Probability Function Research Articles

ANALYSIS OF RUMOR PROPAGATION DYNAMICS IN COMPLEX NETWORKS

Considering that rumors propagation is affected by many factors in real life, based on the SIRS infectious disease model in complex networks, an extended ISRI rumor propagation model is proposed by using the probability function to define the influence mechanisms such as trust mechanism, and suspicion mechanism. First, dynamic equations are established for homogeneous and heterogeneous networks, and the rumor and rumor-free equilibrium points in the two networks are analyzed, respectively. Then, the basic reproduction number [Formula: see text] is obtained by using the next generation matrix and derivative calculation methods. Next, the lyapunov function is constructed to discuss the local stability and global stability of the equilibrium point, and the influence of different parameters on the basic reproduction number [Formula: see text]. In addition, we selected ER network and BA network and found that population flow has a significant impact on the speed and scale of rumor propagation. At the same time, the trust mechanism can improve the propagation speed and scale, while the skepticism mechanism can inhibit the propagation speed, and it is more obvious in the BA network. The interaction between these mechanisms further affects the propagation characteristics of rumors in the network.

Investigating the effect of termination capacitor on E–H mode transition in radio frequency inductively coupled plasma

In this work, the effects of stringing termination capacitors on the external circuit parameters, plasma parameters, and mode transition in radio frequency (RF) inductively coupled Ar discharges are investigated. It has been demonstrated that at low pressure (1 Pa), in the absence of termination capacitors, the plasma parameters and external circuit parameters exhibit a continuous variation with increasing RF power. The plasma density is observed to decrease with decreasing capacitance value in the E mode when the termination capacitor is inserted, while the plasma density is increased with decreasing capacitance value in the H mode. During the E–H mode transition process, both the plasma parameters and the external circuit parameters undergo a discontinuous change characterized by a distinct “jump” in each parameter. By increasing and then decreasing RF power, the evolution of each parameter creates a significant hysteresis. As the termination capacitance decreases, the power threshold of the H–E mode transition decreases, resulting in a larger hysteresis loop. The termination capacitor, which is connected in series at the end of the coil, can alter the voltage distribution on the RF antenna. This alteration results in a reduction in the potential difference between the coil and the “common ground,” which effectively diminishes the electrostatic field. Furthermore, the electron energy probability function indicates that the addition of the termination capacitor results in a reduction in the proportion of energetic electrons in the E mode, accompanied by a reduction in the plasma potential.

New probabilistic methods for quantitative climate reconstructions applied to palynological data from Lake Kinneret

Abstract. Quantitative local paleoclimate reconstructions are an important tool for gaining insights into the climate history of the Earth. The complex age–sediment–depth and proxy–climate relationships must be described in an appropriate way. Bayesian hierarchical models are a promising method for describing such structures. In this study, we present a new age–depth transformation in a Bayesian formulation by determining the uncertainty information of depths in lake sediments at a given age. This enables data-driven smoothing of past periods, which allows better interpretation. We introduce a systematic, machine-learning-based way to establish probabilistic transfer functions which connect spatial distributions of temperature and precipitation to the spatial presence of specific biomes. This includes consideration of various machine learning (ML) algorithms for solving the classification problem of biome presence and absence, taking into account uncertainties in the proxy–climate relationship. For the models and biome distributions used, a simple feedforward neural network provides the optimal choice of the classification problem. Based on this, we formulate a new Bayesian hierarchical model that generates local paleoclimate reconstructions. This is applied to plant-based proxy data from the lake sediment of Lake Kinneret (LK). Here, a priori information on the recent climate in this region and data on arboreal pollen from this lake are used as boundary conditions. To solve this model, we use Markov chain Monte Carlo (MCMC) sampling methods. During the inference process, our new method generates taxa weights and biome climate ranges. The former shows that less weight needs to be given to Olea europaea to ensure the influence of the other taxa. In contrast, the highest weights are found in Quercus calliprinos and Amaranthaceae, resulting in appropriate flexibility under the given boundary conditions. In terms of climate ranges, the posterior probability of the Mediterranean biome reveals the greatest change, with an average boreal winter (December–February) temperature of 10∘C and an annual precipitation of 700 mm for Lake Kinneret during the Holocene. The paleoclimate reconstruction for this period shows comparatively low precipitation of about 400 mm during 9–7 and 4–2 cal ka BP. The respective temperatures fluctuate much less and stay around 10 °C.

