Spatial Operators Research Articles

Application of high-order SF-SFDTD scheme to solving a time-dependent SchrFDTD scheme , Wu

The finite-difference time-domain 2, 2 (FDTD (2, 2)) method with second-order numerical accuracy in time and space has been extensively employed in the field of quantum mechanics to solve the Schrödinger equation. Nevertheless, the presence of the Courant-Friedrichs-Lewy (CFL) condition imposes limitations on the grid size in the computational space, thereby constraining the admissible range of time steps. Accordingly, the efficiency of the FDTD(2, 2) method significantly decreases. In addition, the second-order numerical accuracy of the FDTD(2, 2) method both in time domain and in space domain often results in significant error accumulation during calculations, thereby undermining the fidelity of the simulation results. To surmount the constraints imposed by the CFL stability conditions and enhance the accuracy of computations, a novel approach termed SF-SFDTD(3, 4) method has been proposed, with 3 and 4 referring to the accuracy in space and time, respectively. This method combines spatial filtering (SF) with the high-order symplectic finite-difference time-domain (SFDTD) method. Its primary objective is to solve the time-dependent Schrödinger equation while ensuring time stability and scalability. The SF-SFDTD(3, 4) method obviates the need for further deriving the iterative formula employed in the conventional SFDTD(3, 4) method. Therefore, the method under consideration exhibits a remarkable degree of compatibility with its traditional counterpart. It is merely necessary to include a spatial filtering operation during each numerical iteration to eliminate spatial high-frequency components arising from the utilization of time step sizes that fail to satisfy the CFL stability condition, thereby ensuring the stability of the numerical scheme. Moreover, when the time step value satisfies the CFL stability condition, the amplitude of the high-frequency component approaches zero, thereby exerting a minimal influence on the accuracy of the computational results. The adoption of time steps that do not meet the CFL stability conditions leads to an amplification in the amplitude of the high-frequency component. However, this finding solely affects the stability of the computational results, and the elimination of these unstable high-frequency components scarcely affect the accuracy of the computational results. The SF-SFDTD(3, 4) retains the simplicity and efficacy inherent in the traditional SFDTD(3, 4) methods, while enhancing computational efficiency. Additionally, the numerical stability and dispersion error of the SF-SFDTD(3, 4) method are analyzed theoretically . Finally, the validity and efficacy of the proposed method are corroborated through numerical illustrations.

4D High-Resolution Imagery of Point Clouds for Automotive mmWave Radar

In the community of automotive millimeter wave radar, the recently developed concept of four-dimensional (4D) radar can provide high-resolution point clouds image with enhanced imaging performance. Currently, the density of point clouds for single-frame image is usually too sparse to satisfy the demands of target classification and recognition due to the limitation of Doppler and angle resolutions. To address the aforementioned issues, a novel algorithm is proposed for 4D high-resolution imagery generation of point clouds with extremely high Doppler and angle resolutions in this paper. For high Doppler resolution with high-dynamic, a novel velocity ambiguity resolution algorithm is proposed using a dual pulse repetition frequency (dual-PRF) waveform design embedded in an innovative time-division multiplexing & Doppler-division multiplexing MIMO (TDM-DDM-MIMO) framework. Meanwhile, an attractive complex-valued deep convolutional network (CV-DCN) of super-resolution direction-of-arrival (DOA) estimation is proposed only using single-frame data. To be specific, a spatial smoothing operator on array data is applied as input of the network, and a CV-DCN is designed to learn the transformation of the spatial spectrum from the end-to-end to effectively protect the spectrum extraction. Furthermore, experimental analysis is performed to confirm the effectiveness of the proposed super-resolution DOA estimation algorithm. Finally, the 4D high-resolution imagery of point clouds is obtained by experiments in the parking lot.

