Geometric multiaxial representation of N-qubit mixed symmetric separable states

Study of an N qubit mixed symmetric separable states is a long standing challenging problem as there exist no unique separability criterion. In this regard, we take up the N-qubit mixed symmetric separable states for a detailed study as these states are of experimental importance and offer elegant mathematical analysis since the dimension of the Hilbert space reduces from 2N to N + 1. Since there exists a one to one correspondence between spin-j system and an N-qubit symmetric state, we employ Fano statistical tensor parameters for the parametrization of spin density matrix. Further, we use geometric multiaxial representation (MAR) of density matrix to characterize the mixed symmetric separable states. Since separability problem is NP hard, we choose to study it in the continuum limit where mixed symmetric separable states are characterized by the P-distribution function λ (ᶿ, Φ) We show that the N-qubit mixed symmetric separable state can be visualized as a uniaxial system if the distribution function is independent of ᶿ, and Φ. We further choose distribution function to be the most general positive function on a sphere and observe that the statistical tensor parameters characterizing the N-qubit symmetric system are the expansion coefficients of the distribution function. As an example for the discrete case, we investigate the MAR of a uniformly weighted two qubit mixed symmetric separable state. We also observe that there exists a correspondence between separability and classicality of states

De novo and inherited mutations in the X-linked gene CLCN4 are associated with syndromic intellectual disability and behavior and seizure disorders in males and females

Variants in CLCN4, which encodes the chloride/hydrogen ion exchanger CIC-4 prominently expressed in brain, were recently described to cause X-linked intellectual disability and epilepsy. We present detailed phenotypic information on 52 individuals from 16 families with CLCN4-related disorder: 5 affected females and 2 affected males with a de novo variant in CLCN4 (6 individuals previously unreported) and 27 affected males, 3 affected females and 15 asymptomatic female carriers from 9 families with inherited CLCN4 variants (4 families previously unreported). Intellectual disability ranged from borderline to profound. Behavioral and psychiatric disorders were common in both child- and adulthood, and included autistic features, mood disorders, obsessive-compulsive behaviors and hetero- and autoaggression. Epilepsy was common, with severity ranging from epileptic encephalopathy to well-controlled seizures. Several affected individuals showed white matter changes on cerebral neuroimaging and progressive neurological symptoms, including movement disorders and spasticity. Heterozygous females can be as severely affected as males. The variability of symptoms in females is not correlated with the X inactivation pattern studied in their blood. The mutation spectrum includes frameshift, missense and splice site variants and one single-exon deletion. All missense variants were predicted to affect CLCN4's function based on in silico tools and either segregated with the phenotype in the family or were de novo. Pathogenicity of all previously unreported missense variants was further supported by electrophysiological studies in Xenopus laevis oocytes. We compare CLCN4-related disorder with conditions related to dysfunction of other members of the CLC family.E.E. Palmer ... E. Haan ... J. Nicholl, M. Shaw ... J. Gecz ... et al

Existence of a lens-shaped cluster of surfaces self-shrinking by mean curvature

We rigorously show the existence of a rotationally and centrally symmetric "lens-shaped" cluster of three surfaces, meeting at a smooth common circle, forming equal angles of 120 degrees, self-shrinking under the motion by mean curvature.Comment: 22 pages, 2 figure

Papyrographic separation and location of antibiotics from plants

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Parametric design study of the Orbiting Astronomical Satellite for Investigating Stellar Systems (OASIS) space telescope

OASIS (Orbiting Astronomical Satellite for Investigating Stellar Systems) is a space-based observatory with a large inflatable primary reflector that will perform high spectral resolution observations at terahertz frequencies. An inflatable metallized polymer membrane serves as the primary antenna with large photon collecting area, followed by aberration correction mirror pair that enables a large field of regards of 0.1 degrees while achieving diffraction limited performance over a wide terahertz wavelength ranging from 80 μm to 660 μm. An analytical model is developed to define a solution space based on the profile of primary reflector which is a function of pressure. The photon collecting area, size and weight of the correction mirror pair, and optical aberrations are governed by a 1st order power arrangement of the telescope and is a function of base radius and clear aperture of the primary reflector. Based on the parametric design study, the figure of merit for the profile of the primary reflector is discussed and a baseline design satisfying the scientific and system requirements is proposed. © The Authors.Open access articleThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

All reflective THz telescope design with an inflatable primary antenna for Orbiting Astronomical Satellite for Investigating Stellar Systems (OASIS) mission

With an inflatable membrane, a space antenna having an order of magnitude larger photon collection area as compared to the state of the art is feasible. An integrated and comprehensive study has been performed by the scientists and engineers team at NASA Goddard, Northrup Grumman, L’Garde and University of Arizona. As a part of the study, optical design for the 19m antenna is overviewed here. © 2021 SPIE.Open access articleThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Analytical and finite element analysis tool for nonlinear membrane antenna modeling for astronomical applications

The uninflated shape configurations of parabolic and spherical membrane mirrors were calculated by solving the inverse problem, i.e., given the design inflation pressure, the membrane material and geometric properties, what must be the initial uninflated shape such that on inflation to the design pressure, the exact desired surface of revolution is obtained. The resulting first order nonlinear differential equation was numerically integrated using the boundary conditions. The initial uninflated shape was then subjected to a forward transformation using FAIM, a proprietary geometric nonlinear membrane finite element code. FAIM has been validated against exact analytical solutions for both small and extremely large deformations that are up to eight orders of magnitude larger compared with the starting undeflected shape. Simulations reveal that to fabricate a very accurate and precise inflated membrane mirror relative to the design parameters, one must not only accurately measure and input the moduli in both meridional and hoop directions but an accurately measured Poisson’s ratio as well. The code was used to guide the membrane mirror design. For very small aperture diameters, the initial uninflated shape may be fabricated by thermo-forming the membrane. For aperture diameters exceeding one meter however, the membrane mirror is built with discrete gores that are joined together with tapes at the seams. This provided the impetus to write a companion computer code FLATE, to calculate the gore shapes using a slight modification of the solution to the inverse transformation equation to account for the presence of the seam tapes. After the gores were determined, the resulting final inflated shape was calculated and verified using FAIM. Sensitivity analyses can now be carried out to determine the resulting surface shape as a function of the different sources of error: gore width, gore length, perimeter attachment uncertainties, thermal effects, variation of material properties over the membrane continuum and inflation pressure changes. The code has been shown to be more robust than equivalent commercial analytical packages in so far as membrane, cable and space-frame element combinations are concerned. In particular, the analytical and finite element codes were used in the preliminary assessment of a membrane optic for the OASIS Mission (Orbiting Astronomical Satellite for Investigating Stellar Systems) [1]. The OASIS is a 20-meter class space observatory operating at high spectral resolution in the terahertz frequencies. Over its nominal 2-year mission it will probe conditions and search for biogenic molecules on hundreds of protoplanetary disks and other solar system objects. © 2021 SPIE.Immediate accessThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]