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The unprecedented predictive success of deep generative models in complex many-body systems, such as AlphaFold3, raises an epistemological question: do these networks merely memorize data distributions via high-dimensional interpolation, or…

We construct six-dimensional superconformal models with non-abelian tensor and hypermultiplets. They describe the field content of (2,0) theories, coupled to (1,0) vector multiplets. The latter are part of the non-abelian gauge structure…

We discuss three mathematical structures which arise in topologically massive abelian gauge theory. First, the euclidean topologically massive abelian gauge theory defines a contact structure on a manifold. We briefly discuss three…

We discuss some of the key topological aspects of a two $(1+1)$-dimensional (2D) self-interacting non-Abelian gauge theory (having no interaction with matter fields) in the framework of {\it chiral} superfield formalism. We provide the…

There is a natural way to study the long distance interactions of gauge theories in the electric (momentum) representation. Here, the main ideas are presented for the Abelian and Yang-Mills gauge theories emphasizing on the structure and…

Comments on NC Abelian Higgs model withdrawn. An improved treatment of NC U(2) adjoint models to appear elsewhere.

A system of replicators with Hebbian random couplings is studied using dynamical methods. The self-reproducing species are here characterized by a set of binary traits and interact based on complementarity. In the case of an extensive…

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…

We extend a non local and non covariant version of the Thirring model in order to describe a many-body system with backward and umklapp scattering processes. We express the vacuum to vacuum functional in terms of a non trivial fermionic…

The description of gravitation in the framework of soliton interaction is considered for two nonlinear field models. These models are Born -- Infeld nonlinear electrodynamics and so-called Born -- Infeld type scalar field model. The last…

The thermodynamic properties of vector (O(2) and Complex Spherical) models with four-body interactions are analyzed. When defined in dense topologies, these are effective models for the nonlinear interaction of scalar fields in the presence…

We introduce an agent-based model of interaction, drawing on the contingency approach from Luhmann's theory of social systems. The agent interactions are defined by the exchange of distinct messages. Message selection is based on the…

Motivated by the Higgs Inflation scenario, we study static spherically-symmetric solutions of the non-Abelian Higgs model coupled non-minimally to Gravity. We find solutions for the self-gravitating sphaleron as well as monopole-like…

A recently proposed extension of the interaction flow method is applied to exemplary cases of selected physical and methodical parameters for the two-dimensional Hubbard model away from half-filling and perfect nesting. In this scheme, the…

Non-Abelian gauge offers a powerful route to engineer novel topological phenomena. Here, we systematically investigate a two-dimensional (2D) non-Hermitian Hatano-Nelson model incorporating SU(2) non-Abelian gauge, demonstrating the…

Actors are embedded in networks of communication: the relations of the actors can be represented as the rows of a matrix, while the column vectors represent their communications. The two systems are structurally coupled in the co-variation:…

The dynamics of abelian vector and antisymmetric tensor gauge fields can be described in terms of twisted self-duality equations. These first-order equations relate the p-form fields to their dual forms by demanding that their respective…

In this paper we discuss nonholonomic contact Lagrangian and Hamiltonian systems, that is, systems with a kind of dissipation that are also subject to nonholonomic constraints. We introduce the so-called contact Eden bracket that allows us…

We introduce an original model of quantum phenomena, a model that provides a picture of a "deep structure", an "underlying pattern" of quantum dynamics. We propose that the source of a particle and all of that particle's possible detectors…

Multi-agent systems in biology, society, and engineering are capable of making decisions through the dynamic interaction of their elements. Nonlinearity of the interactions is key for the speed, robustness, and flexibility of multi-agent…