We've heard a lot about how Brexit will affect the UK's finances. But what impact will it have on the EU's? Simon Wilson reports.
How big is the EU's budget?
In the three most recent years for which full accounts are available (2014 to 2016), the EU spent on average €141bn a year; around €1trn during the current seven-year budget agreement (known as the Multiannual Financial Framework, MFF) that covers the years 2014 to 2020. That's around one percentage point of GDP across the 28 member states, or just 2% of all public spending by governments in the bloc.
Compared with the UK, that makes the EU a fiscal minnow: it spends around a sixth of what the UK does (£828bn projected in the current financial year). And despite its status as a supranational institution, national governments manage 80% of the money in the EU budget.
Where does it get its money?
The majority (67%) comes from the coffers of each member state, based on a standard proportion of its annual gross national income (GNI). That proportion must not legally exceed 1.23% of GNI, and it's a bit less than that (1.02% in 2014-2015). This system means, broadly speaking, that richer countries pay in more and get fewer direct benefits.
In addition to direct transfers, the EU levies customs duties on imports (accounting for 14% of income) – in other words, it generates revenue from protectionist measures – and takes a slice of each state's VAT revenues (11%). It gets another 5% from fines, interest on late payments, and contributions from non-member states (such as Norway and Israel) for access to specific EU programmes.
What does it spend it on?
Of the €141bn annual spend (in 2014-2016), €41.5bn a year (30%) went direct to farmers under the common agricultural policy and another €11.8bn (9%) went to rural development. Structural funds made up €47.8bn (34%) a year, which goes on things such as new energy, transport or communications infrastructure, and grants to small businesses to promote competitiveness.
Another smaller, but significant, chunk goes on Horizon 2020, the EU's main research and innovation programme, accounting for €9.2bn (7%). In some countries this spending is vital. In Slovakia, Bulgaria and Hungary, for example, transfers from the EU account for more than 4% of GDP. And in Portugal, Croatia, Lithuania and Poland, EU structural funds account for at least 60% of public investment.
How big a hole will Brexit make?
Gross, the UK contributes around €18.2bn a year (on figures from the Centre for European Reform). After accounting for what we get back, the UK's departure will leave a funding gap of about €10bn or €11bn a year (some projections put it at €12bn, or even €13bn). In other words, Brexit means the loss of a major, large, relatively rich country – an overall net contributor to the EU – and a funding gap for Brussels in the region of 8%.
How will they fill it?
Gradually, they hope, and without big, painful cuts in spending, by increasing the (gross) contributions made by member states (from about 1% of GNI now, to a level capped annually at 1.08%). A recent paper for the Bruegel think tank calculates that – assuming modest annual economic growth – GNI for the post-Brexit EU27 will be 28.1% higher in 2021-2027 than in 2014-2020, due to inflation and growth.
Under this scenario, the EU could keep its budget at the historic level of 1% of GNI and still protect all of its existing spending in real terms, with a bit left over. That's the optimistic scenario. The pessimistic one is that the bloc stagnates, there's no Brexit deal and the Brexit black hole turns out to be more like €14bn a year – €100bn over the seven-year period.
By chance, Brexit (assuming it happens in March 2019) will coincide with a period of intense negotiation – for which, read bitter wrangling – over the next Multiannual Financial Framework, covering the years 2021-2027. The EU is already beset by political divisions between west and east, over issues including immigration, border security, and the populist-authoritarian turn in the likes of Poland and Hungary.
Negotiations over the next budget are all but certain to exacerbate these, since the Commission wants to rebalance spending away from eastern Europe (a beneficiary of much largesse since the "A10" enlargement of 2004) towards the south (badly hurt by the crisis and years of ensuing austerity).
What is it planning to cut?
The Commission's draft proposals were published in May, proposing a budget of €1.279trn. The main points are a 5% cut to the common agricultural policy (and a reskewing to favour smaller farms) and a 7% cut to cohesion funds (together with new criteria that would see funding to eastern European and Baltic countries slashed in several cases). Those cuts will be used to fund the EU's major new priority: it wants to expand its coast and border guard from 1,200 to 10,000 staff, and almost triple its budget for border management, migration and refugee flows from €12bn to €33bn (over the seven years).
Where could it get more cash?
Budget commissioner Gunther Oettinger "wants to create several new sources of income" – including by imposing a tax on non-recyclable plastics, and also by redirecting revenues from selling carbon pollution permits to the EU. The Commission wants to phase out rebates for rich countries (such as the Netherlands, Denmark and Austria).
It also wants to create a "rule of law" mechanism that links budget payments to a country's respect for "EU values", although Brussels insists this won't be used to target the likes of Hungary and Poland, with which it has wrangled over issues including judicial independence. Negotiating all this could make Brexit look like a piece of cake.


text:
Q: Use proxy middleware with gulp connect I am trying to use gulp-connect to forward all requests to api/ to localhost:3000. I found an example at https://github.com/AveVlad/gulp-connect/issues/27
and setup my connect task like this:
gulp.task('connect', function(){
    connect.server({
        root: './app',
    middleware: function(connect, o) {
      return [ (function() {
        var url = require('url');
        var proxy = require('proxy-middleware');
        var options = url.parse('http://localhost:3000/api');
        options.route = 'api';
        return proxy(options);
      })()]
    }
    });
});

Running this task warns that connect deprecated connect(middleware): use app.use(middleware) instead node_modules/gulp-connect/index.js:39:19 and this task does not forward requests as expected.
I looked at the connect source to see if I could work around the depreciation, but it is beyond my level in js:
 ConnectApp.prototype.server = function() {
    var app, middleware;
    middleware = this.middleware();
    app = connect.apply(null, middleware);
    server = http.createServer(app);
    app.use(connect.directory(typeof opt.root === "object" ? opt.root[0] : opt.root));
    server.listen(opt.port);
    this.log("Server started http://" + opt.host + ":" + opt.port);
    if (opt.livereload) {
      tiny_lr.Server.prototype.error = function() {};
      lr = tiny_lr();
      lr.listen(opt.livereload.port);
      return this.log("LiveReload started on port " + opt.livereload.port);
    }
  };

I cannot figure out how to change my gulp-file to use app.use(middleware), the app variable is not exported by the connect module.

A: I couldn't get middleware to work correctly even when using the github source. I did get the same result with modrewrite
var modRewrite = require('connect-modrewrite');

gulp.task('connect', function() {
  connect.server({
    root: './app',
    port: 8000,
    middleware: function() {
      return [
        modRewrite([
          '^/api/(.*)$ http://localhost:3000/api/v1/$1 [P]'
        ])
      ];
    }
  });
});

A: This is a reported issue that should be fixed in the next gulp-connect release on NPM :
https://github.com/AveVlad/gulp-connect/commit/9bd7da765d6763bbee566cc5fc03b873ccf93e37
https://github.com/AveVlad/gulp-connect/issues/67

A: This is my config to start an express server with livereload (using nodemon) and proxy all API requests to the server.
gulp.task('connect', function () {
    var connect = require('connect');

    // Start the Node server to provide the API
    var nodemon = require('gulp-nodemon');
    nodemon({ cwd: '../server', script: 'app.js', ignore: ['node_modules/*'], ext: 'js' })
        .on('restart', function () {
            console.log('Node server restarted!')
        });

    var app = connect()
        // proxy API requests to the node server
        .use(require('connect-modrewrite')(['^/api/(.*)$ http://localhost:3000/api/$1 [P]']))
        .use(require('connect-livereload')({ port: 35729 }))
        .use(connect.static('../client'))
        .use(connect.static('../client/.tmp'))
        .use(connect.directory('../client'));

    require('http').createServer(app)
        .listen(9000)
        .on('listening', function () {
            console.log('Started connect web server on http://localhost:9000');
        });
});

A: A solution given by chimurai on Github is to use the http-proxy-middleware package to do that.
For example :
var gulp = require('gulp');
var connect = require('gulp-connect');
var proxy = require('http-proxy-middleware');

gulp.task('connect', function() {
    connect.server({
        root: ['./app'],
        middleware: function(connect, opt) {
            return [
                proxy('/api', {
                    target: 'http://localhost:3000',
                    changeOrigin:true
                })
            ]
        }

    });
});

gulp.task('default', ['connect']);

redpajama_set_name: RedPajamaStackExchange


text:
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redpajama_set_name: RedPajamaGithub


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Justin Needham, MD
Justin Needham, MD is a board-certified Ophthalmologist who specializes in cataract and refractive surgery, including LASIK, PRK, Implantable Collamer Lenses, Refractive Lens Exchange and Cataract Surgery.
Dr. Needham has recently joined Milan Eye Center after a distinguished career in the US Army. He received his medical degree from our nation's military medical school, Uniformed Services University in Bethesda, MD. After serving as a flight surgeon in Germany, Dr. Needham was selected ahead of his peers to attend ophthalmology residency at Madigan Army Medical Center, Ft. Lewis, WA. Following residency training, Dr. Needham was immediately selected for a teaching position at Brooke Army Medical Center in San Antonio, TX. In addition to providing comprehensive cataract and refractive surgery in the clinic, he also delivered lectures and taught cataract surgery to the ophthalmology residents.
His military service continued when he was promoted to Major and assigned as the Chief of Ophthalmology and of the Warfighter Refractive Eye Surgery Program at Fort Stewart, GA. While assigned to Ft. Stewart, Dr. Needham performed thousands of refractive surgery and cataract procedures on soldiers, retirees and family members from Ft. Stewart, Ft. Jackson, Ft. Benning, and surrounding military bases.
As both an Ophthalmologist and refractive surgery patient himself, Dr. Needham understands the incredible life-changing benefits of refractive surgery; and he looks forward to sharing his years of experience and dedication to safe, high-quality surgery with each and every patient.
Milan Eye Center
1995 Mall of Georgia Boulevard, Suite A
Buford, GA 30519 USA
Email – JNeedham@MilanEyeCenter.com
About: Justin Needham, MD Bio

redpajama_set_name: RedPajamaCommonCrawl


text:
<?php
/**
 * Description of Schedule_model
 *
 * @author User
 */
class Schedule_model extends CI_Model {
  function remove_periods($db_data){ // Премахва периодите на текущя потребител за текущия и следващи месеци
    $this->db->delete('schedules',$db_data);
  }

  function save_periods($db_data){
    $this->db->insert_batch('schedules',$db_data);
  }

  function read_periods(){
    $this->db->where('schedule_date >=', date('Y-m').'-01');
    $this->db->where('worker_id', $_SESSION['worker_id']);
    $query=$this->db->get('schedules');

