Related papers: Mathematical Model for Hit Phenomena
There is increasing evidence that human activity in general, and narrative in particular, can be treated as a dynamical system in the physics sense; a system whose evolution is described by an action integral, such that the average of all…
Constant and symmetric price impact functions, most commonly used in agent-based market modelling, are shown to give rise to paradoxical and inconsistent outcomes in the simplest case of arbitrage exploitation when open-hold-close actions…
This paper proposes a theory of stock market predictability patterns based on a model of heterogeneous beliefs. In a discrete finite time framework, some agents receive news about an asset's fundamental value through a noisy signal. The…
Large Internet video delivery systems serve millions of videos to tens of millions of users on daily basis, via Video-on-Demand and live streaming. Video popularity evolves over time. It represents the workload, as welll as business value,…
Processes of mass communications in complicated social or sociobiological systems such as marketing, economics, politics, animal populations, etc. as a subject for the special scientific discipline - "mediaphysics" - are considered in its…
Here we numerically study a model of excitable media, namely, a network with occasionally quiet nodes and connection weights that vary with activity on a short-time scale. Even in the absence of stimuli, this exhibits unstable dynamics,…
A mathematical framework for the physics of nonequilibrium phenomena is gradually being developed. This review is meant to shed light on some aspects of Response Theory, on the theory of Fluctuation Relations, on the so-called "t-mixing"…
Can we predict the future popularity of a song, movie or tweet? Recent work suggests that although it may be hard to predict an item's popularity when it is first introduced, peeking into its early adopters and properties of their social…
We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the…
Fake news can have a significant negative impact on society because of the growing use of mobile devices and the worldwide increase in Internet access. It is therefore essential to develop a simple mathematical model to understand the…
A new agent-based, bounded-confidence model for discrete one-dimensional opinion dynamics is presented. The agents interact if their opinions do not differ more than a tolerance parameter. In pairwise interactions, one of the pair, randomly…
Many widely used models amount to an elaborate means of making up numbers--but once a number has been produced, it tends to be taken seriously and its source (the model) is rarely examined carefully. Many widely used models have little…
This paper discusses the mathematical representation of an empirically observed phenomenon, referred to as Incremental Similarity. We discuss this feature from the viewpoint of stochastic processes and present a variety of non-trivial…
Statistical modeling of physical laws connects experiments with mathematical descriptions of natural phenomena. The modeling is based on the probability density of measured variables expressed by experimental data via a kernel estimator. As…
Probabilistic graphical models are a powerful concept for modeling high-dimensional distributions. Besides modeling distributions, probabilistic graphical models also provide an elegant framework for performing statistical inference;…
Human mobility is a fundamental aspect of social behavior, with broad applications in transportation, urban planning, and epidemic modeling. Represented by the gravity model and the radiation model, established analytical models for…
Crime remains one of the significant problems that countries are grappling with globally. With shrinking economies and increasing poverty, crime has been on the rise in many countries. In this paper, we propose a system of non-linear…
The paper discusses the main ideas of the chaos theory and presents mainly the importance of the nonlinearities in the mathematical models. Chaos and order are apparently two opposite terms. The fact that in chaos can be found a certain…
In this paper we consider the modeling of opinion dynamics over time dependent large scale networks. A kinetic description of the agents' distribution over the evolving network is considered which combines an opinion update based on binary…
We propose and analyze numerically a simple dynamical model that describes the firm behaviors under uncertainty of demand forecast. Iterating this simple model and varying some parameters values we observe a wide variety of market dynamics…