) and for small π (usually ≤0. The mean and variance of the poisson distribution are both equal to m. 28 flaws per square foot. For… Clarke began by dividing an area into thousands of tiny, equally sized plots. Poisson Distribution The Poisson Distribution is a widely employed distribution that is used to describe the probability of events that are a result of a rate that occurs over time such as: Product demand Demand for services Number of telephone calls that come over a switchboard Number of accidents. So how exactly do I determine the likelihood of an. Some notations used in Poisson distribution are: λ is the rate at which an event occurs, t is the length of a time interval, And X is the number of events in that time interval. , is given, and you are asked to calculate a probability of n events happening in a given time/number of pages/number of miles cycled, then the Poisson Distribution is used. The mle agrees with the method of moments in this case, so does its sampling distribu-. , occurences) has no such limitation. For the binomial distribution, these functions are pbinom, qbinom, dbinom, and rbinom. As you can see, the Poisson distribution is very helpful in calculating the probability for discrete data. This kind of projection is well suited to Poisson statistics. Discrete and Cumulative Probability Calculator for the Poisson Distribution. That said, it can also be one of the more complex ways to calculate a potential winner, and it is isn't perfect. Poisson regression does not handle cases where some participate and others do not, and among those who do not, had they participated, would likely produce an outcome greater than zero. DIST(x,mean,cumulative) The POISSON. So we can't actually find the derivative of the Poisson Distribution, since differentiation only works for continuous functions. The function returns one number. Poisson distribution vs. Although it has been replaced, the Poisson function is still available in Excel 2010 (stored in the list of compatibility functions), to allow compatibility with earlier versions of Excel. The Poisson Calculator makes it easy to compute individual and cumulative Poisson probabilities. LOL! Rand is a built in FUNCTION in Excel. If X1, X2,…,Xn are independent Poisson random variables with parameters λ1, λ2,… λn, then their sum is also a Poisson random variable with parameter λ1 +λ2+…+λn. Note that because this is a discrete distribution that is only defined for integer values of x, the percent point function is not smooth in the way the percent point function typically is for a continuous distribution. (You can also use. Poisson distribution Where do you meet this distribution? Accident : The number of soldiers killed by horse-kicks each year in each corps; Queuing Theory: Number of phone calls per minute, number of access to web sever per minute. Multinomial Distribution. DIST() function in Excel to answer probability questions regarding the Poisson distribution. The mean and variance of the poisson distribution are both equal to m. Poisson Distribution Fitting. Events occur independently. It should be possible to implement a Possison regression model in Excel using a combination of the Poisson distribution and the built-in optimization routines. Poisson Regression Poisson regression is a form of a generalized linear model where the response variable is modeled as having a Poisson distribution. B) Excel Function: Excel provides the following function for the Poisson distribution: POISSON(x, μ, cum) where μ = the mean of the distribution and cum takes the values TRUE and FALSE. Normal distributions are bell shaped (that's why they are sometimes called bell curves), and have a symmetrical distribution with one single peak. We'll use this result to approximate Poisson probabilities using the normal distribution. The authors employed prevalence of leprosy as the variable of interest for monitoring the Leprosy elimination program. Poisson method (Excel) 05/24/2019; 2 minutes to read +1; In this article. This distribution became useful as it models events, particularly uncommon events. In the original version of this page (and the corresponding Excel spreadsheet), I took no special action. Solution This can be written more quickly as: if X ~ Po()3. A common application of the Poisson distribution is predicting the number of events over a specific time, such as the number of cars arriving at a toll plaza in 1 minute. Analysis of sports data by using bivariate Poisson models Dimitris Karlis Athens University of Economics and Business, Greece and Ioannis Ntzoufras University of the Aegean, Chios, Greece [Received November 2001. An Introduction to Excel's Normal Distribution Functions Excel provides several worksheet functions for working with normal distributions or 'bell-shaped curves. Poisson can be a very useful tool when approaching statistical analysis with Excel. The Excel equations were wrong. Today we will learn how you can make a statistical distribution of test scores using excel. What is Monte Carlo Simulation? Monte Carlo Simulation is a process of using probability curves to determine the likelihood of an outcome. Use the poissrnd function to generate random numbers from the Poisson distribution with the average rate 20. =SKEW(H4:H547) = 0. DIST functions in Excel, but not an inverse Poisson distribution function. A common application of the Poisson distribution is predicting the number of events over a specific time, such as the number of cars arriving at a toll plaza in one minute. 1 The Poisson Distribution. It is a pre-built integrated probability distribution function (pdf) in excel that is categorized under Statistical functions. Events occur independently. The use of the Poisson Distribution allows one to compare low numbers of deaths in a strata, thereby deriving more meaningful conclusions from the information. by Marco Taboga, PhD. However, for certain distributions, the mean suffices (for example Poisson's distribution), or, if not, the asymmetry coefficient is also required (Weibull's distribution for example). Poisson distribution Where do you meet this distribution? Accident : The number of soldiers killed by horse-kicks each year in each corps; Queuing Theory: Number of phone calls per minute, number of access to web sever per minute. We will solve a problem with data that is distributed exponentially with a mean of 0. The base name is an abbreviation of the distribution name. The commands follow the same kind of naming convention, and the names of the commands are dbinom, pbinom, qbinom, and rbinom. Consider a Poisson distribution with #μ=3#. Until now, the value of L entered into Excel was 95 for 95% confidence levels, rather than the correct 97. , normal distribution ), that may generally take a value of any real number, it can assume only a countably infinite number of values. It will calculate the Poisson probability mass function. VAT 24%: Buy from Web Store: Mathematical tool for calculating various sports betting probabilities based on Poisson distribution and statistics database. It is a valid statistical model if all the following conditions exist:. In our case, these will be numbers between 10 and 40. If the random variable, x, has an Exponential distribution then the reciprocal (1/x) has a Poisson Distribution. jumps can be modelled by a Poisson processes. 5,TRUE) where I assume that since 11 is the average in 2 hours then 5. Ideally I would reverse this calculation inputing the required probability and obtain x (the spares level required). 519, False) to find the expected value where x is the number of passengers. In other words, if an event occurs, it does not affect the probability of another event occurring in the same time period. Today we will learn how you can make a statistical distribution of test scores using excel. The diagonal line shows where the data would fall if they perfectly followed the Poisson distribution. , for some real > 0, each X i has the density4 f X (x) = exp(x) for x 0. The difference is that in the Poisson distribution, the outcomes occur over a continuous sample space. xla and Formlist. Many of the examples used are already available in functions that come with Excel. The usual way to calculate a Poisson distribution in real life situations is with software like IBM SPSS. In Excel, binomial distributions let you calculate probabilities in two situations. 0425 is the answer. Hi, my task is as follows: For calibration, I take microscopic images of a fluorescent solution. This shows an example of a Poisson distribution with various parameters. The same arguments can be applied to derive conﬁdence bounds and intervals for the negative binomial parameter p, for the Poisson parameter λ, for the ratio of two Poisson parameters, ρ= λ 1/λ 2, and for the parameter Dof the hypergeometric distribution. As per wikipedia, the Poisson distribution, named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event. Simtools adds statistical functions and procedures for doing Monte Carlo simulation and risk analysis in spreadsheets. DIST function is categorized under Excel Statistical functions. Why doesn't Excel have a POISSON. Transformed Gamma Distribution. Excel 2003 is an improvement over previous versions, but not enough has been done that its use for statistical purposes can be recommended. Suppose you have two rates that you assume are Poisson and you want to test that they are di erent. As a financial analyst, POISSON. Normal Approximation of the Binomial Distribution in Excel 2010 and Excel 2013. - If you analyze business data…and especially if you perform any kind of simulation…it's useful to know about the POISSON distribution. It will calculate the Poisson probability mass function. Then the probability of times occurrence of the same event in the same interval is known as follows. Poisson vs Binomial Betting Strategy Thanks to late French Mathematician Simon Denis Poisson , we’re able to calculate the probability of sports betting wagers using Poisson distribution. Poisson Distribution Formula in Excel (With Excel Template) Here we will do another example of the Poisson Distribution in Excel. Since the mean and variance of a Poisson distribution are equal, data that conforms to a Poisson distribution must have an index of dispersion approximately equal to 1. Thanks to the ingenious works of French Mathematician Simeon Denis Poisson in the 19th century, sportsbetting enthusiasts can calculate the probability of sports betting wagers using the Poisson distribution betting strategy. Suppose an event can occur several times within a given unit of time. Excel VBA Statistics and Mathematics Examples This page contains simple Excel VBA Statistics and Mathematics examples. The Poisson distribution with parameter λ can be approximated by a Normal distribution with mean λ and variance λ, for large values of λ. The Poisson distribution has a probability density function (PDF) that is discrete and unimodal. Understanding Exponential Distribution. So how exactly do I determine the likelihood of an. A convenient approach to the calculation is to calculate the mean value "a" of the observation for which the observation of value x=0 is 10% probable. The Poisson distribution is a family of discrete probability distributions. These are: • The number of events that occur in any time interval is independent of the number of events in any other disjoint interval. Returns the Poisson distribution. Although it has been replaced, the Poisson function is still available in Excel 2010 (stored in the list of compatibility functions), to allow compatibility with earlier versions of Excel. In probability theory and statistics, the Poisson binomial distribution is the discrete probability distribution of a sum of independent Bernoulli trials that are not necessarily identically distributed. Poisson Approximation for the Binomial Distribution • For Binomial Distribution with large n, calculating the mass function is pretty nasty • So for those nasty "large" Binomials (n ≥100) and for small π (usually ≤0. To switch between random and static values for all open workbooks use either method: "Rolling dice" icon (Random/Static Standard (F9) Recalculation). Models based on the bivariate Poisson distribution are used for modelling sports data. Example of Binomial Distribution and Probability This Tutorial will explain the Binomial Distribution, Formula, and related Discrete Probabilities Suppose you toss a coin over and over again and each time you can count the number of "Heads" you get. For example, if we want to know the distribution for "ﬁshing with runs," we would run our Excel program many times,. Corrupt Excel File Repair Software repairs corrupt Microsoft Excel documents, Restore Corrupt Excel Files and supported all versions of Microsoft Excel such as Excel 97, MS Excel 2003, Excel XP, Excel 2000, and Excel 95. In other words, for every natural value that I get, the. It is a pre-built integrated probability distribution function (pdf) in excel that is categorized under Statistical functions. Poisson Approximation for the Binomial Distribution • For Binomial Distribution with large n, calculating the mass function is pretty nasty • So for those nasty “large” Binomials (n ≥100) and for small π (usually ≤0. Mean and Standard Deviation of Poisson Random Variables (Jump to: Lecture | Video) Here's my previous example: At a theme park, there is a roller coaster that sends an average of three cars through its circuit every minute between 6pm and 7pm. Not show how it works? Here are the steps for using Excel’s POISSON. If , the ratio is equal to the rate of decay of the Poisson distribution. Given a Poisson distribution with mean , then the number of events in half that time period follows a Poisson distribution with mean /2. Like the binomial distribution and the normal distribution, there are many Poisson distributions. 1 The Poisson Distribution. For this example, you're looking for pr(1), so. In the Poisson model, everybody participates in the y j = exp(b 0 + X j b + ε j) process. Test for a Poisson Distribution. We will see how to calculate the variance of the Poisson distribution with parameter λ. Using Probability Theory & Poisson Distribution to win money! I’ve been gambling casually on football for the past 8 years or so, and not making a great job of it! I’ve had a few decent returns but I’m almost certainly quite a bit down over the total time I’ve been betting. Internal Report SUF–PFY/96–01 Stockholm, 11 December 1996 1st revision, 31 October 1998 last modiﬁcation 10 September 2007 Hand-book on STATISTICAL. Poisson Distribution. WorksheetFunction. Some notations used in Poisson distribution are: λ is the rate at which an event occurs, t is the length of a time interval, And X is the number of events in that time interval. A common application of the Poisson distribution is predicting the number of events over a specific time, such as the number of cars arriving at a toll plaza in one minute. However, there are other Poisson distributions for which the fit is even closer. So, for example, an observed event count of zero would result in a 95% Poisson CI of 0 to 3. In other words, if an event occurs, it does not affect the probability of another event occurring in the same time period. Poisson distribution Where do you meet this distribution? Accident : The number of soldiers killed by horse-kicks each year in each corps; Queuing Theory: Number of phone calls per minute, number of access to web sever per minute. Today we look at the GAMMAINV function. 7183) μ is the mean number of "successes" x is the number of "successes" in question. Poisson Distribution Using Excel In this tutorial we will be solving Poisson Distribution problems using Excel. The suffix is either DIST or INV. The punter is safe in the knowledge that Poisson can be used to predict the score of a football match. If its True then the function will find the cumulative mass function. Returns the Poisson distribution. Poisson handles zeros that arise in correspondence to the model. Software Add-ins About SIMTOOLS and FORMLIST. Poisson random variable is typically used to model the number of times an event happened in a time interval. •The Poisson regression model is another GENERALIZED LINEAR MODEL. , normal distribution ), that may generally take a value of any real number, it can assume only a countably infinite number of values. Test for a Poisson Distribution. What is Poisson distribution. Returns the Poisson distribution. How many such events will occur during a fixed time interval? Under the right circumstances, this is a random number with a Poisson distribution. Location, Scale, and Shape Parameters. RiskBinomial, RiskBernoulli Functions. txt, or in excel. DIST is useful in forecasting revenue. A common application of the Poisson distribution is predicting the number of events over a specific time, such as the number of cars arriving at a toll plaza in 1 minute. Thus, the zip model has two parts, a. I have an excel spreadsheet that uses poisson to figure out the probability of correct scores in soccer matches. Poisson Distribution Calculator. Using Excel, R & Python for checking Poisson Distribution. These distributions differ in their location and scale parameters: the mean ("average") of the distribution defines its location, and the standard deviation ("variability") defines the scale. View Notes - POISSON DISTRIBUTION EXCEL from STATISTICS 361 at California State University, Monterey Bay. Hi there, I have seen in Excel 2010 that there is a Possion Distribution function that I want to use (POISSON. One commonly used discrete distribution is that of the Poisson distribution. Mathematical tool for calculating various sports betting probabilities based on Poisson distribution and statistics database. Maher (1982) on Modelling Association Football scores using Poisson predictive model and i tried to duplicate it on excel as we all know that there is a Poisson Distribution Formula in Excel, right ? I share with you my predictive model for the English Premier League 2016-2017.


