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This study examines population and small sample properties of the standardized fifth and sixth moments – the "higher moments" – for assessing univariate normality against bimodal and selected unimodal alternatives. Population parameters and distributions for selected bimodal mixtures are calculated and contrasted with those for the normal distribution. Using Gram-Charlier series expansion methods, an omnibus goodness of fit test incorporating the higher moments is specified and Monte Carlo simulation used to compare test power with parametric tests based on the standardized third and fourth sample moments: the asymptotic and size corrected versions of the Jarque-Bera score test and the omnibus D'Agostino K2 test. The studentized range and directional tests using the third through sixth moments are also considered. The results demonstrate that incorporating the fifth and sixth moments can provide enhanced parametric normality test power for bimodal normal mixture alternatives but not for various unimodal alternatives. [ABSTRACT FROM AUTHOR]

Supercooled large droplets (SLDs) under natural icing conditions have the characteristics of easy deformation in motion and easy splashing on impact, and a bimodal droplet size distribution that has received less attention. The modified form of the Rosin-Rammler function was improved to achieve a more accurate nonlinear fitting of the SLD distribution curve. The droplet size distribution was divided into non-equipartition continuous multiple components. The drag source term of each component was coupled with the overall droplet size distribution, and the Eulerian equations of each component of SLDs were solved simultaneously. A new coupled Eulerian method for non-equipartition continuous multi-size droplets was proposed to simulate the impact characteristics of SLDs, and the SLD collection coefficients were validated. Effects of the ratio between the number of large and small droplet components and the number of all components on the simulation results were investigated to select a better combination based on stable convergence calculation steps and the calculation time. This new method was added to the multi-step icing numerical method, and the accuracy and robustness of the method in icing shape prediction were verified based on the freezing drizzle, median volume diameter < 40 μm (FZDZ, MVD < 40 μm) icing condition. Airfoil icing characteristics based on the bimodal and monomodal distribution were compared, and the icing shapes at the leading edge were similar. Still, the upper and lower limits of the icing shapes with the bimodal distribution were nearer to the trailing edge and the ice layer was thicker there. [ABSTRACT FROM AUTHOR]

In this paper, the solutions of an extended form of the Fractional-order Neutron Point Kinetics (FNPK) equation in terms of Caputo-time derivatives of the same order are investigated. Instead of using a Caputo derivative, a distributed-order fractional derivative in the Caputo sense was employed in the term of the FNPK equation which is multiplied by the reactivity. This term plays an important role in the description of neutron kinetics during the start-up, shutdown, and steady-state processes in nuclear reactors. The extended (DFNPK) model was solved using the beta, normal, bimodal and Dirac delta distributions to investigate their effect on the transient state solutions of the neutron density. Regardless of the distribution used, the most significant finding is that a destabilizing effect on the neutron density is induced when the mode (or the instant of application of the Dirac delta) of the distribution tends to one while maintaining the orders of the Caputo-time derivatives constant. What defines the destabilizing effect are large magnitude oscillations, a rapid decay, and an oscillation-free steady state with a monotonic increase that is parallel to but somewhat above the trend determined by the FNPK equation. The extended model is anticipated to be effective for modeling neutron density dispersion in a highly heterogeneous medium that may be described using distributed derivatives. [ABSTRACT FROM AUTHOR]

Garnet is an exceptionally useful mineral for reconstructing the evolution of metamorphic rocks that have experienced multiple tectonic or thermal events. Understanding how garnet crystallizes and its mechanical behaviour is important for establishing a petrological and temporal record of metamorphism and deformation and for recognizing multiple geologic stages within the growth history of an individual crystal. Here, we integrate fine‐scale microstructural (electron backscatter diffraction [EBSD]) and microchemical (Laser Ablation Inductively Coupled Plasma Mass Spectrometry [LA‐ICP‐MS] mapping) data obtained on a polycyclic garnet‐bearing micaschist from the Alpine belt. Results suggest that fragmentation of pre‐Alpine garnet porphyroblasts occurred during the late pre‐Alpine exhumation and/or the onset of the Alpine burial, such that the older pre‐Alpine garnet fragments were transported/redistributed during Alpine deformation and acted as nucleation sites for Alpine garnet growth. These processes produced a bimodal garnet size distribution (millimetre‐ and micrometre‐sized grains). Thermodynamic modelling indicates that Alpine garnet grew during the final stage of burial (from 1.9 GPa 480°C to 2.0 GPa 520°C) and early exhumation (down to 1.6 GPa 540°C) forming continuous idioblastic rims on and sealing fractures in pre‐Alpine garnet grains. We propose that fragmentation–overgrowth processes in polycyclic rocks, coupled with ductile deformation, may produce a bimodal garnet size distribution in response to fragmentation and re‐distribution of pre‐existing grains; these clasts can act as new nucleation sites during a subsequent orogenic cycle. [ABSTRACT FROM AUTHOR]

The given text is a list of references and acknowledgments for a research article on the topic of human brain size and evolution. It includes various studies and papers that have explored the changes in brain size over time, as well as the factors that may have influenced these changes. The article discusses different perspectives and theories on the subject, including the impact of climate change and the transition to complex societies. The references cover a wide range of topics related to human evolution and brain morphology, providing a comprehensive overview of the current research in the field. [Extracted from the article]

