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Hypercomplex algebras have recently been gaining prominence in the field of deep learning owing to the advantages of their division algebras over real vector spaces and their superior results when dealing with multidimensional signals in…
This paper is concerned with the axiomatic basis of structures within Hypercompositional Algebra. It is proven that the axioms employed in the definition of numerous hypercompositional structures lack independence. Accordingly, novel…
The paper introduces a new 4d dynamical system leading to a typical 4d strange attractor. Its focal statement appears in its total disconnection from previous 3D nonlinear systems.
We introduce both an exactly solvable model and a coupled-layer construction for an exotic, three-dimensional phase of matter with immobile topological excitations that carry a protected internal degeneracy. Unitary transformations on this…
A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…
We consider three Ginibre ensembles (real, complex and quaternion-real) with a deformed measure and relate them to the known integrable systems via presenting partition functions of these ensembles in form of fermionic expectation values.…
Disordered hyperuniform systems are exotic states of matter that completely suppress large-scale density fluctuations like crystals, and yet possess no Bragg peaks similar to liquids or glasses. Such systems have been discovered in a…
The purpose of this contribution is to initiate the study of integrable deformations for different superstring theory formalisms that manifest the property of (classical) integrability. In this paper we choose the hybrid formalism of the…
In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems,…
Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
Disordered hyperuniform structures are an exotic state of matter having suppressed density fluctuations at large length-scale similar to perfect crystals and quasicrystals but without any long range orientational order. In the past decade,…
Our work is concerned with simplicial complexes that describe higher-order interactions in real complex systems. This description allows to go beyond the pairwise node-to-node representation that simple networks provide and to capture a…
The notions of holomorphic symplectic structures and hypercomplex structures on Courant algebroids are introduced and then proved to be equivalent. These generalize hypercomplex triples and holomorphic symplectic 2-forms on manifolds…
The superspace geometry relevant to the heterotic string is reviewed from the point of view of the off-shell supermultiplet structure of $N=1,d=10$ supergravity. The anomaly-modified seven-form Bianchi identity is analysed at order $\a'^3$…
While "complexity science" has achieved significant successes in several interdisciplinary fields such as economics and biology, it is only a very recent observation that legal systems -- from the way legal texts are drafted and connected…
We discuss the nature of structure and organization, and the process of making new Things. Hyperstructures are introduced as binding and organizing principles, and we show how they can transfer from one situation to another. A guiding…
During modeling of dynamical systems, often two or more model architectures are combined to obtain a more powerful or efficient model regarding a specific application area. This covers the combination of multiple machine learning…
Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two…
A long-term research proposal on the algebraic structure, the representations and the possible applications of paraparticle algebras is structured in three modules: The first part stems from an attempt to classify the inequivalent gradings…