Identification of particulate matter (PM10 and PM2.5) sources using bivariate polar plots and k-means clustering in a South American megacity: Metropolitan Area of Lima-Callao, Peru.

The identification of different air pollution sources is essential to effectively control atmospheric pollution, particularly in megacities of emerging countries with rapid economic development, such as the Metropolitan Area of Lima-Callao (MALC). The objective of this research was to identify the main sources of particulate matter pollution by applying bivariate polar plots and the k-means clustering algorithm. These statistical techniques were applied to hourly in situ data of four variables collected over a 5-year period (2015-2019) by the Automatic Air Quality Monitoring Network of the MALC: wind direction, wind speed, PM10, and PM2.5 concentrations. Average PM10 concentrations ranged from 34μgm-3 (CDM station) to 126.7μgm-3 (VMT station), while average PM2.5 concentrations ranged from 16.8μgm-3 (CDM station) to 41.2μgm-3 (ATE station). The diurnal variation of PM presented two peaks, one in the morning (from 0800 to 1000h) and the other at night (from 1900 to 2300h), with the highest concentrations of PM10 recorded at the ATE (0800h: 155.8μgm-3) and VMT (2100h: 154.6μgm-3) stations, and PM2.5 at the ATE station (0800h: 60.3μgm-3 and 2300h: 37.5μgm-3). The results showed that the contributions of PM10 are directly related to emissions from industrial activities, automotive fleet, construction, demolition, wind erosion, and the suspension and resuspension of particulates from unpaved roads. Meanwhile, high concentrations of PM2.5 are mainly attributed to vehicle exhaust emissions, industrial emissions, secondary particulate formation, and drag by the action of the winds. The major source of particulate matter contamination is the vehicle fleet, and within this, automobiles, station wagons, combi vans, and 2 and 3-wheel motorcycles are those that have the greatest contribution. These results were supported by non-parametric statistical tests such as Kruskal-Wallis and Mann-Whitney U and validated by the conditional bivariate probability function. The findings of this work may help to implement pollution prevention and control strategies in the future within this South American megacity.

A Puccinia striiformis f. sp. tritici Effector with DPBB Domain Suppresses Wheat Defense

Wheat (Triticum aestivum L.) is a primary crop globally. Among the numerous pathogens affecting wheat production, Puccinia striiformis f. sp. tritici (Pst) is a significant biotic stress agent and poses a major threat to world food security by causing stripe rust or yellow rust disease. Understanding the molecular basis of plant–pathogen interactions is crucial for developing new means of disease management. It is well established that the effector proteins play a pivotal role in pathogenesis. Therefore, studying effector proteins has become an important area of research in plant biology. Our previous work identified differentially expressed candidate secretory effector proteins of stripe rust based on transcriptome sequencing data from susceptible wheat (Avocet S) and resistant wheat (Avocet YR10) infected with Pst. Among the secreted effector proteins, PSTG_14090 contained an ancient double-psi beta-barrel (DPBB) fold, which is conserved in the rare lipoprotein A (RlpA) superfamily. This study investigated the role of PSTG_14090 in plant immune responses, which encodes a protein, here referred to as Pst-DPBB, having 131 amino acids with a predicted signal peptide (SP) of 19 amino acids at the N-terminal end, and the DNA sequence of this effector is highly conserved among different stripe rust races. qRT-PCR analysis indicated that expression levels are upregulated during the early stages of infection. Subcellular localization studies in Nicotiana benthamiana leaves and wheat protoplasts revealed that it is distributed in the cytoplasm, nucleus, and apoplast. We demonstrated that Pst-DPBB negatively regulates the immune response by functioning in various compartments of the plant cells. Based on Co-IP and structural predictions and putative interaction analyses by AlphaFold 3, we propose the probable biological function(s). Pst-DPBB behaves as a papain inhibitor of wheat cysteine protease; Pst-DPBB has high structural homology to kiwellin, which is known to interact with chorismate mutase, suggesting that Pst-DPBB inhibits the native function of the host chorismate mutase involved in salicylic acid synthesis. The DPBB fold is also known to interact with DNA and RNA, which may suggest its possible role in regulating the host gene expression.

