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A quasiclassical approximation is constructed to describe the eigenvalues of the magnetic Laplacian on a compact Riemannian manifold in the case when the magnetic field is not given by an exact 2-form. For this, the multidimensional WKB method in the form of Maslov canonical operator is applied. In this case, the canonical operator takes values in sections of a nontrivial line bundle. The constructed approximation is demonstrated for the Dirac magnetic monopole on the two-dimensional sphere., Comment: 18 pages, v2: minor revisions

Motivated by problems in optimization we study the sparsity of the solutions to systems of linear Diophantine equations and linear integer programs, i.e., the number of non-zero entries of a solution, which is often referred to as the $\ell_0$-norm. Our main results are improved bounds on the $\ell_0$-norm of sparse solutions to systems $A x = b$, where $A \in \mathbb{Z}^{m \times n}$, $b \in \mathbb{Z}^m$ and $x$ is either a general integer vector (lattice case) or a non-negative integer vector (semigroup case). In the lattice case and certain scenarios of the semigroup case, we give polynomial time algorithms for computing solutions with $\ell_0$-norm satisfying the obtained bounds.

In the paper we present the results of extensive studies of palladium-rich Pd1-xFex alloy films epitaxially grown on MgO single-crystal substrate. In a composition range of x = 0.01-0.07 these materials are soft ferromagnets, the saturation magnetization and magnetic anisotropy of which can be tuned by its composition. Vibrating sample magnetometry was used to study temperature dependences of spontaneous magnetic moment and to establish the temperature of magnetic ordering (Curie temperature). Ferromagnetic resonance (FMR) measurements at low temperatures in the in-plane and out-of-plane geometries revealed the four-fold in-plane magnetic anisotropy with the easy directions along the <110> axes of the substrate. The modelling of the angular dependence of the field for resonance allowed to extract the cubic and tetragonal contributions to the magnetic anisotropy of the films and establish their dependence on the concentration of iron in the alloy. Experimental data are discussed in the framework of existing theories of dilute magnetic alloys. Using the anisotropy constants established from FMR, the magnetic hysteresis loops are reproduced utilizing the Stoner-Wohlfarth model thus indicating the predominant coherent magnetic moment rotation at low temperatures. The obtained results compile a database of magnetic properties of a palladium-iron alloy considered as a material for superconducting spintronics., Comment: 20 pages, 7 figures, submitted to Journal of Alloys and Compounds

The propagation of focused wave groups in intermediate water depth and the shoaling zone is experimentally and numerically considered in this paper. The experiments are carried out in a two-dimensional wave flume and wave trains derived from Pierson-Moskowitz and JONSWAP spectrum are generated. The peak frequency does not change during the wave train propagation for Pierson-Moskowitz waves; however, a downshift of this peak is observed for JONSWAP waves. An energy partitioning is performed in order to track the spatial evolution of energy. Four energy regions are defined for each spectrum type. A nonlinear energy transfer between different spectral regions as the wave train propagates is demonstrated and quantified. Numerical simulations are conducted using a modified Boussinesq model for long waves in shallow waters of varying depth. Experimental results are in satisfactory agreement with numerical predictions, especially in the case of wave trains derived from JONSWAP spectrum., Comment: 36 pages, 13 figures, 1 table, 38 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

Density functional theory (DFT) is one of the most widely used tools to solve the many-body Schrodinger equation. The core uncertainty inside DFT theory is the exchange-correlation (XC) functional, the exact form of which is still unknown. Therefore, the essential part of DFT success is based on the progress in the development of XC approximations. Traditionally, they are built upon analytic solutions in low- and high-density limits and result from quantum Monte Carlo numerical calculations. However, there is no consistent and general scheme of XC interpolation and functional representation. Many different developed parametrizations mainly utilize a number of phenomenological rules to construct a specific XC functional. In contrast, the neural network (NN) approach can provide a general way to parametrize an XC functional without any a priori knowledge of its functional form. In this work, we develop NN XC functionals and prove their applicability to 3-dimensional physical systems. We show that both the local density approximation (LDA) and generalized gradient approximation (GGA) are well reproduced by the NN approach. It is demonstrated that the local environment can be easily considered by changing only the number of neurons in the first layer of the NN. The developed NN XC functionals show good results when applied to systems that are not presented in the training/test data. The generalizability of the formulated NN XC framework leads us to believe that it could give superior results in comparison with traditional XC schemes provided training data from high-level theories such as the quantum Monte Carlo and post-Hartree-Fock methods., Comment: Added "Data availability" section. Added some details to article. Fixed typo in abstract. Added new references

