Over a billion people live in slums, with poor sanitation, education, property rights and working conditions having direct impact on current residents and future generations. A key problem in relation to slums is slum mapping. Without delineations of where all slum settlements are, informed decisions cannot be made by policymakers in order to benefit the most in need. Satellite images have been used in combination with machine learning models to try and fill the gap in data availability of slum locations. Deep learning has been used on RGB images with some success but since labeled satellite images of slums are relatively low quality and the physical/visual manifestation of slums significantly varies within and across countries, it is important to quantify the uncertainty of predictions for reliable application in downstream tasks. Our solution is to train Monte Carlo dropout U-Net models on multispectral 13-band Sentinel-2 images from which we can calculate pixelwise epistemic (model) and aleatoric (data) uncertainty in our predictions. We trained our model on labelled images of Mumbai and verified our epistemic and aleatoric uncertainty quantification approach using altered models trained on modified datasets. We also used SHAP values to investigate how the different features contribute towards the model’s predictions and this showed that certain short-wave infrared and red-edge image bands are powerful features for determining the locations of slums within images. Having created our model with uncertainty quantification, in the future it can be applied to downstream tasks and decision-makers will know where predictions have been made with low uncertainty, giving them greater confidence in its deployment.

: Mistrust, amplified by numerous artificial intelligence (AI) related incidents, has caused the energy and industrial sectors to be amongst the slowest adopter of AI methods. Central to this issue is the black-box problem of AI, which impedes investments and fast becoming a legal hazard for users. Explainable AI (XAI) is a recent paradigm to tackle this challenge. Being the backbone of the industry, the prognostic and health management (PHM) domain has recently been introduced to XAI. However, many deficiencies, particularly lack of explanation assessment methods and uncertainty quantification, plague this young field. In this paper, we elaborate a framework on explainable anomaly detection and failure prognostic employing a Bayesian deep learning model to generate local and global explanations from the PHM tasks. An uncertainty measure of the Bayesian model is utilized as marker for anomalies expanding the prognostic explanation scope to include model’s confidence. Also, the global explanation is used to improve prognostic performance, an aspect neglected from the handful of PHM-XAI publications. The quality of the explanation is finally examined employing local accuracy and consistency properties. The method is tested on real-world gas turbine anomalies and synthetic turbofan data failure prediction. Seven out of eight of the tested anomalies were successfully identified. Additionally, the prognostic outcome showed 19% improvement in statistical terms and achieved the highest prognostic score amongst best published results on the topic.

Projected future sea level rise and marine storminess is a serious threat for beaches as they induce beach flooding and erosion. Among other factors, wave runup play an important role in beach evolution and must be robustly assessed. However, little attention has been paid to the uncertainties associated to its characterization and how do they compare to other sources of uncertainty. As a first step towards this goal, we have quantified the impact of several sources of error in the estimation of wave runup on sandy beaches. Understanding what factors are more influential in the quality of the results will help to determine the main sources of uncertainty in beach flooding projections. To reach that goal, a calibrated state-of-the-art numerical modelling system has been setup for two beaches in the Mallorca islands (NW Mediterranean). The system has been forced with the best available information of nearshore incoming waves and has been validated against observations to define the benchmark quality. To determine the key factors affecting the quality of the system’s results, different systems configurations have been tested with different degrees of complexity.Our results show that using the most sophisticated modelling system with the best information on boundary conditions, bottom bathymetry, and submerged vegetation leads to a swash RMSE comparable to the standard deviation of the observed swash. We have also found that the choice of lateral boundary conditions (i.e., source of information for the incoming waves) can double the RMSE and induce large biases. Our results also show that using a simple empirical approach usually underestimates the wave runup. However, in locations with vegetated seabed there is a compensation error, and the empirical approach can lead to acceptable results if forced by nearshore waves. In addition, we have compared the error estimates obtained with uncertainties associated to projected sea level rise. Our findings suggest that the uncertainty associated with wave runup modelling should be considered in the assessment of the total uncertainty of future beach flooding, since the analysis performed indicates that this uncertainty can account for between 16% to 60% of the uncertainties linked to mean sea level projections.

Surrogate model based optimization method is widely-used to accelerate the design and optimization process~\cite{marler2004survey}. The input of regression model used in the surrogate model are numbers, which requires users to parametrize the geometries. In this paper, a new parameterization-free surrogate model is introduced and its corresponding uncertainty quantification and sensitivity analysis method are discussed. The input of new surrogate model methods is surface mesh of simulation domain. \Gls{gnns} is used to extract geometric information, and \Gls{cnns} is used to predict contours. This framework bypasses parameterization,as a consequence, uncertainties introduced by manual parameterization is reduced. However, such changes compared with conventional surrogate model methods impose great challenge on uncertainties quantification and sensitivity analysis. Uncertainties quantification in this paper means the error bar of prediction results, which is calculated by Gaussian Process Regression method in current surrogate method. In this paper, a new quantification method achieved by Kullback-Leibler divergence (KLD) is introduced. And the sensitivity analysis is conducted by Automatic Differentiation, which gives a Jacobian matrix of inputs. The method and analysis mentioned above are demonstrated by a low-pressure steam turbine rotator and its exhaust system.

We consider a class of density-driven flow problems. We are particularly interested in the problem of the salinization of coastal aquifers. We consider the Henry saltwater intrusion problem with uncertain porosity, permeability, and recharge parameters as a test case. The reason for the presence of uncertainties is the lack of knowledge, inaccurate measurements, and inability to measure parameters at each spatial or time location. This problem is nonlinear and time-dependent. The solution is the salt mass fraction, which is uncertain and changes in time. Uncertainties in porosity, permeability, recharge, and mass fraction are modeled using random fields. This work investigates the applicability of the well-known multilevel Monte Carlo (MLMC) method for such problems. The MLMC method can reduce the total computational and storage costs. Moreover, the MLMC method runs multiple scenarios on different spatial and time meshes and then estimates the mean value of the mass fraction. The parallelization is performed in both the physical space and stochastic space. To solve every deterministic scenario, we run the parallel multigrid solver ug4 in a black-box fashion. We use the solution obtained from the quasi-Monte Carlo method as a reference solution.

Industrial dynamical systems often exhibit multi-scale response due to material heterogeneities, operation conditions and complex environmental loadings. In such problems, it is the case that the smallest length-scale of the systems dynamics controls the numerical resolution required to effectively resolve the embedded physics. In practice however, high numerical resolutions is only required in a confined region of the system where fast dynamics or localized material variability are exhibited, whereas a coarser discretization can be sufficient in the rest majority of the system. To this end, a unified computational scheme with uniform spatio-temporal resolutions for uncertainty quantification can be very computationally demanding. Partitioning the complex dynamical system into smaller easier-to-solve problems based of the localized dynamics and material variability can reduce the overall computational cost. However, identifying the region of interest for high-resolution and intensive uncertainty quantification can be a problem dependent. The region of interest can be specified based on the localization features of the solution, user interest, and correlation length of the random material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update our prior knowledge on the localized region of interest using measurements and system response. To address the computational cost of the Bayesian inference, we construct a Gaussian process surrogate for the forward model. Once, the localized region of interest is identified, we use polynomial chaos expansion to propagate the localization uncertainty. We demonstrate our framework through numerical experiments on a three-dimensional elastodynamic problem

Validation of the TROPOspheric Monitoring Instrument (TROPOMI) SIF product is a necessity to evaluate its feasibility in various applications. A few validation works have been conducted through direct comparison with in-situ SIF retrievals or cross-comparison with similar satel-lite-based SIF or vegetation index (VI) products. Nevertheless, the influence of the geolocation mismatch between the validation pixel and reference data on validation results was never con-sidered. This study, for the first time, quantifies the geolocation shift of the TROPOMI validation pixel based on a geometric location matching method and then the uncertainty caused by the ge-olocation mismatch. The results indicate that the geolocation shift of the TROPOMI pixel shows large temporal variations, with a standard deviation of 2.45 km and 1.96 km in the across- and along-track directions. The mean shifts are 0.07 km and 0.25 km in the across- and along-track directions respectively, indicating eastward shifts in the across-track direction and northward shifts in the along-track direction in general. More than half (42/54) of the time periods showed relative uncertainty larger than 5%, with the maximum even reaching 55.7%. Hence, the uncertainty caused by geolocation mismatch should be fully considered in the validation of satellite SIF products, especially over heterogeneous surfaces.

Early spaceborne laser altimetry mission development starts in pre-phase A design, where diverse ideas are evaluated against mission science requirements. A key challenge is predicting realistic instrument performance through forward modeling at arbitrary spatial scale. Analytical evaluations compromise accuracy for speed, while radiative transfer modeling is not applicable at global scale due to computational expense. Instead of predicting arbitrary properties of a lidar measurement, we develop a baseline theory to predict only the distribution of uncertainty specifically for the terrain elevation retrieval based on terrain slope and fractional canopy cover features through a deep neural network gaussian mixture model, also known as a mixture density network (MDN). Training data was created from differencing geocorrected GEDI L2B elevation measurements with 32 independent reference lidar datasets in the contiguous U.S. from the National Ecological Observatory Network. We trained the MDN and selected hyperparameters based on regional distribution predictive capability. On average, the relative error of equivalent standard deviation of predicted regional distributions was 15.9%, with some anomalies in accuracy due to generalization and insufficient feature diversity and correlation. As an application, we predict the percent of elevation residuals of a GEDI-like lidar within a given mission threshold from 60°S to 78.25°N, which correlate to qualitative understanding of prediction accuracy and instrument performance.

In this paper we perform numerous numerical studies for the problem of low-rank matrix completion. We compare the Bayesian approaches and a recently introduced de-biased estimator which provides a useful way to build confidence intervals of interest. From a theoretical viewpoint, the de-biased estimator comes with a sharp minimax-optimal rate of estimation error whereas the Bayesian approach reaches this rate with an additional logarithmic factor. Our simulation studies show originally interesting results that the de-biased estimator is just as good as the Bayesian estimators. Moreover, Bayesian approaches are much more stable and can outperform the de-biased estimator in the case of small samples. However, we also find that the length of the confidence intervals revealed by the de-biased estimator for an entry is absolutely shorter than the length of the considered credible interval. These suggest further theoretical studies on the estimation error and the concentration for Bayesian methods as they are being quite limited up to present.

Raman-based Distributed Temperature Sensing (DTS) is a valuable tool for field testing and validating heat transfer models in Borehole Heat Exchanger (BHE) and Ground Source Heat Pump (GSHP) applications. However, temperature uncertainty is rarely reported in the literature. In this paper, a new calibration method is proposed for single-ended DTS configurations, along with a method to remove fictitious temperature drifts due to ambient air variations. The methods are implemented for a Distributed Thermal Response Test case study in an 800 m deep coaxial BHE. The results show that the calibration method and temperature drift correction are robust and give adequate results, with a temperature uncertainty of ± 0.58, 0.74, 1.1 and 1.7 K found at depths of 200, 300, 500 and 800 m, respectively. The temperature uncertainty increases non-linearly with depth and is dominated by the uncertainty in the calibrated parameters for depths larger than 200 m. The paper also offers insights into thermal features observed during the DTRT, including a heat flux inversion along the borehole depth and the slow temperature homogenization under circulation. Distributed temperature measurements and their uncertainties are useful tools in determining the strengths and drawbacks of ground heat transfer models.

While the foundations of climate science and ethics are well established, fine-grained climate predictions, as well as policy-decisions, are beset with uncertainties. This chapter maps climate uncertainties and classifies them as to their ground, extent and location. A typology of uncertainty is presented, centered along the axes of scientific and moral uncertainty. This typology is illustrated with paradigmatic examples of uncertainty in climate science, climate ethics and climate economics. Subsequently, the chapter discusses the IPCC’s preferred way of representing uncertainties and evaluates its strengths and weaknesses from a risk management perspective. Three general strategies for decision-makers to cope with climate uncertainty are outlined, the usefulness of which largely depends on whether or not decision-makers find themselves in a context of deep uncertainty. The chapter concludes by offering two recommendations to ease the work of policymakers, faced with the various uncertainties engrained in climate discourse.

