Sample Problems Research Articles

Algorithmic reconstruction of the fiber of persistent homology on cell complexes

Let K be a finite simplicial, cubical, delta or CW complex. The persistence map PH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{PH}$$\\end{document} takes a filter f:K→R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f:K\\rightarrow \\mathbb {R}$$\\end{document} as input and returns the barcodes of the sublevel set persistent homology of f in each dimension. We address the inverse problem: given target barcodes D, computing the fiber PH-1(D)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{PH}^{-1}(D)$$\\end{document}. For this, we use the fact that PH-1(D)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{PH}^{-1}(D)$$\\end{document} decomposes as a polyhedral complex when K is a simplicial complex, and we generalise this result to arbitrary based chain complexes. We then design and implement a depth-first search that recovers the polytopes forming the fiber PH-1(D)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{PH}^{-1}(D)$$\\end{document}. As an application, we solve a corpus of 120 sample problems, providing a first insight into the statistical structure of these fibers, for general CW complexes.

Relevant sampling in a reproducing kernel subspace of Orlicz space

In this paper, we aim to provide a general paradigm for dealing with the sampling and random sampling problem in a reproducing kernel subspace of Orlicz space [Formula: see text]. We consider the function space [Formula: see text] as the image of an idempotent integral operator on [Formula: see text], where the integral kernel satisfies certain off-diagonal decay and regularity conditions. The model example of such reproducing kernel subspace of [Formula: see text] includes the finitely generated shift-invariant space and signal space with a finite rate of innovation. We show that a signal in [Formula: see text] can be stably reconstructed from its samples at distinct points separated by a sufficiently small gap. Next, we deduce that the random sampling inequality holds with a high probability for the class of functions in [Formula: see text] concentrated on a cube [Formula: see text], when the samples collected at i.i.d. random points are drawn on [Formula: see text] of order [Formula: see text].

CTGGAN: Controllable Text Generation with Generative Adversarial Network

Controllable Text Generation (CTG) aims to modify the output of a Language Model (LM) to meet specific constraints. For example, in a customer service conversation, responses from the agent should ideally be soothing and address the user’s dissatisfaction or complaints. This imposes significant demands on controlling language model output. However, demerits exist among traditional methods. Promoting and fine-tuning language models exhibit the “hallucination” phenomenon and cannot guarantee complete adherence to constraints. Conditional language models (CLM), which map control codes into LM representations or latent space, require training the modified language models from scratch and a high amount of customized dataset is demanded. Decoding-time methods employ Bayesian Rules to modify the output of the LM or model constraints as a combination of energy functions and update the output along the low-energy direction. Both methods are confronted with the efficiency sampling problem. Moreover, there are no methods that consider the relation between constraints weights and the contexts, as is essential in actual applications such as customer service scenarios. To alleviate the problems mentioned above, we propose Controllable Text Generation with Generative Adversarial Networks (CTGGAN), which utilizes a language model with logits bias as the Generator to produce constrained text and employs the Discriminator with learnable constraint weight combinations to score and update the generation. We evaluate the method in the text completion task and Chinese customer service dialogues scenario, and our method shows superior performance in metrics such as PPL and Dist-3. In addition, CTGGAN also exhibits efficient decoding compared to other methods.

An Improved SAR Ship Classification Method Using Text-to-Image Generation-Based Data Augmentation and Squeeze and Excitation

Synthetic aperture radar (SAR) plays a crucial role in maritime surveillance due to its capability for all-weather, all-day operation. However, SAR ship recognition faces challenges, primarily due to the imbalance and inadequacy of ship samples in publicly available datasets, along with the presence of numerous outliers. To address these issues, this paper proposes a SAR ship classification method based on text-generated images to tackle dataset imbalance. Firstly, an image generation module is introduced to augment SAR ship data. This method generates images from textual descriptions to overcome the problem of insufficient samples and the imbalance between ship categories. Secondly, given the limited information content in the black background of SAR ship images, the Tokens-to-Token Vision Transformer (T2T-ViT) is employed as the backbone network. This approach effectively combines local information on the basis of global modeling, facilitating the extraction of features from SAR images. Finally, a Squeeze-and-Excitation (SE) model is incorporated into the backbone network to enhance the network’s focus on essential features, thereby improving the model’s generalization ability. To assess the model’s effectiveness, extensive experiments were conducted on the OpenSARShip2.0 and FUSAR-Ship datasets. The performance evaluation results indicate that the proposed method achieves higher classification accuracy in the context of imbalanced datasets compared to eight existing methods.

