Gaussian Distribution Research Articles

Early-season yield fluctuations of strawberry (Fragaria ×ananassa Duch.) follow a bimodal Gaussian model

Strawberries (Fragaria ×ananassa Duch.) are highly perishable and require intensive labor inputs for harvesting. Therefore, yield forecasting is critical for improving labor management and marketing decision-making in strawberry production. In Florida, United States, strawberry yields during winter months have a unique distribution pattern characterized by multiple waves. We hypothesized that individual yield waves can be described using Gaussian distribution, a model that represents a symmetrical bell-shaped curve. Two short-day cultivars (‘Florida Radiance’ and ‘Florida Brilliance’) and one day-neutral cultivar (‘Florida Beauty’) were grown in west-central Florida. Harvesting was performed 30 times, generally twice a week from November through February. Yield data were converted to weekly values prior to model fitting. The first two yield waves were described by a bimodal Gaussian distribution model, which was then converted into two unimodal Gaussian distribution models. The goodness of fit was very high (R2 = 0.934–0.959) for both yield waves in all tested cultivars. Different yield distribution patterns of the tested cultivars were characterized quantitatively by estimating not only the yield but also the timing and duration of each yield wave. Our modeling approach provides insights into understanding cultivar-dependent fruiting phenology, yielding capacity, and fruit earliness. Such information can help optimize yield distribution through breeding and reduce yield gaps by using different cultivars or staggered planting dates. The model developed here only applies to the first two waves of fruit production. Future research will aim to model the following yield waves to fully characterize the strawberry yield distribution.

SupSpec: A Python Package for Measuring the Doppler Shifts of Supernova Spectral Lines

Here we present an open-source Python package, SupSpec, which aids in finding the velocity structure of spectral features throughout supernova (SN) ejecta. This code is designed to require minimal user interaction and can ingest an arbitrarily large number of spectra. By fitting a Gaussian distribution to the spectral sequence of a single SN over time, it finds the “velocity structure”—the evolution of the velocity of a specific absorption feature over time. SupSpec is available on GitHub and on Zenodo.

On Superposition Lattice Codes for the K-User Gaussian Interference Channel

In this study, we work with lattice Gaussian coding for a K-user Gaussian interference channel. Following the procedure of Etkin et al., in which the capacity is found to be within 1 bit/s/Hz of the capacity of a two-user Gaussian interference channel for each type of interference using random codes, we work with lattices to take advantage of their structure and potential for interference alignment. We mimic random codes using a Gaussian distribution over the lattice. Imposing constraints on the flatness factor of the lattices, the common and private message powers, and the channel coefficients, we find the conditions to obtain the same constant gap to the optimal rate for the two-user weak Gaussian interference channel and the generalized degrees of freedom as those obtained with random codes, as found by Etkin et al. Finally, we show how it is possible to extend these results to a K-user weak Gaussian interference channel using lattice alignment.

Discrete trapping levels of localized states in amorphous silicon nitride

The spectrum of localized hole states (traps) in amorphous silicon nitride, a-Si3N4, is experimentally studied using the method of thermally stimulated depolarization. The experiment is compared with theoretical calculations using three models of the energy spectrum of traps: discrete spectrum (monoenergetic trap), continuous spectrum, and Gaussian trap distribution. The experiment is quantitatively described by a model of a discrete spectrum of traps with an energy of 1.15 eV and a width of no more than 0.01 eV. In the case of a continuous and Gaussian spectrum of traps, the contribution to depolarization is made by the deepest traps. The blurring of the trap energy level in a-Si3N4 due to the absence of long-range order (fluctuations in the Si–N bond length and fluctuations in the N–Si–N and Si–N–Si angles) does not exceed 0.01 eV.