    $periods=array();
    $arr = $query->result_array();
    foreach ($arr as $row){
      $periods['address_'.$row['schedule_date']] = $row['address'];
      $periods["begin_".$row['schedule_date']."_".substr($row['begin_hour'],0,5)]=
               ((strtotime($row['end_hour'])-strtotime($row['begin_hour']))/1800)."_".
               substr($row['begin_hour'],0,5).' ÷ '.substr($row['end_hour'],0,5);
      $periods["end_".$row['schedule_date']."_".substr($row['end_hour'],0,5)]='';
    }
    return $periods;
  }
}


text:
Leadership: Vision, Meaning and Reality
(Alternate title: Organizational Leadership for Twenty First Century)
Proposed for Indian Institute of Bangalore
PGP II, Term II or III
Instructor: Prof. S. Manikutty
Managers within organizations have to take tough decisions. The toughest decisions within organizations are not the result of "rational/logical" analysis which requires a "Eureka!" response. These decisions are a result of answers to multiple questions bordering on what is right and what is wrong. Strangely and ironically, they cannot be clearly compartmentalized or categorized as "right" or "wrong".
As a manager, you too will face a similar situation when you have to take a tough decision … and the situation will worsen when there will arise a need to take the most difficult decision involving a choice between right and right and between wrong and wrong. The choice will call for a compromise. Additionally you will also need to assess the situation and respond to the following questions: what is the difference between a sound compromise and a sell out? When do ethical ends justify dubious means? When do you take a stand?
These are only some of the questions that you will face and which managers face all the time. However, when you take on the role of a leader, these become the key questions. As you reflect and look for appropriate answers to these key questions, some other questions spring to the fore, which simultaneously need to be addressed: What is leadership? How is a leader different from a manager? How does one prepare to become a leader? Does a leader have a vision? Does a leader share a vision? What is meant by vision? Do you dare to dream? When can/do you dream and when do you come to ground realities? Is it worthwhile to dream for a seemingly unrealistic vision? Or is it better to be "practical" and choose "not to be"? Is a leader just a hero? What is the difference between success and satisfaction? When is ambition a propelling, creative force and when does it become destructive? The list is endless and these are only some of the questions that need to be resolved by students aspiring to be leaders.
This course, or for that matter, any course, cannot, by itself, provide answers to these questions. But it does not follow that it is no use asking them, or debating them. This course seeks to provide an opportunity to you to develop a deeper understanding of the dilemmas, complexities and subtleties of responsible leadership. It provides an opportunity to think, reflect and expand your mental horizon. It trains you to ask questions for which you very well know there are no concrete answers. You also know that it makes sense to ask these questions, debate and arrive at responses that help develop judgement, understanding and stimulate the senses to enable you to consider issues in the right perspective. In short, it seeks to enable you to take not more correct decisions, but better decisions (hopefully!).
Another important contribution of the course, hopefully, will be that the course will introduce you to the world of literature and show how to interpret great works of literature and draw lessons from them. Literature is not only fascinating to read (especially when it is not to be read for examinations in degree courses!) but also immensely rewarding in the process of self development.
1. To understand key concepts in leadership such as world view, vision, illusion, meaning, reality, myths, legends, symbols, rituals, beliefs, values, attitudes, will, ambition, virtue, responsibility, cleverness, intrigue, jealousy, personality, roles etc. with input from humanities.
2. To use such concepts in understanding the role of leadership and impact of culture on modern organizational life.
3. To understand relationships between organizational needs, role demands and personality differences, and
4. (Most important) To develop skills for selecting and interpreting great works of literature so as to learn meaningfully from humanities to assume a leadership role.
The course approaches the whole topic of leadership through a study of literature. Why literature? Many works of literature give glimpses of the different aspects of leadership. They present the dilemmas of life. In many of the literary pieces you will read in this course, you will not find clear, inspiring tales of heroism or sainthood, although in some readings there are. Many of the characters in these works are simple people like you and me, with strengths and flaws. They are, in Nietzsche's phrase, "human, all too human". That is why they reflect life in its true reality. These works of literature will puzzle, fascinate and challenge you to interpret the situation and the characters in as conservative or radical a manner as possible.
Interpretation forms the essence of the course. These pieces of literature give insights into the thoughts and feelings of common and lofty people who are either leaders or are on the path to attaining leadership positions with common follies but great successes and failures narrated/presented in a highly readable and fascinating style.
In this course, students will form study groups and each group will take up at least one work and analyse it fully, reflect over it and present their understandings to the class. But before doing so, they have to meet the instructor, as a group, at least one day prior to the class and discuss what they propose to present in the class. These presentations will be for about 20 to 30 minutes, followed by discussions and supplementary inputs by the instructor.
The class discussions tend to become quite interesting, with novel ideas and points of view presented with a new perspective. Interestingly, most students attending the course are quite astonished at their own ability to understand and interpret literature and see its relevance for gaining a holistic perspective of diverse situations, a must for all managers and leaders.
A film titled "The Making of the Mahatma" will form a part of the course. In addition, films on the following readings will be screened to those interested. These screenings will be purely optional and outside the main course outline. The films available are: Don Quixote, Joan of Arc, Othello, To Kill a Mocking Bird, Sidhartha, Lord of the Flies and Good Bye, Mr. Chips. The feedback on these films from the earlier batches has been that they enhanced the appreciation of the main readings tremendously. However, they are NOT a substitute for the main readings.
Grading Scheme
The following will be the grading scheme followed:
15% Class Presentations: This segment will consist of two sub segments:
the class presentation itself and
a brief written report on your own presentation, in about 3-4 pages, submitted as a group. These two segments will carry equal weight, of 7.5% each.
The presentations made by the various groups will be evaluated based on
the quality of their interpretation (rather than merely summarising the reading)
the issues generated for discussions and
the innovative elements introduced to make the presentations more effective. This will be a group grade in which all the members of a group will receive the same grade, unless there are good reasons to believe that some of the members have not contributed at all or only in an insignificant way to the group's output.
The written report will not be a mere repeat of your presentation, but will also include the significant points raised during the class discussion in that session. The evaluation of this report will be based on the clarity of the report and the extent to which the class discussions have been incorporated.
20% Individual class participation and attendance: This will be based on the interest taken in the class and the quality of contributions to the discussions.
25% Term Paper: The term papers will be a group effort, and could be on any of the topics on leadership, may be one of those covered in the class, may be not. They could be based on a theme encompassing more than one reading given in the class or other material, or they could be a detailed reflective elaboration on one of the readings done in the class, including the presentation made in the class and the discussions. A group can choose to write on its own presentation or on one of the presentations of any other group. The grade will be a group grade.
40% End Term Examination: This could be either of the class room, or take home type. Of course, this will be an individual evaluation.
1. Management Education and Humanities
1. Manikutty, S & Sampat P. Singh (2009). The Essence of Leadership: Explorations from Literature. Delhi: Macmillan. Chapter 1, "The Essence of Leadership: Awakening the Human Spirit" .
2. Warren Bennis and Robert Thomas, "The Crucibles of leadership", Harvard Business Review, September 2002.
2. Managers and Leaders
1. Manikutty, S & Sampat P. Singh (2009). The Essence of Leadership: Explorations from Literature. Delhi: Macmillan. Chapter 2, "From a Manager to a Leader".
2. Singh, S P (1999). "Learning Leadership and Decision-Making from Literature," Vikalpa, July - September, 24(3), 3-10.
These first two sessions do not use any literature as such; they set the stage for the course and dwell upon the distinctions between managers and leaders, role of values and are a "how to" guide for appreciating literature.
3. Leaders in the Making
Film: Shyam Benegal, "The Making of the Mahatma".
Duration of the film: three hours.
This film traces the process of development of an ordinary boy named M.K. Gandhi into a Mahatma, of whom Einstein said that future generations might not believe that such a person actually walked on the face of this earth. How he became a leader, and what dilemmas he faced are vividly brought out in this film.
4. Discussion on the Film
5. Dreams and Reality
Cervantes: Don Quixote
Sheldon Kopp: Tale of a Mad Knight
Excerpts from Ortega's Meditations on Quixote
Don Quixote is a synonym for the eccentric, "unrealistic" dreamer who lives in his own world. But the classic novel raises the question: Would the world be much better without such dreamers and cranks? Who is in fact the dreamer and who, the realist? Why does this eccentric inspire the world today so much so that it continues to be translated into a record number of languages, and people continue to read it? And still feel nothing but affection for this mad knight?
We are using only a school edition of this long novel. Interpretation is facilitated by the readings by Ortega Gasset and Sheldon Kopp.
6. Heroism and Martyrdom
George Bernard Shaw: Saint Joan
Joan d'Arc is the person best known for her uniting France as a nation against Englad, and goading a Dauphin, utterly without self respect, into becoming the King of France, and started a process that eventually resulted in the driving away of the English, and the end of the Hundred Years' War. She is still "the soul of France". But she was burnt at the stake as a heretic before she was out of her teens, and before her vision became a reality. What do we learn from this heretic turned Saint?
7. Vision and Action
Girish Karnad: Tughlak
Here is another dreamer, another visionary. But why do we feel so different towards him as compared to, say, Joan or Don Quixote? What are the qualities he possesses? Does he possess any such quality/qualities that led to his failure, and prevented him from becoming a leader who could command respect rather than fear?
8. Ends and Means
Vishakadatta: The Signet Ring of Rakshasa
Chanakya has fascinated people for the last two centuries. For him, end justified the means. No holds barred. Yet he comes as a sharp contrast from Tughlaq. Why? In this immortal play, we look at when ends may justify means.
9. Freedom and Social Responsibility
Brecht: Life of Galileo
Galileo was threatened to be burnt at the stake for his view that challenged the beliefs of the Church on many issues, notably on whether the earth was the centre of the universe, and Man, the chosen of God, or the earth was merely one of the many planets, revolving around the Sun, in an empty space. He was tried by the Church for heresy, recanted and led a life devoted to further advances in physics which did not offend the church. What is the responsibility of the leader when it comes to personal choices? Did Galileo sell out or did he choose a course of action that led to a better world, all things considered?
10. Private versus Public Life
Arthur Miller: All My Sons
Capitalism has its ugly side. It is never uglier than when it forces people to take decisions endangering others' lives. But some of these lives may be those of the near and dear. How do leaders take decisions that need a choice between what organizations demand and what they want to do? In this powerful play by Arthur Miller, we explore many of these uncomfortable issues.
11. Ambition and Purpose
Chinua Achebe: Things Fall Apart
In this novel set in Africa, we explore the raw ambitions of a man which still lead him nowhere. We explore such questions as: What is character? What is ambition? When does it become all destroying? Usually in this story, participants compare with some people they know, and, sometimes, with themselves.
12. Reconciliation of Conflicting Demands
Jean Paul Sartre: Dirty Hands
In this play by Jean Paul Sartre, the dilemmas of leadership in reconciling conflicting demands and the conflict between idealism and compromise to reach the goals is dramatically brought out. A young idealist from an aristocratic background joins the "party" for its ideological appeal, but is confronted by the way the party is compromising its basic ideals, and how ruthlessly individual leaders pursue their own agendas.
13. Success and Satisfaction
Milind Bokil: Thirsting for Water
Success is one thing. Satisfaction is wholly different. They are neither mutually exclusive nor necessary complements. In the short story, we explore the makings of a leader who becomes a leader almost by accident, but who derives satisfaction. We contrast her to another character in the story who is outwardly successful. Building further on Things Fall Apart, the story pushes the point of the need for a balance between success and satisfaction.
Ideals and Reality – I
Iravati Karve: Yuganta, Chapters "Final Effort" (on Bhishma), Kunti and Draupadi.
15. Ideals and Reality – II
Iravati Karve: Yuganta, Chapters on Karna, Ashwathama (Paradharmo) and Krishna.
These two sessions are based on an interpretation of the immortal classic, Mahabharatha by Irawati Karve. We come across the famous characters such as Bhishma, Kunti, Draupadi, Karna and Krishna. Everyone has his or her own flaws. But how does one keep these flaws under control? How does one achieve a perspective and a balance between ends and means? These are the themes explored in the play. No one forgets the interpretations of the characters in the play, especially that of Krishna, the master strategist.
16. Taking a Stand
Sophocles: Antigone
In this classic Greek play by Sophocles, two inflexible characters take positions and their positions are irreconcilable. It leads to a tragic series of events Greek tragedies are famous for. What were the real issues they were taking a stand for? Could they have achieved those yet reconciling with the other person's viewpoint? Or are ideals, by their very nature, incapable of any compromise? These issues arise when one takes a stand on a matter of principle, and this play beautifully brings out the complexities involved in resolving them.
17. Self and Ethics
Bimal Kar: Satyadas
In this powerful short story, we explore the meaning of ethics, self respect and the way one gets rich but gets degraded in the process. It raises powerful questions on the meaning of the term character.
18. Leadership as a personal Journey
Read: Hermann Hesse, Sidhartha.
Sidhartha (not Goutam Buddha) is a brilliant Brahmin boy who, after learning and mastering the scriptures, is dissatisfied and goes in search of truth. He masters sensual pleasures, becomes a successful businessman, and finds the truth still eludes him. He meets a high class courtesan, Kamala, and later discovers that he has become a boy's parent through Kamala. He continues in search of truth, and eventually meets a boatman, who asks him to listen to and learn from the river. Also made into a great film (available to be shown).
19. Leadership, Passion and Discipline
In this session, a DVD titled "Passion and Discipline" by James March, Stanford University will be screened. This effectively brings out most of the lessons in leadership we have learned in the course.
20. Organizational Leadership: A Sum up
a) Manikutty, S (2003). "From a Manager to a Leader: Bridging a Gulf or
Jumping a Chasm?" Vikalpa, October - December, 28(4), 53-6.
b) Collins J (2001). "Level 5 Leadership- The Triumph of Humanity and Fierce
Resolve," Harvard Business Review, January, 67-76.
This will be a wrap up session. Some other works of literature will also be mentioned for further reading.
For the course, which is based on readings from literature, the following will be the books needed to be purchased. What are not mentioned here are photocopied materials. These are not very expensive books. I can give more details reg publishers etc in due course.
List of books needed to be procured
1. Don Quixote (Macmillan edition)
2. Saint Joan
3. Tughlaq
4. Life of Galileo
5. All My Sons
6. Things Fall Apart
7. The Dirty Hands
8. Yuganta
9. Antigone
10. Sidhartha
11. The Essence of Leadership (to be given only at the end of the course)
12. The Little Prince (to be given only at the end of the course)
Prof. S. Manikutty
Professor, Business Policy Area (Retd.)
Ahmedabad 380015.
E Mail: manikuti@iimahd.ernet.in
.Mr. S.V. Chandrasekhar
PGP Office
Indian Institute of Management Bangalore
Dear Mr. Chandrasekhar,
As discussed, I am sending all the materials to be photocopied and distributed for the course LVMR.
Thanking you and with regards,
(S. Manikutty)
: ~acad
~acad -> 英文說故事比賽 第八篇 snow white
different aspects
various groups
complexities involved
difference between success
themes explored
members have
whole topic


