Probability Distributions Of Parameters Research Articles

Three-body binary formation in clusters: analytical theory

ABSTRACT Binary formation in clusters through triple encounters between three unbound stars, ‘three-body’ binary formation, is one of the main dynamical formation processes of binary systems in dense environments. In this paper, we use an analytical probabilistic approach to study the process for the equal mass case and calculate a probability distribution for the orbital parameters of three-body-formed binaries, as well as their formation rate. For the first time, we give closed-form analytical expressions to the full orbital parameter distribution, accounting for both energy and angular momentum conservation. This calculation relies on the sensitive dependence of the outcomes of three-body scatterings on the initial conditions: here we compute the rate of three-body binaries from ergodic interactions, which allow for an analytical derivation of the distribution of orbital parameters of the binaries thus created. We find that soft binaries are highly favoured in this process and that these binaries have a superthermal eccentricity distribution, while the few hard three-body binaries have an eccentricity distribution much closer to thermal. The analytical results predict and reproduce simulation results of three-body scattering experiments in the literature well.

Parametric description of intermittent probability distribution functions in solar wind and magnetohydrodynamic turbulence

ABSTRACT In this work, we find empirical evidence that the scale-dependent statistical properties of solar wind and magnetohydrodynamic (MHD) turbulence can be described in terms of a family of parametric probability distribution functions (PDFs) known as Normal Inverse Gaussian (NIG). Understanding these PDFs is one of the most important goals in turbulence theory, as they are inherently connected to the intermittent properties of solar wind turbulence. We investigate the properties of PDFs of Elsasser increments based on a large statistical sample from solar wind observations and high-resolution numerical simulations of MHD turbulence. In order to measure the PDFs and their corresponding properties, three experiments are presented: fast and slow solar wind for experimental data and a simulation of reduced MHD (RMHD) turbulence. Conditional statistics on a 23-yr-long sample of WIND data near 1 au and high-resolution pseudo-spectral simulation of steadily driven RMHD turbulence on a $2048^3$ mesh are used to construct scale-dependent PDFs. The empirical PDFs are fitted to NIG distributions, which depend on four free parameters. Our analysis shows that NIG distributions accurately capture the evolution of the PDFs, with scale-dependent parameters, from large scales characterized by a Gaussian distribution, turning to exponential tails within the inertial range and stretched exponentials at dissipative scales. We also show that empirically-measured NIG parameters exhibit well-defined scaling properties that are similar across the three empirical data sets, which may be indicative of universal behaviour.

