Refinement Strategy Research Articles

Inaccuracy Matters: Accounting for Solution Accuracy in Event-Triggered Nonlinear Model Predictive Control

We consider the effect of using approximate system predictions in event-triggered control schemes. These approximations often result from using numerical transcription methods for solving continuous-time optimal control problems. Mesh refinement can guarantee upper bounds on the error in the differential equations that model the system dynamics. We employ the accuracy guarantees of a mesh refinement scheme to show that the proposed event-triggering scheme, which compares the measured system with approximate state predictions, can be used with a guaranteed strictly positive inter-update time. Furthermore, if knowledge of the employed transcription scheme or the approximation errors are available, then better online estimates of inter-update times can be obtained. We also detail a method of tightening constraints on the approximate system trajectory to guarantee constraint satisfaction of the continuous-time system. This is the first work to incorporate prediction accuracy in triggering metrics to guarantee reliable lower bounds for inter-update times and perform solution-dependent constraint tightening.

Nonlinear Program Construction and Verification Method Based on Partition Recursion and Morgan's Refinement Rules

The traditional program refinement strategy cannot be refined to an executable program, and there are issues such as low verification reliability and automation. To solve the above problems, this paper proposes a nonlinear program construction and verification method based on partition recursion and Morgan's refinement rules. First, we use recursive definition technique to characterize the initial specification. The specification is then transformed into GCL(Guarded Command Language) programs using loop invariant derivation and Morgan's refinement rules. Furthermore, VCG (Verification Condition Generator) is used in the GCL program to generate the verification condition automatically. The Isabelle theorem prover then validates the GCL program's correctness. Finally, the GCL code generates a C++ executable program automatically via the conversion system. The effectiveness of this method is demonstrated using binary tree preorder traversal program construction and verification as an example. This method addresses the problem that the construction process's loop invariant is difficult to obtain and the refinement process is insufficiently detailed. At the same time, the method improves verification process automation and reduces the manual verification workload.

Exploring the transcriptomic changes underlying recombinant vaccine efficacy against Teladorsagia circumcincta in 3-month-old lambs

Teladorsagia circumcincta is an abomasal parasitic nematode that can cause serious issues in small ruminant production, which are aggravated by drug resistance. Vaccines have been suggested as a feasible, long-lasting alternative for control since adaptation to the host’s immune mechanisms by helminths develops at a much slower pace than anthelmintic resistance. Recently, a T. circumcincta recombinant subunit vaccine yielded over a 60% reduction in egg excretion and worm burden and induced strong humoral and cellular anti-helminth responses in vaccinated 3-month-old Canaria Hair Breed (CHB) lambs, but Canaria Sheep (CS) of a similar age were not protected by the vaccine. Here, we compared the transcriptomic profiles in the abomasal lymph nodes of such 3-month-old CHB and CS vaccinates 40 days after infection with T. circumcincta to understand differences in responsiveness at the molecular level. In the CS, differentially expressed genes (DEG) identified were related to general immunity processes such as antigen presentation or antimicrobial proteins and down-regulation of inflammation and immune response through regulatory T cell-associated genes. However, upregulated genes in CHB vaccinates were associated with type-2 oriented immune responses, i.e., immunoglobulin production, activation of eosinophils, as well as tissue structure and wound repair-related genes and protein metabolism pathways such as DNA and RNA processing. These results highlight potentially more optimal timing and orientation of immune responses in CHB sheep compared to CS associated with vaccine-induced protection. The data obtained in this study thus deepens our understanding of variations in responsiveness to vaccination in young lamb and provides insights for vaccine refinement strategies.

Learning to Propose and Refine for Accurate and Robust Tracking via an Alignment Convolution

Precise and robust feature extraction plays a key role in high-performance tracking to analyse the videos from drones, surveillance and automatic driving, etc. However, most existing Siamese network-based trackers mainly focus on constructing complicated network models and refinement strategies, while using comparatively simple and heuristic conventional or deformable convolutions to extract features from the sampling positions that may be far away from a target region. Consequently, the coarsely extracted features may introduce background noise and degrade the tracking performance. To address this issue, we present a propose-and-refine tracker (PRTracker) that combines anchor-free style proposals at the coarse level, and alignment convolution-driven refinement at the fine level. Specifically, at the coarse level, we design an anchor-free model to effectively generate proposals that provide more reliable interested regions for further verifying. At the fine level, an alignment convolution-based refinement strategy is adopted to improve the convolutional sampling positions of the proposals, thus making the classification and regression of them more accurate. Through using alignment convolution, the convolution sampling positions of the proposals can be efficiently and effectively re-localized, thus improving the accuracy of the extracted features. Finally, a simple yet robust target mask is designed to make full use of the initial state of a target to further improve the tracking performance. The proposed PRTracker achieves a competitive performance against six tracking benchmarks (i.e., UAV123, VOT2018, VOT2019, OTB100, NfS and LaSOT) at 75 FPS.

