Probability Density Plots Research Articles

International Air Cargo Volume Forecasting based on the Stacking Fusion Model

Accurate forecasting of international air cargo volumes is crucial for air cargo carriers, which optimizes operational efficiency and profitability and strengthens market competitiveness and risk response capabilities. This study focuses on the open-source cargo data of over 100 international airlines in India from January 2015 to March 2017. Firstly, the missing data must be dealt with. Then, histograms and probability density plots are used to depict the distribution of the cargo volume and analyze the dynamics of the cargo volume of each company at annual and quarterly levels. Subsequently, key factors affecting cargo volumes are analyzed, with a special focus on the cargo performance of the Top 5 airlines, which is visualized in box plots. Given the time-series nature of cargo data, this study adopts the data sequential partitioning method. It innovatively utilizes the Stacking ensemble learning framework, integrating regression models such as Random Forest, Decision Tree, Extreme Gradient Boosting, and K-Nearest Neighbor as the base learners. The meta-learner is constructed to integrate the outputs of each base model, and the hyperparameters of the model are optimized by grid search and cross-validation. Comparison results show that the Stacking model has a higher R² value and lower MSE than any single base learners, indicating that it is more effective in international air cargo volume prediction. The prediction model based on stacking ensemble learning provides an effective strategy for improving air cargo prediction accuracy.

Reconstruction of microcontinents during the assembly of Rodinia: A case study from the Central Tianshan Block

There are multiple Precambrian microcontinents within the Central Asian Orogenic Belt (CAOB), and the paleogeographic locations of those in the southwest CAOB (e.g. Central Tianshan Block, Yili Block, Aktau-Mointy terrane, Erementau-Niyaz terrane and Kokchetav terrane) remain controversial. The Central Tianshan Block is one of the representative Precambrian microcontinents in the southwest CAOB. It can be divided into the western Central Tianshan Block and eastern Central Tianshan Block. To investigate their relationships and paleogeographic locations, we collected metasedimentary rocks from the Kekesu Group in western Central Tianshan Block. The results of zircon LA–ICP–MS U-Pb dating, combining with previously obtained magmatic ages, suggest that the Kekesu Group was deposited during the latest Mesoproterozoic to earliest Neoproterozoic (ca. 1010–969 Ma). Detrital zircon populations of Kekesu Group were dominated by 2.0–0.9 Ga grains with an age peak at 1474 Ma. The Archean to end-Paleoproterozoic zircon grains had variable εHf(t) values from +9.7 to −8.7, and most of the Mesoproterozoic zircons had positive εHf(t) values (+13.9 to +2.4). The Kekesu Group in western Central Tianshan Block has similar zircon age populations and εHf(t) values to those in eastern Central Tianshan Block. In combination with magmatism, these data suggest that western and eastern Central Tianshan Block had similar tectonic affinities and locations during the earliest Neoproterozoic. We compiled 4566 concordant detrital zircon U-Pb age data of Mesoproterozoic to early Neoproterozoic strata from microcontinents in the southwest CAOB and potential sources. The zircon age probability density plots, kernel density estimates and multidimensional scaling plot suggest that the Central Tianshan and Yili blocks had similar sources mainly derived from the Musgrave Province in central Australia in the latest Mesoproterozoic to early Neoproterozoic, and were possibly located near Australia during assembly of Rodinia. The sources for the Erementau-Niyaz and Kokchetav terranes were probably mainly within the northern Laurentia in the latest Mesoproterozoic to earliest Neoproterozoic.

