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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

It is known that the interplay of the spin-orbit-coupling (SOC) and mean-field self-attraction creates stable two-dimensional (2D) solitons (ground states) in spinor Bose-Einstein condensates. However, SOC destroys the system's Galilean invariance, therefore moving solitons exist only in a narrow interval of velocities, outside of which the solitons suffer delocalization. We demonstrate that the application of a relatively weak moving optical lattice (OL), with the 2D or quasi-1D structure, makes it possible to greatly expand the velocity interval for stable motion of the solitons. The stability domain in the system's parameter space is identified by means of numerical methods. In particular, the quasi-1D OL produces a stronger stabilizing effect than its full 2D counterpart. Some features of the domain are explained analytically. Comment: to be published in Journal of Physics B: At. Mol. Opt. Phys

In this paper we developed the resolvent method for super-operator equations with their applications in quantum optics. Our approach is based on the novel concept of linear super-operator acting on the Hilbert subspace of vector or scalar linear operators satisfying physically reasonable commutation relations. The super-operator equations for the electromagnetic (EM) field operators are formulated for the problems of quantum antenna emission and quantum light scat-tering by a dielectric body. The general solution of super-operator equation is presented in terms of the classical resolvent. In contrast to the classical case, it includes the ancillary components associated with the quantum noise even in the absence of absorption. The reason for it lies in the energy exchange between different spatial regions with various bases for the field presentation (it looks like losses or gain from the point of view of the correspondent region). A number of examples (two-element dipole antenna, plane dielectric layer, and dielectric cylinder with circular cross section) which demonstrate the physical mechanism of the appearance of noise are considered. It is shown, that antenna emission or scattering transforms the coherent properties of quantum light. This opens a new way of controlling the coherence in a direction dependent manner, a feature that can be useful in various applications of quantum technologies, including, quantum radars and lidars, and quantum antennas. Comment: 26 pages with 4 figures

During a cosmological first-order phase transition, particles of the plasma crossing the bubble walls can radiate a gauge boson. The resulting pressure cannot be computed perturbatively for large coupling constant and/or large supercooling. We resum the real and virtual emissions at all leading-log orders, both analytically and numerically using a Monte-Carlo simulation. We find that radiated bosons are dominantly soft and that the resulting retarding pressure on relativistic bubble walls is linear both in the Lorentz boost and in the order parameter, up to a log. We further quantitatively discuss IR cut-offs, wall thickness effects, the impact of various approximations entering the calculation, and comment on the fate of radiated bosons that are reflected. Comment: 26 pages, 8 figures, plus appendices and references. v2: additional references added, matches JHEP publication

We present a deterministic $O(\log \log \log n)$-round low-space Massively Parallel Computation (MPC) algorithm for the classical problem of $(\Delta+1)$-coloring on $n$-vertex graphs. In this model, every machine has a sublinear local memory of size $n^{\phi}$ for any arbitrary constant $\phi \in (0,1)$. Our algorithm works under the relaxed setting where each machine is allowed to perform exponential (in $n^{\phi}$) local computation, while respecting the $n^{\phi}$ space and bandwidth limitations. Our key technical contribution is a novel derandomization of the ingenious $(\Delta+1)$-coloring LOCAL algorithm by Chang-Li-Pettie (STOC 2018, SIAM J. Comput. 2020). The Chang-Li-Pettie algorithm runs in $T_{local}=poly(\log\log n)$ rounds, which sets the state-of-the-art randomized round complexity for the problem in the local model. Our derandomization employs a combination of tools, most notably pseudorandom generators (PRG) and bounded-independence hash functions. The achieved round complexity of $O(\log\log\log n)$ rounds matches the bound of $\log(T_{local})$, which currently serves an upper bound barrier for all known randomized algorithms for locally-checkable problems in this model. Furthermore, no deterministic sublogarithmic low-space MPC algorithms for the $(\Delta+1)$-coloring problem were previously known. Comment: 44 pages, appeared at PODC 2021