Let $(\Omega, \mu)$, $(\Delta, \nu)$ be measure spaces and $\{\tau_\alpha\}_{\alpha\in \Omega}$, $\{\omega_\beta\}_{\beta \in \Delta}$ be 1-bounded continuous Parseval frames for a Hilbert space $\mathcal{H}$. Then we show that \begin{align}\label{UE} \log (\mu(\Omega)\nu(\Delta))\geq S_\tau(h)+S_\omega (h)\geq -2 \log \left(\frac{1+\displaystyle \sup_{\alpha \in \Omega, \beta \in \Delta}|\langle\tau_\alpha , \omega_\beta\rangle|}{2}\right) , \quad \forall h \in \mathcal{H}_\tau \cap \mathcal{H}_\omega, \end{align} where \begin{align*} &\mathcal{H}_\tau := \{h_1 \in \mathcal{H}: \langle h_1 , \tau_\alpha \rangle \neq 0, \alpha \in \Omega\}, \quad \mathcal{H}_\omega := \{h_2 \in \mathcal{H}: \langle h_2, \omega_\beta \rangle \neq 0, \beta \in \Delta\},\\ &S_\tau(h):= -\displaystyle\int\limits_{\Omega}\left|\left \langle \frac{h}{\|h\|}, \tau_\alpha\right\rangle \right|^2\log \left|\left \langle \frac{h}{\|h\|}, \tau_\alpha\right\rangle \right|^2\,d\mu(\alpha), \quad \forall h \in \mathcal{H}_\tau, \\ & S_\omega (h):= -\displaystyle\int\limits_{\Delta}\left|\left \langle \frac{h}{\|h\|}, \omega_\beta\right\rangle \right|^2\log \left|\left \langle \frac{h}{\|h\|}, \omega_\beta\right\rangle \right|^2\,d\nu(\beta), \quad \forall h \in \mathcal{H}_\omega. \end{align*} We call Inequality (\ref{UE}) as \textbf{Continuous Deutsch Uncertainty Principle}. Inequality (\ref{UE}) improves the uncertainty principle obtained by Deutsch \textit{[Phys. Rev. Lett., 1983]}. We formulate Kraus conjecture for 1-bounded continuous Parseval frames. We also derive continuous Deutsch uncertainty principles for Banach spaces.

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

Measurement uncertainty is typically expressed in terms of a symmetric interval , where denotes the measurement result and the expanded uncertainty. However, in the case of heteroscedasticity, symmetric uncertainty intervals can be misleading. In this paper, a different approach for the calculation of uncertainty intervals is introduced. This approach is applicable when a validation study has been conducted with samples with known concentrations. It will be shown how, under certain circumstances, asymmetric uncertainty intervals arise quite naturally and lead to more reliable uncertainty intervals.

Let $(\Omega, \mu)$, $(\Delta, \nu)$ be measure spaces. Let $(\{f_\alpha\}_{\alpha\in \Omega}, \{\tau_\alpha\}_{\alpha\in \Omega})$ and $(\{g_\beta\}_{\beta\in \Delta}, \{\omega_\beta\}_{\beta\in \Delta})$ be unbounded continuous 1-Schauder frames for a Banach space $\mathcal{X}$. Then for every $x \in ( \mathcal{D}(\theta_f) \cap\mathcal{D}(\theta_g))\setminus\{0\}$, we show that \begin{align}\label{UB} \mu(\operatorname{supp}(\theta_f x))\nu(\operatorname{supp}(\theta_g x)) \geq \frac{1}{\left(\displaystyle\sup_{\alpha \in \Omega, \beta \in \Delta}|f_\alpha(\omega_\beta)|\right)\left(\displaystyle\sup_{\alpha \in \Omega , \beta \in \Delta}|g_\beta(\tau_\alpha)|\right)}. \end{align} where \begin{align*} &\theta_f:\mathcal{D}(\theta_f) \ni x \mapsto \theta_fx \in \mathcal{L}^1(\Omega, \mu); \quad \theta_fx: \Omega \ni \alpha \mapsto (\theta_fx) (\alpha):= f_\alpha (x) \in \mathbb{K},\\ &\theta_g: \mathcal{D}(\theta_g) \ni x \mapsto \theta_gx \in \mathcal{L}^1(\Delta, \nu); \quad \theta_gx: \Delta \ni \beta \mapsto (\theta_gx) (\beta):= g_\beta (x) \in \mathbb{K}. \end{align*} We call Inequality (\ref{UB}) as \textbf{Unbounded Donoho-Stark-Elad-Bruckstein-Ricaud-Torr\'{e}sani Uncertainty Principle}. Along with recent \textbf{Functional Continuous Uncertainty Principle} (derived in [arXiv:2308.00312v1 [math.FA], 1 August 2023]), Inequality (\ref{UB}) also improves Ricaud-Torr\'{e}sani uncertainty principle \textit{[IEEE Trans. Inform. Theory, 2013]}. In particular, it improves Elad-Bruckstein uncertainty principle \textit{[IEEE Trans. Inform. Theory, 2002]} and Donoho-Stark uncertainty principle \textit{[SIAM J. Appl. Math., 1989]}.

The hot wire anemometer is a commonly used device for measuring air speed in laboratories. In this paper, the relationship between air speed and the hot wire temperature in different air speed ranges was analyzed based on the theory of thermal equilibrium. A measurement circuit and hot wire shape were designed based on the principle of the hot wire anemometer, and the linear relationship between current and temperature in the hot wire at different air speeds was verified in an adjustable air speed field. The measured current was used to represent air speed. The designed hot wire anemometer was experimentally validated to provide measurement results that match the theoretical values in different air speed ranges. Finally, the sensitivity of the anemometer in different measurement ranges was determined based on the uncertainty of the instrument's sensitivity and the measurement formula.

Bluecat is a recently proposed methodology to upgrade a deterministic model (D-model) into stochastic (S-model), based on the hypothesis that the information contained in a time series of observations and the concurrent predictions by the D-model is sufficient to support this upgrade. Prominent characteristics of the methodology are its simplicity and transparency, which allow easy use in practical applications, without sophisticated computational means. Here we utilize the Bluecat methodology and expand it in order to be combined with climatic model outputs, which often require extrapolation out of the range of values covered by observations. We apply the expanded methodology to the precipitation and temperature processes in a large area, namely the entire territory of Italy. The results showcase the appropriateness of the method for hydroclimatic studies, as regards the assessment of the performance of the climatic projections, as well as their stochastic conversion with simultaneous bias correction and uncertainty quantification.

Projects are rarely executed exactly as planned. Often, the actual durations of a project’s activities differ from the planned ones, resulting in costs stemming from the inaccurate estimation of the activities’ completion dates. While monitoring the project at various inspection points is pricy, it can lead to better estimation of the project completion time, hence saving on costs. Nonetheless, identifying the optimal inspection points is a difficult task, as it requires evaluating a large number of the project’s path options, even for small-scale projects. This paper proposes an analytical method for identifying the optimal project inspection points by using Information Theory measures. We search for monitoring (inspection) points that can maximize the information about the estimated project’s duration or completion time. The proposed methodology is based on a simulation-optimization scheme using a Monte Carlo engine that simulates potential activities’ durations. An exhaustive search is performed of all possible control points to find those with the highest expected information gain on the project duration. The proposed algorithm’s complexity is not affected the number of activities, and can address large projects with hundreds or thousands of activities. Numerical experimentation and analysis of various parameters are presented.

Starting from unidentified objects moving inside a two-dimensional Euclidean manifold, we propose a simple method to detect the topological changes that occur during their reciprocal interactions and shape morphing. This method, which allows the detection of topological holes development and disappearance, makes it possible to solve the uncertainty due to disconnectedness, lack of information and absence of objects’ sharp boundaries, i.e., the three troubling issues which prevent scientists to select the required proper sets/subsets during their experimental assessment of natural and artificial dynamical phenomena, such as fire propagation, wireless sensor networks, migration flows, neural networks’ and cosmic bodies’ analysis.

The relativistic effects of the dynamical properties of light at angular incidence were analyzed from the perspectives of Bohr indeterminacy and Heisenberg uncertainties and statistical dispersion. It was found that these effects report minimal uncertainties that agree with one or the other according to the angular range of incidence and that decrease with increasing refringence of the medium, constituting a specific relativistic uncertainty at angular incidence. An anomaly is indicated for the uncertainty principle in the Quantum Theory (QT) setting for small angles of incidence, where the accuracy of the angular position does not imply an increase in the uncertainty of the linear momentum. The anomalies arise because TQ does not predict the alternation between the classical and relativistic regimes of photon inertia at angular incidence. Specific relativistic uncertainty particularizes the uncertainty principle in the transmission of light between media pairs at angular incidence for the relativistic scenario, considering an observer that registers the relativistic effects of measurements that interfere with the observed system, in another inertial referential.

This research addresses the strategic issue of why key decision-makers fail to foresee potential extreme ‘black swan’ events. Following a review of the literature, a conceptual framework is developed that identifies two types of organisational blindness that are reflected in Tetlock’s hedgehog cognitive thinking style, being the oversimplification of uncertainty (e.g., inductive biases) and an unquestioned, top-down, reference narrative. This framework is tested using a case study approach and qualitative analysis of secondary data sources available from the Royal Commission of Inquiry and other published reports following the 2010 methane explosion at the Pike River Coal Ltd’s mine (Pike) in New Zealand, that killed 29 miners and caused the loss of all funds invested. The results indicate that the combined effect of both blindness’s meant that Pike’s collective intelligence was limited, and for the three key decision-makers at the Pike River mine, some type of extreme ‘black swan’ event was apparently inevitable. This research provides theoretical and practical contributions to the analysis of business and public policy decision-making under uncertainty.

Let $(\Omega, \mu)$, $(\Delta, \nu)$ be measure spaces. Let $(\{f_\alpha\}_{\alpha\in \Omega}, \{\tau_\alpha\}_{\alpha\in \Omega})$ and $(\{g_\beta\}_{\beta\in \Delta}, \{\omega_\beta\}_{\beta\in \Delta})$ be continuous 1-Schauder frames for a Banach space $\mathcal{X}$. Then for every $x \in \mathcal{X}\setminus\{0\}$, we show that \begin{align*} \mu(\operatorname{supp}(\theta_f x)) \geq \frac{1}{\displaystyle\sup_{\alpha \in \Omega, \beta \in \Delta}|f_\alpha(\omega_\beta)|}, \quad \nu(\operatorname{supp}(\theta_g x))\geq \frac{1}{\displaystyle\sup_{\alpha \in \Omega , \beta \in \Delta}|g_\beta(\tau_\alpha)|}. \end{align*} where \begin{align*} &\theta_f: \mathcal{X} \ni x \mapsto \theta_fx \in \mathcal{L}^1(\Omega, \mu); \quad \theta_fx: \Omega \ni \alpha \mapsto (\theta_fx) (\alpha):= f_\alpha (x) \in \mathbb{K},\\ &\theta_g: \mathcal{X} \ni x \mapsto \theta_gx \in \mathcal{L}^1(\Delta, \nu); \quad \theta_gx: \Delta \ni \beta \mapsto (\theta_gx) (\beta):= g_\beta (x) \in \mathbb{K}. \end{align*} This solves a problem asked by K. M. Krishna in the paper 'Functional Continuous Uncertainty Principle' \textit{[arXiv:2308.00312v1]}.

Let $(\Omega, \mu)$, $(\Delta, \nu)$ be measure spaces. Let $(\{f_\alpha\}_{\alpha\in \Omega}, \{\tau_\alpha\}_{\alpha\in \Omega})$ and $(\{g_\beta\}_{\beta\in \Delta}, \{\omega_\beta\}_{\beta\in \Delta})$ be continuous p-Schauder frames for a Banach space $\mathcal{X}$. Then for every $x \in \mathcal{X}\setminus\{0\}$, we show that \begin{align}\label{CUE} \mu(\operatorname{supp}(\theta_f x))^\frac{1}{p} \nu(\operatorname{supp}(\theta_g x))^\frac{1}{q} \geq \frac{1}{\displaystyle\sup_{\alpha \in \Omega, \beta \in \Delta}|f_\alpha(\omega_\beta)|}, \quad \nu(\operatorname{supp}(\theta_g x))^\frac{1}{p} \mu(\operatorname{supp}(\theta_f x))^\frac{1}{q}\geq \frac{1}{\displaystyle\sup_{\alpha \in \Omega , \beta \in \Delta}|g_\beta(\tau_\alpha)|}. \end{align} where \begin{align*} &\theta_f: \mathcal{X} \ni x \mapsto \theta_fx \in \mathcal{L}^p(\Omega, \mu); \quad \theta_fx: \Omega \ni \alpha \mapsto (\theta_fx) (\alpha):= f_\alpha (x) \in \mathbb{K},\\ &\theta_g: \mathcal{X} \ni x \mapsto \theta_gx \in \mathcal{L}^p(\Delta, \nu); \quad \theta_gx: \Delta \ni \beta \mapsto (\theta_gx) (\beta):= g_\beta (x) \in \mathbb{K} \end{align*} and $q$ is the conjugate index of $p$. We call Inequality (\ref{CUE}) as \textbf{Functional Continuous Uncertainty Principle}. It improves the Functional Donoho-Stark-Elad-Bruckstein-Ricaud-Torr\'{e}sani Uncertainty Principle obtained by M. Krishna in \textit{[arXiv:2304.03324v1, 2023]}. It also answers a question asked by Prof. Philip B. Stark to the author.