Statistical analysis on Alzheimer's disease

Alzheimer's disease is a progressive neurodegenerative disease that occurs mostly in the elderly and has memory impairment as the main clinical symptom. There is no ideal treatment for Alzheimer's disease, so early prevention is important. In this paper, we use brain structural information to diagnose Alzheimer's disease features and cognitive-behavioral characteristics, which is important for early and accurate diagnosis of mild cognitive impairment. To investigate the factors influencing Alzheimer's disease, a correlation analysis model was developed after preprocessing the missing values of the data. First, the data features were viewed, the missing values of the data were analyzed, and the useless features were removed and the missing values of the remaining features were filled with the average value. To verify the accuracy of the subsequent intelligent diagnosis model and clustering model, this paper divides the training set and test set according to PTID. Finally, the top ten important features are selected and the Spearman coefficients are chosen according to the distribution of the features for correlation analysis. Machine learning methods were utilized to build an Alzheimer's classification model to solve the problem of intelligent diagnosis of Alzheimer's disease. The pre-processed dataset in the above paper was trained with the model, and five methods of logistic regression, support vector machine, KNN classification, decision tree classification and XGB were utilized to build the classification model, and the accuracy, recall and F1 value of each model were visualized and compared, among which the accuracy of XGB model reached 83%, which is reasonable for the intelligent diagnosis of the disease. A K-Means-based clustering model for disease types was established using the K-Means clustering algorithm, clustering CN, MCI and AD into three major classes, and then refining MCI into three subclasses. The optimal K-values and random seeds were firstly found using the elbow principle, then the cluster analysis was performed using the feature values and data sets selected after preprocessing, and finally the MCI in MCI was extracted and sub-clustered into three subclasses SMC, EMCI and LMCI. In order to investigate the evolution pattern of different categories of diseases over time, patients with 3 categories of diseases are screened separately for analysis in this paper. Firstly, by combining the results above and reviewing the data, the features irrelevant to this task and columns containing a large number of missing values were removed, the remaining features were selected and probability density plots were drawn, and all discrete features and all features that were essentially zero were continued to be screened out. After that, the 15 features of CN, MCI and AD diseases were plotted separately over time to reveal their evolution patterns over time. We reviewed the relevant literature, sorted out and summarized the existing studies at home and abroad, and summarized the criteria for determining the five stages of Alzheimer's disease and the early intervention of the disease.

Timescales and mechanisms of felsic lower continental crust formation: Insights from U-Pb geochronology of detrital zircon (Malenco Unit, eastern Central Alps)

Burial of supracrustal sedimentary material is one of the processes that contribute to the formation of the lower continental crust. We investigate the rate of this process in Permian lower continental crust from the Malenco Unit (eastern Central Alps) by constraining the age of protolith deposition and subsequent high-grade metamorphism of felsic, garnet-rich granulites. Detrital zircon cores, many of which are small (<50 μm), were dated by SIMS and yield concordant dates ranging from 387 ± 21 Ma (2σ) to 2380 ± 16 Ma, with the vast majority of the dates falling in the range 450–1000 Ma. For the seven cores in each sample that gave the youngest concordant dates, replicate analyses were carried out. None of these cores had all measured U-Pb dates agree within error, indicating significant disturbance by the Permian granulite facies metamorphism. A 206Pb/238U age of 424 ± 6 Ma for a core with two overlapping replicate analyses is the best available constraint on the maximum depositional age of the sedimentary protolith. This maximum depositional age also coincides with the first significant population in the probability density plot of detrital core dates, which is a double peak at ∼425 Ma and ∼450 Ma.Zircon detrital cores are separated from metamorphic overgrowths by a small seam of zircon that is riddled with tiny inclusions of quartz, biotite and muscovite. The first generation of metamorphic zircon rims has a 206Pb/238U age of 272.9 ± 2.8 Ma, displays steep heavy rare earth element (HREE) patterns and a moderate negative Eu-anomaly, and returns Ti-in-zircon temperatures of 740–780 °C. The second generation of metamorphic rims has a 206Pb/238U age of 263.8 ± 2.6 Ma, a flat HREE pattern and a pronounced negative Eu-anomaly, and gave Ti-in-zircon temperatures of 780–810 °C. Collectively these observations indicate that the first zircon rim formed on the prograde path at the onset of partial melting where muscovite was present but the rocks contained little garnet and no K-feldspar. Therefore, the metapelites resided at lower amphibolite facies, subsolidus conditions up until the intrusion of a Permian gabbro, which was emplaced shortly after the formation of the first generation of metamorphic zircon and caused heating to granulite facies conditions and widespread partial melting. There is no record of high-pressure metamorphism preceding granulite facies conditions, indicating that felsic lower crust in the Malenco unit was not formed by relamination.The Malenco unit was situated at the north-eastern active margin of Gondwana 420 Ma ago. Subduction-related accretion of sediments at lower crustal levels shortly after their deposition could explain the formation of this felsic lower crust that resided at subsolidus conditions for up to 100 My prior to Permian extension, gabbro intrusion and granulite facies metamorphism.