Design of Quantum Gates Using Quantum Scattering Theory

Given two Hamiltonians \(H_0,H_1=H_0+V\) corresponding respectively to a free particle Hamiltonian and the free particle Hamiltonian plus its interaction energy with a scattering centre, we can compute the S-matrix, i.e., the matrix that determines the quantum mechanical amplitude of the process involving a particle coming from a free particle state at an infinite distance from the scattering centre at time \(t=-\infty\), entering into an initial scattered state, interacting with the scattering centre, entering into a final scattered state, and then escaping away to infinity at time \(t\rightarrow\infty\) to a final free particle state. Such amplitudes were first studied by Lippmann and Schwinger (Steven Weinberg, The Quantum Theory of Fields, Vol. 1, W.O. Amrein, Hilbert Space Methods in Quantum Mechanics) and then analyzed in a mathematically precise way by [T. Kato], [W. Amrein], and [K.B. Sinha]. In this paper, we first derive the Lippmann-Schwinger equation for the input and output scattered states in terms of the input and output free particle states using intuitive arguments originally due to Lippmann and Schwinger, and then, using rigorous operator theoretic arguments revolving around the spectral theorem for unbounded self-adjoint operators in a Hilbert space, we obtain an elegant formula for the scattering matrix elements in terms of the interaction potential and the free particle Hamiltonian between two free particle states corresponding to the same measure. We then discuss a computationally more efficient method based on the Dyson series expansion (Steven Weinberg, The Quantum Theory of Fields, Vol. 1), which works even in the case when the interaction Hamiltonian is time varying, in contrast to the Lippmann-Schwinger method, for calculating the S-matrix. We assume that the scattering potential, which can be time varying, can be controlled by incorporating control parameters and explain how the resulting unitary S-matrix can be made to approximate a given unitary gate in infinite-dimensional Hilbert space by optimizing the Hilbert-Schmidt/Frobenius norm distance between the given gate and the S-matrix gate, in which the latter is approximated by a truncated Dyson series. Of course, the S-matrix given by the Dyson series is a Taylor series functional expansion in the interaction potential and hence is a highly nonlinear function of the control parameters, and hence we propose numerical methods for such optimization. We then observe that if the control parameters are taken as random variables with joint moments, then the TPCP map involving statistical averaging of the adjoint action of the S-matrix acting on an initial mixed state w.r.t. the probability distribution of the control parameters will result in a final mixed state that is linear in the statistical moments of the control parameters, and hence optimization w.r.t. these moments can be easily carried out. Our method of TPCP map design is to optimize the sum of Frobenius distance squares between a sequence of desired output mixed states and the S-matrix based formula for the TPCP map acting on the corresponding input mixed states w.r.t. the statistical moments of the control parameters. We then generalize this method to include the case of TPCP maps obtained from the Hudson-Parthasarathy quantum noisy Schrödinger equation. In summary, we simulate the S-matrix gate for independent realizations of the control parameters having a probability distribution defined by their joint moments obtained by the above optimization procedure and apply the adjoint action of these independent S-matrices on a given input state, and take their ensemble average to obtain a good approximation to the action of the desired TPCP map on any given input state. This suggests that TPCP maps of arbitrarily large size can be realized using scattering experiments in the laboratory.

Verification Test and Research on Fitting Curve of Shear and Tensile Synthesis Method

Based on the recommended curve of concrete compressive strength tested by shear and tensile composite method, this paper combined with concrete specimens of different strength grades, ages and batches produced by several test verification units, adopted the in vitro shear and tensile test method introduced by the regulations, and used basically the same test equipment to collect the single shear and tensile strength and the compressive strength of cube specimens under the same conditions. Each batch was divided into 15 or 30 specimens. Through the collected test data, the conversion strength of the single shear, pull-out and shear tensile composite methods were calculated respectively. The relative error of a single specimen was calculated based on the average strength of each batch of concrete. The error distribution types and errors of each company were systematically studied, and finally the relative error data of each company were summarized, and the probability distribution parameters of the error of the Shear and tensile synthesis method were understood through probability distribution analysis, and the relationship between the error of the shear and tensile synthesis method, the single shear method and the pull method, and the influence degree on the conversion strength of the shear and tensile synthesis method were shown by using three-dimensional coordinates. Using the test data of "shear and tensile synthesis method", "single shear method" and "pull-out method", the scatter plot is drawn, and the error size is compared to explore the direction of further improving the detection accuracy of "shear and tensile synthesis method".

2-D probabilistic inversion of MT data and uncertainty quantification using the Hamiltonian Monte Carlo method

SUMMARY Bayesian methods provide a valuable framework for rigorously quantifying the model uncertainty arising from the inherent non-uniqueness in the magnetotelluric (MT) inversion. However, widely used Markov chain Monte Carlo (MCMC) sampling approaches usually require a significant number of model samples for accurate uncertainty estimates, making their applications computationally challenging for 2-D or 3-D MT problems. In this study, we explore the applicability of the Hamiltonian Monte Carlo (HMC) method for 2-D probabilistic MT inversion. The HMC provides a mechanism for efficient exploration in high-dimensional model space by making use of gradient information of the posterior probability distribution, resulting in a substantial reduction in the number of samples needed for reliable uncertainty quantification compared to the conventional MCMC methods. Numerical examples with synthetic data demonstrate that the HMC method achieves rapid convergence to the posterior probability distribution of model parameters with a limited number of model samples, indicating the computational advantages of the HMC in high-dimensional model space. Finally, we applied the developed approach to the COPROD2 field data set. The statistical models derived from the HMC approach agree well with previous results obtained by 2-D deterministic inversions. Most importantly, the probabilistic inversion provides valuable quantitative model uncertainty information associated with the resistivity structures derived from the observed data, which facilitates model interpretation.

