Fusion Coefficients Research Articles

Fault diagnosis for multi-axis carving machine systems with Gaussian mixture hidden Markov models: A data-model interactive perspective

This paper is concerned with sensor fault diagnosis problems for multi-axis carving machine systems (MACMSs) with repetitive machining tasks. A novel fault diagnosis method that combines the multi-feature fusion technology and Gaussian mixture hidden Markov models (GMHMMs) is proposed, which is inspired by a data- and model-driven collaborative perspective. With fault-sensitive features first extracted from both the time domain and time–frequency domain, the composite health index (CHI) is constructed to facilitate the understanding of the time-varying evolution. Then, GMHMMs are established to characterize the probabilistic relationship between the hidden states and CHI. To achieve high-precision fault classification, a well-designed global objective function is adopted to dynamically optimize both the CHI construction and classifier model training in a closed-loop feedback mechanism. Specifically, the fusion coefficients with range and equality constraints are integrated as part of the model parameters into the global optimization objective function, thereby reducing the search range and improving convergence speed. Besides, the well-trained GMHMMs interact with each other to capture the correlation information between different faults, and are utilized for online fault diagnosis. Finally, experiments are conducted on a self-developed multi-axis carving machine platform. The results exhibit outstanding performance in comparison with existing methods, particularly attaining a diagnostic accuracy of 95.37%.

Urban Land Use Classification Model Fusing Multimodal Deep Features

Urban land use classification plays a significant role in urban studies and provides key guidance for urban development. However, existing methods predominantly rely on either raster structure deep features through convolutional neural networks (CNNs) or topological structure deep features through graph neural networks (GNNs), making it challenging to comprehensively capture the rich semantic information in remote sensing images. To address this limitation, we propose a novel urban land use classification model by integrating both raster and topological structure deep features to enhance the accuracy and robustness of the classification model. First, we divide the urban area into block units based on road network data and further subdivide these units using the fractal network evolution algorithm (FNEA). Next, the K-nearest neighbors (KNN) graph construction method with adaptive fusion coefficients is employed to generate both global and local graphs of the blocks and sub-units. The spectral features and subgraph features are then constructed, and a graph convolutional network (GCN) is utilized to extract the node relational features from both the global and local graphs, forming the topological structure deep features while aggregating local features into global ones. Subsequently, VGG-16 (Visual Geometry Group 16) is used to extract the image convolutional features of the block units, obtaining the raster structure deep features. Finally, the transformer is used to fuse both topological and raster structure deep features, and land use classification is completed using the softmax function. Experiments were conducted using high-resolution Google images and Open Street Map (OSM) data, with study areas on the third ring road of Shenyang and the fourth ring road of Chengdu. The results demonstrate that the proposed method improves the overall accuracy and Kappa coefficient by 9.32% and 0.17, respectively, compared to single deep learning models. Incorporating subgraph structure features further enhances the overall accuracy and Kappa by 1.13% and 0.1. The adaptive KNN graph construction method achieves accuracy comparable to that of the empirical threshold method. This study enables accurate large-scale urban land use classification with reduced manual intervention, improving urban planning efficiency. The experimental results verify the effectiveness of the proposed method, particularly in terms of classification accuracy and feature representation completeness.

SimpleTrackV2: Rethinking the Timing Characteristics for Multi-Object Tracking.