Designing PostGIS Database System with Fuzzy Theory to Support Accessibility Tools for Urban Pedestrians

The combination of fuzzy logic and crowdsourcing can be a powerful tool for generating geospatial data for pedestrians with mobility challenges in urban areas. Although potentially useful, information about the accessibility of paths that is generated through crowdsourcing is susceptible to a high degree of imprecision. Spatial data management is required for such systems, which supports the management of uncertain data. Fuzzy theory allows us to model ambiguous information. To fill this gap, an improved method based on a fuzzy relational PostGIS database (FPostGIS) is proposed. The method includes extensions to represent imprecise data within an entity-relationship (ER) data model specifically tailored for path accessibility, and a set of steps for the derivation of FPostGIS from this extended ER model. According to the case study, this methodology has been applied in the design and development of decision support application within the Maps for Easy Paths (MEP) project. This application stores and retrieves accessibility information about a particular path and allows performing spatial operations and analysis inside the database.

The Rough with the Smooth of the Light Cone String

The polynomials in the generators of a unitary representation of the Poincaré group constitute an algebra which maps the dense subspace D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal D$$\\end{document} of smooth, rapidly decreasing wavefunctions to itself. This mathematical result is highly welcome to physicists, who previously just assumed their algebraic treatment of unbounded operators be justified. The smoothness, however, has the side effect that a rough operator R, which does not map a dense subspace of D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal D$$\\end{document} to itself, has to be shown to allow for some other dense domain which is mapped to itself both by R and all generators. Otherwise their algebraic product, their concatenation, is not defined. Canonical quantization of the light cone string postulates operators -iX1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-\ extrm{i}X^1$$\\end{document} and P-=(P0-Pz)/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P^-=(P^0 - P^z)/2$$\\end{document} and as their commutator the multiplicative operator R=P1/(P0+Pz)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R=P^1/(P^0 + P^z)$$\\end{document}. This is not smooth but rough on the negative z-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z-$$\\end{document}axis of massless momentum. Using only the commutation relations of Pm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P^m$$\\end{document} with the generators -iMiz\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-\ extrm{i}M_{iz}$$\\end{document} of rotations in the Pi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P^i$$\\end{document}-Pz\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P^{z}$$\\end{document}-plane we show that on massless states the operator R is inconsistent with a unitary representation of SO(D-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(D-1)$$\\end{document}. This makes the algebraic determination of the critical dimension, D=26\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D=26$$\\end{document}, of the bosonic string meaningless: if the massless states of the light cone string admit R then they do not admit a unitary representation of the subgroup SO(D-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(D-1)$$\\end{document} of the Poincaré group. With analogous arguments we show: Massless multiplets are inconsistent with a translation group of the spatial momentum which is generated by a self-adjoint spatial position operator X\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{X}$$\\end{document}.

Completing Dirac’s work. The Dirac electron is a 2D hologram

The QED-physical (QED-P) theory [J. H. Wilson, Phys. Essays 35, 5 (2022)] is actually the theory Dirac sought in 1962 in his attempt to predict the muon as an “extensible model of the electron.” Recently, Lerche attempted to produce a classical solution to Dirac’s equation for the radial motion of an extensible, basically classical, model of the electron. Both Dirac and Lerche proceeded in the wrong, classical direction in this effort. The QED-P center of charge (CoC) position operator is derived directly from the Dirac equation (DE) CoC velocity operator, cα with no ad hoc assumptions. QED-P was integrated with QED into a single theory, and that integration is proved by the highly accurate estimates of QED that are dependent on the DE velocity operator cα. Both QED and QED-P are based directly on the same Dirac Equation (DE) four current c(α,I) that QED couples with an external electromagnetic field. QED uses covariant perturbation theory to produce highly accurate results, except for the electron selfenergy, which is infinite. The DE velocity operator, cα, is the spatial part of the free electron four current, and has highly unusual properties compared to classical velocity vectors. QED could not produce highly accurate answers without the 4 × 4 complex matrix cα as the electron CoC “velocity” operator. QED-P simply integrates the same Dirac equation four current used so successfully in QED, and produces the discrete internal spatial and time coordinate operators (ISaTCOs) to give the electron field’s internal structure a very specific, but highly, nonclassical geometric description, with no ad hoc assumptions. QED and QED-P are complementary theories, and both are proven to be true by the accurate results of QED. The physical interpretation of QED-P is discussed in this paper as a two-dimensional, rapidly vibrating “point” charge, that is always located on a 2D CoC sphere in the electron rest frame, oscillating rapidly through eight eigenvalues with an ISaTCO period of ∼10−22 s. The fact that the CoC’s eight ISaTCO spatial eigenvectors are always are located on a 2D shell encompassing the electron’s 3D “space” inside the CoC’s 2D shell is a direct consequence of the DE, and nothing else. In this paper, it is shown that the “discrete” ISaTCOs produce a one dimensional, discrete quantum harmonic oscillator with its ISaTCOs always located on a 2D CoC shell. The CoC shell is an “2D hologram” emerging from a 3D volume inside the 2D CoC shell with a vibrational electronic clock” producing an internal phase that is propagated throughout space/time. The QED-P point electron charge rotates 720° to complete one internal electron discrete period. The electron’s spin and magnetic moment [J. H. Wilson, Phys. Essays 29, 402 (2016); ibid. 31(1), 59‐67 (2018); ibid. 34, 17 (2021)] are generated by the CoC ISaTCO in QED-P, and there is no need for “intrinsic” properties. The QED-P electron properties described above d are far different than the standard model’s very small point particle with intrinsic properties of spin and magnetic moment.

