Sudden cardiac arrest (SAC) is a leading cause of mortality. In recent years, though, many lives have been saved through the use of defibrillators by random bystanders. As a result, defibrillators have been popping up in various locations. In this work we propose a state mandate demanding the presence of a defibrillator at every pharmacy store and argue that it could greatly enhance and augment the impact of the defibrillator network. We support our claim via detailed calculations of the immediate (a defibrillator readily available) and partial (a defibrillator available at a reasonable distance) population coverage achievable by the implementation of our proposal, taking the Argolis area in Peloponnese Greece as a case study. Our findings indicate that, in addition to other benefits, the use of pharmacies to establish a defibrillator network could bring an eight-fold increase in the immediate population coverage of defibrillators and would provide immediate / partial access to a defibrillator to 18 / 24 incidents of SCA per year that would otherwise lead to death, potentially leading to the saving of numerous lives. Alternative scenaria are also discussed.

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.

Accurate and consistent rainfall observations are vital for climatological studies in support of better planning and decision making. However, estimation of accurate spatial rainfall is limited by sparse rain gauge distributions. Satellite rainfall products can thus potentially play a role in spatial rainfall estimation but their skill and uncertainties need to be under-stood across spatial-time scales. This study aimed at assessing the temporal and spatial performance of seven satellite products (TARCAT (Tropical Applications of Meteorology using SATellite and ground-based observations (TAMSAT) African Rainfall Climatology And Time series), Climate Hazards Group InfraRed Precipitation with Station data (CHIRPS), Tropical Rainfall Measuring Mission (TRMM-3B43), Climate Prediction Center (CPC) Morphing (CMORPH), the Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks- Climate Data Record (PERSIANN-CDR), CPC Merged Analysis of Precipitation (CMAP) and Global Precipitation Climatology Project (GPCP) using gridded (0.05o) rainfall data over East Africa for 15 years(1998-2012). The products’ error distributions were qualitatively compared with large scale horizontal winds (850 mb) and elevation patterns with respect to corresponding rain gauge data for each month during the ‘long’ (March-May) and ‘short’ (October-December) rainfall seasons. For validation only rainfall means extracted from 284 rain gauge stations were used, from which qualitative analysis using continuous statistics of Root Mean Squared Difference, Standard deviations, Correlations, coefficient of determinations (from scatter plots) were used to evaluate the products’ performance. Results revealed rainfall variability dependence on wind flows and modulated by topographic influences. The products’ errors showed seasonality and dependent on rainfall intensity and topography. Single sensor and coarse resolution products showed lowest performance on high ground areas. All the products showed low skills in retrieving rainfall during ‘short’ rainfall season when orographic processes were dominant. CHIRPS, CMORPH and TRMM performed well, with TRMM showing the best performance in both seasons. There is need to reduce products’ errors before applications.

This article explores the profound implications of Dr. Anthony Fauci's testimony before the U.S. House Select Subcommittee on the Coronavirus Pandemic, where he admitted that key COVID-19 policies lacked scientific backing. By analyzing the foundation of these decisions, the piece delves into the broader issues of scientific evidence, hypothesis validation, and the societal consequences of implementing unverified measures. It raises critical questions about the role of scientific rigor and accountability in policy-making, urging a reflection on our approach to scientific inquiry and decision-making in public health.

The systematic sampling is used as a method to get the quantitative results from the tissues and the radiological images. Systematic sampling on real line (R) is a very attractive method within which the biomedical imaging is consulted by the practitioners. For the systematic sampling on R, the measurement function (MF) is occurred by slicing the three-dimensional object equidistant systematically. The currently used covariogram model in variance approximation proposed by [28,29] is tested for the different measurement functions in a class to see the performance on the variance estimation of systematically sampled R. This study is an extension of [17], and an exact calculation method is proposed to calculate the constant λ(q,N) of confidence interval in the systematic sampling. The exact value of constant λ(q,N) is examined for the different measurement functions as well. As a result, it is observed from the simulation that the proposed MF should be used to check the performances of the variance approximation and the constant λ(q,N). Synthetic data can support the results of real data.

Quantum gravity theories rely on a minimal measurable length for their formulations, which clashes with the classical formulation of the uncertainty principle and with Lorentz invariance from general relativity. These incompatibilities led to the development of the generalized uncertainty principle (GUP) from string theories and its various modifications. GUP and covariant formulations of the uncertainty principle are discussed, together with implications for space-time quantization.

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.

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.

A time interval only description necessarily needs its own independent definitions, without one moment time coordinates to it. In this paper derived are time interval only set properties, including commutation relations, addition, multiplication and derivatives. Time interval only set commutation relations, consistent with one moment time set properties, are introduced by defining correspondence relations for these sets. Time development and equilibrium within the time interval description depend on the well-known ‘mean velocity theorem’ and the time interval version of the Legendre transform. In contrast, usually applied is only the traditional vector and one moment time coordinate kinematic approach from Newton’s laws. The main results of this paper are correspondences and time interval only set commutation relations. All other properties are derived from these results, while for the time interval only set, different from the one moment time set the canonical property is not valid. The time interval only description can be applied assuming spherical symmetric star-source radiation propagation, with finite time intervals for realistic measurement events. From time development with (a-)symmetry of time intervals, and from Curie’s principle, change can be described with a set theoretic approach. Time interval only set properties include the time interval only version of Noether charges and structure constants. A time interval only description for wave propagation, including group-velocity, for zero and non-zero mass wave particles, relates to the properties of the time interval only set. A second result in terms of the time interval only description is propagation wave energy equivalence with gravitation energy, derived from time interval only set commutation relations. A time interval approach, however including one moment time description dependence, was introduced in earlier publications of this author. In part 1 investigated are the time interval only set and its properties, a forthcoming part 2 to application of the time interval only description to specific groups of stars as emission sources.

Probabilistic inference problems have very broad practical applications. To solve this kind of problems under conditions of certainty, an effective mathematical apparatus has been developed. In real situations, obtaining deterministic estimates of relevant probabilities is often difficult; therefore, problems with handling uncertain estimates of probabilities appear. This paper examines the problem of probabilistic inference with probability trees provided that the initial probabilities are given in the form of intervals of their possible values.

The demonstration of compliance of rolling stock against disturbance limits for railway signaling, and in particular track circuits, is subject to a large deal of variability, caused by the diverse values of the electrical parameters of the railway line and resulting transfer functions, as well as operating conditions of rolling stock during tests. Instrumental uncertainty is evaluated with a Type B approach and shown to be much less than the experimental variability. Repeated test runs in acceleration, coasting, cruising, braking conditions are considered, deriving both max-hold (spread) and sample dispersion curves compared to the respective mean values (Type A approach to the evaluation of uncertainty). The major source of variability affecting a significant portion of the spectrum is caused by the superposed oscillations of the onboard LC filter, for which different choices of the transformation window duration are discussed. The test runs and the acquired data covered overall 1 day of tests along about 300 km of the Italian 3 kV DC railway network.