Estimation of traditional numerical characteristics of lognormal distribution laws of a one-dimensional random variable in conditions of large volume statistical data

The efficiency of estimating the numerical characteristics of a family of the lognormal distribution law of a onedimensional random variable under conditions of large volumes of statistical data is considered. To circumvent the problem of large samples, methods of discretization the range of values of a random variable based on the formulas of Sturges, Brooks-Carruthers, Heinhold-Gaede and the formula proposed by the authors of this article are used. Data arrays have been generated that make it possible to evaluate the numerical characteristics of the laws of distribution of random variables, taking into account their discrete values. Based on the transformed data arrays, estimates of the mathematical expectation, standard deviation, skewness and kurtosis coefficients were calculated. Estimates of the numerical characteristics of the considered distribution laws under the conditions of a continuous and discrete random variable are compared for different volumes of initial statistical data. The effectiveness of methods for estimating the numerical characteristics of the family of the lognormal distribution law based on the initial statistical data and on the results of transformations of these data using known discretization formulas has been established. The reliability of the comparison of the effectiveness indicators of the studied methods was confirmed by using the Kolmogorov-Smirnov criterion. It is shown that the discretization formula proposed by the authors of this article is better and more effective compared to traditional methods.

A building change detection framework with patch-pairing single-temporal supervised learning and metric guided attention mechanism

Building change detection (CD) aims to detect changes in buildings from bi-temporal pairwise images obtained at different times. Typically, a deep learning-based building CD algorithm requires bi-temporal samples with significant building changes for training. However, obtaining such bi-temporal samples is challenging because building changes have a low probability of occurrence. Fortunately, it is relatively simple to obtain single-temporal samples that include a substantial number of buildings. By using these single-temporal building samples, pseudo bi-temporal building change samples can be generated, which can effectively address the problem of limited available bi-temporal building change samples. In view of that, this study proposes a metric guided single-temporal supervised learning framework that uses single-temporal building samples for building CD. In the proposed framework, patch-pairing single-temporal supervised learning (PPSL) adopts a patch-pairing method to construct pseudo bi-temporal building change samples, while equipping the network to effectively suppresses the negative impact of geometric offset and radiation difference in real samples. To further suppress the impact of radiation difference and enhance the effectiveness of our framework, a metric-guided spatial attention module (MGSAM) is designed to minimize the intra-class feature differences between temporal samples and augment the spatial context modeling ability. The proposed method is verified by experiments on different datasets, and the results demonstrate that the proposed method can outperform the existing methods and achieve superior performance.

A digital twin library of mechanical transmission system for the application of small sample fault diagnosis problem

Timely and accurate fault diagnosis of transmission systems is crucial to ensuring the systems’ reliability, safety, and economic viability. However, intelligent fault diagnosis algorithms require a lot of labeled data for training, which may not be available and accessible, especially for many critical devices. This hinders the application of some excellent diagnosis methods in real industry. Digital twin (DT), as an advanced cyber-physical integration method, can be utilized to generate rich fidelity data with virtual models to overcome the dilemma of insufficient data, especially for the small sample problem. We propose the DT library to model the mechanical transmission system with various faults for the data augmentation of the small sample problem. In the library, common components in mechanical transmission systems are modular and digitalized into several differential equations. They can compose a mechanical transmission system digital twin (TSDT) and be injected with various faults to simulate the transmission signal, and even replace the physical experimental platform. The simulation data is used as a pre-training dataset, which can be imported into the transfer learning method for the fault diagnosis. After several verifications, it can be concluded that the simulation data from TSDT is effective in transfer ability and fault feature learning, which significantly improves fault recognition accuracy in the small sample problem.

