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Marco Pedroni

Publications and source records attributed to Marco Pedroni.

At least 19 recordsLinked to original sources
arXiv2026

An involutivity theorem for a class of Poisson quasi-Nijenhuis manifolds

This note aims to continue our study about the applications of Poisson quasi-Nijenhuis geometry to the theory of classical completely integrable systems. More precisely, we will present new versions of the deformation and involutivity theorems, under the hypothesis that the closed 2-form triggering the deformation and the closed 3-form defining the Poisson quasi-Nijenhuis structure are factorized. These results will be supplemented by several examples of involutive Poisson quasi- Nijenhuis manifolds.

math-ph↗
arXiv2026

Can Semantic Methods Enhance Team Sports Tactics? A Methodology for Football with Broader Applications

This paper explores how semantic-space reasoning, traditionally used in computational linguistics, can be extended to tactical decision-making in team sports. Building on the analogy between texts and teams -- where players act as words and collective play conveys meaning -- the proposed methodology models tactical configurations as compositional semantic structures. Each player is represented as a multidimensional vector integrating technical, physical, and psychological attributes; team profiles are aggregated through contextual weighting into a higher-level semantic representation. Within this shared vector space, tactical templates such as high press, counterattack, or possession build-up are encoded analogously to linguistic concepts. Their alignment with team profiles is evaluated using vector-distance metrics, enabling the computation of tactical ``fit'' and opponent-exploitation potential. A Python-based prototype demonstrates how these methods can generate interpretable, dynamically adaptive strategy recommendations, accompanied by fine-grained diagnostic insights at the attribute level. Beyond football, the approach offers a generalizable framework for collective decision-making and performance optimization in team-based domains -- ranging from basketball and hockey to cooperative robotics and human-AI coordination systems. The paper concludes by outlining future directions toward real-world data integration, predictive simulation, and hybrid human-machine tactical intelligence.

cs.AI↗
arXiv2025

From Extraction to Synthesis: Entangled Heuristics for Agent-Augmented Strategic Reasoning

We present a hybrid architecture for agent-augmented strategic reasoning, combining heuristic extraction, semantic activation, and compositional synthesis. Drawing on sources ranging from classical military theory to contemporary corporate strategy, our model activates and composes multiple heuristics through a process of semantic interdependence inspired by research in quantum cognition. Unlike traditional decision engines that select the best rule, our system fuses conflicting heuristics into coherent and context-sensitive narratives, guided by semantic interaction modeling and rhetorical framing. We demonstrate the framework via a Meta vs. FTC case study, with preliminary validation through semantic metrics. Limitations and extensions (e.g., dynamic interference tuning) are discussed.

cs.AI↗
arXiv2025

Recommending Actionable Strategies: A Semantic Approach to Integrating Analytical Frameworks with Decision Heuristics

We present a novel approach for recommending actionable strategies by integrating strategic frameworks with decision heuristics through semantic analysis. While strategy frameworks provide systematic models for assessment and planning, and decision heuristics encode experiential knowledge,these traditions have historically remained separate. Our methodology bridges this gap using advanced natural language processing (NLP), demonstrated through integrating frameworks like the 6C model with the Thirty-Six Stratagems. The approach employs vector space representations and semantic similarity calculations to map framework parameters to heuristic patterns, supported by a computational architecture that combines deep semantic processing with constrained use of Large Language Models. By processing both primary content and secondary elements (diagrams, matrices) as complementary linguistic representations, we demonstrate effectiveness through corporate strategy case studies. The methodology generalizes to various analytical frameworks and heuristic sets, culminating in a plug-and-play architecture for generating recommender systems that enable cohesive integration of strategic frameworks and decision heuristics into actionable guidance.

cs.AI↗
arXiv2024

Poisson quasi-Nijenhuis manifolds, closed Toda lattices, and generalized recursion relations