Improved Caps for Improved Subdivision Surfaces

The quest for a finite number of bicubic (bi-3) polynomial pieces to smoothly fill multi-sided holes after a fixed number of surface subdivision steps has motivated a number of constructions of finite surface caps. Recent bi-3 and bi-4 subdivision algorithms have improved surface shape compared to classic Catmull–Clark and curvature-bounded ‘tuned’ subdivision. Since the older subdivision algorithms exhibit artifacts that obscure the shortcomings of corresponding caps, it is worth re-visiting their multi-sided fill surfaces. The improved caps address the challenge so that either bi-3 or bi-4 data can be accommodated, as needed. The derivation illustrates the subtle fundamental trade off between formal algebraic mathematical smoothness constraints and good shape in the large.

Self-supervised Blind2Unblind deep learning scheme for OCT speckle reductions.

As a low-coherence interferometry-based imaging modality, optical coherence tomography (OCT) inevitably suffers from the influence of speckles originating from multiply scattered photons. Speckles hide tissue microstructures and degrade the accuracy of disease diagnoses, which thus hinder OCT clinical applications. Various methods have been proposed to address such an issue, yet they suffer either from the heavy computational load, or the lack of high-quality clean images prior, or both. In this paper, a novel self-supervised deep learning scheme, namely, Blind2Unblind network with refinement strategy (B2Unet), is proposed for OCT speckle reduction with a single noisy image only. Specifically, the overall B2Unet network architecture is presented first, and then, a global-aware mask mapper together with a loss function are devised to improve image perception and optimize sampled mask mapper blind spots, respectively. To make the blind spots visible to B2Unet, a new re-visible loss is also designed, and its convergence is discussed with the speckle properties being considered. Extensive experiments with different OCT image datasets are finally conducted to compare B2Unet with those state-of-the-art existing methods. Both qualitative and quantitative results convincingly demonstrate that B2Unet outperforms the state-of-the-art model-based and fully supervised deep-learning methods, and it is robust and capable of effectively suppressing speckles while preserving the important tissue micro-structures in OCT images in different cases.

An extended tuned subdivision scheme with optimal convergence for isogeometric analysis

This paper presents an extended tuned subdivision scheme for quadrilateral meshes that recovers optimal convergence rates in isogeometric analysis while preserving high-quality limit surfaces. Convergence rates can be improved for subdivision surfaces through proper mask tuning with a lower subdominant eigenvalue λ. However, such a tuning might affect the quality of limit surfaces if the tuning parameters are restricted to one-ring refined control vertices only. In this work, we further relax Catmull–Clark subdivision rules for 2-ring refined vertices with additional degrees of freedom in tuning masks with limit surfaces towards curvature continuity at extraordinary positions. Curvatures are bounded near extraordinary positions of valences N≤7, and a relaxation approach is proposed to suppress the local curvature variation for N≥8. We compare the proposed tuned subdivision scheme with several state-of-the-art schemes in terms of both surface qualities and applications in isogeometric analysis. Laplace–Beltrami equations with prescribed test solutions are adopted for verification of analysis results, and the proposed scheme recovers optimal convergence rates in the L2-norm with considerably lower absolute solution error than other schemes. As to surface quality, the proposed scheme has significant improvements compared with other schemes with optimal convergence rates for isogeometric analysis. The proposed scheme produces tighter curvature bounds with comparable reflection lines to the prevalent Catmull–Clark subdivision.

