Related papers: Geometry of Friston's active inference
We give a geometric interpretation of the Stanley--Reisner correspondence, extend it to schemes, and interpret it in terms of the field of one element.
We give an a geometric interpretation of the Hasse-Arf theorem for function fields using the recently proved Oort conjecture.
In this paper, a geometric interpretation is provided of a new rational Landen transformation. The convergence of its iterates is also established.
We provide geometrical interpretation of the Master Theorem to solve divide-and-conquer recurrences. We show how different cases of the recurrences correspond to different kinds of fractal images. Fractal dimension and Hausdorff measure are…
In earlier work, we constructed invariants of irreducible representations of the Kauffman skein algebra of a surface. We introduce here an inverse construction, which to a set of possible invariants associates an irreducible representation…
We elaborate on a recently proposed geometric framework for scalar effective field theories. Starting from the action, a metric can be identified that enables the construction of geometric quantities on the associated functional manifold.…
We give a complete geometrical description of the effective Hamiltonians common in nuclear shell model calculations. By recasting the theory in a manifestly geometric form, we reinterpret and clarify several points. Some of these results…
Starting from an axiomatic perspective, \emph{fluctuation geometry} is developed as a counterpart approach of inference geometry. This approach is inspired on the existence of a notable analogy between the general theorems of…
To present a survey on known results from the theory of transposed Poisson algebras, as well as to establish new results on this subject, are the main aims of the present paper. Furthermore, a list of open questions for future research is…
We will pursue a way of building up an algebraic structure that involves, in a mathematical abstract way, the well known Grassmann variables. The problem arises when we tried to understand the grassmannian polynomial expansion on the scope…
We study underlying geometric structures for integral variational functionals, depending on submanifolds of a given manifold. Applications include (first order) variational functionals of Finsler and areal geometries with integrand the…
A solution to the more than 300-years old problem of geometric and physical interpretation of fractional integration and differentiation (i.e., integration and differentiation of an arbitrary real order) is suggested for the…
Phenomenology is the rigorous descriptive study of conscious experience. Recent attempts to formalize Husserlian phenomenology provide us with a mathematical model of perception as a function of prior knowledge and expectation. In this…
This is an elementary geometrical proof of Birkhoff theorem. It is hardly important, but the pictures behind are quite nice.
Combinatorial interpretation of the fibonomial coefficients recently proposed by the present author results here in combinatorial interpretation of the recurrence relation for fibonomial coefficients . The presentation is provided with…
We show that the Boltzmann factor has a geometrical origin. Its derivation follows from the microcanonical picture. The Maxwell-Boltzmann distribution or the wealth distribution in human society are some direct applications of this new…
Structure functions are the essential objects for understanding the deep inelastic scattering processes, providing valuable insight into the partonic structure of hadrons. A direct calculation of the Compton amplitude provides a…
We explain how the action of the Heisenberg algebra on the space of q-deformed wedges yields the Heisenberg crystal structure on charged multipartitions, by using the boson-fermion correspondence and looking at the action of the Schur…
New simple proofs are given to some elementary approximate and explicit inversion formulas for Riesz potentials. The results are applied to reconstruction of functions from their integrals over Euclidean planes in integral geometry.
We develop a method to derive the on-shell invariant quantum action of the supergravity in such a way that the quartic ghost interaction term is explicity determined. First, we reinvestigate the simple supergravity in terms of a principal…