Probabilistic Information Research Articles

Glyphosate/AMPA adsorption on magnetite under different conditions: The effect of pH and electrolytes

As a result of the frequent use, glyphosate (GLY) and its major metabolite, aminomethylphosphonic acid (AMPA), have emerged as ubiquitous environmental contaminants worldwide. Glyphosate, applied in agriculture, adsorbs on soil minerals, such as iron oxides, facilitating its fixation in soils and preventing leaching into groundwater sources. However, the adsorption capacity of various types of soils exhibits substantial variability. In this work the adsorption of GLY and AMPA on magnetite nanoparticles (MNPs) was studied under different conditions: at pH ∼ 6 and ∼ 8, and in the presence of 10 mmol/L NaCl, an indifferent electrolyte, and 10 mmol/L CaCl2, which contains a specific cation mainly present in soils. The pH-dependent zeta potential measurements revealed the difference between the effect of Na+ and Ca2+ ions on the charge state and aggregation of MNPs. The adsorption of GLY/AMPA shows significant pH dependence, with the bound amounts decreasing rapidly above pH ∼ 7 in both 10 mmol/L NaCl and CaCl2 solutions. The phosphonate adsorption capacity of MNPs, as determined from the fitting of the Langmuir isotherm equation, was approximately 0.35 mmol/g and 0,09 mmol/g at pH ∼ 6 and pH ∼ 8, respectively. The diverse bound amounts at different pHs are of environmental importance: under alkaline soil conditions, the mobilization of GLY may be more probable. GLY and AMPA bind to the surface of MNPs via complex formation at ≡Fe-OH sites, primarily involving phosphate groups, preferably at acidic pH, where the MNPs carry positive charges, and the near-surface concentration of phosphonate anions is higher due to electrostatic attraction. Furthermore, in the presence of Ca2+ ions, Ca-bridging occurs, as supported by the findings from the ATR-FTIR spectra. Additionally, it is worth noting that the complex formation between Ca2+ and phosphonates in the solution phase reduces the probability of Ca-bridge and surface complex formation, hindering the fixation of GLY/AMPA in soils.

Critical Sample-Size Analysis for Uncertainty Aerodynamic Evaluation of Compressor Blades with Stagger-Angle Errors

Many probability-based uncertainty quantification (UQ) schemes require a large amount of sampled data to build credible probability density function (PDF) models for uncertain parameters. Unfortunately, the amounts of data collected as to compressor blades of aero-engines are mostly limited due to the expensive and time-consuming tests. In this paper, we develop a preconditioner-based data-driven polynomial chaos (PDDPC) method that can efficiently deal with uncertainty propagation of limited amounts of sampled data. The calculation accuracy of a PDDPC method is closely related to the sample size of collected data. Therefore, the influence of sample size on this PDDPC method is investigated using a nonlinear test function. Subsequently, we consider the real manufacturing errors in stagger angles for compressor blades. Under three different operating conditions, the PDDPC method is applied to investigate the effect of stagger-angle error on UQ results of multiple aerodynamic parameters of a two-dimensional compressor blade. The results show that as the sample-size of measured data increases, UQ results regarding aerodynamic performance obtained by the PDDPC method gradually converge. There exists a critical sample size that ensures accurate UQ analysis of compressor blades. The probability information contained in the machining error data is analyzed through Kullback–Leibler divergence, and the critical sample size is determined. The research results can serve as a valuable reference for the fast and cheap UQ analysis of compressor blades in practical engineering.

Uncertainty in the association between socio-demographic characteristics and mental health.

Questionnaires are among the most basic and widespread tools to assess the mental health of a population in epidemiological and public health studies. Their most obvious advantage (firsthand self-report) is also the source of their main problems: the raw data requires interpretation, and are a snapshot of the specific sample's status at a given time. Efforts to deal with both issues created a bi-dimensional space defined by two orthogonal axes, in which most of the quantitative mental health research can be located. Methods aimed to assure that mental health diagnoses are solidly grounded on existing raw data are part of the individual validity axis. Tools allowing the generalization of the results across the entire population compose the collective validity axis. This paper raises a different question. Since one goal of mental health assessments is to obtain results that can be generalized to some extent, an important question is how robust is a questionnaire result when applied to a different population or to the same population at a different time. In this case, there is deep uncertainty, without any a priori probabilistic information. The main claim of this paper is that this task requires the development of a new robustness to deep uncertainty axis, defining a three-dimensional research space. We demonstrate the analysis of deep uncertainty using the concept of robustness in info-gap decision theory. Based on data from questionnaires collected before and during the Covid-19 pandemic, we first locate a mental health assessment in the space defined by the individual validity axis and the collective validity axis. Then we develop a model of info-gap robustness to uncertainty in mental health assessment, showing how the robustness to deep uncertainty axis interacts with the other two axes, highlighting the contributions and the limitations of this approach. The ability to measure robustness to deep uncertainty in the mental health realm is important particularly in troubled and changing times. In this paper, we provide the basic methodological building blocks of the suggested approach using the outbreak of Covid-19 as a recent example.

