Phone: +49<PHONE_NUMBER>4
Want to start learning or have a question about whether English with Russell is right for you? Send me an email:
Email: Russell@rustybass.com


@import general._ @import models._ @import controllers._ @** * Displays an address on a map. The address should be the street address (preferably minimalistic, * as unnecessary text in the address will break the map) and the city is obvious. *@ @(address: String, city: String)(implicit lang: Lang) @scripts = { } @mainBody(title = Messages("maps.displayAddress.title", address, city), moreScripts = scripts, hasFooter = false) { @headingSmall(Messages("general.applicationName"))


ROCKY III Starring: Sylvester Stallone, Mr. T, Hulk Hogan, Burgess Meredith.
Most movies seem to release a third movie just so it can be called a trilogy. ROCKY III seems to kind of fit in that category, but manages to be slightly unique. The ROCKY formula of "Rocky loses fight/Rocky trains/Rocky wins fight" is carried out to the letter. Also the 'tradition' of showing the last five minutes or so from the past ROCKY film is used as well. This movie begins with a series of clips showing how famous Rocky (Sylvester Stallone) has become... Even showing a brief appearance on Sesame Street!!
Then it moves on with Rocky being in a fixed fight with Thunderlips (Hulk Hogan).  Rocky's trainer (Burgess Meredith) tells Rocky not to fight, but the Italian Stallion doesn't listen.
Somewhere along the line after this several things happen. Rocky's longtime trainer dies, causing Rocky to train with his former opponent Apollo Creed. Rocky's wife complains to her husband that he should fight. The final fight ensues between Clubber and Rocky. Guess who wins? The winner's name rhymes with 'Smocky'.
The movie is entertaning mainly because of Clubber Lang's over the top performance. The dramatic aspect has been toned down considerably since ROCKY II and now action seems to be the strong point of the film. Which is good if you like fighting scenes. The last match is quite decent actually.
If you liked the previous films, rent this one. It's well worth seeing if you are a fan of the series. But if you can't stand Rocky shouting "Adrianne!!!" one more time, see something else.
*** out of ****.
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New Game
Games Won:
Games Lost:
Reset Score
Check Guess
Unscramble:
wwww
Remaining Tries:
4
Keep Trying! You win!! You lost, the word was: wwww.
Words Used


The Red Team Village has several stations (mini hands-on workshops) at DEF CON 30 with numerous exercises where attendees can practice their skills and learn new ones. Most stations run for a period of one (1) hour. You will have different opportunities to participate in multiple stations at the Red Team Village during DEF CON 30. All the stations will take place at the Flamingo Mesquite Room (3rd floor).
| TIME | STATION 1 | STATION 2 | STATION 3 | STATION 4 |
|---|---|---|---|---|
| 12PM | Station Setup | Station Setup | Station Setup | Station Setup |
| 1PM | Attack and Defend with the Command and Control (C2) Matrix | HackerOps | Quiet Recon: Gathering everything you need with LDAP and native AD services | OSINT Skills Lab Challenge |
| 2PM | Attack and Defend with the Command and Control (C2) Matrix | HackerOps | Cyber Resilience Bootcamp | OSINT Skills Lab Challenge |
| 3PM | Hacking Modern WebApps with WebSploit Labs | HackerOps | Cyber Resilience Bootcamp | OSINT Skills Lab Challenge |
| 4PM | Hacking Modern WebApps with WebSploit Labs | HackerOps | Hacking APIs: How to break the chains of the web | OSINT Skills Lab Challenge |
| 5PM | Station Turndown | Station Turndown | Station Turndown | Station Turndown |
| TIME | STATION 1 | STATION 2 | STATION 3 | STATION 4 |
|---|---|---|---|---|
| 10am | Offensive Wireless Security 101 | Hacking WebApps with WebSploit Labs | Chill out and networking | OSINT Skills Lab Challenge |
| 11am | Cyber Resilience Bootcamp | Hacking WebApps with WebSploit Labs | Chill out and networking | OSINT Skills Lab Challenge |


---
layout: post
title: I would never work for Jason Calacanis
date: 2010-12-03 17:10:00.000000000 -05:00
comments: true
categories: []
published: true
---
After watching an interview with Jason Calacanis, I can safely say that I would never want to work for him, and never want to model my company to be anything remotely like his. Don't get me wrong, I am not knocking Jason personally, I just think his work values are wack. Correction, I think his values (or those that I can see by his public persona) are wack.
There I said it.
In a world that is flat, where the best technical talent can go anywhere, who on earth would want to go and work for a company whose CEO specifically states that he has no interest in employees that want 'balance'. Talk about a shitty job experience.
The worst part about all of this, is that I am yet to see Jason produce the 'high quality' product that his supposed "abnormal" (his words, not mine) work ethic produces. Perhaps that's valuable in journalism where you have to fight for the best leads to break the best stories - so I can see how that MIGHT be applicable at Weblogs, Inc. but even that is pushing it.
Jason also equated not wanting to sell your soul and work 80 hour weeks to being 'normal', i.e. it's not exceptional and you don't produce outstanding results being 'normal'.
I guess when you have F U money, you really can say and do anything without caring about the repercussions, but I don't think Jason realizes that the best leaders inspire (not intimidate).
I am yet to hear of anyone 'brag' that they work at Mahalo. All the instances I have seen of people discussing their jobs at Mahalo, it has usually been followed with '....yeah...I know'.
I am still in disbelief that he really believes this.
But...I guess, coming from the guy that thought he could pay for Digg's top users, it isn't much of a shock.


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I have created these animations to serve as idle animations. I made sure to use real people as reference then I would go home and practice the same thing. This allowed me to really know the animation. I also recorded myself doing these animations for reference while I made the animations. The hardest part of animating the toon guy was making it seem like he was listening to music without making every action on beat because then it doesn't look as real. I made both of these characters in Adobe Fuse.


Hello everyone,
Following instructions from the site I am trying to build an an energy monitor measuring current only although I have a few questions to ask.
- how do I attach the current sensor to my breadboard?
-Also how do I go about calibrating my monitor and what is the point of calibration as I have seen some people talk about calibration on this site.
Would be very glad if I can get some help and advice
Thank you very much
Re: Arduino energy monitor
It's all explained here:
http://openenergymonitor.org/emon/buildingblocks/ct-sensors-interface
Re: Arduino energy monitor
I assume your current transformer (current sensor) has a 3-connection 3.5mm jack plug? You need a matching socket. You should get one from most electronic component suppliers as "3.5 mm stereo jack socket". Only the tip (centre) and sleeve (body) connections are used for the standard YHDC SCT-013-000 c.t.
[Edit: Or of course you could remove the plug and solder the wires - only the red and white are used!]
Calibration is necessary because the components used are only accurate to within specified limits - usually 1% but possibly 5%. When several components can affect the signal you are measuring, the tolerances can add up (worst case) or cancel each other out (best case) - but there's no knowing which!
There's more on calibration here: http://openenergymonitor.org/emon/modules/emontx/firmware/calibration and the full theory on how to calculate the numbers (which is a good check that everything is working correctly) is here: http://openenergymonitor.org/emon/buildingblocks/ct-and-ac-power-adaptor...
[N.B. I have deleted the duplicate thread].


