To the Times:
No one is pointing a finger at poor curricula, particularly in math. PA Coalition for Mainstream Math, NYC HOLD, and Haverford High School Students and Parents for Traditional Math Choice have been voicing their concerns for years. School districts with the greatest success at the fifth, eighth and 11th-grade level are using traditional curricula.
Can you imagine how much money would be saved in public education if only curricula with proven track records of success were used? Can you imagine how many more of our children would succeed if they were being taught with what works for the most amounts of students? All districts should be looking at the top districts -- Unionville, Tredyffrin-Easttown, Downingtown Area.
Haverford High School replaced Integrated Math (controversial reform program) with College Preparatory Math (CPM) the most controversial reform program in 2007/2008. 2011/2012 PSSA scores reflect the first test year of full immersion in the program ninth-11th grade. Students were told and guidelines were put in place that if one did not test proficient or advanced on their 11th-grade PSSA they must be enrolled in remedial math to graduate. Larry Feinberg (video news PSSA) referred to this as a successful measure for students to take the test seriously. Thirty-point-two percent of the 414 present seniors at Haverford tested basic or below basic. That would mean 125 students, should be taking remedial math this year. Haverford High School will never make AYP. Students, parents, money, and teachers are not the problem. Many failing schools are using poor curricula. CPM has no proven track record of success (significantly raised standardized test scores) anywhere.
In 2007/2008 with the poor (per Rotoli/Brown) Integrated Math Curriculum, 11th-grade math scores: Advanced 40.2 percent proficient 31.5 percent basic 16.4 percent below basic 11.9- percent. In 2011/2012 with (endorsed by the NCTM, "exemplary" repeated multiple times in many meetings) CPM math curriculum -11th-grade math scores: advanced 43.5 percent proficient 26.3 percent basic 12.6 percent below basic 17.6 percent.
A visit to an Algebra I classroom in CPM would blow your mind. Students discover math in groups, versus being taught. A peek at Algebra I Connections, Volume 1, one of the useless texts that accompanies this course, would be the stamp to send your children directly to private, charter, cyber -- anywhere but Haverford. The language, examples and math that are on the PSSA, PSAT, Keystone and SAT are not there. You do not need to be a rocket scientist or professor at Bryn Mawr to see this.
Parents of Haverford High School students can not be held accountable. They have to leap through fire to get a test home. There is no transparency.
Our district used Twin Valley High School's (Elverson) track record of success with CPM to select this program. What do you think? Would you want this for your children or should you get a voucher? Our district's superintendent uses district success as a whole to spin doctor poor performance of our high school "keep the eye on the prize" Haverford Patch. This is not fair to our students who, were as a whole, high achievers in elementary school and crash by 11th grade due to poor curricula.


Hi, my name is Bethany Fetrow. Currently, I am teaching Algebra I & Honors Algebra 2. This is my 9th year teaching, and my 6th year at Marlington High School. I graduated from Marlington High School in 2008 and Kent State University in 2012.
I am married to Nathan Fetrow. We have 3 children Adalynn, Ava, & Asher. Please feel free to contact me at any time during the school year!


Adaptive FEM Discretization in Solving PDE-based Optimization Problems
We address the basics and recent developments of "goal-oriented" adaptivity by the Dual Weighted Residual (DWR) method for the solution of PDE-based optimization problems. By the Lagrangian formalism the optimization problem is reformulated as a saddle-point boundary value problem (KKT system) that is discretized by a Galerkin finite element method. The accuracy of the discretization is controlled by residual-based a posteriori error estimates which contain primal and dual cell-residuals and associated sensitivity factors. The resulting local error indicators then assist the construction of economical meshes for evaluating and optimizing the quantities of physical interest. This opens the way towards systematic model reduction in the solution of optimization problems. The main features of this approach will be illustrated by examples from flow control and parameter estimation. Recent developments concern the inclusion of control and state constraints, the treatment of nonstationary optimal control problems, the balancing of discretization and iteration errors, and the adaptive choice of regularization parameters.


