Proper Distributions Research Articles

A self-consistent dynamical model of the Milky Way disc adjusted to Gaia data

Context. Accurate astrometry achieved by Gaia for many stars in the Milky Way provides an opportunity to reanalyse the Galactic stellar populations from a large and homogeneous sample and to revisit the Galaxy gravitational potential. Aims. This paper shows how a self-consistent dynamical model can be obtained by fitting the gravitational potential of the Milky Way to the stellar kinematics and densities from Gaia data. Methods. We derived a gravitational potential using the Besancon Galaxy Model, and computed the disc stellar distribution functions based on three integrals of motion (E, Lz, I3) to model stationary stellar discs. The gravitational potential and the stellar distribution functions are built self-consistently, and are then adjusted to be in agreement with the kinematics and the density distributions obtained from Gaia observations. A Markov chain Monte Carlo (MCMC) is used to fit the free parameters of the dynamical model to Gaia parallax and proper motion distributions. The fit is done on several sets of Gaia data, mainly a subsample of the GCNS (Gaia catalogue of nearby stars to 100 pc) with G < 17, together with 26 deep fields selected from eDR3, widely spread in longitudes and latitudes. Results. We are able to determine the velocity dispersion ellipsoid and its tilt for subcomponents of different ages, both varying with R and z. The density laws and their radial scale lengths for the thin and thick disc populations are also obtained self-consistently. This new model has some interesting characteristics that come naturally from the process, such as a flaring thin disc. The thick disc is found to present very distinctive characteristics from the old thin disc, both in density and kinematics. This lends significant support to the idea that thin and thick discs were formed in distinct scenarios, as the density and kinematics transition between them is found to be abrupt. The dark matter halo is shown to be nearly spherical. We also derive the solar motion with regards to the Local Standard of Rest (LSR), finding U⊙ = 10.79 ± 0.56 km s−1, V⊙ = 11.06 ± 0.94 km s−1, and W⊙ = 7.66 ± 0.43 km s−1, in close agreement with recent studies. Conclusions. The resulting fully self-consistent gravitational potential, still axisymmetric, is a good approximation of a smooth mass distribution in the Milky Way and can be used for further studies, including finding streams, substructures, and to compute orbits for real stars in our Galaxy.

Kinematic data rebuild the nuclear star cluster as the most metal-rich region of the Galaxy

Context.The Galactic centre (GC) is located at only 8 kpc from Earth and constitutes a unique template with which to understand Galactic nuclei. Nevertheless, the high crowding and extinction towards the GC hamper the study of its main stellar components, the nuclear stellar disc (NSD) and the nuclear star cluster (NSC).Aims.Recent work has suggested that the NSD and the NSC can be distinguished along the line of sight towards the NSC via the different extinction of their stars. This motivated us to analyse the proper motion, radial velocity, and the metallicity distributions of the different extinction groups.Methods.We use photometric, kinematic, and metallicity data to distinguish between probable NSD and NSC stars in a region centred on the NSC.Results.We detected two different extinction groups of stars and obtained that they have significantly different proper motion distributions, in agreement with the expected kinematics for the NSD and the NSC. We also derived radial velocity maps that appear to be different for the two components, and found different metallicities for each of them, with the largest one measured for the most extinguished group of stars. We obtained that the metallicity distribution of each extinction group is best fitted by a bimodal distribution, indicating the presence of two metallicity components for each of them (a broad one slightly below solar metallicity, and a more metal-rich, narrower one that is largest for the high-extinction group of stars).Conclusions.We conclude that both extinction groups are distinct GC components with different kinematics and metallicity, and correspond to the NSD and the NSC. Therefore, it is possible to distinguish them via their different extinction. The high mean metallicity, [M/H] ∼ 0.3 dex, obtained for the metal-rich stars of the NSC supports the proposition that this component is arguably the most metal-rich region of the Galaxy.

Iterative Landmark-Based Umbrella Sampling (ILBUS) Protocol for Sampling of Conformational Space of Biomolecules.