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### Nonlinear shallow water equation

The name of the equation pretty much gives the quantities that matter in this scenario: the nonlinearity and shallowness. For the standard input of the water wave equation with velocity potential as the unknown, we have:

$\nabla^2 \phi=0$ as governing equation;

$\eta_t+\phi_x\eta_x+\phi_y\eta_y-\phi_z=0$ as kinematic boundary condition (KBC) at free surface;

$\phi_t+g\eta+\frac{1}{2}(\nabla \phi)^2+\frac{p}{\rho}=0$ as dynamics boundary condition (DBC) at free surface.

In order to quantify the effect of nonlinearity and shallowness, non-dimensional form of the equation is introduced by using normalized variables:

$(x, y)\leftarrow (x, y)/l,\quad z\leftarrow z/h, \quad t\leftarrow ct/l, \quad \eta\leftarrow \eta/a,\quad \phi\leftarrow h\phi/(alc)$

where $l$ is characteristic length scale, $a$ is wave amplitude, $h$ is water depth, $c$ is shallow water celerity by linear theory $c=\sqrt{gh}$. The quantity that evaluates nonlinearity is defined as

$\epsilon=a/h$

and that for shallowness is

$\delta=(h/l)^2$

Now the equations become

$\Delta(\phi_{xx}+\phi_{yy})+\phi_{zz}=0$

$\phi_t+\frac{\epsilon}{2}(\phi_x^2+\phi_y^2)+\frac{\epsilon}{2\delta}\phi_z^2+\eta$, for $z=1+\epsilon\eta$    (DBC)

$\delta[\eta_t+\epsilon(\phi_x\eta_x+\phi_y\eta_y)]-\phi_z=0$, for $z=1+\epsilon\eta$   (KBC)

If the unknown $\phi$ is expanded with $\delta$:

$\phi=\phi_0+\delta\phi_1+\delta^2\phi_2+\dots$

One can find for zero order term $\phi_0$, governing equations gives:

$\phi_{0zz}=0$

combining homogeneous Neumann boundary condition at the bottom, this means $\phi_{0z}=0$ all over the region, and $\phi_0$ is independent of vertical location. If denote

$u(x,y,t)=\phi_{0x}, \quad v(x,y,t)=\phi_{0y}$

we have for $\phi_1$:

$\phi_1=-z^2/2(u_x+v_y),\quad \phi_2=z^4/24[(\nabla^2u)_x+(\nabla^2v)_y]$

All above results come from the governing equation and bottom boundary condition, and have nothing to do with free surface boundary conditions, i.e. they are concluded by the fact of flow being incompressible, irrotational, and having immiscible bottom. Now, if we put the expansion of $\phi$ in free surface boundary condition equations, and retain only up to 2nd order of $\delta$, $\epsilon$ in KBC, and up to 1st order of $\delta$, $\epsilon$ in DBC, combing the definition notation of $(u,v)$, we have:

$u_t+\epsilon(uu_x+vv_x)+\eta_x-1/2\delta(u_{txx}+v_{txy})=0$

$v_t+\epsilon(uu_y+vv_y)+\eta_y-1/2\delta(u_{txy}+v_{tyy})=0$

$\eta_t+[u(1+\epsilon\eta)]_x+[v(1+\epsilon\eta)]_y=\delta/6[(\nabla^2u)_x+(\nabla^2v)y]$

In above equations if we take $\delta\rightarrow 0$ and $\epsilon\rightarrow 0$, i.e., assuming linearity and shallowness, we have the linear wave equation for $\eta$:

$\eta_{tt}-c^2(\eta_{xx}+\eta_{yy})=0$

On the other hand, the 1D version of above equations is so called Boussinesq equations:

$u_t+\epsilon uu_x+\eta_x-1/2\delta u_{txx}=0$

$\eta_t+[u(1+\epsilon\eta)]_x=\delta/6 u_{xxx}$

format: plain


text:
# OSL noise_turbulence function

I found that people use noise_turbulence function in noise writing. Also i noticed that it was used in wave texture node implementation using osl here:https://svn.blender.org/svnroot/bf-blender/trunk/blender/intern/cycles/kernel/shaders/node_wave_texture.osl

But there's no any function like that in OSL-Languagespec. So how to write something similar?

