Related papers: A stochastic model of discussion
We consider a Levy flyer of order alpha that starts from a point x0 on an interval [O,L] with absorbing boundaries. We find a closed-form expression for the average number of flights the flyer takes and the total length of the flights it…
We present a new microscopic stochastic model for an ensemble of interacting investors that buy and sell stocks in discrete time steps via limit orders based on individual forecasts about the price of the stock. These orders determine the…
The L\'evy walk process for the lower interval of the time of flight distribution ($\alpha<1$) and with finite resting time between consecutive flights is discussed. The motion is restricted to a region bounded by two absorbing barriers and…
In this work, we propose an approach for detecting conversation groups in social scenarios like cocktail parties and networking events, from overhead camera recordings. We posit the detection of conversation groups as a learning problem…
The L\'evy walk model is a stochastic framework of enhanced diffusion with many applications in physics and biology. Here we investigate the time averaged mean squared displacement $\bar{\delta^2}$ often used to analyze single particle…
The analysis of social networks, in particular those describing face-to-face interactions between individuals, is complex due to the intertwining of the topological and temporal aspects. We revisit them both, using public data recorded by…
The so-called Deffuant model describes a pattern for social interaction, in which two neighboring individuals randomly meet and share their opinions on a certain topic, if their discrepancy is not beyond a given threshold $\theta$. The…
Population dynamics of individuals undergoing birth and death and diffusing by short or long ranged twodimensional spatial excursions (Gaussian jumps or L\'{e}vy flights) is studied. Competitive interactions are considered in a global case,…
We consider a preferential cluster growth in a one-dimensional stochastic model describing the dynamics of a binary chain with long-range memory. The model is driven by data corresponding to emotional patterns observed during online…
The L\'evy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha>1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a…
A biological competition model where the individuals of the same species perform a two-dimensional Markovian continuous-time random walk and undergo reproduction and death is studied. The competition is introduced through the assumption…
We propose models describing the collective dynamics of two opposing groups of individuals with stochastic communication. Individuals from the same group are assumed to align in a stochastic manner, while individuals from different groups…
Social dynamics determined by voting in a stochastic environment is analyzed for a society composed of two cohesive groups of similar size. Within the model of random walks determined by voting, explicit formulas are derived for the capital…
A L\'evy random medium, in a given space, is a random point process where the distances between points, a.k.a. targets, are long-tailed. Random walks visiting the targets of a L\'evy random medium have been used to model many (physical,…
We study a stochastic multiplicative system composed of finite asynchronous elements to describe the wealth evolution in financial markets. We find that the wealth fluctuations or returns of this system can be described by a walk with…
A class of stochastic individual-based models, written in terms of coupled velocity jump processes, is presented and analysed. This modelling approach incorporates recent experimental findings on behaviour of locusts. It exhibits nontrivial…
In this paper, we focus on the stochastic block model (SBM),a probabilistic tool describing interactions between nodes of a network using latent clusters. The SBM assumes that the networkhas a stationary structure, in which connections of…
This article is concerned with a mutualism ecological model with Levy noise. The local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is studied.…
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…
The ordinary contact process is used to model the spread of a disease in a population. In this model, each infected individual waits an exponentially distributed time with parameter 1 before becoming healthy. In this paper, we introduce and…