Non‐Markovian Dynamics in Fiber Delay‐Line Buffers

AbstractThe non‐Markovian effect is studied on a two‐photon polarization entangled state, in which one photon from the pair is stored in a fiber delay‐line buffer. A model of a photonic qubit coupled to fiber birefringence and a fiber reservoir representing the environment is proposed. Analytically, a non‐Markovian probability function is derived for the buffered photon and its paired photon. To verify the probability function, full quantum state tomography of the photon pairs is performed. The probability function fits well with the experimental data and physical values. These results indicate that the quantum system operates slightly above the threshold for a non‐Markovian transition. We observe a unique polarization dynamic of the buffered photon. Measures of quantum mutual information are further exploited to study the quantumness of the photon pairs. Werner's well‐known separability criterion occurs at a buffer time of about 0.9 ms. These results imply that quantum discord can surpass Werner's criterion, and hence, quantum bi‐partite correlation can exist for buffer times greater than 0.9 ms.

An Extension of Some Truncated Distributions Family With Application

This paper represents a suggested a combination of continuous distributions based on Truncated Gompertz-G (tgo-gd[0,1]) and Truncated Gompertz-Weibull (tgo-wd) distributions. Some of the main properties of the suggested combination such as the distribution function (cdf), the probability function (pdf), survival function (Sf), hazard function (Hrf), quintile function (Qf), moment generating function (mgf), skewness ,, kurtosis , entropy, and maximum likelihood estimator (MLE) for the proposed combination of tgo-wd[0,1] have been presented. As well, an experimentally estimation for the parameters of the distributions using MLE have been studied. After the application, the potentiality of the proposed family by means of one real data sets are shown more flexibility in compare with the other models.

Predicting Remaining Useful Life and Optimizing Preventive Maintenance for Multistage Manufacturing Processes

ABSTRACTA multistage manufacturing process (MMP) is a sequential manufacturing process where products enter a machine in each stage and go through multiple stages for their production. In MMP, the machines even with possessing remaining useful life (RUL) at the current stage have to stop production when all the machines in their previous stage fail to operate. A majority of the relevant studies focus on predicting RUL without considering the characteristics of MMP; thus, hardly provide predictive RUL and optimum replacement time for stage‐level maintenance. The proposed method aims to predict RUL and optimize replacement time for stage‐level maintenance under the MMP structure. It consists of three steps: (1) detection and prediction models for caution and breakdown alarms are generated from historical data, (2) RUL of currently running machines and the probability distribution of RUL at stage level is estimated by analyzing current data with the detection and prediction models, and (3) an optimal replacement time at the stage level is derived based on the probability function of RUL. The proposed method is demonstrated in a hypothetical case study to derive the optimal machine replacement time and validated in a real case study.

Matematiksel Modellemeler Yoluyla Bediüzzaman’ın Yedinci Söz Eserinin Kavram Analizleri

In this article, Bedüzzaman Said Nursi's work The Seventh Word is discussed in terms of mathematical modeling. Thus, it is aimed to analyze a text belonging to human sciences from a different perspective with mathematical modeling. The relationships between the concepts in the text are modeled with mathematical approaches such as network theory, heat map, concept map, Probability and Utility Function, differential equation, Sierpinski triangle, fractals. The concepts and judgment sentences in the researched text are visualized. How each produced graph and shape is produced, which model is used and the obtained result are interpreted. It has become debatable how such an analysis can contribute to future research or how similar studies can be expanded. Document analysis and descriptive analysis are used in the research. Keywords: The Seventh Word, mathematical modeling, network theory, fractal geometry.

