Multidimensional Grid Research Articles

Multidimensional optimization-improved grid star map recognition algorithm

In high-precision celestial navigation, star map recognition algorithms are crucial. We identified limitations in the classical grid star map recognition algorithm (CGSMRA) concerning star sorting method, selection strategy, scoring criterion, and screening mechanisms. To address these, we developed a multidimensional optimization-improved grid star map recognition algorithm (MOIGSMRA). We evaluated MOIGSMRA through five experiments: template matching efficiency, companion star recognition, recognition accuracy, attitude determination accuracy, and overall performance. Compared to CGSMRA, MOIGSMRA demonstrated superior results. This study offers a method to optimize attitude determination algorithms for star sensors and provides a theoretical and experimental foundation for improving star recognition accuracy.

Exploring Quantized Massless Photonic Wave-Particle Duality, Inertial Mass Resistance to Motion, and the Speed of Light as Representations of a Higher Dimensional Hyperspace Axis within Subspace Field Unification

This paper explores the potentially interlinked, multidimensional nature of three fundamental qualities of reality. First, wave-particle duality is examined as an intrinsic extension of the fundamental two-dimensional electromagnetic wavelength, which permeates into a three-dimensional quantum manifestation of photonic particles. Second, the speed of light is considered as a limiting factor imposed by a multidimensional hyperspatial subspace ether grid, where the tensile locality restricts light's travel. Third, the movement of mass-carrying particles through this subspace ether grid is analyzed as being responsible for inertial resistance—specifically, resistance to changes in motion, including acceleration, deceleration, and changes in relative velocity.This paper then postulates that the massless motion of photonic energy packets at the speed of light, and the inertial resistance of mass-carrying hadronic particles to changes in relative motion, are opposite dimensional aspects of a unified subspace field theory. These aspects, though seemingly distinct, are proposed to occupy opposing sides of the same intersecting hyperspatial axis, within a higher-dimensional etheric reality.

Two‐step simulation combining large eddy simulation and population balance Monte Carlo for nanoparticle synthesis in flame spray pyrolysis

AbstractA two‐step simulation approach combining large eddy simulation (LES) for turbulent flame and multidimensional/multivariate population balance Monte Carlo (PBMC) for nanoparticle dynamics is proposed to explore the detailed flame fields and particle dynamics of zirconia nanoparticles in a flame spray pyrolysis (FSP) reactor. The turbulent combustion of gas and spray are simulated by the nonlinear LES‐partially stirred reactor model. Thereafter, the differentially weighted PBMC is applied for the first time to describe the spatially resolved formation and growth of nanoparticles using the flame fields derived from LES as an input. An efficient submodel for particle spatial transport in multidimensional grids is adopted and tested to account for the effect of thermophoresis, convective and diffusion of the nanoparticles. This methodology is successfully applied to an FSP case, demonstrating a reliable level of fidelity when compared to experiments and other model. Simulation results are discussed, in particular the flame fields and the size, morphology, as well as polydisperse primary particle and aggregates size distribution.

M3DIS - A grid of 3D radiation-hydrodynamics stellar atmosphere models for stellar surveys. I. Procedure, validation, and the Sun

Large-scale stellar surveys, such as SDSS-V, 4MOST, WEAVE, and PLATO, require accurate atmospheric models and synthetic spectra of stars for accurate analyses of fundamental stellar parameters and chemical abundances. The primary goal of our work is to develop a new approach to solve radiation-hydrodynamics (RHD) and generate model stellar spectra in a self-consistent and highly efficient framework. We build upon the Copenhagen legacy RHD code, the MULTI3D non-local thermodynamic equilibrium (NLTE) code, and the DISPATCH high-performance framework. The new approach allows us to calculate 3D RHD models of stellar atmospheres on timescales of a few thousand CPU hours and to perform subsequent spectrum synthesis in local thermodynamic equilibrium (LTE) or NLTE for the desired physical conditions within the parameter space of FGK-type stars. We compare the 3D RHD solar model with other available models and validate its performance against solar observations, including the centre-to-limb variation of intensities and key solar diagnostic lines of H and Fe. We show that the performance of the new code allows to overcome the main bottleneck in 3D NLTE spectroscopy and enables calculations of multi-dimensional grids of synthetic stellar observables for comparison with modern astronomical observations.

