{% include 'includes/_navbar.html' %}
In sabermetrics, there are a variety of statistics used to evaluate the skill of a batter. Statistics such as batting average, slugging, on-base percentage, strikeouts, and other similar statistics evaluate the overall skill of a batter. None of these statistics consider a batter’s ability to hit varying types of pitches, just the batter’s ability to hit pitches as a whole. Some pitchers may be able to effectively hit all types of pitches, while others may only be able to be effective pitchers for fastballs. The Speciality Score statistic aims to gauge a batter’s ability to hit "speciality" pitches such as curveballs, sliders, changeups, and so on. Batters with high batting skill for these speciality pitches will have a high speciality score while batter with less skill for these pitches will have a lower speciality score.
This statistic could be used to identify batters with a unique batting skill as compared to other batters. A team manager could use this information to ensure that the team is well-balanced in terms of batting ability: a team needs batters that are able to excel against specialty pitches. Pitchers could also benefit from this information by using against batters with low specialty scores. If a pitcher is going to pitch to a batter who has a low specialty score, then he can throw specialty pitches to the batter.
The statistic is presented with a website: http://specialtyscore.herokuapp.com/. A user can access the website and read some information about the statistic and how it is calculated. A user can enter a Major League Baseball player’s name and see his Specialty Score. The Specialty Scores will be available for all players that have enough Statcast data for which we can calculate their score (AB > 200).
To calculate the Specialty Score statistic we first needed to merge data across all available Statcast data that we could find. This consisted of the 2014 - 2018 batting data.
Afterwards, we removed all of the rows from the database where the pitch_type field contained a NaN value because if the pitch did not have a recorded pitch type the data was useless for our calculation. We then also had to do a bit of preprocessing on the pitch_type field itself by removing all values that contained a digit because there existed quite a few anomalous entries that looked similar to 2412_1214. To do this we first removed the "_" contained within these entries. We then iterated again over each value and removed each entry that was purely a digit, 2412_1214 becomes 24121214. This allowed us to just have the pitch types themselves which could be used for the Specialty Score calculation.
We then create another column called hit type that reads from the pitching description to determine if the ball was hit successfully. Essentially we have a conditional that checks if the description contains the word "hit" and the hit was not a ball or foul ball.  If the ball was successfully hit we then increment the successful hit counter with respect to the thrown pitch type for that batter.
After getting a count for the number of times that a player has seen each pitch type and the count for the number of successful hits we then begin to calculate the percentage of each pitch type that was successfully hit by each batter. This is simply done by just taking the total number of successfully hit balls for each pitch type and dividing it by the total number of times that the player saw and then multiplying by 100 to get a percentage.
The final calculation is what makes up the Specialty Score statistic itself. Each of the percentage hit calculations for each pitch type is passed through a weighted sum where,
What is great about the Specialty Score statistic is that the analyst of a team can work with their team manager and pitchers to adjust the weights of specialty pitches to come up with a Speciality Score that is more useful for their pitcher against some batter.


7.5. A Hard Information Flow Problem (WORK IN PROGRESS)¶
Sometimes, passing the right information up and down the tree to control a recursive function gets complicated. The information flow itself is simple enough, but deciding what to pass might be tricky.
A more difficult example is illustrated by the following problem. Given an arbitrary binary tree we wish to determine if, for every node \(A\), are all nodes in \(A\)’s left subtree less than the value of \(A\), and are all nodes in \(A\)’s right subtree greater than the value of \(A\)? (This happens to be the definition for a binary search tree.) Unfortunately, to make this decision we need to know some context that is not available just by looking at the node’s parent or children.
As shown by Figure 7.6.1, it is not enough to verify that \(A\)’s left child has a value less than that of \(A\), and that \(A\)’s right child has a greater value. Nor is it enough to verify that \(A\) has a value consistent with that of its parent. In fact, we need to know information about what range of values is legal for a given node. That information might come from any of the node’s ancestors. Thus, relevant range information must be passed down the tree. We can implement this function as follows.
static <E extends Comparable<E>> boolean checkBST(BSTNode<E> rt, E low, E high) {
if (rt == null) { return true; } // Empty subtree
E rootval = rt.value();
if ((rootval.compareTo(low) <= 0) || (rootval.compareTo(high) > 0)) {
return false; // Out of range
}
if (!checkBST(rt.left(), low, rootval)) {
return false; // Left side failed
}
return checkBST(rt.right(), rootval, high);
}


Global Pop
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Applies to all types of file references, including links to CSS files, image sources, and background images.
| File Path | What it means |
|---|---|
| pointB.css | pointB.css is located in the current folder |
| css/pointB.css |
pointB.css is located in a folder called css The css folder is located in the current folder |
| css/other/pointB.css | pointB.css is located in a folder called other that is located in a folder called css that is located in the current folder |
| ../pointB.css | pointB.css is located in a folder one level up from the current folder |
| ../../pointB.css | pointB.css is located in a folder two levels up from the current folder |
<link rel="stylesheet" href="file-path-here.css" />
selector {
display: inline;
}
Examples: <span />, <em />, <strong />,
<a />, <img />
selector {
width: 300px;
}
selector {
height: 100px;
}
Set a width on a block element, then use auto as a margin.
selector {
width: 300px;
margin: auto;
}
selector {
display: block;
}
Examples: <div />, <section />, <p />, <h1 />, <h2 />, <h3 />, <h4 />, <h5 />, <h6 />, and almost everything else
Both padding and margin use the same syntax. Substitute 'margin' for 'padding' to apply margins instead.
One value:
selector {
padding: all;
}
Two values:
selector {
padding: topAndBottom leftAndRight;
}
Four values:
selector {
padding: top right bottom left;
}
Can also specify padding-top, padding-right, padding-bottom, or padding-left to apply padding to individual sides.
selector {
border: thickness style color;
}
Can also specify border-top, border-right, border-bottom, or border-left to apply a border to individual sides.


Notebooks
Story: Dorothea Bleek - Book BC151_A3_007
Dorothea Bleek - Book BC151_A3_007
Title
Dorothea Bleek - Book BC151_A3_007
Collection
Summary
Notebook. Mostly words and sentences, some personal information. Bechuanaland.
Comments
1) p.1: 5.7.1913. Makolo, at Legombe; 2) p.6v: Information about Makolo and the place she comes from, Kary [?] a village, about a man called Moshe'u from the same place who does not speak the language any more; 3) p.22: names of women and girls, 4) p.30: 9.7.13. Matchunki [?] gives some personal information and words; 5) p.43: 10.7.13. ; 6) p.48: 11.7.13.  There are none left now. They play no musical instruments'; 7) p.61 & op. an illustration and a description of a spring trap or snare; 8) p.78: 13 July; 9) p.81: Pusho [?] 'the man with the schock[?] head and skin dress'; 10) p.88: on '|xum', the cut between the eyebrows - 'this cut is given in order to make them see better for shooting.'; 11) p. 117: 15.7.13; 12) p.135: 16th July
Contributors
Date
1913-07-01T00:00:00.000
Categories
Words and sentences, History (personal)
Story Pages
1-143


Coffee shop in Jioufen
问题描述 :
Cheer manages a coffee shop in Jioufen. As she is the only assistant in the shop, it is a big problem for her to mix up raw materials into a cup of coffee.
To simplify the problem, we can assume that Cheer has n kinds of raw material, and the i-th raw material has been assigned with a value ai denoting its level of deliciousness.
For some unknown reason, Cheer believe that a kind of coffee is perfect if and only if the value of its all kinds of raw materials are co-prime with each other. A kind of perfect coffee also can be made without any of these raw materials, only by water.
Now given n kinds of raw material and their value of deliciousness, find out how many distinct kinds of perfect coffee can be made by them. Note that two kinds of coffee are considered distinct if and only if the raw material sets of them are distinct.
To simplify the problem, we can assume that Cheer has n kinds of raw material, and the i-th raw material has been assigned with a value ai denoting its level of deliciousness.
For some unknown reason, Cheer believe that a kind of coffee is perfect if and only if the value of its all kinds of raw materials are co-prime with each other. A kind of perfect coffee also can be made without any of these raw materials, only by water.
Now given n kinds of raw material and their value of deliciousness, find out how many distinct kinds of perfect coffee can be made by them. Note that two kinds of coffee are considered distinct if and only if the raw material sets of them are distinct.
输入:
There are at most 75 test cases.
For each case, The first line contains one integer n indicating the number of kind of raw material.
The next line contains n integers separated by space, denoting deliciousness values: a1, a2, …, an
(1 <= n <= 60, 1 <= ai <= 231-1)
The input ends with n = 0
For each case, The first line contains one integer n indicating the number of kind of raw material.
The next line contains n integers separated by space, denoting deliciousness values: a1, a2, …, an
(1 <= n <= 60, 1 <= ai <= 231-1)
The input ends with n = 0
输出:
There are at most 75 test cases.
For each case, The first line contains one integer n indicating the number of kind of raw material.
The next line contains n integers separated by space, denoting deliciousness values: a1, a2, …, an
(1 <= n <= 60, 1 <= ai <= 231-1)
The input ends with n = 0
For each case, The first line contains one integer n indicating the number of kind of raw material.
The next line contains n integers separated by space, denoting deliciousness values: a1, a2, …, an
(1 <= n <= 60, 1 <= ai <= 231-1)
The input ends with n = 0
样例输入:
2 2 2 3 1 2 3 3 2 3 4 0
样例输出:
3 8 6HintFor the first case, there 3 distinct kinds of perfect coffee: none of these raw materials, only with the first kind of raw material, and only with the second kind of raw material. Coffee with both the first kind of raw material and the second is not considered as perfect coffee, because the deliciousness levels of first kind of raw material and the second are not co-prime.
素数的一个题，看了题解也没有软用
#include <iostream> #include <cstdio> #include <algorithm> #include <cstring> using namespace std; #define LL long long const int maxn =60; int a[maxn]; LL to[maxn]; int num[maxn]; LL ans; bool gcd(int a,int b){ return b==0?a!=1:gcd(b,a%b); } LL DFS(int n,LL p){ if(n==-1) return 1; LL res=DFS(n-1,p); if(p&(1LL<<n)) return res; if((p|to[n])==p) return res*num[n]; else return res+DFS(n-1,(p|to[n]))*(num[n]-1); } int main() { int n; while(~scanf("%d",&n)&&n){ for(int i=0;i<n;i++) scanf("%d",a+i); sort(a,a+n); int m=0; num[0]=2; for(int i=1;i<n;i++){ if(a[i]==a[m]) num[m]++; else { a[++m]=a[i]; num[m]=2; } } memset(to,0,sizeof(to)); for(int i=0;i<=m;i++) { for(int j=0;j<i;j++) if(gcd(a[j],a[i])) to[i]|=1LL<<j; } ans=0; printf("%I64d\n",DFS(m,0)); } return 0; }
版权声明：stay positive,work harder than everybody else
参考：http://blog.csdn.net/a197p/article/details/47303583
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1）4999是传闻，到某些无良媒体嘴里就成事实了，还做调查问卷。
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ADMIRAL files can be accessed from Linux as a network share:
If using GNOME, use the "Places > Connect to server ..." menu command. A popup window will appear. From the "Service type"
drop-down menu, select "Windows share". Under "Server" enter %{HOSTFULLNAME}
and under
"Share" enter data
. Under "Username" enter username and under "Domain" enter
%{WORKGROUP}
and then click on "Connect". Another popup window will then appear,
into which the password for username should be entered.
Once connected, a user will be able to read/write files in their own private area,
and also to read all files in the shared
and collab
areas.
For advanced users, it is also possible to mount the filesystem directly, using the command:
mount.cifs //${HOSTNAME}/data mountpoint -o rw,user=username,password=userpass,nounix,forcedirectio
where mountpoint has already been created.