Black-and-white thinking not only boxes in our ability to be creative, to empathize, and to see the complexities of the world, but also limits the number and quality of options in the future.
Using an ongoing chronological list of US soldiers who have been killed in the Iraq war (http://www.icasualties.org/Iraq/Fatalities.aspx), I printed their first names in the area surrounding the outline of Iraq (the original piece includes names of US soldiers killed through 6/1/2007; the adjunct piece includes the names from 6/1/07 to the present). Inside Iraq I wrote the first names of only a small portion of the tens of thousands of Iraqi civilians who have been killed (from a list at http://www.iraqbodycount.org/database).


text:
6 Million Memorials
Home: Six million memorials ~ Landscapes of Memory
An introduction to Holocaust memorials
Berlin Memorials
Grunewald Gleis 17/Platform 17
Jewish Museum - Berlin
Judisches Gemendehaus, Fasanen Strasse
Levetzowstrasse Deportation Memorial
Memorial to Murdered Parliament Members 1933-1945
Münchener Strasse Memorials
Otto Weidt's Workshop for the blind
Roßenstraße
Sachsenhausen Concentration Camp
Sachsenhausen Death March memorial
Stolpersteine (Stumbling stones)
The National Memorial to the Victims of Tyranny and War - Neuewache
Train to life/Trains to death, Friedrichstraße
Wannsee Haus
Wasser tower
Wittenberg Platz
Films as memorials
Jersey memorial to Guernsey deportees
Recommended related reading
UK Holocaust Memorials
'Sanctuary' - St Botolph without Aldgate Church
Anish Kapoor Holocaust Memorial - Liberal Jewish Synagogue
Anne Frank - British Library
Freddie Gilroy and the Belsen Stragglers, Scarborough
Holocaust Centre, Beth Shalom
Holocaust Exhibition - Imperial War Museum
Holocaust Exhibition - Imperial War Museum North
Holocaust Memorial Garden, Hyde Park, London
Jersey memorial
Jewish Museum, London
Kindertransport - the arrival Memorial
Lidice Memorial - Hackney, London
National Memorial Arboretum
Raoul Wallenberg Memorial
Wiener Library
"To forget the dead would be akin to killing them a second time." (Elie Wiesel)
'Landscapes of memory' is a study of Holocaust memorials in the UK and in the vicinity of Berlin, these countries represent a cross section of experiences including those of victims, perpetrators and liberators.
This project started as post doctoral research at the University of Leeds funded by Leeds Humanity Research Institute and is ongoing.
Kate has just led a study group in Berlin leading discussions and debates around a variety of memorials and is alos involved in ensuring a legacy of survivors stories with the HSFA in Leeds.
Another aspect of this project will be working as part of the steering group to make the art installation by Antonia Stowe entitled 6 million + in our hands and will be a permanent memorial to the Holocaust and subsequent genocides to be situated in Kirklees. www.facebook.com/6MillionPlus
Kate has recently become involved in a network run by the University of Leicester The Extremes of Human Cruelty Research Network draws together academics, practitioners, and other interested parties, from a variety of disciplines and backgrounds to explore shared interests in human evil and cruelty. It aims to showcase the existing work and research of the contributors, provide a forum to develop collaborative projects, generate debate and discussion, and attract further scholars, practitioners and researchers with interests in these areas. http://www2.le.ac.uk/departments/criminology/research/current-projects/extremes-of-human-cruelty
Please get in touch if you have any thoughts, ideas or questions and find the facebook page (www.facebook.com/MemorialisingTheSixMillion).
Dr Kate Vigurs
e.k.vigurs@leeds.ac.uk
The Memory Void
Jewish Museum, Berlin
Subpages (4): An introduction to Holocaust memorials Events and news! Introduction to the Holocaust Talks


text:
Sites in 3 states eyed for permanent child detention centers
by: JEFF MARTIN, Associated Press
Posted: Jul 3, 2019 / 04:50 PM UTC / Updated: Jul 3, 2019 / 07:04 PM UTC
FILE – In this Feb.19, 2019 file photo, children line up to enter a tent at the Homestead Temporary Shelter for Unaccompanied Children in Homestead, Fla. A government spokesman says President Donald Trump's administration is evaluating vacant properties near five U.S. cities as potential permanent sites to hold unaccompanied migrant children. Department of Health and Human Services spokesman Mark Weber said Wednesday that property is being assessed in and around Atlanta; Phoenix; Dallas; Houston; and San Antonio, Texas. (AP Photo/Wilfredo Lee, File)
ATLANTA (AP) — President Donald Trump's administration is evaluating vacant properties near five U.S. cities as potential permanent sites to hold hundreds of unaccompanied migrant children, a government spokesman said Wednesday.
Property is being assessed in and around Atlanta; Phoenix; Dallas; Houston; and San Antonio, Texas, Department of Health and Human Services spokesman Mark Weber said.
Properties that can hold up to 500 children are being requested in bidding documents. Buildings must have up to 100,800 square feet (9,400 square meters) of space and the properties must include about 2 acres (0.8 hectares) for outdoor recreation.
Existing migrant detention facilities, especially those housing minors, have become a flashpoint in the 2020 presidential race. Several Democratic candidates last week visited a sprawling child migrant detention center in south Florida while they were in the state for the first round of their party's debates.
Lawmakers and migrant advocates have issued scathing criticism about how the teens are treated, saying the center is more like a prison than a "shelter," the term preferred by the facility's operator and the government. They also said they witnessed deplorable conditions at migrant facilities in Texas. Protests have sprung up around the country with demonstrators demanding that the centers be shut down.
Proposals for the new sites in Georgia, Texas and Arizona are for long-term facilities. Federal officials are seeking 20-year leases for most of the sites, a sign that acrimony surrounding immigration policies could continue for years.
It's troublesome that the government "is looking for permanent, long-term structures like this, given its track record on abuses and child neglect that we have seen nationally," said Jerry Gonzalez, executive director of the Georgia Association of Latino Elected Officials.
"Clearly the abuses that we have seen should not be tolerated and I don't think that this administration is capable of administrating a program in a humane way," Gonzalez said. "Other nations around the world have done better by those seeking refuge, and this nation certainly is not doing enough to respect human rights norms."
Gonzalez anticipates there could be protests in Georgia as plans for the facility proceed.
"The search for and addition of permanent licensed facilities is being pursued to reduce the potential need for temporary influx shelters in the future," Weber said.
The plan for the Georgia facility calls for 125 bedrooms, with each of them housing up to four children. About 167 employees would work there, and there would be a counselor's office for every 12 children. Food would be provided in three shifts for each meal in a 2,000-square-foot (610-square-meter ) dining room, documents show.
Government officials are requesting proposals from a specific region in Georgia that's generally south and west of the city. That area is accessible to Atlanta's airport and Interstate 20, a route that connects the state with Texas and western states.
Associated Press Writer Ricardo Alonso-Zaldivar in Washington contributed.
by BRADY McCOMBS, Associated Press / Jul 15, 2019
SALT LAKE CITY (AP) — A tech worker charged in the death of a Utah college student made his first court appearance Monday as friends of the slain woman held hands in the front row.
Ayoola A. Ajayi appeared by video from jail alongside a court-appointed attorney during a quick hearing Monday to set a future court date. He did not speak or enter a plea to murder, kidnapping and other charges.
NEW YORK (AP) — New York's mayor fended off criticism Monday for being in Iowa campaigning for president while Manhattan was in the grips of a major power outage.
Bill de Blasio said on MSNBC that he was in frequent contact with agencies handling the emergency and that he thinks first responders did an "incredible job."