The aim of this article is to propose a core game theory model of transaction costs wherein it is indicated how direct costs determine the probability of loss and subsequent transaction costs. The existence of optimum is proven, and the way in which exposure influences the location of the optimum is demonstrated. The decisions are described as a two-player game and it is discussed how the transaction cost sharing rule determines whether the optimum point of transaction costs is the same as the equilibrium of the game. The dispute between actors regarding changing the share of transaction costs to be paid by each party is modeled by a non-cooperative bargaining game. Requirements of efficient transaction cost sharing rules are defined, and it is posited that solution exists which is not unique. Policy conclusions are also devised based on principles of design of institutions to influence the nature of transaction costs.

We define life as the amplification of quantum uncertainty up to macroscopic scales. A living being is any amplifier that achieves this goal. We argue that everything we know about life can be explained from this idea. We study a ladder mechanism to estimate the probability that the amplification occurs spontaneously in nature. The amplification mechanism is so sensitive to small variations of its own parameters that it acts as a bifurcation itself, i.e. it implies that the universe is either everywhere dead or alive wherever possible. Since the first option is excluded by the existence of life on earth, we infer that the universe hosts a huge number of inhabited planets (possibly one per star on average). We also investigate models of conscious and unconscious learning processes, as well as the structure of the brain and evolution. Finally, we address the problem of creating artificial life.

This paper examines a persuasion game between two agents with one-sided asymmetric information, where the informed agent can reveal her private information prior to playing a Battle-of-the-Sexes coordination game. We find that in the presence of strategic uncertainty in coordination there exists an equilibrium where there is no 'unraveling' of information. We provide a purification argument for this mixed strategy equilibrium to strengthen the central result, which is robust to several extensions, including both-sided asymmetric information and imprecise information revelation.

Energy Measurement and Verification (M&V) aims to make inferences about the savings achieved in energy projects, given the data and other information at hand. Traditionally, a frequentist approach has been used to quantify these savings and their associated uncertainties. We demonstrate that the Bayesian paradigm is an intuitive, coherent, and powerful alternative framework within which M&V can be done. Its advantages and limitations are discussed, and two examples from the industry-standard International Performance Measurement and Verification Protocol (IPMVP) are solved using the framework. Bayesian analysis is shown to describe the problem more thoroughly and yield richer information and uncertainty quantification than the standard methods while not sacrificing model simplicity. We also show that Bayesian methods can be more robust to outliers. Bayesian alternatives to standard M&V methods are listed, and examples from literature are cited.

The design flood concept (DF) provides for an essential tool in designing the hydraulic works, in defining the reservoir operation programs and for a reliable flood hazard identification. Under a simplified approach, the maximum discharge and the floods volume are statistically processed to reasonably define the DF. Yet, the integral hydrograph provides additional key temporal and quantitative details of important significance for flood management and particularly for the res-ervoirs operation and associated risks of failures. The procedure presented in this paper (as applied on a set of compatibly shaped hydrographs) involves the following key stages: (i) normalize the floods, (ii) define similar flood shape classes and (iii) evaluate the average dimensionless flood (ADF) for each class. The ADFs are finally transformed into a set of (DF)s. Many statistical distributions approximate acceptably the frequent values of the maximum discharges or the flood volumes, yet displaying a significant spread for medium or rare probabilities of exceedance (PE). This scattering, which can be explained by the epistemic uncertainty, defines an area of uncertainty both for measured and extrapolated values. In considering upper and lower values of the uncertainty in-tervals as limits for maximum discharges and flood volumes, then by combining them compatibly, a set of DFs - as completely defined hydrographs, with different shapes - results for each PE. The herein proposed procedure defines both one peak DF and multi-peaks DF. Subsequently, such DFs do assist water managers in examining and establishing tailored approaches for a variety of input hydrographs. Among the DFs that would correspond to a same PE, the most compact floods arise a special interest, for they are basic in defining the set of safe operation rules for hydraulic structures.

Integrating large-scale wind energy in modern power systems is demanding more efficient mathematical models to properly address classical assumptions in power system problems. In particular, there are two main assumptions in power system problems with wind integration that have not been adequately studied yet; First, non-linear AC power flow equations have been linearized in most of the literature. Such simplifications can lead to inaccurate power flow calculations that may result in other technical issues. Second, wind power uncertainties are inevitable and have been mostly modelled using the traditional uncertainty modelling approaches, that may not be suitable for large-scale wind power integration. In this paper, we address both challenges: we present a tight second-order conic relaxation (SOCR) for optimal power flow (OPF) problem, and simultaneously, implement the new effective budget of uncertainty approach for uncertainty modelling that determines the maximum wind power admissibility first and then addresses the uncertainty in the model. To the best of our knowledge, this is the first study that proposes an effective robust second-order conic programming (ERSOCP) model that simultaneously addresses the issues of power flow linearization and wind power uncertainty with the new paradigm on the budget of uncertainty approach. Our numerical results show the merit of the proposed model against traditional linearized power flow equations as well as traditional uncertainty modelling approaches.

To verify the reliability of the proposed stitching linear scan method for roundness measurement of small cylindrical workpieces, measurement uncertainties of the workpieces with various dimension are conducted. The cross-sectional circle of a cylindrical workpiece is divided into several equal arcs to be measured. Thus, the arc profile can be characterized according to the measured arcs. The roundness profile of the cylindrical part can be obtained by stitching these arc profiles together. Firstly, the measurement uncertainty of the workpiece with a diameter 1.5 mm and length 5.8 mm is evaluated to be 0.095 μm which can meet the uncertainty target of 0.1 μm. Considering the uncertainty of θx and θz which are the alignment around X-axis and Z-axis respectively changing with workpiece dimension changing, relevant uncertainties are carried out. As a result, there is no limitation with respect to workpiece diameter theoretically If the alignment can reach θz = θx = ±0.1° without considering the measurable range of the machine.

Properties of coherent states for the Heisenberg group over a field of $p$-adic numbers are investigated. It turns out that coherent states form an orthonormal basis. The family of all such bases is parametrized by a set of self-dual lattices in the phase space. The Wehrl entropy $S_W$ is considered and its properties are investigated. In particular, it is proved that $S_W\geq 0$ and vanishes only on coherent states. For a pair of different bases of coherent states, an entropic uncertainty relation is obtained. It is shown that the lower bound for the sum of the corresponding Wehrl entropies is given by the distance between the lattices. The proof uses the fact that the bases of coherent states corresponding to a pair of lattices are mutually unbiased.

The Ocean Color - Simultaneous Marine and Aerosol Retrieval Tool (OC-SMART) is a robust data processing platform that supports a large array of multi-spectral and hyper-spectral sensors. It provides accurate aerosol optical depths and remote sensing reflectances (Rrs estimates) that can be used to generate products such as absorption coefficients due to phytoplankton and detritus/Gelbstoff as well as backscattering coefficients due to particulate matter. The OC-SMART platform yields improved performance in complex environments by utilizing scientific machine learning (SciML) in conjunction with comprehensive radiative transfer computations. This paper expands the capability of OC-SMART by quantifying uncertainties in ocean color retrievals. Bayesian inversion is used to relate measured top of atmosphere radiances and a priori data to estimate posterior probability density functions and associated uncertainties. A framework of the methodology and implementation strategy is presented and uncertainty estimates for Rrs retrievals are provided to demonstrate the approach by applying it to MODIS, OLCI Sentinel-3, and VIIRS sensor data.

Land cover data are important basic data for earth system science and other fields. Multi-source remote sensing images have become the main data source for land cover classification. There are still many uncertainties in the scale effect of image spatial resolution on land cover classification. Since it is difficult to obtain multiple spatial resolution remote sensing images of the same area at the same time, the main current method to study the scale effect of land cover classification is to use the same image resampled to different resolutions, however errors in the resampling process lead to uncertainty in the accuracy of land cover classification. To study the land cover classification scale effect of different spatial resolutions of multi-source remote sensing data, we selected 1 m and 4 m of GF-2, 6 m of SPOT-6, 10 m of Sentinel-2 and 30 m of Landsat-8 multi-sensor data, and explored the scale effect of image spatial resolution on land cover classification from two aspects of mixed image element decomposition and spatial heterogeneity. For the study area, we compared the classification obtained from GF-2, SPOT-6, Sentinel-2, and Landsat-8 images at different spatial resolutions based on GBDT and RF. The results show that (1) GF-2 and SPOT-6 had the best classification results, and the optimal scale based on this classification accuracy was 4–6 m; (2) the optimal scale based on linear decomposition depended on the study area; (3) the optimal scale of land cover was related to spatial heterogeneity, i.e., the more fragmented and complex was the space, the smaller the scale needed; and (4) the resampled images were not sensitive to scale and increase the uncertainty of the classification. These findings have implications for land cover classification and optimal scale selection, scale effects and landscape ecology uncertainty studies.

Groundwater models serve as support tools to among others: assess water resources, evaluate management strategies, design remediation systems and optimize monitoring networks. Thus, the assimilation of information from observations into models is crucial to improve forecasts and reduce uncertainty of their results. As more information is collected routinely due to the use of automatic sensors, data loggers and real time transmission systems; groundwater modelers are becoming increasingly aware of the importance of using sophisticated tools to perform model calibration in combination with sensitivity and uncertainty analysis. Despite their usefulness, available approaches to perform this kind of analyses still present some challenges such as non-unique solution for the parameter estimation problem, high computational burden and a need of a deep understanding of the theoretical basis for the correct interpretation and use of their results, in particular the ones related to uncertainty analysis. We present a brief derivation of the main equations that serve as basis for this kind of analysis. We demonstrate how to use them to estimate parameters, assess the sensitivity and quantify the uncertainty of the model results using an example inspired by a real world setting. We analyze some of the main pitfalls that can occur when performing such kind of analyses and comment on practical approaches to overcome them. We also demonstrate that including groundwater flow estimations, although helpful in constraining the solution of the inverse problem as shown previously, may be difficult to apply in practice and, in some cases, may not provide enough information to significantly constrain the set of potential solutions.

Based on a previous risk calculation study along a road corridor, risk is recalculated using stochastic simulation by introducing variability for most of the parameters in the risk equation. This leads to an exceedance curve comparable to that of catastrophe models. This approach introduces uncertainty into the risk calculation in a simple way, which can be used for poorly documented cases to fulfil lack of data. This approach seems to tend to minimize risk or to question risk calculations.

A Robust Optimization framework with original concepts and fundamentals also admitting a fusion of ideals from relative regret models and static robust optimization, containing conservatism concepts is disclosed. The algorithm uses a fine-tune strategy to tune the model so the robustness and a target ideality can be mutually achieved with a specified risk. The framework comprises original concepts, a mathematical approach and an algorithm. The statistical treatment of the data with the original concepts from the framework make it able to make short, middle or long-term decision-making setting. The framework has high tractability since the algorithm forces the creation of a setting that makes a robust optimization with the specified risk. The framework can be applied in linear and nonlinear mathematical models since that the objective function is monotonic in the domain of the active convex region. Several examples are solved to best understand the framework and all results demonstrated high tractability and performance. There is a wide range of applications. Along all the text, there is a profound discussion about its philosophy, objective, original concepts, fields of application, statistical and probabilistic fundamentals.

This paper introduces a surrogate model to reduce the huge computational load in the process of simulation-optimization and uncertainty analysis. First, the groundwater numerical simulation model was established, calibrated and verified in the northeast of Hetao Plain. Second, two surrogate models of simulation model were established using support vector regression (SVR) method, one (surrogate model A, SMA) was used to describe the corresponding relationship between the pumping rate and average groundwater table drawdown, and another (surrogate model B, SMB) was used to express the corresponding relationship between the hydrogeological parameter values and average groundwater table drawdown. Third, an optimization model was established to search an optimal groundwater exploitation scheme using the maximum total pumping rate as objective function and the limitative average groundwater table drawdown as constraint condition, the SMA was invoked by the optimization model for obtaining the optimal groundwater exploitation scheme. Finally, the SMB was invoked in the process of uncertainty analysis for assessing the reliability of optimal groundwater exploitation scheme. Results show that the relative error and root mean square error between simulation model and the two surrogate models are both less than 5%, which is a high approximation accuracy. The SVR surrogate model developed in this study could not only considerably reduce the computational load, but also maintain high computational accuracy. The optimal total pumping rate is 7947 m3/d and the reliability of optimal scheme is 40.21%. This can thus provide an effective method for identifying an optimal groundwater exploitation scheme and assessing the reliability of scheme quickly and accurately.

