We introduce a new identification strategy for uncertainty shocks to explain macroeconomic volatility in financial markets. The Chicago Board Options Exchange Volatility Index (VIX) measures market expectations of future volatility, but traditional methods based on second-moment shocks and time-varying volatility of the VIX often fail to capture the non-Gaussian, heavy-tailed nature of asset returns. To address this, we construct a revised VIX by fitting a double-subordinated Normal Inverse Gaussian Lévy process to S\&P 500 option prices, providing a more comprehensive measure of volatility that reflects the extreme movements and heavy tails observed in financial data. Using an axiomatic approach, we introduce a general family of risk-reward ratios, computed with our revised VIX and fitted over a fractional time series to more accurately identify uncertainty shocks in financial markets.

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.

Motivated from Deutsch entropic uncertainty principle and several product uncertainty principles, we derive an uncertainty principle for the product of entropies using functions.

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.

Let X be a 3-product space. Let A : D(A) ⊆ X → X , B : D(B) ⊆ X → X and C : D(C) ⊆ X → X be possibly unbounded 3-self-adjoint operators. Then for all x ∈ D(ABC) ∩ D(ACB) ∩ D(BAC) ∩ D(BCA) ∩ D(CAB) ∩ D(CBA) with ⟨x, x, x⟩ = 1, we show that (1) ∆x(3, A)∆x(3, B)∆x(3, C) ≥ |⟨(ABC − aBC − bAC − cAB)x, x, x⟩ + 2abc|, where ∆x(3, A) := ∥Ax − ⟨Ax, x, x⟩x∥, a := ⟨Ax, x, x⟩, b := ⟨Bx, x, x⟩, c := ⟨Cx, x, x⟩. We call Inequality (1) as 3-Heisenberg-Robertson-Schrodinger uncertainty principle. Classical HeisenbergRobertson-Schrodinger uncertainty principle (by Schrodinger in 1930) considers two operators whereas Inequality (1) considers three operators.

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 $(\{f_n\}_{n=1}^\infty, \{\tau_n\}_{n=1}^\infty)$ and $(\{g_n\}_{n=1}^\infty, \{\omega_n\}_{n=1}^\infty)$ be unbounded continuous p-Schauder frames ($0<p<1$) for a disc 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} \|\theta_f x\|_0\|\theta_g x\|_0 \geq \frac{1}{\left(\displaystyle\sup_{n,m \in \mathbb{N} }|f_n(\omega_m)|\right)^p\left(\displaystyle\sup_{n, m \in \mathbb{N}}|g_m(\tau_n)|\right)^p}, \end{align} where \begin{align*} & \theta_f: \mathcal{D}(\theta_f) \ni x \mapsto \theta_fx \coloneqq \{f_n(x)\}_{n=1}^\infty\in \ell^p(\mathbb{N}), \quad \theta_g: \mathcal{D}(\theta_g) \ni x \mapsto \theta_gx \coloneqq \{g_n(x)\}_{n=1}^\infty\in \ell^p(\mathbb{N}). \end{align*} Inequality (1) is unexpectedly different from both bounded uncertainty principle \textit{[arXiv:2308.00312v1]} and unbounded uncertainty principle \textit{[arXiv:2312.00366v1]} for Banach spaces.

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.

Global warming may increase the potential evapotranspiration (Etp), thereby affecting the amount of clean water resources available in a region. In this study, the systematic biases in temperature outputs of 24 global climate models (GCMs) under 3 emission scenarios are corrected by using 8 bias correction methods. The trend of Etp in Yangzi River Delta in the 21st century is projected by using 4 Etp calculation formulas. The uncertainty of the projections is estimated and decomposed by using multi-way analysis of variance. The influence of uncertainty on the projected change signal is quantified by using the signal-to-noise ratio. The results show that, relative to the reference period (1971~2000), the annual mean daily Etp in Yangzi River Delta will increase by 0.14~0.17mm/d during the period 2021~2050 and by 0.21~0.41mm/d during the period 2061~2090, respectively. During 2021~2050, the uncertainty of Etp increase projections is dominantly contributed by the main effects of GCM (63%) and Etp calculation formula (24%). During 2061~2090, it is mainly contributed by the main effect of GCM (36%), followed by the main effects of emission scenario (34%) and Etp calculation formula (18%). The increase projections of Etp are generally reliable and robust during the two projection periods.

