Spatial Points Research Articles

Topology optimization via implicit neural representations

Along with the rapid development of artificial intelligence (AI) technology, scientific research enters a new era of AI. Topology optimization (TO) and AI technology are recently showing a growing trend of cross development, which has received continuous attentions from relative researchers. In this paper, we introduce a concept of Implicit Neural Representations from AI into TO field and establish a novel TO framework which is named as TOINR. In TOINR, the Topology Description Function is the inherent combination factor, which is constructed by a Neural Network (NN) and determines the topology statuses of structural materials in the design domain. We adopt sine as a periodic activation function combined with MLP as the architecture of the NN. The inputs of NN are a predefined set of spatial points’ coordinates, while the outputs are the implicit representations of corresponding topological boundaries. Along with updating NN’s parameters (i.e., design variables), the structural topologies iteratively evolve according to the responses analysis results and optimization functions. A boundary-adaptive multi-resolution finite element analysis method is developed to improve the physical response accuracy. At each step of TOINR, we ensure the computational differentiability. Thus, the automatic differentiation is used in sensitivity analysis. The multi-penalty function approach is applied to handle objects with constraints. Besides, we design an adaptive adjustment scheme for learning rates to enhance the stability of the optimization process. Numerical examples illustrate that TOINR can stably obtain optimized structures for different problems with high performance and robustness.

Frame rate effects and their compensation on super-resolution microvessel imaging using ultrasound localization microscopy

Ultrasound localization microscopy (ULM) breaks the diffraction limit and allows imaging microvasculature at micrometric resolution while preserving the penetration depth. Frame rate plays an important role for high-quality ULM imaging, but there is still a lack of review and investigation of the frame rate effects on ULM. This work aims to clarify how frame rate influences the performance of ULM, including the effects of microbubble detection, localization and tracking. The performance of ULM was evaluated using an in vivo rat brain dataset (15.6 MHz, 3 tilted plane waves (−5°, 0°, +5°), at a compounded frame rate of 1000 Hz) with different frame rates. Quantification methods, including Fourier ring correlation and saturation parameter, were applied to analyze the spatial resolution and reconstruction efficiency, respectively. In addition, effects on each crucial step in ULM processing were further analyzed. Results showed that when frame rates dropped from 1000 Hz to 250 Hz, the spatial resolution deteriorated from 9.9 μm to 15.0 μm. Applying a velocity constraint was able to improve the ULM performance, but inappropriate constraint may artificially result in high apparent resolution. For the dataset, compared with the results of 1000 Hz frame rate, the velocity was underestimated at 100 Hz with 47.18% difference and the saturation was reduced from 55.00% at 1000 Hz to 43.34% at 100 Hz. Analysis showed that inadequate frame rate generated unreliable microbubble detection, localization and tracking as well as incomplete track reconstruction, resulting in the deterioration in spatial resolution, the underestimation in velocity measurement and the decrease in saturation. Finally, a guidance of determining the frame rate requirement was discussed by considering the required spatial sampling points based on vessel morphology, clutter filtering method, tracking algorithm and acquisition time, which provides indications for future clinical application of ULM method.

Gaussian filtering method of evaluating the elastic/elasto-plastic properties of sintered nanocomposites with quasi-continuous volume distribution

In this work, combing the Gaussian filtering algorithm and the cutting quantile functions, a new technique is developed to efficiently generate the RVE of randomly distributed metal matrix nanocomposites (MMNCs) with quasi-continuous volume distribution. The procedures of filtering the random point matrix, generating the random field, separating the spatial points into constituents, and imposing the periodic boundary conditions are numerically implemented in detail. By contrasting the elastic/elasto-plastic properties of the sintered AgNPs composites with those determined by experimental measurements and analytical models, the proposed numerical homogenization model is verified. The results show that the proposed algorithm can control the distributions of the reinforcement size and the matrix volume fractions by tailoring the Gaussian widths and cutting levels. Meanwhile, the ratio of the Gaussian widths to the RVE length σ/L make influences on the resulting elastic/elasto-plastic properties of the MMNCs, and for the sintered AgNPs composites, σ/L = 2.5 is the critical value of its convergence. Additionally, the proposed method can be also extended to predict the other physical properties of MMNCs including conduction and diffusion.

