text:
# difference between dummy variable categories that weren't omitted

Assume we have a categorical variable (one-hot encoded) with three or more categories. {race1, race2, ..., race-n} To avoid the dummy variable trap, assume we omitted race1. Knowing the coefficients of race2,3,...n would help us compare each to race1.

What I'm trying to understand/figure-out is how to compare in the same model without rerunning the regression, the difference between race2 and race3.

• Why not use repeated contrasts instead of dummy variables (aka indicator or onehot contrasts)? See brief explanation of some popular contrast types within answer stats.stackexchange.com/a/221868/3277 – ttnphns Apr 28 '18 at 18:42

Assume your outcome variable Y is continuous and the model includes only the race factor, so that:

Y = beta0 + beta1* race2 + beta2*race3 + ... +
beta-n-1*race-n + error

Then:

beta0 = mean value of Y when race is equal to
race1

beta0 + beta1 = mean value of Y when race is
equal to race2

beta0 + beta2 = mean value of Y when race is
equal to race3

and so on.

If you are interested in the difference in the mean value of Y between race3 and race2, that will be given by:

(beta0 + beta2) - (beta0 + beta1) = beta2 - beta1

So you can set your contrast as:

c = (0, -1, 1, 0, ..., 0)

where the length of the contrast vector is the same as the number of beta coefficients in the model.

Comment:

When a model includes dummy variables used to encode the effect of a categorical variable, what that really means is that the model actually consists of a series of sub-models - one sub-model for each category of that variable. To write down each sub-model, simply set all the dummy variables to zero and then set each dummy variable to 1 in turns (while setting all other dummy variables to zero).

For the model:

Y = beta0 + beta1* race2 + beta2*race3 + ... +
beta-n-1*race-n + error   (*),

the race variable is categorical with n categories and the dummy variables race2, ..., race-n are used to encode its effect on Y. (The race1 dummy variable was omitted from the model, reflecting the fact that race1 is treated as a reference category.)

Here are the n sub-models that can be derived from model (*).

Sub-model 1 corresponds to race = race1 and is obtained by setting all dummy variables in model (*) to 0. Its equation is given by:

Y = beta0 + error

In this sub-model, beta0 represents the mean value of Y when race = race1.

Sub-model 2 corresponds to race = race2 and is obtained by setting the dummy variable for race2 to 1 in model (*) and all other dummy variables to 0. Its equation is given by:

Y = beta0 + beta1 + error

In this sub-model, beta0 + beta1 represents the mean value of Y when race = race2.

...

Sub-model n corresponds to race = race-n and is obtained by setting the dummy variable for race-n to 1 in model (*) and all other dummy variables to 0. Its equation is given by:

Y = beta0 + beta-n + error

In this sub-model, beta0 + beta-n represents the mean value of Y when race = race-n.

The above sub-models help elucidate the interpretation of the parameters beta0, beta0 + beta1, ..., beta0 + beta2. Now we can construct differences between any of these parameters and interpret them. For example:

• (beta0 + beta1) - (beta0) = beta1 represents the difference in the mean value of y among people for whom race = race2 and those for whom race = race1.
• (beta0 + beta2) - (beta0 + beta1) = beta2 - beta1 represents the difference in the mean value of y among people for whom race = race3 and those for whom race = race2.
• would beta2 - beta1 be the coefficient of race3 if race2 was the reference in that case? I don't see how that works? – mamdouh alramadan May 5 '18 at 5:32
• I added a comment to my original answer which should help you understand more about how dummy variables work. – Isabella Ghement May 5 '18 at 17:47

There are several ways to do this, but they all entail constructing linear combinations of the coefficients, such as their difference. This is doable since the original regression gives you the covariances between coefficients in addition to their standard errors, so that you can use the formula for linear combinations of correlated random variables.

Here's an example showing this with Stata, where we are interested in comparing the effect on price of repair record of 4 versus 5 (with 1 as the base category).

. sysuse auto
(1978 Automobile Data)

. reg price i.rep78

Source |       SS           df       MS      Number of obs   =        69
-------------+----------------------------------   F(4, 64)        =      0.24
Model |  8360542.63         4  2090135.66   Prob > F        =    0.9174
Residual |   568436416        64     8881819   R-squared       =    0.0145
Total |   576796959        68  8482308.22   Root MSE        =    2980.2

------------------------------------------------------------------------------
price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
rep78 |
2  |   1403.125   2356.085     0.60   0.554    -3303.696    6109.946
3  |   1864.733   2176.458     0.86   0.395    -2483.242    6212.708
4  |       1507   2221.338     0.68   0.500    -2930.633    5944.633
5  |     1348.5   2290.927     0.59   0.558    -3228.153    5925.153
|
_cons |     4564.5   2107.347     2.17   0.034     354.5913    8774.409
------------------------------------------------------------------------------

. test _b[4.rep78] =  _b[5.rep78]

( 1)  4.rep78 - 5.rep78 = 0

F(  1,    64) =    0.02
Prob > F =    0.8899

. lincom  _b[4.rep78] - _b[5.rep78]

( 1)  4.rep78 - 5.rep78 = 0

------------------------------------------------------------------------------
price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) |      158.5   1140.558     0.14   0.890    -2120.026    2437.026
------------------------------------------------------------------------------

. margins a.rep78

Model VCE    : OLS

Expression   : Linear prediction, predict()

------------------------------------------------
|         df           F        P>F
-------------+----------------------------------
rep78 |
(1 vs 2)  |          1        0.35     0.5536
(2 vs 3)  |          1        0.15     0.6984
(3 vs 4)  |          1        0.16     0.6886
(4 vs 5)  |          1        0.02     0.8899
Joint  |          4        0.24     0.9174
|
Denominator |         64
------------------------------------------------

--------------------------------------------------------------
|            Delta-method
|   Contrast   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
rep78 |
(1 vs 2)  |  -1403.125   2356.085     -6109.946    3303.696
(2 vs 3)  |  -461.6083    1185.87     -2830.656     1907.44
(3 vs 4)  |   357.7333   888.5353      -1417.32    2132.787
(4 vs 5)  |      158.5   1140.558     -2120.026    2437.026
--------------------------------------------------------------

You can also look at ratios of coefficients (though doing this by hand ges trickier since this is a non-linear combination of random variables):

. nlcom  ratio_4_5:_b[4.rep78]/_b[5.rep78]

ratio_4_5:  _b[4.rep78]/_b[5.rep78]

------------------------------------------------------------------------------
price |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
ratio_4_5 |   1.117538   .9271601     1.21   0.228    -.6996625    2.934738
------------------------------------------------------------------------------

format: plain


text:
## Intermediate Algebra (6th Edition)

$f(9)=28.4$ This tells us that 28.4 percent of college students are taking at least one online course in 2009 (which is x=9 years after 2000).
We can find $f(9)$ by plugging $x=9$ into the given equation for $f(x)$. $f(x)=2.7x+4.1$ $f(9)=2.7\times9+4.1=24.3+4.1=28.4$


text:
120 (number)

Jump to navigation Jump to search
 ← 119 120 121 →
Cardinalone hundred twenty
Ordinal120th
(one hundred twentieth)
Factorization23 × 3 × 5
Divisors1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Greek numeralΡΚ´
Roman numeralCXX
Binary11110002
Ternary111103
Senary3206
Octal1708
DuodecimalA012
Hexadecimal7816
The 120-cell (or hecatonicosachoron) is a convex regular 4-polytope consisting of 120 dodecahedral cells

120, read as one hundred [and] twenty, is the natural number following 119 and preceding 121.

In the Germanic languages, the number 120 was also formerly known as "one hundred". This "hundred" of six score is now obsolete, but is described as the long hundred or great hundred in historical contexts.[1]

In mathematics

120 is

• the factorial of 5 i.e. 5 × 4 × 3 × 2 × 1
• 120 is the sum of a twin prime pair (59 + 61) and the sum of four consecutive prime numbers (23 + 29 + 31 + 37), four consecutive powers of 2 (8 + 16 + 32 + 64), and four consecutive powers of 3 (3 + 9 + 27 + 81).
• 120 is divisible by the number of primes below it, 30 in this case. However, there is no integer which has 120 as the sum of its proper divisors, making 120 an untouchable number.
• The sum of Euler's totient function φ(x) over the first nineteen integers is 120.
• As it is a factorial and one less than a square, it, with 11, is one of the few Brown number pairs.
• 120 appears in Pierre de Fermat's modified Diophantine problem as the largest known integer of the sequence 1, 3, 8, 120. Fermat wanted to find another positive integer that, when multiplied by any of the other numbers in the sequence, yields a number that is one less than a square. Leonhard Euler also searched for this number, but failed to find it, but did find a fractional number that meets the other conditions, 777480/28792.
• The internal angles of a regular hexagon (one where all sides and all angles are equal) are all 120 degrees.

