Gaussian Distribution Research Articles

Explainable finite mixture of mixtures of bounded asymmetric generalized Gaussian and Uniform distributions learning for energy demand management

We introduce a mixture of mixtures of bounded asymmetric generalized Gaussian and uniform distributions. Based on this framework, we propose model-based classification and model-based clustering algorithms. We develop an objective function for the minimum message length (MML) model selection criterion to discover the optimal number of clusters for the unsupervised approach of our proposed model. Given the crucial attention received by Explainable AI (XAI) in recent years, we introduce a method to interpret the predictions obtained from the proposed model in both learning settings by defining their boundaries in terms of the crucial features. Integrating Explainability within our proposed algorithm increases the credibility of the algorithm’s predictions since it would be explainable to the user’s perspective through simple If-Then statements using a small binary decision tree. In this paper, the proposed algorithm proves its reliability and superiority to several state-of-the-art machine learning algorithms within the following real-world applications: fault detection and diagnosis (FDD) in chillers, occupancy estimation and categorization of residential energy consumers.

‘The ‘Vector-Model’ wavefunction: spatial description and wavepacket formation of quantum-mechanical angular momenta’

We introduce the concept of an asymptotic spatial angular-momentum wavefunction, Xmjφ,θ,χ=eimφδθ−θm eij+12χ, which treats j in the jm state as a three-dimensional entity; φ, θ, χ are the Euler angles, and θm is the Vector-Model polar angle, given by cosθm=m/j. A wealth of geometric information about j can be deduced from the eigenvalues and spatial transformation properties of the Xmjφ,θ,χ. Specifically, the Xmjφ,θ,χ wavefunction gives a computationally simple description of the sizes of the particle and orbital-angular-momentum wavepackets (constructed from Gaussian distributions in j and m ), given by effective wavepacket angular uncertainty relations for ΔmΔφ, ΔjΔχ, and ΔφΔθ. The Xmjφ,θ,χ also predicts the position of the particle-wavepacket angular motion in the orbital plane, so that the particle-wavepacket rotation can be experimentally probed through continuous and non-destructive j -rotation measurements. Finally, we use the Xmj(φ,θ,χ) to determine geometrically well-known asymptotic expressions for Clebsch–Gordan coefficients, Wigner d-functions, the gyromagnetic ratio of elementary particles, g=2, and the m -state-correlation matrix elements. Interestingly, for low j, even down to j=1/2, these expressions are either exact (the last two) or excellent approximations (the first two), showing that the Xmj(φ,θ,χ) give a useful spatial description of quantum-mechanical angular momentum, and provide a smooth connection with classical angular momentum.

Dynamic simulation-assisted Gaussian mixture alignment approach for fault diagnosis of rotation machinery under small samples

Abstract Obtaining a substantial number of actual samples for rotating machinery in an industrial setting can be challenging, particularly when faulty samples are acquired under hazardous working conditions. The issue of insufficient samples hinders the effective training of reliable fault diagnosis models, impeding the industrial implementation of advanced intelligent methods. This study proposes an innovative Dynamic Simulation-assisted Gaussian Mixture Alignment model (DSGMA) to address the challenge of applying fault diagnosis technologies, with its performance mined by advanced transfer algorithms. Specifically, we establish a fault dynamics model for rotating machinery and acquire a substantial amount of simulated data as the source domain to facilitate the training of the deep neural network model. Subsequently, we propose a Gaussian mixture-guided domain alignment approach that assigns a domain-independent Gaussian distribution to each category as prior knowledge, with the parameters calculated using limited actual samples. Diagnostic knowledge is transferred from the source domain to the target domain by minimizing the Kullback-Leibler divergence between the features of the simulated samples and the Gaussian mixture priors. Furthermore, the DSGMA model incorporates Gaussian clustering loss to augment the clustering capability of samples belonging to the same category from real devices and enhances the computational stability of the parameters in the Gaussian mixture model. The efficacy of the DSGMA method is validated using three publicly available datasets and compared against five widely adopted methods. The experimental findings illustrate that DSGMA exhibits superior diagnostic and robust capabilities, facilitating efficient fault diagnosis under scenarios of small samples.