We propose a new approach to obtain the nanoscale morphology of rough surfaces from low-temperature adsorption experiments. Our method is based on one of the most realistic models of rough surfaces formulated in terms of random correlated processes and random surface density functional theory (RS-DFT) as a theoretical adsorption model. We consider the roughness in the normal direction, the correlation length of the lateral surface structure and the specific surface area as tuning parameters of RS-DFT to fit the experimental data in the low pressure range, where the influence of the surface geometry is the most crucial. One of the major advantages of the proposed approach over published methods is the best-fit detailed geometry of rough surfaces, which provides full information for further atomistic modeling. The obtained geometry correctly reflects how the nanoroughness of silica materials depends on the synthesis conditions. We demonstrate that the surface fractal dimension observed in many experiments is natural for the correlated random surface model. We investigated the surface geometry of popular silica materials synthesized at different conditions. The obtained roughness parameters and fractal dimensions coincide well with the published experimental data. Analysis of the best fit specific surface area reveals the mechanism of adsorption on rough surfaces and provides a new strategy for the search of optimal storage materials.

The partition function $p(n)$ has been a testing ground for applications of analytic number theory to combinatorics. In particular, Hardy and Ramanujan invented the "circle method" to estimate the size of $p(n)$, which was later perfected by Rademacher who obtained an exact formula. Recently, Chan and Wang considered the fractional partition functions, defined by $\sum_{n = 0}^\infty p_{\alpha}(n)x^n := \prod_{k=1}^\infty (1-x^k)^{-\alpha}$. In this paper we use the Rademacher circle method to find an exact formula for $p_\alpha(n)$ and study its implications, including log-concavity and the higher-order generalizations (i.e., the Tur\'an inequalities) that $p_\alpha(n)$ satisfies., Comment: Fixed typos and made minor stylistic changes

Purpose: To characterize the mean topographical shape of the human limbus of a normal eye and ascertain whether it depends on age and refractive power. Setting: Academic institution. Design: Prospective case series. Methods: 74 subjects aged from 20 to 84 years and with no previous ocular surgeries were included in this study. The left eye was measured four times with a corneo scleral topographer (Eye Surface Profiler). From the raw anterior eye height data of each measurement, topographical limbus was demarcated and fitted in three dimensions to a circle, an ellipse and a Fourier series. Root mean square error (RMSE) was calculated to evaluate the goodness of fit. In addition, white to white (WTW) corneal diameter was taken from the readings of the measuring device and compared with the topographical limbus. For statistical analysis, subjects were grouped as young and older, and also according their equivalent sphere correction. Results: From the considered models, second order Fourier series resulted in the most accurate model to describe the shape of the human limbus. The difference between the topographical limbus diameter and the WTW corneal diameter amounted on average and standard deviation to 0.33 mm and 0.24 mm. Statistically significant differences among eye quadrants were found. No statistically significant difference in horizontal and vertical meridian between age groups (P=0.71 and P=0.082, respectively) or between myopes and emmetropes (P=0.78 and P=0.68, respectively) were found. Conclusions: Human limbus is not symmetrical and its shape is subject dependent but not related to age and eye refractive power.

