Sparse Set Research Articles

Deposition path-dependent lightweight support design and its implication to self-support topology optimization

Abstract This paper presents a lightweight support design method for material extrusion-type three-dimensional printed panel structures that innovatively involves the deposition path curvature information for support point determination. Specifically, this support design method provides a robust segmentation algorithm to divide the filament deposition paths into segments based on the curvature sign alternating condition, and then searches for the fewest support points for the filaments counting on the experimentally calibrated relationship between the maximum allowable self-support distance and the local mean curvature. The proposed method features in generating thin-walled skeleton-ray styled support structures that are lightweight while providing firm support for the panels. More importantly, the support design method provides a new type of self-support criterion for structural topology optimization involving non-designable planar panels, i.e., only a sparse point set would be sufficient to support the panel. Consequently, more materials could be spent on enhancing the load-bearing capacity instead of being wasted on oversupporting. The achievable structural performances from self-support topology optimization with this new self-support criterion can improve significantly. Support design and printing tests were conducted on a few panel structures that validated the improved support effect compared with equal-volume supports generated by commercial software. Equidistant and gap-free deposited filaments, no filament collapse due to insufficient support, and no isolated voids reflect the improved support effect. The improved self-support topological design was also validated through a comparative numerical case study, and a compliance reduction of 7.76% was achieved.

A non-linear version of Bourgain’s projection theorem

We prove a version of Bourgain’s projection theorem for parametrized families of C^2 maps, which refines the original statement even in the linear case by requiring non-concentration only at a single natural scale. As one application, we show that if A is a Borel set of Hausdorff dimension close to 1 in \mathbb{R}^2 or close to 3/2 in \mathbb{R}^3 , then for y\in A outside of a very sparse set, the pinned distance set \{|x-y|:x\in A\} has Hausdorff dimension at least 1/2+c , where c is universal. Furthermore, the same holds if the distances are taken with respect to a C^2 norm of positive Gaussian curvature. As further applications, we obtain new bounds on the dimensions of spherical projections, and an improvement over the trivial estimate for incidences between \delta -balls and \delta -neighborhoods of curves in the plane, under fairly general assumptions. The proofs depend on a new multiscale decomposition of measures into “Frostman pieces” that may be of independent interest.

Transfer learning driven design optimization for inertial confinement fusion

Transfer learning is a promising approach to create predictive models that incorporate simulation and experimental data into a common framework. In this technique, a neural network is first trained on a large database of simulations and then partially retrained on sparse sets of experimental data to adjust predictions to be more consistent with reality. Previously, this technique has been used to create predictive models of Omega [Humbird et al., IEEE Trans. Plasma Sci. 48, 61–70 (2019)] and NIF [Humbird et al., Phys. Plasmas 28, 042709 (2021); Kustowski et al., Mach. Learn. 3, 015035 (2022)] inertial confinement fusion (ICF) experiments that are more accurate than simulations alone. In this work, we conduct a transfer learning driven hypothetical ICF campaign in which the goal is to maximize experimental neutron yield via Bayesian optimization. The transfer learning model achieves yields within 5% of the maximum achievable yield in a modest-sized design space in fewer than 20 experiments. Furthermore, we demonstrate that this method is more efficient at optimizing designs than traditional model calibration techniques commonly employed in ICF design. Such an approach to ICF design could enable robust optimization of experimental performance under uncertainty.

Scalable estimation and inference for censored quantile regression process

Censored quantile regression (CQR) has become a valuable tool to study the heterogeneous association between a possibly censored outcome and a set of covariates, yet computation and statistical inference for CQR have remained a challenge for large-scale data with many covariates. In this paper, we focus on a smoothed martingale-based sequential estimating equations approach, to which scalable gradient-based algorithms can be applied. Theoretically, we provide a unified analysis of the smoothed sequential estimator and its penalized counterpart in increasing dimensions. When the covariate dimension grows with the sample size at a sublinear rate, we establish the uniform convergence rate (over a range of quantile indexes) and provide a rigorous justification for the validity of a multiplier bootstrap procedure for inference. In high-dimensional sparse settings, our results considerably improve the existing work on CQR by relaxing an exponential term of sparsity. We also demonstrate the advantage of the smoothed CQR over existing methods with both simulated experiments and data applications.