A multi-institutional machine learning algorithm for prognosticating facial nerve injury following microsurgical resection of vestibular schwannoma

Vestibular schwannomas (VS) are the most common tumor of the skull base with available treatment options that carry a risk of iatrogenic injury to the facial nerve, which can significantly impact patients’ quality of life. As facial nerve outcomes remain challenging to prognosticate, we endeavored to utilize machine learning to decipher predictive factors relevant to facial nerve outcomes following microsurgical resection of VS. A database of patient-, tumor- and surgery-specific features was constructed via retrospective chart review of 242 consecutive patients who underwent microsurgical resection of VS over a 7-year study period. This database was then used to train non-linear supervised machine learning classifiers to predict facial nerve preservation, defined as House-Brackmann (HB) I vs. facial nerve injury, defined as HB II–VI, as determined at 6-month outpatient follow-up. A random forest algorithm demonstrated 90.5% accuracy, 90% sensitivity and 90% specificity in facial nerve injury prognostication. A random variable (rv) was generated by randomly sampling a Gaussian distribution and used as a benchmark to compare the predictiveness of other features. This analysis revealed age, body mass index (BMI), case length and the tumor dimension representing tumor growth towards the brainstem as prognosticators of facial nerve injury. When validated via prospective assessment of facial nerve injury risk, this model demonstrated 84% accuracy. Here, we describe the development of a machine learning algorithm to predict the likelihood of facial nerve injury following microsurgical resection of VS. In addition to serving as a clinically applicable tool, this highlights the potential of machine learning to reveal non-linear relationships between variables which may have clinical value in prognostication of outcomes for high-risk surgical procedures.

Optimization of robotic path planning and navigation point configuration based on convolutional neural networks.

This study introduces a novel approach for enhancing robotic path planning and navigation by optimizing point configuration through convolutional neural networks (CNNs). Faced with the challenge of precise area coverage and the inefficiency of traditional traversal and intelligent algorithms (e.g., genetic algorithms, particle swarm optimization) in point layout, we proposed a CNN-based optimization model. This model not only tackles the issues of speed and accuracy in point configuration with Gaussian distribution characteristics but also significantly improves the robot's capability to efficiently navigate and cover designated areas with high precision. Our methodology begins with defining a coverage index, followed by an optimization model that integrates polygon image features with the variability of Gaussian distribution. The proposed CNN model is trained with datasets generated from systematic point configurations, which then predicts optimal layouts for enhanced navigation. Our method achieves an experimental result error of <8% on the test dataset. The results validate effectiveness of the proposed model in achieving efficient and accurate path planning for robotic systems.

Controlling three-dimensional magnetic island appearance with external current drive in the Chinese first quasi-axisymmetric stellarator

In this study, the impact of a non-inductive current drive, such as electron cyclotron current drive, on three-dimensional (3D) magnetic islands in the high-β equilibrium of the Chinese First Quasi-axisymmetric Stellarator (CFQS) was investigated using the HINT code. In the case of a high-β equilibrium (volume-averaged plasma beta <β> ∼ 0.74% and bootstrap current I bs∼ 24.5 kA), two m/n = 4/2 rational surfaces with large magnetic islands develop (Wang et al 2021 Nucl. Fusion 61 036021). The islands can be effectively controlled using a constant or a Gaussian current density profile, depending on the direction and amplitude of the current. With a constant current density amounting to a total current of −6 kA, the rotational transform profile can be modified such that the m/n = 4/2 rational surface is eliminated and the island is suppressed. For the Gaussian current density profile, the magnetic island can also be suppressed using a smaller total current of ∼−2 kA to adjust the iota profile. These results suggest that in the CFQS stellarator, the external current drive might be an efficient approach for controlling 3D magnetic islands and consequently improving plasma confinement.