Point cloud data from 3D LiDAR sensors are one of the most crucial sensor modalities for versatile safety-critical applications such as self-driving vehicles. Since the annotations of point cloud data is an expensive and time-consuming process, therefore recently the utilisation of simulated environments and 3D LiDAR sensors for this task started to get some popularity. With simulated sensors and environments, the process for obtaining an annotated synthetic point cloud data became much easier. However, the generated synthetic point cloud data are still missing the artefacts usually exist in point cloud data from real 3D LiDAR sensors. As a result, the performance of the trained models on this data for perception tasks when tested on real point cloud data is degraded due to the domain shift between simulated and real environments. Thus, in this work, we are proposing a domain adaptation framework for bridging this gap between synthetic and real point cloud data. Our proposed framework is based on the deep cycle-consistent generative adversarial networks (CycleGAN) architecture. We have evaluated the performance of our proposed framework on the task of vehicle detection from a bird's eye view (BEV) point cloud images coming from real 3D LiDAR sensors. The framework has shown competitive results with an improvement of more than 7% in average precision score over other baseline approaches when tested on real BEV point cloud images., Comment: Under review for IEEE SMC 2019

A numerical method for simulation of bubble dynamics in three-dimensional potential flows is presented. The approach is based on the boundary element method for the Laplace equation accelerated via the fast multipole method implemented on a heterogeneous CPU/GPU architecture. For mesh stabilization, a new smoothing technique using a surface filter is presented. This technique relies on spherical harmonics expansion of surface functions for bubbles topologically equivalent to a sphere (or Fourier series for toroidal bubbles). The method is validated by comparisons with solutions available in the literature and convergence studies for bubbles in acoustic fields. The accuracy and performance of the algorithm are discussed. It is demonstrated that the approach enables simulation of dynamics of bubble clusters with thousands of bubbles and millions of boundary elements on contemporary personal workstations. The algorithm is scalable and can be extended to larger systems., Comment: This paper is intended to be published in some journal and prepared in the format required by Computational Mechanics

We show that for both the unary relation of transcendence and the finitary relation of algebraic independence on a field, the degree spectra of these relations may consist of any single computably enumerable Turing degree, or of those c.e. degrees above an arbitrary fixed $\Delta^0_2$ degree. In other cases, these spectra may be characterized by the ability to enumerate an arbitrary $\Sigma^0_2$ set. This is the first proof that a computable field can fail to have a computable copy with a computable transcendence basis.

We obtain a polynomial-time algorithm that, given input (A, b), where A=(B|N) is an integer mxn matrix, m

Purpose: To develop and test a new method for characterizing tear film surface quality with high speed videokeratoscopy utilizing a fractal dimension approach. Methods: The regularity of the reflected pattern in high speed videokeratoscopy (E300, Medmont) depends on tear film stability. Thus determining tear film stability can be addressed by estimating the fractal dimension of the reflected pattern. The method is tested on 39 normal subjects. The results of the fractal dimension approach are compared with those obtained using previously proposed automated method, based on a gray level co-occurrence matrix approach, and with subjective results obtained by two operators which were assessing the video recordings in ideal conditions. Results: fractal dimension method was less affected by eye movements and changes in the videokeratoscopic image background than gray level co-occurrence matrix method. Median difference of the non-invasive break-up time between manual and automated methods was 0.03 s (IQR = 4.47 s.) and 0.0 s (IQR = 2.22 s.) for gray level co-occurrence matrix and fractal dimension approaches, respectively. Correlation coefficient with manual non-invasive break-up time was r2 = 0.86 (p < 0.001) for gray level co-occurrence matrix approach, and r2 = 0.82 (p < 0.001) for fractal dimension approach. Significant statistical difference was found between non-invasive break-up measurements of manual and gray level co-occurrence matrix method (p = 0.008). Conclusions: The proposed method has the potential to characterize tear film dynamics in more detail compared to previous methods based on high speed videokeratoscopy. It showed good correlation with manual assessment of tear film.