Computer simulations of biomolecules such as molecular dynamics often suffer from insufficient sampling. Due to limited computational resources, insufficient sampling prevents obtaining proper equilibrium distributions of observed properties. To deal with this problem, we proposed a simulation protocol for efficient resampling of collected off-equilibrium trajectories. These trajectories are utilized for the initial mapping of the conformational space, which is later properly resampled by the introduced Iterative Landmark-Based Umbrella Sampling (ILBUS) method. Reconstruction of static equilibrium properties is achieved by the multistate Bennett acceptance ratio (MBAR) method, which enables efficient use of simulated data. The ILBUS protocol is geometry-based and does not demand any additional collective variable or a dimensional-reduction technique. The only requirement is a set of suitably spaced reference conformations, which serve as landmarks in the mapped conformational space. Additionally, the ILBUS protocol encompasses an iterative process that optimizes the force constant used in the umbrella sampling simulation. Such tuning is an inherent feature of the protocol and does not need to be performed by the user in advance. Furthermore, even the simulations with suboptimal force constants can be used in estimates by MBAR. We demonstrate the feasibility and the performance of this approach in the study of the conformational landscape of the alanine dipeptide, met-enkephalin, and adenylate kinase.

The Type II Topp-Leone-G Power Series Distribution with Applications on Bladder Cancer

Statistical distributions are important in modeling the real life of an item and therefore proper distributions that provide useful information for sound conclusions and decisions are needed. For that reason, the demand for developing new generalized distributions have become appropriate for data that have both monotonic and non-monotonic hazard rate functions. In this paper, we develop a new distribution called the Type II Topp-Leone-G Power Series (TIITLGPS) distribution by compounding the Type II Topp-Leone-G (TIITLG) distribution with the power series distribution. Statistical properties of the TIITLGPS distribution are obtained. A variety of shapes for the densities and hazard rate are presented of the considered special case. A simulation study to examine the efficiency of the maximum likelihood estimates is also conducted. Finally, the bladder cancer data example is analyzed for illustrative purposes, it is displayed that the introduced distribution provides better fit when compared to other non-nested distributions considered in this work.

Estimation of P(Y

ABSTRACT The problem of estimating a stress-strength parameter is considered under the assumption that both stress and strength variables follow independent lognormal distributions. The maximum likelihood estimator of this parametric function is obtained and based on its asymptotic distribution, approximate intervals are constructed. Properties of a heuristic estimator are studied as well. Bootstrap intervals are also constructed. Bayes estimator is derived against proper and improper prior distributions. We further compute credible intervals of stress–strength parameter using importance sampling. The empirical Bayes procedure is also discussed. Proposed point and interval estimators are compared numerically using Monte Carlo simulations. Analysis of a real data set is presented for illustration purposes.

Tail-Weighted Wind Speed Distribution by Mixture Model with Constrained Maximum Likelihood

In order to reduce the estimation uncertainty for the wind energy output, the accurate assessment of the wind speed distribution plays an important role. Due to the influence of the complex terrain, the wind speed data in mountainous area may show the heavy tail. The tail has an important effect on the annual energy production of the wind turbine because of the power output being the cubic of the wind speed. Hence the heavy tail should be highlighted before choosing the proper distributions. To characterize the heavy tail, the box plot, QQ plot and conditional mean exceedance are used. In addition, the wind climate in the mountainous area is very complicated and typically mixed by local storms and large-scale wind flows. The distribution of the wind speed is prone to exhibit bimodal or even multi-modal nature. The conventional unimodal distributions such as Weibull may not well portray these distributions. The mixture distribution has more flexibilities to handle this challenge. Both generalized extreme value distribution and generalized Pareto distribution are considered to formulate the mixture distribution in modeling the tail. The maximum likelihood method and the constrained maximum likelihood method are used to estimate distribution parameters. The comprehensive evaluation criteria are adopted to determine the most appropriate distribution of four sets of wind speed in the mountainous area of Yunnan, China. Graphical tools, such as histogram density curve and QQ plot, are also used for evaluation. Results show that heavy tail distribution should be considered for the wind data in mountainous areas and the proposed mixture model with the constrained maximum likelihood method for the parameter estimation will be superior for the wind energy potential estimation.

