Gaussian Distribution Research Articles

Cluster-Based Oversampling with Area Extraction from Representative Points for Class Imbalance Learning

Class imbalance learning is challenging in various domains where training datasets exhibit disproportionate samples in a specific class. Resampling methods have been used to adjust the class distribution, but they often have limitations for small disjunct minority subsets. This paper introduces AROSS, an adaptive cluster-based oversampling approach that addresses these limitations. AROSS utilizes an optimized agglomerative clustering algorithm with the Cophenetic Correlation Coefficient and the Bayesian Information Criterion to identify representative areas of the minority class. Safe and half-safe areas are obtained using an incremental k-Nearest Neighbor strategy, and oversampling is performed with a truncated hyperspherical Gaussian distribution. Experimental evaluations on 70 binary datasets demonstrate the effectiveness of AROSS in improving class imbalance learning performance, making it a promising solution for mitigating class imbalance challenges, especially for small disjunct minority subsets.

The role of asymptomatic carriers on the dynamics of a lymphatic filariasis model incorporating control strategies

This study presents a mathematical model to investigate the patterns of transmission in lymphatic filariasis. The model considers chronic, acute, and asymptomatic individuals and integrates key control strategies. Random synthetic data is generated robustly through numerical solutions to closely replicate real-world scenarios and encompass uncertainties. The synthetic data adheres to a Gaussian distribution to ensure validity and reliability. Following the derivation of the basic and effective reproduction number using the next generation matrix approach, Latin Hypercube Sampling (LHS) and the Partial Rank Correlation Coefficient (PRCC) algorithm is utilized to assess the parameters that significantly influence the model outputs. The study examine the trajectories of different population compartments through numerical simulations over time, with particular emphasis on the role played by asymptomatic individuals in the transmission of the disease. To assess the potential for disease elimination, the study introduces a range of strategies involving protective measures, treatment interventions, and mosquito control. These strategies are determined through sensitivity analysis. The findings demonstrate that the simultaneous implementation of all control measures has a noteworthy effect in managing lymphatic filariasis. In conclusion, the proposed model enhances understanding of lymphatic filariasis dynamics and informs effective control strategies.

Predictive Model for EV Charging Load Incorporating Multimodal Travel Behavior and Microscopic Traffic Simulation

A predictive model for the spatiotemporal distribution of electric vehicle (EV) charging load is proposed in this paper, considering multimodal travel behavior and microscopic traffic simulation. Firstly, the characteristic variables of travel time are fitted using advanced techniques such as Gaussian mixture distribution. Simultaneously, the user’s multimodal travel behavior is delineated by introducing travel purpose transfer probabilities, thus establishing a comprehensive travel spatiotemporal model. Secondly, the improved Floyd algorithm is employed to select the optimal path, taking into account various factors including signal light status, vehicle speed, and the position of starting and ending sections. Moreover, the approach of multi-lane lane change following and the utilization of cellular automata theory are introduced. To establish a microscopic traffic simulation model, a real-time energy consumption model is integrated with the aforementioned techniques. Thirdly, the minimum regret value is leveraged in conjunction with various other factors, including driving purpose, charging station electricity price, parking cost, and more, to simulate the decision-making process of users regarding charging stations. Subsequently, an EV charging load predictive framework is proposed based on the approach driven by electricity prices and real-time interaction of coupled network information. Finally, this paper conducts large-scale simulations to analyze the spatiotemporal distribution characteristics of EV charging load using a regional transportation network in East China and a typical power distribution network as case studies, thereby validating the feasibility of the proposed method.

Investigation of fibre distribution and orientation in SFRC specimens and their influence on flexural properties

The distribution and orientation of fibres were qualitatively estimated using statistical methods, and finite element analysis was conducted to evaluate the flexural behaviours based on these characteristics. The results demonstrate that the fibres disperse well in the concrete matrix when the water-to-binder ratio is 0.35, and the concrete mixture is prepared by sequentially adding coarse/fine aggregates, powder materials, water and steel fibres. In contrast to the order of fibre addition, the water-to-binder ratio significantly influences the fibre distribution coefficient and orientation factor. A water-to-binder ratio of 0.35 results in a higher orientation factor ( gh) of 0.7. Furthermore, statistical analysis reveals that the orientation of fibres on the cutting section follows a Gaussian distribution, with the peak occurring at approximately 40° to 50°. Finite element analysis revealed that the orientation distribution of fibre affects not only the flexural strength, more significantly, the post-cracking flexural stiffness.

Learning Robust and Sparse Principal Components with the α-Divergence.