A high-throughput focused collimator for OAR-sparing preclinical proton FLASH studies: commissioning and validation

Objective. To fabricate and validate a novel focused collimator designed to spare normal tissue in a murine hemithoracic irradiation model using 250 MeV protons delivered at ultra-high dose rates (UHDRs) for preclinical FLASH radiation therapy (FLASH-RT) studies. Approach. A brass collimator was developed to shape 250 MeV UHDR protons from our Varian ProBeam. Six 13 mm apertures, of equivalent size to kV x-ray fields historically used to perform hemithorax irradiations, were precisely machined to match beam divergence, allowing concurrent hemithoracic irradiation of six mice while sparing the contralateral lung and abdominal organs. The collimated field profiles were characterized by film dosimetry, and a radiation survey of neutron activation was performed to ensure the safety of staff positioning animals. Main results. The brass collimator produced 1.2 mm penumbrae radiation fields comparable to kV x-rays used in preclinical studies. The penumbrae in the six apertures are similar, with full-width half-maxima of 13.3 mm and 13.5 mm for the central and peripheral apertures, respectively. The collimator delivered a similar dose at an average rate of 52 Gy s−1 for all apertures. While neutron activation produces a high (0.2 mSv h−1) initial ambient equivalent dose rate, a parallel work-flow in which imaging and setup are performed without the collimator ensures safety to staff. Significance. Scanned protons have the greatest potential for future translation of FLASH-RT in clinical treatments due to their ability to treat deep-seated tumors with high conformality. However, the Gaussian distribution of dose in proton spots produces wider lateral penumbrae compared to other modalities. This presents a challenge in small animal pre-clinical studies, where millimeter-scale penumbrae are required to precisely target the intended volume. Offering high-throughput irradiation of mice with sharp penumbrae, our novel collimator-based platform serves as an important benchmark for enabling large-scale, cost-effective radiobiological studies of the FLASH effect in murine models.

Aspects Regarding the Physical Parameters and Wear in the Work Process of the Disc Openers for Seeding Machines

This paper primarily presents statistics on the variation of physical characteristics (dimensions and mass) for the coulter discs of double-disc seeders. This statistic was calculated based on actual measurements of the probability density and cumulative probability for the mass of the discs, their average thickness, and outer diameter. These parameters (m = 4000 g, g = 4 mm, D = 380 mm) are tracked from the design phase to the actual realization phase, being the parameters specified in the purchase phase by users from agricultural machinery distributors. The standard deviation and deviation from the mean for a cumulative normal (Gaussian) distribution were calculated, and an analysis was made for the decrease of the mentioned parameters in discs already used for sowing cereals on an area of 80 hectares, due to the wear that appeared as a trace of the contact with the soil and the abrasive wear caused by it. Testing of disk parameters using both logarithmic and Gaussian distributions was performed, and test results are presented through appropriate graphs. With small deviations (which appeared for known or unknown reasons), it can be stated that the distribution of the mentioned parameters is generally a normal-type distribution. If the new discs are 15″ in diameter, experts recommend that they be replaced when they reach a diameter of less than 14.5 inches. This study can provide a reference for improving the physical characteristics of opener discs of seed drills in no-till conditions and beyond.

A Bayesian Merging of Earthquake Magnitudes Determined by Multiple Seismic Networks

Abstract We introduce a Bayesian algorithm designed to integrate earthquake magnitudes of the same type reported by various seismic networks, aiming to create unified and standardized catalogs suitable for widespread use. The fundamental concept underpinning this algorithm is the utilization of the inherent consistency within each individual network’s magnitude determination process. Assuming that the magnitudes for an earthquake measured by all networks conform to a Gaussian distribution, with a linear function of the unknown true magnitude serving as its mean, we derive the posterior probability distribution of the true magnitude under four different assumptions for the prior distribution: the uninformative uniform distribution, the unbounded Gutenberg–Richter (GR) magnitude–frequency law, the GR magnitude–frequency relationship restricted by the detection rate, and the truncated GR law as priors. We assess the robustness of the method by a test on several synthetic catalogs and then use it to merge the catalogs compiled by five seismic networks in Italy. The results demonstrate that our proposed magnitude-merging algorithm effectively combines the catalogs, resulting in robust and unified data sets that are suitable for seismic hazard assessment and seismicity analysis.

