Related papers: A short-ranged memory model with preferential grow…
In this paper we develop an Expectation Maximization(EM) algorithm to estimate the parameter of a Yule-Simon distribution. The Yule-Simon distribution exhibits the "rich get richer" effect whereby an 80-20 type of rule tends to dominate.…
The diffusion of ideas and language in society has conventionally been described by S-shaped models, such as the logistic curve. However, the role of sub-exponential growth -- a slower-than-exponential pattern known in epidemiology -- has…
Motivated by the psychological literature on the "peak-end rule" for remembered experience, we perform an analysis within a random walk framework of a discrete choice model where agents' future choices depend on the peak memory of their…
Memories are stored, retained, and recollected through complex, coupled processes operating on multiple timescales. To understand the computational principles behind these intricate networks of interactions we construct a broad class of…
Active systems across scales, ranging from molecular machines to human crowds, are usually modeled as assemblies of self-propelled particles driven by internally generated forces. However, these models often assume memoryless dynamics and…
This article presents a new continuous-time modelling framework for multivariate time series of counts which have an infinitely divisible marginal distribution. The model is based on a mixed moving average process driven by L\'{e}vy noise -…
Popularity describes the dynamics of mass attention, and is a part of a broader class of population dynamics in ecology and social science literature. Studying accurate model of popularity is important for quantifying spreading of novelty,…
The paper is a follow-up of the recently introduced kernel-based framework to identify nonlinear input-output systems regularized by desirable input-output incremental properties. Assuming that the system has fading memory, we propose to…
We study the evolution of the population genealogy in the classic neutral Moran Model of finite size and in discrete time. The stochastic transformations that shape a Moran population can be realized directly on its genealogy and give rise…
Solar flares, email exchanges, and many natural or social systems exhibit bursty dynamics, with periods of intense activity separated by long inactivity. These patterns often follow power- law distributions in inter-event intervals or event…
In some social networks, the opinion forming is based on its own and neighbors' (initial) opinions, whereas the evolution of the individual opinions is also influenced by the individual's past opinions in the real world. Unlike existing…
The random utility model (RUM, McFadden and Richter, 1990) has been the standard tool to describe the behavior of a population of decision makers. RUM assumes that decision makers behave as if they maximize a rational preference over a…
The mathematical model of a linear system with the short memory about own stochastic behavior is proposed. It is assumed that the system is under a continual influence of independent stochastic impulses. In a short memory approximation the…
The purpose of this paper relies on the study of long term yield curves modeling. Inspired by the economic litterature, it provides a financial interpretation of the Ramsey rule that links discount rate and marginal utility of aggregate…
Memory has a great impact on the evolution of every process related to human societies. Among them, the evolution of an epidemic is directly related to the individuals' experiences. Indeed, any real epidemic process is clearly sustained by…
We propose a single chunk model of long-term memory that combines the basic features of the ACT-R theory and the multiple trace memory architecture. The pivot point of the developed theory is a mathematical description of the creation of…
This paper studies a one-sector optimal growth model with i.i.d. productivity shocks that are allowed to be unbounded. The utility function is assumed to be non-negative and unbounded from above. The novel feature in our framework is that…
We propose a stochastic model of web user behaviors in online social systems, and study the influence of attraction kernel on statistical property of user or item occurrence. Combining the different growth patterns of new entities and…
We study a random graph model with preferential edge attachment and detachment through the embedding into a generalized Yule model. We show that the in-degree distribution of a vertex chosen uniformly at random follows a power law in the…
Time evolution of number of species (genera, families, and others), population of them, and size distribution of present ones and life times are studied in terms of a new model, where population of each genetic taxon increases by a (random)…