Probability Distribution Of Distance Research Articles

A novel Hellinger distance-based regret theory method for spherical fuzzy decision making model and its application in logistics

Actual decision making problems are often based on the company decision maker’s behavior factors, such as risk attitude, subjective preference, etc. Regret theory can well express the behavior of the decision maker. In this pursuit, a novel decision making method was developed, based on the regret theory for the multi-attribute decision making problem, in which attribute values were expressed by spherical fuzzy numbers. Distance measurement not only has extensive applications in fields such as pattern recognition and image processing, but also plays an important role in the research of fuzzy decision theory. The existing distance measures of spherical fuzzy set either have special cases of anti-intuition or are more complex in calculation, so finding suitable distance measures is also an important research topic in the decision-making theory of spherical fuzzy set. For this reason, we first establish a new distance of spherical fuzzy sets based on Hellinger distance of probability distribution. A decision maker’s perception utility value function is proposed using the new distance formula, which is used to measure the regretful and rejoice value. Then we establish an optimization model for solving the attribute weights, when the information of attribute weight was partially known. Subsequently, the comprehensive perceived utility values were utilized to rank the order of the alternatives. Finally, a numerical example of assessment of logistics providers is used to show that the new decision making method is effective and feasible.

Lightweight Knowledge Distillation-Based Transfer Learning Framework for Rolling Bearing Fault Diagnosis.

Compared to fault diagnosis across operating conditions, the differences in data distribution between devices are more pronounced and better aligned with practical application needs. However, current research on transfer learning inadequately addresses fault diagnosis issues across devices. To better balance the relationship between computational resources and diagnostic accuracy, a knowledge distillation-based lightweight transfer learning framework for rolling bearing diagnosis is proposed in this study. Specifically, a deep teacher-student model based on variable-scale residual networks is constructed to learn domain-invariant features relevant to fault classification within both the source and target domain data. Subsequently, a knowledge distillation framework incorporating a temperature factor is established to transfer fault features learned by the large teacher model in the source domain to the smaller student model, thereby reducing computational and parameter overhead. Finally, a multi-kernel domain adaptation method is employed to capture the feature probability distribution distance of fault characteristics between the source and target domains in Reproducing Kernel Hilbert Space (RKHS), and domain-invariant features are learned by minimizing the distribution distance between them. The effectiveness and applicability of the proposed method in situations of incomplete data across device types were validated through two engineering cases, spanning device models and transitioning from laboratory equipment to real-world operational devices.

Approximating Projections of Conformational Boltzmann Distributions with AlphaFold2 Predictions: Opportunities and Limitations.

Protein thermodynamics is intimately tied to biological function and can enable processes such as signal transduction, enzyme catalysis, and molecular recognition. The relative free energies of conformations that contribute to these functional equilibria evolved for the physiology of the organism. Despite the importance of these equilibria for understanding biological function and developing treatments for disease, computational and experimental methods capable of quantifying the energetic determinants of these equilibria are limited to systems of modest size. Recently, it has been demonstrated that the artificial intelligence system AlphaFold2 can be manipulated to produce structurally valid protein conformational ensembles. Here, we extend these studies and explore the extent to which AlphaFold2 contact distance distributions can approximate projections of the conformational Boltzmann distributions. For this purpose, we examine the joint probability distributions of inter-residue contact distances along functionally relevant collective variables of several protein systems. Our studies suggest that AlphaFold2 normalized contact distance distributions can correlate with conformation probabilities obtained with other methods but that they suffer from peak broadening. We also find that the AlphaFold2 contact distance distributions can be sensitive to point mutations. Overall, we anticipate that our findings will be valuable as the community seeks to model the thermodynamics of conformational changes in large biomolecular systems.

