Related papers: Polynomial Life: the Structure of Adaptive Systems
We study systems of interacting reinforced stochastic processes, where agents' decisions evolve under reinforcement, network-mediated interactions, and environmental influences. In competitive environments with irreducible networks, we…
We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally…
Characterizing structural and dynamic properties of proteins and large macromolecular assemblies is crucial to understand the molecular mechanisms underlying biological functions. In the field of Structural Biology, no single method…
Extremal principles are fundamental in our interpretation of phenomena in nature. One of the best known examples is the second law of thermodynamics, governing most physical and chemical systems and stating the continuous increase of…
Biological systems often choose actions without an explicit reward signal, a phenomenon known as intrinsic motivation. The computational principles underlying this behavior remain poorly understood. In this study, we investigate an…
The first part of the book is devoted to the symmetry approach to classification of scalar integrable evolution PDEs with two independent variables. In the second part systems of evolution equations with polynomial homogeneous right-hand…
Some of the most common mathematical models in biology, chemistry, physics, and engineering, are polynomial dynamical systems, i.e., systems of differential equations with polynomial right-hand sides. Inspired by notions and results that…
Conventional economic and socio-behavioural models assume perfect symmetric access to information and rational behaviour among interacting agents in a social system. However, real-world events and observations appear to contradict such…
The free energy principle, and its corollary active inference, constitute a bio-inspired theory that assumes biological agents act to remain in a restricted set of preferred states of the world, i.e., they minimize their free energy. Under…
This technical note considers the sampling of outcomes that provide the greatest amount of information about the structure of underlying world models. This generalisation furnishes a principled approach to structure learning under a…
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
In this paper I elaborated on the idea of David Harel and Amir Pnueli to think systems and their interaction from the point of view of their compositional behaviour. The obvious idea to base the composition of systems on the concept of…
Alignment interactions in active matter are typically modeled as relaxational dynamics toward local consensus. In unbounded systems, this makes alignment effectively decoupled from local density and therefore unable to sustain self-confined…
We present experiments on the collective dynamics of macroscopic photoactive self-propelled particles subjected to spatiotemporally varying excitation. The particles move within an arena divided into two regions with different illumination…
The collective response of a system is profoundly shaped by the interaction dynamics between its constituent elements. In physics, tailoring these interactions can enable the observation of unusual phenomena that are otherwise inaccessible…
We investigate the dynamics of forward or backward self-similar systems (iterated function systems) and the topological structure of their invariant sets. We define a new cohomology theory (interaction cohomology) for forward or backward…
A portrait is a combinatorial model for a discrete dynamical system on a finite set. We study the geometry of portrait moduli spaces, whose points correspond to equivalence classes of point configurations on the affine line for which there…
The capacity of an embodied agent to understand, predict, and interact with its environment is fundamentally contingent on an internal world model. This paper introduces a novel framework for investigating the formation and adaptation of…
Active inference helps us simulate adaptive behavior and decision-making in biological and artificial agents. Building on our previous work exploring the relationship between active inference, well-being, resilience, and sustainability, we…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…