Thank you


text:
ASPECT
Changes after the latest release (v2.4.0)

This is the list of changes made after the release of ASPECT version 2.4.0. All entries are signed with the names of the author.

1. New: ASPECT now has a cmake option ASPECT_INSTALL_EXAMPLES that allows to build and install all cookbooks and benchmarks. This will include building all shared libraries during 'make' and installing all files to the installation location on 'make install'. This is helpful for installations that are used for teaching and tutorials.
(Rene Gassmoeller, 2023/03/13)

2. New: Plugins in shared libraries now build libmy_plugin.debug.so or libmy_plugin.release.so depending on the current build type. The "Additional shared libraries" parameter value does not need to be adjusted, because ASPECT automatically loads the correct library when "./libmy_plugin.so" is specified.
(Timo Heister, 2023/03/09)

3. New: ASPECT now supports a DebugRelease build type that creates a debug build and a release build of ASPECT at the same time. It can be enabled by setting the CMake option CMAKE_BUILD_TYPE to DebugRelease or by typing "make debugrelease".
(Timo Heister, 2023/03/03)

4. New: There is a new initial composition plugin that reads in a slab model (e.g. Slab2) and converts it to a compositional field.
(Arushi Saxena, Rene Gassmoeller, Juliane Dannberg, 2023/03/03)

5. New: The signal start_timestep can be used to get a callback at the beginning of each timestep.
(Timo Heister, 2023/02/22)

6. Fixed: The depth average postprocessor would crash when trying to compute the quantities "adiabatic_temperature", "adiabatic_pressure", "adiabatic_density", and "adiabatic_density_derivative" for a single depth slice. It would also compute these quantities at equidistant positions along a depth profile from the surface to the bottom of the model, even if user defined depth bounds were specified in the input file. This was fixed so that adiabatic quantities are computed like all other depth averaged quantities by iterating over all cells in the model domain and averaging the properties spatially. As a consequence some functions in the adiabatic conditions interface that contained the bugs and were only used by the depth average postprocessor have been deprecated.
(Rene Gassmoeller, 2023/02/21)

7. New: ASPECT detects when refinement does not actually change the mesh and skips the redundant computation.
(Timo Heister, 2023/02/13)

8. Fixed: The Allow fixed temperature on outflow boundaries = false option (and the equivalent option for composition) now also work in time steps where the mesh is refined. In addition, if this parameter is set to false, fixed temperature/composition are now no longer applied to the boundary in cases where the flow normal to the boundary is zero (as is the case in time step 0).
(Juliane Dannberg, Rene Gassmoeller, 2023/02/03)

9. New: The PhaseFunction class now includes helper functions n_phases_for_each_composition() and n_phases().
(Bob Myhill, 2023/01/22)

10. New: ASPECT has new introspection functions get_indices_for_fields_of_type and get_names_for_fields_of_type. There is also a new utilities function called compute_only_composition_fractions that takes a vector of compositional field values and a list of indices that designates which of those fields correspond to chemical compositions. It then calculates the missing fraction corresponding to the background field, and returns the full vector of fractions.
(Bob Myhill, 2023/01/19)

11. New: The "Compositional fields / Types of fields" parameter in ASPECT has a new type called "strain".
(Bob Myhill, 2023/01/19)

12. New: There is now a new mesh refinement plugin called "Nonadiabatic temperature threshold" that uses the temperature anomaly (compared to the adiabat) to mark additional cells for refinement.
(Juliane Dannberg, 2023/01/17)

13. New: There is now a new additional material model output called ShearHeatingOutputs that contains the fraction of the deformation work that is released as shear heating rather than being converted into other forms of energy, to be filled by the material model. The boundary_area_change_work_fractions variable (which provides the same information) has been removed from the DislocationViscosityOutputs in the grain size material model.
(Juliane Dannberg, 2023/01/12)

14. Added: The 'adiabatic' initial temperature plugin can now use a spatially variable top boundary layer thickness read from a data file or specified as a function in the input file. Additionally, the boundary layer temperature can now also be computed following the plate cooling model instead of the half-space cooling model.
(Daniel Douglas, John Naliboff, Juliane Dannberg, Rene Gassmoeller, 2022/12/06)

15. New: Added a particle property 'grain size' that tracks grain size evolution on particles using the 'grain size' material model.
(Juliane Dannberg, Rene Gassmoeller, 2022/12/06)

(Rene Gassmoeller, 2022/12/02)

17. Improved: The interpolation from particles to fields used to be done field-by-field, creating a lot of overhead in the interpolation algorithms. Now all particle properties are interpolated to fields at the same time, significantly reducing the time required for interpolation for models with many particle properties.
(Rene Gassmoeller, 2022/10/10)

18. New: We now support tangential velocity boundary conditions with GMG for more geometries, such as 2D and 3D chunks.
(Timo Heister, Haoyuan Li, Jiaqi Zhang, 2022/09/13)

19. Changed: Moved composition velocity statistics postprocessor from cookbook to main code. Compatibility of the postprocessor's input parameter "Names of slab compositional fields" is broken by renaming it to the more general "Names of selected compositional fields".
(Elodie Kendall and Anne Glerum, 2022/07/29)

20. New: The graphical output of a computation with mesh deformation can now be optionally done on the undeformed reference mesh ("set Output undeformed mesh = true") and the displacement can be written as a separate vector field ("set Output mesh displacement = true").
(Timo Heister, 2022/07/16)

21. Changed: In our plugin systems, we have many factory functions that create objects and returned raw pointers; in many but not all places, these returned raw pointers were then converted to std::unique_ptrs. This has been changed now by (hopefully) consistently letting factory functions return std::unique_ptrs right away, and then dealing with them at the receiving end.
(Wolfgang Bangerth, 2022/07/07)

22. New: There is now a postprocessor that outputs the total volume of the computational domain.
(Anne Glerum, 2022/06/28)


text:
Topology Seminars - Miami University
Spring 2012

Thursday, April 19, 2012      3:15 pm - Rm 118 BAC

Title: ON DISCRETELY GENERATED BOX PRODUCTS
Abstract:  This is a joint  work  with  R. Wilson.  We will prove that an
arbitrary box  product  of monotonically normal spaces is discretely  generated.
In  particular,  any  finite  product  of monotonically normal spaces is
discretely  generated.  Therefore there exist countable spaces not embeddable
into a box product of real lines.

Topology Seminar
Topology Seminars - Miami University
Spring 2012

Thursday, January 26, 2012      3:15 pm - Rm 118 BAC
Thursday, January 19, 2012      3:15 pm - Rm 118 BAC

Title: How much do discrete subspaces of a space characterize its topology?
Abstract: We will give a cycle of talks on topological properties determined to some
extent by discrete subspaces of a given space. The first property we are going to talk
about is discrete generability which is a convergence property with a flavor of a global one.
A space $X$ is discretely generated if for any $A\subset X$ and any point $x\in \overline A$
there exists a discrete subset $D\subset A$ such that $x\in \overline D$. It is evident that
discretely generated spaces form a class that contains both Frechet-Urysohn spaces and
scattered spaces so discrete generability is a local property with components of a global one.
We will present a survey of both recent and old results on discrete generability; the material
of the respective lectures is supposed to be sufficient to give a reasonably complete view of
the area.

Topology Seminars - Miami University
Fall 2011

Thursday, November 17, 2011      3:15 pm - Rm 118 BAC
Thursday, November 3, 2011      3:15 pm - Rm 118 BAC
Thursday, October 27, 2011      3:15 pm - Rm 118 BAC
Thursday, October 6, 2011      3:10 pm - Rm 118 BAC
Thursday, September 8, 2011      3:10 pm - Rm 118 BAC
Thursday, September 1, 2011      3:10 pm - Rm 118 BAC
Friday, August 26, 2011      3:10 pm - Rm 118 BAC

Title: How much do discrete subspaces of a space characterize its topology?
Abstract: We will give a cycle of talks on topological properties determined to some
extent by discrete subspaces of a given space. The first property we are going to talk
about is discrete generability which is a convergence property with a flavor of a global one.
A space $X$ is discretely generated if for any $A\subset X$ and any point $x\in \overline A$
there exists a discrete subset $D\subset A$ such that $x\in \overline D$. It is evident that
discretely generated spaces form a class that contains both Frechet-Urysohn spaces and
scattered spaces so discrete generability is a local property with components of a global one.
We will present a survey of both recent and old results on discrete generability; the material
of the respective lectures is supposed to be sufficient to give a reasonably complete view of
the area.