Probability distribution of dependency distance and dependency type in translational language

As a “third code”, translational language attracts considerable attention in linguistics research due to its distinctive features. Adopting the quantitative linguistic approach, the current study examines its features by investigating the mean dependency distance (MDD), as well as the probability distribution of the individual dependency distances (DDs) and distribution of a high-frequency dependency type in translational language. The MDD and the distributions were tested in a self-built corpus which contains parallel and comparable language materials in both Chinese-English and English-Chinese translations. The results show that: (1) compared with source texts and native texts, translated texts in both translation directions yield an MDD in between; (2) both the distribution of DDs and that of the dependency type nsubj follow the Zipf-Alekseev distribution in translated texts, as in source texts and native texts; (3) the in-between feature is further confirmed by parameters a and b in Chinese-English translation materials when fitting the distribution of DDs to Zipf-Alekseev distribution; (4) translational texts in both directions show higher a and lower b than their source and native texts when fitting the DD Distribution of dependency type nsubj to Zipf-Alekseev distribution. These findings suggest that, on the one hand, dependency distance minimization (DDM) occurs in translational language, which is consistent with native language and reflects a general tendency of natural languages to reduce cognitive load; on the other hand, translational language presents distinctive feature in nsubj type, but in most cases, it is subject to the gravitational pull of both source and target language systems, exhibiting a “compromise” feature in between. The current study highlights the contribution of syntactic quantitative methods to deeper understanding of the complexity of translational language and its cognitive underpinnings.

Unveiling local and global conformational changes and allosteric communications in SOD1 systems using molecular dynamics simulation and network analyses

BackgroundAmyotrophic lateral sclerosis (ALS) is a serious neurodegenerative disorder affecting nerve cells in the brain and spinal cord that is caused by mutations in the superoxide dismutase 1 (SOD1) enzyme. ALS-related mutations cause misfolding, dimerisation instability, and increased formation of aggregates. The underlying allosteric mechanisms, however, remain obscure as far as details of their fundamental atomistic structure are concerned. Hence, this gap in knowledge limits the development of novel SOD1 inhibitors and the understanding of how disease-associated mutations in distal sites affect enzyme activity.Methods: We combined microsecond-scale based unbiased molecular dynamics (MD) simulation with network analysis to elucidate the local and global conformational changes and allosteric communications in SOD1 Apo (unmetallated form), Holo, Apo_CallA (mutant and unmetallated form), and Holo_CallA (mutant form) systems. To identify hotspot residues involved in SOD1 signalling and allosteric communications, we performed network centrality, community network, and path analyses.Results: Structural analyses showed that unmetallated SOD1 systems and cysteine mutations displayed large structural variations in the catalytic sites, affecting structural stability. Inter- and intra H-bond analyses identified several important residues crucial for maintaining interfacial stability, structural stability, and enzyme catalysis. Dynamic motion analysis demonstrated more balanced atomic displacement and highly correlated motions in the Holo system. The rationale for structural disparity observed in the disulfide bond formation and R143 configuration in Apo and Holo systems were elucidated using distance and dihedral probability distribution analyses.Conclusion: Our study highlights the efficiency of combining extensive MD simulations with network analyses to unravel the features of protein allostery.

Investigating comparisons on the coal and gangue in various scenarios using multidimensional image features

Online intelligent recognition of coal and gangue is an important aspect of coal mine intelligent development. Current research focuses more on improving recognition accuracy through optimizing image processing algorithms, but there is limited research on the characteristics of coal gangue materials themselves, particularly the comparative analysis of their appearance in images under different scenarios. Therefore, this paper proposes a multi-dimensional feature-based analysis method for coal-gangue images, which can be used to evaluate the characteristics and distinguishability of coal and gangue images. Firstly, the original feature space of coal and gangue images is constructed based on 55 global image feature operators. Then, the characteristics of coal and gangue images in both the original space and the two-dimensional space after dimensionality reduction are analyzed using the similarity between the left and right sides of the split violin plot and the distance of probability distributions. At the same time, different types of features are compared and analyzed in terms of their impact on classification performance when used as inputs with various machine learning classifiers. Furthermore, by leveraging the interpretability of tree models, the contribution of different feature types to coal gangue classification tasks is analyzed. The proposed method is applied to analyze a large number of raw coal images collected from three different conditions. The experimental results demonstrate that the distinguishability of coal gangue images varies under different scenarios, and the distance between the two distributions in the reduced space effectively measures this distinguishability. In coal gangue images, the contribution of color features and texture features to the classification task is related to the type of coal, with texture features playing a more significant role in classifying coking coal compared to thermal coal. However, overall, color features dominate the classification task. These findings are further validated in experiments using machine learning classifiers, which are crucial for designing more refined classification algorithms.