JefiGPU: Jefimenko's equations on GPU

We have implemented a GPU version of the Jefimenko's equations — JefiGPU. Given the proper distributions of the source terms ρ (charge density) and J (current density) in the source volume, the algorithm gives the electromagnetic fields in the observational region (not necessarily overlaps the vicinity of the sources). To verify the accuracy of the GPU implementation, we have compared the obtained results with that of the theoretical ones. Our results show that the deviations of the GPU results from the theoretical ones are around 5%. Meanwhile, we have also compared the performance of the GPU implementation with a CPU version. Finally, we have studied the parameter dependence of the execution time and memory consumption on one NVIDIA Tesla V100 card. Our code can be consistently coupled to RBG (Relativistic Boltzmann equations on GPUs) and many other GPU-based algorithms in physics. Program summaryProgram Title: JefiGPUCPC Library link to program files:https://doi.org/10.17632/6vnghzknx4.1Developer's repository link:https://github.com/Juenjie/CRBMGCode Ocean capsule:https://codeocean.com/capsule/9007956Licensing provisions: Apache-2.0Programming language: PythonNature of problem: Jefimenko's equations are numerically stable with given sources ρ (charge density) and J (current density). Providing proper sources, Jefimenko's equations can give the electromagnetic fields without boundary conditions. However, the relevant integrations of the Jefimenko's equations involve a 4D space-time which is both memory and time consuming. With the help of the state-of-art GPU technique, these integrations can be evaluated with acceptable accuracy and execution time. In the present work, we have implemented a GPU version of the Jefimenko's equations and tested the accuracy and the performance of the code.Solution method: The GPU code mainly deals with the implementation of the integrations in Jefimenko's equations. Each CUDA kernel corresponds to a spatial point of E and B. The integrations involving the source region and the retarded time are performed in each CUDA kernel. Ray, Numba and Cupy packages are used to manipulate the scaling of GPU allocation and evaluation.

The design and evaluation of three-dimensional corner joints used in wooden furniture frames: Experimental and numerical

This study aimed to design and evaluate the detachable corner joints used in wooden furniture frames, including a commonly used detachable joint (control) form using mortise and tenon with plug reinforcement and three novel proposed joints, i.e., novel joint I ~ III, which adopted in-line double-hole nuts, metal sheet connector, and embedded nuts and screws respectively, via numerical and experimental methods. The numerical analysis results indicated that the optimal proposed joint (novel joint І) had good mechanical performance when subjected to bending load with proper stress distributions and relatively low maximum stress compared with the other two proposed joints. The experimental results showed that the bending load resistance of the control and the optimal proposed joints were 1920 N (0.14) and 4390 N (0.05), respectively. The bending moment capacity and bending stiffness of the optimal joints were remarkably higher than the bending moment capacity and bending stiffness of the control joint. In addition, the combination of the numerical and experimental methods could effectively simplify the steps of furniture connection design and development and save costs in terms of time and materials.

ADP-Ribosylation Factor Family of Small GTP-Binding Proteins: Their Membrane Recruitment, Activation, Crosstalk and Functions.

Members of the ADP-ribosylation factor (ARF) family of guanine-nucleotide binding proteins play critical roles in various cellular processes, especially in regulating the secretory, and endocytic pathways. The fidelity of intracellular vesicular trafficking depends on proper activations and precise subcellular distributions of ARF family proteins regulated by guanine nucleotide exchange factors (GEFs) and GTPase-activating proteins (GAPs). Here we review recent progress in understanding the membrane recruitment, activation, crosstalk, and functions of ARF family proteins.

