Cumulative Distribution Research Articles

Determining probability density functions with adiabatic quantum computing

The two main approaches to quantum computing are gate-based computation and analog computation, which are polynomially equivalent in terms of complexity, and they are often seen as alternatives to each other. In this work, we present a method for fitting one-dimensional probability distributions as a practical example of how analog and gate-based computation can be used together to perform different tasks within a single algorithm. In particular, we propose a strategy for encoding data within an adiabatic evolution model, which accommodates the fitting of strictly monotonic functions, as it is the cumulative distribution function of a dataset. Subsequently, we use a Trotter-bounded procedure to translate the adiabatic evolution into a quantum circuit in which the evolution time t is identified with the parameters of the circuit. This facilitates computing the probability density as derivative of the cumulative function using parameter shift rules.

How Rilling and Biochar Addition Affect Hydraulic Properties of a Clay‐Loam Soil

ABSTRACTRill erosion is a significant problem worldwide as it determines relevant amounts of soil loss on hillslopes. Although, in the last few years, many studies have focused on rill erosion and biochar as soil amendment, their influence on soil hydrological properties and relevance on soil conservation strategies is still uncertain. In this paper, the effects of rill formation and biochar addition on the physical and hydraulic properties of a clay‐loam soil were assessed by laboratory measurements (water retention, hydraulic conductivity, minidisk infiltrometer data and 1H Nuclear Magnetic Resonance (NMR) relaxometry with the fast field cycling (FFC) setup) and field tests (rill formation tests at the plot scale). The rilled and non‐rilled soils did not show any difference in the volume of pores with a diameter (d) > 300 μm, but the former showed a smaller volume for the pores in the size range between 300 and 0.2 μm. As compared with an untreated rilled soil, the addition of 5% (w w−1) biochar in the soil in which the rill is incised did not change the volume of pores with d > 300 μm, while there were more pores of both 30 ≤ d ≤ 300 μm and 0.2 ≤ d ≤ 30 μm. Moreover, there were less pores with d < 0.2 μm. Shaping the rill did not influence the hydraulic conductivity of the nearly saturated soil (pressure head, h = −1 cm), while it determined a significant decrease of the soil ability to transmit water in more unsaturated conditions (h ≤ −3 cm). The addition of biochar to the soil improved, in general, the soil aptitude to transmit water, regardless of the pore size. However, this improvement was statistically irrelevant in the case of a transport process governed by larger pores. The hydrological measurements also demonstrated that the addition of a large amount of biochar (5%) impedes soil characteristics alteration as the changes due to rilling are balanced by adding biochar in the soil. NMR was also used to measure the structural and functional connectivity of the original soil, the biochar and a mixture with three biochar concentrations (i.e., BC = 1%, 3% and 5% w w−1) traditionally applied in agronomical activity. These measurements revealed that the mixture of soil and biochar was characterised by longitudinal relaxation time (T1) values, which are related to pore sizes, longer than those measured for the soil. In addition, the soil empirical cumulative frequency distribution of T1 was always skewed towards shorter T1 values, thereby suggesting that the macro‐pore component (i.e., the largest T1 values) was never dominant while biochar addition increased the size of mesopores and micropores. Biochar concentrations larger than 3% (w w−1) did not produce appreciable changes in the pore distribution inside the mixture. The biochar component improved the structural connectivity up to BC = 5%, while decreased the functional connectivity up to BC = 3%. A relationship between the water volume contained in soil pores and the NMR data were established for the micropores (d ≤ 0.2 μm). The biochar‐amended soil was characterised by fewer small pores, but these micropores were greater than those in non‐treated soil.

Automatic Adaptive Algorithm for Delineation of Cerebral-Spinal Fluid Regions for Non-contrast Magnetic Resonance Imaging Volumetry and Cisternography in Mice.