We derive an uncertainty principle for Lipschitz maps acting on subsets of Banach spaces. We show that this nonlinear uncertainty principle reduces to the Heisenberg-Robertson-Schrodinger uncertainty principle for linear operators acting on Hilbert spaces.

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.

A game problem of structural design is defined as a problem of playing against external circumstances. The scalar criterion serves the function of the payoff function. There are two classes of players, the “ordinal” and “cardinal” players. The ordinal players, designated as the "operator" and "nature," endeavor to respectively minimize or maximize the payoff function, operating within the constraints of limited resources. The fundamental premise of this study is that the probability distribution governing nature's "choice" of states remains unknown. Statistical decision theory addresses decision-making scenarios where these probabilities, whether or not they are known, must be considered. The solution to the substratum game is expressed as a value of the game. The value of the game is contingent upon the design parameters. The cardinal players, "designers", oversee the design parameters. For the se single cardinal player, the pursuit of the maximum and minimum values of the game reduces to the problem of optimal design. In the event that there are multiple cardinal players with conflicting objectives, a superstratum game emerges, which addresses the interests of the superstratum players. The optimal design problems for games with closed forms are presented. The game formulations could be applied for optimal design with uncertain loading.

ECOCLIMAP-SG+ is a new 60~m land use land cover dataset, which covers a continental domain, and represents the 33 labels of the original ECOCLIMAP-SG dataset. ECOCLIMAP-SG is used in HARMONIE-AROME, the numerical weather prediction model used operationally by Met Éireann and other national meteorological services. ECOCLIMAP-SG+ was created using an agreement-based method to combine information from many maps to overcome variations in semantic and geographical coverage, resolutions, formats, accuracies, and representative periods. In addition to ECOCLIMAP-SG+, the process generates an agreement score map, which estimates the uncertainty of the land cover labels in ECOCLIMAP-SG+ at each location in the domain. This work presents the first evaluation of ECOCLIMAP-SG and ECOCLIMAP-SG+ against the following trusted land cover maps: LUCAS 2022, the Irish National Land Cover 2018 dataset, and an Icelandic version of ECOCLIMAP-SG. Using a set of primary labels, ECOCLIMAP-SG+ outperforms ECOCLIMAP-SG regarding the F1-score against LUCAS 2022 over Europe and the Irish national land cover 2018 dataset. Similarly, it outperforms ECOCLIMAP-SG against the Icelandic version of ECOCLIMAP-SG for most of the represented secondary labels. The score map shows that the quality ECOCLIMAP-SG+ is hetereogeneous. It could be improved once new maps once they become available but we do not control when they will be available. Therefore, the second-part of this publication series aims at improving the map using machine learning.

