Vector-based Research Articles

Terahertz spoof plasmonic neural network for diffractive information recognition and processing

All-optical diffractive neural networks, as analog artificial intelligence accelerators, leverage parallelism and analog computation for complex data processing. However, their low space transmission efficiency or large spatial dimensions hinder miniaturization and broader application. Here, we propose a terahertz spoof plasmonic neural network on a planar diffractive platform for direct multi-target recognition. Our approach employs a spoof surface plasmon polariton coupler array to construct a diffractive network layer, resulting in a compact, efficient, and easily integrable architecture. We designed three schemes: basis vector classification, multi-user recognition, and MNIST handwritten digit classification. Experimental results reveal that the terahertz spoof plasmonic neural network successfully classifies basis vectors, recognizes multi-user orientation information, and directly processes handwritten digits using a designed input framework comprising a metal grating array, transmitters, and receivers. This work broadens the application of terahertz plasmonic metamaterials, paving the way for terahertz on-chip integration, intelligent communication, and advanced computing systems.

MIGP: Metapath Integrated Graph Prompt Neural Network

Graph neural networks (GNNs) leveraging metapaths have garnered extensive utilization. Nevertheless, the escalating parameters and data corpus within graph pre-training models incur mounting training costs. Consequently, GNN models encounter hurdles including diminished generalization capacity and compromised performance amidst small sample datasets. Drawing inspiration from the efficacy demonstrated by self-supervised learning methodologies in natural language processing, we embark on an exploration. We endeavor to imbue graph data with augmentable, learnable prompt vectors targeting node representation enhancement to foster superior adaptability to downstream tasks. This paper proposes a novel approach, the Metapath Integrated Graph Prompt Neural Network (MIGP), which leverages learnable prompt vectors to enhance node representations within a pretrained model framework. By leveraging learnable prompt vectors, MIGP aims to address the limitations posed by mall sample datasets and improve GNNs’ model generalization. In the pretraining stage, we split symmetric metapaths in heterogeneous graphs into short metapaths and explicitly propagate information along the metapaths to update node representations. In the prompt-tuning stage, the parameters of the pretrained model are fixed, a set of independent basis vectors is introduced, and an attention mechanism is employed to generate task-specific learnable prompt vectors for each node. Another notable contribution of our work is the introduction of three patent datasets, which is a pioneering application in related fields. We will make these three patent datasets publicly available to facilitate further research on large-scale patent data analysis. Through comprehensive experiments conducted on three patent datasets and three other public datasets, i.e., ACM, IMDB, and DBLP, we demonstrate the superior performance of the MIGP model in enhancing model applicability and performance across a variety of downstream datasets. The source code and datasets are available in the website.11https://github.com/hzw-ai/MIGP, with password: MIGPNN2024.

Equiangular Basis Vectors: A Novel Paradigm for Classification Tasks

Equiangular Basis Vectors: A Novel Paradigm for Classification Tasks

Non‐destructively characterizing sandstones, orthoquartzites, agates, and petrified wood for provenance research: Perspectives from the Southeastern Coastal Plain, United States

AbstractSiliceous sandstone (including quartzites), petrified wood, and agates located in Alabama and Mississippi were utilized as a toolstone resource during every recognized cultural period in the Lower Mississippi Valley region of the Southeastern United States. Regrettably, these materials have not been the focus of many provenance‐related investigations. Recent analyses of quartzite and sandstone from other regions in North America and from the Pyrenees were successful in discriminating sources using petrographic techniques. The current study examines the application of visible/near‐infrared reflectance and Fourier transform infrared reflectance (FTIR) spectroscopy on sourcing siliceous materials besides chert, particularly sandstones, orthoquartzites (quartz sandstone), petrified woods, and agates. This source characterization investigation focuses on a case study involving materials gathered from eight distinct collection sites, encompassing nine different siliceous resources collected in Alabama and Mississippi. These materials were sourced from two distinct geological formations: the Hattiesburg and Tallahatta. Results demonstrate the ability of non‐destructive reflectance spectroscopy and introduces a new outlier modeling method that detects, clusters, and separately models outliers with their own set of basis vectors. Principal component analyses, least absolute shrinkage and selection operator regression, linear discriminant function analysis (LDA), and random forest classification are used in this paper to better identify outlier elements as well as discriminate for stone materials accurately (between 67% and 100%). Although this is the first reflectance spectroscopy investigation used to characterize these materials for provenance applications, the preliminary results compare favorably with other provenance techniques whose aim is to quantify between‐formation (inter) and within‐formation (intra) outcrop variation. The quantified and differentiated sources, based on the hyperspectral signatures of the material, will provide a better understanding of prehistoric reliance on these lithic resources and produces a proxy to determine mobility, social interaction, and other past behavior.