Development of a new tuning method for an radio frequency quadrupole accelerator

Tuning is a critical step in the low-power test of the radio frequency quadrupole (RFQ) accelerator. A 163 MHz RFQ for boron neutron capture therapy (BNCT) at Lanzhou University has been fully assembled. Its designed output energy is 2.6 MeV, and the designed output current in continuous wave mode is 30 mA. Before the feeding of high power, a low-power tuning was performed. First, based on the analysis of the tuning algorithm, a new tuning code capable of tuning the RFQ longitudinal field distribution to any desired target field distribution has been developed using Matlab. The tuning code mainly consisted of two parts: the data processing module and the tuning module, including sub-functions such as smoothing processing function and Fourier expansion function. Among them, the smoothing function based on the Gaussian distribution can effectively eliminate random errors in the measured voltage distribution, thereby optimizing the tuning procedure. Then, a new bead-pull system which can directly track the cavity phase shift was built. The bead-pull system was mainly composed of a vector network analyzer, a stepper motor, etc. Finally, the field unflatness of the RFQ was controlled below 1% after 4 times of tuning. The experiment also measured the radio-frequency performance of the RFQ cavity after installing the fixed copper tuners. The results showed that the RFQ operation frequency was 162.937 MHz, the unflatness of the quadrupole voltage was ±0.74%, and the asymmetry of the dipole voltage was ±1.19%, all of which met the requirements of beam dynamics.

DILA: Dynamic Gaussian Distribution Fitting and Imitation Learning-Based Label Assignment for tiny object detection

With the rapid advancement of deep learning technology, significant achievements have been made in the field of general object detection. However, challenges still remain in the detection of tiny objects. There are two main drawbacks: (1) static prior information makes the localization of tiny objects relatively fixed; (2) Intersection over Union (IoU) is highly sensitive to deviations in tiny objects. To this end, we propose a Dynamic Gaussian Distribution Fitting and Imitation Learning-Based Label Assignment (DILA) strategy for Tiny Object Detection. Specifically, to address the positional deviation of effective receptive fields at different network layers during Gaussian modeling, DILA first designs an Adaptive Dynamic Calculation Strategy (ADCS) to compute estimation factors for the effective receptive field in different feature spaces, dynamically modeling prior information using Gaussian distribution. Then, DILA introduces a new Balance of Gaussian Scaling-aware Metric (BGSM) to measure the similarity between tiny bounding boxes and predefined anchors, instead of using IoU, which is highly sensitive to tiny pixel shifts, for sample assignment, thereby providing a more accurate basis for label assignment. Finally, a Detail Information Imitation Compensation Module (DIM) is presented to improve and compensate for the detailed information of tiny objects that troubles label assignment, achieving balanced learning for tiny objects. The proposed DILA strategy can be seamlessly integrated into various anchor-based detectors. Extensive experiments were conducted on three publicly available datasets for tiny object detection. The results indicate that when DILA is embedded into Faster RCNN, it outperforms other state-of-the-art methods in terms of detection performance for tiny objects, achieving an improvement in average precision of 10.3%, 1.5%, and 4.2% on AI-TOD, SODA-D, and VisDrone2019, respectively. The source codes and results are available at: https://github.com/chnu-cpl/DILA.

Charged compact star with Gaussian density profile showing spin retardation

A charged compact star is modelled within the framework of general relativity and electromagnetism to investigate the intricate complexities arising from charge accumulation through the accretion of surrounding charged baryonic matter, charged dark matter, or both. The Einstein-Maxwell field equations are solved for the compact star PSRJ0740+6620 in anisotropic regime by employing a Gaussian type density profile over a coherent background. A radially modulated exponential function is used as a seed ansatz for coherently connecting the class-one type metric. The structural stability and feasibility are then probed through physical bounds on stellar parameters at equilibrium. The key findings associated with charge accretion emphasised: (i). the existence of a transition zone close to mass M∈[1.262,1.271]M⊙ and radius R∈[12.497,12.505]km, indicating the formation of a core–shell type stellar structure (ii). the plane shifting of intrinsic force fields and (iii) the spin retardation, both suggest a non-vanishing spin-charge coupling between the stellar spin and the accreted charge, whether it be from baryonic matter, dark matter, or both.