On the road with fellow travelers without the hassle.
We want to know our users as best as possible.
Our team checks profiles and reviews.
The identity of each participant is confirmed.
So you know for sure, with whom you get into the car.
About us
The website is created with the purpose to help all
(to drivers and passengers),
to carry out trips in the necessary direction.
Drivers can find to themselves fellow travelers,
and fellow travelers can find the driver of the passing vehicle,
for a joint trip.


General
The Azure Map app has been built as a Commercial app. This SERVICE is provided by Jason Chin and is intended for use as is.
This page is used to inform users regarding the policies with the collection, use, and disclosure of Personal Information if anyone decided to use this Service.
If you choose to use the Service, then you agree to the collection and use of information in relation to this policy. The Personal Information that may be collected is used for providing and improving the Service. It will not use or share your information with any third party except as described in this Privacy Policy.
Information Collection and Use
For a better experience, while using the Service, you may be required to provide us with certain personally identifiable information, including but not limited to Location Services. The information that is requested will be retained on your device only and is not collected by the developer in any way.
The app does not use third party services that may collect information used to identify you. Only frameworks provided by Apple has been used.
Log Data
Whenever you use the Service, in a case of an error in the app, the data and information in your phone's Log Data may be collected. This Log Data may include information such as your device Internet Protocol (“IP”) address, device name, operating system version, the configuration of the app when utilising the Service, the time and date of your use of the Service, and other statistics.
Cookies
Cookies are files with a small amount of data that are commonly used as anonymous unique identifiers. These are sent to your browser from the websites that you visit and are stored on your device's internal memory.
This Service does not use these “cookies” explicitly. However, the app may use third party code and libraries that use “cookies” to collect information and improve their services. You have the option to either accept or refuse these cookies and know when a cookie is being sent to your device. If you choose to refuse our cookies, you may not be able to use some portions of this Service.
Service Providers
Third-party companies and individuals may be employed due to the following reasons:
* To facilitate the Service;
* To provide the Service on our behalf;
* To perform Service-related services; or
* To assist us in analysing how our Service is used.
These third parties may have access to your Personal Information. The reason is to perform the tasks assigned to them on our behalf. However, they are obligated not to disclose or use the information for any other purpose.
Security
Your trust in providing us your Personal Information is valued and we ensure that your Personal Information is protected. But remember that no method of transmission over the internet, or method of electronic storage is 100% secure and reliable, and no guarantee can be provided for its absolute security.
Links to Other Sites
This Service may contain links to other sites. If you click on a third-party link, you will be directed to that site. Note that these external sites are not operated by me. Therefore, I strongly advise you to review the Privacy Policy of these websites. I have no control over and assume no responsibility for the content, privacy policies, or practices of any third-party sites or services.
Children’s Privacy
These Services do not address anyone under the age of 13. Personally identifiable information from children under 13 are not knowingly collected. In the case that it was discovered that a child under 13 has provided his/her personal information, it will be deleted immediately from the storage. If you are a parent or guardian and you are aware that your child has provided the developer with personal information, please contact the developer so that necessary actions can be taken.
Changes to This Privacy Policy
The Privacy Policy may be updated from time to time. Thus, you are advised to review this page periodically for any changes. Notification of any changes will be posted in the new Privacy Policy on this page. These changes are effective immediately after they are posted on this page.
Contact Us
If you have any questions or suggestions about my Privacy Policy, do not hesitate to contact me at<EMAIL_ADDRESS>This privacy policy page was created at privacypolicytemplate.net and modified/generated by App Privacy Policy Generator (https://app-privacy-policy-generator.firebaseapp.com)


If you want to create your own tool for building or extracting files from UMOD installers, you'll need knowledge about their internal structure.
A UMOD installer file consists of three parts:
The UMOD installer must contain a file Manifest.ini
that describes the target locations of the files, the installed mod's
requirements and other details, and Manifest.int
that contains the textual captions and descriptions used in the installer. See
/Creating on how to set up those files.
Described in reverse order of their appearance in the file, since this is the order they'll be parsed when reading the UMOD file.
The UMOD file header is 20 bytes long. The header is stored in the last 20 bytes of the file (hence the quotes around the term "header").
| Offset | Length | Type | Description |
| 0 | 4 | unsigned int | Magic number. Used to verify this file as a UMOD installer. Always 0x9FE3C5A3. |
| 4 | 4 | unsigned int | Byte offset of file directory in the UMOD file. (See below.) |
| 8 | 4 | unsigned int | Total byte size of the UMOD file. |
| 12 | 4 | unsigned int | UMOD file version. |
| 16 | 4 | unsigned int | CRC32 checksum over the file content. |
Mychaeel: That CRC32 checksum needs further investigation... It's just a guess that the checksum goes over the file content (first part of UMOD file) only. Besides, I've been running into problems trying to verify UnrealScript source code TextBuffer checksums using a standard CRC32 algorithm with a standard seed – or I didn't feed it the right data. Any help?
The file directory describes the files stored in the first part of the UMOD file. Its byte offset in the UMOD file is given in the file "header" (see above).
The directory consists of an index-type file count (the index data type is described below), followed by variable-size records, each describing one file in the UMOD installer.
| Offset | Length | Type | Description |
| 0 | variable | index | Length of file name (including trailing null byte). |
| variable | char | File name, with trailing null byte. | |
| 4 | unsigned int | Byte offset of file in UMOD file. | |
| 4 | unsigned int | Byte length of file. | |
| 4 | unsigned int | Bit field describing file flags. (See below.) |
Mychaeel: Feel free to investigate and contribute information about the file flags. (I know that they have to be set to 0x03
for Manifest.ini
and Manifest.int
to prevent those files from being copied to the user's System directory, and set to
0x00 for all other files.)
The files are stored without compression starting from byte 0 of the file, one after another, with no padding or separators between them. Their respective byte offsets in the file are specified by the file directory (see above).
Specifications of the integer and index values can be found: Package File Format/Data Details


Ocala events
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Problems and Promise of the American Middle School | RAND
The middle school years represent a critical time for young teens. Middle schools have been blamed for the increase in student behavior problems and cited as .
http://www.rand.org/pubs/research_briefs/RB8025/index1.htmlImplications of Middle School Behavior Problems for High School ...
and estimate a recursive bivariate probit model that 1) relates middle school behavior problems to high school graduation and 2) models later employment in .
http://data.e-rockford.com/upload/files/1/middle%20school.pdf
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May 4picture of chevrolet nomas 1955
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Ocala's best venues
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Why Do Most Behavior Problems Spring Up Around Middle School?
Young boys and girls usually exhibit problematic behaviors such as stealing, lying, fighting, using bad language, skipping class, and bullying. They display .
http://www.teach-nology.com/prodevelopment/middle_level/ -
Strategies for Improving Student Behavior
major implications for middle school educators seeking to improve student behavior.2 . specific with-it behaviors are confronting problems before they become .
http://go.hrw.com/resources/go_sc/gen/HSTPR054.PDF -
Middle School Children's Problem-Solving Behavior: A ... - JStor
35, No. 3, 187-219. Middle School Children's. Problem-Solving Behavior: A Cognitive Analysis from a Reading. Comprehension Perspective. Stephen J. Pape .
http://www.jstor.org/stable/30034912paradise park leessummit mo
98 people's favorite
-
ResearchBrief:Middle School Entry Year and Student Behavior
May 29, 2007 . While there was a jump in behavior problems for all students when they entered middle school, students entering in the 6th grade experienced .
http://www.ascd.org/publications/researchbrief/v5n05/toc.aspx -
The Impact of Discipline in the Behavior of Middle School Students ...
Nov 6, 2006 . Implementing Family-Centered Interventions within the Public Middle School: Linking Service Delivery to Change in Student Problem Behavior .
http://voices.yahoo.com/the-impact-discipline-behavior-middle-105163.html