Damage detection for high-speed railway standard box girders based on time–frequency characteristics of train-induced strain

This paper presents a novel approach for detecting damage in high-speed railway standard box girders by leveraging the time–frequency characteristics of train-induced strain. Based on the mechanical and deformation characteristics of high-speed railway box girders, the method involves segmenting the box girder into distinct components based on plate element analysis to identify their damage separately. It utilizes coefficients derived from wavelet transforms as indicators sensitive to damage, and employs the particle swarm optimization algorithm (PSO) to determine the ideal frequency intervals in terms of number and position. Within these optimal frequency intervals, the sum of wavelet coefficients is only sensitive to damage features while remaining unaffected by environmental and operational variations. A convolutional denoising autoencoder is employed to remove noise from the strain time–frequency image, improving the robustness of the proposed method. By utilizing the Gaussian inverse cumulative distribution function to estimate confidence boundary (CB) for damage features (DF), outliers are detected, allowing for precise damage localization and quantification. A case study for the high-speed railway box girder show that the proposed method can effectively identify, locate and quantify damage across all components in the critical key section by using data acquired from just 4 strain sensors. This method holds promise for facilitating the development of effective maintenance strategies for high-speed railway box girders.

Grant-Free Random Access Enhanced by Massive MIMO and Non-Orthogonal Preambles

Massive multiple input multiple output (MIMO) enabled grant-free random access (mGFRA) stands out as a promising random access (RA) solution, thus effectively addressing the need for massive access in massive machine-type communications (mMTCs) while ensuring high spectral efficiency and minimizing signaling overhead. However, the bottleneck of mGFRA is mainly dominated by the orthogonal preamble collisions, since the orthogonal preamble pool is small and of a fixed-sized. In this paper, we explore the potential of non-orthogonal preambles to overcome limitations and enhance the success probability of mGFRA without extending the length of the preamble. Given the RA procedure of mGFRA, we analyze the factors influencing the success rate of mGFRA with non-orthogonal preamble and propose to use two types of sequences, namely Gold sequence and Gaussian distribution sequence, as the preambles for mGFRA. Simulation results demonstrate the effectiveness of these two types pf non-orthogonal preambles in improving the success probability of mGFRA. Moreover, the system parameters’ impact on the performance of mGFRA with non-orthogonal preambles is examined and deliberated.

Simulation algorithms for stationary sequences with distributions in the form of a mixture of Gaussian distributions

Abstract In this paper, we present three algorithms for simulation of intervals of stationary vector and scalar sequences with partial distributions of their subsequences of fixed length in the form of a mixture of Gaussian distributions. The first algorithm is based on superposition of two Gaussian vector processes and the second and third ones use the method of conditional distributions and the method of superpositions to simulate the mixtures and to select realizations for approximate construction of conditional realizations. Some properties of these algorithms are presented.

Enhancing microscale additive manufacturing: Electrolyte-column localized electrochemical deposition for microwire and microdevice substrate connection

Electrochemical deposition is a microscale additive manufacturing technology. Due to the excellent performance of electrodeposited coating layers which exhibit no thermal stress, low porosity, and minimal microcracks, electrodeposition has been used in the connections of microdevices to solve the problems of shrinkage and deformation of microparts caused by thermal stress generated by conventional connections. Due to the low efficiency of Meniscus-Confined electrodeposition, a novel connection process for microwires and microdevice substrate using electrolyte-column localized electrochemical deposition (ECL-ECD) is proposed. The connecting mechanism is determined through simulation and experimentation. Simulation results indicated that the current density in the connection area exhibited a Gaussian distribution and the deposition layer preferentially grew at the interface between the microwire and the substrate. A high-speed camera was used to observe the liquid beam throughout the experiment, the results indicated that the microwires didn’t affect the stability of the liquid beam, and the ECL-ECD had excellent domain fixation. Smooth and dense surfaces on the connection area of the microwire and substrate were obtained at a current density of 50–60 A/dm2. Performance testing results showed that the connection point has excellent corrosion resistance and electrical properties. When the deposition time was short, the microwire was detached from the deposition area due to relatively thin deposition layer thickness and the tensile strength was only 133.82 MPa during the tensile testing. When the appropriate deposition process parameters were chosen, the fracture occurred on the microwire under tensile load and the fracture strength was 198.84 MPa, which equals the tensile strength of the microwire and indicated that the connection point can provide sufficient strength. The experimental results demonstrated that ECL-ECD can provide an effective and reliable connection process for the microwires interconnection.