Wear life prediction of piston ring and cylinder liner based on integration of experiment and bench test data

The wear data of piston ring-cylinder liner (PRCL) of high-power diesel engines faces the problems of small samples, randomness, and underutilization, which leads to the wear life prediction of PRCL has been a difficult task in the engineering field. A wear life prediction method of PRCL based on the integration of experimental data and bench test data is proposed. First, a large amount of wear data is rapidly obtained through accelerated wear tests on specimens, and the distribution type of wear depth of PRCL is determined. Secondly, based on Rhee's wear equation, the nonlinear relationship between time, load, temperature, and wear depth is considered, and the acceleration models of temperature and load were introduced as the Arrhenius model and the inverse power law model, respectively. The wear life prediction model (WLPM) for specimens and parts with stochasticity is developed. The eigenvalues of WLPM’s parameters of specimens and parts were utilized to construct the mapping relationship from the specimen to the part. Finally, the Bayesian statistical method is used to merge the wear data of specimens and the parts, and the WLPM of specimens and the mapping relationship are taken as the a priori information, the bench data are taken as the new sample information, and the MCMC-Gibbs sampling method is used to estimate the mapping-based WLPM of parts. The results show that through the validation test, the method predicts the wear depth of PRCL with 100 % falling into the 95 % confidence interval better than the WLPM prediction results of a single specimen or part, and the errors of predicting the mean wear life of PRCL are all within 10 %. The method can provide a reference for the quality evaluation and engineering application of PRCL.

ACQ: Improving generative data-free quantization via attention correction

Data-free quantization aims to achieve model quantization without accessing any authentic sample. It is significant in an application-oriented context involving data privacy. Converting noise vectors into synthetic samples through a generator is a popular data-free quantization method, which is called generative data-free quantization. However, there is a difference in attention map between synthetic samples and authentic samples. This is always ignored and restricts the quantization performance. First, since synthetic samples of the same class are prone to have homogenous attention, the quantized network can only learn limited intra-class visual features. Second, synthetic samples in eval mode and training mode exhibit different attention. Hence, the statistical distribution matching tends to be inaccurate. ACQ is proposed in this paper to fix the attention of synthetic samples. Regarding intra-class attention homogeneity, we introduce an attention center matching loss aimed at achieving coarse-grained matching of attention of synthetic samples. Additionally, we have devised an adversarial loss based on pairs of samples with identical conditions. On one hand, this mechanism prevents the generator from mode collapse due to excessive attention on conditional information. On the other hand, it augments the separation between intra-class samples, thus further enhancing intra-class attention diversity. To improve the attention similarity of synthetic samples in different network modes, we introduce a consistency penalty to guarantee accurate statistical distribution matching. The experimental results demonstrate that ACQ effectively improves the attention problems of synthetic samples. Under various training settings, ACQ achieves the best quantization performance. For the 4-bit quantization of Resnet18 and Resnet50, ACQ reaches 67.55 % and 72.23 % accuracy, respectively.

Small Sample Methods in Multilevel Analysis

Bayesian methods have been said to solve small sample problems in frequentist methods by reflecting prior knowledge in the prior distribution. However, there are dangers in strongly reflecting prior knowledge or situations where much prior knowledge cannot be used. In order to address the issue, in this article, we considered to apply two Bayesian methods, one with weakly informative prior for random effect parameters (BayesW) and another with non-informative prior (BayesN) and compared their performance of parameter recovery with restricted maximum likelihood (REML) method, a frequentist-based estimation method commonly used in multilevel analysis. Specifically, we conducted two simulation studies using a two-level linear multilevel model and compared the performance of the BayesW, the BayesN, and the REML in various conditions that include scenarios of small sample data with a combination of small sample size both at level-1 and level-2. The results showed that the REML performed better than the BayesW, which showed overall better performance than the BayesN, in terms of convergence, bias, and coverage in some small sample scenarios. Therefore, based on the results of the present study, it is recommended to use the REML when adapting the two-level linear multilevel model and analyzing real-world data with small samples.