In this paper, novel robust principal component analysis (RPCA) methods are proposed to exploit the local structure of datasets. The proposed methods are derived by minimizing the α-divergence between the sample distribution and the Gaussian density model. The α-divergence is used in different frameworks to represent variants of RPCA approaches including orthogonal, non-orthogonal, and sparse methods. We show that the classical PCA is a special case of our proposed methods where the α-divergence is reduced to the Kullback-Leibler (KL) divergence. It is shown in simulations that the proposed approaches recover the underlying principal components (PCs) by down-weighting the importance of structured and unstructured outliers. Furthermore, using simulated data, it is shown that the proposed methods can be applied to fMRI signal recovery and Foreground-Background (FB) separation in video analysis. Results on real world problems of FB separation as well as image reconstruction are also provided.

Generalized fused Lasso for grouped data in generalized linear models

Generalized fused Lasso (GFL) is a powerful method based on adjacent relationships or the network structure of data. It is used in a number of research areas, including clustering, discrete smoothing, and spatio-temporal analysis. When applying GFL, the specific optimization method used is an important issue. In generalized linear models, efficient algorithms based on the coordinate descent method have been developed for trend filtering under the binomial and Poisson distributions. However, to apply GFL to other distributions, such as the negative binomial distribution, which is used to deal with overdispersion in the Poisson distribution, or the gamma and inverse Gaussian distributions, which are used for positive continuous data, an algorithm for each individual distribution must be developed. To unify GFL for distributions in the exponential family, this paper proposes a coordinate descent algorithm for generalized linear models. To illustrate the method, a real data example of spatio-temporal analysis is provided.

Translational exploration of fully biological restoration of cardiac rhythm via ion channel gene therapy

Abstract 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. For the systemic delivery group, BioICD-expressing cells were homogeneously distributed over the tissue with fixed total expression percentage. For the local delivery group, circular areas were given BioICD-expressing cells, randomly patterned in a Gaussian distribution. In both groups spiral waves were initiated and subsequently studied for 10 seconds. For systemic delivery, an additional set of simulations was performed for 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 >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 <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.

Enhancing Broiler Weight Estimation through Gaussian Kernel Density Estimation Modeling

The management of individual weights in broiler farming is not only crucial for increasing farm income but also directly linked to the revenue growth of integrated broiler companies, necessitating prompt resolution. This paper proposes a model to estimate daily average broiler weights using time and weight data collected through scales. In the proposed model, a method of self-adjusting weights in the bandwidth calculation formula is employed, and the daily average weight representative value is estimated using KDE. The focus of this study is to contribute to the individual weight management of broilers by intensively researching daily fluctuations in average broiler weight. To address this, weight and time data are collected and preprocessed through scales. The Gaussian kernel density estimation model proposed in this paper aims to estimate the representative value of the daily average weight of a single broiler using statistical estimation methods, allowing for self-adjustment of bandwidth values. When applied to the dataset collected through scales, the proposed Gaussian kernel density estimation model with self-adjustable bandwidth values confirmed that the estimated daily weight did not deviate beyond the error range of ±50 g compared with the actual measured values. The next step of this study is to systematically understand the impact of the broiler environment on weight for sustainable management strategies for broiler demand, derive optimal rearing conditions for each farm by combining location and weight data, and develop a model for predicting daily average weight values. The ultimate goal is to develop an artificial intelligence model suitable for weight management systems by utilizing the estimated daily average weight of a single broiler even in the presence of error data collected from multiple weight measurements, enabling more efficient automatic measurement of broiler weight and supporting both farms and broiler demand.

A Review on Laser Beam Shaping Application in Laser Powder Bed Fusion

Laser powder bed fusion (L‐PBF) is extensively adopted in the aerospace and automobile industries for producing metallic components. The L‐PBF process involves rapid melting and solidification of metallic powders using a laser source to produce dense parts. Most industrial L‐PBF systems use a fiber‐based laser source that emits a Gaussian beam distribution. However, the conventional Gaussian beam used in L‐PBF processes presents inherent limitations that can impact the quality and properties of the final products. This review aims to provide a theoretical background of laser beam shaping techniques and explores the application of alternative beam shapes in L‐PBF. It investigates how different beam profiles affect the melt pool geometry, process stability, productivity, mechanical properties, microstructure, and surface roughness of fabricated parts. Additionally, it discusses different types of beam‐shaping techniques and elements utilized to generate distinct beam shapes. Furthermore, different constraints and limitations that hinder the full exploitation of beam shaping are critically discussed. By analyzing the impact of beam shaping in L‐PBF, this review provides insight into optimizing the AM process, enhancing part quality, and improving processing performance. It will also help readers to overview the research gaps, challenges, and promising future directions in laser beam shaping applications in L‐PBF.This review comprehensively covers and presents the current research trend of laser beam shaping applications in L‐PBF. It delves into the opportunities, challenges, limitations, and futures prospects of beam shaping applications. Furthermore, presents the methods and techniques used to modulate the laser beam profile, including spatial and temporal.This article is protected by copyright. All rights reserved.