Knowledge control in informatics in military and civilian universities

The article provides a comparative analysis of the results of learning control in higher military and civilian universities. The analysis and comparison of control methods of testing were used. It was found that even the simplest paper-based tests allow effective comparative assessment of knowledge and provide a much deeper differentiation of knowledge assessment than the five-point grading system.The cheapness and efficiency of the test used at Krasnodar Air Force Institute for Pilots are achieved by dividing it into three parts: a questionnaire, a response sheet, and a test stencil. The questionnaire is a reusable document, and the response sheet is small in size.The use of basic Microsoft Office programs in the test showed that the mastery of these programs among students is increasing year by year. It turned out that the mastery of these programs depends little on the main process of learning.When checking the knowledge in the field of computer science, the primary testing is basic. But in general, the control of residual knowledge with the help of testing can objectively establish the effectiveness of teaching any subject.The article conducted a mathematical analysis of the test results and plotted probability density plots, which were approximated by a smooth mathematical function. This clear view of the distribution of the indicator leads to an understanding of how well the knowledge is learned by students.

Quantum Classical Transition for Mixed States: The Scaled Von Neumann Equation

In this work, we proposed a smooth transition wave equation from a quantum to classical regime in the framework of von Neumann formalism for ensembles and then obtained an equivalent scaled equation. This led us to develop a scaled statistical theory following the well-known Wigner–Moyal approach of quantum mechanics. This scaled nonequilibrium statistical mechanics has in it all the ingredients of the classical and quantum theory described in terms of a continuous parameter displaying all the dynamical regimes in between the two extreme cases. Finally, a simple application of our scaled formalism consisting of reflection from a mirror by computing various quantities, including probability density plots, scaled trajectories, and arrival times, was analyzed.

Developing a probabilistic decision-making model for reinforced sustainable supplier selection

The competitive environment and recent regulations require corporations to implement sustainable and reinforced solutions in their business operations and, thereby, sustainable supplier selection (SSS) has become a critical concern of companies. This study introduces a neoteric approach by extending the SSS framework containing the three widespread indicators, i.e., economic, social, and environmental sustainability dimensions (S), with additional three genuine aspects such as innovation (I), lean principles (L), and knowledge management (K), namely the S-ILK framework. To deal with probabilistic uncertainty, a novel Monte Carlo (MC) aided hybrid multi-criteria decision analysis model was constructed. MC simulation with Beta-PERT distribution was integrated with the Analytical Hierarchy Process (AHP) and Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) to identify criteria weights and perform supplier evaluations, respectively. Hence, criteria weights and supplier evaluation scores were illustrated as probability density plots instead of crisp values with MC aided decision-making model. The findings emphasized the role of economic sustainability and knowledge management capabilities of suppliers, which require a diligent investigation of life cycle cost of production and quality of knowledge management systems of suppliers. This study contributes to theory by highlighting interpersonal uncertainty through MC simulation and to practice by informing industry professionals about urgent needs for focusing on the innovation, knowledge management, and lean capabilities of suppliers. The proposed S-ILK framework can be regarded as a roadmap for companies to enhance their sustainability performance with innovative solutions, increased data quality, and continuous improvement with lean principles.

Strength Damage and Acoustic Emission Characteristics of Water-Bearing Coal Pillar Dam Samples from Shangwan Mine, China

Long-term erosion and repeated scouring of water significantly affect the technical properties of coals, which are the essential elements that must be considered in evaluating an underground reservoir coal column dam’s standing sustainability. In the paper, the coal pillar dam body of the 22 layers of coal in the Shangwan Coal Mine is studied (22 represents No. 2 coal seam), and the water content of this coal pillar dam body is simplified into two types of different water content and dry–wet cycle. Through acoustic emission detection technology and energy dissipation analysis method, the internal failure mechanism of coal water action is analyzed. This study revealed three findings. (1) The crest pressure, strain, and resilient modulus in the coal sample were inversely related to the water content along with the dry–wet cycle number, while the drying–wetting cycle process had a certain time effect on the failure to the sample. (2) As the moisture content and the dry–wet cycle times incremented, three features were shown: first, the breakage pattern is the mainly stretching fracture for the coal specimen; second, the number and absolute value of acoustic emission count peaks decrease; third, the RA-AF probability density plot (RA is the ratio of AE Risetime and Amplitude, and AF is the ratio of AE Count and Duration) corresponds more closely to the large-scale destruction characteristics for the coal samples. (3) A higher quantity of wet and dry cycles results in a smoother energy dissipation curve in the compacted and flexible phases of the crack, indicating that this energy is released earlier. The research results can be applied to the long-term sustainability assessment of the dams of coal columns for underground reservoirs and can also serve as valuable content to the excogitation of water-bearing coal column dams under similar engineering conditions.

