Refinement Algorithm Research Articles

Improved local refinement for S-splines-based isogeometric analysis

S-splines (Simple splines) is a generalization of T-splines that solves the problem of additional control points propagation in T-spline’s local refinement algorithm. However, when applying S-splines to isogeometric analysis (IGA), the existing local refinement algorithm for S-splines can result in a matrix with an extremely large condition number. This paper provides a solution to this problem by introducing an improved local refinement algorithm. The improvement is achieved through an optimized postprocessing process for decomposing the blending functions before insertion. We also prove that the improved local refinement algorithm can preserve the linear independence of blending functions, the partition of unity, and create nested spline spaces during local refinement. Numerical experiments show that the resulting S-splines require fewer degrees of freedom than T-splines and analysis-suitable T-splines under the same error. Additionally, the condition numbers of the matrices are much smaller than those with the original S-splines local refinement algorithm.

Use of Artificial Intelligence in the Advancement of Breast Surgery and Implications for Breast Reconstruction: A Narrative Review.

Breast reconstruction is a pivotal part of the recuperation process following a mastectomy and aims to restore both the physical aesthetic and emotional well-being of breast cancer survivors. In recent years, artificial intelligence (AI) has emerged as a revolutionary technology across numerous medical disciplines. This narrative review of the current literature and evidence analysis explores the role of AI in the domain of breast reconstruction, outlining its potential to refine surgical procedures, enhance outcomes, and streamline decision making. A systematic search on Medline (via PubMed), Cochrane Library, Web of Science, Google Scholar, Clinical Trials, and Embase databases from January 1901 to June 2023 was conducted. By meticulously evaluating a selection of recent studies and engaging with inherent challenges and prospective trajectories, this review spotlights the promising role AI plays in advancing the techniques of breast reconstruction. However, issues concerning data quality, privacy, and ethical considerations pose hurdles to the seamless integration of AI in the medical field. The future research agenda comprises dataset standardization, AI algorithm refinement, and the implementation of prospective clinical trials and fosters cross-disciplinary partnerships. The fusion of AI with other emergent technologies like augmented reality and 3D printing could further propel progress in breast surgery.

RIS-Aided Near-Field Localization Under Phase-Dependent Amplitude Variations

We investigate the problem of reconfigurable intelligent surface (RIS)-aided near-field localization of a user equipment (UE) served by a base station (BS) under phase-dependent amplitude variations at each RIS element. Through a misspecified Cramér-Rao bound (MCRB) analysis and a resulting lower bound (LB) on localization, we show that when the UE is unaware of amplitude variations (i.e., assumes unit-amplitude responses), severe performance penalties can arise, especially at high signal-to-noise ratios (SNRs). Leveraging Jacobi-Anger expansion to decouple range-azimuth-elevation dimensions, we develop a low-complexity approximated mismatched maximum likelihood (AMML) estimator, which is asymptotically tight to the LB. To mitigate performance loss due to model mismatch, we propose to jointly estimate the UE location and the RIS amplitude model parameters. The corresponding Cramér-Rao bound (CRB) is derived, as well as an iterative refinement algorithm, which employs the AMML method as a subroutine and alternatingly updates individual parameters of the RIS amplitude model. Simulation results indicate fast convergence and performance close to the CRB. The proposed method can successfully recover the performance loss of the AMML under a wide range of RIS parameters and effectively calibrate the RIS amplitude model online with the help of a user that has an a-priori unknown location.

DetonationFoam: An open-source solver for simulation of gaseous detonation based on OpenFOAM

