Analysis of the Caratheodory s theorem on dynamical system trajectories under numerical uncertainty

Osinenko, Pavel; Devadze, Grigory; Streif, Stefan

doi:10.1109/jas.2018.7511135

Cited by 4 publications

(3 citation statements)

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“…The authors in Reference 17 proposed an unused and useful verification for the Caratheodory's hypothesis on the presence and uniqueness of directions of dynamical frameworks. Tragically, the key concern is numerical instability.…”

Section: Related Workmentioning

confidence: 99%

A probabilistic approach: Uncertain navigation of the uncertain web

Boulaares

Sassi

Benslimane

et al. 2022

Concurrency and Computation

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Summary In the era of Internet Technology (IT), uncertainty management is a challenge in many fields. These include e‐commerce, social and sensor networks, scientific data production and mining, object tracking, data integration, geo‐located services, and recently Internet and Web of Things.3$$ {}^3 $$ Due to the uncertain data published on the web, web resources are diverse. Hence, identical resources could be available from heterogeneous platforms and heterogeneous resources could represent the same objects. These resources are hugely heterogeneous, conflict, inconsistent, or have incompatible formats. This uncertainty is inherently related to many facts, such as information extraction and integration. Hence, with web resources proliferation on the web, referencing through the uncertain web has become increasingly difficult. The traditional techniques used for the classical web could not handle uncertain navigation. Generally, it's implicitly represented, decided randomly, or even neglected. Harnessing these uncertain resources to their full potential in order to handle the uncertain navigation, raises major challenges that relate to each phase of their life cycle: creation, representation, and navigation. In this article, we establish a probabilistic approach to model and interpret uncertain web resources. We present operators to compute response uncertainty. Finally, we create algorithms in order to validate resources and achieve uncertain hypertext navigation.

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Section: Related Workmentioning

confidence: 99%

A probabilistic approach: Uncertain navigation of the uncertain web

Boulaares

Sassi

Benslimane

et al. 2022

Concurrency and Computation

View full text Add to dashboard Cite

show abstract

“…La teoría de ecuaciones diferenciales de Carathéodory contiene, a día de hoy, casi un siglo de resultados matemáticos. Desde el punto de vista de los sistemas dinámicos se han realizado muchos estudios en estabilidad, análisis númerico y teoría de bifurcación (véase, por ejemplo, Filippov [26], Osinenko et al [46], Pötzsche y Rasmussen [49], Pötszche [48], entre otros). Los resultados obtenidos en esta memoria pueden ser aplicados en estas direcciones.…”

Section: Summary In Spanishunclassified

“…The theory of Carathéodory differential equations embraces almost one century of mathematical results. From a dynamical systems point of view, it also includes studies of stability, numerical analysis and bifurcation theory (see for example Filippov [26], Osinenko et al [46], Pötzsche and Rasmussen [49], Pötszche [48]). We believe that the topological framework and results contained in this work could be applied also in these directions.…”

Section: Introductionmentioning

confidence: 99%