In a world filled with uncertainties, Ebb&Flow emerged as a story of convergence, intertwining dementia research, caregiving, and artistic exploration into a tripartite creative knowledge exchange. This study delves into the complexities of uncertainty in dementia care and research through a collaborative project involving artists, researchers, carers, and individuals with lived experience of dementia. Initiated by the Trellis:Arbor program, Ebb&Flow sought to co-created a human space addressing the multifaceted nature of uncertainty. The sea, with its unpredictable nature, served as a guiding metaphor for the project, reflecting the unpredictability of dementia and life. Over three months, through paintings, writings, and digital mediums, participants documented the changing emotions, challenges, and discoveries they encountered daily. The project fostered an environment where uncertainties were openly discussed, building supportive and resilient communities through participatory co-creation and methodological exchange. Key activities included a digital logbook, allowing participants to document and share their experiences of uncertainty, and the creation of the Ebb&Flow card deck—a compilation of personal stories and insights that serve as a legacy of shared experiences. Each card facilitated dialogue, understanding, and connection, bridging gaps between those affected by dementia and the broader community. The project culminated in a final exhibition and sharing event, where participants, researchers, and the public celebrated the journey's outcomes through stories and artworks. Throughout this journey, we observed that embracing uncertainty and fostering empathy through creative collaboration profoundly impacted participants, enhancing empathy and resilience. This project underscores the transformative potential of integrating artistic practices with scientific research to address the emotional and psychological burdens of dementia and research environments. Ebb&Flow demonstrates that even in the face of the unknown, a united community can find strength, solace, and understanding, highlighting the power and beauty of unity in exploring and expressing the multifaceted experiences of dementia and life.

In this paper, we present a multi-task model that predicts disparities and confidence levels in deep stereo matching simultaneously. We do this by combining its successful model for each separate task and obtaining a multitask model that can be trained with a proposed loss function. We show the advantages of this model compared to training and predicting disparity and confidence sequentially. This method enables an improvement of 15% to 30% in the area under the curve (AUC) metric when trained parallel rather than sequential. In addition, the effect of weighting the components in the loss function on the stereo and confidence performance is investigated. By improving the confidence estimate, the practicality of stereo estimators for creating distance images is increased.

With advancements in digital technologies such as 5G communications, big data, and cloud computing, the components of network operation systems have become increasingly complex, significantly complicating system monitoring and maintenance. Correspondingly, automated log anomaly detection has become a crucial means to ensure stable network operation and protect them from malicious attacks or failures. Conventional machine learning and deep learning methods assume consistent distributions between the training and testing data, adhering to a closed-set recognition paradigm. Nevertheless, in realistic scenarios, systems may encounter new anomalies that were not present in the training data, especially in log anomaly detection. Inspired by evidential learning, we propose a novel anomaly detector called LogEDL, which supervises training of the model through an evidential loss function. Unlike traditional loss functions, the evidential loss function not only focuses on correct classification, but also quantifies the uncertainty of predictions. This enhances the robustness and accuracy of the model in handling anomaly detection tasks, while achieving functionality similar to open-set recognition. To evaluate the proposed LogEDL method, we conduct extensive experiments on three datasets, i.e., HDFS, BGL, and Thunderbird, to detect anomalous log sequences. Experimental results demonstrate that our proposed LogEDL achieves state-of-the-art performance in anomaly detection.

Khosravi, Drnov\v{s}ek and Moslehian [\textit{Filomat, 2012}] derived Buzano inequality for Hilbert C*-modules. Using this inequality we derive Deutsch entropic uncertainty principle for Hilbert C*-modules over commutative unital C*-algebras.

Let $\{\tau_n\}_{n=1}^\infty$ and $\{\omega_m\}_{m=1}^\infty$ be two modular Parseval frames for a Hilbert C*-module $\mathcal{E}$. Then for every $x \in \mathcal{E}\setminus\{0\}$, we show that \begin{align}\label{UE} \|\theta_\tau x \|_0 \|\theta_\omega x \|_0 \geq \frac{1}{\sup_{n, m \in \mathbb{N}} \|\langle \tau_n, \omega_m\rangle \|^2}. \end{align} We call Inequality (\ref{UE}) as \textbf{Noncommutative Donoho-Stark-Elad-Bruckstein-Ricaud-Torr\'{e}sani Uncertainty Principle}. Inequality (\ref{UE}) is the noncommutative analogue of breakthrough Ricaud-Torr\'{e}sani uncertainty principle \textit{[IEEE Trans. Inform. Theory, 2013]}. In particular, Inequality (\ref{UE}) extends Elad-Bruckstein uncertainty principle \textit{[IEEE Trans. Inform. Theory, 2002]} and Donoho-Stark uncertainty principle \textit{[SIAM J. Appl. Math., 1989]}.