Diameter‐free estimates for the quadratic Vinogradov mean value theorem

Let s ⩾ 3 $s \geqslant 3$ be a natural number, let ψ ( x ) $\psi (x)$ be a polynomial with real coefficients and degree d ⩾ 2 $d \geqslant 2$ , and let A $A$ be some large, non-empty, finite subset of real numbers. We use E s , 2 ( A ) $E_{s,2}(A)$ to denote the number of solutions to the system of equations ∑ i = 1 s ( ψ ( x i ) − ψ ( x i + s ) ) = ∑ i = 1 s ( x i − x i + s ) = 0 , \begin{equation*}\hskip2.5pc \sum _{i=1}^{s} (\psi (x_i) - \psi (x_{i+s}) )= \sum _{i=1}^{s} (x_i - x_{i+s} ) = 0, \end{equation*} where x i ∈ A $x_i \in A$ for each 1 ⩽ i ⩽ 2 s $1 \leqslant i \leqslant 2s$ . Our main result shows that E s , 2 ( A ) ≪ d , s | A | 2 s − 3 + η s , \begin{equation*}\hskip6pc E_{s,2}(A) \ll _{d,s} |A|^{2s -3 + \eta _{s}}, \end{equation*} where η 3 = 1 / 2 $\eta _3 = 1/2$ , and η s = ( 1 / 4 − 1 / 7246 ) · 2 − s + 4 $\eta _{s} = (1/4- 1/7246)\cdot 2^{-s + 4}$ when s ⩾ 4 $s \geqslant 4$ . The only other previously known result of this flavour is due to Bourgain and Demeter, who showed that when ψ ( x ) = x 2 $\psi (x) = x^2$ and s = 3 $s=3$ , we have E 3 , 2 ( A ) ≪ ε | A | 3 + 1 / 2 + ε , \begin{equation*}\hskip6pc E_{3,2}(A) \ll _{\epsilon } |A|^{3 + 1/2 + \epsilon }, \end{equation*} for each ε > 0 $\epsilon > 0$ . Thus, our main result improves upon the above estimate, while also generalising it for larger values of s $s$ and more wide-ranging choices of ψ ( x ) $\psi (x)$ . The novelty of our estimates is that they only depend on d $d$ , s $s$ and | A | $|A|$ , and are independent of the diameter of A $A$ . Thus, when A $A$ is a sparse set, our results are stronger than the corresponding bounds that are provided by methods such as decoupling and efficient congruencing. Consequently, our strategy differs from these two lines of approach, and we employ techniques from incidence geometry, arithmetic combinatorics and analytic number theory. Amongst other applications, our estimates lead to stronger discrete restriction estimates for sparse sequences.

Deep Patch-based Global Normal Orientation

The accuracy and consistency of point cloud normals are both vital for various successful applications. Great progresses have been achieved recently for accurate unoriented normal estimation by deep learning. However, inferring global consistent orientation directly with deep networks, just as many deep orienters have done, leads to unsatisfactory results since these work only focused on the local geometry of each point. In this paper, we propose a multi-task network which can aggregate global and local information for consistent normal orientation. Specifically, given a query point, a local branch and a global branch take a local patch and a coarse global sub-sampling relative to the query point as input, respectively. Then an unoriented normal and an oriented normal are inferred from the local and global network branches, respectively. Normal estimation from the local branch, as an auxiliary task, boosts the performance of normal orientation. Since the sparse global sample set is as lightweight as a local patch, our network is patch-based. Thus it can be trained on small datasets and be applied to large-scale point clouds straightforwardly. While previous deep orienters whose inputs are whole point clouds cannot achieve it. Extensive experiments on multiple synthetic datasets and raw scanning data demonstrate that our algorithm outperforms the state-of-the-art methods. Our source code, pre-trained model and datasets are available at https://github.com/joycewangsy/DPGO .