Recent researches proved that the underbridge geometry can be reconstructed by mounting a 3D laser scanner on a motorized cart travelling on a walkway located under the bridge. The walkway is moved by a truck and the accuracy of the bridge model depends on the accuracy of the trajectory of the scanning head with respect to a fixed reference system. In this paper, we describe the metrological characterization of a method that uses non-contact systems to identify the relative motion of the cart with respect to the walkway; the orientation of the walkway with respect to the bridge is determined using inclinometers and optical rails, while the position of the truck with respect to the bridge is measured using a conventional odometer. The measurement uncertainty of the proposed system was initially evaluated by numerical simulations and successively verified by experiments in laboratory conditions. The complete system has then been tested in operative conditions; the validity of the proposed approach has been demonstrated by comparing the geometry of buildings reconstructed with the proposed system with the geometry obtained with a static scan. Results evidenced that the errors are approximately 6 mm.

Market uncertainty has a significant impact on market performance. Previous studies put much efforts in investigations on market uncertainty related to information asymmetry and risk. However, they have neglected the uncertainty inherent in market transactions, which is also an important aspect of market performance, besides quantity of transactions and market efficiency. In this paper, we put forward the concept of transaction entropy to measure the market uncertainty and see how it changes with price. The definition of transaction entropy is the ratio of total information entropy of all traders to quantity of transactions, reflecting the level of uncertainty in making transactions. And the transaction entropy is the lowest at equilibrium, it will be decreasing in a shortage market, and increasing in a surplus market. Additionally, we make a comparison of total entropy of the centralized market with that of the decentralized market, revealing that the price filtering mechanism could effectively reduce market uncertainty. Overall, the introduction of transaction entropy enriches our understanding of market uncertainty and facilitates a more comprehensive assessment of market performance.

Let $(\{f_j\}_{j=1}^n, \{\tau_j\}_{j=1}^n)$ and $(\{g_k\}_{k=1}^n, \{\omega_k\}_{k=1}^n)$ be two p-orthonormal bases for a finite dimensional Banach space $\mathcal{X}$. If $ x \in \mathcal{X}\setminus\{0\}$ is such that $\theta_fx$ is $\varepsilon$-supported on $M\subseteq \{1,\dots, n\}$ w.r.t. p-norm and $\theta_gx$ is $\delta$-supported on $N\subseteq \{1,\dots, n\}$ w.r.t. p-norm, then we show that \begin{align}\label{ME} &o(M)^\frac{1}{p}o(N)^\frac{1}{q}\geq \frac{1}{\displaystyle \max_{1\leq j,k\leq n}|f_j(\omega_k) |}\max \{1-\varepsilon-\delta, 0\},\\ &o(M)^\frac{1}{q}o(N)^\frac{1}{p}\geq \frac{1}{\displaystyle \max_{1\leq j,k\leq n}|g_k(\tau_j) |}\max \{1-\varepsilon-\delta, 0\},\label{ME2} \end{align} where \begin{align*} \theta_f: \mathcal{X} \ni x \mapsto (f_j(x) )_{j=1}^n \in \ell^p([n]); \quad \theta_g: \mathcal{X} \ni x \mapsto (g_k(x) )_{k=1}^n \in \ell^p([n]) \end{align*} and $q$ is the conjugate index of $p$. We call Inequalities (\ref{ME}) and (\ref{ME2}) as \textbf{Functional Donoho-Stark Approximate Support Uncertainty Principle}. Inequalities (\ref{ME}) and (\ref{ME2}) improve the finite approximate support uncertainty principle obtained by Donoho and Stark \textit{[SIAM J. Appl. Math., 1989]}.

Introduction: Lack of certainty or knowledge in health professions generates uncertainty, affecting clinical practice in decision-making (diagnostic or therapeutic), intervention design and therapeutic communication. In nursing, the lack of information to predict prognosis and outcome of interventions generates uncertainty: recognizing and managing it is essential for individualized, safe, and effective care. Objective: to assess uncertainty and the perception of a debriefing within the same shift ("intrathoracic pass") as a proposal for improvement. Method: ad-hoc survey of nursing professionals and Auxiliary Nursing Care Technicians (ANC). Variables: age, work experience, PRU scale (Physisicians' Reactions to Uncertainty) and additional question on intrathoracic pass. Results: Sample: 61 nurses and 10 TCAE (90.14 % female, 9.86 % male; mean age 35.18, standard deviation SD=13.04). Mean professional experience 11.74 years (SD=12.21); 56.33% had ≤4 years of experience. Origin: 49.30% Intensive Care Units (ICU), 11.27% Hospitalization, 7.04% Emergency, 1.41% Primary Care and 30.99% Other Services. The mean level of uncertainty was 27.99 points (max. possible 75; SD=7.50), with stress (mean=25.55, max. possible: 40; SD=5.24) and anxiety (mean=15.80, max. possible: 25; SD=3.05) as major manifestations. The association uncertainty-age (r=0.339; p=0.004) and uncertainty-experience (r=0.391; p=0.001) correlated negatively (the older and more experienced, the less uncertainty), with no significant differences between degrees or services. 91.55% stated that the intra-day pass was useful to reduce uncertainty during the working day. Conclusion: Uncertainty is frequent in nursing, and implementing the intrashift pass is perceived as a competent strategy.

Let $(\{f_j\}_{j=1}^n, \{\tau_j\}_{j=1}^n)$ and $(\{g_k\}_{k=1}^n, \{\omega_k\}_{k=1}^n)$ be two p-orthonormal bases for a finite dimensional Banach space $\mathcal{X}$. Let $M,N\subseteq \{1, \dots, n\}$ be such that \begin{align*} o(M)^\frac{1}{q}o(N)^\frac{1}{p}< \frac{1}{\displaystyle \max_{1\leq j,k\leq n}|g_k(\tau_j) |}, \end{align*} where $q$ is the conjugate index of $p$. Then for all $x \in \mathcal{X}$, we show that \begin{align}\label{FGJU} (1) \quad \quad \quad \quad \|x\|\leq \left(1+\frac{1}{1-o(M)^\frac{1}{q}o(N)^\frac{1}{p}\displaystyle\max_{1\leq j,k\leq n}|g_k(\tau_j)|}\right)\left[\left(\sum_{j\in M^c}|f_j(x)|^p\right)^\frac{1}{p}+\left(\sum_{k\in N^c}|g_k(x) |^p\right)^\frac{1}{p}\right]. \end{align} We call Inequality (1) as \textbf{Functional Ghobber-Jaming Uncertainty Principle}. Inequality (1) improves the uncertainty principle obtained by Ghobber and Jaming \textit{[Linear Algebra Appl., 2011]}.

As a fundamental, overall, and strategic issue facing human society, human migration is a key factor affecting the development of countries and cities given constantly changing population numbers. The fuzziness of the spatiotemporal attributes of human migration limits the pool of open-source data for human migration prediction, leading to a relative lag in human migration prediction algorithm research. This study expands the definition of human migration research, reviews the progress of research into human migration prediction, and classifies and compares human migration algorithms based on open-source data. It also explores the critical uncertainty factors restricting the development of human migration prediction. Given the effect of human migration prediction, in combination with artificial intelligence and big data technology, the paper concludes with specific suggestions and countermeasures aimed at enhancing human migration prediction research results to serve economic and social development and national strategy.

One of the most common forms of dementia is Alzheimer’s disease (AD), which leads to progressive mental deterioration. Unfortunately, there is no definitive diagnosis and cure that can stop the condition progressing. The diagnosis is often performed based on the clinical history and neuropsychological data, including magnetic resonance imaging (MRI). Deep neural networks (DNN) algorithms are gaining popularity for medical diagnosis, and have been used widely for the analysis of MRI data. DNNs can extract hidden features from thousands of training images automatically. However, they cannot judge how confident they are about their predictions. To use DNNs in safety-critical applications such as medical diagnosis, uncertainty quantification of DNNs predictions is crucial. For this purpose, Monte Carlo dropout (MCD) has been widely used, however, it may lead to overconfident and miss calibrated results. This paper proposes a framework in which the MCD algorithm’s hyper-parameters are optimized during training using Bayesian optimization for the first time. The conducted optimization leads to assigning high predictive entropy to erroneous predictions and making it possible to recognize risky predictions. The proposed framework is used for AD diagnosis, which has not been done before. We compare our method with some existing methods in the literature based on different uncertainty quantification criteria. The results of comprehensive experiments on the Kaggle dataset using a deep model pre-trained on the ImageNet dataset show that the proposed algorithm can quantify uncertainty much better than the existing methods.

This paper is a response to the EPR paper titled: "Can quantum-mechanical description of physical reality be considered complete?", published in Physical Review in 1935. A quantum-mechanical (QM) measurement function describes a distribution of local results and each empirical measurement process produces one result as exact as allowed by a measuring instrument calibrated to a non-local unit standard. Repeating these empirical measurements produces a bell shaped distribution of measurement results. Each of these distributions can be compared to the other. To precisely compare a QM measurement function describing a distribution of eigenvectors to a distribution of repetitive empirical measurement results, it is necessary to determine, by calibration, the precision of the eigenvectors to the same standard as the empirical results, because each eigenvector evidences uncertainty relative to a standard. When the calibration process is recognized as formal as well as empirical, QM measurement function results and metrology measurement process results are unified.

Problem. Image biomarker analysis, also known as radiomics, is a tool for tissue characterization and treatment prognosis that relies on routinely acquired clinical images and delineations. Due to the uncertainty in image acquisition, processing, and segmentation (delineation) protocols, radiomics often lacks reproducibility. Radiomics harmonization techniques have been proposed as a solution to reduce these sources of uncertainty and/or their influence on the prognostic model performance. A relevant question is how to estimate the protocol-induced uncertainty of a specific image biomarker, what the effect is on the model performance, and how to optimize the model given the uncertainty. In this manuscript, we show how protocol uncertainty can drastically reduce prognostic model performance. We introduce an effect-size measure η that assesses the protocol-induced uncertainty versus the measurable effect. Methods. Two non-small cell lung cancer (NSCLC) cohorts, composed of 421 and 240 patients respectively, were used for training and testing. Per patient, a Monte Carlo algorithm was used to generate three hundred synthetic contours with a surface dice tolerance measure less than 1.18 mm with respect to the original GTV. These contours were subsequently used to derive 104 radiomic features, which were ranked on their relative sensitivity to contour perturbation, expressed in the parameter η. The top four (low η) and the bottom four (high η) features were selected for two models based on Cox proportional hazards model. To investigate the influence of segmentation uncertainty on the prognostic model, we trained and tested the setup in 5000 augmented realizations (using a Monte Carlo sampling method); the log-rank test was used to assess the stratification performance and stability to segmentation uncertainty. Results. Although both low and high η setup showed significant testing set log-rank p-values (p=0.01) in the original GTV delineations (without segmentation uncertainty introduced), in the model with high uncertainty to effect ratio only around 30% of the augmented realizations resulted in model performance with p < 0.05 in the test set. In contrast, the low η setup performed with log-rank p < 0.05 in 90% of the augmented realizations. Moreover, the high η setup classification was uncertain for 50% of the subjects in the testing set (for 80% agreement rate), whereas the low η setup was uncertain only in 10% of the cases. The code and part of the data are available at https://github.com/Maastro-CDS-Imaging-Group/sure. Discussion. Estimating image biomarker model performance based only on the original GTV segmentation without considering segmentation uncertainty may be deceiving. The model might result in a significant stratification performance, but can be unstable for delineation variations, which are inherent to manual segmentation. Simulating segmentation uncertainty using the method described allows for more stable image biomarker estimation, selection, and model development. The segmentation uncertainty estimation method described here is universal and can be extended to estimate other protocol uncertainties (such as image acquisition and pre-processing).