In science

120 is the atomic number of unbinilium, an element yet to be discovered.

In electrical engineering, each line of the three-phase system are 120 degrees apart from each other.

Three soap films meet along a Plateau border at 120${\displaystyle ^{\circ }}$ angles.

In religion

• The cubits of the height of the Temple building (II Chronicles 3:4)
• The age at which Moses died (Deut. 34:7).
• By extension, in Jewish tradition, to wish someone a long life, one says, "Live until 120"
• The number of Men of the Great Assembly who canonized the Books of the Tanakh and formulated the Jewish prayers
• The number of talents of gold that the Queen of Sheba gave to Solomon in tribute (I Kings 10:10)
• The number of princes King Darius set over his kingdom (Daniel 6:2)
• The summed weight in shekels of the gold spoons offered by each tribal prince of Israel (Num. 7:86).
• In astrology, when two planets in a person's chart are 120 degrees apart from each other, this is called a trine. This is supposed to bring good luck in the person's life.[7]

120 is also:

References

1. ^ Gordon, E V (1957). Introduction to Old Norse. Oxford: Clarendon Press. pp. 292–293. Archived from the original on 2016-02-23. Retrieved 2022-09-04.
2. ^ "Sloane's A002182 : Highly composite numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
3. ^ "Sloane's A004394 : Superabundant numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
4. ^ "Sloane's A004490 : Colossally abundant numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
5. ^ "Sloane's A036913 : Sparsely totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
6. ^ "Sloane's A005820 : 3-perfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
7. ^ "Astrology And The Black Man". Afro American. January 31, 1970. Retrieved December 30, 2010.
8. ^ The Game Court, National Basketball Association, retrieved 2014-04-07.
9. ^ Porter, Darwin; Danforth Prince (2009). Frommer's Austria. Hoboken, New Jersey: Frommer's. p. 482. ISBN 978-0-470-39897-5.


text: Consider two axially loaded columns, namely, $1$ and $2$, made of a linear elastic material with Young’s modulus $2 \times 10^5$ MPa, square cross-section with side $10$ mm, and length $1$ m. For column $1$, one end is fixed and the other end is free. For Column $2$, one end is fixed and the other end is pinned. Based on the Euler’s theory, the ratio (up to one decimal place) of the buckling load of Column $2$ to the buckling load of Column $1$ is ________


text:
### Show Posts

This section allows you to view all posts made by this member. Note that you can only see posts made in areas you currently have access to.

### Messages - Zihan Wan

Pages: [1]
1
##### Quiz-6 / Re: Q6 TUT 5101
« on: November 17, 2018, 04:19:43 PM »
solution is attached

2
##### Term Test 1 / Re: TT1 Problem 3 (night)
« on: October 19, 2018, 11:28:22 AM »
For(c), C is an arbitrary real number that is derived when looking for the formula for v, a real-valued function. So in the end, there will a term of the form Ci, a pure imaginary number, not an arbitrary constant.
Just my thought.

3
##### Term Test 1 / Re: TT1 Problem 4 (night)
« on: October 19, 2018, 11:10:10 AM »
$-3^{3}*2\pi$

4
##### Term Test 1 / Re: TT1 Problem 4 (night)
« on: October 19, 2018, 10:55:58 AM »
-54pi

5
##### Term Test 1 / Re: TT1 Problem 3 (night)
« on: October 19, 2018, 10:55:04 AM »
that should be i2z

6
##### Term Test 2 / Re: TT2--P1
« on: March 22, 2018, 04:51:13 PM »
y(0)=0,y'(0)=pi
but you are solving like y'(0)=0

7
##### Quiz-1 / TUT 0501
« on: January 25, 2018, 04:54:59 PM »
Find the general solution of the given differential equation, and use it to determine how solutions behave as t→∞
ty′+2y=sin(t), t>0

Pages: [1]


text:
# Villager or not - Single label classification using the fastai framework

Last post we created a dataset for a ‘villager or not a villager’ classification task. This time we’ll train a model and see how well we can get a neural network to recognize said villager. We’ll use a resnet34 model created with the fastai framework, the same as from lesson 1 in the fastai deep learning course 2019.

This code is on Github. I did most of the work on a Google Colab notebook.

Here’s the code for creating a neural net and training it on the dataset:

from fastai.datasets import untar_data, download_data
from fastai.vision import ImageDataBunch, cnn_learner, get_image_files, imagenet_stats, models, error_rate

drive.mount('/content/gdrive', force_remount=False)

path = untar_data('https://joalon.se/datasets/villager-or-not');
training_path = path/'training'
fnames = get_image_files(training_path)
pat = r'/([^/]+)_\d+.png\$'

data = ImageDataBunch.from_name_re(training_path, pat=pat, fnames=fnames)
data.normalize(imagenet_stats)

learn = cnn_learner(data, models.resnet34, metrics=error_rate)

learn.unfreeze()
learn.fit_one_cycle(10)

learn.save('/content/gdrive/My Drive/Villager or not/first-villager-model')

Here you can see it running:

Note! I did have to add a GPU to the colab notebook, otherwise the training time for each epoch was 10 minutes instead of 10 seconds.

Let’s see how it did, we can plot a confusion matrix:

interp = ClassificationInterpretation.from_learner(learn)
interp.plot_confusion_matrix()

That’s cool, it’s gotten 5 images wrong in the whole set. In the last post we concluded that the image generation was a bit flawed, now is a good time to check which images the model was most confused about.

interp.plot_top_losses(9, figsize=(15,11))

Not very strange that these images have a high loss, they’re clearly wrongly labelled. It’s the perfect time to use a cool widget from the fastai library called the ImageCleaner to do some relabeling:

ds, idxs = DatasetFormatter().from_toplosses(learn)
ImageCleaner(ds, idxs, path)

I had to spend quite some time relabeling images. The generator wasn’t as good as I expected, this model has probably overfit to be able to do so good on the wrongly labeled images.

Note: I couldn’t run the ImageCleaner on Google Colab since it doesn’t allow running widgets so, to run it, I had to use my laptop. Unfortunately I don’t have a current GPU so I had to install pytorch as CPU only:

pip3 install https://download.pytorch.org/whl/cpu/torch-1.1.0-cp37-cp37m-linux_x86_64.whl
pip3 install fastai

Pytorchs website has a really good tool for getting installation instructions for your own environment:

The ImageCleaner widget doesn’t actually change your dataset on disk, it creates a cleaned.csv file in the training path which can be loaded and retrained with:

df = pd.read_csv(path/'cleaned.csv', header='infer')

db = (ImageList.from_df(df, path)
.split_none()
.label_from_df()
.databunch(bs=64))

learn = cnn_learner(db, models.resnet34, metrics=error_rate)
learn.unfreeze()
learn.fit_one_cycle(10)

learn.save('villager-or-not')
learn.export()

We’ll need the export.pkl file from executing learn.export() to create a production model and run predictions on.

To finally test our model let’s grab a couple of screenshots the model hasn’t seen before to run inference with. I took some from the AoE 2 Wiki and cropped them. The champion is a unit the model hasn’t seen before, it’ll be interesting to see how it handles that.

The directory you’re running the following code in should contain the aforementioned export.pkl.

from fastai.vision import load_learner, open_image
from PIL import Image


text:
# Part 3.3HTML forms

A form is a way of collecting information. In fact, a form could be the most crucial part of a website as it provides multiple ways of collecting information.

Like a paper form, for instance a survey or a contract, a HTML form has specific functionalities and inputs. This article will discuss these.

## Forms

Below is a sample form and the code used to generate it.

HTML
<form action="" method="post">
Name: <input name="t1" type="text">

Favourite Colour: <input name="t2" type="color">

Age: <input name="t3" type="number">

Email: <input name="t4" type="email">

</form>

This form will likely display differently per browser, as a lot of the elements are not supported in all of the browsers.

### Action

The action attribute is used to specify a page to navigate and pass the information to.

The action attribute should point to some page that uses some server side language, such as PHP, to perform some tasks on the information, such as inserting it into a MySQL database.

In order for a form action to occur, the form must have a way of submitting the form such as submit button.

### Method

The method attribute is used to specify the way that the form will submit the information to the page or script that the form is submitting to.

By using the post method, the client will not see what variables are being passed to the page when it is done, whereas the get method will show these parameters in the URL.