On Univariate Gaussian Mixture Model for Diabetic Patients in Yola, Adamawa State

Finite Mixture Model serves as a potent statistical tool for modeling intricate data distributions through the amalgamation of multiple Gaussian components. The aim of this work is to use finite mixture of normal distribution to model data on diabetic patients from Modibbo Adama University Teaching Hospital, Yola, Adamawa State, so as to expose latent sub-groups. The model is first used on synthetic data and subsequently on diabetic patients data. The diabetic data set consists of 553 cases of diabetes mellitus. The variables measured: Age(years), Mass of a patient(kg/meters), glucose level (plasma glucose con- centration, a 2-hour in an oral glucose tolerance test), pressure (Diastolic blood pressure mmHg), insulin (2-hour serum insulin mu U/ml) and class variable (0 or 1) treating 0 as false or negative and 1 treated as true or positive test for diabetes. The synthetic data is obtained from Gaussian distribution. The results showed that there is presence of heterogeneity in the data by showing the presence of 2 sub-groups.

A robust self-supervised approach for fine-grained crack detection in concrete structures

This work addresses a critical issue: the deterioration of concrete structures due to fine-grained cracks, which compromises their strength and longevity. To tackle this problem, experts have turned to computer vision (CV) based automated strategies, incorporating object detection and image segmentation techniques. Recent efforts have integrated complex techniques such as deep convolutional neural networks (DCNNs) and transformers for this task. However, these techniques encounter challenges in localizing fine-grained cracks. This paper presents a self-supervised 'you only look once' (SS-YOLO) approach that utilizes a YOLOv8 model. The novel methodology amalgamates different attention approaches and pseudo-labeling techniques, effectively addressing challenges in fine-grained crack detection and segmentation in concrete structures. It utilizes convolution block attention (CBAM) and Gaussian adaptive weight distribution multi-head self-attention (GAWD-MHSA) modules to accurately identify and segment fine-grained cracks in concrete buildings. Additionally, the assimilation of curriculum learning-based self-supervised pseudo-labeling (CL-SSPL) enhances the model's ability when applied to limited-size data. The efficacy and viability of the proposed approach are demonstrated through experimentation, results, and ablation analysis. Experimental results indicate a mean average precision (mAP) of at least 90.01%, an F1 score of 87%, and an intersection over union threshold greater than 85%. It is evident from the results that the proposed method yielded at least 2.62% and 4.40% improvement in mAP and F1 values, respectively, when tested on three diverse datasets. Moreover, the inference time taken per image is 2 ms less than that of the compared methods.

Liouville models of particle-laden flow

Langevin (stochastic differential) equations are routinely used to describe particle-laden flows. They predict Gaussian probability density functions (PDFs) of a particle's trajectory and velocity, even though experimentally observed dynamics might be highly non-Gaussian. Our Liouville approach overcomes this dichotomy by replacing the Wiener process in the Langevin models with a (small) set of random variables, whose distributions are tuned to match the observed statistics. This strategy gives rise to an exact (deterministic, first-order, hyperbolic) Liouville equation that describes the evolution of a joint PDF in the augmented phase-space spanned by the random variables and the particle position and velocity. Analytical PDF solutions for canonical models of particle-laden flows serve to establish a relationship between the Langevin and Liouville approaches. Finally, our framework is used to derive a new analytical PDF model for fluidized homogeneous heating systems.

Hybrid Method of Uncertainty Propagation for Near-Earth Conjunction Analysis

In this research, several existing semi-analytical dynamics and uncertainty propagation techniques are combined with conjunction models to achieve fast and accurate probability of collision results. Initial Gaussian uncertainty associated with two objects is split into smaller Gaussian distributions using Gaussian mixture models to achieve mixture components that will maintain linearity over longer propagation times. These mixture components are propagated forward using second-order state transition tensors that can capture the nonlinearity in the propagation accurately by taking into account the desired dynamics. The dynamic solution and these tensors are computed using the Deprit–Lie averaging approach, including transformations between mean and osculating states, which accounts for perturbations due to solar radiation pressure and J2. This simplified dynamic system allows fast and accurate propagation by combining the speed of propagation with averaged dynamics and the accuracy of short-period variation addition. Combined, these mathematical tools are used to propagate the object’s uncertainties forward. The final distributions are compared using analytical conjunction methods to compute the probability of collision, which is then compared to the Monte Carlo result to confirm the method’s validity.

Deep Learning With Physics-Embedded Neural Network for Full Waveform Ultrasonic Brain Imaging.

