Different Types Of Uncertainty Research Articles

Rock slope stability analysis adopting Eurocode 7, a limit state design approach for an open pit

In this paper we compare the partial factors approach of Eurocode 7 with a traditional deterministic limit equilibrium analysis approach and probabilistic approach. The example case is a simplistic model profile of an open pit mine cut slope configuration. The controlling parameters in a structurally dictated failure mechanism were introduced as random variables in the model, to account for the different types of uncertainties arising in rock engineering data. The limit equilibrium method was used in this study to conduct rock slope stability analysis, while the impact of naturally uncertain and variable parameters, among others water pressure and earthquake activities were considered. Different scenarios from the best to the worst-case were analysed and later compared. The sensitivity analysis revealed the importance of the joint failure plane, joint roughness coefficient and joint friction angle and how the actions (groundwater pressure and earthquake action) affect the slope’s stability. These results emphasize some advantages of the approach, and the potential further embracement from the rock engineering fraternity.

Bumpless stabilisation of uncertain switched positive linear systems under synchronous and asynchronous switching

This paper deals with stabilising uncertain Switched Positive Linear Systems (SPLSs) with a bumpless transfer controller. The contribution of this study is to improve switching controller robustness at the switching instances and also guarantee the –gain performance of the positive systems. Positive systems are widespread; most of the biological, economic systems, disease, etc., have nonnegative variables belonging to this class of systems. Positive Systems modelling encounters different types of uncertainties; therefore, stability analysis and stabilisation of uncertain SPLSs are crucial in analysing positive systems. The stability of the SPLSs can be guarantee by using multiple copositive Lyapunov functions with the Dwell Time (DT) strategy. The stability of the SPLS has been investigated under synchronous and asynchronous switching modes. The so-called asynchronous switching means that the switches between the candidate controllers and system modes are asynchronous. Also, the –gain performance of the system is derived. Finally, two illustrative examples are provided to demonstrate the proposed scheme’s effectiveness compared with the foremost existing solutions.

How to measure uncertainty in uncertainty sampling for active learning

Various strategies for active learning have been proposed in the machine learning literature. In uncertainty sampling, which is among the most popular approaches, the active learner sequentially queries the label of those instances for which its current prediction is maximally uncertain. The predictions as well as the measures used to quantify the degree of uncertainty, such as entropy, are traditionally of a probabilistic nature. Yet, alternative approaches to capturing uncertainty in machine learning, alongside with corresponding uncertainty measures, have been proposed in recent years. In particular, some of these measures seek to distinguish different sources and to separate different types of uncertainty, such as the reducible (epistemic) and the irreducible (aleatoric) part of the total uncertainty in a prediction. The goal of this paper is to elaborate on the usefulness of such measures for uncertainty sampling, and to compare their performance in active learning. To this end, we instantiate uncertainty sampling with different measures, analyze the properties of the sampling strategies thus obtained, and compare them in an experimental study.

Communicating Uncertainties About the Effects of Medical Interventions Using Different Display Formats.

Communicating uncertainties in scientific evidence is important to accurately reflect scientific knowledge , increase public understanding of uncertainty, and to signal transparency and honesty in reporting. While techniques have been developed to facilitate the communication of uncertainty, many have not been empirically tested, compared for communicating different types of uncertainty, or their effects on different cognitive, trust, and behavioral outcomes have not been evaluated. The present study examined how a point estimate, imprecise estimate, conflicting estimates, or a statement about the lack of evidence about treatment effects, influenced participant's responses to communications about medical evidence. For each type of uncertainty, we adapted three display formats to communicate the information: tables, bar graphs, and icon arrays. We compared participant's best estimates of treatment effects, as well as effects on recall, subjective evaluations (understandability and usefuleness), certainty perceptions, perceptions of trustworthiness of the information, and behavioral intentions. We did not find any detrimental effects from communicating imprecision or conflicting estimates relative to a point estimate across any outcome. Furthermore, there were more favorable responses to communicating imprecision or conflicting estimates relative to lack of evidence, where participants estimated the treatment would improve outcomes by 30-50% relative to a placebo. There were no differences across display formats, suggesting that, if well-designed, it may not matter which format is used. Future research on specific display formats or uncertainty types and with larger sample sizes would be needed to detect small effects. Implications for the communication of uncertainty arediscussed.