Contents
We need a library for that...
Underscore.js to the rescue
Performance
Language independent concepts
Functional programming
Underscore.js: under the hood
Alternatives
Summary
We need a library for that...
Before looking at Underscore.js more closely let's first discuss the context in which it can be useful. We will see what problems we may have and that it actually solves them well. Because, who knows maybe we don't need Underscore.js at all and you can already stop reading the article?
Here is our problem. Let's say that as part of some other larger project we would like to write code that analyzes text and outputs some important information like the list of all the used words in the alphabetical order, the top 10 most frequently used words, the total number of words, etc.
This is what our first attempt at solving the problem might look like if we never heard of functional programming in general and Underscore.js and corresponding JavaScript APIs in particular.
The text we would like to analyze:
[sourcecode language="javascript"]
var text = "Alice was beginning to get very tired of sitting \
by her sister on the bank, and of having nothing to do: once \
or twice she had peeped into the book her sister was reading, \
but it had no pictures or conversations in it, \
'and what is the use of a book,' thought Alice \
'without pictures or conversations?'\
\
So she was considering in her own mind (as well as she could, \
for the hot day made her feel very sleepy and stupid), whether \
the pleasure of making a daisy-chain would be worth the trouble \
of getting up and picking the daisies, when suddenly a White \
Rabbit with pink eyes ran close by her.";
[/sourcecode]
And the code that analyzes the text:
[sourcecode language="javascript"]
function textWords(text) {
var words = text.match(/[a-zA-Z\-]+/g);
for (var i = 0; i < words.length; i++) {
words[i] = words[i].toLowerCase();
}
return words;
}
function wordsFrequencies(words) {
var frequencies = {},
currentWord = null;
for(var i = 0; i < words.length; i++) {
currentWord = words[i];
frequencies[currentWord] =
(frequencies[currentWord] || 0) + 1;
}
return frequencies;
}
function sortedListOfWords(wordsFrequencies) {
var words = [];
for (var key in wordsFrequencies) {
if (wordsFrequencies.hasOwnProperty(key)) {
words.push(key);
}
}
return words.sort();
}
function topTenWords(wordsFrequencies) {
var frequencies = [],
result = [];
for (var key in wordsFrequencies) {
if (wordsFrequencies.hasOwnProperty(key)) {
frequencies.push([key, wordsFrequencies[key]]);
}
}
frequencies = frequencies.sort(function(freq1, freq2) {
return (freq1[1] < freq2[1])
? 1
: (freq1[1] > freq2[1] ? -1 : 0);
});
for (var i = 0; i < 10; i++) {
result[i] = frequencies[i];
}
return result;
}
function analyzeText(text) {
var words = textWords(text),
frequencies = wordsFrequencies(words),
used = sortedListOfWords(frequencies),
topTen = topTenWords(frequencies);
console.log("Word count = ", words.length);
console.log("List of used words = ", used);
console.log("Top 10 most used words = ", topTen);
}
analyzeText(text);
[/sourcecode]
This should be self explanatory, but still let's look at one of the methods more closely, in particular we will be interested in low level implementation details:
[sourcecode language="javascript"]
function wordsFrequencies(words) {
var frequencies = {},
currentWord = null;
for(var i = 0; i < words.length; i++) {
currentWord = words[i];
frequencies[currentWord] =
(frequencies[currentWord] || 0) + 1;
}
return frequencies;
}
[/sourcecode]
Here we just iterate through the list of all words and for each word increment its frequency value stored in frequencies. Note, that this implementation contains the details how we exactly increment the index when getting the next word and this is pretty low level. It is first not important to our implementation and second very likely can be reused in many other use cases. This is precisely the reason why JavaScript has it already abstracted into a separate function Array.prototype.forEach. Let's rewrite wordsFrequencies using this function instead:
[sourcecode language="javascript"]
function wordsFrequencies(words) {
var frequencies = {};
words.forEach(function(word) {
frequencies[word] = (frequencies[word] || 0) + 1;
});
return frequencies;
}
[/sourcecode]
No doubt the implementation became somewhat clearer without an extra index variable i and currentWord. But actually even this version can be made shorter and the low level implementation details of how exactly frequencies changes with each processed word can also be partially hidden. For that we will use the Array.prototype.reduce function:
[sourcecode language="javascript"]
function wordsFrequencies(words) {
return words.reduce(function(frequencies, word) {
frequencies[word] = (frequencies[word] || 0) + 1;
return frequencies;
}, {});
}
[/sourcecode]
It seems like we improved this part quite a bit. But now we notice that in another place of our code we read the list of all the keys of an object, and there is also a separate Object.keys function provided by JavaScript to do that, and instead of:
[sourcecode language="javascript"]
for (var key in wordsFrequencies) {
if (wordsFrequencies.hasOwnProperty(key)) {
frequencies.push([key, wordsFrequencies[key]]);
}
}
[/sourcecode]
we can write:
[sourcecode language="javascript"]
frequencies = Object.keys(wordsFrequencies).map(function(key) {
return [key, wordsFrequencies[key]];
});
[/sourcecode]
Much more readable. And here we also used the Array.prototype.map function.
Now below is the whole version of our program rewritten using the JavaScript standard methods we mentioned above:
[sourcecode language="javascript"]
function textWords(text) {
return text.match(/[a-zA-Z\-]+/g).map(function(word) {
return word.toLowerCase();
});
}
function wordsFrequencies(words) {
return words.reduce(function(frequencies, word) {
frequencies[word] = (frequencies[word] || 0) + 1;
return frequencies;
}, {});
}
function sortedListOfWords(wordsFrequencies) {
return Object.keys(wordsFrequencies).sort();
}
function topTenWords(wordsFrequencies) {
var frequencies = [],
result = [];
frequencies = Object.keys(wordsFrequencies)
.map(function(key) {
return [key, wordsFrequencies[key]];
}).sort(function(freq1, freq2) {
return (freq1[1] < freq2[1])
? 1
: (freq1[1] > freq2[1] ? -1 : 0);
});
for (var i = 0; i < 10; i++) {
result[i] = frequencies[i];
}
return result;
}
function analyzeText(text) {
var words = textWords(text),
frequencies = wordsFrequencies(words),
used = sortedListOfWords(frequencies),
topTen = topTenWords(frequencies);
console.log("Word count = ", words.length);
console.log("List of used words = ", used);
console.log("Top 10 most used words = ", topTen);
}
analyzeText(text);
[/sourcecode]
The program became shorter and much more clear. However, if we look carefully, we can notice that there are still a few places with lots of low-level details, for example:
[sourcecode language="javascript"]
function topTenWords(wordsFrequencies) {
var frequencies = [],
result = [];
frequencies = Object.keys(wordsFrequencies)
.map(function(key) {
return [key, wordsFrequencies[key]];
}).sort(function(freq1, freq2) {
return (freq1[1] < freq2[1])
? 1
: (freq1[1] > freq2[1] ? -1 : 0);
});
for (var i = 0; i < 10; i++) {
result[i] = frequencies[i];
}
return result;
}
[/sourcecode]
still has low level details related to sorting and getting the first 10 elements.
Moreover this function clearly does too much at once and almost asks to split it in two functions. And having 10 hardcoded in the body of the function is clearly far from perfect. Notice that this became much more evident only after we partially re-factored the code of the original function and abstracted away some of the implementation details. For now we will stop here with our re-factoring and return to this function later when we will use Underscore.js in the process.
Unfortunately the standard JavaScrit, while providing a number of useful functions such as map, reduce, filter, etc. still lacks some other functions and the API is a bit limited.
For example in the case of topTenWords function above we miss the function for taking first n elements from an array which is quite common to many languages, see take from the standard Clojure library or take from the standard Ruby library.
This is where Underscore.js comes to the rescue.
Underscore.js to the rescue
Underscore.js can be installed as a Node module:
[sourcecode]
npm install underscore
[/sourcecode]
Or you can just include the minified source on your page:
[sourcecode]
[/sourcecode]
The source code for the library can be found on Github github.com/jashkenas/underscore
Underscore.js does just what we need: it provides a large number of convenient functions that we can use to get rid of low level implementation details in our programs. There is some intersection with the standard JavaScript API, but Underscore.js provides far more useful functions than we can find in the standard JavaScript. For example, the last function we considered for getting the top 10 frequent words can be rewritten as follows:
[sourcecode language="javascript"]
function wordsAndFrequenciesDescending(wordsFrequencies) {
return _.sortBy(_.map(_.keys(wordsFrequencies),
function(key) {
return [key, wordsFrequencies[key]];
}),
_.property("1")).reverse();
}
function topWords(wordsFrequencies, number) {
return _.take(
wordsAndFrequenciesDescending(wordsFrequencies),
number
);
}
[/sourcecode]
Notice that it is now more terse and expressive. _.keys corresponds to Object.keys, _.map to Array.prototype.map we encountered before, etc. Also we see that Underscore.js does include the take method we mentioned before and which was missing from the standard JavaScript API. The function by which we sort became much shorter and clearer as well thanks to using the _.property function provided by Underscore.js.
Another thing that we immediately notice about Underscore.js is that rather than adding methods to JavaScript objects, Underscore.js provides external methods that take an object as a parameter.
Underscore.js also allows to use a more object-oriented style by wrapping an object and making its functions available on the resulting wrapper object as methods. When invoked each such method returns another wrapper object that contains the intermediate computation result and on which we can again invoke Underscore.js methods. This way we can chain computations.
For example, compare:
[sourcecode language="javascript"]
var object = {
"key1": "value1",
"key2": "value2",
"key3": "value3"
};
_(object).keys();
_.keys(object);
[/sourcecode]
Both ways of calling keys in this case are valid. You can read more about wrapping objects with Underscore.js and chaining in the documentation.
And here is the full version of our initial program rewritten using Underscore.js functions.
[sourcecode language="javascript"]
function textWords(text) {
return _.map(text.match(/[a-zA-Z\-]+/g), function(word) {
return word.toLowerCase();
});
}
function wordsFrequencies(words) {
return _.reduce(words, function(frequencies, word) {
frequencies[word] = (frequencies[word] || 0) + 1;
return frequencies;
}, {});
}
function sortedListOfWords(wordsFrequencies) {
return _.sortBy(_.keys(wordsFrequencies));
}
function wordsAndFrequenciesDescending(wordsFrequencies) {
return _.sortBy(_.map(_.keys(wordsFrequencies),
function(key) {
return [key, wordsFrequencies[key]];
}),
_.property("1")).reverse();
}
function topWords(wordsFrequencies, number) {
return _.take(
wordsAndFrequenciesDescending(wordsFrequencies),
number
);
}
function analyzeText(text) {
var words = textWords(text),
frequencies = wordsFrequencies(words),
used = sortedListOfWords(frequencies),
topTen = topWords(frequencies, 10);
console.log("Word count = ", words.length);
console.log("List of used words = ", used);
console.log("Top 10 most used words = ", topTen);
}
analyzeText(text);
[/sourcecode]
The functions became much more succinct and clear and the low level implementation details are now well hidden.
Actually, it is possible to make (thanks for pointing this out, rooktakesqueen) the code even more expressive. Using the _.chain function we can re-write wordsAndFrequenciesDescending as follows:
[sourcecode language="javascript"]
function wordsAndFrequenciesDescending(wordsFrequencies) {
return _.chain(wordsFrequences)
.keys()
.map(function(key) {
return [key, wordsFrequencies[key]];
})
.sortBy(_.property('1'))
.reverse()
.value();
}
[/sourcecode]
And... That's it, if you have managed to follow the article this far, you already have a good grasp of what Underscore.js is and how it can help you with writing your code. You can always get more information about Underscore.js by reading its annotated source code or documentation. The number of provided functions is considerably larger than what we discussed so far, in particular there are separate functions for objects, arrays, collections and functions, as well as a few generic utility functions.
Even more functions can be found in underscore-contrib. Although the functions there may be less generic and suitable only for a particular type of problems. If you cannot find some function in Underscore.js, check it out, it may already contain what you need. But this part is out of the scope of the present article.
What follows below is more detailed discussion about the style of programming promoted by Underscore.js, performance, implementation details of the library, etc. Read it if you would like to have more advanced understanding of the library.
Performance
Underscore.js provides us high level abstract functions that make our code clearer and shorter, that is it makes us as developers more productive, but what about the computer productivity? Is our code performant enough? Let's use jsperf to test that in our case and see some results for the three implementations above:
Here is the link to the test cases and the full results http://jsperf.com/underscore-js-vs-map-reduce-keys-vs-low-level
We immediately see that using the native map, reduce and keys is from 1.5 to 2 times faster than the Underscore.js version.
Suprisingly enough in the case of our program for Chrome and IE10 using native map, reduce and keys is even faster than the low level implementation. But actually it does make sense, because those native methods are implemented as native code which is somewhat faster than trying to write the same logic in JavaScript.
Although this does not always seem to be true, and the low level implementation can still be much faster than the native forEach and reduce if the arrays are large enough and contain only numbers as another benchmark demonstrates http://jsperf.com/foreach-vs-reduce-vs-for-loop
The main result here is that the performance of all the three approaches is of the same order, i.e. is comparable. Then if we get more readability with Underscore.js or native functions we probably should use them as we do not loose much in performance and in the case of Chrome we actually win.
Based on this benchmark the recommendation will be consider avoiding writing your own loops, as they are much less expressive, more complicated and do not always guarantee better performance.