Bridging between Soft and Hard Thresholding by Scaling

In this article, we developed and analyzed a thresholding method in which soft thresholding estimators are independently expanded by empirical scaling values. The scaling values have a common hyper-parameter that is an order of expansion of an ideal scaling value that achieves hard thresholding. We simply call this estimator a scaled soft thresholding estimator. The scaled soft thresholding is a general method that includes the soft thresholding and non-negative garrote as special cases and gives an another derivation of adaptive LASSO. We then derived the degree of freedom of the scaled soft thresholding by means of the Stein's unbiased risk estimate and found that it is decomposed into the degree of freedom of soft thresholding and the reminder connecting to hard thresholding. In this meaning, the scaled soft thresholding gives a natural bridge between soft and hard thresholding methods. Since the degree of freedom represents the degree of over-fitting, this result implies that there are two sources of over-fitting in the scaled soft thresholding. The first source originated from soft thresholding is determined by the number of un-removed coefficients and is a natural measure of the degree of over-fitting. We analyzed the second source in a particular case of the scaled soft thresholding by referring a known result for hard thresholding. We then found that, in a sparse, large sample and non-parametric setting, the second source is largely determined by coefficient estimates whose true values are zeros and has an influence on over-fitting when threshold levels are around noise levels in those coefficient estimates. In a simple numerical example, these theoretical implications has well explained the behavior of the degree of freedom. Moreover, based on the results here and some known facts, we explained the behaviors of risks of soft, hard and scaled soft thresholding methods.

Fault Location in Power Networks Using a Sparse Set of Digital Fault Recorders

This paper presents a robust fault location method that can be used for radial or meshed power systems. It addresses several challenges encountered in previous work such as signal attenuation by power transformers, measurement errors, the impact of Inverter Based Power Sources (IBPSs), differentiating faults from other events. This is accomplished via a KMeans clustering of DFRs and using a weighted directed tree model enabling accurate fault location. The proposed algorithm is tested on both transmission and distribution systems under different fault scenarios.

A framework for numerical and experimental correlation of mode shapes with low spatial resolution: a catamaran’s case study

This work presents a framework for correlating numerical and experimental mode shapes with low spatial resolution using the Local Correspondence of Modes and Modal Coordinates (LCMC). As a case study, an operational modal analysis of a catamaran was performed. Thirteen global natural frequencies and their respective modes were identified in the range between 1 and 50 Hz, using only six sensors placed on its main deck. Thus, due to experimental modes’ spatial incompleteness, this required its full numerical model to be assembled and reduced using the System Equivalent Reduction Expansion Process to its main deck. Consequently, the reduced numerical modal matrix was used to fill in the gaps in the sparse set of the experimental modes, creating the mixed modal matrix. Then, this matrix was correlated and expanded using LCMC to the degrees of freedom (DOFs) that have not been measured. As a result, the spatial resolution of the catamaran’s experimental mode shapes was successfully increased from 6 to 174 DOFs. In general, the use of LCMC improved the Modal Assurance Criteria (MAC) of the correlated modes matrix compared to the MAC of the mixed modal matrix.

Decompositions of quasirandom hypergraphs into hypergraphs of bounded degree

We prove that any quasirandom uniform hypergraph H H can be approximately decomposed into any collection of bounded degree hypergraphs with almost as many edges. In fact, our results also apply to multipartite hypergraphs and even to the sparse setting when the density of H H quickly tends to 0 0 in terms of the number of vertices of H H . Our results answer and address questions of Kim, Kühn, Osthus and Tyomkyn; and Glock, Kühn and Osthus as well as Keevash. The provided approximate decompositions exhibit strong quasirandom properties which are very useful for forthcoming applications. Our results also imply approximate solutions to natural hypergraph versions of long-standing graph decomposition problems, as well as several decomposition results for (quasi)random simplicial complexes into various more elementary simplicial complexes such as triangulations of spheres and other manifolds.