Matrix In R - Arithmetic Operations / Addition And Subtraction On Matrices In R
Keep in touch and stay productive with Teams and Officeeven when you're working remotely. Learn how to collaborate with Office Tech support scams are an industry-wide issue where scammers trick you into paying for unnecessary technical support services. You can help protect yourself from scammers by verifying that the contact is a Microsoft Agent or Microsoft Employee and that the phone number is an official Microsoft global customer service number. I am trying to find the difference between an estimated number and the actual number.
The formula pulls that total number into a vlc spices, however the formula isn't working at all and just calculates the total number as 0.
Total of X Actual of X Change between total and actual 0 0. Did this solve your problem? Yes No. Sorry this didn't help. April 14, Keep in touch and stay productive with Teams and Officeeven when you're working remotely. Site Feedback. Tell us about your experience with our site. This thread is locked. You can follow the question or vote as helpful, but you cannot reply to this thread.
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How satisfied are you with this response? This site in other languages x.If you want to get a job as a data scientist, you need to master basic data manipulation operations.
My favorite commands Part3: ‘sweep’ function in R
Ideally, you should be able to write them rapidly, and from memory no looking them up on Google! A very common data manipulation task is manipulating columns of a dataframe. Specifically, you need to know how to add a column to a dataframe.
Adding a column to a dataframe in R is not hard, but there are a few ways to do it. This can make it a little confusing for beginners … you might see several different ways to add a column to a dataframe, and it might not be clear which one you should use.
In my opinion, the best way to add a column to a dataframe in R is with the mutate function from dplyr. This is a minor thing, but little details can make a difference. First, I typically like to avoid capital letters in variable names and dataset names. Now that we have our dataset, let's add a new variable. You'll see here that we're using the mutate function. After we specify the dataframe that we're going to mutate, we specify exactly how we will change it. We are calculating it by dividing the price variable by the sqft variable.
Basically, mutate modifies a dataframe by creating a new variable. That's all that it does. When you call mutate, the first argument is the name of the dataframe that we want to modify. The second argument is a "name value pair. A name and a value. A variable name and a value associated with it. Name value pair. The variable that we create can be relatively simple or complex.We often want to combine values of and perform calculations on rasters to create a new output raster.
This tutorial covers how to subtract one raster from another using basic raster math and the overlay function. It also covers how to extract pixel values from a set of locations - for example a buffer region around plot locations at a field site. You will need the most current version of R and, preferably, RStudio loaded on your computer to complete this tutorial. Download Dataset. Set Working Directory: This lesson assumes that you have set your working directory to the location of the downloaded and unzipped data subsets.
An overview of setting the working directory in R can be found here. If available, the code for challenge solutions is found in the downloadable R script of the entire lesson, available in the footer of each lesson page. We often want to perform calculations on two or more rasters to create a new output raster.
For example, if we are interested in mapping the heights of trees across an entire field site, we might want to calculate the difference between the Digital Surface Model DSM, tops of trees and the Digital Terrain Model DTM, ground level. The resulting dataset is referred to as a Canopy Height Model CHM and represents the actual height of trees, buildings, etc.
We will need the raster package to import and perform raster calculations. We can perform raster calculations by simply subtracting or adding, multiplying, etc two rasters. In the geospatial world, we call this "raster math". Notice that the range of values for the output CHM is between 0 and 30 meters.
Does this make sense for trees in Harvard Forest? It's often a good idea to explore the range of values in a raster dataset just like we might explore a dataset that we collected in the field. However, raster math is a less efficient approach as computation becomes more complex or as file sizes become large. The overlay function is more efficient when:. The overlay function takes two or more rasters and applies a function to them using efficient processing methods. The syntax is. Let's perform the same subtraction calculation that we calculated above using raster math, using the overlay function.
How do the plots of the CHM created with manual raster math and the overlay function compare? Data Tip: A custom function consists of a defined set of commands performed on a input object. Custom functions are particularly useful for tasks that need to be repeated over and over in the code. The writeRaster function by default writes the output file to your working directory unless you specify a full file path.
Data are often more interesting and powerful when we compare them across various locations. Let's compare some data collected over Harvard Forest to data collected in Southern California. Then compare the two sites. This will help you keep track of data from different sites! Skip to main content. Learning Objectives After completing this tutorial, you will be able to: Be able to to perform a subtraction difference between two rasters using raster math.
Know how to perform a more efficient subtraction difference between two rasters using the raster overlay function in R. Install R Packages raster: install. Challenge: Explore CHM Raster Values It's often a good idea to explore the range of values in a raster dataset just like we might explore a dataset that we collected in the field. What is the distribution of all the pixel values in the CHM?We look at some of the basic operations that you can perform on lists of numbers.
It is assumed that you know how to enter data or read data files which is covered in the first chapter, and you know about the basic data types. Once you have a vector or a list of numbers in memory most basic operations are available. Most of the basic operations will act on a whole vector and can be used to quickly perform a large number of calculations with a single command. There is one thing to note, if you perform an operation on more than one vector it is often necessary that the vectors all contain the same number of entries.
First, the vector will contain the numbers 1, 2, 3, and 4. We then see how to add 5 to each of the numbers, subtract 10 from each of the numbers, multiply each number by 4, and divide each number by 5. If you want to take the square root, find e raised to each number, the logarithm, etc. Note that you can do the same operations with vector arguments.Column Subtraction of Whole Numbers
For example to add the elements in vector a to the elements in vector b use the following command:. The operation is performed on an element by element basis. Note this is true for almost all of the basic functions. So you can bring together all kinds of complicated expressions:. You need to be careful of one thing. When you do operations on vectors they are performed on an element by element basis. One ramification of this is that all of the vectors in an expression must be the same length.
If the lengths of the vectors differ then you may get an error message, or worse, a warning message and unpredictable results:. As you work in R and create new vectors it can be easy to lose track of what variables you have defined. To get a list of all of the variables that have been defined use the ls command:.
Finally, you should keep in mind that the basic operations almost always work on an element by element basis. There are rare exceptions to this general rule. For example, if you look at the minimum of two vectors using the min command you will get the minimum of all of the numbers. There is a special command, called pmin, that may be the command you want in some circumstances:.
Given a vector of numbers there are some basic commands to make it easier to get some of the basic numerical descriptions of a set of numbers. Here we assume that you can read in the tree data that was discussed in a previous chapter.
It is assumed that it is stored in a variable called tree :. Each column in the data frame can be accessed as a vector. The following commands can be used to get the mean, median, quantiles, minimum, maximum, variance, and standard deviation of a set of numbers:.
The summary command is especially nice because if you give it a data frame it will print out the summary for every vector in the data frame:.
Here we look at some commonly used commands that perform operations on lists. The commands include the sortminmaxand sum commands. First, the sort command can sort the given vector in either ascending or descending order:.
The min and the max commands find the minimum and the maximum numbers in the vector:. R Tutorial 3. Basic Operations and Numerical Descriptions 3. Basic Operations 3. Basic Numerical Descriptions 3. Operations on Vectors. Basic Operations and Numerical Descriptions.In this article we shall learn how to perform arithmetic operations on matrices in R Introduction In my previous articleswe all have seen what a matrix is and how to create matrices in R.
We have also seen how to rename matrix rows and columns, and how to add rows and columns, etc. Now, we shall learn and discuss how to perform arithmetic operations like addition and subtraction on two matrices in R. We shall also see how it works, using examples in R Studio. Let's get started now Step 1 - Creating Two Different Matrices First, we shall create two matrices which we will use while performing arithmetic operations.
Now, we can use it for our arithmetic operations on these matrices. Let's look at the below images first. The below code will add the two matrices. We have already done addition of two matrices. Now, let us visualize how it has performed the addition operation, using the below images. For example, the yellow color has been used to highlight the element of the first row and first column in both matrices.
After addition, the dimension is also the same as it was, i. Subtracting of Matrices Subtraction of matrices behaves almost the same as it behaves in the case of the addition of two matrices in R.
The below code shows how to perform the subtraction operations in matrices in R. Summary In this article, we have seen how to perform simple arithmetic operations on matrices in R. We have seen and visualized the addition and subtraction operation on matrices in R. I hope you learned and enjoyed it. I look forward to seeing your feedback. View All. Suraj Kumar Updated date, Aug 13 In this article, we have seen how to perform simple arithmetic operations on matrices in R.
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Subtract a constant from values in a channel? Active Participant. I need to subtract a constant from the values in a channel. The only way I can think to do it is to do the subtraction in a FOR loop - not very elegant.
I tried using the calculator in the analysis form, but I can't see how to do it there. It seems like scaling an array should be a built in analysis function, but I don't see it. Please help. Message 1 of Re: Subtract a constant from values in a channel? Hello George, you were right. The calculator is the solution. It is much faster than the for loop! Message 2 of Thanks that works great. But now how do I refer to the channel just created? I'm trying to find a command or variable that refers to the last channel or at least to the total number of channels.
Message 3 of NI Employee. This variable specifies teh maximum channel number. Therefore, it will correspond with the channel that you just created.
It only takes a minute to sign up. Such questions are better at StackOverflow in the R tag. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Adding a value to each element of a column in R [closed] Ask Question. Asked 5 years, 4 months ago. Active 5 years, 4 months ago. Viewed 75k times. The result I am after is: 6 7 8 9 10 It shouldn't be too hard but I don't know what function to use. Kyra Kyra 61 1 1 gold badge 1 1 silver badge 3 3 bronze badges.
I think you didn't even tried to solve it on your own. And indeed, that's the solution to your problem. Active Oldest Votes. Stephan Kolassa Stephan Kolassa This should bring you up to speed very quickly. Good luck! The Overflow Blog. Q2 Community Roadmap.
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This game has odds allocated to the outcome of matches which are in turn multiplied by the value of bet placed.
You choose an outcome of each match with respective odds.
The matches chosen must be a minimum of 3 and a maximum of 7
Payment is made for the correct outcome of matches with respective odds.
Outcome of all matches bet on must be correct.
The outcome per match is the result as per 90mins plus injury time.
Result for Cancelled / Abandoned match is given a default odd of 1


A professor at Oxford University, Sir Andrew Wiles has been awarded £500,000 prize because he easily cracked a 300-year-old mystery mathematical problem for academics known as ‘epochal moment’.
Norwegian Academy of Science and Letters has awarded him the Abel Prize for his proof of Fermat’s Theorem, which was published in the year 1994. This report was published on March 18, 2016.
This 62-year-old professor would be awarded a cheque of 6 million Norwegian Krone and the award from Norway’s Crown Prince Haakon in the month of May in Oslo.
Sir Andrew expresses gratitude and says it is an honor to receive this Prize and join the group of previous laureates who have made immense contributions to this field.
This equation was his passion since a long time, and he overwhelmed when he solved it. He always hoped that his solution would inspire several young people to opt for mathematics and work on the challenges of this fascinating and beautiful subject.
The academy stated that they awarded this prize to Sir Andrew as it was a stunning proof of Fermat’s Last Theorem and opened a new chapter in number theory. This breakthrough was made by Sir Andrew while he was working in Princeton.
This was first formulated by Pierre de Fermat, the French mathematician in 1637 and the theorem states that there are no whole number solutions to this equation which reads xn+yn= zn when the value of n is greater than 2.
Not only was ‘Wiles’ proof a turning point in his career but was also an epochal moment. The academy stated that culmination of this remarkable journey began three decades earlier.
This Prize was created in the year 2002 and is named after Niels Henrik Abel, the Norwegian mathematician, who died in the year 1829.


An explainer on the basics of compound interest, with historical anecdotes.
The Power of Compound Interest
In my journey through personal finance, one concept continually stands out as a cornerstone of wealth building: compound interest. Often referred to as the eighth wonder of the world, compound interest is a powerful force that can turn modest savings into substantial wealth over time. But what exactly is compound interest, and how does it work? Let’s delve into its basics and explore some fascinating historical anecdotes that underscore its importance.
The Basics of Compound Interest
At its core, compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. In simpler terms, it’s “interest on interest.” This differs from simple interest, where interest is calculated solely on the principal amount.
For example, suppose you invest $1,000 at an annual compound interest rate of 5%. After the first year, you earn $50 in interest, bringing your total to $1,050. In the second year, you earn interest not just on your initial $1,000 but also on the $50 interest from the first year. So, your interest for the second year is $52.50, making your total $1,102.50. This process continues each year, with the interest accumulating at an increasing rate.
Historical Anecdotes: The Magic of Compounding
Albert Einstein’s Admiration
Albert Einstein famously declared compound interest the most powerful force in the universe. He is often quoted as saying, “He who understands it, earns it; he who doesn’t, pays it.” While there is no documented evidence of Einstein actually saying this, the sentiment accurately reflects his admiration for the concept.
The Legend of the Chessboard
One of the most famous historical anecdotes illustrating the power of compound interest is the legend of the chessboard and the inventor of the game of chess. As the story goes, the inventor was asked by the ruler of the land what he wanted as a reward. The inventor, understanding the power of exponential growth, asked for one grain of rice to be placed on the first square of the chessboard, two on the second, four on the third, and so on, doubling on each subsequent square.
The ruler, underestimating this request, agreed, only to realize later that the total amount of rice needed would surpass the world’s supply. This story, whether fact or fable, brilliantly illustrates how compound interest can lead to enormous numbers over time.
Savings and Investment
In practical terms, understanding and utilizing compound interest is crucial for anyone looking to grow their wealth. Whether it’s through a high-yield savings account, retirement fund, or other investment vehicles, the earlier you start, the more significant the compounding effect.
Conversely, compound interest can work against you when it comes to loans and debts. Credit card debt, for example, can quickly spiral out of control due to the compounding of interest on unpaid balances.
The Bottom Line
Compound interest is more than just a financial concept; it’s a fundamental principle that can shape your financial future. It teaches patience, the value of time, and the importance of starting early. Whether you’re saving for retirement, investing in the stock market, or paying down debt, understanding the mechanics and implications of compound interest is crucial.
Remember, the true magic of compound interest lies not just in its mathematical formula but in its ability to transform modest savings into a substantial nest egg over time. It’s a reminder that in the world of finance, sometimes the most powerful forces are not the loudest or the most immediate, but those that quietly work in the background, steadily growing your wealth.


