Analytical approach to the model of scientific revolutions

Kondratiuk, Paweł; Siudem, Grzegorz; Hołyst, Janusz A.

doi:10.1103/physreve.85.066126

Cited by 11 publications

(9 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, all these companies are located now much more closely to the SZG vertex than earlier, i.e. during the nucleation process [45][46][47] 2007-01-25 (cf. also our earlier considerations given in Refs.…”

Section: B Dominant Role Of the Szg Companymentioning

confidence: 99%

Temporal condensation and dynamic λ-transition within the complex network: an application to real-life market evolution

et al. 2015

View full text Add to dashboard Cite

Abstract. We fill a void in merging empirical and phenomenological characterisation of the dynamical phase transitions in complex networks by identifying and thoroughly characterising a triple sequence of such transitions on a real-life financial market. We extract and interpret the empirical, numerical, and analytical evidences for the existence of these dynamical phase transitions, by considering the medium size Frankfurt stock exchange (FSE), as a typical example of a financial market. By using the canonical object for the graph theory, i.e. the minimal spanning tree (MST) network, we observe: (i) the (initial) dynamical phase transition from equilibrium to non-equilibrium nucleation phase of the MST network, occurring at some critical time. Coalescence of edges on the FSE's transient leader (defined by its largest degree) is observed within the nucleation phase; (ii) subsequent acceleration of the process of nucleation and the emergence of the condensation phase (the second dynamical phase transition), forming a logarithmically diverging temporal λ-peak of the leader's degree at the second critical time; (iii) the third dynamical fragmentation phase transition (after passing the second critical time), where the λ-peak logarithmically relaxes over three quarters of the year, resulting in a few loosely connected sub-graphs. This λ-peak (comparable to that of the specific heat vs. temperature forming during the equilibrium continuous phase transition from the normal fluid I 4 He to the superfluid II 4 He) is considered as a prominent result of a non-equilibrium superstar-like superhub or a dragon-king's abrupt evolution over about two and a half year of market evolution. We capture and meticulously characterise a remarkable phenomenon in which a peripheral company becomes progressively promoted to become the dragon-king strongly dominating the complex network over an exceptionally long period of time containing the crash. Detailed analysis of the complete trio of the dynamical phase transitions constituting the λ-peak allows us to derive a generic nonlinear constitutive equation of the dragon-king dynamics describing the complexity of the MST network by the corresponding inherent nonlinearity of the underlying dynamical processes.

show abstract

Section: B Dominant Role Of the Szg Companymentioning

confidence: 99%

Temporal condensation and dynamic λ-transition within the complex network: an application to real-life market evolution

et al. 2015

View full text Add to dashboard Cite

show abstract

“…Although one-dimensional systems are frequently used to model social dynamics [17][18][19][20][21], such an approach often suffers from over-simplicity, e.g., one finds no evidence to support the idea that agents related to social interactions are to be distributed on a chain. In this paper we give clear reasons for choosing this very topology.…”

Section: Introductionmentioning

confidence: 99%

Finite size induces crossover temperature in growing spin chains

2014

Self Cite

View full text Add to dashboard Cite

We introduce a growing one-dimensional quenched spin model that bases on asymmetrical one-side Ising interactions in the presence of external field. Numerical simulations and analytical calculations based on Markov chain theory show that when the external field is smaller than the exchange coupling constant J there is a nonmonotonous dependence of the mean magnetization on the temperature in a finite system. The crossover temperature Tc corresponding to the maximal magnetization decays with system size, approximately as the inverse of the Lambert W function. The observed phenomenon can be understood as an interplay between the thermal fluctuations and the presence of the first cluster determined by initial conditions. The effect exists also when spins are not quenched but fully thermalized after the attachment to the chain. By performing tests on real data we conceive the model is in part suitable for a qualitative description of online emotional discussions arranged in a chronological order, where a spin in every node conveys emotional valence of a subsequent post.

show abstract

“…Still, more recent years have seen the appearance of the first models of idea diffusion in scientific communities, including approaches that make use of the Master equation [45] and population dynamics [92] instead of agent models. Among the agent models, several just try to describe the statistical features observed in the studies that measured number of papers and how they are connected by proposing simple rules of influence [26,82,83,67] such as, per example, copying the citations of read papers.…”

Section: Existing Models For Describing Scientific Practicesmentioning

confidence: 99%

Modelling Epistemic Systems

Martins

2013

Intelligent Systems Reference Library

View full text Add to dashboard Cite

In this Chapter, I will explore the use of modeling in order to understand how Science works. I will discuss the modeling of scientific communities, providing a general, non-comprehensive overview of existing models, with a focus on the use of the tools of Agent-Based Modeling and Opinion Dynamics. A special attention will be paid to models inspired by a Bayesian formalism of Opinion Dynamics. The objective of this exploration is to better understand the effect that different conditions might have on the reliability of the opinions of a scientific community. We will see that, by using artificial worlds as exploring grounds, we can prevent some epistemological problems with the definition of truth and obtain insights on the conditions that might cause the quest for more reliable knowledge to fail.

show abstract

Analytical approach to the model of scientific revolutions

Cited by 11 publications

References 25 publications

Temporal condensation and dynamic λ-transition within the complex network: an application to real-life market evolution

Temporal condensation and dynamic λ-transition within the complex network: an application to real-life market evolution

Finite size induces crossover temperature in growing spin chains

Modelling Epistemic Systems

Contact Info

Product

Resources

About