Is meta-worry relevant to interpersonal problems? Testing the metacognitive model of generalized anxiety disorder in an analogue- and a clinical sample of GAD

ABSTRACT Interpersonal problems are common in individuals with generalized anxiety disorder (GAD) and improved interpersonal functioning is an important goal in treatment. In the metacognitive model of worry and generalized anxiety disorder, emotional distress and psychological dysfunction are related to two distinct types of worry. Particular emphasis is put on meta-worry which refers to “worry about worrying” or appraisal of worrying as threatening in itself. Meta-worry impairs effective mental regulation and might therefore be an important predisposition to self-regulate via others and thereof interpersonal problems. In the current study, we tested the prediction that meta-worry is uniquely associated with interpersonal problems in two samples. The first consisted of 135 individuals with analogue GAD and the second of 56 individuals with a diagnosis of GAD. Using hierarchical linear regressions controlling for anxiety, depression and worry, meta-worry showed a unique relationship with interpersonal problems in both samples. These findings indicate that meta-worry may be relevant to formulate and treat interpersonal problems in individuals with GAD.

Abnormal line loss identification and category classification of distribution networks based on semi-supervised learning and hierarchical classification

Line loss refers to the electrical energy that is dissipated as heat during the transmission and distribution of electricity through power lines. However, unusual causes, such as grid topology mismatch and communication failure, can cause abnormal line loss. Efficient abnormal line loss detection contributes not only to minimizing energy wastage and reducing carbon emissions but also to maintaining the stability and reliability of the entire distribution network. In actual situations, the cause of abnormal line loss is not labeled due to the expensive labor cost. This paper proposes a hierarchical abnormal line loss identification and category classification model, considering the unlabeled and unbalanced sample problem. First, an abnormal line loss identification model-based random forest is established to detect whether the line loss is abnormal. Then, an abnormal line loss category classification model is developed with semi-supervised learning for line loss abnormal category classification, considering the unlabeled samples. The real dataset in China is utilized to validate the performance of the proposed model. Its reliability implies the potential to be applied to real-world scenarios to improve the management level and safety of the power grid.

Monte Carlo on manifolds in high dimensions

We introduce an efficient numerical implementation of a Markov Chain Monte Carlo method to sample a probability distribution on a manifold (introduced theoretically in Zappa, Holmes-Cerfon, Goodman (2018) [53]), where the manifold is defined by the level set of constraint functions, and the probability distribution may involve the pseudodeterminant of the Jacobian of the constraints, as arises in physical sampling problems. The algorithm is easy to implement and scales well to problems with thousands of dimensions and with complex sets of constraints provided their Jacobian retains sparsity. The algorithm uses direct linear algebra and requires a single matrix factorization per proposal point, which enhances its efficiency over previously proposed methods but becomes the computational bottleneck of the algorithm in high dimensions. We test the algorithm on several examples inspired by soft-matter physics and materials science to study its complexity and properties.

FVCNet: Detection obstacle method based on feature visual clustering network in power line inspection

AbstractPower line inspection is an important means to eliminate hidden dangers of power lines. It is a difficult research problem how to solve the low accuracy of power line inspection based on deep neural network (DNN) due to the problems of multi‐view‐shape, small‐size object. In this paper, an automatic detection model based on Feature visual clustering network (FVCNet) for power line inspection is established. First, an unsupervised clustering method for power line inspection is proposed, and applied to construct a detection model which can recognize multi‐view‐shape objects and enhanced object features. Then, the bilinear interpolation method is used to Feature enhancement method, and the enhanced high‐level semantics and low‐level semantics are fused to solve the problems of small object size and single sample. In this paper, FVCNet is applied to the MS‐COCO 2017 data set and self‐made power line inspection data set, and the test accuracy is increased to 61.2% and 82.0%, respectively. Compared with other models, especially for the categories that are greatly affected by multi‐view‐shape, the test accuracy has been improved significantly.