If you still have doubts, in general, when performance considerations enter your decision making, please, remember, as a rule we should optimize only the 10% of the code that takes 90% of the execution time, otherwise we are wasting our development time, do not win much performance-wise and make our code unnecessary complicated.
Language independent concepts
If you are familiar with any other languages than JavaScript you might have seen already something similar to the functions we used above. Ruby has its Enumerable module which defines many of the similar methods, Java has Guava and in fact almost everybody in the Java world tries to develop their own version of Underscore.js without even sometimes realizing it, Scala has many of these methods included into the standard library, etc.
If you look carefully at what we discussed so far, you will see that there is not much that is JavaScript specific. We just talked about collections, functions, passing functions into other functions and creating higher level functions, that is functions that can accept other functions as arguments. In fact, we can define functions like map, filter, reduce, etc. in any other language that has the concepts mentioned above.
A large part of the philosophy and ideas behind Underscore.js is thus language independent and quite generic. But of course, in order to be practically useful it also has a sizable JavaScript-specific part which is still needed by JavaScript developers, for example, take a look at the _.toArray and _.isDate functions.
That ideas and philosophy are in large part inspired by Functional Programming (FP), which is a development paradigm that views functions as the primary building block of programs.
For some languages that currently do not treat functions as important enough, for example, Java, it is stil possible to emulate passing functions into functions and create something similar to Underscore.js but it will look much uglier and will be quite cumbersome to use, for example, compare the different versions of a program that converts a collection of strings into a collection of lengths of each string:
the Java version (using the Functional Java library):
[sourcecode language="java"]
Array.map().f(new F() {
@Override
public Integer f(String arg) {
return arg.length();
}
}).f(array("a", "ab", "abc")).array(Integer[].class));
[/sourcecode]
the Scala version:
[sourcecode language="scala"]
Array("a", "ab", "abc").map(_.length())
[/sourcecode]
the Ruby version:
[sourcecode language="ruby"]
["a", "ab", "abc"].map {|str| str.length}
[/sourcecode]
and the JavaScript one:
[sourcecode language="javascript"]
["a", "ab", "abc"].map(function(str) {
return str.length;
});
[/sourcecode]
Now it is clearly time for a bit of critism in the direction of JavaScript. You can see that while JavaScript version is comparable to the Scala one it is still a bit more wordy and includes syntactic noise such as function and return keywords. But here Underscore.js will not help us much, as we cannot easily circumvent the core language limitations. And we can only feel sorry for poor Java developers until they finally get lambdas in Java 8.
Functional programming
This is a generic programming paradigm in which the primary (or at least one of the primary) building blocks that are used to create new programs are functions.
Another things often talked about in relation to Functional Programming (FP) are immutability and referential transparency.
We will not go into many details what those mean, and provide only a brief explanation, but please, feel free to take a deep dive and explore more on your own.
In a couple of words the basic principles of FP can be summed up as follows:
- You can substitute a function invocation with the body of the function withouth changing the results of the computation (referential transparency)
- There is no shared state in the program, functions accept as arguments and produce immutable objects
- There is no notion of time, the actual scheduling of when various parts of the program will be evaluated does not affect the results of the computation as long as each function gets all of its arguments before its invocation
- Functions can be passed as arguments into other functions and can be returned from functions (in other words, functions are "first-class citizens")
The programs in FP are more like mathematical statements or formulas then a set of imperative instructions that should be executed one by one.
Many of the languages considered "functional" do not follow all of the outlined principles to begin with. For example, even in Scala it is possible to have mutable shared state although there is considerable language support for immutability. Quite often the theoretical beauty of FP has to make some room for practical concerns: writing something to disk or sending a network message obviously do require to have the notion of time in programs.
It is relatively clear that JavaScript only satisfies the last requirement. We can of course try to create programs that have no shared state and will be referentially transparent in JavaScript but it will require additional efforts from our side as the developers and we are not restricted to violate those principles by the language itself.
That said, having functions as "first-class citizens" in JavaScript is actually quite a powerful feature already. It moves us considerably in the direction of FP, and we can always try to follow the rest of the principles of FP when it suits us best. Definitely Underscore.js provides a great deal of help here.
Underscore.js: under the hood
Let's now take a look at the implementation details of Underscore.js. There we can find some good examples of functional style of programming but normally the library tries to avoid using its own functions when implementing other functions because of the performance concerns, so some of the examples we will see will be what we call here "low-level". And this is perfectly acceptable because many libraries depend on Underscore.js and here the performance actually does play an important role, it is even probably more important than readability.
The full source code of Underscore.js is available in the github repository https://github.com/jashkenas/underscore
One example of the functional approach used in Underscore.js is the union function:
[sourcecode language="javascript"]
_.union = function() {
return _.uniq(_.flatten(arguments, true));
};
[/sourcecode]
The implementation clearly explains what the function does: given a few arrays it first concatenates those arrays with _.flatten and then removes non-unique elements with _.uniq.
Another good example of the functional style is a number of functions that deal with grouping, let's look at the code for _.groupBy:
[sourcecode language="javascript"]
// An internal function used for aggregate "group by" operations.
var group = function(behavior) {
return function(obj, iterator, context) {
var result = {};
iterator = lookupIterator(iterator);
each(obj, function(value, index) {
var key = iterator.call(context, value, index, obj);
behavior(result, key, value);
});
return result;
};
};
// Groups the object's values by a criterion. Pass either
//a string attribute to group by, or a function that
//returns the criterion.
_.groupBy = group(function(result, key, value) {
_.has(result, key)
? result[key].push(value)
: result[key] = [value];
});
[/sourcecode]
group is quite an interesting function. It accepts another function that alters its behavior and then returns a function that accepts an object and an iterator. The third argument context is optional, it can specify on which object the iterator should be invoked, i.e. the value of this inside the iterator function. This function returned from group when it is invoked calls the provided iterator to get the key for each value it gets from the target object on which it was invoked. If object is an array, then value will be an element of that array. Once we have key and value we use the provided behavior to process them and maybe alter the result which we first initialize to an empty object. In the end we return result.
We call functions that accept other functions as arguments "higher-order" functions. Then, speaking in the language of Functional Programming, group is just a higher-order function that returns another higher-order function once it is invoked.
This may sound too complicated, but once we look at a concrete example of how _.groupBy is defined and used, everything becomes much clearer.
We see that _.groupBy is just a function returned by the group function which we customize with a specific behavior that for each key and value pushes that value into the array of values stored in result[key]. This way we get all the values stored in the result grouped into corresponding arrays which can be accessed as properties on the result object.
An example of how the _.groupBy function is used:
[sourcecode language="javascript"]
//Result: {"even":[0,2,4],"odd":[1,3]}
_.groupBy([0, 1, 2, 3, 4], function(value) {
return (value % 2 == 0) ? "even" : "odd";
});
[/sourcecode]
Here we provide the concrete iterator function that specifies how to map each value to a key. In this case this is a function that determines for each value whether it is odd or even.
The rest of the grouping functions _.indexBy and _.countBy are defined in a very similar fashion:
[sourcecode language="javascript"]
// Indexes the object's values by a criterion, similar
// to `groupBy`, but for when you know that your index
// values will be unique.
_.indexBy = group(function(result, key, value) {
result[key] = value;
});
// Counts instances of an object that group by
// a certain criterion. Passeither a string attribute
//to count by, or a function that returns the criterion.
_.countBy = group(function(result, key) {
_.has(result, key) ? result[key]++ : result[key] = 1;
});
[/sourcecode]
You can actually see what they do by doing an analysis of code similar to what we have just done with _.groupBy.
But as we mentioned not everything in Underscore.js is written in a functional style. An example of this is the _.object function that allows to create an object from provided arrays of properties in two ways:
[sourcecode language="javascript"]
//Result: {"key1": "value1",
// "key2": "value2", "key3": "value3"}
_.object([
["key1", "value1"],
["key2", "value2"],
["key3", "value3"]
]);
//Result: {"key1": "value1",
// "key2": "value2", "key3": "value3"}
_.object(["key1", "key2", "key3"],
["value1", "value2", "value3"]);
[/sourcecode]
The current implementation is as follows:
[sourcecode language="javascript"]
_.object = function(list, values) {
if (list == null) return {};
var result = {};
for (var i = 0, length = list.length; i < length; i++) {
if (values) {
result[list[i]] = values[i];
} else {
result[list[i][0]] = list[i][1];
}
}
return result;
};
[/sourcecode]
Which is quite low level and complicated. If we were to rewrite this using the functional style, we would get a shorter and cleaner version:
[sourcecode language="javascript"]
_.object = function(list, values) {
if (list == null) return {};
var pairs = values
? _.zip(list, _.take(values, list.length))
: list;
return _.reduce(pairs, function(result, pair) {
result[pair[0]] = pair[1];
return result;
}, {});
};
[/sourcecode]
But this version turns out to be almost 10 times slower because of using of the _.zip and _.take functions which are themselves a bit slow. In the end we sacrifice the readability and functional purity for the performance and choose to leave the current implementation in place. The corresponding performance test that demonstrates the comparative performance of the two implementations
can be found here http://jsperf.com/underscore-object-implementations
Here we will stop with exploring the internal workings of Underscore.js as the parts of the library that we reviewed are already quite representative, but feel free to review the rest of the code.
Alternatives
There are a number of alternative helper libraries or APIs that you can use, but Underscore.js is by far the most popular one and the one where you can count on good support and the availability of the need features. De-facto this library has become a standard, for example, it is the most dependent upon Node module.
But as we have seen among the drawbacks may be a bit of a loss of the functional purity in the implementation, large API and slightly worse than native performance. Also not everybody can like the default Underscore.js style when we have to execute external functions on each object. And surely there are always alternatives.
One of them is the Lo-Dash library (thanks jcready for the reference). Personally I did not use it much, but it looks quite interesting and seems to do all of the things that Underscore.js does and sometimes even a bit more. A quick benchmark http://jsperf.com/reduce-underscore-js-vs-lo-dash shows that _.reduce is 2 times faster in Lo-Dash than in Underscore.js when the benchmark is run in Chrome, but at the same time in Firefox the two libraries do not have noticable performance differences.
Yet another alternative you may consider is Lazy.js (thanks brtt3000), it seems to be the fastest library available based on the benchmarks provided on its site comparing it both with Underscore.js and Lo-dash. If your main concern is performance you may give this library a try.
Also you can always just use the native methods analogous to those provided by Underscore.js: map, reduce, filter, etc. Modern browsers support them well and Underscore.js itself falls back to the native implementations for its functions when it is possible for performance reasons. But be mindful that the performance win will not be more than 50% - 100% which can be relatively insignificant if the hot spots of your application lie elsewhere.
If you want to have a small core of well-defined functions and more of a functional paradigm, then consider using, for example, fn.js https://github.com/eliperelman/fn.js, a "JavaScript library built to encourage a functional programming style & strategy."
Summary
We have seen that:
- Writing our own loops and low level code makes our programs less readable and not always faster
- Instead the native higher-order functions should be used or a specialized library like Underscore.js
- With Underscore.js the resulting code is much more maintainable, as a result the development productivity grows
- The performance cost of using Underscore.js is acceptable in most cases
- It would be good to include functions similar to some of the Underscore.js functions into the language standard and support them natively
If you find yourself writing many loops and iterating over arrays a lot in your project you should definitely give Underscore.js a try and see how your code improves.
The code examples from this article can be found on github github.com/antivanov/misc/tree/master/JavaScript/Underscore.js
Links
Underscore.js
Lo-Dash
Lazy.js
"Functional JavaScript: Introducing Functional Programming with Underscore.js" book