We present HAETAE (Hyperball bimodAl modulE rejecTion signAture schemE), a new lattice-based signature scheme. Like the NIST-selected Dilithium signature scheme, HAETAE is based on the Fiat-Shamir with Aborts paradigm, but our design choices target an improved complexity/compactness compromise that is highly relevant for many space-limited application scenarios. We primarily focus on reducing signature and verification key sizes so that signatures fit into one TCP or UDP datagram while preserving a high level of security against a variety of attacks. As a result, our scheme has signature and verification key sizes up to 39% and 25% smaller, respectively, compared than Dilithium. We provide a portable, constanttime reference implementation together with an optimized implementation using AVX2 instructions and an implementation with reduced stack size for the Cortex-M4. Moreover, we describe how to efficiently protect HAETAE against implementation attacks such as side-channel analysis, making it an attractive candidate for use in IoT and other embedded systems.

In order to improve the wear resistance of coarse-grained WC–Co cemented carbides, the fine WC powder were used to reinforce the metallic binder. These WC–Co-based cemented carbides having bimodal WC grain size distributions were synthesized by liquid phase sintering. For comparison, the cemented carbides having unimodal WC grain size distributions were synthesized. The microstructure, hardness, fracture toughness and wear resistance of these cemented carbides were investigated. The results show that adding fine WC powder is an effective method to improve the wear resistance of coarse-grained WC–Co cemented carbides. The WC size, mean free path and fracture toughness decrease with the addition of fine WC powder, while the hardness exhibits an opposite trend. The impact-wear coefficient of bimodal distribution cemented carbides is noticeably lower than that of the unimodal one with the same hardness, which means that the cemented carbides with bimodal grain structure have better combination of hardness and impact-abrasive wear resistance. The impact-abrasive wear mechanism of the bimodal cemented carbides is that the fine WC grains prevent abrasive wear and the coarse WC grains prevent impact wear. [ABSTRACT FROM AUTHOR]

Silicon nitride (Si 3 N 4) ceramics, with different ratios of fine and coarse α-Si 3 N 4 powders, were prepared by spark plasma sintering (SPS) and heat treatment. Further, the influence of coarse α-Si 3 N 4 powder on densification, microstructure, mechanical properties, and thermal behavior of Si 3 N 4 ceramics was systematically investigated. Compared with fine particles, coarse particles exhibit a slower phase transition rate and remain intact until the end of SPS. The remaining large-sized grains of coarse α-Si 3 N 4 induce extensive growth of neighboring β-Si 3 N 4 grains and promote the development of large elongated grains. Noteworthy, an appropriate number of large elongated grains distributed among fine-grained matrix forms bimodal microstructural distribution, which is conducive to superior flexural strength. Herein, Si 3 N 4 ceramics with flexural strength of 861.34 MPa and thermal conductivity of 65.76 W m−1 K−1 were obtained after the addition of 40 wt% coarse α-Si 3 N 4 powder. [ABSTRACT FROM AUTHOR]

This work focuses on increasing the solids content of water‐based coating materials such as paints, other coatings or adhesives while attempting to reduce the amount of surfactant in the final latex. The synthesis of a latex with a bimodal particle size distribution was carried out by combining RAFT and classical emulsion polymerization processes. By employing the RAFT polymerization, the population of small particles was created by self‐ordering the block copolymer chains, consisting of a hydrophilic block based on methacrylic acid or sodium 4‐styrenesulfonate and another hydrophobic block based on styrene. The final latex was made by adding a pre‐emulsion prepared from the latex of small particles and a mixture of monomers and surfactants to the latex of large particles made via conventional emulsion polymerization. The final bimodal latex thus obtained had a solids content of 65% mass with a viscosity value of around 2.0 Pa.s at a shear rate of 20 s−1. [ABSTRACT FROM AUTHOR]

The atomization of metastable superheated water injected into the atmosphere through a convergent-divergent nozzle at a temperature of 240–260°C was studied experimentally. The dispersion structure of the atomization plume is bimodal with a predominance of submicron droplets, whose proportion increases with increasing temperature and reaches 80% at the nozzle outlet at a water temperature of 260°C. The influence of droplet coagulation on the distribution of the proportion of large droplets along the length of the atomization plume was estimated. [ABSTRACT FROM AUTHOR]

The existing literature establishes the pattern that exporters in developed countries sell most of their output in their own domestic markets; however, recent evidence suggests that the export intensity distributions of 47 countries exhibit peaks at each end. In this study, we study the characteristics of pure exporters, namely exporters at the right‐hand peak of the distribution. We use Thailand's firm‐level panel data covering the period from 2007 through 2017 to estimate factors that explain the likelihood that a firm self‐selects to be a pure exporter. We do not find evidence that firm‐level productivity can explain the decision to become a pure exporter. Rather, the main factors that determine the decision are the capital–labour ratio, the amount of labour, foreign ownership, investment promotion and firm age. [ABSTRACT FROM AUTHOR]