This study aims to investigate whether 16 weeks of High-Intensity Interval Training (HIIT) implemented on Physical Education classes (PEC), can improve physical fitness in high-school adolescents This study was a two-arm randomized controlled trial design with adolescents (15-17 years old). Twelve classes were randomized to either a 16 weeks of HIIT (HIIT-G, n = 106 students) implemented on PEC warm-up or a control group (CG, n = 123 students) of usual PEC warm-up. The HIIT sessions ranged from 14 to 20 all-out bouts intervals, adopting a 2:1 work-to-rest ratio. Post-intervention measures revealed a significant difference between groups in CRF and girls from HIIT-G increased their cardiorespiratory fitness (CRF) with significant difference between female groups and a medium to large effect size. The main findings from this study indicate that brief whole-body HIIT of an extremely low volume, over 16 weeks, can improve CRF in adolescent girls.

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.

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.

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.

This work investigates the stability conditions for linear systems with time-varying delays via augmented Lyapunov-Krasovskii functional(LKF). Two types of augmented LKFs with cross terms in integral are suggested to improve the stability conditions for interval time-varying linear systems. Through this work, the compositions of the LKFs are considered to enhance the feasible region of stability criterion for linear systems. Mathematical tools such as Wirtinger-based integral inequality(WBII), zero equalities, reciprocally convex approach, and Finsler’s lemma are utilized to solve the problem of stability criteria. Two sufficient conditions are derived to guarantee the asymptotic stability of the systems using linear matrix inequality(LMI). First, asymptotic stability criteria are induced by constructing the new augmented LKFs in Theorem 1. And then simplified LKFs in Corollary 1 are proposed to show the effectiveness of Theorem 1. Second, asymmetric LKFs are shown to reduce the conservatism and the number of decision variables in Theorem 2. Finally, the advantages of the proposed criteria are verified by comparing maximum delay bounds in two examples. Two numerical examples show that the proposed Theorem 1 and 2 obtained less conservative results than existing outcomes. Also, Example 2 shows that the asymmetric LKF methods of Theorem 2 can provide larger delay bounds and fewer decision variables than Theorem 1’s in some specific systems.

In this paper, a continuous power management for a decentralized DC microgrid (DCMG) is proposed to achieve voltage regulation and power balance even under system uncertainty and voltage sensor failure. The DCMG system achieves a continuous power management through only the primary controller to reduce the computational burden of each power agent. To enhance the reliability and resilience of the DCMG system under voltage sensor failure, a DC bus voltage (DCV) sensor fault detection algorithm is proposed. In this algorithm, the DCV sensor failure is detected by comparing the measured DCV with the estimated DCV. When the power agent identifies the DCV sensor failure, it changes the operation properly according to the proposed control mode decision algorithm to maintain the stability of the DCMG system. When uncertain conditions such as the power variation of the distributed generations, sudden grid disconnection, DCV sensor failure, electricity price change, and critical battery status occur, the DCMG system is changed to transitional operation modes. These transitional operation modes are employed to transmit the power agent information to other agents without digital communication links (DCLs) and to accomplish power sharing even under such uncertain conditions. In the transitional operation modes of the DCMG system, the DCV levels are temporarily shifted to an appropriate level, enabling each power agent to detect the uncertainty conditions, and subsequently to determine its operation modes based on the DCV levels. Simulation and experimental results under different test conditions confirm the reliability and effectiveness of the proposed control scheme.

This study presents the first U-Pb (CA-ID-TIMS) radioisotopic dating of zircon grains extracted from tonsteins (altered volcanic ashfalls) within the uppermost Permian coal interval of the Minusinsk Coal Basin (Siberia, Russia). Petrographic, structural, and mineralogical analyses confirm the volcanic ash origin of the tonsteins. The parent pyroclastic material is identified as rhyolite-pantellerite for tonstein I-22 and dacite-rhyodacite for tonstein I-12. Morphological analysis of zircon crystals, along with cathodoluminescence and melt inclusion studies, confirms their volcanic origin and crystallisation temperatures of 700–900ºC. New radioisotopic dates of 261.4 ± 0.7 Ma and 261.3 ± 0.4 Ma clarify the age of the Izykh Formation, enabling its direct correlation with the Capitanian Stage of the International Chronostratigraphic Chart. The results emphasise the possible discontinuity of the coal-bearing succession of southern Angaraland and highlight the potential for further stratigraphic refinement through continued radioisotopic dating of tonsteins.

Early diagnosis of paroxysmal atrial fibrillation (PAF) could suggest patients to receive timely interventions in clinical practice. Various PAF onset prediction algorithms might benefit from accurate heart rate variability (HRV) analysis and machine learning classification but to be challenged in real-time monitoring scenarios. The aim of this study is to present an end-to-end deep learning based PAFNet model that integrates a sliding window technique on raw R-R interval of electrocardiogram (ECG) segments to achieve a real-time prediction of PAF onsets. This integration enable the deep convolutional neural network (CNN) to be customized as a light-weight architecture that accommodates the size of sliding windows simply by altering the input layer, specifically its effectiveness in making a new prediction with each new heartbeat. Catering to potential influence of input sizes, three CNN models were trained using 50, 100, and 200 R-R intervals, respectively. For each model, the performance of automated algorithms was evaluated for PAF prediction using a ten-fold cross-validation. As a results, a total of 56,381 PAFN-type and 56,900 N-type R-R interval segments was collected from publicly accessible ECG databases, and a promising prediction performance of the automated algorithm with a 100 R-R intervals was achieved in terms of the sensitivity of 97.12%, the specificity of 97.77%, and the accuracy of 97.45%, respectively. Importantly, the automated algorithm with a sliding windows step of 1 could process one sample in only 23.1 milliseconds and identify the onset of PAF at least 45 minutes in advance. The present results suggest that the sliding window technique on raw R-R interval sequences along by deep learning based algorithms may offers the possibility of providing an accurate, real-time, and end-to-end clinical tool for mass monitoring of PAF.