Purpose: To describe a new methodology for tear-film dynamics assessment by observing fluorescein decay rate over time and to understand the relationship between the newly defined tear fluorescein washout rate (TFWR)and other measures of the tear film behaviour. Methods: Forty subjects (24F/16M) aged (mean +/- standard deviation) 31.8 +/- 14.2 years volunteered for the study. It consisted of the review of medical history, McMonnies questionnaire (McMQ), slit lamp examination, and TFWR using a newly-developed fluorescein profilometry. The repeatability of TFWR measurements was assessed. TFWR estimates were contrasted against patient age, McMQ score, daytime, fluorescein tear film breakup time (FTBUT), tear meniscus height (TMH) and blink frequency. Results: Mean repeatability of the method was 28.13 +/- 9.59%. The group mean TFWR was 39 +/- 23% at 30-s mark after the beginning of measurements, ranging from 1.4% to 83%. This indicates that TFWR is highly subject-dependent. Statistically significant correlations were found between the percentage TFWR and McMQ score (r2 =0.214, p = 0.001) as well as FTBUT (r2 =0.136, p = 0.009). No statistically significant correlations were found between TFWR and age, daytime, TMH, and blink frequency. Conclusions: Fluorescein profilometry allows clinicians to follow dynamic changes in the tear film on the entire ocular surface and may be used for qualitative assessment of the tear film dynamics.

Introduction. The aim is to provide a summary of methods available for the assessment of tear turnover and tear clearance rates. The review defines tear clearance and tear turnover and describes their implication for ocular surface health. Additionally, it describes main types of techniques for measuring tear turnover, including fluorescein tear clearance tests, techniques utilizing electromagnetic spectrum and tracer molecule and novel experimental techniques utilizing optical coherence tomography and fluorescein profilometry. Areas covered. Internet databases (PubMed, Science Direct, Google Scholar) and most frequently cited references were used as a principal resource of information on tear turnover rate and tear clearance rate, presenting methodologies and equipment, as well as their definition and implications for the anterior eye surface health and function. Keywords used for data-search were as follows: tear turnover, tear clearance, fluorescein clearance, scintigraphy, fluorophotometry, tear flow, drainage, tear meniscus dynamics, Krehbiel flow and lacrimal functional unit. Expert Commentary. After decades, the topic of tear turnover assessment is reintroduced. Recently, new techniques have been developed to propose less invasive, less time consuming and simpler methodologies for the assessment of tear dynamics that have the potential to be utilized in a clinical practice. Keywords. Fluorescein clearance test, fluorophotometry, tear clearance, tear film dynamics, tear turnover, scintigraphy, optical coherence tomography.

Purpose: To assess the early-phase of tear clearance rate (TCR) with anterior segment optical coherence tomography (OCT) and to determine the association between TCR and other clinical measures of the tear film in a group of young subjects with different levels of tear film quality. Methods: TCR was classified as the percentage decrease of the inferior tear meniscus height 30s after instillation of 5uL 0.9% saline solution. Fifty subjects (32F and 18M) aged (mean +/- standard deviation) 25.5 +/- 4.3 years volunteered for the study. It consisted of a review of medical history, Ocular Surface Disease Index (OSDI) questionnaire, tear film osmolarity measurements, slit lamp examination and TCR estimation based on dynamic measurements of the lower tear meniscus with OCT. Estimates of TCR were contrasted against subject age and tear film measures commonly used for dry eye diagnosis, which includes OSDI score, fluorescein tear film break-up time (FBUT), tear meniscus height (TMH), blinking frequency, tear film osmolarity and corneal staining. Results: The group mean TCR was 29 +/- 13% and 36 +/- 19% respectively after 30 and 60 s margin after saline solution instillation. Statistically significant correlations were found between TCR and FBUT (r2=0.319, p<0.001), blinking frequency (r2=0.138, p<0.01), tear film osmolarity (r2=0.133, p<0.01) and age (r2=0.095, p<0.05). Conclusions: Anterior segment optical coherence tomography allows following changes of tear meniscus morphology post saline solution instillation and evaluating the TCR. OCT based TCR might be used as additional measure of the lacrimal functional unit.

The Guillemin-Uribe trace formula is a semiclassical version of the Selberg trace formula and more general Duistermaat-Guillemin formula for elliptic operators on compact manifolds, which reflects the dynamics of magnetic geodesic flows in terms of eigenvalues of a natural differential operator (the magnetic Laplacian) associated with the magnetic field. In this paper, we give a survey of basic notions and results related with the Guillemin-Uribe trace formula and provide concrete examples of its computation for two-dimensional constant curvature surfaces with constant magnetic fields and for the Katok example., Comment: 37 pages, v2: minor corrections, references added