Single Gaussian Distribution Research Articles

Context normalization: A new approach for the stability and improvement of neural network performance

Deep neural networks face challenges with distribution shifts across layers, affecting model convergence and performance. While Batch Normalization (BN) addresses these issues, its reliance on a single Gaussian distribution assumption limits adaptability. To overcome this, alternatives like Layer Normalization, Group Normalization, and Mixture Normalization emerged, yet struggle with dynamic activation distributions. We propose ”Context Normalization” (CN), introducing contexts constructed from domain knowledge. CN normalizes data within the same context, enabling local representation. During backpropagation, CN learns normalized parameters and model weights for each context, ensuring efficient convergence and superior performance compared to BN and MN. This approach emphasizes context utilization, offering a fresh perspective on activation normalization in neural networks. We release our code at https://github.com/b-faye/Context-Normalization.

Influence of the growth rate during Nb film pulsed laser deposition on the sapphire R-plane

Optimal conditions for obtaining high quality epitaxial Nb thin films on the monocrystalline sapphire R-plane by pulsed laser deposition in ultrahigh vacuum have been determined. The ratio of room temperature resistance to the residual resistance (RRR) on the substrate temperature has the maximum at about 630 °C. The RRR dependence on the growth rate has the maximum at growth rates of 3–6 nm/min. In epitaxial Nb films, there is a simultaneous increase in the value of RRR and growth misorientation of Nb(001) relatively sapphire R-plane. At the maximum value of RRR, the shapes of Nb X-ray diffraction (XRD) peaks (002) and (011) are symmetrical and close to the Gaussian distribution; at lower RRR values, the shapes of XRD peaks become asymmetrical and cannot be approximated by a single Gaussian distribution, and their shape can be described by the sum of several Gaussian functions. For all obtained films, full width at half maximum (FWHM) of Nb (002) and Nb (011) peaks are 0.2o and 0.4о, respectively. FWHM of Nb (002) rocking curves is 0.4o.

Probabilistic Prediction and Assessment of Train-Induced Vibrations Based on Mixture Density Model

This study presents a probabilistic prediction method for train-induced vibrations by combining a deep neural network (DNN) with the mixture density model in a cascade fashion, referred to as the DNN-RMDN model in this paper. A benchmark example is conducted to demonstrate and evaluate the prediction performance of the DNN-RMDN model. Subsequently, the model is applied to a case study to investigate and compare the uncertainties of train-induced vibrations in the throat area and testing line area of a metro depot. After training, the model is capable of accurately predicting the probability density function (PDF) of train-induced vibrations at different distances from the track and at different frequencies. Utilizing the predicted PDF, probabilistic assessments can be performed to ascertain the likelihood of surpassing predefined limits. By employing a mixture density model instead of a single Gaussian distribution, the DNN-RMDN model achieves more accurate prediction of the PDF for train-induced vibrations. The proposed probabilistic assessment framework can effectively assist in vibration screening during the planning phase and in selecting and designing vibration mitigation measures of appropriate levels.

A novel constrained skew-Gaussian filter and its application to maneuverable reentry vehicle tracking

The state of the system generally satisfies specific constraints imposed by material properties or physical laws, so the application of these constraints can improve the accuracy of state estimation. In this paper, a novel recursive filter referred as constrained high-degree cubature skew-Gaussian filter (CHCSGF) is proposed, which achieves soft-constrained state estimation by compressing the probability density of unconstrained states with constraint information. First, the probability density of the state under inequality soft constraints is modeled as a skew-Gaussian (SG) distribution, rather than truncated or single Gaussian distributions. Then, a recursive constrained SG filter is developed to handle inequality soft constraints in linear systems. Addressing nonlinear challenges, a 5th-degree spherical-radial cubature approximation method is presented to numerically calculate SG-weighted integrals for the nonlinear transformation of SG distribution. Finally, the CHCSGF algorithm is proposed using this method to tackle nonlinear filtering problems. The CHCSGF is applied to reentry trajectory tracking to improve estimation accuracy by dealing with heat flow, dynamic pressure and overload constraints during reentry flight. Simulation results demonstrate that the CHCSGF achieves higher estimation accuracy than unconstrained methods under nonlinear inequality soft constraints, and is robust to the constraints with a prior error. Compared to particle filter and moving horizon estimation, the computational complexity of CHCSGF is significantly reduced.