SGPAC: generalized scalable spatial GroupBy aggregations over complex polygons

This paper studies the spatial group-by query over complex polygons. Given a set of spatial points and a set of polygons, the spatial group-by query returns the number of points that lie within the boundaries of each polygon. Groups are selected from a set of non-overlapping complex polygons, typically in the order of thousands, while the input is a large-scale dataset that contains hundreds of millions or even billions of spatial points. This problem is challenging because real polygons (like counties, cities, postal codes, voting regions, etc.) are described by very complex boundaries. We propose a highly-parallelized query processing framework to efficiently compute the spatial group-by query on highly skewed spatial data. We also propose an effective query optimizer that adaptively assigns the appropriate processing scheme based on the query polygons. Our experimental evaluation with real data and queries has shown significant superiority over all existing techniques.

A spatial obesity risk score for describing the obesogenic environment using kernel density estimation: development and parameter variation

BackgroundOverweight and obesity are severe public health problems worldwide. Obesity can lead to chronic diseases such as type 2 diabetes mellitus. Environmental factors may affect lifestyle aspects and are therefore expected to influence people’s weight status. To assess environmental risks, several methods have been tested using geographic information systems. Freely available data from online geocoding services such as OpenStreetMap (OSM) can be used to determine the spatial distribution of these obesogenic factors. The aim of our study was to develop and test a spatial obesity risk score (SORS) based on data from OSM and using kernel density estimation (KDE).MethodsObesity-related factors were downloaded from OSM for two municipalities in Bavaria, Germany. We visualized obesogenic and protective risk factors on maps and tested the spatial heterogeneity via Ripley’s K function. Subsequently, we developed the SORS based on positive and negative KDE surfaces. Risk score values were estimated at 50 random spatial data points. We examined the bandwidth, edge correction, weighting, interpolation method, and numbers of grid points. To account for uncertainty, a spatial bootstrap (1000 samples) was integrated, which was used to evaluate the parameter selection via the ANOVA F statistic.ResultsWe found significantly clustered patterns of the obesogenic and protective environmental factors according to Ripley’s K function. Separate density maps enabled ex ante visualization of the positive and negative density layers. Furthermore, visual inspection of the final risk score values made it possible to identify overall high- and low-risk areas within our two study areas. Parameter choice for the bandwidth and the edge correction had the highest impact on the SORS results.DiscussionThe SORS made it possible to visualize risk patterns across our study areas. Our score and parameter testing approach has been proven to be geographically scalable and can be applied to other geographic areas and in other contexts. Parameter choice played a major role in the score results and therefore needs careful consideration in future applications.

The influence of flow velocity on the response of rheophilic fish to visual cues.

The strong association with visual cues exhibited by fish that prefer to inhabit flowing water (rheophilic species) may help reduce the energetic costs of maintaining position due to the provision of spatial points of reference. If this "Station Holding Hypothesis" is true, a positive relationship between the association with visual cues and flow velocity is expected. This hypothesis was tested experimentally by quantifying the response of common minnow (Phoxinus phoxinus) and brown trout (Salmo trutta) to visual cues under three flow velocities. In contradiction to the prediction, there was no evidence that the association with strong visual cues was positively related to flow velocity when fish were presented with vertical black stripes in an open channel flume, although interspecific variation in response was observed. The association with visual cues was relatively weak in trout, compared to minnow that spent 660% more time associated with the zone in which visual cues were present during the treatment, than the control when visual cues were absent. Trout tended to be more exploratory and made short visits to the area where visual cues were present, whereas minnow associated with the cues for longer. The strong association with visual cues independent of flow velocity exhibited by minnow and the weak association across all velocities by trout suggest that this behaviour is unlikely to reflect a strategy to minimise the energetic cost of maintaining position in flowing water. Minnow may have used the visual cues as a proxy indicator of physical structure that provides alternative benefits, such as refuge from predators. Trout may have employed alternative cues (e.g. mechanosensory) to seek more energetically favourable regions of the experimental area, reducing the importance of stationary visual stimuli.

Synchronization of spatiotemporal chaos and reservoir computing via scalar signals

Reservoir computing turns out to be a powerful data-driven tool for model-free prediction and synchronization of chaotic systems. However, recent studies of synchronization using reservoir computing mainly focus on low-dimensional chaotic systems, the relevant research on spatiotemporally chaotic systems that are more common in nature is still missing. Here, we investigate synchronization of spatiotemporally chaotic systems via reservoir computing instead of dynamical equations. By transmitting scalar driving signals at a finite number of spatial points, we realize three types of synchronization, including the one between the trained reservoir computer and its learned spatiotemporally chaotic system, the one between the trained reservoir computers, and the cascading one among the learned system and the trained reservoir computers. Our method can not only be used to confirm whether the trained reservoir computer has captured the features of the spatiotemporally chaotic system but also is of great significance for application in complex networks and secure communication. The results are illustrated numerically with two benchmark dynamical systems.