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Data Science projects are either pure analytics projects, or Software projects, or both.
Three typical data science project phases are understanding the data, creating a software component and then a story telling part:
There are two other steps which I left out as I don't have any rules to follow or tools that simplify the job: Getting access to the data and data cleaning.
Please also note that waterfall does not work: The project phases are likely not "pure", but slightly mixed. While you will have an exploratory phase in the beginning, you will also need to communicate your findings (story telling).
In the following, I will highlight some of the tools to simplify the project phases and mention what you should do to make the project successful.
Understanding the Setting
Before there is Data, you have a proces which generates the data. You have a business with a history. Changes which needed to be done. Not the nice and clean way, but ASAP. Understanding how the setting helps you to ask reasonable questions in the next step.
Understanding the Data
Exploratory Data Analysis happens when you
first get a dataset and already have it in a format you can work with. The
linked article already contains quite a bit of software, especially
Pandas, Ipython notebooks and edapy
are useful at this step.
I would create an own repository for this phase. This repository contains code and some artifacts like images or maybe small parts of the dataset and is unlike typical software repositories:
- No tests: What exactly would you test for? The only thing I could think of is boundary and distribution checks, e.g. defining that an "age" has to be non-negative and below 200 and should have its median between 20 and 40.
- No reviews: It is super hard to review IPython notebooks. Don't get me wrong - you should talk about your findings and you should give co-workers access to your code, but it does not make sense to expect them to fully go through your code. Code for understanding data is likely dirty, because most data is dirty.
It's hard to tell when this project phase is over. One artifact that should be created at the end of this project phase is a data loading script. It should take the data from your typical sources and return it in a format you can directly work with. This could be CSV to Pandas dataframes. The dataframe should be cleaned already. The data loading script will be pasted in the subsequent software project and should get a software review as it is a core part of the software development.
If you happen to be in a pure exporatory project - meaning somebody told you to have a look in the data and find interesting things - be aware that this is hard. Make clear that stakeholders understand that you need regular feedback to see if you are on the right track. I would say at least once a day. Pure EDA projects have a high potential to be unsatisfying for everybody.
Ask Stakeholders for Hypotheses. Hypothesis checking is a lot more "work as usual" where you can build up knowledge and finish the task.
Software Projects
For forecasting, classification and regression you are in a supervised machine learning tasks. As it is machine learning, you have to have an optimization metric. In some cases it will be possible to have the same optimization metric as what your stakeholders use to measure how well this part is doing. If this is possible, do it: Use the same metric!
Having the same metric to optimize likely leads to better results and gives your stakeholders an easier time understanding your results. It directly contributes to the "story telling" aspect.
As with any software project, you should have tests, code reviews, a proper project structure and get deployed / used somewhere.
The main difference to typical software projects is the model you create. That model is perceived as a black box by stakeholders.  I recommend reading The Mythos of Model Interpretability to get some nice conceptual ideas about black boxes. To summarize:
- Data Scientists understand their models: We wrote them. There is no way to create a complex piece of software that works without understanding it.
- Black Boxes are common: If we define a black box as something where we don't know 100% instantly and intuitively what happens, then there are a lot of black boxes. Humans, for example. But still you trust your doctor.
- Error types are important: For a human doctor, you know in which way he might do errors. He might be psychologically ill, most likely he will just not pay enough attention and thus diagnose something common where you might have an issue which is uncommon. For machine learning models, it can be the other way around. While overfitting is a problem we are aware of, the model can be fooled to make a very unusual prediction.
So there are two sides of this problem: On the one hand, it is hard to make sure that a model is trustworthy. You have to have the right metric(s), you have to make sure the software works as expected. On the other hand, if you have a trustworthy model, you have to convince your stakeholders that it is trustworthy.
Building Trust
For this part, you have to talk a lot with your stakeholders. They have to get a basic understanding how your model works. It is especially important to emphasize that a model is not a rule-based system. At least not necessarily. Decisions can be made in a non-linear way which makes questions such as "what is the most important feature" problematic.
Model Lab
You can build trust by giving access to your model. If you can give your stakeholders an easy to use interface in which they can enter / manipulate features and see the output of a model, they will either build more trust in your model or you will get some examples where your model fails. Either way, it is a win for the project.
This wireframe is an idea for a web service which allows data scientists to share models with stakeholders in a way that they can "poke" it. They see what the input of the model is, they can manipulate the input and see the output. Please also note that the URL contains the models parameters and thus can be shared.
How can such a web service look from a software perspective?
Each model consists of a package with a model.py
which contains an
infer(input_dict)
function and a description.json
:
{
"name": "Titanic Survival Model",
"parameters": [
{
"name": "Pclass",
"label": "Pclass",
"type": "int",
"comment": "Passenger Class: 1 (First Class) is the most expensive one, 3 is the cheapest"
},
{
"name": "age",
"label": "age",
"type": "float",
"comment": ""
},
{
"name": "SibSp",
"label": "SibSp",
"type": "float",
"comment": "# of siblings / spouses aboard the Titanic"
},
{
"name": "Parch",
"label": "Parch",
"type": "float",
"comment": "# of parents / children aboard the Titanic"
},
{
"name": "Fare",
"label": "Fare",
"type": "float",
"comment": ""
}
],
"output": [
{
"name": "Survival Probability",
"comment": "Survival probability in [0, 1], where 0 means the model is certain that the passenger did not survive and 1 means it is certain that the passenger survived."
}
],
"archetypes": [
{
"name": "The mother",
"parameters": {
"Pclass": 1,
"age": 42,
"SibSp": 12.34,
"Parch": 3.141,
"Fare": 2.141
}
}
],
"info": {
"text": "The model was trained on the values of 123 passangers of the titanic where it is known if the did / did not survive.\n\nThe model is an SVM with C = 1.234."
}
}
Types that should be supported:
int
float
image
binary
(any file upload)ext:FOO
(files with the extension FOO)
Story Telling
Story Telling is the part where you, as a data scientist, make your insights accessible, easy to understand and interpret in the correct way by your stakeholders. It can be about visualizations, but also about choosing the right metrics and reasonable numbers to share. I think I'll make another blog post about this topic as Python has many visualization packages.