Elastic Shape Analysis of Tree-Like 3D Objects Using Extended SRVF Representation.

How can one analyze detailed 3D biological objects, such as neuronal and botanical trees, that exhibit complex geometrical and topological variation? In this paper, we develop a novel mathematical framework for representing, comparing, and computing geodesic deformations between the shapes of such tree-like 3D objects. A hierarchical organization of subtrees characterizes these objects - each subtree has a main branch with some side branches attached - and one needs to match these structures across objects for meaningful comparisons. We propose a novel representation that extends the Square-Root Velocity Function (SRVF), initially developed for Euclidean curves, to tree-shaped 3D objects. We then define a new metric that quantifies the bending, stretching, and branch sliding needed to deform one tree-shaped object into the other. Compared to the current metrics such as the Quotient Euclidean Distance (QED) and the Tree Edit Distance (TED), the proposed representation and metric capture the full elasticity of the branches (i.e., bending and stretching) as well as the topological variations (i.e., branch death/birth and sliding). It completely avoids the shrinkage that results from the edge collapse and node split operations of the QED and TED metrics. We demonstrate the utility of this framework in comparing, matching, and computing geodesics between biological objects such as neuronal and botanical trees. We also demonstrate its application to various shape analysis tasks such as (i) symmetry analysis and symmetrization of tree-shaped 3D objects, (ii) computing summary statistics (means and modes of variations) of populations of tree-shaped 3D objects, (iii) fitting parametric probability distributions to such populations, and (iv) finally synthesizing novel tree-shaped 3D objects through random sampling from estimated probability distributions.

Effect of uncertainties in cable corrosion and material strength on seismic fragility of long-span cable-stayed bridges in marine environments

This paper presents an investigation into the seismic fragility of cable-stayed bridges and considers the complex uncertainties in cable corrosion and material strength. Under certain assumptions and using the limited measured data available for steel corrosion, a cable corrosion model is established. The probability distribution of several parameters, including the corrosion rate, corrosion initiation time, chloride concentration, and cable replacement in the corrosion model, is considered. In addition, the influence of the stress level of cables is also considered in the model by the amplification coefficient of the corrosion rate. To consider the effect of the uncertainties in cable corrosion and material strength on the seismic fragility of this bridge, the uniform design (UD) method is used to generate reasonable bridge samples and to build probabilistic seismic demand models. The results indicate that cable corrosion has a significant impact on the seismic fragility of cable-stayed bridges. The seismic fragility of girders and piers are the smallest and the highest among all bridge components, respectively. The material strength uncertainties have a significant influence on the seismic fragility of bridge components. The coupling between the uncertainties in cable corrosion and material strength does not increase the seismic fragility of the bridge components in most cases because of the cancellation effect of the two uncertainties to some extent. In addition, cable replacement has a significant influence on the seismic fragility of bridge components. In order to correctly evaluate the performance of cable-stayed bridges in service, it is necessary to consider the uncertainties in cable corrosion and material strength in a seismic fragility analysis of long-span cable-stayed bridges with different service periods.

A facies‐constrained geostatistical seismic inversion method based on multi‐scale sparse representation

AbstractGeostatistical seismic inversion is an important method for establishing high‐resolution reservoir parameter models. There is no accurate representation method for reservoir structural features, and prior information about structural features cannot be incorporated into geostatistical inversion. Based on the assumption of the sparsity of stratigraphic sedimentary features, the same type of structural feature is used to represent the sedimentary pattern of reservoirs within the same facies. Different sparse representation patterns are used to represent the differences in sedimentary patterns between facies. Although changes in depositional environment might result in the multi‐scale characteristics of geological structures for varying sedimentary rhythms, this paper proposes a facies‐constrained geostatistical inversion method based on multi‐scale sparse representation to better accommodate such situation. Using the method of sparse representation combined with wavelet transform, the multi‐scale sedimentary structural features of reservoirs are learned from well‐logging data. Seismic facies and multi‐scale features are used as prior information for geostatistical inversion. Further, the likelihood function is constructed using seismic data to obtain the posterior probability distribution of reservoir parameters. Finally, the accurate inversion result is obtained by using multi‐scale sparse representation as a constraint in the posterior probability distribution of reservoir parameters. Compared with conventional geostatistical methods, this algorithm can better match the structural features of reservoir parameters with varying geological conditions. Field data tests have shown the effectiveness of this method in improving the accuracy and resolution of reservoir parameter structural features.