Efficient Solution of Surface Erosion in Particle-Laden Hypersonic Flows

The standard approach for simulating hypersonic dust erosion problems using mixed Eulerian–Lagrangian two-phase solvers may be too computationally expensive for routine simulations, and particularly for uncertainty quantification (UQ) analyses. For efficient analyses, a new approach for predicting the surface dust erosion in hypersonic flows with a sparse set of particles is presented and demonstrated on a problem from literature involving the ExoMars Schiaparelli entry vehicle. This new approach, referred to here as the Trajectory Control Volume (TCV) method, is verified against traditional approaches based on Monte Carlo and is shown to require over three orders of magnitude fewer samples to obtain the same results. An example UQ and global nonlinear sensitivity analysis is performed with the new TCV approach. This analysis, which is not feasible with previous approaches, demonstrates the computational efficiency of the approach for UQ problems as well as provides some insight into the driving factors behind dust erosion. UQ and sensitivity results indicate that accurate characterization of material composition and size distribution for dust environments is key to reducing uncertainty in predicted surface recession due to dust impingement.

Improving estimates of the ionosphere during geomagnetic storm conditions through assimilation of thermospheric mass density

Dynamical changes in the ionosphere and thermosphere during geomagnetic storm times can have a significant impact on our communication and navigation applications, as well as satellite orbit determination and prediction activities. Because of the complex electrodynamics coupling processes during storms, which cannot be fully described with the sparse set of thermosphere–ionosphere (TI) observations, it is crucial to accurately model the state of the TI system. The approximation closest to the true state can be obtained by assimilating relevant measurements into physics-based models. Thermospheric mass density (TMD) derived from satellite measurements is ideal to improve the thermosphere through data assimilation. Given the coupled nature of the TI system, the changes in the thermosphere will also influence the ionosphere state. This study presents a quantification of the changes and improvement of the model state produced by assimilating TMD not only for the thermosphere density but also for the ionosphere electron density under storm conditions. TMD estimates derived from a single Swarm satellite and the Coupled Thermosphere Ionosphere Plasmasphere electrodynamics (CTIPe) physics-based model are used for the data assimilation. The results are presented for a case study during the St. Patricks Day storm 2015. It is shown that the TMD data assimilation generates an improvement of the model’s thermosphere density of up to 40% (measured along the orbit of the non-assimilated Swarm satellites). The model’s electron density during the course of the storm has been improved by approximately 8 and 22% relative to Swarm-A and GRACE, respectively. The comparison of the model’s global electron density against a high-quality 3D electron density model, generated through assimilation of total electron content, shows that TMD assimilation modifies the model’s ionosphere state positively and negatively during storm time. The major improvement areas are the mid-low latitudes during the storm’s recovery phase.Graphical

Comparison of trend models for geotechnical spatial variability: Sparse Bayesian Learning vs. Gaussian Process Regression

This paper compares two probabilistic models for the trend function of geotechnical spatial variability: sparse Bayesian learning (SBL) vs. Gaussian process regression (GPR). For the SBL model (MSBL), the spatial trend is represented as the weighted sum of a sparse set of basis functions (BFs). For the GPR model (MGPR), the spatial trend is represented as a stationary normal random field. The comparison between these two models is based on their Bayesian evidence. The comparison results show that MSBL usually outperforms MGPR with a larger Bayesian evidence when the underlying trend function can be represented by sparse BFs. This usually happens for one-dimensional (1D) simulated examples and 1D real cone penetration test (CPT) examples. However, MGPR usually outperforms MSBL when the spatial trend can not be well represented by sparse BFs. This usually happens for 2D and 3D real CPT examples. Another important contribution of the current paper is the derivations of Kronecker-product formulae for the GPR method. These formulae resolve the issue of the high computational cost for 3D GPR analyses.

