Exact solutions for two-body problems in 1D deformed space with minimal length

We reduce two-body problem to the one-body problem in general case of deformed Heisenberg algebra leading to minimal length.Two-body problems with delta and Coulomb-like interactions are solved exactly. We obtain analytical expression for the energy spectrum for partial cases of deformation function. The dependence of the energy spectrum on the center-of-mass momentum is found. For special case of deformation function, which correspondes to cutoff procedure in momentum space it is shown that this dependence is more likely to observe for identical particles

Sliding to predict: vision-based beating heart motion estimation by modeling temporal interactions

Purpose: Technical advancements have been part of modern medical solutions as they promote better surgical alternatives that serve to the benefit of patients. Particularly with cardiovascular surgeries, robotic surgical systems enable surgeons to perform delicate procedures on a beating heart, avoiding the complications of cardiac arrest. This advantage comes with the price of having to deal with a dynamic target which presents technical challenges for the surgical system. In this work, we propose a solution for cardiac motion estimation. Methods: Our estimation approach uses a variational framework that guarantees preservation of the complex anatomy of the heart. An advantage of our approach is that it takes into account different disturbances, such as specular reflections and occlusion events. This is achieved by performing a preprocessing step that eliminates the specular highlights and a predicting step, based on a conditional restricted Boltzmann machine, that recovers missing information caused by partial occlusions. Results: We carried out exhaustive experimentations on two datasets, one from a phantom and the other from an in vivo procedure. The results show that our visual approach reaches an average minima in the order of magnitude of 10-7 while preserving the heart’s anatomical structure and providing stable values for the Jacobian determinant ranging from 0.917 to 1.015. We also show that our specular elimination approach reaches an accuracy of 99% compared to a ground truth. In terms of prediction, our approach compared favorably against two well-known predictors, NARX and EKF, giving the lowest average RMSE of 0.071. Conclusion: Our approach avoids the risks of using mechanical stabilizers and can also be effective for acquiring the motion of organs other than the heart, such as the lung or other deformable objects.Peer ReviewedPostprint (published version

Formulation of the Spinor Field in the Presence of a Minimal Length Based on the Quesne-Tkachuk Algebra

In 2006 Quesne and Tkachuk (J. Phys. A: Math. Gen. {\bf 39}, 10909, 2006) introduced a (D+1)-dimensional $(\beta,\beta')$-two-parameter Lorentz-covariant deformed algebra which leads to a nonzero minimal length. In this work, the Lagrangian formulation of the spinor field in a (3+1)-dimensional space-time described by Quesne-Tkachuk Lorentz-covariant deformed algebra is studied in the case where $\beta'=2\beta$ up to first order over deformation parameter $\beta$. It is shown that the modified Dirac equation which contains higher order derivative of the wave function describes two massive particles with different masses. We show that physically acceptable mass states can only exist for $\beta<\frac{1}{8m^{2}c^{2}}$. Applying the condition $\beta<\frac{1}{8m^{2}c^{2}}$ to an electron, the upper bound for the isotropic minimal length becomes about $3 \times 10^{-13}m$. This value is near to the reduced Compton wavelength of the electron $(\lambda_c = \frac{\hbar}{m_{e}c} = 3.86\times 10^{-13} m)$ and is not incompatible with the results obtained for the minimal length in previous investigations.Comment: 11 pages, no figur

V-ANFIS for Dealing with Visual Uncertainty for Force Estimation in Robotic Surgery

Accurate and robust estimation of applied forces in Robotic-Assisted Minimally Invasive Surgery is a very challenging task. Many vision-based solutions attempt to estimate the force by measuring the surface deformation after contacting the surgical tool. However, visual uncertainty, due to tool occlusion, is a major concern and can highly affect the results' precision. In this paper, a novel design of an adaptive neuro-fuzzy inference strategy with a voting step (V-ANFIS) is used to accommodate with this loss of information. Experimental results show a significant accuracy improvement from 50% to 77% with respect to other proposals.Peer ReviewedPostprint (published version