Two Ways To Understand Reachable Matrix

Last week we have learned how to use adjacency matrix to represent a social network. One question is why the power of matrix can indicate the reachability of social networks. Actually, the matrix mentioned in the class is named reachable matrix.

Let's see how it works. Here, I assume all of us have known the way to do matrix multiplication.

1. The First Way
One simple way to calculate reachable matrix is to regard it as logical operations,(And, Or, Not). We regard 0 and 1 represents false and true respectively.(you can also understand in this way: 0 represents two nodes are not connected; 1 represents two nodes are connected)

Another thing that should be declared is that in logic algebra, numeric operations of multiplication x*y, addition x + y are equal to the respective logical operations of conjunction x∧y, disjunction x∨y. The relevant logic operation rules are shown as below:

Let's review the example, here is a matrix:

Graph below is generated by matrix above: 

The two steps matrix within logic calculation:(which means the reachability going through two steps)

We can see that in X, n6 and n3 are not connected but in X^2 they are. So let's analyze the elements m'63(i=6, j=3).(using m for the elements in X matrix; using m' for the elements in X^2 matrix)

• m'63
  
  m'63=(m61∧m13)∨(m62∧m23)∨(m63∧m33)∨(m64∧m43)∨(m65∧m53)∨(m66∧m63)
  We have know that n6 is not connected with n3 within one step, So if n6 is connected with n3 within two steps, there must be at least one node nx which connects n3 and is connected by n6.
  
  Now look at the calculation process. It means if n6 n1 are connected and at the same time n1 n3 are connected; OR n6 n2 are connected and at the same time n2 n3 are connected;OR....., then n6 n3 are connected.
  
  In this process, only (m62∧m23) is equal to 1, others are all zero. So the path should be 6->2->3.

The thinking way is the same with the situation of more steps.

2. The Second Way
Another way to think this is to multiple matrix in normal way. With the foundation above, we can deepen our understanding.

The two steps matrix within normal way calculation:

With the knowledge in FIRST PART, we have understood the meaning of non-zero elements. Now let's analyze the elements m'16 and m'22

• m'16
  m'16=m11*m16+m12*m26+m13*m36+m14*m46+m15*m56+m16*m66
  We can see that only :
  
  m12*m26 =1
  m15*m56 =1
  Others are all equal to zero. So 
  m'16=m12*m26+m15*m56=2
  And you must find that 2 represents that there are two paths which make n1 n6 connected. Obviously, the paths can be 1->2->6 and 1->5->6
  
  
• m'22
  It is easy to find that two paths are 2->3->2 and 2->6->2

The thinking way is the same with the situation of more steps.

If you have any question, pls feel free to discuss with me.

Hope you enjoy this!

Difference Between Individual Work And Group Work

We've learned about communication and socail behavior on the Internet in last 2 lectures. And we had  activities which help us understand some theory deeply. After that, I thought more about what we learned in the class, and I'd like to share my view with others.

In this post, I will answer the questions mentioned in the class.

Answers of Activities

The answer of these two activities are shown as below (the answers are the same)

Q1. What is the definition of Social Cloud?

A1. A Social Cloud is a resource and service sharing framework utilizing relationships established between members of a social network.

Q2. What are the possible applications of a Social Cloud?

A2. A Social Computation Cloud

   A Social Storage Cloud

   A Social Collaborative Cloud

   A Social Cloud for Public Science

   An Enterprise Social Cloud

Difference In Epistemic Aims

Firstly, I want to mention about the JTB theory.

A subject S knows that a proposition P is true if and only if:
 1.P is true
 2.S believes that P is true, and
 3.S is justified in believing that P is true

In individual work, the epistemic aim is understanding the reading material,  finding out the answer of question and forming belief. In this process, our behavior reflect the second point of JTB theory: believe our answer is true.

In group work, I do think the epistemic aim changes. Since we have already understood the material and found the answer, understanding and finding out can't be regarded as our aim. In most case, we consider the answer which most people give as right. In this process, what we do is justifing whether our answer is true or not. So it reflects the third point of JTB theory: we are justified in believing our answer is true.

Difference In Epistemic Cognition

In individual work, people have no chance to communicate with others about their idea, and they might not be very sure about their answer, their idea, their view, etc. at the stage of certainty of knowing and criteria of knowing. And there are less things inspires people to generate new ideas.

However, in group work, by sharing their own ideas with others, people can find an answer more quick; by learning from others and discussing the issue with others, people can produce new knowledge more easily.

Our group changed our focus point after knowing our answers are the same. We discussed things we wanted to know and problems from the article etc..

 

Difference In Processes

I think the activities might not reflect the social behavior completely.The first reason is that in the second activity we have already find our own answer. The second reason is that the questions are very simple.

Firstly, you may notice a phenomenon that there are always few people doing nothing in a group work.(what we say "打酱油" in Chinese) So, If the article in Activity Two is different from Activity One, people mentioned above may show this character.

Secondly, as many students said, the questions are quite easy and almost everyone could affirm the answer. Students always check answers of advanced math homework during their university life. Why? Because the questions are very complicated and confirmation degree of such questions is lower than simple questions. In addition, with many controversial issue, different people hold different stand. So when questions given are complicated or controversial, the difference between  individual work and group work will be more obvious.