Thursday, October 20, 2011      3:15 pm - Rm 118 BAC

Thursday, October 13, 2011      3:15 pm - Rm 118 BAC
Tuesday, September 27, 2011      3:15 pm - Rm 118 BAC
Thursday, September 22, 2011      3:15 pm - Rm 118 BAC

Title: Noetherian type and other order-theoretic'' cardinal functions I, II, III, IV
Abstract:  A topological space has {\sl countable Noetherian type}'' if it
has a base where no element is contained in infinitely many elements of that base.
Study of this property goes back to the Russian School of General Topology of the
70-80s (Malykhin, Peregudov and Shapirovskii ${\ldots}$) and was taken up independently
by the American School in the 90s. Some fundamental questions about it remain open.
For example, if $X^2$ has countable Noetherian type, does $X$ need to have countable
Noetherian type too?  We will offer some partial answers to this question of Balogh,
Bennett, Burke, Gruenhage, Lutzer and Mashburn, both in the positive and in the
negative. This definition suggests introducing a cardinal function. Time permitting
we will show how this function is related to the Suslin Number (of homogeneous compacta)
and present an independence result regarding the value of this function on certain
countably supported box products.

This is joint work with Dave Milovich and Menachem Kojman.

Wednesday, October 12, 2011      3:15 pm - Rm 118 BAC

Friday, October 7, 2011      3:15 pm - Rm 118 BAC
Wednesday, September 28, 2011      3:15 pm - Rm 118 BAC
Friday, September 16, 2011      3:15 pm - Rm 118 BAC

Speaker: Daniel Farley Miami University
Title: Some iterated monodromy groups of intermediate growth I, II, III, IV
Abstract:  In a 1968 paper, John Milnor defined the growth function
of a finitely generated group, and asked whether every group has polynomial
or exponential growth. Grigorchuk produced the first examples of groups with
intermediate growth; that is, he found groups whose growth functions were
neither bounded above by polynomials, nor bounded below by exponential
functions. Grigorchuk's examples were subgroups of the automorphism group of
the infinite rooted binary tree.

In Nekrashevych's 2005 monograph, Self-similar groups, he defined the
{\sl iterated monodromy group} (IMG) of a post-critically finite complex
polynomial. (A polynomial $f$ is {\sl post-critically finite} if the set of
forward iterates $f(f(f(f...(f(c))))$ is finite, for each critical point $c$.)
The iterated monodromy group of a quadratic post-critically finite polynomial
acts on the infinite rooted binary tree, like Grigorchuk's groups.

Bux and Perez showed that the iterated monodromy group of $z^{2} + i$ has
intermediate growth. This gave the first positive evidence for a conjecture
which Bux and Perez attribute to Nekrashevych:

If $p(z) = z^{2} + c$ is a post-critically finite quadratic polynomial and $0$
is not a post-critical point of $p$, then IMG$(p)$ has intermediate growth.

In this talk (or series of talks), I will confirm this conjecture for two more
post-critically finite polynomials. I will make the talks as self-contained as
possible. The results come from undergraduate research in SUMSRI that I supervised
during the summer.

Thursday, October 6, 2011      3:10 pm - Rm 118 BAC

Thursday, September 8, 2011      3:10 pm - Rm 118 BAC
Thursday, September 1, 2011      3:10 pm - Rm 118 BAC
Friday, August 26, 2011      3:10 pm - Rm 118 BAC

Title: How much do discrete subspaces of a space characterize its topology?
Abstract: We will give a cycle of talks on topological properties determined to some
extent by discrete subspaces of a given space. The first property we are going to talk
about is discrete generability which is a convergence property with a flavor of a global one.
A space $X$ is discretely generated if for any $A\subset X$ and any point $x\in \overline A$
there exists a discrete subset $D\subset A$ such that $x\in \overline D$. It is evident that
discretely generated spaces form a class that contains both Frechet-Urysohn spaces and
scattered spaces so discrete generability is a local property with components of a global one.
We will present a survey of both recent and old results on discrete generability; the material
of the respective lectures is supposed to be sufficient to give a reasonably complete view of
the area.

Thursday, September 8, 2011      3:10 pm - Rm 118 BAC

Thursday, September 1, 2011      3:10 pm - Rm 118 BAC

Friday, August 26, 2011      3:10 pm - Rm 118 BAC

Abstract: We will give a cycle of talks on topological properties determined to some
A space $X$ is discretely generated if for any $A\subset X$ and any point $x\in \overline A$
there exists a discrete subset $D\subset A$ such that $x\in \overline D$. It is evident that


text:
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# In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,

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In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

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Updated on: 02 Oct 2018, 05:20
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In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336, what is the perimeter of the triangle?

A. 58
B. 77
C. 82
D. 84
E. 92

Originally posted by arnavrayaca on 02 Oct 2018, 02:51.
Last edited by Bunuel on 02 Oct 2018, 05:20, edited 1 time in total.
Renamed the topic and edited the question.
Director
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Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

### Show Tags

02 Oct 2018, 06:35
arnavrayaca wrote:
In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336, what is the perimeter of the triangle?

A. 58
B. 77
C. 82
D. 84
E. 92

Formula used:- Area of scalene triangle=$$\sqrt{s(s-a)(s-b)(s-c)}$$
Here, a=28, b=30, c=x(say)
$$s=\frac{a+b+c}{2}=29+\frac{x}{2}$$

So, $$(29+\frac{x}{2})(29-\frac{x}{2})(\frac{x}{2}+1)(\frac{x}{2}-1)=336^2$$
Or, $$\left(29^2-\frac{x^2}{4}\right)\left(\frac{x^2}{4}-1\right)=336^2$$
Solving for x, we have x=26.

Hence perimeter=26+28+30=84

Ans. (D)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336, &nbs [#permalink] 02 Oct 2018, 06:35
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text:
# Maclaurin and Taylor series – Edexcel FP2

#### 6. Maclaurin and Taylor series – Edexcel Further Pure Mathematics 2 (FP2)

What students need to learn:
Third and higher order derivatives.

Derivation and use of Maclaurin series.
The derivation of the series expansion of $$e^x , \sin x, \cos x, ln (1 + x)$$ and other simple functions may be required.

Derivation and use of Taylor series.
The derivation, for example, of the expansion of $$\sin x$$ in ascending powers of $$(x − \pi)$$ up to and including the term in $$(x − \pi)^3$$ .

Use of Taylor series method for series solutions of differential equations.
Students may, for example, be required to find the solution in powers of $$x$$ as far as the term in $$x^4$$ , of the differential equation
$$\dfrac{d^2y}{dx^2} + x \dfrac{dy}{dx} + y = 0$$ ,
such that $$y = 1$$, $$\dfrac{dy}{d x} = 0$$ at $$x = 0$$.


text:
# How many commuting nilpotent matrices are there?

To be precise, fix $n$, fix a field $k$.

What is the maximal dimension of a subspace of the vector space of all $n\times n$ matrices formed by commutative nilpotent matrices? By commutative I mean all the products of matrices in this subspace are commutative.

(I feel like this can be formulated in terms of Lie algebras, but I don't find a good one. And I think the down-to-earth formulation might make it more accessible.)

-
Commuting matrices can be simultaneously trigonalized over the algebraic closure. If the matrices are nilpotent, their trigonalizations will be strictly upper triangular (because any nonzero entries on the diagonal would survive taking powers, contradicting the nilpotency). So the maximal dimension is $\frac{n\left(n-1\right)}{2}$. –  darij grinberg Sep 18 '10 at 22:12
I get this point, but upper triangular matrices don't necessarily commute with each other, right? –  Yuhao Huang Sep 18 '10 at 22:25
"Commutative" is not a property of a matrix, but of a set of matrices, so I would rather you state the property you want more precisely. –  Qiaochu Yuan Sep 18 '10 at 22:28
I think the substitution of "commuting" for "commutative" would address Qiaochu's concern. –  Charles Staats Sep 18 '10 at 22:35
Related questions: mathoverflow.net/questions/19591/…, mathoverflow.net/questions/19755/…. It came up there that you can achieve the maximal dimension for a commutative subalgebra, 1 plus the floor of n^2/4, by taking scalars plus 2-by-2 block strictly upper triangular matrices. (Apparently the proof of maximality is due to Schur.) Now you can throw out the multiples of the identity to obtain an example of commuting nilpotents having dimension the floor of n^2/4. –  Jonas Meyer Sep 19 '10 at 0:28

Try the matrices of the form ${0A\choose 00}$ with A an m by n block (with |m-n|≤1 for maximal dimension).
A book "Commutative Matrices", Acad. Press, 1968 by Suprunenko and Tyshkevich (translation from Russian) is devoted, largely, to this question. My cursory look at it tells that the problem seems to be complicated - there are only partial results for small $n$ and particular classes of algebras, expressed in terms of some cumbersome-looking invariants.


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HCS 230 Communication Opinion Paper

# HCS 230 Communication Opinion Paper

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HCS 230 Communication Opinion Paper

****ESSAY EXCERPT*****

Communication takes place when one person transmits ideas and or feelings to another person or group. The process of communication is broken down into three elements the first one would be the source, this is the sender, the speaker, the transmitter, and the instructor. The symbols used in composing and transmitting the message, this includes words or signs. The last would be the receiver; this includes the listener, the reader, and the student. The source I communication is the sender, speaker, transmitter, or the instructor. Communication can be achieved through symbols, which are visual and oral codes. The receiver is the listener, reader, or the student. Some of the barriers to effective communication include the lack of common experience, the confusion between the symbol and the symbolized object, the overuse of abstracts, and the interference. The lack of common experience is the biggest issue when it comes to effective communication. Confusion between the symbol and the symbolized object is when one word is confused with what is really represented. The overuse of abstractions, are words that are more general then specific. Interference is made up of factors that are outside the direct control of the instructor.

