Shape Of Distribution Research Articles

Cumulant method for identifying spatial distributions of laser beam intensity

The article considers the identification of spatial distributions of laser beam intensity, which is of significant practical importance for laser developers when certifying radiation sources. As an identification parameter, a measure of similarity of the measured axisymmetric distributions of laser radiation intensity with a given Gaussian distribution is proposed and investigated. To determine this measure, it is not necessary to first find the beam width at the waist. A mathematical apparatus for identification based on the use of cumulants of spatial intensity distributions is developed. A feature of the method is a limited number of cumulants of the Gaussian distribution, which makes it attractive for practical application. A comparative analysis of a number of two-dimensional distributions with a Gaussian distribution is carried out and it is shown that even with a small number of measured cumulants, high sensitivity of the method to the shapes of intensity distributions is ensured. A similarity measure for continuous one- dimensional intensity distributions of arbitrary shape is presented. The asymmetry measure of two-dimensional spatial distributions of laser beam intensity based on the ratio of moments and cumulants of the fourth and second orders is considered. The proposed measure of similarity of the measured axisymmetric intensity distributions with the Gaussian distribution is an alternative to the well-known propagation coefficient M 2 and can be used together with this coefficient.

Surrogate model-based assessment of particle damage behaviour of Al[sbnd]Zn[sbnd]Mg alloy

Recent research has found some intermetallic compound particles with even stronger hydrogen trapping capacity (e.g., Al7Cu2Fe) than the age-hardening precipitates that are reported to be the origin of hydrogen embrittlement in aluminium. Such intermetallic compound particles can reduce hydrogen concentration at the interface between the precipitates and aluminium by absorbing hydrogen in their interiors, thus preventing the hydrogen embrittlement of aluminium. However, this cannot be achieved if the particles, which have absorbed large amounts of hydrogen, are damaged due to hydrogen embrittlement. In this study, the hydrogen embrittlement of aluminium was observed in situ by X-ray CT, and the damage behaviour was analysed of all the particles that were located in the gauge section of a single tensile specimen. After exhaustive quantification of the size, shape, and spatial distribution of the particles, coarsening processes identified highly correlated design variables. Subsequently, particle damage behaviour was analysed utilizing a surrogate model using a support vector machine. The damage to Al7Cu2Fe particles could be described only by design variables representing size and shape, while those representing spatial distribution were removed through the coarsening processes. No change was observed in the damage behaviour of Al7Cu2Fe particles with increasing hydrogen concentrations, and it was concluded that the dispersion of Al7Cu2Fe particles is effective in preventing hydrogen embrittlement of aluminium. The contribution of damaged particles to the formation of fracture surfaces and the damage behaviour of Mg2Si particles, where damage is accelerated by hydrogen, were also analysed.

Malware classification through Abstract Syntax Trees and L-moments

The ongoing evolution of malware presents a formidable challenge to cybersecurity: identifying unknown threats. Traditional detection methods, such as signatures and various forms of static analysis, inherently lag behind these evolving threats. This research introduces a novel approach to malware detection by leveraging the robust statistical capabilities of L-moments and the structural insights provided by Abstract Syntax Trees (ASTs) and applying them to PowerShell. L-moments, recognized for their resilience to outliers and adaptability to diverse distributional shapes, are extracted from network analysis measures like degree centrality, betweenness centrality, and closeness centrality of ASTs. These measures provide a detailed structural representation of code, enabling a deeper understanding of its inherent behaviors and patterns. This approach aims to detect not only known malware but also uncover new, previously unidentified threats. A comprehensive comparison with traditional static analysis methods shows that this approach excels in key performance metrics such as accuracy, precision, recall, and F1 score. These results demonstrate the significant potential of combining L-moments derived from network analysis with ASTs in enhancing malware detection. While static analysis remains an essential tool in cybersecurity, the integration of L-moments and advanced network analysis offers a more effective and efficient response to the dynamic landscape of cyber threats. This study paves the way for future research, particularly in extending the use of L-moments and network analysis into additional areas.

Effect of a traveling magnetic field on the parameters of doped tellurium gallium arsenide single crystals grown by the chokhralsky method

The effect of a traveling magnetic field on the parameters of Te-doped GaAs single crystals in the carrier density range of 5 × 1017–2 × 1018 cm–3 has been studied. A traveling magnetic field was induced in a melt by a graphite inductor located in the setup chamber around the main heater. It is shown that a high-frequency magnetic field slightly reduces the dislocation density in the crystals without changing the shape of the dislocation distribution over their cross sections. The magnetic field affects the impurity distribution along the crystal axis, almost doubling the distance between the striation bands from 9 µm in the absence of magnetic field to 17 µm in a field with a frequency of 300 Hz.