The classical uncertainty principle inequalities were imposed as a mathematical constraint over the general relativity geodesic equation. In this way, the uncertainty principle was reformulated in terms of the proper space-time length element, Planck length and a geodesic-derived scalar, leading to a geometric expression for the uncertainty principle (GeUP). This re-formulation confirmed the necessity for a minimum length for the space-time line element in the geodesic, dependent on a geodesic-derived scalar which made the expression Lorentz-covariant. In agreement with quantum gravity theories, GeUP required the imposition of a perturbation over the background Minkowski metric unrelated to classical gravity. When applied to the Schwarzschild metric, a geodesic exclusion zone was found around the singularity where uncertainty in space-time diverged to infinity.

Background: The COVID-19 pandemic has hit the Spanish economy hard. The result is an unprecedented economic and social crisis due to uncertainty about the remedy, and due to the socio-economic effects on people’s lives. Methods: We performed a retrospective analysis of the macro-economic impact of COVID-19 in 2020, using the principal indicators of the Spanish economic and productive model. National statistics were examined in the search for impacts or anomalies occurring since the beginning of the pandemic. To estimate the strength of the impact on each of the indicators analysed, we used Bayesian structural time series. Results: In 2020, the cumulative impact on the Gross Domestic Product was of -11.41% [95% credible interval: -13.46; -9.29]. The indicator for Business Turnover fell by -9.37% [-12.71; -6.07]. The reduction in business activity was related to the sharp fall in demand. The Spanish employment market was strongly affected; our estimates showed a cumulative increase of 11.9% [4.27; 19.45] in the rate of unemployment during 2020. The autonomous communities which are economically the most heavily dependent on the services sector were those which recorded the worst indicators. Conclusions: Our estimates portray a dramatic situation in our country, and show all too clearly the fragility of a productive system which has to make the behavioural changes that are necessary to confront the COVID-19 pandemic.

The incorporation of wind generation introduces challenges to the operation of the power system due to its uncertain characteristics. Therefore, the development of methods to accurately model the uncertainty is necessary. In this paper, the spatio-temporal Kriging and analog approaches are used to forecast wind power generation and used as input to solve an economic dispatch problem, considering the uncertainties of wind generation. Spatio-temporal Kriging takes into account the spatial and temporal information given by the database to enhance wind forecasts. We evaluate the performance of using the spatio-temporal Kriging, and comparisons are carried out versus other approaches in the framework of the economic power dispatch problem, for which simulations are developed on the modified IEEE 3-bus and IEEE 24-bus test systems. The results show that the use of Kriging-based spatio-temporal models in the context of economic power dispatch can provide an opportunity for lower operating costs in the presence of uncertainty when compared to other approaches.

This paper focuses on quantifying the uncertainty in the specific absorption rate values of brain induced by the uncertain positions of the electroencephalography electrodes placed on patient's scalp. To avoid running a large number of simulations, an artificial neural network architecture for uncertainty quantification involving high-dimensional data is proposed in this paper. The proposed method is demonstrated to be an attractive alternative to conventional uncertainty quantification methods because of its considerable advantage in the computational expense and speed.

Uncertainty is the main source of risk of geological hazards in tunnel engineering. Uncertainty information not only affects the accuracy of evaluation results, but also affects the reliability of decision-making schemes. Therefore, it is necessary to evaluate and control the impact of uncertainty on risk. In this study, the problems in existing entropy-hazard model such as inefficient decision-making and failure of decision-making are analysed, and an improved uncertainty evaluation and control process are proposed. Then the tolerance cost, the key factor in the decision-making model, is also discussed. It is considered that the amount of change in risk value (R1) can better reflect the psychological behaviour of decision-makers. Thirdly, common attribute decision models, such as the expected utility-entropy model, are analysed, and then the viewpoint of different types of decision-making issues that require different decision methods is proposed. The well-known Allais paradox is explained by the proposed methods. Finally, the engineering application results show that the uncertainty control idea proposed here is accurate and effective. This research indicates a direction for further research into uncertainty, and risk control, issues affecting underground engineering works.

SLEUTH Model (slope, landuse, exclusion, urban extent, transportation and hillshade) is an important tool for landuse planning and land policy. To evaluate the performance of SLEUTH model, implementation of Sensitivity Analysis (SA) is essential. The main limitation of SA in SLEUTH application is a lack of insight into model input self-modification parameters (SMPs) variation, namely, uncertainty involved in the model transfer metrics and model presumptions, which often misled the decision makers and model users. To address this issue, this study divided the forward process into two stages. Firstly, during the transfer process ①, the contribution scores of five SMPs were drawn, and parameters highly sensitive to model output were given. Apart from that, the recommended initial value for SMPs of 0.11, 0.2, 0.87, 1.13, 15, 1.01, 0.49 were found to be subordinated to such a heterogeneous urban area simulation. Secondly, during the transfer process ②, SMP caused imagery metrics indicated the disparity between parameters with Fixed Reference and with Successive Reference. Reversely, it derives reasonable threshold for the best fit values of five prediction coefficients’ initialization by comparing the real image with the predicted one. The framework of SLEUTH model transfer mechanism not only could distinguish highly sensitive SMPs with higher contribution scores, but also could give parametric analysis for simulation imagery based on metrics. The study was found to be a practical tool for quantization response of model input variables for modelling complex urban systems. So, this insight can help geographic information scientists decide how to find out the inner forward transfer mechanism of SLEUTH model for further make good use of it and improve the model.

Hydro-climatic projections in West Africa are attributed with high uncertainties that are difficult to quantify. This study assesses the influence of the parameter sensitivities and uncertainties of three rainfall runoff models on simulated discharge in current and future times using meteorological data from 8 Global Climate Models. The IHACRES Catchment Moisture Deficit (IHACRES-CMD) model, the GR4J and the Sacramento model were chosen for this study. During model evaluation, 10,000 parameter sets have been generated for each model and used in a sensitivity and uncertainty analysis using the Generalized Likelihood Uncertainty Estimation (GLUE) method. Out of the three models, IHACRES-CMD recorded the highest Nash-Sutcliffe Efficiency (NSE) of 0.92 and 0.86 for the calibration (1997-2003) and the validation (2004-2010) period respectively. The Sacramento model was able to adequately predict low flow patterns on the catchment while the GR4J and IHACRES-CMD over and under estimate low flow respectively. The use of multiple hydrological models to reduce uncertainties caused by model approaches is recommended along with other methods of sustainable river basin managements.

Future projections from climate models and recent studies shows impact of climate change on rainfall indices estimation. This study assesses the simulations of rainfall indices based on the Coupled Model Intercomparison Project CMIP5 and CMIP3 in the some of subbasin Hamedan Province West of Iran. The analysis of the rainfall indices are: simple rainfall intensity, very heavy rainfall days, maximum one-day rainfall and rainfall frequency has been carried out in this study to evaluating the impact of climate change on rainfall indices events. Relative change in three rainfall indices is investigated by GCMs under various greenhouse gas emission scenarious A1B and B1 and RCP8.5, RCP8.5 scenarios for the future periods 2020–2045 and 2045-2065. The final results show that each of rainfall indices differs in stations under the three GCMs model (GIAOM, MIHR, MPEH5) and emission scenarios A1B and B1, and RCP2.5, RCP8.5 scenarios. Relative change of daily intensity index varies from -9.93% - 25%, very heavy rainfall days 20.71% - 25.9% and yearly rainfall depth -15.71% - 13% can be observed at study area in 50y for future periods (2046–2065). Rainfall indices of sum wet days, nday >1mm and maximum one-day rainfall are projected to decrease under the senariuos B1,A1B and sum wet days, simple daily intensity and heavy Rainfall days>10 projected to decrease under the RCP2.6.

Errors during manufacture of high value components are not acceptable nowadays in driving industries such as energy and transportation. Sectors such as aerospace, automotive, shipbuilding, nuclear power, large science facilities or wind power manufacture complex and accurate components that demand close measurements and fast feedback into manufacturing processes. New measuring technologies are already available in machine tools, including integrated touch probes and fast interface capabilities. They shall provide the possibility to measure the workpiece during or after the manufacturing process, maintaining the original setup of the workpiece and avoiding the manufacturing process from being interrupted to transport the workpiece to a measuring position. However, the traceability of the measurement process on a machine tool is not ensured yet and measurement data is still not fully reliable for process control or product validation. Due to the similarity between a coordinate measuring machine and a machine tool, some of the methods applied for a correct assessment of uncertainty in coordinate measuring machines are adapted to the challenges of a machine tool. The scientific objective is to determine the uncertainty on a machine tool measurement and, in this way, convert it into a machine integrated traceable measuring process. This paper reviews the fundamentals of machine tool metrology.

Visualizing geo-spatial data embedded into a three-dimensional terrain is challenging. The problem becomes even more complex when uncertainty information needs to be presented as well. This paper addresses the question of how to visually communicate all three aspects: the 3D terrain, the geo-spatial data, and the data-associated uncertainty. We argue that visualizing all aspects with a high degree of detail will likely exceed the visual budget. Therefore, we propose a visualization strategy based on prioritizing a selected aspect and presenting the remaining two with less detail. We discuss various design options that allow us to obtain differently prioritized visual representations. Our approach has been implemented as a tool for rapid visualization prototyping in the context of avionics applications. Practical solutions are described for a use case related to the visualization of 3D terrain and uncertain weather data.

In this paper, aiming at the safety evaluation of ultimate bearing safety capacity of ultra-high-performance-concrete (UHPC) composite pile bridge foundation, the symmetrical reliability method with forward and inverse analysis considering the randomness of parameters is proposed to evaluate the safety performance of composite pile foundation. The proposed method, consid-ering the randomness of parameters, was used to calculate the safety factor of ultimate bearing capacity of composite pile foundation to meet the prescribed target reliability requirements. An example was used to verify the correctness of the proposed method. The proposed method was applied to an actual engineering example and the sensitivity of the parameters were analyzed, the calculation results show that: ignoring the randomness of the parameters will overestimate the safety of the composite pile foundation; the target reliability index has a great influence on the safety of composite pile foundation; the influence of statistical parameters of random variables on the safety of UHPC composite pile foundation cannot be neglected; the initial iteration value of the safety factor has no effect on the final calculation result. The proposed method has high ac-curacy and applicability, and provides an effective way for the safety factor estimation of ultimate carrying capacity of UHPC composite pile foundation.

Estimating peak flow for a catchment is commonly undertaken using the design event method, however this method does not allow for the understanding of uncertainty in the result. This research first presents a simplified method of fragments approach to rainfall disaggregation that ignores the need to consider seasonality, offering a greater diversity in storm patterns within the resulting sub-daily rainfall. By simulating 20 iterations of the disaggregated sub-daily rainfall within a calibrated continuous simulation hydrologic model, we were able to produce multiple long series of stream flow at the outlet of the catchment. With this data, we investigated the use of both the annual maximum and peaks over threshold approaches to flood frequency analysis and found that for a one in 100 year annual exceedance probability peak flow, the peaks over threshold method (333m3/s ±50m3/s) was significantly less uncertain than the annual maximum method (427m3/s ±100m3/s). For the one in 100 year annual exceedance probability, the median peak flow from the peaks over threshold method (333m3/s) produced an outcome comparable to the design event method peak flow (328m3/s), indicating that this research offers an alternative approach to estimating peak flow, with the additional benefit of understanding the uncertainty in the estimation. Finally, the paper highlighted the impact that length and period of streamflow has on peak flow estimation and noted that previous assumptions around the minimum length of gauged streamflow required for flood frequency analysis may not be appropriate in particular catchments.

Abstract Background. There is an inherent limit in the accuracy of our measurements, set by nature itself and predicted by Heisenberg's uncertainty principle, which defines the properties of nature in the microcosmos. There is a fundamental limit to the accuracy with which complementary phys-ical quantities of a particle can be predicted from their initial conditions. As classical physics is essentially considered at borderline of quantum mechanics, so the power of uncertainty princi-ple is limited in describing everyday life perceived or managed phenomena. Method. In this study, we apply Heisenberg's uncertainty principle to children under diagnostic uncertainty re-garding appendicitis. We analyze this phenomenon in clinical practice. Results. Medical practice is full of uncertainty. False negative decisions correlate with delays in treatment and adverse outcomes in children with atypical appendicitis. On the other hand, false-positive surgery deci-sions result in negative appendectomies. With improvement of technology, the incidence of complicated appendicitis or negative appendectomies due to diagnostic uncertainty has de-creased but cannot be ignored or eliminated. Conclusion. According to the principle, there is a fundamental limit to the accuracy with which the complementary variables of negative appen-dectomy and complicated appendicitis can be observed or measured simultaneously. What does all this mean for the physician?