Maddison Lackey
CIT 230 - Assignment Portal
Lesson 2:
Semantic HTML and Basic CSS
Lesson 3:
HTML Markup Validation Assignment


An excellent position paper on web applications from Mozilla and Opera (via).
So much of the stuff I've been reading lately has been about formlizing and standardizing the web. How boring! Useful, perhaps, maybe even important... but horribly boring. It's nice to see them talking about real issues in application development, which is the most interesting direction for the web (the document distribution side of the web works just fine right now).
As far as advanced web-based UIs go right now, we're still in a dark period, IMHO. It's like the table-based layouts of the 90's -- they work, but it's a precarious position, and burdensome and distracting for the developer.
Anyway, I'll have to keep an eye on Web Forms


-
Best Engineering Poster
Award, The Korean-American Scientists and Engineers Association, Jan 2017
-
ACM International Joint
Conference on Pervasive and Ubiquitous Computing Travel Grant, Seattle WA,
2014
-
Graduate Student Tuition
Fellowship, College of Natural Sciences and Mathematics, University of
Houston, 2011, 2012, 2013, 2014, 2015
-
1 st Outstanding
Undergraduate Awards Winner 2nd/3rd place, SEJONG University, Jan 2004
-
2 nd Outstanding
Undergraduate Awards Winner 2nd/3rd place, SEJONG University, Jan 2005


flixel.util.FlxPath
- type
- class
This is a simple path data container. Basically a list of points that
a FlxObject can follow. Also has code for drawing debug visuals.
FlxTilemap.findPath() returns a path object, but you can
also just make your own, using the add() functions below
or by creating your own array of points.
Static Methods
- parameters
Object
The Object which will follow this path
Nodes
Array of points which will construct path.
Speed
How fast to travel along the path in pixels per second.
Mode
Optional, controls the behavior of the object following the path using the path behavior constants. Can use multiple flags at once, for example PATH_YOYO|PATH_HORIZONTAL_ONLY will make an object move back and forth along the X axis of the path only.
AutoRotate
Automatically point the object toward the next node. Assumes the graphic is pointing upward. Default behavior is false, or no automatic rotation.
Instance Methods
- parameters
X
X position of the new path point in world coordinates.
Y
Y position of the new path point in world coordinates.
- parameters
X
X position of the new path point in world coordinates.
Y
Y position of the new path point in world coordinates.
Index
Where within the list of path nodes to insert this new point.
- parameters
Node
The point in world coordinates you want to add to the path.
AsReference
Whether to add the point as a reference, or to create a new point with the specified values.
- parameters
Node
The point in world coordinates you want to add to the path.
Index
Where within the list of path nodes to insert this new point.
AsReference
Whether to add the point as a reference, or to create a new point with the specified values.
- parameters
Camera
The camera object the path will draw to.
- returns
- The first node in the path.
- parameters
Node
The point object you want to remove from the path.
- returns
- The node that was excised. Returns null if the node was not found.
- parameters
Index
Where within the list of path nodes you want to remove a node.
- returns
- The node that was excised. Returns null if there were no nodes in the path.
- parameters
Object
Nodes
Optional, can specify all the points for the path up front if you want.
- returns
- parameters
NodeIndex
The index of the new node out of path.nodes.
- returns
- The last node in the path.


Ian Wright bravely reveals he cried 'for days' after not making England's Euro 96 squad
Last night, Wright left viewers saddened - by admitting he cried for days following his omission from the England squad for Euro 1996
by James Rodger, https://www.facebook.com/jamesrodgerjournalistIan Wright has bravely opened up on I'm A Celebrity... Get Me Out Of Here! over his biggest sporting heartbreak.
The former footballer turned broadcaster is now a frequent pundit on BBC One highlights show Match of the Day.
And Wright, who was awarded an MBE, is currently competing on I'm A Celeb alongside nine other stars.
His campmates include Caitlyn Jenner, Kate Garraway and James Haskell.
Last night, Wright left viewers saddened - by admitting he cried for days following his omission from the England squad for Euro 1996.
Ian said: "To be honest I just wanted to win the FA Cup and the League and then in the end I won the FA Cup a couple of times, won the Premier League and played for England.”
But Ian added: “I couldn’t believe I got left out of (Euro) 96, I cried for days. He (Glenn Hoddle) took Robbie Fowler and Les Ferdinand who are obviously top players, unbelievable players but I was devastated.”
Caitlyn said: “Ian, James and myself all some from a sports background so for me, I’m always intrigued by people who have achieved so much in sport and I want to hear their story.”
Rugby union star James said: “I think everyone, especially the three of us appreciates what it took to get to the levels we did. We have definitely got a common ground, it’s nice to share that and hear from two people I really admire.”