text:
2017 might be the year NM fixes its "Swiss cheese" Tax policy.
February 28, 2017 Economy and Job Creation
Rep. Jason Harper introduced a 347 page bill (HB 412) that has the potential to fix our states "Swiss cheese" tax policy and reform the state GRT. Jobs are created when businesses can rely on a consistent tax policy, and out-of-state businesses are not scared off by our GRT.
Redundant Regulations diminish Job Creation
The City of ABQ is trying to weed out redundant regulations by bringing "clarity and predictability" to development regulations within the city. Existing planning and regulatory documents create a stack of paper several feet high. The new regulations would be considerably more concise and easier to understand making it more likely that there will be more development and job creation in the city.
Teenage 'Mobbing' Murder
February 21, 2017 Family
Seven families have a significant problem-- one family because a family member was murdered and 6 boys from other families who participated in "mobbing" which led to murder. All families have had their lives irrevocably changed. The prosecutor, Callaway, described the awful actions of the boys this way, "I think that in their minds, they had this 'Grand Theft Auto'(perception)," referring to the violent video game.
Equalizing the GRT
Because receipts from some types of sales are not taxed, others must be taxed so heavily that NM's capacity to compete with surrounding states is compromised as to some heavily taxed industries. You can bet that when an out of state business is negotiating with NM about opening a plant here, a diminution of the GRT is on the table. Daily, existing NM businesses are adversly affected by the GRT. An effort is underway to equalize the GRT and thereby lower them.
The Cartels Next Door
Cartels in Mexico earn billions in profits as they traffic drugs throughout not only this country but several others. The cartels are comparable in size and reach to an international corporation; law enforcement's best efforts find difficulty in keeping track of them. Many families in New Mexico have been affected by illicit drug use. The ABQ Journal began a 6-part investigative series on the criminal enterprise causing havoc across the country.
What Happened to Our Economic Freedom?
It's been 8 years since the Great Recession, yet U.S. economy has been inching along, with productivity flagging and millions being locked out the labor market. Heritage Foundation periodically compares economic freedom among countries throughout the world. (and by extension, in NM)
Mining Act Reclamation Program
The Mining and Minerals Division of EMNRD usually posts reports about the number of new mines created since the 1994 state mining act. This year they didn't, so we reached out and learned that the 2016 Draft of the Annual Reporting of MARP to the NM Mining Commission, like earlier reports, will state that as to regular mining no new operations have been approved since 1994. (Note, potash is not covered by the act.)
Manufacturer to Bring 175 Jobs to Belen
A plastics manufacturer, Keter Plastics, has acquired the Solo Cup Building south of Belen and is going to bring 175 jobs to New Mexico. Keter will invest at least $36 million in the project. The City of Belen was instrumental in bringing about the project. See the article in the Albuquerque Journal by Marie C. Baca, AJ, 1/12/17.
Is New Mexico Moving in The Right Direction?
An increasingly large portion of New Mexico's leaders say it isn't according to an Albuquerque Journal front page article by Ellen Marks titled, " Is New Mexico Moving in the Right Direction?" Whereas 36% of business leaders thought the state was on the wrong track in 2015, now 58% think New Mexico is on the wrong track.
RESTRICTING COMPETITION AND REDUCING JOB CREATION
February 3, 2017 Member Analysis
NEW MEMBER ANALYSIS COMING SOON The national unemployment rate is 4.6%. Yet New Mexico's unemployment rate is 6.6%. The question is whether over the next few years, as President Trump attempts to create more jobs in the nation, New Mexico will fall further behind the nation or whether it will catch up. Since the publication of our two ads on January 15th, we have been contacted by multiple readers. Some have recounted stories related to the difficulty in starting businesses in the state -- and, consequently, the difficulty of creating jobs here. One such response came from Bruce J. Fischer, a former job creator in Texas who moved to New Mexico. This is his report: "Many thanks for publishing your article Sunday in the Albuquerque Journal discussing New Mexico's problems. I am a perfect example of your statement that 'businesses here often live in an adverse regulatory environment.' Briefly, here is my story. I owned and operated a small design-build construction … [Read more...]


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In part 1 of this eBook series, learn the essential components of strategy, planning and investment management.
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text:
NIH research initiative seeks diversity in collecting DNA from 1 million
Rachel Z. Arndt
Dr. Christian Hinrichs, assistant clinical investigator at the Center for Cancer Research at the National Cancer Institute, helped develop advanced, cutting-edge procedures to cure two women of a rare form of cervical cancer.
The National Institutes of Health on Sunday will launch a massive research initiative to gather the health records and DNA of 1 million people, with a focus on including communities underrepresented in medical research.
The All of Us Research Program aims to advance precision medicine. The initiative has $1.45 billion over 10 years in congressional funding, and the NIH will start making the data openly available to researchers in 2019.
In a conference call Tuesday morning, NIH Director Dr. Francis Collins announced the official launch date of the initiative, which comes after nearly a year of beta testing during which the agency improved communications, the website user experience and staffing for the project.
Collins and others from the agency emphasized that the initiative would involve an especially diverse cohort.
"There are far too many unanswered questions about health disparities that disproportionately affect underrepresented communities," said Dr. Dara Richardson-Heron, the NIH's chief engagement officer. "We can begin to chip away at health disparities."
To enroll people from these underrepresented communities, the NIH has partnered with community organizations, provider groups and medical centers to educate their members and patients.
The agency has also focused on building trust, as some potential participants may worry that their data could be used against them. Agency representatives have assured them that past "errors" in medical research shouldn't stymie future advances.
"Safeguarding participants' privacy and data is our top responsibility," All of Us Director Eric Dishman said.
The NIH will give patients access to their data. "We think of it as your right and your choice to have your information back if you choose," Dishman said.
The agency has learned from private initiatives that preceded it in the precision health and data space, including Geisinger's National Precision Health Initiative that launched in 2017.
But All of Us is distinct from other programs because of its scale and diversity, Dishman said. He's aiming for 70% to 75% of participants to come from communities underrepresented in medical research.
Biden administration to focus on risk factors for Alzheimer's
How Chicago's sewers are helping predict COVID outbreaks
Modern Healthcare Alert: Sign up for this breaking news email to be kept in the loop as urgent healthcare business news unfolds.


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text:
\section{Introduction}
In this  tutorial I cover a few recent papers in the field of network embedding. Network embedding is a collective term for techniques for mapping graph nodes to vectors of real numbers in a multidimensional space. To be useful, a good embedding should preserve the structure of the graph. The vectors can then be used as input to various network and graph analysis tasks, such as link prediction. The papers I discuss develop methods for the online learning of such embeddings. These developments in online learning of network embeddings have major applications for the analysis of graphs and networks, including online social networks.

Recently, researchers have adapted ideas and techniques from word embeddings to the domain of network embeddings. This tutorial will cover these recent developments. Specifically, I cover the following papers:

\begin{table}[h]
\centering
\label{papers}
\begin{tabular}{p{2.5in}p{1.5in}}
\textbf{Title} & \textbf{Where, Who, When} \\
\textsc{DeepWalk}{}: Online Learning of Social Representations  & KDD \citet{perozzi2014deepwalk}  \\
\hline
LINE: Large-scale Information Network Embedding &    WWW, \citet{tang2015line}  \\
\hline
node2vec: Scalable Feature Learning for Networks   &    KDD, \citet{grover2016node2vec}  \\
\hline
struc2vec: Learning Node Representations from Structural Identity   &  KDD, \citet{ribeiro2017struc2vec} \\
\hline
metapath2vec: Scalable representation learning for heterogeneous networks
& KDD, \citet{dong2017metapath2vec} \\
\hline
\end{tabular}
\caption{Reviewed Papers}
\end{table}

The papers use various methods to sample the nodes and create node contexts. Subsequently, machine learning techniques perform the embedding. The first paper, ``\textsc{DeepWalk}{}: Online Learning of Social Representations'', is a seminal paper that generalizes a well-known NLP word embedding technique, \textit{word2vec}{}, to graph theory. The second and third papers, ``LINE: Large-scale Information Network Embedding''  and ``node2vec: Scalable Feature Learning for Networks'', improve upon \textsc{DeepWalk}{} in a substantial way.

The papers were presented at SIGKDD and WWW conferences (2014, 2015, and 2016) and are highly-cited: 471, 362, and 268 in Google Scholar; 374, 330, and 139 in Microsoft Academic. The latter service is reputed to be more reliable.

The last two papers reviewed are ``struc2vec:  Learning Node Representations from Structural Identity'' and ``metapath2vec:  Scalable representation learning for heterogeneous networks''.