By Ronald Goldman
Taking a unique, extra beautiful procedure than present texts, An built-in creation to special effects and Geometric Modeling specializes in photos, modeling, and mathematical tools, together with ray tracing, polygon shading, radiosity, fractals, freeform curves and surfaces, vector equipment, and transformation options. the writer starts with fractals, instead of the common line-drawing algorithms present in many normal texts. He additionally brings the turtle again from obscurity to introduce numerous significant techniques in special effects.
Supplying the mathematical foundations, the ebook covers linear algebra issues, resembling vector geometry and algebra, affine and projective areas, affine maps, projective alterations, matrices, and quaternions. the most pictures components explored contain mirrored image and refraction, recursive ray tracing, radiosity, illumination types, polygon shading, and hidden floor tactics. The ebook additionally discusses geometric modeling, together with planes, polygons, spheres, quadrics, algebraic and parametric curves and surfaces, optimistic strong geometry, boundary documents, octrees, interpolation, approximation, Bezier and B-spline equipment, fractal algorithms, and subdivision concepts.
Making the cloth obtainable and proper for years yet to come, the textual content avoids descriptions of present pix and designated programming languages. in its place, it offers photos algorithms in accordance with well-established actual types of sunshine and cogent mathematical tools.
Read Online or Download An Integrated Introduction to Computer Graphics and Geometric Modeling (Chapman & Hall/CRC Computer Graphics, Geometric Modeling, and Animation Series) PDF
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Additional info for An Integrated Introduction to Computer Graphics and Geometric Modeling (Chapman & Hall/CRC Computer Graphics, Geometric Modeling, and Animation Series)
An Integrated Introduction to Computer Graphics and Geometric Modeling (Chapman & Hall/CRC Computer Graphics, Geometric Modeling, and Animation Series) by Ronald Goldman


Hadi Jorati was educated in Classical Arabic, Classical Persian, and Ottoman Turkish. He studied Mathematics and Physics (BA), then completed a PhD in Mathematics at Princeton University under Elias Stein. Afterwards, he joined the faculty of the University of British Columbia as a visiting researcher, where he taught for several years before switching fields and joining Yale NELC to work on his second doctorate with Dimitri Gutas.
Jorati is interested the social and intellectual history of the Islamic Civilization -- science, education, and institutions of learning in the East in the Medieval and pre-Modern period. He has previously worked on Umar Khayyam's mathematical career, the Anwā' tradition as the Arabic science of the stars, patronage in al-Biruni's works, al-Kindi's work in Meteorology, textual criticism of Ilkhanid historiography, and Ottoman Astronomy. Jorati's PhD dissertation is on the social history of science and the career of Nasir al-Din Tusi. His other interests include the Alexander legend between Eastern cultures, Arabic and Persian gnomologia, and the Persianate heritage of the Indian subcontinent.


Haymik Help Multiplies
Te Puke Inventor
Haymik help multiplies
Following a very positive reaction to his highly innovative Haymik Maths Helper 20, Te Puke inventor Bevan John has added to his repertory.
The original Haymik Maths Helper has been very well received by schools, teachers and other learning institutions plus families throughout the country. The maths helper is a slide rule which works by aligning an arrow on the slide with a number on the top board As an example, to add 6 and 3, the arrow on the slide is aligned with 6, on the top board. Reading off the slide, the 3 becomes aligned with 9>, the answer on the top board. Bevan says the same principle works in reverse for subtraction.
Bevan invented the Haymik Helper through seeking to help his grandson Hayden, then aged five, get the hang of addition and subtraction. After studying an old slide rule he began to devise a much simpler, streamlined version. Hayden soon had the help he needed and during the next couple of years Bevan perfected the device, which is a real, hit with kids and continues to receive high praise from many teachers. It is named in honour of Hayden and his sister Mikyla.
Bevan has kept busy demonstrating and promoting the Haymik Helper and is always keen to get feedback. It was through such response from a teacher keen to see more advanced calculations that Bevan began to formulate what has become the Haymik Maths Helper 30 and he has also devised a set of Haymik multipliers.
The Haymik Helper 30 offers the added advantage of being able to align a double-headed arrow with a number on the top or bottom board. For example: to add 15 and 7, the arrow on the slide is aligned to 15 on the bottom board. This action aligns 7 with the answer on the bottom board, 22. A small10 by the arrow allows for more advanced problem solving to be undertaken.
The set of multipliers offers an easy to use and simple way of learning the times tables. Bevan says the multipliers have the added advantage of allowing children to visualise that multiplication is nothing more than repetitive addition. He says that it is the visualisation process that is the real key and being able to see how things add up gives users the confidence to tackle more problems. He has been delighted to find that the process clearly rubs off in most cases, encouraging users to enjoy a continuing and creative interest in maths.
"The helper encourages them to become innovative and flexible problem solvers as there are different ways to solve particular problems." A growing list of testimonials reflect the impact Haymik Helpers are having.
One school comments that the original device is a great help for beginners and also for some older students who struggle with maths. Fun and enjoyment are other common words used in feedback and bilingual versions have also been very well received.
With interest in the Haymik Helpers now well established nationally, Bevan is considering export potential. He is also continually setting his inventive mind to creating other teaching devices and is also keen to move into the literacy field as well.
4 Seddon Street.
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University Hospital Hamburg-Eppendorf, Germany
Over its now three years of existence and development, the ‘qpcR’ package for the R statistical environment has matured into a quantitative real-time PCR (qPCR) data analysis software that houses nearly 70 functions and example datasets assisting in qPCR analysis. The versatile R statistical language makes it relatively effortless to implement published algorithms or new ideas in a short time, and test these new algortihms by the 20 included datasets derived from many different PCR platforms. The package includes in its current version (1.3-4) many ‘replications’ of widely-used methods (i.e. window-of-linearity, REST approach, exponential fitting, sigmoidal fitting, threshold cycle estimation by second derivative maximum, Cy0, comparative quantitation, ratio calculation in a batch format, etc). All of these methods have been compared with the original versions, as to ensure result compatibility/identity. Many implemented functions have also been officially approved by the original authors. The talk will focus on somewhat exotic implementations of qPCR quantitation that are relatively new. While some of them are already published (but not necessarily available in a software), we will introduce methods that are still under development or amenable to public discussion in respect to their general applicability within the qPCR community. The methods that will be presented with short examples are:
1) Monte-Carlo simulation of error propagation (short).
2) Bootstrapping qPCR fits.
3) The development of a tilted threshold, which gives significantly better calibration values from high dilution line by an iterative process.
4) A six-parameter sigmoidal model which models the baseline slope accurately.
5) The MAK2/MAK3 mechanistic models from Boggy et al.
6) The maxRatio method from Shain et al.
7) Several methods for automatic tagging of unsuccessful runs.
8) Using the PRESS statistic for goodness-of-fit.
9) The exceptional speed of R when analyzing high-throughput data. We show this this on a dataset with 9000 runs (raw fluorescence data), whose import, model fitting, quality control (failed runs detection), threshold cycle and efficiency calculation takes about 10 minutes.
10) The importance of weighting when fitting nonlinear models to qPCR data.
Some these methods will be presented as short animations, to clarify things. We will also show the feasibility of the methods by testing them on a cohort of datasets.
|Back to Data Analysis: qPCR Biostatistics & Bioinformatics|