Effect of soil-building interaction on dynamic earth pressure on basement walls

This study investigates dynamic earth pressure on basement walls by considering soil-structure interaction, a factor that is often overlooked by conventional methods like Mononobe-Okabe, Seed and Whitman, and Wood. Superstructure, basement, and soil were numerically simulated in a single model to evaluate the inertial and kinematic effects of buildings on dynamic earth pressure on the basement walls. The numerical model was validated using data from a centrifuge test and an instrumented building. Then, a parametric study was performed, with the height, width, and basement depth of the building varied with six input motions. The results showed that the inertia of the building increased dynamic thrust. Furthermore, the dynamic thrust showed a similar trend with the displacement response spectrum curve of the ground surface acceleration as the building height increased, while the distribution shape transitioned from triangular to inverted triangular. Additionally, wider buildings had increased dynamic earth pressure, while deeper buildings exhibited smaller normalized dynamic thrust.

Emergence of economic and social disparities through competitive gift-giving

Several tiers of social organization with varying economic and social disparities have been observed. However, a quantitative characterization of the types and the causal mechanisms for the transitions have hardly been explained. While anthropologists have emphasized that gift exchange, rather than market exchange, prevails in traditional societies and shapes social relations, few mathematical studies have explored its consequences for social organizations. In this study, we present a simple model of competitive gift-giving that describes how gifts bring goods to the recipient and honor to the donor, and simulate social change. Numerical simulations and an analysis of the corresponding mean-field theory demonstrate the transitions between the following four phases with different distribution shapes of wealth and social reputation: the band, without economic or social disparities; the tribe, with economic but without social disparities; the chiefdom, with both; and the kingdom, with economic disparity and weak social disparity except for an outlier, namely, the “monarch”. The emergence of strong disparities is characterized by power law distributions and is attributed to the “rich get richer” process. In contrast, the absence of such a process leads to exponential distributions due to random fluctuations. The phases depend on the parameters characterizing the frequency and scale of gift interactions. Our findings provide quantitative criteria for classifying social organizations based on economic and social disparities, consistent with both anthropological theory and empirical observations. Thus, we propose empirically measurable explanatory variables and characteristic indices for the evolution of social organizations. The constructive model, guided by social scientific theory, can provide the basic mechanistic explanation of social evolution and integrate theories of the social sciences.

Kinetic-scale diagnostics of destabilization of electromagnetic electron whistler-cyclotron modes in the presence of hybrid non-thermal non-extensive electrons

Temperature anisotropies exist in all the solar terrestrial regions and act as a source of free energy that plays a pivotal role for the destabilization of various plasma modes, one of them is the electromagnetic electron whistler-cyclotron instability. In this paper, the kinetic-scale diagnostic of parallel propagating electromagnetic electron whistler-cyclotron instability is numerically investigated in hybrid non-thermal non-extensive non-collisional magnetized plasmas. The dielectric response function (DRF) of right handed circularly polarized whistler instability (WI) is derived by the incorporation of Vlasov–Maxwell model for both super-extensive (q<1, α≠0) and sub-extensive (q>1, α≠0) bi-Cairns–Tsallis distributed plasma (bi-CTDP) systems. The unstable solutions of WI are obtained through the exact numerical analysis of DRF to compute the oscillatory/real frequency and growth rate. The dependence of pertinent parameters, i.e., non-thermality (q), non-extensivity (α), temperature anisotropy ratio (δe) and (α,q)-dependent plasma beta (β∥eα,q), on the destabilization of whistler mode are examined in detail. The prevalence of hybrid non-thermal non-extensive electrons population plays a substantial role in altering the characteristics of whistler-cyclotron instability in bi-CTDP system as compared to other non-thermal/non-equilibrium plasma systems. The nature and characteristics of the instabilities and waves are substantially influenced by the shape of particle velocity distributions, particularly on kinetic scale. The hybrid non-thermal non-extensive character of electrons distribution remarkably support the instability growth. We observed the highest growth rate of WI in super-extensive bi-CTDP in contrast to other non-thermal plasma distributions. A detailed comparison of the present findings with the other models, e.g. bi-Cairns, bi-nonextensive, and bi-Maxwellian plasmas is also unveiled in the present research.

