A New Model of Science of Science

Jinshan Wu

School of Systems Science

Beijing Normal University

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

MultilayerFramework

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

MultilayerFramework

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

TotalCharactersTotalFrequencies

Back to the new model of Sci${^2}$

  • Measure creativity, novalty of papers/authors, coreness or fundamentality concepts of a discipline
  • Show the more general hierarchical structure of a discipline
  • Suggest plausible concepts/links to work on
  • All become a math problem over the new model?
  • Solve it and test it?

Questions

  • Thank you for your time and critical input
  • Together, we can make a difference to Science of Science

IESS|The Big Physics Team