Diffusion of biogas for freight transport in Sweden: A user perspective

Current freight transport is highly dependent on fossil fuels and there is a need for a transition to alternative fuels and technologies. Biogas is a type of biofuel that has the potential to reduce climate emissions from freight transport, while providing additional benefits such as recycling of nutrients and increased energy security. This paper uses theories on the diffusion of green technologies to analyse the barriers and drivers for the increased use and diffusion of biogas in freight transport. The empirical focus is on the region of Västra Götaland in Sweden, and qualitative interviews have been conducted with demand-side actors such as transport buyers, haulage companies and vehicle manufacturers. The results confirm the important barriers observed in previous research, such as the higher costs of biogas, financial uncertainties and lack of infrastructure, as well as the interplay between barriers. The main drivers are an increased focus on sustainability both within the sector and from wider society, as well as the environmental properties of biogas. Specific barriers have also been identified such as a fragmented freight market structure with a mix of large and small transport companies, tight profit margins and reduced capacity for investments. There is also a division of labour and responsibilities between transport companies and transport buyers, which makes it unclear who will drive the transition to alternative fuels. In general, the study shows that the different types of uncertainty are perceived by the actors as being a significant barrier that needs to be better conceptualised in diffusion theory.

Investigating the relationships between uncertainty types and risk management strategies in cross-border e-commerce logistics

PurposeDue to its fast growth, cross-border e-commerce (CBEC) is becoming a popular internationalization model, especially in those destination markets with impressive e-commerce development like China. However, CBEC also brings new logistics challenges and uncertainty. This paper aims to understand how companies cope with logistics uncertainty in this field and whether the different types of uncertainty influence the risk management strategies adopted to face them.Design/methodology/approachA survey targeting online exporters to China and third-party forwarding logistics service providers (3PFLs) is conducted. A structural equation model (SEM) analysis is performed to test the possible relationship between the adopted risk management strategies and the types of uncertainty. The type, industry and size of the company, as well as the distance between the company's home country and China, are used as control variables in the study. Survey results are enriched via interviews with some of the respondents.FindingsThe risk management strategies adopted are dependent on the type of logistics uncertainty that the companies face and, to a minor extent, on the industry the company operates in. Conversely, no significant influence is exerted by other types of control factors, i.e. home country, company size or company type.Originality/valueThe paper investigates logistics uncertainty and risk management approaches in the novel context of CBEC. A systematic review of relevant sources of uncertainty is offered to help both scholars and practitioners understand the current complexities of CBEC. From a theoretical perspective, the paper models the investigated concepts in light of the contingency approach. From a practical perspective, results can be of interest since the list of proposed items can support risk identification and evaluation while the interviews with managers can provide insights on risk management practices.

KETIDAKPASTIAN DAN KOMPLEKSITAS RANTAI PASOK DALAM KINERJA OPERASIONAL YANG BERKELANJUTAN

The purpose of this research plan is analyzing the different types of uncertainties and complexity in the supply chain and provide suggestion on strategies to deliver superior operational performance (OP) in disruption and dynamic situation using symmetrical and asymmetrical modeling approaches. Symmetrical modeling is applied via PLS-SEM in order to assess the theoretical relationships among the latent variables, while asymmetrical modeling is applied via fuzzy set qualitative comparative analysis (fsQCA) to emphasize their combinatory causal relation. This research contributes by providing an illustration of a PLS-SEM and fsQCA based estimation for the rapidly emerging field of sustainable supply chain management. This study assumes to provide empirical support for resource dependence theory (RDT) in explaining the relation between SCU and SCS as well as SCO and SCC which leads to sustainable OP. From a methodological standpoint, this study also illustrates predictive validation testing of models using holdout samples and testing for causal asymmetry.