A data-driven polynomial chaos method for uncertainty quantification of a subsonic compressor cascade with stagger angle errors

The probability-based uncertainty quantification (UQ) methods require a large amount of sampled data to construct the probability distribution of uncertain input parameters. However, it is a common situation that only limited and scarce sampled data are available in engineering applications due to expensive tests. In the present paper, the Data-Driven Polynomial Chaos (DDPC) method is adopted, which can propagate input uncertainty in the case of scarce sampled data. The calculation accuracy and convergence of the self-developed DDPC method are validated by a nonlinear test function. Subsequently, the DDPC method is applied to investigate the uncertain impact of stagger angle errors on the aerodynamic performance of a subsonic compressor cascade. A family of manufacturing error data of stagger angles was obtained from the real compressor blades. Based on the limited measurement data, the DDPC method combined with Computational Fluid Dynamics (CFD) simulation is employed to quantify the performance impact of the compressor cascade. The results show that the performance dispersion under off-design conditions is more prominent than that under design conditions. The actual aerodynamic performance deviating from the nominal performance is not a small probability event, and the probability of deviating from the nominal loss coefficient and exit flow angle by more than 1% can reach up to 47.6% and 36.8% under high incidence i = 7°. Detailed analysis shows that stagger angle errors have a significant effect on the flow state near the leading edge, resulting in variations in separation bubble size and boundary layer thickness.

Susceptibility of AutoML mortality prediction algorithms to model drift caused by the COVID pandemic

BackgroundConcept drift and covariate shift lead to a degradation of machine learning (ML) models. The objective of our study was to characterize sudden data drift as caused by the COVID pandemic. Furthermore, we investigated the suitability of certain methods in model training to prevent model degradation caused by data drift.MethodsWe trained different ML models with the H2O AutoML method on a dataset comprising 102,666 cases of surgical patients collected in the years 2014–2019 to predict postoperative mortality using preoperatively available data. Models applied were Generalized Linear Model with regularization, Default Random Forest, Gradient Boosting Machine, eXtreme Gradient Boosting, Deep Learning and Stacked Ensembles comprising all base models. Further, we modified the original models by applying three different methods when training on the original pre-pandemic dataset: (1) we weighted older data weaker, (2) used only the most recent data for model training and (3) performed a z-transformation of the numerical input parameters. Afterwards, we tested model performance on a pre-pandemic and an in-pandemic data set not used in the training process, and analysed common features.ResultsThe models produced showed excellent areas under receiver-operating characteristic and acceptable precision-recall curves when tested on a dataset from January-March 2020, but significant degradation when tested on a dataset collected in the first wave of the COVID pandemic from April-May 2020. When comparing the probability distributions of the input parameters, significant differences between pre-pandemic and in-pandemic data were found. The endpoint of our models, in-hospital mortality after surgery, did not differ significantly between pre- and in-pandemic data and was about 1% in each case. However, the models varied considerably in the composition of their input parameters. None of our applied modifications prevented a loss of performance, although very different models emerged from it, using a large variety of parameters.ConclusionsOur results show that none of our tested easy-to-implement measures in model training can prevent deterioration in the case of sudden external events. Therefore, we conclude that, in the presence of concept drift and covariate shift, close monitoring and critical review of model predictions are necessary.