Turnitin
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--- title: BioNetVisA workshop 2019 layout: default ---
The workshop presentations are available here
BioNetVisA workshop brings together different actors of network biology from database providers, networks creators, computational biologists, biotech companies involved in data analysis and modeling to experimental biologists, clinicians that use systems biology approaches. The participants are exposed to the different paradigms of network biology and the latest achievements in the field.
The goal of BioNetVisA workshop is to build a discussion around various approaches for biological knowledge formalisation, data integration and analysis; compatibility between different methods and biological networks resources available the field; applicability for concrete research and clinical projects depending on scientific question and type of high-throughput data.
The BioNetVisA workshop aims at identifying bottlenecks and proposing short- and long-term objectives for the community as discussing questions about accessibility of available tools for wide range of user in every-day standalone application in biological and clinical labs. In addition, the possibilities for collective efforts by academic researchers, clinicians, biotech companies and future development directions in the field will be discussed during the round table panel.
The workshop targets computational systems biologists, molecular and cell biologists, clinicians and a wide audience interested in update and discussion around current status of network biology, pathway databases, and related analysis tools, including visualization, statistical analysis and dynamic modelling. No computational background is required to attend the workshop.
Graphical representation of biological knowledge
Molecular interaction and pathway databases
Comprehensive signalling networks
Networks annotation and curation
High-throughput data visualization, analysis and interpretation in the context of networks
Multi-scale networks (genome, epigenome, transcriptome, proteome, metabolome...)
Network modelling
Machine learning/Artificial Intelligence approaches in network biology
Basic research and clinical application of networks
Microbiome and networks
Single-cell data and network inference
Metabolomics and networks
Human microbiome
Networks for drug repositioning
| October 24 | Abstract submission deadline Submit now! |
| OCtober 25 | Abstract acceptance notification |
| October 28 | Workshop's final program announcement |
| October 30 | Workshop's registration deadline (no fee) Register here |
| October 31 | BioNetVisA 2019 |
| Session 1: Pathway resources and maps construction in the AI era |
| 08:50 - 09:00 Opening |
| 09:00 - 09:30 Deriving structured representations from natural language to aid scientific discovery: Case studies from reconstructing large pathway maps Abstract Sucheendra Kumar Palaniappan The Systems Biology Institute, Tokyo, Japan |
| Session 2: AI for network-based drug discovery and repositioning |
| 09:30 - 10:00 Pharma Databases Integration coupled with human curation for Drug Development/Repurposing Abstract Junhyung Park 3BIGS CO., LTD. Suwon, Republic of Korea |
| 10:00 - 10:30 Network-based and data-driven drug discovery by machine learning Abstract Yoshihiro Yamanishi Kyushu Institute of Technology, Fukuoka, Japan |
| 10:30 - 11:00 Network-based knowledge for drug discovery: Application in pharmaceutical industry Abstract Tatsuya Ando Takeda Pharmaceuticals, Tokyo, Japan |
| 11:00 - 11:15 Break |
| Session 3: Cancer evolution and medical applications of systems biology |
| 11:15 - 11:45 The Reconstruction of Cancer Phylogenies Abstract David Wedge Big Data Institute, University of Oxford, UK |
| 11:45 - 12:15 Challenges to integrating systems biology and artificial intelligence in medical applications Abstract Yoshiyuki Asai Yamaguchi University, Yamaguchi, Japan |
| Session 4: Big data: integration, visualization interpretation |
|---|
| 12:15 - 12:45 Multi-omics and medical data integration and visualization Abstract Reinhard Schneider Luxembourg Centre for Systems Biomedicine, Luxembourg |
| 12:45 - 14:00 Lunch |
| 14:00 - 15:00 Keynote Joint analysis of large single-cell dataset collections Abstract Peter Kharchenko Harvard medical school, Boston, USA |
| 15:00 - 15:30 Multiscale molecular exploration of medulloblastoma tumors Abstract Emmanuel Barillot Institut Curie, Paris, France |
| Session 5: Modelling of biological and disease networks |
|---|
| 15:30 - 16:00 Towards Predictive Biology: Applications and challenges of mechanistic modeling and machine learning Abstract Ayako Yachie The Systems Biology Institute, Tokyo, Japan |
| 16:00 - 16:15 Break |
| 16:15 - 16:45 A universal network mechanism governing heterogenous ErbB signaling dynamics Abstract Hiroaki Imoto Institute for Protein Research, Osaka University, Osaka, Japan |
| 16:45 - 17:05 Mapping Interactions at Genome Scale for a Specific Biological Context: A Case Study in Epithelial-Mesenchymal Transition Abstract Ian Overton Queen's University Belfast, Belfast, UK |
| 17:05 - 17:25 Merging data-based and mechanistic modelling to study osteoarthritis (OA) development and predict potential intervention targets Abstract Raphaelle Lesage/a> Katholieke Universiteit Leuven, Leuven, Belgium |
| 17:30 - 18:00 Round table discussion and closing remarks |
We invite to submit your abstract for a talk in the topics described above.
The submission deadline is on August 1st 2019
Submitted abstracts will be reviewed by the scientific program committee and a notification of acceptance for a talk will be provided to the corresponding author by August 12th, 2018.
Number of poster abstracts will be also selected for flash poster presentations (3 minutes of topic advertisement).
Abstract format:
Title
List of authors (the first author is the presenting author)
Affiliations
Abstract text in unstructured format (maximum 300 words)
Submission process
The link below will take you to the EasyChair submission page. Once logged, click on the 'Submission' tab to start the submission process. Enter authors, title without HTML elements, abstract up to 300 words, keywords, and select up to three relevant topic sessions.
To assist us with creating the abstract booklet, please upload the same abstract as a word document in the section called "Upload Paper" using this TEMPLATE
When the form is adequately filled out, press the 'Submit' button. You will receive an email from the conference "EasyChair". This email is solely a notification that EasyChair for BioNetVisA2019 has received the abstract.
The free-of-charge registration is obligatory for all participants (speakers, poster presenters, audience).
The registration deadline is on October 20th 2019
Emmanuel Barillot (Institut Curie, France)
Hioraki Kitano (RIKEN Center for Integrative Medical Sciences, Japan)
Alfonso Valencia (Spanish National Bioinformatics Institute, Madrid, Spain)
Samik Ghosh (Systems Biology Institute, Tokyo, Japan)
Inna Kuperstein (Institut Curie, France)
Luis Cristobal Monraz Gomez (Institut Curie, France)
Robin Haw (Ontario Institute for Cancer Research, Canada)
Andrei Zinovyev (Institut Curie, France)
Patrick Kemmeren (Princess Maxima Center for Pediatric Oncology, Utrecht, Netherlands)
Okinawa Insitute of Science and Technology Graduate University, Okinawa, Japan
1919-1 Tancha, Onna-son, Kunigami-gun, Okinawa, Japan 904-0495
https://www.oist.jp/access-map
Room: B250


The answer is no. The above magnetic field is not a solution to the GS equation even if the plasma pressure in the GS equation is set to zero. The above expression is a solution to the GS equation in the limit of infinite aspect ratio and zero plasma pressure. Finite aspect ratio and plasma pressue introduce the Shafranov shift (see Sec. 10).


SFrame.
to_numpy
Converts this SFrame to a numpy array
This operation will construct a numpy array in memory. Care must be taken when size of the returned object is big.
out : numpy.ndarray
A Numpy Array containing all the values of the SFrame


Activate Wi-Fi ?
- Enabling Wi-Fi allows access to all device contents without the need
to connect the USB cable.
- In order for iMazing to automatically access devices they must be connected
to the same Wi-Fi network as the computer.
- USB cable can be connected or disconnected at anytime during transfers as iMazing automatically switches between USB and Wi-Fi.


Instructions Step 1: Make the proper connection by clicking the node as instructed below. If the wire is misplaced, click the node number to deattach the nodes' wire.
From
1
2
3
4
6
7
9
10
To
3
4
12
5
7
8
11
12
Step 2: Click "Check" button.
if connection is correct, an alert appers. Click ok. Now, go to step 4.
if connection is wrong, an alert appers. Click ok. Now, go to step 3.
Step 3: Check the connection, if incorrect, click on node number to remove any particular connection(s) or click on reset button and start from step 1. Step 4: Switch on the MCB. Step 5: Move the slider to change the load values Step 7: Take readings from Rotor, Voltmeter, Ammeter, Watt-meter and load values. Step 8: Click "Add to table 1" button to insert the values in the table 1. Step 9: Click "Add to table 2" button to insert the values in the table 2. Step 10: Follow the procedure from step 6 to step 8, till you have the >=6 readings on the table. Step 11: After taking minimum 6 readings, click the "Graph" buttons(1, 2, and 3). Step 11: Click "Print" button, to print the full connections with graph and table in landscape mode.


Okay, gather round,
everybody, gather round.
Gather round, please.
I have a, uh, a presentation.
lose your attention in
about three minutes,
I slept 26 hours last night.
You still seem very sleepy.
Can I start my presentation?
Where's the easel?
No, no, I'm not using an easel... don't interrupt.
You want me to go get the projector?
No, I don't want the projector.
Let me start my presentation,
which is actually about that.
It's about innovation.
Let me do my thing, okay?
Stop interrupting.
Okay, so, um, as we all know,
um, tomorrow is St. Paddy's Day,
traditionally our
most profitable day.
However, recently, profits
have been declining.
Every year.
And we need to change.
We need innovation.
We need to move Paddy's
from the past and into...
the future,
a mobile Paddy wagon.
Now, these days, people like
to have things on demand.
So instead of having
to go to a bar,
we will bring the bar to you.
Ooh, is that, like, a car
service type of thing?
Where we pick people up and
take 'em around from bar to bar
and jack up the prices?
The Paddy's wagon is the bar.
No, Dennis.
If we want to make money,
we need to honor ancient
Irish traditions,
like serving an irresponsible
amount of booze to people
who are genetically predisposed
to having alcohol problems.
- Right.
- You see,
St. Patrick started
that tradition,
and that's why we
celebrate him today.
Yeah... No, that's
not what he did.
No, he-he played
the flute for some kids,
and then he lured them
into a cave somewhere,
- and he diddled them.
- Nah.
You got him mixed up with the Pied Piper.
Right.
St. Patrick didn't
play the flute.
He drove the kids
out of Ireland.
And then he molested 'em.
No, no, if-if St. Patrick
molested kids,
I feel like, in the olden days
of the Catholic Church,
All right, all right,
look, g-guys, uh,
He drove the snakes
out of Ireland.
I kind of want to just do
the traditional thing
of, like, sticking
around the bar
and-and trying to catch the leprechaun.
No, no!
because he doesn't exist.
Guys, please...
You know what...
I don't even know
if I've set up
my glue traps for him yet.
I mean, can you believe him?
Okay, wait.
Who cares? Look, I'm trying to...
You know what,
actually... I might
want to get myself a flute.
I was thinking the same thing.
We've been talking... you were?
Yeah, because I-I feel like
it's a really fun...
I know we're kind of old, but...

Everybody go get a flute!
...in the sixth grade,
I feel like it's kind of simple.
Frank, look...
All right, let me
explain it to you, at least.
No, he's gone.
Okay.
So, Frank, here's the plan.
for the Web site.
And that will entice
future end users
to comment
and spread brand awareness
over various
social media platforms.
Why don't we just take cash?
No, no, no, no. What I'm talking
about's way simpler than cash.
It's-it's streamlined.
I'm lost. It's... I'm
trying to explain it to you
and I feel like you're not
even listening. I-I...
: Top o' the morning,
you filthy lads.
I'm fixing to have a whale of
a time in this here mobile pub.
I'm so sorry... what is this?
 Why?
'Cause it's fun.
No.
I thought that's the thing
about St. Patrick's Day...