Multi-object tracking tasks aim to assign unique trajectory codes to targets in video frames. Most detection-based tracking methods use Kalman filtering algorithms for trajectory prediction, directly utilizing associated target features for trajectory updates. However, this approach often fails, with camera jitter and transient target loss in real-world scenarios. This paper rethinks state prediction and fusion based on target temporal features to address these issues and proposes the SimpleTrackV2 algorithm, building on the previously designed SimpleTrack. Firstly, to address the poor prediction performance of linear motion models in complex scenes, we designed a target state prediction algorithm called LSTM-MP, based on long short-term memory (LSTM). This algorithm encodes the target's historical motion information using LSTM and decodes it with a multilayer perceptron (MLP) to achieve target state prediction. Secondly, to mitigate the effect of occlusion on target state saliency, we designed a spatiotemporal attention-based target appearance feature fusion (TSA-FF) target state fusion algorithm based on the attention mechanism. TSA-FF calculates adaptive fusion coefficients to enhance target state fusion, thereby improving the accuracy of subsequent data association. To demonstrate the effectiveness of the proposed method, we compared SimpleTrackV2 with the baseline model SimpleTrack on the MOT17 dataset. We also conducted ablation experiments on TSA-FF and LSTM-MP for SimpleTrackV2, exploring the optimal number of fusion frames and the impact of different loss functions on model performance. The experimental results show that SimpleTrackV2 handles camera jitter and target occlusion better, achieving improvements of 1.6%, 3.2%, and 6.1% in MOTA, IDF1, and HOTA, respectively, compared to the SimpleTrack algorithm.

Entanglement and pseudo entanglement dynamics versus fusion in CFT

The fusion rules and operator product expansion (OPE) serve as crucial tools in the study of operator algebras within conformal field theory (CFT). Building upon the vision of using entanglement to explore the connections between fusion coefficients and OPE coefficients, we employ the replica method and Schmidt decomposition method to investigate the time evolution of entanglement entropy (EE) and pseudo entropy (PE) for linear combinations of operators in rational conformal field theory (RCFT). We obtain a formula that links fusion coefficients, quantum dimensions, and OPE coefficients. We also identify two definition schemes for linear combination operators. Under one scheme, the EE captures information solely for the heaviest operators, while the PE retains information for all operators, reflecting the phenomenon of pseudo entropy amplification. Irrespective of the scheme employed, the EE demonstrates a step-like evolution, illustrating the effectiveness of the quasiparticle propagation picture for the general superposition of locally excited states in RCFT. From the perspective of quasiparticle propagation, we observe spontaneous block-diagonalization of the reduced density matrix of a subsystem when quasiparticles enter the subsystem.

A novel interactive prognosis framework with nonlinear Wiener process and multi-sensor fusion for remaining useful life prediction

Accurate remaining useful life (RUL) prediction plays a vital role in increasing the system operation safety and reducing maintenance costs. In industrial applications, there is usually a large amount of multi-sensor data generated. Therefore, how to construct an appropriate health index (HI) based on multi-sensor signals is very important for the RUL prediction. However, existing works treat sensor selection, HI construction, and degradation modeling independently as unrelated parts, which may result in the combination of sensors selected not constituting an optimal HI or the constructed HI not matching the degradation model. In addition, most existing works treat prior units as a whole to obtain a unique set of sensor combinations and fusion coefficients, which cannot reflect unit-to-unit heterogeneity, thus affecting the accuracy of RUL prediction. Therefore, a novel interactive feedback framework is established to construct HI, where the sensor selection, fusion coefficient calculation, and nonlinear Wiener process degradation modeling are incorporated into the feedback. Furthermore, an adaptive weight selection method based on particle swarm optimization and leave-one-out cross-validation (PSO-LV) is proposed to adjust the fusion coefficients in real-time. Then, the RUL is estimated by updating model parameters online, detecting degradation trends, and deriving the probability density function (PDF) of the RUL. Finally, two examples of engine datasets are provided to verify the effectiveness of the proposed method.

Integrity monitoring for decentralized redundant IMUs/GNSS integrated navigation system with correlated measurements

In civil aviation systems, the inertial measurement unit (IMU)/Global Navigation Satellite System (GNSS) integrated navigation remains the most effective navigation scheme. Based upon this, the utilization of redundant IMUs and a multi-constellation system can significantly enhance navigation and integrity performance. However, redundant IMUs/GNSS integrated navigation systems are susceptible to more complex failure modes, including GNSS faults (satellite and constellation faults) and IMU faults. Additionally, dealing with correlated measurements between redundant constructions presents a challenging issue. Therefore, we propose an integrity monitoring method for decentralized redundant IMUs/GNSS integrated navigation systems. This method considers GNSS faults and IMU fault in the integrity monitoring process, specifically designed for decentralized filter construction with redundancy. Furthermore, due to the correlated measurements between redundant filters, optimal fusion coefficients are determined by considering the unbiased estimate and minimizing the trace covariance of the primary filter. An optimal allocation scheme for continuity risk is also established to improve navigation and integrity performance. Simulation results demonstrate the feasibility and effectiveness of the proposed integrity monitoring method. Moreover, in the context of correlated measurements, the integrated navigation system also exhibits superiority.