In this study, we employ the GARCH-MIDAS (Generalised Autoregressive Conditional Heteroskedasticity variant of Mixed Data Sampling) model to explore the predictability of commodity return volatility in relation to US climate policy uncertainty (CPU). Our analysis utilizes the 20-day annualized realized commodity volatility returns of nine global commodities (Aluminium, Cocoa, Coffee, Copper, Cotton, Rice, Soybean, Sugar, and Wheat) to construct the GARCH-MIDAS model, with Climate Policy Uncertainty (CPU) serving as the predictive variable. The outcomes of our investigation reveal a consistently positive and statistically significant relationship between CPU and the selected commodities. This implies that CPU effectively serves as a robust predictor of volatility in commodity returns. The implications drawn from our results suggest that climate change policies play a pivotal role in influencing economic activities within the commodity market. This underscores the substantial impact of climate change considerations on investment decisions and further emphasizes the integral role of climate change in shaping economic choices.

Let $\mathcal{X}$ be a Banach space. Let $\{\tau_j\}_{j=1}^n, \{\omega_k\}_{k=1}^m\subseteq \mathcal{X}$ and $\{f_j\}_{j=1}^n$, $\{g_k\}_{k=1}^m\subseteq \mathcal{X}^*$ satisfy $ |f_j(\tau_j)|\geq 1$ for all $ 1\leq j \leq n$, $|g_k(\omega_k)|\geq 1 $ for all $1\leq k \leq m$. If $x \in \mathcal{X}\setminus \{0\}$ is such that $x=\theta_\tau\theta_f x=\theta_\omega\theta_g x$, then we show that \begin{align}\label{FKDB} \|\theta_fx\|_0\|\theta_gx\|_0\geq \frac{\bigg[1-(\|\theta_fx\|_0-1)\max\limits_{1\leq j,r \leq n,j\neq r}|f_j(\tau_r)|\bigg]^+\bigg[1-(\|\theta_g x\|_0-1)\max\limits_{1\leq k,s \leq m,k\neq s}|g_k(\omega_s)|\bigg]^+}{\left(\displaystyle\max_{1\leq j \leq n, 1\leq k \leq m}|f_j(\omega_k)|\right)\left(\displaystyle\max_{1\leq j \leq n, 1\leq k \leq m}|g_k(\tau_j)|\right)}. \end{align} We call Inequality (\ref{FKDB}) as \textbf{Functional Kuppinger-Durisi-B\"{o}lcskei Uncertainty Principle}. Inequality (\ref{FKDB}) improves the uncertainty principle obtained by Kuppinger, Durisi and B\"{o}lcskei \textit{[IEEE Trans. Inform. Theory (2012)]} (which improved the Donoho-Stark-Elad-Bruckstein uncertainty principle \textit{[SIAM J. Appl. Math. (1989), IEEE Trans. Inform. Theory (2002)]}). We also derive functional form of the uncertainity principle obtained by Studer, Kuppinger, Pope and B\"{o}lcskei \textit{[EEE Trans. Inform. Theory, (2012)]}.

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.

: 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.

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.