Fig. \ref{fig:outline} shows a time outline of the papers reviewed in this tutorial.

\begin{figure}
    \centering
    \includegraphics[width=4.5in]{outline.png}
    \caption[caption]{Paper outline}
    \label{fig:outline}
\end{figure}

The papers use \textit{\textit{word2vec}{}}, an algorithm designed for performing word embedding. Thus, I first give a brief introduction to this technique. The original \textit{word2vec}{} papers are \citet{mikolov2013efficient} and \citet{mikolov2013distributed}. Since many of the descriptions in these papers are ``somewhat cryptic and hard to follow'' \citep{goldberg2014word2vec}, a small cottage industry of pre-prints explaining \textit{word2vec}{} has sprung up, including \cite{rong2014word2vec} and \cite{goldberg2014word2vec}.

\section{\textit{word2vec}{}}
Traditional natural language processing systems treat words as discrete symbols. Words are then represented as one-hot vectors in a very high dimension space. With a vocabulary of $V$ different words, the space is of dimension $V$, and each word is represented by a vector of length $V$ with a single component of 1 and $V-1$ components of 0.

In contrast, vector space models embed words in a low, $d$-dimension real-numbers vector space such that words which are semantically similar are represented by closer vectors. This embedding is based on the principle of co-occurrence: the assumption that words with related semantic meanings appear close to each other in texts. This assumption is famously summarized by British linguist J. R. Firth's famous statement that ``you shall know a word by the company it keeps'' \citep{firth1957papers}.

\textit{word2vec}{} (\citet{mikolov2013efficient}, \citet{mikolov2013distributed}) is a machine learning model for the efficient learning of word embeddings given raw text. There are two versions of \textit{word2vec}{}, Continuous Bag-of-Words (CBOW) and Skip-gram. Here I focus on Skip-gram, since this is the model used by \textsc{DeepWalk}{} and \textit{node2vec}{}.

Given a word $w$ we look at its context-words $c \in C(w)$ using a sliding window of size $2 \times k$: the  $k$ words preceding $w$, and the $k$ words following $w$. A typical parameter for this window parameter is $k=5$. When we consider the conditional probabilities $p(c|w)$, the goal is to find the parameters $\theta$ of $p(c|w, \theta)$ such that the following is maximized:
\begin{equation}
    \argmax_\theta
     \prod_{c \in C(w)} p(c|w;\theta)
\end{equation}
For the entire corpus $T$ we have:
\begin{equation}
    \argmax_\theta \prod_{w \in T}
    \left( \prod_{c \in C(w)} p(c|w;\theta) \right)
\end{equation}
which we can also write as
\begin{equation}
    \argmax_\theta \prod_{(w, c)\in D} p(c|w;\theta)
    \label{eq:node2vec}
\end{equation}
where $D$ is the set of all the $(w, c)$ pairs of (word, context-word). In a corpus $T$ with a vocabulary of $V$ words, we have approximately $2 \times k \times V$ such pairs.

The approach taken by  $word2vec$ is to parameterize the model using a classical soft-max neural network:
\begin{equation}
    p(c|w;\theta) = \frac
    {e^{\vec{v_c} \cdot \vec{v_w}}}
    {\sum\limits_{c^\prime \in C} e^{\vec{v_c^\prime} \cdot \vec{v_w}}}
\end{equation}
where $\vec{v_w}$ and $\vec{v_c}$ are the vector representations of the words and the context-words, both in $\mathbb{R}^d$.
The input layer thus consists of $V$ neurons where each word is represented by a one-hot vector. The output layer has $V$ neurons, one for each context word, and acts as a soft-max classifier. The hidden layer has $d$ neurons, where $d$ is the size of the embedding space. This is shown in Fig. \ref{fig:word2vec}.
\begin{figure}
    \centering
    \includegraphics[width=3.5in]{NN.png}
    \caption[caption]{\textit{word2vec}{} neural network}
    \label{fig:word2vec}
\end{figure}

As is usually the case, the objective function is easier to optimize after taking its log. This step is omitted here for sake of brevity. Following the optimization, the $V \times d$ weights of the $d$ neurons of the hidden layer serve as the vector representations. The hidden layer basically serves as an auto-encoder that produces the word embeddings. The outputs from the final layer are not needed.

Due to the time complexity of the training (there are $V \times V \times d$ parameters to be computed), it is impractical to scale the training of the network to very large corpora. The authors describe two tricks for better computation efficiency. The first is hierarchical softmax, an efficient way of computing softmax (\citet{mnih2008probabilistic} and \citet{morin2005hierarchical}). Hierarchical softmax reduces the complexity of computation per training instance per context word from $O(V)$ to $O(\log V)$. The second is negative-sampling, where only a sample of the output vectors are updated per iteration. These two improvements make it possible to train the model on very large amounts of text.
\footnotetext{The figures in this tutorial are drawn by the author, unless otherwise stated}

\subsection{A Note on Terminology}
There is some confusion regarding terminology in this cutting-edge field, especially between \textit{graph embedding} and \textit{node embedding}. It would perhaps be more consistent to use \textit{node embedding} for the mapping of nodes to vectors, in the same way that \textit{word embedding} is used in NLP. Indeed, some authors use this term. Others, however, use graph embedding. This is confusing since graph embedding is also used to denote the mapping of entire graphs into a single vector (in much the same way that \textit{document embedding} maps an entire document into a vector and thus allows to find distances between documents). Another factor adding to the confusion is that graph embedding is a well establish topic in the mathematical field of topological graph theory.

In this tutorial I chose to use yet another term, \textit{network embedding}, to describe the mapping of the nodes to vectors, as this currently seems to be the most popular term in the machine learning community.

\section{\textsc{DeepWalk}{}}

\textit{word2vec}{} is a huge success, and inspires many derivative works in related fields. One of the most intriguing developments is \textsc{DeepWalk}{} \citep{perozzi2014deepwalk}, a new online learning method for embedding of graphs, with an emphasis on graphs representing social networks.

The problem of network embedding can be formalized as follows: given a graph $G(V,E)$ with a set $V$ of nodes and a set $E$ of edges, compute a mapping $f(v \in V) \longrightarrow \mathbb{R}^d$ such that the structure of $G$ is preserved as much as possible.
Vast literature in the field covers multiple techniques for attacking the problem of network embeddings \citep{fouss2016algorithms}. For example, \emph{spectral methods} use the eigenvectors of various graph matrices to compute the embeddings, thus offering exact solutions following a closed-form formulation. Another approach is to use the analogy between nodes and edges to physical spring networks, resulting in \emph{force-directed methods}.

\textsc{DeepWalk}{}, on the other hand, gets its inspiration from NLP and generalizes the \textit{word2vec}{} model to graphs using an analogy between documents and graphs, as shown in Table \ref{table:analogy}: a document is seen as a graph of words. In the \textit{word2vec}{} model, words are used to estimate the likelihood of the nearby context-words in the sentence.
In much the same way, \textsc{DeepWalk}{} uses nodes to estimate the likelihood of nearby nodes in the graph. To paraphrase J. R. Firth, ``you shall know a node by the company it keeps''. The nearby nodes are sampled using random walks. The assumption is that sampling from multiple random walks captures the structure of the graph.
\begin{table}[h]
\centering
\begin{tabular}{ll}
NLP          & Graph Theory \\ \hline
Corpora/Documents      & Networks/Graphs\\
Words        & Nodes/Vertices\\
Word co-occurrence & Node neighborhood\\
Sentences & Random walks
\end{tabular}
\caption{Analogy between NLP and Graph Theory}
\label{table:analogy}
\end{table}

The \textsc{DeepWalk}{} algorithm generates random walks for each node $v \in V$. Each random walk starts from the origin node $v$ and then advances to a node uniformly selected from its immediate neighbors. The length of the walks is $T$. Thus, each such random walk generates an ordered list of nodes:
\begin{equation}
    RW(v) = (v=u_1, u_2, ..., u_{T}).
\end{equation}
Each walk is a ``sentence'' of nodes. Similarly for the words in \textit{word2vec}{}, for each node $u_{i}$ within this ``sentence'', the algorithm then looks at a window of $k$ neighboring nodes before and after $u_j$, which comprise the set of our ``context-nodes'':
\begin{equation}
    C(u_{i}) = \{u_{i-k}, ..., u_{i+k}\}
\end{equation}
We would then like to find $\theta$ that maximizes:
\begin{equation}
    \argmax_\theta
     \prod_{u \in RW(v)} p(u^\prime \in C(u)|u_;\theta)
\end{equation}
For the entire graph $G$ we have:
\begin{equation}
    \argmax_\theta \prod_{v \in G}
    \left( \prod_{u \in RW(v)} p(u^\prime \in C(u)|u_;\theta) \right)
\end{equation}
which we can also write as
\begin{equation}
    \argmax_\theta \prod_{(u^\prime, u)\in D} p(u^\prime|u;\theta)
    \label{eq:deepwalk}
\end{equation}
where $D$ is the set of all (node, context-node) pairs discovered in all the random walks of all the nodes.
To improve sampling, $\gamma$ random walks per node $v$ are performed. $\gamma$, $T$, and $k$ are all hyper-parameters of the algorithm. In total, $\gamma  \times |V|$ random walks  of length $T$ are generated, and there are approximately $\gamma \times |V| \times T \times k$ (node, context-node) pairs.

As can be seen, \textsc{DeepWalk}'s Equation \eqref{eq:deepwalk} is equivalent to \textit{node2vec}{} Skip-gram{}'s Equation \eqref{eq:node2vec}, and indeed the same neural network is used to compute the embeddings for the nodes, with some mandatory adjustments (for example, the input layer is the one-hot representations of the nodes). \subsection{Experiments}
The original motivation for \textsc{DeepWalk}{} is solving the following social graph multi-label classification problem: we are given a graph $G(V,E)$ of a social network and node attributes
$X \in \mathbb{R}^{|V| \times S}$ (where $S$ is the size of the feature space). There is also a set of labels $\mathcal{Y}$. Some of the nodes are labeled with $y \in \mathcal{Y}$. The task is to predict the labels of the other (unlabeled) nodes.\footnote{In fact, the paper mentions that the label output is $Y \in \mathbb{R}^{|V| \times \mathcal{Y}}$. I found this confusing, if not wrong, since the labels are not real numbers but belong to a discrete set of labels.}

This problem is known as a \textit{relational classification problem}. Traditional approaches use the graph
structure for classification. In this paper, we first learn the embedding of the nodes
$X_E \in \mathbb{R}^{|V| \times d}$,
and these are then treated as additional features. $X_E$ is thus combined with the attributes $X$ as input to any standard classification algorithm.