Across Time and Space: Senju ’s Approach for Scaling Iterative Stencil Loop Accelerators on Single and Multiple FPGAs

Stencil-based applications play an essential role in high-performance systems as they occur in numerous computational areas, such as partial differential equation solving. In this context, Iterative Stencil Loops (ISLs) represent a prominent and well-known algorithmic class within the stencil domain. Specifically, ISL-based calculations iteratively apply the same stencil to a multi-dimensional point grid multiple times or until convergence. However, due to their iterative and intensive nature, ISLs are highly performance-hungry, demanding specialized solutions. Here, Field Programmable Gate Arrays (FPGAs) represent a valid architectural choice as they enable the design of custom, parallel, and scalable ISL accelerators. Besides, the regular structure of ISLs makes them an ideal candidate for automatic optimization and generation flows. For these reasons, this article introduces Senju , an automation framework for the design of highly parallel ISL accelerators targeting single-/multi-FPGA systems. Given an input description, Senju automates the entire design process and provides accurate performance estimations. The experimental evaluation shows remarkable and scalable results, outperforming single- and multi-FPGA literature approaches under different metrics. Finally, we present a new analysis of temporal and spatial parallelism trade-offs in a real-case scenario and discuss our performance through a single- and novel specialized multi-FPGA formulation of the Roofline Model.

Cops and Robber on butterflies, grids, and AT-free graphs

Cops and Robber is a well-studied two player pursuit-evasion game played on a graph. In this game, a set of cops, controlled by the first player, tries to capture the position of a robber, controlled by the second player. The cop number of a graph is the minimum number of cops required to capture the robber in the graph. A group of cops guard a subgraph if they can ensure that the robber cannot enter the subgraph without getting captured immediately.We study the applications of guarding to provide new bounds and improve existing bounds for several graph classes. In particular, we show that the cop number for butterfly networks and for solid grids is two. We also construct a partial grid with cop number 3 establishing that partial grids have same cop number as their superclass planar graphs. We also consider three well-studied variants of Cops and Robber: Cops and Fast Robber, Cops and Attacking Robber, and Surrounding CnR. We improve the existing bounds for the cop number of multidimensional grids for both Cops and Attacking Robber and Surrounding CnR. Finally, we consider Cops and Fast Robber on AT-free graphs to improve the existing bounds on the cop number for this game.

A Fast Algorithm for Aperiodic Linear Stencil Computation using Fast Fourier Transforms

Stencil computations are widely used to simulate the change of state of physical systems across a multidimensional grid over multiple timesteps. The state-of-the-art techniques in this area fall into three groups: cache-aware tiled looping algorithms, cache-oblivious divide-and-conquer trapezoidal algorithms, and Krylov subspace methods. In this article, we present two efficient parallel algorithms for performing linear stencil computations. Current direct solvers in this domain are computationally inefficient, and Krylov methods require manual labor and mathematical training. We solve these problems for linear stencils by using discrete Fourier transforms preconditioning on a Krylov method to achieve a direct solver that is both fast and general. Indeed, while all currently available algorithms for solving general linear stencils perform Θ( NT ) work, where N is the size of the spatial grid and T is the number of timesteps, our algorithms perform o ( NT ) work. To the best of our knowledge, we give the first algorithms that use fast Fourier transforms to compute final grid data by evolving the initial data for many timesteps at once. Our algorithms handle both periodic and aperiodic boundary conditions and achieve polynomially better performance bounds (i.e., computational complexity and parallel runtime) than all other existing solutions. Initial experimental results show that implementations of our algorithms that evolve grids of roughly 10 7 cells for around 10 5 timesteps run orders of magnitude faster than state-of-the-art implementations for periodic stencil problems, and 1.3× to 8.5× faster for aperiodic stencil problems. Code Repository: https://github.com/TEAlab/FFTStencils

Machine learning for rapid inference of critical dimensions in optical metrology of nanopatterned surfaces