GMConv: Modulating Effective Receptive Fields for Convolutional Kernels.

In convolutional neural networks (CNNs), the convolutions are conventionally performed using a square kernel with a fixed N × N receptive field (RF). However, what matters most to the network is the effective receptive field (ERF), which indicates the extent to which input pixels contribute to an output pixel. Inspired by the property that ERFs typically exhibit a Gaussian distribution, we propose a Gaussian Mask convolutional kernel (GMConv). Specifically, GMConv utilizes the Gaussian function to generate a concentric symmetry mask that is placed over the kernel to refine the RF. We analyze the RFs of CNN kernels in different CNN layers and evaluate our approach through extensive experiments on image classification and object detection tasks. Over several tasks and standard base models, our approach compares favorably against the standard convolution. For instance, using GMConv for AlexNet and ResNet-50, the top-1 accuracy on ImageNet classification is boosted by 0.98% and 0.85% , respectively.

“The “Vector-Model” Wavefunction: spatial description and wavepacket formation of quantum-mechanical angular momenta”

Abstract We introduce the concept of an asymptotic spatial angular-momentum wavefunction, X_m^j (φ,θ,χ)=Exp[imφ] δ(θ-θ_m ) Exp[i(j+1/2)χ], which treats j in the |jm⟩ state as a three-dimensional entity; φ, θ, χ are the Euler angles, and θ_m is the Vector-Model polar angle, given by cos⁡θ_m =m/|j|. A wealth of geometric information about j can be deduced from the eigenvalues and spatial transformation properties of the X_m^j (φ,θ,χ). Specifically, the X_m^j (φ,θ,χ) wavefunctions give 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 X_m^j (φ,θ,χ) also predict 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 X_m^j (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 X_m^j (φ,θ,χ) give a useful spatial description of quantum-mechanical angular momentum, and provide a smooth connection with classical angular momentum.

Effect of the global electroneutrality condition on electromigration Taylor-Aris dispersion in a microcapillary with finite Debye layer thickness.

In this work, the electromigration dispersion (EMD) due to the charged electrolytes in microchannels is considered without using the thin electrical double layer assumption. The electrokinetic flow and transport of ions are actuated within a rectangular micro-/nanochannel having a negative surface charge density under the influence of an external electric field. Due to the local variation of the conductivity and the nonvalidity of the electroneutrality condition, the local electric field varies as a function of the solute concentration, wall surface charge density, valency, and Debye layer length. The resulting electrokinetic flow due to the external electric field drives the fluid along with the charged species, where the Taylor-Aris dispersion separates the solutes into their different constituents. The local concentration dependence of the electric field leads to the formation of concentration profiles that are slightly asymmetric with respect to the standard Gaussian distribution. Including a finite Debye layer thickness has an effect on the advection of the species as well as the diffusion of the species. It is found that in cases where Debye layers are thicker, the species advects faster within the microchannel. This might give valuable insights into the nature of the EMD. Our model aims to predict the evolution of ionic concentration at all positions within the channel. A study of the higher-order statistics in skewness and kurtosis has also been conducted to obtain a better understanding of the idealized model consisting of a buffer solution.

An improved GNSS ambiguity best integer equivariant estimation method with Laplacian distribution for urban low-cost RTK positioning

The integer least squares (ILS) estimation is commonly used for carrier phase ambiguity resolution (AR). More recently, the best integer equivariant (BIE) estimation has also attracted an attention for complex application scenarios, which exhibits higher reliability by a weighted fusion of integer candidates. However, traditional BIE estimation with Gaussian distribution (GBIE) faces challenges in fully utilizing the advantages of BIE for urban low-cost positioning, mainly due to the presence of outliers and unmodeled errors. To this end, an improved BIE estimation method with Laplacian distribution (LBIE) is proposed, and several key issues are discussed, including the weight function of LBIE, determination of the candidates included based on the OIA test, and derivation of the variance of LBIE solutions for reliability evaluation. The results show that the proposed LBIE method has the positioning accuracy similar to the BIE using multivariate t-distribution (TBIE), and significantly outperforms the ILS-PAR and GBIE methods. In an urban expressway test with a Huawei Mate40 smartphone, the LBIE method has positioning errors of less than 0.5 m in three directions and obtains over 50% improvements compared to the ILS-PAR and GBIE methods. In an urban canyon test with a low-cost receiver STA8100 produced by STMicroelectronics, the positioning accuracy of LBIE in three directions is 0.112 m, 0.107 m, and 0.252 m, respectively, with improvements of 17.6%, 27.2%, and 26.1% compared to GBIE, and 23.3%, 28.2%, and 30.6% compared to ILS-PAR. Moreover, its computational time increases by 30–40% compared to ILS-PAR and is approximately half of that using TBIE.