Eigensolutions and Thermodynamic Properties of Kratzer Plus Generalized Morse Potential

In this study, we apply the parametric Nikiforov-Uvarov method to obtain the bound state solution of Schrödinger wave equation in the presence of Kratzer plus generalized Morse potential (KPGM). The energy eigen equation and the corresponding normalised wave function were obtained in closed form. The resulting energy eigen equation was used to study partition function and other thermodynamic properties such as vibrational mean energy, vibrational specific heat capacity, vibrational mean free energy and vibrational entropy for the proposed potential as applied to lithium hydride diatomic molecule. The thermodynamic plots obtained were in excellent agreement to work of existing literatures. The wave function and probability density plots for the diatomic molecules were obtained through a well designed and implemented maple programme.

Investigation of the spatial distribution pattern of 3D microcracks in single-cracked breakage

The implementation of multi-crack recognition requires a theoretical basis from single-crack failure results. This study investigates the spatial distribution pattern of microcracks in single-crack-damaged coal specimens subjected to uniaxial compression. The distribution mechanism of the induced microcracks is analysed in terms of macrocracks and stress states. Gaussian and Weibull distributions are selected to explore the spatial distribution of microcracks, and quantile–quantile plots are used to study the probability density plots. The results show that the updated data better demonstrate the distribution characteristics of the ellipsoid shape visually, and the microcracks are observed to converge near the envelope. Linear distribution features are found in the scattered points of the quantile–quantile plots. The goodness-of-fit tests indicate that both Gaussian and Weibull distributions can be assigned to describe the microcrack distribution on the new axis. The probability density distribution results show that the shape is preferred to obey Gaussian distribution , whereas Weibull distribution exhibits a greater possibility of shape variation. The study results can enhance the existing knowledge on crack spatial distribution of acoustic emission positioning results associated with rock materials. In addition, the statistical results can interpret the cracks by recognising them with a specified distribution pattern.

Molecular self-diffusivity and separation of CH4/H2S in metal organic framework MIL-47(V)

The loading dependence of self-diffusion coefficient (Ds), diffusion selectivity (sdiff), and structural properties of pure CH4, H2S, and their mixtures in MIL-47(V) material were investigated using Molecular Dynamics (MD) simulations. The preferential adsorption sites of gas molecules in the lattice, as well as the molecular structure of gases were determined using Radial Distribution Functions (RDFs). The diffusion behavior of gas molecules diffusing in the lattice was further investigated utilizing the 2D probability density plots and free energy profiles derived by the Histogram Sampling method. Furthermore, the findings of our computational study are examined and compared to previous research.

Approximate Solutions, Thermal Properties, and Superstatistics Solutions to Schrödinger Equation

In this work, we apply the parametric Nikiforov-Uvarov method to obtain eigensolutions and total normalized wave function of Schrödinger equation expressed in terms of Jacobi polynomial using Coulomb plus Screened Exponential Hyperbolic Potential (CPSEHP), where we obtained the probability density plots for the proposed potential for various orbital angular quantum number, as well as some special cases (Hellmann and Yukawa potential). The proposed potential is best suitable for smaller values of the screening parameter α . The resulting energy eigenvalue is presented in a close form and extended to study thermal properties and superstatistics expressed in terms of partition function Z and other thermodynamic properties such as vibrational mean energy U , vibrational specific heat capacity C , vibrational entropy S , and vibrational free energy F . Using the resulting energy equation and with the help of Matlab software, the numerical bound state solutions were obtained for various values of the screening parameter ( α ) as well as different expectation values via Hellmann-Feynman Theorem (HFT). The trend of the partition function and other thermodynamic properties obtained for both thermal properties and superstatistics were in excellent agreement with the existing literatures. Due to the analytical mathematical complexities, the superstatistics and thermal properties were evaluated using Mathematica 10.0 version software. The proposed potential model reduces to Hellmann potential, Yukawa potential, Screened Hyperbolic potential, and Coulomb potential as special cases.