Comment on “Fusion-fission dynamics of Pt188,190 through fission fragment mass distribution measurements”

Kavita [] analyze the width of the mass distributions of fission fragments from Si28+Gd160 and C12+Hf178 collisions. The authors report that the distributions “are reproducible with a single Gaussian at all studied energies”. However, the fits presented in the figures show functions that do not correspond to single-Gaussian distributions. A critical analysis, presented here, sheds doubts on the characterization of the mass distributions. Published by the American Physical Society 2024

An adaptive fault detection model based on variational auto-encoders and unsupervised transfer learning

Aiming at the problem of insufficient generalization of fault detection in traditional machine learning, an SDN controller fault detection method based on unsupervised transfer learning is proposed. The method mainly includes two parts. (1) A Gaussian mixture variational autoencoder based on the autoregressive flow is proposed. First, the encoder and decoder of variational autocoding are improved with gated recurrent units, and the improved variational autocoding can process time series data. Secondly, the gated recurrent unit is improved by using the gravitational search algorithm, which speeds up the search of the weight of the gated recurrent unit. Further, considering that the latent space of the variational autoencoder is a single Gaussian distribution, and the complex data in reality is often too simple to be represented by a single Gaussian distribution. (2) Aiming at the problem of poor generalization of fault detection models in practical scenarios, a domain adaptive fault detection algorithm based on multi-kernel maximum mean difference and intra-class distance constraints is proposed. Map the features into the manifold space to eliminate the distortion of the features in the original space. After mapping, the distance between fields needs to be measured, and the maximum mean difference of a single kernel cannot determine which kernel function is more suitable for the current task in practical applications. Therefore, the maximum mean difference based on multi-core is introduced to measure between the two fields. The experimental results show that the algorithm proposed improves the accuracy about 5% compared with the previous algorithm.

MIT-FRNet: Modality-invariant temporal representation learning-based feature reconstruction network for missing modalities

The investigation of missing modalities aims to extract valuable feature information from missing multi-modal data, it is a focal point in multi-modal learning. Existing missing modalities processing methods primarily focused on multi-modal fusion schemes to achieve optimal performance, but they faced the following two key challenges: (1) how to improve the robustness of incomplete multi-modal sequence representation, (2) how to effectively learn modality-invariant representations to mitigate heterogeneity between modalities. In this paper, we propose a modality-invariant temporal representation learning-based feature reconstruction network called MIT-FRNet for the missing modalities to tackle these challenges. In the MIT-FRNet, we first extract the latent features for each modality considering intra-modality and inter-modality, and then introduce an encoder-decoder framework to address the first challenge, it reconstructs missing element features via taking the incomplete modal sequences as input and implementing the inter-modal and cross-modal attention mechanisms for feature extraction. And then, through treating each timestamp as a single Gaussian distribution, we design a fine-grained similarity constraint based on distribution-level modality-invariant representations to learn effective modality-invariant representations, thereby addressing the second challenge. Finally, the efficiency of proposed model is validated through the classification results after multi-modal fusion that involves using a gate encoder to pass it and followed by a vector fusion to fuse it. Extensive experiments on public benchmark datasets demonstrate that the proposed MIT-FRNet method achieves promising results under varying missing rates while exhibiting good convergence.

Hybrid Variable Monitoring Mixture Model for Anomaly Detection in Industrial Processes.