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Translator: xiaodp
Author: labuladong
This article is an advanced version of “Details of Backtracking Algorithms” before. The previous one isn’t clear enough, so you don’t need to read it and just read this article.
Ponder carefully and you will find that the backtracking problems follow the same pattern, that is, have the same framework.
Let’s go straight to the framework backtracking follows. Solving a backtracking problem is actually a traversal process of a decision tree. Now you only need to think about 3 terms:
Path: the selection that have been made.
Selection List: the selection you can currently make.
End Condition: the condition under which you reach the bottom of the decision tree, and can no longer make a selection.
It doesn’t matter if you don’t understand the explanation of the 3 terms. I will use the two classic backtracking algorithm problems,Permutation
and N Queen Problem
to help you understand what they mean. Before this, you just keep them in mind.
Here shows the pseudocode of the framework:
result = []
def backtrack(Path, Seletion List ):
if meet the End Conditon:
result.add(Path)
return
for seletion in Seletion List:
select
backtrack(Path, Seletion List)
deselect
The core is the recursion in the for loop. It makes a selection
before the recursive call and undoes the selection
after the recursive call, which is especially simple.
Then what makes a selection
and undo the selection
means? and what is the underlying principle of this framework? Let’s use Permutation
to solve your questions and explore the underlying principle in detail.
You must have learned the permutations and combinations. As we know, for N unique numbers, the number of full permutations is N!.
note
: For simplicity and clarity, the full permutation problem we are discussing this time does not contain duplicate numbers.
Think about how we find out all the permutations. If you are given three numbers [1,2,3]
, you may follow these steps:
In fact, this is the ‘’backtracking’’. You can use it even without a teacher! The following figure shows the backtracking tree:
Just traverse this tree from the root to the leaves and record the numbers on the paths, and you will get all the permutations. We might as well call this tree a “decision tree” for backtracking for you’re actually making decisions on each node. For instance, if you are now at the red node, you will making a decision between the “1” branch and “3” branch. Why only 1 and 3? Because the “2” branch is behind you, you have made this selection before, and the full permutation is not allowed to reuse numbers.
Now you can understand the terms mentioned before more specifically: [2]
is the “Path”, which records the selections you have made; [1,3]
is the “Selection List”, which means the current selections you can make; End Condition
is to traverse to the bottom of the decision tree(here is when the Selection List is empty).
If you understand these terms, you can use the “Path” and “Selection List” as attributes of each node in the decision tree. For example, the following figure lists the attributes of several nodes
The function backtrack()
we defined is actually like a pointer. It is necessary to walk on the tree and maintain the attributes of each node correctly. Whenever it reaches the bottom of the tree, its “Path” is a full permutation.
Furthermore, how to traverse a tree? it should not be difficult. Recall from the previous article Framework Thinking of Learning Data Structures, various search problems are actually tree traversal problems, and the multi-tree traversal framework is:
void traverse(TreeNode root) {
for (TreeNode child : root.childern)
// Operations needed for preorder traversal
traverse(child);
// Operations needed for postorder traversal
}
The so-called preorder traversal and postorder traversal are just two very useful time points. The following picture will make you more clear:
Preorder travers is executed at the time point before entering a node, and postorder traversal is executed at the time point after leaving a node.
Recalling what we just said:“Path” and “Selection List” are attributes of each node. If want the function to maintain the attributes of the node correctly, we must do something at these two special time points:
Now, do you understand the core framework of backtracking?
for seletion in Seletion List:
# select
Remove this seletion from the Seletion List
Path.add(seletion)
backtrack(Path, Seletion List)
# deselect
Path.remove(seletion)
Add the seletion to the Seletion List
As long as we make a selection before recursion and undo the previous selection after recursion, we can get the Selection List and Path of each node correctly.
Here shows the code for the full permutation:
List<List<Integer>> res = new LinkedList<>();
/* The main method, enter a set of unique numbers and return their full permutations */
List<List<Integer>> permute(int[] nums) {
// record Path
LinkedList<Integer> track = new LinkedList<>();
backtrack(nums, track);
return res;
}
// Path: recorded in track
// Seletion List: those elements in nums that do not exist in track
// End Condition: all elements in nums appear in track
void backtrack(int[] nums, LinkedList<Integer> track) {
// trigger the End Condition
if (track.size() == nums.length) {
res.add(new LinkedList(track));
return;
}
for (int i = 0; i < nums.length; i++) {
// exclude illegal seletions
if (track.contains(nums[i]))
continue;
// select
track.add(nums[i]);
// enter the next level decision tree
backtrack(nums, track);
// deselect
track.removeLast();
}
}
We made a few changes here: instead of explicitly recording the “selection List”, we use nums
and track
to deduce the current selection list:
So far, we have explained the underlying principle of the backtracking through the full permutation problem. Of course, this algorithm is not very efficient, and using the contains
method for linked list requires O(N) time complexity. There are better ways to achieve the purpose by exchanging elements which are more difficult to understand. I won’t discuss them in this article. If you are interested, you can google related knowledge by yourself.
However, it must be noted that no matter how optimized, it conforms to the backtracking framework, and the time complexity cannot be lower than O(N!).Because exhaustion of the entire decision tree is unavoidable. This is also a feature of backtracking. Unlike dynamic programming having overlapping subproblems which can be optimized, backtracking is purely violent exhaustion, and time complexity is generally high.
After understanding the full permutation problem, you can directly use the backtracking framework to solve some problems. Let’s take a brief look at the N Queen
problem.
 Thus, a solution requires that no two queens share the same row, column, or diagonal.
This problem is essentially similar to the full permutation problem. If we build a decision tree, each layer of the decision tree represents each row on the chessboard. And the selection that each node can make is to place a queen on any column of the row.
Apply the backtracking framework directly:
vector<vector<string>> res;
/* Enter board length n, return all legal placements */
vector<vector<string>> solveNQueens(int n) {
// '.' Means empty, and 'Q' means queen, initializing the empty board.
vector<string> board(n, string(n, '.'));
backtrack(board, 0);
return res;
}
// Path:The rows smaller than row in the board have been successfully placed the queens
// Seletion List: all columns in 'rowth' row are queen's seletions
// End condition: row meets the last line of board(n)
void backtrack(vector<string>& board, int row) {
// trigger the End Condition
if (row == board.size()) {
res.push_back(board);
return;
}
int n = board[row].size();
for (int col = 0; col < n; col++) {
// exclude illegal seletions
if (!isValid(board, row, col))
continue;
// select
board[row][col] = 'Q';
// enter next row decision
backtrack(board, row + 1);
// deselect
board[row][col] = '.';
}
}
This part of the code is actually similar to the full permutation problem. The implementation of the isValid()
is also very simple.：
/*Is it possible to place a queen on board [row] [col]? */
bool isValid(vector<string>& board, int row, int col) {
int n = board.size();
// Check if share the same column
for (int i = 0; i < n; i++) {
if (board[i][col] == 'Q')
return false;
}
// Check if share the same right diagonal
for (int i = row - 1, j = col + 1;
i >= 0 && j < n; i--, j++) {
if (board[i][j] == 'Q')
return false;
}
// Check if share the same left diagonal
for (int i = row - 1, j = col - 1;
i >= 0 && j >= 0; i--, j--) {
if (board[i][j] == 'Q')
return false;
}
return true;
}
The function backtrack()
still looks like a pointer walking in the decision tree. The position traversed by the backtrack()
can be represented byrow
and col
, and the unqualified condition can be pruned by the isValid()
:
If you are facing such a chunk of solution code directly, you may feel very puzzled. But if you understand the framework of backtracking, it is not difficult to understand the solution code. Based on the framework, the changes are just the way of making selection and excluding illegal selections. As long as you keep the framework in mind, you are left with only minor issues.
When N = 8, it is the eight queens problem. Gauss, the mathematics prince , spent his whole life not counting all possible ways to place, but our algorithm only needs one second .But don’t blame Gauss, the complexity of this problem is indeed very high. Look at our decision tree, although there is a pruning by the isValid()
, the worst time complexity is still O(NN + 1).And it cannot be optimized. If N = 10, the calculation is already rather time consuming.
When we don’t want to get all legal answers but only one answer, what should we do ? For example, the algorithm for solving Sudoku is too complicated to find all the solutions and one solution is enough.
In fact, it is very simple. Just modify the code of the backtracking slightly:
// Returns true after finding an answer
bool backtrack(vector<string>& board, int row) {
// Trigger End Condition
if (row == board.size()) {
res.push_back(board);
return true;
}
...
for (int col = 0; col < n; col++) {
...
board[row][col] = 'Q';
if (backtrack(board, row + 1))
return true;
board[row][col] = '.';
}
return false;
}
After this modification, as long as an answer is found, subsequent recursion of the for loop will be blocked. Maybe you can slightly modify the code of the N queen problem and write an algorithm to solve Sudoku?
Backtracking is a multi-tree traversal problem. The key is to do some operations at the positions of pre-order traversal and postorder traversal. The algorithm framework is as follows:
def backtrack(...):
for seletion in seletions List:
select
backtrack(...)
deselect
When writing the backtrack()
function, you need to maintain the “Path” you have traveled and the “selection List” you currently have. When the “End Condition” is triggered, record the “Path” in the result set.
Think carefully, is the backtracking and dynamic programming somehow similar? We have repeatedly emphasized in the series of articles about dynamic planning that the three points that need to be clear in dynamic programming are “State”, “selection” and “Base Case”. Do they correspond to the “Path” that has passed, and the current “selection List” And “End Condition”?
To some extent, the brute-force solution phase of dynamic programming is a backtracking. When some problems have overlapping sub-problems, you can use dp table or memo to greatly prune the recursive tree, which becomes dynamic programming. However, today’s two problems do not have overlapping subproblems, that is, the problem of backtracking, and the high complexity is inevitable.