Einstein was skeptical of part of quantum mechanics, and he believed that Heisenberg’s uncertainty principle did not reflected the full depth of reality. He famously stated, ”God does not play dice with the universe.” However, since quantum mechanics has passed so many experimental tests, most physicists today assume that Einstein was wrong. Nevertheless, we will demonstrate that Heisenberg’s uncertainty principle must be modified to unify gravity with quantum mechanics. This modification leads to the Certainty-Uncertainty principle where the certainty part is strongly linked to gravity. This means Einstein likely was right in his intuition also on this point. The key is to understand that the de Broglie wavelength is not the actual wavelength of matter but merely a derivative of the true matter wavelength, namely the Compton wavelength. Furthermore, one must understand that the gravitational constant, first introduced in 1873, is simply a composite constant needed to rectify the incomplete definition of kilogram mass introduced into Newtonian gravity in 1873.

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 uncertainty in the secondary path of an Active Noise Control (ANC) headphone affects the waterbed effect and stability of the feedback system. This study focuses on the uncertainty of the secondary path when real users wear headphones, and proposes a new uncertainty constraint based on the measured results of the secondary path transfer function under different wearing conditions of dummy head and limited subjects. This constraint and a cascaded second-order infinite impulse response filter with fixed coefficients are used to formulate a control strategic function, which is optimized by the Improved Grey Wolf Optimizer (IGWO) algorithm to obtain the optimal controller with better noise reduction performance. The proposed method and simulation model are validated based on the experimental test results. The results demonstrate that the safety factor and waterbed suppressing factor contained in the proposed uncertainty constraint ensures more stable noise reduction and effective suppression of the waterbed effect for new subjects without a priori data.

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.

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).

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.

Uncertainty relations in hydrodynamics are numerically studied. We first give a review for the formulation of the generalized uncertainty relations in the stochastic variational method (SVM), following the work by two of the present authors [Phys.\ Lett.\ A\textbf{382}, 1472 (2018)]. In this approach, the origin of the finite minimum value of uncertainty is attributed to the non-differentiable (virtual) trajectory of a quantum particle and then both of the Kennard and Robertson-Schr\"{o}dinger inequalities in quantum mechanics are reproduced. The same non-differentiable trajectory is applied to the motion of fluid elements in the Navier-Stokes-Fourier equation or the Navier-Stokes-Korteweg equation. By introducing the standard deviations of position and momentum for fluid elements, the uncertainty relations in hydrodynamics are derived. These are applicable even to the Gross-Pitaevskii equation and then the field-theoretical uncertainty relation is reproduced. We further investigate numerically the derived relations and find that the behaviors of the uncertainty relations for liquid and gas are qualitatively different. This suggests that the uncertainty relations in hydrodynamics are used as a criterion to classify liquid and gas in fluid.

In the century and a half since Maxwell first conjured his “finite being” which Lord Kelvin subsequently dubbed a “daemon”, researchers have explored the connections between non-equilibrium thermodynamics, entropy, and information theory. In recent years various Thermodynamic Uncertainty Relations (TURs) have been derived to inform upon the relationship between the entropy production and the precision possible in thermodynamic machines and processes. In this paper the recently derived TURs are applied to the hypothetical thermodynamic economy as described by Parker [1]. The TURs define the lower bound on the total entropy production of the economy. Changes in this entropy production rate has consequences on the stability of the economic system and plays a central role in the business cycle. This new perspective has important implications for policy makers, researchers, and other economic actors.

In this paper we establish information theoretical bridges between 1) Thermal Heisenberg uncertainties $\Delta x \Delta p$ (at temperature $T$), and 2) LMC structural quantifiers. After having achieved such purpose, we determine to what an extent our bridges can be extended to both the semi classical and classical realms. Also, we find a strict bound relating a special LMC structural quantifier to quantum uncertainties.

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

The e-commerce sector is in a constant state of growth and evolution, particularly within its subdomain of online food delivery. As such, ensuring customer satisfaction is critical for companies working in this field. One way to achieve this is by providing accurate delivery time estimation. While companies can track couriers via GPS, they often lack real-time data on traffic and road conditions, complicating delivery time predictions. To address this, a range of statistical and machine learning techniques are being employed, including neural networks and specialized expert systems, with different degree of success. One issue with neural networks and machine learning models is their heavy dependence on vast, high quality data. To mitigate this issue we propose two Bayesian generalized linear models to predict time of the delivery. Utilizing a linear combination of predictor variables, we generate practical range of outputs with Hamiltonian Monte Carlo sampling method. These models offer a balance of generality and adaptability, allowing for tuning with expert knowledge. They were compared with PSIS-LOO and WAIC criteria. Results show that both models accurately estimated delivery times from the dataset, while maintaining numerical stability. Model with more predictor variables proved to be more accurate.

The introduction of ChatGPT in academia has raised significant concerns, particularly regarding issues like plagiarism and the ethical use of generative text for academic purposes. Existing literature has predominantly focused on ChatGPT adoption, leaving a notable gap in addressing the strategies users employ to mitigate these emerging challenges. To bridge this gap, this research utilizes the Uncertainty Reduction Theory (URT) to formulate user strategies for reducing uncertainty. These strategies include both interactive and passive approaches. Concurrently, the study identifies key sources of uncertainty, which include concerns related to transparency, information accuracy, and privacy. Additionally, it introduces the concepts of seeking clarification and consulting peer feedback as mediating roles to facilitate reduced uncertainty. We tested these hypotheses with a sample of Indonesian users (N = 566) using structural equation modeling via Smart-PLS 4.0 software. The results confirm that interactive Uncertainty Reduction Strategies (URS) are more effective in reducing uncertainty when using ChatGPT compared to passive URS. Transparency concerns, information accuracy, and privacy concerns are identified as factors that increase the level of uncertainty. In contrast, consulting peer feedback is the most effective strategy for reducing uncertainty compared to seeking clarification at the individual-system level. Insights from the mediating effects confirm that consulting peer feedback significantly mediates uncertainty sources to reduce uncertainty. The study discusses various strategies for the ethical use of ChatGPT by users in the educational context and contributes significantly to theoretical development.

In this paper, we shall introduce the interval-valued spatial error model. Based on the idea of least square method of single-valued case, we give the parameter estimator for interval-valued spatial error model. The theoretical properties of the proposed estimator are proved. Finally, we give the numerical analysis and a real example.

Studying concurrent systems is to sort the read/write and control events in the concurrent system according to the order, or in partial order, or in strict order. Because of the concurrency of events and the timeliness of writing events, there will be overlap between events, which requires interval order analysis. A single start and end sequence to represent the entire hierarchical order structure as well as all equivalent spaced order observations.a single sequence of beginnings and endings to represent the entire stratified order structures as well as all equivalent interval order observations. Mazurkiewicz traces and Comtracks are hierarchical traces, but they cannot describe interval traces. In a few sentences of this summary, we can tell the problems (petri interval traces with data), the previous work (Mazurkiewicz traces, Comtracks), the reasons that cannot be solved, and our own solutions (DPN: Petri nets with data, interval traces). This paper focuses on a BE (Beginnings and Endings) sequence representing an equivalent class of runs, or targets. Our goal is to have a BE sequence to represent the entire hierarchical order structure, that is, all equivalent observable interval orders.