Internet of things-based robust semi-analytical over ubiquitous data for indoor positioning geomagnetic

In the era of the Internet of Things (IoT), there is an increasingly urgent demand for high-precision and ubiquitous indoor positioning. However, robust technical solutions have yet to emerge, with one challenge being the effective use of geomagnetic information to address indoor personnel orientation. As known, outdoor environments with open spaces can utilize geomagnetic resolution-based methods for orientation, but indoor environments often suffer from significant magnetic distortions, rendering such methods impractical. To address this issue, this paper proposes a semi-analytical orientation method. The method initially integrates the analytical orientation results with the geometric relationship of corridor structures extracted based on spatial context information, obtaining corrected orientation results. This is achieved by measuring magnetic distortions and determining the fusion coefficient. Furthermore, the paper thoroughly analyzes the impact of different fusion coefficients on the orientation results. Test results indicate that compared to existing methods, the proposed approach exhibits better robustness, effectively improving orientation accuracy, and is widely applicable to path-based or corridor-based positioning and orientation scenarios.

Diesel engine quality abnormal patterns recognition based on feature fusion and adaptive decision fusion

The current assembly process of marine diesel engines is low in intelligence and the control chart pattern classifier with unstable performance, which makes it difficult to control and identify the quality control chart pattern. This paper proposes a new assembly quality control diagram recognition method based on an adaptive decision model to address these problems. Through characteristics and changes of the diesel engine assembly process analyses, the triangular norm is used to fuse the extracted shape features and statistical features to reduce the influence of data fluctuation and imbalance on pattern recognition. An adaptive decision fusion model of the assembly process is established by defining multiple weights with considering the complexity and uncontrollability of the diesel engine assembly process. Based on these, the fusion coefficients within the adaptive decision model are optimized by the Ant Lion Optimization algorithm (ALO) to improve the decision efficiency and classification precision. To validate the proposed model, diesel engine exhaust pressure is selected as a case for abnormal pattern recognition, and the ability of the model is discussed in terms of recognition accuracy and stability.

Row–column duality and combinatorial topological strings

Integrality properties of partial sums over irreducible representations, along columns of character tables of finite groups, were recently derived using combinatorial topological string theories (CTST). These CTST were based on Dijkgraaf-Witten theories of flat G-bundles for finite groups G in two dimensions, denoted G-TQFTs. We define analogous combinatorial topological strings related to two dimensional topological field theories (TQFTs) based on fusion coefficients of finite groups. These TQFTs are denoted as R(G)-TQFTs and allow analogous integrality results to be derived for partial row sums of characters over conjugacy classes along fixed rows. This relation between the G-TQFTs and R(G)-TQFTs defines a row-column duality for character tables, which provides a physical framework for exploring the mathematical analogies between rows and columns of character tables. These constructive proofs of integrality are complemented with the proof of similar and complementary results using the more traditional Galois theoretic framework for integrality properties of character tables. The partial row and column sums are used to define generalised partitions of the integer row and column sums, which are of interest in combinatorial representation theory.

Multi-scale convolutional neural networks and saliency weight maps for infrared and visible image fusion

Image fusion is the fusion of multiple images from the same scene to produce a more informative image, and infrared and visible image fusion is an important branch of image fusion. To tackle the issues of diminished luminosity in the infrared target, inconspicuous target features, and blurred texture of the fused image after the fusion of infrared and visible images. This paper introduces a novel effective fusion framework that merges multi-scale Convolutional Neural Networks (CNN) with saliency weight maps. First, the method measures the source image features to estimate the initial saliency weight map. Then, the initial weight map is segmented and optimized using a guided filter before being further processed by CNN. Next, a trained Siamese convolutional network is used to solve the two key problems of activity measure and weight assignment. Meanwhile, a multi-layer fusion strategy is designed to effectively retain the luminance of the infrared target and the texture information in the visible background. Finally, adaptive adjustment of the fusion coefficients is achieved by employing saliency. The experimental results show that the method outperforms the state-of-the-art algorithms in terms of both subjective visual quality and objective evaluation effects.

