The symmetrization map $$\pi :{\mathbb{C}}^2\rightarrow {\mathbb{C}}^2$$ is defined by (z_1,z_2)=(z_1+z_2,z_1z_2).$$ closed symmetrized bidisc $$\Gamma$$ the of unit $$\overline{{\mathbb{D}}^2}$$ , that is, $$\begin{aligned} \Gamma = \pi (\overline{{\mathbb{D}}^2})=\{ (z_1+z_2,z_1z_2)\,:\, |z_i|\le 1, i=1,2 \}. \end{aligned}$$ A pair commuting Hilbert space operators (S, P) for which a spectral...

— It is shown that it is possible to achieve complete formal symmetrization in the electron and proton quantum theory by means of a new quantization process. The meaning of Dirac equations is somewhat modified and there is no longer any reason to speak of negative-energy states nor to assume, for any other types of particles, especially neutral ones, the existence of antiparticles, correspondin...

schwartz-jampel syndrome, (sjs) is a rare disorder characterized by myotonia, joint contracture, facial dysmorphism and growth retardation, we present three siblings (two sisters and one brother) 19,24 and 27 years old from consanguineous healthy parents with sjs. their clinical features were similar to those previously described. motor and sensory nerve conduction study (ncs) were compatible w...

Many machine learning data sets are embedded in high-dimensional spaces, and require some type of dimensionality reduction to visualize or analyze the data. In this paper, we propose a novel framework for multiscale dimensionality reduction based on diffusion wavelets. Our approach is completely data driven, computationally efficient, and able to directly process non-symmetric neighborhood rela...

We argue that symmetrization of an incoming microstate with similar states in a sea of microstates contained in a macroscopic detector can produce an effective image, which does not contradict the no-cloning theorem, and such a combinatorial set can then be used with first passage random walk interactions suggested in an earlier work to give the right quantum mechanical weight for measured eige...

LFA-1 activation plays a major role in reducing the velocity of rolling leukocytes and causing firm adhesion to the endothelium. The signaling cascades that cause LFA-1 activation during this process have been described through mostly correlative experiments, but the precise occurrence and location of LFA-1 activation in response to specific signals has not been directly shown. Tim Springer’s g...