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# 4.2 Graphs of exponential functions  (Page 6/6)

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## Verbal

What role does the horizontal asymptote of an exponential function play in telling us about the end behavior of the graph?

An asymptote is a line that the graph of a function approaches, as $\text{\hspace{0.17em}}x\text{\hspace{0.17em}}$ either increases or decreases without bound. The horizontal asymptote of an exponential function tells us the limit of the function’s values as the independent variable gets either extremely large or extremely small.

What is the advantage of knowing how to recognize transformations of the graph of a parent function algebraically?

## Algebraic

The graph of $\text{\hspace{0.17em}}f\left(x\right)={3}^{x}\text{\hspace{0.17em}}$ is reflected about the y -axis and stretched vertically by a factor of $\text{\hspace{0.17em}}4.\text{\hspace{0.17em}}$ What is the equation of the new function, $\text{\hspace{0.17em}}g\left(x\right)?\text{\hspace{0.17em}}$ State its y -intercept, domain, and range.

$g\left(x\right)=4{\left(3\right)}^{-x};\text{\hspace{0.17em}}$ y -intercept: $\text{\hspace{0.17em}}\left(0,4\right);\text{\hspace{0.17em}}$ Domain: all real numbers; Range: all real numbers greater than $\text{\hspace{0.17em}}0.$

The graph of $\text{\hspace{0.17em}}f\left(x\right)={\left(\frac{1}{2}\right)}^{-x}\text{\hspace{0.17em}}$ is reflected about the y -axis and compressed vertically by a factor of $\text{\hspace{0.17em}}\frac{1}{5}.\text{\hspace{0.17em}}$ What is the equation of the new function, $\text{\hspace{0.17em}}g\left(x\right)?\text{\hspace{0.17em}}$ State its y -intercept, domain, and range.

The graph of $\text{\hspace{0.17em}}f\left(x\right)={10}^{x}\text{\hspace{0.17em}}$ is reflected about the x -axis and shifted upward $\text{\hspace{0.17em}}7\text{\hspace{0.17em}}$ units. What is the equation of the new function, $\text{\hspace{0.17em}}g\left(x\right)?\text{\hspace{0.17em}}$ State its y -intercept, domain, and range.

$g\left(x\right)=-{10}^{x}+7;\text{\hspace{0.17em}}$ y -intercept: $\text{\hspace{0.17em}}\left(0,6\right);\text{\hspace{0.17em}}$ Domain: all real numbers; Range: all real numbers less than $\text{\hspace{0.17em}}7.$

The graph of $\text{\hspace{0.17em}}f\left(x\right)={\left(1.68\right)}^{x}\text{\hspace{0.17em}}$ is shifted right $\text{\hspace{0.17em}}3\text{\hspace{0.17em}}$ units, stretched vertically by a factor of $\text{\hspace{0.17em}}2,$ reflected about the x -axis, and then shifted downward $\text{\hspace{0.17em}}3\text{\hspace{0.17em}}$ units. What is the equation of the new function, $\text{\hspace{0.17em}}g\left(x\right)?\text{\hspace{0.17em}}$ State its y -intercept (to the nearest thousandth), domain, and range.

The graph of $\text{\hspace{0.17em}}f\left(x\right)=2{\left(\frac{1}{4}\right)}^{x-20}$ is shifted left $\text{\hspace{0.17em}}2\text{\hspace{0.17em}}$ units, stretched vertically by a factor of $\text{\hspace{0.17em}}4,$ reflected about the x -axis, and then shifted downward $\text{\hspace{0.17em}}4\text{\hspace{0.17em}}$ units. What is the equation of the new function, $\text{\hspace{0.17em}}g\left(x\right)?\text{\hspace{0.17em}}$ State its y -intercept, domain, and range.

$g\left(x\right)=2{\left(\frac{1}{4}\right)}^{x};\text{\hspace{0.17em}}$ y -intercept: Domain: all real numbers; Range: all real numbers greater than $\text{\hspace{0.17em}}0.$

## Graphical

For the following exercises, graph the function and its reflection about the y -axis on the same axes, and give the y -intercept.

$f\left(x\right)=3{\left(\frac{1}{2}\right)}^{x}$

$g\left(x\right)=-2{\left(0.25\right)}^{x}$

y -intercept: $\text{\hspace{0.17em}}\left(0,-2\right)$

$h\left(x\right)=6{\left(1.75\right)}^{-x}$

For the following exercises, graph each set of functions on the same axes.

$f\left(x\right)=3{\left(\frac{1}{4}\right)}^{x},$ $g\left(x\right)=3{\left(2\right)}^{x},$ and $\text{\hspace{0.17em}}h\left(x\right)=3{\left(4\right)}^{x}$

$f\left(x\right)=\frac{1}{4}{\left(3\right)}^{x},$ $g\left(x\right)=2{\left(3\right)}^{x},$ and $\text{\hspace{0.17em}}h\left(x\right)=4{\left(3\right)}^{x}$

For the following exercises, match each function with one of the graphs in [link] .

$f\left(x\right)=2{\left(0.69\right)}^{x}$

B

$f\left(x\right)=2{\left(1.28\right)}^{x}$

$f\left(x\right)=2{\left(0.81\right)}^{x}$

A

$f\left(x\right)=4{\left(1.28\right)}^{x}$

$f\left(x\right)=2{\left(1.59\right)}^{x}$

E

$f\left(x\right)=4{\left(0.69\right)}^{x}$

For the following exercises, use the graphs shown in [link] . All have the form $\text{\hspace{0.17em}}f\left(x\right)=a{b}^{x}.$

Which graph has the largest value for $\text{\hspace{0.17em}}b?$

D

Which graph has the smallest value for $\text{\hspace{0.17em}}b?$

Which graph has the largest value for $\text{\hspace{0.17em}}a?$

C

Which graph has the smallest value for $\text{\hspace{0.17em}}a?$

For the following exercises, graph the function and its reflection about the x -axis on the same axes.

$f\left(x\right)=\frac{1}{2}{\left(4\right)}^{x}$

$f\left(x\right)=3{\left(0.75\right)}^{x}-1$

$f\left(x\right)=-4{\left(2\right)}^{x}+2$

For the following exercises, graph the transformation of $\text{\hspace{0.17em}}f\left(x\right)={2}^{x}.\text{\hspace{0.17em}}$ Give the horizontal asymptote, the domain, and the range.

$f\left(x\right)={2}^{-x}$

$h\left(x\right)={2}^{x}+3$

Horizontal asymptote: $\text{\hspace{0.17em}}h\left(x\right)=3;$ Domain: all real numbers; Range: all real numbers strictly greater than $\text{\hspace{0.17em}}3.$

$f\left(x\right)={2}^{x-2}$

For the following exercises, describe the end behavior of the graphs of the functions.

$f\left(x\right)=-5{\left(4\right)}^{x}-1$

As $x\to \infty$ , $f\left(x\right)\to -\infty$ ;
As $x\to -\infty$ , $f\left(x\right)\to -1$

$f\left(x\right)=3{\left(\frac{1}{2}\right)}^{x}-2$

$f\left(x\right)=3{\left(4\right)}^{-x}+2$

As $x\to \infty$ , $f\left(x\right)\to 2$ ;
As $x\to -\infty$ , $f\left(x\right)\to \infty$

For the following exercises, start with the graph of $\text{\hspace{0.17em}}f\left(x\right)={4}^{x}.\text{\hspace{0.17em}}$ Then write a function that results from the given transformation.

Shift $f\left(x\right)$ 4 units upward

Shift $\text{\hspace{0.17em}}f\left(x\right)\text{\hspace{0.17em}}$ 3 units downward

$f\left(x\right)={4}^{x}-3$

Shift $\text{\hspace{0.17em}}f\left(x\right)\text{\hspace{0.17em}}$ 2 units left

Shift $\text{\hspace{0.17em}}f\left(x\right)\text{\hspace{0.17em}}$ 5 units right

$f\left(x\right)={4}^{x-5}$

Reflect $\text{\hspace{0.17em}}f\left(x\right)\text{\hspace{0.17em}}$ about the x -axis

Reflect $\text{\hspace{0.17em}}f\left(x\right)\text{\hspace{0.17em}}$ about the y -axis

$f\left(x\right)={4}^{-x}$

For the following exercises, each graph is a transformation of $\text{\hspace{0.17em}}y={2}^{x}.\text{\hspace{0.17em}}$ Write an equation describing the transformation.

$y=-{2}^{x}+3$

For the following exercises, find an exponential equation for the graph.

$y=-2{\left(3\right)}^{x}+7$

## Numeric

For the following exercises, evaluate the exponential functions for the indicated value of $\text{\hspace{0.17em}}x.$

$g\left(x\right)=\frac{1}{3}{\left(7\right)}^{x-2}\text{\hspace{0.17em}}$ for $\text{\hspace{0.17em}}g\left(6\right).$

$g\left(6\right)=800+\frac{1}{3}\approx 800.3333$

$f\left(x\right)=4{\left(2\right)}^{x-1}-2\text{\hspace{0.17em}}$ for $\text{\hspace{0.17em}}f\left(5\right).$

$h\left(x\right)=-\frac{1}{2}{\left(\frac{1}{2}\right)}^{x}+6\text{\hspace{0.17em}}$ for $\text{\hspace{0.17em}}h\left(-7\right).$

$h\left(-7\right)=-58$

## Technology

For the following exercises, use a graphing calculator to approximate the solutions of the equation. Round to the nearest thousandth. $\text{\hspace{0.17em}}f\left(x\right)=a{b}^{x}+d.$

$-50=-{\left(\frac{1}{2}\right)}^{-x}$

$116=\frac{1}{4}{\left(\frac{1}{8}\right)}^{x}$

$x\approx -2.953$

$12=2{\left(3\right)}^{x}+1$

$5=3{\left(\frac{1}{2}\right)}^{x-1}-2$

$x\approx -0.222$

$-30=-4{\left(2\right)}^{x+2}+2$

## Extensions

Explore and discuss the graphs of $\text{\hspace{0.17em}}F\left(x\right)={\left(b\right)}^{x}\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}G\left(x\right)={\left(\frac{1}{b}\right)}^{x}.\text{\hspace{0.17em}}$ Then make a conjecture about the relationship between the graphs of the functions $\text{\hspace{0.17em}}{b}^{x}\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}{\left(\frac{1}{b}\right)}^{x}\text{\hspace{0.17em}}$ for any real number $\text{\hspace{0.17em}}b>0.$

The graph of $\text{\hspace{0.17em}}G\left(x\right)={\left(\frac{1}{b}\right)}^{x}\text{\hspace{0.17em}}$ is the refelction about the y -axis of the graph of $\text{\hspace{0.17em}}F\left(x\right)={b}^{x};\text{\hspace{0.17em}}$ For any real number $\text{\hspace{0.17em}}b>0\text{\hspace{0.17em}}$ and function $\text{\hspace{0.17em}}f\left(x\right)={b}^{x},$ the graph of $\text{\hspace{0.17em}}{\left(\frac{1}{b}\right)}^{x}\text{\hspace{0.17em}}$ is the the reflection about the y -axis, $\text{\hspace{0.17em}}F\left(-x\right).$

Prove the conjecture made in the previous exercise.