Briefly about Myself
Achievements
Stat-gram--An Instagram Micro-service.
Stat-gram is a microservice tool for Business and Influencers on Instagram platform. We're using AI to help Business get better leads and create a bridge with Marketing and Management tools, saving valuable time spent in comunication in Business.
JobMarket-Analytics--LinkedIn.
Scraping Data from Job-Listing such Indeed, Google, mainly LinkedIn. The Goal was uncover trends and gaps on Job market to help candidates be more competitive against resume-scan software. Next phase is train a model on our data and create a online aplication.
Data TextMining-SentmentAnalysis--Twitter.
Create a scripit using Python that extract Tweets related to the prime minister of India, "Narendra Modi" and get Insights about his popularity. In fact, after 4 months the Idia Election happened, and we find out that our Polarity chart indicator was super accurate.
Projects
Tech


X position: m
Y position: m
Z position: m
Cable length: m
Density: kg/m
Tension in A: = N
Tension in B: = N


GPU particle simulation of vibratory audio wave motion using ThreeJS and the Web Audio API. Allows for large particle counts by computing positions with a shader, using PhysicsRenderer and Render-To-Texture. Inspired by Chladni or Cymatic patterns.
VisualizeDeep Deterministic Gradient Policy (Actor-Critic) machine learning racing driver, implemented for the racing simulator "TORCS". Uses an actor-critic network implemented in Keras and TensorFlow with OpenAI Gym environment interface to train a racing AI using reinforcement learning.
LearnImage courtesy of Engadget
Multi-Projector Zoom Alignment created for Christie Digital, used to automatically align 2 or more projectors for 3D cinemas. Runs C# computer vision processing to align the size of a test pattern on both projectors, with a WPF interface. Emphasis on performance for potential future embedded uses, using dotMemory and dotTrace profiling tools.
WatchA gallery of personal photography, with a responsive tiled hexagon layout and CSS-only lightbox effect. Pictures of travels, novelties, and simple beauties.
Explore


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The Greet® Meetings app stores and processes personal data that you have provided to us, in order to provide our Service. It’s your responsibility to keep your phone and access to the app secure. We therefore recommend that you do not jailbreak or root your phone, which is the process of removing software restrictions and limitations imposed by the official operating system of your device. It could make your phone vulnerable to malware/viruses/malicious programs, compromise your phone’s security features and it could mean that the Greet® Meetings app won’t work properly or at all.
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With respect to Nandi Mechatronics Pvt. Ltd.’s responsibility for your use of the app, when you’re using the app, it’s important to bear in mind that although we endeavour to ensure that it is updated and correct at all times, we do rely on third parties to provide information to us so that we can make it available to you. Nandi Mechatronics Pvt. Ltd. accepts no liability for any loss, direct or indirect, you experience as a result of relying wholly on this functionality of the app.
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These terms and conditions are effective as of 2020-07-17
Contact Us
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SUPERCHARGE COVID-19 TESTING
In the fight against the Coronavirus, one of the biggest challenges are the so called Superspreaders. These are people who are infected, but do not show any symptoms. In Austria people with no symptoms are not tested, due to a shortage of material and medical staff for the RT-PCR tests. Until now, we found 8000 infected people in Austria, but only a few of the Superspreaders. Mass testing will increase the detection of Superspeaders and therefore prevent them from spreading the disease without even noticing.
To increase the testing capacity, SUPER develops a Machine Learning based solutions for COVID-19 detection from CT scans and X-Ray Images.
This project is still under development and shouldn't be used for medical diagnosis yet.


GOLDENEYE A film review by Andrew Hicks Copyright 1995 Andrew Hicks / Fatboy Productions
(**1/2 out of four)
I haven't seen many other James Bond movies to compare this new one to (translation: zero), but it stands on its own as a decent action flick. I did find it an uneven movie to be mainly appreciated by middle-aged adults who grew up on the Connery Bond films of the 60's and are in need of something to cling on to in light of the recent wave of P.C.-laden movies and sex-killer flicks. And I was pretty much proven right when my mom asked me how I liked it and I said "It was okay." She replied, "Are you kidding? I loved that movie." And yes, I do still see movies with my mother. What's it to you?
GOLDENEYE, at least, plays the outdated Bond movie staples for laughs. What else can you do but snicker at a movie with a White-Anglo-Saxon-Protestant hero, an abnormal ratio of cigarette smokers to non-smokers, helpless women, Russian villains, absurd high-tech gadgets, explosions, red convertible sports cars and ridiculously far-fetched death defying scenes? Add in a beautiful yet villainous masochist woman (Xenia Onatopp) who gets off on her fights with Bond and the movie may as well be a time machine to a long-forgotten era. I was waiting for them to talk about President Nixon or hot pants.
Pierce Brosnan does a good job of playing 007 (which represents his agent number and his I.Q.) here and, as usual, James Bond gets all the chicks while making the world safe for kids to play in the streets. And what does he get for his efforts? People call him a "sexist, misogynist dinosaur." This time, Bond has to protect the world from a missile system that short circuits all the world's electricity, undoing the progress the world has made in the last century. Please, this movie is far enough in the Stone Age already.
-- Visit the Movie Critic at LARGE website at http://www.missouri.edu/~c667778/movies.html
The review above was posted to the
rec.arts.movies.reviews newsgroup (de.rec.film.kritiken for German reviews).
The Internet Movie Database accepts no responsibility for the contents of the
review and has no editorial control. Unless stated otherwise, the copyright
belongs to the author.
Please direct comments/criticisms of the review to relevant newsgroups.
Broken URLs inthe reviews are the responsibility of the author.
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Related links: index of all rec.arts.movies.reviews reviews


Search inside Yourself questions
Did you connect with any of the analogies for the mind?
Don't think so
What learnings did you take from the chapter?
- Emotional awareness: Recognizing one's emotion and their effects
- Accurate self-assessment: Knowing one's strengths and limits
- Self-confidence:A strong sense of one's self-worth and capabilities
How did you find the body scanning
A bit like meditating except with specific instructions.


I had never had the pleasure of attending one before, but I never
expected drugs to be sold so openly at music festivals. My journey to
Spookstock 7 was long an uneventful, and mostly was spent mentally
preparing for whatever psychedelic experiences I might have. I was
actually doubtful that I would be able to find any doses at all, as
it's fairly uncommon in my home state. I was not to be disappointed.
I awoke to the rising sun at about seven o'clock, on the second day of
the festival. I had arrived at the campground at midnight the night
before, to something like an all-night music and drug party, and
hadn't slept much in the intervening time. I was feeling strangely
refreshed anyway, for some reason. I think it was something about the
atmosphere of this place; everyone I met seemed to non-verbally
acknowledge the strange, subtle connectedness that the psychedelic
state awakens me to. It was, perhaps, the change that was refreshing.
Not many people I normally interact with have been awakened in this
way.
As I climbed out of my friend R's car, stretched, and stumbled around,
I encountered three new arrivals, camped out in the space next to
us. were yelling at passerby, 'Molly! Mescaline!'. (T-1:00)
'Mescaline', I thought. That was definitely on my long, but
shortening, list of 'Substances To Experience Before I Die'.
In addition to the connectedness, everyone here is just extremely
friendly, too. Maybe it's all the good pot and beautiful scenery. I
don't know. Anyway, I talked to this 'mescaline' guy for a while, and
he invited me over to his campsite, and offered me some hot chocolate.
He told me that what he actually had was MDMA, Peyote extract, and
2C-B, which he explained was like synthetic mescaline.
However, I already knew 2C-B well from my research. I had never
experienced it, though. It is indeed chemically similar to mescaline,
but it has its own unique and interesting effects, also. I knew that
it's effects are described as 'Somewhere between MDMA and LSD, but
completely unlike a combination of the two.' He agreed to sell me one
of his few doses. I took it on the spot, and proceeded up the hill to
the site where people had been gathered around the bonfire the night
before. I knew there would be a good aura up there. (T0:00)
As a bit of background information, I've been having a mild identity
crisis over the past few months. A lot of my friendships had changed
suddenly, and I found myself more alone than I'd ever been. I realized
at this point that I had been defining myself too much by the people I
was associating with, and, in the absence of them, I wasn't entirely
sure who I was, where I was, or even why I was alive. It was very
disconcerting, to say the least.
The embers of the bonfire of the night before were still smoldering
when I arrived, and about ten of my fellow early morning trippers had
been drawn up here as well. They were all sitting around it, smiling,
sometimes talking sporadically, but mostly just relaxing and being
generally amicable towards the world. I'd never met any of these
people before, but the seemed friendly enough.
A kid in glasses and an all-over print t-shirt welcomed me over. This
was the first time I'd seen the camp in the daytime, and I must say,
it is beautiful beyond description. It was a perfect day. Clear, blue
sky with a warm sun beating down its pure energy onto us. The
greenest, softest grass I'd ever seen encircled the fire like a
carpet, stretching away into the woods at the bottom of the
hill. Birds were flying in an unbelievable dance of life far above us,
as the fire crackled in what I thought was a wise and especially
soothing manner. I was definitely beginning to feel the effects of the
drug now. (T+0:30-0:40)
All of my previous trips have been with tryptamine compounds, and what
I found is that, if 2C-B is any indication, phenethylamines are much
more pleasant. Much warmer, much friendlier, less 'glitchy', and with
less distracting visual activity. That's not to say the visual
activity is not there. If anything, it was much more intense than with
other drugs I've tried. However, I was able to ignore it much more
easily. It wasn't as mesmerizing as what I would see on, for
example, LSD. This was a good thing, as it lets me focus more on my
soul, which is what I came here to do.
When it finally arrived, after maybe 45 minutes, The come-up was fast
and fairly intense; almost overwhelming. I felt the energy of it
washing over me in waves, and it felt amazing. If I had been in a more
neutral or hostile setting, things probably would have been
frightening at this point, but I knew that everyone around me
understood, and was supportive of my state of mind. This made it much
easier to bare my soul, and slip into a pleasant state of openness and
unity with my surroundings. (T+0:40-1:00)
Before I had been there thirty minutes, the kid in the glasses and an
old hippie got together with a guitar and a drum, and started playing
music.  Everyone
laughed in that kind of spaced-out way, they switched instruments, and
then proceeded to play the most beautiful music I've ever heard. The
trees swayed, the wind blew, the birds swooped and dove in intricate
patterns, and it seemed as though the whole valley was dancing to the
beat of our collective soul.
Colors ... are amazing. Acid never did the colors thing for me, but on
this ... the grass was the greenest green I have ever seen. I'll never
forget it, as long as I'm alive. The world is a beautiful place, if
only you can eliminate your bias and stop filtering the beauty through
your worldview for a moment. I am in love with this place.
The birds ... its almost as if they act as a single organism, some
kind of a pseudo-hive mind. Every one of them has a soul, but,
together, they are something greater. Something ... beyond ... mere
birds. They are a collective. WE are a collective. We are at peace.
It was quickly apparent that 2C-B is also much more of an intoxicant
than LSD is, at least for me. My memory was dramatically affected, and
somehow in-sync with the waves of energy crashing over my
consciousness. The rest of the trip was superimposed upon sets of
clearly-defined waves of beauty, awareness, and clarity. It was as if
I was in a movie, and, at points, I would suddenly 'awaken' in a new
place, as if a cutscene or transition had taken place. I was fully
sane, conscious, and aware in the intervening time, and I remember it
clearly, but it's not nearly as important as when I was on the crest
of a wave of energy. Its as if I was coming to orgasmic revelations,
every twenty minutes or so.
I remember clearly, at the peak of my come-up, two older clean-shaven
men came over and sat down around the campfire with us. For some
reason, it was obvious to me that they were undercover cops. Looking
back, I'm not sure if they actually were. However, a man in camoflogue
came over to the campfire, talking in a walkie-talkie, convincing me
beyond a doubt that we were surrounded by some kind of undercover SWAT
team.
He reached down behind a log where a kid was sitting, and picked up a
bag of weed. 'What's this?' he said. 'Will you please stand up, sir?'
I was sure that we were getting busted, and was really high at this
point, so it was kind of starting to freak me out. But, it turns out,
the guy was just selling weed. 'Crappy weed is what it is. Nugget
delivery service!' he said. 'Somebody buy some nuggets!' I didn't see
or hear about anyone get arrested during the entire festival. The guys
that I suspected were cops even smoked some of the pot with us. (T+1:30)
As I started to come down from the crest of my first wave, I wandered
away from the campfire, and walked down 'Shakedown Street', the place
where all the vendors are set up. Everyone's face was severely
distorted, but not in a menacing way. It was an obvious drug effect,
so it didn't cause me much worry. The people didn't seem to notice
that I was tripping, or just simply didn't care. I felt a strange
benevolence towards everyone, tinged with a hint of suspisciousness,
as I still suspected there were more undercover cops around here,
somewhere. I didn't have anything on me, so it wasn't a fear, but
rather an understandable delusion that I held for twenty minutes or
so. There probably were cops around there, with all the drug
trafficking going on. However, I recognized it as a drug-induced
delusion, and brushed it off before I left Shakedown.
Eventually, I ended up by the creek that runs through the bottom of
the valley. It's nothing like the creeks from my home state, all muddy
and brown. No, this one was perfectly, unbelievably clear, like in a
dream. Three more dudes were sitting by the creekside playing drums,
and again, it seemed like they were playing to the beat of the
river. Through the music, it seemed to me that they had uncovered the
secret heartbeat of nature. Why hadn't I heard this before? (T+2:00)
I sat there for nearly two hours, in the sun, listening to the drums,
the river, and watching the golden spiderwebs of the morning sky dance
across the perfectly clear water. I bathed in the radiance of the
heartbeat, its warm, pulsating waves. The energy of that time was
absolutely amazing.
I find that, personally, with the exception of Ayahuasca, the 'comeup'
of psychedelics in general is not nearly as useful, in terms of
introspection, as the 'comedown'. That is, the comeup is more
enjoyable, but, if I take anything away from the experience, I'm going
to learn it while descending back to sobriety. That turned out to be
especially true with this substance. During the last four hours or so,
I spent a lot of time wandering around, both in the campground, and in
my mind.
I realized that my identity crisis was more an issue of where I was
derived from. That is, I need to be part of a collective, a culture,
perhaps, or a group of friends, but I cannot be OF that culture. Much
like the flock of birds on the hill, I need to enter into it,
independently, as a developed person, and bring something new to
it. Any other way, I would either be defined by cultural norms, or an
outcast. I need to push out my identity to those around me, rather
than pulling in theirs. This was my problem, and the realization of
this greatly settled my soul, and still does, as I write this more
than a month later.
After the sun had ascended so far into the sky that I could no longer
justify calling this a 'perfect morning', I ended up back at the
campsite of the people who had sold me the 2C-B. They were rolling up
a blunt. Perfect. Everything had that shiny, plastic sheen of order,
yet identity, about it. They invited me over to smoke. It was a
wonderful, communal experience. I felt close with everything. I had a
very intense feeling of having arrived home, at long last. (T+4:20)
There was what seemed to be an extremely long period of intoxication,
after the main effects had ended. This may or may not have been a
product of all the marijuana I had smoked over the course of the day,
though I suspect it was not. I had the same 'waves of energy' feeling,
but without any of the visual activity, or really anything other than
a mild feeling of drunkenness. It was not unpleasant in the slightest,
but it did seem to go on well past the peak of the experience. I was
just confused as to how I could still feel like I was tripping hard,
but without any kind of visuals at all.
I finally was completely sober around 3 or 4 PM. The world retained
its beauty, however, and, strangely, the grass retained its surreal
green color. Even today, I will occasionally come across a
particularly green patch of grass in the morning or evening, with the
sun falling across it just right, and I will again be overwhelmed with
the beauty of the world.
All in all, I think this was hands-down the best trip of my life. I
didn't learn as much from this substance as I did from Ayahuasca, and
it wasn't nearly as intense as LSD or psilocybin mushrooms, but,
rather, a soft, warm day spent in paradise. I'm glad I had the
opportunity to experience this. Highly recommended.
Experience Reports are the writings and opinions of the individual authors who submit them.
Some of the activities described are dangerous and/or illegal and none are recommended by Erowid.


