Microscopic and Macroscopic Simulation of Competition between Languages

Description of spreading dynamics by microscopic network models and macroscopic branching processes can differ due to coalescence

Spreading processes are conventionally monitored on a macroscopic level by counting the number of incidences over time. The spreading process can then be modeled either on the microscopic level, assuming an underlying interaction network, or directly on the macroscopic level, assuming that microscopic contributions are negligible. The macroscopic characteristics of both descriptions are commonly assumed to be identical. In this work, we show that these characteristics of microscopic and macroscopic descriptions can be different due to coalescence, i.e., a node being activated at the same time …

Spin models as microfoundation of macroscopic financial market models

Macroscopic price evolution models are commonly used for investment strategies. There are first promising achievements in defining microscopic agent based models for the same purpose. Microscopic models allow a deeper understanding of mechanisms in the market than the purely phenomenological macroscopic models, and thus bear the chance for better models for market regulation. We exemplify this strategy in a case study, deducing a macroscopic Langevin equation from a microscopic spin market model closely related to the Ising model. The interplay of the microscopic and the macroscopic view allow…

从微观社会力模型到宏观连续模型研究人行流

From microscopic social force models to macroscopic continuum models for pedestrian flow

本文基于微观社会力模型推导出介观和宏观连续模型，通过调整相互作用力探讨不同尺度模型间的联系，并通过数值实验验证模型的有效性。

Agent Based Models of Language Competition: Macroscopic descriptions and Order-Disorder transitions

We investigate the dynamics of two agent based models of language competition. In the first model, each individual can be in one of two possible states, either using language $X$ or language $Y$, while the second model incorporates a third state XY, representing individuals that use both languages (bilinguals). We analyze the models on complex networks and two-dimensional square lattices by analytical and numerical methods, and show that they exhibit a transition from one-language dominance to language coexistence. We find that the coexistence of languages is more difficult to maintain in the …

Modeling self-organized systems interacting with few individuals: from microscopic to macroscopic dynamics

In nature self-organized systems as flock of birds, school of fishes or herd of sheeps have to deal with the presence of external agents such as predators or leaders which modify their internal dynamic. Such situations take into account a large number of individuals with their own social behavior which interact with a few number of other individuals acting as external point source forces. Starting from the microscopic description we derive the kinetic model through a mean-field limit and finally the macroscopic system through a suitable hydrodynamic limit.

Fractional calculus ties the microscopic and macroscopic scales of complex network dynamics

A two-state master equation based decision making model has been shown to generate phase transitions, to be topologically complex and to manifest temporal complexity through an inverse power-law probability distribution function in the switching times between the two critical states of consensus. These properties are entailed by the fundamental assumption that the network elements in the decision making model imperfectly imitate one another. The process of subordination establishes that a single network element can be described by a fractional master equation whose analytic solution yields the…

微观模型中交通波的宏观表现

Macroscopic Manifestations of Traffic Waves in Microscopic Models

本研究分离跟车动力学，提出关联微观与宏观尺度的层级测试方法，建立不稳定区微观模型宏观流量生成方法，基于三类基础场景研究非平衡交通波在基本图的表现，揭示常用微观模型的约化基本图特征，为理解交通波提供因果明确的分析路径。

Modeling self-organization in pedestrians and animal groups from macroscopic and microscopic viewpoints

This paper is concerned with mathematical modeling of intelligent systems, such as human crowds and animal groups. In particular, the focus is on the emergence of different self-organized patterns from non-locality and anisotropy of the interactions among individuals. A mathematical technique by time-evolving measures is introduced to deal with both macroscopic and microscopic scales within a unified modeling framework. Then self-organization issues are investigated and numerically reproduced at the proper scale, according to the kind of agents under consideration.

Highway traffic data: macroscopic, microscopic and criticality analysis for capturing relevant traffic scenarios and traffic modeling based on the highD data set

This work provides a comprehensive analysis on naturalistic driving behavior for highways based on the highD data set. Two thematic fields are considered. First, some macroscopic and microscopic traffic statistics are provided. These include the traffic flow rate and the traffic density, as well as velocity, acceleration and distance distributions. Additionally, the dependencies to each other are examined and compared to related work. The second part investigates the distributions of criticality measures. The Time-To-Collision, Time-Headway and a third measure, which couples both, are analyzed…

二阶多车道交通流模型：从微观到宏观尺度

Second-order multilane traffic flow models: from the microscopic to the macroscopic scale

研究多车道车辆交通建模，从微观到宏观描述，推导出两个二阶宏观模型，通过数值实验和与经验数据对比，发现模型2在定量拟合上更优，能再现复杂交通现象，为交通流分析提供有力工具。

Relating the microscopic rules in coalescence-fragmentation models to the macroscopic cluster size distributions which emerge

Coalescence-fragmentation problems are of great interest across the physical, biological, and recently social sciences. They are typically studied from the perspective of the rate equations, at the heart of such models are the rules used for coalescence and fragmentation. Here we discuss how changes in these microscopic rules affect the macroscopic cluster-size distribution which emerges from the solution to the rate equation. More generally, our work elucidates the crucial role that the fragmentation rule can play in such dynamical grouping models. We focus on two well-known models whose frag…