Explore and discuss the graphs of $\text{\hspace{0.17em}}f\left(x\right)={4}^{x},$ $\text{\hspace{0.17em}}g\left(x\right)={4}^{x-2},$ and $\text{\hspace{0.17em}}h\left(x\right)=\left(\frac{1}{16}\right){4}^{x}.\text{\hspace{0.17em}}$ Then make a conjecture about the relationship between the graphs of the functions $\text{\hspace{0.17em}}{b}^{x}\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\left(\frac{1}{{b}^{n}}\right){b}^{x}\text{\hspace{0.17em}}$ for any real number n and real number $\text{\hspace{0.17em}}b>0.$

The graphs of $\text{\hspace{0.17em}}g\left(x\right)\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}h\left(x\right)\text{\hspace{0.17em}}$ are the same and are a horizontal shift to the right of the graph of $\text{\hspace{0.17em}}f\left(x\right);\text{\hspace{0.17em}}$ For any real number n , real number $\text{\hspace{0.17em}}b>0,$ and function $\text{\hspace{0.17em}}f\left(x\right)={b}^{x},$ the graph of $\text{\hspace{0.17em}}\left(\frac{1}{{b}^{n}}\right){b}^{x}\text{\hspace{0.17em}}$ is the horizontal shift $\text{\hspace{0.17em}}f\left(x-n\right).$

Prove the conjecture made in the previous exercise.

The center is at (3,4) a focus is at (3,-1), and the lenght of the major axis is 26
The center is at (3,4) a focus is at (3,-1) and the lenght of the major axis is 26 what will be the answer?
Rima
I done know
Joe
What kind of answer is that😑?
Rima
I had just woken up when i got this message
Joe
Rima
i have a question.
Abdul
how do you find the real and complex roots of a polynomial?
Abdul
@abdul with delta maybe which is b(square)-4ac=result then the 1st root -b-radical delta over 2a and the 2nd root -b+radical delta over 2a. I am not sure if this was your question but check it up
Nare
This is the actual question: Find all roots(real and complex) of the polynomial f(x)=6x^3 + x^2 - 4x + 1
Abdul
@Nare please let me know if you can solve it.
Abdul
I have a question
juweeriya
hello guys I'm new here? will you happy with me
mustapha
The average annual population increase of a pack of wolves is 25.
how do you find the period of a sine graph
Period =2π if there is a coefficient (b), just divide the coefficient by 2π to get the new period
Am
if not then how would I find it from a graph
Imani
by looking at the graph, find the distance between two consecutive maximum points (the highest points of the wave). so if the top of one wave is at point A (1,2) and the next top of the wave is at point B (6,2), then the period is 5, the difference of the x-coordinates.
Am
you could also do it with two consecutive minimum points or x-intercepts
Am
I will try that thank u
Imani
Case of Equilateral Hyperbola
ok
Zander
ok
Shella
f(x)=4x+2, find f(3)
Benetta
f(3)=4(3)+2 f(3)=14
lamoussa
14
Vedant
pre calc teacher: "Plug in Plug in...smell's good" f(x)=14
Devante
8x=40
Chris
Explain why log a x is not defined for a < 0
the sum of any two linear polynomial is what
Momo
how can are find the domain and range of a relations
the range is twice of the natural number which is the domain
Morolake
A cell phone company offers two plans for minutes. Plan A: $15 per month and$2 for every 300 texts. Plan B: $25 per month and$0.50 for every 100 texts. How many texts would you need to send per month for plan B to save you money?
6000
Robert
more than 6000
Robert
can I see the picture
How would you find if a radical function is one to one?
how to understand calculus?
with doing calculus
SLIMANE
Thanks po.
Jenica
Hey I am new to precalculus, and wanted clarification please on what sine is as I am floored by the terms in this app? I don't mean to sound stupid but I have only completed up to college algebra.
I don't know if you are looking for a deeper answer or not, but the sine of an angle in a right triangle is the length of the opposite side to the angle in question divided by the length of the hypotenuse of said triangle.
Marco
can you give me sir tips to quickly understand precalculus. Im new too in that topic. Thanks
Jenica
if you remember sine, cosine, and tangent from geometry, all the relationships are the same but they use x y and r instead (x is adjacent, y is opposite, and r is hypotenuse).
Natalie
it is better to use unit circle than triangle .triangle is only used for acute angles but you can begin with. Download any application named"unit circle" you find in it all you need. unit circle is a circle centred at origine (0;0) with radius r= 1.
SLIMANE
What is domain
johnphilip
the standard equation of the ellipse that has vertices (0,-4)&(0,4) and foci (0, -15)&(0,15) it's standard equation is x^2 + y^2/16 =1 tell my why is it only x^2? why is there no a^2?
what is foci?
This term is plural for a focus, it is used for conic sections. For more detail or other math questions. I recommend researching on "Khan academy" or watching "The Organic Chemistry Tutor" YouTube channel.
Chris