Upgrade of Thomson Scattering Diagnostic on HL-2A

The Thomson scattering diagnostic of the HL-2A tokamak device was upgraded to improve its multi-point diagnostic capability, including new collection optics, fibers bundles, and data analysis code. The small old collection lens was replaced by a six-piece lens with a Cooke optical design. The aperture of its first standard sphere face is 310.125 mm, which successfully increases the amount of collected scattering light by about three times. The new collection optic module allows for up to twenty-six spatial points. A kind of Y-type fiber bundle has also been used to ensure that the fiber end-face matches the image of the laser beam exactly. Additionally, the new data analysis code can provide preview results in seconds. Finally, the multi-point Te diagnostic ability has been significantly improved.

An Image Post-Processing Approach Based on Fully Dense U-Net for Microwave Induced Thermo-Acoustic Tomography

In microwave induced thermo-acoustic tomography (TAT), circular scanning sensor array is the general signal acquiring mode. For higher sensitivity, large aperture detectors are widely preferred in the real TAT imaging system. However, large aperture of detector usually results in the limited spatial sampling points. Meanwhile, for considering the safety and comfort, the microwave radiation power is also limited. Due to these limitations, the signal to noise ratio (SNR) of TA signals may not be ideal to reconstruct an image with satisfactory quality. In addition, the TA image often suffers the artifacts resulted by sparsely sampling data. Herein, we propose a deep learning-based scheme to process the TA images which are reconstructed with time reversal (TR) method. Since the obvious artifacts removing performance in photoacoustic tomography (PAT), fully dense U-Net (FD U-Net) is employed to be the base deep learning architecture. Due to the amount limitation of real experimental TA data, the network is mainly trained by synthetic data which are generated in TAT simulating scheme. Furthermore, in order to ensuring the trained network could correctly detect the targets in the TA image, we propose a scheme termed data augmentation FD U-Net (DAFD U-Net) in which a few experimental TA images are added to the training procedure and perform data augmentation.The performance of DAFD U-Net is verified by an experimental image. Results show that the proposed scheme could significantly improve the quality of TAT image.

Inversion in an uncertain ocean using Gaussian processes.

Gaussian processes (GPs) can capture correlation of the acoustic field at different depths in the ocean. This feature is exploited in this work for pre-processing acoustic data before these are employed for source localization and environmental inversion using matched field inversion (MFI) in an underwater waveguide. Via the application of GPs, the data are denoised and interpolated, generating densely populated acoustic fields at virtual arrays, which are then used as data in MFI. Replicas are also computed at the virtual receivers at which field predictions are made. The correlations among field measurements at distinct spatial points are manifested through the selection of kernel functions. These rely on hyperparameters, that are estimated through a maximum likelihood process for optimal denoising and interpolation. The approach, employing Gaussian and Matérn kernels, is tested on synthetic and real data with both an exhaustive search and genetic algorithms and is found to be superior to conventional beamformer MFI. It is also shown that the Matérn kernel, providing more degrees of freedom because of an increased number of hyperparameters, is preferable over the frequently used Gaussian kernel.

RI-LIO: Reflectivity Image Assisted Tightly-Coupled LiDAR-Inertial Odometry

In this letter, we propose RI-LIO, a new reflectivity image assisted tightly-coupled LiDAR-inertial odometry (LIO) framework that introduces additional reflectivity texture information to efficiently reduce the drift of geometric-only methods. To achieve this, we construct an iterated extended Kalman filter framework by blending the point-to-plane geometric measurement and the reflectivity image measurement. Specifically, the geometric measurement is defined as the distance from the raw point of a new scan to its nearest neighbor plane in the global incremental kd-tree map. The searched nearest neighbor point is used to render a sparse reflectivity image after LiDAR motion distortion information is given by its corresponding raw point. Then, the reflectivity measurement is built to align the sparse reflectivity image with the dense reflectivity image of the current scan by minimizing the photometric errors directly. In addition, based on the mechanism of high-resolution LiDAR, a corrected spherical projection model is proposed to project spatial points into the image frame. Finally, extensive experiments are conducted in structured, unstructured and challenging open field scenarios. The results demonstrate that the proposed method outperforms existing geometric-only methods in terms of robustness and accuracy, especially in the rotation direction.

