Classical Indicators Research Articles

Heterogeneous Network Motif Coding, Counting, and Profiling

Network motifs, as a fundamental higher-order structure in large-scale networks, have received significant attention over recent years. Particularly in heterogeneous networks, motifs offer a higher capacity to uncover diverse information compared to homogeneous networks. However, the structural complexity and heterogeneity pose challenges in coding, counting, and profiling heterogeneous motifs. This work addresses these challenges by first introducing a novel heterogeneous motif coding method, adaptable to homogeneous motifs as well. Building upon this coding framework, we then propose GIFT, a heterogeneous network motif counting algorithm. GIFT effectively leverages combined structures of heterogeneous motifs through three key procedures: neighborhood searching, motif combination, and redundant motif filtering. We apply GIFT to count three-order and four-order motifs across eight distinct heterogeneous networks. Subsequently, we profile these detected motifs using four classical motif-based indicators. Experimental results demonstrate that by appropriately selecting motifs tailored to specific networks, heterogeneous motifs emerge as significant features in characterizing the underlying network structure.

Microcrediting and Investment Analysis in the Context of Environmental, Social, and Corporate Governance

This article is devoted to the analysis and development of ranking criteria for microcredit organizations to increase their investment attractiveness. The need to solve problematic issues is associated with the need to minimize risks before the start of the lending process through the correct selection of participants in the credit transaction. This study used the methods of content analysis and interpretation, correlation analysis and regression modeling, ranking, and clustering to assess the factors affecting the effectiveness of microcredit organizations. The most attention is paid to identifying key indicators that help improve the quality of financial services provided and their availability for various categories of borrowers. The results show that factors related to lending volumes and borrower characteristics have a significant impact on the quality of microcredit organizations. Of interest is the interpretation of classical financial indicators of microcredit organizations in the context of the principles of environmental, social, and corporate governance (ESG). The proposed approaches and conclusions can be used to improve the practice of microfinance and develop management and regulation strategies in this area.

Is It Possible to Establish an Economic Trend Correlating Territorial Assessment Indicators and Earth Observation? A Critical Analysis of the Pandemic Impact in an Italian Region

The paper is set within the methodological framework of the Territorial Impact Assessment (TIA) process, which is an instrument designed to facilitate sustainable and cohesive policy-making choices at the European level. The article is developed within the context of a European H2020-RICE cooperative project, which utilises the STeMA (Sustainable Territorial Economic/Environmental Management Approach) TIA methodology to investigate the potential relationship between statistical economic indicators, specifically Gross Domestic Product, and related parameters (metadata), and Earth Observation (EO) data. The objective is to provide evidence of socioeconomic trends during the Coronavirus 2019 pandemic in the Lazio Region (Italy), with a particular focus on the metropolitan area of the Rome capital city Rome. In line with the pertinent European context and the scientific literature on the subject, the paper examines the potential for combining classical and Earth observation indicators to assess macroeconomic dimensions of development, specifically in terms of gross domestic product (GDP). The results of the analysis indicate the presence of certain correlations between grey data and EO information. The STeMA-TIA approach allows for the measurement and correlation of both qualitative and quantitative statistical indicators with typological functional areas (in accordance with European Commission-EC and Committee of Ministers responsible for Spatial/Regional Planning—CEMAT guidance) at the NUTS (Nomenclature des unités territoriales statistiques) 2 and 3 levels. This facilitates the territorialisation of information, enabling the indirect comparison of data with satellite data and economic trends. A time series of data was gathered and organised for the purpose of facilitating comparison between different periods, beginning with 2019 and extending to the present day. In order to measure and monitor the evolution of the selected territorial economies (the Lazio Region), a synthetic index (or composite indicator) was developed in the economic and epidemic dimensions. This index combines single values of indicators according to a specific STeMA methodology. It is important to note that there are some critical observations to be made about the impact on GDP, due to the discrepancy between the indicators in the two fields of observation.

Balancing economic benefits and environmental costs: Introducing carbon footprint indicators in tourist market targeting

We argue that governments’ decisions to target certain tourist markets must consider both benefits and costs. We design a composite indicator methodology to assess economic benefits, using six classic indicators of market desirability (leadership, dynamism, seasonality, length of stay, expenditure and connectivity), which we complement with two carbon footprint indicators indicative of some of the costs incurred by the planet (CO2e per tourist night and CO2e per tourist trip). We model how target market decisions should change as the weight given to carbon costs changes from zero (current scenario) to 25% and 50% in the set of indicators used to select target markets. Adding carbon data in a cost-benefit analysis makes regional and national markets much more attractive than distant markets due to their low carbon footprints, despite shorter tourist stays or lower expenditures. Our method can inform government strategies to decarbonize while maintaining a clear market focus.