A DiffeRential Evolution Adaptive Metropolis (DREAM)-based inverse model for continuous release source identification in river pollution incidents: Quantitative evaluation and sensitivity analysis

The identification of continuous pollution sources for rivers is of great concern for emergency response. Most studies focused on instantaneous river pollution sources and associated incidents. There is a dire need to address continuous pollution sources, as pollutant discharge may impose a major impact on the water ecosystem. Therefore, in this study, a novel inverse model is proposed to identify the continuous point sources in river pollution incidents that would estimate the source strength, location, release time, and spill time. The proposed inverse model combines the advanced DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm and the forward transport advection-dispersion equation to infer the posterior probability distribution of source parameters for quantifying uncertainties. In addition, the performance of the DREAM-based model is compared with those of the Metropolis-Hastings (MH)-based and genetic algorithm (GA)-based models. The results show that the DREAM-based model performs accurately for both the hypothetical and the field tracer cases. The comparative analysis shows that the DREAM-based model performs better in saving computation time, improving the accuracy of results, and reconstructing pollutant concentrations. Observation errors significantly influence the accuracy of the identification results from the DREAM-based model. In addition, a comprehensive sensitivity analysis of the DREAM-based model is conducted. The identification results from the DREAM-based model are sensitive to the dispersion coefficient and river velocity. The accuracy of the inverse model could be improved by increasing the monitoring number and by monitoring locations closer to the spill site. The findings of this study can improve decision-making during emergency responses to sudden river pollution incidents.

Taking cues from machine learning, compartmental and time series models for SARS-CoV-2 omicron infection in Indian provinces

SARS-CoV-2, the virus responsible for COVID-19, posed a significant threat to the world. We analyzed COVID-19 dissemination data in the top ten Indian provinces by infection incidences using the Susceptible-Infectious-Removed (SIR) model, an Autoregressive Integrated Moving Average (ARIMA) time series model, a machine learning model based on the Random Forest, and distribution fitting. Outbreaks are expected to continue if the Basic Reproduction Number (R0) > 1, and infection waves are anticipated to end if the R0 < 1, as determined by the SIR model. Different parametric probability distributions are also fitted. Data collected from December 12, 2021, to March 31, 2022, encompassing data from both before and during the implementation of strict control measures. Based on the estimates of the model parameters, health agencies and government policymakers can develop strategies to combat the spread of the disease in the future, and the most effective technique can be recommended for real-world application for other outbreaks of COVID-19. The best method out of these could be also implemented further on the epidemiological data of other similar infectious agents.

Accounting for hydroclimatic properties in flood frequency analysis procedures

Abstract. Flood hazard is typically evaluated by computing extreme flood probabilities from a flood frequency distribution following nationally defined procedures in which observed peak flow series are fit to a parametric probability distribution. These procedures, also known as flood frequency analysis, typically recommend only one probability distribution family for all watersheds within a country or region. However, large uncertainties associated with extreme flood probability estimates (&gt;50-year flood or Q50) can be further biased when fit to an inappropriate distribution model because of differences in the tails between distribution families. Here, we demonstrate that hydroclimatic parameters can aid in the selection of a parametric flood frequency distribution. We use L-moment diagrams to visually show the fit of gaged annual maxima series across the United States, grouped by their Köppen climate classification and the precipitation intensities of the basin, to a general extreme value (GEV), log normal 3 (LN3), and Pearson 3 (P3) distribution. Our results show that in real space basic hydroclimatic properties of a basin exert a significant influence on the statistical distribution of the annual maxima. The best-fitted family distribution shifts from a GEV towards an LN3 distribution across a gradient from colder and wetter climates (Köppen group D, continental climates) towards more arid climates (Köppen group B, dry climates). Due to the diversity of hydrologic processes and flood-generating mechanisms among watersheds within large countries like the United States, we recommend that the selection of distribution model be guided by the hydroclimatic properties of the basin rather than relying on a single national distribution model.

