Invariance is one of the most important notions in applications of mathematics. It is one of the key concepts in modern physics, is a computational tool that helps in solving complex equations, etc. In view of its importance, it is desirable to come up with a definition of invariance which is as general as possible. In this paper, we describe how to formulate a general notion of invariance in c...

The Meta-Schr\"odinger algebra arises as the dynamical symmetry in transport processes which are ballistic a chosen `parallel' direction and diffusive all other `transverse' directions. time-space transformations of this Lie its infinite-dimensional extension, meta-Schr\"odinger-Virasoro algebra, constructed. We also find representation suitable for non-stationary systems by proposing generalis...

We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with admit scale-free formulation of the functional integral and effective action in terms invariant fields. They correspond to exact scaling solutions renormalization flow equations. Such are highly predictive since all relevant parameters for deviations from solution vanish....

Watermarking has increased dramatically in recent years in the Internet and digital media. Watermarking is one of the powerful tools to protect copyright. Local image features have been widely used in watermarking techniques based on feature points. In various papers, the invariance feature has been used to obtain the robustness against attacks. The purpose of this research was based on local f...

Invariance to geometric transformations is a highly desirable property of automatic classifiers in many image recognition tasks. Nevertheless, it is unclear to which extent state-of-the-art classifiers are invariant to basic transformations such as rotations and translations. This is mainly due to the lack of general methods that properly measure such an invariance. In this paper, we propose a ...