Related papers: The Architecture of Complex Systems
Random networks are a powerful tool in the analytical modeling of complex networks as they allow us to write approximate mathematical models for diverse properties and behaviors of networks. One notable shortcoming of these models is that…
We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…
Collaboration networks are studied as an example of growing bipartite networks. These have been previously observed to have structure such as positive correlations between nearest-neighbour degrees. However, a detailed understanding of the…
Short-term survival and an exuberant plunge into building our future are generating a new kind of unintended consequence -- hidden fragility. This is a direct effect of the sophistication and structural complexity of the socio-technical…
We advocate the use of qualitative models in the analysis of large biological systems. We show how qualitative models are linked to theoretical differential models and practical graphical models of biological networks. A new technique for…
The relationship between topology and dynamics of complex systems has motivated continuing interest from the scientific community. In the present work, we address this interesting topic from the perspective of simple games, involving two…
We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.
Large-scale network systems describe a wide class of complex dynamical systems composed of many interacting subsystems. A large number of subsystems and their high-dimensional dynamics often result in highly complex topology and dynamics,…
In this paper, we report on a study of the road networks of the provinces of Canada as complex networks. A number of statistical features have been analyzed and compared with two random models. In addition, we have also studied the…
We review the theory of neural networks, as it has emerged in the last ten years or so within the physics community, emphasizing questions of biological relevance over those of importance in mathematical statistics and machine learning…
The last two decades witnessed tremendous advances in the Information and Communications Technologies. Beside improvements in computational power and storage capacity, communication networks carry nowadays an amount of data which was not…
Recent results on finite open group transformations are reviewed.
Tensor networks provide extremely powerful tools for the study of complex classical and quantum many-body problems. Over the last two decades, the increment in the number of techniques and applications has been relentless, and especially…
Complex software systems are among most sophisticated human-made systems, yet only little is known about the actual structure of 'good' software. We here study different software systems developed in Java from the perspective of network…
Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…
Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…
Just as a herd of animals relies on its robust social structure to survive in the wild, similarly robustness is a crucial characteristic for the survival of a complex network under attack. The capacity to measure robustness in complex…
Great part of the interest in complex networks has been motivated by the presence of structured, frequently non-uniform, connectivity. Because diverse connectivity patterns tend to result in distinct network dynamics, and also because they…
An exposition of the mathematics underpinning the neural network architecture of a GPT-3-style LLM.
We give a brief review on recent developments in the three-dimensional minimal model program.