ELCT-YOLO: An Efficient One-Stage Model for Automatic Lung Tumor Detection Based on CT Images

Research on lung cancer automatic detection using deep learning algorithms has achieved good results but, due to the complexity of tumor edge features and possible changes in tumor positions, it is still a great challenge to diagnose patients with lung tumors based on computed tomography (CT) images. In order to solve the problem of scales and meet the requirements of real-time detection, an efficient one-stage model for automatic lung tumor detection in CT Images, called ELCT-YOLO, is presented in this paper. Instead of deepening the backbone or relying on a complex feature fusion network, ELCT-YOLO uses a specially designed neck structure, which is suitable to enhance the multi-scale representation ability of the entire feature layer. At the same time, in order to solve the problem of lacking a receptive field after decoupling, the proposed model uses a novel Cascaded Refinement Scheme (CRS), composed of two different types of receptive field enhancement modules (RFEMs), which enables expanding the effective receptive field and aggregate multi-scale context information, thus improving the tumor detection performance of the model. The experimental results show that the proposed ELCT-YOLO model has strong ability in expressing multi-scale information and good robustness in detecting lung tumors of various sizes.

Multifidelity Algorithm for the Sensitivity Analysis of Multidisciplinary Problems

AbstractThe present article proposes an algorithm for the sensitivity analysis of a multidisciplinary problem, in which the derivative-based global sensitivity indices are computed with multifidelity Gaussian process models. Two levels of fidelity are used to estimate the indices, where the low-fidelity samples are obtained by stopping the multidisciplinary analysis solver before convergence. A dedicated refinement strategy for the multifidelity Gaussian process is proposed to ensure the accuracy of the sensitivity index estimation. This algorithm is tested on three multidisciplinary problems of increasing complexity (one analytical and two representative engineering design problems), and proved to be both reliable in detecting the noninfluential variables and computationally efficient, compared to classical Monte Carlo integration and to three other candidate algorithms.

Heatmap-Guided Selective Feature Attention for Robust Cascaded Face Alignment

Face alignment methods have been actively studied using coordinate and heatmap regression tasks. Although these regression tasks have the same objective for facial landmark detection, each task requires different valid feature maps. Therefore, it is not easy to simultaneously train two kinds of tasks with a multi-task learning network structure. Some studies have proposed multi-task learning networks with two kinds of tasks, but they do not suggest an efficient network that can train them simultaneously because of the shared noisy feature maps. In this paper, we propose a heatmap-guided selective feature attention for robust cascaded face alignment based on multi-task learning, which improves the performance of face alignment by efficiently training coordinate regression and heatmap regression. The proposed network improves the performance of face alignment by selecting valid feature maps for heatmap and coordinate regression and using the background propagation connection for tasks. This study also uses a refinement strategy that detects global landmarks through a heatmap regression task and then localizes landmarks through cascaded coordinate regression tasks. To evaluate the proposed network, we tested it on the 300W, AFLW, COFW, and WFLW datasets and obtained results that outperformed other state-of-the-art networks.

Adaptive density-based robust topology optimization under uncertain loads using parallel computing

This work presents an efficient parallel implementation of density-based robust topology optimization (RTO) using adaptive mesh refinement (AMR) schemes permitting us to address the problem with modest computational resources. We use sparse grid stochastic collocation methods (SCMs) for transforming the RTO problem into a weighted multiple-loading deterministic problem at the collocation points. The calculation of these deterministic problems and the functional sensitivity is computationally expensive. We combine distributed-memory parallel computing and AMR techniques to address the problem efficiently. The former allows us to exploit the computational resources available, whereas the latter permits us to increase performance significantly. We propose the parallel incremental calculation of the deterministic problems and the contribution to the functional sensitivity maintaining a similar memory allocation to the one used in the deterministic counterpart. The cumulative computing uses buffers to adapt the evaluation at the collocation points to the parallel computing resources permitting the exploitation of the embarrassing parallelism of SCMs. We evaluate the deterministic problems in a coarse mesh generated for each topology optimization iteration to increase the performance. We perform the regularization and design variable update in a fine mesh to obtain an equivalent design to the one generated in such a mesh. We evaluate the proposal in two- and three-dimensional problems to test its feasibility and scalability. We also check the performance improvement using computational buffers in parallel computing nodes. Finally, we compare the proposal to the same approach using different preconditioners without AMR schemes showing significant performance improvements.