Mapping high marsh and salt pannes/flats along the northern Gulf of Mexico coast

Coastal wetlands are predicted to undergo extensive transformation due to climate and land use change. Baseline maps of coastal wetlands can be used to help assess changes. Found in the upper portion of the estuarine zone, high marsh and salt pannes/flats provide ecosystem goods and services and are particularly important to fish and wildlife. We developed the first map of high marsh and salt pannes/flats along the northern Gulf of Mexico using regional models that included spectral indices related to greenness and wetness from optical satellite imagery, elevation data, irregularly flooded wetland probability information, and synthetic aperture radar backscatter. We found the greatest relative coverage of high marsh along the Texas coast (30% to 65%) and the Florida Panhandle (40%), whereas the greatest relative coverage of salt pannes/flats was along the lower Texas coast (74%) and the middle Texas coast (15%). As part of this effort, we also developed a map that highlighted irregularly flooded wetlands dominated by Juncus roemerianus (black needlerush) for part of the study area. Both maps had an overall accuracy of around 80%. Our results advance the understanding of estuarine marsh zonation and provide a baseline for assessing future transformations.

Identification of mental disorders in South Africa using complex probabilistic hesitant fuzzy N-soft aggregation information

This paper aims to address the challenges faced by medical professionals in identifying mental disorders. These mental health issues are an increasing public health concern, and middle-income nations like South Africa are negatively impacted. Mental health issues pose a substantial public health concern in South Africa, putting forth extensive impacts on both individuals and society broadly. Insufficient funding for mental health remains the greatest barrier in this country. In order to meet the diverse and complex requirements of patients effective decision making in the treatment of mental disorders is crucial. For this purpose, we introduced the novel concept of the complex probabilistic hesitant fuzzy N-soft set (CPHFNSS) for modeling the unpredictability and uncertainty effectively. Our approach improves the precision with which certain traits connected to different types of mental conditions are recognized by using the competence of experts. We developed the fundamental operations (like extended and restricted intersection, extended and restricted union, weak, top, and bottom weak complements) with examples. We also developed the aggregation operators and their many features, along with their proofs and theorems, for CPHFNSS. By implementing these operators in the aggregation process, one could choose a combination of characteristics. Further, we introduced the novel score function, which is used to determine the optimal choice among them. In addition, we created an algorithm with numerical illustrations for decision making in which physicians employ CPHFNS data to diagnose a specific condition. Finally, comparative analyses confirm the practicability and efficacy of the technique that arises from the model developed in this paper.

Intermolecular interactions and the weakly bound precursor states of elementary physicochemical processes

This study concerns the importance of the precursor (or pre-reactive) state of elementary physicochemical processes whose basic features, as structure, stability, and trapping effect of reagents, are controlled by the balance of intermolecular forces that arise at long range and operate at intermediate and short separation distances. The detailed formulation of such forces, determining formation probability and dynamical evolution of the precursor state, is of relevance in molecular science and difficult to be treated by quantum chemistry. Such a problem has been tackled by us exploiting the phenomenological approach, which employs semi-empirical and empirical formulas to represent strength, range and angular dependence of the leading interaction components involved. In addition to the study of transport phenomena, part of the attention is addressed to chemi-ionization (or Penning ionization) reactions for which neutral reagents lead to atomic and/or molecular ions plus electrons as products. Chemi-ionizations are bimolecular processes occurring in several environments of interest, where a reagent is a species, formed in excited-metastable electronic states by collisions with energetic electrons or cosmic rays. For such reactions all crucial electronic rearrangements, affecting stability and evolution of the weakly bound precursor state, here coincident with the reaction transition state, are characterized with a high detail. The results of the present study are of interest for many other processes, whose precursor states and their relevant features are difficult to characterize, often masked by several other effects.Graphical abstract