Spatialization of Imperial Power: Spatial Reconstruction and Power Operation of Jinshan Temple during the Southern Inspection Tours of Emperor Kangxi

The Kangxi Southern Inspection Tours strengthened the Qing Dynasty’s control over Jiangnan Buddhism, thereby promoting the standardization and officialization of Jiangnan temples and externalizing imperial power through images and physical space. Taking Jinshan Temple as an example, this study combines spatial analysis of architecture and image analysis used by art historians to examine the transformation between physical and pictorial spaces in Jinshan Temple, revealing the spatial operation of imperial power. The intervention of imperial power sparked the space reconstruction of Jinshan Temple through a process of “merger-occupation-infiltration-adjustment”. Thus, the control measures of Kangxi are revealed, including the emphasis on the geographical significance of the temple, space occupation of royal buildings, change in landscape, and the adaptation of monks by adjusting their imagination of the sacred space. By determining the spatial reconstruction, we observe that the spatial strategy of power reflects Kangxi’s religious attitude toward Buddhism of “neither promoting nor suppressing, but treating it reasonably” 朕惟置之焉能有無之間, which may enrich our understanding of the influence of Kangxi’s Southern Inspection Tours on Jiangnan’s religious space.

Numerical modelling of advection diffusion equation using Chebyshev spectral collocation method and Laplace transform

In this article a numerical method for numerical modelling of advection diffusion equation is developed. The proposed method is based on Laplace transform (LT) and Chebyshev spectral collocation method (CSCM). The LT is used for time-discretization and the CSCM is used for discretization of spatial derivatives. The LT is used to transform the time variable and avoid the finite difference time stepping method. In time stepping technique the accuracy is achieved for very small time step which results in a very high computational time. The spatial operators are discretized using CSCM to achieve high accuracy as compared to other methods. The method is composed of three primary stages: firstly the given problem is transformed into a corresponding inhomogeneous elliptic problem by using the LT; secondly the CSCM used to solve the transformed problem in LT domain; finally the solution obtained in LT domain is converted to time domain via numerical inverse LT. The inversion of LT is generally an ill-posed problem and due to this reason various numerical inversion methods have been developed. In this article we have utilized the contour integration method which is one of the most efficient methods. The most important feature of this approach is that it handles the time derivative with the Laplace transform rather than the finite difference time stepping approach, avoiding the untoward impact of time steps on stability and accuracy of the method. Five test problems are used to validate the efficiency and accuracy of the proposed numerical scheme.