Regional investment risk evaluation based on compound risk correlation coefficient and migration learning approach

The high profit of regional investment is often accompanied by high risks, and the prior assessment of investment risks is conducive to avoid investment risks. However, the traditional evaluation methods usually only focus on individual risk factors, and it is difficult to evaluate and manage risks on the whole. Therefore, the study introduces deep learning algorithm, first build regional investment risk evaluation index system, then according to the characteristics of risk evaluation, design based on deep learning regional investment risk evaluation model, the final use parameter based migration learning algorithm and composite correlation coefficient to improve the evaluation model, solve the problem of insufficient training samples. The test results showed that the randomly selected 50 test samples with two different risk assessment models were 0.80 and 0.86, the deep learning algorithm tested 0.84, and the transfer learning improved model tested was 0.92, with the highest accuracy. This shows that the deep learning regional investment risk evaluation model improved by transfer learning effectively solves the problem of insufficient training data and improves the accuracy of prediction evaluation. In the field of venture capital, the model can help investors to evaluate and predict investment risks more accurately and improve the effect of investment decisions.

Multi-Level Feature-Refinement Anchor-Free Framework with Consistent Label-Assignment Mechanism for Ship Detection in SAR Imagery

Deep learning-based ship-detection methods have recently achieved impressive results in the synthetic aperture radar (SAR) community. However, numerous challenging issues affecting ship detection, such as multi-scale characteristics of the ship, clutter interference, and densely arranged ships in complex inshore, have not been well solved so far. Therefore, this article puts forward a novel SAR ship-detection method called multi-level feature-refinement anchor-free framework with a consistent label-assignment mechanism, which is capable of boosting ship-detection performance in complex scenes. First, considering that SAR ship detection is susceptible to complex background interference, we develop a stepwise feature-refinement backbone network to refine the position and contour of the ship object. Next, we devise an adjacent feature-refined pyramid network following the backbone network. The adjacent feature-refined pyramid network consists of the sub-pixel sampling-based adjacent feature-fusion sub-module and adjacent feature-localization enhancement sub-module, which can improve the detection capability of multi-scale objects by mitigating multi-scale high-level semantic loss and enhancing low-level localization features. Finally, to solve the problems of unbalanced positive and negative samples and densely arranged ship detection, we propose a consistent label-assignment mechanism based on consistent feature scale constraints to assign more appropriate and consistent labels to samples. Extensive qualitative and quantitative experiments on three public datasets, i.e., SAR Ship-Detection Dataset (SSDD), High-Resolution SAR Image Dataset (HRSID), and SAR-Ship-Dataset illustrate that the proposed method is superior to many state-of-the-art SAR ship-detection methods.

A new model for spatial rods incorporating surface energy effects

A new non-classical model for spatial rods incorporating surface energy effects is developed using a surface elasticity theory. A variational formulation based on the principle of minimum total potential energy is employed, which leads to the simultaneous determination of the equilibrium equations and complete boundary conditions. The newly developed spatial rod model contains three surface elasticity constants to account for surface energy effects. The new model recovers the classical elasticity-based Kirchhoff rod model as a special case when the surface energy effects are not considered. To illustrate the new spatial rod model, two sample problems are analytically solved by directly applying the general formulas derived. The first one is the buckling of an elastic rod of circular cross-section with fixed-pinned supports, and the other is the equilibrium analysis of a helical rod deformed from a straight rod. An analytical formula is derived for the critical buckling load required to perturb the axially compressed straight rod, and two closed-form expressions are obtained for the force and couple needed in deforming the helical rod. These formulas reduce to those based on classical elasticity when the surface energy effects are suppressed. For the buckling problem, it is found that the critical buckling load predicted by the current new model is always higher than that given by the classical elasticity-based model, and the difference between the two sets of predicted values is significantly large when the radius of the rod is sufficiently small but diminishes as the rod radius increases. For the helical rod problem, the numerical results reveal that the force and couple predicted by the current model are, respectively, significantly larger and smaller than those predicted by the classical model when the rod radius is very small, but the difference is diminishing with the increase of the rod radius.