A method of accuracy error compensation for the time interval is examined, allowing to eliminate the dependence of accuracy error on the duration of measured intervals and minimising the influence of destabilising factors - ambient temperature changes and the initial deviation of the meter clock generator frequency from the nominal value. The compensation method is based on a calibration procedure that measures precise time intervals under conditions of changing ambient temperature. Then the dependence of the accuracy error on temperature for a particular meter is recorded. Based on these data, a correction table is compiled containing correction factors and temperature values at which these factors were determined. Under real measurement conditions, the correction factor corresponding to the current temperature is determined from the table for measured results correction. The table with correction factor values could be stored in the memory of the meter or processing computer. Experimental verification of the method showed that applying a correction for a meter with a standard XO class clock generator (certificated instability of ±50 ppm) can obtain an equivalent clock generator instability of ±0.15 ppm. The application of the method is efficient in cases where the use of high-end clocking to ensure the required measurement accuracy is not economically feasible.

Since the beginning of the 21th century, infrared Nd:YVO4 pulsed lasers have been widely applied especially in some actual industrial processes. In the working process of a laser-aided etching device, the “match-head” effect must be effectively controlled by suppressing the first giant pulse for a solid-state Q-switched laser. In the process of optimizing the infrared Nd:YVO4 pulsed laser by adjusting the slope parameters of the radio frequency (RF) modulation to suppress the first giant pulse, it has been come across that some abnormal horizontally polarized emission with a very short time appears before the formal vertically polarized emission when the gate signal is artificially started. Actually, abnormal horizontally polarized emission will bring some unexpected machining traces during the production process and even greater dangers. The experimental results show that with the increase of the slope duration of a RF signal, the existence time of abnormal output horizontal polarized light will be shortened, and the horizontal giant pulse and vertical giant pulse are well suppressed. When the slope duration is greater than 0.18 ms both horizontal and vertical giant pulses will disappear. The horizontal polarized light can be thoroughly suppressed when the slope duration is greater than 13.7 ms. Compared with the method of adding polarizer to eliminate abnormal output horizontal polarized light, this method does not add elements in the laser, ensuring that the laser volume is relatively small, and does not affect the quality of the normal output laser. The research conclusion is thought to be of great practical significance especially for processing transparent materials.

This article investigates robust optimality and duality for a class of nonsmooth multiobjective programming problems with vanishing constraints under data uncertainty (in short, UNMPVC) via convexificators. Using the properties of convexificators, we introduce generalized standard Abadie constraint qualification (in short, GS-ACQ) for the considered problem UNMPVC. Moreover, we introduce generalized robust version of nonsmooth stationary conditions, namely, weakly stationary point (in short, RW-Stationary), T-stationary point (in short, RT-Stationary), M-stationary point (in short, RM-Stationary) and S-stationary point (in short, RS-Stationary) for UNMPVC. By employing GS-ACQ, we establish that the RS-Stationary is the necessary first-order optimality condition for a local Pareto solution of UNMPVC. Moreover, under generalized convexity assumptions, we establish sufficient optimality criteria for UNMPVC. Furthermore, we formulate the Wolfe-type (in short, WRD) and Mond-Weir-type (in short, MWRD) robust dual models corresponding to the primal problem UNMPVC.

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.

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 relationship between the returns and volatility of stocks, gold, bonds, and Bitcoin (BTC) to changes in inflation, interest rates (SBI), and exchange rates is a compelling topic, encompassing factors such as inter-asset interactions, and the roles of assets as hedge or safe-haven. We aims the inter-assetscorrelation using Granger Causality Test and the role of hedge or safe-haven assets against uncertainty using GARCH for normal condition and quantile regression in crisis. Last, we built an optimal portfolio using the Arbitrage Pricing Model (APT) consists of 28% stocks, 16% gold, 27% bonds, and 29% BTC, with returns 1.7796% over the Rf. Monthly trading records from 2018 until 2023 are used. The results demonstrate a correlation between the returns of gold and bonds with BTC, while stock volatility is found to correlate with BTC volatility. Furthermore we found a negative correlation between gold returns and exchange rates, though gold shows no correlation with other variables, indicating its effectiveness as a hedge in normal conditions. The bond serve primarily as a diversifier against exchange rate and inflation in normal, bearish, and bullish market conditions. These findings suggest that gold and bonds are more stable instruments and serve as risk mitigation strategy for BTC.

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.

We show that one of the two important uncertainty principles derived by Maccone and Pati \textit{[Phys. Rev. Lett., 2014]} can be derived for arbitrary maps defined on subsets of $\mathcal{L}^p$ spaces for $1< p<\infty$. Our main tool is the Clarkson inequalities. We also derive a nonlinear uncertainty principle for weak parallelogram spaces and Type-p Banach spaces.

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]}.

We provide a comprehensive framework for forecasting five minute load using Gaussian processes with a positive definite kernel specifically designed for load forecasts. Gaussian processes are probabilistic, enabling us to draw samples from a posterior distribution and provide rigorous uncertainty estimates to complement the point forecast, an important benefit for forecast consumers. As part of the modeling process, we discuss various methods for dimension reduction and explore their use in effectively incorporating weather data to the load forecast. We provide guidance for every step of the modeling process, from model construction through optimization and model combination. We provide results on data from the PJMISO for various periods in 2018. The process is transparent, mathematically motivated, and reproducible. The resulting model provides a probability density of five-minute forecasts for 24 hours.

In this paper, we will revisit the derivation of Heisenberg's uncertainty principle. We will see how the Heisenberg principle collapses at the Planck scale by introducing a minor modification. The beauty of our suggested modification is that it does not change the main equations in quantum mechanics; it only gives them a Planck scale limit where uncertainty collapses. We suspect that Einstein could have been right after all, when he stated, ``God does not throw dice." His now-famous saying was an expression of his skepticism towards the concept that quantum randomness could be the ruling force, even at the deepest levels of reality. Here we will explore the quantum realm with a fresh perspective, by re-deriving the Heisenberg principle in relation to the Planck scale. We will show how this idea also leads to an upper boundary on uncertainty, in addition to the lower boundary. These upper and lower boundaries are identical for the Planck mass particle; in fact, they are zero, and this highlights the truly unique nature of the Planck mass particle. Further, there may be a close connection between light and the Planck mass particle: In our model, the standard relativistic energy momentum relation also seems to apply to light, while in modern physics light generally stands outside the standard relativistic momentum energy relation. We will also suggest a new way to look at elementary particles, where mass and time are closely related, consistent with some of the recent work in experimental physics. Our model leads to a new time operator that does not appear to be in conflict with the Pauli objection. This indicates that both mass and momentum come in quanta, which are perfectly correlated to an internal Compton `clock' frequency in elementary particles.