Around the World in 80 Days
by Jules Verne
Around the World in 80 Days (French: Le tour du monde en quatre-vingts jours) is a classic adventure novel by the French writer Jules Verne, first published in 1873. In the story, Phileas Fogg of London and his newly employed French valet Passepartout attempt to circumnavigate the world in 80 days on a £20,000 wager set by his friends at the Reform Club.
Source: Verne, J. (1873) Around the World in 80 Days Paris, France: Routledge
- Chapter 1: In Which Phileas Fogg and Passepartout Accept Each Other, the One as Master, the Other as Man Around the World in 80 Days
- Phineas Fogg and his sole servant, Passepartout, become acquainted.
- Chapter 2: In Which Passepartout is Convinced that He Has at Last Found His Ideal
- Impressed by his new employer's composure, Passepartout feels he may have finally found an ideal situation.
- Chapter 3: In Which a Conversation Takes Place Which Seems Likely to Cost Phileas Fogg Dear
- An argument at the Reform Club results in a strange wager by Phileas Fogg.
- Chapter 4: In Which Phileas Fogg Astounds Passepartout, His Servant
- Phileas Fogg returns home to inform Passeportout of their upcoming expedition. Upon arriving at the local train station, Phileas is surprised to encounter a member of the Reform Club. Passepartout is admonished for his forgetfulness.
- Chapter 5: In Which New Species of Funds, Unknown to the Moneyed Men, Appears on ‘Change’
- As Phlieas Fogg departs by train amidst rumors and speculation regarding the nature of his journey. Phileas suddenly finds himself a suspect in a robbery.
- Chapter 6: In Which Fix, the Detective, Betrays a Very Natural Impatience
- In Suez, Detective Fox anxiously awaits the arrival of the Mongolia, believing the guilty party is on board. Passepartout approaches Detective Fix in an attempt to locate the British Consulate.
- Chapter 7: Which Once More Demonstrates the Uselessness of Passports as Aids to Detectives
- Detective Fix informs the consulate of his suspicions regarding Phileas Fogg.
- Chapter 8: In Which Passepartout Talks Rather More, Perhaps, Than is Prudent
- Detective Fix accompanies Passepartout on his errands in an attempt to better understand Phileas Fogg.
- Chapter 9: In Which the Red Sea and the Indian Ocean Prove Propitious to the Designs of Phileas Fogg
- As the Mongolia passes through the Red Sea, Phileas and Passepartout each pass the time in their own way. Having had his passport stamped, Phileas Fogg offers some incentive to the engineer to expedite the voyage to Bombay.
- Chapter 10: In Which Passepartout is Only Too Glad to Get Off with the Loss of His Shoes
- Phileas, having had his passport stamped, has a meal at the train station while Passepartout once again runs errands. A cultural misstep by Passepartout results in an incident at the temple and gives Detective Fix further grounds to obtain an arrest warrant.
- Chapter 11: In Which Phileas Fogg Secures a Curious Means of Conveyance at a Fabulous Price
- In Bombay, Phileas and Passepartout are joined by a Brigadier General, who proceeds to share his opinions with Phileas Fogg. Passepartout makes an alarming discover fearing that Phileas may be in danger of losing his wager.
- Chapter 12: In Which Phileas Fogg and His Companions Venture Across the Indian Forests, and What Ensued
- Phileas and Passepartout journey through India on an elephant. Sir Francis' explanation of the the suttee appalls both Passepartout and Phileas.
- Chapter 13: In Which Passepartout Receives a New Proof That Fortune Favors the Brave
- Phileas' heroic profession is quickly backed by both Sir Francis and Passepartout. As the Parsee guide divulges greater details about the condemned woman's life, Phileas becomes more determined to rescue Aouda. Passepartout devises an intricate plan to save Aouda.
- Chapter 14: In Which Phileas Fogg Descends the Whole Length of the Beautiful Valley of the Gangs Without Ever Thinking of Seeing It
- Phileas, Sir Francis, and Passepartout, having been successful in their rescue attempt, proceed on their journey accompanied by a liberated Aouda. Phileas' show of generosity towards the guide further pleases Passepartout. As time passes, Aouda awakens from her drug induced state, thankful of her rescuers actions.
- Chapter 15: In Which the Bag of Banknotes Disgorges Some Thousands of Pounds More
- Phileas and Passepartout are detained upon arrival in Calcutta, but quickly depart to Hong Kong after posting bond, much to detective Fix's disappointment.
- Chapter 16: In Which Fix Does Not Seem to Understand in the Least What is Said to Him
- Now aboard the Rangoon, Phileas and his fellow travelers proceed on their trip to Hong Kong, with Phileas spending a great deal of time with Aouda in the process. Still awaiting the arrival of an arrest warrant, Detective Fix quietly boards the Rangoon still pursuing Phileas Fogg.
- Chapter 17: Showing What Happened on the Voyage from Singapore to Hong Kong
- Passepartout questions Detective Fix's motivation after discovering him on the Rangoon. An oblivious Phileas continues to spend time with Aouda. The Rangoon enters high seas.
- Chapter 18: In Which Phileas Fogg, Passepartout, and Fix Go Each About His Business
- Passepartout, devoted to the completion of his master's objective, insists on helping the crew of the Rangoon in an attempt to expedite the voyage. Unable to locate a relative in Hong Kong, Aouda decides to accompany Phileas to Europe. Detective Fix is further agitated by the travelers' reserving of space on the Carnatic.
- Chapter 19: In Which Passepartout Takes a Too Great Interest in His Master, and What Comes of It
- Passepartout explores Hong Kong, admiring the diversity of its residents. Detective Fix finally divulges his true identity to Passepartout.
- Chapter 20: In Which Fix Comes Face to Face with Phileas Fogg
- Phileas continues to spend time with Aouda as they explore the streets of Hong Kong. Having missed the Carnatic's departure, Phileas is forced to find transport elsewhere. A deal is struck to arrange travel to Shanghai.
- Chapter 21: In Which the Master of the “Tankadere” Runs Great Risk of Losing a Reward of Two Hundred Pounds
- After a period of calm seas aboard the Tankadere, Phileas and Aouda arrive in Shanghai. Detective Fix is greatly affected by Phileas' kindness, evening offering to pay for his passage.
- Chapter 22: In Which Passepartout Finds Out that, Even at the Antipodes, It is Convenient to Have Some Money in One’s Pocket
- Passepartout awakes to find that he is alone aboard the Carnatic, eventually arriving in Yokohama.
- Chapter 23: In Which Passepartout’s Nose Becomes Outrageously Long
- The morning after arriving in Yokohama, a hungry Passepartout attempts to secure his next meal. Passepartout is reunited with his master and Aouda.
- Chapter 24: During Which Mr. Fogg and Party Cross the Pacific Ocean
- Phileas, Aouda, and Passepartout board the General Grant as they prepare to travel to America. Aouda tells Passepartout of her travels with Phileas. Detective Fix, disappointed by the sudden change of jurisdiction, continues to pursue Phileas and his fellow travelers, resulting in an altercation with Passepartout. Detective Fix finds has a change of heart in regards to Phileas Fogg's wager. Phileas reaches the half-way point.
- Chapter 25: In Which a Slight Glimpse is Had of San Francisco Around the World in 80 Days
- Phileas, Aouda, and Passepartout arrive in America, taking rooms and traveling out into the streets of San Francisco. After encountering Detective Fix, Phileas and Aouda find themselves in the midst of some political upheaval.
- Chapter 26: In Which Phileas Fogg and Party Travel by the Pacific Railroad
- The travelers continue on their journey across the American continent with some interruption.
- Chapter 27: In Which Passepartout Undergoes, at a Speed of Twenty Miles an Hour, a Course of Mormon History
- As the trip continues, Passepartout attends a lecture by a Mormon elder in Utah. After a tour of Salt Lake City, the travelers pick up another passenger before leaving town.
- Chapter 28: In Which Passepartout Does Not Succeed in Making Anybody Listen to Reason
- Unlike his fellow travelers, Phileas remains calm as the troubled journey continues. Aouda spots a familiar face on the train, prompting Passepartout and Detective Fox to take action.
- Chapter 29: In Which Certain Incidents Are Narrated Which Are Only to be Met with on American Railroads
- Phileas' game of whist is suddenly interrupted by Colonel Proctor, who he quickly challenges to a duel. A surprise attack forces the two to temporarily forget their differences. Passepartout is successful in his mission once again.
- Chapter 30: In Which Phileas Fogg Simply Does His Duty
- Following a valiant fight against the Sioux's attack, Phileas leads a party to rescue the captured prisoners. Phileas' successful rescue of Passepartout is greatly received by Aouda. Phileas plans the next leg of his trip.
- Chapter 31: In Which Fix, the Detective, Considerably Furthers the Interests of Phileas Fogg
- With the party now stranded at Fort Kearney, Fix presents a proposal to Phileas. The travelers continue heading east but still do not arrive in time to board the China.
- Chapter 32: In Which Phileas Fogg Engages in a Direct Struggle with Bad Fortune
- Having missed the China, Phileas searches for an alternative passage to Liverpool.
- Chapter 33: In Which Phileas Fogg Shows Himself Equal to the Occasion
- The travelers board the Henrietta, with Phileas eventually taking the helm as captain. Phileas brokers a deal with the captain, eventually arriving in Liverpool with time to spare.
- Chapter 34: In Which Phileas Fogg at Last Reaches London
- Passeportout and Aouda protest the arrest of Phileas, who is being held in the Custom House of Liverpool. With the real thief captured, Phileas is finally released to conclude his journey.
- Chapter 35: In Which Phileas Fogg Does Not Have to Repeat His Orders to Passepartout Twice
- Phileas, having arrived back home, sets Aouda up in the guest room before shutting himself up in his room to ponder his predicament. After a proposal by Aouda, Phileas admits his true feelings.
- Chapter 36: In Which Phileas Fogg’s Name is Once More at a Premium on Change
- With Phileas' whereabouts unknown, the members of the Reforms Club, as well as all of London, anxiously await news on the fate of Phileas.
- Chapter 37: In Which It is Shown That Phileas Fogg Gained Nothing by His Tour Around the World, Unless it Were Happiness
- Having won his wager, Phileas prepares for his wedding. The events just prior to Phileas' arrival at the Reform Club are presented to the reader.


Go to the source code of this file.
Compounds | |
| struct | CharScanType |
| Information about a key. More... | |
| class | TDisplay |
| Display information. More... | |
| struct | TEvent |
| Information about events. More... | |
| class | TEventQueue |
| Information about mouse. More... | |
| struct | KeyDownEvent |
| Information about key presses. More... | |
| struct | MessageEvent |
| Information about message events. More... | |
| struct | MouseEventType |
| Information about mouse events. More... | |
| class | TScreen |
| The interface to the system. More... | |
Variables | |
| const int | evMouseDown = 0x0001 |
| const int | evMouseUp = 0x0002 |
| const int | evMouseMove = 0x0004 |
| const int | evMouseAuto = 0x0008 |
| const int | evKeyDown = 0x0010 |
| const int | evCommand = 0x0100 |
| const int | evBroadcast = 0x0200 |
| const int | evNothing = 0x0000 |
| const int | evMouse = 0x000f |
| const int | evKeyboard = 0x0010 |
| const int | evMessage = 0xFF00 |
| const int | mbLeftButton = 0x01 |
| const int | mbRightButton = 0x02 |
| const int | meMouseMoved = 0x01 |
| const int | meDoubleClick = 0x02 |
Definition in file system.h.
|
|
Broadcast event.
|
|
|
Command event.
|
|
|
Key pressed.
|
|
|
Keyboard event.
|
|
|
Message (command, broadcast, or user-defined) event.
|
|
|
Mouse event.
|
|
|
Periodic event while mouse button held down.
|
|
|
Mouse button pressed.
|
|
|
Mouse changed location.
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|
Mouse button released.
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Event already handled.
|


The ReceptionReception
The reception will also be held at the Diplomat Banquet Center. Hors d'oeuvres and drinks will be available immediately following the ceremony while the newly weds and the rest of the wedding party leave for photographs. Food will be served buffet style beginning around 6:30 P.M. Followed by DJ assisted dancing, cake cutting, and final farewells.
Speeches will be delivered before the buffet by the best man, Jordan Hunter, and the maid of honor, Kristi Young. The couple will have their first dance, followed by Stephanie dancing with her father, and then Will dancing with his aunt.