Detonation has promising applications in advanced propulsion systems, and numerical simulation is widely used to gain insights into the complex interaction between the hydrodynamic flow and chemical reactions involved in detonation. In this work, detonationFoam, an open-source solver for accurate and efficient simulation of compressible reactive flow and detonation are developed based on OpenFOAM. detonationFoam can simulate compressible, multi-component, reactive flow and it can accurately evaluate the detailed transport coefficients using the mixture-averaged transport model. Compared to rhoCentralFoam, the improved HLLC-P approximate Riemann solver is used in detonationFoam and it helps to accurately resolve shock waves appearing in detonation. Besides, the adaptive mesh refinement and dynamic load balancing algorithms are used in detonationFoam, which greatly improves the computational efficiency. Validation tests including homogenous ignition, unsteady diffusion, shock tube problem, premixed flame, planar detonation, double Mach reflection, detonation cellular structure and oblique detonation wave are conducted. These tests demonstrate that detonationFoam can be used to accurately and efficiently to simulate the compressible, multi-component reactive flow and detonation processes. Program summaryProgram Title: detonationFoamCPC Library link to program files:https://doi.org/10.17632/x45zh4nz28.1Developer's repository link:https://github.com/JieSun-pku/detonationFoamLicensing provisions: GPLv3Programming language: C++Nature of problem: Gaseous detonation involves different length scales and complicated chemistry. To accurately and efficiently simulate the gaseous detonation, adaptive mesh refinement needs to be conducted and detailed chemistry should be considered. Besides, the severe load imbalance caused by the chemical source term evaluation may greatly reduce the computation efficiency.Solution method: An open-source solver, detonationFoam is developed based on OpenFOAM. The species equations considering detailed chemistry are solved in detonationFoam and thereby detonation in a compressible, multi-component, reactive flow can be simulated. The adaptive mesh refinement technique and the dynamic load balancing algorithm are incorporated into detonationFoam. It is demonstrated that detonationFoam can accurately and efficiently simulate gaseous detonation.

Min-Deviation-Flow in Bi-directed Graphs for T-Mesh Quantization

Subdividing non-conforming T-mesh layouts into conforming quadrangular meshes is a core component of state-of-the-art (re-)meshing methods. Typically, the required constrained assignment of integer lengths to T-Mesh edges is left to generic branch-and-cut solvers, greedy heuristics, or a combination of the two. This either does not scale well with input complexity or delivers suboptimal result quality. We introduce the Minimum-Deviation-Flow Problem in bi-directed networks (Bi-MDF) and demonstrate its use in modeling and efficiently solving a variety of T-Mesh quantization problems. We develop a fast approximate solver as well as an iterative refinement algorithm based on matching in graphs that solves Bi-MDF exactly. Compared to the state-of-the-art QuadWild [Pietroni et al. 2021] implementation on the authors' 300 dataset, our exact solver finishes after only 0.49% (total 17.06s) of their runtime (3491s) and achieves 11% lower energy while an approximation is computed after 0.09% (3.19s) of their runtime at the cost of 24% increased energy. A novel half-arc-based T-Mesh quantization formulation extends the feasible solution space to include previously unattainable quad meshes. The Bi-MDF problem is more general than our application in layout quantization, potentially enabling similar speedups for other optimization problems that fit into the scheme, such as quad mesh refinement.

Acceleration of iterative refinement for singular value decomposition

We propose fast numerical algorithms to improve the accuracy of singular vectors for a real matrix. Recently, Ogita and Aishima proposed an iterative refinement algorithm for singular value decomposition that is constructed with highly accurate matrix multiplications carried out six times per iteration. The algorithm runs for the problem that has no multiple and clustered singular values. In this study, we show that the same algorithm can be run with highly accurate matrix multiplications carried out five times. Also, we proposed four algorithms constructed with highly accurate matrix multiplications, two algorithms with the multiplications carried out four times, and the other two with the multiplications carried out five times. These algorithms adopt the idea of a mixed-precision iterative refinement method for linear systems. Numerical experiments demonstrate speed-up and quadratic convergence of the proposed algorithms. As a result, the fastest algorithm is 1.7 and 1.4 times faster than the Ogita-Aishima algorithm per iteration on a CPU and GPU, respectively.

Deep learning and hybrid approach for particle detection in defocusing particle tracking velocimetry

The present work aims at the improvement of particle detection in defocusing particle tracking velocimetry (DPTV) by means of a novel hybrid approach. Two deep learning approaches, namely faster R-CNN and RetinaNet are compared to the performance of two benchmark conventional image processing algorithms for DPTV. For the development of a hybrid approach with improved performance, the different detection approaches are evaluated on synthetic and images from an actual DPTV experiment. First, the performance under the influence of noise, overlaps, seeding density and optical aberrations is discussed and consequently advantages of neural networks over conventional image processing algorithms for image processing in DPTV are derived. Furthermore, current limitations of the application of neural networks for DPTV are pointed out and their origin is elaborated. It shows that neural networks have a better detection capability but suffer from low positional accuracy when locating particles. Finally, a novel Hybrid Approach is proposed, which uses a neural network for particle detection and passes the prediction onto a conventional refinement algorithm for better position accuracy. A third step is implemented to additionally eliminate false predictions by the network based on a subsequent rejection criterion. The novel approach improves the powerful detection performance of neural networks while maintaining the high position accuracy of conventional algorithms, combining the advantages of both approaches.