New method for dependence assessment in human reliability analysis based on linguistic hesitant fuzzy information

Human reliability analysis (HRA) is a proactive approach to model and evaluate human systematic errors, and has been extensively applied in various complicated systems. Dependence assessment among human errors plays a key role in the HRA, which relies heavily on the knowledge and experience of experts in real-world cases. Moreover, there are ofthen different types of uncertainty when experts use linguistic labels to evaluate the dependencies between human failure events. In this context, this paper aims to develop a new method based on linguistic hesitant fuzzy sets and the technique for human error rate prediction (THERP) technique to manage the dependence in HRA. This method handles the linguistic assessments given by experts according to the linguistic hesitant fuzzy sets, determines the weights of influential factors by an extended best-worst method, and confirms the degree of dependence between successive actions based on the THERP method. Finally, the effectiveness and practicality of the presented linguistic hesitant fuzzy THERP method are demonstrated through an empirical healthcare dependence analysis.

Tolerance for Uncertainty, Personality Traits and Specialty Choice Among Medical Students

The objective was to explore the tolerance for uncertainty in its different aspects (risk, ambiguity and complexity) in medical students at different times of their careers, and to relate these tolerance levels with their predominant personality traits and specialty choices. A secondary objective was to build a hypothetical model aimed at explaining the potential relationships of dependency between gender, personality traits, tolerance for uncertainty and specialty choice using a structural equation modeling (SEM) analysis. A prospective cross-sectional study including two cohorts of second-year (n = 155) and sixth-year (n = 157) medical students was performed during 2017 at the Buenos Aires University School of Medicine. Both student cohorts completed instruments assessing tolerance for different types of uncertainty: (1) complexity (Tolerance for Ambiguity scale); (2) risk (Pearson Risk Attitude scale); and (3) ambiguity (Ambiguity Aversion in Medicine scale). Information on age, gender and specialty choice in sixth-year medical students was included, plus the Big Five Inventory-10 (BFI-10) personality test. Sixth-year students showed significantly lower scores than second-year students at tolerance for complexity (p = 0.0003) and ambiguity (p = 0.008). Sixth-year students choosing a surgical specialty were associated with low tolerance for risk and ambiguity, and moderate for complexity. Conversely, students choosing a clinical specialty were related with high tolerance for risk, moderate for ambiguity, and low for complexity. Logistic regression analysis including the uncertainty questionnaires plus BFI-10 categories demonstrated that only the "neuroticism" personality trait was independently associated with a surgical specialty choice (OR: 1.31, 95%CI: 1.03-1.67). The final SEM that best represented the data showed good fit statistics: chi-square (p = 0.108), and RMSEA (p = 0.047). Tolerance for uncertainty in its different dimensions was associated with personality traits and specialty choice among medical students. A SEM analysis could satisfactorily explain the hypothetical relationships of dependency between gender, personality traits, tolerance for uncertainty, and specialty choice.

Uncertainty and exchange rate volatility: Evidence from Mexico

This paper analyzes the effect of different types of uncertainty by implementing an in-depth case study of Mexican peso US dollar exchange rate volatility. The paper exploits unique data from the Banco de México's Survey of Professional Forecasters to construct four distinct, direct knightian uncertainty measures, and two macro surprise measures. These measures, as well as text-based and financial data based measures common in the literature, are used to test for distinct uncertainty effects. Exchange rate volatility during 1999–2018 is regressed onto uncertainty measures capturing both domestic and international, economic and political uncertainty. The main results show higher knightian uncertainty leads to higher exchange rate volatility. While both domestic and international measures affect exchange rate volatility, international uncertainty measures based on text and financial data (the global EPU and the VIX) and our novel survey-based knightian measure of domestic political uncertainty dominate. The paper also presents evidence of an amplifying effect of domestic economic uncertainty on exchange rate volatility during recession periods. The results are robust to different exchange rate volatility measures and different specifications.

Better the devil you know than the devil you don't: Neural processing of risk and ambiguity

Risk and ambiguity are inherent in virtually all human decision-making. Risk refers to a situation in which we know the precise probability of potential outcomes of each option, whereas ambiguity refers to a situation in which outcome probabilities are not known. A large body of research has shown that individuals prefer known risks to ambiguity, a phenomenon known as ambiguity aversion. One heated debate concerns whether risky and ambiguous decisions rely on the same or distinct neural circuits. In the current meta-analyses, we integrated the results of neuroimaging research on decision-making under risk (n = 69) and ambiguity (n = 31). Our results showed that both processing of risk and ambiguity showed convergence in anterior insula, indicating a key role of anterior insula in encoding uncertainty. Risk additionally engaged dorsomedial prefrontal cortex (dmPFC) and ventral striatum, whereas ambiguity specifically recruited the dorsolateral prefrontal cortex (dlPFC), inferior parietal lobe (IPL) and right anterior insula. Our findings demonstrate overlapping and distinct neural substrates underlying different types of uncertainty, guiding future neuroimaging research on risk-taking and ambiguity aversion.