In this paper, Ti-48Al-2Cr-2Nb alloy with ultrafine/fine-scale bimodal grain structure was prepared by high-energy ball milling and hot-pressing sintering. The microstructure, room temperature mechanical properties and fracture mechanism of the alloy were investigated by means of XRD, SEM, TEM, and compressive tests. The results show that the TiAl alloy with ultrafine/fine grained bimodal structure is mainly composed of equiaxed γ-TiAl grains, dispersed island-like α2-Ti3Al phase and a small amount of lamellar γ/α2 microstructure, and possesses satisfied room temperature compressive properties, with the yield strength, fracture strength, and compression rate of 2047, 2693 MPa, and 4.85%, respectively. The fracture morphology is smooth, and the tear layer is small and thin, showing the fracture forms of translamellar and intergranular/interlamellar fractures. [ABSTRACT FROM AUTHOR]

In this paper, a new form of alpha-beta-skew-Laplace distribution is proposed under Balakrishnan [3] mechanism and investigated some of its related distributions. The moments, distributional properties and some extensions of the proposed distribution have also studied. Finally, the suitability and the appropriateness of the proposed distribution has tested by conducting data fitting experiment and comparing the values of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) with the values of some other related distributions. Likelihood Ratio test is used for discriminating between the nested models. [ABSTRACT FROM AUTHOR]

Background: Flatfoot (Pes Planus), often regarded as a physiological deviation in children, is of concern to parents because there is no test to predict the development of foot arch. This study aimed to use a new diagnostic flatfoot criterion to determine 1) how the footprint index changes during the development of foot arches, 2) what factors can predict a foot arch development, and 3) whether foot arch development could be a process of body growth. Methods: 572 children were enrolled in a prospective longitudinal study of anthropometrical parameters and physical fitness twice at age of 6.7 and 8.2 years. The bimodal frequency distribution of the Chippaux-Smirak index (CSI) of the footprint was used to define flatfoot as CSI 0.61. Body measurements and physical fitness tests were compared between children with flatfeet who developed foot arches and children who did not. Results: Of 263 children with flatfeet, the CSI significantly changed from 0.72 to 0.46 in 70 children who developed foot arches over 1.5 years and the others had minimal change in the index. Children with foot arch development had a lower initial CSI, improved boys' performance in one-leg balance, and less increase in girls’ body height than children who remained flatfooted, whereas sex and weight were similar in both groups. Conclusion: This longitudinal study with the bimodal distribution of the CSI investigated how the development of foot arch advances in children around age 7. A significant and unique pattern in change of the CSI suggests involvement of a maturational stage in foot arch development. Along with the improved performance in one-leg balance, the unidirectional transition from flatfoot to non-flatfoot is associated with improvement in motor control of the ankle. Trial registration: Chinese Clinical Trial Registry (ChiCTR–OCS–14004300).

Purpose: The laser diffraction method has become increasingly popular during the last decades to measure the grain size distribution of various environmental particles originating from sediments, soils or river suspended sediments. However, the measurement of multimodal samples containing sands is still an issue. The aim of this study is to discuss the limits of the laser diffraction method in measuring the sand fraction of bimodal samples. Materials and methods: A systematic comparison of four commercially available laser diffraction instruments (Cilas 1190L, Fritsch Analysette 22 Nanotec, Malvern Mastersizer 3000, and Sequoia Lisst 200X) is performed on 12 unimodal and bimodal samples of glass beads and silica-rich natural sands. Results: Measured grain size distributions differ between the four instruments. Most important differences occur in bimodal samples containing a sand fraction, where some instruments have major difficulties to estimate the proportion of the fine towards coarse mode correctly, with errors up to 100%. Conclusion: In accordance with the observation of coarse particles accumulating in low-velocity areas within the sampling tank, the creation of an imperfect suspension within the sampling tank is considered as a main reason for the differences. The choice of the most suitable measurement parameters is crucial to obtain accurate and precise measurements. However, these parameters cannot be compared between the instruments, nor exist precise user guidelines. Therefore, testing several measurement parameters before analyzing novel sample compositions using laser diffraction is recommended. [ABSTRACT FROM AUTHOR]

The effects of body force/external pressure gradient on the statistical behaviours of the reaction progress variable variance and the terms of its transport equation have been investigated for different turbulence intensities using DNS data of statistically planar flames. Since the extent of flame wrinkling increases with the strengthening of body force promoting unstable stratification, the scalar variance has been found to decrease under strong body force promoting stability. This trend is particularly strong for low turbulence intensities where the probability density function of the reaction progress variable cannot be approximated by a bimodal distribution. Therefore, an algebraic relation for the reaction progress variable variance, derived based on a presumed bimodal probability density function of reaction progress variable, cannot be used for general flow conditions. The contributions of chemical reaction and scalar dissipation rates in the scalar variance transport equation remain leading order source and sink, respectively for all cases irrespective of the strength and direction of the body force. The counter-gradient type transport is found to weaken with increasing body force magnitude when the body force is directed from the heavier unburned gas to the lighter burned gas side of the flame brush, and vice versa. Although a scalar dissipation rate-based reaction rate closure can be utilised to model the reaction rate contribution to the scalar variance transport accurately, the dissipation rate contribution due to the gradient of the Favre-averaged reaction progress variable cannot be ignored and it plays a key role for large magnitudes of body force promoting stable stratification. An algebraic closure of the scalar dissipation rate, originally proposed for high Damköhler number combustion, has been modified for the thin reaction zones regime combustion by incorporating the effects of Froude number. This model has been shown to predict the scalar dissipation rate accurately for all cases considered here. [ABSTRACT FROM AUTHOR]