In this study, we conducted a comprehensive analysis of the spatial distribution of soil organic carbon stock (SOC stock) and the associated uncertainties in two soil layers (0–10 cm and 0–30 cm; SOC stock 10 and SOC stock 30 respectively), in Valchiavenna, an alpine valley located in northern Italy . We employed the digital soil mapping (DSM) approach within different machine learning models, including multivariate adaptive regression splines (MARS), random forest (RF), support vector regression (SVR), and elastic net (ENET). Our dataset comprised soil data from 110 profiles, with SOC stock calculations for all sampling points based on bulk density (BD), whether measured or estimated, considering the presence of rock fragments. As environmental covariates for our research we utilized environmental variables, in particular geomorphometric parameters derived from a digital elevation model (with a 20 m pixel resolution), land cover data, and climat-ic maps. To evaluate the effectiveness of our models, we evaluated their capacity to predict SOC stock 10 and SOC stock 30 using the coefficient of determination (R2). The results for the SOC stock 10 were as follows: MARS 0.39, ENET 0.41, RF 0.69, and SVR 0.50. For the SOC stock 30, the corresponding R2 values were: MARS 0.45, ENET 0.48, RF 0.65, and SVR 0.62. Additionally, we calculated the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) for further assessment. To map the spatial distribution of SOC stock and address uncertainties in both soil layers, we chose the RF model, due to its better performance, as indicated by the highest R2 and the lowest RMSE and MAE. The resulting SOC stock maps using the RF model demonstrated an accuracy of RMSE = 1.35 kg.m-2 for the SOC stock 10 and RMSE= 3.36 kg.m-2 for the SOC stock 30. To further evaluate and illustrate the precision of our soil maps, we conducted an uncertainty assessment and mapping by analyzing the standard deviation (SD) from 50 iterations of the best-performing RF model. This analysis effectively highlighted the high accuracy achieved in our soil maps. The maps of uncertainty demonstrated that the RF model better predicts the SOC stock 10 compared to the SOC stock 30.

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.

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.

The adaptive implementation of the Monte Carlo Method (AMCM) has been applied to optimize the calibration uncertainty of a positive displacement meter against a standard tank in an ISO 17025 accredited volume laboratory. These meters are used for custody transfer in liquid hydrocarbon logistics where any reduction in the uncertainty estimation may have an important economic impact. Several innovations are proposed when applying AMCM; regulation of AMCM convergence by applying the Student's t-distribution, validation of repeatability and filtering of outliers by performing 50 iterations of the AMCM, and characterization of the measurand's Probability Density Function (PDF) which results in a Flatten Gaussian. This work proves that GUM method does not assign the correct PDF. The uncertainty estimation is reduced 7.1 % compared to GUM method.

Tungsten balls with sub-100-μm diameter can function as probe tips for micro-coordinate measuring machines (CMMs) to measure ultraprecise workpieces such as ceramic bearings with a high aspect ratio. A high-precision measuring system was proposed to evaluate the roundness error of the self-made tungsten ball tips. The principles and mathematical models of the measuring system are illustrated, and the fabrication principle of tungsten balls is introduced. An analysis was conducted on the maximum allowable contact force and bending strength of the tungsten ball tips, and the elastic mechanism was designed based on the analysis. A ruby probe with a sphericity error of 130 nm (A-5003-0577, Renishaw Corporation) used as a reference sphere was measured to verify the system's effectiveness. Repeated measurement experiments were performed for two tungsten ball tips. The results show the roundness error of the tungsten ball-A is between 568.3 and 586.2 nm with a standard deviation of 6.6 nm while the tungsten ball-B’s roundness error is between 898.5 and 958.0 nm with a standard deviation of 19.7 nm. The uncertainty is calculated as 125.8 nm. The developed system can stably measure the roundness of the tungsten ball tips.

This research aims to propose a novel approach to evaluate and minimize the scrap rate in the industrial production of premium food cans with distortion printing. Beyond cost considerations, a critical aspect of modern food can manufacturing is the aesthetic quality of the graphical display. In addition to traditional formability requirements, a waving requirement is defined. Detailed real production conditions are provided and discussed. The material of interest is a double cold-reduced (DR) low-carbon steel sheet and chromium-coated tin-free steel with a thickness of 0.16 mm. These sheets are laminated on both sides with PET film before distortion printing on the exterior. A material parameter identification method is proposed and illustrated to address the challenges in characterizing such a thin sheet. The thickness profile and flange length are key criteria for this identification. Digital image correlation (DIC) and a microscope are used to measure the thickness distribution and flange length. Within the manufacturing system, uncertainties arising from material properties and forming processes can lead to scraps or defects. Finite element analysis (FEA) is adopted for process analysis and validated with experiment. Uncertainty propagation via metamodeling, employing radial basis function (RBF) neural networks, is adopted for the scrap rate evaluation. The study concludes with process optimization recommendations to reduce scrap.

