The human visual system uses eye movements to gather visual information. They act as visual scanning processes and can roughly be divided into two different types: small movements around fixation points and larger movements between fixation points. The processes are often modeled as random walks, and recent models based on heavy tail distributions, also known as Levý flights, have been used in ...

The local, covariant, continuous, anticommuting and nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for all the fields of a (0 + 1)-dimensional spinning relativistic particle are obtained in the framework of augmented superfield approach to BRST formalism. The trajectory of this super-particle is parametrized by a monotonically increasing parameter τ that is em...

This article provides further generalized Weierstrass relations for a spin manifold S immersed in a higher dimensional spin manifold M ; we show that kernel of a certain Dirac operator defined over S, which we called submanifold Dirac operator, gives the data of the immersion. In the derivation, we use a relation between the generalized Weierstrass relations and the Frobenious reciprocity of Cl...

We show that the holonomy invariance of a function on the tangent bundle of a manifold, together with very mild regularity conditions on the function, is equivalent to the existence of local parallelisms compatible with the function in a natural way. Thus, in particular, we obtain a characterization of generalized Berwald manifolds. We also construct a simple example of a generalized Berwald ma...

We present a new proof of a strengthened version of D.V. Anosov's multiphase averaging theorem, originally stated for systems of ODEs with slow variables evolving in R and fast variables evolving on a smooth immersed manifold. Our result allows the fast variables to belong to an arbitrary smooth compact Riemannian manifold, and the vector eld to have only Sobolev regularity. This is accomplishe...