CFD modeling of air flow, humidity, CO2 and NH3 distributions in a caged laying hen house with tunnel ventilation system

In poultry houses, the ventilation system should provide a favorable standard living environment for hens. In addition to uniform distribution of velocity and temperature, concentration of gaseous CO2 and NH3 pollutants and the humidity distribution, which affect the air quality in the poultry house, are of prime importance. In previous numerical studies on caged laying hen houses with tunnel ventilation system, these five concerns have not been examined concurrently. To address all of these issues, in this numerical study a previously studied laying hen house with 4 rows of cages equipped with tunnel ventilation system using evaporative cooling pads has been considered in summer. 3D numerical simulations indicated the deficiency of previous models for provision of proper temperature and velocity distributions also ignoring investigation of humidity and concentration of gaseous pollutants. Thus three new models were proposed, in which the position and number of evaporative cooling pads and exhaust fans and their capacity were altered. Evaluation showed that the second new model, in which 15 fans are on the east wall and three evaporative cooling pads are on the west wall, provides the best performance. In this model, the speed at the levels of the birds is 2.5 m.s-1 and the maximum temperature is 308 K. Also, the relative humidity is between 60 and 75%, which is 10% lower than that of the original model of previous study and CO2 and NH3 concentrations are within the tolerable range everywhere. The CFD techniques utilized in this study may be extended to simulate other poultry houses with any ventilation system such as tunnel, mixed or any other inlet/outlet arrangements, however for the results to be reliable simulation should involve air flow, thermal and humidity fields as well as CO2 and NH3 concentrations.

Estimating Vat Refunds the Case of South Africa

This study intends to estimate VAT refund levels in South Africa in an ideal situation where there are well-equipped, incorruptible officials and a proper VAT system is in place. Understanding the dynamics behind the behaviour of VAT and its main drivers is crucial and could have a huge benefit to the country’s economy with regards to closing the tax gap related to this tax type. Using the data from various sources (VAT refunds and some macroeconomic variables), a Vector Autoregression (VAR) model was used to estimate the level of VAT refunds in South Africa. The model estimates VAT refunds for the period 2021/22 to be R242.7 billion, while the VAT refunds forecast for the period 2022/23 and 2023/24 amounts to R254.6 billion and R267.3 billion, respectively. Furthermore, VAT refunds contribute on average 17.5% to the total tax for the forecast period of 2021/22-2023/24. The study also indicates that the growth in VAT refunds is influenced by the growth in domestic VAT collections, increasing employment rate and the growth in both agriculture and construction GDP. The estimated level of VAT refunds can serve as an important consideration in the national budgeting processes in South Africa. Adequate provisions can be made to enable proper planning and distributions to government departments. To our knowledge, this study is the first of its kind for South Africa. In summary, the South African tax authority should not deviate from the primary goal of building sound VAT systems based on improved voluntary compliance through effective systems of self-assessment

ER proteins decipher the tubulin code to regulate organelle distribution

Organelles move along differentially modified microtubules to establish and maintain their proper distributions and functions1,2. However, how cells interpret these post-translational microtubule modification codes to selectively regulate organelle positioning remains largely unknown. The endoplasmic reticulum (ER) is an interconnected network of diverse morphologies that extends promiscuously throughout the cytoplasm3, forming abundant contacts with other organelles4. Dysregulation of endoplasmic reticulum morphology is tightly linked to neurologic disorders and cancer5,6. Here we demonstrate that three membrane-bound endoplasmic reticulum proteins preferentially interact with different microtubule populations, with CLIMP63 binding centrosome microtubules, kinectin (KTN1) binding perinuclear polyglutamylated microtubules, and p180 binding glutamylated microtubules. Knockout of these proteins or manipulation of microtubule populations and glutamylation status results in marked changes in endoplasmic reticulum positioning, leading to similar redistributions of other organelles. During nutrient starvation, cells modulate CLIMP63 protein levels and p180–microtubule binding to bidirectionally move endoplasmic reticulum and lysosomes for proper autophagic responses.

Unsupervised lexical acquisition of relative spatial concepts using spoken user utterances

This paper proposes methods for unsupervised lexical acquisition for relative spatial concepts using spoken user utterances. A robot with a flexible spoken dialog system must be able to acquire linguistic representation and its meaning specific to an environment through interactions with humans as children do. Specifically, relative spatial concepts (e.g. front and right) are widely used in our daily lives, however, it is not obvious which object is a reference object when a robot learns relative spatial concepts. Therefore, we propose methods by which a robot without prior knowledge of words can learn relative spatial concepts. The methods are formulated using a probabilistic model to estimate the proper reference objects and distributions representing concepts simultaneously. The experimental results show that relative spatial concepts and a phoneme sequence representing each concept can be learned under the condition that the robot does not know which located object is the reference object. Additionally, we show that two processes in the proposed method improve the estimation accuracy of the concepts: generating candidate word sequences by class n-gram and selecting word sequences using location information. Furthermore, we show that clues to reference objects improve accuracy even though the number of candidate reference objects increases.