Response to Shariff’s comments to my paper on his isotropic invariants (Shariff, 2023)

In the paper by Shariff (Q. J. Mech. Appl. Math. 76, 143–161, 2023) a functional basis of vectors and symmetric tensors based on eigenvectors of the first tensor is proposed. In the paper by Itskov (Mech. Soft Mater. 6(4), 1–3, 2024) a counterexample is reported demonstrating that the proposed terms do not generally represent isotropic invariants and cannot thus serve as a functional basis of symmetric tensors. In the latest response (Mech. Soft Mater. 6, 4, 2024) Shariff shows many examples of symmetric tensors for which his functional basis is valid but he does not really oppose the counterexample.

Symmetry breaking of bound states in the continuum in luminescence response of photonic crystal slabs with embedded Ge nanoislands

Bound states in the continuum (BIC) have attracted a great deal of attention in all-dielectric nanophotonics due to their ability to provide spectral features with a very high-quality factor. By definition, BIC cannot be observed in the far field because of the symmetry mismatch with the modes propagating in free space. Despite this, in systems with slightly reduced symmetry, the condition for BIC is lifted, which gives rise to the high-quality resonant features in their optical response. In particular, in photonic crystal slabs, which support the BIC states, the symmetry reduction allows modification of light propagation, reflection, or emission. In this work, using the photonic crystal slabs with embedded Ge nanoislands, we have shown the ability to control their light emission features by symmetry breaking. It was demonstrated that such symmetry breaking due to a change in the basis vectors of the photonic crystal unit cell or a change in the unit cell internal structure could provide independent control knobs to alter the spectral position of photonic crystal modes, their dispersion, and degeneracy. The obtained results reveal additional ways to manage the light emission of active media in photonic crystal slabs.

Assessing the stability of direction finding by virtual magnetic dipoles when using a dielectrically opaque radio direction finder radome

The implementation of highly mobile direction finding systems based on UAVs is an important and urgent task, however, antenna systems that are installed on UAVs lead to a decrease in aerodynamic efficiency, which can lead to a decrease in operating time and flight range. To solve this problem, fairings are used, which cannot always be realized on the basis of dielectrically transparent materials. All this, combined with the electrical nature of wave scattering near the UAV, leads to distortion of the field characteristics, significantly complicating direction finding. This paper proposes the use of the method of virtual antenna arrays based on virtual magnetic dipoles, which are formed on the basis of vector antennas to increase the accuracy of direction finding. This research was funded by Russian Science Foundation, No. 19-79-109, https://rscf.ru/project/19-79-10109 /.

Memory‐efficient compression of 𝒟ℋ2‐matrices for high‐frequency Helmholtz problems

AbstractDirectional interpolation is a fast and efficient compression technique for high‐frequency Helmholtz boundary integral equations, but requires a very large amount of storage in its original form. Algebraic recompression can significantly reduce the storage requirements and speed up the solution process accordingly. During the recompression process, weight matrices are required to correctly measure the influence of different basis vectors on the final result, and for highly accurate approximations, these weight matrices require more storage than the final compressed matrix. We present a compression method for the weight matrices and demonstrate that it introduces only a controllable error to the overall approximation. Numerical experiments show that the new method leads to a significant reduction in storage requirements.

3D modelling of ground magnetic-source airborne TEM data for anisotropic media based on the rational Krylov method

With the rapid development of the transient electromagnetic method (TEM), the numerical simulations of three-dimensional anisotropic media have garnered attention. This study used the rational Krylov method to realise the three-dimensional modelling of the ground magnetic-source airborne transient electromagnetic data for arbitrary anisotropic media. First, based on Maxwell's equations, a time-domain electromagnetic equation was derived for anisotropic media. The finite difference method was employed to discretise the equation, and the electromagnetic field was then expressed as the product of an exponential matrix and a vector related to the source. Subsequently, the rational Arnoldi algorithm was adopted to construct the rational Krylov subspace orthogonal basis vectors, and the electromagnetic fields at different times were obtained based on a model reduction strategy. The accuracy of the proposed algorithm was verified through the comparisons of its results with those of other software packages. We calculated the response for different anisotropic parameters of the typical three-dimensional anisotropic models, and analysed the influence of the anisotropic media on the ground magnetic-source airborne transient electromagnetic data. The proposed three-dimensional forward TEM algorithm provides important technical support for identifying the anisotropic geological bodies and lays the foundation for further inversion research.