Discriminating between “drizzle or rain” and sea salt aerosols in Cloudnet for measurements over the Barbados Cloud Observatory

Abstract. The highly sensitive Ka-band cloud radar at the Barbados Cloud Observatory (BCO) frequently reveals radar reflectivity signals below −50 dBZ within the convective sub-cloud layer. These so-called haze echoes are signals from hygroscopically grown sea salt aerosols. Within the Cloudnet target classification scheme, haze echoes are generally misclassified as precipitation (target class: “drizzle or rain”). We present a technique to discriminate between “drizzle or rain” and sea salt aerosols in Cloudnet that is applicable to marine Cloudnet sites. The method is based on deriving heuristic probability functions utilizing a combination of cloud radar reflectivity factor, radar mean Doppler velocity, and the ceilometer attenuated backscatter coefficient. The method is crucial for investigating the occurrence of precipitation and significantly improves the Cloudnet target classification scheme for measurements at the BCO. The results are validated against the amount of precipitation detected by the Virga-Sniffer tool. We analyze data for measurements at BCO covering 2 years (July 2021–July 2023). A first-ever statistical analysis of the Cloudnet target classification product including the new “haze echo” target over 2 years at the BCO is presented. In the atmospheric column above the BCO, “drizzle or rain” is on average more frequent during the dry season compared to the wet season due to the higher occurrence of warm clouds contributing to the amount of precipitation. Haze echoes are identified about 4 times more often during the dry season compared to the wet season. The frequency of occurrence of “drizzle or rain” in Cloudnet caused by misclassified haze echoes is overestimated by up to 16 %. Supported by the Cloudnet statistics and the results obtained from the Virga-Sniffer tool, 48 % of detected warm clouds in the dry and wet season precipitate. The proportion of precipitation evaporating fully before reaching the ground (virga) is higher during the dry season.

Characterization of Rock Pore Geometry and Mineralization Process via a Random Walk-Based Clogging Scheme

Among the technologies for carbon neutral, CO2 geological sequestration is one of the most promising. The mechanisms of CO2 behavior within pore space are complex and influenced by multiple factors, with the geometric structure of porous formations being particularly critical to the technology’s efficiency. Among several important and challenging problems in geological sequestration, this work addresses the issue of selecting lithologies based on their geometrical structure. This study proposes a mathematical approach to characterize the geometric structure of porous rock and fluid flow using a random walk (RW) method. Our approach simulates the time evolution of particle flow through highly disordered and heterogeneous digital rock models under a pressure gradient imposed between inlet and outlet surfaces. Through RW simulations, a probabilistic model for mineralization via a clogging (pore-filling) model is introduced, to examine the accumulation of particles within porous structures over time: single-phase clogging and multiple-phase clogging. In single-phase clogging, the porosity decrease can be described as a monotonically non-increasing function of the deposition probability. However, this is no longer true in the multiple-phase strategy because large deposition probability blocks the capillaries near the inlet surface, preventing the fluid from easily invading easily the outlet. In this study, numerical studies conducted on four types of natural rocks—Bentheimer, Doddington, Estaillades, and Ketton—revealed that Ketton exhibits the highest permeability. Our results suggest that Bentheimer, Doddington, and Ketton formations are suitable candidates for CO2 sequestration, while Estaillades is less favorable from a geometric standpoint. The methods presented in this work contribute to effectively identifying natural rocks with geometric structures advantageous for CO2 storage.