Magnetic resonance imaging (MRI) is an invaluable method of choice for anatomical and functional in vivo imaging of the brain. Still, accurate delineation of the brain structures remains a crucial task of MR image evaluation. This study presents a novel analytical algorithm developed in MATLAB for the automatic segmentation of cerebrospinal fluid (CSF) spaces in preclinical non-contrast MR images of the mouse brain. The algorithm employs adaptive thresholding and region growing to accurately and repeatably delineate CSF space regions in 3D constructive interference steady-state (3D-CISS) images acquired using a 9.4 Tesla MR system and a cryogenically cooled transmit/receive resonator. Key steps include computing a bounding box enclosing the brain parenchyma in three dimensions, applying an adaptive intensity threshold, and refining CSF regions independently in sagittal, axial, and coronal planes. In its original application, the algorithm provided objective and repeatable delineation of CSF regions in 3D-CISS images of sub-optimal signal-to-noise ratio, acquired with (33 μm)3 isometric voxel dimensions. It allowed revealing subtle differences in CSF volumes between aquaporin-4-null and wild-type littermate mice, showing robustness and reliability. Despite the increasing use of artificial neural networks in image analysis, this analytical approach provides robustness, especially when the dataset is insufficiently small and limited for training the network. By adjusting parameters, the algorithm is flexible for application in segmenting other types of anatomical structures or other types of 3D images. This automated method significantly reduces the time and effort compared to manual segmentation and offers higher repeatability, making it a valuable tool for preclinical and potentially clinical MRI applications. Key features • This protocol presents a fully automatic adaptive algorithm for the delineation of CSF space regions in 3D-CISS in vivo images of the mouse brain. • The algorithm represents an analytical method for adaptive CSF regions separation based on cumulative distribution of brain image intensities and contrast calculation-based slice-wise region growing. • Users can interactively alter the input parameters to modify the algorithm's output in a variety of 3D brain MR and μCT or CT images. • The algorithm is implemented in MATLAB 2021a and is compatible with all versions up to 2024a.

A novel method for evaluating asphalt pavement structural performance based on vehicle vibration

ABSTRACT Fast, accurate, and high-frequency detection for evaluating pavement structural performance is vital for road maintenance decision-making. Traditional detection methods make it challenging to balance the detection speed, frequency, and cost. Pavement condition identification technology based on vehicle vibration has become increasingly mature and can overcome the above problems. This study aims to evaluate the structural performance of asphalt pavement. A vehicle-based test system based on two-axle vibration sensing was developed. The vibration signal from the vehicle driving in the asphalt pavement was generated. Further, the deep signal features was extracted based on the expression of the probability distribution. The evolutionary characteristics of probability density distribution and cumulative distribution were summarized. The main conclusions are as follows: The theoretical model analyzed the correlation between the probability density and the pavement modulus. Further, estimate the peak of the probability density (PKDE) and the cumulative distribution fitting value (CDF0). The estimated indexes’ correlation coefficients were calculated by matching the dynamic deflection index of 10 road sections. As a result, PKDE has a robust correlation with a correlation coefficient of 0.81. Therefore, the vehicle vibration probability distribution expression method proposed is effective for structural performance evaluation and has high application feasibility.

A comparative analysis of deterministic and probabilistic approaches for estimating seepage flow in earth dams using a hybrid finite element method

Purpose Computing seepage discharge in earth dams involves inherent complexities and challenges that require the use of probabilistic algorithms to accurately capture their uncertain characteristics and identify optimal solutions. This study aims to investigate the impact of uncertainty in seepage flow estimation using a novel hybrid approach, combining the analysis of Laplacian equations with the probabilistic finite element method (PFEM) and a metaheuristic algorithm. Design/methodology/approach To achieve this purpose, a finite element-based FORTRAN program was developed to model the problem using the Galerkin finite element method, which was validated using laboratory findings. Subsequently, Monte Carlo loops were incorporated into each model, consisting of 2000 iterations and the probability distribution function and cumulative distribution function were computed for each sub-model. A total of 138 earth dams were analysed to investigate the influence of different characteristics on seepage, including variations in dam geometry, soil permeability and water levels (both downstream and upstream). Effective seepage flow (ESF), was introduced in both deterministic and probabilistic models. Findings The findings indicated that the downstream slope has a more significant impact on ESF than the upstream slope, with a difference of 1.29%. Additionally, the ratio of dam height to bottom width (H/B) directly affects the ESF, resulting in a 20% increase in ESF for every 16% increase in H/B. Originality/value This study introduces a novel hybrid approach for estimating seepage flow in earth dams by integrating the Unlike traditional deterministic models, which often overlook the inherent .PFEM with a metaheuristic algorithman advanced uncertainties in seepage characteristics, this research effectively captures these uncertainties throughprobabilistic framework.

