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Numerical simulation of superconducting devices is a powerful tool for understanding the principles of their work and improving their design. We present a new pseudospectral method for two-dimensional magnetization and transport current superconducting strip problems with an arbitrary current-voltage relation, spatially inhomogeneous strips, and strips in a nonuniform applied field. The method is based on the bivariate expansions in Chebyshev polynomials and Hermite functions. It can be used for numerical modeling magnetic flux pumps of different types and investigating AC losses in coated conductors with local defects. Using a realistic two-dimensional version of the superconducting dynamo benchmark problem as an example, we showed that our new method is a competitive alternative to finite element methods. Comment: 20 pages

We address dynamics of Bose-Einstein condensates (BECs) loaded into a one-dimensional four-color optical lattice (FOL) potential with commensurate wavelengths and tunable intensities. This configuration lends system-specific symmetry properties. The analysis identifies specific multi-parameter forms of the FOL potential which admits exact solitary-wave solutions. This newly found class of potentials includes more particular species, such as frustrated double-well superlattices, and bi-chromatic and three-color lattices, which are subject to respective symmetry constraints. Our exact solutions provide options for controllable positioning of density maxima of the localized patterns, and tunable Anderson-like localization in the frustrated potential. A numerical analysis is performed to establish dynamical stability and structural stability of the obtained solutions, which makes them relevant for experimental realization. The newly found solutions offer applications to the design of schemes for quantum simulations and processing quantum information. Comment: 7 pages, 6 figures

We investigate the relations between algebraic structures, spectral invariants, and persistence modules, in the context of monotone Lagrangian Floer homology with Hamiltonian term. Firstly, we use the newly introduced method of filtered continuation elements to prove that the Lagrangian spectral norm controls the barcode of the Hamiltonian perturbation of the Lagrangian submanifold, up to shift, in the bottleneck distance. Moreover, we show that it satisfies Chekanov type low-energy intersection phenomena, and non-degeneracy theorems. Secondly, we introduce a new averaging method for bounding the spectral norm from above, and apply it to produce precise uniform bounds on the Lagrangian spectral norm in certain closed symplectic manifolds. Finally, by using the theory of persistence modules, we prove that our bounds are in fact sharp in some cases. Along the way we produce a new calculation of the Lagrangian quantum homology of certain Lagrangian submanifolds, and answer a question of Usher. Comment: 71 pages, 6 figures

In this paper we prove the generalized Kaplansky conjecture for the Jordan algebras of the type $J_n$ in particular for self adjoint $2\times 2$ matrices over $\R$, over $\C$, $\HH$ and $\Oct$. In fact, we prove that the image of multilinear polynomial must be either $\{0\}$, $\mathbb{R}$, the space of pure elements $V$, or $J_n$.

Metallography is crucial for a proper assessment of material's properties. It involves mainly the investigation of spatial distribution of grains and the occurrence and characteristics of inclusions or precipitates. This work presents an holistic artificial intelligence model for Anomaly Detection that automatically quantifies the degree of anomaly of impurities in alloys. We suggest the following examination process: (1) Deep semantic segmentation is performed on the inclusions (based on a suitable metallographic database of alloys and corresponding tags of inclusions), producing inclusions masks that are saved into a separated database. (2) Deep image inpainting is performed to fill the removed inclusions parts, resulting in 'clean' metallographic images, which contain the background of grains. (3) Grains' boundaries are marked using deep semantic segmentation (based on another metallographic database of alloys), producing boundaries that are ready for further inspection on the distribution of grains' size. (4) Deep anomaly detection and pattern recognition is performed on the inclusions masks to determine spatial, shape and area anomaly detection of the inclusions. Finally, the system recommends to an expert on areas of interests for further examination. The performance of the model is presented and analyzed based on few representative cases. Although the models presented here were developed for metallography analysis, most of them can be generalized to a wider set of problems in which anomaly detection of geometrical objects is desired. All models as well as the data-sets that were created for this work, are publicly available at https://github.com/Scientific-Computing-Lab-NRCN/MLography. Comment: arXiv admin note: substantial text overlap with arXiv:2003.04226 Same text as last submission, changed the author list to correspond to the pdf

An emerging challenge for time-to-event data is studying semi-competing risks, namely when two event times are of interest: a non-terminal event time (e.g. age at disease diagnosis), and a terminal event time (e.g. age at death). The non-terminal event is observed only if it precedes the terminal event, which may occur before or after the non-terminal event. Studying treatment or intervention effects on the dual event times is complicated because for some units, the non-terminal event may occur under one treatment value but not under the other. Until recently, existing approaches (e.g., the survivor average causal effect) generally disregarded the time-to-event nature of both outcomes. More recent research focused on principal strata effects within time-varying populations under Bayesian approaches. In this paper, we propose alternative non time-varying estimands, based on a single stratification of the population. We present a novel assumption utilizing the time-to-event nature of the data, which is weaker than the often-invoked monotonicity assumption. We derive results on partial identifiability, suggest a sensitivity analysis approach, and give conditions under which full identification is possible. Finally, we present non-parametric and semi-parametric estimation methods for right-censored data. Comment: 35 pages, 3 figure, 3 tables

We describe how the observed polarization properties of an astronomical object are related to its intrinsic polarization properties and the finite temporal and spectral resolutions of the observing device. Moreover, we discuss the effect that a scattering screen, with non-zero magnetic field, between the source and observer has on the observed polarization properties. We show that the polarization properties are determined by the ratio of observing bandwidth and coherence bandwidth of the scattering screen and the ratio of temporal resolution of the instrument and the variability time of screen, as long as the length over which the Faraday rotation induced by the screen changes by $\sim\pi$ is smaller than the size of the screen visible to the observer. We describe the conditions under which a source that is 100\% linearly polarized intrinsically might be observed as partially depolarized, and how the source's temporal variability can be distinguished from the temporal variability induced by the scattering screen. In general, linearly polarized waves passing through a magnetized scattering screen can develop a significant circular polarization. We apply the work to the observed polarization properties of a few fast radio bursts (FRBs), and outline potential applications to pulsars. Comment: 15 pages, 9 figures. Accepted for publication in MNRAS