We present two involutivity theorems in the context of Poisson quasi-Nijenhuis %(PqN) manifolds. The second one stems from recursion relations that generalize the so called Lenard-Magri relations on a bi-Hamiltonian manifold. We apply these results to the closed (or periodic) Toda lattices of type $A_n^{(1)}$, $C_n^{(1)}$, $A_{2n}^{(2)}$ and, for the ones of type $A^{(1)}_n$, we show how this geometrical setting relates to their bi-Hamiltonian representation and to their recursion relations.

math-ph↗
arXiv2021

Poisson quasi-Nijenhuis deformations of the canonical PN structure

We present a result which allows us to deform a Poisson-Nijenhuis manifold into a Poisson quasi-Nijenhuis manifold by means of a closed 2-form. Under an additional assumption, the deformed structure is also Poisson-Nijenhuis. We apply this result to show that the canonical Poisson-Nijenhuis structure on R^2n gives rise to both the Poisson-Nijenhuis structure of the open (or non periodic) n-particle Toda lattice, introduced by Das and Okubo [6], and the Poisson quasi-Nijenhuis structure of the closed (or periodic) n-particle Toda lattice, described in our recent work [7].

math-ph↗
arXiv2019

On the Geometry of Extended Self-Similar Solutions of the Airy Shallow Water Equations

Self-similar solutions of the so called Airy equations, equivalent to the dispersionless nonlinear Schrödinger equation written in Madelung coordinates, are found and studied from the point of view of complete integrability and of their role in the recurrence relation from a bi-Hamiltonian structure for the equations. This class of solutions reduces the PDEs to a finite ODE system which admits several conserved quantities, which allow to construct explicit solutions by quadratures and provide the bi-Hamiltonian formulation for the reduced ODEs.

math-ph↗
arXiv2019

Poisson pencils: reduction, exactness, and invariants

We study the invariants (in particular, the central invariants) of suitable Poisson pencils from the point of view of the theory of bi-Hamiltonian reduction, paying a particular attention to the case where the Poisson pencil is exact. We show that the exactness is preserved by the reduction. In the Drinfeld-Sokolov case, the same is true for the characteristic polynomial of the pencil, which plays a crucial role in the definition of the central invariants. We also discuss the bi-Hamiltonian structures of a generalized Drinfeld-Sokolov hierarchy and of the Camassa-Holm equation.

math-ph↗
arXiv2013

Fundamental solutions and local solvability for nonsmooth Hörmander's operators

We consider operators of the form $L=\sum_{i=1}^{n}X_{i}^{2}+X_{0}$ in a bounded domain of R^p where X_0, X_1,...,X_n are nonsmooth Hörmander's vector fields of step r such that the highest order commutators are only Hölder continuous. Applying Levi's parametrix method we construct a local fundamental solution γ for L and provide growth estimates for γ and its first derivatives with respect to the vector fields. Requiring the existence of one more derivative of the coefficients we prove that γ also possesses second derivatives, and we deduce the local solvability of L, constructing, by means of γ, a solution to Lu=f with Hölder continuous f. We also prove $C_{X,loc}^{2,α}$ estimates on this solution.

math.AP↗
arXiv2012

An inertia 'paradox' for incompressible stratified Euler fluids

The interplay between incompressibility and stratification can lead to non-conservation of horizontal momentum in the dynamics of a stably stratified incompressible Euler fluid filling an infinite horizontal channel between rigid upper and lower plates. Lack of conservation occurs even though in this configuration only vertical external forces act on the system. This apparent paradox was seemingly first noticed by Benjamin (J. Fluid Mech., vol. 165, 1986, pp. 445-474) in his classification of the invariants by symmetry groups with the Hamiltonian structure of the Euler equations in two dimensional settings, but it appears to have been largely ignored since. By working directly with the motion equations, the paradox is shown here to be a consequence of the rigid lid constraint coupling through incompressibility with the infinite inertia of the far ends of the channel, assumed to be at rest in hydrostatic equilibrium. Accordingly, when inertia is removed by eliminating the stratification, or, remarkably, by using the Boussinesq approximation of uniform density for the inertia terms, horizontal momentum conservation is recovered. This interplay between constraints,action at a distance by incompressibility, and inertia is illustrated by layer-averaged exact results, two-layer long-wave models, and direct numerical simulations of the incompressible Euler equations with smooth stratification.