Effective process monitoring is both a prerequisite and a guarantee for high system reliability. In modern industrial processes, binary variables may appear together with continuous variables, making process monitoring more intractable. Recently, a model named hybrid variable monitoring (HVM) has been proposed to conduct anomaly detection with both continuous and binary variables. Although the performance of HVM has been significantly improved after using the information of binary variables, it assumes that every continuous variable obeys a single Gaussian distribution and each binary variable obeys a single Bernoulli distribution. It is difficult for practical processes to satisfy such strict assumptions. To overcome this problem, this study proposes an improved algorithm called HVM mixture model (HVMMM). The HVMMM contains multiple components with the assumption of an HVM for every component. Compared with the HVM, the HVMMM is suitable for more general situations and has a more accurate characterization of the data features. Subsequently, the expectation-maximization (EM) algorithm is adopted for parameter learning for multiple components. The mathematical expressions of the parameters are derived in detail. In addition, the improvement on the monitoring performance caused by multiple components is analyzed. Finally, a numerical example and a practical case are used to demonstrate the effectiveness and efficiency of HVMMM. After multiple components are considered, the fault detection rate increases by 5.49% in the numerical example and the false alarm rate reduces by 1.6% in the practical case.

Quality-driven Gaussian mixture variational probabilistic network for soft sensor application in PET/PA6 polymerization process

Variational autoencoder has been widely used to build soft sensor models as a deep unsupervised feature extractor in recent years. However, the vanilla VAE employs a single diagonal Gaussian distribution as the approximate posterior in its latent feature space, which may lead to inferior performance when solving complex non-Gaussian multimode modeling problem. To address the issue, this paper proposes a quality-driven Gaussian mixture variational probabilistic network-based (QGMVPN) soft sensor model. First, Gaussian mixture density with diagonal covariance matrices and Householder transformations are implemented to characterize the distributions of non-Gaussian multimode feature. Then, a quality-driven strategy is designed to extract quality-related features and a novel gating mechanism is employed to enhance the nonlinear representation ability. Last, the trained decoder, coupled with the sampling space, is directly applied to soft sensor modeling owing to the special extra input of the decoder. The effectiveness of QGMVPN-based model is demonstrated on two polymerization datasets.

A novel genetic marginalized particle filter method for state of charge and state of energy estimation adaptive to multi-temperature conditions of lithium-ion batteries

Power lithium-ion batteries are widely used in various fields, the battery management system (BMS) is the main object of battery energy management and safety monitoring, so the accurate collaboration of state of charge (SoC) and state of energy (SoE) is estimated to be essential for the BMS system. In this work, a novel genetic marginal particle filter (GMPF) algorithm to estimate SoC and SoE accurately. The forgetting factor recursive least square (FFRLS) algorithm is used to identify the second-order Thevenin equivalent model parameter, and the genetic algorithm is used to improve the re-sampling process of the traditional particle filtering (PF) algorithm, according to the Rao-Blackwell theory in statistical science, the marginalization of part of the linear state variables during the calculation of particle filtering, the distribution of the post-test is similar to a single Gaussian distribution. The GMPF algorithm is verified under the conditions of the hybrid pulse power characteristic (HPPC) and the Beijing bus dynamic stress test (BBDST) with 15 °C, 25 °C, and 35 °C respectively, and experimental results show that the improved GMPF algorithm can effectively realize the collaborative estimation of the SoC and SoE of power lithium-ion batteries. The mean absolute error of SoC and SoE estimation is always less than 1.56 %, the root-mean-square error is always less than 1.58 %. And the GMPF algorithm is suitable for temperature environments of 15 °C to 35 °C.

