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In this work, the calculation of complexity on atomic systems is considered. In order to unveil the increasing of this statistical magnitude with the atomic number due to the relativistic effects, recently reported in [A. Borgoo, F. De…
Let $M$ be a cancellative and commutative monoid (written additively). The monoid $M$ is atomic if every non-invertible element can be written as a sum of irreducible elements (often called atoms in the literature). Weaker versions of…
A self-organization is an universal phenomenon in nature and, in particular, is highly important in materials systems and biology. We proposed a new theory that allowed us to model the most challenging cases of atomic self-assembling whose…
In resisting attempts to explain the unity of a whole in terms of a multiplicity of interacting parts, quantum mechanics calls for an explanatory concept that proceeds in the opposite direction: from unity to multiplicity. It concerns the…
Process Philosophy endeavours to replace the classical ontology of substances by a process ontology centered on notions of changes and transitions. We argue, that the substantial and processual approach are mutually complementary. Here,…
There are two ways to turn a categorical model for pure quantum theory into one for mixed quantum theory, both resulting in a category of completely positive maps. One has quantum systems as objects, whereas the other also allows classical…
Quantum theory has the property of "local tomography": the state of any composite system can be reconstructed from the statistics of measurements on the individual components. In this respect the holism of quantum theory is limited. We…
In physics, there is the prevailing intuition that we are part of a unique external world, and that the goal of physics is to understand and describe this world. This assumption of the fundamentality of objective reality is often seen as a…
In the initial stages of its development, atomic theory had to bypass the laws of classical electromagnetism in an ad hoc manner in order to explain the stability of atoms. In quantum mechanics, however, the classical theory may find again…
It is argued that the three main quantum interpretations, Copenhagen, de Broglie-Bohm, and Many-Worlds, support the Principle Q (Quantum): Not all what matters for physical phenomena is contained in space-time. This principle underpins…
In the algebraic theory of codes and formal languages, the set $Q$ of all primitive words over some alphabet $\zi $ has received special interest. With this survey article we give an overview about relevant research to this topic during the…
Chemical bonding is a nonlocal phenomenon that binds atoms into molecules. Its ubiquitous presence in chemistry, however, stands in stark contrast to its ambiguous definition and the lack of a universal perspective for its understanding. In…
Except for crystalline or random structures, an agreed definition of complexity for intermediate and hence interesting cases does not exist. We fill this gap with a notion of complexity that characterises shapes formed by any finite number…
Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial…
It is asserted that consciousness functionally is a vision. Biologically it is a sensation of work of a brain that converts external and internal signals into visual output. However, as we well know, human consciousness includes meaning…
Decomposition of text into atomic propositions is a flexible framework allowing for the closer inspection of input and output text. We use atomic decomposition of hypotheses in two natural language reasoning tasks, traditional NLI and…
In 1929 Szilard pointed out that the physics of the observer may play a role in the analysis of experiments. The same year, Bohr pointed out that complementarity appears to arise naturally in psychology where both the objects of perception…
Formulations of quantum mechanics can be characterized as realistic, operationalist, or a combination of the two. In this paper a realistic theory is defined as describing a closed system entirely by means of entities and concepts…
Elementary Cycles Theory is a self-consistent, unified formulation of quantum and relativistic physics. Here we introduce its basic quantum aspects. On one hand, Newton's law of inertia states that every isolated particle has persistent…
Quantifying the evolution and complexity of materials is of importance in many areas of science and engineering, where a central open challenge is developing experimental complexity measurements to distinguish random structures from evolved…