In this paper we define a new auction, called the Draw auction. It is based on the implementation of a draw when a minimum price of sale is not reached. We find that a Bayesian Nash equilibrium is reached in the Draw auction when each player bids his true personal valuation of the object. Furthermore, we show that the expected profit for the seller in the Draw auction is greater than in second-price auctions, with or without minimum price of sale. We make this affirmation for objects whose valuation can be modeled as a bimodal density function in which the first mode is much greater than the second one. Regarding the Myerson auction, we show that the expected profit for the seller in the Draw auction is nearly as good as the expected profit in the optimal auction, with the difference that our method is much more simple to implement than Myerson's one. All these results are shown by computational tests, for whose development we have defined an algorithm to calculate Myerson auction. [ABSTRACT FROM AUTHOR]

Aims: This study investigated insulinoma‐associated‐2 autoantibody (IA‐2A) and zinc transporter 8 autoantibody (ZnT8A) distribution in patients with type 1 diabetes (T1D) and latent autoimmune diabetes (LAD) and the autoantibodies' association with clinical characteristics and HLA‐DR‐DQ genes. Materials and Methods: This cross‐sectional study recruited 17,536 patients with diabetes from 46 hospitals across China. A total of 189 patients with T1D and 58 patients with LAD with IA‐2A positivity, 126 patients with T1D and 86 patients with LAD with ZnT8A positivity, and 231 patients with type 2 diabetes (T2D) were selected to evaluate islet autoantibodies, clinical phenotypes, and HLA‐DR‐DQ gene frequency. Results: IA‐2A was bimodally distributed in patients with T1D and LAD. Patients with low IA‐2A titre LAD had lower fasting C‐peptide (FCP) (p < 0.01), lower postprandial C‐peptide (PCP) (p < 0.001), and higher haemoglobin A1c (HbA1c) levels (p < 0.05) than patients with T2D. Patients with high IA‐2A titre LAD were younger than patients with low IA‐2A titre LAD (p < 0.05). Patients with low IA‐2A titre T1D had lower FCP (p < 0.01), lower PCP (p < 0.01), and higher HbA1c levels (p < 0.05) than patients with high IA‐2A titre LAD. HLA‐DR‐DQ genetic analysis demonstrated that the frequency of susceptible HLA haplotypes was higher in IA‐2A‐positive patients (p < 0.001) than in patients with T2D. Patients with high ZnT8A titre LAD had lower FCP (p = 0.045), lower PCP (p = 0.023), and higher HbA1c levels (p = 0.009) and a higher frequency of total susceptible haplotypes (p < 0.001) than patients with low ZnT8A titre LAD. Conclusions: IA‐2A in patients with T1D and LAD was bimodally distributed, and the presence of IA‐2A could demonstrate partial LAD clinical characteristics. ZnT8A titre had a certain predictive value for islet functions in patients with LAD. [ABSTRACT FROM AUTHOR]

Accurate classification of maturity status and estimation of size at 50% maturity for male crabs are important to the management of North Pacific crab stocks, which form the basis of several economically valuable fisheries. We demonstrate a straightforward maturity classification approach applied to male Tanner crabs (Chionoecetes bairdi), based on the use of log-transformed chela height distributions calculated via kernel density functions. The linear equation defining the relationship between the minima of these chela height distributions, and the midpoint of the corresponding carapace width bins is then used to estimate the incidence of maturity by size group across the population. We demonstrate the performance of this approach relative to two other currently applied methodologies. Finally, we apply this method to assess annual size at 50% maturity in eastern Bering Sea male Tanner crabs, and spatiotemporal trends in this parameter. We demonstrate the existence of high interannual and spatial variability in this population metric and find evidence of a decline in size at maturity in the western stock.

Bimodal data sets are very common in different areas of knowledge. The crude birth rates data, fish length data, egg diameter data, the eruption and interruption times of the Old Faithful geyser, are examples of this type of data. In this paper, a new class of symmetric density functions for modeling bimodal data as described above are presented. From density functions with support on [ 0 , + ∞) , the symmetry is getting by reflecting the density function in the negative semi-axis with their respective normalization. In this way, if the primitive density function is unimodal, then the resulting density will be bimodal. We introduce asymmetry parameters and study their behavior, in particular the values of their modes and some other statistical values of interest. The cases for densities generated by Gamma, Weibull, Log-normal, and Birnbaum-Saunders densities, among others are studied. Statistical inference is performed from a classical perspective. A small simulation study to evaluate the benefits and limitations of the new proposal. In addition, an application to a data set related to the fetal weight in grams obtained through ultrasound in a sample of 500 units is also presented; the results show the great usefulness of the model in practical situations. [ABSTRACT FROM AUTHOR]

Particle size inversion of dynamic light scattering (DLS) is a typically ill-posed problem. Regularization is an effective method to solve the problem. The regularization involves imposing constraints on the fitted autocorrelation function data by adding a norm. The classical regularization inversion for DLS data is constrained by the L2 norm. In the optimization equation, the norm determines the smoothness and stability of the inversion result, affecting the inversion accuracy. In this paper, the Lp norm regularization model is constructed. When p is 1, 2, 10, 50, 100, 1000, and ∞, respectively, the influence of their norm models on the inversion results of data with different noise levels is studied. The results prove that overall, the inversion distribution errors show a downward trend with the increase of p. When p is larger than 10, there is no significant difference in distribution error. Compared with L2, L∞ can provide better performance for unimodal particles with strong noise, although this does not occur in weak noise cases. Meanwhile, L∞ has lower sensitivity to noise and better peak resolution, and its inverse particle size distribution is closer to the true distribution for bimodal particles. Thus, L∞ is more suitable for the inversion of DLS data. [ABSTRACT FROM AUTHOR]