This paper consists of two parts. In part I some new relations for a field theory with time intervals are derived. One concept of field theory evaluated is complementarity, another is field operators both defined within a time interval description. Part II includes specific results and commentary. Discussed are time interval dependent wave propagation surfaces for star source emission waves and derived is a metric propagation surface area requirement. The results allow to consider one same field that like gravitation within General Relativity applies to both non zero and zero mass. The associated field energy is space time dependent for non zero mass, and is related to a space time dependent metric tensor for zero mass wave particles. Defined is internal energy transfer where wave particle numbers increase linearly and mass and momentum diminish, decrease inversely with the distance from the wave emission source. The commentary are applications related to cosmological overall volume and temperature dependence.

The Ramanujan primes are the least positive integers Rn having the property that if m ≥ Rn, then π_m − π_(m/2) ≥ n. This document develops several bounds related to the Ramanujan primes, sharpening the currently known results. The theory presented is by no means exhaustive, however it provides insights for future research work. Alternatively, we may say that it is a road map which may be followed to make further discoveries.

In the manufacturing industry, orders are typically scheduled and delivered through batches, and the probability of machine failure under high-load operation is high. On this basis, we focus on a single machine batch scheduling problem with a maintenance interval (SMBSP-MI). The studied problem is expressed by three-field representation as 1|B,MI|\sum{F_j+\mu}m, and the optimization objective is to minimize total flow time and delivery costs. Firstly, 1|B,MI|\sum{F_j+\mu}m is proved to be NP-hard by Turing reduction. Secondly, shortest processing time (SPT) order is shown the optimal scheduling of SMBSP-MI, and a dynamic programming algorithm based on SPT (DPA-SPT) with the time complexity of O(n^3T_1) is proposed. A small-scale example is designed to verify the feasibility of DPA-SPT. Finally, DPA-SPT is approximated to a fully-polynomial dynamic programming approximation algorithm based on SPT (FDPAA-SPT) by intervals partitioning technique. The proposed FDPAA-SPT runs in O(\frac{n^5}{\varepsilon^2})\ time with the approximation (1+\varepsilon).

Interval-valued functions have been widely used to accommodate data inexactness in optimization and decision theory. In this paper, we study interval-valued vector optimization problems, and derive their relationships to interval variational inequality problems, of both Stampacchia and Minty types. Using the concept of interval approximate convexity, we establish necessary and sufficient optimality conditions for local strong quasi and approximate $LU$-efficient solutions to nonsmooth optimization problems with interval-valued multiobjective functions.

Type-2 fuzzy sets were introduced by L. Zadeh aiming at modelling some settings in which fuzzy sets (usually called type-1 fuzzy sets) are not sufficient to reflect certain uncertainty degrees - loosely speaking, they are fuzzy sets whose membership degrees are ordinary fuzzy sets. On the other hand, fiber bundles are topological entities of extreme importance in Mathematics itself and many other scientific areas, like Physics (General Relativity, Field Theory etc.), finance modelling, and statistical inference. The present work introduces a conceptual link between the two ideas and conjectures about the potential mutual benefits that can be obtained from this viewpoint.As an objective and usable product of the presented ideas, it is described a framework for defining type-2 fuzzy hedges, proper to operate on interval type-2 fuzzy sets.

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.

In this article, we consider a class of nonsmooth interval-valued multiobjective semi-infinite programming problems with vanishing constraints (in short, NIMSIPVC). We introduce the VC-Abadie constraint qualification (in short, VC-ACQ) for NIMSIPVC and employ it to establish Karush-Kuhn-Tucker (in short, KKT)-type necessary optimality conditions. Related to NIMSIPVC, we formulate interval-valued vector Lagrange type dual and scalarized Lagrange type dual problems. Subsequently, we establish weak, strong, and converse duality results relating NIMSIPVC and corresponding dual problems. In addition, we introduce the notions of saddle points for interval-valued vector Lagrangian and scalarized Lagrangian of NIMSIPVC. Moreover, we establish the saddle point optimality criteria for NIMSIPVC. Various non-trivial examples are provided to demonstrate the validity of established results. To the best of our knowledge, optimality conditions, Lagrange type duality, and saddle point optimality criteria for NIMSIPVC have not been investigated yet via Clarke subdifferentials.

In recent years retarded gravity has explained many of the mysteries surrounding the "missing mass" related to galactic rotation curves, the Tully-Fisher relations, and gravitational lensing phenomena. Indeed a recent paper analyzing 143 galaxies, has demonstrated that retarded gravity will suffice to explain the galaxies rotation curves without the need to postulate dark matter for multiple types of galaxies. Moreover, it also demystified the "missing mass" related to galactic clusters and elliptic galaxies in which excess matter wad derived through the virial theorem. Here we give a mathematical criterion which specifies the cases for which retardation is important for gravity (and when it is not). The criterion takes the form of an "uncertainty" relation.

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 $\mathcal{X}$ 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)]}.

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]}.

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.

Deterministic simulations using the SWAN model were conducted along a stretch of the Tietê-Paraná waterway in the Ilha Solteira dam reservoir, São Paulo, Brazil, to assess the water waves generated by winds. Simultaneously employs a probabilistic metamodeling approach (PCE) and Sobol indices, to quantify uncertainty of the five involved physical parameters (wind velocity and direction, bottom friction (JONSWAP), whitecapping and depth-induced breaking index). In the deterministic part, Janssen’s formulation yielded the most successful and accurate estimations of wave heights. Probabilistic analysis underscored the importance of wind data and the whitecapping parameter in model calibration, with a significant influence of wind speed indicated by Sobol indices. The results not only refined the model calibration process, but also allowed the creation of contour maps for wave height and period that offer practical pre-project applications. This work advances understanding of wind wave hydrodynamics deterministically and probabilistically, with good concordance and performance indices compared to field data, despite being scarce.