First U-Pb Detrital Zircon Ages from Kamlial Formation (Kashmir, Pakistan): Tectonic Implications for Himalayan Exhumation

This study reports the first-ever detrital zircon provenance investigation of sandstones of the Kamlial Formation, exposed in Kashmir Basin along the Kohala–Bagh road section (Muzaffarabad, Pakistan). Analysis of probability density plots of detrital U-Pb zircon ages displayed a major age population clustered around ≈400–1200 Ma and a minor age population clustered around ≈1600–1900 Ma. In addition, scattered ages existed between ≈2000 and 3000 Ma. This age pattern resembled strongly the Himalayan sources, including the Tethys Himalaya, Greater/Higher Himalaya, and Lesser Himalaya. The younger ages (&lt;150 Ma) present in the studied samples indicated the Asian provenance. The Lesser Himalayan component (≈166–1900 Ma) was more pronounced in the 2015KM03 and 2015KM04 samples, representing the middle to the upper portion of the formation. The recycled orogen provenance of the Kamlial Formation as deduced from the sandstone petrography supports the mixed detrital zircon provenance. Considering the provenance, we propose a tectonic model that suggests that large-scale exhumation occurred in the Himalaya as a result of Panjal thrust activation during 25–14 Ma (age of Kamlial Formation), which uplifted the hinterland zone that acted as a source area that fed the foreland basin, where the Kamlial Formation deposited.

The experience of using additive technologies for three-dimensional reconstruction of the lungs in the clinical practice of a tuberculosis dispensary

The aim was to study the volume of blood loss and the duration of a surgical session in patients with destructive pulmonary tuberculosis using threedimensional anatomical models of the lungs. Methods. The study was conducted in 2020 – 2021 in the State Budgetary Healthcare Institution of the Nizhniy Novgorod region “Nizhny Novgorod Regional Clinical Tuberculosis Dispensary” as part of an internal grant from the Federal State Budgetary Educational Institution of Higher Education “Privolzhsky Research Medical University” of the Ministry of Health of the Russian Federation. The prospective clinical study included 80 patients. All patients were divided into two groups. The main group included 40 patients. Preoperative lung reconstruction was performed for these patients. Thoracic surgeons used the three-dimensional anatomical models of the lungs to study the syntopy of healthy and diseased tissue (visual assessment) and prepare for the surgical session (cutting the model with a scalpel). Threedimensional preoperative lung reconstruction was not performed for the other 40 patients in the control group. In this group, the thoracic surgeons did not use 3D anatomical models of the lungs. Comparison of the results in the control and the main group was carried out using the Mann – Whitney U-test and Spearman and Kendall correlation tests. The obtained data are described with absolute and relative values, boxplots reflecting median (Me) and interquartile interval (IQI), scatter plots with trend lines, and probability density plots. The level of statistical significance of differences for testing the hypotheses was chosen at p &lt; 0.05. Results. It was shown that the volume of blood loss (U = 590; p = 0.042) and the duration of surgery (U = 587; p = 0.041) in patients of the main group are smaller than in patients in the control group. A moderate correlation was established between the volume of blood loss and the duration of the surgical session (ρ = 0.54; p &lt; 0.001) in the main group using the Spearman’s test. Kendall’s test also showed a positive correlation (τ = 0.42; p &lt; 0.001). Conclusion. The established differences between the main group and control group in the volume of blood loss and the duration of surgery due to the inclusion of polymer models of the lungs in preoperative preparation of thoracic surgeons confirm our hypothesis about the effect of additive technologies on the above parameters and indicate the significance of the applied reconstruction method.

Evaluating the Use of Uncertainty Visualisations for Imputations of Data Missing At Random in Scatterplots.