The authors compared the performance of \textsc{DeepWalk}{} with five other baseline methods:
\begin{itemize}
\item Spectral Clustering of the normalized graph Laplacian \citep{tang2011leveraging}
\item Modularity Matrix \citep{tang2009relational}
\item $k$-means clustering  of the adjacency matrix  \citep{tang2009scalable},
\item Weighted-vote relational neighbor \citep{macskassy2003simple},
\item Na\"ive majority
\end{itemize}

The classification method used with \textsc{DeepWalk}{} is a one-vs-rest logistic regression, and the parameters selected are $d=128$ (number of dimensions), $T=50$ (length of random walks), $w=10$ (window size), $\gamma = 80$ (number of random walks per node).

Three test datasets are used for the multi-label classification task: \textsc{BlogCatalog}, \textsc{Flickr}, and \textsc{YouTube}. The results show that \textsc{DeepWalk}{} has strong performance that is almost as good as or exceeds the leading method, Spectral Clustering. In addition, it needs relatively few labels to perform well. It also has the advantage that it is computationally feasible to perform this embedding on huge networks such as \textsc{YouTube}, which is computationally unfeasible for spectral clustering.

\section{LINE}
While the analogy of graphs and texts is useful, networks do not possess the linear property of text. So while the neighborhood of a word can be quite accurately sampled using a sliding window, social and other large networks are not linear, and thus sampling their structure is more challenging.
Following the introduction of \textsc{DeepWalk}{}, many other researchers have started to use similar NLP-inspired methods for network embedding. One of the problems with \textsc{DeepWalk}{} is that it uses unbiased random walks for generating the node contexts. In that way, it is similar to a depth-first search (DFS).
The work by \cite{tang2015line} tries to solve this issue by preserving first-order and second-order node proximities.

The first-order proximity of two nodes is defined to be the weight of the edge between them (1 for unweighted graphs), and zero if they do not share an edge. For example,  nodes 6 and 7 in Fig. \ref{fig:line} should be embedded closely since they are connected by a ``heavy'' edge (compared to nodes 7 and 8, for example).
\begin{figure}[h]
    \centering
    \includegraphics[width=2in]{LINE.png}
    \caption{First-order and second-order proximities}
    \label{fig:line}
\end{figure}

The second-order proximity is defined by the common neighborhood of two nodes. Referring back to Fig. \ref{fig:line}, nodes 5 and 6 have a high second-order proximity since they share a lot of neighbors, even thought they are not directly connected. Thus, they should also be embedded closely together in the embedding space.

In mathematical terms, the first order proximity between any two nodes $v_i$ and $v_j$ is defined by LINE to be the following joint probability:
\begin{equation*}
    p_1(v_i, v_j)=\frac{1}{1+exp(-\vec{v_i}^T \cdot \vec{v_j})}
\end{equation*}
where $\vec{v}$ is the vector representation of node $v$ in $\mathbb{R}^d$.
Ideally, this probability would be equal to the empirical probability induced by the edge weights:
\begin{equation*}
    \hat{p_1}(v_i, v_j)=\frac{w_{ij}}{W}
\end{equation*}
where $w_ij$ is the weight of the edge between the two nodes and $W$ is a normalization factor.
The embedding should try and minimize the distance between the two distributions $p_1(\cdot, \cdot)$ and $\hat{p_1}(\cdot, \cdot)$. LINE uses KL-divergence to measure distance between distributions, and so we get that the distance to optimize is:
\begin{equation*}
 O_1 = - \sum_{(i,j) \in E} w_{ij} \log (p_1(v_i, v_j))
\end{equation*}
For the second-order proximity, the authors choose the neighbors of each node to provide ``context'' in the \textit{word2vec}{} sense. The development for this is quite tedious, so we will skip it here. The reader is referred to Section 4.1.2 in \cite{tang2015line}. The result is the following objective function for the second order proximity:
\begin{equation*}
 O_2 = - \sum_{(i,j) \in E} w_{ij} \log (p_2(v_j| v_i))
\end{equation*}
Where, similarly to the Skip-gram{} model, the conditional probability between two nodes is given by:
\begin{equation*}
 p_2(v_j|v_i)=\frac{\exp ( \vec{v_j}^\prime \cdot \vec{v_i})}{ \sum_{k=1}^{|V|}   \exp ( \vec{{v\prime}_k^T} \cdot \vec{v_i})}
\end{equation*}
The second-order proximity thus defines a conditional probability $p(v_j|v_i)$ over all other context nodes $v_k$.

\subsection{Embedding and Experiments}
In LINE, the embedding for the first-order and second-order proximities (i.e. maximizing for $O_1$ and $O_2$) is done separately. Solving for $O_2$ is done using asynchronous stochastic gradient algorithm (ASGA) with various performance optimization tricks, including edge sampling.
The vectors from the two models are then concatenated for each node. As the authors note, this approach is not very ``principled'', and a better approach that would minimize $O_1$ and $O_2$ simultaneously is more appropriate.

LINE is compared against baseline methods for performing various tasks. The data includes a Language Network from the entire English Wikipedia, Social Networks (Flickr and YouTube), and Citation Networks. Algorithms for comparison included graph embedding using matrix factorization, \textsc{DeepWalk}{}, and various variations of the LINE algorithm. The results show clearly that the LINE network embedding that include both first-order and second-order proximities outperform all other methods in classification tasks.

\section{\textit{node2vec}{}}

Following \textsc{DeepWalk}{} and LINE, \citet{grover2016node2vec} had the insight that a better capture of a node's neighborhood can be achieved by carefully biasing the random walks. This leads to latent representations that better capture the network structure. \textit{node2vec}{} indeed achieves excellent performance in multiple social graph tasks.

Assuming that we want a sample of $k$ nodes from the neighborhood of each node. Two extreme strategies are Breadth-First Sampling (BFS) and Depth-First Sampling (DFS). BFS samples the immediate $k$ neighbors of the node, and thus helps in understanding its local structure. DFS samples $k$ increasingly distant nodes, and thus identifies a more global community structure. A rich sample that combines the properties of BFS and DFS is the intuition behind the creation of the biased random walk.

Let us recall that the random walk proposed by \textsc{DeepWalk}{} had the following uniform probability of advancing from node $u_i$ to node $u_{i+1}$:
\begin{equation}
    P(u_{i+1} = v | u_i = w) =
  \begin{cases}
     \frac{1}{d(w)} & \text{if $(v,w) \in E$}\\
     0 & \text{otherwise}
   \end{cases}
\end{equation}
where $d(w)$ is the degree of node $w$.

In contrast, the random walk proposed by \textit{node2vec}{} has two parameters that control the walk, $p$ and $q$. Assume that in the random walk we just advanced from node $t$ to node $v$. There are three possibilities for the next node in the walk:
we can (1) go from $v$ back to $t$, (2) advance to a third node $x$, a common neighbor of both $t$ and $v$,
or (3) advance to a third node $x$, a neighbor of $v$ but not of $t$.
The parameters $p$ and $q$ control the probabilities for each of these types of transitions.

More specifically, assuming identical edge weights, the \textit{unnormalized} transition probability from node $v$ to node $x$, having arrived from node $t$, is:
\begin{equation}
    \pi_{vx}^t=
  \begin{cases}
     \frac{1}{p} & \text{if $d(t,x) = 0$}\\
     1 & \text{if $d(t,x) = 1$}\\
     \frac{1}{q} & \text{if $d(t,x) = 2$}
   \end{cases}
\end{equation}
where $p$ is the \textit{return parameter}, which controls the likelihood of the walk to backtrack to the previous node; and $q$ is the \textit{in-out parameter}, which decides whether to favor nodes closer to $t$. See Fig. \ref{fig:transprops} for an example of the transition properties.
By controlling these two parameters, the randoms walks can achieve a balance of the benefits of both BFS and DFS, and thus more accurately represent the local and global graph properties.
\begin{figure}[h]
    \centering
    \includegraphics[width=2in]{Transitions.png}
    \caption{Unnormalized transition probabilities from node $v$, after just transitioning from node $t$}
    \label{fig:transprops}
\end{figure}
The rest of the exposition in \citet{grover2016node2vec} follows similar path to \textsc{DeepWalk}{}, i.e., it uses the \textit{word2vec}{} neural network model with a hidden layer that calculates the latent vector representations. Optimization is done using stochastic gradient descent (SGD). The algorithm also borrows \textit{word2vec}{}'s negative sampling trick to achieve scaling to graphs with millions of nodes.

\subsection{Edge Features}
In addition to biased random walks, one of the interesting contributions of \textit{node2vec}{} is the
extension of feature learning to edges. For this goal, a binary operator $\circ$ is defined on the vector representations $f(v)$ and $f(u)$ of \textit{any} two nodes $v$ and $u$, with the aim of generating a vector representation of the pair $(u,v)$ such that $g(u,v) : V \times V \longrightarrow \mathbb{R}^{d^\prime}$. Several choices for this binary operators where $d=d^\prime$ are shown in Table \ref{table:edge}. The operator is defined whether or not the edge actually exists in the graph, paving the way for the use of this representation in a link prediction task.

\begin{table}[h]
\centering
\begin{tabular}{ll}
Operator          & Definition  \\ \hline
Average     & $\frac{f_i(u) + f_i(v)}{2}$ \\
Hadamard    & $f_i(u) * f_i(v)$ \\
Weighted-L1    & $|f_i(u) - f_i(v)|$ \\
Weighted-L2    & $|f_i(u) - f_i(v)|^2$ \\
\hline
\end{tabular}
\caption{Different operators showing the $i$th component of $g(u,v)$}
\label{table:edge}
\end{table}

\subsection{Experiments}
The authors test \textit{node2vec}{} with two tasks. The first is a multi-label classification task, similar to the one used with \textsc{DeepWalk}{}. In this task, the node feature representations are input to a one-vs-rest logistic regression classifier. Three datasets are tested: \textsc{BlogCatalog} (10,312 nodes, 39 different labels); \textsc{Protein-Protein Interaction (PPI)} (3,890 nodes, 50 different labels); and \textsc{Wikipedia} (4,777 nodes, 40 different labels).

The baseline algorithms tested against are:
\begin{itemize}
\item \textsc{DeepWalk}{}
\item Spectral Clustering of the normalized graph Laplacian \citep{tang2011leveraging}
\item LINE
\end{itemize}
With the right selection of $p$ and $q$, \textit{node2vec}{} outperforms all other contenders. The performance gain for BlogCatalog and Wikipedia is a staggering 22\%.