Entropy-Based Anomaly Detection for Gaussian Mixture Modeling

Gaussian mixture modeling is a generative probabilistic model that assumes that the observed data are generated from a mixture of multiple Gaussian distributions. This mixture model provides a flexible approach to model complex distributions that may not be easily represented by a single Gaussian distribution. The Gaussian mixture model with a noise component refers to a finite mixture that includes an additional noise component to model the background noise or outliers in the data. This additional noise component helps to take into account the presence of anomalies or outliers in the data. This latter aspect is crucial for anomaly detection in situations where a clear, early warning of an abnormal condition is required. This paper proposes a novel entropy-based procedure for initializing the noise component in Gaussian mixture models. Our approach is shown to be easy to implement and effective for anomaly detection. We successfully identify anomalies in both simulated and real-world datasets, even in the presence of significant levels of noise and outliers. We provide a step-by-step description of the proposed data analysis process, along with the corresponding R code, which is publicly available in a GitHub repository.

Investigating the distribution of double neutron stars and unconventional component mass

ABSTRACTThe mass distribution of double neutron stars (DNSs) can help us to understand the evolution of binary systems, which can also contain information about DNSs induced by gravitational wave radiation. Henceforth, for the 25 pairs of DNS systems so far discovered by radio observations, we have only statistically analysed 13 systems with precisely measured masses of two-component NSs, by employing the classical Gaussian mixture models based on the Akaike and Bayesian information criteria. The result infers that the mass distributions for recycled and non-recycled NSs follow a double-Gaussian and single-Gaussian distribution, respectively. In the conventional scenario of DNS formation, the mass of the first formed recycled NS is higher than that of the second-formed companion NS. However, there exist some unconventional cases with a reverse mass ratio. To explore the phenomenon of this ‘unconventional component mass’ of DNSs, we employed Monte Carlo sampling. We find that the unconventional DNS systems occupy about 27.7 per cent of all DNSs, which could be a useful reference for the future gravitational wave detection by LIGO/Virgo. Furthermore, we discuss a possible explanation for the unconventional DNS mass ratio, which involves the recycling process and its birth rate. This also has an implication for the mass distribution of the DNS progenitors.

Plücker coordinates of the best-fit Stiefel tropical linear space to a mixture of Gaussian distributions

In this research, we investigate a tropical principal component analysis (PCA) as a best-fit Stiefel tropical linear space to a given sample over the tropical projective torus for its dimensionality reduction and visualization. Especially, we characterize the best-fit Stiefel tropical linear space to a sample generated from a mixture of Gaussian distributions as the variances of the Gaussians go to zero. For a single Gaussian distribution, we show that the sum of residuals in terms of the tropical metric with the max-plus algebra over a given sample to a fitted Stiefel tropical linear space converges to zero by giving an upper bound for its convergence rate. Meanwhile, for a mixtures of Gaussian distribution, we show that the best-fit tropical linear space can be determined uniquely when we send variances to zero. We briefly consider the best-fit topical polynomial as an extension for the mixture of more than two Gaussians over the tropical projective space of dimension three. We show some geometric properties of these tropical linear spaces and polynomials.

An efficient fault-tolerant distributed Bayesian filter based on conservative fusion

This paper proposes a fault-tolerant distributed Bayesian filter for multi-sensor state estimation using a peer-to-peer sensor network with incoherent local estimates problems. The proposed approach uses a Gaussian mixture rather than a single Gaussian distribution to represent the fusion result, which can effectively reduce the negative impact of corrupted local estimates on the fusion results. The resulting filter performs Bayesian recursion via Gaussian mixture. To accommodate a heterogeneous sensor network, we develop a novel arithmetic average fusion employing a set of covariance-dependent weighting coefficients, where the fusion error covariance is effectively reduced in the case of fusing information with different qualities. For intersensor communication, a partial flooding scheme is investigated, in which only valid-likely Gaussian components are disseminated and fused between neighbor sensors. Theoretically, it is shown that under reasonable assumptions, the presented fault-tolerant distributed estimator can guarantee local stability with the exponentially bounded estimation error in the mean square. The effectiveness and superiority of our approach are validated through both simulation and experiment scenarios.