### Names

Elements in the form all need a name attribute in order for their data to be passed to a server side script. Giving this attribute to the element allows the script to then obtain the value the user has given to the input or whatever.

## Label

The label element is used alongside some other element to describe that element. This is particularly useful for checkboxes or radio buttons because they are generally quite small unless they have text attached to them.

The label element binds text to another element by surrounding it:

HTML
<input type="radio" name="opt1" value="1"> Use default settings

## Input

The input element is perhaps the most used of all. This is because it offers a wide variety of different options. Specifying information about what type of input to receive is done through the type attribute.

### Text

The default for the input element is text. This implies that the type attribute is text, although it need not be specified. However, for strictness it is advised that a type is given.

Declaring a text input is defined below:

HTML

<input type="text">

<input>

### Special types

There are a range of special types that can be applied to an input element that in turn restrict the text that is inserted. In theory, these are all elements inherited from the basic text input element described before. This can be seen as an advantage because they appear in the same way. The vast majority of these types are being introduced with HTML5 and so not all browsers support these correctly.

#### Email

The email input validates an email address as the user types it, ensuring it has a valid structure. It checks for the @ character in particular. This is a particularly useful input type because it saves on writting a JavaScript function to perform this task. This is validated on the submission of the form and not when the user is inputting their information.

HTML
<input type="email">

#### Number

A numeric value can be checked using an input that accepts only numeric values. By defining the type to accept only numeric values, the system will prevent characters from the alphabet and symbols.

HTML
<input type="number">

#### Telephone

The telephone input allows the input of telephone numbers. This ensures that input follows the structure of a valid telephone number.

HTML
<input type="tel">

#### Date

A date input element will allow the selection of a date.

This element is very badly supported as of early 2014, but intends to be improved for cross browser support. The element's purpose is to make a single way of collecting a date from the user, as jQuery solutions are inadequate due to their lack of integrated support (albeit they are cross browser compatible).

A screenshot of its use in Google Chrome is pictured:

HTML
<input type="date">

#### Time

An element similar to the date element. This will allow users to insert a time in the form of hours and minutes.

HTML
<input type="time">

### Input Buttons

There are two inputs that are buttons.

#### Button

HTML
<input type="button" value="Button" onclick="alert('Test');">

The onclick is a JavaScript function that specifies what to do when clicked. The input where the  type is equal to button does not do anything on its own, it must have some event handler attached to it.

#### Submit

The submit type works very differently to the button type. The difference is that if this type of button is given to an input and placed within a form element, the button will act as the submit method for the form. Such an example is shown below:

HTML
<form action="test.php" method="post">
Name:
<input type="text" name="name">

<input type="submit" value="Submit">
</form>

#### Reset

HTML
<form>
Name:
<input type="text" name="name" value="Jamie">

<input type="reset" value="Reset values">
</form>

## Further input types

### Range input

Another way of obtaining an input, such as a number within a range is using the range input type.

HTML
<form>
Range:
<input type="range" name="value" max="150">

</form>

The current value is 50

### File input

HTML
<form enctype="multipart/form-data">
File:
<input type="file" name="file">

</form>

Files can be uploaded using the file type for the input. Take note of the fact that the form has enctype="multipart/form-data" as well.

These files will need processing on the server.

### Hidden inputs

Hidden inputs are input boxes that users cannot set the value for (unless they edit the HTML). Technically speaking, these are an unsecure way of storing temporary information, and so information can be passed around the pages quite easily, although certain information should not be passed this way such as a password.

The following sample use some JavaScript, although the purpose of this sample is not to show the JavaScript but to show how hidden elements can be addressed.

HTML
<form>
<input type="hidden" name="hidden" id="hidden" value="Hidden element">
<button onclick="getHidden();">Get value of hidden element</button>
</form>

There are a collection of special input types. These types are used perhaps the most as they offer the end user the cleaniest and easiest ways of selecting information.

### Checkboxes

Check boxes are an interesting way of getting a Boolean (true or false) input. A check box can be seen as a switch.

HTML
<form>

</form>

One of the most important features of the checkbox input type is that it works alone. If a second checkbox is required, it cannot be directly associated to the first checkbox without special code, unlike radio buttons.

A radio button is a standard way of choosing between multiple options.

It also provides a value, but it can be a range of different values. Giving multiple radio button inputs the same name means that they work as an array. Giving them a value attribute means that they have different values.

HTML
<form>
Use default settings <input type="radio" name="opt1" value="1">

Use basic settings <input type="radio" name="opt1" value="0">

</form>

## Text areas

The textarea is a totally different input. It's structure is in no way similar to the input element. The textarea element is used to collect a larger amount of text than just a standard text input field. In some ways, it can be seen as being a text editor field somewhat similar to an application on a desktop PC such as Notepad. It is not a rich text editor, so RTL/RTF are not allowed as content.

Text areas can be useful for collecting information such as email content for instance in a contact form, but as with any input, verification and validation absolutely should be applied to the input to prevent attacks. One of the most notable features of the text area field over the input field is that it supports multiline by default. Not only that, but it convert the multiline to the correct format so that if it is stored in a database, the information can be retrieved including the line breaks.

One of the most important features is that unlike an input field, the textarea field is given a default value by simply inserting it between the opening and closing tags.

HTML
<form>
<textarea name="textarea1">This is a text area</textarea>
</form>

A drop down box or option box is one of the more advanced form inputs that exists to offer an alternative to radio buttons for multiple choice. As such, the option field allows the choice of an option from a list.

Drop down lists are limited in some ways, but when it comes to larger lists, such as a country selector, radio buttons struggle to compete. The following quotations are from this website here.

When drop-down lists grow larger than 15 options they become difficult to scan and navigate. Some users will have to start scrolling inside the drop-down list which is a slow and painful experience.

When drop-down lists have less than 7 options they suffer from a lack of up-front information. The user has to click in order to see the available options.

A drop down menu must be correctly implemented with at least a required minimum and at most a maximum number of choices so that it does not look bare or cluttered. According to the aforementioned website, if a drop down list has less than 7 options, consider using radio buttons instead.

In web development, a drop down menu is referred to by it's tag name of select.

HTML
<form>
<select name="age">
<option value="18">18 - 25</option>
<option value="26">26 - 32</option>
<option value="32">32+</option>
</select>
</form>

## Selection lists

Further to dropdown lists, the <select> element can be used to create a selection list in which the user may choose multiple items.

Creating a 'selection list' is easy and very similar to that of the ordinary dropdown box, and allows the user to pick multiple items.

To change a select element from a standard dropdown to a list, simply add the attribute multiple to the tag:

HTML
<form>
<select name="subjects" multiple>
<option value="Computer Science">Computer Science</option>
<option value="Egnlish">English</option>
<option value="French">French</option>
<option value="History">History</option>
<option value="Mathematics">Mathematics</option>
<option value="Modern Studies">Modern Studies</option>
</select>
</form>

Holding down the Control key on the keyboard allows the user to pick multiple individual options and holding down the shift key allows the user to pick multiple options at once.

Code preview
Feedback 👍
Comments are sent via email to me.


text:
#### Publisher 2007, file too large.

I have recently installed publisher 2007. When I try to save any files bigger
than 1.5MB it takes a long time in trying to save it and then gives the
message: The file is too large. Delete some objects and save again. I never
experienced this problem with Publisher 2003.

Any suggestions/help will be appriciated.

 0
E (96)
2/11/2008 12:34:00 PM
publisher 21446 articles. 6 followers.

5 Replies
245 Views

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MVP Microsoft [Publisher]
Tech Editor for "Microsoft Publisher 2007 For Dummies"

"Mr. E" <Mr. E@discussions.microsoft.com> wrote in message
news:C0DEBB6E-695D-425B-A754-4AB1C45C3CF2@microsoft.com...
>I have recently installed publisher 2007. When I try to save any files
>bigger
> than 1.5MB it takes a long time in trying to save it and then gives the
> message: The file is too large. Delete some objects and save again. I
> never
> experienced this problem with Publisher 2003.
>
> Any suggestions/help will be appriciated.

 0
jl_paules (2768)
2/11/2008 1:49:47 PM
192 MB of RAM.

"JoAnn Paules" wrote:

> How much RAM are you running?
>
> --
>
> JoAnn Paules
> MVP Microsoft [Publisher]
> Tech Editor for "Microsoft Publisher 2007 For Dummies"
>
>
> "Mr. E" <Mr. E@discussions.microsoft.com> wrote in message
> news:C0DEBB6E-695D-425B-A754-4AB1C45C3CF2@microsoft.com...
> >I have recently installed publisher 2007. When I try to save any files
> >bigger
> > than 1.5MB it takes a long time in trying to save it and then gives the
> > message: The file is too large. Delete some objects and save again. I
> > never
> > experienced this problem with Publisher 2003.
> >
> > Any suggestions/help will be appriciated.
>
>
>

 0
MrE (1)
2/11/2008 3:01:03 PM
192?
Pub recommends 256 which really means 512 (and that's still pretty slim)

Try turning off other programs that may be running in the background.