Application of reverse cumulative distribution curve and scaled logit model in determining optimal immunogenic dose and prediction of protection of EV71 vaccines

ABSTRACT Background This study proposes the reverse cumulative distribution curve (RCDC) for optimal dose selection and a scaled logit model for estimating protection in EV71 vaccine development. Research design and methods Data were from a phase 2 trial involving infants and young children randomized to receive either 640 U with or without adjuvant, 320 U with adjuvant, 160 U with adjuvant EV71 vaccines, or placebo. RCDCs were constructed using neutralizing antibody titers 28 days post-vaccination. Robustness of RCDC parameters was assessed via coefficient of variation for the area under the curve (AUC), the relative optimal point, median on the curve, and antibody titer of the point of maximum curvature, with geometric mean titer (GMT) as control. The scaled logit model estimated protection against EV71-associated disease for the selected optimal dose. Results The AUC and relative optimal point demonstrated greater robustness than GMT. The 640 U with adjuvant dose had the highest AUC (0.64, 95% CI: 0.61-0.66), sum of coordinates of the relative optimal point (1.40, 95% CI: 1.34-1.43), and the highest estimated protection (93.36%, 95% CI: 79.91-97.86). Conclusions AUC and relative optimal point of RCDC are effective for early vaccine dose screening, with protection estimated by the scaled logit model.

BC-DISTRIBUTION FUNCTION AND BC-REARRANGEMENT OF BC-MEASURABLE FUNCTIONS WITH HYPERBOLIC NORM

This paper investigates the distribution function and nonincreasing rearrangement of -valued functions equipped with the hyperbolic norm. The concept of the distribution function for -valued functions is introduced, which characterizes the cumulative distribution of values taken by the function. Next, it is delved into the nonincreasing rearrangement of -valued functions with the hyperbolic norm. By exploring the nonincreasing rearrangement of -valued functions, we determined how the hyperbolic norm influences the rearrangement process and its impact on the function’s behavior and properties.

Vibration Serviceability Assessment of Floor Structures: Simulation of Human-Structure-Environment Interactions Using Agent-Based Modeling.

A rapidly growing body of experimental evidence in the literature shows that the effects of humans interacting with vibrating structures, other humans, and their surrounding environment can be critical for reliable estimation of structural vibrations. The Interaction-based Vibration Serviceability Assessment framework (I-VSA) was proposed by the authors in 2017 to address this, taking into account human-structure dynamic interactions (HSI) to simulate the structural vibrations experienced by each occupant/pedestrian. The I-VSA method, however, had limited provisions to simulate simultaneously multiple modes of structure in HSI, to simulate human-human and human-environment interactions, and the movement pattern of the occupants/pedestrians. This study proposes a new Agent-based Vibration Serviceability Assessment framework, termed AVSA, to address the following limitations: (a) allowing for multiple modes of structure to be simulated simultaneously, (b) to simulate effects of vibrations on gait parameters and walking pattern/routes, and (c) to simulate human-environment interactions, and movement patterns for any desired interior layout and use case. The AVSA framework was used to simulate the response and to assess the vibration serviceability of a lightweight floor under a combination of sitting and walking traffic, where three vertical modes of vibrations were engaged simultaneously. The results of the simulations show that for all tests, the experimental Cumulative Distribution Functions of the vibrations experienced by the participants are within the 95% confidence interval predicted by the AVSA method. The proposed method provides a generic and flexible framework to simulate simultaneously different interaction modalities, different human tasks and postures, and multiple modes of structure and the human body.

Days at Home After Transcatheter Mitral Valve Repair Versus Medical Therapy Alone in Heart Failure.