Approximately half of head and neck squamous cell carcinoma (HNSCC) cases recur, and most of them recur within the first two years after treatment. Although it has been suggested that the interval to recurrence after radical treatment and prognosis in patients with HNSCC are associated, investigations are insufficient. In this study, patients diagnosed with HNSCC at Kyushu University Hospital were retrospectively analyzed (n = 500). A total of 234 patients experienced recurrence, with 110 and 124 patients experiencing early recurrence (ER) (recurrence within 2–6 months) and late recurrence (LR) (recurrence after 7 months), respectively. There were two independent risk factors for poor prognosis in the multivariate analyses: ER (hazard ratio [HR] = 3.200, 95% confidence interval [CI] = 1.570–6.521, p = 0.001) and no radiotherapy (HR = 0.374, 95% CI = 0.191–0.733, p = 0.004). In patients with recurrent HNSCC, a short interval to recurrence is a risk factor for poor prognosis and survival. This study demonstrated the prognostic value of ER in patients. During the selection of treatment for patients with recurrence, the recurrent area, initial treatment content, and strategy of changing salvage therapy depending on the recurrence status should be considered.

The analysis and measurement of poverty is a crucial issue in the field of social science. Poverty is a multidimensional notion that can be measured using composite indicators relevant to synthesizing statistical indicators. Subjective choices could, however, affect these indicators. We propose interval-based composite indicators to avoid the problem, enabling us in this context to obtain robust and reliable measures. Based on a relevant conceptual model of poverty we have identified, we will consider all the various factors identified. Then, considering a different random configuration of the various factors, we will compute a different composite indicator. We can obtain a different interval for each region based on the distinct factor choices on the different assumptions for constructing the composite indicator. So we will create an interval-based composite indicator based on the results obtained by the Monte-Carlo simulation of all the different assumptions. The different intervals can be compared, and various rankings for poverty can be obtained. For their parameters, such as center, minimum, maximum, and range, the poverty interval composite indicator can be considered and compared. The results demonstrate a relevant and consistent measurement of the indicator and the shadow sector's relevant impact on the final measures.

Knee osteoarthritis (OA) is the most common joint disease worldwide. Exercise therapy has been identified as a first-line treatment option in patients suffering from knee OA. High-intensity interval training (HIIT) is an innovative exercise modality with potential in improving various disease-related outcomes. The purpose of this review is to explore the impact of HIIT on knee OA symptoms and physical functioning. A comprehensive search of scientific electronic databases was conducted to identify the articles on the effects of HIIT on knee OA. Thirteen studies were included in this review. Nine compared the effects of HIIT with those of low-intensity training, moderate-intensity continuous training, or a control group. Three evaluated the effects of HIIT alone. Eight reported a decrease in knee OA symptoms, and eight reported an increase in physical functioning. HIIT was shown to improve knee OA symptoms and physical functioning, but also aerobic capacity, muscle strength, and quality of life with minimal or no adverse events. However, compared to other exercise modalities, no clear superiority of HIIT was found. HIIT is a promising exercise strategy in patients with knee OA: anyway, the actual quality of evidence remains very low, and more high-quality studies are needed to confirm these promising outcomes.

In this article, we show the existence of fixed point for the derivative of interval-valued functions. Meanwhile, the fixed point inquiry will utilize the common fixed point methods under the condition of compatibility of the hybrid composite mappings in the sense of the Hausdorff metric. Some examples are given to support the usability of the result of this research .

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

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

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.

Pharmacy personnel often answer telephones to respond to pharmacy customers (subjects) who received messages from automated systems. This research examines the communication process in terms of how users interact and engage with pharmacies after receiving automated messages. No study has directly addressed automated telephone calls and subjects’ interactions. The purpose of this study is to test the interpersonal communication (IC) process of uncertainty in subjects in receipt of automated telephone calls from pharmacies. Subjects completed a survey of validated scales for Satisfaction (S); Relevance (R); Quality (Q); Need for Cognitive Closure (NFC). Relationships between S, R, Q, NFC, and subject preference to an automated telephone call (ATC) were analyzed to determine whether subjects contacting pharmacies display information seeking behavior. This research demonstrates that seeking information occurs if subjects: are dissatisfied with the content of the ATC; perceive that the Q of the ATC is high; perceive that the Q of ATC is high, and like receiving the ATC or with high NFC, and do not like receiving ATCs. Other interactions presented complexities amongst uncertainty and tolerance of NFC within the IC process.

Classifiers face a myriad of challenges in today’s data-driven world, ranging from overfitting and high computational costs to low accuracy, imbalanced training datasets, and the notorious black box effect. Furthermore, many traditional classifiers struggle with the robust handling of noisy and missing feature values. In response to these hurdles, we present classification methods that leverage the power of feature partitioning learning and outranking measures. Our classification algorithms offer an innovative approach, eliminating the need for prior domain knowledge by automatically discerning feature intervals directly from the data. These intervals capture essential patterns and characteristics within the dataset, empowering our classifiers with newfound adaptability and insight. In addition, we employ outranking measures to mitigate the influence of noise and uncertainty in the data. Through pairwise comparisons of alternatives on each feature, we enhance the robustness and reliability of our classification outcomes. The developed classifiers are empirically evaluated on several data sets from UCI repository and are compared with well-known classifiers including k Nearest Neighbors (K-NN), Support Vector Machine (SVM), Random Forest (RF), Neural Network (NN), Naive Bayesian (NB) and Nearest Centroid (NC). The experiments result demonstrate that the classifiers based on feature interval learning and outranking approaches are robust to imbalanced data and to irrelevant features and achieve comparably and even better performances than the well-known classifiers in some cases. Moreover, our proposed classifiers produce more explainable models whilst preserving high predictive performance levels.

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 $(\{f_j\}_{j=1}^n, \{\tau_j\}_{j=1}^n)$ 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]}.

This paper addresses the alliance route network design problem considering uncertainty of unit transportation cost. An alliance route network is constructed based on the hub-and-spoke (HS) network , in which airlines can achieve inter-area passenger transport through their international gateways. The design problem is formulated with a robust model containing a set of uncertain cost parameters. The model is established based on the three-subscript model of the HS network. A case study collected from real-world data is used to test the proposed model. The results show that the robust solution can reduce the impact of cost uncertainty.

Formaldehyde (HCHO) is one of the most important carcinogenic air contaminants. However, the lack of global surface concentration of HCHO monitoring is currently hindering researches on outdoor HCHO pollution. Traditional methods are either too naïve or data-demanding for a global scale research. To alleviate this issue, we trained two fully-connected neural networks respectively for deriving point and interval estimation of surface HCHO concentration in 2019, where vertical column density data from TROPOMI, in-situ data from HAPs (harmful air pollutants) monitoring network and ATom mission are utilized. Our result shows that the global surface HCHO average concentration is 2.30 μg/m3. Furthermore, in terms of regions, the concentration in Amazon Basin, North China, South-east Asia, Bay of Bengal, Central and Western Africa are among the highest. Our study makes up for the global shortage of surface HCHO monitoring and helps people have a clearer understanding of surface concentration distribution of HCHO. In addition, with the help of quality-driven algorithm, interval estimation of surface HCHO concentration is believed to bring confidence to our results. As an early work adopting interval estimation in AI-driven atmospheric pollutant research and the first to map global HCHO surface distribution, our paper will pave way for rigorous study on global ambient HCHO health risk and economic loss, thus providing basis for pollutant controlling policies worldwide.

