Related papers: A simple model of knowledge percolation
From some observations on economic behaviors, in particular changing economic conditions with time and space, we develop a very simple model for the evolution of economic entities within a geographical type of framework. We raise a few…
The growth of science and technology is a recombinative process, wherein new discoveries and inventions are built from prior knowledge. Yet relatively little is known about the manner in which scientific and technological knowledge develop…
Clustering provides a common means of identifying structure in complex data, and there is renewed interest in clustering as a tool for the analysis of large data sets in many fields. A natural question is how many clusters are appropriate…
Science is increasingly dominated by teams. Understanding patterns of scientific collaboration and their impacts on the productivity and evolution of disciplines is crucial to understand scientific processes. Electronic bibliography offers…
One of the most intriguing dynamics in biological systems is the emergence of clustering, the self-organization into separated agglomerations of individuals. Several theories have been developed to explain clustering in, for instance,…
In this paper, we generalize epistemic logic so that it can help reason about ways of combining common knowledge and distributed knowledge such as "common distributed knowledge", "distributed common knowledge", "distributed common…
When presented with information of any type, from music to language to mathematics, the human mind subconsciously arranges it into a network. A network puts pieces of information like musical notes, syllables or mathematical concepts into…
Percolation is a paradigmatic model in disordered systems and has been applied to various natural phenomena. The percolation transition is known as one of the most robust continuous transitions. However, recent extensive studies have…
Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…
Collective phenomena emerge from the interaction of natural or artificial units with a complex organization. The interplay between structural patterns and dynamics might induce functional clusters that, in general, are different from…
We analyze a distributed information network in which each node has access to the information contained in a limited set of nodes (its neighborhood) at a given time. A collective computation is carried out in which each node calculates a…
This is an evolving document. It is devoted to summarizing patterns and laws of knowledge growth. By examining a variety of parameters in data sources such as Wikipedia and Microsoft Academic Graph, we can get deeper insights of how…
We consider the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over…
In formal epistemology, group knowledge is often modelled as the knowledge that the group would have, if the agents shared all their individual knowledge. However, this interpretation does not account for relations between agents. In this…
A new ``Percolation with Clustering'' (PWC) model is introduced, where (the probabilities of) site percolation configurations on the leaf set of a binary tree are rewarded exponentially according to a generic function, which measures the…
In domains with high knowledge distribution a natural objective is to create principle foundations for collaborative interactive learning environments. We present a first mathematical characterization of a collaborative learning group, a…
Knowledge distillation aims to transfer useful information from a teacher network to a student network, with the primary goal of improving the student's performance for the task at hand. Over the years, there has a been a deluge of novel…
A self-organized model with social percolation process is proposed to describe the propagations of information for different trading ways across a social system and the automatic formation of various groups within market traders. Based on…
Knowledge plays a critical role in artificial intelligence. Recently, the extensive success of pre-trained language models (PLMs) has raised significant attention about how knowledge can be acquired, maintained, updated and used by language…
Macroscopic properties of heterogeneous media are frequently modelled by regular lattice models, which are based on a relatively small basic cluster of lattice sites. Here, we extend one of such models to any cluster's size kxk. We also…