Application of interval-valued triangular fuzzy numbers and their functional to the healthcare problems

Aim. In healthcare field there exist different types of uncertainty due to medical error generated by human and technologies. In general the crisp value generate loss of precision and inaccuracy about result and therefore the available data is not sufficient to assessed clinical process up to desired degree of accuracy. Therefore fuzzy set theory play as an important and advance role in accuracy of results in healthcare related problems. Methods. Here for more accuracy of result, we use functional fuzzy numbers in this paper. This study uses a new fuzzy fault tree analysis for patient safety risk modelling in healthcare. In this paper we will use level (λ, ρ) interval-valued triangular fuzzy number, their functional, t-norm operation and centre of gravity defuzzification method to evaluate fuzzy failure probability and estimate reliability of system. The effectiveness of these methods is illustrated by an example related to healthcare problems and then we analyse the result obtained with the other existing techniques. Tanaka et al.’s approach has been used to give the rank of basic events of the considered problems. Also, we use functional of fuzzy numbers to analyse the change in fuzzy failure probability. Results. The paper examines the application of the failure tree, t-norm and functional fuzzy numbers in the context of interval-valued triangular fuzzy numbers. The research examined two types of healthcare-specific problems and the corresponding defuzzification techniques for the purpose of reliability analysis using the existing methods. The authors concluded that t-norm is not associated with significant accumulation and identified how a functional fuzzy number affects reliability. Similarly, using the V index method, the least critical events were found for each system.

The uncertainty–investment relationship: scrutinizing the role of firm size

PurposeThe objective of this paper is threefold. First, it aims to empirically study whether firm-specific/idiosyncratic uncertainty, macroeconomic/aggregate uncertainty and political uncertainty have an adverse influence on firms' investment decisions in Pakistan. After establishing this, it scrutinizes whether the uncertainty effects on investment are different for firms of different sizes. Finally, it investigates whether any heterogeneity exists in the uncertainty impacts across different industries.Design/methodology/approachThe empirical analysis is based on an unbalanced panel data of 468 nonfinancial firms listed at the Pakistan Stock Exchange (PSX) during the period 2000–2018. Departing from the literature, the paper builds a time-varying composite volatility/uncertainty index based on the principal component analysis (PCA) by utilizing the constructed volatility series for sales, cash flows and return on assets to gauge firm-specific uncertainty for each firm included in the analysis. Likewise, the paper develops a PCA-based composite index for macroeconomic uncertainty by using the conditional variance series of consumer price index (CPI), industrial production index (IPI), the interest rate and the exchange rate obtained by estimating the (generalized) autoregressive conditional heteroscedastic, (G)ARCH, models. Finally, political uncertainty is measured by political risk components maintained by the Political Risk Services Group. The empirical framework of the paper augments the standard investment equation by incorporating all three types of uncertainty. Firms are grouped into small, medium and large categories based on firms' total assets and the size indicators are generated. Next, the indicators are multiplied by each uncertainty measure to quantify the differential effects of uncertainty across firm size. Firms are also differentiated by sectors to explore the sector-based asymmetries in the uncertainty effects. The “robust two-step system generalized method of moments (2SYS GMM) (dynamic panel data) estimator” is applied to estimate the empirical models.FindingsThe results provide robust and strong evidence of the detrimental influence of all three types of uncertainty on investment. Yet, it is observed that the strength of the influence considerably varies across uncertainty types. In particular, compared to firm-specific uncertainty, both macroeconomic and political uncertainties have more unfavorable effects. The analysis also reveals that the effects of all three types of uncertainty are quite different at small, medium and large firms. Specifically, it is observed that although the investment of all firms is influenced adversely by magnified uncertainty, the adverse effects of all three kinds of uncertainty are quite stronger at small firms than medium and large firms. These findings support the phenomenon of size-based asymmetries in the effects of uncertainty on investment. The results also provide evidence that either type of uncertainty quite differently affects the investment policy of firms in different sectors.Practical implicationsThe findings help different stakeholders to know how different types of uncertainty differently affect corporate firms' investments. Further, they suggest that firm size has a vital role in ascertaining the adverse effects of uncertainty on investment. The paper identifies to which type of uncertainty investors and policymakers should care more about and to which types of firms and industries they should concern more during volatile times. Firms should have more fixed assets and expand their size to mitigate the detrimental effects on investment of internal and external uncertainties. The government should enhance the political stability to induce firms for a higher level of investment, which, in turn, will result in higher growth of the economy.Originality/valueThe originality of the paper is credited to four aspects. First, unlike most previous studies that have utilized a single volatility measure, this paper constructs composite uncertainty indices based on the weights determined by the PCA. Second, it examines the effect of political uncertainty over and above the effects of idiosyncratic and aggregate (macroeconomic uncertainty) for an emerging economy. Third, and most important, it provides first-hand empirical evidence on the role of firm size in establishing the asymmetric effects of uncertainty on investment. Finally, it provides evidence on the industry-based heterogeneity in the uncertainty effects.