Most real-world datasets contain missing values yet most exploratory data analysis (EDA) systems only support visualising data points with complete cases. This omission may potentially lead the user to biased analyses and insights. Imputation techniques can help estimate the value of a missing data point, but introduces additional uncertainty. In this work, we investigate the effects of visualising imputed values in charts using different ways of representing data imputations and imputation uncertainty-no imputation, mean, 95% confidence intervals, probability density plots, gradient intervals, and hypothetical outcome plots. We focus on scatterplots, which is a commonly used chart type, and conduct a crowdsourced study with 202 participants. We measure users' bias and precision in performing two tasks-estimating average and detecting trend-and their self-reported confidence in performing these tasks. Our results suggest that, when estimating averages, uncertainty representations may reduce bias but at the cost of decreasing precision. When estimating trend, only hypothetical outcome plots may lead to a small probability of reducing bias while increasing precision. Participants in every uncertainty representation were less certain about their response when compared to the baseline. The findings point towards potential trade-offs in using uncertainty encodings for datasets with a large number of missing values. This paper and the associated analysis materials are available at: https://osf.io/q4y5r/.

Disentangle the sediment mixing from geochemical proxies and detrital zircon geochronology

Detrital zircon UPb geochronology and geochemical proxies derived from immobile elements and isotopes are commonly applied to trace sediment sources because of their durability and stability in most earth surface processes and environments. However, little is known on whether these different tracers can contain identical or similar provenance signals for sediments of interest. This study presents the UPb ages of detrital zircons from a grain-size fraction of 63–125 μm and elemental and Nd isotopic compositions for bulk sediments from the Mulanxi, a small mountainous river in southeast China. We aim to retrieve provenance signals preserved by different tracers and to test whether they are robust in discriminating the effect of sediment mixing in this tidal-dominated river. Our results show that detrital zircons in the Mulanxi catchments and estuarine have two major age groups at 90–110 Ma and 120–150 Ma. Moreover, the results of probability density plots (PDPs) suggest there is no significant difference in detrital zircon UPb ages between the sediments from non-tidal and tidal reaches. The detrital zircon age distributions in the Mulanxi catchments are significantly different from those in the Changjiang (Yangtze River) catchments and in the inner shelf mud belt of the East China Sea which have distinct multiple age populations. A statistical multidimensional scaling (MDS) analysis suggests there is no a source-to-sink connection between the Changjiang and Mulanxi zircons. On the contrary, the geochemical proxies of Sc/Th, Cr/Th, and Nd isotopes reveal different sediment sources between the non-tidal and tidal reaches of Mulanxi, with the fine tidal-reach sediments having mixed sources from the offshore mud and the Mulanxi River, while the coarse-grained sediments from the non-tidal upstream being completely contributed by the Mulanxi. The contradictory results from these different provenance proxies suggest their implications and limitations for sediment source tracing. Detrital zircon ages can track the ‘inherited’ source signals of zircons and relating coarse fractions in sediments, but they are less sensitive to source changes in fine fractions than the geochemical proxies of Nd isotopes, Sc/Th and Cr/Th ratios. It is therefore essential and a prerequisite to carefully evaluate all possible factors controlling detrital sediment compositions, and to weigh the pros and cons of different tracers for sediment provenance discrimination especially in dynamic Small Mountainous Rivers (SMRs) and continental margins.

Agrometeorological Conditions and Agroclimatic Trends for the Maize and Wheat Crops in the Balkan Region

The Balkan peninsula is a transitional zone, in terms of bioclimatic conditions, with an extended and dynamic agricultural sector. Its potential is in peril due to climate change and socioeconomic factors. To assess and evaluate the agrometeorological conditions and the related trends which affect the widely cultivated wheat and maize, a big dataset with high spatiotemporal analysis was utilized. The thermal indices of Growing Degree Days (GDD) and Heat Stress Index (HSI) along with the main frost parameters (frost days, last spring frost, first autumn frost, and free of frost days) were calculated over ten countries for 42 years on a daily basis over a grid of 25 × 25 km. The results indicate a clear cultivations’ expansion ability to northern areas, and higher altitudes and an increased risk of heat caused plants’ injuries. The thermal indices’ trends for maize and wheat cultivation are always positive (Maize: GDD 7.26–11.05 units/yr, HSI 0.52–3.51 units/yr Wheat: GDD 7.2–12.7 units/yr, HSI 0.22–1.77 units/yr). The free of frost (FFD) season is getting longer (trend −0.04 to 0.34 d/yr) because of earlier last spring frost and delayed first autumn frost. The results consist of spatial and temporal illustrations, along with summary statistics and probability density plots for the entire study area and per country.