Decomposing the linear momentum transfer components in break-up fusion reactions: An experimental study of the F19+Tb159 system

In the present work, measurement and analysis of forward recoil range distribution of various reaction residues populated in the interaction of $^{19}\mathrm{F}$ projectile with $^{159}\mathrm{Tb}$ target nucleus have been performed. The aim is to disentangle the contribution of complete fusion (CF) and incomplete fusion (ICF) components at two different above-barrier energies $\ensuremath{\approx}83$ and 94 MeV. The recoil-catcher technique with off-line $\ensuremath{\gamma}$-ray spectroscopy has been performed. The complete and incomplete fusion events have been identified by full and partial linear momentum transfer, respectively. A single Gaussian distribution has been observed in case of residues populated via complete fusion processes. However, the recoil range distribution for $\ensuremath{\alpha}$-emitting channels was found to be deconvoluted into more than one Gaussian peak indicating the involvement of both full and partial linear momentum transfer components due to the presence of CF and ICF processes. The analysis of data suggests that projectile breaks up as soon as it comes near the vicinity of target nuclear field leading to different linear momentum transfer components. Further, the analysis done within the framework of universal fusion function indicates a significant break-up fusion probability of $^{19}\mathrm{F}$ projectile. As such, at lower energies $^{19}\mathrm{F}$ is found to behave similar to other $\ensuremath{\alpha}$-cluster beams.

Modality-invariant temporal representation learning for multimodal sentiment classification

Multimodal sentiment classification is a notable research field that aims to refine sentimental information and classify the sentiment tendency from sequential multimodal data. Most existing sentimental recognition algorithms explore multimodal fusion schemes that achieve good performance. However, there are two key challenges to overcome. First, it is essential to effectively extract inter- and intra-modality features prior to fusion, while simultaneously reducing ambiguity. The second challenge is how to learn modality-invariant representations that capture the underlying similarities. In this paper, we present a modality-invariant temporal learning technique and a new gated inter-modality attention mechanism to overcome these issues. For the first challenge, our proposed gated inter-modality attention mechanism performs modality interactions and filters inconsistencies from multiple modalities in an adaptive manner. We also use parallel structures to learn more comprehensive sentimental information in pairs (i.e., acoustic and visual). In addition, to address the second problem, we treat each modality as a multivariate Gaussian distribution (considering each timestamp as a single Gaussian distribution) and use the KL divergence to capture the implicit temporal distribution-level similarities. These strategies are helpful in reducing domain shifts between different modalities and extracting effective sequential modality-invariant representations. We have conducted experiments on several public datasets (i.e., YouTube and MOUD) and the results show that our proposed method outperforms the state-of-the-art multimodal sentiment categorization methods.

Findings of inhomogeneity in barrier height of Schottky junction Al/rGO-SnO2 having anomaly in theoretical and experimental value of Richardson constant: A Gaussian approach

In this research, the temperature dependent dynamical behavior of Schottky junction Al/rGO-SnO2 has been investigated with thermionic emission (TE) theory within the temperature regime 303 K to 423 K at interval 20 K. During analysis of electrical charge transport behavior an anomalous change is observed in the value of ideality factor and barrier height with rising temperature for the junction. Experimentally derived Richardson constant (of the order 10-5A/m2K2) using TE theory is exceptionally substandard to the theoretical (of the order 106A/m2K2) values. The beauty of this work is to find out the underline physics for this discrepancy in measurement of Richardson constant (might arose due to inhomogeneity in barrier of metal-semiconductor junction) by assuming the Gaussian distribution of the barrier height with TE theory at the junction. It is obvious that the occurrence of barrier inhomogeneity across the junction leading charge transport phenomena which mostly impacting upon the parameters of Schottky diodes and its nature because of intrinsic formation of ripples and ridges. In this study, it is found that the charge transport mechanism is highly follows the single Gaussian distribution. The material characterization and its Schottky behavior in normal temperature had been published elsewhere.