Write a 700- to 1,050-word paper on health care communication.

How does effective communication incorporate the basic elements of communication?

How do the basic elements of effective communication differ from the basic rules of health care communication?

How might a provider encourage a reluctant consumer to communicate candidly?

How might cultural differences influence communication?

Cite a minimum of two sources, one from the University Library and the other from the course textbooks or Electronic Reserve Readings, to support your opinion.

HCS 230
SubjectWiz

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#### Oh Snap! This Answer is Locked

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Excerpt from file: HCS 230 Communication Opinion Paper Write a 700- to 1,050-word paper on health care communication. Answer the following questions in your paper: How does effective communication incorporate the basic elements of communication? How do the basic elements of effective communication differ from the

Filename: 11279223.docx

Filesize: < 2 MB

Print Length: 6 Pages/Slides

Words: 607

Surround your text in *italics* or **bold**, to write a math equation use, for example, $x^2+2x+1=0$ or $$\beta^2-1=0$$

Use LaTeX to type formulas and markdown to format text. See example.


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# How can I improve rendering speeds of a Voxel/Minecraft type game?

I'm writing my own clone of Minecraft (also written in Java). It works great right now. With a viewing distance of 40 meters I can easily hit 60 FPS on my MacBook Pro 8,1. (Intel i5 + Intel HD Graphics 3000). But if I put the viewing distance on 70 meters, I only reach 15-25 FPS. In the real Minecraft, I can put the viewing disntance on far (= 256m) without a problem. So my question is what should I do to make my game better?

The optimisations I implemented:

• Only keep local chunks in memory (depending on the player's viewing distance)
• Frustum culling (First on the chunks, then on the blocks)
• Only drawing really visible faces of the blocks
• Using lists per chunk that contain the visible blocks. Chunks that become visible will add itself to this list. If they become invisible, they are automatically removed from this list. Blocks become (in)visible by building or destroying a neighbour block.
• Using lists per chunk that contain the updating blocks. Same mechanism as the visible block lists.
• Use nearly no new statements inside the game loop. (My game runs about 20 seconds until the Garbage Collector is invoked)
• I'm using OpenGL call lists at the moment. (glNewList(), glEndList(), glCallList()) for each side of a kind of block.

Currently I'm even not using any sort of lighting system. I heard already about VBO's. But I don't know exactly what it is. However, I'll do some research about them. Will they improve performance? Before implementing VBO's, I want to try to use glCallLists() and pass a list of call lists. Instead using thousand times glCallList(). (I want to try this, because I think that the real MineCraft doesn't use VBO's. Correct?)

Are there other tricks to improve performance?

VisualVM profiling showed me this (profiling for only 33 frames, with a viewing distance of 70 meters):

Profiling with 40 meters (246 frames):

Note: I'm synchronising a lot of methods and code blocks, because I'm generating chunks in another thread. I think that acquiring a lock for an object is a performance issue when doing this much in a game loop (of course, I'm talking about the time when there is only the game loop and no new chunks are generated). Is this right?

Edit: After removing some synchronised blocks and some other little improvements. The performance is already much better. Here are my new profiling results with 70 meters:

I think it is pretty clear that selectVisibleBlocks is the issue here.

Martijn

Update: After some extra improvements (like using for loops in stead of for each, buffering variables outside loops, etc...), I now can run viewing distance 60 pretty good.

I think I'm going to implement VBO's as soon as possible.

PS: All source code is available on GitHub:
https://github.com/mcourteaux/CraftMania

• Can you give us a profile shot at 40m so we can see what might be scaling up faster than another? – James Jan 19 '12 at 20:39
• Maybe too specified, but if you consider, is just asking techniques of how to speedup a 3D game, sound interesting. But the title may scare ppl. – Gustavo Maciel Jan 19 '12 at 20:45
• @Gtoknu: What do you suggest as title? – Martijn Courteaux Jan 19 '12 at 20:51
• Depending on who you ask, some people would say that Minecraft really isn't that fast, either. – thedaian Jan 19 '12 at 20:51
• I think something like "Which techniques can speed up a 3D game" should be a lot better. Think of something, but try not to use the word "best" or try to compare to some other game. We can't tell exactly what they use on some games. – Gustavo Maciel Jan 19 '12 at 21:04

You mention doing frustum culling on individual blocks — try throwing that out. Most rendering chunks should be either entirely visible or entirely invisible.

Minecraft only rebuilds a display list/vertex buffer (I don't know which it uses) when a block is modified in a given chunk, and so do I. If you're modifying the display list whenever the view changes, you're not getting the benefit of display lists.

Also, you appear to be using world-height chunks. Note that Minecraft uses cubical 16×16×16 chunks for its display lists, unlike for load and save. If you do that, there's even less reason to frustum cull individual chunks.

(Note: I have not examined the code of Minecraft. All of this information is either hearsay or my own conclusions from observing Minecraft's rendering as I play.)

Remember that your rendering executes on two processors: CPU and GPU. When your frame rate is insufficient, then one or the other is the limiting resource — your program is either CPU-bound or GPU-bound (assuming it isn't swapping or having scheduling problems).

If your program is running at 100% CPU (and doesn't have an unbounded other task to complete), then your CPU is doing too much work. You should try to simplify its task (e.g. do less culling) in exchange for having the GPU do more. I strongly suspect this is your problem, given your description.

On the other hand, if the GPU is the limit (sadly, there aren't usually convenient 0%-100% load monitors) then you should think about how to send it less data, or require it to fill fewer pixels.

• Great reference, your research on it mentioned on your wiki was very helpful to me! +1 – Gustavo Maciel Apr 17 '12 at 5:47
• @OP: only render visible faces (not blocks). A pathological but monotonic 16x16x16 chunk will have nearly 800 visible faces, while the contained blocks will have 24,000 visible faces. Once you've done that, Kevin's answer contains the next most important improvements. – AndrewS Jul 29 '14 at 17:54
• @KevinReid There are some programs to help with performance debugging. AMD GPU PerfStudio for example tells you if its CPU or GPU bound and on GPU what component is the bound(texture vs fragment vs vertex, etc) And I am sure Nvidia has something similar too. – akaltar Jul 7 '15 at 10:02

What's calling Vec3f.set so much? If you're building what you want to render from scratch each frame then that's definitely where you'd want to start to speed it up. I'm not much of an OpenGL user and I don't know much about how Minecraft renders, but it seems that the math functions you using are killing you right now (just look how much time you spend in them and the number of times they get called - death by a thousand cuts calling them).

Ideally your world would be segmented up such that you can group stuff to render together, building Vertex Buffer Objects and re-using them across multiple frames. You'd only need to modify a VBO if the world it represents changes somehow (like the user edits it). You can then create/destroy VBO's for what you're representing as it comes into range of being visible to keep memory consumption down, you'd only take the hit as the VBO was created rather than every frame.

If the "invocation" count is correct in your profile, you're calling an awful lot of things an awful lot of times. (10 million calls to Vec3f.set... ouch!)

• I use this method for tons of things. It simply sets the three values for the vector. This is much better than allocating each time a new object. – Martijn Courteaux Jan 19 '12 at 22:07

My description (from my own experimentation) here is applicable:

For voxel rendering, what is more efficient: pre-made VBO or a geometry shader?

Minecraft and your code likely uses the fixed function pipeline; my own efforts have been with GLSL but the gist is generally applicable, I feel:

(From memory) I made a frustum that was a half-block bigger than the screen frustum. I then tested the center-points of each chunk (minecraft has 16*16*128 blocks).

The faces in each has spans in an element-array VBO (many faces from chunks share the same VBO until it is 'full'; think like malloc; those with the same texture in the same VBO where possible) and the vertex indices for the north faces, south faces and so on are adjacent rather than mixed. When I draw, I do a glDrawRangeElements for the north faces, with the normal already projected and normalized, in a uniform. Then I do the south faces and so on, so the normals are not in any VBO. For each chunk, I only have to emit the faces that will be visible - only those in the center of the screen need to draw left and right sides, for example; this is simple GL_CULL_FACE at an application level.

The biggest speedup, iirc, was culling interior faces when polygonizing each chunk.

Also important is texture-atlas management and sorting faces by texture and putting the faces with the same texture in the same vbo as those from other chunks. You want to avoid too many texture changes and sorting the faces by texture and so on minimizes the number of spans in the glDrawRangeElements. Merging adjacent same-tile faces into bigger rectangles was also a big deal. I talk about merging in the other answer cited above.

Obviously you only polygonize those chunks that have ever been visible, you may discard those chunks that haven't been visible for a long time, and you re-polygonize chunks that are edited (as this is a rare occurrence compared to rendering them).