Particle-in-cell method for plasmas in the one-dimensional electrostatic limit

We discuss the particle-in-cell (PIC) method, which is one of the most widely used approaches for the kinetic description of plasmas. The positions and velocities of the charged particles take continuous values in phase space, and spatial macroscopic quantities, such as the charge density and self-generated electric fields, are calculated at discrete spatial points of a grid. We discuss the computer implementation of the PIC method for one-dimensional plasmas in the electrostatic regime and discuss a desktop application (PlasmAPP), which includes the implementation of different numerical and interpolation methods and diagnostics in a graphical user interface. To illustrate its functionality, the electron-electron two-stream instability is discussed. Readers can use PlasmAPP to explore advanced numerical methods and simulate different phenomena of interest.

Prior-Driven NeRF: Prior Guided Rendering

Neural radiation field (NeRF)-based novel view synthesis methods are gaining popularity. NeRF can generate more detailed and realistic images than traditional methods. Conventional NeRF reconstruction of a room scene requires at least several hundred images as input data and generates several spatial sampling points, placing a tremendous burden on the training and prediction process with respect to memory and computational time. To address these problems, we propose a prior-driven NeRF model that only accepts sparse views as input data and reduces a significant number of non-functional sampling points to improve training and prediction efficiency and achieve fast high-quality rendering. First, this study uses depth priors to guide sampling, and only a few sampling points near the controllable range of the depth prior are used as input data, which reduces the memory occupation and improves the efficiency of training and prediction. Second, this study encodes depth priors as distance weights into the model and guides the model to quickly fit the object surface. Finally, a novel approach combining the traditional mesh rendering method (TMRM) and the NeRF volume rendering method was used to further improve the rendering efficiency. Experimental results demonstrated that our method had significant advantages in the case of sparse input views (11 per room) and few sampling points (8 points per ray).

Improving upon the effective sample size based on Godambe information for block likelihood inference

We consider the effective sample size, based on Godambe information, for block likelihood inference which is an attractive and computationally feasible alternative to full likelihood inference for large correlated datasets. With reference to a Gaussian random field having a constant mean, we explore how the choice of blocks impacts this effective sample size. This is done by introducing a column-wise blocking method which spreads out the spatial points within each block, instead of keeping them close together as the existing row-wise blocking method does. It is seen that column-wise blocking can lead to considerable gains in effective sample size and efficiency compared to row-wise blocking, while retaining computational simplicity. Analytical results in this direction are obtained under the AR (1) model. The insights so found facilitate the study of other one-dimensional correlation models as well as correlation models on a plane, where closed form expressions are intractable. Simulations are seen to provide support to our conclusions.

Numerical solutions of the time‐dependent Schrödinger equation with position‐dependent effective mass

AbstractNumerical solution of the time‐dependent Schrödinger equation with a position‐dependent effective mass is challenging to compute due to the presence of the non‐constant effective mass. To tackle the problem we present operator splitting‐based numerical methods. The wavefunction will be propagated either by the Krylov subspace method‐based exponential integration or by an asymptotic Green's function‐based time propagator. For the former, the wavefunction is given by a matrix exponential whose associated matrix–vector product can be approximated by the Krylov subspace method; and for the latter, the wavefunction is propagated by an integral with retarded Green's function that is approximated asymptotically. The methods have complexity per step with appropriate algebraic manipulations and fast Fourier transform, where is the number of spatial points. Numerical experiments are presented to demonstrate the accuracy, efficiency, and stability of the methods.

Open-Circuit Radial Stray Magnetic Flux Density Based Noninvasive Diagnosis for Mixed Eccentricity Parameters of Interior Permanent Magnet Synchronous Motors in Electric Vehicles

By measuring the open-circuit radial stray magnetic flux density (RSMFD) of three spatial points, a novel diagnostic method for the eccentricity of interior permanent magnetic motors (IPMSMs) in electric vehicles is proposed. Outperforming traditional methods, the proposed method can noninvasively diagnose not only the severities of static eccentricity (SE), dynamic eccentricity (DE), and mixed eccentricity (ME), but also the eccentricity location. In this article, diagnosis results are described through three eccentricity parameters: SE ratio, DE ratio, and SE angle. First, an analytical model of the open-circuit RSMFD of the IPMSM is proposed, with its accuracy validated by experiments. The pattern of the impact of the eccentricity parameters on the open-circuit RSMFD is analyzed to form the basis of the proposed method. Then, an eccentricity prototype motor, which can continuously emulate the eccentricity according to any listed eccentricity parameters, is developed. A test rig is built to collect the open-circuit RSMFD and validate the analytical calculation results. Finally, an eccentricity diagnostic model based on the open-circuit RSMFD is established. The diagnosis results proved the noninvasiveness, effectiveness, and viability of the proposed method.

