Related papers: A model for dynamical evolution of science in spac…
Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…
In this paper, we examine how patterns of scientific collaboration contribute to knowledge creation. Recent studies have shown that scientists can benefit from their position within collaborative networks by being able to receive more…
Population structure induced by both spatial embedding and more general networks of interaction, such as model social networks, have been shown to have a fundamental effect on the dynamics and outcome of evolutionary games. These effects…
Free actions of finite groups on spheres give rise to topological spherical space forms. The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. In this article, we present a…
Exact string solutions are presented, where moduli fields are varying with time. They provide examples where a dynamical change of the topology of space is occurring. Some other solutions give cosmological examples where some dimensions are…
The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge…
The notion of a coherent space is a nonlinear version of the notion of a complex Euclidean space: The vector space axioms are dropped while the notion of inner product is kept. Coherent spaces provide a setting for the study of geometry in…
The selection of research topics by scientists can be viewed as an exploration process conducted by individuals with cognitive limitations traversing a complex cognitive landscape influenced by both individual and social factors. While…
In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by…
Despite persistent efforts in revealing the temporal patterns in scientific careers, little attention has been paid to the spatial patterns of scientific activities in the knowledge space. Here, drawing on millions of papers in six…
Due to the fact that the numbers of annually published papers have witnessed a linear growth in some citation networks, a geometric model is thus proposed to predict some statistical features of those networks, in which the academic…
Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…
One of the most interesting scientific challenges nowadays deals with the analysis and the understanding of complex networks' dynamics. A major issue is the definition of new frameworks for the exploration of the dynamics at play in real…
A topological dynamical system induces two natural systems, one is on the hyperspace and the other one is on the probability space. The connection among some dynamical properties on the original space and on the induced spaces are…
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…
Science mapping (SM), the study of the organization and development of science and technology, is a rapidly developing field within information science. The volume of available data allows this methodology to empirically address such issues…
Ecological systems show a variety of characteristic patterns of biodiversity in space and time. It is a challenge for theory to find models that can reproduce and explain the observed patterns. Since the advent of island biogeography these…
Hyperspaces form a powerful tool in some branches of mathematics: lots of fractal and other geometric objects can be viewed as fixed points of some functions in suitable hyperspaces - as well as interesting classes of formal languages in…
The editorial handling of papers in scientific journals as a human activity process is considered. Using recently proposed approaches of human dynamics theory we examine the probability distributions of random variables reflecting the…
We study the cosmological stability of a class of theories with a dynamical preferred frame. For a range of actions, we find cosmological solutions which are compatible with observations of the recent history of the Universe: a matter…