Boundary rigidity for Randers metrics

If a non-reversible Finsler norm is the sum of a reversible Finsler norm and a closed 1-form, then one can uniquely recover the 1-form up to potential fields from the boundary distance data. We also show a boundary rigidity result for Randers metrics where the reversible Finsler norm is induced by a Riemannian metric which is boundary rigid. Our theorems generalize Riemannian boundary rigidity results to some non-reversible Finsler manifolds. We provide an application to seismology where the seismic wave propagates in a moving medium.

Effects of Multiple Filters on Liver Tumor Segmentation From CT Images

Segmentation of liver tumors from Computerized Tomography (CT) images remains a challenge due to the natural variation in tumor shape and structure as well as the noise in CT images. A key assumption is that the performance of liver tumor segmentation depends on the characteristics of multiple features extracted from multiple filters. In this paper, we design an enhanced approach based on a two-class (liver, tumor) convolutional neural network that discriminates tumor as well as liver from CT images. First, the contrast and intensity values in CT images are adjusted and high frequencies are removed using Hounsfield units (HU) filtering and standardization. Then, the liver tumor is segmented from entire images with multiple filter U-net (MFU-net). Finally, a quantitative analysis is carried out to evaluate the segmentation results using three different methods: boundary-distance-based metrics, size-based metrics, and overlap-based metrics. The proposed method is validated on CT images from the 3Dircadb and LiTS dataset. The results demonstrate that the multiple filters are useful for extracting local and global feature simultaneously, minimizing the boundary distance errors, and our approach demonstrates better performance in heterogeneous tumor regions of CT images.

PROCEDURE FOR ESTIMATING THE BOUNDARY DISTANCE OF SHORE RADIO STATIONS IN VHF RANGE FOR THE SHORE-TO-SHIP DIRECTION

Сформулирована и детализирована методика оценивания граничной дальности береговых ОВЧ радиостанций в направлении Берег-Судно, которая основана на зависимостях напряженности поля, полученных эмпирическим путем. Определены численные значения граничной дальности ОВЧ радиосвязи применительно к типовому судовому радиооборудованию и шумовой обстановке вблизи судовой антенны. Проведена оценка максимальных допусков определения граничной дальности ОВЧ радиосвязи. The procedure for estimating the boundary distance of the shore VHF radio stations in the shore-to-ship direction, which is based on the dependences of the electromagnetic field strength obtained empirically, has been formulated and detailed. Numerical values of the boundary distance of VHF radio communication in relation to typical ship radio equipment and the noise environment near the ship's antenna are determined. The estimation of the maximum tolerances for determining the boundary distance of VHF radio communication is carried out.

Recognition of Multiscale Dense Gel Filament-Droplet Field in Digital Holography With Mo-U-Net

Accurate particle detection is a common challenge in particle field characterization with digital holography, especially for gel secondary breakup with dense complex particles and filaments of multi-scale and strong background noises. This study proposes a deep learning method called Mo-U-net which is adapted from the combination of U-net and Mobilenetv2, and demostrates its application to segment the dense filament-droplet field of gel drop. Specially, a pruning method is applied on the Mo-U-net, which cuts off about two-thirds of its deep layers to save its training time while remaining a high segmentation accuracy. The performances of the segmentation are quantitatively evaluated by three indices, the positive intersection over union (PIOU), the average square symmetric boundary distance (ASBD) and the diameter-based prediction statistics (DBPS). The experimental results show that the area prediction accuracy (PIOU) of Mo-U-net reaches 83.3%, which is about 5% higher than that of adaptive-threshold method (ATM). The boundary prediction error (ASBD) of Mo-U-net is only about one pixel-wise length, which is one third of that of ATM. And Mo-U-net also shares a coherent size distribution (DBPS) prediction of droplet diameters with the reality. These results demonstrate the high accuracy of Mo-U-net in dense filament-droplet field recognition and its capability of providing accurate statistical data in a variety of holographic particle diagnostics. Public model address: https://github.com/Wu-Tong-Hearted/Recognition-of-multiscale-dense-gel-filament-droplet-field-in-digital-holography-with-Mo-U-net.

Exact Solution of the Schrödinger Equation for Composition of Coulomb and Oscillator Potentials

The spherically symmetric potential is considered whose dependence on the distance r is described by the smooth composition of Coulomb at r < r0 and oscillator at r > r0 potentials. The boundary distance r0 is determined by the parameters of these potentials. The exact continuous solution of the radial Schrödinger equation is expressed in terms of the confluent hypergeometric functions. The discrete energy levels are obtained. The graphic illustrations for the energy spectrum and the radial wave functions are presented.

A Boundary Distance-Based Symbolic Aggregate Approximation Method for Time Series Data

A large amount of time series data is being generated every day in a wide range of sensor application domains. The symbolic aggregate approximation (SAX) is a well-known time series representation method, which has a lower bound to Euclidean distance and may discretize continuous time series. SAX has been widely used for applications in various domains, such as mobile data management, financial investment, and shape discovery. However, the SAX representation has a limitation: Symbols are mapped from the average values of segments, but SAX does not consider the boundary distance in the segments. Different segments with similar average values may be mapped to the same symbols, and the SAX distance between them is 0. In this paper, we propose a novel representation named SAX-BD (boundary distance) by integrating the SAX distance with a weighted boundary distance. The experimental results show that SAX-BD significantly outperforms the SAX representation, ESAX representation, and SAX-TD representation.

Meshless method using fundamental solution applied to computational simulation of groundwater flow of real aquifers: study case (Guariroba’s APA and Juazeiro do Norte)

ABSTRACT We investigated the influence of fictitious boundary distance, a parameter of MFS, to determine piezometric levels of two unconfined sedimentary aquifers assuming Dupuit-Forchheimer and steady-state flow hypothesis. Two study areas were modelled: Guariroba’s Environmental Protection Area, in Mato Grosso do Sul State, Brazil, and Juazeiro do Norte City, in Ceará State, Brazil. It was observed that in order to use the MFS as a numerical method in modeling groundwater flow, it is necessary to determine the best distance value of the fictitious boundary. This value can be chosen from the use of field data within the analyzed domain, where the relative error is a parameter to be minimized. Applying this methodology and comparing with the results of the MODFLOW application for the same set of initial data, we concluded that the MSF allows to estimate the piezometric level values within the analyzed domains and that the results of the statistical comparison between them point to the need to investigate the representativeness of both methods to determine which one is most appropriate for modelling the groundwater flow in each region.