--
~~~~~~~~~~~~~~~~~~
Rob Giordano
Microsoft MVP Expression

"Mr. E" <MrE@discussions.microsoft.com> wrote in message
news:18F75548-1E64-4107-95BD-579A282B7034@microsoft.com...
| 192 MB of RAM.
|
| "JoAnn Paules" wrote:
|
| > How much RAM are you running?
| >
| > --
| >
| > JoAnn Paules
| > MVP Microsoft [Publisher]
| > Tech Editor for "Microsoft Publisher 2007 For Dummies"
| >
| >
| > "Mr. E" <Mr. E@discussions.microsoft.com> wrote in message
| > news:C0DEBB6E-695D-425B-A754-4AB1C45C3CF2@microsoft.com...
| > >I have recently installed publisher 2007. When I try to save any files
| > >bigger
| > > than 1.5MB it takes a long time in trying to save it and then gives
the
| > > message: The file is too large. Delete some objects and save again. I
| > > never
| > > experienced this problem with Publisher 2003.
| > >
| > > Any suggestions/help will be appriciated.
| >
| >
| >

 0
webmaster911 (1600)
2/11/2008 3:06:10 PM
I had a feeling that was going to be the problem.

--

JoAnn Paules
MVP Microsoft [Publisher]
Tech Editor for "Microsoft Publisher 2007 For Dummies"

"Rob Giordano (Crash)" <webmaster@siriussystems.invalid> wrote in message
news:uqf8g$LbIHA.1208@TK2MSFTNGP03.phx.gbl... > 192? > Pub recommends 256 which really means 512 (and that's still pretty slim) > > Try turning off other programs that may be running in the background. > > -- > ~~~~~~~~~~~~~~~~~~ > Rob Giordano > Microsoft MVP Expression > > > > > > "Mr. E" <MrE@discussions.microsoft.com> wrote in message > news:18F75548-1E64-4107-95BD-579A282B7034@microsoft.com... > | 192 MB of RAM. > | > | "JoAnn Paules" wrote: > | > | > How much RAM are you running? > | > > | > -- > | > > | > JoAnn Paules > | > MVP Microsoft [Publisher] > | > Tech Editor for "Microsoft Publisher 2007 For Dummies" > | > > | > > | > "Mr. E" <Mr. E@discussions.microsoft.com> wrote in message > | > news:C0DEBB6E-695D-425B-A754-4AB1C45C3CF2@microsoft.com... > | > >I have recently installed publisher 2007. When I try to save any > files > | > >bigger > | > > than 1.5MB it takes a long time in trying to save it and then gives > the > | > > message: The file is too large. Delete some objects and save again. > I > | > > never > | > > experienced this problem with Publisher 2003. > | > > > | > > Any suggestions/help will be appriciated. > | > > | > > | > > >   0 jl_paules (2768) 2/11/2008 3:32:13 PM See if enlarging your swap file helps (virtual memory). Look in the system folder in the control panel. It is also helpful to change the display view in Publisher. View, pictures. Your video driver maybe failing. Read the fourth FAQ here: http://ed.mvps.org/Static.aspx?=Publisher/FAQs Microsoft recommends 256 MB of RAM to run Publisher 2007 correctly. Windows sets the Virtual Memory to three times the amount of RAM you have installed. -- Mary Sauer MSFT MVP http://office.microsoft.com/ http://msauer.mvps.org/ news://msnews.microsoft.com "Mr. E" <Mr. E@discussions.microsoft.com> wrote in message news:C0DEBB6E-695D-425B-A754-4AB1C45C3CF2@microsoft.com... >I have recently installed publisher 2007. When I try to save any files bigger > than 1.5MB it takes a long time in trying to save it and then gives the > message: The file is too large. Delete some objects and save again. I never > experienced this problem with Publisher 2003. > > Any suggestions/help will be appriciated.   0 mary-sauer (6480) 2/11/2008 3:55:07 PM  Reply: Similar Artilces: Exporting CRM Opportunity List to Office Excel 2007 We have CRM 3.0 Server. Our users are using CRM Web Client to access their leads, opportunities, quotes and orders. Using the Export toolbar button in CRM, users who have Office 2003 installed on their PCs are able to export opportunity lists to Excell perfectly all right, however users who have Office 2007 installed are not able to do that! Is this a limitation in CRM 3.0 ? Is there a workaround (If any)? Any possible risks when using or applying this workaround (If any)? "luai7" <luai7@discussions.microsoft.com> wrote in message news:6CADFDC5-8439-4B5F-955A-D6DBF... 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text:
# On avoiding the intended (but unwanted) effect of \outer

David Carlisle d.p.carlisle at gmail.com
Fri Oct 18 18:26:50 CEST 2019

On Fri, 18 Oct 2019 at 17:15, Taylor, P <P.Taylor at rhul.ac.uk> wrote:
>
> David Carlisle wrote:
> > You could save yourself some bytes, and some expansion steps.
> >
> > \edef \imagebox #1{\expandafter\noexpand\csname newbox\endcsname #1\setbox #1}
> >
> > David
>
> Confused (as always), David.  Your definition is 77 characters, mine is
> 56.   I assume that the "bytes saved" must therefore be in TeX's
> internal memory, but we have for quite some time not been restricted to
> 640kB,

You got a new machine?

> so are there any real-world situations in which saving those few
> bytes (and some expansion steps) is more important that writing clear,
> simple, didactic code ?

I wouldn't say anything with `\csname` in it counts as clear simple or didactic,

The edef definition was intended to be didactic notably highlighting
that \outer does not stop definitions having that token, just stops
the token appearing in certain scanning contexts so you can give
\imagebox the definition that you intended, you just need to write it
differently.

By far the clearest and simplest version would be to repeat the
one-line definition of \newbox without \outer, then just use \newbox
directly or use a format that has done that for you already:-)

>
> ** Phil.

David


text:
# Density operator in second quantization form [closed]

In first quantization the particle density operator is

$$n(x)=\sum_{\alpha}\delta^{3}(\vec{x}-\vec{x}_{\alpha})$$

In second quantization I have:

$$n(\vec{x})=\sum_{\alpha,i,j}\langle i|_{\alpha}\delta^{3}(\vec{x}-\vec{x}_{\alpha})|j\rangle_{\alpha}|i\rangle_{\alpha}\langle j|_{\alpha}$$

I know that

$$\sum_{\alpha}|i\rangle_{\alpha}\langle j|_{\alpha}=a_{i}^{\dagger}a_j$$

How can I introduce the creation and annihilation operators in the first equation?, the sum depend on $$\alpha$$.

I need to show that

$$n(\vec{x})=\psi^{\dagger}(\vec{x})\psi(\vec{x})$$

## closed as off-topic by Emilio Pisanty, Jon Custer, sammy gerbil, user191954, Kyle KanosNov 20 '18 at 10:55

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – Emilio Pisanty, Jon Custer, sammy gerbil, Community, Kyle Kanos
If this question can be reworded to fit the rules in the help center, please edit the question.

• You should double-check your second equation. The excerpt $)l\rangle$ should almost certainly read $)|j\rangle$. – Emilio Pisanty Nov 18 '18 at 21:22

I don't think your sum on alpha is supposed to collapse into the expression you are trying to show, here is my approach:

A single particle operator such as $$n$$ may be written in second quantized form according to

$$n = \sum_{\alpha , \beta} \langle \alpha | n | \beta \rangle a_{\alpha}^{\dagger} a_{\beta}$$

for some complete set of states {$${\alpha , \beta}$$}. Equivalently, we may write this using the field operators

$$n = \int dx dy \langle x | n | y \rangle \psi(x)^{\dagger} \psi(y) = \sum_{i} \int dx dy \delta(x-x_i)\langle x | y \rangle \psi(x)^{\dagger} \psi(y) = \sum_{i} \psi(x_i)^{\dagger} \psi(x_i)$$

For completeness, I should define the field operator

$$\psi(x) = \sum_i \langle x| i \rangle a_i$$

This may help as well.

• thanks, i am not sure of my expression. I supposed that the second equation depend on alpha becouse I and j are states of the particles and different particles must have different states or not? – F.Mark Nov 20 '18 at 0:35


text:
# Constrain chess moves to board width with xskak and chessboard

I'm using xskak and chessboard to typeset a game. How can I constrain the printing of the moves to the with of the board? I'm basically looking to constrain the width of the text box. In the image below you can see that the moves extend both left and right of the area over the board.

Here is the MWE for this game:

\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{5mm}
\usepackage{xskak}
\usepackage{chessboard}
\begin{document}
\begin{preview}
\newchessgame
\mainline{1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 a6 6. Be3 e6
7. g4 e5 8. Nf5 g6 9. g5}\\
\chessboard[label=False]
\end{preview}
\end{document}

Thanks!

You can just put the movements into a \parbox of the desired width:

Here's the code:

\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{5mm}
\usepackage{xskak}
\usepackage{chessboard}
\begin{document}
\begin{preview}
\newchessgame
\parbox{60mm}{
\mainline{1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 a6 6. Be3 e6
7. g4 e5 8. Nf5 g6 9. g5}
}

\chessboard[label=False]
\end{preview}
\end{document}