A simple equilibration procedure leading to polynomial-degree-robust a posteriori error estimators for the curl-curl problem

We introduce two a posteriori error estimators for Nédélec finite element discretizations of the curl-curl problem. These estimators pertain to a new Prager–Synge identity and an associated equilibration procedure. They are reliable and efficient, and the error estimates are polynomial-degree-robust. In addition, when the domain is convex, the reliability constants are fully computable. The proposed error estimators are also cheap and easy to implement, as they are computed by solving divergence-constrained minimization problems over edge patches. Numerical examples highlight our key findings, and show that both estimators are suited to drive adaptive refinement algorithms. Besides, these examples seem to indicate that guaranteed upper bounds can be achieved even in non-convex domains.

Enhanced full-inversion-based ultrasound elastography for evaluating tumor response to neoadjuvant chemotherapy in patients with locally advanced breast cancer

PurposeAn enhanced ultrasound elastography technique is proposed for early assessment of locally advanced breast cancer (LABC) response to neoadjuvant chemotherapy (NAC). MethodsThe proposed elastography technique inputs ultrasound radiofrequency data obtained through tissue quasi-static stimulation and adapts a strain refinement algorithm formulated based on fundamental principles of continuum mechanics, coupled with an iterative inverse finite element method to reconstruct the breast Young’s modulus (E) images. The technique was explored for therapy response assessment using data acquired from 25 LABC patients before and at weeks 1, 2, and 4 after the NAC initiation (100 scans). The E ratio of tumor to the surrounding tissue was calculated at different scans and compared to the baseline for each patient. Patients’ response to NAC was determined many months later using standard clinical and histopathological criteria. ResultsReconstructed E ratio changes obtained as early as one week after the NAC onset demonstrate very good separation between the two cohorts of responders and non-responders to NAC. Statistically significant differences were observed in the E ratio changes between the two patient cohorts at weeks 1 to 4 after treatment (p-value < 0.001; statistical power greater than 97%). A significant difference in axial strain ratio changes was observed only at week 4 (p-value = 0.01; statistical power = 76%). No significant difference was observed in tumor size changes at weeks 1, 2 or 4. ConclusionThe proposed elastography technique demonstrates a high potential for chemotherapy response monitoring in LABC patients and superior performance compared to strain imaging.

Compressed Training for Dual-Wideband Time-Varying Sub-Terahertz Massive MIMO

6G operators may use millimeter wave (mmWave) and sub-terahertz (sub-THz) bands to meet the ever-increasing demand for wireless access. Sub-THz communication comes with many existing challenges of mmWave communication and adds new challenges associated with the wider bandwidths, more antennas, and harsher propagations. Notably, the frequency- and spatial-wideband (dual-wideband) effects are significant at sub-THz. This paper presents a compressed training framework to estimate the time-varying sub-THz MIMO-OFDM channels. A set of frequency-dependent array response matrices are constructed, enabling channel recovery from multiple observations across subcarriers via multiple measurement vectors (MMV). Using the temporal correlation, MMV least squares (LS) is designed to estimate the channel based on the previous beam support, and MMV compressed sensing (CS) is applied to the residual signal. We refer to this as the MMV-LS-CS framework. Two-stage (TS) and MMV FISTA-based (M-FISTA) algorithms are proposed for the MMV-LS-CS framework. Leveraging the spreading loss structure, a channel refinement algorithm is proposed to estimate the path coefficients and time delays of the dominant paths. To reduce the computational complexity and enhance the beam resolution, a sequential search method using hierarchical code-books is developed. Numerical results demonstrate the improved channel estimation accuracy of MMV-LS-CS over state-of-the-art techniques.