Although economic uncertainty and social media use are recognized as having a significant impact on religiosity, their role in religiosity has yet to be extensively examined in developing countries. This study explored the effects of economic uncertainty and social media use on religiosity in the Chinese context. By analyzing the publicly available data from the Chinese General Social Survey and World Values Survey, the findings showed that economic uncertainty significantly increased people's religious beliefs, while social media use had no significant impact on religious beliefs. Furthermore, social media use did not significantly moderate the relationship between economic uncertainty and religious belief. In contrast, educational level positively moderated the relationship between economic uncertainty and religious belief. These findings differ in part from the results of previous studies, presenting new evidence for theoretical integration in the field and revealing potential group differences in the strength of the relationship between economic uncertainty and religious belief.

Uncertain fractional differential equation (UFDE) is an excellent tool for describing complicated dynamic systems. This paper analyzes the valuation problems of currency option based on UFDE under optimistic value criterion. Firstly, an uncertain fractional currency model is formulated to describe the dynamics of foreign exchange rate. Then, the pricing formulae of European, American and Asian currency option are obtained under optimistic value criterion, respectively. Finally, numerical simulations are provided to illustrate the validity of our theoretical results.

The paper presents an error model of a measurement chain containing link performing discrete wavelet transform algorithm which is most often the last stage of measurement signal processing. The goal is to determine the uncertainty budget of the input quantities of the wavelet transform algorithm. The error model takes into account parts of analog, analog-to-digital and digital processing, describing the properties of subsequent fragments of the chain using their transmittance and processing functions. The proposed model enables the description of both deterministic and non-deterministic properties of signal errors. The proposed model was validated using an example measurement chain created for this purpose.

Optical current sensors have been developed and improved in recent decades, and their use has been widespread in power systems, including smart grids. Like any measuring instrument or system, the result of its measurements is associated with a measurement uncertainty, which quantifies its precision. This article presents a review of the main uncertainty contributions that affect the quality and performance of optical current sensors.

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.

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.

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.

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.

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.

We assessed machine learning techniques (MLTs) for downscaling global climate model’s precipitation to local level in Bolivia. The skill, assumptions and uncertainty of the process are analyzed. Additionally, future projections are delivered. For that, an ensemble of 20 global climate models (GCMs) from CMIP6, with random forest (RF) and support vector machines (SVM), is used on four zones (highlands, Andean slopes, Amazon lowlands and Chaco lowlands). The downscaled series’ skill is evaluated in terms of relative errors. The uncertainty is analyzed through variance decomposition. MLTs’ skill is adequate in most cases, especially for the highlands and the Andean slopes. Moreover, RF tends to outperform SVM. Stationary assumptions are robust in the highlands and Andean slopes. Perfect prognosis assumption is poor in the highlands and Andean slopes; topographical complexity appears to be the reason. Regarding uncertainties, MLTs are the dominant source. In future projections, the highlands show shorter dry spell lengths with more frequent but less intense high rainfall events and higher annual rainfall. The Andean slopes exhibit an increased annual rainfall with a reduction in the high precipitation intensities but an increased frequency. The Amazon lowlands present a decrease in annual rainfall, and the Chaco lowlands an increase.