In addition to the classification task, the authors also experiment with a link prediction task using the various edge features operators that are described above. Three datasets are tested: \textsc{Facebook} (4,039 nodes; 88,234 edges); \textsc{PPI} (19,706 nodes; 390,633 edges); \textsc{arXiv} (18,722 nodes; 198,110 edges). They compare \textit{node2vec}{} performance against the baseline algorithms using the different operators in Table \ref{table:edge}, as well as against the standard link prediction scores: Common Neighbors, Jaccard's coefficient, Adamic-Adar Score, and Preferential Attachment. The \textit{node2vec}{} method with the Hadarmard operator outperforms all the other methods, in some cases with impressive improvements.

\section{\textit{struc2vec}{}}
Another interesting network embedding work is \textit{struc2vec}{} \citep{ribeiro2017struc2vec}, which focuses on the role of nodes in a network. Nodes in networks have specific roles. These roles can be identified through structural identity. For example, in an airport network, some nodes serve as hubs. Two hubs can be far away (hop-wise), but still have structural similarity. In social networks, roles of users are can also be identified by the structure. For example, in a graph representing a company structure, mid-level managers have a typical structure within the graph.
\begin{figure}
    \centering
    \includegraphics[width=2in]{automorphism.png}
    \caption{Node roles in graphs}
    \label{fig:automorphism}
\end{figure}
Consider the graph in Fig. \ref{fig:automorphism}. The red and green nodes are structurally equivalent. They belong to an isomorphism. The blue and black nodes, while not structurally \textit{equivalent}, are structurally \textit{similar}.

\textit{struc2vec}{} is a framework for representations based on structural similarity.  The goal of \textit{struc2vec}{} is to preserve the identity of the nodes' structure when projecting them into Euclidean space, even if they are not close. Embeddings such as \textsc{DeepWalk}{} and \textit{node2vec}{} capture neighborhood relations.
However two nodes that are structurally similar but very distant will not be close in the vector space. In addition, nodes that are close to each other in the graph can be structurally dissimilar, and thus should not be close in the Euclidean space.
This is the problem that \textit{struc2vec}{} is trying to solve. In other words, the embedding done by the former methods depends on the hop distance between nodes. \textit{struc2vec}{} does not take into account this distance.

To compute the representations, \textit{struc2vec}{} builds a special graph - the \textit{context graph} - that represents structural similarities between nodes. The goal is to create a context graph where nodes are close to each other if they are structurally similar. Once the context graph is constructed, the embedding is done once again using the \textit{word2vec}{} algorithm. That is, random walks are performed in the context graph in order to build "sentences", followed by online learning using \textit{word2vec}{}'s Skip-gram{} algorithm. Thus, the main contribution of \textit{struc2vec}{} is the construction of the context graph.

Given the original graph $G(V, E)$ with diameter $K$, the context graph $M$ is a multi-layer graph with $K+1$ layers. Each layer includes all the nodes in $G$. Within each layer, weighted edges represents structural similarity between nodes. Edges also exist between the corresponding nodes of each layer. We will now describe the four steps used in \textit{struc2vec}{}. Our emphasis is on the construction of the context graph, since this is the main contribution of the paper.

\subsection{Step 1: Computing Structural Similarity}
The first step looks at the structural similarity between nodes. For each node $v$, we look at the $N_k(v)$, which is the set of nodes which are $k$-distant from u ($N_0(v) = {v}$). These form ``rings'' around each node. For each such ring, we look at the ordered degree sequence $DS(N_k(v))$ of the nodes participating in the ring.

Referring again to Fig. \ref{fig:automorphism}, let's focus for example on the $black$ node. When $k=0$, $N_0(black) = \{black\}$, and its degree is 4, thus $DS(N_0(black)) = (4)$. Moving to $k=1$, we look at the nodes whose distance to $black$ is $1$. We see that:
\begin{equation*}
    N_1(black) = \{red, blue, green, yellow\}
\end{equation*}
and their degrees are 4, 3, 4, and 1, respectively. Thus, the ordered degree list is:
\begin{equation*}
    DS(N_1(black)) = (4, 4, 3, 1)
\end{equation*}

Once we compute $DS(N_k(v)) \quad (k=0, 1, ..., K)$, for all $v$, we can measure the structural similarities between every pair of nodes $u, v$ by comparing their degree sequences. To measure the distance between two degree sequences $A = DS(N_k(u))$ and $B = DS(N_k(v))$, and noting that these sequences are not necessarily of the  same length, the authors suggest using Dynamic Time Warping (DTW), a technique to match elements of two sequences of different lengths. The technique minimizes the sum of the distances between matched elements $a \in A$ and $b \in B$. The distance between two elements is designed in \textit{struc2vec}{} so that node degrees of 1001 and 1002 are more similar than node degrees of 1 and 2 by using $\big(max(a,b)/min(a,b)\big)-1$ as the distance between the two matched degrees in the sequences.

Now that the distance between two degree sequences is defined, the \textit{structural distance}
 between two nodes is defined hierarchically as:
\begin{equation*}
    f_k(u,v)=f_{k-1}(u,v)+g\big(DS(N_k(u)), DS(N_k(v))\big).
\end{equation*}
$g$ is the distance function between two degree sequences as described above.

\subsection{Step 2: Constructing the Context Graph}
Now that we defined a structural distance between nodes, we can move on to build the context graph. The context graph  $M$ is a multilayer graph with $K$ layers. Each layer is a complete graph consisting of all the nodes $u \in V$ in the original graph $G$. Thus, each node $u \in V$ is represented in $M$ by $K+1$ nodes $u_k \quad (k=0, 1, ..., K$), one in each layer.

To illustrate, Fig. \ref{fig:multilayer} shows the first three layers of the context graph $M$ for our example graph $G$. Each of the nodes in the original graph $G$ is represented in each of the layers in $M$. The dashed arrows show how the $red$ node is replicated in each layer. Other nodes are similarly replicated. Within the $k$th layer, the weight of an edge between nodes $u_k$ and $v_k$ is a function of the structural distance $f_k(u,v)$. Thus, each layer is a complete sub-graph with weighted, undirected edges that correspond to the structural similarity between the nodes.

Assuming $u_k$ and $v_k$ in layer $k$ are the nodes representing $u$ and $v$, the weight of their connecting edge is calculated as follows:
\begin{equation*}
    w(u_k,v_k)=e^{-f_k(u,v)}, \quad k=0, 1, ..., K
\end{equation*}
Nodes that are structurally similar will have larger weights within the multiple layers of $M$.

Edges also exist between the different layers, but they are directed and exist only between the corresponding nodes $u_0, ..., u_k, u_{k+1}$ that represent the same node $u$ in $G$. Each node is linked to the corresponding node in the layer just above (for $k<K$) and just below (for $k>0$). These directed edges are also weighted. The weights between the same node in different layers is given by:
\begin{equation}
    w(u_k, u_{k+1}) = log(\Gamma_k(u)+e), \quad k=0, ..., K-1
    \label{eq:moveup}
\end{equation}
\begin{equation}
    w(u_k, u_{k-1}) = 1, \quad k=1, ..., K
    \label{eq:movedown}
\end{equation}
where $\Gamma_k(u)$ is the number of edges connected to $u_k$ whose weight is larger than the average edge weight in layer $k$, and is thus a measure of the number of similar nodes in layer $k$. If $u_k$ has many similar nodes, the weight going to the upper level will be larger. In a higher level, the number of similar nodes can only decrease.

Fig. \ref{fig:multilayer} shows these up/down links between the various representations of the red node in the multi-layer graph. Similar links exist also for the other nodes, but they are not shown in the figure.

\begin{figure}[h]
    \centering
    \includegraphics[width=3.5in]{multilayer.png}
    \caption{Node roles in graphs}
    \label{fig:multilayer}
\end{figure}
\subsection{Step 3: Generate Context}
Once the context graph $M$ is constructed, the rest of the procedure is similar to \textsc{DeepWalk}{}. Random walks are generated in $M$ to create the context of nodes. A hyperparamter $q$ determines whether the walk will change a layer or stay within the layer. The weights of the edges determine the probabilities of advancing to the next nodes.
With probability $q$ the walk stays within the same node, and in that case the probability of moving from $u$ to $v$ is given by
\begin{equation}
    p_k(u,v)=\frac{e^{-f_k(i,v)}}{Z_k(u)}
\end{equation}
$Z_k(u)$ is a normalization factor.
Thus, in each step, the walk will prefer to walk to nodes which are structurally similar.
With probability $1-q$, the walk will move up or down a layer to its corresponding node in layer $k-1$ or $k+1$ according to the weights given in \eqref{eq:moveup} and \eqref{eq:movedown}.

\subsection{Step 4: Learn Representations}
In \textit{struc2vec}{} the Skip-gram{} approach is  used by generating sets of independent and relatively short random walks in $M$. Multiple random walks are generated for each node, starting with layer $0$. These are the ``sentences''. These sentences are then used as input to the \textit{word2vec}{} algorithm to train a neural network and learn the latent representing of the nodes by maximizing the probability of nodes within a context.

\subsection{Optimization}
$M$ is a huge graph. It has $(K+1)n$ nodes and $\frac{1}{2}(K+1)\big(n(n-1)\big)+2nK$ edges\footnote{The paper has a typo in these numbers, which I verified by corresponding with one of the authors (Savarese). In section (3.2) of the paper the number of nodes in  $M$ is listed as $Kn$ nodes and the number of edges is $\frac{1}{2}K\big(n(n-1)\big)+2n(K-1)$. Thus, the authors mistakenly use $K$ layers instead of $K+1$ layers.}. To reduce the time to generate and store the multi-layer graph and context for nodes, the authors propose three optimizations:
\begin{itemize}
    \item Reduce the length of degree sequences by compressing them into a list of 2-tuples $(d, count)$, which means that the sequence has $count$ nodes of degree $d$ for each such tuple.
    \item Reduce the number of edges in the multilayer graph (only $log(n)$ neighbors per node).
    \item Reduce the number of layers in the multilayer graph.
\end{itemize}
These optimizations enable the \textit{struc2vec}{} algorithm to scale quasi-linearly, and the authors were able to analyze networks with millions of nodes.
\begin{figure}[h]
    \centering
    \includegraphics[width=3.5in]{doublekarate.png}
    \caption{Mirrored Karate network (from \citet{ribeiro2017struc2vec}}
    \label{fig:karate}
\end{figure}

\begin{figure}
    \centering
    \includegraphics[width=3.5in]{struc2veccompare.png}
    \caption{Comparison of Node Representations (from \citet{ribeiro2017struc2vec}}
    \label{fig:struc2compare}
\end{figure}

\subsection{Experiments}
The authors ran different experiments which demonstrated the superiority of \textit{struc2vec}{} for the task. In one of the experiments, they created a graph composed of two copies of  Zachary's Karate network \citep{zachary1977information}, connected by a single edge, as shown in Fig. \ref{fig:karate}. The result of the \textit{struc2vec}{} embedding was compared to \textsc{DeepWalk}{} and \textit{node2vec}{}. A result of the embedding is shown in Fig. \ref{fig:struc2compare}. Since the Karate network was duplicated, the resulting mirror network has two identical nodes for each role. These was captured by \textit{struc2vec}{}, as can be seen by the pairs of nodes embedded closely in part (c) of the figure. The top embeddings, for (a) \textsc{DeepWalk} and (b) \textit{node2vec}{} do not capture the structural equivalence and mostly focus on the graph distances.