Thermal Decomposition of Calcium Carbonate at Multiple Heating Rates in Different Atmospheres Using the Techniques of TG, DTG, and DSC

To grasp the decomposition reaction rule of calcium carbonate in cement raw material, the thermogravimetric analyzer (TG), derivative thermogravimetric (DTG), and differential scanning calorimeter (DSC) were used for analysis. Calcium carbonate samples were heated linearly at multiple heating rates of 10, 20, 30, and 40 °C/min in the atmospheres of N2 and 70% N2 + 30% O2, respectively. The decomposition kinetics was investigated using a double extrapolation method. Kinetic parameters of the thermal decomposition and the most probable mechanism function were determined in two different atmospheres. The results show that TG, DTG, and DSC curves moved to a higher temperature with the increase in heating rate, and the addition of O2 in the reaction atmosphere had almost no effect on the change in the decomposition curve. Additionally, the activation energy of the initial state in the formation of the new nucleus obtained using the double extrapolation method was 232.13 kJ/mol in the N2 atmosphere, and the most probabilistic mechanistic function was G(α) = 1 − (1 − α)1/2. The chemical reaction process was consistent with the contracted cylinder mechanism model of phase boundary reaction. Moreover, the activation energy of the initial state in the formation of the new nucleus was 233.79 kJ/mol in the 70% N2 + 20% O2 atmosphere, and the chemical reaction process was consistent with that of the N2 atmosphere. Therefore, these results could determine the decomposition temperature and decomposition rate of calcium carbonate. This was important for understanding the thermal stability and processing temperature range of polymer materials, especially the application and potential in production and scientific research.

Autocorrelation properties of temporal networks governed by dynamic node variables

We study synthetic temporal networks whose evolution is determined by stochastically evolving node variables—synthetic analogues of, e.g., temporal proximity networks of mobile agents. We quantify the long-timescale correlations of these evolving networks by an autocorrelative measure of network-structural memory. Several distinct patterns of autocorrelation arise, including power-law decay and exponential decay, depending on the choice of node-variable dynamics and connection probability function. Our methods are also applicable in wider contexts; our temporal network models are tractable mathematically and in simulation, and our long-term memory quantification is analytically tractable and straightforwardly computable from temporal network data. Published by the American Physical Society 2025

Partial imaging and Thomason conditionals

Abstract The main goal of this article is to give an adequate semantic treatment of Thomason conditionals, that is, conditionals where the consequent asserts the agent’s ignorance or disbelief on the antecedent. These conditionals present a challenge to the conventional epistemic view of conditionals, as outlined by the Ramsey test. We argue that we can give a correct treatment of this type of conditional by taking a probabilistic approach and applying the probability function Jeffrey Imaging as a way of supposing the antecedent. We demonstrate how this method not only unifies the treatment of different types of conditionals while maintaining consistency with the Ramsey test’s core insights, but also sheds light on the general nature of partial supposition.

A robust and powerful metric for distributional homogeneity

AbstractAssessing the homogeneity of two random vectors is a fundamental task in statistical inference. In this work, we introduce a weighted multivariate Cramér‐von Mises type metric that transforms each variable through a marginal mixture distribution function and integrates the squared difference in probability functions of these transformed variables. Notably, our metric exhibits scale invariance, rendering it robust against outliers and heterogeneity. The expression for our metric is straightforward and possesses a closed‐form representation. It is non‐negative and attains a value of zero if and only if the two random vectors are identically distributed. Moreover, our metric employs an ‐norm expression, which significantly enhances its effectiveness in high‐dimensional scenarios compared to traditional methods relying on the ‐norm. We validate the efficacy of our proposed approach through extensive simulation studies and empirical data analysis.

Digital Image Correlation and Reliability-Based Methods for the Design of Structural Beams Made from Recycled Concrete Using Aggregates from Precast Rejects

The use of recycled aggregates in the manufacture of concrete is presented as a solution to reduce the consumption of resources and waste in the construction sector and contribute to a lower environmental impact. This work aims to explore the possibility of producing structural beams from recycled concrete using aggregates from precast concrete rejects and to improve their design using advanced characterisation techniques. To this end, the experimental data coming from mechanical test and the use of the digital image correlation approach are combined with a robust reliability-based method. The full-field data provided by the digital image correlation approach allow to determine the probabilistic density functions of the mechanical data. From these data, a predictive analysis of the maximum strength and deflection of flexural beams is carried out based on robust design techniques. This approach uses analytical theoretical models and a Monte Carlo-based simulation strategy that allows the prediction of the behaviour of the beams. This methodology was validated by manufacturing six beams with the previously analysed recycled concrete, HA-30, and testing them in the laboratory. All the beams showed behaviour within the predicted range: around 49.7 kN maximum load and just over 9.3 mm maximum deflection. These results demonstrate the robustness of the approach as well as the feasibility of using precast rejects for the manufacture of structural elements.