Transcatheter edge-to-edge repair of the mitral valve (mTEER) reduced a hierarchical end point that included death and heart failure hospitalization in COAPT (Cardiovascular Outcomes Assessment of the MitraClip Percutaneous Therapy for Heart Failure Patients With Functional Mitral Regurgitation Trial). However, the magnitude to which mTEER increases the number of days a patient spends at home (DAH) in the first few years after treatment, a patient-centered end point not captured routinely in clinical trials, has not been evaluated. We compared 1- and 2-year DAH among patients with functional mitral regurgitation and heart failure randomized to mTEER plus medical therapy versus medical therapy alone (control) by linking the COAPT trial to comprehensive health care claims data. We linked data from COAPT trial participants to Medicare fee-for-service claims. DAH was calculated as the number of days alive and spent outside a hospital, skilled nursing facility, inpatient rehabilitation, long-term acute care hospital, emergency department, or observation stay after randomization. Treatment groups were compared using quantile regression to calculate the area under the curve of cumulative distribution functions. We linked 271 patients (mTEER 136/302, control 135/312) for a 2-year follow-up. Mean±SD DAH at 1 year was 312.0±95.6 in mTEER and 298.1±107.5 in controls with similar area under the curve (difference 13.9 days [-10.5 to 38.3], P=0.26). DAH at 2 years was 577.2±235.6 in mTEER and 518.2±253.0 in control with a higher area under the curve in mTEER (difference 59.0 days [0.07 to 117.9], P=0.0497). In the COAPT trial linked to Medicare claims, patients randomized to mTEER spent a similar number of DAH at 1 year but more time at home at 2 years compared with medical therapy alone.

Glitches and Glitching Clusters in Rotation-powered Pulsars

Abstract The study of pulsar glitch phenomena serves as a valuable probe into the dynamic properties of matter under extreme high-density conditions, offering insights into the physics within neutron stars. Providing theoretical explanations for the diverse manifestations observed in different pulsars has proven to be a formidable challenge. By analyzing the distribution of glitch sizes and waiting times, along with the evolution of cumulative glitch sizes over time, we have uncovered a long-term clustering phenomenon for pulsar glitches. This perspective allows us to approach the distinct glitch representations in various pulsars from a unified standpoint, connecting the same periodicity of observational data to the randomness. Without relying on specific physical models, we utilized the coefficient of variation to numerically determine optimal clustering numbers and clustering periods for sample pulsars. Our analysis involving 27 pulsars has revealed a clear linear relationship between the glitch cluster period and characteristic age. Of interest, the cumulative distribution of functions of cluster sizes and interval times have the same patterns, which can be synchronously fitted by Gaussian processes. These results may indicate novel understandings of glitches and the resulting processes.

Significant Wave Height Retrieval in Tropical Cyclone Conditions Using CYGNSS Data

The retrieval of global significant wave height (SWH) data is crucial for maritime navigation, aquaculture safety, and oceanographic research. Leveraging the high temporal resolution and spatial coverage of Cyclone Global Navigation Satellite System (CYGNSS) data, machine learning models have shown promise in SWH retrieval. However, existing models struggle with accuracy under high-SWH conditions and discard a significant number of such observations due to low quality, which limits their effectiveness in global SWH retrieval, particularly for monitoring tropical cyclone (TC) events. To address this, this study proposes a daily global SWH retrieval framework through the enhanced eXtreme Gradient Boosting model (XGBoost-SC), which incorporates Cumulative Distribution Function (CDF) matching to introduce prior distribution information and reduce errors for SWH values exceeding 3 m. An enhanced loss function is employed to improve accuracy and mitigate the distribution bias in low-SWH retrieval induced by CDF matching. The results were tested over one million sample points and validated against the European Centre for Medium-Range Weather Forecasts (ECMWF) SWH product. With the help of CDF matching, XGBoost-SC outperformed all models, significantly reducing RMSE and bias while improving the retrieval capability for high SWHs. For SWH values between 3–6 m, the RMSE and bias were 0.94 m and −0.44 m, and for values above 6 m, they were 2.79 m and −2.0 m. The enhanced performance of XGBoost-SC for large SWHs was further confirmed in TC conditions over the Western North Pacific and in the Western Atlantic Ocean. This study provides a reference for large-scale SWH retrieval, particularly under TC conditions.

Joint Power and Delay Optimization‐Based Resource Allocation in Mu‐MIMO‐OFDM System: Deep Convolutional Red Piranha Pyramid‐Dilated Neural Network