“RULES-BASED MOTION” REANIMATION OF THE CARPUS

Using a reverse engineering capability to quantify the factors that control the rigid body mechanics of the wrist, a mathematical forward animation capability and model of wrist motion that allows the carpus to move under its own rules is being developed. This characterises the isometric connections, from which was developed the Stable Central Column Theory of Carpal Mechanics - which incorporates the Law of Rules Based Motion.This work has now advanced to the ability to reapply the extracted rules to allow rules-based rigid body reanimation of an individual wrist. As each wrist is unique, there is a given reality that each reanimation must be based on an individual wrist's unique rules, and the aspiration to create a standard or normal wrist is unrealistic.Using True Life Anatomy (Adelaide, Aust) analysis software, the specific rules (morphology / connectivity / interaction / loading) of individual wrists have been characterised, and then reapplied in a rigid body reanimation environment using Adams (MSC Software, U.S.) software.In the preliminary application of this biomechanics environment, by using the reverse engineering / forward reanimation process, wrist motion can be recreated - based purely on the unique rules, extracted from individual wrists. Instability of the proximal scaphoid was evident in several of the animations, and there was confirmation that the spatial attachment points of the isometric constraints are very exacting. The actual attachment and specific morphology of the carpal bones varied between individual wrists.Using a reverse engineering and then forward reanimation process, we have been able to recreate wrist motion using the rigid body mechanics based on the Law of Rules Based Motion. Further work is required, but the potential to apply “what if” virtual surgery options to an individual injured wrist and more precisely characterise and test solutions to wrist dysfunction are becoming realised.

Mesh-free least-squares reverse-time migration

AbstractThe reflectivity of the subsurface can be precisely determined using least-squares reverse-time migration (LSRTM). As LSRTM necessitates solving the wave equation, the numerical solution method of the wavefield directly determines the quality of the migration image. The conventional LSRTM method usually uses the finite difference method based on a regular grid to calculate the wavefield. Due to the stepwise approximation of an irregular surface with a regular grid, scattering noise may occur in the propagation of the wavefield, which affects the quality of the image. In addition, the conventional LSRTM cannot effectively handle the models with rugged topography. The finite difference method generated by radial basis functions (FD-RBF) is a mesh-free method and can construct interpolation functions to solve the wave equations numerically according to arbitrarily distributed spatial coordinate points. Therefore, we use the FD-RBF method to develop a mesh-free LSRTM approach to eliminate the influence of the inherent limitation of a regular grid on the imaging. Numerical examples show that the mesh-free LSRTM method can better represent the curved or steep interface within the model and is also suitable for models with rugged topography. The LSRTM method can provide higher-quality images and effectively reduce the memory required for calculations.

Damage evolution process of fiber-reinforced backfill based on acoustic emission three-dimensional localization

The spatial localization of the damage evolution caused by a fiber-reinforced backfill is critical for the prediction of the rupture location in a mining area filling. Acoustic emission (AE) three-dimensional localization tests under uniaxial compression were conducted on various fiber-reinforced backfills to study the damage evolution process. The general characteristics of energy count and the law of evolution for the spatial localization damage of fiber-reinforced backfills were derived by analyzing the time sequence evolution process of energy count and the spatial distribution of the AE events. The results show that the time-series evolution process of the backfill energy count can be approximately divided into the three periods: rising, quiet, and active. The damage mode of the fiber-reinforced backfill in uniaxial compression is determined as ductile damage, and the penetration mode is determined as shear + tension penetration. The evolution of the spatial distribution of the AE events of a backfill can not only reflect the spatial location of damage during the entire loading process but also determine the degree of damage at a certain location according to the density of spatial points. The results of this study can provide a theoretical basis for the prediction of rupture localization for mine filling.

Two-step calibration method of the extrinsic parameters with high accuracy for a bistatic non-orthogonal shafting laser theodolite system.

Motivated by the increasing demands on the precision of 3D large-scale measurement, the extrinsic parameters calibration with high accuracy of the bistatic non-orthogonal shafting laser theodolite (N-theodolite) system is required. A two-step method is proposed to achieve the extrinsic parameters calibration with high accuracy in this paper. In the first step, by analyzing and setting the approximate emitted point during the motion of the laser axis in local space, the calculation of the initial extrinsic parameters can be simplified. In the second step, the above results are taken as the initial values of optimization, and the distances between the spatial laser points provided by PSD sensors with high accuracy in global space are used to construct the unconstrained optimal objective function. The proposed method is validated with the measurement experiment of the bistatic N-theodolite system, the average error of 3D coordinate measurement is less than 0.4 mm, and the average error of distance measurement is less than 0.3 mm within 5 m.