Reference:

[1]http://en.wikipedia.org/wiki/Justified_true_belief

[2]http://www.dic123.com/A/7/7F/7FD_25815.html

[3]http://www.docin.com/p-438217766.html

Cogntion of 3 Levels & Current Social Networks

Last two weeks we mainly learned about social psychology and cognition. Firstly, let's review the basic concept of cognition and have a better understand of it. Then I'll analyze the current social networks with relevant knowledge.

Part 1.

As the picture below showing, cognition can be divided into three different levels.



fig1. Hierarchy of Cognition

Even though a detail explanation of these 3 levels were given in the class, it was still very hard to understand the concept very clearly, especially the highest level--epistemic cognition. In my view, from the bottom up, the cognition is from wide to deep. It also indicates that the higher the level is, the more difficulty to reach the level.

 

To understand this more specifically, let's think about the library.

• There are a huge number of books in a library, and we can regard them as data which in the bottom of the triangle model. We feel this like an ocean containing all the data that we need and we don't need.
• We try to find books we need, read those books and get useful information from the book. And this can be regarded as the middle of the triangle model. During this period, we may deal with those information in many ways (e.g. categorize information, take notes, and  keep them in mind).
• After we gain the information from books, we could come with new ideas by ourselves. Discussing with others is also a good way to help us create new ideas. We make information become systemic and orderly, then transform information as knowledge. This process is just like the top of the triangle model. Another appropriate description of the 3rd level would be a  Chinese proverb: "Consider the past, and you shall know the future. "(温故而知新)

Part 2.

Now we get a clear view of 3 levels cognition, so let's see how current social networks reflecting these 3 levels.

Here I will analyze one of the most popular SNS--Weibo.com in Mainland China. It has the same function with twitter.com, but is localized in many details. In this case, the  presentation of 3 levels depends on different users (only high level users are considered in this passage).  



fig2. Interface of weibo.com

• In the home page, we can see numerous messages posted by the people we following. Those messages can be regarded as data in the bottom of triangle model. In this stage, messages are in a mess, and we can not distinguish which we would be more interested at our first sight.
• In the 2nd stage, we read the messages and find those interesting ones then retweet them or/and mark them as our favourite. And tags are also available. This kind of behavior helps information spread very rapidly.
• In the 3rd stage, users may use the function of twteet, comment and reply to share their ideas, to discuss their point of views. The authenticity of the information is usually uncertain, but I think the majority of high level users (within epistemic cognition level) can discriminate easily while still some users operate without thinking. Users on the 3rd level transform the useful information as knowledge, improve their thinking capacity and discernment.

In conclusion, we can see that current SNS has contained the elements of 3 levels cognition, but the showing level of cognition depends on user quality. We also can see that high level users contribute more in SNS (they seldom spread rumors), so in order to facilitate the development of SNS the future trend would be guiding low level users to high level. However, there is no such method now. I'm dying to know it. How about you?

Reference
[1] Class Notes (week3, week4)
[2] http://www.quora.com/Cognition/What-is-Epistemic-Cognition

Viewing Differences Between Social Media With Social Networking From Digg.com

Digg.com delivers the most interesting and talked about stories on the Internet right now. The Internet is full of great stories, and Digg helps users find, read, and share the very best ones. It is a typical web2.0 website and it combines social media with social networking very well.

We have gained a clear concept of both social media and social networking, but not web2.0. So I will introduce this first.

Web 2.0 is a concept that takes the network as a platform for information sharing, interoperability, user-centered design, and collaboration on the Internet or World Wide Web. A Web 2.0 site allows users to interact and collaborate with each other in a social media dialogue as creators (prosumers) of user-generated content in a virtual community, in contrast to websites where users (consumers) are limited to the passive viewing of content that was created for them. Examples of Web 2.0 include social networking sites, blogs, wikis, video sharing sites, hosted services, web applications, mashups and folksonomies. 

Users on digg.com participate in social interaction.
They generate content by submit a link to Digg, to share a new story for other users on Digg.

fig.1

They give stories a digg to show their preference, and share stories for friends on facebook or tweet.

fig.2

By generating stories, digging stories, sharing stories,  users change their traditional way to discover news, read news and share news. Meanwhile, the information is disseminated by these social interaction.

As we can see, digg.com will select the most popular stories and show them on the home page of digg.com., so users can always read those most interesting and talked about stories. However, there is no relationship between users of digg, they are just like strangers and contribute to digg index as a whole. To another words, users can not build a relationship on digg.com, they can just see what majority interested in and can't find those who have the same interest, what they focus on is the content rather than connection. From this aspect, digg.com shows obvious features of social media and web2.0.

To make this social media more sociable, digg.com cooperates with facebook and tweet. To facilitate the share of information on digg.com, it puts a share button below every story. Instead of building new relationship, it introduce the users' existent connection from other social network(FB and TW).Users can easily click the button and share it on their facebook or tweet.

In terms of social networking, like facebook and tweet(focus on connection), users share stories from digg to facebook or tweet, discover those who have the same interest, build and enhance their relationship.

In conclusion, information from social media helps people to discover the possibility of    connection and social networking builds and enhances that connection. Stories from digg help people to find like-minded friends, facebook helps people keep relationship with these friends, new stories from digg make people find more common character, interaction on facebook deepen the relationship...The process forms a positive circle, so I think social media like digg and social networking like facebook and tweet facilitate the development of each other.

Reference:

[1]http://digg.com/about

[2]http://en.wikipedia.org/wiki/Web_2.0

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