In this paper, aiming at the safety evaluation of ultimate bearing safety capacity of composite pile bridge foundation, the symmetrical reliability method with forward and inverse analysis con-sidering the randomness of parameters is proposed to evaluate the safety performance of com-posite pile foundation. The proposed method, considering 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. Through the example calculation of the safety coefficient of pile foundation, the results show that the statistical characteristics of random vari-ables that affect the safety coefficient of pile foundation have a significant impact. The degree of the safety coefficient depends on the probability distribution type and distribution parameters of the random parameters, among which the more important is the variation characteristics of the random variables. The stronger the parameter variability, the lower the safety level of the struc-ture. During design and evaluation, it is necessary to measure the safety reserve of pile founda-tions in accordance with engineering practice to ensure the safe construction and well operation of the pile.

Modern automotive systems should must satisfy strict reliability requirements. Most of the real vehicle systems and safety-critical networks have complex interconnections. Sensitivities and probabilistic uncertainties of reliability of System with Complex Interconnections (SwCI) can be investigated by the Monte-Carlo Simulation (MCS). The paper focuses on sensitivities and parametrical uncertainties of SwCIs reliability. The proposed method can be used forimplemented in the investigation of uncertainties of SwCIs reliability – in other wordsi.e., for in the determination of critical system elements and to estimateion of the Required Number of Spare Parts (RNSP) of the system, which depends on the probability of allowable spare equipment shortage.

Intelligence is a human construct to represent the ability to achieve goals. Given this wide berth, intelligence has been defined countless times, studied in a variety of ways and represented using numerous measures. Understanding intelligence ultimately requires theory and quantification, both of which have proved elusive. I develop a framework -- the Theory of Intelligences (TIS) -- that applies across all systems from physics, to biology, humans and AI. TIS likens intelligence to a calculus, differentiating, correlating and integrating information. Intelligence operates at many levels and scales and TIS distils these into a parsimonious macroscopic framework centered on solving, planning and their optimization to accomplish goals. Notably, intelligence can be expressed in informational units or in units relative to goal difficulty, the latter defined as goal complexity relative to system (individual or benchmarked) ability. I present general equations for intelligence and its components, and a simple expression for the evolution of intelligence traits. The measures developed here could be the basis for further refinements to gauge different facets of intelligence for any step-wise transformation of information. I argue that "proxies" such as environment, technology, society and collectives are essential to a general theory of intelligence and to possible evolutionary transitions in intelligence, particularly in humans. I conclude with testable predictions of TIS and offer several speculations.

A new approach based on input-output (IO) analysis has emerged to estimate the carbon footprints of companies and their products from cradle to gate. While they rely on the same principles as the GHG Protocol, they use a distributed iterative framework to improve the footprint estimations and reduce their uncertainty. While optimal estimations would result if all the world’s companies would enter such a system, this paper shows how such a distributed system could apply to the real world where many enterprises would stay out of the system. We show how it would increase the quality of the estimations with respect the GHG Protocol by integrating scope 1 and scope 2 data of the value chains in the footprint estimations and reducing the part of remaining scope 3 data. To help analyzing uncertainty, we show how to use the scope 1/2/3 decomposition to estimate the biases and the standard deviations of the computed production intensities. We illustrate the model on macroeconomic data for 44 sectors and two regions (Europe and Rest of World), using the Inter-Country Input-Output database (ICIO). Such a system would necessarily rely on Information and Communication Technology since the companies would be permanently interconnected in a large-scale meshed network, using an application protocol for data exchange.

This research aimed to investigate the relationship between climate policy uncertainty (CPU), clean energy (ENERGY), carbon emission allowance prices (CARBON), and Bitcoin returns (BTC) for the period from August 2012 to August 2022. The empirical analysis strategies utilized in this study included the Fourier Bootstrap ARDL long-term coefficient estimator, Fourier Granger Causality, and Fourier Toda Yamamoto Causality methods. Following the confirmation of cointegration among the variables, we observed a positive relationship between BTC and CARBON, a positive relationship between BTC and CPU, and a negative relationship between BTC and ENERGY. In terms of causal associations, we identified one-way causality running from CARBON to BTC, BTC to CPU, and BTC to the ENERGY variable. The study underscores the potential benefits and revenue opportunities for investors seeking diversified investment strategies in light of climate change concerns. Furthermore, it suggests actionable strategies for policymakers, such as implementing carbon taxes and educational campaigns, to foster a transition towards clean energy sources within the cryptocurrency mining sector and thereby mitigate environmental impacts.