Clinical impact of DVH uncertainties

Dose-volume histograms (DVH), along with dose and volume metrics, are central to radiotherapy planning. As such, errors have the potential to significantly impact the selection of appropriate treatment plans. Dose distributions that pass tests in one TPS may fail the same tests when transferred to another, even if using identical structures and dose grid information. This work shows the design and implementation of methods for assessing the accuracy of dose and volume computations performed by treatment planning systems (TPS), and other analytical tools. We demonstrate examples where differences in calculations between systems can change the assessment of a plan’s clinical acceptability. Our work also provides a more detailed DVH analysis of single targets than earlier published studies. This is relevant for SRS plans and small structure dose assessments. Very small structures are a particular problem because of their coarse digital representation, and the impact of this is thoroughly examined.Reference DVH curves were derived mathematically, based on Gaussian dose distributions centered on spherical structures. The structures and dose distributions were generated synthetically, and imported into RayStation, MasterPlan, and ProKnow. Corresponding DVHs were analytically derived and taken as ground truth references, for comparison with the commercial DVH calculations. Two commonly used dose metrics PCI and MGI were used to determine the limit of calculation accuracy for small structures. In addition, to measure the DVH differences between a larger range of commercial DVH calculators, the D95 metric from a set of real clinical plans was compared across both the 3 DVH calculators under test, and across a further six TPSs from other hospitals.We show that even slight deviations between the results of DVH calculators can lead to plan check failures, and we illustrate this with the commonly used D95 planning metric. We present clinical data across eight planning systems that highlight instances where plan checks would pass in one software and fail in another due to DVH calculation differences. For the smallest volumes tested, errors of up to 20% were observed in the DVHs. RayStation was tested down to a 3 mm radius sphere (≈0.1 cc) and this showed close to 10% error, reducing to 1% for 10 mm radius (≈4.0 cc) and 0.1% for 20 mm radius (≈33 cc). In clinical plans, the variation in D95 was up to 9% for the smallest volumes, and typically around 2% in the range 0.5 cc-20 cc, and 1% in 20 cc-70 cc, falling to <0.1% for large volumes. Paddick Conformity Index (PCI) and Modified Gradient Index (MGI) are commonly used plan quality indicators for very small volumes. For volumes ≈0.1 cc we observed errors of up to 40% in PCI, and up to 75% in MGI.Our study extends the range of tested DVH calculators in published work, and shows their performance over a wider range of volume sizes. We provide quantitative evidence of the critical need to test the accuracy of DVH calculators in the TPS before clinical use. This work is particularly relevant for both stereotactic plan evaluation and for assessment of small volume doses in published dose constraint recommendations. We demonstrate that significant errors can occur in DVHs for volumes less than 1 cc, even if the volumes themselves are calculated accurately. Even for large structures, deviations between the outputs of DVH calculators can lead to indicated or reported plan check failures if they do not include appropriate tolerances. We urge caution in the use of DVH metrics for these very small volumes and recommend that appropriate DVH uncertainty tolerances are set in organ dose constraints when using them to evaluate clinical plans.

Noncommutative wormhole in de Rham-Gabadadze-Tolley like massive gravity

The wormhole solution in dRGT massive gravity is examined in this paper in the background of non-commutative geometry. In order to derive the wormhole model, along with the zero tidal force, we assume that the matter distribution is given by the Gaussian and Lorentzian distributions. The shape function in both models involves the massive gravity parameters m2c1 and m2c2. But the spacetime loses its asymptotic flatness due to the action of the massive gravity parameter. It is noticed that the asymptotic flatness is affected by the repulsive effect induced in the massive gravitons that push the spacetime geometry very strongly. We observed that each model violates the null energy criteria, indicating the presence of exotic matter which is necessary to sustain the wormholes. The exotic matter is measured using the volume integral quantifier. Moreover, it is discovered that the model is stable under the hydrostatic equilibrium condition by utilizing the TOV equation. Finally, our research encompassed an exploration of the repulsive influence exerted by gravity. Our findings demonstrated that the presence of repulsive gravity results in a negative deflection angle for photons following null geodesics. Remarkably, we consistently observed negative values for the deflection angle across all values of r0 in the two scenarios examined. This consistent negativity unequivocally signifies the manifestation of the repulsive gravity effect.

