There has been a longstanding interest in building systems that can handle uncertain data. Traditional database systems inherently assume exact data and harbour fundamental limitations when it comes to handling uncertain data. In this dissertation, we present a probabilistic database model that can compactly represent uncertainty models in full generality. Our representation is associated with ...

Parametric quantum circuits play a crucial role in the performance of many variational algorithms. To successfully implement such algorithms, one must design efficient that sufficiently approximate solution space while maintaining low parameter count and circuit depth. In this paper, develop method to analyze dimensional expressivity parametric circuits. Our technique allows for identifying sup...

Local symmetries are primarily defined in the case of spacetime, but several authors have them outside this context, sometimes with help groupoids. We show that, many cases, local can be as global symmetries. also that groups used, rather than groupoids, to handle Examples given for graphs and networks, color symmetry tilings. The definition physics is discussed.

A bstract We explore the notion of approximate global symmetries in quantum field theory and gravity. show that a variety conjectures about gravity, including weak gravity conjecture, distance magnetic axion versions conjecture can be motivated by assumption generalized should strongly broken within context low-energy effective theory, i.e. at characteristic scale less than Planck where effects...

The moment map is a mathematical expression of the concept of the conservation associated with the symmetries of a Hamiltonian system. The abstract moment map is defined from G-manifold M to dual Lie algebra of G. We will interested study maps from G-manifold M to spaces that are more general than dual Lie algebra of G. These maps help us to reduce the dimension of a manifold much more.

we de ne approximate xed point in fuzzy norm spaces and prove the existence theorems, we also consider approximate pair constructive map- ping and show its relation with approximate fuzzy xed point.

ˆe world around us consists of objects of vastly varying shapes, sizes, and geometric complexity. A natural question is how to capture such geometric variations? We propose algorithms for capturing, comparing, and analyzing such D geometry. In the rst part of this thesis, we propose algorithms to automate the various stages of a standard shape acquisition pipeline. Typically, a D scanner capt...

The detection of motion from image sequences is usually performed using a time differential method or calculating the difference from a background reference image. These algorithms often perform poorly in the presence of temporal clutter. This paper describes a technique that measures the irregularity of an intensity sequence to detect motion. We demonstrate that static background, interesting ...

In this paper, new classes of symmetries for partial differential equations (PDE) which can be written in a conserved form are introduced. These new symmetries called nonclassical potential symmetries, are neither potential symmetries nor nonclassical symmetries. Some of these symmetries are carried out for the Burgers equation ut + uux − uxx = 0. (1) by studying the nonclassical symmetries of ...