Adaptive Mesh Generation Technique for Efficient Electromagnetic Computation in RFIC Designs

A novel adaptive mesh generation technique for efficient electromagnetic simulation of radio-frequency integrated circuits (RFICs) is herein presented. By exploring the geometrical and physical characteristics of RFICs, some adaptive mesh treatments, such as mesh projection, edge refinement, via polymerization, etc., are utilized to improve the accuracy and efficiency of electromagnetic computations. For strong coupling structures, such as two conductors in close proximity for a relatively large area, a projection-based mesh scheme is introduced to improve the accuracy of numerical integration. Moreover, the current most likely concentrates near the edges of conductors due to the edge effect. To better model the edge effect, an edge refinement scheme is applied. For via arrays that appear common in RFICs, an automatic via aggregation approach is adopted to improve computational efficiency yet still keep good computational accuracy. Finally, some numerical examples are given to validate the computational accuracy and efficiency of the novel adaptive mesh generation technique.

Point-normal subdivision curves and surfaces

This paper proposes to generalize linear subdivision schemes to nonlinear subdivision schemes for curve and surface modeling by refining vertex positions together with refinement of unit control normals at the vertices. For each round of subdivision, new control normals are obtained by projections of linearly subdivided normals onto unit circle or sphere while new vertex positions are obtained by updating linearly subdivided vertices along the directions of the newly subdivided normals. Particularly, the new position of each linearly subdivided vertex is computed by weighted average of end points of circular or helical arcs that interpolate the positions and normals at the old vertices at one ends and the newly subdivided normal at the other ends. The main features of the proposed subdivision schemes are three folds: (1) The point-normal (PN) subdivision schemes can reproduce circles, circular cylinders and spheres using control points and control normals; (2) PN subdivision schemes generalized from convergent linear subdivision schemes converge and can have the same smoothness orders as the linear schemes; (3) PN C2 subdivision schemes generalizing linear subdivision schemes that generate C2 subdivision surfaces with flat extraordinary points can generate visually C2 subdivision surfaces with non-flat extraordinary points. Experimental examples have been given to show the effectiveness of the proposed techniques for curve and surface modeling.

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.

Evolving Guide Subdivision

AbstractTo overcome the well‐known shape deficiencies of bi‐cubic subdivision surfaces, Evolving Guide subdivision (EG subdivision) generalizes C2 bi‐quartic (bi‐4) splines that approximate a sequence of piecewise polynomial surface pieces near extraordinary points. Unlike guided subdivision, which achieves good shape by following a guide surface in a two‐stage, geometry‐dependent process, EG subdivision is defined by five new explicit subdivision rules. While formally only C1 at extraordinary points, EG subdivision applied to an obstacle course of inputs generates surfaces without the oscillations and pinched highlight lines typical for Catmull‐Clark subdivision. EG subdivision surfaces join C2 with bi‐3 surface pieces obtained by interpreting regular sub‐nets as bi‐cubic tensor‐product splines and C2 with adjacent EG surfaces. The EG subdivision control net surrounding an extraordinary node can have the same structure as Catmull‐Clark subdivision: two rings of 4‐sided facets around each extraordinary nodes so that extraordinary nodes are separated by at least one regular node.

Verification of Fuzzy Decision Trees

In recent years, there have been major strides in the safety verification of machine learning models such as neural networks and tree ensembles. However, fuzzy decision trees (FDT), also called soft or differentiable decision trees, are yet unstudied in the context of verification. They present unique verification challenges resulting from multiplications of input values; in the simplest case with a piecewise-linear splitting function, an FDT is piecewise-polynomial with degree up to the depth of the tree. We propose an abstraction-refinement algorithm for verification of properties of FDTs. We show that the problem is NP-Complete, like many other machine learning verification problems, and that our algorithm is complete in a finite precision setting. We benchmark on a selection of public data sets against an off-the-shelf SMT solver and a baseline variation of our algorithm that uses a refinement strategy from similar methods for neural network verification, finding the proposed method to be the fastest. Code for our algorithm along with our experiments and demos are available on GitHub at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/autonlab/fdt_verification</uri> .