Multidimensional Scaling (MDS): A quantitative approximation of zircon ages to sedimentary provenance with some examples from Mexico

During the last decades, provenance studies have proven to be an invaluable tool to evaluate modern and ancient sedimentary environments and to reconstruct the paleogeography and evolution of different tectonic settings. Whereas in the past provenance studies were mainly based on qualitative comparisons of whole-rock sandstone detrital modes, the advance and implementation of microanalytical techniques driven by the community during the last ~15 years permit the quantification of detrital-mineral ages and the isotopic characterization by in situ analysis. The combination of ages, isotopes, and mineral chemistry of individual detrital components provides a better understanding and reconstruction of source-to-sink systems. However, the introduction of these largely accessible microanalytical techniques has produced a large amount of data that requires proper management to be objectively interpreted. While a quantitative comparison between the age distributions of detrital sample pairs can be easily performed by Kolmogorov-Smirnov (K–S) statistics, comparing multi-samples data sets requires a more complex statistical approach. One of those is Multidimensional Scaling analysis (MDS), which allows, by using K–S statistics, to compare the dissimilarity between two or more samples. To compare among samples, a dissimilarities matrix, based on the stress from the ideal fit, is constructed. Dissimilarities are graphically represented in a “map” that tends to group more similar samples, pulling apart those that are more dissimilar. We contribute with three examples from the Mexican geology, showing how MDS can be used to evaluate in a more objective way the provenance of clastic rocks. We show that the MDS is more suitable than the visual comparison of probability density plots and kernel density estimations in marking the similarities and differences between the available samples; thus, it is a more suitable approach to reconstruct more rigorously the evolution of source-to-sink systems. Particularly, we examine fluvial to deep-marine Triassic strata, Paleozoic–lower Mesozoic metasedimentary rocks of the Ayú and Acatlán complexes, and Upper Jurassic–Cretaceous successions of the Pacific continental margin. The MDS challenges the scenario in which all Triassic submarine fan deposits of Mexico were part of a giant single fan developed along the Mexican Pacific margin, and supports the idea that the western margin of Pangea was drained by different fluvial systems that supplied distinct submarine fans. Applied to the Paleozoic–lower Mesozoic metasedimentary rocks of southern Mexico, this approach shows major dissimilarities between the Ayú and the Acatlán complexes, supporting the idea that these are likely two different tectonic complexes. Finally, the MDS suggests that two distinct and independent provenance domains were established in Mexico during the development of the Upper Jurassic–Early Cretaceous Arperos back-arc basin, and that such a detrital signature compartmentalization was lost by the end of Early Cretaceous time with the advent of compressive tectonics and the development of orogenic belts.

Exponentiated–Exponential Logistic Distribution: Some Properties and Application

This study proposes new distribution which is generated from exponentiated-exponential-X family of distribution. It is explored various shape and behavior of the observed distribution through probability density plot, hazard rate function and quantile function. Further we have investigated some mathematical properties, estimation of the parameters and associated confidence interval using maximum likelihood estimation (MLE) method of the exponentiatedexponential-logistic distribution (EELD).

An exploration of the utility of speleothem age distributions for palaeoclimate assessment

Abstract Age distributions of speleothem growth frequency are often employed as proxies for past climate variation. However, their interpretation can be influenced by many variables such as the type of probability density estimator used, the number of samples studied, and indeed the nature of the sampling itself. In order to explore the utility of speleothem age distributions in this context, we constructed a synthetic speleothem growth dataset by randomly generating U-Th ages, based on a known climatic forcing to evaluate whether the most basic climatic information could be recovered by subsequent sampling of this dataset under differing conditions. This modelling approach allows us to separately examine the influences of sample size, the type of probability density estimator, and its parameterisation on the shape of the resulting age distribution. Our model demonstrates that periodic Quaternary climate fluctuations can be recovered from growth frequency distributions derived from as few as 120–150 radiometric ages. To construct such distributions, a kernel density estimator may more accurately represent speleothem growth frequency than the commonly employed probability density plot, because peaks in the latter often reflect data precision rather than data density. For U-Th ages, randomizations of the activity ratios can be used to reintroduce chronometric or analytical uncertainty into the Kernel Density Estimator in a Monte-Carlo simulation.