Feature-vector for the MeanShift

The article gives the description of the feature vector, which is suitable for the MeanShift procedure, uses all the color information of the RGB24 format and has a dimension exceeding only 1.5 times the dimension of the smallest 512-dimensional vector used for the Kernel Based Object Tracking procedure. For the described feature vector, a function of similarity of two elliptical areas of the frame is built. For the similarity function, formulas are found for the gradient vector - the mean shift vector, which indicates the direction of the growth of similarity in four-dimensional space of all elliptical regions covering the object in the frame. Knowing the greatest value of the similarity function of two elliptical regions, the length of the displacement vector in the four dimensional space of all elliptical regions was found. To this vector the previous point in space must be moved at the current moment, i.e. the values of the coordinates of the center and the dimensions of the ellipse, in order to obtain the best similarity of the current elliptical area from the previous one. Finally, so as to implement Kernel Based Object Tracking, an algorithm of successive iterations (Newton's method) has been developed, which allows finding the parameters of the ellipse that really has the best similarity. The experiments were carried out and their results were presented and discussed

New coordinates for a simpler canonical derivation of the Hawking effect

In order to achieve a Hamiltonian-based canonical derivation of the Hawking effect, one usually faces multiple hurdles. Firstly, the spacetime foliation using Schwarzschild time does not lead to hyper-surfaces which are always spacelike. Secondly, the null coordinates which are frequently used in covariant approach, do not lead to a true matter Hamiltonian. Recently, an exact canonical derivation was presented using the so-called near-null coordinates. However, there too one faces the difficulty of having to deal with non-vanishing matter diffeomorphism generator as the spatial decomposition involves a non-zero shift vector. Here we introduce a new set of coordinates which allows one to perform an exact canonical derivation of Hawking effect without having to deal with matter diffeomorphism generator.

Nonlinear electro-magneto-mechanical constitutive modelling of monolayer graphene

Using the classical theory of invariants for the specific class of graphene's symmetry, we constitutively characterize electro-magneto-mechanical interactions of graphene at continuum level. Graphene's energy depends on five arguments: the Finger strain tensor, the curvature tensor, the shift vector, the effective electric field intensity and the effective magnetic induction. The Finger strain tensor describes in- surface phenomena, the curvature tensor is responsible for the out-of-surface motions, while the shift vector is used due to the fact that graphene is a multilattice. The electric and the magnetic fields are described by the effective electric field intensity and the effective magnetic induction, respectively. An energy with the above arguments that also respects graphene's symmetries is found to have 42 invariants. Using these invariants, we evaluate all relevant measures by finding derivatives of the energy with respect to the five arguments of the energy. We also lay down the field equations that should be satisfied. These are the Maxwell equations, the momentum equation, the moment of momentum equation and the equation ruling the shift vector. Our framework is general enough to capture fully coupled processes in the finite deformation regime.