Influence of Magnetic Polarization on Diagrams of Inductive and Electromagnetic Logs

Abstract ––We present the results of the study of the effect of induced magnetic polarization of clay beds under the influence of an external harmonic electromagnetic field (frequencies 70 and 875 kHz). A two-stage numerical modeling procedure is proposed. At the first stage we determine the effective relative magnetic permeability of a synthetic sample with inclusions of clay particles. In this case a 3D heterogeneous mesh sample is generated. Then we numerically model a spatial distribution of an electric field. The electromotive force (EMF) induced in the measuring coil is calculated from this distribution. Relative magnetic permeability is determined by comparison with EMF of homogeneous samples with different values of magnetic permeability. It has been found that during the electric field excitation by an alternating current coil, the effect of induced magnetic polarization appears in the sample with clay particles. Its manifestation is that the effective magnetic permeability becomes complex. At the second stage we calculate the EMF diagram of the three-coil logging probe in the macro-model ‘clay cap – reservoir’. Magnetic permeability of the clay cap is given by a complex value. In the generated logs, extremes appear in the vicinity of the bottom of the clay cap; they do not correspond to the distribution of electrical conductivity and magnetic permeability in the given model. They can be incorrectly interpreted when analyzing real logs into individual formations. Numerical modeling at all stages is performed by the Vector Finite Element Method on a consistent adaptive tetrahedral partition and the first-order Webb vector basis.

Flux distribution tallies using proper orthogonal decomposition in Monte Carlo calculations

ABSTRACT In this paper, a new tallying method for a neutron flux distribution using the proper orthogonal decomposition is proposed for dimensionality reduction. The target spatial flux distribution is expanded by orthogonal basis vectors. Expansion coefficients are tallied during the random walk of the Monte Carlo calculation. The orthogonal basis vectors are extracted from the pre-calculated snapshots by the singular value decomposition. The proposed method is verified in the multi-group Monte Carlo calculation with the one-dimensional heterogeneous whole core geometry as a feasibility study. The flux distribution for each of the assemblies and energy groups is expanded by the basis vectors. The fewer basis vectors obtained from snapshots can reconstruct the target distribution well compared with the conventional Legendre polynomials used in the functional expansion tallies. The dimension of the solution in the proposed method is reduced by a factor of twenty compared with the conventional cell tally. In addition, the statistical error is reduced through dimensionality reduction thanks to the methodological feature of the proposed method. The results indicate that the proposed method has the capability of dimensionality reduction to tally the finely discretized flux distribution.

Observation of 2 µm multiple annular structured vortex pulsed beams by cavity-mode tailoring.

In the past few years, annular structured beams have been extensively studied due to their unique "doughnut" structure and characteristics such as phase and polarization vortices. Especially in the 2 µm wavelength range, they have shown promising applications in fields such as novel laser communication, optical processing, and quantum information processing. In this Letter, we observed basis vector patterns with orthogonality and completeness by finely cavity-mode tailoring with end-mirror space position in a Tm:CaYAlO4 laser. Multiple annular structured beams including azimuthally, linearly, and radially polarized beams (APB, LPB, and RPB) operated at a Q-switched mode-locking (QML) state with a typical output power of ∼18 mW around 1962 nm. Further numerical simulation proved that the multiple annular structured beams are the coherent superposition of different Hermitian Gaussian modes. Using a self-made M-Z interferometer, we have demonstrated that the obtained multiple annular beams have a vortex phase with orbital angular momentum (OAM) of l = ±1. To the best of our knowledge, this is the first observation of vector and scalar annular vortex beams in the 2 µm solid-state laser.

A Study on the Average Number of LLL-based Using Statistical Learning

Lattice-based Cryptography is known as one of the key technologies in modern cryptography. This encryption scheme has the basis vectors from the lattice as the public key and a short-length vector in the lattice consisting of an integer combination of the basis vectors as the secret key. To break this encryption, we need to solve the Shortest Vector Problem (SVP), known as NP-hard. Therefore, instead of finding the shortest vector, LLL algorithm is often used to find a vector of sufficiently short length to break the encryption. The LLL algorithm is a well-known method for breaking this encryption, but there is still no clear answer to the question of how many times the LLL algorithm needs to be used to obtain the desired level of secret key, the average number of the (, )-LLL bases in dimension n is a tool to measure the probability that the LLL algorithm solves the SVP. We can expect that this number indicates how many times the appropriate algorithm should run. There is a formula for this, but it contains some functions that take a long time to compute. We apply linear regression to the formula of the average number of the (, )-LLL bases in dimension n, and therefore we obtain some formulas to approximate the average number of the (, )-LLL is based on dimension n, which contains simple functions. When the dimensions are high, our model is much better regarding the computation time.

