The purpose of the presentation
to introduce the core ideas behind the new model of science of science
to collect critical feedbacks
to push forward the specific projects along this line of thinking
You may ask questions anytime
The Framework: Overview
The Framework: Each Layer
The concept layer: concepts with their logical conenctions, such as theorems connected by ‘prove’
The paper layer: papers connected by citations
The author layer: researchers connected by mentor-mentee relation
Inter layer connections: author-writes-paper, paper-studies-concepts
The Framework: What can be done
Cluserting papers and concepts into topics/fields/discciplines
Evaluate creativity of papers/authors
Get an overview of the whole field, for researchers and administrators
Help the development of science, ultimately
Can also help teachers/learners
The Framework: why a model
A math model for the major elements of Science of Science
A scientometric question becomes a math problem in terms of this math model
Solve it, test it, generalize it into a class of questions and a method of analysis
In short, a math language for the data, questions, method of analysis, ways of thinking
Examples: several systems
Math theorems, connected by ‘prove’, with papers, authors
Chemical reations/reactants connected by reactants/reactions
Diseases-medicine/treatment network
Chinese characters connected by their forms
English words with etymological relation
Examples: method of analysis
Collect data to build up the network, infrastructure
Ask questions and represent them in terms of the network
Seek ways to solve the question
Test, and systemize it of necessary
Network analysis: A combination of direct and indirect connections
Network of Chinese characters
Network of Chinese characters
Optimal learning orders, even personalized
Adaptice diagnostic testing system
Even helps to determine what to learn
Learning orders
From the network, we know $a^{i}_{j}=1,0$ when $i$ is/is not a component of $j$
Normalize each column to get $\tilde{A}$
Solve the following to get $\tilde{W}$, the learning order while $W$ is the known usage frequencies
\begin{equation}
\tilde{W}= \left(1-\tilde{A}\right)^{-1}W= W + \tilde{A}W+\tilde{A}^{2}W+\tilde{A}^{3}W + \cdots
\end{equation}
Effectively, this calculation considers usage frequency, hierarchical structure and degree
Learning orders
Total number of characters and total usage frequencies
Questions
Thank you for your time and critical input
Together, we can make a difference to Science of Science
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