| Characters | Meaning |
|---|---|
. |
Has one of the following meanings:
Note that the ES2018 added the |
\d |
Matches any digit (Arabic numeral). Equivalent to |
\D |
Matches any character that is not a digit (Arabic numeral). Equivalent to |
\w |
Matches any alphanumeric character from the basic Latin alphabet, including the underscore. Equivalent to |
\W |
Matches any character that is not a word character from the basic Latin alphabet. Equivalent to |
\s |
Matches a single white space character, including space, tab, form feed, line feed, and other Unicode spaces. Equivalent to |
\S |
Matches a single character other than white space. Equivalent to |
\t |
Matches a horizontal tab. |
\r |
Matches a carriage return. |
\n |
Matches a linefeed. |
\v |
Matches a vertical tab. |
\f |
Matches a form-feed. |
[\b] |
Matches a backspace. If you're looking for the word-boundary character (\b ), see Boundaries. |
\0 |
Matches a NUL character. Do not follow this with another digit. |
\cX |
Matches a control character using caret notation, where "X" is a letter from A–Z (corresponding to codepoints |
\xhh |
Matches the character with the code hh (two hexadecimal digits). |
\uhhhh |
Matches a UTF-16 code-unit with the value hhhh (four hexadecimal digits). |
\u{hhhh} or \u{hhhhh} |
(Only when the u flag is set.) Matches the character with the Unicode value U+hhhh or U+hhhhh (hexadecimal digits). |
\ |
Indicates that the following character should be treated specially, or "escaped". It behaves one of two ways.
To match this character literally, escape it with itself. In other words to search for |
| Characters | Meaning |
|---|---|
^ |
Matches the beginning of input. If the multiline flag is set to true, also matches immediately after a line break character. For example, This character has a different meaning when it appears at the start of a group. |
$ |
Matches the end of input. If the multiline flag is set to true, also matches immediately before a line break character. For example, |
\b |
Matches a word boundary. This is the position where a word character is not followed or preceded by another word-character, such as between a letter and a space. Note that a matched word boundary is not included in the match. In other words, the length of a matched word boundary is zero. Examples:
To match a backspace character ( |
\B |
Matches a non-word boundary. This is a position where the previous and next character are of the same type: Either both must be words, or both must be non-words, for example between two letters or between two spaces. The beginning and end of a string are considered non-words. Same as the matched word boundary, the matched non-word boundary is also not included in the match. For example, |
Note: The ?
character may also be used as a quantifier.
| Characters | Meaning |
|---|---|
x(?=y) |
Lookahead assertion: Matches "x" only if "x" is followed by "y". For example, / |
x(?!y) |
Negative lookahead assertion: Matches "x" only if "x" is not followed by "y". For example, |
(?<=y)x |
Lookbehind assertion: Matches "x" only if "x" is preceded by "y". For example, |
(?<!y)x |
Negative lookbehind assertion: Matches "x" only if "x" is not preceded by "y". For example, |
| Characters | Meaning |
|---|---|
x|y |
Matches either "x" or "y". For example, |
[xyz] |
A character set. Matches any one of the enclosed characters. You can specify a range of characters by using a hyphen, but if the hyphen appears as the first or last character enclosed in the square brackets it is taken as a literal hyphen to be included in the character set as a normal character. It is also possible to include a character class in a character set. For example, For example, For example, |
|
|
A negated or complemented character set. That is, it matches anything that is not enclosed in the brackets. You can specify a range of characters by using a hyphen, but if the hyphen appears as the first or last character enclosed in the square brackets it is taken as a literal hyphen to be included in the character set as a normal character. For example, The ^ character may also indicate the beginning of input. |
(x) |
Capturing group: Matches A regular expression may have multiple capturing groups. In results, matches to capturing groups typically in an array whose members are in the same order as the left parentheses in the capturing group. This is usually just the order of the capturing groups themselves. This becomes important when capturing groups are nested. Matches are accessed using the index of the the result's elements ( Capturing groups have a performance penalty. If you don't need the matched substring to be recalled, prefer non-capturing parentheses (see below).
|
\n |
Where "n" is a positive integer. A back reference to the last substring matching the n parenthetical in the regular expression (counting left parentheses). For example, |
(?<Name>x) |
Named capturing group: Matches "x" and stores it on the groups property of the returned matches under the name specified by For example, to extract the United States area code from a phone number, we could use |
(?:x) |
Non-capturing group: Matches "x" but does not remember the match. The matched substring cannot be recalled from the resulting array's elements ([1], ..., [n] ) or from the predefined RegExp object's properties ($1, ..., $9 ). |
| Characters | Meaning |
|---|---|
x* |
Matches the preceding item "x" 0 or more times. For example, |
x+ |
Matches the preceding item "x" 1 or more times. Equivalent to |
x? |
Matches the preceding item "x" 0 or 1 times. For example, If used immediately after any of the quantifiers |
x{n} |
Where "n" is a positive integer, matches exactly "n" occurrences of the preceding item "x". For example, |
x{n,} |
Where "n" is a positive integer, matches at least "n" occurrences of the preceding item "x". For example, |
x{n,m} |
Where "n" is 0 or a positive integer, "m" is a positive integer, and |
|
|
By default quantifiers like
|
// Non-binary values \p{UnicodePropertyValue} \p{UnicodePropertyName=UnicodePropertyValue} // Binary and non-binary values \p{UnicodeBinaryPropertyName} // Negation: \P is negated \p \P{UnicodePropertyValue} \P{UnicodeBinaryPropertyName}
General_Category
(gc
), Script
(sc
), or Script_Extensions
(scx
).Decimal_Number
for the General_Category
property may be written Nd
, digit
, or Decimal_Number
). For most values, the UnicodePropertyName
part and equals sign may be omitted. If a UnicodePropertyName
is specified, the value must correspond to the property type given.


Robo Resume.
DataBase Edition-Login Page.
Invalid username and password.
You have been logged out.
User
Password
Sign In


MagicCMS.Core Namespace
Classes
| Class | Description | |
|---|---|---|
| AjaxJsonResponse |
Class AjaxJsonResponse. Object return by MagicCMS Ajax requests.
|
|
| ClauseValue |
Where clause value. Clause value of a query clause
|
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| CMS_Config |
Class CMS_Config. Wrapper class for MagicCMS application configuration setting.
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| ControlExtensions | ||
| MagicCMSConfiguration |
Wrap Class for MagicCMSConfiguration Configuration Section in Web.config
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| MagicCmsSelect2 |
Class MagicCmsSelect2. Object used to populate select2 lists.
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| MagicGmap3Marker |
Class MagicGmap3Marker. Used tu simplify handling of MagicPost with [MagicCMS.MagicPost.Tipo] = [MagicCMS.MagicPostTypeInfo.Geolocazione]
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| MagicGmap3MarkerOptions |
Class MagicGmap3MarkerOptions.
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| MagicKeyword |
Class MagicKeyword. Wrapper class for storing and indexing [MagicCMS.MagicPost.Tags] assigned to a MagicPost.
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| MagicKeywordCollection |
Class MagicKeywordCollection.
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| MagicLanguage |
Class MagicLanguage.
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| MagicLanguageCollection |
Class MagicLanguageCollection.
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| MagicLog |
Class MagicLog. The MagicCMS log table register every write action and every error that happens in a MagicCMS application.
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| MagicLogCollection |
Class MagicLogCollection.
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| MagicOrdinamento |
Order clauses for MagicPosts recotd sets
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| MagicPost |
Wrapper class for MagicPost the MagicCMS main object.
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| MagicPostCollection | ||
| MagicPostHTML_Encoded |
Wrapper of MagicPost class. Returns HTML encoded version of MagicPost HTML properties
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| MagicPostTypeInfo |
MagicPostTypeInfo is a wrapper class for MagicPost Tipo definition. It manages MagicPost types definitions stored in
MagicCMS database.
"Tipo" is the key property of MagicPost. Trough MagicPost type definition table where you can:
MagicPostTypeInfo class define a number of integer constants corresponding to unique IDs of MagicPost type definition inserted by default in database types table. In this way developers can exploit the advantages of editor code completion and enjoy a more friendly approach to MagicPost types. Generally you can freely define, rename and add new MagicPost type definitions. The MagicCMS back end offers to you a friendly interface to do this. However few types are handled by MagicCMS engine in some special way. See MagicPostTypeInfo Fields documentation for details. |
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| MagicPostTypeInfoCollection | ||
| MagicPrerogativa |
Class MagicPrerogativa.
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| MagicSession |
Class MagicSession. Hamdles typed session variables.
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| MagicTransDictionary |
Class MagicTransDictionary.
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| MagicTransDictionaryCollection |
Class MagicTransDictionaryCollection.
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| MagicTranslation |
Class MagicTranslation.
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| MagicTranslationCollection | ||
| MagicUser | ||
| MagicUserCollection |
Class MagicUserCollection.
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| MagicUtils |
Class MagicUtils.
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| MagicVoto |
Class MagicVoto.
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| MenuIcon | ||
| MenuInfo |
Class MenuInfo.
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| MenuInfoCollection |
Class MenuInfoCollection. Represents a collection of menu items (a main menu or a sub menu).
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| Miniatura |
Class Miniatura. Wrapper class for MagicCMS image miniatures management.
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| MiniaturaInfo |
Class MiniaturaInfo. Extract basic informations by Miniatura
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| WhereClause |
Where clause class. Create and handle not injectable sql queries .
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| WhereClauseCollection |
Class WhereClauseCollection. Group of clause that construct a not injectable SQL query
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Enumerations
| Enumeration | Description | |
|---|---|---|
| ClauseValueType |
Where clause value types. Clause value type of a query clause.
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| LogAction |
Enum LogAction. Define action logged in MagicLog
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| MagicPostTypeInfoOrder | ||
| MagicPostWhichUrl |
Enum MagicPostWhichUrl
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| MagicSearchActive | ||
| MagicTagContainer | ||
| MbUserLoginResult |
Enumeration: User login states
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| MenuIconType |
Enum MenuIconType
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Classes
PxFlags.h File Reference
#include "
foundation/Px.h
"
This graph shows which files directly or indirectly include this file:
Go to the source code of this file.
Classes
class
PxFlags< enumtype, storagetype >
Container for bitfield flag variables associated with a specific enum type.
More...
packman-repo
PxShared-public
1.1.trunk.29467035
include
foundation
PxFlags.h
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www.nvidia.com


Your Roots Are Showing
An exploration of polynomial roots and pretty fractals
An exploration of polynomial roots and pretty fractals
Polynomials are a function of the form a_0 + a_1x + a_2x^2 + ... + a_nx^n, a_n \neq 0
e.g. x+5 = y
The root of a polynomial p is a value a such that p(a) = 0.
e.g. The root of x+5 = 0 is -5, because the expression is only true if we set x equal to -5.
It's often handy to know for what values a function will evaluate to 0. As a simple example, the trajectory of a projectile can be modelled with a quadratic equation, and the roots will tell you where the projectile will hit the ground.
More useful, factoring equations is at the heart of RSA, a widely use cryptographic scheme.
More interesting, it's used to find the eigenvalues of a matrix.
The number of times a polynomial has a root at a given point.
e.g. (x+1)(x+1)(x+1) = x^3 + 3x^2 + 3x + 1 has multiplicity 3 at x = -1.
The one I understand best: x < max(a_i) (Cauchy)
In 1824, Niels Henrik Abel (with help from LaGrange and Ruffini) proved that it was not possible to algebraically find the roots of polynomial of degree greater than 5.
The basic idea: x_{n+1} = x_n + \frac{f(x_n)}{f'(x_n)}
x_{n+1} = g(x_n) where g(x_n) = x_n - \frac{f(x_n)}{f'(x_n)}
Draw a secant line between a, b | a< \alpha, b> \alpha , and set x-axis intercept as new a.
Choose values a, b | a < \alpha, b> \alpha, determine whether root is above or below \frac{a-b}{2}, and then set \frac{a-b}{2} to be the new a or b.
The set of complex numbers c such that z_{n+1} = {z_n}^2 + c remains bounded (doesn't diverge under iteration)(I think)
Finding polynomial roots is an ill-conditioned problem. This means that small errors can dramatically affect results.
In plain english: by creating a polynomial (x-1)(x-2)(x-3) ... (x-n), we know that it has roots at the integers up to n.
As we've seen, finding roots is really more of an art than a science.