• I like the idea of your frustum optimisation. But aren't you mixing up the terms "block" and "chunk" in your explanation? – Martijn Courteaux Jan 20 '12 at 22:55
• probably yes. A chunk of blocks is a block of blocks in English. – Will Jan 21 '12 at 15:02

Where are all your comparisons (BlockDistanceComparator) coming from? If it's from a sort function, could that be replaced with a radix sort (which is asymptotically faster, and not comparison based)?

Looking at your timings, even if the sorting itself isn't that bad, your relativeToOrigin function is being called twice for each compare function; all of that data should be computed once. It should be faster to sort an auxiliary structure e.g.

struct DistanceIndexPair
{
float m_distanceSquaredFromOrigin;
int m_index;
};

and then in pseudoCode

// for i = 0..numBlocks
//     distanceIndexPairs[i].m_distanceSquaredFromOrigin = ...;
///    distanceIndexPairs[i].m_index = i;
// sort distanceIndexPairs
// for i = 0..numBlocks
//    sortedBlock[i] = unsortedBlocks[ distanceIndexPairs.m_index ]

Sorry if that's not a valid Java struct (I haven't touched Java since undergrad) but hopefully you get the idea.

• I find this amusing. Java doesn't have structs. Well, there is something called like that in the Java world but it has to do with databases, not the same thing at all. They can create a final class with public members, I guess that works. – Theraot May 18 '17 at 11:32

Yeah use VBOs and CULL facing, but that goes for pretty much every game. What you want to do is only render the cube if it is visible to the player, AND if the blocks are touching in a specific way (let's say a chunk that you cannot see because it's underground) you add the vertices of the blocks and make it almost like a "bigger block", or in your case- a chunk. This is called greedy meshing and it drastically increases performance. I am developing a game (voxel-based) and it uses a greedy meshing algorithm.

Instead of rendering everything like this:

It renders it like this:

The downside to this is that you have to do more calculations per chunk on the initial world build, or if the player removes/adds a block.

## pretty much any type of voxel engine needs this for good performance.

What it does is checks to see if the block face is touching another block face, and if so: only render as one (or zero) block face(s). It is an expensive touch when you are rendering chunks really fast.

public void greedyMesh(int p, BlockData[][][] blockData){

for(int side=0; side<6; side++){
for(int x=0; x<blockData.length; x++){
for(int y=0; y<blockData[0].length; y++){
for(int z=0; z<blockData[0][0].length; z++){
if(data[x][y][z] > Material.AIR && !mask[x][y][z][side] && blockData[x][y][z].faces[side]){
if(side == 0 || side == 1){
int width = 0;
int height = 0;
loop:
for(int i=y; i<blockData[0].length; i++){
if(i == y){
for(int j=z; j<blockData[0][0].length; j++){
if(!mask[x][i][j][side] && blockData[x][i][j].id == blockData[x][y][z].id && blockData[x][i][j].faces[side]){
width++;
}else{
break;
}
}
}else{
for(int j=0; j<width; j++){
if(mask[x][i][z+j][side] || blockData[x][i][z+j].id != blockData[x][y][z].id || !blockData[x][i][z+j].faces[side]){
break loop;
}
}
}
height++;
}
for(int i=0; i<height; i++){
for(int j=0; j<width; j++){
}
}

if(side == 0)
meshes.get(p).add(new Mesh(new VoxelVector3i(x+1, y, z), new VoxelVector3i(x+1, y+height, z+width), new VoxelVector3i(1, 0, 0), Material.getColor(data[x][y][z])));
else
meshes.get(p).add(new Mesh(new VoxelVector3i(x, y, z+width), new VoxelVector3i(x, y+height, z), new VoxelVector3i(-1, 0, 0), Material.getColor(data[x][y][z])));
}else if(side == 2 || side == 3){
int width = 0;
int height = 0;
loop:
for(int i=x; i<blockData.length; i++){
if(i == x){
for(int j=z; j<blockData[0][0].length; j++){
if(!mask[i][y][j][side] && blockData[i][y][j].id == blockData[x][y][z].id && blockData[i][y][j].faces[side]){
width++;
}else{
break;
}
}
}else{
for(int j=0; j<width; j++){
if(mask[i][y][z+j][side] || blockData[i][y][z+j].id != blockData[x][y][z].id || !blockData[i][y][z+j].faces[side]){
break loop;
}
}
}
height++;
}
for(int i=0; i<height; i++){
for(int j=0; j<width; j++){
}
}

if(side == 2)
meshes.get(p).add(new Mesh(new VoxelVector3i(x, y+1, z+width), new VoxelVector3i(x+height, y+1, z), new VoxelVector3i(0, 1, 0), Material.getColor(data[x][y][z])));
else
meshes.get(p).add(new Mesh(new VoxelVector3i(x+height, y, z+width), new VoxelVector3i(x, y, z), new VoxelVector3i(0, -1, 0), Material.getColor(data[x][y][z])));
}else if(side == 4 || side == 5){
int width = 0;
int height = 0;
loop:
for(int i=x; i<blockData.length; i++){
if(i == x){
for(int j=y; j<blockData[0].length; j++){
if(!mask[i][j][z][side] && blockData[i][j][z].id == blockData[x][y][z].id && blockData[i][j][z].faces[side]){
width++;
}else{
break;
}
}
}else{
for(int j=0; j<width; j++){
if(mask[i][y+j][z][side] || blockData[i][y+j][z].id != blockData[x][y][z].id || !blockData[i][y+j][z].faces[side]){
break loop;
}
}
}
height++;
}
for(int i=0; i<height; i++){
for(int j=0; j<width; j++){
}
}

if(side == 4)
meshes.get(p).add(new Mesh(new VoxelVector3i(x+height, y, z+1), new VoxelVector3i(x, y+width, z+1), new VoxelVector3i(0, 0, 1), Material.getColor(data[x][y][z])));
else
meshes.get(p).add(new Mesh(new VoxelVector3i(x, y, z), new VoxelVector3i(x+height, y+width, z), new VoxelVector3i(0, 0, -1), Material.getColor(data[x][y][z])));
}
}
}
}
}
}
}

• And is it worth it? It seems like an LOD system would be more appropriate. – MichaelHouse Jun 5 '17 at 22:45

It would seem that your code is drowning in objects and function calls. Gauging the numbers, it doesn't seem like there is any in-lining happening.

You could try to find a different Java environment, or simply mess with the settings of the one you have, but a plain and simple way of making your code, not fast, but a good deal less slow is at least internally in Vec3f to stop coding OOO*. Make every method self containing, don't call any of the other methods just to perform some menial task.

Edit: While there is overhead all over the place it would seem that ordering the blocks before rendering is the worst performance eater. Is that really necessary? If so you should probably start out by going through a loop and calculate each blocks distance to origin, and then sort by that.

*Overly Object Oriented

• Yep, you'll save memory, but lose CPU! So OOO is not too good in realtime games. – Gustavo Maciel Jan 20 '12 at 0:00
• As soon as you start profiling (and not just sampling), any inlining that the JVM normally does vanishes. It's kind of like quantum theory, can't measure something without chaning the outcome :p – Michael Jan 20 '12 at 0:28
• @Gtoknu That is not universally true, at some level of OOO the function calls start to take up more memory than inline code would. I'd say there is a good part of the code in question that is around the break even point for memory. – aaaaaaaaaaaa Jan 20 '12 at 0:36

You could also try to break down Math operations down to bitwise operators. If you have 128 / 16, try to make a bitwise operator: 128 << 4. This will help a lot with your problems. Don't try to make things run at full speed. Make your game update at a rate of 60 or something, and even break that down for other things, but you would have to do destroying and or placing voxels or you would have to make a todo-list, which would bring down your fps. You could do an update rate of about 20 for entities. And something like 10 for world updates and or generation.


text:
location:  Publications → journals
Search results

Search: MSC category 15 ( Linear and multilinear algebra; matrix theory )

 Expand all        Collapse all Results 26 - 37 of 37

26. CJM 2003 (vol 55 pp. 1000)

Graczyk, P.; Sawyer, P.
 Some Convexity Results for the Cartan Decomposition In this paper, we consider the set $\mathcal{S} = a(e^X K e^Y)$ where $a(g)$ is the abelian part in the Cartan decomposition of $g$. This is exactly the support of the measure intervening in the product formula for the spherical functions on symmetric spaces of noncompact type. We give a simple description of that support in the case of $\SL(3,\mathbf{F})$ where $\mathbf{F} = \mathbf{R}$, $\mathbf{C}$ or $\mathbf{H}$. In particular, we show that $\mathcal{S}$ is convex. We also give an application of our result to the description of singular values of a product of two arbitrary matrices with prescribed singular values. Keywords:convexity theorems, Cartan decomposition, spherical functions, product formula, semisimple Lie groups, singular valuesCategories:43A90, 53C35, 15A18

