Related papers: Mathematical Model for Hit Phenomena
We introduce and analyse a three-body consensus model (3CM) for non-linear consensus dynamics on hypergraphs. Our model incorporates reinforcing group effects, which can cause shifts in the average state of the system even in if the…
The broad concept of emergence is instrumental in various of the most challenging open scientific questions -- yet, few quantitative theories of what constitutes emergent phenomena have been proposed. This article introduces a formal theory…
Face-to-face interaction networks describe social interactions in human gatherings, and are the substrate for processes such as epidemic spreading and gossip propagation. The bursty nature of human behavior characterizes many aspects of…
We analyze a mathematical model to understand the dynamics of bullying in schools. The model considers a population divided into four groups: susceptible individuals, bullies, individuals exposed to bullying, and violent individuals.…
The mathematical modeling of crowds is complicated by the fact that crowds possess the behavioral ability to develop and adapt moving strategies in response to the context. For example, in emergency situations, people tend to alter their…
Natural conversations between humans often involve a large number of non-verbal nuanced expressions, displayed at key times throughout the conversation. Understanding and being able to model these complex interactions is essential for…
In this communication, some economic models given by functional mappings are addressed. These are models for random markets where agents trade by pairs and exchange their money in a random and conservative way. They display the exponential…
We model the communication of narratives as a cheap-talk game under model uncertainty. The sender has private information about the true data generating process of publicly observable data. The receiver is uncertain about how to interpret…
Recently research on bubble and its burst attract much interest of researchers in various field such as economics and physics. Economists have been regarding bubble as a disorder in prices. However, this research strategy has overlooked an…
Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct…
We suggest that the broad distribution of time scales in financial markets could be a crucial ingredient to reproduce realistic price dynamics in stylised Agent-Based Models. We propose a fractional reaction-diffusion model for the dynamics…
A first attempt at obtaining market--directional information from a non--stationary solution of the dynamic equation "future price tends to the value that maximizes the number of shares traded per unit time" [1] is presented. We demonstrate…
Pragmatics and non-literal language understanding are essential to human communication, and present a long-standing challenge for artificial language models. We perform a fine-grained comparison of language models and humans on seven…
Internet platforms' traffic defines important characteristics of platforms, such as price of services, advertisements, speed of operations. The traffic is usually estimated with the help of the traditional time series models (ARIMA,…
Two and a half millennia ago Pythagoras initiated the scientific study of the pitch of sounds; yet our understanding of the mechanisms of pitch perception remains incomplete. Physical models of pitch perception try to explain from…
A model for the spreading of online information or "memes" on multiplex networks is introduced and analyzed using branching-process methods. The model generalizes that of [Gleeson et al., Phys.Rev. X., 2016] in two ways. First, even for a…
Suspense is a crucial ingredient of narrative fiction, engaging readers and making stories compelling. While there is a vast theoretical literature on suspense, it is computationally not well understood. We compare two ways for modelling…
This paper presents a probabilistic analysis of what we call the "repeated solicitation model". To give a specific context, suppose B is a direct marketing company with a list of S sales prospects. At epoch 1, B sends a solicitation to…
We introduce a mathematical model on the dynamics of demand and supply incorporating collectability and saturation factors. Our analysis shows that when the fluctuation of the determinants of demand and supply is strong enough, there is…
From the climate system to the effect of the internet on society, chaotic systems appear to have a significant role in our future. Here a method of statistical learning for a class of chaotic systems is described along with underlying…