1 ) A cash collection was made around a room with everyone putting a note into a bag. People put in either a €20, a €10 or a €5 note.
I asked the collector how much was in the collection and he told me that if I pulled out a note at random that there would be a 1 in 12 chance of getting a €20 note. He said there would be a 1 in 4 chance of getting a €10 note and a 2 in 3 chance of getting a €5.
I protested that I needed more information. He conceded that four people had put in €20 notes and he refused to tell me any more.
Can you figure out how much money was in the bag?
2) You are travelling to Britain and you change €500 into Sterling. The exchange sells you Sterling notes at 0.76 £/€ and takes a £2 commission.
On your trip you spend half your Sterling, and when you return you change it back to euro at 0.79 £/€ and the exchange takes €3 commission.
How much are you left with in Euro?
3 ) if a builder builds a 100 houses and he numbers them 1-100 .How many number 9’s does he need.
4) If there were twice as many elephants as monkeys, 4 times as many lions as elephants and 3 times as many horses as lions. If there were 3 monkeys . how many legs in total (on animals only ) did Moses take into the Arc.
5 ) what is the combined total nuber of crossbars in school (on gaelic and soccer goals) plus number of classes in school (ie number that get register taken in mornings) plus the number of Ms Horns room
6 ) Use the numbers only once to add subtract multiply or divide the follow numbers to make
75,4,9,5,6,8 to make 422 (You don’t have to use all the numbers)


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We Can Work It Out - Calibration as Artistic Method by Anna
summing over L4:3 i,incoming particle i o, outgoing particle o The square of is c^2 times the invariant mass square, is a very useful quantity as it is both conserved and Lorentz invariant!, for v=0 Remark: Taylor expanding for small v we get: 2015-07-29 Momentum Practice Problems Perform the following practice problems on a seperate sheet of notebook paper. Make sure you include the formula, the numbers plugged into the formula, 2009-10-23 2020-01-17 2008-08-19 Now consider a similar problem involving momentum conservation. A 0.150-kg baseball moving at a speed of 45.0 m/s crosses the plate and strikes the 0.250-kg catcher's mitt (originally at rest). The catcher's mitt immediately recoils backwards (at the same speed as the ball) before the catcher applies an external force to stop its momentum.
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All rights reserved. Registration on or use of this site constitutes acceptance The impulse momentum theorem states that an impulse acting on any system changes the momentum of the entire system. Impulse is the effect of a net force ac The impulse momentum theorem states that an impulse acting on any system changes the Before one can face the problem of four-momentum conservation, one must thus first of all construct a mathematically well-defined energy-momentum tensor, Preview of what kind of problems we will deal with. • decay.
welcome back we will now do a momentum problem in two dimensions so let's see what we have here so we have this ball a and we could maybe even think of it as this is maybe what's going on on the surface of a pool table we have ball a and it's moving with its ten kilograms so these numbers are the mass of the balls this is a 10 kilogram ball and it's moving to the right at 3 meters per second and then it hits this … The length of this four-vector is an invariant. The momenta of two particles in a collision can then be transformed into the zero-momentum frame for analysis, a significant advantage for high-energy collisions. For the two particles, you can determine the length of the momentum-energy 4-vector, which is an invariant under Lorentz transformation.
Acconeer - beQuoted
The electron and positron fuse briefly to form a single particle, labelled X. For the case when Ee = 50 GeV, Ep = 100 GeV and m is negligible, calculate the four-vector momentum of X i the lab frame, and its rest mass. Then balancing the four momentum i get P1 + P2 = P3 squaring i get P1^2 + P2^2 +P1.P2 =P3^2 .
Lectures on quantum mechanics... - LIBRIS
∑K = ½(8 kg)(6 m/s)2, +, ½(4 kg)(9 m/s)2 Since the description of this problem makes no mention of the existence or even the possibility of a third The law of momentum conservation can be used as a model for predicting the Both the person and the medicine ball move across the ice with a velocity of 4 20 Dec 2013 We present a matrix formalism, inspired by the Minkowski four-vectors of special relativity, useful to solve classical physics problems related to Using the four-velocity, we can define a current density8 four-vector as.
Four LiU researchers will share more than SEK 21 million from the Swedish Research Council's funding for the humanities and social sciences. MOMENTUM PLUS Unlock added customization, integrations, widgets, and more!
We again have the problem of the speed of light not being equal to one in our units. The answer, which we will derive below, is that the Momentum-Energy 4-vector is Litany For Momentum Problems [©2004 RJ Bieniek] 1. Since momentum methods are most often used to solve problems involving a collision, an explosion, or an impulsive event, draw separate sketches of the physical the physical situation before and after the “event”.
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Set the management momentum. 07.08.19. But as the mass is equal to the Minkowski metric length of the four-momentum can avoid potential problems until the full extent of the law becomes more clear. Four LiU researchers will share more than SEK 21 million from the Swedish Research Council's funding for the humanities and social sciences. MOMENTUM PLUS Unlock added customization, integrations, widgets, and more!
Law of Conservation of Momentum Problems. Q1. There are cars with masses 4 kg and 10 kg respectively that are at rest. A car having the mass 10 kg moves 4.


Learn to Play Casino Game Variations
Once you think of casino game, you probably think of poker. But the truth is, there are hundreds of casino game types. The most used casino game is blackjack. Blackjack is probably the easiest casino games to understand and play, so it is often the first choice for most new casino goers. Blackjack can also be played with live dealers, but because you do not get to interact with the dealer during the game, this type of casino game is not for everyone.
You can find three main categories of casino games: table games, gaming machines, and random chance games. Table games are the ones that are played on a casino floor and include blackjack, baccarat, and the slots. Gaming machines are operated by way of a casino employee and also have a residence edge. Random chance games are the ones that are randomly selected from a deck, and there is a good possibility that you could think of a random outcome.
Slots are a popular casino game because the house edge on them is low in comparison to other games. That means that the casino will lose more money in the event that you bet on the incorrect number. This makes slots a “low risk” gambling option for people who find themselves just starting out. Blackjack, on the other hand, includes a high house edge, so it’s easier to choose another card game.
A binomial distribution is another type of casino game that determines the results of a casino game in a probabilistic manner. In a binomial distribution, the outcome of a round of a number of rounds is called the “binomial distribution logarithmically distributed.” In a binomial distribution, you can find twenty-two random variables A and B and their values, one for each round of the game. The probability density function because of this distribution uses the binomial equation to calculate the expected value for every variable. This is like roulette, where the best possible result is actually a “red” or “white” aswell.
One of the most important statistics in casino games falls under the category of statistical likelihood. It’s simply the ratio of expected wins against expected losses. Normally, this is called the home edge. When calculating this, you take the difference in the middle of your expected winnings and expected losses and divide it by the amount of time you’ve been playing the overall game.
Some casino games belong to the realm of chance such as 카지노 신규 쿠폰 slots and blackjack. Slots are one of the earliest casino games which were invented by man. The reason it took casino developers so long to develop this game is basically because no cards were involved! All players gamble with their own cards and coins, with the bets being transferred to the house. Blackjack, just like the famous casino game, is played with poker chips and is among the oldest games on earth. No card games have already been around longer than the slots.
Video Poker can be area of the casino game house. Like all video gaming, video poker requires skills and strategic thinking. Video Poker, though, has some interesting variations. For example, the house is rolling out a variation of craps called Craps Go Long that allows players who play video poker for fun to strategize in ways much like traditional craps.
Other variations of video poker games are the keno, slots, baccarat, and poker. While these games are all fun, they’re not exactly high stakes games. So, if you are looking for a casino game where one can win big, you should think about the slots or the keno. Most of all, to be able to learn a little more about gambling, don’t hesitate to search for a casino game forum.