An anti Si/Zr-poisoning strategy of Al grain refinement by the evolving effect of doped complex

The issue of how to avoid the poisoning phenomenon of α-Al grain refinement caused by special elements (such as Si and Zr) has always been the focus of research attention. In this work, the anti Si/Zr-poisoning of α-Al grain refinement was achieved by the evolving effect of a doped TCB complex, which is constituted by B-doped TiC (B-TiC) and C-doped TiB2 (C-TiB2). The results indicate that B-TiC in the TCB complex can release Ti atoms in Al melts, and the unique C-TiB2 particles have a reproduction subsequently. The released Ti atoms by B-TiC during the evolution process act as the solute, limiting the grain growth and assisting in the refinement of the α-Al grains. Furthermore, the density functional theory calculations show that the C atoms in the interior of C-TiB2 tend to enhance the adhesion energy of the C-TiB2/Al interface, improving the nucleation potency for α-Al on C-TiB2 in the Al-Si alloys or Zr-containing Al alloys. The average grain sizes of Al-7Si-0.4Mg and Al-5Cu-0.15Zr with inoculated TCB complex can be refined to 84 ± 7 μm and 63 ± 4 μm from 784 ± 58 μm and 402 ± 32 μm, respectively. Thus, the anti Si/Zr-poisoning of Al grain refinement is synergistically realized based on the dynamically evolving TCB complex. These findings provide a new direction for the grain refinement of the Al-Si alloys or Zr-containing Al alloys, as well as guidance on further research and development of grain refiners.

High-performance GPU computing of phase-field lattice Boltzmann simulations for dendrite growth with natural convection

The effect of natural convection on dendrite morphology is investigated through three-dimensional large-scale phase-field lattice Boltzmann simulations using a block-structured adaptive mesh refinement scheme with the mother-leaf method in a parallel-GPU environment. The simulations confirmed that downward buoyancy enhances the growth of the primary and secondary arms, and upward buoyancy delays the growth of those arms. In addition, the effect of natural convection on the solidification morphologies gradually decreased as the primary arm tip reached the top of the computational domain and finally stopped. Furthermore, in the longer simulation under purely isothermal diffusive conditions, detachment of the secondary arms owing to curvature-driven fragmentation was observed. A large-scale non-isothermal dendrite growth simulation was also conducted, wherein it was observed that the tip growth rate of the primary arm was delayed, and the secondary arm spacing was larger than that in the isothermal condition.

Clinically Relevant Myocardium Segmentation in Cardiac Magnetic Resonance Images.

Deep learning approaches have shown great success in myocardium region segmentation in Cardiac MR (CMR) images. However, most of these often ignore irregularities such as protrusions, breaks in contour, etc. As a result, the common practice by clinicians is to manually correct the obtained outputs for the evaluation of myocardium condition. This paper aims to make the deep learning systems capable of handling the aforementioned irregularities and satisfy desired clinical constraints, necessary for various downstream clinical analysis. We propose a refinement model which imposes structural constraints on the outputs of the existing deep learning-based myocardium segmentation methods. The complete system is a pipeline of deep neural networks where an initial network performs myocardium segmentation as accurate as possible and the refinement network removes defects from the initial output to make it suitable for clinical decision support systems. We experiment with datasets collected from four different sources and observe consistent final segmentation outputs with improvement up to 8% in Dice Coefficient and up to 18 pixels in Hausdorff Distance due to the proposed refinement model. The proposed refinement strategy leads to qualitative and quantitative improvements in the performances of all the considered segmentation networks. Our work is an important step towards the development of a fully automatic myocardium segmentation system. It can also be generalized for other tasks where the object of interest has regular structure and the defects can be modelled statistically.

Improved adaptive tessellation rendering algorithm.

The human body model in the virtual surgery system is generally nested by multiple complex models and each model has quite complex tangent and curvature change. In actual rendering, if all details of the human body model are rendered with high performance, it may cause the stutter due to insufficient hardware performance. If the human body model is roughly rendered, the details of the model cannot be well represented. In order to realize the real-time rendering of complex models in virtual surgical systems, this paper proposes an improved adaptive tessellation rendering algorithm, which includes offline and online parts. The offline part mainly completes data reading and data structure constructing. The online part performs the surface subdivision operation in-real time for each frame, which includes the subdivision operation of the control points and surface evaluation. The offline part simplifies the subdivision step by recording the surface subdivision hierarchy using a quadtree and using control templates to record control point information. The online part reduces computation time by using a matrix to record topological relationships between vertices and vertex weights. The online part can compress the time complexity of traversing the quadtree of different subdivision levels to O⁢(n⁢log⁡n) by establishing an association with the quadtree of each subdivision level and using the greedy algorithm to complete the traversal of the quadtree. Finally, the adaptive tessellation rendering algorithm proposed in this paper is compared with other commonly used tessellation algorithms. The algorithm has advantages in computational efficiency and graphical display.