HSH-UNet: Hybrid selective high order interactive U-shaped model for automated skin lesion segmentation

The use of computer-assisted clinical dermatologists to diagnose skin diseases is an important aid. And computer-assisted techniques mainly use deep neural networks. Recently, the proposal of higher-order spatial interaction operations in deep neural networks has attracted a lot of attention. It has the advantages of both convolution and transformers, and additionally has the advantages of efficient, extensible and translation-equivariant. However, the selection of the interaction order in higher-order interaction operations requires tedious manual selection of a suitable interaction order. In this paper, a hybrid selective higher-order interaction U-shaped model HSH-UNet is proposed to solve the problem that requires manual selection of the order. Specifically, we design a hybrid selective high-order interaction module HSHB embedded in the U-shaped model. The HSHB adaptively selects the appropriate order for the interaction operation channel-by-channel under the computationally obtained guiding features. The hybrid order interaction also solves the problem of fixed order of interaction at each level. We performed extensive experiments on three public skin lesion datasets and our own dataset to validate the effectiveness of our proposed method. The ablation experiments demonstrate the effectiveness of our hybrid selective higher order interaction module. The comparison with state-of-the-art methods also demonstrates the superiority of our proposed HSH-UNet performance. The code is available at https://github.com/wurenkai/HSH-UNet.

Surface phase-field surfactant fluid model and its practical closest point type finite difference computation

To investigate the fluid surfactant material on three-dimensional objects, we herein develop a simple and practical model based on phase-field method and design its efficient algorithm. The binary fluids and surfactant are represented by two order parameters. The fluid evolution is governed by the incompressible Navier–Stokes equations. To achieve high-performance computation, a linear semi-implicit scheme with stabilizers is proposed for the phase-field type equations in time. The projection method with pressure correction is used to decouple the velocity and the pressure. Based on the closest-point type embedded narrow domain method and a simple pseudo-Neumann boundary treatment, the calculation on curved surface is extended into a narrow band region including the surface. The surface spatial operators are approximately replaced by the standard spatial operators. In the three-dimensional narrow band, the finite difference method is used to discretize the equations on staggered grids. The mass compensation and vector projection techniques are designed to obtain physically meaningful solutions. In each time iteration, the proposed algorithm is efficient to implement. Numerical results indicate that the proposed method is capable to simulate surfactant-laden phase separation, fluid instabilities, and coarsening dynamics with variable mobility on various surfaces.

A WENO SPH scheme with improved transport velocity and consistent divergence operator

The Arbitrary Lagrangian–Eulerian Smoothed Particle Hydrodynamics (ALE-SPH) formulation can guarantee stable solutions preventing the adoption of empirical parameters such as artificial viscosity. However, the convergence rate of the ALE-SPH formulation is still limited by the inaccuracy of the SPH spatial operators. In this work, a Weighted Essentially Non-Oscillatory (WENO) spatial reconstruction is then adopted to minimise the numerical diffusion introduced by the approximate Riemann solver (which ensures stability), in combination with two alternative approaches to restore the consistency of the scheme: corrected divergence SPH operators and the particle regularisation guaranteed by the correction of the transport velocity. The present work has been developed in the framework of the DualSPHysics open-source code. The beneficial effect of the WENO reconstruction to reduce numerical diffusion in ALE-SPH schemes is first confirmed by analysing the propagation of a small pressure perturbation in a fluid initially at rest. With the aid of a 2-D vortex test case, it is then demonstrated that the two aforementioned techniques to restore consistency effectively reduce saturation in the convergence to the analytical solution. Moreover, high-order (above second) convergence is achieved. Yet, the presented scheme is tested by means of a circular blast wave problem to demonstrate that the restoration of consistency is a key feature to guarantee accuracy even in the presence of a discontinuous pressure field. Finally, a standing wave has been reproduced with the aim of assessing the capability of the proposed approach to simulate free-surface flows.

Numerical calculation and fast method for the magnetohydrodynamic flow and heat transfer of fractional Jeffrey fluid on a two-dimensional irregular convex domain

In this paper, we study the magnetohydrodynamic (MHD) flow and heat transfer of the fractional Jeffrey fluid in a straight channel, of which the cross section is a two-dimensional irregular convex domain. We consider a spatial fractional operator to modify the classical Fourier's law of thermal conduction, and obtain the time-space fractional coupled model. The fractional coupled model is solved numerically by the L2−1σ method in the temporal direction and the unstructured mesh finite element method in the spatial direction. Besides, we prove the stability and convergence of the numerical scheme. In order to reduce the computational time, a fast method is proposed. Finally, a numerical example is given to verify the theoretical analysis and the efficiency of the fast method. Furthermore, an example is considered to discuss the effects of the fractional parameters on the MHD flow and heat transfer of the fractional Jeffrey fluid.