Over the last couple of months I’ve been getting my feet wet with linear programming and mathematical optimisation. I got a sense of how it all worked from this Discrete Optimisation course in Coursera and googling around I discovered that there are a ton of tools out there to help you solve optimisation problems. Makes sense, why would you want to implement a solving algorithm from scratch when some of the best minds in the history of mankind have already given it a shot?
Solvers, as these tools are often called, can reach the hundreds of thousands of dollars and they are worth every penny! But since I wanted to play with one without forking up the dough, I narrowed my search down to open-source options.
Hans Mittelmann from the Arizona State University performs regular automated benchmarks on different mathematical optimisation tools. He publishes the benchmarks at http://plato.asu.edu/bench.html. Following what I read in the results, I picked Google Optimization Tools (OR-Tools) because it performed fairly well and well, because if you’re looking for a sinister tool to model and solve hard problems in the human world, you can rarely go wrong with Google.
GLOP has C++ and Python APIs. I’m better at Python and I expected to quickly put together a web front-end for this, so I picked the latter one.
TL;DR. Just gimme the code
I picked a variation of the knapsack problem: a grocery-shopping example in which you try to maximise the number of calories you can buy with a limited budget. I got the problem from this blog post:
Basically: You walk into a grocery store with a grocery bag and some cash, to buy groceries for a week. You need to follow these rules:
1. Your bag can hold ten pounds.
2. You have $100
3. You need about 2000 calories a day, so a weekly shopping trip is about 14,000 calories.
4. You must purchase at least 4 ounces of each grocery item.
These are the groceries you can by and their price per pound:
Ham: 650 cals, $4 Lettuce: 70 cals, $1.5 Cheese: 1670 cals, $5 Tuna: 830 cals, $20 Bread: 1300 cals, $1.20
Follow the instructions at https://developers.google.com/optimization/introduction/installing. You will need Python and Python setuptools installed in your machine.
Coding the problem
We can split the coding of the problem into 6 elements:
1. Identify the problem
We tell or-tools that we are attempting to solve a linear programming problem. We create a solver variable that is going to contain all the necessary items to solve the problem.
from ortools.linear_solver import pywraplp solver = pywraplp.Solver('SolveSimpleSystem',pywraplp.Solver.GLOP_LINEAR_PROGRAMMING)
2. Ingest the input
We are going to send our table of possible groceries, calories and prices as a nested list:
food = [['ham',650, 4], ['lettuce',70,1.5], ['cheese',1670,5], ['tuna',830,20], ['bread',1300,1.20]]
3. Configure the decision variables
We need 5 decision variables which contain how many pounds of each product you are going to buy. Instead of creating 5 variables, we can create a list of size 5 (the size of the food list). Each item in the list will contain a decision variable.
Each decision variable will be created with a call to the NumVar method of the solver variable, passing the minimum amount of groceries we can buy, the maximum (infinity), and a unique name for the variable (contained in the previously-defined food list).
#food is a list of groceries, calories and prices variable_list = [] * len(food) for i in range(0, len(food)): #you must buy at least minShop of each variable_list[i] = solver.NumVar(minShop, solver.infinity(), str(food[i]))
They pythonic way of writing that loop is using a list comprehension. However I’m using the loop for readability.
#same thing but with comprehension variable_list=[solver.NumVar(minShop, solver.infinity(), str(food[i])) for i in range(0, len(food))]
4. Configure the constraints
This is where most of the magic happens. We will create one constraint per “rule” specified in the problem description.
In linear programming each constraint is specified in terms of addition of the decision variables:
lower bound <= var1+var2+var3 <=upper bound
In the knapsack problem, the conversion is pretty straightforward. In some other cases, you have to re-think and re-model your problem in these terms.
We will create a list of 3 constraints, calling Constraint(lower bound, upper bound) for each one, and then walk the variables list and call SetCoefficient for each of the variables.
#Define the constraints constraint_list= #Constraint 1: totalWeight<maxWeight #ham + lettuce + cheese + tuna + bread <= maxWeight constraint_list.append(solver.Constraint(0, maxWeight)) for i in range(0, len(food)): constraint_list.SetCoefficient(variable_list[i],1) #Constraint 2: totalPrice<=maxCost constraint_list.append(solver.Constraint(0, maxCost)) for i in range(0, len(food)): constraint_list.SetCoefficient(variable_list[i],food[i]) #Constraint 3: totalCalories>=minCals constraint_list.append(solver.Constraint(minCals, minCals + 100)) for i in range(0, len(food)): constraint_list.SetCoefficient(variable_list[i],food[i])
Note that the 4th rule of the problem, “You must purchase at least 4 ounces of each grocery item,” is already coded in the variables definition.
5. Configure the objective function
Similar to the constraint definition, the goal function is specified in terms of addition of the decision variables:
goal = Maximize/Minimize (var1+var2+var3)
If we wish to minimize cost, we walk our variable list, get the price from the food list, and set the objective.
for i in range(0, len(variable_list[)): objective.SetCoefficient(variable_list[i], food[i]) objective.SetMinimization()
Say we wanted to maximize calories intake. We would do the same, but taking the calories value from the food list, and setting a maximization goal
# Define our objective: maximizing calories for i in range(0, len(food)): objective.SetCoefficient(variable_list[i], food[i]) objective.SetMaximization()
After all these configuration steps, we just call the solve method against the solver variable and print out a solution if we find it.
result_status = solve(solver) if result_status == solver.OPTIMAL: print('Successful solve.') # The problem has an optimal solution. print(('Problem solved in %f milliseconds' % solver.wall_time())) # The objective value of the solution. print(('Optimal objective value = %f' % solver.Objective().Value())) # The value of each variable in the solution. var_sum=0 for variable in variable_list: print(('%s = %f' % (variable.name(), variable.solution_value()))) var_sum+=variable.solution_value() print(('Variable sum = %f' % var_sum)); print('Advanced usage:') print(('Problem solved in %d iterations' % solver.iterations())) for variable in variable_list: print(('%s: reduced cost = %f' % (variable.name(), variable.reduced_cost()))) activities = solver.ComputeConstraintActivities() for i, constraint in enumerate(constraint_list): print(('constraint %d: dual value = %f\n' ' activity = %f' % (i, constraint.dual_value(), activities[constraint.index()]))) elif result_status == solver.INFEASIBLE: print('No solution found.') elif result_status == solver.POSSIBLE_OVERFLOW: print('Some inputs are too large and may cause an integer overflow.')
We got a solution, but you need to know a little bit of python to run this program, change its inputs or read the solution. Wouldn’t it be nice to have some sort of user-friendly UI? This will be the subject of future posts.
Containerizing the solution with docker


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The poem is not about math, but has a mathematical form called the Fib. This form is based on the Fibonacci sequence (1,1,2,3,5,8,…). Each verse has six lines and twenty syllables, with each line having the syllable count of the corresponding Fibonacci number. I’ve written three stanzas in this form, and I’ve added a little rhyming to twist it up.
see the light –
it is a warning
of the fast approaching day – blight!
each night. Time soon brought
the light. Stop time! Let darkness stay
no light crest
horizon. My bane
is morning light. Haste sun to west!


For each sampler, we will use the same code to plot sampler paths. The block below loads the relevant libraries and defines a function for plotting the sampler's trajectory across the posterior.
The Turing model definition used here is not especially practical, but it is designed in such a way as to produce visually interesting posterior surfaces to show how different samplers move along the distribution.
ENV["GKS_ENCODING"] = "utf-8" # Allows the use of unicode characters in Plots.jl using Plots using StatsPlots using Turing using Random using Bijectors # Set a seed. Random.seed!(0) # Define a strange model. @model function gdemo(x) s² ~ InverseGamma(2, 3) m ~ Normal(0, sqrt(s²)) bumps = sin(m) + cos(m) m = m + 5 * bumps for i in eachindex(x) x[i] ~ Normal(m, sqrt(s²)) end return s², m end # Define our data points. x = [1.5, 2.0, 13.0, 2.1, 0.0] # Set up the model call, sample from the prior. model = gdemo(x) # Evaluate surface at coordinates. evaluate(m1, m2) = logjoint(model, (m=m2, s²=invlink.(Ref(InverseGamma(2, 3)), m1))) function plot_sampler(chain; label="") # Extract values from chain. val = get(chain, [:s², :m, :lp]) ss = link.(Ref(InverseGamma(2, 3)), val.s²) ms = val.m lps = val.lp # How many surface points to sample. granularity = 100 # Range start/stop points. spread = 0.5 σ_start = minimum(ss) - spread * std(ss) σ_stop = maximum(ss) + spread * std(ss) μ_start = minimum(ms) - spread * std(ms) μ_stop = maximum(ms) + spread * std(ms) σ_rng = collect(range(σ_start; stop=σ_stop, length=granularity)) μ_rng = collect(range(μ_start; stop=μ_stop, length=granularity)) # Make surface plot. p = surface( σ_rng, μ_rng, evaluate; camera=(30, 65), # ticks=nothing, colorbar=false, color=:inferno, title=label, ) line_range = 1:length(ms) scatter3d!( ss[line_range], ms[line_range], lps[line_range]; mc=:viridis, marker_z=collect(line_range), msw=0, legend=false, colorbar=false, alpha=0.5, xlabel="σ", ylabel="μ", zlabel="Log probability", title=label, ) return p end;
Gibbs sampling tends to exhibit a "jittery" trajectory. The example below combines
PG sampling to traverse the posterior.
c = sample(model, Gibbs(HMC(0.01, 5, :s²), PG(20, :m)), 1000) plot_sampler(c)
Hamiltonian Monte Carlo (HMC) sampling is a typical sampler to use, as it tends to be fairly good at converging in a efficient manner. It can often be tricky to set the correct parameters for this sampler however, and the
NUTS sampler is often easier to run if you don't want to spend too much time fiddling with step size and and the number of steps to take. Note however that
HMC does not explore the positive values μ very well, likely due to the leapfrog and step size parameter settings.
c = sample(model, HMC(0.01, 10), 1000) plot_sampler(c)
The HMCDA sampler is an implementation of the Hamiltonian Monte Carlo with Dual Averaging algorithm found in the paper "The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo" by Hoffman and Gelman (2011). The paper can be found on arXiv for the interested reader.
c = sample(model, HMCDA(200, 0.65, 0.3), 1000) plot_sampler(c)
Metropolis-Hastings (MH) sampling is one of the earliest Markov Chain Monte Carlo methods. MH sampling does not "move" a lot, unlike many of the other samplers implemented in Turing. Typically a much longer chain is required to converge to an appropriate parameter estimate.
The plot below only uses 1,000 iterations of Metropolis-Hastings.
c = sample(model, MH(), 1000) plot_sampler(c)
As you can see, the MH sampler doesn't move parameter estimates very often.
The No U-Turn Sampler (NUTS) is an implementation of the algorithm found in the paper "The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo" by Hoffman and Gelman (2011). The paper can be found on arXiv for the interested reader.
NUTS tends to be very good at traversing complex posteriors quickly.
c = sample(model, NUTS(0.65), 1000) plot_sampler(c)
The only parameter that needs to be set other than the number of iterations to run is the target acceptance rate. In the Hoffman and Gelman paper, they note that a target acceptance rate of 0.65 is typical.
Here is a plot showing a very high acceptance rate. Note that it appears to "stick" to a mode and is not particularly good at exploring the posterior as compared to the 0.65 target acceptance ratio case.
c = sample(model, NUTS(0.95), 1000) plot_sampler(c)
An exceptionally low acceptance rate will show very few moves on the posterior:
c = sample(model, NUTS(0.2), 1000) plot_sampler(c)
The Particle Gibbs (PG) sampler is an implementation of an algorithm from the paper "Particle Markov chain Monte Carlo methods" by Andrieu, Doucet, and Holenstein (2010). The interested reader can learn more here.
The two parameters are the number of particles, and the number of iterations. The plot below shows the use of 20 particles.
c = sample(model, PG(20), 1000) plot_sampler(c)
Next, we plot using 50 particles.
c = sample(model, PG(50), 1000) plot_sampler(c)