Fusion rules and shrinking rules of topological orders in five dimensions

As a series of work about 5D (spacetime) topological orders, here we employ the path-integral formalism of 5D topological quantum field theory (TQFT) established in Zhang and Ye, JHEP04 (2022) 138 to explore non-Abelian fusion rules, hierarchical shrinking rules and quantum dimensions of particle-like, loop-like and membrane-like topological excitations in 5D topological orders. To illustrate, we focus on a prototypical example of twisted BF theories that comprise the twisted topological terms of the BBA type. First, we classify topological excitations by establishing equivalence classes among all gauge-invariant Wilson operators. Then, we compute fusion rules from the path-integral and find that fusion rules may be non-Abelian; that is, the fusion outcome can be a direct sum of distinct excitations. We further compute shrinking rules. Especially, we discover exotic hierarchical structures hidden in shrinking processes of 5D or higher: a membrane is shrunk into particles and loops, and the loops are subsequently shrunk into a direct sum of particles. We obtain the algebraic structure of shrinking coefficients and fusion coefficients. We compute the quantum dimensions of all excitations and find that sphere-like membranes and torus-like membranes differ not only by their shapes but also by their quantum dimensions. We further study the algebraic structure that determines anomaly-free conditions on fusion coefficients and shrinking coefficients. Besides BBA, we explore general properties of all twisted terms in 5D. Together with braiding statistics reported before, the theoretical progress here paves the way toward characterizing and classifying topological orders in higher dimensions where topological excitations consist of both particles and spatially extended objects.

Fake News Detection based on Deep Learning

The rapid popularization of the Internet has broken the professional threshold of information dissemination, enabling more and more people to easily obtain information, share and express views through social media, which has greatly enriched people's daily life. However, due to the huge number of users of social media, false news fabricated for various purposes is emerging in endlessly. Moreover, with the progress of technology, false news is no longer simply spread in the form of text, but more spread through the combination of text, pictures and video, which greatly increases the confusion of false news. The experiment in this paper is based on tensorflow to detect false news. During the experiment, LR was used to obtain the fusion coefficients of CNN and LSTM models, that is the regression coefficient of LR, and then calculated the optimal threshold with the fused model on the verification set. In addition, in terms of model selection, lightgbm and xgboost were selected to train the model on the training set for false news, and predicted the news text on the testing set. The results of three experiments show that the effect of using xgboost model is the best, and the F1 score obtained in the experiment is the highest.

Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions

We discuss a variety of codimension-one, non-invertible topological defects in general 3+1d QFTs with a discrete one-form global symmetry. These include condensation defects from higher gauging of the one-form symmetries on a codimension-one manifold, each labeled by a discrete torsion class, and duality and triality defects from gauging in half of spacetime. The universal fusion rules between these non-invertible topological defects and the one-form symmetry surface defects are determined. Interestingly, the fusion coefficients are generally not numbers, but 2+1d TQFTs, such as invertible SPT phases, $${\mathbb {Z}}_N$$ gauge theories, and $$U(1)_N$$ Chern-Simons theories. The associativity of these algebras over TQFT coefficients relies on nontrivial facts about 2+1d TQFTs. We further prove that some of these non-invertible symmetries are intrinsically incompatible with a trivially gapped phase, leading to nontrivial constraints on renormalization group flows. Duality and triality defects are realized in many familiar gauge theories, including free Maxwell theory, non-abelian gauge theories with orthogonal gauge groups, $${{{\mathcal {N}}}}=1,$$ and $${{{\mathcal {N}}}}=4$$ super Yang-Mills theories.