When there is uncertainty in the value of parameters of the input random components of a stochastic simulation model, two-level nested simulation algorithms are used to estimate the expectation of performance variables of interest. In the outer level of the algorithm (n) observations are generated for the parameters, and in the inner level (m) observations of the simulation model are generated with the value of parameters fixed at the value generated in the outer level. In this article, we consider the case in which the observations at both levels of the algorithm are independent, showing how the variance of the observations can be decomposed into the sum of a parametric variance and a stochastic variance. Next, we derive central limit theorems that allow us to compute asymptotic confidence intervals to assess the accuracy of the simulation-based estimators for the point forecast and the variance components. Under this framework, we derive analytical expressions for the point forecast and the variance components of a Bayesian model to forecast sporadic demand; and we use these expressions to illustrate the validity of our theoretical results by performing simulation experiments using this forecast model.

A fundamental tool in mathematical physics is the logarithmic Sobolev inequality. A quantitative version proven by Carlen with a remainder involving the Fourier-Wiener transform is equivalent to an entropic uncertainty principle more general than the Heisenberg uncertainty principle. In the stability, the remainder is in terms of an entropy, not a metric. Recently, a stability result for H¹ was obtained by Dolbeault, Esteban, Figalli, Frank, and Loss in terms of an L^p norm. Afterwards, Brigati, Dolbeault, and Simonov discussed the stability problem involving a stronger norm. A full characterization with a necessary and sufficient condition to have H¹ convergence is identified in this paper. Moreover, an explicit H¹ bound via a moment assumption is shown. Also, the L^p stability of Dolbeault, Esteban, Figalli, Frank, and Loss is proven to be sharp.

The perception in pair trading is to recognize two stocks that move together, and their prices will converge to a mean value in future. However, finding the mean-reverted point at which the value of the pair will converge, and optimal boundaries of the trade is not easy. As uncertainty and model misspecifications may lead to losses. To cater for the problems, this study employs the novel entropic approach that utilizes entropy as penalty function for the misspecification of the model. The use of entropy as a measure of risk in pair trading is a nascent idea and this study utilizes daily data for 64 companies listed on PSX for the years 2017, 2018, and 2019, respectively to compute the returns based on the entropic approach. These companies cover the major sectors including Cement, Chemical, Automobile Assembler, Food and Personal Care Products, Oil and Gas Marketing Companies, Oil and Gas Exploration Companies Ltd, Power Generation and Distribution, Refinery and Pharmaceuticals. The returns to these stocks are then evaluated and compared with the Buy and Hold strategy. The results show positive and significant returns from pair trading using an entropic approach.

Science evolves over a gentle arc spanning centuries, with scientists building upon and extending the hypotheses and discoveries of their forebears when nurturing their own work from ideation to crystallization and finally implementation. However, evidence suggests several limitations of our modern academic pursuits including major inertia and epistemological biases to implement even major advancements. For instance, the transformative uncertainty principles of quantum mechanics are yet to be satisfactorily integrated in modern analyses and publications, even almost a century after Heisenberg received the Nobel prize for these. Another example is ever expanding reliance on mathematics to validate the hypotheses of Physics, and undermine the opinions to the contrary. In addition, modern science limits itself to the era post fifteenth century and hastily rejects premodern achievements despite glaring examples. This reluctance and inertia to capitalize on existing knowledge is a challenge that imperils our intellectual pursuits. A salient facet of science is "the willingness to admit ignorance". Only on this foundational principle can science meaningfully evolve. It is time we take a step back to evaluate widely accepted and foundational premises of modern science and institute structured processes to implement the treasure trove of knowledge amassed by our predecessors. This essay highlights some of the opportunities that can and should be availed capitalizing upon the recent developments of computational and analytical capabilities along with artificial intelligence.

The minimum requirement for uncertainty estimation is to use only intermediate precision (R_w), especially for measurands lacking a reference measurement system such as thyroid functions tests (TFT). In this study, measurement uncertainty (MU) for TSH and FT4 from long-term internal quality control (IQC) data was estimated while reference change values (RCV) were calculated from estimated MU. Furthermore, intermediate precision (R_w) was used to establish appropriate risk-based QC frequency. Twenty fore months of third party IQC data were collected retrospectively, on the Abbott ARCHITECT i1000sr analyzer from INSTITUT PASTEUR OF MSILA laboratory, ALGERIA. The MU, RCV and sigma-metric were estimated simply from the intermediate precision (R_w), while a nomogram relating sigma performance to run size was used to establish QC frequency. The MU for the TSH and FT4 was 12% and 8% respectively. The U _one-sided for the TSH and FT4 was 10%, 6.6% respectively. MU and U _one-sided of TSH and FT4 met quality requirements for permissible uncertainty (pU %) and allowable total error (ATE %). When monitoring thyroid replacement therapy, an upward minimum change (RCV) of 54% and 22% or a downward of 35% and 18% in serum TSH and FT4 respectively, would be considered significant. Optimal QC strategy for serum TSH was selected to run 4 QC materials every 190 patients sample and to use a multi-rule (1_3s/2_2s/R_4s/4_1s). Our results suggest that MU estimation from long-term IQC alone may be acceptable for TFT to assist physician in results interpretation and to establish appropriate QC frequency.

The study's motivation is to gauge the nexus between economic policy uncertainty and financial innovation for the period 2004M1 to 2018M12 in BRIC nations. For establishing a long-run cointegration study applied Autoregressive Distributed Lagged (ARDL) and asymmetry effects of economic policy uncertainty investigated following nonlinear framework known as NARDL. Furthermore, directional causality is established by performing a non-granger causality test. Cointegration test results of Fpss, Wpss, and tBDM confirmed the long-run association between EPU and financial innovation. On the other hand, the Wald test results proved asymmetry effects furring from EPU to financial innovation both in the long-run and short-run. Referring to asymmetry effects that positive and negative shocks in financial innovation, the study revealed that negative linkage between shocks in EPU and financial innovation in the long-run but short-run effects are insignificant. Furthermore, financial innovation measured by R&D investment exhibits positive linked with shocks in EPU, implying that uncertainty induces innovation in the economy. Refers to directional causality estimation, the study revealed evidence supporting the feedback hypothesis between EPU and financial innovation in all sample countries.

In this paper, we consider a make-to-order supply chain which satisfies demand that is dependent on both price and quoted lead -time. The manufacturer chooses the lead -time and the order quantity, and the retailer sets the revenue shares. The interactions between the manufacturer and the retailer are modelled as a Nash Game, and the existence and uniqueness of pure strategy equilibrium are demonstrated. A mechanism that enables the supply chain to coordinate the decisions of the members is developed. Lastly, we also analyze how the supply chain system parameters impact the optimal supply chain decisions and the supply chain performance.

Coastal inundation is an increasing problem. Sea-level rise will greatly increase the frequency and depth of inundation, forcing vulnerable communities to adapt. Communities will need to decide when and how to adapt. The process of decision-making along adaptive pathways is now being used internationally to plan for adaptation over time by anticipating decision points in the future however it unfolds. This process requires risk and uncertainty considerations to be transparent in the scenarios used in such planning. We outline a framework for uncertainty identification and management within coastal hazard assessments which recognizes different types of decision and identifies the types of uncertainty that must be accounted for, such as statistical, scenario and deep uncertainty types. We show how coastal-inundation hazard can be mapped and presented in a way that clearly separates sources of uncertainty, so that they are transparent within a dynamic adaptive pathways planning process. Traditional coastal inundation maps show inundated area only. We present maps of inundation depth and frequency which clearly show the degree of exposure, where that exposure occurs, and how much sea-level rise can be tolerated. The new uncertainty framework and mapping techniques can better identify decision points and their expected time range, which provides more useful input to the adaptation process than traditional coastal inundation assessments.

Sustainability is a characteristic manifested in the ability to maintain the necessary level of performance for construction companies when risk factors arise during the implementation of investment and construction projects. The risk factors that arise during the implementation of in-vestment and construction projects differ in nature, degree of influence, and other characteristics. Ignoring these factors and measures to manage them often leads to critical consequences in the form of disruptions in the timing of work. Risk is a combination of the probability and consequences of the occurrence of adverse events. The article considers the concept of risk as a potential possibility of occurrence of adverse situations and related consequences when exposed to these factors. Risk factors are characterized by surprise, discreteness of changes, the presence of threshold values, upon reaching which a transition to a different mode of operation is required. The article discusses the risk factors arising at the construction stage, their classification. A methodology has been developed that includes conducting a survey in the form of a questionnaire in order to collect information about risk factors that affect the implementation of investment and construction projects. Experts with experience in the construction sector were involved in the survey. The processing of the survey results made it possible to assess the significance of various risk factors in investment and construction projects. Thus, statistical and expert methods were used in the study. The results showed that financial, technical, legal, economic, managerial and natural factors have the greatest impact on investment and construction projects. It is recommended to pay special attention to the listed factors when developing measures aimed at preventing risks and their consequences. The methodology described in the study can be used by construction companies in strategic planning. The analysis of the stability of construction companies, depending on their use of various ways to counteract risk factors, allowed us to develop a number of practical recommendations to reduce the impact of the studied factors on achieving the goals of investment and construction projects.

This paper presents a novel algorithm, the multi-objective nonlinear interval PageRank (MONIPR) Algorithm. This algorithm extends the conventional PageRank (PR) algorithm, integrating nonlinear interval computation and multi-objective considerations into the computation process. The MONIPR algorithm bridges a research gap in integrating nonlinear interval approaches and multi-objective problems into the PR algorithm, which were traditionally treated separately. In addition, this research adopts the constrained interval arithmetic proposed to address the limitations of the conventional PR algorithm, which tends to overlook uncertainties and results in deterministic outcomes. In addition, we use a numerical example to demonstrate the proposed algorithm, contrasting it with the conventional approaches. A numerical example demonstrates the algorithm's performance by comparing the rank intervals obtained with the traditional crisp Markov chain and PR algorithm. The results highlight the ability of the proposed algorithm to provide a range of possible rank intervals, considering both uncertainty and multi-objectives. The findings suggest potential applications in decision-making, uncertainty quantification, and systems analysis.

Let $\{f_j\}_{j=1}^n$ and $\{g_k\}_{k=1}^m$ be Parseval p-frames for a finite dimensional Banach space $\mathcal{X}$. Then we show that \begin{align}\label{UE} \log (nm)\geq S_f (x)+S_g (x)\geq -p \log \left(\displaystyle\sup_{y \in \mathcal{X}_f\cap \mathcal{X}_g, \|y\|=1}\left(\max_{1\leq j\leq n, 1\leq k\leq m}|f_j(y)g_k(y)|\right)\right), \quad \forall x \in \mathcal{X}_f\cap \mathcal{X}_g, \end{align} where \begin{align*} &\mathcal{X}_f\coloneqq \{z\in \mathcal{X}: f_j(z)\neq 0, 1\leq j \leq n\}, \quad \mathcal{X}_g\coloneqq \{w\in \mathcal{X}: g_k(w)\neq 0, 1\leq k \leq m\},\\ &S_f (x)\coloneqq -\sum_{j=1}^{n}\left|f_j\left(\frac{x}{\|x\|}\right)\right|^p\log \left|f_j\left(\frac{x}{\|x\|}\right)\right|^p, \quad S_g (x)\coloneqq -\sum_{k=1}^{m}\left|g_k\left(\frac{x}{\|x\|}\right)\right|^p\log \left|g_k\left(\frac{x}{\|x\|}\right)\right|^p, \quad \forall x \in \mathcal{X}_g. \end{align*} We call Inequality (1) as \textbf{Functional Deutsch Uncertainty Principle}. For Hilbert spaces, we show that Inequality (1) reduces to the uncertainty principle obtained by Deutsch \textit{[Phys. Rev. Lett., 1983]}. We also derive a dual of Inequality (1).

Nowadays, the selection of web services with uncertain quality of service (QoS) is gaining a lot of attention in the service-oriented computing paradigm (soc). In fact, searching for a service composition that fulfills a complex user’s request is known to be NP-Complete. The search time is mainly dependent on the number of the requested tasks, the size the available services, and the size of the QoS realizations (i.e., sample size). To handle this problem, we propose a two-stage approach that reduces the search space using heuristics for ranking the tasks’ services and a bat algorithm metaheuristic for selecting the final near optimal compositions. The fitness used by the metaheuristic aims to fulfill all the global constraints of the user. The experimental study shows that the ranking heuristics, termed “fuzzy pareto dominance” and "Zero-order stochastic dominance", are highly effective than the other heuristics and most of the existing state-of-the-art methods.