Simple analytical theory for micelles with widespread radial distribution of charged heads

Modeling aggregation of ionic micelles in solution is an important task that has been attracting attention for years. The molecular-thermodynamic micellization models describe the electrostatic interactions within the Poisson-Boltzmann theory that does not take into account fluctuations of the surfactant heads in the micelle. In this work we apply the statistical field theory to spherical micelles where the charged heads of surfactant molecules undergo fluctuations in the diffuse coronae. From this theory, a simple equation is derived for the electrostatic contribution to the standard free energy of aggregation. The results from the new theory are compared with the numerical results and analytical approximations of the Poisson-Boltzmann theory for the spheres of varying charge and curvature in the ranges relevant to micelles and over a broad interval of solution salinity. The new electrostatic free energy term is employed in the classical molecular-thermodynamic model to describe spherical micelles in the aqueous solution of ionic surfactant with added salt. We introduce an empirical correction that takes into account the effect of fluctuations on the hydrophobic part of the aggregation free energy. Modeling aggregation equilibrium for the spherical SDS micelles in the aqueous solution of salt, we illustrate the performance of the new theory. We compare our results with the structural MD-data and experimental hydrodynamic radii to show that our model with the fluctuating surfactant heads can reflect a realistic picture of the micellar structure and gives reasonable size-estimates for the spherical ionic micelles if proper charge distributions are considered.

The Impact of Climate Change on Hydro-Meteorological Droughts Using Copula Functions

Climate change has made many alterations to the climate of earth, including hydro-climatic extreme events. To investigate the impact of climate change on hydro-meteorological droughts in the Kamal-Saleh dam basin in Markazi province, Iran, proportional to future climate conditions, a new and comprehensive index was developed with the aim of accurately estimating drought in a more realistic condition. This aggregate drought index (ADI) represented the main meteorological and hydrological characteristics of drought. Temperature and precipitation projections for future climates were simulated by five CMIP5 models and downscaled over the study area during 2050s (2040–2069) and 2080s (2070–2099) relative to the baseline period (1976–2005). By fitting five univariate distribution functions on drought severity and duration, proper marginal distributions were selected. The joint distribution of drought severity and duration was chosen from five types of copula functions. The results revealed that in future, severe droughts are expected to frequently occur in a shorter period.

Bayesian inference of heterogeneous epidemic models: Application to COVID-19 spread accounting for long-term care facilities

We propose a high dimensional Bayesian inference framework for learning heterogeneous dynamics of a COVID-19 model, with a specific application to the dynamics and severity of COVID-19 inside and outside long-term care (LTC) facilities. We develop a heterogeneous compartmental model that accounts for the heterogeneity of the time-varying spread and severity of COVID-19 inside and outside LTC facilities, which is characterized by time-dependent stochastic processes and time-independent parameters in ∼1500 dimensions after discretization. To infer these parameters, we use reported data on the number of confirmed, hospitalized, and deceased cases with suitable post-processing in both a deterministic inversion approach with appropriate regularization as a first step, followed by Bayesian inversion with proper prior distributions. To address the curse of dimensionality and the ill-posedness of the high-dimensional inference problem, we propose use of a dimension-independent projected Stein variational gradient descent method, and demonstrate the intrinsic low-dimensionality of the inverse problem. We present inference results with quantified uncertainties for both New Jersey and Texas, which experienced different epidemic phases and patterns. Moreover, we also present forecasting and validation results based on the empirical posterior samples of our inference for the future trajectory of COVID-19.

Compact cascaded meta-surface system for controlling the spin and orbital angular momentum of electromagnetic fields simultaneously.