A new approach to probabilistic classification based on Gaussian process and support vector machine

This paper proposes three algorithms that combine the Support Vector Machine (SVM) and Gaussian Process (GP) in a unified framework to classify large datasets efficiently and obtain probabilistic information on the classification results. The first algorithm works in two steps. In Step 1, the algorithm judiciously selects a sample of size m from the training dataset of size n, where m ≪ n. Step 2 then runs a Gaussian Process Classification (GPC) on the selected sample. The second algorithm is based on the first one, where instead of a standard GPC, a sparse GPC (a low-cost variant of standard GPC) is run in Step 2. The third algorithm is based on manipulating the Gaussian Process Regression (GPR) to classify the data. Unlike GPC, GPR uses an exact inference method that greatly reduces the computational complexity. We have experimented with seven datasets to compare the performance of the proposed algorithms with the existing state-of-the-art methodologies. In addition to providing probabilistic information, the proposed algorithms have proved to be computationally efficient, especially in the training phase, where they consistently deliver faster results than the existing algorithms. The accuracies provided by the proposed algorithms are satisfactory, and at times even surpass the accuracy obtained by the existing algorithms.

Complete loss of E-cadherin expression in a rare case of metastatic malignant meningioma: a case report

BackgroundHematogenous tumor spread of malignant meningiomas occurs very rarely but is associated with very poor prognosis.Case presentationWe report an unusual case of a patient with a malignant meningioma who developed multiple metastases in bones, lungs and liver after initial complete resection of the primary tumor. After partial hepatic resection, specimens were histologically analyzed, and a complete loss of E-cadherin adhesion molecules was found. No oncogenic target mutations were found. The patient received a combination of conventional radiotherapy and peptide receptor radionuclide therapy (PRRT). Due to aggressive tumor behavior and rapid spread of metastases, the patient deceased after initiation of treatment.ConclusionsE-cadherin downregulation is associated with a higher probability of tumor invasion and distant metastasis formation in malignant meningioma. Up to now, the efficacy of systemic therapy, including PRRT, is very limited in malignant meningioma patients.

A fuzzy group decision-making framework for computer network security evaluation with probabilistic linguistic information

The computer network security evaluation is a classical multiple attribute group decision making (MAGDM) problems. Recently, the Exponential TODIM TODIM (ExpTODIM) method has been used to cope with MAGDM issues. The probabilistic linguistic term sets (PLTSs) are used as a tool for characterizing uncertain information during the computer network security evaluation. In this manuscript, the probabilistic linguistic ExpTODIM (PL-ExpTODIM) is built to solve the MAGDM under PLTSs. In the end, a numerical case study for computer network security evaluation is given to validate the proposed method. The main contribution of this paper is constructed: (1) the Exponential TODIM TODIM (ExpTODIM) method is extended to the PLTSs; (2) the probabilistic linguistic ExpTODIM (PL-ExpTODIM) method is defined to solve the MAGDM under PLTSs; (3) In the end, a numerical case study for computer network security evaluation is given to validate the proposed method.

FRB 20210405I: a nearby Fast Radio Burst localized to sub-arcsecond precision with MeerKAT

ABSTRACT We present the first sub-arcsecond localized Fast Radio Burst (FRB) detected using MeerKAT. FRB 20210405I was detected in the incoherent beam using the MeerTRAP pipeline on 2021 April 05 with a signal to noise ratio of 140.8 and a dispersion measure of 565.17 pc cm−3. It was detected while MeerTRAP was observing commensally with the ThunderKAT large survey project, and was sufficiently bright that we could use the ThunderKAT 8 s images to localize the FRB. Two different models of the dispersion measure in the Milky Way and halo suggest that the source is either right at the edge of the Galaxy, or outside. This highlights the uncertainty in the Milky Way dispersion measure models, particularly in the Galactic Plane, and the uncertainty of Milky Way halo models. Further investigation and modelling of these uncertainties will be facilitated by future detections and localizations of nearby FRBs. We use the combined localization, dispersion measure, scattering, specific luminosity, and chance coincidence probability information to find that the origin is most likely extra-galactic and identify the likely host galaxy of the FRB: 2MASS J1701249−4932475. Using SALT spectroscopy and archival observations of the field, we find that the host is a disc/spiral galaxy at a redshift of z = 0.066.

