Intertwined isospectral potentials in an arbitrary dimension

The method of intertwining with n-dimensional (nD) linear intertwining operator L is used to construct nD isospectral, stationary potentials. It has been proven that differential part of L is a series in Euclidean algebra generators. Integrability conditions of the consistency equations are investigated and the general form of a class of potentials respecting all these conditions have been specified for each n=2,3,4,5. The most general forms of 2D and 3D isospectral potentials are considered in detail and construction of their hierarchies is exhibited. The followed approach provides coordinate systems which make it possible to perform separation of variables and to apply the known methods of supersymmetric quantum mechanics for 1D systems. It has been shown that in choice of coordinates and L there are a number of alternatives increasing with $n$ that enlarge the set of available potentials. Some salient features of higher dimensional extension as well as some applications of the results are presented.Comment: 14 pages, Latex fil

Two families of superintegrable and isospectral potentials in two dimensions

As an extension of the intertwining operator idea, an algebraic method which provides a link between supersymmetric quantum mechanics and quantum (super)integrability is introduced. By realization of the method in two dimensions, two infinite families of superintegrable and isospectral stationary potentials are generated. The method makes it possible to perform Darboux transformations in such a way that, in addition to the isospectral property, they acquire the superintegrability preserving property. Symmetry generators are second and fourth order in derivatives and all potentials are isospectral with one of the Smorodinsky-Winternitz potentials. Explicit expressions of the potentials, their dynamical symmetry generators and the algebra they obey as well as their degenerate spectra and corresponding normalizable states are presented.Comment: 22 pages, only four typos are correcte

Pupil Localisation and Eye Centre Estimation using Machine Learning and Computer Vision

Various methods have been used to estimate the pupil location within an image or a real-time video frame in many fields. However, these methods lack the performance specifically in low-resolution images and varying background conditions. We propose a coarse-to-fine pupil localisation method using a composite of machine learning and image processing algorithms. First, a pre-trained model is employed for the facial landmark identification to extract the desired eye-frames within the input image. We then use multi-stage convolution to find the optimal horizontal and vertical coordinates of the pupil within the identified eye-frames. For this purpose, we define an adaptive kernel to deal with the varying resolution and size of input images. Furthermore, a dynamic threshold is calculated for reliable identification of the best-matched candidate. We evaluated our method using various statistical and standard metrics along-with a standardized distance metric we introduce first time in this study. Proposed method outperforms previous works in terms of accuracy and reliability when benchmarked on multiple standard datasets. The work has diverse artificial intelligence and industrial applications including human computer interfaces, emotion recognition, psychological profiling, healthcare and automated deception detection

Evaluation of biventricular myocardial performance index in patients with Behçet's disease

Objective: The global function of both left ventricular (LV) and right ventricular (RV) functions were compared in patients with Behçet's disease (BD) versus healthy controls. Methods: Biventricular function was evaluated by measurement of the myocardial performance index (MPI) evaluated from tissue Doppler echocardiographic measurements in 24 BD patients and was compared with measurements in 24 age- and sex-matched healthy controls. Results: Significantly higher MPI values were associated with ventricular dysfunction. The study demonstrated impaired RV function in patients with BD compared with healthy controls, whereas normal LV function was observed both in patients with BD and in healthy controls. Conclusion: Early noninvasive evaluation of the properties of BD during the asymptomatic phase of this inflammatory disease may have prognostic value in the management of patients. © 2012 Field House Publishing LLP

A study of the bound states for square potential wells with position-dependent mass

A square potential well with position-dependent mass is studied for bound states. Applying appropriate matching conditions, a transcendental equation is derived for the energy eigenvalues. Numerical results are presented graphically and the variation of the energy of the bound states are calculated as a function of the well-width and mass.Comment: To appear in Phys. Lett. A (Present e-mail of A.G: [email protected]