We propose a compact cascaded meta-surface system (CCMS) to produce well converged orbital angular momentum (OAM) vortex waves with tailored spin angular momentum (SAM) by integrating a meta-surface lens (ML) with an assistant meta-mirror (AM). Specifically, the co-linearly polarized (LP) waves from the feed would be reflected by the ML firstly and then twisted into the cross-LP counterparts by the AM to penetrate the ML for the perfect synthesis of the OAM vortex beams while performing the linear-to-circular polarization conversion. Especially, the CCMS can pack the ML and the AM closely together with a quarter of the ML focal length when we apply proper phase distributions on the AM. In addition, the proposed CCMS can readily be extended to the generation of multiple circularly polarized OAM vortex waves with different modes. Our design should thus pave the way for building up more efficient wireless communication systems with expanded channel capacity.

On the existence of posterior mean for Bayesian logistic regression

Abstract Existence conditions for posterior mean of Bayesian logistic regression depend on both chosen prior distributions and a likelihood function. In logistic regression, different patterns of data points can lead to finite maximum likelihood estimates (MLE) or infinite MLE of the regression coefficients. Albert and Anderson [On the existence of maximum likelihood estimates in logistic regression models, Biometrika 71 1984, 1, 1–10] gave definitions of different types of data points, which are complete separation, quasicomplete separation and overlap. Conditions for the existence of the MLE for logistic regression models were proposed under different types of data points. Based on these conditions, we propose the necessary and sufficient conditions for the existence of posterior mean under different choices of prior distributions. In this paper, a general wide class of priors, which are informative priors and non-informative priors having proper distributions and improper distributions, are considered for the existence of posterior mean. In addition, necessary and sufficient conditions for the existence of posterior mean for an individual coefficient is also proposed.

Statistical Inference of Truncated Normal Distribution Based on the Generalized Progressive Hybrid Censoring.

In this paper, the parameter estimation problem of a truncated normal distribution is discussed based on the generalized progressive hybrid censored data. The desired maximum likelihood estimates of unknown quantities are firstly derived through the Newton–Raphson algorithm and the expectation maximization algorithm. Based on the asymptotic normality of the maximum likelihood estimators, we develop the asymptotic confidence intervals. The percentile bootstrap method is also employed in the case of the small sample size. Further, the Bayes estimates are evaluated under various loss functions like squared error, general entropy, and linex loss functions. Tierney and Kadane approximation, as well as the importance sampling approach, is applied to obtain the Bayesian estimates under proper prior distributions. The associated Bayesian credible intervals are constructed in the meantime. Extensive numerical simulations are implemented to compare the performance of different estimation methods. Finally, an authentic example is analyzed to illustrate the inference approaches.

Evaluation of Fractal Variance-Distance Model in Identifying Geochemical Anomalies of Calamine Mehdiabad Mining Complex, Central Iran

In this paper, a power-law relation modeling called the vario-fractal model is introduced in order to understand the discrepancies between the linear and non-linear distribution of the elements and its application for mineral exploration in the calamine Zn-Pb ore-deposit. From a hypothetical viewpoint, since geochemical zonation of the supra- and sub-ore elements is a crucial evaluation criterion for concealed/underlying mineralization potentials, this hypothesis can be tested by delineating the fractal surfaces of elements as the geometric evidence of primary geochemical zonation of elements in the calamine mine. A comparison of the linear regression results with the Poisson distribution coefficients indicate the relative tendency of the elements towards a non-linear distribution. Therefore, a logarithmic equation derived from the variance-distance relationship (power-law) is used here for the delineation of fractal surfaces of elements as the geometric features related to proper self-organized distributions. In this research work, the vario-fractal expression of geochemical zonation has trace-element tendencies to the non-linear distribution. The results obtained show that the calamine’s fractional surfaces are mostly of self-organized types, situated at 2 < FD < 3 as fractal surfaces, although 3 of the elements appear in the quasi-fractal populations called Brownies” here. Moreover, the calamine’s fractal surfaces can be extended throughout the anomalous regions or may be distributed as limited types of the finalized model, which is a fractal-based pattern of geochemical zonation of the elements for evaluation of the hypogenic mineralization potential and has been prioritized to 6 target-areas containing 10 elements with real fractal surfaces and 3 more at near Brownies and then validated by the mineralogical evidence.