Analyzing and Visualizing Uncertain Knowledge: The Use of TEI Annotations in the PROVIDEDH Open Science Platform

The underlying uncertainty in digital humanities research data affects decision-making and persists during a project’s lifecycle. This uncertainty is inevitable since most empirical claims cannot be assessed against an absolute truth (Drucker 2011; Binder et al. 2014). This situation has been previously recognized together with the need to report the degrees of uncertainty that accompany such claims (Blau 2011). Although TEI makes it possible to annotate text with notions of certainty or precision, examples of actual projects taking advantage of this are scarce. There are many possible explanations for uncertainty’s lack of visibility in computationally supported humanities research; among them, the need for tools specifically designed to address the goal of defining and managing uncertainty stands out. Thus, efforts to provide technical support for humanities research should focus on managing and making uncertainty more transparent, rather than removing it. Another challenge is the fact that there is no agreement on a generic taxonomy for the different types of uncertainty that researchers may face. Various researchers across disciplines, working on varying projects and data sets, can use different categories to classify the uncertainties present in a particular case. In this paper, we introduce a collaborative platform for collective annotation of TEI data sets. We briefly present the flexible taxonomy of uncertainty used in the platform and describe two data sets used for its testing. Then we describe use cases of annotations available on the platform, and how they translate into TEI annotations. Creating and interpreting annotations with and without uncertainty should now be easier, especially for researchers who do not know TEI markup.

Revisiting Ellsberg’s and Machina’s Paradoxes: A Two-Stage Evaluation Model Under Ambiguity

In this paper, a two-stage evaluation (TSE) model for decision making under ambiguity is proposed. Events in state space are classified into risky and ambiguous events, which correspond to different types of uncertainty generated by different sources. In this TSE model, uncertainty of two different types are evaluated by decision maker (DM) in different stages. In the first stage, DM evaluates more uncertain consequences of an act locally by applying local subjective expected utility (SEU) models, which are then embedded into the second-stage evaluation based on SEU defined globally over all events. To axiomatize such a model, the small domain SEU over risky acts is extended to both risky and nonrisky (ambiguous) acts. When evaluating a risky act, TSE model reduces to Savage’s SEU with one stage. When evaluating an ambiguous act, local SEU with a different uncertainty aversion defined on ambiguous events gives TSE model some flexibility in describing preferences. It can be shown that TSE model can accommodate Ellsberg’s paradoxes and Machina’s paradoxes in the literature. When applied to portfolio selection problem, TSE model enjoys some nice properties other models do not have. This paper was accepted by Manel Baucells, decision analysis.

Aleatoric and epistemic uncertainty in machine learning: an introduction to concepts and methods

The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often referred to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of attempts so far at handling uncertainty in general and formalizing this distinction in particular.