Visualizing the Value of Diagnostic Tests and Prediction Models, Part I. Introduction and Expected Gain in Utility as a Function of Pre-Test Probability.

Visualizing the Value of Diagnostic Tests and Prediction Models, Part I. Introduction and Expected Gain in Utility as a Function of Pre-Test Probability.

The quenching effect of oxygen addition on an argon capacitively coupled plasma: experimental and computational study of the argon metastable atom kinetics

Abstract The effect of oxygen admixture in an argon capacitively coupled radio-frequency plasma is investigated experimentally and computationally in a symmetrical discharge cell, at pressures ⩽ 10 Pa. In the experiments, tunable diode laser absorption spectroscopy is applied to monitor the densities of the Ar 1s5 ( → 772.376 nm 2p6) and 1s3 ( → 772.421 nm 2p2) metastable atoms in the plasma as a function of the oxygen content in the working gas. In order to enhance computational efficiency, the modelling is divided into two steps. First, the electron energy probability function (EEPF) is obtained from a particle-in-cell/Monte Carlo collision simulation of the Ar/O2 plasma without considering the dynamics of the excited levels of Ar atoms. As the second step, this EEPF is fed into a code that solves the balance equations of Ar atoms in numerous excited levels. These equations comprise the effects of diffusion, direct and stepwise excitation processes, stepwise and pooling ionization, as well as radiative transfer between the various Ar atomic levels, and the quenching of the excited Ar atoms by O2 molecules. Using this approach is justified by the fact that the EEPF is insensitive to the excited level dynamics at low pressures, as shown in previous studies. The measurements and simulations are found to yield consistent results, indicating the correctness of the literature values of the quenching coefficient of Ar 1s5 and 1s3 by oxygen molecules.

Variation law of micro-void distribution characteristics in early stage of spallation damage

The development trend of spallation damage mechanics is to construct a physical model that couples information with micro-mesoscale structure of materials, which also promotes the development of numerical calculation methods, experimental techniques and theoretical research. The mechanism responsible for plastic deformation and failure of structural metal materials at high strain rates is complex and ainfluenced by heterogeneities in the micro-mesoscale structure that comprises the distribution of grain boundaries, interfaces, and pre-existing densities voids. The distribution of these mesoscale heterogeneities can provide either strengthening behavior or void nucleation sites and influence spall failure behavior. Due to the lack of evolutionary information of micro-mesoscopic void distribution characteristics, the current spallation damage model is not only restricted in its application in extreme environments with high strain rates, high pressures, and shock, but also does not effectively provide some information about the correlation between material damage and final material fragmentation particle size, which is of very concern in engineering. Therefore, it is urgent to develop a spallation damage model that can reflect the variation law of micro-mesoscopic void distribution characteristics in damaged materials. The probability distribution function of void nucleation based on cosine function is given in this work by analyzing various influencing factors in the process of void nucleation, combining the characteristics of early void growth, and considering the convenience of analytical solution. The analytical calculation results of the new probability function of void nucleation are consistent not only with the results of the variation of void number with time calculated by molecular dynamics, but also with the experimental results of tantalum spallation in the early stage of damage development, that is to say, the new probability function of void nucleation can reflect the variation law of micro-void distribution characteristics in the early stage of spallation damage to a certain extent.

Joint Probability Functions for Scenarios Arising From Multi‐State Series and Multi‐State Parallel Systems

Joint Probability Functions for Scenarios Arising From Multi‐State Series and Multi‐State Parallel Systems