Phase-field lattice-Boltzmann study on dendritic growth of hcp metals under gravity-driven natural convection

A phase-field lattice-Boltzmann method coupled with the parallel-adaptive mesh refinement algorithm is developed to simulate the equiaxed and columnar dendritic growth of hcp metal alloys. The effect of gravity-driven natural convection on the dendritic growth is discussed separately and also coupled with forced convection. The simulated results show the asymmetric dendritic growth of hcp metal alloys in two dimensions under gravity-driven natural convection, and reveal the evolution process of solute segregation and solute plumes. It can be concluded that the solute plume formation is determined by the competition between the solute blocking of dendrites and solute transport of the melt flow. Introducing an appropriate forced convection can eliminate the solute plume formation and dampen the local fluctuation of solute concentration in front of the dendrite tips. It is also found that the gravity-driven natural convection enriches the diversity of the 3D dendritic morphology of hcp metal alloys.

RIS-Aided Cell-Free Massive MIMO System: Joint Design of Transmit Beamforming and Phase Shifts

This article studies a reconfigurable intelligent surface (RIS)-aided cell-free massive multiple-input multiple-output system and formulate the max&#x2013;min fairness problem that maximizes the minimum achievable rate among all the users by jointly optimizing the transmit beamforming at access points and the phase shifts at RISs. To address such a challenging problem, we first study the special single-user scenario and propose an algorithm that can transform the optimization problem into a semidefinite program (SDP) or an integer linear program for the cases of continuous or discrete phase shifts, respectively. Then, in order to solve the optimization problem for the multiuser scenario with continuous phase shifts, we propose an alternating optimization algorithm, which can alternately transform the problem into a second-order-cone program and an SDP. Finally, for the multiuser scenario with discrete phase shifts, we design a zero-forcing-based successive refinement algorithm, which can find the suboptimal transmit beamforming and phase shifts by means of alternating optimization. Numerical results show that compared with the benchmark schemes of random phase shifts and without using the RIS, the proposed algorithms can significantly increase the minimum achievable rate. It is also demonstrated that, compared with the case of programming continuous phase shifts, using 2-bit discrete phase shifts can practically achieve the same performance.

Adaptive isogeometric methods with C1 (truncated) hierarchical splines on planar multi-patch domains

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well suited for the representation of complex geometries, and to maintain high continuity on general domains special constructions on multi-patch geometries must be used. In this paper, we focus on adaptive isogeometric methods with hierarchical splines, and extend the construction of [Formula: see text] isogeometric spline spaces on multi-patch planar domains to the hierarchical setting. We replace the hypothesis of local linear independence for the basis of each level by a weaker assumption, which still ensures the linear independence of hierarchical splines. We also develop a refinement algorithm that guarantees that the assumption is fulfilled by [Formula: see text] splines on certain suitably graded hierarchical multi-patch mesh configurations, and prove that it has linear complexity. The performance of the adaptive method is tested by solving the Poisson and the biharmonic problems.

Picking point recognition for ripe tomatoes using semantic segmentation and morphological processing

Identifying picking points is the key to the intelligent picking of ripe tomatoes and an important guarantee of efficient and lossless picking. A semantic segmentation model with the improved Swin Transformer V2 and a picking point recognition algorithm based on the connection of tomato fruit, calyx and stem are proposed for the problem of picking point recognition of ripe tomatoes in complex environments. Firstly, the tomato fruit, calyx and stem are accurately identified by an improved semantic segmentation model. On the one hand, the SeMask module is integrated into the traditional Swin Transformer V2 architecture for incorporating semantic information of the image into the encoder to improve the segmentation performance. On the other hand, UPerNet is used as the decoder of the model to improve the prediction results by integrating the feature selection module and feature alignment module into the decoder. Secondly, the calyx regions and stem regions of ripe tomatoes are extracted by a connected component labeling algorithm and morphological processing. Finally, the picking points located on the tomato lateral stems are extracted by the image refinement algorithm, deburring algorithm and position constraints of the tomato calyxes. The results of the ablation and comparison experiments show that the improved semantic segmentation model proposed in this paper has the best performance on Mean Intersection over Union (MIoU) and Mean Pixel Accuracy (MPA) with 82.5% and 89.79%, respectively. After accurately identifying tomato fruits, calyxes and stems, the picking point recognition algorithm proposed in this paper has 97.43% and 86.04% on precision and recall, respectively. This research provides an effective picking point recognition method for tomato harvesting robots.