Mixture texture model with weighted generalized inverse Gaussian distribution for target detection

With the improvement of radar resolution, the amplitude distribution of sea clutter has begun to exhibit significant heavy-tailed characteristics. Existing models for sea clutter amplitude distribution do not sufficiently solve this problem, which results in a diminished target detection probability in two-step generalized likelihood ratio test (GLRT) based target detectors. To address this issue and to enhance the radar target detection capabilities, we propose a new compound-Gaussian clutter model based on a weighted mixture of generalized inverse Gaussian distributions to model the texture. The CG-WGIG model demonstrates greater flexibility and effectively captures the characteristics of sea clutter amplitude distributions with heavy tails, thus affording a better fit. We combine this model with the two-step GLRT criterion to propose a GLRT detector endowed with a weighted generalized inverse Gaussian texture (GLRT-WGIG), specifically tailored for detecting range-spread targets (RSTs). We have conducted a rigorous mathematical proof to demonstrate that the constant false alarm rate (CFAR) characteristic of the proposed GLRT-WGIG detector is independent of the covariance matrix, thereby ensuring its robustness in various operational scenarios. Using measured data, we demonstrate that the proposed model and detector are flexible and outperform the existing methods in terms of fitting and detection performance, where we obtain a mean 12.02% MSE of fitting performance promotion.

Flexible density peak clustering for real-world data

In density based clustering, the density peak algorithm has attracted much attention due to its effectiveness and simplicity, and a vast amount of clustering approaches have been proposed based on this algorithm. Some of these works require manual selection of cluster centers with a decision graph, where human involvement leads to uncertainty in clustering results. In order to avoid human involvement, some other algorithms depend on user-specified number of clusters to determine cluster centers automatically. However, it is well known that accurate estimation of number of clusters is a long-standing difficulty in data clustering. In this paper we present a sequential density peak clustering algorithm to extract clusters one by one, thereby determining the number of clusters automatically and avoiding manual selection of cluster centers in the meanwhile. Starting from a density peak, our algorithm generates an initial cluster surrounding the density peak in the first step, and then obtains the final cluster by expanding the initial cluster based on the relative density relationship among neighboring data points. With a peeling-off strategy, we obtain all the clusters sequentially. Our algorithm works well with clusters of Gaussian distribution and is therefore potential for clustering of real-world data. Experiments with a large number of synthetic and real datasets and comparisons with existing algorithms demonstrate the effectiveness of the proposed algorithm.

Spatial Autoregressive Model with Mixture of Gaussian Distribution for the Random Effect: Formulation, Estimation and Application

Spatial Autoregressive Model with Mixture of Gaussian Distribution for the Random Effect: Formulation, Estimation and Application

Charged particle reflection in a magnetic mirror

We study the reflection of electrons in a magnetic field mirror. It is a field with a gradient from a lowest value B0 to a largest one Bm. With this purpose, Montecarlo simulations are made. We use a number of 5,000 particles with random pitch angles. The frequency distribution of these random values follows a Gaussian distribution centered at \theta = 0 and with standard deviation \sigma. Various values of \sigma and also different values of the B0 /Bm ratio are used in the simulations. The simulations show that \sigma has an important influence on the confinement of charged particles, for the different B0 /Bm ratios here studied. However, the percent of reflected particles differs from a B0 /Bm ratio to another in the whole range of \sigma, although for \sigma = 10 the differences between different ratios are small (&lt;5%). The number of reflected particles increases very rapidly with \sigma, in the range of 10° to 40°. For the \sigma range from 20° to 40°, the percent of reflected particles is \leq 20% larger for B0 /Bm = 0.10 than for the 0.55 ratio.

Microstructure and Optical Properties of Au:N Doped Diamond-Like Carbon Films: Effect of Working Pressure

In recent years, the incorporation of impurities (metallic or non-metallic) into diamond-like carbon films for industrial and biological applications has garnered considerable attention from researchers. In this study, gold nanoparticles and nitrogen impurities were introduced into diamond-like carbon using a co-deposition method involving Radio Frequency Plasma-Enhanced Chemical Vapor Deposition (RF-PECVD) and Radio Frequency Sputtering (RF-sputtering),modifying the working pressure from 14.5 to 19.5 mTorr. X-ray Diffraction (XRD) patterns confirmed the presence of gold nanocrystals in the samples. The surface morphology of the films was analyzed using images obtained from Scanning Electron Microscopy (SEM) and Atomic Force Microscopy (AFM) subjected to statistical and fractal analyses. These investigations revealed non-symmetric Gaussian distributions of the grains, demonstrating a multifractal nature in all samples, as well as a complex relationship between film roughness and working pressure. Films prepared at working pressures of 16.5 and 18.5 mTorr exhibited the roughest and smoothest surfaces, respectively. Fast Fourier Infrared (FTIR) spectroscopy was used to identify functional groups and to estimate the sp2/sp3 ratio. Raman spectra show D and G bands associated with the disordered graphitic carbon of the DLC, with the intensity of the G band being higher than that of the D band, indicating a higher sp2 bonding content compared to sp3 bonding. Subsequently, the absorption UV-visible spectrum of the samples was examined, confirming the presence of gold nanoparticles in the films, as evidenced by the occurrence of a Localized Surface Plasmon Resonance peak, whose location dependent on the working pressure used during deposition. These observations are consistent with other microscopic and structural analyses.