Fast estimation of array shape and direction of arrival using sparse Bayesian learning for manoeuvring towed line array

AbstractThe sparse Bayesian learning (SBL) algorithm has demonstrated its advantage in the direction of arrival (DOA) estimation. However, it requires a lot of computational cost to iteratively estimate the SBL hyperparameters from measurement data. This paper focuses on fast estimating the array shape and DOAs using SBL for a short towed line array (TLA) during manoeuvring. A parabolic model is utilised to describe the bent TLA whose bow as a hyperparameter is estimated in the SBL iterative process. Then, the basis vector pruning strategy is considered in the iteration to reduce computational cost by neglecting the impossible directions of signal presence. The converged speed of the joint estimation algorithm is further improved by approximately calculating the posterior probability density with the message passing approach. The effectiveness of the optimising joint estimation algorithm is verified using the experimental results from South China Sea.

A method for determining the actual coordinate system of spiral bevel gears by the measured positions of eight tooth surfaces

Abstract The coordinate system for the measurement of spiral bevel gear (SBG) by gear measuring center (GMC) is discussed and the misalignment between the actual coordinate system and the theoretical coordinate system of the SBG is analyzed. The misalignment can cause measurement errors and cannot be neglected in SBG precision measurements. To calculate the misalignment and accurately establish the actual coordinate system, a novel re-fitting method based on the measured positions of eight tooth surfaces is proposed. First, eight sets of gear axis direction vectors and original points can be obtained from the measurement of eight tooth surfaces, by the single tooth surface matching method. Second, the actual axis vector and the original point of the gear can be obtained, by re-fitting those eight sets of gear axis vectors and original points. Then, the actual coordinate system can be established by the actual gear axis direction vector and the original point. The least square method is used to calculate the original point, and a basis vector fitting method is proposed to solve the gear axis direction vector. Finally, two groups of preset coordinate system deviation tests are carried out to verify the accuracy and feasibility of the fitting algorithm. The results show that the fitting error of the original point is far less than 1 × 10 − 1 μ m and the fitting error of the angle is far less than 1 × 10 − 7 degree, which are superior to the design accuracy of the GMC. Therefore, the proposed algorithm can be applied to improve the measurement accuracy of current GMC.

მდ. ჩოხელთხევის, ნადიბაანის ხევის და ნაღვარევის ხევის ღვარცოფული ნაკადების ფორმირების ფაქტორები და ანალიზი

The article presents the research and analysis of the formation factors of the mudflows of the right tributaries of the Tetri Aragvi River, Chokhelt Khevi River, Nadibaan Khevi River and Naghvarevi Khevi River, in order to develop modern methods of assessing, modeling and forecasting the expected risks, which is based on the data of field studies in 2023. The signs of influence of the geological and geomorphological structure, climatic and hydrographic characteristics of the studied valleys on the formation of alluvial flows are presented. Based on these data, some reference values are obtained, which determine the risks of occurrence of mudflows. The material presented in the article will be the basis for the creation of the basic vector data necessary for modeling the expected mudflows with RAMMS computer program.

Multi-index modeling and optimization of thermal performance of shell-and-tube heat accumulator based on MANOVA

