9 citations · 15 across the 26 of their papers we have counts for
27 papers
Information Loss under Gauge Reduction of Discrete Electromagnetic Fields
Jean-Pierre Magnot
We study relative entropy under gauge reduction in Whitney-discretized electromagnetism. The discrete Hodge decomposition separates exact gauge directions from harmonic and coexact…
Chern--Simons Fluctuations and Information Geometry in Discrete Electromagnetism
Jean-Pierre Magnot
We construct helicity-conditioned statistical states for a Whitney-discretized electromagnetic field on a closed oriented three-manifold. The simplicial de Rham complex provides ex…
Diffeological Tangent Spaces and Distributional Linearization for Lifted Euler--Reynolds Limits
Alireza Ahmadi, Jean-Pierre Magnot, Bijan Davvaz
We develop a diffeological framework for the geometry of Euler--Reynolds subsolutions of the incompressible Euler equations. Passing to a lifted formulation in which the velocity,…
Entropy Geometry and Normalized Means on Infinite-Dimensional Hamiltonian Manifolds
Jean-Pierre Magnot
We propose a geometric--analytic framework for equilibrium statistical mechanics on infinite-dimensional Hamiltonian systems. In situations where no suitable -additive invariant…
Graph-Series Semantics and Abel Regularization for Recursive Hybrid Quantum Programs
Jean-Pierre Magnot
We introduce a graded graph-series semantics for recursive hybrid quantum programs interpreted in the quantum orchestra monad. Finite terminating executions are represented by dire…
Diffeologies on Locally Convex Spaces and Smooth Multiplication of Distributions
Alireza Ahmadi, Bijan Davvaz, Jean-Pierre Magnot
We investigate the canonical and -diffeologies on Hausdorff locally convex spaces and their applications to Schwartz distributions. We prove that a Hausdorff locally conv…
Spherical Milnor Spaces II: Projective Quotients and Higher Topological Structures
Jean-Pierre Magnot
We study projective and semidirect quotients of the spherical Milnor construction and develop a step-by-step lifting obstruction from their explicit spherical local sections. The r…
On spherical Milnor Classifying Spaces I: differential geometry
Jean-Pierre Magnot
We compare the original product-subset diffeology on the Milnor join of Magnot--Watts with the locally finite final diffeology on a signed spherical model. The canonical squaring m…
Spectral Cut-off Oscillatory Integrals for Non-Autonomous Hamiltonian Evolution Equations
Jean-Pierre Magnot
We develop a spectral cut-off and time-slicing construction for non-autonomous Hamiltonian evolution equations. Let \(H_0\) be a positive self-adjoint reference operator with compa…
Remarks on pairwise comparisons, transition amplitudes, and qubit states
Jean-Pierre Magnot
We discuss a pairwise-comparison viewpoint on finite families of qubit states. Starting from transition amplitudes between pure states, we distinguish three associated levels of co…
Pairwise-comparison-valued cosurfaces: a projective framework for multi-scale relational structures
Jean-Pierre Magnot
We introduce cosurfaces with values in the group \(\PC_n(H)\) of \(H\)-valued reciprocal pairwise comparison matrices. The composition law is covariant on upper triangular coeffici…
Noisy Nonreciprocal Pairwise Comparisons: Scale Variation, Noise Calibration, and Admissible Ranking Regions
Jean-Pierre Magnot
Pairwise comparisons are widely used in decision analysis, preference modeling, and evaluation problems. In many practical situations, the observed comparison matrix is not recipro…
Effective dynamics and defect expansions for polynomial PDEs on thin annuli
Jean-Pierre Magnot
We develop a geometric and analytic framework for polynomial partial differential equations posed on thin annuli in the plane. Using renormalized Sobolev inner products, we constru…
A Lorentzian SU(3)-covariant noncommutative KP hierarchy and hypercomplex gauge fields
Jean-Pierre Magnot
We propose a formal framework for a noncommutative Kadomtsev--Petviashvili (KP) hierarchy which is covariant under the action of and compatible with a Lorentzian structure…
Preliminaries on Pre-Hilbert Structures on Polynomial Spaces and Associated Laplacians
Jean-Pierre Magnot
We study orthogonal polynomial systems arising from general pre-Hilbert inner products on polynomial spaces, beyond the classical framework of measures. To each such inner product…
On the geometry of profinite diffeological spaces
Anahita Eslami-Rad, Jean-Pierre Magnot, Enrique G. Reyes
We consider the class of profinite diffeological spaces, that is, diffeological spaces which diffeologies are deduced by pull-back of diffeologies on finite-dimensional manifolds t…
Poisson structures on weak Sobolev loop spaces and applications to integrable systems
Jean-Pierre Magnot
We develop a framework for Poisson geometry on loop spaces of low regularity, extending Mokhov's classical constructions from smooth loops to weak Sobolev spaces $W^{s,p}(\mathbb{S…
Contextuality, Holonomy and Discrete Fiber Bundles in Group-Valued Boltzmann Machines
Jean-Pierre Magnot
We propose a geometric extension of restricted Boltzmann machines (RBMs) by allowing weights to take values in abstract groups such as \( \mathrm{GL}_n(\mathbb{R}) \), \( \mathrm{S…
Diffeological Generalized Formal Series: An Overview
Jean-Pierre Magnot
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new t…
Linearizations and optimization problems in diffeological spaces
Jean-Pierre Magnot
By generalizing the notion of linearization, a concept originally arising from microlocal analysis and symbolic calculus, to diffeological spaces, we make a first proposal setting…
On strict ranking by pairwise comparisons
Jean-Pierre Magnot
We attack the problem of getting a strict ranking (i.e. a ranking without equally ranked items) of items from a pairwise comparisons matrix. Basic structures are described, a f…
Kadomtsev-Petviashvili hierarchies with non-formal pseudo-differential operators, non-formal solutions, and a Yang-Mills--like formulation
Jean-Pierre Magnot, Enrique G. Reyes
We start from the classical Kadomtsev-Petviashvili hierarchy posed on formal pseudo-differential operators, and we produce two hierarchies of non-linear equations posed on non-form…
On smooth infinite dimensional grassmannians, splittings and non-commutative generalized cross-ratio mappings
Jean-Pierre Magnot
We describe basic diffeological structures related to splittings and Grassmannians for infinite dimensional vector spaces. We analyze and expand the notion of non-commutative cross…
On random pairwise comparisons matrices and their geometry
Jean-Pierre Magnot
We describe a framework for random pairwise comparisons matrices, inspired by selected constructions releted to the so called inconsistency reduction of pairwise comparisons (PC) m…