Modelling is challenging topic and using parametric models is important stage to reach flexible function for modelling. Weibull distribution has shape and scale parameters which play the main role for modelling. Bimodality parameter is added and so bimodal Weibull distribution can capture real data set with bimodality which can be actually combination of two populations. The properties of the proposed distribution and estimation method are examined extensively to show its usability in modelling accurately and safely for practitioners. After examination as first stage in modelling issue, it is appropriate to use bimodal Weibull for modelling bimodality in real data sets if it exists. Two estimation methods including objective functions are used to estimate the parameters of shape, scale and bimodality parameters of function. The second stage in modelling is overcome by using heuristic algorithms for optimization of function according to parameters due to the fact that converging to global point of objective function is performed by heuristic algorithms from stochastic optimization. Real data sets are provided to show the modelling competence of objective functions from bimodal forms of Weibull and Gamma distributions having well defined shape, scale and bimodality parameters and potentially less parameters when compared with the existing distributions. [ABSTRACT FROM AUTHOR]

Aftershocks, background earthquakes, and their spatiotemporal parameters have been studied for decades for the purpose of hazard assessment and forecasting. Methods for determining these parameters or seismic attributes are becoming increasingly sophisticated and varied; some optimize the results to fit observations using trial and error, while others do the same by giving prescriptions for a limited region. Here, we propose a method that is potentially useful in general hazard assessment and forecasting applications. We categorized the earthquakes into two groups, aftershocks (triggered events) and background earthquakes, by introducing the network distance, i.e., the shortest distance between two events of equal magnitude within a modified interevent time, into the k-means clustering, which couples the modified interevent time and magnitude hierarchically. Our results show a bimodal distribution consisting of a power law at shorter network distances and a lognormal distribution at longer network distances, implying that earthquakes of magnitudes larger than the characteristic magnitude, found to be 4.5 for Taiwan and 4.3 for California, may be only weakly linked to other same magnitude earthquakes and hence are hard to be triggered even by events of larger size. [ABSTRACT FROM AUTHOR]

In this paper, we introduce bimodal extensions, one symmetric and one asymmetric, of the logistic distribution. We define this new density and study some basic properties. We draw inferences from the moment estimator and maximum likelihood approaches. We present a simulation study to assess the behaviour of the moment and maximum likelihood estimators. We also study the singularity of the Fisher information matrix for particular cases. We offer applications in real data and compare them with a mixture of logistics distributions. [ABSTRACT FROM AUTHOR]

Quantitative analysis of error sources in wave measurement intercomparison under real-world conditions remains challenging due to various factors such as spatial and temporal offsets in the field, diverse configurations of wave sensors and platforms, and distinct measurement algorithms. This study introduces a modified error analysis method based on sampling variability. Measurements from two co-deployed Datawell Waverider buoys at the National Marine Test Site (Weihai) in China offer an opportunity to assess the spatial variability error. The results reveal that for non-directional wave parameters, like significant wave height and mean zero-crossing period, the wave conditions in the field can be considered stationary, with random errors primarily arising from inherent sampling variability. Spatial offsets significantly impact directional wave parameters at peak frequencies, with large deviations (greater than 20°) in peak wave direction primarily attributed to bimodal distribution. For data with significant wave heights exceeding 0.5 m, random errors in the mean wave direction at the same frequency can be mainly attributed to sampling variability. The bulk directional wave parameters weighted by the energy spectrum demonstrate lower sensitivity to spatial offsets, and there is excellent agreement between the bulk mean directions when considering only the unimodal distribution data. • Wave intercomparison of two co-deployed Datawell Waverider buoys was analyzed. • Random error of non-directional parameters mainly arises from sampling variability. • The directional wave parameters at peak frequencies are sensitive to spatial offsets. • Excellent agreement between the bulk mean direction of unimodal distribution data. [ABSTRACT FROM AUTHOR]

In this work, we propose a new bimodal distribution with support in the real line. We obtain some properties of the model, such as moments, quantiles, and mode, among others. The computational implementation of the model is presented in the tpn package of the software R. We perform a simulation study in order to assess the properties of the maximum likelihood estimators in finite samples. Finally, we present an application to a bimodal data set, where our proposal is compared with other models in the literature. [ABSTRACT FROM AUTHOR]

A number of soils and parent rocks at different stages of weathering were investigated for the formation of heterogeneous wettability under residual hydrophobic contamination in situ. The aim of the study was to determine specific wetting contact angles of soils and parent rocks under different conditions. The wetting contact angle was measured by the captive bubble method, which implied attaching an air bubble to the specially prepared horizontal surface of a water-placed specimen with subsequent measuring the wetting contact angle according to the profile of the bubble's photo. The soil specimens were artificially hydrophobized using media containing less than 1 wt % of oil degradation products with adapted microflora. Leached chernozem, alluvial silty loam, bentonite, dolomite–clayey marl, ornamental marl, and phyllite were studied. Based on the Pearson's goodness-of-fit criterion, good angular data approximation by both the von Mises–Tikhonov distribution and the normal distribution was found. The dependence of the types and parameters of statistical distributions of the wetting contact angle on hydrophobization conditions of the specimens was revealed. The formation of the specimens' hydrophobicity exclusively under introduced organic matter and incomplete water saturation conditions was found; at the same time, a high heterogeneity of wettability and hydrophobic areas at wetting contact angles above 129° was manifested. The results of the study can be useful for assessing and predicting the impact of soil hydrophobic contaminants and amendments, as well as for advancing methods for determining the wetting contact angle on the soil surface. [ABSTRACT FROM AUTHOR]