REAL ANALYTIC DISCRETE CHOICE MODELS OF DEMAND: THEORY AND IMPLICATIONS

We demonstrate that a large class of discrete choice models of demand can be approximated by real analytic demand models. We obtain this result by combining (i) a novel real analytic property of the mixed logit and the mixed probit models with any distribution of random coefficients and (ii) an approximation property of finite mixtures of Gumbel and Gaussian distributions. To illustrate some of the implications of this result, we discuss how real analyticity facilitates nonparametric and semi-nonparametric identification, extrapolation to hypothetical counterfactuals, numerical implementation of demand inverses, and numerical implementation of the maximum likelihood estimator.

Normal quantum channels and Markovian correlated two-qubit quantum errors

We study general ‘normally’ (Gaussian) distributed random unitary transformations. These distributions can be defined in terms of a diffusive random walk in the respective group manifold. On the one hand, a Gaussian distribution induces a unital quantum channel, which we will call ‘normal’. On the other hand, the diffusive random walk defines a unital quantum process, generated by a Lindblad master equation. In the single qubit case, we show different distributions may induce the same quantum channel.In the case of two qubits, we study normal quantum channels, induced by Gaussian distributions in SU(2)⊗SU(2) . They provide an appropriate framework for modeling quantum errors with classical correlations. In contrast to correlated Pauli errors, for instance, they conserve their Markovianity, and they lead to very different results in error correcting codes. This is illustrated with an application to entanglement distillation.

Determination of dynamic collapse limit states using the energy-based method for multi-story RC frames subjected to column removal scenarios

The Alternative Load Path method is widely adopted to perform progressive collapse analyses for reinforced concrete (RC) frame structures subjected to column removal scenarios. Considering that the progressive collapses are usually dynamic phenomena, nonlinear dynamic analyses can yield the most accurate results. However, the associated computational cost is high. Alternatively, the energy-based method (EBM) can be employed to efficiently calculate the maximum dynamic responses. Unfortunately, collapse or dynamic limit states (DLS) cannot be directly determined when the EBM is adopted for the progressive collapse analyses, because it is essentially a quasi-static approach. To tackle this issue, in this paper an EBM-Intersection Point-based (EBM-IP-based) method is proposed to effectively determine the DLS. The method is considering that the dynamic instability will occur once the dynamic capacity curve exceeds the corresponding static capacity curve. Hence, it is possible to determine the DLS by making a correction on the intersection point of the aforementioned two curves without performing nonlinear dynamic time-history analyses. Compared with the other energy components, the kinetic energy at the moment of the peak displacement response is relatively small and the effectiveness of the EBM is verified. Through both static pushdown analyses and incremental dynamic analyses for 48 column removal scenarios of six different multi-story RC frames, the effectiveness of the proposed EBM-IP-based method is verified and the associated coefficients are calibrated. Statistical information and (joint) probabilistic density functions (PDF) of the coefficients are identified. Further, stochastic analyses are carried out in order to quantify the model uncertainties when adopting the EBM-IP-based method. On the basis of all the calculation results, a Gumbel distribution is adopted to capture the PDF of the model uncertainty in relation to displacements, while a lognormal distribution is adopted to fit the PDF of the model uncertainty in terms of resistances. Moreover, a multi-variate Gaussian distribution model with two components is employed to fit the joint PDF.