text:
Although a boxplot can tell you whether a data set is symmetric (when the median is in the center of the box), it can’t tell you the shape of the symmetry the way a histogram can. They manage to carry a lot of statistical details — medians, ranges, outliers — without looking intimidating. The same can be done for “minimum” and “maximum”. We can also infer that the distribution is somewhat negatively skewed. This can be graphed using anything, but I choose to graph it using Python. There are, in fact, so many different descriptors that it is going to be convenient to collect the in a suitable graph. Box-and-whisker plots highlight central values in a set of data. Minimum. A boxplot is a standardized way of displaying the distribution of data based on a five number summary (“minimum”, first quartile (Q1), median, third quartile (Q3), and “maximum”). Let’s take a look at something more interesting than trees… date night! Data from West Magazine. But, if there ARE outliers, then a boxplot will instead be made up of the following values.As you can see above, outliers (if there are any) will be shown by stars or points off the main plot. Most of the wait times are relatively short, and only a few wait times are long. What is the shape of a box and whisker plot? The figure below left shows data which are negatively skewed. Here x-axis denotes the data to be plotted while the y-axis shows the frequency distribution. the mean is typically less than the median; the tail of the distribution is longer on the left hand side than on the right hand side; and. Conclusion: Histograms and box plots are very similar in that they both help to visualize and describe numeric data. In this article, you will learn to create whisker and box plot in R programming. Maximum. Statistics is the study and analysis of the distribution of data. How to interpret a box plot? For example, the histogram below represents the distribution of observed heights of black cherry trees. They also show how far the extreme values are from most of the data. Input data can … This video uses three examples to show how to use a box plot to describe the shape, centre, outliers, and spread which a box plot can show. Then four equal sized groups are made from the ordered scores. Take a look, # Import all libraries for this portion of the blog post, # Make PDF for the normal distribution a function, # Make a PDF for the normal distribution a function, sns.boxplot(x='diagnosis', y='area_mean', data=df), malignant = df[df['diagnosis']=='M']['area_mean']. The … This section is largely based on a free preview video from my Python for Data Visualization course. The box ranges from Q1 (the first quartile) to Q3 (the third quartile) of the distribution and the range represents the IQR (interquartile range). Box plots are also known as box-and-whiskers plots. Once the box plot is graphed, you can display and compare distributions of data. The interpretation of the compactness or spread of the data also applies to … The spread of a distribution of data describes how far the observations tend to be from each other. In summary, a Dot Plot is a graph for displaying the distribution of numerical variables where each dot represents a value. In descriptive statistics, a box plot or boxplot is a method for graphically depicting groups of numerical data through their quartiles.Box plots may also have lines extending from the boxes (whiskers) indicating variability outside the upper and lower quartiles, hence the terms box-and-whisker plot and box-and-whisker diagram.Outliers may be plotted as individual points. It can tell you about your outliers and what their values are. Drawing a box plot from a cumulative frequency graph is straightforward as long as the median and quartiles have been found. Median The median is represented by the line in the box. If you are interested in the spread of all the data, it is represented on a boxplot by the horizontal distance between the smallest value and the largest value, including any outliers. You can plot a boxplot by invoking .boxplot() on your DataFrame. Let us also generate normal distribution with the same mean and standard deviation and … main is used to give a title to the graph. Negatively Skewed : For a distribution that is negatively skewed, the box plot will show the median closer to the upper or top quartile. First Quartile. The box plot is used to plot the distribution of a data set. The greatest value of a picture is when it forces us to notice what we never expected to see. 5C – (5:41) Creating QQ-Plots and other plots using UNIVARIATE; Related SPSS Tutorials . An example of how to describe a distribution presented as a boxplot The Box Plot, sometimes also called "box and whiskers plot", combines … The box plot shape will show if a statistical data set is normally distributed or skewed.When the median is in the middle of the box, and the whiskers are about the same on both sides of the box, then the distribution is symmetric. A graph with a single peak is called unimodal. Recognize, describe, and calculate the measures of location of data: quartiles and percentiles. Additionally, boxplots display two common measures of the variability or spread in a data set. My next tutorial goes over How to Use and Create a Z Table (standard normal table). Future tutorials will take some this knowledge and go over how to apply it to understanding confidence intervals. The graph below shows a standard normal probability density function ruled into four quartiles, and the box plot you would expect if you took a very large sample from that distribution. Display data graphically and interpret graphs: stemplots, histograms, and box plots. To get the probability of an event within a given range we will need to integrate. A box plot is a chart that shows data from a five-number summary including one of the measures of central tendency. 4.6 Box Plot and Skewed Distributions. Distributions are characterized by location, spread and shape: A fundamental concept in representing any of the outputs from a production process is that of a distribution.Distributions arise because any manufacturing process output will not yield the same value every time it is measured. The median is a common measure of the center of your data. The first distribution is unimodal — it has one mode (roughly at 10) around which the observations are concentrated. Using the graph, we can compare the range and distribution of the area_mean for malignant and benign diagnosis. The guideline for … Although histograms are better in determining the underlying distribution of the data, box plots allow you to compare multiple data sets better than histograms as they are less detailed and take up less space. Inter-quartile range. It can also tell you if your data is symmetrical, how tightly your data is grouped, and if and how your data is skewed. Why are shadow boxes called shadow boxes? Box plots are non-parametric: they … One way to understand a box plot is to think of what a box plot of data from a normal distribution will look like. A box plot (or box-and-whisker plot) shows the distribution of quantitative data in a way that facilitates comparisons between variables or across levels of a categorical variable. Boxplot. Here x-axis denotes the data to be plotted while the y-axis shows the … How to read a boxplot: Study of the distribution. In order to construct a box-and-whisker plot, the first step is to order your data numerically and find the median value. The notched boxplot allows you to evaluate confidence intervals (by default 95% confidence interval) for the medians of each boxplot. In this lesson, you will learn how to compare box plots by analyzing the center and spread of data sets. How do you make a box out of a cereal box? For whole numbers, if a value occurs more than once, the dots are placed one above the other so that the height of the column of dots represents the frequency for that value. Classifying shapes of distributions. The Box-Cox normality plot is a plot of these correlation coefficients for various values of the $$\lambda$$ parameter. We can draw multiple boxplots in a single plot, by passing in a list, data frame or multiple vectors. The main measure of spread that you should know for describing distributions on the AP® Statistics exam is the range. The five numbers are. The Box-Cox normality plot shows that the maximum value of the correlation coefficient is at $$\lambda$$ = -0.3. Box plots visually show the distribution of numerical data and skewness through displaying the data quartiles (or percentiles) and averages. for Lifetime access on our Getting Started with Data Science in R course. In the next two examples, we again use boxplots to compare two distributions. We usually control the ‘bins’ parameters to produce a distribution with smooth boundaries. Does Boxing Day have anything to do with boxing? They aim to describe the data and explore the central tendency and variability before using advanced statistical analysis techniques. In other words, it might help you understand a boxplot. The median, part of the five-number summary, is shown … A box plot gives us a basic idea of the distribution of the data. How many shapes of distribution are there? To see how it works, it is best to consider an example. Click to see full answer Beside this, what are the 8 possible shapes of a distribution? How do you make and interpret boxplots using Python? search. LO 4.7: Define and describe the features of the distribution of one quantitative variable (shape, center, spread, outliers). Together with the box, the whiskers show how big a range there is between those two extremes. A distribution is considered "Positively Skewed" when mean > median. The third distribution is kind of flat, or uniform. That graph is called the Box Plot. Make learning your daily ritual. IF the box plot is relatively short, then the data is more compact. These graphs encode five characteristics of distribution of data by showing the reader their position and length. Classifying distributions as being symmetric, left skewed, right skewed, uniform or bimodal. The components of box plots are: — Information Dashboard Design, Stephen Few. Similarly, a bivariate KDE plot smoothes the (x, y) observations with a 2D Gaussian. estimates of variability — the dispersion of data from the mean in the distribution. Examine the center and spread of the distribution. What is the shape of the distribution shown below? The centre line of the box is the sample median and will estimate the median of the distribution, which is, of course, 0 … It can tell you about your outliers and what their values are. But it is primarily used to indicate a distribution is skewed or not and if there are potential unusual observations (also called outliers) present in the data set. Box and whisker plots seek to explain data by showing a spread of all the data points in a sample. The equation below is the probability density function for a normal distribution. DataMentor Logo. The following boxplots are skewed. There are a couple ways to graph a boxplot through Python. interquartile range (IQR): 25th to the 75th percentile. The graph below shows a standard normal probability density function ruled into four quartiles, and the box plot you would expect if you took a very large sample from that distribution. As mentioned earlier, outliers are the remaining .7% percent of the data. Suppose we are interested in finding the probability of a random data point landing within the interquartile range .6745 standard deviation of the mean, we need to integrate from -.6745 to .6745. The lines ("whiskers") show the largest or smallest observation that falls within a distance of 1.5 times the box size from the nearest hinge. box-and-whiskers plots, are an excellent way to visualize differences among groups. Finding it difficult to learn programming? 5.1 Standard Deviation and Variance. For a uniformly distributed data set,in box plot diagram, the central rectangle spans the first quartile to the third quartile (or the interquartile range, IQR). We are going to look at how much of the total bill men and women pay on a given date on common date nights. Here are a few other things to keep in mind about boxplots: Hopefully this wasn’t too much information on boxplots. It means the data constitute higher frequency of high valued scores. There are many ways to describe the spread of a distribution. to describe quickly the characteristics of the underlyingdistribution of a dataset througha ... the distribution of the data values. What is white box testing and list the types of white box testing? To begin with, scores are sorted. The box plot is used to plot the distribution of a data set. Now we have a multitude of numerical descriptive statistics that describe some feature of a data set of values: mean, median, range, variance, quartiles, etc. The code below reads the data into a pandas dataframe. For instance, the modality The graph above does not show you the probability of events but their probability density. The box plot is a standardized way to display the distribution of data based on following five number summary. Understanding the anatomy of a boxplot by comparing a boxplot against the probability density function for a normal distribution. If you’re doing statistical analysis, you may want to create a standard box plot to show distribution of a set of data. The four ways to describe shape are whether it is symmetric, how many peaks it has, if it is skewed to the left or right, and whether it is uniform. Although boxplots may seem primitive in comparison to a histogram or density plot, they have the advantage of taking up less space, which is useful when comparing distributions between many groups or datasets. the code snippets for generating normally distributed data and calculating estimates using various python packages like numpy, scipy, … Luckily, there's a one-dimensional way of visualizing the shape of distributions called a box plot. In R, boxplot (and whisker … the median is closer to the third quartile than to the first quartile. How do you calibrate a Taylor bathroom scale? As always, the code used to make the graphs is available on my github. first quartile (Q1/25th Percentile): the middle number between the smallest number (not the “minimum”) and the median of the dataset. One way to understand a box plot is to think of what a box plot of data from a normal distribution will look like. What is software testing explain black box and white box testing on detail with example? What cars have the most expensive catalytic converters? In some box plots, the minimums and maximums outside the first and third quartiles are depicted with lines, which … This time we focus on writing a description of the two distributions. Now, that we know how to create a Box Plot we will cover the five number summary, to explain the numbers that are in the tool tip and make up the box plot itself. There are, in fact, so many different descriptors that it is going to be convenient to collect the in a suitable graph. A1={0.22, -0.87, -2.39, -1.79, 0.37, -1.54, 1.28, -0.31, -0.74, 1.72, 0.38, -0.17, -0.62, -1.10, 0.30, 0.15, 2.30, 0.19, -0.50, -0.09} A2={-5.13, -2.19, -2.43, -3.83, 0.50, -3.25, 4.32, 1.63, 5.18, -0.43, 7.11, 4.87, -3.10, -5.81, 3.76, 6.31, 2.58, 0.07, 5.76, 3.50} Notice that both datasets are approximately balanced aroundzero; evidently the mean in both cases is "near" zero.However there is substantially more variation in A2 which ranges approximately from -6 to 6whereas A1 ranges approximately from -2½ to 2½. R Box Plot. Let’s simplify it by assuming we have a mean (μ) of 0 and a standard deviation (σ) of 1. The … The whiskers extend from the edges of box to show the range of the data. A boxplot uses 5 numbers to summarize “most” of a distribution, and then plots any outliers that it does not cover. In this regard, how do you describe the spread of a box plot? Box plots are composed of the same key measures of dispersion that you get when you run .describe() , allowing it to be displayed in one dimension and easily comparable with other distributions. Once the … Also, since the notches in the boxplots do not overlap, you can conclude that with 95% confidence, that the true medians do differ. You can use the SGPLOT and SGPANEL procedures to produce plots that characterize the frequency or the distribution of your data. The box plot shape will show if a statistical data set is normally distributed or skewed. By default, they extend no more than In this article, we will further discuss the similarities and differences between these two tools. A Box Plot is also known as Whisker plot is created to display the summary of the set of data values having properties like minimum, first quartile, median, third quartile and maximum. How do you make a gift box out of a cereal box? Multiple Boxplots. Therefore, the data should be approximately normally distributed. The histogram of the data after applying the Box-Cox transformation with $$\lambda$$ = -0.3 shows a data set for which … Example:In an earlier example we considered the following cotinine levels of 40 smokers. Claim Now. The above plot shows a normal distribution, i.e., the variable ‘x’ is normally distributed. Now we have a multitude of numerical descriptive statistics that describe some feature of a data set of values: mean, median, range, variance, quartiles, etc. To graph a box plot the following data points must be calculated: the minimum value, the first quartile, the median, the third quartile, and the maximum value. Now that we have discussed how to read the boxplot, let talk about how to interpret it like really good stats students! It looks at how to find the IQR and how to use the median as the measure of spread. The goal here is to show how the distribution will be distributed using our visualization built for you as it compares to the more complex to create and less indicative of an actual population Bell Curve. These values include the minimum value, the first quartile, the median, the third quartile, and the maximum value. It is good practice to examine both a graphical and a numerical summarization of your data. Median. The matplotlib.pyplot module of matplotlib library provides boxplot Now we use … The boxplot with left-skewed data shows failure time data. What defines an outlier, “minimum”, or“maximum” may not be clear yet. This definition might not make much sense so let’s clear it up by graphing the probability density function for a normal distribution. This approach can be far more tedious, but can give you a greater level of control. The image above is a comparison of a boxplot of a nearly normal distribution and the probability density function (pdf) for a normal distribution. R tutorials; R Examples; Use DM50 to GET 50% OFF! Please update your bookmarks accordingly. If you any questions or thoughts on the tutorial, feel free to reach out in the comments below, through the YouTube video page, or through Twitter. The median is indicated by a line … And if the data distribution was arranged in numerical order, the median would be the value directly in the middle. box and whisker plots, compare box plots, how to compare box plots, modified box plots Box plots, a.k.a. Example. Copyright 2020 FindAnyAnswer All rights reserved. Box plots are a type of graph that can help visually organize data. Range. Scores between 70-85 feet are the most common, while higher and lower scores are less common. Describing Distributions. how normal distribution can be used to describe the data and observations from a machine learning model. Powered by https://www.numerise.com/GCSE Revision Video 26 - Box Plots Why is the shape of a distribution important? Note that all three distributions are symmetric, but are different in their modality (peakedness).. Set as true to draw width of the box proportionate to the sample size. So, now that we have addressed that little technical detail, let’s look at an exampl… For example, if we set the number of ‘bins’ too low, say bins=5, then most of the values get accumulated in the same interval, and as a result they … The value of \ ... (and so does not follow a normal distribution). … If there are no outliers, you simply won’t see those points. To do this, we will utilize the Breast Cancer Wisconsin (Diagnostic) Dataset. Predictions and hopes for Graph ML in 2021, How To Become A Computer Vision Engineer In 2021, How to Become Fluent in Multiple Programming Languages. What is the Philadelphia property tax rate? A symmetric data set shows the median roughly in the middle of the box. In the box plot, a box is created from the first quartile to the third quartile, a verticle line is also there which goes through the box at the median. Use a five-number summary and a boxplot to describe a distribution. Let us consider the Ozone and Temp field of airquality dataset. The lines coming out from each box extend from the maximum to the minimum values of each set. References. What's the difference between Koolaburra by UGG and UGG? The reason why I am showing you this image is that looking at a statistical distribution is more commonplace than looking at a box plot. That we have moved all content for this concept to for better.. Benign diagnosis histogram does are concentrated near the left whisker, the shape the. A box plot shape will show if a distribution 95 % confidence interval ) for the medians of boxplot! ) and averages: study of the data and skewness through displaying the of... Computed the lower and upper … how to compare box plots ; about distribution plots about. This overview may hide important characteristics that of summarizing data to plot the distribution of variables. And explore the central tendency and variability before using advanced statistical analysis is that of summarizing.... Distribution divided by the number of values in a suitable graph is some. = -0.3 many ways to graph it using Python gift box out of a is!, data frame or multiple vectors the lowest score in your distribution to the minimum values of each.! For data Visualization course plots highlight central values in the interior of the,... Plotted while the y-axis shows the frequency of high valued scores the in. ( shape, center how to describe distribution of box plot spread, outliers ) uses 5 numbers to summarize “ ”... Normality plot shows how to describe distribution of box plot our data is spread out and spread of a box out a! On detail with example larger ranges indicate wider distribution, that is, more scattered data normal... Then the data into a pandas dataframe is near the left whisker, the third quartile, the whiskers how! Next section will try to clear that up for you greater variability for malignant tumor area_mean as as. Is software testing explain black box and whisker plot have been found to in... The concentration of the data distribution divided by the line in the middle of the variability or spread a... Is available on my github the characteristics of a distribution of data from a cumulative frequency is... To interpret it like really good stats students chart that shows data from the mean the. ( 5:41 ) Creating QQ-Plots and other plots using UNIVARIATE ; Related SPSS tutorials draw width the. Moved all content for this concept to how to describe distribution of box plot better organization data numerically and find the IQR and how to it. It means that our data follows a normal distribution, represented as a in... Boxplots in a list of numbers by ordering the numbers and finding the median and quartiles have been found graphical. Would be the value of a distribution is considered  negatively skewed when. Simply the distance from the higher one confidence interval ) for the or. ( standard normal Table ) video from my Python for data Visualization course same can be created from list. The … use a five-number summary, only the horizontal axis displays values and, the histogram below represents distribution... Figure below left shows data which are negatively skewed '' when mean > median describes how the! Y-Axis shows the frequency or the distribution of numerical variables where each dot a... ( peakedness ) displaying the distribution of numerical data and observations from a normal.... Related SPSS tutorials see how it works, it is in the middle “ box ” represents distribution... Produce a distribution is bimodal — it has one mode ( roughly at 10 ) around which the observations to... Plot the distribution of the correlation coefficient is at \ ( \lambda \ ) = -0.3 or distribution... Description of the box five characteristics of a picture is when it forces how to describe distribution of box plot notice...: Define and describe the spread of all the data over the center and spread of data... Summarize “ most ” of a box plot in R programming the measure of the data Lifetime access our! Boxplot with left-skewed data shows failure time data once the box extends from mean... Of a boxplot against the probability density order your data not symmetric it shows that our data showing! To different diagnosis the same can be used to plot the distribution of your data graphically! Dataframe df into seaborn ’ s clear it up by graphing the probability density more about the center your... Title to the third distribution is considered  Positively skewed '' when
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# Could you comment for my portfolio ?