In educational measurement, exploring the method of generating multiple high-quality parallel tests has become a research hotspot. One purpose of this research is to construct parallel forms item by item according to a seed test, using two proposed item selection heuristic methods [minimum parameters–information–distance method (MPID) and minimum information–parameters–distance method (MIPD)]. Moreover, previous research addressing test assembly issues has been limited mainly to situations in which the information curve of the item pool or seed test has a normal or skewed distribution. However, in practice, the distributions of information curves for tests are diverse. These include multimodal distributions, the most common type of which is the bimodal distribution. Therefore, another main aim of this article is to extend the information curves of unimodal distributions to bimodal distributions. Thus, this study adopts simulation research to compare the results of two item, response, theory (IRT)-based item matching methods (MPID and MIPD) using different information curve distributions for item pools or seed tests. The results show that the MPID and MIPD methods yield rather good performance in terms of both two statistical targets when the information curve has a unimodal distribution, and two new methods yield better performance than two existing methods in terms of test information functions target when the information curve has a bimodal distribution. [ABSTRACT FROM AUTHOR]

Carbon slurries as “flowable electrodes” have been used recently in a few electrochemical systems, e.g., electrochemical flow capacitors (EFCs) for energy storage and flow-electrode capacitive deionization (FCDI) for water treatment. These slurries typically have three parts: activated carbon particles, a conductive additive such as carbon black, and an aqueous electrolyte solution. Previously, a particle-based computational model that employs Stokesian dynamics was developed to describe the particle motion and interaction, while simultaneously solving for the charge transfer inside an electrical network of moving particles. In this work, we develop a unified expression of the dynamically varying electrical network. Furthermore, we incorporate a group of smaller particles as the conductive additive, whose effect on the charge transfer of the slurry is studied. The results suggest that at lower concentrations, the small particles may enhance charge transfer by filling interstitial spaces and bridging contacts of large particles; however, at higher concentrations, the benefits are not as clear since direct contacts of the large particles play the dominant role in charge transfer. [ABSTRACT FROM AUTHOR]

In educational measurement, exploring the method of generating multiple high-quality parallel tests has become a research hotspot. One purpose of this research is to construct parallel forms item by item according to a seed test, using two proposed item selection heuristic methods [minimum parameters–information–distance method (MPID) and minimum information–parameters–distance method (MIPD)]. Moreover, previous research addressing test assembly issues has been limited mainly to situations in which the information curve of the item pool or seed test has a normal or skewed distribution. However, in practice, the distributions of information curves for tests are diverse. These include multimodal distributions, the most common type of which is the bimodal distribution. Therefore, another main aim of this article is to extend the information curves of unimodal distributions to bimodal distributions. Thus, this study adopts simulation research to compare the results of two item, response, theory (IRT)-based item matching methods (MPID and MIPD) using different information curve distributions for item pools or seed tests. The results show that the MPID and MIPD methods yield rather good performance in terms of both two statistical targets when the information curve has a unimodal distribution, and two new methods yield better performance than two existing methods in terms of test information functions target when the information curve has a bimodal distribution.

This letter addresses the use of the Sentinel-1 time series with the aim of proposing an automatic and unsupervised coastline detection method that averages the dynamical variations of coastal areas over a limited period of time, e.g., one year. First, we propose applying a temporal averaging filter that allows the temporal variations in coastal areas, e.g., due to tides or vegetation, to be encapsulated, and, at the same time, the speckle to be reduced, without decreasing the spatial resolution of the synthetic aperture radar (SAR) time series. Then, based on the distinctive backscattering values of the sea and land pixels, we will employ an iterative hierarchical tiling method in order to accurately characterize the two classes using bimodal distribution. The distribution is then segmented by a thresholding and region-growing procedure to separate the sea and land classes. A large-scale quantitative comparison between the SAR-derived and open street map (OSM) coastlines allows for a numerical evaluation of the results, i.e., an overall agreement ranging from 80% to 90%. In addition, Sentinel-2 images are used to evaluate the estimated SAR coastline qualitatively. Furthermore, the benefits of having an accurate SAR coastline are shown in the case of two well-known Earth observation-monitoring applications, ship detection, and floodwater mapping. [ABSTRACT FROM AUTHOR]

This study reports the crack-free fabrication of a new high gamma prime precipitation hardened Ni-based superalloy by Laser Powder Bed Fusion (LPBF) process. In the as-built condition, scanning electron microscopy and electron backscattered diffraction analysis indicated the presence of elongated columnar grains with an orientation along 〈1 0 0〉 direction. Following the sub-solvus heat treatment cycle determined using Thermo-Calc software, crack-free microstructure with columnar grains was observed along 〈1 0 0〉 orientation. High-resolution scanning electron microscope analysis revealed a bimodal distribution of gamma prime precipitates and a uniform distribution of carbide precipitates in the heat-treated samples. As a result of heat treatment, hardness increased from 365 HV to 508 HV. The heat-treated samples also displayed excellent yield strength, ultimate tensile strength, and elongation of 939 MPa, 1368 MPa, and 23% respectively at room temperature. Mechanical testing at elevated temperatures confirmed the yield strength, tensile strength, and elongation reached 80 MPa, 106 MPa, and 34% respectively at 1121 °C. The stress rupture test of the heat-treated samples revealed good creep properties with rupture times of 559 h and 75 h, respectively, at 927 °C and 982 °C, for stresses of 152 MPa and 138 MPa.