Characterizing urban acoustic environments by clustering sensor node measurements

Equivalent sound pressure levels have been widely used to assess the impact of the sonic environment on persons. At the same time, it has been demonstrated that sound sensor networks allow to extract a wealth of information about the living environment. Nevertheless it has not been clearly demonstrated how to summarize this information. To this end, we used advanced non-linear clustering methods to group 15-minute sound environments based on a wide range of classical acoustic indicators such as peak levels, statistical levels, spectral center of gravity. Machine learning methods identifying the sound sources that are present based on 1/3 octave band levels measured at 125 msec interval, are then used to better understand why these clusters emerge. The methodology is applied to 150 bedroom window measurements gathered in the Equal-Life project. Preliminary results show that groups of pre-school children with specific cognitive development and mental health are related to different diurnal patterns of sound environment clusters. These results can be interpreted in the larger context of living environments extracted from environmental sound sensing networks.

Non-invasive, pre-symptomatic detection of potato cyst nematode infection in tomato using chlorophyll fluorescence analysis.

Potato cyst nematodes (PCN) are notorious pathogens in all major potato production areas worldwide. Mainly due to the low mobility of this soil pathogen, PCN infestations are mostly observed as patches ('foci') that only cover a fraction of the acreage. In-field pre-symptomatic localization of this pathogen is valuable as it would allow for the localized application of control measures. Although the mapping of foci is technically feasible, it is unpractical as it would take the analysis of numerous soil samples. We investigated whether chlorophyll fluorescence (Chl-F) could be suitable as a rapid, non-destructive method for early PCN detection. To this end, the impact of four Globodera pallida densities on the Chl-F of tomato was investigated in a phenotyping greenhouse for 26 days. Furthermore, classical plant performance indicators biomass and root surface area were compared with Chl-F. Thermal dissipation ('NPQ_Lss') and actual photosynthetic rate ('QY_Lss') responded at 1 DPI, while QY_Lss was most sensitive to low PCN infection levels. Chl-F parameters responded more readily to PCN infection than biomass and root surface area. The efficiency of photosystem II (QY_max) and the potential activity of photosystem II (Fv/Fo) initially increased at low PCN infection levels, whereas a sharp decrease was observed at higher infestation levels. Hence, our data suggest that low PCN levels promoted plant performance before becoming detrimental at higher levels. While Chl-F allowed for early and sensitive PCN detection, it remains to be investigated whether these signals can be distinguished from those produced by other below-ground stressors in the field.

Impact of Nonthermal Plasma Treatment on the Oxidation of Lipids with Different Unsaturation Degrees.

Nonthermal plasma (NTP) treatment of food presents a new technology for the industry but raises concerns about lipid oxidation due to the presence of reactive species. Considering the critical role of the degree of unsaturation in lipid oxidation, this study investigates NTP-induced oxidation across various unsaturated lipids. These lipids are six oil samples primarily containing one of the following methylesters: oleate, linoleate, linolenate, arachidonate, eicosapentaenoate, and docosahexaenoate. Samples were treated with a nonthermal surface dielectric barrier discharge. Plasma-induced effects were first examined by classical lipid oxidation indicators, such as the peroxide value and p-anisidine value. The specific volatile oxidation products, including hexanal, nonanal, trans-2-hexenal, and methyl 9-oxononanoate, were determined to further elucidate the impact of ozone-related oxidation. Monitoring the production of selected nonvolatile oxidation products, such as epoxy-, oxo-, and hydroxy fatty acid methylesters, confirmed that plasma treatment facilitated the decomposition of lipid hydroperoxide. Generally, the level of plasma-induced oxidation increased in parallel with the unsaturation degree of the studied samples, except for the quantity of individual volatile carbonyls. The long-term effect of NTP treatment was investigated by a stability test, revealing that the oxidative stability depended on the input gas of plasma treatment, the sensitivity of the treated sample, and the presence of antioxidants. Except for the focus on the NTP impact, this study offered a case study of a comprehensive investigation into lipid oxidation.