play unblocked 2048. Best of recent times game 2048. Enjoy unblocked io games with yohoho.gold
Properties of .io games
.IO games come in all shapes and colors, but they do have some shared properties:
Players grow by eating or otherwise killing other players
The game takes place in an arena.
Most games use HTML5 technology to run in any modern browser.
The games are fiercely competitive and feature real-time multiplayer gameplay.
The 2048 game consists of 4x4 16 squares. By combining the same numbers in the same row and column, try to double the numbers. Play 2048 by using the arrow keys on the computer and dragging with your finger on mobile devices and mobile phones. You can play the 2048 game by combining the numbers and unloading the squares that are numbers. Every time, try to take your 2048 game record to the next level.
A new figure comes to one of the empty squares with each move. If all the squares are full and no new numbers are found, the game is over. To do this, multiply two numbers that are the same in every move and get a new number. Thus, the value of the numbers on the screen is increased. In addition, an empty square is created for the new figure. Follow this logic and try to get the 2048 number.


Working with equations
Adding equations to a model
You add equations to your model using the Math view’s equation table. The Concept equation solver solves both geometric and non-geometric equations. As a result, you can add functional properties to your models. You can mix and match dimensions and variables in equations. New variables included in your equations are automatically added to the Math view’s parameter table.
In this lesson, we will use equations to compute the maximum fiber stress (normal stress) in a simple rectangular beam. We will assume that the beam is a simply supported beam with a point load (P) at the center.
In step 1 of this lesson, we will draw the cross section of the beam. In step 2, we will create a new math group to contain our equations, and then add the equations to the model.
Step 1: Draw the beam
- If needed, start a new file by clicking the Create a new model tool from the main toolbar or selecting New from the File menu.
- Using the Rectangle tool draw a small rectangle by clicking two points in the sketch area that define the upper left and lower right diagonal points of the rectangle. Don't worry about exact values of the dimensions yet.
Observe that the dimensions for the rectangle also appear in the parameter table (the upper portion of the Math view).
Next, we will identify the primary datum surface of the part by placing a fixed point and Line At Angle constraint on one of the lines. We will not place datums in this simple example. For information about datums, see Enventive Concept Help.
- Add a Fixed Point and
- Observe that the DOF (degrees of freedom) display in the upper right of the Concept window reads 0, indicating the model is fully constrained. The display also shows that our model has one Fixed Point and one Line At Angle constraint.
In the Parameter table, click anywhere in the row for the Line At Angle dimension. The name and value are shown in the Enter/Edit Parameter area at the top of the Math View. In the Name field, change the dimension's name to LAA. Press Enter to accept the change.
To keep our example simple as we proceed, we will change the dimension values to small whole numbers. Name the width dimension b and change its value to 1. Concept asks if you want to scale the model.
From this message, click Scale. This will also change the height dimension so that its size remains relative to the width dimension.
Name the height dimension h and change its value to 4. The Parameter table should now look like the following.
- Right-click in the sketch and select Zoom All from the shortcut menu to resize the display of the drawing. Reposition the dimensions so that your sketch looks similar to the following:
- Save the file as Beam.enb.
You have completed sketching a simple model of a beam. Next, we'll add equations to the model.
Step 2: Add equations to the model
Add a new math group by selecting New Group... from the Group drop-down at the top of the Math view.
Type Beam Equations as the name of the new group in the New Math Group dialog that opens, and click OK.
The new Beam Equations group is added to the Group drop-down list.
To add the height and width dimensions to the Beam Equations group, extend-select (hold down the Ctrl key while clicking on the dimensions in either the sketch or parameter table) the h and b dimensions, and then select the box next to Beam Equations in the Properties Explorer.
Select Beam Equations from the Group drop-down list to make the group active. Note that the Beam Equations group now contains the b and h dimensions.
In the equation table (the lower portion of the Math view), click the New Equation button to open the Equation Editor dialog, and type the basic beam equation for stress (S): S=M*c/Ix. (Note: You can copy each equation from this page and paste it into the Equation Editor.)
Press Enter or click OK to add the equation. Note that the variables included in the equation have been added to the parameter table.
Enter the following equations in the same way you did for the S equation:
- Area moment of Inertia about the x axis (Ix): Ix=b*h^3/12
- Value of distance to the neutral axis (c): c=h/2
Moment (M): M=P*L/4
After you have entered all the equations, the Beam Equations group will contain the following entries.
In the parameter table, enter 1000 as the value for load (P) and 200 as the value for beam length (L). Based on the P and L values, Concept computes the moment (M) and stress (S) values.
This lesson illustrates how to analyze the variability of the computed parameters we created in Adding Equations to a Model.
- Select Default Tolerances... from the Edit menu, and click the Dimensions tab to see the default settings for dimensions.
Change the default tolerance for linear dimensions to 0.01. Click OK to save your changes.
Select the P variable from the parameter table.
- In the Property Explorer’s Tolerance area, select +/- or Symmetric from the Type selection list, and specify a tolerance of +/- 50 as shown below.
- In the same way you set the tolerance for the P variable, set the L variable's tolerance to +/- 0.1.
Click the maximize button in the upper right corner of the Modules view to maximize the view so you can see the entire tolerance analysis report. To see the Advanced Contributor section, scroll to the right of the report.
To see the sub-contributors for the complex contributors b and h, click the expand button to the left of their rows.
- Click the Restore button in the upper right corner of the maximized spreadsheet to return the Modules view to its normal docked size.
- Save the file.
Back-solving to derive a parameter value
In this lesson, you’ll learn how to back-solve from a computed variable to derive the value of a dimensional parameter. Continuing to work with the file we used in the previous lessons, Adding Equations to a Model and Tolerance Analysis, we’ll solve for the beam height that will produce a specific stress level. You will also learn how to add text to your sketch, which is particularly useful for sharing information about a model with other team members.
Back-solve to drive the beam height
In the Math view’s parameter table, unlock the h dimension by clicking on the lock symbol in the L (Lock Status) column.
- Observe that the values of the S, c, and Ix variables also become unlocked. If we review the equations, we see that this occurs because these variables are interdependent. Entering a value for one of these variables (and thereby locking that variable) will drive the values of the other variables.
To drive the values with the stress (S) variable, type 10000 as the value for S, and press Enter to accept the change.
The status for S becomes Locked. The variables that are now driven by the value of S (h, c, and Ix) are changed to Derived status, and their values are recalculated based on the value we entered for S.
Observe in the Sketch view that the height of the beam has changed in response to the new value of S, which now drives the beam height.
Add text to the sketch
In this part of the lesson, we'll add a note to the sketch to tell other team members that we used equations to find the height of the beam.
- Select the Sketch Text tool from the Sketch view toolbar.
- Select the line that has its height set by the h dimension.
- In the Sketch Text dialog that appears, type the text shown in the following illustration, then click OK. (Note: If you do not select an object when placing the Sketch Text, you will not have options to show a leader line or move the text with the object.)
- If needed, zoom out or pan to see the text in its entirety.
- Move the text as desired by clicking and dragging it using the Select tool. (You can return to the Select tool at any time by pressing Esc on your keyboard.)
Click on the text to see its properties in the Properties Explorer. To better format the text, add line breaks by pressing Enter to break the lines as shown in the following illustration.
The text now appears as shown below.
Congratulations! You have successfully completed the Equations tutorial.
For extra practice, work through the attached labs that explore additional methods of computing beam stress.