ABSTRACTIn general, Multi‐User Multiple Input Multiple Output Orthogonal Frequency Division Multiplexing (MU‐MIMO‐OFDM) enables multiple users to simultaneously communicate with a single base station using multiple antennas and OFDM modulation. Nevertheless, resource allocation challenges such as power management and delay optimization arise within MU‐MIMO‐OFDM systems, requiring sophisticated solutions to ensure efficient use of resources and optimal system performance. Thus, joint power and delay optimization‐based resource allocation using a Deep Convolutional Pyramid‐Dilated Neural Network (DCPDNN) with Red piranha optimization and Optimal Delay Scheduling conflict graphs Algorithm (DCPDNN‐RPO‐ODSCGA) in MU‐MIMO‐OFDM system is proposed in this presented research. The proposed mechanism is performed in two stages: power allocation and delay optimization. In the first stage, through a Deep Convolutional Pyramid‐Dilated Neural Network (DCPDNN), which aims to maximize throughput, the network resources are distributed to user equipment (UEs) based on power and transmission rate. To reduce the loss function, Red Piranha Optimization (RPO) is proposed to optimize the layers of DCPDNN. In the second stage, the Optimal Delay Scheduling conflict graphs Algorithm (ODSCGA) is proposed for the optimizing delay in the MU‐MIMO‐OFDM system. The multiracial envelope procedure and service curve for traffic flows in the uplink transmission are used in the ODSCGA approach to estimate the delay‐bound value. Ideas like the maximal weight independent set and optimal conflict graph are also utilized. The simulations of DCPDNN‐RPO‐ODSCGA were conducted using MATLAB software. Thus, the proposed approach has attained higher spectral capacity, higher fairness index, and increased cumulative distribution function (CDF), 29.74%, 32.98%, and 16.46% lower loss rate, 28.05%, 24.09%, and 17.45% improved energy efficiency, 15.09%, 13.78%, and 12.05% lower processing time than other conventional approaches like MPQM‐SCA, Hyb‐BF‐DSA, and SIA‐FDBD methods, respectively.

On the Equivalence of Likelihood‐Based Confidence Bands for Fatigue‐Life and Fatigue‐Strength Distributions

ABSTRACTFatigue data arise in many research and applied areas, and there have been statistical methods developed to model and analyze such data. The distributions of fatigue life and fatigue strength are often of interest to engineers designing products that might fail due to fatigue from cyclic‐stress loading. Based on a specified statistical model and the maximum likelihood method, the cumulative distribution function (cdf) and quantile function (qf) can be estimated for the fatigue‐life and fatigue‐strength distributions. Likelihood‐based confidence bands can then be obtained for the cdf and qf. This paper provides equivalence results for confidence bands for fatigue‐life and fatigue‐strength models. These results are useful for data analysis and computing implementation. We show (a) the equivalence of the confidence bands for the fatigue‐life cdf and the fatigue‐life qf, (b) the equivalence of confidence bands for the fatigue‐strength cdf and the fatigue‐strength qf, and (c) the equivalence of confidence bands for the fatigue‐life qf and the fatigue‐strength qf. Then we illustrate the usefulness of those equivalence results with two examples using experimental fatigue data.

Iterative Application of UMAP-Based Algorithms for Fully Synthetic Healthcare Tabular Data Generation

Building on a previously developed partially synthetic data generation algorithm utilizing data visualization techniques, this study extends the novel algorithm to generate fully synthetic tabular healthcare data. In this enhanced form, the algorithm serves as an alternative to conventional methods based on Generative Adversarial Networks (GANs) or Variational Autoencoders (VAEs). By iteratively applying the original methodology, the adapted algorithm employs UMAP (Uniform Manifold Approximation and Projection), a dimensionality reduction technique, to validate generated samples through low-dimensional clustering. This approach has been successfully applied to three healthcare domains: prostate cancer, breast cancer, and cardiovascular disease. The generated synthetic data have been rigorously evaluated for fidelity and utility. Results show that the UMAP-based algorithm outperforms GAN- and VAE-based generation methods across different scenarios. In fidelity assessments, it achieved smaller maximum distances between the cumulative distribution functions of real and synthetic data for different attributes. In utility evaluations, the UMAP-based synthetic datasets enhanced machine learning model performance, particularly in classification tasks. In conclusion, this method represents a robust solution for generating secure, high-quality synthetic healthcare data, effectively addressing data scarcity challenges.

Radiomic Consensus Clustering in Glioblastoma and Association with Gene Expression Profiles.