Abstract Bimodal gene expression (where a gene expression distribution has two maxima) is associated with phenotypic diversity in different biological systems. A critical issue, thus, is the integration of expression and phenotype data to identify genuine associations. Here, we developed tools that allow both: i) the identification of genes with bimodal gene expression and ii) their association with prognosis in cancer patients from The Cancer Genome Atlas (TCGA). Bimodality was observed for 554 genes in expression data from 25 tumor types. Furthermore, 96 of these genes presented different prognosis when patients belonging to the two expression peaks were compared. The software to execute the method and the corresponding documentation are available at the Data access section.

Particle size inversion of dynamic light scattering (DLS) is a typically ill-posed problem. Regularization is an effective method to solve the problem. The regularization involves imposing constraints on the fitted autocorrelation function data by adding a norm. The classical regularization inversion for DLS data is constrained by the L2 norm. In the optimization equation, the norm determines the smoothness and stability of the inversion result, affecting the inversion accuracy. In this paper, the Lp norm regularization model is constructed. When p is 1, 2, 10, 50, 100, 1000, and ∞, respectively, the influence of their norm models on the inversion results of data with different noise levels is studied. The results prove that overall, the inversion distribution errors show a downward trend with the increase of p. When p is larger than 10, there is no significant difference in distribution error. Compared with L2, L∞ can provide better performance for unimodal particles with strong noise, although this does not occur in weak noise cases. Meanwhile, L∞ has lower sensitivity to noise and better peak resolution, and its inverse particle size distribution is closer to the true distribution for bimodal particles. Thus, L∞ is more suitable for the inversion of DLS data.

Abstract We study a five-parameter model called the Weibull Burr XII (WBXII) distribution, which extends several models, including new ones. This model is quite flexible in terms of the hazard function, which exhibits increasing, decreasing, upside-down bathtub, and bathtub shapes. Its density function allows different forms such as left-skewed, right-skewed, reversed-J, and bimodal. We aim to provide some general mathematical quantities for the proposed distribution, which can be useful to real data analysis. We develop a shiny application to provide interactive illustrations of the WBXII density and hazard functions. We estimate the model parameters using maximum likelihood and derive a profile log-likelihood for all members of the Weibull-G family. The survival analysis application reveals that the WBXII model is suitable to accommodate left-skewed tails, which are very common when the variable of interest is the time to failure of a product. The income application is related to player salaries within a professional sports league and it is peculiar because the mean of the player’s salaries is much higher than for most professions. Both applications illustrate that the new distribution provides much better fits than other models with the same and less number of parameters.

Conductive copper paste is a promising material for use in electronic devices, replacing silver or other metal pastes, because of its high conductivity, low electro-migration, and cost. However, the high sintering temperature and the need of an inert sintering atmosphere limit the commercial application of copper paste. In this study, a copper thick film paste for use on alumina was developed using a mixture of copper nanoparticles (50 nm in size) and microparticles (1 μm in size). With this paste, the sintering temperature was as low as 500 °C when the pressure was at ambient pressure. It was found that the bimodal copper film offered the best volume resistivity of 6.26 × 10−8 Ω·m at a weight ratio of micro- to nanoparticles of 2:1. Glass frits were used as an additive to improve the adhesion strength between the copper film and the alumina substrate with minimal change in electrical performance. [ABSTRACT FROM AUTHOR]

The regional adaptive (RAPT) algorithm is particularly useful in sampling from multimodal distributions. We propose an adaptive partitioning of the sample space, to be used in conjunction with the RAPT sampler and its variants. The adaptive partitioning consists in defining a hyperplane that is orthogonal to the line joining averaged coordinates in two separate regions and that goes through a point such that both averaged coordinates are equally Mahalanobis‐distant from this point. This yields an adaptive process that is robust to the choice of initial partition, stabilizes rapidly and is implemented at a marginal computational cost. The ergodicity of the sampler is verified through the simultaneous uniform ergodicity and diminishing adaptation conditions. The approach is compared to the RAPT algorithm with fixed regions and to the RAPT with online recursion (RAPTOR) through various examples, including a real data application. In short, our main contribution is the development of an alternative version of RAPTOR that seems to have no obvious downside and runs 15–35% faster in the examples considered. [ABSTRACT FROM AUTHOR]