EDIT In light of the comments below, perhaps you want to use something like this:

\documentclass{article}
\usepackage{xskak}

\begin{document}

\newchessgame
\hspace*{7mm}\mainline{1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6}\\
\hspace*{7mm}\mainline{5. Nc3 a6 6. Be3 e6 7. g4 e5 8. Nf5 g6 9.  g5}
\par\leavevmode\vspace*{-60mm}
\chessboard[label=False]

\end{document}

This produces:

Note that I have removed the use of preview and used two \mainline commands to control the line spacing.

• Thanks, is there a way to offset the position of the parbox so that the left side of the text is flush with the left side of the board? Or the parbox is centered over the board? Apr 28, 2019 at 5:42
• When in doubt try a random LaTeX command! For example, try putting \hspace*{6mm} before the \parbox command. Is there a reason why you are using the preview package? I've not seen it before and would not have guessed that you needed it.
– user30471
Apr 28, 2019 at 6:09
• I am using preview because the code didn't seem to work without it (I get no pages of output written). Do you know what preview actually does, I copied it from an example? Apr 28, 2019 at 6:30
• Thanks for the tip on the \hspace*, I'm new enough at LaTeX that I don't know which random commands to try. Apr 28, 2019 at 6:35
• Do you know how to make the text box line break only right before a move number? Do you know how to reduce the vertical space between the text and the diagram? Or should I accept this answer now and ask these as separate questions? Apr 28, 2019 at 6:36


text:
## anonymous 5 years ago how do you solve this: 2x-3 = (3+x)/2

1. anonymous

multiply by 2, subtract an x and add a 3

2. anonymous

thank you

3. anonymous

x=3

4. anonymous

5. anonymous

I don't think so

6. anonymous

The point is, you want to get all your x terms on one side and your non-variable terms on the other

7. anonymous

$2*(2x-3)=[(3+x)/2]*2$

8. anonymous

then it goes to : 4x-6=3+x

9. anonymous

thank you so much, i understand now

10. anonymous

the get x by itself...so subtract -x to the left so next step: 3x=9

11. anonymous

do i get a medal :)

12. anonymous

yes! but i don't know how to give one

13. anonymous

i need help with this one too please: 2x-1= 1/3(5-3x) + 4

14. anonymous

Ok, well why don't you tell us how to start this one

15. anonymous

Oh, and is it $\frac{1}{3(5-3x)}$ or $\frac{1}{3}(5-3x)$

16. anonymous

the second one

17. anonymous

Ok. So which part do you want to tackle first? (There's lots of different paths to the same answer)

18. anonymous

Overall goal is to get all the x terms on one side and the non-x terms on the other side

19. anonymous

You tell me what to do, and I'll write the new equation.

20. anonymous

$2x-1= \frac{1}{3}(5-3x) + 4$

21. anonymous

i don't know how to start that's why i'm asking

22. anonymous

That's ok. Just pick a term that is in the wrong place

23. anonymous

We want everything with an x on the left, and everything without an x on the right

24. anonymous

Pick a term, any term.

25. anonymous

3x

26. anonymous

Ah, that term is a little tricky because it's part of a factor in a product. We will need to expand that product out first before we can work with that term directly

27. anonymous

But that's ok!

28. anonymous

That just means we need to distribute the 1/3 to each of the terms in the other factor

29. anonymous

So what do we get when we distribute that 1/3?

30. anonymous

3-9x?

31. anonymous

no. we have to multiply each term in the left factor by 1/3 $\frac{1}{3}(5-3x) = \frac{1}{3}*5 - \frac{1}{3}*3x$

32. anonymous

Does that make sense? So what do we have when we simplify that product?

33. anonymous

i'm not sure...

34. anonymous

a(b+c) = ab + ac Right? Basic multiplicative distribution

35. anonymous

ok so would it be 5/3 -x?

36. anonymous

yes

37. anonymous

So now we have: $2x-1= \frac{5}{3}-x + 4$

38. anonymous

so the whole thing would be : 2x-1 = 5/3-x+4?

39. anonymous

Yes

40. anonymous

Can you solve from there? or do you need more help with it?

41. anonymous

maybe a little more

42. anonymous

Ok, so pick a term that's in the wrong place

43. anonymous

how would i combine 5/3 + 4 that's the next step right?

44. anonymous

You can certainly do that yes.

45. anonymous

There is no 'next step'. There are a lot of ways to do it. If you want to do that next, go for it =)

46. anonymous

ok so how do you do it?

47. anonymous

How do you add $$\frac{5}{3} + 4$$

48. anonymous

You have to change the denominator of the 4 to match the 3 in the 5/3

49. anonymous

We do this using the trick of multiplying by 1.

50. anonymous

$$4 \times 1 = ?$$

51. anonymous

4

52. anonymous

Ok, so if we multiply by 1 we won't have changed the value, right?

53. anonymous

right

54. anonymous

Ok, so what is $$\frac{3}{3}$$

55. anonymous

1

56. anonymous

So you're saying then that if I multiply 4 by 3/3 I will still have 4?

57. anonymous

$4\times \frac{3}{3} = \frac{4\times 3}{3} = \frac{12}{3}$

58. anonymous

And 12/3 does equal 4, but it's in a different form that is now easy to add to 5/3

59. anonymous

60. anonymous

yes so the answer would be 17/3

61. anonymous

Well, the sum of those two terms would be 17/3 yes

62. anonymous

So we have: $2x-1= \frac{17}{3}-x$

63. anonymous

then irt would be 3x-1= 17/3

64. anonymous

Certainly

65. anonymous

it would be 3x = 1 17/3?

66. anonymous

yeah, but I dun like mixed numbers

67. anonymous

Can you do the same trick to the 1 we did to the 4 to make it easy to add to the 17/3

68. anonymous

isn't it 20/9?

69. anonymous

x = 20/9 is correct yes.

70. anonymous

you don't divide that by 3?

71. anonymous

72. anonymous

It was 3x = 20/3

73. anonymous

oh ok i thought it was 3x = 1 17/3? and then you divide by 3 on both sides to get x

74. anonymous

$$3x = 1+\frac{17}{3}$$$\implies 3x = 1\times \frac{3}{3} + \frac{17}{3}$$\implies 3x = \frac{1\times 3}{3} + \frac{17}{3}$$\implies 3x = \frac{3}{3} + \frac{17}{3}$$\implies 3x = \frac{20}{3}$

75. anonymous

Then you divide by 3 on both sides

76. anonymous

77. anonymous

yes thanks

78. anonymous

but how do you divide 3 on both sides, that what i want to know

79. anonymous

dividing by 3 is the same as multiplying by 1/3

80. anonymous

nope. $3x \times \frac{1}{3} = \frac{20}{3} \times \frac{1}{3}$ $x = \frac{20}{9}$ $3x \div 3 = \frac{20}{3} \div 3$ $x = 6.\bar{6}\bar{6} \div 3 = 2.\bar{2}\bar{2} = \frac{20}{9}$


text:
# How do you solve x+4y-z=7, x+y+z=2 and -2x-2y+2z=-8 using matrices?

Oct 14, 2016

Please see the explanation for the process.
$x = 2 , y = 1 , z = - 1$

#### Explanation:

Write $x + 4 y - z = 7$ into the first row of an augmented matrix:

[ (1,4,-1,|,7) ]

Write $x + y + z = 2$ into the second row:

[ (1,4,-1,|,7), (1,1,1,|,2) ]

Write $- 2 x - 2 y + 2 z = - 8$ into the third row:

[ (1,4,-1,|,7), (1,1,1,|,2), (-2, -2, 2, |, -8) ]

Multiply row 1 by -1 and add to row 2:

[ (1,4,-1,|,7), (0,-3,2,|,-5), (-2, -2, 2, |, -8) ]

Multiply row 1 by 2 and add to row 3:

[ (1,4,-1,|,7), (0,-3,2,|,-5), (0, 6, 0, |, 6) ]

Divide row 3 by 6 and swap with row 2:

[ (1,4,-1,|,7), (0, 1, 0, |, 1), (0,-3,2,|,-5) ]

Multiply row 2 by 3 and add to row 3:

[ (1,4,-1,|,7), (0, 1, 0, |, 1), (0,0,2,|,-2) ]

Divide row 3 by 2:

[ (1,4,-1,|,7), (0, 1, 0, |, 1), (0,0,1,|,-1) ]

Add row 3 to row 1:

[ (1,4,0,|,6), (0, 1, 0, |, 1), (0,0,1,|,-1) ]

Multiply row 2 by -4 and add to row 1:

[ (1,0,0,|,2), (0, 1, 0, |, 1), (0,0,1,|,-1) ]

$x = 2 , y = 1 , z = - 1$


text:
# NANOSCOPIC IMAGING OF BIOMOLECULES AND CELLS WITH STORM

Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/33401

Files Size Format View
abstract.gif 23.93Kb GIF image

