arXiv subjects

Carlo Cattani

Publications and source records attributed to Carlo Cattani.

8 recordsLinked to original sources

arXiv2026

A Delayed Generalized Lotka--Volterra Model for Threshold Instability and Structural Recognition

This paper develops a delayed generalized Lotka--Volterra model for systems in which structural change and recognition of change are not synchronized. The starting point is the idea that a system may accumulate internal transformations while remaining locally stable at the level of interpretation, governance, or perception. Instability becomes effective only when accumulated structural stress crosses a threshold and is recognized after a delay. We introduce a vector of civilizational state variables including systemic complexity, informational entropy, systemic pressure, resilience, and legitimacy. Their interaction is modeled through a delayed generalized Lotka--Volterra system. The delays represent the temporal separation between structural variation and its cognitive, institutional, or social effects. A composite instability functional is then defined, and threshold crossing is interpreted as the transition from latent instability to recognized instability. The paper studies positivity, equilibria, linearization, and local stability of the delayed system. Particular attention is given to delay-induced instability: even when the corresponding non-delayed system is locally stable, sufficiently large delays may destabilize the equilibrium and generate oscillatory or nonlinear behavior. The model provides a mathematical framework for delayed recognition, threshold instability, and the emergence of crises in complex adaptive systems.

math.DS↗

arXiv2026

A Dynamical Framework for Cognitive Processes Based on Transformations and Semantic Equivalence

This paper proposes a structural and dynamical framework for modeling cognitive processes within a cybernetic perspective. Cognitive states are represented as elements of a state space evolving through an iterative update rule of the form \[ X_{t+1} = \pi\big(F(f(X_t))\big), \] where $f$ describes internal transformations, $F$ represents interpretative mappings, and $\pi$ enforces semantic equivalence. The model is interpreted as a feedback system integrating transformation, observation, and stabilization. A categorical formulation is introduced to capture compositional structure, while the associated dynamics are analyzed through fixed-point arguments and contraction conditions ensuring stability. To demonstrate the operational character of the framework, a computational illustration is provided, together with a qualitative analysis of the induced dynamics. A concrete linguistic application shows how context-dependent interpretation can be modeled as a trajectory toward a stable semantic class. The proposed approach connects dynamical systems, category theory, and cognitive modeling, and provides a unified representation of cognition as a feedback-driven process evolving toward invariant interpretations.

cs.AI↗

arXiv2025

The Fractal Lie Derivative: Theory and Applications

This paper presents a new Lie theoretic approach to fractal calculus, which in turn yields such new results as a Fractal Noether's Theorem, a setting for fractal differential forms, for vector fields, and Lie derivatives, as well as k-fractal jet space, and algorithms for k-th fractal prolongation. The symmetries of the fractal nonlinear $n$-th $\alpha$-order differential equation are examined, followed by a discussion of the symmetries of the fractal linear $n$-th $\alpha$-order differential equation. Additionally, the symmetries of the fractal linear first $\alpha$-order differential equation are derived. Several examples are provided to illustrate and highlight the details of these concepts.

math.GM↗

arXiv2022

Linear canonical wavelet transform and the associated uncertainty principles

We define a novel time-frequency analyzing tool, namely linear canonical wavelet transform (LCWT) and study some of its important properties like inner product relation, reconstruction formula and also characterize its range. We obtain Donoho-Stark's and Lieb's uncertainty principle for the LCWT and give a lower bound for the measure of its essential support. We also give Shapiro's mean dispersion theorem for the proposed LCWT.

math.FA↗

arXiv2021

A generalized novel approach based on orthonormal polynomial wavelets with an application to Lane-Emden equation

Capturing solution near the singular point of any nonlinear SBVPs is challenging because coefficients involved in the differential equation blow up near singularities. In this article, we aim to construct a general method based on orthogonal polynomials as wavelets. We discuss multiresolution analysis for wavelets generated by orthogonal polynomials, e.g., Hermite, Legendre, Chebyshev, Laguerre, and Gegenbauer. Then we use these wavelets for solving nonlinear SBVPs. These wavelets can deal with singularities easily and efficiently. To deal with the nonlinearity, we use both Newton's quasilinearization and the Newton-Raphson method. To show the importance and accuracy of the proposed methods, we solve the Lane-Emden type of problems and compare the computed solutions with the known solutions. As the resolution is increased the computed solutions converge to exact solutions or known solutions. We observe that the proposed technique performs well on a class of Lane-Emden type BVPs. As the paper deals with singularity, non-linearity significantly and different wavelets are used to compare the results.

math.NA↗

arXiv2021

Clifford wavelets for fetal ECG extraction

Analysis of the fetal heart rate during pregnancy is essential for monitoring the proper development of the fetus. Current fetal heart monitoring techniques lack the accuracy in fetal heart rate monitoring and features acquisition, resulting in diagnostic medical issues. The challenge lies in the extraction of the fetal ECG from the mother's ECG during pregnancy. This approach has the advantage of being a reliable and non-invasive technique. For this aim, we propose in this paper a wavelet/multi-wavelet method allowing to extract perfectly the feta ECG parameters from the abdominal mother ECG. The method is essentially due to the exploitation of Clifford wavelets as recent variants in the field. We prove that these wavelets are more efficient and performing against classical ones. The experimental results are therefore due to two basic classes of wavelets and multi-wavelets. A first-class is the classical Haar Schauder, and a second one is due to Clifford valued wavelets and multi-wavelets. These results showed that wavelets/multiwavelets are already good bases for the FECG processing, provided that Clifford ones are the best.

physics.med-ph↗

arXiv2013

Correct light deflection in Weyl conformal gravity

The conformal gravity fit to observed galactic rotation curves requires γ>0. On the other hand, conventional method for light deflection by galaxies gives a negative contribution to Schwarzschild value for γ>0, which is contrary to observation. Thus, it is very important that the contribution to bending should in principle be positive, no matter how small its magnitude is. Here we show that the Rindler-Ishak method gives a positive contribution to Schwarzschild deflection for γ>0, as desired. We also obtain the exact local coupling term derived earlier by Sereno. These results indicate that conformal gravity can potentially test well against all astrophysical observations to date.

gr-qc↗

arXiv2010

Light bending in the galactic halo by Rindler-Ishak method

After the work of Rindler and Ishak, it is now well established that the bending of light is influenced by the cosmological constant Λ appearing in the Schwarzschild-de Sitter spacetime. We show that their method, when applied to the galactic halo gravity parametrized by a constant γ, yields exactly the same γ- correction to Schwarzschild bending as obtained by standard methods. Different cases are analyzed, which include some corrections to the special cases considered in the original paper by Rindler and Ishak.

gr-qc↗