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This article is concerned with the existence, status and description of the so-called emergent phenomena believed to occur in certain principally planar electronic systems. In fact, two distinctly different if inseparable tasks are…

We describe the geometric structures involved in the variational formulation of physical theories. In presence of these structures, the constitutive set of a physical system can be generated by a family of functions. We discuss conditions,…

We investigate the Galois coverings of piecewise algebras and more particularly their behaviour under derived equivalences. Under a technical assumption which is satisfied if the algebra is derived equivalent to a hereditary algebra, we…

Complex data usually results from the interaction of objects produced by different generating mechanisms. Here we introduce a universal, unsupervised and parameter-free model-oriented approach, based upon the seminal concept of algorithmic…

We study the homology of simplicial complexes built via deterministic rules from a random set of vertices. In particular, we show that, depending on the randomness that generates the vertices, the homology of these complexes can either…

In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…

Effect algebras form an algebraic formalization of the logic of quantum mechanics. For lattice effect algebras E we investigate a natural implication and prove that the implication reduct of E is term equivalent to E. Then we present a…

Many systems involve numerous interacting parts and the whole system can have properties that the individual parts do not. I take this novelty as the defining characteristic of an emergent property. Other characteristics associated with…

When a large number of similar entities interact among each other and with their environment at a low scale, unexpected outcomes at higher spatio-temporal scales might spontaneously arise. This nontrivial phenomenon, known as emergence,…

We study the asymptotic nature of geometric structures formed from a point cloud of observations of (generally heavy tailed) distributions in a Euclidean space of dimension greater than one. A typical example is given by the Betti numbers…

"Emergence", the phenomenon where a complex system displays properties, behaviours, or dynamics not trivially reducible to its constituent elements, is one of the defining properties of complex systems. Recently, there has been a concerted…

We present a mathematical framework for quantum mechanics in which the basic entities and operations have physical significance. In this framework the primitive concepts are states and effects and the resulting mathematical structure is a…

We report numerical investigations of wave turbulence in a vibrating plate. The possibility to implement advanced measurement techniques and long time numerical simulations makes this system extremely valuable for wave turbulence studies.…

We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…

Recent experimental advances in neuroscience have opened new vistas into the immense complexity of neuronal networks. This proliferation of data challenges us on two parallel fronts. First, how can we form adequate theoretical frameworks…

We present a way of topologizing sets of Galois types over structures in abstract elementary classes with amalgamation. In the elementary case, the topologies thus produced refine the syntactic topologies familiar from first order logic. We…

Structural causal models postulate noisy functional relations among a set of interacting variables. The causal structure underlying each such model is naturally represented by a directed graph whose edges indicate for each variable which…

We consider the problem of causal discovery (structure learning) from heterogeneous observational data. Most existing methods assume a homogeneous sampling scheme, which leads to misleading conclusions when violated in many applications. To…

Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…

Effect algebras form a formal algebraic description of the structure of the so-called effects in a Hilbert space which serves as an event-state space for effects in quantum mechanics. This is why effect algebras are considered as logics of…