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The present study introduces fractal interpolation function as an attractor of the iterated function system involving a finite number of Reich contractions on a complete metric space. Some amendments are made concerning the results of Reich ...$$

This research reports on the recent development of black-box optimization methods based on single-step deep reinforcement learning and their conceptual similarity to evolution strategy (ES) techniques. It formally introduces policy-based ...

In recent years, owing to the frequent flow of digital images worldwide over the transmission media, it has become essential to secure them from leakages. Moreover, many applications like military image databases, confidential video conferencing, ...

A rigorous numerical algorithm, formally verified with Isabelle/HOL, is used to certify the computations that Tucker used to prove chaos for the Lorenz attractor. The verification is based on a formalization of a diverse variety of mathematics and ...

A considerable amount of research has been carried out in harvesting the benefit of chaos theory in image encryption. However, there are not many schema that effectively maximize the advantages of Lorenz system. In this paper, we present one such image ...

This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivative of long time averaged "statistical" quantities to ...

We present an algorithm for computing rigorous solutions to a large class of ordinary differential equations. The main algorithm is based on a partitioning process and the use of interval arithmetic with directed rounding. As an application, we prove ...