A radiological study of the natural history of diffuse idiopathic skeletal hyperostosis (DISH): a story of incomplete fusion

Introduction: DISH is an ankylosing disease, when fractured can be challenging to manage. A retrospective radiological study was conducted to evaluate the natural history and radiological characteristics of DISH on Computed tomography (CT). Methods: Paired CT scans with DISH that are separated at least two years apart were used to perform the following radiological measurements: Degree of disc space fusion, Osteophyte and vertebral body linear attenuation coefficients (LAC), and Osteophyte axial area size and location. Results: 164 patients were analysed with a mean duration of 4.49 years between scans. 38.14% (442/1159) of disc spaces had at least partial calcification. Most osteophytes were right sided before becoming more circumferential over time. The average fusion score was 54.17. Most of the changes in fusion occurred in the upper and lower thoracic regions. The thoracic region when compared to the lumbar region had a greater proportion of its disc spaced being fully fused. Disc level osteophyte areas were larger than Body level osteophytes. Disc osteophytes size growth rate drops over time from 10.89mm2/year in Stage 1 to 3.56mm2/year in Stage 3. Stage 3 disc spaces (−11.01HU/year) was also found to have had a reduction in their LAC over time when compared to Stage 1 disc spaces (17.04HU/year). This change in osteophyte LAC was not mirrored in the change in vertebral body LAC. We predict that the age of onset and complete thoracolumbar ankylosis of DISH to be 17.96 years and 100.59 years, respectively. Conclusion: DISH ankylosis of the spine a slow process that starts in the mid to lower thoracic region before extending cranially and caudally. After the bridging osteophyte has fully formed, remodelling of the osteophyte occurs.

ALFPN: Adaptive Learning Feature Pyramid Network for Small Object Detection

Object detection has become a crucial technology in intelligent vision systems, enabling automatic detection of target objects. While most detectors perform well on open datasets, they often struggle with small-scale objects. This is due to the traditional top-down feature fusion methods that weaken the semantic and location information of small objects, leading to poor classification performance. To address this issue, we propose a novel feature pyramid network, the adaptive learnable feature pyramid network (ALFPN). Our approach features an adaptive feature inspection that incorporates learnable fusion coefficients in the fusion of different levels of feature layers, aiding the network in learning features with less noise. In addition, we construct a context-aligned supervisor that adjusts the feature maps fused at different levels to avoid scaling-related offset effects. Our experiments demonstrate that our method achieves state-of-the-art results and is highly robust for the small object detection on the TT-100K, PASCAL VOC, and COCO datasets. These findings indicate that a model’s ability to extract discriminant features is positively correlated with its performance in detecting small objects.

Pansharpening Based on Adaptive High-Frequency Fusion and Injection Coefficients Optimization

The purpose of pansharpening is to fuse a multispectral (MS) image with a panchromatic (PAN) image to generate a high spatial-resolution multispectral (HRMS) image. However, the traditional pansharpening methods do not adequately take consideration of the information of MS images, resulting in inaccurate detail injection and spectral distortion in the pansharpened results. To solve this problem, a new pansharpening approach based on adaptive high-frequency fusion and injection coefficients optimization is proposed, which can obtain an accurate injected high-frequency component (HFC) and injection coefficients. First, we propose a multi-level sharpening model to enhance the spatial information of the MS image, and then extract the HFCs from the sharpened MS image and PAN image. Next, an adaptive fusion strategy is designed to obtain the accurate injected HFC by calculating the similarity and difference of the extracted HFCs. Regarding the injection coefficients, we propose injection coefficients optimization scheme based on the spatial and spectral relationship between the MS image and PAN image. Finally, the HRMS image is obtained through injecting the fused HFC into the upsampled MS image with the injection coefficients. Experiments with simulated and real data are performed on IKONOS and Pléiades datasets. Both subjective and objective results indicate that our method has better performance than state-of-the-art pansharpening approaches.

