Related papers: Scale-invariance underlying the logistic equation …
A large computer program is typically divided into many hundreds or even thousands of smaller units, whose logical connections define a network in a natural way. This network reflects the internal structure of the program, and defines the…
The frequency and magnitude of weather extreme events have increased significantly during the past few years in response to anthropogenic climate change. However, global statistical characteristics and underlying physical mechanisms are…
Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were…
To understand the growing phenomena of new vocabulary on nationwide online social media, we analyzed monthly word count time series extracted from approximately 1 billion Japanese blog articles from 2007 to 2019. In particular, we first…
Test-time compute scaling has emerged as a powerful paradigm for enhancing mathematical reasoning in large language models (LLMs) by allocating additional computational resources during inference. However, current methods employ uniform…
In this paper, we study the statistical evolution of the large-scale structure (LSS), focusing on the joint probability distribution function (PDF) of the coarse-grained cosmic field and its role in constructing effective dynamics. As the…
A celebrated and controversial hypothesis conjectures that some biological systems --parts, aspects, or groups of them-- may extract important functional benefits from operating at the edge of instability, halfway between order and…
Here we describe how some important scaling laws observed in the distribution of languages on Earth can emerge from a simple computer simulation. The proposed language dynamics includes processes of selective geographic colonization,…
The paper investigates the properties of a class of resource allocation algorithms for communication networks: if a node of this network has $x$ requests to transmit, then it receives a fraction of the capacity proportional to $\log(1+x)$,…
Understanding how language model performance varies with scale is critical to benchmark and algorithm development. Scaling laws are one approach to building this understanding, but the requirement of training models across many different…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
Emergent technologies such as solar power, electric vehicles, and artificial intelligence (AI) often exhibit exponential or power function price declines and various ``S-curves'' of adoption. We show that under CES and VES utility, such…
In this chapter the complex systems are discussed in the context of economic and business policy and decision making. It will be showed and motivated that social systems are typically chaotic, non-linear and/or non-equilibrium and therefore…
Even though people in our contemporary, technological society are depending on communication, our understanding of the underlying laws of human communicational behavior continues to be poorly understood. Here we investigate the…
Many real-world processes evolve in cascades over complex networks, whose topologies are often unobservable and change over time. However, the so-termed adoption times when blogs mention popular news items, individuals in a community catch…
We present a theory for the growth dynamics of the World Wide Web that takes into account the wide range of stochastic growth rates in the number of pages per site, as well as the fact that new sites are created at different times. This…
A birth-death lattice gas model about the influence of an environment on the fitness and concentration evolution of economic entities is analytically examined. The model can be mapped onto a high order logistic map. The control parameter is…
A large-scale service system with multiple customer classes and multiple server pools is considered, with the mean service time depending both on the customer class and server pool. The allowed activities (routing choices) form a tree (in…
An important side effect of the evolution of the human brain is an increased capacity to form opinions in a very large domain of issues, which become points of aggressive interpersonal disputes. Remarkably, such disputes are often no less…
Scalar inferences (SI) are a signature example of how humans interpret language based on unspoken alternatives. While empirical studies have demonstrated that human SI rates are highly variable -- both within instances of a single scale,…