83 Uncertainty Representation in Mild Cognitive Impairment: Comparing Internally Cued versus Externally Driven Uncertainty

Objective:Choice response time (RT) increases linearly with increasing information uncertainty, which can be represented externally or internally. Using a card-sorting task, we previously showed that Alzheimer’s disease (AD) dementia patients were more impaired relative to cognitively normal older adults (CN) under conditions that manipulated internally cued rather than externally driven uncertainty, but this study was limited by a between-subjects design that prevented us from directly comparing the two uncertainty conditions. The objective of this study was to assess internally cued and externally driven cued uncertainty representations in CN and mild cognitive impairment (MCI) patients.Participants and Methods:Older participants (age > 60 years; N=49 CN, N=33 MCI patients) completed a card-sorting task that separately manipulated externally cued uncertainty (i.e., the number of sorting piles with equal probability of each stimulus type) or internally cued uncertainty (i.e., the probability of each stimulus type with fixed number of sorting piles) at three different uncertainty loads (low, medium, high). Exploratory analyses separated MCI patients by etiology into possible/probable cortical neurodegenerative process (i.e., AD, frontotemporal dementia; N=13) or nonneurodegenerative process (i.e., vascular, psychiatric, sleep, medication effect; N=20).Results:CN and MCI patients maintained a high level of accuracy on both tasks (M accuracy > .94 across conditions). MCI patients performed more slowly than CN on the externally and internally cued tasks, and both groups showed a significant positive association between uncertainty load and RT (p’s < .05). There was a group x load x uncertainty condition interaction (p = .05). For CNs, the slope of the linear association between load and RT was significantly steeper in the externally cued compared to internally cued condition. For MCI patients in contrast, RTs increased with load to a similar degree in both conditions. Exploratory analyses showed the MCI-neurodegenerative patients were significantly slower than MCI-nondegenerative and CN (p < .001). While the group x load x condition interaction was significant when comparing all three groups (p < .05), this was driven by the differences between CN and MCI patients described above; the MCI-neurodegenerative and non-neurodegenerative groups did not significantly differ in the strength of the RT-load association between the externally or internally cued conditions.Conclusions:Overall, CN participants showed greater RT slowing with increasing load of externally driven than internally cued uncertainty. Though they were slower than CNs, MCI patients (even those with a possible/probable cortical neurodegenerative condition) were able to accurately perform an internally cued uncertainty task and did not show differential slowing compared to an externally driven task. This provides preliminary evidence that internal representations of probabilistic information are intact in patients with MCI due to a neurodegenerative condition, meaning they may not depend on cortical processes. Future work will increase the sample sizes of the MCI-neurodegenerative and non-degenerative groups.

Inpatient nurses' preferences and decisions with risk information visualization.

We examined the influence of 4 different risk information formats on inpatient nurses' preferences and decisions with an acute clinical deterioration decision-support system. We conducted a comparative usability evaluation in which participants provided responses to multiple user interface options in a simulated setting. We collected qualitative data using think aloud methods. We collected quantitative data by asking participants which action they would perform after each time point in 3 different patient scenarios. More participants (n = 6) preferred the probability format over relative risk ratios (n = 2), absolute differences (n = 2), and number of persons out of 100 (n = 0). Participants liked average lines, having a trend graph to supplement the risk estimate, and consistent colors between trend graphs and possible actions. Participants did not like too much text information or the presence of confidence intervals. From a decision-making perspective, use of the probability format was associated with greater concordance in actions taken by participants compared to the other 3 risk information formats. By focusing on nurses' preferences and decisions with several risk information display formats and collecting both qualitative and quantitative data, we have provided meaningful insights for the design of clinical decision-support systems containing complex quantitative information. This study adds to our knowledge of presenting risk information to nurses within clinical decision-support systems. We encourage those developing risk-based systems for inpatient nurses to consider expressing risk in a probability format and include a graph (with average line) to display the patient's recent trends.

A Transdiagnostic Study of Effort-Cost Decision-Making in Psychotic and Mood Disorders.