Visualization of concrete internal defects based on unsupervised domain adaptation algorithm for transfer learning of experiment-simulation hybrid dataset of impact echo signals

Detecting concrete internal defects through deep learning analysis of impact echo signals faces two challenges: (1) the traditional signal processing method such as wavelet transform (WT) fails to reflect data-sensitive damage characteristics due to the uncertainty principle and (2) the limited labeled data acquired from real structures impedes network training. To address the first challenge, this paper proposes the WT-based synchrosqueezing transform (WT-SST) for the conversion of time-series data to the time-frequency spectrogram, which can provide effective features for the network in time and frequency domains simultaneously. To overcome the second challenge, numerical simulation data are supplemented for the augment of labeled data. To minimize the effect of data variance between experiments and simulations, this paper uses an unsupervised domain adaptation (DA) network for the transfer training of labeled simulation data (original domain) and unlabeled experimental data (target domain). The DA network extracts domain-invariant features by maximizing the domain recognition error and minimizing the probability distribution distance. The damage probability is calculated by the trained model to produce a 2D defect contour image of concrete specimens, and the three-dimensional visualization of internal defects by estimating the defect depth based on the defect area of contour image. Finally, the recognition precision, recall, F1-score, and accuracy of the model of unsupervised DA network trained by a hybrid dataset reaches 89.4%, 88.4%, 88.9%, and 94.7%, respectively.

The correlation parameter of renewal processes and structures with positive and negative periodicity

The correlation parameter (CP) as a generalization of the concepts of correlation time and correlation length is calculated for the renewal point structure by studying the spectral density. This structure is a generalization of the renewal process and is characterized by the probability distribution of distances between neighboring points. These distances can be negative. A non-monotonic dependence of the CP on the periodicity parameter is obtained. The results of calculating CPs using spectral densities for various renewal structures are in good agreement with the results of the general formula for quasi-symmetric distributions.

A Probabilistic Transformation of Distance-Based Outliers

The scores of distance-based outlier detection methods are difficult to interpret, and it is challenging to determine a suitable cut-off threshold between normal and outlier data points without additional context. We describe a generic transformation of distance-based outlier scores into interpretable, probabilistic estimates. The transformation is ranking-stable and increases the contrast between normal and outlier data points. Determining distance relationships between data points is necessary to identify the nearest-neighbor relationships in the data, yet most of the computed distances are typically discarded. We show that the distances to other data points can be used to model distance probability distributions and, subsequently, use the distributions to turn distance-based outlier scores into outlier probabilities. Over a variety of tabular and image benchmark datasets, we show that the probabilistic transformation does not impact outlier ranking (ROC AUC) or detection performance (AP, F1), and increases the contrast between normal and outlier score distributions (statistical distance). The experimental findings indicate that it is possible to transform distance-based outlier scores into interpretable probabilities with increased contrast between normal and outlier samples. Our work generalizes to a wide range of distance-based outlier detection methods, and, because existing distance computations are used, it adds no significant computational overhead.