Scatterometry-based metrology has the capability to perform high-throughput inspection of large-area nanopatterned surfaces. It utilizes physics-based dependencies between reflectance spectra of light scattered from nanopatterned surfaces and the geometric parameters, or so-called Critical Dimensions (CDs), of such nanopatterns. This paper proposes a novel method for rapid and accurate inference of CDs of complex nanopatterned surfaces through the use of a Machine Learning (ML)-based inverse problem mapping, coupled with the use of a strategic feature selection algorithm, which also originated from the ML domain. Specifically, Latin Hypercube Sampling was utilized to create a multi-dimensional grid of CDs which are used as inputs for physics-based simulations of scattered light spectra for nanopatterned surfaces with those CDs. Simulation results are used to build the training data for the ML model relating simulated reflectance spectra with the corresponding CDs. The Extreme Gradient Boosting (XGBoost) algorithm was utilized to realize the aforementioned mapping. In addition, most informative spectral wavelengths were selected using Recursive Feature Elimination (RFE) algorithm based on the feature importance scores obtained from XGBoost. Capabilities of the newly proposed approach were evaluated through inspection of a semiconductor wafer sample with hourglass patterns, which are characterized by eight CDs. It was observed that the proposed method is capable of real-time CD metrology of large-area nanostructured surfaces with complex nanopatterns, with accuracy and repeatability comparable to that of Scanning Electron Microscopy.

A Novel Clustering Method Based on Adjacent Grids Searching.

Clustering is used to analyze the intrinsic structure of a dataset based on the similarity of datapoints. Its widespread use, from image segmentation to object recognition and information retrieval, requires great robustness in the clustering process. In this paper, a novel clustering method based on adjacent grid searching (CAGS) is proposed. The CAGS consists of two steps: a strategy based on adaptive grid-space construction and a clustering strategy based on adjacent grid searching. In the first step, a multidimensional grid space is constructed to provide a quantization structure of the input dataset. The noise and cluster halo are automatically distinguished according to grid density. Moreover, the adaptive grid generating process solves the common problem of grid clustering, in which the number of cells increases sharply with the dimension. In the second step, a two-stage traversal process is conducted to accomplish the cluster recognition. The cluster cores with arbitrary shapes can be found by concealing the halo points. As a result, the number of clusters will be easily identified by CAGS. Therefore, CAGS has the potential to be widely used for clustering datasets with different characteristics. We test the clustering performance of CAGS through six different types of datasets: dataset with noise, large-scale dataset, high-dimensional dataset, dataset with arbitrary shapes, dataset with large differences in density between classes, and dataset with high overlap between classes. Experimental results show that CAGS, which performed best on 10 out of 11 tests, outperforms the state-of-the-art clustering methods in all the above datasets.

Beyond Discrete Genres: Mapping News Items onto a Multidimensional Framework of Genre Cues

In the contemporary media landscape, with the vast and diverse supply of news, it is increasingly challenging to study such an enormous amount of items without a standardized framework. Although attempts have been made to organize and compare news items on the basis of news values, news genres receive little attention, especially the genres in a news consumer’s perception. Yet, perceived news genres serve as an essential component in exploring how news has developed, as well as a precondition for understanding media effects. We approach this concept by conceptualizing and operationalizing a non-discrete framework for mapping news items in terms of genre cues. As a starting point, we propose a preliminary set of dimensions consisting of “factuality” and “formality”. To automatically analyze a large amount of news items, we deliver two computational models for predicting news sentences in terms of the said two dimensions. Such predictions could then be used for locating news items within our framework. This proposed approach that positions news items upon a multidimensional grid helps deepening our insight into the evolving nature of news genres.

Regional Well-Being Disparities in Morocco and its OECD Partners.

This article proposes a multidimensional analysis grid to assess regional disparities, transcending monetary considerations. This grid agrees overall with the common framework that prevails in the literature review that we have carried out. It is built around four dimensions of well-being: economy (development, labor market, human capital and innovation), social (health, living conditions and gender), environment and governance. Our analysis of regional disparities was based on the synthesis of fifteen indicators by constructing a Synthetic Index of Well-being (SIWB) by combining its four dimensions using an aggregative-compensative approach. This analysis covers Morocco, 35 of the OECD member countries and their 389 regions between 2000 and 2019. We have assessed the dynamics of Moroccan regions compared to those of the benchmark. Thus, we have highlighted the gaps to be made up in relation to the different areas of well-being as well as their thematic variations.