The convenience, safety, and affordability of ultrasound imaging make it a vital non-invasive diagnostic technique for examining soft tissues. However, significant differences in acoustic impedance between the skull and soft tissues hinder the successful application of traditional ultrasound for brain imaging. In this study, we propose a physics-embedded neural network with deep learning based full waveform inversion (PEN-FWI), which can achieve reliable quantitative imaging of brain tissues. The network consists of two fundamental components: forward convolutional neural network (FCNN) and inversion sub-neural network (ISNN). The FCNN explores the nonlinear mapping relationship between the brain model and the wavefield, replacing the tedious wavefield calculation process based on the finite difference method. The ISNN implements the mapping from the wavefield to the model. PEN-FWI includes three iterative steps, each embedding the F CNN into the ISNN, ultimately achieving tomography from wavefield to brain models. Simulation and laboratory tests indicate that PEN-FWI can produce high-quality imaging of the skull and soft tissues, even starting from a homogeneous water model. PEN-FWI can achieve excellent imaging of clot models with constant uniform distribution of velocity, randomly Gaussian distribution of velocity, and irregularly shaped randomly distributed velocity. Robust differentiation can also be achieved for brain slices of various tissues and skulls, resulting in high-quality imaging. The imaging time for a horizontal cross-sectional imag e of the brain is only 1.13 seconds. This algorithm can effectively promote ultrasound-based brain tomography and provide feasible solutions in other fields.

Multi-Scale Object Detection in Remote Sensing Images Based on Feature Interaction and Gaussian Distribution

Remote sensing images are usually obtained from high-altitude observation. The spatial resolution of the images varies greatly and there are scale differences both between and within object classes, resulting in a diversified distribution of object scales. In order to solve these problems, we propose a novel object detection algorithm that maintains adaptability to multi-scale object detection based on feature interaction and Gaussian distribution in remote sensing images. The proposed multi-scale feature interaction model constructs feature interaction modules in the feature layer and spatial domain and combines them to fully utilize the spatial and semantic information of multi-level features. The proposed regression loss algorithm based on Gaussian distribution takes the normalized generalized Jensen–Shannon divergence with Gaussian angle loss as the regression loss function to ensure the scale invariance of the model. The experimental results demonstrate that our method achieves 77.29% mAP on the DOTA-v1.0 dataset and 97.95% mAP on the HRSC2016 dataset, which are, respectively, 1.12% and 1.41% higher than that of the baseline. These experimental results indicate the effectiveness of our method for object detection in remote sensing images.

Versatile Descent Algorithms for Group Regularization and Variable Selection in Generalized Linear Models

This paper proposes an adaptively bounded gradient descent (ABGD) algorithm for group elastic net penalized regression. Unlike previously proposed algorithms, the proposed algorithm adaptively bounds the Fisher information matrix, which results in a flexible and stable computational framework. In particular, the proposed algorithm (i) does not require orthogonalization of the predictors, and (ii) can be easily applied to any combination of exponential family response distribution and link function. The proposed algorithm is implemented in the grpnet R package (available from CRAN), which implements the approach for common response distributions (Gaussian, binomial, and Poisson), as well as several response distributions not previously considered in the group penalization literature (i.e., multinomial, negative binomial, gamma, and inverse Gaussian). Simulated and real data examples demonstrate that the proposed algorithm is as or more efficient than existing methods for Gaussian, binomial, and Poisson distributions. Furthermore, using two genomic examples, I demonstrate how the proposed algorithm can be applied to high-dimensional multinomial regression problems with grouped predictors. R code to reproduce the results is included as supplementary materials.

Thermodynamic work of partial resetting

Partial resetting, whereby a state variable x(t) is reset at random times to a value ax(t) , 0⩽a⩽1 , generalizes conventional resetting by introducing the resetting strength a as a parameter. Partial resetting generates a broad family of non-equilibrium steady states (NESS) that interpolates between the conventional NESS at strong resetting (a = 0) and a Gaussian distribution at weak resetting (a → 1). Here such resetting processes are studied from a thermodynamic perspective, and the mean cost associated with maintaining such NESS are derived. The resetting phase of the dynamics is implemented by a resetting potential Φ(x) that mediates the resets in finite time. By working in an ensemble of trajectories with a fixed number of resets, we study both the steady-state properties of the propagator and its moments. The thermodynamic work needed to sustain the resulting NESS is then investigated. We find that different resetting traps can give rise to rates of work with widely different dependencies on the resetting strength a. Surprisingly, in the case of resets mediated by a harmonic trap with otherwise free diffusive motion, the asymptotic rate of work is insensitive to the value of a. For general anharmonic traps, the asymptotic rate of work can be either increasing or decreasing as a function of the strength a, depending on the degree of anharmonicity. Counter to intuition, the rate of work can therefore in some cases increase as the resetting becomes weaker (a→1) although the work vanishes at a = 1. Work in the presence of a background potential is also considered. Numerical simulations confirm our findings.