The Determination of Reward Function in AGV Motion Control Based on DQN

Motion control is a very important part in the field of AGV(Automated Guided Vehicle). A good motion control method can make the movement of AGV more stable. Network models of reinforcement learning is one of the methods to solve the problem of AGV in motion control. This paper introduces the Markov Decision Process and the role of reward function. Besides, it studies and analyzes several classic reinforcement learning cases. DQN(Deep Q-Learning Network) which belongs to deep reinforcement learning network model is adopted. We set up several sets of comparative experiments with different reward functions by using sparse reward setting method, formalized reward setting method and reward coefficient variation reward setting method. Also we adjust the time of training. Through comparison, a reward function suitable for solving the problem of AGV motion control is obtained. In the field of AGV motion control, reinforcement learning model can converge faster and make more correct decisions. The reward function is verified in the simulation environment built by ROS(Robot Operating System).

A Probabilistic Autoencoder for Type Ia Supernova Spectral Time Series

We construct a physically parameterized probabilistic autoencoder (PAE) to learn the intrinsic diversity of Type Ia supernovae (SNe Ia) from a sparse set of spectral time series. The PAE is a two-stage generative model, composed of an autoencoder that is interpreted probabilistically after training using a normalizing flow. We demonstrate that the PAE learns a low-dimensional latent space that captures the nonlinear range of features that exists within the population and can accurately model the spectral evolution of SNe Ia across the full range of wavelength and observation times directly from the data. By introducing a correlation penalty term and multistage training setup alongside our physically parameterized network, we show that intrinsic and extrinsic modes of variability can be separated during training, removing the need for the additional models to perform magnitude standardization. We then use our PAE in a number of downstream tasks on SNe Ia for increasingly precise cosmological analyses, including the automatic detection of SN outliers, the generation of samples consistent with the data distribution, and solving the inverse problem in the presence of noisy and incomplete data to constrain cosmological distance measurements. We find that the optimal number of intrinsic model parameters appears to be three, in line with previous studies, and show that we can standardize our test sample of SNe Ia with an rms of 0.091 ± 0.010 mag, which corresponds to 0.074 ± 0.010 mag if peculiar velocity contributions are removed. Trained models and codes are released at https://github.com/georgestein/suPAErnova.

Sparse Sonomyography-Based Estimation of Isometric Force: A Comparison of Methods and Features

Noninvasive methods for estimation of joint and muscle forces have widespread clinical and research applications. Surface electromyography (sEMG) provides a measure of the neural activation of muscles which can be used to estimate the force produced by the muscle. However, sEMG based measures of force suffer from poor signal-to-noise ratio and limited spatiotemporal specificity. In this paper, we propose a sonomyography or ultrasound imaging-based offline approach for estimating continuous isometric force from a sparse set of ultrasound scanlines. Our approach isolates anatomically relevant features from A-mode scanlines isolated from B-mode images, thus greatly reducing the dimensionality of the feature space and the computational complexity involved in traditional ultrasound-based methods. We evaluate the performance of four regression methodologies for force prediction using the reduced sonomyographic feature set. We also evaluate the feasibility of a practical wearable sonomyography-based system by simulating the effect of transducer placement and varying the number of transducers used in force prediction. Our results demonstrate that Gaussian process regression models outperform other regression methods in predicting continuous force levels from just four equispaced transducers in offline settings. We believe that these findings will aid in the design of wearable, robust and computationally efficient sonomyography-based force prediction systems.

Denoising multiplexed microscopy images in n-dimensional spectral space.