Making what is visible invisible, this is a question that has appealed to both designers and artists. In the emotion visualization projects, we are dealing with this question, where the invisible corresponds to emotional states of people. Making emotions visible, and maybe tangible, might increase emotional self-awareness of people and ease emotional communication between them.
We are working with AR, thinking that it will become a widely used technology in the future and by using this technology seeing information such as emotional states embedded in our regular vision will become something very common.
I have been implementing prototypes of our ideas on HoloLens, using Unity. Below are two strategies we have been exploring for making emotions visible in AR.
Initially we came up with the Emotionscape concept, a hypothetical emotionally responsive space. In this concept, the spatial attributes change to reflect emotional states - either what the user experiencing, what another collocated person's experiencing or one that is selected by the user. Our work has been accepted as poster presentations to VRST'17 and CHI'18 .
While imagining spatial emotion representations, we realized it would also be interesting to visualize the emotional states of people within separately - in fact this could have more use cases and could have a more general applicability. Therefore, we started with a series of exploratory workshops on how people would like to visualize their emotional states and created an emotion visualization design framework for AR based on the outcomes of the workshops and literature. Now, we are evaluating the framework and are planning to prototype our work in HoloLens.
As a part of a fellow student Seyma Tasel's project, I built a personal space creation prototype on HoloLens.


This week, we present another collection of remarkable contributions made through Utopian. These contributions include entries from the Blog, Graphics, Analysis and Development categories. Consider checking them out and using them as an example to improve your own contributions to Utopian.
Staff Picks
Got upvotes but no payout? An overview of the situation around the minimum payout threshold by @crokkon [analysis]
Without exception, @crokkon creates amazing pieces of analytical work. In this post, his main point of interest was a payout threshold in the Steem blockchain, exploring why not all posts are paid out if they didn’t receive enough STUs. @crokkon explore the threshold that has been set at 0.02 STU for any post and comment to be paid out. He presents the count of posts and the time they were created, and has interesting observations.
Total payout: 100.28 STU Number of votes: 119
1UP News: Fundition Campaign, New Platform Account And UP Token Distribution Explained by @steem-1up [blog]
Steem-1up is the descendant of utopian-1up, following the idea of 1UP. Its aim is to create a hivemind curation system for different communities. Thus, in accordance with the new branding, the older Steem account has retired. New updates are going to be published with the new account. However, they still deliver the same type of comprehensive updates with beautiful custom images. The post is also a part of the Fundition campaign to support the development of the project.
Total payout: 100.28 STU Number of votes: 119
Logo for lightsteem by @oups [graphics]
@oups has participated in the task request for lightsteem, which is a lightweight Python library for Steem. @emrebeyler, the creator and developer of lightsteem has asked for a new logo to represent his project. We can see that the actual logo is clean and simple, and the presentation follows the idea of simplicity, too. You can read about the initial idea, the process of creating the logo, and the color ranges that were used to make the logo best possible.
Total payout: 2.02 STU (Not voted yet) Number of votes: 28
Announcing Finally Network - Turn your Steem blog into a website by @sambillingham [development]
@sambillingham has proved in the past that his projects have potential and are useful to the community. He has worked on Steem-based projects, and Finally Network is no different. Continuing to develop new projects that utilise the Steem blockchain will show that the blockchain can be used for different kinds of projects. Finally Network aims to provide a simple way to create a custom website for Steem users. The creator compares the idea to Squarespace, and at the moment has provided an MVP of the project, which may change according to received feedback.
Total payout: 20.45 STU (Not voted yet) Number of votes: 631
Steem Use-a-Thon by Byteball - Weekly Update 3 by @byteball.org [blog]
The folks at @byteball.org continue to updates about the use-a-thon, and these are some of the most extensive regular updates we could wish for. Byteball also brings up the topic of creating your own token, which you can use as you wish. Further, the post covers the regular updates from the participants and as always, announces a weekly prize for the winner of the week.
Total payout: 5.47 STU (Not voted yet) Number of votes: 147
Building an asyncsteem python web app with micro-transaction-based steem user authentication, Redis and Jinja2 by @mattockfs [tutorials]
Another great tutorial by @mattockfs. The author provides a quick comparison between Steemconnect and micro-transaction approaches for authentication. He bases the tutorial on building a micro transactions authentication system under a Python implementation, as an alternative and better approach to authenticate users instead of delegating authority via steemconnect.
Total payout: 1.40 STU (Not voted yet) Number of votes: 19
Utopian.io Post Statistics
The staff picked contributions are only a small (but exceptional) example of the mass of contributions reviewed and rewarded by Utopian.io.
- Overall, the last week saw a total of 189 posts, with 172 of them rewarded through an upvote by @utopian-io.
- In total, Utopian.io distributed an approximate of 1512.15 STU to contributors.
- The highest payout seen on any Utopian.io contribution this week was 125.752 STU, with a total of 94 votes received from the community.
- The contribution that attracted the most engagement was 1UP Airdrop For Communities: Steem Monsters Spotlight, with no less than 25 comments in its comment threads.
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class: center, middle, inverse, title-slide # Class 1: Data visualization and exploration ### Julie Josse, Gaël Varoquaux, and Bénédicte Colnet ### Lundi 18 Janvier 2021 --- # Purpose of this class At the end of this class you will be able to perform a ***data exploration*** in `R`. -- This term first appeared in a book from John Tukey (1977): *"Practice of inspecting, and exploring your data, before stating hypotheses, fitting predictors, and other more ambitious inferential goals. It typically includes the computation of simple summary statistics which capture some property of interest in the data, and visualization."* Note that this is *assumption-free*. -- It includes being able to: - Load and preview data; - Visualize data; - Compute basic statistical metrics such as mean, median, correlation coefficient. These are called **point estimates**; - Understand what is behind a confidence interval; - Run standard statistical tests; - Be aware of typical bias (Simpson paradox); - Understand what a p-value means. --- # Notations We will (try to!) have as less as possible the need of mathematical formula for this class. -- The core material in statistics and machine learning is *data* (and it can be dirty data!):