Research suggests that effort-cost decision-making (ECDM), the estimation of work required to obtain reward, may be a relevant framework for understanding motivational impairment in psychotic and mood pathology. Specifically, research has suggested that people with psychotic and mood pathology experience effort as more costly than controls, and thus pursue effortful goals less frequently. This study examined ECDM across psychotic and mood pathology. We hypothesized that patient groups would show reduced willingness to expend effort compared to controls. People with schizophrenia (N = 33), schizoaffective disorder (N = 28), bipolar disorder (N = 39), major depressive disorder (N = 40), and controls (N = 70) completed a physical ECDM task. Participants decided between completing a low-effort or high-effort option for small or larger rewards, respectively. Reward magnitude, reward probability, and effort magnitude varied trial-by-trial. Data were analyzed using standard and hierarchical logistic regression analyses to assess the subject-specific contribution of various factors to choice. Negative symptoms were measured with a clinician-rated interview. There was a significant effect of group, driven by reduced choice of high-effort options in schizophrenia. Hierarchical logistic regression revealed that reduced choice of high-effort options in schizophrenia was driven by weaker contributions of probability information. Use of reward information was inversely associated with motivational impairment in schizophrenia. Surprisingly, individuals with major depressive disorder and bipolar disorder did not differ from controls. Our results provide support for ECDM deficits in schizophrenia. Additionally, differences between groups in ECDM suggest a seemingly similar behavioral phenotype, reduced motivation, could arise from disparate mechanisms.

Nucleation Work on Curved Substrates

Nucleation is the initial phase transition process when nuclei of a new phase form within an undercooled or supersaturated parent phase under appropriate conditions. Nucleation most often occurs through a heterogeneous process on active centers on which the probability of nucleus formation is high. In general, the origin of active centers may be difficult to distinguish. In this work, we consider the formation of crystalline nuclei in a melt on various curved substrates. Knowledge of excess free energy plays a key role in understanding the process of formation of clusters and it is not easy to express this quantity in a considered system. Excess free energy is often approximated within the framework of capillarity approximation based on interfacial energy, which depends on interatomic interactions near the interface, as well as the misfit between melts, surface roughness, temperature, composition, etc., near the phase interface. The formation of nuclei requires overcoming a certain energy (nucleation) barrier that is a consequence of balancing the volume and the interfacial free energy. Knowing the nucleation barrier (W) is crucial for understanding this process, as nuclei predetermine the physical properties of a newly formed phase. W is typically expressed as a function of the nucleus radius; however, in nucleation kinetics, one needs to determine (W) as a function of the number of molecules forming the nucleus. We analyze nucleation work on various substrates (flat, convex, and concave) for crystallization from an aluminum melt to show that the formation of nuclei is the most probable on concave substrates. An analytical expression for W can be easily applied to other systems under consideration. We show that under the same conditions, the critical radius of nuclei is identical for various substrate, in contrast with the critical number of molecules forming a nucleus.

Machine Learning Enables Accurate Prediction of Quinone Formation during Drug Metabolism.

Metabolism helps in the elimination of drugs from the human body by making them more hydrophilic. Sometimes, drugs can be bioactivated to highly reactive metabolites or intermediates during metabolism. These reactive metabolites are often responsible for the toxicities associated with the drugs. Identification of reactive metabolites of drug candidates can be very helpful in the initial stages of drug discovery. Quinones are soft electrophiles that are generated as reactive intermediates during metabolism. Quinones make up more than 40% of the reactive metabolites. In this work, a reliable data set of 510 molecules was used to develop machine learning and deep learning-based predictive models to predict the formation of quinone-type metabolites. For representing molecules, two-dimensional (2D) descriptors, PubChem fingerprints, electro-topological state (E-state) fingerprints, and metabolic reactivity-based descriptors were used. Developed models were compared to the existing Xenosite web server using the untouched test set of 102 molecules. The best model achieved an accuracy of 86.27%, while the Xenosite server could achieve an accuracy of only 52.94% on the test set. Descriptor analysis revealed that the presence of greater numbers of polar moieties in a molecule can prevent the formation of quinone-type metabolites. In addition, the presence of a nitrogen atom in an aromatic ring and the presence of metabolophores V51, V52, and V53 (SMARTCyp descriptors) decrease the probability of quinone formation. Finally, a tool based on the best machine learning models was developed, which is accessible at http://14.139.57.41/quinonepred/.

