Related papers: Interaction spaces: towards a universal mathematic…

Dynamical systems are a broad class of mathematical tools used to describe the evolution of physical and computational processes. Traditionally these processes model changing entities in a static world. Picture a ball rolling on an empty…

As AI systems enter into a growing number of societal domains, these systems increasingly shape and are shaped by user preferences, opinions, and behaviors. However, the design of AI systems rarely accounts for how AI and users shape one…

To study implementations and optimisations of interaction net systems we propose a calculus to allow us to reason about nets, a concrete data-structure that is in close correspondence with the calculus, and a low-level language to create…

Complex systems' modeling and simulation are powerful ways to investigate a multitude of natural phenomena providing extended knowledge on their structure and behavior. However, enhanced modeling and simulation require integration of…

The growing complexity of modern practical problems puts high demands on the mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice becomes…

We study the dynamics of a system composed of interacting units each with a complex internal structure comprising many subunits. We consider the case in which each subunit grows in a multiplicative manner. We propose a model for such…

Network theory provides tools which are particularly appropriate for assessing the complex interdependencies that characterise our modern connected world. This article presents an introduction to network theory, in a way that doesn't…

The transition structure of an automaton can be used to create a natural topology to the set of states of an automaton, generating, this way, a topological space. Probabilistic automata can also be modeled in terms of measure theory. A…

We review and develop a selection of models of systems with competition and cooperation, with origins in economics, where deep insights can be obtained by the mathematical methods of game theory. Some of these models were touched upon in…

Explanations have gained an increasing level of interest in the AI and Machine Learning (ML) communities in order to improve model transparency and allow users to form a mental model of a trained ML model. However, explanations can go…

We consider the basic features of complex dynamical and control systems. Special attention is paid to the problems of synthesis of dynamical models of complex systems, construction of efficient control models, and to the development of…

As full AI-based automation remains out of reach in most real-world applications, the focus has instead shifted to leveraging the strengths of both human and AI agents, creating effective collaborative systems. The rapid advances in this…

The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a great variety of complex systems has been successfully described as networks whose…

Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range models. Therefore…

Traffic jams on roadways, echo chambers on social media, crowds of moving pedestrians, and opinion dynamics during elections are all complex social systems. These applications may seem disparate, but some of the questions that they motivate…

As large language models (LLMs) continue to make significant strides, their better integration into agent-based simulations offers a transformational potential for understanding complex social systems. However, such integration is not…

We offer an insight into our mathematical endeavors, which aim to advance the foundational understanding of energy systems in a broad context, encompassing facets such as charge transport, energy storage, markets, and collective behavior.…

Interface theories are powerful frameworks supporting incremental and compositional design of systems through refinements and constructs for conjunction, and parallel composition. In this report we present a first Interface Theor -- |Modal…

Transformers play a central role in the inner workings of large language models. We develop a mathematical framework for analyzing Transformers based on their interpretation as interacting particle systems, which reveals that clusters…

The development of AI agents based on large, open-domain language models (LLMs) has paved the way for the development of general-purpose AI assistants that can support human in tasks such as writing, coding, graphic design, and scientific…