• Formations of heart-shaped film and fountain are attributed to two films merging. • Evolution of fountain and size characteristics of splashes are revealed. • Splashes volume concentration shows a bimodal distribution after fountain breakup. The technology of liquid film by jet impingement is widely applied in aerospace, electronics and cleaning. In this paper, the spreading and evolution of the liquid films formed by two continuous jets impinging obliquely on a vertical wall are experimentally studied. The effects of the jet Weber number, jet inclination angle, nozzles spacing and angle between two jets on the films are examined. Results show that three flow patterns are observed as the experimental conditions vary, including two separated liquid films, a heart-shaped liquid film and a heart-shaped film with the fountain sheet breakup. The formation of a heart-shaped liquid film is attributed to the merging of two films and results in the spreading area and length of the film increasing suddenly. The fountain sheet forms when two liquid films merge, and develops with the increase of the jet Weber number. When the balance between the surface tension on the fountain sheet and the inertial force as well as gravity that form the fountain is disrupted, the fountain sheet breaks up, and causes the splashing rate to increase suddenly. The volume concentration of the splashing droplet size displays the bimodal distribution after the occurrence of the fountain sheet breakup, which indicates the existence of two splashing droplet formation mechanisms in the systems, the surface wave and fountain sheet breakup. The height variation of the left and right peaks of the bimodal distribution reflects the competition between the two splashing generation mechanisms. [ABSTRACT FROM AUTHOR]

To reveal the inhibitory effect of stoichiometric methane/air explosions, NaHCO 3 with a bimodal distribution were selected as inhibitors. A 5 L vertical transparent duct was used. All the results revealed that Blend 82 , whose mass fraction contained 80% OP 500 – 600 and 20% OP 200 – 220 NaHCO 3 , exhibited the optimal inhibitory effect. For the bimodal distribution of NaHCO 3 , assessing the inhibitory effect solely on the basis of a single particle size parameter is unreliable. Synergistic effects between particles of different sizes should be considered when the interaction index I S < 1. Multiple size classes of bimodal NaHCO 3 were proposed for use in response surface methodology to predict the inhibitory effect of methane/air flames. Furthermore, we employed a detailed chemical kinetic model to quantify the endothermic and chemical effects of NaHCO 3 on the laminar burning velocity of methane/air flames and established a good relationship between the explosion parameters and laminar flame properties. [Display omitted] • An optimal mass ratio exists between OP 500 – 600 and OP 200 – 220 in NaHCO 3 blends. • Synergistic effects between two inhibitors with different sizes are quantified. • Drop ratios in overpressure can be predicted via response surface methodology. • The endothermic effect of NaHCO 3 is considered in the kinetic calculations. • A correlation between explosion parameters and laminar flame properties is found. [ABSTRACT FROM AUTHOR]

Transcription is a pivotal step in gene expression yet a complex biochemical process. It occurs often in a bursty manner, leading to cell-to-cell variability important for the cells surviving in complex environments. Quantitative experiments of such stochastic transcription call for model analysis in a systematic rather than case-by-case fashion. Here we analyze two general yet biologically-reasonable classes of stochastic transcription models: the first class called promoter models considers that promoter structure is general, and the second class called queuing models considers that waiting-time distributions are general. For the former, we show that there are conjugate relationships between models with different transcription exits. This property well reveals the mechanic principle of stochastic transcription in complex cases of transcription factor regulation. For the latter, we establish an integral equation for the mRNA moment-generating function, through which stationary mRNA moments of any orders can be analytically derived. Finally, we analyze parametric regions for robust unimodality and bimodality. The overall analysis not only lays a foundation for quantitative analysis of stochastic transcription but also reveals how the upstream promoter kinetics impact the downstream expression dynamics.

Aftershocks, background earthquakes, and their spatiotemporal parameters have been studied for decades for the purpose of hazard assessment and forecasting. Methods for determining these parameters or seismic attributes are becoming increasingly sophisticated and varied; some optimize the results to fit observations using trial and error, while others do the same by giving prescriptions for a limited region. Here, we propose a method that is potentially useful in general hazard assessment and forecasting applications. We categorized the earthquakes into two groups, aftershocks (triggered events) and background earthquakes, by introducing the network distance, i.e., the shortest distance between two events of equal magnitude within a modified interevent time, into the k-means clustering, which couples the modified interevent time and magnitude hierarchically. Our results show a bimodal distribution consisting of a power law at shorter network distances and a lognormal distribution at longer network distances, implying that earthquakes of magnitudes larger than the characteristic magnitude, found to be 4.5 for Taiwan and 4.3 for California, may be only weakly linked to other same magnitude earthquakes and hence are hard to be triggered even by events of larger size.

In this paper, we introduce bimodal extensions, one symmetric and one asymmetric, of the logistic distribution. We define this new density and study some basic properties. We draw inferences from the moment estimator and maximum likelihood approaches. We present a simulation study to assess the behaviour of the moment and maximum likelihood estimators. We also study the singularity of the Fisher information matrix for particular cases. We offer applications in real data and compare them with a mixture of logistics distributions.

In this paper, a new form of alpha-beta-skew distribution is proposed under Balakrishnan (2002) mechanism and investigated some of its related distributions. The most important feature of this new distribution is that it is versatile enough to support both unimodal and bimodal as well as multimodal behaviors of the distribution. The moments, distributional properties and some extensions of the proposed distribution have also been studied. Finally, the suitability of the proposed distribution has been tested by conducting data fitting experiment and comparing the values of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) with the values of some other related distributions. Likelihood Ratio testis used for discriminating between normal and the proposed distributions. [ABSTRACT FROM AUTHOR]