 Title: NANOSCOPIC IMAGING OF BIOMOLECULES AND CELLS WITH STORM Creators: Zhuang, Xiaowei Issue Date: 2008 Publisher: Ohio State University Abstract: Optical microscopy is one of the most widely used imaging methods in biological research. Several advantages, such as the exquisite molecular specificity, the relatively fast time resolution and the noninvasive imaging nature, make light microscopy a particularly powerful tool for cell, tissue and animal imaging. However, the spatial resolution of far-field optical microscopy, classically limited by the diffraction of light to $\sim$300\,nm, is substantially larger than typical molecular length scales in cells, leaving many biological problems beyond the reach of light microscopy. To increase the image resolution, we have developed a new form of high resolution light microscopy, stochastic optical reconstruction microscopy (STORM). STORM uses photo-switchable fluorescent probes to temporally separate the otherwise spatially overlapping images of individual molecules, allowing the construction of high-resolution images. The imaging process includes multiple imaging cycles. In each cycle, only a fraction of the fluorophores are switched on, such that each of the active fluorophores is optically resolvable from the rest. This allows the position of these fluorophores to be determined with nanometer accuracy. Over the course of many activation cycles, the positions of numerous fluorophores are determined and used to construct a super-resolution image. Using this concept, we have achieved three-dimensional fluorescence imaging of molecular complexes and cells with $\sim$20\,nm lateral and $\sim$50\,nm axial resolutions. Furthermore, we have discovered a family of photo-switchable probes with distinct spectral properties and demonstrated multicolor super-resolution imaging. This new form of fluorescence microscopy allows molecular interactions in cells and cell-cell interactions in tissues to be imaged at the nanometer scale. Description: Author Institution: Department of Chemistry and Chemical Biology, Howard Hughes Medical Institute, Harvard University, Cambridge, MA 02138 URI: http://hdl.handle.net/1811/33401 Other Identifiers: 2008-MA-03


text:
Evalutaion of a real integral using the residue theorem

1. Nov 1, 2011

asmani

Evaluate the following integral using the residue theorem:

Any hint?

2. Nov 1, 2011

lurflurf

2i sin(x)=eix-e-ix
and
(n+1)undu=dun+1
with u=eix is
(n+1)einxdeix=dei(n+1)x

3. Nov 2, 2011

asmani

Sorry, I can't see how to use these facts. Can you give any further hint, please?
Besides, what contour should be chosen?

Thanks

Last edited: Nov 2, 2011
4. Nov 2, 2011

lurflurf

contour is unit circle
let
z=ei x
dx=dz/(i z)
sin(x)=((z-1/z)/(2i))
sin2n(x)=((z-1/z)/(2i))2n

$$\int_0^\pi \sin^{2n}(x) dx=\frac{1}{2}\int_{-\pi}^\pi \sin^{2n}(x) dx=\oint_{|z|=1}\left( \frac{z-\frac{1}{z}}{2i}\right)^{2n}\frac{dz}{2i z}$$

5. Nov 3, 2011

Thanks!


text:
José Carlos Cruz Costa

Associate Professor

University of Minho

jcosta@math.uminho.pt
(+351) 253 604344
.

PhD in Informatics, 1998, University of Paris 6

The research activity has been developed mainly in the area of Finite Semigroup Theory, having also been explored connections with the areas of Formal Languages and Automata Theory and Combinatorics on Words

Publications

Recognizing pro-𝖱 closures of regular languages

Forum Mathematicum | 2022

José Costa

Marc Zeitoun

On ω -Identities over Finite Aperiodic Semigroups with Commuting Idempotents

Springer Proceedings in Mathematics and Statistics | 2021

J.C. Costa

The Overlap Gap Between Left-Infinite and Right-Infinite Words

International Journal of Foundations of Computer Science | 2021

The word problem for κ -terms over the pseudovariety of local groups

Semigroup Forum | 2021

M.L. Teixeira


text:
# August 17, 2020

## Revising the Pareto Chart

—A look at the statistics underlying the Pareto Chart and how to improve it.

In Data Measurement and Analysis for Software Engineers, I go through Part 4 of a talk by Dennis J. Frailey. Part 4 covers statistical techniques for data analysis that are well suited for software. A number of references provided in Dennis’ talks are valuable for understanding measurement: A Look at Scales of Measurement explores the use of ordinal scales of defect severity. Part 4 makes reference to Revising the Pareto Chart, a paper by Leland Wilkinson. Wilkinson’s revision includes introducing acceptance intervals to address his concerns with the Pareto Chart.

## The Pareto Chart

Joseph Juran proposed the Pareto Chart on the left and then updated it to the diagram on the right.

Both versions are in Juran’s Quality Handbook. Both charts are from Wilkinson’s paper. Neither chart includes acceptance intervals but the one on the right eliminates dual scales plots and better conveys intent.

## Improving the Pareto Chart

Wilkinson proposes improving the Pareto chart by introducing acceptance intervals. An acceptance interval is derived from the assumption that all categories are equally probable before sorting the data by frequency. This interval is generated using the Monte Carlo Method.

The creation of a Pareto Chart involves sorting of unordered categorical data. A comparison to sorted but equally probably occurrences of unordered categorical data provides a way to identify outliers. This comparision is designed to challenge the notion that the most frequently occurring issue is the one to address. This is important when the costs of remedies are not uniform.

Wilkinson wanted to acheive two goals in revising the Pareto chart.

1. To point out there is no point in attacking the vital few failures unless the data fits a Pareto or similar power distribution.
2. To improve the Pareto chart so that acceptance intervals could be incorporated.

Wilkinson provides a way to compare the data distribution of the Pareto against a random distribution to identify when the data does not fits a Pareto distribution. The lack of fit provides motivation to dig a little deeper into the data and hopefully improve decision making.

What follows is an exploration of Wilkinson’s approach, including a Jupyter Notebook that I believe faithfully reproduces Wilkinson’s experiments.

## Reproducing the Results

Wilkinson’s thesis challenges the wisdom of attacking Category 1 if frequencies are random and costs are not uniform. It seeks to remedy this by introducing acceptance intervals derived from assuming that all categories are equally probable before sorting.

From the paper:

Recall that the motivation for the Pareto chart was Juran’s interpretation of Pareto’s rule, that a small percent of defect types causes most defects. To identify this situation, Juran sorted the Pareto chart by frequency. Post-hoc sorting of unordered categories by frequency induces a downward trend on random data, however, so care is needed in interpreting heights of bars.

Wilkinson provides a recipe for reproducing his results. His results provide an opportunity to explore how to employ different statistics to generate acceptance intervals. What follows is how I reproduced these results.

1. Use a multinomial distribution with $$n = 40$$ and $$\mbox{p-values} = \{ 1/6, 1/6, 1/6, 1/6, 1/6, 1/6 \}$$ for each category. The identical p-value ensure all categories are equally probable.

In this case, the multinomial is a random variable $$X$$, such that $$X = x_{i}, \forall i, 1 \ge i \le 6$$.

2. For $$N = 40000$$ trials, generate a multinomial $$X_{i}, \forall i, 1 \ge i \le N$$ and sort each trial from the highest to lowest value. This ensures the Pareto ordering is imposed upon the random data generated during each trial.

In my experiment, the order statistics changed up to the $$30000^{th}$$ to $$35000^{th}$$ trial. My experiments were with 20,000 and 40,000 trials. The charts below capture the results of 40,000 trials.

3. Order each trial from smallest to largest. This simulates a Pareto distribution using random data.

4. Calculate the lower $$1 - \frac{\alpha}{2}$$ and upper $$\frac{\alpha}{2}$$ frequencies, where $$\alpha = 0.05$$ and $$Z = 1.96$$.

A non-parametric way of generating these frequencies uses the formula $$Y = N \pm Z \times \sqrt{N \times p \times (1 - p)}$$, where $$p = \frac{\alpha}{2}$$. In this case, Y is the position of the $$Y^{th}$$ value in the ordered trials created in the previous step.

Importantly, this step identifies the $$95^{th}$$ percentile using a $$95\%$$ confidence interval. This is not a prediction interval for future events. It shows only where the $$95^{th}$$ percentile is likely to lie.

(Category 1 is the top subplot.) The interesting artifact in the frequency by category chart is the banding introduced by sorting the multinomial in each trial. This sorting applies the Pareto method to random data.

By comparison, the unsorted distribution:

The unsorted distribution has bands that are of equal range for every category. The sorted distribution has the effect of limiting bands in each category to a much narrower range.

Order statistics include minimum and maximum frequency along with range and median. It’s unclear whether these statistics were used to ensure the Monte Carlo simulation stablized. It’s possible that only the upper and lower frequencies were used.

These charts compute their statistic for the $$n^{th}$$ trial of each category. This computation includes all trials from $$1$$ through $$n, n \le N$$. Similarly, the $$n + 1^{st}$$ trial includes all trials from $$1$$ through $$n + 1$$.

The minimum value of all trials up to and including the $$n^{th}$$ trial.

The maximum value of all trials up to and including the $$n^{th}$$ trial.

The median of all trials up to and including the $$n^{th}$$ trial. It is $$Y_{\frac{n + 1}{2}}$$ if $$n$$ is odd; $$\frac{1}{2}(Y_{\frac{n}{2}} + Y_{\frac{n + 1}{2}})$$ otherwise.

