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The question of a possible excitation and emergence of fractional type dynamics, as a more realistic framework for understanding emergence of complex systems, directly from a conventional integral order dynamics, in the form a continuous…
Magnetostatic normal modes are investigated here in elongated rods. The dipolar field resulting from the dipole-dipole interactions is calculated numerically in points of the axis connecting opposite rod face centers (\emph{central axis})…
This work introduces a Hamiltonian approach to regularization and linearization of central-force particle dynamics through a new canonical extension of the so-called "projective decomposition". The regularization scheme is formulated within…
We classify the three-dimensional representations of the modular group that are reducible but indecomposable, and their associated spaces of holomorphic vector-valued modular forms. We then demonstrate how such representations may be…
Composition is an important feature of a specification language, as it enables the design of a complex system in terms of a product of its parts. Decomposition is equally important in order to reason about structural properties of a system.…
A broad class of systems, including ecological, epidemiological, and sociological ones, are characterized by populations of individuals assigned to specific categories, e.g., a chemical species, an opinion or an epidemic state, that are…
Starting from space-discretisation of Maxwell's equations, various classical formulations are proposed for the simulation of electromagnetic fields. They differ in the phenomena considered as well as in the variables chosen for…
Flow forming involves complicated tooling/workpiece interactions. Purely analytical models of the tool contact area are difficult to formulate, resulting in numerical approaches that are case-specific. Provided are the details of an…
Modal analysis has long been consolidated as a basic tool to interpret dynamics and build low-order models of mechanical, thermal, and fluid systems. Eigenmodes arising from the spectral decomposition of the underlying linearized dynamics…
There exist two ways of defining regular variation of a time series in a star-shaped metric space: either by the distributions of finite stretches of the series or by viewing the whole series as a single random element in a sequence space.…
The literature on concurrency theory offers a wealth of examples of characteristic-formula constructions for various behavioural relations over finite labelled transition systems and Kripke structures that are defined in terms of fixed…
Concept-based interpretability methods offer a lens into the internals of foundation models by decomposing their embeddings into high-level concepts. These concept representations are most useful when they are compositional, meaning that…
In the recent development in a various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In this paper, we consider the deformations which have two purposes: to have them like…
A new type of artificial molecule is proposed, which consists of coupled defect atoms in photonic crystals, named as photonic molecule. Within the major band gap, the photonic molecule confines the resonant modes that are closely analogous…
Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…
This paper presents ReasonFormer, a unified reasoning framework for mirroring the modular and compositional reasoning process of humans in complex decision-making. Inspired by dual-process theory in cognitive science, the representation…
A method to derive features of modal eigenvalue traces from known and understood solutions is proposed. It utilizes the concept of subduction from point group theory to obtain the symmetry properties of a target structure from those of a…
We define localized modulation maps and modulation spaces of symbols suited to the study of Rieffel's deformation quantization pseudodifferential calculus. They are used to generate Hilbert space representations for the quantized…
After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…
We use holography to derive effective theories of fluctuations in spontaneously broken phases of systems with finite temperature, chemical potential, magnetic field and momentum relaxation in which the order parameters break translations.…