A novel Bayesian computational approach for bridge-randomized quantile regression in high dimensional models

A bridge-randomized penalization that employs a prior for the shrinkage parameter, as opposed to the conventional bridge penalization with a fixed penalty, often delivers more superior performance compared to many other traditional shrinkage methods. In this paper, we develop an efficient Bayesian computational algorithm via the two-block Markov Chain Monte Carlo method for the bridge-randomized penalization in quantile regression to perform inference in the high-dimensional ‘large-p’ and ‘large-p-small-n’ settings. To construct a fully Bayesian formulation, we utilize the asymmetric Laplace distribution as an auxiliary error distribution and the generalized Gaussian distribution prior for the regression coefficients. Simulation studies encompassing a wide range of scenarios indicate that the proposed method performs at least as well as, and often better than, other existing procedures in terms of both parameter estimation and variable selection. Finally, a real-data application is provided for illustrative purposes.

Exploring translational approaches for fully biological cardiac rhythm restoration through ion channel gene therapy

Abstract Funding Acknowledgements Type of funding sources: Public grant(s) – EU funding. Main funding source(s): European Research Council (Starting grant 716509) to D.A. Pijnappels Background Recently it was demonstrated how the heart itself could be enabled to quickly restore its rhythm by realizing a biologically-integrated cardiac defibrillator (BioICD) through modification and subsequent expression of ion channels in cardiomyocytes [1]. By incorporating these frequency-dependent depolarizing ion channels, abnormal cardiac rhythm could be rapidly detected and terminated to restore sinus rhythm in a fully biological and shock-free manner. However, from a translational point of view, it remains unclear how such rhythm restoration can be realized via ion channel gene therapy. Purpose To explore and understand the importance of the distribution and number of BioICD-expressing cardiomyocytes in realizing fully biological restoration of cardiac rhythm. Methods To this purpose, two different realistic gene therapy configurations, i.e. those corresponding to systemic and local transgene delivery, were tested in a digital twin of human ventricular cardiac monolayers. In the systemic delivery group, BioICD-expressing cells were uniformly distributed over the tissue at different total expression percentages. In the local delivery group, circular areas were populated with BioICD-expressing cells, randomly arranged in a Gaussian distribution. Spiral waves were initiated in both groups and studied for 10 seconds. An additional set of simulations for the systemic delivery group involved an adapted BioICD ion channel with a slower opening and faster closing rate. Results Upon comparing both gene therapy methods, the systemic approach showed a gradually increasing arrhythmia termination chance with increasing BioICD-expression percentage, while local delivery did not result in termination. Instead, local delivery resulted in islands of ionic heterogeneity, causing attraction and anchoring of the spiral waves in a size and distance-dependent manner. Building on the results of the systemic approach, different ion channel parameters were tried, which resulted in normal rhythm being restored in all cases for &amp;gt;50% BioICD expressing cells. Time till termination was inversely related to the percentage, resulting in only 4.3s and 2.5s for 50% and 100%, respectively. Regarding termination, it was observed that conduction blocks appeared throughout the tissue and subsequently connected to force arrhythmic waves to terminate, while this process remained incomplete in the &amp;lt;50% groups. Conclusion This study reveals that wide-spread distribution of BioICD-expressing cardiomyocytes is required for the realization of fully biological self-restoration of cardiac rhythm, of which the efficiency is ion-channel-dynamics- and dosage-dependent. Local expression, however, results in stabilization of spiral wave activity. Further exploration of this emerging concept of biological cardioversion may not only expand our understanding of cardiac arrhythmias, but also pave the way to breakthrough advances in arrhythmia management.