Vision Transformer-Based Ensemble Learning for Hyperspectral Image Classification

Hyperspectral image (HSI) classification, due to its characteristic combination of images and spectra, has important applications in various fields through pixel-level image classification. The fusion of spatial–spectral features is a topic of great interest in the context of hyperspectral image classification, which typically requires selecting a larger spatial neighborhood window, potentially leading to overlaps between training and testing samples. Vision Transformer (ViTs), with their powerful global modeling abilities, have had a significant impact in the field of computer vision through various variants. In this study, an ensemble learning framework for HSI classification is proposed by integrating multiple variants of ViTs, achieving high-precision pixel-level classification. Firstly, the spatial shuffle operation was introduced to preprocess the training samples for HSI classification. By randomly shuffling operations using smaller spatial neighborhood windows, a greater potential spatial distribution of pixels can be described. Then, the training samples were transformed from a 3D cube to a 2D image, and a learning framework was built by integrating seven ViT variants. Finally, a two-level ensemble strategy was employed to achieve pixel-level classification based on the results of multiple ViT variants. Our experimental results demonstrate that the proposed ensemble learning framework achieves stable and significantly high classification accuracy on multiple publicly available HSI datasets. The proposed method also shows notable classification performance with varying numbers of training samples. Moreover, herein, it is proven that the spatial shuffle operation plays a crucial role in improving classification accuracy. By introducing superior individual classifiers, the proposed ensemble framework is expected to achieve even better classification performance.

48 Psychometric properties of DCTclock™ with commonly used neuropsychological tests and their combined ability to predict Beta-Amyloid Positron Emission Tomography Status

Objective:Sensitive and non-invasive methods of screening for early-stage Alzheimer’s disease (AD) are urgently needed. The digital clock drawing test (DCTclockTM) is an established and well-researched neuropsychological tool that can aid in early detection of dementia. Other simple, yet sensitive, neuropsychological measures able to detect early stages of AD include Trail Making Tests (TMT). We investigated the psychometric properties of DCTclockTM with TMT-A and TMT-B. We then sought to understand the degree to which neuropsychological tools (i.e., DCTclockTM, TMT-A, and B) versus the Montreal Cognitive Assessment (MoCA) predict beta-amyloid (Aß) positron emission tomography (PET) status (positive or negative) in cognitively normal individuals.Participants and Methods:Participants included a sample of cognitively normal older adults (n= 59, M age = 69.2, F = 64%) recruited from the Butler Memory and Aging Program. The Linus Health DCTclockTM uses a digital pen to capture traditional clock drawing test performance and advanced analytics to evaluate the drawing process for indicators of cognitive difficulty. DCTclockTM may have overlapping cognitive properties with TMT measures, like efficiency, processing speed, and spatial reasoning. We compared latency measures (i.e., process efficiency, clock face speed, average latency, and processing speed) and spatial reasoning of the DCTclockTM to z-scores of TMT-A and TMT-B to detect any overlapping psychometric properties. Verbal fluency was included for discriminant validity. We then ran logistic regressions on a subset of the sample to compare neuropsychological tests (DCTclockTM total score [score that captures overall performance], TMT-A/B, and verbal fluency) to the MoCA, a commonly used cognitive screening tool, in determining PET status.Results:Highly correlated (r > .7) DCTclockTM variables were excluded. We found statistically significant correlations between some DCTclockTM measures and TMT-A/B, like DCTclockTM drawing process efficiency and TMT-A and TMT-B (r= .45, p< .001, r=.29, p< .026, respectively), and DCTclockTM average latency and TMT-A and TMT-B (r=.3, p< .024, r= .26, p< .044, respectively). No statistically significant associations were found between any DCTclockTM measures and verbal fluency, or between DCTclockTM spatial reasoning and TMT-A/B. We then investigated the effect of these neuropsychological tests (DCTclockTM total score, TMT-A/B, verbal fluency) and age on the likelihood of PET positivity (subset of sample, total PET, n=31). The model was statistically significant (x2 (5) = 15.35, p< .01). The model explained 53% (Nagelkerke R2) of the variance in PET status and correctly classified 74.2% of cases. DCTclockTM was the only significant predictor (p< .02), after controlling for TMT-A, TMT-B, verbal fluency, and age. Comparatively, there was no effect of MoCA and age (total PET, n= 29) on the likelihood of PET positivity.Conclusions:Overall, these results suggest psychometric convergence on elements of DCTclockTM and TMT-A/B, while there was no association in spatial operations between DCTclockTM and TMT measures. Further, when compared to the MoCA, DCTclockTM and these commonly used neuropsychological tests (verbal fluency and TMT-A/B) were better predictors of PET status, primarily driven by the DCTclockTM. Digitized neuropsychological tools may provide additional metrics not captured by pen-and-paper tests that can detect AD-associated pathology.