We derive a quantum speed limit for unitary evolution for the case of mixed quantum states using the stronger uncertainty relation for mixed quantum states. This bound can be optimized over different choices of Hermitian operators for a better bound. We illustrate this with some examples and show its better performance with respect to three existing bounds for mixed quantum states.

Let $(\{f_j\}_{j=1}^n, \{\tau_j\}_{j=1}^n)$ and $(\{g_k\}_{k=1}^m, \{\omega_k\}_{k=1}^m)$ be p-Schauder frames for a finite dimensional Banach space $\mathcal{X}$. Then for every $x \in \mathcal{X}\setminus\{0\}$, we show that \begin{align}\label{UE} \|\theta_f x\|_0^\frac{1}{p}\|\theta_g x\|_0^\frac{1}{q} \geq \frac{1}{\displaystyle\max_{1\leq j\leq n, 1\leq k\leq m}|f_j(\omega_k)|}\quad \text{and} \quad \|\theta_g x\|_0^\frac{1}{p}\|\theta_f x\|_0^\frac{1}{q}\geq \frac{1}{\displaystyle\max_{1\leq j\leq n, 1\leq k\leq m}|g_k(\tau_j)|}. \end{align} where \begin{align*} \theta_f: \mathcal{X} \ni x \mapsto (f_j(x) )_{j=1}^n \in \ell^p([n]); \quad \theta_g: \mathcal{X} \ni x \mapsto (g_k(x) )_{k=1}^m \in \ell^p([m]) \end{align*} and $q$ is the conjugate index of $p$. We call Inequality (\ref{UE}) as \textbf{Functional Donoho-Stark-Elad-Bruckstein-Ricaud-Torr\'{e}sani Uncertainty Principle}. Inequality (\ref{UE}) improves Ricaud-Torr\'{e}sani uncertainty principle \textit{[IEEE Trans. Inform. Theory, 2013]}. In particular, it improves Elad-Bruckstein uncertainty principle \textit{[IEEE Trans. Inform. Theory, 2002]} and Donoho-Stark uncertainty principle \textit{[SIAM J. Appl. Math., 1989]}.

This paper is a response to the EPR paper titled: "Can quantum-mechanical description of physical reality be considered complete?", published in Physical Review in 1935. A quantum-mechanical (QM) measurement function describes a distribution of local results, while each empirical measurement process produces one result as exact as allowed by a measuring instrument calibrated to a non-local unit standard. Repeating these empirical measurements produces a Gaussian distribution of measurement results. The QM and empirical measurement result distributions can be compared. To precisely compare a QM measurement function describing a distribution of eigenvectors to a distribution of repetitive empirical measurement results, it is necessary to determine, by calibration, the precision of the eigenvectors to the same standard as the empirical results, because each eigenvector evidences uncertainty relative to a standard. When the calibration process is recognized as formal as well as empirical, QM measurement function results and metrology measurement process results are unified.

The question whether a given set of test items can be considered “identical” is often addressed in terms of the homogeneity of the test material from which said items were taken. However, for some types of matrices – in particular, for matrices consisting of minute separate particles, only some of which carry the analyte under consideration – even in the case of homogenous test material, an irreducible source of variability between test items may remain: the fundamental variability. In this paper, the concept of fundamental variability is explained, and procedures for reducing and characterizing it are described.

Validation of satellite sea surface salinity (SSS) products is typically based on comparisons with in-situ measurements at a few meters depth, that are mostly done at a single location and time. The difference in term of spatio-temporal resolution between the in-situ near-surface salinity and the two-dimensional satellite SSS results in a sampling mismatch uncertainty. The Climate Change Initiative (CCI) project has merged SSS from three satellite missions. Using an optimal interpolation, weekly and monthly SSS and their uncertainties are estimated at a 50 km spatial resolution over the global ocean. Over the 2016-2018 period the mean uncertainty on weekly CCI SSS is 0.13, whereas the standard deviation of weekly CCI minus in-situ Argo salinities is 0.24. Using high resolution SSS simulations, we estimate the expected uncertainty due to the CCI versus Argo sampling mismatch. Most of the largest spatial variability of the satellite minus Argo salinity are observed in regions with large mismatch. A quantitative validation is performed by considering the statistical distribution of the CCI minus Argo salinity normalized by the sampling and retrieval uncertainties. This quantity should follow a Gaussian distribution with a standard deviation of 1, if all uncertainty contributions are properly considered. We find that 1) the sampling mismatch can explain most of the observed differences between Argo and CCI data, especially for monthly products and in dynamical regions (river plumes, fronts), 2) overall, the uncertainties are well estimated in CCI version 3, much better compared to CCI version 2. There are a few dynamical regions where discrepancies remain, and where the satellite SSS, their associated uncertainties and the sampling mismatch estimates should be further validated.

Among many research areas to which Ron Yager contributed are decision making under uncertainty (in particular, under interval and fuzzy uncertainty) and aggregation – where he proposed, analyzed, and utilized the use of Ordered Weighted Averaging (OWA). The OWA algorithm itself provides only a specific type of data aggregation. However, it turns out that if we allows several OWA stages one after another, we get a scheme with a universal approximation property – moreover, a scheme which is perfectly equivalent to deep neural networks. In this sense, Ron Yager can be viewed as a (grand)father of deep learning. We also show that the existing schemes for decision making under uncertainty are also naturally interpretable in OWA terms.

The frame construction of an apartment complex that consists of multiple buildings encounters various uncertainties, owing to the complex relationships among units of work. Currently, the period of such a construction is calculated based on the number of floors of the highest building in the complex. This study quantitatively analyzes an apartment frame construction period using a queue model and evaluates the validity of the estimated period. In this regard, a methodology is proposed for analyzing the construction period by applying the concept of a customer and a server. A case study on the duration of an apartment frame construction is conducted with Korea Land and Housing Corporation, which has supplied the largest number of apartments in South Korea. It was found that the stable state of a queue system was observed when the rate of server utilization was applied to the basement and aboveground floors. However, a stable state was not reached on the ground floor. This study includes non-working days in its calculation and quantitatively analyzes uncertainty factors during construction. Therefore, the findings can be practically utilized to quantitatively plan the durations of work units in an apartment frame construction.

The article contains the results of experimental studies for a multi-opening orifice with substitute constriction factor of β = 0.5 (m = 0.25), mounted in a DN50 hydraulic measuring flume. Flow measurements were taken for a progressing turbulent flow within Reynolds numbers (Re = 4700...19500). Based on experimental data, flow characteristics as well as discharge coefficient C characteristics were determined. Relative expanded uncertainty of determining a discharge coefficient C was estimated within the changes of volume flow qv from 0.35 dm3/s to 0.68 dm3/s. The value does not exceed 1.25% within the changes of Reynolds numbers 9800 ≤ Re ≤ 19500.

The entropy models have been recently adopted in many studies to evaluate the distribution of the shear stress in circular channels. However, the uncertainty in their predictions and their reliability remains an open question. We present a novel method to evaluate the uncertainty of four popular entropy models, including Shannon, Shannon-Power Low (PL), Tsallis, and Renyi, in shear stress estimation in circular channels. The Bayesian Monte-Carlo (BMC) uncertainty method is simplified considering a 95% Confidence Bound (CB). We developed a new statistic index called as FREE_opt-based OCB (FOCB) using the statistical indices Forecasting Range of Error Estimation (FREE) and the percentage of observed data in the CB (N_in), which integrates their combined effect. The Shannon and Shannon PL entropies had close values of the FOCB equal to 8.781 and 9.808, respectively, had the highest certainty in the calculation of shear stress values in circular channels followed by traditional uniform flow shear stress and Tsallis models with close values of 14.491 and 14.895, respectively. However, Renyi entropy with much higher values of FOCB equal to 57.726 has less certainty in the estimation of shear stress than other models. Using the presented results in this study, the amount of confidence in entropy methods in the calculation of shear stress to design and implement different types of open channels and their stability is determined.

Additive manufacturing (AM) is a promising new technology that is having a very fast growth from home workshops to high-tech cutting-edge factories. As any manufacturing technique, adequate metrology services are needed to assure the quality of items manufactured by AM. One of the most widely used instruments to measure the characteristics of surfaces manufactured with AM is the confocal microscope. In this paper, authors present a whole calibration procedure for confocal microscopes designed to be implemented preferably in workshops or industrial environments rather than in research and development departments. Because of that, it is as simple as possible. The procedure is designed without forgetting any of the key aspects that need to be taken into account and based on classical reference material standards. These standards can be easily found in industrial dimensional laboratories and easily calibrated in accredited calibration laboratories.

The experiments of Project 8 have been excellent, but the expected goals still difficult to achieve. So much so that some of the results at your fingertips were also missing. In view of this, the focus of this article is to clarify several easy confused concepts. Only in this way, we can reasonably explain the experimental data. The main points are as follows: 1. The value c of the light speed in vacuum and a particle with zero static mass, both of which do not exist in the reality. That is to say, the so-called a photon's static mass is equal to zero but has energy, which is a paradox that confuses two different definitional domains. 2. In the reality, photons are high-speed particles generated by electromagnetic radiation. They must have the characteristics of (static) mass, energy and wave, in order to describe the main body to aim at photons from different angles. 3. After any main body comes into being electromagnetic radiation, its static mass will inevitably decrease accordingly. 4. The charge-mass ratio of an electron is a physical constant, which is the ratio of its charge to the amount of matter, and is not affected by relativistic effects and electromagnetic radiation. 5. The uncertainty of moving electrons is caused by random electromagnetic radiations. Finally, it is pointed out that if the cyclotron frequency of a single electron is measured, and at the same time, its de Broglie wavelength or frequency can also be measured, then its static mass can be obtained. Even so, the expected goals are still difficult to achieve, because random electromagnetic radiations are always taking away continually the matter composition of the single electron being measured. However, this was precisely a result of the research obtained by Project 8, and had universality, which should be reflect on.

Phenomenon of vacuum fluctuations of virtual particles in high energy physics has been mathematically modeled by a third order differential equation. Aim of present theory is to unravel underlying mathematical equation capable of explaining microscopic phenomenon of vacuum fluctuations. Solution of such a differential equation after applying appropriate boundary conditions gives an acceptable wave function i.e. . Operation of energy and time operator on this wave function proves that these operators do not hold commutative property. Time energy uncertainty principle has been derived by calculating variance of energy and time for the same wave function.

Model-based design has received considerable attention in biological and chemical industries over the last two decades. However, the parameter uncertainties of first-principle models are critical in model-based design and have led to the development of robustification concepts. Various strategies were introduced to solve the robust optimization problem. Most approaches suffer from either unreasonable computational expense or low approximation accuracy. Moreover, they are not rigorous and do not consider robust optimization problems where parameter correlation and equality constraints exist. In this work, we propose a highly efficient framework for solving robust optimization problems with the so-called point estimation method (PEM). The PEM has a fair trade-off between computation expense and approximation accuracy and can be easily extended to problems of parameter correlations. From a statistical point of view, moment-based methods are used to approximate robust inequality and equality constraints. We also suggest employing the information from global sensitivity analysis to further simplify robust optimization problems with a large number of uncertain parameters. We demonstrate the performance of the proposed framework with two case studies where one is to design a heating/cooling profile for the essential part of a continuous production process and the other is to optimize the feeding profile for a fed-batch reactor of the penicillin fermentation process. The results reveal that the proposed approach can be used successfully for complex (bio)chemical problems in model-based design.

The purpose of this paper is to evaluate the timing of innovative investment in technology product life cycles using a compound binomial option with management flexibility. Considering the business cycles changes in the macroeconomic will affect consumer purchasing power. The focus is how to evaluate the optimal investment strategy and the project value. It was applied to different product stages (three stages including production innovation, manufacture innovation, and operation innovation) and factored to different risks to build a technology innovation strategy model. An aim of this study is the options premium of the best strategy timing for each innovation stage. Its application of the compound binomial options for the manufacture innovation will only be considered after the execution of the production innovation. The same condition is applied to the operation innovation, which will only be considered after the execution of the manufacture innovation. Then, this paper constructs the dynamic investment sequential decision model, assesses the feasibility of an investment strategy, and makes a decision on the appropriate project value and options premium for each stage under the possible change of Gross Domestic Product (GDP). This paper investigates the product life cycle innovation investment topic by using the compound binomial options method and will provide a more flexible strategy decision compared with other trend forecast criteria.