DynamicAug: Enhancing Transfer Learning Through Dynamic Data Augmentation Strategies Based on Model State

Transfer learning has made significant advancements, however, the issue of overfitting continues to pose a major challenge. Data augmentation has emerged as a highly promising technique to counteract this challenge. Current data augmentation methods are fixed in nature, requiring manual determination of the appropriate intensity prior to the training process. However, this entails substantial computational costs. Additionally, as the model approaches convergence, static data augmentation strategies can become suboptimal. In this paper, we introduce the concept of Dynamic Data Augmentation (DynamicAug), a method that autonomously adjusts the intensity of data augmentation, taking into account the convergence state of the model. During each iteration of the model’s forward pass, we utilize a Gaussian distribution based sampler to stochastically sample the current intensity of data augmentation. To ensure that the sampled intensity is aligned with the convergence state of the model, we introduce a learnable expectation to the sampler and update the expectation iteratively. In order to assess the convergence status of the model, we introduce a novel loss function called the convergence loss. Through extensive experiments conducted over 27 vision datasets, we have demonstrated that DynamicAug can significantly enhance the performance of existing transfer learning methods.

A new analytical wind turbine wake model considering the effects of coriolis force and yawed conditions

Wind turbine wakes significantly affect power production and impose higher loads on downstream turbines. Therefore, the development of accurate and efficient wake models is important for optimizing wind farm layouts and predicting wind turbine performance. This study introduces a novel analytical wake model for yawed wind turbines that incorporates the effects of the Coriolis force. The wake deflection in the far wake region is derived through the application of the principles of mass and momentum conservation. In the near wake, the deflection is assumed to be linear with distance. A Gaussian distribution is assumed for the velocity deficit within the wind turbine wake. Two approaches have been proposed to estimate the onset of the far wake region. While the first approach employs a simplified empirical formula, the second approach utilizes an iteration-based method. The proposed analytical wake model has been validated against computational fluid dynamics (CFD) results. Subsequently, the effects of several important parameters on the wake deflection have been systematically investigated. Overall, the simulation results showed a satisfactory agreement between the CFD results and those obtained from the proposed model. Furthermore, the study concluded that the Coriolis force can exert significant effects on wake deflection, particularly in the far wake region, confirming previous findings from numerical simulations. Due to its simplicity and computational efficiency, the proposed model can be readily used in several applications, including wind farm layout optimization, control and risk assessment.

Predictive Modelling on Competitor Analysis Performance by using Generalised Linear Models and Machine Learning Approach

Competitive analysis in digital and technology is trending in the business field. However, the field of digital and technology in the business world is vast and challenging to analyse. The purpose of this research is first to identify the success factor which represent the company performance. Second, is to identify the significant services provided by the company to their business user. Then, based on the first and second objectives, a predictive modelling is developed to produce the best solution to their business user. The research is implementing a case study from Telecommunication Company and using data science life cycle methodology. The statistical modelling that is used to develop the competitor’s analysis model is generalised linear model (GLM) which integrated with machine learning approach. Furthermore, the synthetic data set is created by using Gamma Distribution, Gaussian Distribution and Poisson Distribution due to some data from the case study is confidential. The synthetic data set is based on existing real data which are from Telecommunication Company sentiment analysis data, were used to investigate the performance of the proposed model. The machine learning technique is used to get the accuracy of the significant GLM which has been developed. The accuracy is tested by using the error rates of the machine learning technique which are Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and R-squared. This research discovered that the business solution to the significant service for the business user and discovered the best statistical model to be used for the business solution. The results show that the Gumbel distribution is the best fit model for the synthetic dataset where the values of RMSE is 1.0574, MAE is 0.9168 and R-squared is 0.3994, and the significant success factor that has been identified by using the GLM is advertising success factor. The model developed can be improved with another type of data set and different sizes of data. Hence, further studies and real-world data are required for better validation.

Blind Super-Resolution Via Meta-Learning and Markov Chain Monte Carlo Simulation.

Learning based approaches have witnessed great successes in blind single image super-resolution (SISR) tasks, however, handcrafted kernel priors and learning based kernel priors are typically required. In this paper, we propose a Meta-learning and Markov Chain Monte Carlo based SISR approach to learn kernel priors from organized randomness. In concrete, a lightweight network is adopted as kernel generator, and is optimized via learning from the MCMC simulation on random Gaussian distributions. This procedure provides an approximation for the rational blur kernel, and introduces a network-level Langevin dynamics into SISR optimization processes, which contributes to preventing bad local optimal solutions for kernel estimation. Meanwhile, a meta-learning based alternating optimization procedure is proposed to optimize the kernel generator and image restorer, respectively. In contrast to the conventional alternating minimization strategy, a meta-learning based framework is applied to learn an adaptive optimization strategy, which is less-greedy and results in better convergence performance. These two procedures are iteratively processed in a plug-and-play fashion, for the first time, realizing a learning-based but plug-and-play blind SISR solution in unsupervised inference. Extensive simulations demonstrate the superior performance and generalization ability of the proposed approach when comparing with state-of-the-arts on synthesis and real-world datasets.