Intermediate-aided allostery mechanism for α-glucosidase by Xanthene-11v as an inhibitor using residue interaction network analysis

Exploring allosteric inhibition and the discovery of new inhibitor binding sites are important studies in protein regulation mechanisms and drug discovery. Structural and network-based analyses of trajectories resulting from molecular dynamics (MD) simulations have been developed to discover protein dynamics, landscape, functions, and allosteric regions. Here, an experimentally suggested non-competitive inhibitor, xanthene-11v, was considered to explore its allosteric inhibition mechanism in α-glucosidase MAL12. Comparative structural and network analyses were applied to eight 250 ns independent MD simulations, four of which were performed in the free state and four of which were performed in ligand-bound forms. Projected two-dimensional free energy landscapes (FEL) were constructed from the probabilistic distribution of conformations along the first two principal components. The post-simulation analyses of the coordinates, side-chain torsion angles, non-covalent interaction networks, network communities, and their centralities were performed on α-glucosidase conformations and the intermediate sub-states. Important communities of residues have been found that connect the allosteric site to the active site. Some of these residues like Thr307, Arg312, TYR344, ILE345, Phe357, Asp406, Val407, Asp408, and Leu436 are the key messengers in the transition pathway between allosteric and active sites. Evaluating the probability distribution of distances between gate residues including Val407 in one community and Phe158, and Pro65 in another community depicted the closure of this gate due to the inhibitor binding. Six macro states of protein were deduced from the topology of FEL and analysis of conformational preference of free and ligand-bound systems to these macro states shows a combination of lock-and-key, conformational selection, and induced fit mechanisms are effective in ligand binding. All these results reveal structural states, allosteric mechanisms, and key players in the inhibition pathway of α-glucosidase by xanthene-11v.

The dynamics of suspensions of prolate spheroidal particles—Effects of volume fraction

The effect of volume fraction on the dynamics of a gravity driven suspension of prolate spheroidal solid particles in a fully periodic domain is examined by fully resolved numerical simulations, for relatively modest Reynolds numbers (around 20, depending on the volume fraction). Three systems are examined, for volume fractions of 2.2% (20 particles), 5.5% (50 particles), and 9.9% (90 particles). The results show a transition from flow at low volume fractions dominated by the hydrodynamic interactions between the particles and the fluid, although modified by collisions, to flow dominated by collisions at higher volume fractions. The distribution of the particles with respect to each other, as measured by the probability distribution of nearest distances, is nearly random at low volume fractions but at high volume fractions, there is more clustering than for a random distribution. At lower volume fractions most of the particles fall broadside on whereas at the highest volume fraction, their orientation is essentially random.

Diachronic quantitative snow avalanche risk assessment as a function of forest cover changes

This work proposes a holistic quantitative snow avalanche risk assessment that evaluates, at reasonable computational costs and for various types of buildings, the impact of forest cover changes on the probability distribution of runout distances, impact pressures and subsequent risk estimates. A typical case study of the French Alps shows that, from a completely deforested to a completely forested path, avalanche risk for a building located downslope decreases by 53–99%, depending on how forest cover is accounted for in avalanche statistical–dynamical modeling. Local forest cover data inferred from old maps and photographs further demonstrates that a 20–60% risk reduction actually occurred between 1825 and 2017 at the site because of the afforestation dynamics, with significant modulations according to the considered building technology. These results (1) assert the protective role of forests against snow avalanches, (2) highlight the potential of combining nature-based solutions with traditional structural measures to reduce risk to acceptable levels at reasonable costs, (3) suggest a significant decrease in risk to settlements in areas that encountered similar forest cover changes and (4) open the door to the quantification of long-term avalanche risk changes as a function of changes of all its hazard, vulnerability and exposure drivers in various mountain context.

Two-stage prediction framework for wind power ramps considering probability distribution distance measurement

The high volatility in wind power and uncertainty of ramp events has brought significant hidden hazards to maintain the stable and safe operation of the power system. In this paper, a two-stage prediction framework is proposed, taking the measurement of the probability density curve and the judgment of ramp-up mode. Aiming at the issue of limited prediction information and the sensitivity of prediction values at extreme points, an uncertainty prediction model for wind power based on a gated recurrent unit quantile regression network is proposed to realize the screening and judgment of ramps based on the prediction results and the divergence measurement of probability density distribution. Faced with notoriously unpredictable ramps and the small-samples poor learning performance, this paper proposes a ramp pattern discrimination model based on a gradient boosting decision tree, which describes the events in a future period from their magnitude and duration. Compared with state-of-the-art ramp forecasting methods, our proposed framework yields highly outstanding performances and realizes the adaptive detection for wind power ramps.