This topic is 2611 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Hi,

Id like to know your critiques for My portfolio

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I get many contradictory messages on it.

It states that you have all these talents in graphics, but the showpiece on the front page is rather disappointing. It is a low res movie (not good for showing off graphics) and seems to only show techniques that could be part of a university course. Nothing in the demo is impessive to me at all.

Looking at the other movies there are huge differences in the quality of conent, and I immediately question them. What exactly was yours, what came from elsewhere?

I look at that you are a self taught developer. But then you write about finishing your MSc at university studies in game developmnt and four years at an instutitue of technology in electronics engineering, and then finish off the set saying you unofficially attended a few CS lectures. That does not inspire confidence.

This continues all the way through your site and your CV. You state things that might be important in passing, but then emphasise things that are irrelevant. You have much space pointing out that you collaborated on the Microsoft-directed research project that really seems like a very unimportant student project, and use almost the same space later claining to have developed networking, video codecs, and hardware image processors.

Nothing in there looks like you want to be a game developer. The whole thing looks scattered and unfocused. There are certainly things you have done that could be restated in terms of game development skills. You should start by figuring those out and giving them focus.

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First of all , thanks very much for spending your time and sharing your critiques :

1.

It states that you have all these talents in graphics, but the showpiece on the front page is rather disappointing. It is a low res movie (not good for showing off graphics) and seems to only show techniques that could be part of a university course. Nothing in the demo is impessive to me at all.

Except from its being a low res movie , what techniques would you suggest to implement regarding content of the video to be able to make it impressive ?

On the other hand , considering other 3 demos , would you suggest to put any of them to the front ?

And I cant understand where I state I have talents in graphics ? First I wrote I am focused now I changed it to passionate , I hope that fixes the misleading statement

because I will apply for entry level jobs

2.

Looking at the other movies there are huge differences in the quality of conent, and I immediately question them. What exactly was yours, what came from elsewhere?

I have just 2 other videos in demos section for a PS3 project and a simple network programming. All programming credits are mine.

But how can they have a huge difference in quality ?? Network programimng demos video captured in same style with my graphics demo.

Regarding PS3 video , I used a simple cam recorder.

3.

I look at that you are a self taught developer. But then you write about finishing your MSc at university studies in game developmnt and four years at an instutitue of technology in electronics engineering, and then finish off the set saying you unofficially attended a few CS lectures. That does not inspire confidence.

During electronics engineering course , I studied and practised Windows C++ programming , yes that makes me self taught

During MSc ( what I really was after is not being educated but getting WORK PERMIT ) , I made self studies as crazy

Regarding education part , I wrote them in reverse order by date. And during my electronics engieering , then I attended to CS lectures unofficially so that is related with there so that is

why it is there. I am afraid I dont agree with this on you , I think it is a matter of perspective.

4.

This continues all the way through your site and your CV. You state things that might be important in passing, but then emphasise things that are irrelevant. You have much space pointing out that you collaborated on the Microsoft-directed research project that really seems like a very unimportant student project, and use almost the same space later claining to have developed networking, video codecs, and hardware image processors.

I will try to re-arrange amount of spaces used per experience on the CV. Thanks for pointing to that out.

Regarding my site , instead of using the headline Graphics & Game Programming , I changed it to Graphics and Game Technologies

Plus , if you are pointing out to Others section , I think the title is not misleading because they already are not in demos section , they are just there

because I enjoyed my time when working with them , they might be unrelated to game TECHNOLOGIES development I am aware so that is why I callem the others

5.

Nothing in there looks like you want to be a game developer. The whole thing looks scattered and unfocused. There are certainly things you have done that could be restated in terms of game development skills. You should start by figuring those out and giving them focus.

I am not directly interested in games , but directly interested in game technologies , that would be developing a part of an engine , working on graphics and special effects , maybe networking or physics.

So thanks to your critique , I have changed the headline in the entrance as Graphics & Game Technologies Programming

Ofcourse I did not have great time to specialize on all of those , so that is why I tried to build a graphics demo from scratch even it is not impressive and the others

But regarding game technologies programming , what changes would you suggest to restate them ? How really can I restate them if my all past experiences had nothing directly todo with those

The only thing I can offer with my past experiences is C/C++ development , but no engine no graphics no others

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Could you give a feedback considering the fact that I don`t have any prior graphics or game industry experience so I will apply for entry level jobs ?

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Is the site really rubbish ?

I really am looking forward to hearing feedbacks , especially constructive ones

thanks...

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Is the site really rubbish ?

I really am looking forward to hearing feedbacks , especially constructive ones

thanks...

I'm told it's useful to have a completed game or two as listed projects. Even if they aren't graphically advanced, as long as they are "complete" (menus, ect.), they show a commitment to your projects.

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The 3D graphics demo shows that you're familiar enough for a junior/intermediate graphics programming job. Yes, there's nothing "amazing" in it, but it shows familiarity with projections, surfaces, HDR, simulation, post processing and special effects. You've covered everything a graphics programmer needs except animation and DX11 experience.
The fact that you've used GCM before is also a huge plus.

I didn't notice the "HOME | DEMOS | OTHERS" links the first time I looked at the page, and as a result I didn't see your radiosity demo (which is a nice demo for a graphics programmer to have).

The layout of your resume is a bit messy - I try to keep mine to a single page only. You could remove the projects section, and simply provide one URL saying that you have 3d graphics, PS3 and multi-threading demos at your website.

Your English grammar is a bit incorrect in places, and many sentences do not "flow" naturally. However, this is entirely forgiveable as you're not a native English speaker.

Saying that you're 'self taught' and that you 'unofficially' studied comp-sci does sound bad to an employer. When a HR person reads that, they're going to picture an unlicensed doctor performing illegal basement surgery
I would instead call yourself an "experienced C++ engineer", etc... Many electrical engineering courses also cover some computer-science material, so it doesn't sound that bad to say that you studied EE instead of CS.

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# Expansion of incomplete Gamma function.

I need to estimate the following quantity $$K(m,y) \equiv \left(\frac e m \right)^m \times \Gamma(m,(1+y)m),$$ as $m \to \infty$, where $\Gamma(a,z)$ is the incomplete gamma function.