The paper examines the various uncertainties encountered in high-frequency trading (HFT) environments and delves into the multiple challenges faced by HFT firms in navigating the Dodd-Frank Wall Street Reform and Consumer Protection Act (referred to as the "Dodd-Frank Act"), particularly during the initial stages of its enactment. These challenges include the ambiguity surrounding the definition of HFT, the lack of clarity regarding regulatory requirements and boundaries, inconsistencies in enforcement resulting from deviations in understanding the content, and the absence of detailed descriptions of the Act’s provisions. These hurdles significantly impact not only the daily operations of HFT firms but also pose higher demands on their long-term strategic planning and risk management. Drawing upon the Data, Information, Knowledge, Wisdom, and Purpose (DIKWP) model, this study employs an innovative analytical framework. Through the comprehensive application of conceptual space, cognitive space, and semantic space, it provides a systematic methodology for identifying and analyzing the aforementioned issues. This approach not only aids firms in better comprehending and adhering to complex regulatory requirements but also enables them to explore new business opportunities and competitive advantages while ensuring compliance.

The goal of the paper is to clarify the observed irrationality of decision making in conflict situations considered as one-step games of two players. To solve such situations, we consider the asymmetry in the relation of the players to their own rewards and the rewards of the opponents. Formalization of the decision-making process is based on recently developed non-commutative operators of multivalued logic algebra. The suggested method is applied to solve the well-known Prisoners’ dilemma game and the other situations of conflict, where it results in the expected strategies.

This study analyzes the relationship between economic policy uncertainty (hereinafter EPU) and corporate value, and verifies the differential effects of EPU on corporate value according to corporate social responsibility (hereinafter CSR) activities. The study period was from 2010 to 2020, and the EPU indexes measured by Baker et al. (2016)'s method and Hexun's CSR scores for companies listed on the Chinese stock market were used. Hexun is one of the three major evaluation agencies in China, and the CSR scores evaluated by this agency have been widely used in previous studies as a representative indicator of Chinese companies' CSR performance. The results of this study are as follows. First, EPU and corporate value were found to have a negative (-) relationship. Second, active CSR activities relieved the negative (-) relationship between EPU and corporate value. Finally, companies were divided into groups according to CSR activity scores to analyze the relationship and according to the result, the negative (-) relationship between EPU and corporate value was greater in the groups with low CSR activity scores than in the groups with high CSR activity scores. A lag model was applied to control endogeneity, and the results were consistent with the main results above. Previous studies have mainly focused on microscopic factors to investigate factors affecting corporate value. This study focused on macroeconomic policies and paid attention to the effects of changes in the macroenvironment caused by economic policy uncertainty on corporate value. In addition, this study is meaningful in that it expanded previous studies related to CSR activities by confirming that active CSR activities can be an advantageous tool for overcoming EPU.

We review our theory of interdependence applied to autonomous human-machine teams, with which we have made several generalizations based on theory that have led to new discoveries, compared to social science which is struggling to break free of its validation crisis, but also has no generalizations to new discoveries with human teams, let alone to human-machine teams. In this invited article, based around the stability of a team, of our discoveries, we review the uncertainty between a team's structure and its performance, our first finding. We generalize that finding to deception, vulnerability, innovation and fittedness. From there, our next generalization is to the quantum likeness of interdependence and quantum mechanics; we move on to Shannon holes, knowledge, and conclude with the value of debate and the need for boundaries to contain debate, to reduce interference, and to protect states of interdependence. After the introduction, we extend our model in Section 2 to energy and time, and we close with a brief review of innovation and future plans.

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]}.