Thermal Infrared Single-Pedestrian Tracking for Advanced Driver Assistance System

Tracking algorithms with low computational complexity and reliable performance are important in developing advanced driver assistance systems (DAS). This paper proposes a method of single-pedestrian tracking using thermal infrared cameras to meet the needs of DAS operating in nighttime and low-visibility conditions. The proposed algorithm uses the background-aware correlation filter (BACF) as the basic tracking framework. In order to address the problem that directly introducing the convolutional features leads to tracking performance degradation in the BACF framework, this paper proposes a fusion scheme to integrate handcrafted and convolutional features to make full use of the advantages of both the features. The proposed scheme combines response maps from convolutional and handcrafted features through fusion coefficients to improve the performance of the trackers based on the single features. In order to calculate fusion coefficients, a novel approach of searching the main peak and interference peaks of a response map is proposed by using local binary pattern values of the response map to locate all local maximum points. Experimental results show that the proposed algorithm outperforms the existing 9 competing tracking algorithms and can be used in vehicle platforms as a module of DAS to improve the safe level of driving in nighttime.

Slit-Strip Ising Boundary Conformal Field Theory 1: Discrete and Continuous Function Spaces

This is the first in a series of articles about recovering the full algebraic structure of a boundary conformal field theory (CFT) from the scaling limit of the critical Ising model in slit-strip geometry. Here, we introduce spaces of holomorphic functions in continuum domains as well as corresponding spaces of discrete holomorphic functions in lattice domains. We find distinguished sets of functions characterized by their singular behavior in the three infinite directions in the slit-strip domains, and note in particular that natural subsets of these functions span analogues of Hardy spaces. We prove convergence results of the distinguished discrete holomorphic functions to the continuum ones. In the subsequent articles, the discrete holomorphic functions will be used for the calculation of the Ising model fusion coefficients (as well as for the diagonalization of the Ising transfer matrix), and the convergence of the functions is used to prove the convergence of the fusion coefficients. It will also be shown that the vertex operator algebra of the boundary conformal field theory can be recovered from the limit of the fusion coefficients via geometric transformations involving the distinguished continuum functions.

Pointwise mutual information sparsely embedded feature selection

Feature selection is an effective approach to dimensionality reduction. Feature selection based on rough sets and fuzzy rough sets is extensively realized by introducing diversified heuristic information. Most existing heuristic feature selection methods ignore the fact that different features have distinct classification abilities when constructing feature evaluation functions. Due to the limitations of search strategies, locally optimal feature subsets are probably selected out. Embedded feature selection based on regression analysis can avoid falling into locally optimal feature subsets to a certain extent. However, only linear relationships between feature space and decision space have been involved. To overcome those problems, a pointwise mutual information sparsely embedded feature selection model (PMISEFS) is proposed in this paper. In this model, the pointwise fuzzy mutual information matrix is constructed based on fuzzy information granules to characterize the discernibility of features as well as the nonlinear relationship between the feature space and decision space for a data set. A classification information matrix is introduced to further describe the consistency between the predicted decision and real decisions of samples. The fuzzy mutual information tensor is embedded sparsely into the decision matrix and the sparsely embedded coefficients, called information fusion coefficients (IFCs) of features, are adaptively learnt by imposing a smooth constraint to avoid over-fitting. An embedded feature selection algorithm is designed to adaptively learn optimal IFCs. Extensive experiments on various benchmark data sets are conducted and experimental results demonstrate the superiority of the proposed model over the state-of-the-art heuristic as well as embedded feature selection methods.

Admissible-level $$\mathfrak {sl}_3$$ minimal models

The first part of this work uses the algorithm recently detailed in arXiv:1906.02935 to classify the irreducible weight modules of the minimal model vertex operator algebra $L_k(\mathfrak{sl}_3)$, when the level $k$ is admissible. These are naturally described in terms of families parametrised by up to two complex numbers. We also determine the action of the relevant group of automorphisms of $\hat{\mathfrak{sl}}_3$ on their isomorphism classes and compute explicitly the decomposition into irreducibles when a given family's parameters are permitted to take certain limiting values. Along with certain character formulae, previously established in arXiv:2003.10148, these results form the input data required by the standard module formalism to consistently compute modular transformations and, assuming the validity of a natural conjecture, the Grothendieck fusion coefficients of the admissible-level $\mathfrak{sl}_3$ minimal models. The second part of this work applies the standard module formalism to compute these explicitly when $k=-\frac32$. We expect that the methodology developed here will apply in much greater generality.