Nonholonomic Optimization

Udrişte, Constantin; Dogarul, Oltin; Феррара, Массимилиано; Ţevy, Ionel

doi:10.1007/3-540-28258-0_8

Cited by 3 publications

(8 citation statements)

References 3 publications

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“…We restricted our study to the Physics domain, but we must stress there exists another active field of research, which translates (via a specific dictionary) the thermodynamical notions and results into economic ones [18,23,63,61,62]. All the content of our paper have a direct correspondence within this economic theory, which remains to be precised and developed in a future paper.…”

Section: Discussionmentioning

confidence: 99%

“…(vii) The maximum entropy (MaxEnt) problem is a fundamental area of investigation in Statistical Mechanics and Information theory. Its classical thermodynamics counterpart is less studied and, in any case, with totally different tools ( [27], Ch.5); mathematical optimization with non-holonomic constraints is a difficult theory, which emerged only recently (see [38,64,70] and references therein).…”

Section: Thermodynamic Interpretations and Applicationsmentioning

confidence: 99%

“…A highly original geometrization path for dynamical systems, via Pfaffian equations and non-holonomic geometry, is the Geometric Dynamics of C. Udriste [60]. In particular, this tool was applied also in the study of the GH equation ( [6,57,58,63,61,62] to quote but a few).…”

Section: Introduction 1motivationmentioning

confidence: 99%

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Fisher-like Metrics Associated with ϕ-Deformed (Naudts) Entropies

et al. 2022

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The paper defines and studies new semi-Riemannian generalized Fisher metrics and Fisher-like metrics, associated with entropies and divergences. Examples of seven such families are provided, based on exponential PDFs. The particular case when the basic entropy is a ϕ-deformed one, in the sense of Naudts, is investigated in detail, with emphasis on the variation of the emergent scalar curvatures. Moreover, the paper highlights the impact on these geometries determined by the addition of some group logarithms.

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Section: Discussionmentioning

confidence: 99%

Section: Thermodynamic Interpretations and Applicationsmentioning

confidence: 99%

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Fisher-like Metrics Associated with ϕ-Deformed (Naudts) Entropies

et al. 2022

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“…Log-Optimal and Rapid Path. To find bounds of significant functions for disease distribution, we can use the technique of optimization of an objective function with nonholonomic constraints [11,12]. One of these functions is the "volume" (SIR product) of disease states.…”

Section: Complexitymentioning

confidence: 99%

“…e mathematical literature that helped us to do this study is classified as follows: stochastic modeling of geometric structures [1][2][3][4], infectious disease flow [5][6][7], differential inclusions [8], geometric dynamics on Riemannian manifolds [9,10], nonholonomic optimization [11,12], and nonholonomic spaces [13].…”

Section: Introductionmentioning

confidence: 99%

Flow, Wind, and Stochastic Connectivity Modeling Infectious Diseases

2021

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We study in this paper the trends of the evolution of different infections using a SIR flow (first-order ODE system), completed by a differential inclusion, a geodesic motion in a gyroscopic field of forces, and a stochastic SIR perturbation of the flow (Itô ODE system). We are interested in mathematical analysis, bringing new results on studied evolutionary models: infection flow together with a differential inclusion, bounds of evolution, dual description of disease evolution, log-optimal and rapid path, epidemic wind (geometric dynamics), stochastic equations of evolution, and stochastic connectivity. We hope that the paper will be a guideline for strategizing optimal sociopolitical countermeasures to mitigate infectious diseases.

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Holonomic and Non-Holonomic Geometric Models Associated to the Gibbs–Helmholtz Equation

Pripoae,

Hirica,

Pripoae

et al. 2023

Mathematics

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By replacing the internal energy with the free energy, as coordinates in a “space of observables”, we slightly modify (the known three) non-holonomic geometrizations from Udriste’s et al. work. The coefficients of the curvature tensor field, of the Ricci tensor field, and of the scalar curvature function still remain rational functions. In addition, we define and study a new holonomic Riemannian geometric model associated, in a canonical way, to the Gibbs–Helmholtz equation from Classical Thermodynamics. Using a specific coordinate system, we define a parameterized hypersurface in R4 as the “graph” of the entropy function. The main geometric invariants of this hypersurface are determined and some of their properties are derived. Using this geometrization, we characterize the equivalence between the Gibbs–Helmholtz entropy and the Boltzmann–Gibbs–Shannon, Tsallis, and Kaniadakis entropies, respectively, by means of three stochastic integral equations. We prove that some specific (infinite) families of normal probability distributions are solutions for these equations. This particular case offers a glimpse of the more general “equivalence problem” between classical entropy and statistical entropy.

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Nonholonomic Optimization

Cited by 3 publications

References 3 publications

Fisher-like Metrics Associated with ϕ-Deformed (Naudts) Entropies

Fisher-like Metrics Associated with ϕ-Deformed (Naudts) Entropies

Flow, Wind, and Stochastic Connectivity Modeling Infectious Diseases

Holonomic and Non-Holonomic Geometric Models Associated to the Gibbs–Helmholtz Equation

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