An integrated approach using empirical wavelet transform and a convolutional neural network for wave power prediction

The prediction of electricity generated from wave energy converters (WECs) has attracted increasing attention along with the improvements in WEC technologies in recent years. There are two typical types of approaches that have been developed to forecast wave energy generation: physical models and data-driven models. This paper gives a brief review of these two approaches and then presents a hybrid deep learning model for wave power prediction by incorporating empirical wavelet transform (EWT) and a convolutional neural network (CNN). The EWT is adopted to decompose the wave power observations into several sub-bands with high and low frequencies, while the CNN model allows to extract spatial features from multi-dimensional grid data instead of one-dimensional time-series data. This paper also presents a physical-based model based on a wave power matrix (WPM) under different wave conditions. The proposed hybrid EWT-CNN model is compared with the physical-based WPM model and other well-established hybrid algorithms. The results from the proposed hybrid model can better predict short-term wave power output than other benchmark models based on time-space domain information; thus, the proposed approach has strong potential to be used in wave energy exploitation.

MSG: A software package for interpolating stellar spectra in pre-calculated grids

While the spectrum of the light emitted by a star can be calculated by simulating the flow of radiation through each layer of the star's atmosphere, this process is computationally expensive. Therefore, it is often far more efficient to pre-calculate spectra over a grid of photospheric parameters, and then interpolate within this grid. MSG (short for Multidimensional Spectral Grids) is a software package that implements this interpolation capability.

Challenging the Curse of Dimensionality in Multidimensional Numerical Integration by Using a Low-Rank Tensor-Train Format

Numerical integration is a basic step in the implementation of more complex numerical algorithms suitable, for example, to solve ordinary and partial differential equations. The straightforward extension of a one-dimensional integration rule to a multidimensional grid by the tensor product of the spatial directions is deemed to be practically infeasible beyond a relatively small number of dimensions, e.g., three or four. In fact, the computational burden in terms of storage and floating point operations scales exponentially with the number of dimensions. This phenomenon is known as the curse of dimensionality and motivated the development of alternative methods such as the Monte Carlo method. The tensor product approach can be very effective for high-dimensional numerical integration if we can resort to an accurate low-rank tensor-train representation of the integrand function. In this work, we discuss this approach and present numerical evidence showing that it is very competitive with the Monte Carlo method in terms of accuracy and computational costs up to several hundredths of dimensions if the integrand function is regular enough and a sufficiently accurate low-rank approximation is available.

Robotic Navigation Based on Experiences and Predictive Map Inspired by Spatial Cognition

Humans and animals have environmental cognition and navigation abilities. These abilities are closely related to the spatial cognitive mechanism of brain. Based on this mechanism, we propose a novel robotic navigation framework based on experiences and predictive map inspired by spatial cognition to accurately construct environment experience and quickly plan path. The grid cell and the place cell are modeled to rapidly integrate self-motion cues. The multidimensional grid coding and one-shot learning rule are utilized for activating the place representation of robot pose. Visual cues provide information for relocation. These information are integrated through experiences which express the topology of the environment, enabling the robot to accurately achieve spatial cognition of complex environment. In order to realize the sequential decision making of hippocampus, the predictive map is introduced to quickly plan the experience sequence to target in dynamic environment. The successor representation model of robot's state is constructed through reinforcement learning. Combined with the goal-based reward function, the shortest path can be replanned to adapt to environment changes. The proposed method is tested in simulated maze, Kitti dataset and corridor environment. Compared with other bionic navigation methods, it has a faster computing speed and higher precision with bionic characteristics. Compared with visual navigation methods, the navigation tasks can robustly be accomplished without complex system design.

Learning Asymmetric and Local Features in Multi-Dimensional Data Through Wavelets With Recursive Partitioning

Effective learning of asymmetric and local features in images and other data observed on multi-dimensional grids is a challenging objective critical for a wide range of image processing applications involving biomedical and natural images. It requires methods that are sensitive to local details while fast enough to handle massive numbers of images of ever increasing sizes. We introduce a probabilistic model-based framework that achieves these objectives by incorporating adaptivity into discrete wavelet transforms (DWT) through Bayesian hierarchical modeling, thereby allowing wavelet bases to adapt to the geometric structure of the data while maintaining the high computational scalability of wavelet methods-linear in the sample size (e.g., the resolution of an image). We derive a recursive representation of the Bayesian posterior model which leads to an exact message passing algorithm to complete learning and inference. While our framework is applicable to a range of problems including multi-dimensional signal processing, compression, and structural learning, we illustrate its work and evaluate its performance in the context of image reconstruction using real images from the ImageNet database, two widely used benchmark datasets, and a dataset from retinal optical coherence tomography and compare its performance to state-of-the-art methods based on basis transforms and deep learning.