The range is $$max - min$$ of all trials up to and including the $$n^{th}$$ trial.

The objective of the study was to stablize the upper and lower frequencies. These frequencies match those in the original paper, implying this method has successfully reproduced the one used in the paper.

The paper says only a “few thousand” Monte Carlo simulations are required to compute the frequency bounds. Indeed, these frequencies stablize at less than 5,000 trials for most of the Monte Carlo runs. An exception exists for Category 3’s lower bound which changes between the $$17500^{th}$$ and $$30000^{th}$$ trial.

The upper frequency bound stablizes before $$5000$$ trials.

The stabilization of the upper and lower bounds happens just after the $$30000^{th}$$ trial. This may be what Wilkinson refers to when he says the statisitc stabilizes in a few thousand trials. I don’t have a better explanation for the explanation of a “few thousand trials”.

In all, the use of so many order statistics may not be necessary as the results imply that the frequency bounds are the focus. An interesting question is whether the use of the non-parametric statistics for these bounds is appropriate.

## Non-Parametric Statistics

Is the non-parametric approach for calculating bounds meaningful? The formula used above works well if the frequency of each trial for each category has a normal distribution. To see this I plotted a histogram for each category.

These distributions look good. Some of the misalignment of the normal is due to rounding.

## Acceptance Levels

What do the acceptance levels look like for these results in comparision to those Wilkinson achieved?

The original acceptance intervals from the paper, with 40 defects allocated to 6 categories.

The experimental version below.

Looks like a good reproduction of the original paper.

## References

Some excellent explanations of the Monte Carlo method.

A look at confidence intervals from percentials:


text:
# BDPReader — Converts BDP in XML format to in-memory BDP object.¶

This module defines the BDPReader class.

class admit.xmlio.BDPReader.BDPReader(file=None)[source]

Class to read in a bdp file (xml style) and convert it to a BDP object in memory. Only the name of the bdp file (including any relative or absolute path) needs to be specified. The given file will be passed to the AdmitParser where it will be parsed. The resulting data will be inserted into a BDP object of the appropriate type (type is determined by the contents of the bdp file). The BDP object is the returned.

Parameters: file : str File name (including any relative or absolute path) of the bdp file to be parsed and converted to a BDP object. Default : None.

Attributes

 File name (including any relative or absolute path) of the bdp file to be parsed and converted to a BDP object.

Methods

 read([file]) Method to convert a bdp file to a BDP object.
read(file=None)[source]

Method to convert a bdp file to a BDP object. Only the file name (including relative or absolute path) needs to be given. The file is then parsed and the data inserted into the appropriate BDP object. The type of BDP is determined from the data in the bdp file itself. The resulting BDP object is returned.

Parameters: file : str File name (including any relative or absolute path) of the bdp file to be parsed and converted to a BDP object. Default : None BDP object of appropriate type based on the given input file.


text: Is interior points of a subset $E$ of a metric space $X$ is always a limit point of $E$? Short scene in novel: implausibility of solar eclipses, How Close Is Linear Programming Class to What Solvers Actually Implement for Pivot Algorithms. Recap Sequences and Convergence in Metric Spaces De nition: A sequence in a set X(a sequence of elements of X) is a function s: N !X. mapping metric spaces to metric spaces relates to properties of subsets of the metric spaces. Since x was arbitrary, there are no limit points. () Conversely, suppose that X - A is open. Take any x Є (a,b), a < x < b denote . Do I need my own attorney during mortgage refinancing? So suppose x is a limit point of A and that x A. The subset [0,1) ofRdoes not have isolated points. We need to show that A contains all its limit points. The closure of A, denoted by A¯, is the union of Aand the set of limit points … If xn! Suppose that A⊆ X. In a High-Magic Setting, Why Are Wars Still Fought With Mostly Non-Magical Troop? Deﬁnition 1.15. Nothing in the definition of a metric space states the need for infinitely many points, however if we use the definition of a limit point as given by my lecturer only metric spaces that contain infinitely many points can have subsets which have limit points. It is contrary of x is limit of . There exists some r > 0 such that B r(x) ⊆ Ac. An (open) -neighbourhood of a point p is the set of all points within … The situation is different in weird topological spaces that are not $T_1$ spaces. Hence, a limit point of the set E is the limit of a sequence of points in E. The converse is not true. There are several variations on this idea, and the term ‘limit point’ itself is ambiguous (sometimes meaning Definition 0.4, sometimes Definition 0.5. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Interior and Boundary Points of a Set in a Metric Space. Given a subset A of X and a point x in X, there are three possibilities: 1. The last two sections have shown how we can phrase the ideas of continuity and convergence purely in terms of open sets. Limit Points and the Derived Set Deﬁnition 9.3 Let (X,C)be a topological space, and A⊂X.Then x∈Xis called a limit point of the set Aprovided every open set Ocontaining xalso contains at least one point a∈A,witha=x. In Brexit, what does "not compromise sovereignty" mean? It turns out that if we put mild and natural conditions on the function d, we can develop a general notion of distance that covers distances between number, vectors, sequences, functions, sets and much more. Third property tells us that a metric must measure distances symmetrically. (Limit points and closed sets in metric spaces) Neighbourhoods and open sets in metric spaces Although it will not be clear for a little while, the next definition represents the first stage of the generalisation from metric to topological spaces. In a metric space,, the open set is replaced with an open ball of radius. Thanks for contributing an answer to Mathematics Stack Exchange! To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Then some -neighbourhood of x does not meet A (otherwise x would be a limit point of A and hence in A). Let M is metric space A is subset of M, is called interior point of A iff, there is which . Proposition A set C in a metric space is closed if and only if it contains all its limit points. [You Do!] A pair, where d is a metric on X is called a metric space. Furthermore any finite metric space based on the definition my lecturer is using, would not have any subsets which contain limit points. I prefer the second definition myself, but the first definition can be useful too, as it makes it immediately clear that finite sets do not have limit points. Definition 3.11Given a setE⊂X. Definition Let E be a subset of a metric space X. If there is no such point then already X= B (x 1) and the claim is proved with N= 1. Don't one-time recovery codes for 2FA introduce a backdoor? x, then x is the only accumulation point of fxng1 n 1 Proof. The definition my lecturer gave me for a limit point in a metric space is the following: Let (X, d) be a metric space and let Y ⊆ X. For your last question in your post, you are correct. Theorem 2.37 In any metric space, an inﬁnite subset E of a compact set K has a limit point in K. [Bolzano-Weierstrass] Proof Say no point of K is a limit point of E. Then each point of K would have a neighborhood containing at most one point q of E. A ﬁnite number of these neighborhoods cover K – so the set E must be ﬁnite. †A set A in a metric space is bounded if the diameter diam(A) = sup{d(x,x˜) : x ∈A,x˜ ∈A} is ﬁnite. We say that a point $x \in X$ is a limit point of $Y$ if for any open neighborhood $U$ of $x$ the intersection $U \cap Y$ contains infinitely many points of $Y$, However I know that the general topological definition of a limit point in a topological space is the following. We say that a point x ∈ X is a limit point of Y if for any open neighborhood U of x the intersection U ∩ Y contains infinitely many points of Y 3. A point, a topological space, is a limit point of if a sequence of points, such that for every open set, containing an such that. A limit of a sequence of points (: ∈) in a topological space T is a special case of a limit of a function: the domain is in the space ∪ {+ ∞}, with the induced topology of the affinely extended real number system, the range is T, and the function argument n tends to +∞, which in this space is a limit point of . As said in comments, both definitions are equivalent in the context of metric spaces. 