Improvement of LED-based photoacoustic imaging using lag-coherence factor (LCF) beamforming.

Owing to its portability, affordability, and energy-efficiency, LED-based photoacoustic (PA) imaging is increasingly becoming popular when compared to its laser-based alternative, mainly for superficial vascular imaging applications. However, this technique suffers from low SNR and thereby limited imaging depth. As a result, visual image quality of LED-based PA imaging is not optimal, especially in sub-surface vascular imaging applications. Combination of linear ultrasound (US) probes and LED arrays are the most common implementation in LED-based PA imaging, which is currently being explored for different clinical imaging applications. Traditional delay-and-sum (DAS) is the most common beamforming algorithm in linear array-based PA detection. Side-lobes and reconstruction-related artifacts make the DAS performance unsatisfactory and poor for a clinical-implementation. In this work, we explored a new weighting-based image processing technique for LED-based PAs to yield improved image quality when compared to the traditionalmethods. We are proposing a lag-coherence factor (LCF), which is fundamentally based on the combination of the spatial auto-correlation of the detected PA signals. In LCF, the numerator contains lag-delay-multiply-and-sum (DMAS) beamformer instead of a conventional DAS beamformer. A spatial auto-correlation operation is performed between the detected US array signals before using DMAS beamformer. We evaluated the new method on both tissue-mimicking phantom (2D) and human volunteer imaging (3D) data acquired using a commercial LED-based PA imagingsystem. Our novel correlation-based weighting technique showed LED-based PA image quality improvement when it is combined with conventional DAS beamformer. Both phantom and human volunteer imaging results gave a direct confirmation that by introducing LCF, image quality was improved and this method could reduce side-lobes and artifacts when compared to the DAS and coherence-factor (CF) approaches. Signal-to-noise ratio, generalized contrast-to-noise ratio, contrast ratio and spatial resolution were evaluated and compared with conventional beamformers to assess the reconstruction performance in a quantitative way. Results show that our approach offered image quality enhancement with an average signal-to-noise ratio and spatial resolution improvement of around 20% and 25% respectively, when compared with conventional CF based DASalgorithm. Our results demonstrate that the proposed LCF based algorithm performs better than the conventional DAS and CF algorithms by improving signal-to-noise ratio and spatial resolution. Therefore, our new weighting technique could be a promising tool to improve the performance of LED-based PA imaging and thus accelerate its clinicaltranslation.

Spatial Blockchain: Enhancing Spatial Queries and Applications through Integrating Blockchain and Spatial Database Technologies

The fusion of spatial data with blockchain technologies presents an innovative approach towards a decentralized, secure, and trustworthy framework for spatial information management. This integration brings spatial representation to the forefront of blockchain, opening avenues for various sectorial applications. However, challenges like slow processing times, restricted query capabilities, and consistency issues have been identified within the blockchain system. Addressing these challenges, we propose an optimized method for spatial queries by leveraging the high-performance capabilities of spatial databases. Unlike conventional off-chain query techniques, our approach synergistically combines hyperledger fabric with a specialized spatial database. This fusion facilitates distributed spatial queries within blockchain framework, incorporating spatial operation functionalities into smart contracts while preserving the distributed nature of nodes and spatial databases. Enhancing system security, we incorporate a dual-stage verification mechanism alongside a salt-hash storage strategy to counteract potential unauthorized alterations. Initial results validate the efficacy of our methodology in terms of performance and security. Building on this foundation, we introduce a rental transaction system that effectively merges spatial data with blockchain, demonstrating the feasibility and potential of integrating spatial information into the blockchain, especially in the realm of real estate.