Multicriteria Recommendation Method of Tourist Routes Based on Tourist Clustering

A multicriteria recommendation algorithm for tourist routes under the multidimensional expanded spatial grid structure model based on fuzzy C-means clustering of tourist preferences is proposed. The purpose of the proposed structure is to improve the multicriteria intelligent recommendation ability of tourist routes under the multidimensional expanded spatial grid structure model of popular tourist core circle. The multidimensional enlarged spatial grid structure model of the well-known tourist core circle is used to develop the tourist correlation model of travel routes under the restricted sample training. Under the popular traveler core circle’s multidimensional enlarged spatial grid structure framework, the mixed kernel use and global kernel use are created to extract the correlation characteristics of tourist route recommendation. Under the multidimensional enlarged spatial grid structure model of the well-known tourist core circle, the adaptive learning of tourist route selection is carried out using the hybrid particle swarm algorithm. To manage the convergence of the suggestion process, maps of logistical chaos are employed, utilizing culture’s universalism and ergodicity resources and examining the aesthetic resources along tourism routes. The simulation results demonstrate that the multidimensional extended spatial grid structure model’s tourism route information recommendation accuracy is decent, and a solid swarm intelligence junction is observed in this analysis, preventing tourism route recommendations from settling for the local optimal solution and enhancing their intelligence and global stability.

Assessment of the Clusterability of Data Using a Multimodal Convolutional Neural Network

Clustering assigns data points into groups called clusters, which define the characteristics of similar data points. Our work defines a model to identify and assess the presence of a clusterable structure initially in a two-dimensional density grid of a data set which is respectively expanded into a multidimensional density grid according the dimensionality of the data set. Clusterability is defined as the tendency of a data set having a structure for successful clustering. Our approach consists of a multimodal, convolutional neural network to assess the clusterability of a data set. Multimodality is the utilization of multiple sources of information. The output of our approach, the created model, also identifies the type of the clusterable structure (none, centroid and density). Our approach does not require an initial clustering of the data to define its clusterability. In the assessment of the clusterability of high-dimensional data, we utilize random rotations accompanied with an ensemble approach. The multiple experiments of various clustering problems illustrate that our proposed approach is capable of assessing the clusterability of data and of identifying the type of the clusterable structure.

Energy dependent ratios of level-density parameters in superheavy nuclei

The nuclear level densities and level-density parameters in fissioning nuclei at their saddle points of fission barriers, ${a}_{f}$, as well as those for neutron, ${a}_{n}$, proton, ${a}_{p}$, and $\ensuremath{\alpha}$-particle, ${a}_{\ensuremath{\alpha}}$, emission residues at the ground states are calculated for isotopic chains of superheavy nuclei with $Z$ = 112--120. The calculations are performed with the superfluid formalism using the single-particle energies obtained from the diagonalization of the deformed Woods-Saxon potential. Spectra were generated at global minima of the adiabatic potential energy surfaces, found by the multidimensional minimization method, and at the proper saddle points, found by the ``immersion water flow'' technique on multidimensional energy grids, with allowed reflection and axial symmetry breaking. The influence of shell effects on the energy dependence of the ratios of level-density parameters corresponding to residues of the considered decay modes to those of neutron emission is studied. As shown, in contrast to the ${a}_{f}/{a}_{n}$ ratio, the ${a}_{p}/{a}_{n}$ and ${a}_{\ensuremath{\alpha}}/{a}_{n}$ ratios do not show characteristic maxima depending on the excitation energy of the compound nucleus being formed. In the case of $\ensuremath{\alpha}$ decay, we identified the collective enhancement caused by cluster degrees of freedom as playing quite an important role. The energetic course of the variability of the level-density parameters before reaching the asymptotic value, not taken into account so far, is of great importance for the estimation of the probabilities of de-excitation cascades via light particles emission in competition with fission and, thus, for the determination of the survival probabilities and finally for the total production cross sections of superheavy nuclei.

Spectral-norm risk rates for multi-taper estimation of Gaussian processes

We consider the estimation of the covariance of a stationary Gaussian process on a multi-dimensional grid from observations taken on a general acquisition domain. We derive spectral-norm risk rates for multi-taper estimators. When applied to one-dimensional acquisition intervals, these show that Thomson's classical multi-taper has optimal risk rates, as they match known benchmarks. We also extend existing lower risk bounds to multi-dimensional grids and conclude that multi-taper estimators associated with certain two-dimensional acquisition domains also have almost optimal risk rates.