This is how addition and subtraction make me feel.
Here's Our Very Best Attempt At Calculating World Title Scenarios
I put every ounce of my third grade math skills into this.
On our Portugal wrap-up post, one commenter made a comically astute observation. Stoner, referencing Ashton's earlier words, said: "While we're still tabulating the scenarios," which really means.... "While we're waiting for someone else to post the scenarios because we can't count." And if that wasn't so hilariously valid, it might have stung a little. The truth is that no one at Stab, besides maybe our savvy leader Sammy Mac, would know their asymptotes from their ellipses.
We are writers; filmers; designers; artists! And numbers, even in their simplest form, are rarely understood by those who choose cultural experiences over cold hard cash.
But I promise you, readers, that I really did try to get this math right. I even drew little diagrams, pie charts, used a TI-89 calculator and everything!
With one contest remaining, here is what will need to happen for any of the four remaining WT contenders (John, Gabby, Jordy, Julian) to win the Title.
- If John makes the final at Pipe: he wins the title.
- If John places 3rd or 5th: Medina can win the title with a Pipe Masters victory.
- If John places 9th: Medina can win with a 2nd or better. Jordy can also win with a Pipe Masters victory, assuming Gabby doesn't place 2nd or better.
- If John places 13th or 25th: Medina can win with a 5th or better. Jordy can also win with a 2nd or better, assuming Gabby doesn't place 3rd or better. Julian can also win with a Pipe Masters victory, assuming Gabby doesn't place 5th or better and Jordy doesn't place 2nd or better.
Essentially, the title is still John's to lose, but with a strangely mediocre history at the Pipe Masters and a rampaging Medina hot on his heels, rest assured John will have an uneasy 43 days in the lead-up to this event. Heavy lies the crown.
Aaaand now feel free to blast my mathematical blunders in the comments...


LOS ANGELES - The estimated jackpot for the Saturday, Sept. 23 drawing of the Powerball lottery is $750 million, the seventh largest prize in the game's history and the 12th largest lottery jackpot in U.S. history.
But according to USC math professor Ken Alexander, buying a ticket at a store where tickets with large jackpots have been sold in the past does not necessarily increase a purchaser's chance of winning a jackpot.
"The chance that a given place will sell a winning lottery ticket is just related to how many tickets they sell," said Alexander.
However, players looking to avoid sharing the jackpot should choose numbers that aren't selected as often, according to Alexander.
He said that lottery players frequently choose the date of their birthdays as one of the numbers, so numbers higher than 31 would be played less.
The odds of matching all five numbers with the Powerball number is 1 in 292.2 million, according to the Mult-State Lottery Association, the organization that conducts the game.
But the overall chance of winning any prize is 1 in 24.9.
If you're looking to grab a ticket in time, sales end at 7 p.m. Saturday evening. The drawing will be held at 7:59 p.m.
The Powerball game is played in 45 states, the District of Columbia, Puerto Rico and U.S. Virgin Islands.
City News Service contributed to this report.


The Finite Element Method using MATLAB by Hyochoong Bang, Young W. Kwon
The Finite Element Method using MATLAB Hyochoong Bang, Young W. Kwon ebook
ISBN: 0849396530, 9780849396533
Solving ODEs with Matlab Instructors Manual - L.F. With Matlab Instructors Manual – L.F. I want to know what does actual mean by "Weak Form"? The finite element method (FEM) has become one of the most important and useful tools for scientists and engineers. IAnd What are we take Test Function while using in Galerkin Method? The analysis of the crash-test with explicit finite element programs such as LS-DYNA helps us to reduce the actual testing on prototypes in the automotive industry. Shampine.pdfSpectral Methods in MATLAB – Lloyd N. Spectral Methods in MATLAB - Lloyd N. This ebook is a matlab tutorial ebook on Finite Element methods. Many electronics design software are based on Finite element methods theory such as Comsol Multiphysics, CST studio, Altium designer and others. I always come across during class of Finite Element Methods. The Finite Element Method using MATLAB - Kwon and Bang.pdf. The faculty members form the most valuable resource of the technical education system. While  uses only free softwares for 3D reconstruction, present work optionally makes use of MATLAB (which is a commercial software) also. The behavior of car stability has been simulated with MATLAB software.
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Online Casino Games – THEIR RESIDENCE Edge
You can find basically three forms of casino games obtainable in casinos today: gambling games, table games, and interactive gaming devices. Gambling games, including slots, roulette, blackjack, baccarat, craps, etc., are usually played by just one individual at the same time in a casino and do not require the continuous presence of the casino staff to play. Table games, which include poker, bridge, roulette, slot machines, etc., require the constant presence of casino staff and players to make sure fairness in odds.
When we consider the game costs, the very first thing we have to consider may be the house edge. The word “house edge” means the percentage of profit a casino makes from each player in the casino. In land-based casinos, where slots are the 블랙잭 most popular games, the house edge is just about 10%. Compared, in online casinos the house edge is even lower, sometimes only a single point. Blackjack, craps, roulette, baccarat, poker, baccarat, slot machines, etc., have smaller houses with smaller percentages.
Slots, video poker, and other gambling games have their own characteristics, which make them more difficult to investigate than other casino games. Analysis requires knowledge of statistics and probability. One of the primary problems encountered in casinos in relation to gambling, especially with regards to slots, is identifying which machine is most beneficial to bet on. Slots are based on random chance, so any two slots could be different ones. It’s quite common for gamblers to lose a lot of money while trying to identify the slot that gives the highest percentage chance of winning.
Analysis of casino games is made more complicated by the truth that casino games are played in stacks. Every card or ticket has an associated price, whether it’s a dollar, five dollars, a dollar bill, a ten dollar bill, etc. We can utilize the arithmetic mean of the costs of all the tickets, which we manage dividing the sum of all the individual prices by the number of tickets in the stack. That’s, we want the typical deviation of the common price. Standard deviation is really a way of measuring how unpredictable changes in the average price are.
The typical deviation of the random variables is also used to determine whether a game includes a house advantage or not. Suppose, we have two sets of numbers: one set is randomly chosen from the number [0,1]. The casino software will assign a spot called keno to each player, which corresponds to their performance in a casino game. By calculating the standard deviation of the numbers from the distribution of the keno numbers, we can determine the amount of house advantage or disadvantage.
We are able to also analyze casino games by considering the house advantage or disadvantage of different casino games. Once you place a bet in a casino game, you take an instantaneous risk. But the risk can vary greatly, depending on how lucky you’re. In roulette, for instance, if you hit on a jackpot, your expected winnings become larger; but if you miss, in that case your expected winnings become smaller. Exactly the same is true for baccarat and poker games.
You can find three different variations of roulette, three different variations of baccarat and three different variations of poker, so we must analyze them separately. Each variation has its own house edge, so that is excatly why the analysis also involves counting the house edge of each game. There are four types of online slots: progressive slots, bonus slots, video slots and progressive slots machines with live dealers. Additionally, there are different variations of online slots, so we ought to analyze them separately. Each kind of slot includes a different house edge.
It might be very interesting to know what type of house edge each of these online casino games have. And that is something you could see out if you spend some time studying the various types of online casino games available. After you know their house edge, you can make an informed decision concerning which game you will most likely win and which one you should avoid. You also need to consider the casino games’ odds, or possibility of winning, because the larger the house edge, the more your odds of losing. Knowing this basic information will help you make more informed choices about casino games.


INTRODUCTION TO BUSINESS STATISTICS 7TH EDITION BY RONALD WEIERS – TEST BANK
Chapter 11: Hypothesis Tests Involving Two Sample Means
1. True or False
When comparing the mean of two dependent samples, we are interested in only one variable: the difference between measurements for each person or object.
2. True or False
A typical example of dependent samples occurs when we have before-and-after measures of the same individuals.
3. True or False
An important factor in choosing between the pooled-variances t-test and the unequal-variances t-test is whether we can assume the population means might be equal.
4. True or False
Although it is often associated only with small-sample tests, the t distribution is appropriate when the population standard deviations are unknown, regardless of how large or small the samples happen to be.
5. True or False
When the population standard deviations are unknown and not assumed to be equal, pooling the sample standard deviations into a single estimate of their common population value is no longer applicable.
6. True or False
When the population standard deviations are unknown and are not assumed to be equal, s1 and s2 must be used to estimate their respective population standard deviations, 1 and 2.
7. True or False
The number of degrees of freedom associated with the unequal-variances t-test for comparing the means of two independent samples is n1 + n2 – 2.
8. True or False
When either test can be applied to the same data, the z-test for comparing the means of two independent samples is preferable to the unequal-variances t-tests, especially when doing the test with computer assistance.
9. True or False
The z-test requires no assumptions about the shape of the population distributions as long as both n1 and n2 are 30.
10. True or False
The z-test approximation to the unequal variance t-test assumes that the population standard deviations, 1 and 2 , are known.