The heat storage process of composite phase change heat accumulators is a complex phenomenon that requires multiple indicators to comprehensively reflect their thermal performance. Current research in this area is not comprehensive enough. There are also limitations in the evaluation indicators used. In this paper, the multi-index modeling, comprehensive evaluation and optimization methods of the heat storage performance of heat accumulators are studied. First, the basic vectors in the vector set of parameters reflecting the heat storage performance are selected as indicator functions, such as heat storage capacity, heat storage time and heat storage residue. Several independent variables are selected from the three aspects of the geometric parameters of the heat accumulator, the operating conditions, and the rib parameters as factors affecting the thermal storage performance. These multi-index dependent variables and independent variables constitute the multi-index form mathematical model group. Second, multivariate analysis of variance (MANOVA) was used to study the constituent terms of the multi-indicator formal mathematical model group. The MANOVA method was used to identify the effects of each independent variable on the thermal performance of the heat accumulators. The MANOVA method was also used to analyze the effect of the interaction between the factors on the multiple indicators of the thermal performance of the thermal storage. Multivariate nonlinear regression analysis was used to construct the multi-indicator mathematical model group reflecting the thermal storage performance based on MANOVA. Finally, the mathematical model group of multiple indicators is normalized and converted into a group of multiple indicator effectiveness functions, and the group of multiple indicator effectiveness functions is mathematically transformed to construct a comprehensive evaluation function that comprehensively responds to the thermal storage performance and seeks an optimization scheme for the thermal storage performance. The maximum value of its comprehensive index is 0.9988, and the corresponding optimal solutions of independent variables are X1 = 24 mm, X2 = 66.7 mm, X3 = 1600 mm, X4 = 0.2 m/s, X5 = 2 mm, X6 = 6.4 mm, and X7 = 46.8 mm.

Model-free three-vector predictive current control of permanent magnet synchronous motor based on improved sliding mode observer

Abstract To address the complexity of vector selection in the conventional predictive current control strategy and the reduction of control system robustness when the motor parameters change, this paper proposes a finite-set model-free three-vector predictive current control method for permanent magnet synchronous motor based on the improved sliding-mode perturbation observer. According to the mathematical model of a permanent magnet synchronous motor under perturbation, a new hyperlocal model is established, and the conventional vector traversal optimization method is optimized to obtain the necessary basic voltage vector by analyzing the function with one judgment. Meanwhile, the sliding mode perturbation observer is designed using the fast exponential convergence law to observe the unknown part. Finally, by experimentally contrasting the proposed technique with the conventional three-vector model predictive current control, the method suggested in this paper can successfully reduce the current pulsation and inhibit the system perturbation caused by the parameter change, ensuring the steady state performance of the motor, as demonstrated by the experimental comparison with the conventional three-vector model predictive current control method.

Double-Vector Model-Free Predictive Current Control Method for Voltage Source Inverters With Sampling Noise Suppression

Model-free predictive current control (MFPCC) methods based on look-up tables (LUTs) have been widely applied in voltage source inverters (VSIs) due to their simple implementation and excellent robustness. However, the performance of the VSIs is affected by the voltage vector used, accuracy of current gradients and sampling noise. In order to improve these, a new double-vector MFPCC method is proposed in this paper. First, a synthetic voltage vector composed of double vectors is applied in each control period to reduce current ripples, where the durations of the double vectors are calculated using predicted current gradients. Next, an extended LUT is designed by using the current gradients of the applied synthetic voltage vectors to update all current gradients of eight basic voltage vectors, so as to increase the accuracy of current gradients. Then, the effect of the sampling noise on MFPCC is analyzed in detail and suppressed by a sliding-mode observer (SMO) for the VSIs. Finally, simulation and experimental results have verified the effectiveness of the proposed method.

A Closed Formalism for Anatomy-Independent Projection and Optimization of Magnetic Stimulation Coils on Arbitrarily Shaped Surfaces.

Transcranial magnetic stimulation (TMS) is a popular method for the noninvasive stimulation of neurons in the brain. It has become a standard instrument in experimental brain research and has been approved for a range of diagnostic and therapeutic applications. These applications require appropriately shaped coils. Various applications have been established or approved for specific coil designs with their corresponding spatial electric field distributions. However, the specific coil implementation may no longer be appropriate from the perspective of available material and manufacturing opportunities or considering the latest understanding of how to achieve induced electric fields in the head most efficiently. Furthermore, in some cases, field measurements of coils with unknown winding or a user-defined field are available and require an actual implementation. Similar applications exist for magnetic resonance imaging coils. This work aims at introducing a complete formalism free from heuristics, iterative optimization, and ad-hoc or manual steps to form practical stimulation coils with individual turns to either equivalently match an existing coil or produce a given field. The target coil can reside on practically any sufficiently large or closed surface adjacent to or around the head. The method derives an equivalent field through vector projection exploiting the well-known Huygens' and Love's equivalence principle. In contrast to other coil design or optimization approaches recently presented, the procedure is an explicit forward Hilbert-space vector projection or basis change. For demonstration, we map a commercial figure-of-eight coil as one of the most widely used devices and a more intricate coil recently approved clinically for addiction treatment (H4) onto a bent surface close to the head for highest efficiency and lowest field energy. The resulting projections are within ≤4% of the target field and reduce the necessary pulse energy by more than 40%.