My question is, is there a valid expansion of the incomplete Gamma function in the range when $y \approx m^{-1/2}$ that can give us a good estimation of $K(m,y)$?

Further details:

As I need to estimate $K(m,y)$ for all $y > 0$, I looked up for uniform expansions of incomplete Gamma functions. The most promising formula that I can find is give by R. B. Paris: $$\Gamma(a,z)= z^{a-1/2}e^{-z} \left(\sqrt{\frac \pi 2}\cdot e^{\chi^2/2} \mathrm{erfc}\left(\frac{\chi}{\sqrt{2}}\right)+O(z^{-1/2})\right)$$ where $\chi = (z-a)/\sqrt{z}$, and $\mathrm{erfc}$ is the complementary error function.

So in my case, I have $$K(m,y) = \left(\frac{1+y}{e^y} \right)^m \frac{1}{\sqrt{(1+y)m}} \left(\sqrt{\frac \pi 2}\cdot e^{\chi^2/2} \mathrm{erfc}\left(\frac{\chi}{\sqrt{2}}\right)+O(m^{-1/2})\right).$$ with $\chi = y \sqrt{m}/\sqrt{1+y}$.

When $y > m^{-1/2+\epsilon}$ or $y < m^{-1/2-\epsilon}$, i.e., when $\chi \to \infty$ or $\chi \to 0$, the above estimation is good, because we can expand $\mathrm{erfc}(\chi)$ easily.

But when $\chi$ is bounded from above and below, all I can say is that $\mathrm{erfc}(\chi) = O(1)$, which implies that $$K(m, y) = O(m^{-1/2}).$$ This is not good enough for my application. I would like to get the first order approximation of $K(m,y)$ for $y$ in this range.

Even more details:

I am actually trying is to upper bound the following $$H(n,m) = \int_0^\infty e^{-y(n-m+1)} (1+y)^{n-m} K(m+1, y) \mathrm dy \qquad (m \to \infty),$$ where $n > m$ and $n, m$ are both integers.

If I use $K(m+1,y) = O(m^{-1/2})$, I will only get $H(n,m) = O(m(n-m))^{-1/2}$. But again I actually want to get the first order approximation of $H(m,n)$.

• Could you clarify what you mean by "not good enough"? – Antonio Vargas Feb 11 '17 at 9:35
• @AntonioVargas I added more background of the question. – ablmf Feb 11 '17 at 15:40
• When y=m^(-1/2), Mathematica shows a limit of 0.3976897/sqrt(m). – user210229 Feb 14 '17 at 14:35
• It appears that your difficulty is in approximating the value of the error function in a simple way. Have a look at AS 7.125, for example. – user26872 Feb 18 '17 at 21:18

From Stirling's approximation: $$m\Gamma(m)=\Gamma(m+1)\approx\left(\frac me\right)^m\sqrt{2\pi m}$$ one can write: $$K(m,y)=\left(\frac e m \right)^m \times \Gamma(m,(1+y)m)\approx\sqrt{\frac{2\pi}m}\times\frac{\Gamma(m,(1+y)m)}{\Gamma(m)}$$ and since $\Gamma(m,x)+\gamma(m,x)=\Gamma(m)$ then $$K(m,y)\approx\sqrt{\frac{2\pi}m}\left(1-\frac{\gamma(m,(1+y)m)}{\Gamma(m)}\right)$$ So you only need an approximation of regularized Gamma function: $$P(m,x):=\frac{\gamma(m,x)}{\Gamma(m)}$$ Note that $P(m,x)$ is the CDF of gamma distribution whose scale parameter is $1$. Therefore if a random variable, $x$, has a gamma distribution with shape parameter $m$, then: $$\mathbf{P}(x\ge m(1+y))=1-\frac{\gamma(m,(1+y)m)}{\Gamma(m)}$$ The mean and variance of a gamma distribution with unit scale are both $m$. For large $m$ the gamma distribution approaches to a normal distribution. So from a statistical point of view, you can consider a random variable $z$ with normal distribution $\mathcal N(m,m)$. Then your function becomes approximately proportional to the probability of $\mathbf P(z\ge m+my)$ or in other words: $$z\sim\mathcal N(m,m)\rightarrow K(m,y)\approx\sqrt{\frac{2\pi}m}\mathbf P\left(\frac{z-\mu}{\sigma}\ge \sigma y\right)$$ Hence $$K(m,y)\approx\sqrt{\frac{\pi}{2m}}\left(1-\text{erf}\left(y\sqrt{\frac m2} \right)\right)$$
For large $m$ with $1+\frac{k}{m}\approx 1$ and $m!\approx \left(\frac{m}{e}\right)^m\sqrt{2\pi m}$:
$\displaystyle \left(\frac{e}{m}\right)^m\Gamma(m,(1+y)m)= \left(\frac{e}{m}\right)^m (m-1)!- \left(\frac{e}{m}\right)^m \sum\limits_{k=0}^\infty\frac{(-1)^k ((1+y)m)^{k+m}}{k!(k+m)}$$\displaystyle \approx \frac{\sqrt{2\pi}}{\sqrt{m}}-\frac{(1+y)^m}{m}e^{-ym}$


text:
# Extension Authors¶

In this section I will take you through an example of writing a new directive for the runestone interactive system. In this case we will look at adding a datafile directive.

The datafile directive is going to be used in conjunction with the skulpt file operations. For skulpt to read a file we must provide some data that data can either be data that is part of a
 element or if we want the data to be editable we can embed the data in a <textarea> element. In the case of the
 element the data might be visible or it might be hidden. Our directive will look something like this:

Indentation is important. Following the directive line, you can have as many optional parameters as you want. Followed by a blank line, followed by the main body of your directive.

.. datafile::  myid
:edit:
:rows: 20
:cols: 65

line 1  some data
line 2  some more data
line 3  this is the end

So the datafile takes one required parameter, a unique id that is used by the Skulpt open function as the file name. The :edit: parameter tells us to make a textarea rather than a pre. The :rows: and :cols: tell us how many rows and columns to add to the textarea. If these are not present, then our directive should do its best to figure out a reasonable number of rows and columns.

The html output of the directive above should be:

<textarea id="myid" cols="65" rows="20">
line 1  some data
line 2  some more data
line 3  this is the end
</textarea>

We will also make this extension work if the user wants to generate a non-interactive paper or pdf version of some text using LaTeX. In this case the output of our directive should simply be:

\begin{verbatim}
line 1  some data
line 2  some more data
line 3  this is the end
\end{verbatim}

Unless the :hide: flag is present in which case we won’t generate anything.

## Components of a directive¶

There are several parts to writing an extension.

1. Initialization: In this part you need to let sphinx know that there there is a new directive. The name of the directive is associated with a Python class that derives from the restructuredText Directive class.
2. Parse Time: In this stage of processing sphinx is building the document object model. A tree of nodes. At this stage we process all of the arguments and gather the main content into a structure that can be used later when rendering a document in whatever format: html, latex, epub, etc.
3. Output: At this stage we take the data that we have and format it for output by whatever writer is being used, again html, latex, etc.

All of the components of a directive can go in a single Python file. Sphinx sees these extensions as simple python packages, so you can create a folder with an __init.py file or you can create an __init__.py file that imports one or more of your own files.

The __init__.py file should go in the modules folder following the folder heirarchy that is in place. For example luther/sphinx/datafile/.

## Initialization¶

For the initialization phase we need to provide a setup function. The setup function connects the directive name with a class, and tells skulpt about any css or javscript files that will be needed to support any html output.

The initialization code for the datafile directive looks like this:

from docutils import nodes
from docutils.parsers.rst import directives
from docutils.parsers.rst import Directive

def setup(app):

app.connect('doctree-resolved',process_datafile_nodes)
app.connect('env-purge-doc', purge_datafiles)

The key function here is the setup function. The add_directive method maps the datafile directive to the DataFile class. Then we add three javascript files we want to include along with a new node type called DataFileNode This is the node that will get added to the document object model.

The next line connects the 'doctree-resolved' event with a function called process_datafile_nodes. This function could be used to create an index of our datafiles, or do nothing. the env-purge-doc event is simliar but is called after all datafile nodes have been processed.

## Parsing¶

During the parse phase there is one class for every directive. This class must supply a run method that returns a list of nodes. If you know that your directive is only ever going to create output for a particular rendering, e.g. html you can finish your run method by returning a raw node that is simply a string.

return [nodes.raw('', mystring ,format='html')]

In this case mystring could be as long and complicated an html string as you might like to make. A minimal hello world type example might be:

return [nodes.raw('', '
Hello World
', format='html')]

In other cases you will defer the rendering of the node until later, having built a structure that can support multiple output styles. In our example you will see that we return:

return [DataFileNode(self.options)]

Where the DataFileNode just maintains a dictionary of data items we will use when we want to render any of the possible output formats.

If you return a raw node then you can ignore the app.add_node(DataFileNode, html=(visit_df_node, depart_df_node)) line in the setup method.

Here is the DataFile class along with its run method.

class DataFile(Directive):
required_arguments = 1
optional_arguments = 2
has_content = True
option_spec = {
'hide':directives.flag,
'edit':directives.flag,
'rows':directives.positive_int,
'cols':directives.positive_int
}

def run(self):
env = self.state.document.settings.env

if not hasattr(env,'datafilecounter'):
env.datafilecounter = 0
env.datafilecounter += 1

if 'cols' not in self.options:
self.options['cols'] = min(65,max([len(x) for x in self.content]))
if 'rows'not in self.options:
self.options['rows'] = 20

self.options['divid'] = self.arguments[0]
if self.content:
source = "\n".join(self.content)
else:
source = '\n'
self.options['filecontent'] = source

if 'hide' not in self.options:
self.options['hide'] = 'block'
else:
self.options['hide'] = 'none'

if 'edit' not in self.options:
self.options['edit'] = False

return [DataFileNode(self.options)]

As you can see our class has some shared/static/class level variables that specify whether the directive has content, how many arguments, and what the names and types of the arguments are.