Tree Frogs Alter Their Behavioral Strategies While Landing On Vertical Perches.

As an arboreal animal, tree frogs face diverse challenges when landing on perches, including variations in substrate shape, diameter, flexibility, and angular distribution, with potentially significant consequences for failed landings. Research on tree frog landing behavior on perches, especially concerning landing on vertical substrates, remains limited. This study investigated the landing strategies (forelimb, abdomen, and hindlimb) of tree frogs on vertical perches, considering perch diameter. Although all three strategies were observed across perches of different diameters, their frequencies differed. Forelimb landing was most common across all perch diameters, with its frequency increasing with perch diameter, while abdomen and hindlimb landing strategies were more prevalent on smaller diameter perches. During the process from take-off to landing, the body axis underwent some deviation owing to the asymmetric movement of the left and right limbs; however, these deviations did not significantly differ among landing strategies. Additionally, different landing strategies led to variations in the landing forces, with abdominal landings generating significantly higher impact forces than the other two strategies. These findings provide insights into the biomechanics and biological adaptations of tree frogs when landing on challenging substrates, such as leaves or branches.

Soil pore dynamics and infiltration characteristics as affected by cultivation duration for Mollisol in northeast China

Elucidating the effects of long-term cultivation on pore structure and infiltration characteristics is essential for understanding soil degradation mechanism and improving cropland sustainability. In this study, we evaluated a number of indicators regarding soil properties, pore structure, and water infiltration during long-term cultivation and the relationship of basic properties and pore structure with soil infiltration in northeast Mollisol region of China. The studied cropland involved four cultivation durations (20, 40, 60, and 100 years) and one forest (FR) as the control. X-ray computed tomography (CT) and mini disk infiltrometer were applied to assess the effects of long-term cultivation on soil pore structure and infiltration characteristics at soil depths of 0–100 cm. The pore properties including soil porosity (TP), pore number (PN), pore size distribution, mean shape factor (MSF), fractal dimension (FA), anisotropy (DA), and Euler number (EN), and infiltration properties including mean (IR), initial (IIR), stable infiltration rate (SIR), and saturated hydraulic conductivity (Ks) were planned to be measured in this study. The results showed that soil organic carbon (SOC) in cropland was significantly lower than that in FR, while bulk density (BD) and mean weight diameter (MWD) exhibited an opposite trend. Long-term cultivation altered the soil pore size and shape distribution, and decreased the macroporosity (>500 μm) and elongated porosity, which suggested that long-term cultivation results in a simpler pore network. FR took a longer time to reach a stable state in infiltration curve over time, while cropland had lower IR, IIR, SIR and Ks, indicating negative effects of cultivation on water infiltration. > 500 μm porosity and elongated porosity were positively correlated with infiltration characteristics (P<0.01). The infiltration parameters were mainly affected by soil pore properties (MSF, PN, and DA) and basic properties (SOC, MWD, and BD), highlighting the importance of pore morphology in the infiltration process. Our results provide new insights into the evolution of soil structure and properties and explanations for water infiltration dynamics under long-term cultivation from the microscale.

3D Vessel Segmentation With Limited Guidance of 2D Structure-Agnostic Vessel Annotations.

Delineating 3D blood vessels of various anatomical structures is essential for clinical diagnosis and treatment, however, is challenging due to complex structure variations and varied imaging conditions. Although recent supervised deep learning models have demonstrated their superior capacity in automatic 3D vessel segmentation, the reliance on expensive 3D manual annotations and limited capacity for annotation reuse among different vascular structures hinder their clinical applications. To avoid the repetitive and costly annotating process for each vascular structure and make full use of existing annotations, this paper proposes a novel 3D shape-guided local discrimination (3D-SLD) model for 3D vascular segmentation under limited guidance from public 2D vessel annotations. The primary hypothesis is that 3D vessels are composed of semantically similar voxels and often exhibit tree-shaped morphology. Accordingly, the 3D region discrimination loss is firstly proposed to learn the discriminative representation measuring voxel-wise similarities and cluster semantically consistent voxels to form the candidate 3D vascular segmentation in unlabeled images. Secondly, the shape distribution from existing 2D structure-agnostic vessel annotations is introduced to guide the 3D vessels with the tree-shaped morphology by the adversarial shape constraint loss. Thirdly, to enhance training stability and prediction credibility, the highlighting-reviewing-summarizing (HRS) mechanism is proposed. This mechanism involves summarizing historical models to maintain temporal consistency and identifying credible pseudo labels as reliable supervision signals. Only guided by public 2D coronary artery annotations, our method achieves results comparable to SOTA barely-supervised methods in 3D cerebrovascular segmentation, and the best DSC in 3D hepatic vessel segmentation, demonstrating the effectiveness of our method.