This article focuses on the issue of motor oils used in the engines of off-road mobile machinery (NRMM), more specifically tractors. The primary goal of the paper is to determine the appropriate replacement interval for these oils. The physical properties of the examined samples were first determined by conventional instruments. Furthermore, the concentration of abrasive metals, contaminants, and additive elements were measured using an optical emission spectrometer. Lastly, the content of water, fuel, glycol, and the products of oxidation, nitration, and sulphation were determined by using infrared spectrometry. The measured values were compared to the limit values. Based on the processing and evaluation of these analyses, the overall condition of the oils was assessed and subsequently the optimal exchange interval of the examined oils was determined. In addition, a risk analysis of the outage was performed. Due to the high yields of crops, farmers can lose a significant amount of product when a tractor is not functioning during the harvest period. This loss for calculated in the paper.

In this study, we present the concept of interval-valued fuzzy soft point and then introduce the notions of neighborhood and quasi-neighbourhood of it in interval-valued fuzzy soft topological spaces. Separation axioms in interval-valued fuzzy soft topology, so-called $q$-$T_{i}$ for $ i=0,1,2,3,4 ,$ is introduced and some of its basic properties are also studied.

This article puts forward the bi-matrix games with crisp parametric payoffs based on interval value function approach. We conclude that the equilibrium solution of the game model can converted into optimal solutions of the pair of the non-linear optimization problem. Finally, experiment results show the efficiency of the model.

This work (in two parts) will review the recently developed predictive modeling methodology called “4th-BERRU-PM” and its applicability to energy systems as exemplified by an illustrative application to the Polyethylene-Reflected Plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The acronym 4th-BERRU-PM designates the “Fourth-Order Best-Estimate Results with Reduced Uncertainties Predictive Modeling” methodology, which yields best-estimate results with reduced uncertainties for the first fourth-order moments (mean values, covariance, skewness, and kurtosis) of the optimally predicted posterior distribution of model results and calibrated model parameters. The 4th-BERRU-PM uses the Maximum Entropy (MaxEnt) principle to incorporate fourth-order experimental and computational information, including fourth (and higher) order sensitivities of computed model responses to model parameters, thus incorporating, as particular cases, the results previously predicted by the second-order predictive modeling methodology 2nd-BERRU-PM, and vastly generalizing the results produced by extant data assimilation and data adjustment procedures. The 4th-BERRU-PM methodology encompasses the scopes of high-order sensitivity analysis (SA), uncertainty quantification (UQ), data assimilation (DA) and model calibration (MC). The application of the 4th-BERRU-PM methodology to energy systems is illustrated by means of the above-mentioned OECD/NEA reactor physics benchmark, which is modeled using the neutron transport Boltzmann equation involving 21976 imprecisely known parameters, the solution of which is representative of “large-scale computations.” The model result (“response”) of interest is the leakage of neutrons through the outer surface of this spherical benchmark, which can be computed numerically and measured experimentally. Part 1 of this work illustrates the impact of high-order sensitivities, in conjunction with parameter standard deviations of various magnitudes, on the determination of the expected value and variance of the computed response in terms of the first four moments of the distribution of the uncertain model parameters. Part 2 of this work will illustrate the capabilities of the 4th-BERRU-PM methodology for combining computational and experimental information, up to and including forth-order sensitivities and distributional moments, for producing best-estimate values for the predicted responses and model parameters while reducing their accompanying uncertainties.

QTc interval measurement is a widely used screening tool to assess the risk of cardiac diseases, arrhythmias, and is a useful biomarker for pharmacovigilance. However, interpretation of QTc is difficult in neonates due to hemodynamic maturational changes and uncertainties on reference values. To describe trends in QTc values throughout infancy (1 year of life), and to explore the impact of (non)-maturational changes and medicines exposure, a structured systematic review (PROSPERO CRD42022302296) was performed. In term neonates, a decrease was observed over the first week of life, whereafter values increased until two months of age, followed by a progressive decrease until six months. A similar pattern, with longer QTc values was observed in preterms. QTc is influenced by cord clamping, hemodynamic changes, therapeutic hypothermia, illnesses and sleep, not by sex. Cisapride, domperidone and doxapram result in QTc prolongation in neo-nates. Further research in this age category is needed to improve primary screening practices, earlier detection of risk factors and precision pharmacovigilance.

This paper investigates the importance of enhancing the safety of research reactors, especially in newcomer countries where experience may be limited. The focus is on the role of Independent Assessment (IA) and assessors in addition to using Best Estimate plus Uncertainty (BEPU) approach in enhancing safety measures. By using the best estimate codes to perform uncertainty calculations, the BEPU technique logically connects nuclear thermal hydraulics and nuclear reactor safety. BEPU is based on an understanding of the phenomena related to the reactor state. Reactor circumstances, such as those related to operations or accidents, could be identified in this way. The IA process, involves experts supporting design, installation, safety analysis, decommissioning, and modification. In order to shape the use of IA process in this study feedback from nuclear professionals was collected through questionnaires, revealing a consensus on the necessity of qualified regulatory bodies in newcomer countries. Additionally, the questionnaires highlighted the potential benefits of IA, such as minimizing accident risks and providing valuable insights for future analyses. The results indicate a global anticipation of increased research reactor construction, particularly in newcomer countries. The study discusses the propagation of input uncertainties, emphasizing the importance of considering various factors and parameters in safety assessments. The BEPU method was applied by using the COBRA-TF code by modeling onset of nucleate boiling (ONB) conditions for VVR-K research reactor. For uncertain parameters; ±1% inlet/initial pressure, ±1% inlet temperature, and ±1% linear heat rate, the ONB temperature in the axial region with the average cladding temperature was calculated to be 114.44℃. Table 2 (our references) provided a value of 114.6℃. The close agreement between the reference value and the COBRA-TF result shows that the model used in the calculation of the reference value and the Chen relation used by COBRA-TF are compatible.

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.

Supplier selection is one of the most important multi criteria decision making (MCDM) problems for decision makers in competitive market. Organizations of today’s world are seeking new ways to reduce negative effects of their organizations to the environment and to reach a greener system. At this point, green supplier selection concept has gained great importance with its ability on incorporating environmental or green criteria into the classical supplier selection practices. Therefore, in this study, it is aimed at proposing a multi-phase MCDM model based on Best-Worst Method (BWM) and interval type-2 fuzzy technique for order preference by similarity to ideal solution (TOPSIS). A case study in a plastic injection molding facility in Turkey is performed to show the applicability of the proposed integrated methodology. The paper ensures insights into the decision making, methodology, and managerial implications. Results of the case study are examined and suggestions for future research are provided.