  WindDirection 	  maxO3 	  T9 	  Ne9 	  Vx15

  North 	  87 	  15.6 	  4 	  -0.6946

  North 	  82 	  NA 	  5 	  -3.0000

  East 	  92 	  15.3 	  2 	  0.5209

  North 	  114 	  16.2 	  1 	  -0.1736

 -- This is the minimum notation you should keep in mind: - `\(n\)` is the number of observation in a data set - `\(p\)` is the number of covariates (= features = caracteristics) by observation - `\(X\)` is usually a matrix of size `\(n\)` x `\(p\)` (you can also find `\(Y\)`, a vector of size `\(n\)` x `\(1\)`, being the variable to explain). A realization of the variable can be denoted `\(x\)` - `\(i\)` denotes the `\(i^{th}\)` observations, for example `\(x_i\)` is the `\(i^{th}\)` element of a sample. --- # Typical statistical quantities ### Empirical mean If we consider a random variable `\(X\)`, we would like to define its average. It can also be seen as a weighted sum of the possible values that `\(X\)` can take. -- Mathematically it is written: `$$\bar{x}=\frac{1}{n} \sum_{i=1}^{n} x_{i}$$` -- ### Standard deviation .pull-left[ It measures how the spread in the data.

From sixsigmadsi.com

 ] .pull-right[ Using the previous notations for the expected value it gives: `$$\sigma=\sqrt{V}=\sqrt{\frac{1}{n} \sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)^{2}}$$` ] --- # Why can't we just use Excel? 🤔 These notations are the very basics for this class, and now we start a real data analysis using `R`, and not `excel`. Why? -- - Not reproducible 🔁 - Hard to merge different data set 🤝 - To clean data is fastidious 🧹 - Not designed for complex visualization 🎨 - It is not free 👛 - And it can be super slow 🐢  -- For this class we use air pollution data, the data are stored in `ozoneNA.csv`. After the class you should be able to reproduce all the commands that will be shown in this class. --- # How to load data? (Classical) data are generally contained within a file in which the individuals are presented in rows and the variables in columns. -- In `R` the data are stored in an object called a `data.frame`. -- The classical way to read a data file is to use the function `read.table` or `read.csv`. ```r ozone <- read.table("ozoneNA.csv", header = TRUE, sep = ",", row.names = 1) ``` -- Here, our data are stored in an `R` object called `ozone`. You can give the name you want to your objects 👶, but try to be consistent and kind with an external reader. -- Make sure you understand each parameter (`header`, `sep`, `row.names`) of the function `read.table()`. When you don't know how to use a function, you can do `?read.table()` to access the documentation. --- # Inspect your object - Let's look at the first 3 rows of `ozone`. (you can also do `head(ozone)`) ```r ozone[1:3, 1:10] # show first 3 rows and 10 first columns ``` ``` ## maxO3 T9 T12 T15 Ne9 Ne12 Ne15 Vx9 Vx12 Vx15 ## 20010601 87 15.6 18.5 NA 4 4 8 0.6946 -1.7101 -0.6946 ## 20010602 82 NA NA NA 5 5 7 -4.3301 -4.0000 -3.0000 ## 20010603 92 15.3 17.6 19.5 2 NA NA 2.9544 NA 0.5209 ``` -- - To access one of the variable, you can use the `$` operator, for example with the temperature at 9am. ```r ozone$T9[1:10] # only the first 10 ``` ``` ## [1] 15.6 NA 15.3 16.2 NA 17.7 16.8 14.9 16.1 18.3 ``` -- Note that this is equivalent as `ozone[, "T9"]` or `ozone[, 2]`. --- # Univariate analysis Here we have at our disposal 112 observations collected during the summer of 2001 in Rennes. The available variables are - maxO3 (maximum daily ozone) - maxO3v (maximum daily ozone the previous day) - T12 (temperature at midday) - T9 - T15 (Temp at 3pm) - Vx12 (projection of the wind speed vector on the east-west axis at midday) - Vx9 and Vx15 as well as the Nebulosity (cloud) Ne9, Ne12, Ne15 -- Before any analysis an important point is to visualize the data. For example you can print the dimension of the dataframe stored in the object `ozone`. ```r dim(ozone) ``` ``` ## [1] 112 12 ``` --- # Univariate analysis `summary()` details the data type of each column. ```r summary(ozone[, 8:12]) # 5 last columns so that it fits in the slide but you can launch everything doing simply summary(ozone) ``` ``` ## Vx9 Vx12 Vx15 maxO3v WindDirection ## Min. :-7.8785 Min. :-7.8785 Min. :-9.000 Min. : 42.00 East :10 ## 1st Qu.:-3.0000 1st Qu.:-3.6941 1st Qu.:-3.759 1st Qu.: 70.00 North:31 ## Median :-0.8671 Median :-1.9284 Median :-1.710 Median : 82.50 South:21 ## Mean :-1.0958 Mean :-1.6853 Mean :-1.830 Mean : 89.39 West :50 ## 3rd Qu.: 0.6919 3rd Qu.:-0.1302 3rd Qu.: 0.000 3rd Qu.:101.00 ## Max. : 5.1962 Max. : 6.5778 Max. : 3.830 Max. :166.00 ## NA's :18 NA's :10 NA's :21 NA's :12 ``` -- Can you already see difference in variable type? 🕵 --- # Useful commands All the column names can be retrieved with the command `names()`. ```r names(ozone) ``` ``` ## [1] "maxO3" "T9" "T12" "T15" "Ne9" "Ne12" ## [7] "Ne15" "Vx9" "Vx12" "Vx15" "maxO3v" "WindDirection" ``` Basic statistics can be computed: ```r mean(ozone$maxO3, na.rm = TRUE) ``` ``` ## [1] 91.23958 ``` -- Note that the option `na.rm = TRUE` is necessary because the data contain missing value. If not the output will be a missing value. -- All the basics statistics are implemented such as `sd()`, `min()`, `median()`, or `max()`. --- # Two important data types The data can be of two types: - **Qualitatives** *For example colors, or gender.* - **Quantitatives** *For exemple a salary, or heigth.* -- ⚠ You have to be careful, whenever you replace colors by numbers (for example red with 0 and blue with 1), the data type will be set to numerical (so quantitative) and the computer can do operation on it. For example blue will be considered bigger than red, which has no meaning. -- 💡 The command `summary()` already allows you to observe your data type, another command is possible with `str()`. -- 🖍 You can change the type of your data from quantitative to qualitative using the command `factor()`. --- # Illustration of the data type on Ozone Inspect qualitative data is basically counting occurences: ```r table(ozone$WindDirection) ``` ``` ## ## East North South West ## 10 31 21 50 ``` -- You can do operation on quantitative variables: ```r test <- ozone$maxO3 + ozone$T9 mean(test, na.rm = TRUE) ``` ``` ## [1] 109.7714 ``` -- By the way, you can create a column composed by operation on other column such as `ozone$my_new_column <- ozone$maxO3 + ozone$T9 * ozone$T12`. --- # Visualization in R Remember you can draw very beautiful plots in `R`. In this class we suggest you to use: - `ggplot2` for static plots; - `gganimate` if you want to do animated plots from static `ggplot`; - `Shiny` to host dynamic visualization of your data (really great to share visualization of a big data base within a team or for external communication). -- Before we detail how to do it, here are example to show you a part of what is possible! --- # Example 1 : time series  --- # Example 2 : scatter plot  --- # Example 3 : population pyramid  --- # Example 4: heat maps  --- # Animated plots These are data linking GDP per capita and life expectancy over years and for different countries. We may want to animate it over time.  --- # Animated plots These are data linking GDP per capita and life expectancy over years and for different countries. We may want to animate it over time. ``` ## Frame 1 (1%) Frame 2 (2%) Frame 3 (3%) Frame 4 (4%) Frame 5 (5%) Frame 6 (6%) Frame 7 (7%) Frame 8 (8%) Frame 9 (9%) Frame 10 (10%) Frame 11 (11%) Frame 12 (12%) Frame 13 (13%) Frame 14 (14%) Frame 15 (15%) Frame 16 (16%) Frame 17 (17%) Frame 18 (18%) Frame 19 (19%) Frame 20 (20%) Frame 21 (21%) Frame 22 (22%) Frame 23 (23%) Frame 24 (24%) Frame 25 (25%) Frame 26 (26%) Frame 27 (27%) Frame 28 (28%) Frame 29 (29%) Frame 30 (30%) Frame 31 (31%) Frame 32 (32%) Frame 33 (33%) Frame 34 (34%) Frame 35 (35%) Frame 36 (36%) Frame 37 (37%) Frame 38 (38%) Frame 39 (39%) Frame 40 (40%) Frame 41 (41%) Frame 42 (42%) Frame 43 (43%) Frame 44 (44%) Frame 45 (45%) Frame 46 (46%) Frame 47 (47%) Frame 48 (48%) Frame 49 (49%) Frame 50 (50%) Frame 51 (51%) Frame 52 (52%) Frame 53 (53%) Frame 54 (54%) Frame 55 (55%) Frame 56 (56%) Frame 57 (57%) Frame 58 (58%) Frame 59 (59%) Frame 60 (60%) Frame 61 (61%) Frame 62 (62%) Frame 63 (63%) Frame 64 (64%) Frame 65 (65%) Frame 66 (66%) Frame 67 (67%) Frame 68 (68%) Frame 69 (69%) Frame 70 (70%) Frame 71 (71%) Frame 72 (72%) Frame 73 (73%) Frame 74 (74%) Frame 75 (75%) Frame 76 (76%) Frame 77 (77%) Frame 78 (78%) Frame 79 (79%) Frame 80 (80%) Frame 81 (81%) Frame 82 (82%) Frame 83 (83%) Frame 84 (84%) Frame 85 (85%) Frame 86 (86%) Frame 87 (87%) Frame 88 (88%) Frame 89 (89%) Frame 90 (90%) Frame 91 (91%) Frame 92 (92%) Frame 93 (93%) Frame 94 (94%) Frame 95 (95%) Frame 96 (96%) Frame 97 (97%) Frame 98 (98%) Frame 99 (99%) Frame 100 (100%) ## Finalizing encoding... done! ```  --- # Visualization using shiny apps Examples: - Models used by the united nation to predict demography: [<ru-blockquote> here </ru-blockquote>](https://bayespop.shinyapps.io/wpp2019explorer/) - An online application to predict covid19 increase made by Prof. Marc Lavielle in France: [<ru-blockquote> here </ru-blockquote>](http://shiny.webpopix.org/covidix/app3/) -- As you can see, these are great tools for your professional life. --- # Visualization: ggplot2 In this class we use the package `ggplot2` (implementation by Hadley Wickam). -- A `ggplot2` object will have the following elements.footnote[This source explains it well: http://www.john-ros.com/]: - `data` the data frame holding the data to be plotted. - `aes` defines the mapping between variables to their visualization. - `geoms` are the objects/shapes you add as layers to your graph. - `stats` are statistical transformations when you are not plotting the raw data, such as the mean or confidence intervals. --- # Histogram - Visualization of a quantitative variable: histogram ```r library(ggplot2) ggplot(ozone, aes(x = maxO3)) + geom_histogram(bins = 10, na.rm = TRUE) ```  --- # Histogram with options - Visualization of a quantitative variable: histogram ```r # library(ggplot2) # you call it only once ggplot(ozone, aes(x = maxO3)) + geom_histogram(bins = 10, # important parameter! alpha = 0.5, # transparency color = "blue", #border fill = "pink", # color to fill na.rm = TRUE) + # do the plot ignoring NAs theme_bw() # you can look for different themes ```  You can find a recap of all the possibilities [<ru-blockquote> here </ru-blockquote>](https://rstudio.com/wp-content/uploads/2015/03/ggplot2-cheatsheet.pdf). --- # Barplot - Visualisation of a categorical variable: barplot ```r ggplot(ozone, aes(x = WindDirection)) + geom_bar(stat = "count", # note the difference! alpha = 0.5, # transparency color = "cyan", fill = "blue") ```  --- # Boxplot A univariate boxplot helps to highlights outliers. ```r ggplot(ozone, aes(y = T12)) + geom_boxplot(outlier.color = "red") + theme_bw() ```  --- # Summarizing data: one variable Let's pause and look at what we saw. -- - Statistic for a quantitative variable *Quartiles, percentile, mean, median, range, variance, standard deviation* -- - Statistics for a categorical variable: *Frequency* -- - Plots - *Quantitative*: boxplot and histogram - *Qualitative*: barplot -- 💪 Never forget that `R` has a very active community that will (almost) always have a solution to your problem. When you don't understand an error message, copy paste your error message in a web browser and you will find a solution. -- Now we would like to analyze several variables **together**. It is a way to highlight associations between the variables! --- # Visualization: boxplot You can observe association between a quantitative and qualitative variable. ```r ggplot(ozone, aes(x = WindDirection, y = maxO3)) + geom_boxplot() + theme_bw() ```  --- # Visualization: violin You can choose many other representations, for example violin plots and superposition of your real data points. ```r ggplot(ozone, aes(x = WindDirection, y = maxO3, color = T12)) + geom_violin() + geom_jitter(alpha = 0.6, width = 0.1)+ theme_bw() ```  --- # Visualization: scatter plot ```r ggplot(ozone, aes(x = T12, y = T15)) + geom_point() + theme_bw() ```  Beyond visualization, you all now a numerical indicator that is usually used to characterize the association between two variables ❓ --- # Bivariate analysis ## Correlation coefficient - Very popular metric - Useful but contains limits - The Pearson coefficient is the most used -- The correlation coefficient between two variables `\(X_1\)` and `\(X_2\)` (for example `T12` and `T15`): `$$\rho_{X_1, X_2}=\frac{\overline{X_1 X_2}- \bar{X_1} \bar{X_2}}{\sigma_{X_1} \sigma_{X_2}}$$` *where `\(\sigma_{X_i}\)` is the empirical standard deviation of `\(X_i\)`* -- - `\(\rho_{X_1, X_2} = 1\)` or `\(-1\)`: implies that a linear equation describes the relationship between `\(Z\)` and `\(Y\)` perfectly - `\(\rho_{X_1, X_2} = 0\)`: no linear relationship between `\(X_1\)` and `\(X_2\)` (⚠ which is different as saying no relation at all!) --- # Correlation (1) ## Application in `R` We can observe the Pearson correlation between temperature at 12pm and 3pm. ```r cor(ozone$T12, ozone$T15, method = "pearson", use = "complete.obs") ``` ``` ## [1] 0.9476315 ``` As expected it shows a high correlation coefficient. We can observe the data to see if it seems coherent. --  Does the linearity seems to be a good hypothesis for these data? --- # Correlation (2) ## An apparently simple example We create a function that simulates two vectors from a Gaussian distribution (mean being 0, and standard deviation being 1) of size `\(n\)`. We first choose `\(n =2\)`, then we do it up to `\(200\)`. We compute the correlation coefficient between each new sampling. --  Comment. What should we do? --- # Correlation (3) You can test if your correlation coefficient is meaningful (statistically speaking). -- First we do this with only 5 observations: ``` ## ## Pearson's product-moment correlation ## ## data: x1 and x2 ## t = 0.792, df = 3, p-value = 0.4862 ## alternative hypothesis: true correlation is not equal to 0 ## 95 percent confidence interval: ## -0.7367073 0.9496858 ## sample estimates: ## cor ## 0.41585 ``` What can we conclude? -- Don't worry if you don't understand how it works for now, we will come back to this later ✅ --- # Correlation (4) ## Test with a bigger data set We repeat the previous test with 10000 observations: ``` ## ## Pearson's product-moment correlation ## ## data: x1 and x2 ## t = 0.3074, df = 9998, p-value = 0.7585 ## alternative hypothesis: true correlation is not equal to 0 ## 95 percent confidence interval: ## -0.01652678 0.02267299 ## sample estimates: ## cor ## 0.003074284 ``` And now? --- # Correlation (5) Back to our `ozone` example: ```r res <- cor.test(ozone$T12, ozone$T15, method = "pearson", use = "complete.obs") res ``` ``` ## ## Pearson's product-moment correlation ## ## data: ozone$T12 and ozone$T15 ## t = 23.552, df = 63, p-value < 0.00000000000000022 ## alternative hypothesis: true correlation is not equal to 0 ## 95 percent confidence interval: ## 0.9152771 0.9678377 ## sample estimates: ## cor ## 0.9476315 ``` What can we conclude? ⚠ >In general always associate a numerical indicator with a graphical display --- # Correlation only reflects linear relationship! Be careful with correlation. For example all the following data have same mean, sd, and correlation coefficient! (package `datasauRus`) .center[![Gapminder](./animated_plot/ex_gganimate.gif)] --- # Correlation is not causation This credo is constantly repeated, but still it remains very important to understand that __an association in data does not imply a causation__. Correlation is one type of association between data. As long as you only observe phenomenon, you can hardly conclude on causation until you perform experiments. -- This funny website proposes a lot of funny associations:

From http://tylervigen.com/spurious-correlations

 --- # Another example - Sleeping with shoes and headache can show a really strong correlation!  -- - Do umbrellas cause car accidents? -- ⚠ Unobserved confounders makes it impossible to separate correlation and causality when correlated to both the outcome and the treatment. --- # An apparently simple conclusion Let's have a look to a well-know paradox! 🕵 -- Covid-19 case fatality rates between China and Italy: 44 672 cases from China with early reports from Italy (9th March).

Screenshot from J. von Kügelgen et al., 2020

 What do you conclude? --- # A paradox? The same data can be represented with age strata.

Screenshot from J. von Kügelgen et al., 2020

 What do you conclude from this graph? --- # The Simpson paradox ## Only seeing can even lead to wrong conclusions! ⚠

Screenshot from J. von Kügelgen et al., 2020

 Complete article: *Simpson's paradox in Covid-19 case fatality rates: a mediation analysis of age-related causal effects* from Julius von Kügelgen, Luigi Gresele, Bernhard Schölkopf --- # Another example: effect of class size (1) Imagine we want to measure the effect of class size on the results of children.

DEPP

 What do you suggest to measure the effect? --- # Another example: effect of class size (2) .pull-left[  The difference is statistically significant. ] -- .pull-right[

DEPP

 ] --- # Break We can pause and resume what we saw. -- - Correlation coefficient is an interesting tool, - ... but it can not resume all type of association and it has to be significant! - Correlation is an association between data, it does not imply a causal link. - Paradox can be hidden in the data, the Simpson paradox is a famous one.