A novel method for determining the depth of kickoff points in cluster wells based on probability analysis

The purpose of this study is to determine the depth range of kickoff points of cluster wells. A probability distribution method is proposed to analyze the control deviation of the closure distance of vertical well sections. A Box-Cox transformation was performed on the positively skewed raw data, and a function of the closure distance probability distribution with the Box-Cox transformation parameter λ and the measured depth was established. The closure distance range was nonlinearly related to the measured depth and the distribution probability. The factors that should be considered in the function when determining the depth of the kickoff points were discussed. An engineering example was used to verify the applicability of the method. The proposed function can be used for assessing the collision risk during the project planning phase and optimizing the number of cluster wells and the wellhead spacing.

Point-of-interest recommendation in location-based social networks based on collaborative filtering and spatial kernel weighting

The growing popularity of location-based social networks (LBSNs), as well as their financial benefits, has led to a variety of methods for point-of-interest (POI) recommendations. A review of various methodologies reveals the role of geography is rarely addressed individually in current procedures. Instead, it is treated as an overall probability distribution of distances between all check-in pairs. On the other hand, despite the increased accuracy, the incorporation of individualized probabilistic distributions complicates matters of recommender systems. To address this issue, the main objective of this study is to introduce a POI recommendation mechanism in LBSNs that could be simple to implement the geographical influence. Furthermore, the method could be easily integrated with collaborative filtering while also increasing the quality of recommendations. Hence, instead of establishing a unique probability function for all check-ins data using the power-law or the Gaussian distribution, a spatial kernel weighting technique inspired by the similarity-weighted average notion, called CFSKW, was introduced and implemented. CFSKW was found on the principle that POIs close to a person's favourite POIs are more likely to be visited. As expected, the proposed method outperformed state-of-the-arts when tested utilizing two Four square datasets, namely New York and Tokyo. Kernel bandwidth and the coefficient of integrating user preference with geographical influence were two critical factors to be tuned. Low bandwidth and a medium to high geographical coefficient, according to the findings, produce better results. In unproportionate density of POIs, like that of the Tokyo dataset, a proposed algorithm based on dynamic bandwidth showed promising results. For the New York dataset, Precision@5 and Recall@5 were obtained as 25.41% and 61.80% using the proposed method, respectively, indicating a 3% and 5.1% improvement over the reference techniques. Precision@5 and Recall@5 were 1.1% and 1.2% better for the Tokyo dataset, respectively, when using a dynamic bandwidth geographical similarity algorithm.

A Two-Stage Transfer Regression Convolutional Neural Network for Bearing Remaining Useful Life Prediction

Recently, deep learning techniques have been successfully used for bearing remaining useful life (RUL) prediction. However, the degradation pattern of bearings can be much different from each other, which leads to the trained model usually not being able to work well for RUL prediction of a new bearing. As a method that can adapt a model trained on source datasets to a different but relative unlabeled target dataset, transfer learning shows the potential to solve this problem. Therefore, we propose a two-stage transfer regression (TR)-based bearing RUL prediction method. Firstly, the incipient fault point (IFP) is detected by a convolutional neural network (CNN) classifier to identity the start time of degradation stage and label the training samples. Then, a transfer regression CNN with multiloss is constructed for RUL prediction, including regression loss, classification loss, maximum mean discrepancy (MMD) and regularization loss, which can not only extract fault information from fault classification loss for RUL prediction, but also minimize the probability distribution distance, thus helping the method to be trained in a domain-invariant way via the transfer regression algorithm. Finally, real data collected from run-to-failure bearing experiments are analyzed by the TR-based CNN method. The results and comparisons with state-of-the-art methods demonstrate the superiority and reliable performance of the proposed method for bearing RUL prediction.