A continuous field adaptive mesh refinement algorithm for isogeometric topology optimization using PHT-Splines

This study proposes a continuous density-field based isogeometric topology optimization (ITO) using Polynomial splines over Hierarchical T-meshes (PHT-Splines). Taking the benefit of isogeometric methods, the design density values for the mesh are defined using spline basis functions as a continuous density function (CDF) through the control points. The material density at the control points will then appear as a facade over the domain, which is further employed to generate a very smooth topology and also to propose a marking criterion for an adaptive mesh refinement (AMR) strategy during the optimization process. During this adaptive meshing, the isogeometric domain mesh is refined during each adaptive step, properly tracking the density variation over the elements and sharpening the boundaries of the optimized topologies. By utilizing the rationale of the Geometry Independent Field approximaTion (GIFT) framework, any complex multi-patch geometry constructed in an industry-standard CAD package using Non-Uniform Rational B-Splines (NURBS) may be imported and discretized using PHT-Splines, including higher dimensions. This helps to maintain the geometrical accuracy through an initial coarse mesh and computational accuracy of the optimization iterations through the local refinement feature of the PHT-Splines. An adaptive first-neighbourhood smoothening algorithm based on the Shepard function is also proposed to obtain manufacturable topologies and to circumvent post-processing stages. The proposed method was observed to provide remarkably smooth topologies with an initial coarse mesh, thereby obtaining a computationally efficient domain to be solved. Compared to existing element density based methods, the proposed method demonstrates a substantial minimization in Degree’s-of-Freedom (DoF) requirement to arrive at clear and realistic solutions. Also, when compared to globally refined solutions, a 50%–90% reduction in DoF is achieved using the adaptive refinement strategy.

Adaptive Nonintrusive Reconstruction of Solutions to High-Dimensional Parametric PDEs

Numerical methods for random parametric PDEs can greatly benefit from adaptive refinement schemes, in particular when functional approximations are computed as in stochastic Galerkin and stochastic collocations methods. This work is concerned with a nonintrusive generalization of the adaptive Galerkin finite element method with residual-based error estimation. It combines the nonintrusive character of a randomized least squares method with the a posteriori error analysis of stochastic Galerkin methods. The proposed approach uses the variational Monte Carlo method to obtain a quasi-optimal low-rank approximation of the Galerkin projection in a highly efficient hierarchical tensor format. We derive an adaptive refinement algorithm which is steered by a reliable error estimator. Opposite to stochastic Galerkin methods, the approach is easily applicable to a wide range of problems, enabling a fully automated adjustment of all discretization parameters. Benchmark examples with affine and (unbounded) lognormal coefficient fields illustrate the performance of the nonintrusive adaptive algorithm, showing the expected convergence rates of single-level strategies.

3D Transient CFD Simulation of an In-Vessel Loss-of-Coolant Accident in the EU DEMO WCLL Breeding Blanket

The in-vessel Loss-of-Coolant Accident (LOCA) is one of the design basis accidents in the design of the EU DEMO tokamak fusion reactor. System-level codes are typically employed to analyse the evolution of these transients. However, being based on a lumped approach, they are unable to quantify localised quantities of interest, such as local pressure peaks on the vacuum vessel walls, to which the failure criteria are linked. To calculate local quantities, the 3D nature of the phenomenon needs to be considered. In this work, a 3D transient model of the in-vessel LOCA from a water-cooled blanket is developed. The model is implemented in the commercial CFD software STAR-CCM+. It simulates the propagation of the water jet in the vessel from the beginning of the accident, thus accounting for the phase change of the water, i.e., from the pressurised liquid phase to the vapour phase inside the vessel, being the latter at a much lower pressure than in the blanket coolant pipes. Due to the large pressure ratio (&gt;1000), shocks are expected; therefore, an Adaptive Mesh Refinement (AMR) algorithm is employed. The physical models (in particular, the multiphase model) are benchmarked to a 2D reference problem before being applied to the 3D EU DEMO-relevant problem. The simulation results show that the pressure peaks in front of the vessel walls are not dangerous as they are below the design limit. The entire evolution of the water jet is followed up to the opening of the burst disks, in order to compare the average pressure evolution with that computed with system-level codes. A comparison with the in-vessel LOCA from a helium-cooled blanket is also carried out, showing that the accident evolution in the water case is less violent than in the helium case.