On Reliability of Repairable Hot Double Redundant System with Arbitrarily Distributed Life- and Repair Times of Its Elements

The article introduces the concept of Marked Markov processes, which are used to study a repairable hot double redundant system with a single repair facility. It is assumed that components’ life- and repair times follow arbitrary distributions. The proposed approach allows for calculating the system’s reliability function, and its mean lifetime, as well as conducting the sensitivity analysis to the shape of input distributions. The new method was validated with numerical examples by comparing it with previously obtained analytical results and showed high accuracy.

Effects of electrochemical machining on high-cycle fatigue of Inconel 718 blades

Blades made from Inconel718 (IN718) are generally machined using electrochemical machining (ECM), and the high-cycle fatigue (HCF) of such blades significantly impacts the service life of aeroengines. In this study, modal analysis was performed to obtain the blade modal shape and stress distribution at first-order frequency, after which blades were machined at different current densities (9.5A/cm2, 18.2A/cm2, 34A/cm2, 46.7A/cm2, 61.2A/cm2, 70.1A/cm2) and then subjected to detailed surface-integrity analysis and fatigue tests. No surface defects (e.g., intergranular corrosion, recast layers) were observed, the microhardness was unchanged, and new residual stress was not found to be introduced to the machined surfaces. The machined surfaces were uneven and contained micro-pits, and high current density contributed to better surface quality. At a constant load of 520 MPa, the blade machined at 70.1A/cm2 had the best fatigue life of 1.4×106. The blades fractured because of micro-pits, and as the surface quality of the blades improved, so did their fatigue performance. Therefore, the fatigue failure mechanism characterized in this work provides a reference for the HCF behavior of blades machined by ECM.

Experimental measurements of gamma-photon production and estimation of electron/positron production on the PETAL laser facility

This article reports the first measurements of high-energy photons produced with the high-intensity PETawatt Aquitaine Laser (PETAL) laser. The experiments were performed during the commissioning of the laser. The laser had an energy of about 400 J, an intensity of 8 × 1018 W·cm−2, and a pulse duration of 660 fs (FWHM). It was shot at a 2 mm-thick solid tungsten target. The high-energy photons were produced mainly from the bremsstrahlung process for relativistic electrons accelerated inside a plasma generated on the front side of the target. This paper reports measurements of electrons, protons and photons. Hot electrons up to ≈35 MeV with a few-MeV temperature were recorded by a spectrometer, called SESAME (Spectre ÉlectronS Angulaire Moyenne Énergie). K- and L-shells were clearly detected by a photon spectrometer called SPECTIX (Spectromètre Petal à Cristal en TransmIssion pour le rayonnnement X). High-energy photons were diagnosed by CRACC-X (Cassette de RAdiographie Centre Chambre-rayonnement X), a bremsstrahlung cannon. Bremsstrahlung cannon analysis is strongly dependent on the hypothesis adopted for the spectral shape. Different shapes can exhibit similar reproductions of the experimental data. To eliminate dependence on the shape hypothesis and to facilitate analysis of the data, simulations of the interaction were performed. To model the mechanisms involved, a simulation chain including hydrodynamic, particle-in-cell, and Monte Carlo simulations was used. The simulations model the preplasma generated at the front of the target by the PETAL laser prepulse, the acceleration of electrons inside the plasma, the generation of MeV-range photons from these electrons, and the response of the detector impacted by the energetic photon beam. All this work enabled reproduction of the experimental data. The high-energy photons produced have a large emission angle and an exponential distribution shape. In addition to the analysis of the photon spectra, positron production was also investigated. Indeed, if high-energy photons are generated inside the solid target, some positron/electron pairs may be produced by the Bethe–Heitler process. Therefore, the positron production achievable within the PETAL laser facility was quantified. To conclude the study, the possibility of creating electron/positron pairs through the linear Breit–Wheeler process with PETAL was investigated.