A provably stable and high-order accurate finite difference approximation for the incompressible boundary layer equations

In this article we develop a high order accurate method to solve the incompressible boundary layer equations in a provably stable manner. We first derive continuous energy estimates, and then proceed to the discrete setting. We formulate the discrete approximation using high-order finite difference methods on summation-by-parts form and implement the boundary conditions weakly using the simultaneous approximation term method. By applying the discrete energy method and imitating the continuous analysis, the discrete estimate that resembles the continuous counterpart is obtained proving stability. We also show that these newly derived boundary conditions removes the singularities associated with the null-space of the nonlinear discrete spatial operator. Numerical experiments that verifies the high-order accuracy of the scheme and coincides with the theoretical results are presented. The numerical results are compared with the well-known Blasius similarity solution as well as that resulting from the solution of the incompressible Navier–Stokes equations.

Offshore geotechnical challenges of the energy transition

Offshore wind is the most mature of the offshore renewable energy technologies and has a significant role to play in the energy transition. 2000 GW of offshore wind capacity is anticipated globally by 2050 in order meet the targets of the Paris Agreement [1]. These ambitions correspond to a 35-fold increase compared to current installed offshore wind capacity, which has taken three decades to achieve, thus requiring an installation rate between now and the mid-century far out-stripping that currently achieved [2]. The pace and scale of offshore wind ambitions to support the energy transition present a range of challenges for the offshore geotechnical sector and the broader offshore wind sector, with impacts across the supply chain regarding availability of raw materials, vessels, equipment and personnel, and across each stage of the life-cycle of the projects from marine spatial planning, site investigation, design, manufacturing, installation, operation and decommissioning. To address these challenges, the sector faces key imperatives, including (i) to determine where best to place future offshore windfarms to meet technical, social and environmental requirements and identify where technology and knowledge gaps exist, (ii) to improve efficiency in deriving geotechnical design parameters in order to alleviate pressures on people, vessels, equipment and labs for site investigation and interpretation of test results; (iii) to improve efficiency of design outcomes, i.e. to achieve greater capacity:weight efficiency for foundations, anchors and mooring systems to ease supply chain, manufacturing and installation pressures, while maintaining necessary reliability; (iv) to improve time efficiency to complete designs in order to make design calculations and processes less time- and personnel-intensive to carry out; and (v) to improve the life-cycle cost of delivering the necessary offshore wind to enable a net zero future through considering the end of engineered life at the design stage. 
 Figure 1 illustrates the magnitude of the projected and necessary growth in offshore wind globally to 2050 in terms of installed offshore wind capacity and number of turbines, with an indication of the associated geotechnical implications for this pace and scale of growth.
 Potential solutions to address the identified challenges and associated imperatives include those to address specifically geotechnical challenges, but also geotechnical solutions to offshore wind challenges beyond the seabed. For example, (i) use of geospatial mapping and analysis to determine the available seabed areas for future offshore windfarms and identify suitable foundations or anchors for particular regions, which can in turn inform on supply chain or critical technology and knowledge gaps [4]; (ii) innovations to increase efficiency of offshore site investigation, including software [5] [6] and hardware approaches [7] to facilitate seabed characterization at meaningful spatial and temporal scales; (iii) innovations in design philosophy, concepts and methods to improve design outcomes for foundations and anchoring systems, including whole life geotechnical design [8], novel moorings and anchors [9] [10] [11] and integrated design [12]; (iv) creation of optimization design tools that can directly address the design question, avoiding numerous ad hoc individual analyses to hone in to a workable solution [13] [14]; and (v) methods to inform on requirements for end of engineered life, e.g. retrieval or stability if left in situ beyond the design life [15] [16], and geospatial mapping to understand the distribution of assets at the end of engineered life in order to plan for recycling or disposal [17].