While neural language models often perform surprisingly well on natural language understanding (NLU) tasks, their strengths and limitations remain poorly understood. Controlled synthetic tasks are thus an increasingly important resource for diagnosing model behavior. In this work we focus on story understanding, a core competency for NLU systems. However, the main synthetic resource for story understanding, the bAbI benchmark, lacks such a systematic mechanism for controllable task generation. We develop Dyna-bAbI, a dynamic framework providing fine-grained control over task generation in bAbI. We demonstrate our ideas by constructing three new tasks requiring compositional generalization, an important evaluation setting absent from the original benchmark. We tested both special-purpose models developed for bAbI as well as state-of-the-art pre-trained methods, and found that while both approaches solve the original tasks (>99% accuracy), neither approach succeeded in the compositional generalization setting, indicating the limitations of the original training data. We explored ways to augment the original data, and found that though diversifying training data was far more useful than simply increasing dataset size, it was still insufficient for driving robust compositional generalization (with <70% accuracy for complex compositions). Our results underscore the importance of highly controllable task generators for creating robust NLU systems through a virtuous cycle of model and data development. Comment: Code and data will be made available at project page: https://tiny.one/8wjxwd7z

Today, Machine Learning (ML) applications can have access to tens of thousands of features. With such feature sets, efficiently browsing and curating subsets of most relevant features is a challenge. In this paper, we present a novel approach to visualize up to several thousands of features in a single image. The image not only shows information on individual features, but also expresses feature interactions via the relative positioning of features.

The virial theorem, and the equipartition theorem in the case of quadratic degrees of freedom, are handy constraints on the statistics of equilibrium systems. Their violation is instrumental in determining how far from equilibrium a driven system might be. We extend the virial theorem to nonequilibrium conditions for Langevin dynamics with nonlinear friction and multiplicative noise. In particular, we generalize the equipartition theorem for confined laser-cooled atoms in the semi-classical regime. The resulting relation between the lowest moments of the atom position and velocity allows to measure in experiments how dissipative the cooling mechanism is. Moreover, its violation can reveal the departure from a strictly harmonic confinement or from the semi-classical regime. Comment: 7 pages, 3 figures

The Rosenzweig-Porter random matrix ensemble serves as a qualitative phenomenological model for the level statistics and fractality of eigenstates across the many-body localization transition in static systems. We propose a unitary (circular) analogue of this ensemble, which similarly captures the phenomenology of many-body localization in periodically driven (Floquet) systems. We define this ensemble as the outcome of a Dyson Brownian motion process. We show numerical evidence that this ensemble shares some key statistical properties with the Rosenzweig-Porter ensemble for both the eigenvalues and the eigenstates. Comment: 7 pages, 3 figures

Motivated from the surrounding property of a point set in $\mathbb{R}^d$ introduced by Holmsen, Pach and Tverberg, we consider the transversal number and chromatic number of a simplicial sphere. As an attempt to give a lower bound for the maximum transversal ratio of simplicial $d$-spheres, we provide two infinite constructions. The first construction gives infintely many $(d+1)$-dimensional simplicial polytopes with the transversal ratio exactly $\frac{2}{d+2}$ for every $d\geq 2$. In the case of $d=2$, this meets the previously well-known upper bound $1/2$ tightly. The second gives infinitely many simplicial 3-spheres with the transversal ratio greater than $1/2$. This was unexpected from what was previously known about the surrounding property. Moreover, we show that, for $d\geq 3$, the facet hypergraph $\mathcal{F}(\mathsf{K})$ of a $d$-dimensional simplicial sphere $\mathsf{K}$ has the chromatic number $\chi(\mathcal{F}(\mathsf{K})) \in O(n^{\frac{\lceil d/2\rceil-1}{d}})$, where $n$ is the number of vertices of $\mathsf{K}$. This slightly improves the upper bound previously obtained by Heise, Panagiotou, Pikhurko, and Taraz. Comment: 22 pages, 2 figures