Hyperspectral fluorescence microscopy images of biological specimens frequently contain multiple observations of a sparse set of spectral features spread in space with varying intensity. Here, we introduce a spectral vector denoising algorithm that filters out noise without sacrificing spatial information by leveraging redundant observations of spectral signatures. The algorithm applies an n-dimensional Chebyshev or Fourier transform to cluster pixels based on spectral similarity independent of pixel intensity or location, and a denoising convolution filter is then applied in this spectral space. The denoised image may then undergo spectral decomposition analysis with enhanced accuracy. Tests utilizing both simulated and empirical microscopy data indicate that denoising in 3 to 5-dimensional (3D to 5D) spectral spaces decreases unmixing error by up to 70% without degrading spatial resolution.

Prognostic Evaluation Based on Dual-Time 18F-FDG PET/CT Radiomics Features in Patients with Locally Advanced Pancreatic Cancer Treated by Stereotactic Body Radiation Therapy.

Background 18F-FDG PET/CT is widely used in the prognosis evaluation of tumor patients. The radiomics features can provide additional information for clinical prognostic assessment. Purpose Purpose is to explore the prognostic value of radiomics features from dual-time 18F-FDG PET/CT images for locally advanced pancreatic cancer (LAPC) patients treated with stereotactic body radiation therapy (SBRT). Materials and Methods This retrospective study included 70 LAPC patients who received early and delayed 18F-FDG PET/CT scans before SBRT treatment. A total of 1188 quantitative imaging features were extracted from dual-time PET/CT images. To avoid overfitting, the univariate analysis and elastic net were used to obtain a sparse set of image features that were applied to develop a radiomics score (Rad-score). Then, the Harrell consistency index (C-index) was used to evaluate the prognosis model. Results The Rad-score from dual-time images contains six features, including intensity histogram, morphological, and texture features. In the validation cohort, the univariate analysis showed that the Rad-score was the independent prognostic factor (p < 0.001, hazard ratio [HR]: 3.2). And in the multivariate analysis, the Rad-score was the only prognostic factor (p < 0.01, HR: 4.1) that was significantly associated with the overall survival (OS) of patients. In addition, according to cross-validation, the C-index of the prognosis model based on the Rad-score from dual-time images is better than the early and delayed images (0.720 vs. 0.683 vs. 0.583). Conclusion The Rad-score based on dual-time 18F-FDG PET/CT images is a promising noninvasive method with better prognostic value.

Correlation in Dose-Response to Rapid- and Long-Acting Insulin for People with Type 1 Diabetes.

In diabetes, it can become necessary to switch between pump- and pen-based insulin treatment. This switch involves a translation between rapid- and long-acting insulin analogues. In standard-of-care translation algorithms, a unit-to-unit conversion is applied. However, this simplification may not fit all individuals. In this paper, we investigate the correlation between dose-response to rapid- and long-acting insulin in the same individual, and compare the correlation across individuals. As a measure of dose-response, we estimate the insulin sensitivity in clinical data from 25 subjects with type 1 diabetes. For parameter estimation, we use maximum likelihood with a continuous-discrete extended Kalman filter and Bergman's minimal model. The results show a weak correlation between insulin sensitivity to rapid- and long-acting insulin across individuals. On this sparse data set, the analysis suggests that the standardized unit-to-unit translation between insulin analogues may not benefit all subjects.

Optimal LiDAR Data Resolution Analysis for Object Classification.

When classifying objects in 3D LiDAR data, it is important to use efficient collection methods and processing algorithms. This paper considers the resolution needed to classify 3D objects accurately and discusses how this resolution is accomplished for the RedTail RTL-450 LiDAR System. We employ VoxNet, a convolutional neural network, to classify the 3D data and test the accuracy using different data resolution levels. The results show that for our data set, if the neural network is trained using higher resolution data, then the accuracy of the classification is above 97%, even for the very sparse testing set (10% of original test data set point density). When the training is done on lower resolution data sets, the classification accuracy remains good but drops off at around 3% of the original test data set point density. These results have implications for determining flight altitude and speed for an unmanned aerial vehicle (UAV) to achieve high accuracy classification. The findings point to the value of high-resolution point clouds for both the training of the convolutional neural network and in data collected from a LiDAR sensor.