Modified artificial bee colony algorithm for solving mixed interval-valued fuzzy shortest path problem

In recent years, numerous researchers examined and analyzed several different types of uncertainty in shortest path (SP) problems. However, those SP problems in which the costs of arcs are expressed in terms of mixed interval-valued fuzzy numbers are less addressed. Here, for solving such uncertain SP problems, first a new procedure is extended to approximate the summation of mixed interval-valued fuzzy numbers using alpha cuts. Then, an extended distance function is introduced for comparing the path weights. Finally, we intend to use a modified artificial bee colony (MABC) algorithm to find the interval-valued membership function of SP in such mixed interval-valued fuzzy network. The proposed algorithm is illustrated via two applications of SP problems in wireless sensor networks and then the results are compared with those derived from genetic and particle swarm optimization (PSO) algorithms, based on three indexes convergence iteration, convergence time and run time. The obtained results confirm that the MABC algorithm has less convergence iteration, convergence time and implementation time compared to GA and PSO algorithm.

Robust Model Predictive Control of DC-DC Floating Interleaved Boost Converter With Multiple Uncertainties

DC-DC Floating Interleaved Boost Converter (FIBC) is recently introduced for converting low-level voltage generated by a renewable energy source to high-level voltage required for AC inverters. Although a desired voltage is expected at the output, designing a proper voltage gain for FIBC is challenging due to different types of uncertainties. For instance, the voltage generated by the energy source and, therefore, the input voltage of FIBC may change by a variety of parameters including external load. Furthermore, parametric uncertainty and measurement noise are other sources which can affect the control procedure. As a result, voltage gain for a fixed switching duty cycle may be uncertain. It demands a robust approach to guarantee the control performance under uncertainties without the need for individually tuning controller for each single converter. In this work, a robust model predictive control is employed to regulate the output voltage at the desired level despite the existing uncertainties. Controller parameters are fixed for any FIBC within the uncertainty range and further tuning is not required for individual converters. In addition, unlike the conventional controllers, the suggested controller is able to handle input-output constraints. Performance of the suggested controller is investigated through simulations carried out in MATLAB and the superiority of the proposed approach is verified over non-robust model predictive framework.

The Role of Transparency, Trust, and Social Influence on Uncertainty Reduction in Times of Pandemics: Empirical Study on the Adoption of COVID-19 Tracing Apps.

BackgroundContact tracing apps are an essential component of an effective COVID-19 testing strategy to counteract the spread of the pandemic and thereby avoid overburdening the health care system. As the adoption rates in several regions are undesirable, governments must increase the acceptance of COVID-19 tracing apps in these times of uncertainty.ObjectiveBuilding on the Uncertainty Reduction Theory (URT), this study aims to investigate how uncertainty reduction measures foster the adoption of COVID-19 tracing apps and how their use affects the perception of different risks.MethodsRepresentative survey data were gathered at two measurement points (before and after the app’s release) and analyzed by performing covariance-based structural equation modeling (n=1003).ResultsWe found that uncertainty reduction measures in the form of the transparency dimensions disclosure and accuracy, as well as social influence and trust in government, foster the adoption process. The use of the COVID-19 tracing app in turn reduced the perceived privacy and performance risks but did not reduce social risks and health-related COVID-19 concerns.ConclusionsThis study contributes to the mass adoption of health care technology and URT research by integrating interactive communication measures and transparency as a multidimensional concept to reduce different types of uncertainty over time. Furthermore, our results help to derive communication strategies to promote the mass adoption of COVID-19 tracing apps, thus detecting infection chains and allowing intelligent COVID-19 testing.

A Fuzzy Multiple Criteria Decision Making Approach with a Complete User Friendly Computer Implementation.

The paper presents the generalization of the almost forty years of experience in the field of setting and solving the multiple criteria decision-making (MCDM) problems in various branches of a human activity under different types of uncertainties that inevitably accompany such problems. Based only on the pragmatic intentions, the authors avoid the detailed descriptions of the known methods for the decision-making, while instead focusing on the most frequently used mathematical tools and methodologies in the decision-making practice. Therefore, the paper may be classified as a special kind of illustrative review of the mathematical tools that are focused on applications and are the most used in the solutions of MCDM problems. As an illustrative example, a complete user-friendly computer implementation of such tools and methodology is presented with application to the simple “buying a cat” problem, which, however, possesses all the attributes of the hierarchical fuzzy MCDM task.