Glioblastoma (GBM) is the most common malignant primary central nervous system tumor with extremely poor prognosis and survival outcomes. Non-invasive methods like radiomic feature extraction, which assess sub-visual imaging features, provide a potentially powerful tool for distinguishing molecular profiles across groups of patients with GBM. Using consensus clustering of MRI-based radiomic features, this study aims to investigate differential gene expression profiles based on radiomic clusters. Patients from the TCGA and CPTAC datasets (n = 114) were included in this study. Radiomic features including T1, T1 with contrast, T2, and FLAIR MRI sequences were extracted using PyRadiomics. Selected radiomic features were then clustered using ConsensusClusterPlus (k-means base algorithm and Euclidean distance), which iteratively subsamples and clusters 80% of the data to identify stable clusters by calculating the frequency in which each patient is a member of a cluster across iterations. Gene expression data (available for n = 69 patients) was analyzed using differential gene expression (DEG) and gene set enrichment (GSEA) approaches, after batch correction using ComBat-seq. Three distinct clusters were identified based on the relative consensus matrix and cumulative distribution plots (Cluster 1, n = 25; Cluster 2, n = 46; Cluster 3, n = 43). No significant differences in patient demographic characteristics, MGMT methylation status, tumor location, or overall survival were identified across clusters. Differentially expressed genes were identified in Cluster 1, which have been previously associated with GBM prognosis, recurrence, and treatment sensitivity. GSEA of Cluster 1 showed an enrichment of genes upregulated for immune-related and DNA metabolism pathways and genes downregulated in pathways associated with protein and histone deacetylation. Clusters 2 and 3 exhibited fewer DEGs which failed to reach significance after multiple testing corrections. Consensus clustering of radiomic features revealed unique gene expression profiles in the GBM cohort which likely represent subtle differences in tumor biology and radiosensitivity that are not visually discernible, underscoring the potential of radiomics to serve as a non-invasive alternative for identifying GBM molecular heterogeneity. Further investigation is still required to validate these findings and their clinical implications.

Dynamic stochastic model of allometric equations and cumulative distribution for biomass-carbon in Pinus hartwegii Lindl., facing climate change

Objective: to construct a dynamic stochastic model with validated biospheric-interaction, estimating allometric equations for the total volumetric increase and cumulative distribution of biomass for Pinus hartwegii Lindl in the states of Mexico and Puebla, considering climate change. Design/ Methodology/ Approach: the methodology included the use of SiBiFor numerical databases, NASA Power data, Ordinary Least Squares mathematical models, the Random-Forest software, Ridge model with regression, R algorithms and Newton volumetric estimation equations. Results: estimated allometric equations were obtained for the total volume of trees in 2023, highlighting the importance of linear regression models and the validity of the variables used. Newton's mathematical equations and theoretical models for excurrent tree-form types were found to have the best accuracy in estimating the total volume of the barked tree. Limitations of the study/ Implications: this study has limitations in terms of generalization to other forest types and the availability of data in Mexico. However, it highlights the importance of understanding forest responses to environmental changes and the need for validated dynamic stochastic models to estimate allometric equations and assess carbon sequestration. Findings/ Conclusions: this study highlights the importance of understanding and assessing the carbon storage capacity of forests, especially in the context of climate change. In addition, it underlines the usefulness of linear regression models and variable validation to estimate carbon sequestration in Pinus hartwegii forests.

An improved empirical quantile mapping approach for bias correction of extreme values in climate model simulations

Abstract Quantifying and correcting biases in modeling simulations is crucial for deriving meaningful findings across various scientific disciplines. Climate model simulations, in particular, often exhibit systemic biases when compared to observations. These biases may persist in future climate simulations, affecting the results of many climate change impact assessment studies. Empirical Quantile Mapping (QM) is a widely used method to correct such biases, mapping quantiles between observed and simulated Cumulative Distribution Functions (CDFs). However, empirical QM faces a fundamental challenge when the CDF of future simulations differs from historical simulations, potentially leading to extreme values falling outside the historical CDF range. To address this issue, our study introduces a novel approach to extrapolate future extreme values for bias correction, preserving the rank order of simulated future extremes. By construction, our approach ensures that bias corrected values are not exaggerated and retain the rank structure of the original simulated data, while preserving climate change signals in the bias corrected outputs. Additionally, our approach includes a technique to adjust the wet-day frequency for precipitation by preserving the ratio of wet-day frequency between observations and historical model simulations.

