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After discussing the significance of interactions to understand complex multiscale stochastic systems (CMSS), we turn our attention to the construction of a Generalised Theory of Interactions (GToI). We define interactions as discrete,…
We study the impact of the coupling topology on the ability of various networked dynamical systems to generate extreme events. By determining the coupling strength that is necessary to generate an extreme event in the collective dynamics of…
Causality has traditionally been a scientific way to generate knowledge by relating causes to effects. From an imaginery point of view, causal graphs are a helpful tool for representing and infering new causal information. In previous…
Existence theory in economics is usually in real domains such as the findings of chaotic trajectories in models of economic growth, tatonnement, or overlapping generations models. Computational examples, however, sometimes converge rapidly…
Assuming that Quantum Mechanics is universal and that it can be applied over all scales, then the Universe is allowed to be in a quantum superposition of states, where each of them can correspond to a different space-time geometry. How can…
This paper gives a generative model of the interpretation of formal logic for data-driven logical reasoning. The key idea is to represent the interpretation as likelihood of a formula being true given a model of formal logic. Using the…
We describe a method for inferring linear causal relations among multi-dimensional variables. The idea is to use an asymmetry between the distributions of cause and effect that occurs if both the covariance matrix of the cause and the…
In this paper, we introduce techniques for animating explosions and their effects. The primary effect of an explosion is a disturbance that causes a shock wave to propagate through the surrounding medium. This disturbance determines the…
Bayesian mechanics provides a framework that addresses dynamical systems that can be conceptualised as Bayesian inference. However, elucidating the requisite generative models is essential for empirical applications to realistic…
The present paper presents a new general conception of interaction between physical systems, differing significantly from that of both classical physics and quantum physics as generally understood. We believe this conception could provide…
We advance a statistical theory of extreme event emergence in random nonlinear wave systems with self-similar intermediate asymptotics. We show, within the framework of a generic (1 + 1)D nonlinear Schrodinger equation with linear gain,…
Understanding the evolution of connectivity in spatiotemporal systems requires mathematical frameworks capable of encoding not only instantaneous interactions but also their cumulative causal structure. In this work, we introduce the…
Due to the fact that the numbers of annually published papers have witnessed a linear growth in some citation networks, a geometric model is thus proposed to predict some statistical features of those networks, in which the academic…
The coexistence relation of quantum effects is a fundamental structure, describing those pairs of experimental events that can be implemented in a single setup. Only in the simplest case of qubit effects an analytic characterization of…
We expose a mechanism for the dynamical generation and control of light states with diverse topologies in spiraling guiding structures. Specifically, we show that spiraling shallow refractive index landscapes induce coupling and periodic…
Many integrable physical systems exhibit Keplerian shear. We look at this phenomenon from the point of view of ergodic theory, where it can be seen as mixing conditionally to an invariant $\sigma$-algebra. In this context, we give a…
Macroscopic equations arising out of stochastic particle systems in detailed balance (called dissipative systems or gradient flows) have a natural variational structure, which can be derived from the large-deviation rate functional for the…
In this paper we study the emergence of coherence in collective motion described by a system of interacting motiles endowed with an inner, adaptative, steering mechanism. By means of a nonlinear parametric coupling, the system elements are…
To describe the flow of a miscible quantity on a network, we introduce the graph wave equation where the standard continuous Laplacian is replaced by the graph Laplacian. This is a natural description of an array of inductances and…
Emergence of various properties is mapped in a two-component system from quantum to mesoscale, using Au-Ag alloys. Experiments are designed so that composition is the primary 'interaction' guiding the evolution of properties across…