Data-Driven Spatial Adaptive Terminal Iterative Learning Predictive Control for Automatic Stop Control of Subway Train With Actuator Saturation

A data-driven spatial adaptive terminal iterative learning predictive control (SATILPC) scheme with actuator saturation is proposed for automatic stop control of the subway train. Considering the outstanding repetitive operation pattern and the unavailable accurate model of a subway train, the unknown train dynamics is firstly transformed into a nonlinear discrete form in spatial domain via the spatial differential operator. Since the train automatic stop control (TASC) only concentrates on the tracking performances of the terminal position and terminal speed, an iterative dynamic linearization approach considering the terminal operation point is devised to formulate the relationship of the train input and output (I/O) into a linear affine form. Then, a terminal iterative learning prediction mechanism is introduced to reconstruct the developed train data model to forecast the future train behaviors through rolling optimization process. As a result, by removing the constraints on the unimportant points, the optimal control input (braking force) can be obtained by minimizing the objective function through terminal I/O data. Further, actuator saturation is considered to address the passenger comfort and the reliable operation of the train. The proposed SATILPC approach is a pure data-driven iterative learning control scheme and no model information is involved in the whole design processes. By utilizing a newly space-based contraction mapping method, the convergence of the proposed approach is strictly proved. Finally, the simulation results further demonstrate the feasibility of the proposed algorithm.

Adaptive Beamforming with Small Samples and Low Complexity for Large-Scale Arrays

In this paper, we propose a novel adaptive beamforming method based on interference plus noise covariance matrix (INCM) reconstruction with few samples and low complexity. Unlike existing techniques, we make use of the fact that large-scale antenna arrays can significantly increase the spectral analysis’s resolution by estimating the steering vector (SV) and power of the interfering signal using the discrete Fourier transform (DFT). In addition, a simple spatial rotation operation is employed to resolve the power “leakage” problem of the DFT spectrum and increase estimation precision. The proposed method achieves a high output SINR by reconstructing an accurate INCM with the advantage of simple implementation and low computation complexity. Finally, we verify the effectiveness of the proposed method by numerical simulation and result analysis.

EMO-MoviNet: Enhancing Action Recognition in Videos with EvoNorm, Mish Activation, and Optimal Frame Selection for Efficient Mobile Deployment.

The primary goal of this study is to develop a deep neural network for action recognition that enhances accuracy and minimizes computational costs. In this regard, we propose a modified EMO-MoviNet-A2* architecture that integrates Evolving Normalization (EvoNorm), Mish activation, and optimal frame selection to improve the accuracy and efficiency of action recognition tasks in videos. The asterisk notation indicates that this model also incorporates the stream buffer concept. The Mobile Video Network (MoviNet) is a member of the memory-efficient architectures discovered through Neural Architecture Search (NAS), which balances accuracy and efficiency by integrating spatial, temporal, and spatio-temporal operations. Our research implements the MoviNet model on the UCF101 and HMDB51 datasets, pre-trained on the kinetics dataset. Upon implementation on the UCF101 dataset, a generalization gap was observed, with the model performing better on the training set than on the testing set. To address this issue, we replaced batch normalization with EvoNorm, which unifies normalization and activation functions. Another area that required improvement was key-frame selection. We also developed a novel technique called Optimal Frame Selection (OFS) to identify key-frames within videos more effectively than random or densely frame selection methods. Combining OFS with Mish nonlinearity resulted in a 0.8-1% improvement in accuracy in our UCF101 20-classes experiment. The EMO-MoviNet-A2* model consumes 86% fewer FLOPs and approximately 90% fewer parameters on the UCF101 dataset, with a trade-off of 1-2% accuracy. Additionally, it achieves 5-7% higher accuracy on the HMDB51 dataset while requiring seven times fewer FLOPs and ten times fewer parameters compared to the reference model, Motion-Augmented RGB Stream (MARS).