Fast and effective protein model refinement using deep graph neural networks

Protein model refinement is the last step applied to improve the quality of a predicted protein model. Currently the most successful refinement methods rely on extensive conformational sampling and thus, take hours or days to refine even a single protein model. Here we propose a fast and effective model refinement method that applies GNN (graph neural networks) to predict refined inter-atom distance probability distribution from an initial model and then rebuilds 3D models from the predicted distance distribution. Tested on the CASP (Critical Assessment of Structure Prediction) refinement targets, our method has comparable accuracy as two leading human groups Feig and Baker, but runs substantially faster. Our method may refine one protein model within ~11 minutes on 1 CPU while Baker needs ~30 hours on 60 CPUs and Feig needs ~16 hours on 1 GPU. Finally, our study shows that GNN outperforms ResNet (convolutional residual neural networks) for model refinement when very limited conformational sampling is allowed.

Microdosimetry modeling with Auger emitters in generalized cell geometry

A microdosimetry model was developed for the prediction of cell viability for irregular non-spherical cells that were irradiated by low energy, short range Auger electrons. Measured cell survival rates for LNCaP prostate cancer were compared to the computational results for the radioisotopes 177Lu and 161Tb (conjugated to PSMA). The cell geometries used for the computations were derived directly from the cell culture images. A general computational approach was developed to handle arbitrary cell geometries, based on distance probability distribution functions (PDFs) derived from basic image processing. The radiation calculations were done per coarse grained PDF bin to reduce computation time, rather than on a pixel/voxel basis. The radiation dose point kernels over the full electron spectrum were derived using Monte Carlo simulations for energies below 50 eV to account for the propagation of Auger electrons over length scales at and below a cellular radius. The relative importance of short range Auger electrons were evaluated between the two nuclide types. The microdosimetry results were consistent with the cell viability measurements, and it was found that 161Tb was more efficient than 177Lu primarily due to the short range Auger electrons. We foresee that imaging based microdosimetry can be used to evaluate the relative therapeutic effect between various nuclide candidates.

Mode III critical distance determination with optimized V-notched specimen under torsional fatigue and size effects on the inverse search probability distribution

An optimized V-notched specimen is proposed for the determination of mode III, or torsional, critical distance. Numerical procedures are provided for the inverse determination of this length, and then for a statistical analysis of the resulting skew-normal distribution, as obtained from (symmetric) normal distributions of the plain and notched specimen strengths. An experimental example is shown on steel 42CrMo4 + QT, with clear evidence of a significantly larger mode III critical distance than mode I. A parametric analysis is then presented to evaluate the effects of size of the specimen on the standard deviation of the inverse search critical distance probability distribution.

Quantum Chaos and the Spectrum of Factoring

AbstractThe factorization ensemble is a set to which integer factorable numbers , having the same trivial factorization complexity, belong. Hence, the Rivest‐Shamir‐Adleman (RSA) cryptographic moduli pertain to this set. A function can be defined therein which will be associated to the energy of a system of ions in a Penning trap. This is the quantum factoring simulator hypothesis connecting quantum mechanics with number theory. Here, a possible setup of the simulator from the magnetron energies of a Coulomb crystal in a cylindrical trap is described. Then, quantum mechanically, these energies may have only discrete values. To test the validity of the simulator hypothesis, evidence of this kind of discreteness from the statistics of the of a large random sample of RSA moduli is reported; indeed, their unfolded distance probability distribution fits to a Gaussian Unitary Ensemble, exactly as required if they actually correspond to the quantum energy levels spacing of a magnetically confined system that exhibits chaos. The confirmation of these predictions is consistent with the quantum simulator hypothesis and, thereby, it points to the existence of a liaison between quantum mechanics and number theory.