NSRGRN: a network structure refinement method for gene regulatory network inference.

The elucidation of gene regulatory networks (GRNs) is one of the central challenges of systems biology, which is crucial for understanding pathogenesis and curing diseases. Various computational methods have been developed for GRN inference, but identifying redundant regulation remains a fundamental problem. Although considering topological properties and edge importance measures simultaneously can identify and reduce redundant regulations, how to address their respective weaknesses whilst leveraging their strengths is a critical problem faced by researchers. Here, we propose a network structure refinement method for GRN (NSRGRN) that effectively combines the topological properties and edge importance measures during GRN inference. NSRGRN has two major parts. The first part constructs a preliminary ranking list of gene regulations to avoid starting the GRN inference from a directed complete graph. The second part develops a novel network structure refinement (NSR) algorithm to refine the network structure from local and global topology perspectives. Specifically, the Conditional Mutual Information with Directionality and network motifs are applied to optimise the local topology, and the lower and upper networks are used to balance the bilateral relationship between the local topology's optimisation and the global topology's maintenance. NSRGRN is compared with six state-of-the-art methods on three datasets (26 networks in total), and it shows the best all-round performance. Furthermore, when acting as a post-processing step, the NSR algorithm can improve the results of other methods in most datasets.

Local linear independence of bilinear (and higher degree) B-splines on hierarchical T-meshes

We generate hierarchical T-meshes by repeatedly inserting new line segments, in order to adapt both the size and the shape of the cells to the specific requirements of the underlying application. The associated spaces of bilinear spline functions are spanned by the locally refined (LR) B-splines of Dokken et al. (2013), which are products of univariate B-splines defined over local knot vectors. Our method guarantees that these functions are linearly independent for the obtained class of hierarchical T-meshes. Furthermore, they even possess the property of local linear independence, since exactly 4 functions take non-zero values on each cell of the mesh, and they form a partition of unity without the need to perform additional scaling or truncation.The correctness of our refinement algorithm is verified by enumerating the (newly introduced) local configurations, which represent the possible topologies of the mesh in the vicinity of a cell. It is then shown that the method works well in all the resulting situations. The fairly large number (385) of cases sheds some light on the challenges associated with linear independence in the context of LR B-spline refinement.Additionally we apply our method to meshes that possess the additional property local semi-regularity (first studied by Weller and Hagen, 1995), where only 49 topologically different situations may arise. However, we observe that the resulting class of hierarchical T-meshes is less flexible, which leads to a substantial amount of excess refinement in applications.Finally we note that the same construction can be applied to generate basis functions for Cs–smooth spline spaces of degree p=2s+1, again with the property of local linear independence.

Fast Direct Localization for Millimeter Wave MIMO Systems via Deep ADMM Unfolding

Massive arrays deployed in millimeter-wave systems enable high angular resolution performance, which in turn facilitates sub-meter localization services. Albeit suboptimal, up to now the most popular localization approach has been based on a so-called two-step procedure, where triangulation is applied upon aggregation of the angle-of-arrival (AoA) measurements from the collaborative base stations. This is mainly due to the prohibitive computational cost of the existing direct localization approaches in large-scale systems. To address this issue, we propose a deep unfolding based fast direct localization solver. First, the direct localization is formulated as a joint <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{2,1}$ </tex-math></inline-formula> norm sparse recovery problem, which is then solved by using alternating direction method of multipliers (ADMM). Next, we develop a deep ADMM unfolding network (DAUN) to learn the ADMM parameter settings from the training data and a position refinement algorithm is proposed for DAUN. Finally, simulation results showcase the superiority of the proposed DAUN over the baseline solvers in terms of better localization accuracy, faster convergence and significantly lower computational complexity.