We consider the evolution of the separation distance between two particles advected by a random velocity field with slowly decaying temporal and spatial correlations in the weak coupling regime. It has been shown in [5] that the motion of a single particle converges to a fractional Brownian motion on a time scale δ−γ with some γ < 2, which is shorter than the classical diffusive time scale δ−2 ...

Gaussian random field on general ultrametric space is introduced as a solution of pseudodifferential stochastic equation. Covariation of the introduced random field is computed with the help of wavelet analysis on ultrametric spaces. Notion of ultrametric Markovianity, which describes independence of contributions to random field from different ultrametric balls is introduced. We show that the ...

The report summarizes the feasibility study performed for AFRL/AOARD regarding the use of Random Finite Set (RFS) filtering approach for tracking orbital space debris. Specifically, we investigate the capability of the RFS approach to accommodate: nonlinear motion and measurement models; unknown and time varying target number; and limited sensor field-of-view. This report shows the capability o...

We discuss D-dimensional Euclidean scalar field interacting with a scale invariant quantized metric. We assume that the metric depends on d-dimensional coordinates where d < D. We show that the interacting quantum fields have more regular short distance behaviour than the free fields. A model of a Gaussian metric is discussed in detail. In particular, in the Φ theory in four dimensions we obtai...

Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information is available display scale-free features. Here we study the scaling properties of the recently introduced scale-free model, that can account for the observed ...

Characterizing the geometric conformation of object complexes requires the description of certain geometric features. These features are most intuitive and provide locality if each is at a restricted range of scale. Thus a complete representation of a geometric entity, such as an object, includes descriptions at multiple scale levels, each describing a residue from the information provided at t...

Many images, of natural or man-made scenes often contain Similar but Genuine Objects (SGO). This poses a challenge to existing Copy-Move Forgery Detection (CMFD) methods which match the key points / blocks, solely based on the pair similarity in the scene. To address such issue, we propose a novel CMFD method using Scaled Harris Feature Descriptors (SHFD) that preform consistently well on forge...