A comprehensive statistical analysis of Malaria dynamics in the Adamawa region of Cameroon, from 2018 to 2022

Malaria remains a prominent public health concern in Cameroon, with the potential for epidemic outbreaks, necessitating a robust understanding of its dynamics. This paper uses routinely collected surveillance data from health facilities in the Adamawa Region since January 2018. By applying statistical analysis, this study aims to enhance comprehension, enable data predictions, and facilitate informed decision-making for public health policy implementation. Focusing on weekly health districts data spanning from 2018 to 2022, our analysis employs key statistical metrics for central tendency, data spread, distribution shape, and variable dependence. The study reveals distinctive trends, highlighting peak malaria transmission periods consistently occurring between August and November each year. The highest weekly recorded case count in any health district reached 1,294. The data exhibits leptokurtic distributions, skewed to the left of the median. And in 2022, 11% of the population was reported to have contracted malaria. Despite an overall region-wide average growth rate of -1.21% over the past five years, maintaining vigilant attention to this critical health issue is imperative. Auto dependence analysis indicates that observations are weekly correlated, assuming the time series as stationary. The stationarity has been confirmed by ADF and KPSS tests that we performed. This comprehensive data analysis helps our understanding of the malaria landscape in the Adamawa Region of Cameroon. The paper also recommends the inclusion of additional variables in data collection for a more holistic perspective. These findings provide a basis for the formulation and implementation of targeted interventions by relevant stakeholders, aiding in the prediction of future cases and ultimately contributing to the effective management of malaria in the region.

Global estimation of dietary micronutrient inadequacies: a modelling analysis

Inadequate micronutrient intakes and related deficiencies are a major challenge to global public health. Analyses over the past 10 years have assessed global micronutrient deficiencies and inadequate nutrient supplies, but there have been no global estimates of inadequate micronutrient intakes. We aimed to estimate the global prevalence of inadequate micronutrient intakes for 15 essential micronutrients and to identify dietary nutrient gaps in specific demographic groups and countries. In this modelling analysis, we adopted a novel approach to estimating micronutrient intake, which accounts for the shape of a population's nutrient intake distribution and is based on dietary intake data from 31 countries. Using a globally harmonised set of age-specific and sex-specific nutrient requirements, we then applied these distributions to publicly available data from the Global Dietary Database on modelled median intakes of 15 micronutrients for 34 age-sex groups from 185 countries, to estimate the prevalence of inadequate nutrient intakes for 99·3% of the global population. On the basis of estimates of nutrient intake from food (excluding fortification and supplementation), more than 5 billion people do not consume enough iodine (68% of the global population), vitamin E (67%), and calcium (66%). More than 4 billion people do not consume enough iron (65%), riboflavin (55%), folate (54%), and vitamin C (53%). Within the same country and age groups, estimated inadequate intakes were higher for women than for men for iodine, vitamin B12, iron, and selenium and higher for men than for women for magnesium, vitamin B6, zinc, vitamin C, vitamin A, thiamin, and niacin. To our knowledge, this analysis provides the first global estimates of inadequate micronutrient intakes using dietary intake data, highlighting highly prevalent gaps across nutrients and variability by sex. These results can be used by public health practitioners to target populations in need of intervention. The National Institutes of Health and the Dutch Ministry of Foreign Affairs.

The effects of processing parameters on the shape of particle size distribution and grinding rate in a stirred mill

The study of particle size distribution (PSD) of materials is a crucial aspect of mineral processing. It not only determines the appropriate beneficiation process and equipment but also has a significant impact on the grade and recovery of concentrate. This study utilizes a pin-stirred mill for the wet fine grinding of limonite to examine four different widths of PSD functions and compares their quantitative descriptions of the PSD. Skewness is a parameter introduced to quantitatively describe the asymmetry of the PSD. This study aims to investigate the effect of the stirrer speed, the density and the size of the grinding media on the shape of the PSD and on the grinding rate. The results show that a lower stirrer speed and a lower density of the grinding media result in a narrower and a more symmetrical PSD of the grinding products. Moreover, the time-dependent approach succeeds in simulating and proving the evolution behavior of the median particle size. It was found that the optimum mixing ratio of the grinding media can effectively adjust the shape of the PSD and improve the grinding efficiency.

A Lightweight Pathological Gait Recognition Approach Based on a New Gait Template in Side-View and Improved Attention Mechanism.