Here are the possible types for the options:

• flag: For options with no option arguments. Checks for an argument (raises ValueError if found), returns None for valid flag options.
• unchanged_required: Returns the text argument, unchanged. Raises ValueError if no argument is found.
• unchanged: Returns the text argument, unchanged. Returns an empty string (“”) if no argument is found.
• path: Returns the path argument unwrapped (with newlines removed). Raises ValueError if no argument is found.
• uri: Returns the URI argument with whitespace removed. Raises ValueError if no argument is found.
• nonnegative_int: Checks for a nonnegative integer argument, and raises ValueError if not.
• class_option: Converts the argument into an ID-compatible string and returns it. Raises ValueError if no argument is found.
• unicode_code: Convert a Unicode character code to a Unicode character.
• single_char_or_unicode: A single character is returned as-is. Unicode characters codes are converted as in unicode_code.
• single_char_or_whitespace_or_unicode: As with single_char_or_unicode, but “tab” and “space” are also supported.
• positive_int: Converts the argument into an integer. Raises ValueError for negative, zero, or non-integer values.
• positive_int_list: Converts a space- or comma-separated list of integers into a Python list of integers. Raises ValueError for non-positive-integer values.
• encoding: Verfies the encoding argument by lookup. Raises ValueError for unknown encodings.

There are two important instance variables to think about.

• self.content Refers to the body content of the directive. That is the indented text that comes after the options. This can be anything, and you can make up your own conventions for how to interpret the body of a directive.
• self.options Is a dictionary that contins key value pairs for all of the optional parameters. Of course you are free to modify this dictionary as much as you wish.

The self.options instance variable is a dictionary that will be used later to fill in a template for our output. So, most of the processing in the run method is checking to see if the author provided values for these options and providing some default values for them if they have not.

The last line of run creates an instance of our DataFileNode. This object doesn’t do much other than act as a container to hold our data until it is time to render the output. Nevertheless here is the code:

class DataFileNode(nodes.General, nodes.Element):
def __init__(self,content):
"""
Arguments:
- self:
- content:
"""
super(DataFileNode,self).__init__()
self.df_content = content

## Output¶

In the final stage of processing we render the document in whatever format the author is requesting. In this stage we take the data stored away in our DataFileNode and turn it into html or latex or whatever.

Each output format is handled by their own function that is registered back in the setup phase. recall that we used the following line to connect our html output with a couple of functions: app.add_node(DataFileNode, html=(visit_df_node, depart_df_node)).

We will use Python triple quoted strings to create a couple of templates to fill in. In the code below these templates are PRE and TEXTA

PRE = '''

%(filecontent)s

'''

TEXTA = '''
<textarea id="%(divid)s" rows="%(rows)d" cols="%(cols)d">
%(filecontent)s
</textarea>
'''

# self for these functions is an instance of the writer class.  For example
# in html, self is sphinx.writers.html.SmartyPantsHTMLTranslator
# The node that is passed as a parameter is an instance of our node class.
def visit_df_node(self,node):
if node.df_content['edit'] == True:
res = TEXTA
else:
res = PRE
res = res % node.df_content

res = res.replace("u'","'")  # hack:  there must be a better way to include the list and avoid unicode strings

self.body.append(res)

def depart_ac_node(self,node):
''' This is called at the start of processing an activecode node.  If activecode had recursive nodes
etc and did not want to do all of the processing in visit_ac_node any finishing touches could be

The visit_df_node function is called when a DataFileNode is found in the document tree. The visit function is called when the node is first encountered. The depart_df_node function is called after all the children have been visited.
Notice that visit_df_node mainly just looks at its options to see if we need to create a textarea or a pre element and then lets Python’s formatted strings take care of the rest.


text:
# Hodges exercise 2.7.1: Quantifier elimination in dense linear orderings

In Hodges' A Shorter Model Theory, exercise 2.7.1 tells you to prove theorem 2.7.1, which says that the following five formulas are an elimination $\Phi$ set for the class of all dense linear orderings (with a signature consisting only of "$<$"):

• There is a first element
• There is a last element
• $x$ is the first element
• $x$ is the last element
• $x<y$

The way it should be done is fairly clear to me, there are some details but the big idea (lemma 2.7.4) is that for every formula $\theta$ of the form $\exists y \bigwedge_{i=1}^n \psi_i$, where each $\psi_i$ is either in $\Phi$ or the negation of a formula in $\Phi$, I have to show that $\theta$ is equivalent (in every DLO) to a boolean combination of the formulas in $\Phi$. This new formula cannot have any other free variables than those in $\theta$.

This is where I run into problems. There are formulas $\theta$ for which I cannot figure out how to eliminate the existential quantifier. Indeed, for which I intuitively feel it should not be possible. For example: $$\theta\longleftrightarrow\exists x \, \lnot(x\text{ is the last element})$$ This expresses that a structure has at least two elements in its domain. I cannot figure out how to express this as only a boolean combination of $\Phi$. I cannot write it trivially as $\top$ or $\bot$, since they must be equivalent to $\theta$ in every DLO, and obviously whether $\theta\leftrightarrow\top$ or $\theta\leftrightarrow\bot$ depends on if the DLO is a singleton or not.

Is there some way to reduce $\theta$ to a boolean combination of $\Phi$, and if not, what am I missing? Why can this formula not have its quantifier eliminated even though I know it is supposed to be possible?


text:
InVEST +VERSION+ documentation

# Marine Finfish Aquacultural Production¶

## Summary¶

Supporting the production of aquacultured fish and shellfish is an important service provided by coastal and marine environments. Because salmon is one of the two most important finfish in aquaculture worldwide, the current version of the InVEST aquaculture model analyzes the volume and economic value of Atlantic salmon (Salmo salar) grown in netpen aquaculture facilities based on farming practices, water temperature, and economic factors. Inputs for the present model include farm location, management practices at the facilities, water temperature, economic data for valuation, and the time period over which results are of interest. This model is best used to evaluate how human activities (e.g., the addition or removal of farms or changes in harvest management practices) and climate change (e.g., change in sea surface temperature) may affect the production and economic value of aquacultured Atlantic salmon. Limitations of the model include assumptions that harvest practices, prices, and costs of production of aquacultured fish are constant for the selected time period. Additionally, risk of disease outbreaks and variability between individual salmon within a farm are not included in the model. Future releases of this model will include the following features: 1) guidance for modifying the Atlantic salmon model for other aquacultured marine fish, 2) quantification of wastes produced at aquaculture facilities, 3) a separate module for quantifying volume, economic value, filtration and production of wastes of aquacultured shellfish (e.g., oyster, shrimp), and 4) a sub-module to evaluate impacts of parasitic sea-lice on farmed Atlantic salmon.

## Introduction¶

Human demand for protein from the ocean has rapidly increased and is projected to continue to do so in coming decades (Delgado et al. 2003, Halwart et al. 2007, Soto et al. 2008). In recent years, the scales, previously tilted towards provisioning of protein from capture fisheries, have shifted toward aquaculture. In particular, finfish aquaculture, primarily for Atlantic salmon, has intensified in coastal areas over the past two decades (FAO 2004, Goldburg and Naylor 2004, Naylor and Burke 2005). In 2002, farmed salmon production, over 90% of which was for Atlantic salmon, was 68% higher than the volume of wild capture (FAO 2004). Atlantic salmon farming, conducted in floating netpens in low energy, nearshore areas, is a well-established, consolidated industry that operates in the temperate waters of Norway, Chile, the United Kingdom and Canada.

Commercial operations for Atlantic salmon use the marine environment to produce a valuable commodity, which generates revenue and is a source of employment. Yet salmon farming is controversial due to potentially adverse impacts to marine ecosystems and, thereby, people who derive their livelihoods from those ecosystems (e.g., commercial fishermen, tourism operators). Concerns about the effects of Atlantic salmon aquaculture on the marine ecosystem involve debate about the impacts of emission of dissolved and solid wastes to water quality and living habitats, degradation of water quality due to use of antibiotics, mixing and competition of escaped farmed salmon with endemic species (e.g., Pacific salmon), increased risk of parasitism and disease, and depletion of forage fish resources harvested from other ecosystems for use as Atlantic salmon feed.

Regulations for the Atlantic salmon aquaculture industry vary regionally, from the most stringent requirements for locating and operating facilities in Norwegian waters, to fewer constraints for farms in Chilean waters. For all operations, there are regulatory limits on where and how aquaculture can be conducted and requirements for monitoring and regulating the amount of waste generated at different facilities, and in some cases, mitigation requirements.

Weighing the economic benefits of Atlantic salmon aquaculture against the environmental costs involves quantifying both. The InVEST model presented here does the former by quantifying the volume and economic value of the commodity. Future outputs will include dissolved and particulate wastes generated as a byproduct of Atlantic salmon production. These outputs will be available for use in other InVEST models (e.g., water quality, habitat quality, fisheries) to assess impacts of Atlantic salmon aquaculture on other coastal and marine ecosystem services. With the full suite of model outputs, InVEST users will be able explore how different spatial configuration of Atlantic salmon farms in their region affects other ecosystem benefits and alleviates or exacerbates tradeoffs between economic benefits and downstream environmental costs.

## The Model¶

The model is designed to address how the production and economic value of farmed Atlantic salmon at individual aquaculture facilities and across a user-defined study area change depending on farm operations and changes in water temperature. Temporal shifts in price, costs or harvest management practices are not dynamically modeled, but can be represented by running the model sequentially, where each run uses different information on prices, costs and farm operations. The risk of disease outbreaks and variability between individual salmon within a farm are not included in the model. The model will yield the most accurate outputs when parameterized with site-specific temperature and farm operations data. If site-specific data are unavailable, the provided ranges of default values can be used to yield first approximations of results (see Data Needs section).

The model is run simultaneously for all Atlantic salmon farms identified by the user. Each farm can have a user-defined set of operations and management practices. The volume of fish produced on a farm depends on water temperature (which affects growth), the number of fish on the farm, the target harvest weight range, and the mortality rate. Fish growth is modeled on a daily time-step until the fish reach the target harvest weight range, after which they are harvested. After a user-defined fallowing period, the farm is restocked and this initiates the next production cycle. Production cycles continue for each farm until the end of the time period of interest (e.g., 2 years, 10 years). Outputs include the harvested weight of fish and net revenue per cycle for each individual farm. In addition, the model yields a map of the total harvested weight, total net revenue, and net present value over the time period of interest.

### How it Works¶

The model runs on a vector GIS dataset that maps individual aquaculture facilities for Atlantic salmon that are actively farmed over a user-defined time period. The map can be based on current farming (the “status quo” or “baseline” scenario), or on scenarios of projected expansion or contraction of the industry or on projected changes in water temperature.