Perspective study on charge time measurement of long-term stored lithium-ion batteries used in electric-powered aircraft assessed and modelled by specific growth model with diffusion process backup

Electrical energy sources and batteries are currently in great demand. The demand is growing, and their use is on the rise in a variety of applications. In contrast, there are limited both production/manufacturing options and an effort to ensure more environmentally friendly acquisition, operation and use. In this article, we study, test, and model the charging process of Li-ION batteries. We study a set of long-term stored Li-ION batteries and compare the data and results with a set of new Li-ION batteries. The charging data are obtained experimentally by long-term testing, and the volume (of the data) is very large and statistically very representative. Modelling of the Li-ION battery charging process is based on specific growth model forms. Furthermore, the charging process is simulated using special forms of the diffusion process, specifically the Geometric Ornstein-Uhlenbeck process, which seems to be the most suitable for this purpose. The research is carried out with the aim to obtain the first passage time (FPT), i.e. the charge time of the battery. The first passage time is further studied with respect to the suitability of its expression using parametric probability distributions. We also acquired the numerical statistics of the charging time FPT as well as the respective parametric distribution. The FPT results obtained for long-term stored and new Li-ION batteries were compared using well-known and lesser-known statistical tests, such as the Kullback-Leibler divergence.

Estimation of Weibull Probability Distribution Parameters with Optimization Algorithms and Foça Wind Data Application

In this study, the scale and shape parameters of the Weibull probability distribution function (W.pdf) used in determining the profitability of wind energy projects are estimated using optimization algorithms and the moment method. These parameters are then used to estimate the wind energy potential in Foça region of İzmir in Turkey. The values of Weibull parameters obtained using Particle Swarm Optimization (PSO), Sine Cosine Algorithm (SCA), Social Group Optimization (SGO), and Bat Algorithm (BA) were compared with the estimation results of the Moment Method (MM) as reference. Root mean square error (RMSE) and chi-square (χ^2) tests were used to compare the parameter estimation methods. The wind speed measurement values of the observation station in Foça were used. As a result of Foça speed data analysis, the annual average wind speed was determined as 6.15 m/s, and the dominant wind direction was found as northeast. Wind speed frequency distributions were compared with the measurement results and calculated with the estimated parameters. When RMSE and χ^2 criteria are evaluated together; it can be said that the BA provides the best performance. It has been discovered as a consequence that the optimization parameters give very good results in potential calculations and wind speed distribution.

Robust adaptive analysis of extreme dynamic responses of wave energy converters

In the current study, a new adaptive binned kernel density estimation method has been introduced. In the proposed new method, Fourier transforms have been utilized to accomplish the convolution rather than performing the convolution by hand. By utilizing the fast Fourier transform, direct and inverse Fourier transforms have been found in a relatively short amount of time when implementing the new method. Upon analyzing the computed results, it has been observed that the newly proposed adaptive binned kernel density estimation distribution curve exhibits a high level of smoothness in the tail region. Furthermore, it demonstrates a strong alignment with the histogram derived from the recorded ocean wave dataset obtained at the NDBC station 46053. These are the major advantages of the proposed new method comparing with other existing methods such as the parametric method, the ordinary KDE method, and Abramson's adaptive KDE method. The specific research gap identified in the field is that none of the existing methods can predict the sea state parameter probability distribution tails both accurately and efficiently, and the proposed new method has successfully addressed this research gap. Upon careful examination of the calculation results, it becomes evident that the projected 50-year extreme power-take-off heaving force value, derived using the newly proposed method, is 1989300N. This value significantly surpasses (by more than 9.5%) the forecasted value of 1816200N obtained through the application of the Rosenblatt-I-SORM contour method. The findings of this study suggest that the newly proposed adaptive binned kernel density estimation method exhibits robustness and demonstrates accurate forecasting capabilities for the 50-year extreme dynamic responses of wave energy converters.

LSSVC: A Learned Spatially Scalable Video Coding Scheme.