Bladder cancer is one of the most common malignant diseases in the urinary system and a highly aggressive neoplasm. The prognosis is not favourable usually and its evolution for particular patients is very difficult to find out. In this paper we propose a dynamic mathematical model that describes the bladder tumor growth and the immune response evolution. This model is customized for a single patient, determining appropriate model parameter values via model calibration. Due to the uncertainty of the tumor evolution, using the calibrated model parameters, we predict the tumor size and the immune response evolution over the next few months assuming three different scenarios: favourable, neutral and unfavourable. In the former, the cancer disappears; in the second a 5mm tumor is expected around the middle of August 2018; in the worst scenario, a 5mm tumor is expected around the end of May 2018. The patient has been cited around June 15th, 2018, to check the tumor size, if it exists.

A simple method for the determination of caffeine in coffee grains by GC-FID is presented in the current work. The method was fully validated according to ISO 17025 requirements and European Commission regulation. The accuracy, as provided by recovery experiments was higher than 93%, and the precision, as provided by the (%)Relative standard deviation under reproducibility conditions, was lower than 5%. All independent parameters that lead in the increase of methods uncertainty were investigated. In the present work all special precautions were taken into account in order to avoid the use of an internal standard. The method was applied in real samples and possible health claims were investigated.

With advances in information technology, big data, mobile communications, and robotics, digital technologies are increasingly being used in factories around the world. This digital transformation is named industry 4.0. Today, industrial companies are looking at how to adopt this era and implement these technologies 4.0 while improving their performance and generating more profits. The objective of this paper is to help companies to better choose the appropriate digital technologies according to their activities using a multi-experts-multi-criteria decision-making approach under hesitant fuzzy information. The proposed model is a generic model based on Multi-Agent Systems allowing to have an idea of the parameters necessary to apply the adopted approach. The adopted approach allows a better representation of uncertainty and subjectivity of experts’ judgments. It would be of great interest, especially, when exact quantitative data are not available. A real case company example is exposed (automotive company) towards putting into practice the proposed approach.

InSAR and associated analytic methods enable relative surface deformation measurements from low Earth orbit with a potential accuracy of centimeters to millimeters. However, assessing the actual accuracy can be quite difficult. The analytic methods are complicated enough that naive analytic error propagation is infeasible, and, in many settings, InSAR practitioners lack sufficient ground truth to assess results. Phase noise due to partial decorrelation from changes in the scattering properties of the ground is a prominent source of accuracy loss. In this paper we present a method to assess the loss of precision due to this component of phase noise. The proposed method consists of generating synthetic data stacks whose statistical properties match those of the actual input SAR data stacks, and then using the synthetic data for an ensemble calculation. The spread of the results of the ensemble calculation indicates the loss of precision. We show examples of the ensemble analysis at a mining operation in South Africa, and demonstrate the ability to estimate the precision of two InSAR deformation retrieval methods on a point-by-point and epoch-by-epoch basis.

Intending to analyze the role of nuclear power in an integrated energy system, we used the IESA-Opt-N cost minimization model focusing on four key themes: system-wide impacts of nuclear power, uncertain technological costs, flexible generation, and cross-border electricity trade. We demonstrate that the Levelized Cost of Energy (LCOE) alone should not be used to demonstrate the economic feasibility of a power generation technology. For instance, under the default techno-economic assumptions, particularly the 5% discount rate and exogenous electricity trade potentials, it is cost-optimal for the Netherlands to invest in 9.6 GWe nuclear capacity by 2050. However, its LCOE is 34 €/MWh higher than offshore wind. Moreover, we found that nuclear power investments can reduce demand for variable renewable energy sources in the short term and higher energy independence (i.e., lower imports of natural gas, biomass, and electricity) in the long term. Furthermore, investing in nuclear power can reduce the mitigation costs of the Dutch energy system by 1.6% and 6.2% in 2040 and 2050, and 25% lower national CO₂ prices by 2050. However, this cost reduction is not significant given the odds of higher nuclear financing costs and longer construction times. In addition, this study has shown that lower financing costs (e.g., EU taxonomy support) considerably reduce the relevance of nuclear cost uncertainties on its investments. Furthermore, we demonstrate that the economic feasibility of national nuclear power investments can vary considerably depending on the cross-border electricity trade assumptions. Additionally, we found that lowering the cost of small modular reactors has more impact on their economic feasibility than increasing their generation flexibility. In conclusion, under the specific assumptions of this study, nuclear power can play a complementary role (in parallel to the wind and solar power) in supporting the Dutch energy transition from the sole techno-economic point of view.

The theories of quantum mechanics and relativity dramatically altered our understanding of the universe ushering in the era of modern physics. Quantum theory deals with objects probabilistically at small scales, whereas relativity deals classically with motion in space and time. We show here that the mathematical structures of quantum theory and of relativity follow together from pure thought, defined and uniquely constrained by the same elementary ``combining and sequencing'' symmetries that underlie standard arithmetic and probability. The key is uncertainty, which inevitably accompanies observation of quantity and imposes the use of pairs of numbers. The symmetries then lead directly to the use of complex \sqrt{-1} arithmetic, the standard calculus of quantum mechanics, and the Lorentz transformations of relativistic spacetime. One dimension of time and three dimensions of space are thus derived as the profound and inevitable framework of physics.

Understanding tourist behaviour during and after major tourism crises is essential to help destinations recover. The COVID-19 pandemic, a period of uncertainty and risk, makes it relevant to assess factors that influence travel intentions. There has been little research on tourist behaviour during health crises and, in particular, on perceived health risk and uncertainty effects on travel intentions. This study was carried out during the first months of the pandemic in Brazil and aims to investigate the role of health risk perception and intolerance of uncertainty on travel intentions for 2020 and 2021. We applied an online survey to 1,150 Brazilian participants from March to May of 2020. Our findings indicate that perceived COVID-19 severity, perceived probability of contracting it, and expected pandemic duration are significant predictors of travel intentions for both years. This paper sheds new light on tourist behaviour in the context of global health crises.

Max Born's statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. While the lat- ter always result from an assumed probability measure, the first include transition probabilities with a purely algebraic origin. Moreover, the gen- eral definition of transition probability introduced here comprises not only the well-known quantum mechanical transition probabilities between pure states or wave functions, but further novel cases. A transition probability that differs from 0 and 1 manifests the typical quantum indeterminacy in a similar way as Heisenberg's and others' un- certainty relations and, furthermore, rules out deterministic states in the same way as the Bell-Kochen-Specker theorem. However, the transition probability defined here achieves a lot more beyond that: it demonstrates that the algebraic structure of the Hilbert space quantum logic dictates the precise values of certain probabilities and it provides an unexpected access to these quantum probabilities that does not rely on states or wave functions.

Soil hydraulic properties are often derived indirectly, i.e. computed from easily available soil properties with pedotransfer functions (PTFs), when those are needed for catchment, regional or continental scale applications. When predicted soil hydraulic parameters are used for the modelling of the state and flux of water in soils, uncertainty of the computed values can provide more detailed information when drawing conclusions. The aim of this study was to update the previously published European PTFs (Tóth et al., 2015, euptf v1.4.0) by providing prediction uncertainty calculation built into the transfer functions. The new set of algorithms was derived for point predictions of soil water content at saturation (0 cm matric potential head), field capacity (both -100 and -330 cm matric potential head), wilting point (-15.000 cm matric potential head), plant available water, and saturated hydraulic conductivity, as well as the Mualem-van Genuchten model parameters of the moisture retention and hydraulic conductivity curve. The minimum set of input properties for the prediction is soil depth and sand, silt and clay content. The effect of including additional information like soil organic carbon content, bulk density, calcium carbonate content, pH and cation exchange capacity were extensively analysed. The PTFs were derived adopting the random forest method. The advantage of the new PTFs is that they i) provide information about prediction uncertainty, ii) are significantly more accurate than the euptfv1, iii) can be applied for more predictor variable combinations than the euptfv1, 32 instead of 5, and iv) are now also derived for the prediction of water content at -100 cm matric potential head and plant available water content.

The energy, momentum and the action associated with the time domain transition radiation fields are investigated. The results show that for a charged particle moving with speed $v$, the longitudinal momentum associated with the transition radiation is approximately equal to $E/c$ for values of $1-v/c$ smaller than about 10^-3 where $E$ is the total radiated energy and c is the speed of light in free space. The action of the transition radiation, defined as the product of the energy dissipated and the duration of the emission, increases as $1-v/c$ decreases and, for an electron, it becomes equal to $h/4\pi$ when $v=c-v_m$ where $v_m$ is the speed associated with the lowest energy state of a particle confined inside the universe and h is the Plank constant. Combining these results with Heisenberg’s uncertainty principle, an expression for the electronic charge based on other fundamental physical constants is derived. The best agreement between the experimentally observed electronic charge and the theoretical prediction is obtained when one assumes that the actual size of the universe is about 250 times larger than the visible universe.

This paper presents a systematic approach to developing big data analytics for manufacturing process-relevant decision-making activities from the perspective of smart manufacturing. The proposed analytics consists of five integrated system components: 1) data preparation system, 2) data exploration system, 3) data visualization system, 4) data analysis system, and 5) knowledge extraction system. The functional requirements of the integrated systems are elucidated. In addition, JAVA- and spreadsheet-based systems are developed to realize the proposed integrated system components. Finally, the efficacy of the analytics is demonstrated using a case study where the goal is to determine the optimal material removal conditions of a dry electrical discharge machining operation. The analytics identified the variables (among voltage, current, pulse-off time, gas pressure, and rotational speed) that effectively maximize the material removal rate. It also identified the variables that do not contribute to the optimization process. The analytics also quantified the underlying uncertainty. In synopsis, the proposed approach results in transparent, big-data-inequality-free, and less resource-dependent data analytics, which is desirable for small and medium enterprises—the actual sites where machining is carried out.

Stray current is a relevant phenomenon in particular for DC electrified transportation systems, affecting the track and infrastructure within the right of way and other structures and installations nearby. It worsens with time and the level of protection depend on timely maintenance, besides correct design choices. The assessment of track insulation is the starting point for both stray current monitoring systems and at commissioning or upon major changes. Standardized methods (ref. EN 50122-2, or IEC 62128-2) are almost unchanged in the last 20 years, but suffer from accuracy issues and variability due to parameters and conditions not under operator’s control. A critical discussion and analysis of the sources of variability and practical constraints is proposed, followed by the evaluation of uncertainty, with the objective not only to assess the accuracy of provided results, but to foster research on innovative, more flexible and accurate, methods.

The adaptive identification method developed to evaluate the parameters of the Bouc-Wen hysteresis (BWH). The adaptive approach based on the use of adaptive observers. We synthesize adaptive identification algorithms using the second Lyapunov method. The boundedness of adaptive system processes shown in coordinate and parametric spaces. We prove exponential dissipativity of processes in an adaptive system. Estimating method proposed for signaling uncertainty in the system.

We survey the main results emerging in the rapidly developing field that considers the geometry of thermodynamics and statistical mechanics. Our ideas of stability depend on variational principles – Maximum Entropy together with Least Action (and the isomorphic Least Exertion) – and this stability (invariance in time) indicates the centrality of the geometries of the systems. We explore a variety of examples of the application of thermodynamics in both macro- and micro-systems, and propose that irreversibility is an intrinsic and fundamental property of the physical realm (instead of being merely emergent). Using the concept of complex time, we examine the underlying mathematical unity of quantum mechanics, statistical mechanics, and geometrical thermodynamics. We show how the Planck and Boltzmann constants provide the fundamental quantum units for the phenomenological characteristics of the two Noether-conserved quantities controlling overall thermodynamic behaviour: respectively, energy and entropy production. We discuss the far-reaching isomorphisms (between all of complex time, temperature and the system symmetry) that always exist for Maximum Entropy systems, even as they exhibit either irreversible (dissipative, yet still dynamically stable) or reversible (including stable and static geometries) behaviours.

In this study, the dependence between Bitcoin (BTC) and economic policy uncertainty (EPU) of USA and China is estimated by applying latest methodology of quantile cross-spectral dependence. The findings indicate a positive return interdependence between BTC and EPU is high in short-term, and this dependence decreases as investment horizons increase from weekly to yearly. The information on above interdependence is also extracted by applying wavelet coherence analysis and the estimation results suggest that correlation between BTC and EPU is positive during short-term investment horizon. Furthermore, more diversification benefits of BTC can be obtained during USA-EPU as compared to China-EPU.