Investigation and optimization of parameters for bidirectional composite vibratory finishing of gears

ABSTRACT To meet the core requirements for uniform and efficient finishing of high-precision gears, a bidirectional composite vibratory finishing (BCVF) process was introduced. The influence of motion parameters (gear rotational speed n, vibration frequency f x and f z , vibration amplitude A x and A z , vibration phase difference ψ), process parameters (media loading height H, gear installation position h), gear parameters and container geometric parameters (cross-sectional shape, size L x × L y ) on the finishing effect was investigated by kinematic analysis and discrete element simulation (DEM). On this basis, the parameters with significant influence were selected and further optimized by gray relational analysis (GRA). Numerical simulations were carried out by orthogonal design, taking the cumulative contact energy and distribution uniformity on gear surface as evaluation indicators for multi-objective optimization. The results indicated that the affecting significance on comprehensive performance was ranked as f x > f z > A x > A z . Besides, the optimal parameter combination was obtained.

Gauss-Benford Rules and Their Harmonic Peers

We research the relationship between the probability functions of the twofold hyperbolic universe, consisting of the logarithmic (real) and harmonic (rational) worlds. Within the logarithmic realm, we study the connection between the Gauss- Kuzmin distribution and Newcomb-Benford law and prove that they are fundamentally equivalent; the former corresponds to the probability decrements of the latter, i.e., log(2,1+1/(k(k+2))) is the difference between the function log(2,1+1/n) evaluated at n=k and n=k+1, where k is the index of a coefficient of a real number’s regular continued fraction expansion and n is a positive numeral written in positional notation. Thus, the binary Newcomb-Benford probability of n=1 is the sum of all the Gauss-Kuzmin masses, of n=2, is the sum of all the Gauss-Kuzmin masses minus the Gauss-Kuzmin mass at k=1, and of n=m, is the sum of all the Gauss-Kuzmin masses minus the sum of the first m-1 ones. Besides, the extrapolation of the Gauss-Kuzmin measure outside the unit interval subsumes Newcomb-Benford’s cumulative distribution function. These findings lead to the Gauss-Benford law, which specifies that the occurrence possibility of a positive real number represented in positional notation is log(2,1+x) (i.e., the Gauss-Kuzmin measure) if x is within the unit interval and log(2,1+1/x) if x is outside. Geometrically, these possibilities indicate proximity to 1. The map between both domain partitions is a sheer inversion, the unique conformal transformation that fixes one and respects the minimum information principle. Moreover, we introduce the Gauss-Benford measure, log(1+1/x,1+y), as the probability of a random variable accumulated between x-1 and x, with density 1/((1+y)ln(1+1/x)), where 0≤x-1<y≤x. We also explore the analogous harmonic rules; the canonical (normalized) harmonic probability of a positive natural q is 1/q, the qth harmonic gap has probability mass 1/(q(q+1)), and the harmonic occurrence possibility of a positive rational number is t if t is in the unit interval and 1/t if t is outside. We build the bridge between the logarithmic and harmonic realms by integrating and normalizing the latter.

Adaptive Ultra-Wideband/Pedestrian Dead Reckoning Localization Algorithm Based on Maximum Point-by-Point Distance

Positioning using ultra-wideband (UWB) signals can be used to achieve centimeter-level indoor positioning. UWB has been widely used in indoor localization, vehicle networking, industrial IoT, etc. However, due to non-line-of-sight (NLOS) and multipath interference problems, UWB cannot provide adequate position information, which affects the final positioning accuracy. This paper proposes an adaptive UWB/PDR localization algorithm based on the maximum point-by-point distance to solve the problems of poor UWB performance and the error accumulation of the pedestrian dead reckoning (PDR) algorithm in NLOS scenarios that is used to enhance the robustness and accuracy of indoor positioning. Specifically, firstly, the cumulative distribution function (CDF) map of localization under normal conditions is obtained through offline pretraining and then compared with the CDF obtained when pedestrians are moving on the line. Then, the maximum point-by-point distance algorithm is used to identify the abnormal base stations. Then, the standard base stations are filtered out for localization. To further improve the localization accuracy, this paper proposes a UWB/PDR algorithm based on an improved adaptive extended Kalman filtering (EKF), which dynamically adjusts the position information through the adaptive factor, eliminates the influence of significant errors on the current position information and realizes multi-sensor fusion positioning. The realization results show that the algorithm in this paper has a solid ability to identify abnormal base stations and that the adaptive extended Kalman filtering (AEKF) algorithm is improved by 81.27%, 58.50%, 29.76%, and 18.06% compared to the PDR, UWB, EKF, and AEKF algorithms, respectively.