Modeling risk potential fields for mandatory lane changes in intelligent connected vehicle environment

In the environment of Intelligent Connected Vehicles (ICVs), the ICV system is capable of gathering, processing, and transmitting the majority of traffic information to each vehicle, thereby empowering drivers to make more informed and secure decisions. Nevertheless, ICVs are still incapable of completely avoiding traffic conflicts and accidents. Consequently, developing a risk assessment model for ICVs is crucial for their deployment. To investigate the dynamic patterns of lane-changing vehicle risks within ICV environments, this study developed a quantitative relationship model based on the Artificial Potential Field (APF) theory. The model correlates the Total Potential Field (TPF) of mandatory lane-changing (MLC) vehicle with the longitudinal/transverse gravitational potential field (LGPF/TGPF) and the longitudinal/transverse repulsion potential field (LRPF/TRPF). Subsequently, three sets of Human Machine Interface (HMI) systems were developed to delineate distinct ICV environments: baseline, warning group, and guidance group. The baseline furnishes fundamental data, the warning group supplements preceding vehicle icons and real-time headway information, whereas the guidance group additionally augments speed and voice guidance functionalities. Following this, a simulated driving experiment involving 43 participants was carried out to simulate MLC scenarios in highway merging sections. Using enumeration and gradient descent methods, the quantitative relationship between different types of risk fields was determined. The findings indicated that the ICV environment significantly impacts the mean values of LGPF, TGPF, LRPF (Leading Vehicle, LV), and TRPF, while insignificantly affecting the mean value of LRPF (Following Vehicle, FV). Nevertheless, a notable discrepancy in the mean value of LRPF (FV) was observed between the warning and guidance groups. Comparative results with lane positions demonstrate that the proposed TPF accurately depicts vehicle lane-changing behaviors. Comparative results with classical risk indicators indicate that TPF more accurately depicts the actual driving risks and variation trends faced by vehicles in different MLC processes. The research findings will be pivotal in improving real-time control and guidance strategies for vehicles in highway merging sections under ICV environments.

Blood Urea Nitrogen-to-Serum Albumin Ratio Predicts Fatal Outcomes in Severe Fever with Thrombocytopenia Syndrome Patients.

There are no effective therapies for severe fever with thrombocytopenia syndrome (SFTS), and existing predictors of mortality are still controversial. This retrospective study aimed to identify reliable early-stage indicators for predicting fatal outcomes in 217 patients hospitalized with an SFTS diagnosis between March 2021 and November 2023; 157 of the patients survived, and 60 died. Demographics, clinical characteristics, and laboratory parameters were reassessed in both groups. The mean age of participants was 64.0 (interquartile range: 54.5-71.0) years, and 42.4% (92/217) were males. Based on a multivariate Cox regression analysis, the blood urea nitrogen-to-serum albumin ratio (BAR) (hazard ratio [HR]:4.751; 95% CI: 2.208-10.226; P <0.001), procalcitonin level (HR: 1.946; 95% CI: 1.080-3.507; P = 0.027), and central nervous system symptoms (HR: 3.257; 95% CI, 1.628-6.513; P = 0.001) were independent risk factors for mortality in SFTS patients. According to a receiver operating characteristic curve analysis, a BAR with an area under the curve of 0.913 (95% CI: 0.873-0.953; P <0.001), a sensitivity of 76.7%, and a specificity of 90.4% showed better predictive performance for fatal outcomes than other classical indicators reported. The Kaplan-Meier survival curve confirmed that an increased BAR was linked with an unfavorable prognosis in SFTS patients (P <0.001 by log-rank test). In conclusion, the results indicate that high BAR levels are markedly related to substandard outcomes and are a reliable and readily accessible predictor of fatal outcomes in SFTS patients.

Years of Life Lost to COVID-19 and Related Mortality Indicators: An Illustration in 30 Countries.

The concept of (potential) years of life lost is a measure of premature mortality that can be used to compare the impacts of different specific causes of death. However, interpreting a given number of years of life lost at face value is more problematic because of the lack of a sensible reference value. In this paper, we propose three denominators to divide an excess years of life lost, thus obtaining three indicators, called average life lost, increase of life lost, and proportion of life lost, which should facilitate interpretation and comparisons. We study the links between these three indicators and classical mortality indicators, such as life expectancy and standardized mortality rate, introduce the concept of weighted standardized mortality rate, and calculate them in 30 countries to assess the impact of COVID-19 on mortality in the year 2020. Using any of the three indicators, a significant excess loss is found for both genders in 18 of the 30countries.