physics.flu-dyn↗
arXiv2011

On the lifting and approximation theorem for nonsmooth vector fields

We prove a version of Rothschild-Stein's theorem of lifting and approximation and some related results in the context of nonsmooth Hormander's vector fields for which the highest order commutators are only Holder continuous. The theory explicitly covers the case of one vector field having weight two while the others have weight one.

math.AP↗
arXiv2010

Natural connections for semi-Hamiltonian systems: The case of the $ε$-system

Given a semi-Hamiltonian system, we construct an $F$-manifold with a connection satisfying a suitable compatibility condition with the product. We exemplify this procedure in the case of the so-called $ε$-system. The corresponding connection turns out to be flat, and the flat coordinates give rise to additional chains of commuting flows

nlin.SI↗
arXiv2009

$F$-manifolds and integrable systems of hydrodynamic type

We investigate the role of Hertling-Manin condition on the structure constants of an associative commutative algebra in the theory of integrable systems of hydrodynamic type. In such a framework we introduce the notion of F-manifold with compatible connection generalizing a structure introduced by Manin.

math.DG↗
arXiv2009

Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality

We consider a family of vector fields defined in some bounded domain of R^p, and we assume that they satisfy Hormander's rank condition of some step r, and that their coefficients have r-1 continuous derivatives. We extend to this nonsmooth context some results which are well-known for smooth Hormander's vector fields, namely: some basic properties of the distance induced by the vector fields, the doubling condition, Chow's connectivity theorem, and, under the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's inequality. By known results, these facts also imply a Sobolev embedding. All these tools allow to draw some consequences about second order differential operators modeled on these nonsmooth Hormander's vector fields.

math.AP↗
arXiv2008

Bi-Hamiltonian Aspects of a Matrix Harry Dym Hierarchy

We study the Harry Dym hierarchy of nonlinear evolution equations from the bi-Hamiltonian view point. This is done by using the concept of an S-hierarchy. It allows us to define a matrix Harry Dym hierarchy of commuting Hamiltonian flows in two fields that projects onto the scalar Harry Dym hierarchy. We also show that the conserved densities of the matrix Harry Dym equation can be found by means of a Riccati-type equation.

nlin.SI↗
arXiv2006

A 3-component extension of the Camassa-Holm hierarchy

We introduce a bi-Hamiltonian hierarchy on the loop-algebra of sl(2) endowed with a suitable Poisson pair. It gives rise to the usual CH hierarchy by means of a bi-Hamiltonian reduction, and its first nontrivial flow provides a 3-component extension of the CH equation.

nlin.SI↗
arXiv2005

Gel'fand-Zakharevich Systems and Algebraic Integrability: the Volterra Lattice Revisited

In this paper we will discuss some features of the bihamiltonian method for solving the Hamilton-Jacobi (H-J) equations by Separation of Variables, and make contact with the theory of Algebraic Complete Integrability and, specifically, with the Veselov--Novikov notion of algebro-geometric (AG) Poisson brackets. The "bihamiltonian" method for separating the Hamilton-Jacobi equations is based on the notion of pencil of Poisson brackets and on the Gel'fand-Zakharevich (GZ) approach to integrable systems. We will herewith show how, quite naturally, GZ systems may give rise to AG Poisson brackets, together with specific recipes to solve the H-J equations. We will then show how this setting works by framing results by Veselov and Penskoi about the algebraic integrability of the Volterra lattice within the bihamiltonian setting for Separation of Variables.

nlin.SI↗