As people age, abnormal gait recognition becomes a critical problem in the field of healthcare. Currently, some algorithms can classify gaits with different pathologies, but they cannot guarantee high accuracy while keeping the model lightweight. To address these issues, this paper proposes a lightweight network (NSVGT-ICBAM-FACN) based on the new side-view gait template (NSVGT), improved convolutional block attention module (ICBAM), and transfer learning that fuses convolutional features containing high-level information and attention features containing semantic information of interest to achieve robust pathological gait recognition. The NSVGT contains different levels of information such as gait shape, gait dynamics, and energy distribution at different parts of the body, which integrates and compensates for the strengths and limitations of each feature, making gait characterization more robust. The ICBAM employs parallel concatenation and depthwise separable convolution (DSC). The former strengthens the interaction between features. The latter improves the efficiency of processing gait information. In the classification head, we choose to employ DSC instead of global average pooling. This method preserves the spatial information and learns the weights of different locations, which solves the problem that the corner points and center points in the feature map have the same weight. The classification accuracies for this paper's model on the self-constructed dataset and GAIT-IST dataset are 98.43% and 98.69%, which are 0.77% and 0.59% higher than that of the SOTA model, respectively. The experiments demonstrate that the method achieves good balance between lightweightness and performance.

Architectural underpinnings of stochastic intergenerational homeostasis.

Living systems are naturally complex and adaptive and offer unique insights into the strategies for achieving and sustaining stochastic homeostasis in different conditions. Here we focus on homeostasis in the context of stochastic growth and division of individual bacterial cells. We take advantage of high-precision long-term dynamical data that have recently been used to extract emergent simplicities and to articulate empirical intra- and intergenerational scaling laws governing these stochastic dynamics. From these data, we identify the core motif in the mechanistic coupling between division and growth, which naturally yields these precise rules, thus also bridging the intra- and intergenerational phenomenologies. By developing and utilizing techniques for solving a broad class of first-passage processes, we derive the exact analytic necessary and sufficient condition for sustaining stochastic intergenerational cell-size homeostasis within this framework. Furthermore, we provide predictions for the precision kinematics of cell-size homeostasis and the shape of the interdivision time distribution, which are compellingly borne out by the high-precision data. Taken together, these results provide insights into the functional architecture of control systems that yield robust yet flexible stochastic homeostasis.

Non-uniform distribution model of rust layer around steel bar circumference and its effect on corrosion-induced concrete cracking

This paper presents a critical review of non-uniform distribution models of rust layer around a reinforcing bar’s circumference and a numerical investigation into the effect of non-uniform distribution of rust on (a) crack patterns and (b) development of concrete surface crack width. Different shapes of rust layer simulated by mathematical models were established based on statistical distribution functions which were compared with the transport-electrochemical model and published testing results. In addition, an advanced 2D finite element model was implemented to simulate crack propagation in concrete caused by rebar corrosion. It is found that non-uniform rust distribution shape around the rebar not only affected concrete surface crack width evolution, but also crack length and crack pattern. Transport-electrochemical model and Gaussian distribution-based model could reasonably simulate rust distribution and associated corrosion-induced cracks. In addition, the authors proposed a simplified semi-empirical model that incorporated an analytical chloride transport model and a Gaussian model to simulate time-dependent advancement of non-uniform rust layer. Furthermore, a parametric study of the effect of elastic stiffness of the rust layer on crack patterns and surface crack width development was also performed.

A hierarchical constrained density regression model for predicting cluster‐level dose‐response

AbstractWith the advent of new alternative methods for rapid toxicity screening of chemicals comes the need for new statistical methodologies which appropriately synthesize the large amount of data collected. For example, transcriptomic assays can be used to assess the impact of a chemical on thousands of genes, but current approaches to analyzing the data treat each gene separately and do not allow sharing of information among genes within pathways. Furthermore, the methods employed are fully parametric and do not account for changes in distribution shape that may occur at high exposure levels. To address the limitations of these methods, we propose Constrained Logistic Density Regression (COLDER) to model expression data from different genes simultaneously. Under COLDER, the dose‐response function for each gene is assigned a prior via a discrete logistic stick‐breaking process (LSBP) whose weights depend on gene‐level characteristics (e.g., pathway membership) and atoms consist of different dose‐response functions subject to a shape constraint that ensures biological plausibility. The posterior distribution for the benchmark dose among genes within the same pathways can be estimated directly from the model, which is another advantage over current methods. The ability of COLDER to predict gene‐level dose‐response is evaluated in a simulation study and the method is illustrated with data from a National Toxicology Program study of Aflatoxin B1.