Physics-guided mixture density networks for uncertainty quantification

This paper proposes a Physics-guided Mixture Density Network (PgMDN) model for uncertainty quantification of regression-type analysis. It integrates a Mixture Density Network for probabilistic modeling and physics knowledge as regularizations. This model can handle arbitrary distribution of data (e.g., strongly non-Gaussian, multi-mode, and truncated distributions). The physics knowledge from parameters and their partial derivatives is used as equality/ inequality constraints. The training of physics-guided machine learning is formulated as a constrained optimization problem. The constrained optimization problem is transformed to an unconstrained one using a dynamic penalty function algorithm. Thus, the commonly used backpropagation algorithm can be used to train the neural network. With the physics constraints, the required training data size can be reduced, and the overfitting problem can be mitigated. This paper demonstrates the application of the PgMDN using a numerical example, an engineering problem for fatigue stress-life curve estimation, an engineering problem for natural frequency prediction of bridges, and an engineering problem for fatigue life prediction of corroded steel reinforcing bars. Some discussions are given to illustrate the effectiveness of incorporating the physics knowledge when data are sparse, the improvement of the dynamic penalty function method compared with the static method, and the benefits achieved from the distribution mixture compared with a single Gaussian distribution.

Neutron spectrum unfolding of the magnetic proton recoil spectrometer using the GRAVEL and MLEM algorithms

The magnetic proton recoil (MPR) spectrometer is a high-resolution neutron spectrometer, which provides critical information about the deuterium–tritium (DT) fusion yield, collective fuel velocity, and ion temperature. For precise measurements, the MPR spectrometer operates in a high-resolution mode; however, its detection efficiency is low. The trade-off between energy resolution and detection efficiency limits its widespread applications. Herein, we apply the spectrum unfolding technique to obtain a precise energy spectrum using the MPR spectrometer in a low-resolution mode and to achieve high detection efficiency. Numerical experiments and Geant4 simulations are conducted to compare the GRAVEL and the maximum likelihood expectation maximization (MLEM) algorithms in different cases. A new stopping criterion for iterations is adopted and works well. The source focuses on the primary DT neutrons with single Gaussian, asymmetric, and dual Gaussian distributions. All the cases demonstrate an accurate and stable unfolded energy spectrum, revealing the potential of the MPR spectrometer in a wide range of applications.

New Coulomb barrier scaling law with reference to the synthesis of superheavy elements

The synthesis of superheavy elements based on fusion reactions and multinucleon transfer reactions is sensitive to the reaction energies, where the Coulomb barrier plays a crucial role as it must be overcome for the projectile and target to contact each other. The Coulomb barrier cannot be measured directly, and the synthesis of superheavy elements is sensitive to it. In this study, we systematically extract the barrier information from the experimental fusion excitation functions by the empirical cross section formula, which is based on a single-Gaussian distribution of fusion barrier heights. A total of 403 sets of experimental data are fitted, among which 243 sets have good results with ${\ensuremath{\chi}}^{2}/pt$ less than one. The extracted fusion barrier is a dynamical barrier, which includes the overall effect of coupled channels. Different from the prediction of the WKJ formula, the new scaling law proposed in this work is almost identical to the CW76 Coulomb barrier at the $z=170--300$ region and reproduces well the centroid barrier extracted from quasielastic scattering. The comparison to the other 14 bare potential models and exploration of the very large $z$ region is also discussed. It is also remarkable to find that the predictions of the DP2015 potential, including of the contributions of the macroscopic and shell correction terms, are highly consistent with the extracted results in this work and the CW76 potential. The numerical results demonstrated that the dynamical fusion barrier and the centroid barrier extracted from the quasielastic reaction (the reaction threshold) could be the same physical quantity for superheavy reactions. This study could provide important references for the synthesis of superheavy nuclei based on fusion reactions and very heavy multinucleon transfer reactions.