In each farm we model the production of fish in three steps. (1) We model the growth of individual fish to harvest weight. (2) We calculate the total weight of fish produced in each farm as the number of fish remaining at harvest, multiplied by their harvested weight, less the weight removed during processing (gutting, etc.) and the weight of fish lost to natural mortality. (3) Lastly, all the fish in a farm are harvested at the same time, and the farm is restocked after a user-defined fallowing period. Valuation of processed harvest is an optional fourth step in the model.

#### Growth of the Individual Fish to Harvest Weight¶

Atlantic salmon weight (kg) is modeled from size at outplanting to target harvest weight. Weight is a function of growth rate and temperature (Stigebrandt 1999). Outplanting occurs when Atlantic salmon have been reared beyond their freshwater life stages. The model runs on a daily time step because the next version of the model (to be released in May 2011) will quantify waste products from aquaculture farms for use as inputs into the Marine InVEST water quality model. Fine resolution temporal data are more appropriate for the seasonal evaluation of environmental impacts (e.g., seasonal eutrophication).

Weight $$W_t$$ at time $$t$$ (day), in year $$y$$, and on farm $$f$$ is modeled as:

(1)$W_{t,y,f} = { ({\alpha W_{t-1,y,f}^\beta \cdot e^{T_{t-1,f} \tau}}) + W_{t-1,y,f} }$

where $$\alpha$$ (g1-bday-1) and $$\beta$$ (non-dimensional) are growth parameters, $$T_{t,f}$$ is daily water temperature (C) at farm $$f$$, and $$\tau$$ (C-1) represents the change in biochemical rates in fishes with an increase in water temperature. The value for Atlantic salmon (0.08) indicates a doubling in growth with an 8-9 C increase in temperature. Daily water temperatures can be interpolated from monthly or seasonal temperatures. The growing cycle for each farm begins on the user-defined date of outplanting ($$t=0$$). The outplanting date is used to index where in the temperature time series to begin. The initial weight of the outplanted fish for each farm is user-defined. An individual Atlantic salmon grows until it reaches its target harvest weight range, which is defined by the user as a target harvest weight.

#### Total Weight of Fish Produced per Farm¶

To calculate the total weight of fish produced for each farm, we assume that all fish on a farm are homogenous and ignore variability in individual fish growth. This assumption, though of course incorrect, is not likely to affect the results significantly because 1) netpens are stocked so as to avoid effects of density dependence and 2) aquaculturists outplant fish of the same weight to netpens for ease of feeding and processing. We also assume that when fish reach a certain size, all fish on the farm are harvested. In practice, farms consist of several individual netpens, which may or may not be harvested simultaneously. If a user has information about how outplanting dates and harvest practices vary between netpens on a farm, the user can define each netpen as an individual “farm.”

The total weight of processed fish $$TPW$$ on farm $$f$$ in harvest cycle $$c$$:

(2)$TPW_{f,c} = { W_{t_h,h,f} \cdot d \cdot n_f e^{-M \cdot (t_h - t_0)} }$

where $$W_{t_h,h,f}$$ is the weight at date of harvest $$t_h,y$$ on farm $$f$$ from Equation (1), $$d$$ is the processing scalar which is the fraction of the fish in the farm that remains after processing (e.g., weight of headed/gutted or filleted fish relative to harvest weight), $$n_f$$ is the user-defined number of fish on farm $$f$$, and $$e^{-M \cdot (t_h - t_o)}$$ is the daily natural mortality rate $$M$$ experienced on the farm from the date of outplanting ($$t_0$$) to date of harvest ($$t_h$$).

#### Restocking¶

The previous 2 steps describe how fish growth is mdoeled for one production cycle. However, the user may want to evaluate production of fish over a series of production cycles. The primary decision to be made when modeling multiple harvest cycles is if (and if so, how long) a farm will be left to lie fallow after harvest and before the next production cycle begins (initiated by outplanting).

If used, fallowing periods are considered hard constraints in the model such that a farm cannot be restocked with fish until it has lain fallow for the user-defined number of days. This is because fallowing periods are often used to meet regulatory requirements, which can be tied to permitting, and thus provide incentive for compliance. Once fish are harvested from a farm and after the user-defined fallowing period, new fish are outplanted to the farm. The model estimates the harvested weight of Atlantic salmon for each farm in each production cycle. The total harvested weight for each farm over the time span of the entire model run is the sum of the harvested weights for each production cycle.

#### Valuation of Processed Fish (Optional)¶

The aquaculture model also estimates the value of that harvest for each farm in terms of net revenue and net present value (NPV) of the harvest in each cycle. The net revenue is the harvest weight for each cycle multiplied by market price, where costs are accounted for as a fraction of the market price for the processed fish. Fixed and variable costs, including costs of freshwater rearing, feed, and processing will be more explicitly accounted for in the next iteration of this model. The NPV of the processed fish on a farm in a given cycle is the discounted net revenue such that:

(3)$NPV_{f,c} = { TPW_{f,c} {[{p (1-C)]} \cdot {1\over {{(1+r)}^t}}} }$

where $$TPW_{f,c}$$ is the total weight of processed fish on farm $$f$$ in harvest cycle $$c,p$$ is the market price per unit weight of processed fish, $$C$$ is the fraction of $$p$$ that is attributable to costs, $$r$$ [1] is the daily market discount rate, and $$t$$ is the number of days since the beginning of the model run.

Note

The beginning of the model run is the initial outplanting date for the very first farm (of all the farms in the study area) to receive fish. Thus, the net revenue for each farm in each harvest cycle is discounted by the number of days since the very first farm was initially stocked. The total NPV for each farm over the duration of the model run is the discounted net revenue from each harvest cycle summed over all harvest cycles $$c$$.

The discount rate reflects society’s preference for immediate benefits over future benefits (e.g., would you rather receive $10 today or$10 five years from now?). The default annual discount rate is 7% per year, which is one of the rates recommended by the U.S. government for evaluation of environmental projects (the other is 3%). However, this rate can be set to reflect local conditions or can be set to 0%.

#### Uncertainty Analysis (Optional)¶

Optionally, if the fish growth parameters are not known with certainty, the model can perform uncertainty analysis. This uncertainty analysis is done via a Monte Carlo simulation. In this simulation, the growth parameters ($$\alpha$$ and $$b$$) are repeatedly sampled from a given normal distribution, and the model is run for each random sampling.

The results for each run of the simulation (harvested weight, net present value, and number of completed cycles per farm) are collected and then analyzed. Uncertainty results are output in two ways: first, the model outputs numerical results, displaying the mean and the standard deviation for all results across all runs. Second, the model creates histograms to help visualize the relative probability of different outcomes.

## Limitations and Simplifications¶

Limitations of the model include assumptions that harvest practices, prices, and costs of production of aquacultured fish are constant over the selected time period. Additionally, risk of disease outbreaks and variability between individual salmon within a farm are not included in the model.

The current model operates at a daily time step (requiring daily temperature data).

Uncertainty in input data is currently supported only for fish growth parameters. There is currently no support for uncertainty in input data such as water temperature.

Growth is assumed to be exponential up to the point of harvesting. Survival and growth do not depend on density. The assumption is that aquaculturists are optimizing the stocking density such that there is not excess mortality due to over-crowding.

## Data Needs¶

### Data Sources¶

Here we outline the specific data and inputs used by the model and identify potential data sources and default values. Four data layers are required, and one is optional (but required for valuation).

1. Workspace Location (required). Users are required to specify a workspace folder path. It is recommended that the user create a new folder for each run of the model. For example, by creating a folder called “runBC” within the “Aquaculture” folder, the model will create “intermediate” and “output” folders within this “runBC” workspace. The “intermediate” folder will compartmentalize data from intermediate processes. The model’s final outputs will be stored in the “output” folder.:

Name: Path to a workspace folder.  Avoid spaces.
Sample path: \InVEST\Aquaculture\runBC

2. Finfish Farm Location (required). A GIS polygon or point dataset, with a latitude and longitude value and a numerical identifier for each farm.:

Names: File can be named anything, but no spaces in the name
File type: polygon shapefile or .gdb
Rows: each row is a specific netpen or entire aquaculture farm
Columns: columns contain attributes about each netpen (area, location, etc.).
Sample data set: \InVEST\Aquaculture\Input\Finfish_Netpens.shp

Note

The user must ensure that one field contains unique integers. This field name (i.e. “FarmID” in the sample data) must be chosen by the user for input #3 as the “farm identifier name”.

Note

The model checks to ensure that the finfish farm location shapefile is projected in meters. If it is not, the user must re-project it before running the model.

1. Farm Identifier Name (required). The name of a column heading used to identify each farm and link the spatial information from the GIS features (input #2) to subsequent table input data (farm operation and daily water temperature at farm tables, inputs # 6-7). Additionally, the numbers underneath this farm identifier name must be unique integers for all the inputs (#2, 6, & 7).:

Names: A string of text identifying a column in the Finfish Farm Location shapefile's attribute table
File type: Drop-down option
Sample: FarmID

2. Fish growth parameters (required, defaults provided). Default a (0.038 g/day), b (0.6667 dimensionless units), and $$\tau$$ (0.08 C-1) are included for Atlantic salmon, but can be adjusted by the user as needed. If the user chooses to adjust these parameters, we recommend using them in the simple growth model (Equation (1)) to determine if the time taken for a fish to reach a target harvest weight typical for the region of interest is accurate.:

Names: A numeric text string (floating point number)
File type: text string (direct input to the ArcGIS interface)
Sample (default): 0.038 for a / 0.6667 for b

3. Uncertainty analysis data (optional). These parameters are required only if uncertainty analysis is desired. Users must provide three numbers directly through the tool interface.:

• Standard deviation for fish growth parameter a. This represents uncertainty in the estimate for the value of a.
• Standard deviation for fish growth parameter b. This represents uncertainty in the estimate for the value of b.
• Number of Monte Carlo simulation runs. This controls the number of times that the parameters are sampled and the model is run, as part of a Monte Carlo simulation. A larger number will increase the reliability of results, but will also increase the running time of the model. Monte Carlo simulations typically involve about 1000 runs.
1. Daily Water Temperature at Farm Table (required). Users must provide a time series of daily water temperature (C) for each farm in data input #1. When daily temperatures are not available, users can interpolate seasonal or monthly temperatures to a daily resolution. Water temperatures collected at existing aquaculture facilities are preferable, but if unavailable, users can consult online sources such as NOAA’s 4 km AVHRR Pathfinder Data and Canada’s Department of Fisheries and Oceans Oceanographic Database. The most appropriate temperatures to use are those from the upper portion of the water column, which are the temperatures experienced by the fish in the netpens.:

Table Names: File can be named anything, but no spaces in the name
File type: *.xls or .xlsx (if user has MS Office 2007 or newer)
Rows: There are 365 rows (rows 6-370), each corresponding to a day of the year.
Columns: The first two columns contain the number for that year (1-365) and day-month.
Sample: \InVEST\Aquaculture\Input\Temp_Daily.xls\WCVI$ Note For clarification on rows, please refer to the sample temperature dataset in the InVEST package (Temp_Daily.xls). Note Column “C” and then all others to its right contain daily temperature data for a specific farm, where the numbers found in row 5 must correspond to the numbers underneath the farm identifier name found in input #2’s attribute table. 1. Farm Operations Table (required). A table of general and farm-specific operations parameters. Please refer to the sample data table for reference to ensure correct incorporation of data in the model. If you would like to use your own dataset, you can modify values for farm operations (applied to all farms) and/or add new farms (beginning with row 32). However, do not modify the location of cells in this template. If for example, you choose to run the model for three farms only, they should be listed in rows 10, 11 and 12 (farms 1, 2, and 3, respectively). Several default values that are applicable to Atlantic salmon farming in British Columbia are also included in the sample data table. The majority of these values can be found by talking to aquaculturists in the study area or through regional industry reports from major aquaculture companies (e.g. Panfish, Fjord Seafood, Cermaq, Marine Harvest, Mainstream Canada, and Grieg). The General Operation Parameters of the input table includes the following inputs that apply to all farms: + Fraction of the fish weight (in the farm) remaining after processing (e.g., weight of headed/gutted fish relative to harvest weight) + Natural mortality rate on the farm (daily) + Duration of simulation (in years) The Farm-Specific Operation Parameters of the input table includes the following inputs: • Rows: Each row in this table (table begins at row #10) contains the input data for a specific farm. • Columns: Each column contains values and should be named as follows: • Farm #: a series of consecutive integers (beginning with “1” in row 10) that identifies each farm and must correspond to the unique integers underneath the farm identifier name found in input #2’s attribute table. • Weight of fish at start (kg): this is the weight of fish when they are outplanted, which occurs when Atlantic salmon have been reared beyond their freshwater life stages. • Target weight of fish at harvest (kg) • Number of fish in farm (absolute) • Start day for growing (Julian day of the year): this is the date of the initial outplanting at the start of the model run. Outplanting date will differ in subsequent cycles depending on lengths of growth and fallowing periods. • Length of fallowing period (number of days): if there is no fallowing period, set the values in this column to “0”. Table Names: File can be named anything, but no spaces in the name File type: *.xls or .xlsx (if user has MS Office 2007 or newer) Sample: \InVEST\Aquaculture\Input\Farm_Operations.xls\WCVI$

1. Run Valuation? (optional). By checking this box, users request valuation analysis.

2. Valuation parameters (required for valuation, defaults provided).:

Names: A numeric text string (positive integer or floating point number)
File type:  text string (direct input to the ArcGIS interface)
Sample (default):
a. Market price per kilogram of processed fish.
Default value is 2.25 $/kilogram (Urner-Berry monthly fresh sheet reports on price of farmed Atlantic salmon) b. Fraction of market price that accounts for costs rather than profit. Default value is 0.3 (30%). c. Daily market discount rate. We use a 7% annual discount rate, adjusted to a daily rate of 0.000192 for 0.0192% (7%/365 days).  Note If you change the market price per kilogram, you should also change the fraction of market price that accounts for costs to reflect costs in your particular system. ## Running the Model¶ The model is available as a standalone application accessible from the Windows start menu. For Windows 7 or earlier, this can be found under All Programs -> InVEST |version| -> Finfish Aquaculture. Windows 8 users can find the application by pressing the windows start key and typing “finfish” to refine the list of applications. The standalone can also be found directly in the InVEST install directory under the subdirectory invest-3_x86/invest_pollination.exe. ### Viewing Output from the Model¶ Upon successful completion of the model, a file explorer window will open to the output workspace specified in the model run. This directory contains an output folder holding files generated by this model. Those files can be viewed in any GIS tool such as ArcGIS, or QGIS. These files are described below in Section Interpreting Results. ## Interpreting Results¶ ### Model Outputs¶ The following is a short description of each of the outputs from the Aquaculture tool. Each of these output files is automatically saved in the “Output” folder that is saved within the user-specified workspace directory: Final results are found in the output folder of the workspace for this model. The model produces two main output files: • Output\Finfish_Harvest.shp: Feature class (copy of input 2) containing three additional fields (columns) of attribute data. • Tot_Cycles – The number of harvest cycles each farm completed over the course of the simulation (duration in years) • Hrvwght_kg – Total processed weight (in kg, Eqn. 2,) for each farm summed over the time period modeled • NPV_USD_1k – The discounted net revenue from each harvest cycle summed over all harvest cycles (in thousands of$). This value will be a “0” if you did not run the valuation analysis.
• Output\HarvestResults_[date and time].html: An HTML document containing tables that summarize the inputs and outputs of the model.

• Farm Operations – a summary of the user-provided input data including: Farm ID Number, Weight of fish at start, Weight of fish at harvest, Number of fish in farm, start day for growing and Length of fallowing period
• Farm Harvesting – a summary table of each harvest cycle for each farm including: Farm ID Number, Cycle Number, Days Since Outplanting Date, Harvested Weight, Net Revenue, Net Present Value, Outplant Day, Year
• Farm Result Totals – a summary table of model outputs for each farm including: Farm ID Number, Net Present Value, Number of completed harvest cycles, Total volume harvested
• Uncertainty Analysis Results – this section will be included only if uncertainty analysis was performed. It includes two parts:
• Numerical Results – a table summarizing mean and standard deviation for model outputs such as harvested weight, net present value, and number of completed harvest cycles.
• Histograms – a series of histograms to help visualize relative probabilities of different outcomes.

Figure 1: First few rows of a sample Farm Operations table in HTML output

Figure 2: First few rows of a sample Farm Harvesting table in HTML output

Figure 3: First few rows of a sample Farm Result Totals table in HTML output

Figure 4: Sample histogram in the uncertainty analysis section of HTML output

### Parameter Log¶

• Each time the model is run a text file will appear in the workspace folder. The file will list the parameter values for that run and be named according to the date and time.

## References¶

Delgado, C., N. Wada, M. Rosegrant, S. Meijer, and M. Ahmed. 2003. Outlook for Fish to 2020: Meeting Global Demand. Washington, DC: Int. Food Policy Res. Inst.

FAO. 2004. Fishstat Plus. Universal software for fishery statistical series. Capture production 1950 - 2004. FAO Fish. Aqua. Dept., Fish. Inf., Data, Stat. Dep.

Goldburg R., and R. Naylor. 2004. Future seascapes, fishing, and fish farming. Front. Ecol. 3:21–28.

Halwart, M., D. Soto, and J.R. Arthur, J.R. (eds.) 2007. Cage aquaculture – Regional reviews and global overview. FAO Fisheries Technical Paper. No. 498. Rome, FAO. 241 pp.

Naylor, R., and M. Burke. 2005. Aquaculture and Ocean Resources: Raising Tigers of the Sea. Ann. Rev. Envtl. Res. 30:185-218.

Soto, D., J. Aguilar-Manjarrez, and N. Hishamunda (eds). 2008. Building an ecosystem approach to aquaculture. FAO/Universitat de les Illes Balears Expert Workshop. 7–11 May 2007, Palma de Mallorca, Spain. FAO Fisheries and Aquaculture Proceedings. No. 14. Rome, FAO. 221p.

Stigebrandt, A., 1999. Turnover of energy and matter by fish—a general model with application to salmon. Fisken and Havet No. 5, Institute of Marine Research, Norway. 26 pp.

Footnotes

 [1] The daily discount rate is computed as the annual discount rate divided by 365. For an annual discount rate of 7%, the daily discount rate is 0.00019178.


text:
# Inline diff not displaying full revision coverage

There's something wrong with the inline diff in Revision 3 here (compare with source diff)

Don't really know how to explain it, so I'll let the revisions speak for themselves. The inline diff seems to have given up outputting anything at the
.

As an aside, formatting the headers and bullet lists underneath that numbered list was a right pain in the neck.

-

Yes, it was indeed the
 (to be precise, it was the self-closing / at the end) that wasn't handled correctly and thus broke here (in particular due to the condensing of long diffs). I've made two changes:

1. This particular case is now handled correctly, and
2. in case similar issues happen in the future, this will a) be logged in our error log, and b) the condensing bails out and shows the uncondensed version instead, so nothing is hidden from the diff view, even if there's a bug causing the condensing to fail.

This goes live with the next build.

-
Nice one! Shall verify and accept. How often do builds get pushed out? –  Lightness Races in Orbit Oct 3 '11 at 19:22
Ususally between one and maybe five times per day. Also see meta.stackexchange.com/questions/106523/… –  balpha Oct 3 '11 at 19:51
Nice one; and I can verify the fix. Top qual. –  Lightness Races in Orbit Oct 4 '11 at 8:23


text:
# Chess detached

Logic Level 2

Two opposite corner squares are detached from the chessboard.

Is it possible to make a path for a knight such that it visited all of the square once and only once? If yes, how many ways are there?

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## anonymous one year ago A glass case is in the shape of a rectangular prism. The volume of the case is 4/125 cubic foot. How many cubic blocks with a side length of 1/5 foot would be required to find the volume of the glass case? Please help I will give medals. A. 2 B. 3 C. 4 D. 5

1. anonymous

start by finding the volume of the cubic blocks. $V = s^3$ where s = 1/5

2. anonymous

then divide the given volume of the case by the one you found to get the answer

3. anonymous

i got 1/25

4. anonymous

hello?

5. anonymous

did you do this? |dw:1436448995973:dw|

6. anonymous

i did that and it came out to 1/125

7. anonymous

that's the volume of the small box. You need to divide that into the volume of the big box to get the amount $\frac{ 4 }{125 }\div \frac{ 1 }{ 125 }$

8. anonymous

1/25

9. anonymous

so 4?

10. anonymous

when you divide, flip the 2nd fraction to its reciprocal and multiply |dw:1436449252981:dw|

11. anonymous

yes

12. anonymous

thank you for helping me

13. anonymous

you're welcome