Machine Learning and Traditional Approaches in Shear Reliability of Steel Fiber Reinforced Concrete Beams

In the field of structural engineering, the exploration of steel fibre reinforced concrete (SFRC) beams has recently intensified, particularly due to their improved tension and shear performance of structure. This study pioneers a novel reliability analysis of shear capacity predictions for SFRC beams, distinctively classifying the datasets into high-strength (HSFRC) and normal-strength (NSFRC) categories. A comprehensive database of 142 HSFRC and 265 NSFRC beams serves as the foundation for this analysis, which critically examines the standard Gaussian distribution in shear design models and proposes the Lognormal and Weibull distributions as more precise alternatives. Employing advanced First-order (FORM) and Second-order Reliability Methods (SORM), the study covers a broad spectrum of load conditions, including dead, live, snow, wind, and seismic loads, to evaluate various empirical, semi-empirical and machine learning proposed shear capacity prediction formulas. One of the key innovations of this research is the development of differentiated resistance coefficients for various risk levels in the reliability analysis, allowing future structural designers to tailor their designs according to specific risk profiles. This approach significantly enhances the balance between economic efficiency and structural safety based on the evolution of different target reliability indexes. The study reveals that existing design equations for SFRC beams generally lean towards conservatism. This study found that formulas derived from machine learning exhibited superior prediction ability compared to traditional theoretically derived regression formulas. When compared the proposed machine learning formulas, the Tarawneh's formula demonstrated better prediction ability than the Kara's formula when applied to larger datasets. However, high predictive power does not necessarily equate to high reliability. Machine learning formulas prioritize predictive accuracy, often at the expense of insufficient redundancy for ensuring safety. Overall, it introduces Kara's formula for NSFRC beams, which stands out with its superior predictive performance, offering an optimal balance of safety and cost-efficiency. Ashour's formula is also identified as a more effective and safer option for HSFRC beams. Complementing these findings, the extensive sensitivity analysis of the collected data not only confirms the robustness of the conclusions but also prepares for the integration of broader datasets in the future.

FP‐Flow: Feature pyramid flow model for fabric defect detection

AbstractFabric defect detection is a crucial aspect of fabric production. At present, deep learning detection methods mostly rely on supervised learning. To tackle this issue, this study proposes an unsupervised fabric defect detection approach based‐on normalising flow. The method only needs to train the mapping of the feature probability distribution of defect‐free samples to a Gaussian distribution. In the inference process, the location of defects can be determined by testing the distance between the probability distribution of image features and the estimated distribution. To adapt to the complex background and various minor defects of the fabric, a feature pyramid structure is adopted. Moreover, considering the gradient vanishing and network degradation caused by deep layers during training, a residual structure is incorporated into the model. Experimental results demonstrate that the feature pyramid flow model outperforms other methods in defect detection across multiple datasets, with an average score rate of 98.7% and 100% for pixel‐level area under the curve (AUC) receiver operating characteristic and image‐level AUC, respectively, compared to an average score rate of 91.1% and 85.4% for other methods.

Optimizing kernel width for new risk-sensitive loss: A generalized algorithmic approach

This paper outlines a novel approach to the development of adaptive filtering algorithms, which minimizes susceptibility to the effects of non-Gaussian measurement noise. Using the generalized Gaussian density (GGD) function as the kernel function, we developed a generalized kernel risk-sensitive loss (GKRSL) criterion by which to derive the generalized minimum kernel risk-sensitive loss (GMKRSL) algorithm. We also developed a variable kernel width algorithm for GMKRSL (VKW-GMKRSL) to address the trade-off between convergence rate and steady-state misalignment resulting from a constant kernel width. In simulations, GMKRSL and VKW-GMKRSL outperformed existing works in system identification performance.