Improving Student Learning Outcomes with the Problem Based Learning Model: Classroom Action Research at the State Islamic Primary School

This research aims to improve student learning outcomes by using a problem based learning model. This research uses a type of classroom action research. The subjects of this research were third grade students of State Islamic Primary School of 41 Aceh Besar. Data collection techniques in this research are observation and tests. Data were analyzed using descriptive statistical techniques. The results of the research show that student learning outcomes in the third grade Theme 8 material at State Islamic primary School of 41 Aceh Besar using the problem based learning model have increased in each cycle. In cycle I, student learning outcomes reached 73.33% but had not yet reached the classical success indicators, then in cycle II student learning outcomes increased, namely reaching 80% but had reached the classical success indicators. These results show that by using a problem-based learning model, student learning outcomes have increased and achieved indicators of success. Therefore, the problem-based learning model can be used as an alternative learning model that can overcome the problem of low student learning outcomes.

Evaluating Consolidation Centers of an Integrated Transportation Network under the Belt and Road Initiative

Following the Belt and Road, the Air Silk Road has also been proposed. The coordinated development of multiple transportation modes, including air, land, and water, will create a strong transportation force in node cities. However, the current insufficient supply of cargo in various regions and the lack of integration among different transportation modes result in low transportation efficiency, which in turn affects the further advancement of the Belt and Road. To investigate these issues and attempt to find a solution, we selected 44 candidate cities from the prefecture-level cities in China as nodes based on relevant government policies, and constructed an integrated transportation network. For each node city, we first calculated the values of six classical indicators and then used the CRITIC to assign weights to each indicator. Subsequently, we employed the TOPSIS method combined with Grey Relational Analysis (GRA) to compute the comprehensive score for each node city. Based on the spatial layout and government policies under the BRI, eight cities, including Wuhan, Chongqing, Tianjin, Shanghai, Guangzhou, Lianyungang, Hefei, and Dalian, were finally recommended as the consolidation centers of the integrated transportation network. It is hoped that the results of this analysis can provide some insights for the government to outline and build the consolidation centers of the integrated transportation network composed of railway, air, highway, and water routes, which in turn can offer insights for elevating the Belt and Road Initiative (BRI) to a new level.

Relationship between classic indicators of health behaviour and contraceptive choices in women in Flanders

BackgroundIn this study we shed light on ongoing trends in contraceptive use in Flanders (Belgium). Building on the fundamental cause theory and social diffusion of innovation theory, we examine socio-economic gradients in contraceptive use and the relationship to health behaviours.MethodsUsing the unique and recently collected (2020) ISALA data, we used multinomial logistic regression to model the uptake of contraceptives and its association to educational level and health behaviour (N:4316 women).ResultsHigher educated women, and women with a healthy lifestyle especially, tend to use non-hormonal contraceptives or perceived lower-dosage hormonal contraceptives that are still trustworthy from a medical point of view. Moreover, we identified a potentially vulnerable group in terms of health as our results indicate that women who do not engage in preventive health behaviours are more likely to use no, or no modern, contraceptive method.DiscussionThe fact that higher educated women and women with a healthy lifestyle are less likely to use hormonal contraceptive methods is in line with patient empowerment, as women no longer necessarily follow recommendations by healthcare professionals, and there is a growing demand for naturalness in Western societies.ConclusionThe results of this study can therefore be used to inform policy makers and reproductive healthcare professionals, since up-to-date understanding of women’s contraceptive choices is clearly needed in order to develop effective strategies to prevent sexually transmitted infections and unplanned pregnancies, and in which women can take control over their sexuality and fertility in a comfortable and pleasurable way.

The Death of Vulcan: NEID Reveals That the Planet Candidate Orbiting HD 26965 Is Stellar Activity* * HD 26965 is also known as 40 Eridani A, which is the host star of the planet Vulcan in the Star Trek universe.

We revisit the long-studied radial velocity (RV) target HD 26965 using recent observations from the NASA-NSF “NEID” precision Doppler facility. Leveraging a suite of classical activity indicators, combined with line-by-line RV analyses, we demonstrate that the claimed 45-day signal previously identified as a planet candidate is most likely an activity-induced signal. Correlating the bulk (spectrally averaged) RV with canonical line activity indicators confirms a multiday “lag” between the observed activity indicator time series and the measured RV. When accounting for this lag, we show that much of the observed RV signal can be removed by a linear detrending of the data. Investigating activity at the line-by-line level, we find a depth-dependent correlation between individual line RVs and the bulk RVs, further indicative of periodic suppression of convective blueshift causing the observed RV variability, rather than an orbiting planet. We conclude that the combined evidence of the activity correlations and depth dependence is consistent with an RV signature dominated by a rotationally modulated activity signal at a period of ∼42 days. We hypothesize that this activity signature is due to a combination of spots and convective blueshift suppression. The tools applied in our analysis are broadly applicable to other stars and could help paint a more comprehensive picture of the manifestations of stellar activity in future Doppler RV surveys.