\section{\textit{metapath2vec}{}}

Finally, we  look into recent work by \cite{dong2017metapath2vec} which embeds \textit{heterogeneous} networks.

In a heterogeneous graph nodes can represent different entities. A classic example is an academic network, where nodes can represent researchers, organizations, papers and conference venues, and edges represent various relations between the entities.
For example, a paper is connected to its author(s), and also to the conference venue where it was presented. Fig. \ref{fig:hetero} shows an mock academic network.

\begin{figure}[h]
    \centering
    \includegraphics[width=4.5in]{hetero.png}
    \caption{An example heterogeneous academic network, with four types of nodes, from left to right: Organizations (O), Authors (A), Papers (P), and Conference Venues (V)}
    \label{fig:hetero}
\end{figure}

The methods we have seen so far (\textsc{DeepWalk}{}, LINE, \textit{word2vec}{}) assume a homogeneous network, where there is only one kind of node (e.g., a person in a social network). The contexts generated for the nodes, and the resulting embedding, do not take into account the different types of nodes and relationships between them. To solve this problem, the authors suggest using a method called \textit{metapath2vec}{}, where random walks will be biased by using meta-paths. A meta-path is a predefined composite relation between nodes. For example, in the context of an academic network, the specific relation Author-Paper-Author in the network defines the notion of co-authorship. Two authors that are connected in this way are co-authors of the same paper (note that authors can also be connected via an organization, but that implies a different relationship). The idea of the meta-path is not new, but here the authors are using it to create random walks, thus generating carefully biased contexts for nodes.

\begin{figure}
    \centering
    \includegraphics[width=4.5in]{metapaths.png}
    \caption{Metapaths for the academic network}
    \label{fig:metapaths}
\end{figure}
This work again uses the Skip-gram{} algorithm, with the necessary adjustments for heterogeneous network. We are now looking to optimize
\begin{equation}
    \argmax_\theta
     \sum_{v \in V} \sum_{t \in T_V} \sum_{c_t \in N_t(v)} \log p(c_t|v;\theta)
\end{equation}
where $N_t(v)$ are the neighbors of $v$ of  the $t$th type. $p(c_t|v;\theta)$ is defined as the softmax function.

As mentioned, the random walks must follow the meta-paths that are hand-designed for the specific network and task. Examples of meta-paths for the academic network are given in Fig. \ref{fig:metapaths}. For example, A-P-A denotes the Author-Paper-Author path. Thus, each specific meta-path semantic creates a bias toward specific relations. Some  meta-paths can be long, for example O-A-P-V-P-A-O (Organization-Author-Paper-Venue-Paper-Author-Organization). These meta-paths are then used to create biased random walks. I.e., the random walks must follow the semantics dictated by the various prescribed meta-paths. For example for A-P-A, the path with start with an author, then choose a paper (at random), then another author (at random). Again, this contexts are fed into a Skip-gram{}-like neural network for the final embedding.

\subsection{Experiments and Results}

\begin{figure}
    \centering
    \includegraphics[width=3.5in]{mp-viz.png}
    \caption{PCA projections of the 128D embeddings of 16 top CS conferences and corresponding high-profile authors \citep{dong2017metapath2vec}}
    \label{fig:mp-viz}
\end{figure}

\begin{figure}
    \centering
    \includegraphics[width=3.5in]{mp-cluster.png}
    \caption{2D t-SNE projections of the 128D embeddings of
48 CS venues, three each from 16 sub-fields. \citep{dong2017metapath2vec}}
    \label{fig:mp-cluster}
\end{figure}

 The authors compared the \textit{metapath2vec}{} performance to \textsc{DeepWalk}{}, LINE, and \textit{node2vec}{}, as well as to PTE (Predictive Text Embedding). The data used for the task consisted of two academic networks, AMiner Computer Science and  DBIS (Database and Information Systems). AMiner contains more than 9 million authors and 3 million papers from thousands of venues. DBIS is much smaller.

\textit{metapath2vec}{} shows impressive results on tasks involving heterogeneous networks, including visualization, classification, and clustering. In Fig. \ref{fig:mp-viz}, PCA is used to project the embeddings of venues and top authors done by the various methods. The embeddings by \textsc{DeepWalk}{} (a) and PTE (b) clustered the authors and venues, but failed to create a meaningful relation between them. \textit{metapath2vec}{} and \textit{metapath2vec+}{} (a variant of \textit{metapath2vec}{}) shows a consistent relationship between each author and its field.

Fig. \ref{fig:mp-cluster} demonstrates how the relations between nodes of a certain type also benefits from \textit{metapath2vec}{}, as the projection of venues naturally lends itself to conferences in the same field being embedded close to each other. Performance in a multi-class classification task also showed superior performance compare to the baseline methods.

\section{Summary}
Methods of network embedding, which are based on research in word embeddings, are described.\footnote{Curiously, the \citet{perozzi2014deepwalk} paper never mentions the term \textit{network embedding} or \textit{graph embedding}, instead focusing on \textit{online learning} and \textit{representation}. The \citet{grover2016node2vec} paper mentions \textit{node embeddings} only once. This perhaps hints at disconnect between different research communities.}
By finding an analogy between documents and graphs, machine learning methods from NLP are successfully generalized to graphs.
The methods, \textsc{DeepWalk}{}, LINE, \textit{node2vec}{}, etc. are able to process very large-scale graphs. Online learning of the latent vector representations of nodes are shown to have superior performance in various tasks, including multiple-label classification and edge prediction. Network embedding is an appropriate target for machine learning, since there are a multitude of underlying patterns in the graphs that are non-trivial to detect programmatically.

A major strength of these network embeddings is the ability to use well-developed data mining and other statistical algorithm (e.g., classification, prediction) for performing network tasks, instead of running discrete, path-, node-, or edge-based graph algorithms. The computational optimization are also an important advantage, as these methods scale to millions of nodes. Some of the issues which still need to be improved upon are the selection of hyper-parameters, and, perhaps most importantly, the interpretability of the embedded vectors. Similarly to word embeddings, while intuitively the method makes sense, there is currently no well-established theory that explains its success.

Extending this research can be done in the direction using network embeddings for different heterogeneous networks, as well as experimenting with the embeddings in other network tasks, e.g. community detection, clustering, and bipartite graph analysis. Also, some of the insights gained from network embeddings (e.g., biased random walks, edge features) can potentially improve methods related to word embeddings back in the NLP domain. Another area for further research is creating  agreed-upon standard benchmarks for comparisons. Currently each paper develops its own experimental configuration. A development of standard benchmarks for network embedding thus has the potential to improve research and results in this area. This lack of standard benchmarks is probably a byproduct of the fact that there is no established theoretical framework for describing and analyzing the various methods and tasks. Finally, these methods are used in static networks. It would be interesting to try and expand methods to dynamic networks, in a way that would not require recalculating embeddings whenever a node or edge are added or removed from the network.

The field of machine-learning-based network embeddings continues to develop, with more techniques appearing regularly.
Finally, the research evolution described, \textit{word2vec}{} (2013) $\rightarrow$ \textsc{DeepWalk}{} (2014) $\rightarrow$ LINE (2015) $\rightarrow$ \textit{node2vec}{} (2016), also demonstrates how quickly ideas propagate within the machine learning community, perhaps a testament to the success of the short-cycle conferences publication ecosystem. I also note that the code, data, and datasets for both the \textsc{DeepWalk}{} and \textit{node2vec}{} papers are available online. Thus, the methods and results can be tested, compared, reproduced, and improved upon. I see this as an essential asset for advancing research in this field.

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redpajama_set_name: RedPajamaArXiv


This classic chart of The Muscular System was illustrated by Peter Bachin in 1947 and continues to be one of the most easily recognized images in medical illustration. Every illustrations is vividly colored and finely detailed. All structures are clearly labeled. The large central illustrations show both anterior and posterior views of the male muscular system. Four smaller illustrations show : the muscles of the right hand, the right half of the diaphragm, muscles of the posterior abdominal wall, muscles of the right foot.


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text:
npc Kahedin
Kahedin
Arthurian characters
Wikipedia, the free encyclopedia
Kahedin is brother to Iseult of Brittany and the son of King
Hoel of Brittany. He had an affair with Brangaine,
the handmaiden of Iseult of Ireland.
first meets Brangaine in the Hall of Images, where he was previously sent to deliver
a message to Iseult of Ireland regarding the arrival of her lover, Sir Tristan.
He conveys the message and Iseult and Tristan spend the night in a wooden cabin.
Meanwhile, Kahedin prepares to spend the night with Brangaine after receiving
favourable advances from her. When they go to bed, however, Kahedin plunges into
a deep sleep and wakes up the following morning to realise that some sorcery must
have been carried out. Out of courtesy, he ignores the happenings of the previous
night and the two couples spend the day together. The same trick is carried out
again that night; on the third night, Iseult manages to convince her maid to surrender
to Kahedin to stop his humiliation. In some versions, Camille, another of the
Queen's handmaidens, is chosen by Kahedin over Brangaine. She also refuses the
knight, wishing to preserve her honour. Iseult then assists by providing Kahedin
with a "magic pillow" after which he falls into a deep
slumber. Kahedin
wakes up the next morning to be taunted by Camille and the ladies of the household;
he travels with Tristan without revealing to him the incident of the previous
Prose Tristan, Kahedin remains Tristan's close companion even after his sister
has been abandoned in Brittany. Like various other knights he falls in love with
the Irish Iseult and eventually dies pining for her.
Worlds of Mankind is owned and created by Mark John Goodwin
text on this page is Open Game Content, and is licensed for public use under the
terms of the Open Game License v1.0a.
System' and the 'd20 System' logo are trademarks of Wizards of
the Coast, Inc.
and are used according to the terms of the d20 System License
A copy of this License can be found at www.wizards.com/d20.