27. CJM 2003 (vol 55 pp. 91)

Choi, Man-Duen; Li, Chi-Kwong; Poon, Yiu-Tung
 Some Convexity Features Associated with Unitary Orbits Let $\mathcal{H}_n$ be the real linear space of $n\times n$ complex Hermitian matrices. The unitary (similarity) orbit $\mathcal{U} (C)$ of $C \in \mathcal{H}_n$ is the collection of all matrices unitarily similar to $C$. We characterize those $C \in \mathcal{H}_n$ such that every matrix in the convex hull of $\mathcal{U}(C)$ can be written as the average of two matrices in $\mathcal{U}(C)$. The result is used to study spectral properties of submatrices of matrices in $\mathcal{U}(C)$, the convexity of images of $\mathcal{U} (C)$ under linear transformations, and some related questions concerning the joint $C$-numerical range of Hermitian matrices. Analogous results on real symmetric matrices are also discussed. Keywords:Hermitian matrix, unitary orbit, eigenvalue, joint numerical rangeCategories:15A60, 15A42

28. CJM 2002 (vol 54 pp. 571)

Li, Chi-Kwong; Poon, Yiu-Tung
 Diagonals and Partial Diagonals of Sum of Matrices Given a matrix $A$, let $\mathcal{O}(A)$ denote the orbit of $A$ under a certain group action such as \begin{enumerate}[(4)] \item[(1)] $U(m) \otimes U(n)$ acting on $m \times n$ complex matrices $A$ by $(U,V)*A = UAV^t$, \item[(2)] $O(m) \otimes O(n)$ or $\SO(m) \otimes \SO(n)$ acting on $m \times n$ real matrices $A$ by $(U,V)*A = UAV^t$, \item[(3)] $U(n)$ acting on $n \times n$ complex symmetric or skew-symmetric matrices $A$ by $U*A = UAU^t$, \item[(4)] $O(n)$ or $\SO(n)$ acting on $n \times n$ real symmetric or skew-symmetric matrices $A$ by $U*A = UAU^t$. \end{enumerate} Denote by $$\mathcal{O}(A_1,\dots,A_k) = \{X_1 + \cdots + X_k : X_i \in \mathcal{O}(A_i), i = 1,\dots,k\}$$ the joint orbit of the matrices $A_1,\dots,A_k$. We study the set of diagonals or partial diagonals of matrices in $\mathcal{O}(A_1,\dots,A_k)$, {\it i.e.}, the set of vectors $(d_1,\dots,d_r)$ whose entries lie in the $(1,j_1),\dots,(r,j_r)$ positions of a matrix in $\mathcal{O}(A_1, \dots,A_k)$ for some distinct column indices $j_1,\dots,j_r$. In many cases, complete description of these sets is given in terms of the inequalities involving the singular values of $A_1,\dots,A_k$. We also characterize those extreme matrices for which the equality cases hold. Furthermore, some convexity properties of the joint orbits are considered. These extend many classical results on matrix inequalities, and answer some questions by Miranda. Related results on the joint orbit $\mathcal{O}(A_1,\dots,A_k)$ of complex Hermitian matrices under the action of unitary similarities are also discussed. Keywords:orbit, group actions, unitary, orthogonal, Hermitian, (skew-)symmetric matrices, diagonal, singular valuesCategories:15A42, 15A18

29. CJM 2001 (vol 53 pp. 758)

Goulden, I. P.; Jackson, D. M.; Latour, F. G.
 Inequivalent Transitive Factorizations into Transpositions The question of counting minimal factorizations of permutations into transpositions that act transitively on a set has been studied extensively in the geometrical setting of ramified coverings of the sphere and in the algebraic setting of symmetric functions. It is natural, however, from a combinatorial point of view to ask how such results are affected by counting up to equivalence of factorizations, where two factorizations are equivalent if they differ only by the interchange of adjacent factors that commute. We obtain an explicit and elegant result for the number of such factorizations of permutations with precisely two factors. The approach used is a combinatorial one that rests on two constructions. We believe that this approach, and the combinatorial primitives that have been developed for the cut and join'' analysis, will also assist with the general case. Keywords:transitive, transposition, factorization, commutation, cut-and-joinCategories:05C38, 15A15, 05A15, 15A18

30. CJM 2001 (vol 53 pp. 470)

Bauschke, Heinz H.; Güler, Osman; Lewis, Adrian S.; Sendov, Hristo S.
 Hyperbolic Polynomials and Convex Analysis A homogeneous real polynomial $p$ is {\em hyperbolic} with respect to a given vector $d$ if the univariate polynomial $t \mapsto p(x-td)$ has all real roots for all vectors $x$. Motivated by partial differential equations, G{\aa}rding proved in 1951 that the largest such root is a convex function of $x$, and showed various ways of constructing new hyperbolic polynomials. We present a powerful new such construction, and use it to generalize G{\aa}rding's result to arbitrary symmetric functions of the roots. Many classical and recent inequalities follow easily. We develop various convex-analytic tools for such symmetric functions, of interest in interior-point methods for optimization problems over related cones. Keywords:convex analysis, eigenvalue, G{\aa}rding's inequality, hyperbolic barrier function, hyperbolic polynomial, hyperbolicity cone, interior-point method, semidefinite program, singular value, symmetric functionCategories:90C25, 15A45, 52A41

31. CJM 2000 (vol 52 pp. 141)

Li, Chi-Kwong; Tam, Tin-Yau
 Numerical Ranges Arising from Simple Lie Algebras A unified formulation is given to various generalizations of the classical numerical range including the $c$-numerical range, congruence numerical range, $q$-numerical range and von Neumann range. Attention is given to those cases having connections with classical simple real Lie algebras. Convexity and inclusion relation involving those generalized numerical ranges are investigated. The underlying geometry is emphasized. Keywords:numerical range, convexity, inclusion relationCategories:15A60, 17B20

32. CJM 2000 (vol 52 pp. 197)

 Sublinearity and Other Spectral Conditions on a Semigroup Subadditivity, sublinearity, submultiplicativity, and other conditions are considered for spectra of pairs of operators on a Hilbert space. Sublinearity, for example, is a weakening of the well-known property~$L$ and means $\sigma(A+\lambda B) \subseteq \sigma(A) + \lambda \sigma(B)$ for all scalars $\lambda$. The effect of these conditions is examined on commutativity, reducibility, and triangularizability of multiplicative semigroups of operators. A sample result is that sublinearity of spectra implies simultaneous triangularizability for a semigroup of compact operators. Categories:47A15, 47D03, 15A30, 20A20, 47A10, 47B10

33. CJM 1999 (vol 51 pp. 506)

Elduque, A.; Iltyakov, A. V.
 On Polynomial Invariants of Exceptional Simple Algebraic Groups We study polynomial invariants of systems of vectors with respect to exceptional simple algebraic groups in their minimal linear representations. For each type we prove that the algebra of invariants is integral over the subalgebra of trace polynomials for a suitable algebraic system (\cf\ \cite{Schw1}, \cite{Schw2}, \cite{Ilt}). Categories:15A72, 17C20

34. CJM 1998 (vol 50 pp. 1323)

Morales, Jorge
 L'invariant de Hasse-Witt de la forme de Killing Nous montrons que l'invariant de Hasse-Witt de la forme de Killing d'une alg{\e}bre de Lie semi-simple $L$ s'exprime {\a} l'aide de l'invariant de Tits de la repr{\'e}sentation irr{\'e}ductible de $L$ de poids dominant $\rho=\frac{1}{2}$ (somme des racines positives), et des invariants associ{\'e}s au groupe des sym{\'e}tries du diagramme de Dynkin de $L$. Categories:11E04, 11E72, 17B10, 17B20, 11E88, 15A66

35. CJM 1998 (vol 50 pp. 929)

Broer, Abraham
 Decomposition varieties in semisimple Lie algebras The notion of decompositon class in a semisimple Lie algebra is a common generalization of nilpotent orbits and the set of regular semisimple elements. We prove that the closure of a decomposition class has many properties in common with nilpotent varieties, \eg, its normalization has rational singularities. The famous Grothendieck simultaneous resolution is related to the decomposition class of regular semisimple elements. We study the properties of the analogous commutative diagrams associated to an arbitrary decomposition class. Categories:14L30, 14M17, 15A30, 17B45

36. CJM 1997 (vol 49 pp. 865)

Goulden, I. P.; Jackson, D. M.
 Maps in locally orientable surfaces and integrals over real symmetric surfaces The genus series for maps is the generating series for the number of rooted maps with a given number of vertices and faces of each degree, and a given number of edges. It captures topological information about surfaces, and appears in questions arising in statistical mechanics, topology, group rings, and certain aspects of free probability theory. An expression has been given previously for the genus series for maps in locally orientable surfaces in terms of zonal polynomials. The purpose of this paper is to derive an integral representation for the genus series. We then show how this can be used in conjunction with integration techniques to determine the genus series for monopoles in locally orientable surfaces. This complements the analogous result for monopoles in orientable surfaces previously obtained by Harer and Zagier. A conjecture, subsequently proved by Okounkov, is given for the evaluation of an expectation operator acting on the Jack symmetric function. It specialises to known results for Schur functions and zonal polynomials. Categories:05C30, 05A15, 05E05, 15A52

37. CJM 1997 (vol 49 pp. 840)

Rodman, Leiba
 Non-Hermitian solutions of algebraic Riccati equation Non-hermitian solutions of algebraic matrix Riccati equations (of the continuous and discrete types) are studied. Existence is proved of non-hermitian solutions with given upper bounds of the ranks of the skew-hermitian parts, under the sign controllability hypothesis. Categories:15A99, 15A63, 93C60
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text:
# Confusing NullSpace Method behaviour

The background of this question is that I'm trying to get the bottom of when the output of NullSpace outputs a list of pairwise orthogonal vectors. On my route to answering this question, I came upon the following weirdness:

The documentation of NullSpace makes the claim (M10)

Possible settings for the Method option include "CofactorExpansion", "DivisionFreeRowReduction", and "OneStepRowReduction". The default setting of Automatic switches among these methods depending on the matrix given.

but the example which follows seems to demonstrate that this is at least partially false.

