Related papers: The averaging principle
This article analyzes the problem of estimating the time until an event occurs, also known as survival modeling. We observe through substantial experiments on large real-world datasets and use-cases that populations are largely…
In nature and human societies, the effects of homogeneous and heterogeneous characteristics on the evolution of collective behaviors are quite different from each other. It is of great importance to understand the underlying mechanisms of…
We introduce a two-parameter ensemble of random discrete-time Markov models that simultaneously captures critical slowing down and broken detailed balance. Extending a previously studied heterogeneous Markov ensemble, we incorporate…
This chapter introduces the \emph{random-order model} in online algorithms. In this model, the input is chosen by an adversary, then randomly permuted before being presented to the algorithm. This reshuffling often weakens the power of the…
There is increasing regulatory interest in whether machine learning algorithms deployed in consequential domains (e.g. in criminal justice) treat different demographic groups "fairly." However, there are several proposed notions of…
The method of model averaging has become an important tool to deal with model uncertainty, for example in situations where a large amount of different theories exist, as are common in economics. Model averaging is a natural and formal…
We present an extensive study of the joint effects of heterogeneous social agents and their heterogeneous social links in a bounded confidence opinion dynamics model. The full phase diagram of the model is explored for two different…
A hybrid model for opinion dynamics in complex multi-agent networks is introduced, wherein some continuous-valued agents average neighbors' opinions to update their own, while other discrete-valued agents use stochastic copying and voting…
In many applications, data can be heterogeneous in the sense of spanning latent groups with different underlying distributions. When predictive models are applied to such data the heterogeneity can affect both predictive performance and…
Molecular phylogenetic and phylogeographic reconstructions generally assume time-homogeneous substitution processes. Motivated by computational convenience, this assumption sacrifices biological realism and offers little opportunity to…
Items in modern recommender systems are often organized in hierarchical structures. These hierarchical structures and the data within them provide valuable information for building personalized recommendation systems. In this paper, we…
We consider homogenization of random surfaces and study the variational principle for graph homomorphisms from subsets of $\mathbb{Z}^m$ into $\mathbb{Z}$, where the underlying uniform measure is perturbed by a random field. Motivated by…
Heterogeneity of many building materials complicates numerical modelling of structural behaviour. The material randomicity can be manifested by different values of material parameters of each material specimen. To capture inherent…
Covarion models of character evolution describe inhomogeneities in substitution processes through time. In phylogenetics, such models are used to describe changing functional constraints or selection regimes during the evolution of…
Agglomeration economies drive urban growth at different spatial scales by enabling productivity gains, knowledge spillovers, and shared inputs among proximate firms and amenities. To develop a unified science of cities it is thus important…
Our societies are heterogeneous in many dimensions such as census, education, religion, ethnic and cultural composition. The links between individuals - e.g. by friendship, marriage or collaboration - are not evenly distributed, but rather…
Natural and artificial collectives exhibit heterogeneities across different dimensions, contributing to the complexity of their behavior. We investigate the effect of two such heterogeneities on collective opinion dynamics: heterogeneity of…
We propose a generic model for multiple choice situations in the presence of herding and compare it with recent empirical results from a Web-based music market experiment. The model predicts a phase transition between a weak imitation phase…
We introduce a very general model of an inhomogenous random graph with independence between the edges, which scales so that the number of edges is linear in the number of vertices. This scaling corresponds to the p=c/n scaling for G(n,p)…
One widely-existed state --``harmony with diversity" in which individuals freely express various viewpoints to sustain integration of social diversity, but at the same time shared values ensure social coherence, can be considered as the…