Came across this story by chance via an article in a Twine update that I was about to delete. Anyway, I caught the name Wolfram so thought I’d take a peek. The name might ring a bell – it’s Wolfram as in Wolfram Research, as in Stephen Wolfram of Mathematica fame. No slouch when it comes to all things mathematical. In any event, apparently in May he will unveil Alpha which, I gather from the article, is a “computational engine” that will actually compute answers to plain language queries. A brief sampling from the article:
For those who are more scientifically inclined, Stephen showed me many interesting examples — for example, Wolfram Alpha was able to solve novel numeric sequencing problems, calculus problems, and could answer questions about the human genome too. It was also able to compute answers to questions about many other kinds of topics (cooking, people, economics, etc.). Some commenters on this article have mentioned that in some cases Google appears to be able to answer questions, or at least the answers appear at the top of Google’s results. So what is the Big Deal? The Big Deal is that Wolfram Alpha doesn’t merely look up the answers like Google does, it computes them using at least some level of domain understanding and reasoning, plus vast amounts of data about the topic being asked about.
It will be interesting to see how (and whether) it actually performs. Given Wolfram’s credentials, the huge effort (undertaken in stealth mode it seems) and data that has gone into it and the positive articles to date (such as the one below) it does sound very promising.
From a legal perspective, it will be interesting to see how content used in the engine has been utilized and how the rights to such content (assuming there is at least some non-public domain material used) have been dealt with. From a tech perspective, it will be very interesting to see what the iron powering this thing will look like, particularly if it starts getting millions of queries a day, how the underlying algorithms work and the extent to which it can evolve and improve over time (I hesitate to use the word “learn”). And from a biz perspective, it will be interesting to see whether Wolfram takes a google-type approach to revenue generation (i.e. ads) or whether he has something else up his sleeve. Check it out for yourself in May.


Издательство: Scholastic Inc., 2017 г. Серия: EarlyLearners Жанр: Изучение иностранного языка
Аннотация к книге "Write and Wipe Counting"
Write and Wipe Counting is perfect for helping children who are learning to write and use the numbers 1-10. The book comes with a wipe-clean pen and the glossy board is easy to clean, so that children can try a page, wipe it clean, and try it again! This interactive book shows children exactly how to write the numbers 1-10, and provides practice in counting and ordering numbers. Читать Write and Wipe Counting.


- a balanced approach to numeracy instruction that combines conceptual understanding, and problem-solving skills.
- engaging our students in real-world problem-solving tasks to help them see the relevance of mathematics in everyday life. Our students are encouraged to apply their knowledge and skills to solve authentic problems, fostering critical thinking, reasoning, and problem-solving abilities.
- cater to individual students’ strengths, interests, and readiness levels.
- engage with parents and caregivers in supporting mathematics development at home. The school may provide resources, strategies, and guidance to involve families in promoting reading and writing habits and creating a literacy-rich environment.


At Harewood C of E Primary School we follow the White Rose Maths (WRM) scheme of learning with linked resources such as Classroom Secrets and Target Maths. We use the mastery approach to teach elements in small steps, through fluency tasks and reasoning challenges.
Formative assessment is a critical part of everyday practice in mathematics and feedback and ‘live-marking’ is offered wherever possible so pupils can see if they have grasped the concept within the lesson and so that they know the next steps forward.
We test the children’s progress termly, using PUMA assessment materials as well as using the White Rose unit assessments to assess prior knowledge and understanding after each unit and identify pupils in need of intervention in these areas.
The WRM scheme is supported by a wide range of resources and websites, including www.classroomsecrets.co.uk, which we subscribe to. We value the importance of mathematical ‘manipulatives’ (e.g. numicon) which are available in all classes and we make use of practical tools where appropriate (i.e. measuring containers, scales, clocks, trundle wheels, scientific data logging equipment etc.).
Differentiation is fluid within each class, dependent on the task at hand and the need of the child. Classes may have the children sat in ability groups or seating plans are considered so pupils needing support are easily accessed by the teacher or support staff. Initial input is whole class and tasks differentiated as necessary. All small steps have both fluency and reasoning resources and short term planning includes challenge and support tasks (or adaptations to the task).
Children’s work is marked regularly (usually the same day) by the teacher, TA, the child or a peer. Throughout the lesson, the teacher and TA (if present) monitor progress, plan opportunities for the pupils to reflect on their progress in the lesson and highlight children for additional support with the aim of same day intervention work if necessary. If the WRM unit assessment scores show a pupil in need of support work then this is planned for these pupils, focusing on the related concepts from previous years to try to close any gaps or previous misconceptions.


From infancy onwards children connect to Mathematics through experiences and daily life. They are learning concepts of size, shape, distance, number and comparisons. These early understandings are crucial for building foundations for developing skills and knowledge, but also for developing attitude, problem solving and Mathematical thinking.
So how can you support this? Help your child to love Mathematics by modelling and including your child in Mathematics from daily life. Encourage them to ask questions, to take risks and to be curious by talking about Mathematics in every day life.
Here are ten ideas for doing just this:
1. When shapes, amounts, size or numbers can be compared ask your child’s opinion. Which toy is bigger? Or smaller? Will it take us longer to walk to the park or to the shop? Do you have more strawberries or less strawberries? Look for things you can compare and share these experiences with your child
2. Develop number sense by counting at every opportunity. Our everyday life is full of opportunities to count. When we dress, when we cook, when we walk to school. Ask your child to count how many bikes there are on the corner? Or how many carrots are in the fridge, better still ask them to count and choose the carrots when shopping. Use coins and notes too and ask them to count out daily how many 1 yuan notes there are in your wallet.
3. Solve problems with your child. Puzzles allow children to develop problem solving skills by using strategic thinking and reasoning skills. Ask them lots of questions about how they are solving these problems and this helps them to explain their ideas. Why do you think that piece goes there? What do you think the picture in this corner will be? What colors can you see?
4. Early addition and subtraction skills come from informal experiences using objects. When sharing food (i.e. singular items: fruit, candy, dumplings) ask children to count how many pieces there are in total. If everyone got one apple how many apples in total? How many plates are on the table? How many shoes are at the door?
5. Identify shapes in real life. When walking or in malls or at the park, play games looking for shapes in real life. As children develop their knowledge explore more complex shapes.
6. Cooking offers a range of mathematical learning experiences. Counting ingredients, measuring ingredients, discussing shapes of resources and creations, comparing sizes.
7. Playing games offers children the opportunity to experience through modelling and practice strategic thinking. Pattern games, sharing games, building games。
8. Sorting activities using shells, buttons, coins, ribbons or any easy to handle objects that your family will enjoy collecting. Then at different times sort them by color, size, shape.
9. Pattern activities: identifying patterns in life at an early age help build a foundation for future Mathematical problem solving、
10. Look for Mathematics in story books. Are they discussing size, comparing amounts, counting? Ask your child to look at the numbers on the page and count with you. Ask your child to count a certain object on the page.
Research has shown that children with a positive attitude about mathematics, who value mistakes and see the fun in Mathematics develop greater fluency and confidence. Helping children to see that Mathematics is more than simply calculating broadens their understandings and expectations.
Well known researcher in Mathematics Learning and Teaching Jo Boaler (2013) states, “The core of mathematics is reasoning – thinking through why methods make sense and talking about reasons for the use of different methods” (Please click “Read More”to download the PDF file) This is why encouraging children to explain their ideas and thinking is so important. For young children this begins by adults modelling this process. When you are using Mathematics skills in daily life tell your children. “Hmm, I do not know if this book will fit into my bag? How can I find out? Can we measure the book and then the bag? What can we measure it with? Our hands. Ok let’s try” This models, and includes your child, in how to solve a problem and use specific skills. The power of involving your child and sharing these experiences can have a big impact.
Just as reading with your child develops a love of books, so can playing and exploring Mathematics in daily life develop a love of Mathematics.
Make Mathematics fun! Celebrate mistakes as learning experiences. Encourage children to ask questions about numbers, shapes, location, pattern and measurement.