First, we make functions that output matrices with null spaces of specified dimensions, just by changing the basis of some trivial projectors:

randMat[dim_,dimNull_] := With[{A=RandomReal[{-1,1},{dim,dim}]}, A.DiagonalMatrix[Array[If[#>dimNull,1,0]&,dim]].Inverse[A]]
randIntMat[dim_,dimNull_] := With[{A=RandomInteger[{-1,1},{dim,dim}]}, A.DiagonalMatrix[Array[If[#>dimNull,1,0]&,dim]].Inverse[A]]

Next, we try NullSpace with all four method options, and output the pairwise dot product of the resulting null space vectors in each case:

MatrixForm /@ Chop /@ Module[{mat = randMat[5, 3]},
With[{null = NullSpace[mat, Method -> #]},
Outer[#1.#2 &, null, null, 1]] & /@ {"CofactorExpansion",
"DivisionFreeRowReduction", "OneStepRowReduction", Automatic}
]

In the case of the RandomReal random matrix version, we get answers like

$$\left\{\{\},\left( \begin{array}{ccc} 6.48185 & 1.67163 & 4.27561 \\ 1.67163 & 4.29849 & 0.35762 \\ 4.27561 & 0.35762 & 4.65582 \\ \end{array} \right),\left( \begin{array}{ccc} 6.48185 & 1.67163 & 4.27561 \\ 1.67163 & 4.29849 & 0.35762 \\ 4.27561 & 0.35762 & 4.65582 \\ \end{array} \right),\left( \begin{array}{ccc} 1. & 0 & 0 \\ 0 & 1. & 0 \\ 0 & 0 & 1. \\ \end{array} \right)\right\}$$

In the case of the RandomInteger random matrix, we get answers like

$$\left\{ \left( \begin{array}{ccc} 2 & 0 & -1 \\ 0 & 2 & -1 \\ -1 & -1 & 3 \\ \end{array} \right),\left( \begin{array}{ccc} 2 & 0 & -1 \\ 0 & 2 & -1 \\ -1 & -1 & 3 \\ \end{array} \right),\left( \begin{array}{ccc} 2 & 0 & -1 \\ 0 & 2 & -1 \\ -1 & -1 & 3 \\ \end{array} \right),\left( \begin{array}{ccc} 2 & 0 & -1 \\ 0 & 2 & -1 \\ -1 & -1 & 3 \\ \end{array} \right) \right\}$$

And if we call N on the integer matrix before invoking NullSpace, we get answers like

$$\left\{\{\},\left( \begin{array}{ccc} 1.55556 & 0.222222 & 0.444444 \\ 0.222222 & 1.88889 & -0.222222 \\ 0.444444 & -0.222222 & 1.55556 \\ \end{array} \right),\left( \begin{array}{ccc} 1.55556 & 0.222222 & 0.444444 \\ 0.222222 & 1.88889 & -0.222222 \\ 0.444444 & -0.222222 & 1.55556 \\ \end{array} \right),\left( \begin{array}{ccc} 1. & 0 & 0 \\ 0 & 1. & 0 \\ 0 & 0 & 1. \\ \end{array} \right)\right\}$$

So clearly in the _Real case, Automatic is doing something different than simply choosing one of the other three options. Most likely it is choosing one of the three and then orthonormalizing the result? Does anyone know what's actually going on here? Thanks!

• The documentation is really not correct for matrices of approximate numbers. In those cases Automatic will use a method based on SVD. This will give orthonormal vectors since the nulls come from vectors in an orthogonal matrix produced by SVD. – Daniel Lichtblau Jan 21 '15 at 20:27
• @DanielLichtblau That makes sense, I guess, based on how stable SVD algorithms are. Is this a guess on your part? – Ian Hincks Jan 21 '15 at 20:39
• No, not a guess. – Daniel Lichtblau Jan 21 '15 at 21:46


text:
# Dependent Types for Extensive Games

Abstract : Extensive games are tools largely used in economics to describe decision processes of a community of agents. In this paper we propose a formal presentation based on the proof assistant COQ which focuses mostly on infinite extensive games and their characteristics. COQ proposes a feature called dependent types'', which means that the type of an object may depend on the type of its components. For instance, the set of choices or the set of utilities of an agent may depend on the agent herself. Using dependent types, we describe formally a very general class of games and strategy profiles, which corresponds somewhat to what game theorists are used to. We also discuss the notions of infiniteness in game theory and how this can be precisely described.
Keywords :
Document type :
Preprints, Working Papers, ...
Domain :

https://hal-ens-lyon.archives-ouvertes.fr/ensl-01391418
Contributor : Pierre Lescanne <>
Submitted on : Tuesday, December 5, 2017 - 10:11:12 AM
Last modification on : Friday, February 8, 2019 - 9:33:19 AM

### Files

dependentTypesForGames.pdf
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### Identifiers

• HAL Id : ensl-01391418, version 3
• ARXIV : 1611.06101

### Citation

Pierre Lescanne. Dependent Types for Extensive Games. 2016. ⟨ensl-01391418v3⟩

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text:
# Thread: Solving a DE by method of variation of parameters

1. ## Solving a DE by method of variation of parameters

I have found the general solution for the equation of $y'' - 9y = (x+1) e^{-x}$ to be

$y(x) = A e^{3x} + B e^{-3x} - \frac{1}{8} e^{-x} x - \frac{3 e^{-x}}{32}$

by the method of undetermined coefficients.

However I need to use the method of variation of parameters, but I am totally confused.

I have the homogeneous equation as: $y_{h} = A e^{3x} + B e^{-3x}$ and so $y_{p} = A(x) e^{3x} + B(x) e^{-3x}$
and
$A'(x) e^{3x} + B'(x) e^{-3x} = 0$
$3A'(x) e^{3x} - 3B'(x) e^{-3x} = (x+1) e^{-x}$

But where do I go now? Can anyone help me with the steps to solve this?

Thank you all in advance.

2. ## Re: Solving a DE by method of variation of parameters

Try multiplying the first equation by 3, then adding the two equations, as this will eliminate $B'(x)e^{-3x}$.


text:
# Regression approximation for the rate of change in occupancy rate of residential market with respect to price

I have historical data on occupancy rates for a given neighborhood, along with characteristics and other local economic variables.

I am looking to estimate the regression equation with occupancy rates as dependent variable and price, level of supply, characteristics and economic vars as independent variables.

D(p) = Rent + Median Income + Supply + # of HH

• Median Income is time fixed effect.

My questions are:

1. How do you interpret the equilibrium price from the regression output? i.e price at which Occupancy rate is 100%. or price elasticity of demand.
2. Interaction term. Given that supply follows rental prices, add supply * rent as interaction term.
3. What other regression methods would make sense for this problem?

## 1 Answer

If the goal of the project is to model housing demand, I would suggest using the actual number of occupied housing units. Census data may calculate occupancy as an algebraic function of supply, that is, occupancy is derived using the supply variable. This may show up as a strong correlation in the model, but it doesn't capture the stochastic properties of housing demand.

1. If you are interested in the price elasticity of housing, just use a log-log regression. Here is a good post about equilibrium price.

2. What is the level of analysis? If you have panel data (historical data for $$n$$ neighborhoods), I would suggest looking into spatial regression.

For a given neighborhood $$x$$, the occupancy rate of the surrounding neighborhoods may affect demand for housing (the negative affects of vacancy "spill over" into $$x$$). Another example, if rent is high in the neighborhoods surrounding $$x$$,a shift in the demand for housing will occur, because people are making a spatial decision regarding where they will live and take into account the housing characteristics of the neighborhoods of a given area. Therefore, to model housing demand, the occupancy rate and independent variables of surrounding neighborhoods may capture the process of housing demand in $$x$$.

This is refereed to as spatial dependence and it can affect the model a lot. I would recommend the software Geoda and GeodaSpace to analyze and run spatial regression models.

• I like the idea of spatial regression. Are there any relevant links, papers you can share? – kms Aug 17 '20 at 5:03
• Anselin, Rey. (2014). Modern Spatial Econometrics in Practice: A Guide to GeoDa, GeoDaSpace and PySAL. That book is a mixture of statistics theory and also serves as a usuer manual for the open source software Geoda, GeodaSpace, and Pysal (a Python package). If you are interested in the heavier statistics theory I would recommend Anselin. (1988). Spatial Econometrics: Methods and Models. It basically laid the foundation for modern spatial econometrics. – Andrew Aug 17 '20 at 9:26