A DFT study of electronic structure, magnetic properties and cyclization reaction of [5]helicene derivatives

A series of 1,14-dimethyl-[5]helicene derivatives comprising radicals ((2,2,6,6-tetramethylpiperidin-1-yl)oxyl, 1,2,3,5-dithiadiazolyl, 1,5-dimethyl-6-oxo-verdazyl and 4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazol-1-oxyl-3-oxide) was investigated by quantum-chemical modeling of their electronic structure, exchange interactions and cyclization reaction. The performed DFT study of 1,14-dimethyl-[5]helicene, supported by DFT/CASSCF and DFT/NEVPT2 calculations, have shown that cyclic form of this compound represents a singlet biradical. The energy barriers of transition between open and cyclic forms of 1,14-dimethyl-[5]helicene radical derivatives are comparable to the values characteristic of enantiomerization reaction, which indicates a high probability of formation of cyclic isomers under thermal conditions. The TD DFT calculations of electronic transitions predicted the presence of non-overlapping bands in the studied isomers that favors switching between them by irradiation. The variation in a number of paramagnetic centers as a result of interconversion of open and cyclic forms, and the presence of structures bearing strong ferromagnetic exchange interactions, make the considered [5]helicene derivatives a suitable basis for molecular electronics devices.

A molecular dynamics simulations study on the modification of aqueous solution structure and dynamics in presence of monovalent salts: An electronic continuum correction approach and effect of ion size

The hydrogen bonding structure and dynamics of water are investigated by varying the concentrations up to 6.18 m for full-charged and the electronic continuum correction with rescaling (ECCR) charged model for NaCl solutions using classical molecular dynamics simulations. We have also considered the seven different (MCl/NaX) salt solutions at 6.18 m with varying monovalent cations (M+) or anions (X-). The first and second solvation shells of water in both full- and ECCR models are affected by NaCl concentrations, and destruction of the tetrahedral network structure is observed. Probability of ion pair formation is higher in KCl and NaF solutions compared to other salts at 6.18 m. The self-diffusion coefficient values of water, Na+ in full-charged, and Cl− in ECCR models are in good agreement with the experimental results. The hydrogen bond lifetime of water does not significantly change with increasing NaCl salt concentrations, but Cl−-water lifetime is significantly lowered in the ECCR model.

Methane hydrate formation in slit-shaped pores: Impacts of surface hydrophilicity

Gas hydrate accumulation and hydrate-based gas storage and transportation technology are intimately linked to the formation process of hydrates in the pore space. However, the molecular mechanism underlying this process remains unclear. Here, we employ molecular simulations to investigate methane hydrate formation in surface-modified silica pores, with specific emphasis on the impact of pore surface characteristics. Our results show that under the same thermodynamic conditions, methane hydrate shows no preference towards either the hydrophobic or hydrophilic pore surface, and tends to nucleate in the central part of the hydrophilic slit. It means that whilst the surface properties can impact the dynamics and structure of the molecules on it, thus affecting methane concentration and, as a result, the probability of cage formation, the confinement effect ultimately controls the nucleation process. Furthermore, the pre-filling of the pores with methane can significantly accelerate hydrate formation. This is because methane bubbles adsorbed in the pores can noticeably elevate methane concentration in solution. Moreover, the hydrophobic surface can help with methane dissolution in water, which can both promote the transportation of molecules between methane bubbles and enhance methane hydrate nucleation. This study enhances understanding of the hydrate formation process in pores, which can aid in the design of gas hydrate promoters or inhibitors that meet the demands of hydrate technologies.

On the Existence of Ternary Compounds in the CaO-BaO-Al<sub>2</sub>O<sub>3</sub> System

In this article in order to verify the probability of the formation of the compound CaBaAl4O8, a thermodynamic analysis of the following possible solid-phase reactions of its formation was carried out: formation of CaBaAl4O8 from the initial components - calcium carbon dioxide, barium carbon dioxide and aluminum oxide; the probability of formation of dual compounds CaAl2O4 and BaAl2O4 from the same raw materials (since the compound CaBaAl4O8 is located on the BaAl2O4-CaAl2O4 conjugate) and the possibility of formation of the compound CaBaAl4O8 from binary compounds CaAl2O4 and BaAl2O4. As a result of our experimental studies, the existence of ternary compounds Вa3CaAl2O7 and ВaCa2Al8O15 was confirmed, and it was found that the Вa3CaAl2O7 compound exists in the system at least up to a temperature of 1400 °C. Thus, our studies have determined an increase in the temperature limits of its existence, in contrast to the data of previous researchers, who indicated 1250 °C as the upper temperature of existence of Вa3CaAl2O7.

Retracted: Emergency Optimization Decision-Making with Incomplete Probabilistic Information under the Background of COVID-19

Retracted: Emergency Optimization Decision-Making with Incomplete Probabilistic Information under the Background of COVID-19