Drought Responses in Three Apple Cultivars Using an Autonomous Sensor-based Irrigation System

Irrigation decision support systems evolving in the domestic temperate tree fruit production industry incorporate measures of soil moisture status, which diverges from classic physiological indicators of edaphic stress. This study used an autonomous sensor-based irrigation system to impose a water deficit (soil matric potential targets of –25, –40, –60, and –80 kPa) on ‘Autumn Gala’, ‘CrimsonCrisp’, and ‘Golden Delicious’ apple (Malus domestica) cultivars grafted to ‘Budagovsky 9’ rootstock in the greenhouse (n = 60). It was hypothesized that relationships between physiological plant function, assessed via infrared gas exchange and chlorophyll fluorescence, and the soil matric potential may be used to advance emerging irrigation decision support systems. Complications arising from defoliation by day 11 at –60 and –80 kPa indicate the generation of substrate-specific soil–water relationships in research applications of autonomous sensor-based irrigation systems. ‘Autumn Gala’ carbon assimilation rates at –80 kPa declined from day 0 to day 8 (9.93 and 5.86 μmol⋅m–2⋅s–1 carbon dioxide), whereas the transpiration rate was maintained, potentially reducing observed defoliation as other cultivars increased transpiration to maintain carbon assimilation. Correlation matrices revealed Pearson’s r ≤ |0.43| for all physiological metrics considered with soil matric potential. Nevertheless, exploratory regression analysis on predawn leaf water potential, carbon assimilation, transpiration, stomatal conductance, and nonphotochemical quenching exposed speculatively useful data and data shapes that warrant additional study. Nonlinear piecewise regression suggested soil matric potential may useful as a predictor for the rate of change in predawn leaf water potential upon exposure to a water deficit. The critical point bridging the linear spans, –30.6 kPa, could be useful for incorporating in emerging irrigation decision support systems.

Assessment of the impact of spent mushroom substrate on biodiversity and activity of soil bacterial and fungal populations based on classical and modern soil condition indicators

Assessment of the impact of spent mushroom substrate on biodiversity and activity of soil bacterial and fungal populations based on classical and modern soil condition indicators

Sensitivity of human-induced vibrations and comfort analysis to partially rigid STS joints in timber-to-timber composite floors

The study of floors vibration serviceability represents a well-known challenging task and has a critical role in comfort analysis, assessment and optimization of pedestrian systems in general. To this aim, several consolidated and/or simplified tools are available in the literature to address the most important aspects. In practice, however, most of assumptions for the analysis and verification are based on the use of rough mechanical models of joints and connections, which have indeed a primary role especially for composite floors. In this paper, the attention is given to timber-to-timber floors with inclined self-tapping screws (STS). A parametric Finite-Element (FE) numerical investigation is carried out by taking into account conventional walking features and a case-study timber-to-timber composite beam, well representative of a one-way wooden floor. A major advantage for structural and pedestrian modelling stages is taken from previous literature efforts, while large attention is spent for structural analysis and vibration serviceability assessment tasks, as a function of the STS mechanical parameters (first of all the secant stiffness). Comparative linear modal and non-linear time history analyses are carried out and addressed towards limit mechanical configurations for STS joints, in terms of vibration frequency considerations, as well as structural response and comfort assessment, based on classical performance indicators. The parametric numerical results are further discussed based on simplified methods provided by selected design standards. A critical analysis of major effects due to partial joint rigidity and floor performance classification is presented, both in terms of expected structural safety and comfort levels for similar systems.

AI-assisted image analysis and physiological validation for progressive drought detection in a diverse panel of Gossypium hirsutum L.