A Boundary Node Method for Solving Interior and Exterior Acoustic Problems

The Boundary Node Method (BNM) is a meshfree scheme for solving Boundary Integral Equations (BIE). BNM simplifies the problem at two levels. Primarily, as BNM aims to solve the integral form of the governing equation, dimensionality of the problem is reduced by one order. Additionally, the mesh-free scheme eliminates the need for meshing, proving particularly beneficial for problems involving complex geometries. In this study, BNM is formulated using Element Free Galerkin (EFG) scheme to solve interior and exterior problems in acoustics. A 3-dimensional linear basis is used to construct moving least square shape functions. This eliminates the need to define additional local or parametric coordinate systems, making the method easily applicable to any arbitrary geometry. To illustrate the capabilities of the proposed method, four example problems are solved. An open pipe at resonance and a simple expansion muffler are analyzed to validate BNM’s performance in solving interior problems. Radiation from a pulsating sphere and radiation from a sphere with harmonic velocity excitation are analyzed as examples of exterior problems. Results from all four sample problems indicate that the BNM scheme proposed for solving acoustic problems is accurate and robust.

An improved V-Net lung nodule segmentation model based on pixel threshold separation and attention mechanism.

Accurate labeling of lung nodules in computed tomography (CT) images is crucial in early lung cancer diagnosis and before nodule resection surgery. However, the irregular shape of lung nodules in CT images and the complex lung environment make it much more challenging to segment lung nodules accurately. On this basis, we propose an improved V-Net segmentation method based on pixel threshold separation and attention mechanism for lung nodules. This method first offers a data augment strategy to solve the problem of insufficient samples in 3D medical datasets. In addition, we integrate the feature extraction module based on pixel threshold separation into the model to enhance the feature extraction ability under different thresholds on the one hand. On the other hand, the model introduces channel and spatial attention modules to make the model pay more attention to important semantic information and improve its generalization ability and accuracy. Experiments show that the Dice similarity coefficients of the improved model on the public datasets LUNA16 and LNDb are 94.9% and 81.1% respectively, and the sensitivities reach 92.7% and 76.9% respectively. which is superior to most existing UNet architecture models and comparable to the manual level segmentation results by medical technologists.

Research on Parkinson's disease recognition algorithm based on sample enhancement

Parkinson's disease patients have early vocal cord damage, and their voiceprint characteristics differ significantly from those of healthy individuals, which can be used to identify Parkinson's disease. However, the samples of the voiceprint dataset of Parkinson's disease patients are insufficient, so this paper proposes a double self-attention deep convolutional generative adversarial network model for sample enhancement to generate high-resolution spectrograms, based on which deep learning is used to recognize Parkinson's disease. This model improves the texture clarity of samples by increasing network depth and combining gradient penalty and spectral normalization techniques, and a family of pure convolutional neural networks (ConvNeXt) classification network based on Transfer learning is constructed to extract voiceprint features and classify them, which improves the accuracy of Parkinson's disease recognition. The validation experiments of the effectiveness of this paper's algorithm are carried out on the Parkinson's disease speech dataset. Compared with the pre-sample enhancement, the clarity of the samples generated by the proposed model in this paper as well as the Fréchet inception distance (FID) are improved, and the network model in this paper is able to achieve an accuracy of 98.8%. The results of this paper show that the Parkinson's disease recognition algorithm based on double self-attention deep convolutional generative adversarial network sample enhancement can accurately distinguish between healthy individuals and Parkinson's disease patients, which helps to solve the problem of insufficient samples for early recognition of voiceprint data in Parkinson's disease. In summary, the method effectively improves the classification accuracy of small-sample Parkinson's disease speech dataset and provides an effective solution idea for early Parkinson's disease speech diagnosis.