Simpson paradox made simple

 -- ➡ The next part of the class is about statistical test, and how to get an information from a limited sample. --- # Statistical tests With the correlation coefficient, we introduced the concept of a statistical test. The typical question to answer is: How we can draw conclusions or make decisions based on finite samples of data? -- A wide variety of usage: - Clinical trials and efficacy; - Economic experiments; - Screening genetic variants for associations with a phenotype, and many others.

Credits: Modern Statistics for Modern Biology, Chap 6., Susan Holmes

 --- # Confidence interval (CI) .pull-left[

Credits: xkcd.com

 ] .pull-right[ * In real life we only get to take ***one*** sample from the population. * Also, we obviously don't know the true population parameter, that's what we are interested in! * What can we do in practice? ] -- Even unobserved, we know that the sampling distribution does exist (or we put hypothesis on it), and with assumptions, we know how it behaves! --- # Point estimates versus CI Until now we have only estimated *point estimates* from our samples: for example sample mean. -- We saw a glimpse of what is a confidence interval with the correlation test. But what does this mean exactly? -- Rather that a point estimate, we could give a range of plausible values for the parameters we are interested in. -- This is what a **confidence interval** (CI) provides. -- With a confidence interval comes a confidence *level*, usually it is 95%. > *Interpreation* Imagine we do 100 times the experiment and construct a confidence interval. 95 out of 100 of the confidence intervals constructed would contain the good value. -- There are several ways to compute a CI, depending on the question asked. --- # Intuition of the notion We can simulate data of a somnifere on the average sleeping time. Here you can see the results of a small study with 30 people included.  What can you conclude? --- # The more data, the bigger the certainty Here we gathered 100 patients in the study.  --- # In practice ```r t.test(control, sample2) ``` ``` ## ## Welch Two Sample t-test ## ## data: control and sample2 ## t = -2.8553, df = 150.78, p-value = 0.004906 ## alternative hypothesis: true difference in means is not equal to 0 ## 95 percent confidence interval: ## -1.1111202 -0.2022729 ## sample estimates: ## mean of x mean of y ## 7.026535 7.683232 ``` -- The command is simple, but then you have to precisely know where to read the results (confidence interval, p-value, hypothesis meaning, and so on). Also, be careful on the fact that it requires hypothesis on your distribution. --- # With ozone data set ```r t.test(ozone$maxO3, conf.level = 0.95)$conf.int ``` ``` ## [1] 85.37665 97.10252 ## attr(,"conf.level") ## [1] 0.95 ```  --- # Conclusion Today you have seen how to perform a simple data exploration with `R` and that being cautious with indicators is important. -- By next class you can train on any data set to perform a simple data analysis. You can find some more (related to economy) on the github `experimentdatar` repository. -- Next class will be about Principal Component Analysis (PCA), clustering and dimension reduction. --- # Ressources Plenty of ressources are available online on data exploration and statistics with `R`. And we gathered some for you here: **Basics** - [<ru-blockquote> TedX on data visualisation </ru-blockquote>](https://www.ted.com/talks/david_mccandless_the_beauty_of_data_visualization?language=fr) - [<ru-blockquote> Starting with Rstudio, advanced statistics </ru-blockquote>](http://larmarange.github.io/analyse-R/) **Funny** - [<ru-blockquote> To play down statistics: *La statistique expliquée à mon chat* </ru-blockquote>](https://www.youtube.com/channel/UCWty1tzwZW_ZNSp5GVGteaA/featured) **Advanced** - [<ru-blockquote> Susan Holmes' book "Modern Statistics for Modern Biology" </ru-blockquote>](http://web.stanford.edu/class/bios221/book/) - [<ru-blockquote> Introduction to econometrics with R (SciencesPo)</ru-blockquote>](https://scpoecon.github.io/ScPoEconometrics/index.html) --- # Credits This class was made with inspiration from: - [<ru-blockquote> Susan Holmes' book "Modern Statistics for Modern Biology" </ru-blockquote>](http://web.stanford.edu/class/bios221/book/) - [<ru-blockquote> Introduction to econometrics with R (SciencesPo)</ru-blockquote>](https://scpoecon.github.io/ScPoEconometrics/index.html) - And datanovia website for the animated plots Thanks to all of them - and others - for open science. --- Next slides are additional ones, it completes the statistical tests part in more details. --- # From CI to hypothesis testing Just like confidence intervals, hypothesis tests are used to make claims about a population based on the information from a sample. -- A hypothesis test consists of a test between two competing hypothesis about a parameter. -- >For example the average income for women and men measured in one sample is different. Is the difference significant? 🤔 -- The usual framework you will find in books is: - The null hypothesis usually states no difference, and we denote it `\(H_{0}\)` (in our little example it would mean that men and women have same average income) - The alternative hypothesis states that it is different, and we denote it `\(H_{1}\)` -- Let's take a simple - but detailed - example to understand the principle: coin tossing --- # An example: coin tossing Imagine I simulate a coin with a probability of head `\(p\)` (this is something you can easily do in `R`). -- You want to know if the coin is fair ( `\(p = 0.5\)` ). What do you do? -- Yes, you start flipping the coin. Results type are: ``` ## [1] "H" "T" "H" "T" "T" "H" ``` -- You do it a lot, for example 100 time. If the coin is fair, you would expect half of the time to get heads. We can compute how many heads you obtained on the 100 flips. ```r table(coinFlips) ``` ``` ## coinFlips ## H T ## 60 40 ``` What do you do? Continue up to 1000 times? Stop and conclude? Was it bad luck? --- # How probable was this realisation? The number of heads obtained in 100 independent tosses of a coin is: `$$P(K=k \mid 100, p)=\left(\begin{array}{c}100 \\ k\end{array}\right) p^{k}(1-p)^{100-k}$$` Where `\(p\)` is the probability of heads. -- >Notations' tips: - The first term reads as: the probability that the observed value for `\(K\)` is `\(k\)`, given the values of `\(n\)` and `\(p\)` ( `\(p\)` is the parameter of our problem). - The big `\(K\)` is all the possible values we can have (here from 0 to 100), and `\(k\)` is the value observed. Statisticians usually write the difference. --- We implement the previous equation. Note that the binomial is already implemented in `R` with `dbinom`:  What is the most probable value? To what corresponds the vertical line? -- But at which point could we consider this was not just bad luck? --- # Formalization Statisticians divide the set of all possible `\(k\)` (0 to 100) in complementary regions: a rejection region and a region of no rejection. -- The common threshold is `\(\alpha = 0.05\)` meaning that if the observed `\(k\)` is in a region which probability is lower than 0.05 then the null-hypothesis is rejected. --

Credits: xkcd cartoons

 >⚠ Remember that the `\(\alpha = 0.05\)` rule is a convention! --- # Visualization of the `\(\alpha\)`  What do you conclude? 🤔 --- # Using implemented function We state the null-hypothesis `\(\mathbb{H}_0: p=0.5\)`. In our example we observe 60 heads. We can use the implemented function: ```r binom.test(x = numHeads, n = numFlips, p = 0.5) ``` ``` ## ## Exact binomial test ## ## data: numHeads and numFlips ## number of successes = 60, number of trials = 100, p-value = 0.05689 ## alternative hypothesis: true probability of success is not equal to 0.5 ## 95 percent confidence interval: ## 0.4972092 0.6967052 ## sample estimates: ## probability of success ## 0.6 ``` We conclude that the coin is fair, but you can observe that it depends on the confidence level you fixed! --- # Confidence interval for a mean For a relative big (>30) sample, the central limit theorem guarantees that the confidence interval is this one: `$$\left[\bar{x}-\frac{\hat{\sigma}}{\sqrt{n}} \times t_{1-\alpha / 2}(n-1) ; \bar{x}+\frac{\hat{\sigma}}{\sqrt{n}} \times t_{1-\alpha / 2}(n-1)\right]$$` With `\(n\)` the sample size, `\(\bar{x}\)` the empirical mean, `\(\hat{\sigma}\)` the empirical standard deviation, and `\(t_{1-\alpha / 2}\)` a parameter from the Student law (beyond the scope of the class). .pull-left[  ] .pull-right[ ```r t.test(ozone$maxO3, conf.level=0.95)$conf.int ``` ``` ## [1] 85.37665 97.10252 ## attr(,"conf.level") ## [1] 0.95 ``` ] --- # p-value

https://towardsdatascience.com/wait-so-whats-a-p-value-6fc50f362df1

 -- >**Rigorous definition** >Consider that null-hypothesis is true. The ***p-value*** is the probability of observing a test statistic more extreme than the one we obtained. >If the p-value falls below the cutoff `\(\alpha\)`, we reject the null hypothesis on the grounds that what we observe is too unlikely to happen under the Null ⚠ Be careful with what is called the p-value hacking and multiple testing.


Constructor Summary
| Public Constructor | ||
| public |
Constructor creates a tile that stores whether the tile is a mine or not, the number of mines adjacent to it, and whether the tile has been flagged or not. |
Member Summary
| Public Members | ||
| public |
Number of mines adjacent to the tile. |
|
| public |
Flag status of the tile. |
|
| public |
A mine or not a mine. |
|
| public |
Revealed status of the tile. |
Method Summary
| Public Methods | ||
| public |
flag() Reverses the flag status of the tile. |
|
| public |
Gets the number of mines adjacent to the tile. |
|
| public |
Gets whether the tile has been flagged or not. |
|
| public |
Gets whether the tile is a mine or not. |
|
| public |
Gets whether the tile has been revealed or not. |
|
| public |
reveal() Reveals the tile, setting revealed to true. |
|
| public |
setAdjacent(adj: number) Sets the number of mines adjacent to the tile. |
|
| public |
setMine() Sets the tile's status to be a mine. POSTCONDITION: isMine is true. |
Public Constructors
public constructor() source
Constructor creates a tile that stores whether the tile is a mine or not, the number of mines adjacent to it, and whether the tile has been flagged or not. POSTCONDITION: isMine, adjNum, flagged, and revealed, all now have set values.
Public Members
Public Methods
public flag() source
Reverses the flag status of the tile. If it has been flagged, set to false. If it has not, set to true. POSTCONDTION: flagged is inverted


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