2. Then, this ball only contains x. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. Philosophical reason behind definition of limit point. It means that no matter how closely we zoom in on a limit point, there will always be another point in its immediate vicinity which belongs to the subset in question. In abstract topological spaces, limit points are defined by the criterion in 1 above (with "open ball" replaced by "open set"), and a continuous function can be defined to be a function such that preimages of closed sets are closed. Am I correct in saying this? Let ϵ>0 be given. 2) Open ball in metric space is open set. The set of limit points of [0,1) is the set [0,1]. We will now define all of these points in terms of general metric spaces. Asking for help, clarification, or responding to other answers. Indeed, there is only one neighborhood of $x$, namely the space $X$ itself; and this space contains a point of $Y$. Cauchy sequences. (a)Show for every >0, Xcan be covered by nitely many balls of radius . Wikipedia says that the definitions are equivalent in a $T_1$ space. Why do exploration spacecraft like Voyager 1 and 2 go through the asteroid belt, and not over or below it? The closed interval [0, 1] is closed subset of, The closed disc, closed square, etc. The points 0 and 1 are both limit points of the interval (0, 1). Equivalent formulation of $T_1$ condition. This can be seen using the definition the other definition too. 1.5 Limit Points and Closure As usual, let (X,d) be a metric space. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Deﬁnition 1.14. A point p is a limit point of the set E if every neighbourhood of p contains a point q ≠ p such that q ∈ E. Theorem Let E be a subset of a metric space X. Interior and Boundary Points of a Set in a Metric Space Fold Unfold. This is the most common version of the definition -- though there are others. We usually denote s(n) by s n, called the n-th term of s, and write fs ngfor the sequence, or fs 1;s 2;:::g. See the nice introductory paragraphs about sequences on page 23 of de la Fuente. Then pick x 2 such that d(x 2;x 1) . Making statements based on opinion; back them up with references or personal experience. Thus this -neighbourhood of x lies completely in X - A which is what we needed to prove. Already know: with the usual metric is a complete space. Compactness Characterization Theorem Suppose that K is a subset of a metric space X, then the following are equivalent: K is compact, K satisfies the Bolzanno-Weierstrass property (i.e., each infinite subset of K has a limit point in K), ; K is sequentially compact (i.e., each sequence from K has a subsequence that converges in K). I'm really curious as to why my lecturer defined a limit point in the way he did. A point in subset $A$of metric space is either limit point or isolated point. Let E be a nonempty subset of a metric space and x a limit point of E. For every $$n\in \mathbf N$$, there is a point $$x_n\in E$$ (distinct from x) such that $$d(x_n, x)<1\slash n$$, so $$x_n\rightarrow x$$. How many electric vehicles can our current supply of lithium power? This is the same as saying that A is contained in a ﬁxed ball (of ﬁnite radius). So suppose that x X - A. A point $x \in X$ is a limit point of $Y$ if every neighborhood of $x$ contains at least one point of $Y$ different from $x$ itself. Definition If A is a subset of a metric space X then x is a limit point of A if it is the limit of an eventually non-constant sequence (ai) of points of A. Definition 3.9A pointcofEis an isolated point ofEifcis not a limit point ofE. Metric Spaces, Topological Spaces, and Compactness sequences in X;where we say (x ) ˘ (y ) provided d(x ;y ) ! Definition It only takes a minute to sign up. 1.2. Informally, a point in a metric space is a limit point of some subset if it is arbitrarily close to other points in that subset. Proof We have deﬁned convergent sequences as ones whose entries all get close to a ﬁxed limit point. Limit Points in a metric space (,) DEFINITION: Let be a subset of metric space (,). A subset A of a metric space X is closed if and only if its complement X - A is open. Deﬁnition 9.4 Let (X,C)be a topological space, and A⊂X.The derived set of A,denoted A, is the set of all limit points of A. What is this stake in my yard and can I remove it? Denition: A limit point of a set Sin a metric space (X;d) is an element x2Xfor which there is a sequence in Snfxgthat converges to x| i.e., a sequence in S, none of whose terms is x, that converges to x. If A is a subset of a metric space X then x is a limit point of A if it is the limit of an eventually non-constant sequence (ai) of points of A. Theorem Let x be a point and consider the open ball with center x and radius the minimum of all distances to other points. (Note that this is easy for a set already known to be compact; see problem 4 from the previous assignment). By the deﬁnition of convergence, 9N such that d„xn;x” <ϵ for all n N. fn 2 N: n Ng is inﬁnite, so x is an accumulation point. Property 2 states if the distance between x and y equals zero, it is because we are considering the same point. The definition my lecturer gave me for a limit point in a metric space is the following: Let $(X, d)$ be a metric space and let $Y \subseteq X$. 1) Simplest example of open set is open interval in real line (a,b). Hence, x is not a limit point. If any point of A is interior point then A is called open set in metric space. Proof Exercise. In this case, x is called a boundary point of A. What exactly does this mean? We need to show that X - A is open. rev 2020.12.8.38145, Sorry, we no longer support Internet Explorer, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. 252 Appendix A. The definitions below are analogous to the ones above with the only difference being the change from the Euclidean metric to any metric. are closed subsets of. A point x is called an isolated point of A if x belongs to A but is not a limit point of A. For any r > 0, B r(x) intersects both A and Ac. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Example 3.8A discrete metric space does not have any limit points. How can I upsample 22 kHz speech audio recording to 44 kHz, maybe using AI? In other words, a point $$x$$ of a topological space $$X$$ is said to be the limit point of a subset $$A$$ of $$X$$ if for every open set $$U$$ containing $$x$$ we have Let (X,ρ) be a metric space. Brake cable prevents handlebars from turning. Example 3.10A discrete metric space consists of isolated points. Table of Contents. Suppose x′ is another accumulation point. Submitting a paper proving folklore results. The set of all cluster points of a sequence is sometimes called the limit set. Proving that a finite point set is closed by using limit points. Let (X;d) be a limit point compact metric space. LIMITS AND TOPOLOGY OF METRIC SPACES so, ¥ å i=0 bi =limsn =lim 1 bn+1 1 b = 1 1 b if jbj < 1. Metric spaces are $T_n$ spaces for $n\in \{ 0,1,2, 2\frac {1}{2}, 3, 3\frac {1}{2},4,5,6 \}.$, Definition of a limit point in a metric space. Let $X$ be a topological space and let $Y \subseteq X$. It is equivalent to say that for every neighbourhood $${\displaystyle V}$$ of $${\displaystyle x}$$ and every $${\displaystyle n_{0}\in \mathbb {N} }$$, there is some $${\displaystyle n\geq n_{0}}$$ such that $${\displaystyle x_{n}\in V}$$. A point ∈ is a limit point of if every neighborhood of contains a point ∈ such that ≠ . Every matrix space is a $T_1$ space since for $x,y\in X$ with $d=d(x,y)$ the neighborhoods $B(x,d/2)$ and $B(y,d/2)$ separate $x$ and $y$. If $${\displaystyle X}$$ is a metric space or a first-countable space (or, more generally, a Fréchet–Urysohn space), then $${\displaystyle x}$$ is cluster point of $${\displaystyle (x_{n})_{n\in \mathbb {N} }}$$ if and only if $${\displaystyle x}$$ is a limit of some subsequence of $${\displaystyle (x_{n})_{n\in \mathbb {N} }}$$. The natural question to ask then would be are all metric spaces $T_1$ spaces? But this is an -neighbourhood that does not meet A and we have a contradiction. MathJax reference. The second one is to be used in this case. Employee barely working due to Mental Health issues, Program to top-up phone with conditions in Python. Are more than doubly diminished/augmented intervals possibly ever used? 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