Traditional block-based spatially scalable video coding has been studied for over twenty years. While significant advancements have been made, the scope for further improvement in compression performance is limited. Inspired by the success of learned video coding, we propose an end-to-end learned spatially scalable video coding scheme, LSSVC, which provides a new solution for scalable video coding. In LSSVC, we propose to use the motion, texture, and latent information of the base layer (BL) as interlayer information for compressing the enhancement layer (EL). To reduce interlayer redundancy, we design three modules to leverage the upsampled interlayer information. Firstly, we design a contextual motion vector (MV) encoder-decoder, which utilizes the upsampled BL motion information to help compress high-resolution MV. Secondly, we design a hybrid temporal-layer context mining module to learn more accurate contexts from the EL temporal features and the upsampled BL texture information. Thirdly, we use the upsampled BL latent information as an interlayer prior for the entropy model to estimate more accurate probability distribution parameters for the high-resolution latents. Experimental results show that our scheme surpasses H.265/SHVC reference software by a large margin. Our code is available at https://github.com/EsakaK/LSSVC.

Extrapolating Metal (Cu, Ni, Zn) Toxicity from Individuals to Populations Across Daphnia Species Using Mechanistic Models: The Roles of Uncertainty Propagation and Combined Physiological Modes of Action.

Mechanistic effect modeling is a promising tool to improve the ecological realism of environmental risk assessment. An open question for the mechanistic modeling of metal toxicity is whether the same physiological mode of action (PMoA) could be assumed for closely related species. The implications of various modeling choices, such as the use of parameter point estimates and assumption of simplistic toxicodynamic models, are largely unexplored. We conducted life-table experiments with Daphnia longispina, Daphnia magna, and Daphnia pulex exposed to the single metals Cu, Ni, and Zn, and calibrated toxicokinetic-toxicodynamic (TKTD) models based on dynamic energy budget theory. We developed TKTD models with single and combined PMoAs to compare their goodness-of-fit and predicted population-level sensitivity. We identified the PMoA reproduction efficiency as most probable in all species for Ni and Zn, but not for Cu, and found that combined-PMoA models predicted higher population-level sensitivity than single-PMoA models, which was related to the predicted individual-level sensitivity, rather than to mechanistic differences between models. Using point estimates of parameters, instead of sampling from the probability distributions of parameters, could also lead to differences in the predicted population-level sensitivity. According to model predictions, apical chronic endpoints (cumulative reproduction, survival) are conservative for single-metal population effects across metals and species. We conclude that the assumption of an identical PMoA for different species of Daphnia could be justified for Ni and Zn, but not for Cu. Single-PMoA models are more appropriate than combined-PMoA models from a model selection perspective, but propagation of the associated uncertainty should be considered. More accurate predictions of effects at low concentrations may nevertheless motivate the use of combined-PMoA models. Environ Toxicol Chem 2024;43:338-358. © 2023 The Authors. Environmental Toxicology and Chemistry published by Wiley Periodicals LLC on behalf of SETAC.

Parametric Information Geometry with the Package Geomstats

We introduce the information geometry module of the Python package Geomstats. The module first implements Fisher–Rao Riemannian manifolds of widely used parametric families of probability distributions, such as normal, gamma, beta, Dirichlet distributions, and more. The module further gives the Fisher–Rao Riemannian geometry of any parametric family of distributions of interest, given a parameterized probability density function as input. The implemented Riemannian geometry tools allow users to compare, average, interpolate between distributions inside a given family. Importantly, such capabilities open the door to statistics and machine learning on probability distributions. We present the object-oriented implementation of the module along with illustrative examples and show how it can be used to perform learning on manifolds of parametric probability distributions.

Designing robust green sustainable supply chain network by bi-objective optimization method

Designing a green supply chain is becoming popular in the context of sustainable development. To address this academic concern, this paper designs a multi-product, multi-echelon green supply chain network (GSCN) from economic and environmental aspects. During the modeling process, the main challenge is to access the accurate probability distributions of uncertain parameters from limited historical data. To overcome this difficulty, this paper develops a distributionally robust design framework for bi-objective GSCN, where the distribution information of uncertain parameter is partially available and characterized by ambiguity sets. For the tractability, this paper discusses robust counterpart reformulation under Wasserstein-distance-based ambiguity sets. Finally, the obtained mixed integer programming model is resolved via commercial optimization software. To validate the proposed optimization framework, we design a meat supply chain network for a Chinese realistic food enterprise. The computational results demonstrate that the proposed distributionally robust model can provide reliable solutions compared with stochastic optimization method.