Drought detection, spanning from early stress to severe conditions, plays a crucial role in maintaining productivity, facilitating recovery, and preventing plant mortality. While handheld thermal cameras have been widely employed to track changes in leaf water content and stomatal conductance, research on thermal image classification remains limited due mainly to low resolution and blurry images produced by handheld cameras. In this study, we introduce a computer vision pipeline to enhance the significance of leaf-level thermal images across 27 distinct cotton genotypes cultivated in a greenhouse under progressive drought conditions. Our approach involved employing a customized software pipeline to process raw thermal images, generating leaf masks, and extracting a range of statistically relevant thermal features (e.g., min and max temperature, median value, quartiles, etc.). These features were then utilized to develop machine learning algorithms capable of assessing leaf hydration status and distinguishing between well-watered (WW) and dry-down (DD) conditions. Two different classifiers were trained to predict the plant treatment-random forest and multilayer perceptron neural networks-finding 75% and 78% accuracy in the treatment prediction, respectively. Furthermore, we evaluated the predicted versus true labels based on classic physiological indicators of drought in plants, including volumetric soil water content, leaf water potential, and chlorophyll a fluorescence, to provide more insights and possible explanations about the classification outputs. Interestingly, mislabeled leaves mostly exhibited notable responses in fluorescence, water uptake from the soil, and/or leaf hydration status. Our findings emphasize the potential of AI-assisted thermal image analysis in enhancing the informative value of common heterogeneous datasets for drought detection. This application suggests widening the experimental settings to be used with deep learning models, designing future investigations into the genotypic variation in plant drought response and potential optimization of water management in agricultural settings.

Condition Monitoring of Wind Turbine Drivetrain Bearings

Abstract As an extremely valuable and reliable energy source, the renewable energy is developing around the world at an unprecedented pace. By the end of 2022, the global installed capacity of offshore wind turbines is expected to reach 46.4 GW, among which 33.9 GW in Europe. Efficiencies in Operations and Maintenance (O&amp;M) offer potential to achieve significant cost savings as it accounts for around 20%–30% of overall offshore wind farm costs. A recent study of approximately 350 offshore wind turbines indicates that gearboxes might have to be replaced as early as 6.5 years. Therefore sensing and condition monitoring (CM) systems are needed in order to obtain reliable information on the state and condition of different critical parts. The development and use of such technologies will allow companies to schedule actions at the right time. The reduced costs of O&amp;M enable the wind energy at a competitive price thus strengthening productivity of the wind energy sector. At the academic level, a plethora of methodologies have been proposed during the last decades focusing toward early and accurate fault detection. Among others, Envelope Analysis is one of the most important methodologies, where the envelope of the vibration signal is estimated, usually after filtering around a selected frequency band excited by impacts due to the faults. Different tools, such as Kurtogram, have been proposed in order to accurately select the optimum filter parameters (center frequency and bandwidth). Cyclostationary analysis and corresponding methodologies, i.e., the cyclic spectral correlation and the cyclic spectral coherence, have been proved as powerful tools for CM. On the other hand the application, test, and evaluation of such tools in general industrial cases is still rather limited. Therefore the main aim of this paper is the application and evaluation of advanced diagnostic techniques and diagnostic indicators, including the Enhanced Envelope Spectrum and the Spectral Flatness on real-world vibration data collected from vibration sensors on gearboxes in multiple wind turbines over an extended period of time of nearly four years. The diagnostic indicators are compared with classical statistic time and frequency indicators, i.e., Kurtosis, Crest Factor, etc. and their effectiveness is evaluated based on the successful detection of two failure events.

Problem-Based Learning Learning Strategy at SMK Plus Al Hadi, Rengel District

Selection of the right learning method is necessary because it will greatly determine the ability of students in learning outcomes. In response to this problem, an appropriate learning model is needed, one of which is the PBL learning model. Formulation of the Problem (1) How is the application of the Problem-Based Learning learning model in PAI learning in Class XI of SMK Plus Al Hadi, Rengel District? (2) How to increase students’ critical thinking from the application of the Problem-Based Learning learning model in PAI learning in Class XI SMK Plus Al Hadi, Rengel District. This study aims (1) to describe the application of the Problem-Based Learning learning model to PAI learning in Class XI of SMK Plus Al Hadi, Rengel District. (2) To explain how to increase students’ critical thinking from the application of the problem-based learning model in PAI learning in Class XI SMK Plus Al Hadi, Rengel District. The analysis of this research data is qualitative and quantitative. Data collection techniques in this study include observation, tests, interviews and documentation. The results of this study were that the percentage of students who scored critical thinking skills met completeness in Cycle I was 65.62%, and in Cycle II it was 96.87%. The percentage of the number of students who met the completeness score in Cycle II had met the classical success indicators