Background: Bayesian Network (BN) modeling is a prominent methodology in computational systems biology. However, the incommensurability of datasets fre- quently encountered in life science domains gives rise to contextual dependence and numerical irregularities in the behavior of model selection criteria (such as MDL, Minimum Description Length) used in BN reconstruction. This renders model features, first and foremost dependency strengths, incomparable and diffi- cult to interpret. In this study, we derive and evaluate a model selection principle that addresses these problems. Results: The objective of the study is attained by (i) approaching model eval- uation as a classification problem, (ii) estimating the effect that sampling error has on the satisfiability of conditional independence criterion, as reflected by Mutual Information, and (iii) utilizing this error estimate to penalize uncertainty with the novel Minimum Uncertainty (MU) model selection principle. We vali- date our findings numerically and demonstrate the performance advantages of the MU criterion. Finally, we illustrate the advantages of the new model evaluation framework on real data examples. Conclusions: The new BN model selection principle successfully overcomes per- formance irregularities observed with MDL, offers a superior average convergence rate in BN reconstruction, and improves the interpretability and universality of resulting BNs, thus enabling direct inter-BN comparisons and evaluations.

The spatial resolution measurement limitation of the position-momentum uncertainty principle is shown to mathematically originate from the Bekenstein entropy bound and the associated second law of thermodynamics, as a special case in which a statistical thermodynamic distribution of energies is specialized to a fixed, definite probe energy equal to the average energy of that distribution. This is used in combination with the Wein displacement law to predict an ultraviolet cutoff for Planck blackbody radiation at about ⅛ of the Wein peak. A new UV photon counting experiment is proposed to test for this. A physical understanding of these results may be provided by a UV-complete, intelligible theory of general relativistic quantum mechanics in which the observation of a blackbody spectrum is simply a remote observation of Hawking radiation emitted from black hole fluctuations in the gravitational vacuum.

In this paper, we propose a method to find all efficient solutions of an interval multiple objective linear programming (IMOLP) problem with interval coefficients in the objective functions, the constraint matrix and the right-hand side vector. The set of all efficient solutions of an IMOLP problem can completely supply information to the decision makers in finding their most preferred solutions but, up to now, not all efficient solutions of an IMOLP problem can be found by known methods. A numerical example is given to illustrate the working of the proposed method.

Confidence interval of is an interval corresponding to a specified confidence and including the true value. It can be used to describe the precision of a statistical quantity and quantify its uncertainty. Although the principle of maximum entropy (POME) has been used for a variety of applications in hydrology, the confidence intervals of the POME quantile estimators have not been available. In this study, the calculation formulas of asymptotic variances and confidence intervals of quantiles based on POME for Gamma, Pearson type 3 (P3) and Extreme value type 1 (EV1) distributions were derived. Monte Carlo Simulation experiments were performed to evaluate the performance of derived formulas for finite samples. Using four data sets for annual precipitation at the Weihe River basin in China, the derived formulas were applied for calculating the variances and confidence intervals of precipitation quantiles for different return periods and the results were compared with those of the methods of moments (MOM) and of maximum likelihood (ML) method. It is shown that POME yields the smallest standard errors and the narrowest confidence intervals of quantile estimators among the three methods, and can reduce the uncertainty of quantile estimators

The responses of inflammatory cytokines and brain-derived neurotrophic factor (BDNF) to a high-intensity interval training (HIIT) session were compared between 7 postmenopausal (57±2 y) and 8 premenopausal females (44±3 y) during the luteal phase of their menstrual cycle, when estrogen and progesterone are highest, and. HIIT consisted of 10 x 1 min running intervals (90% maximum heart rate) separated by 1 min recovery intervals. Blood samples were collected at baseline (fasted), pre-exercise (postprandial), and 0, 30 and 90 min post-HIIT and analyzed for interleukin (IL-6) and 10 (IL-10), tumour necrosis factor-alpha (TNF-α) and BDNF. IL-6 significantly increased from pre-exercise to 0 min post-HIIT in postmenopausal (+40%, p=0.01) but 30 min post-HIIT in premenopausal females (+60%, p=0.02). IL-6 remained elevated at 90 min post-HIIT in premenopausal (+104%, p=0.05) and to a higher degree in postmenopausal (+385%, p&lt;0.001). IL-10 showed no response. TNF-α increased from pre- to 0 min post-HIIT (+10%, p=0.05), then decreased to below pre-exercise at 30 min (-10%, p=0.02) and 90 min (-5%, p=0.04) in both groups. BDNF increased immediate post-HIIT in premenopausal (+60%, p&lt;0.001) but not postmenopausal females. The differences in IL-6 and BDNF response to HIIT between pre and postmenopausal females provide evidence of the role of female reproductive hormones in the regulation of these exercise-induced responses.

(1) Methadone is a chiral synthetic opioid primarily used to treat heroin and prescription-opioid addiction: the (R)-enantiomer (Levomethadone) activates the µ-opioid receptor more potently than the (S)-enantiomer, which is a more potent blocker of the hERG potassium channels, resulting in QTc prolongation. The purpose of this study is to assess the effect of methadone on the QTc interval and to investigate the benefits of Levomethadone. (2) The electrocardiograms of 165 patients taking methadone at various dosages and for different periods of time were examined: the QTc value was manually measured and then adjusted using Bazett's formula. (3) Data analysis revealed a linear association between the dosage of methadone and QTc length; no correlation was found between the QTc value and gender, age, or duration of therapy. 14% of the sample (23 patients) showed a prolongation of the QTc interval. 10 of the 23 patients with QTc elongation underwent a change of therapy from Methadone to Levomethadone: in 90% of these patients, a normalization in the QTc length was established. (4) This study confirmed the role of methadone, specifically its dosage, in QTc prolongation and the efficiency of Levomethadone as an adequate therapeutic substitute in these circumstances. This study validates the importance of a careful electrocardiographic monitoring in methadone-treated patients.

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.

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.

This study uses the social impact theory to analyse consumer behaviour amidst Covid-19. Fear of scarcity has changed consumer buying behaviour in crisis times such as the now abating global health crisis – i.e., Covid-19. The study asserts that the existing five-stage model of consumer purchasing decisions does not fit neatly in turbulent times. It proposes a shortened four-stage process of need recognition, purchase, ownership and satisfaction as a better and more adaptable fit. Cutting out information search and evaluation of alternatives in the old model, and replacing these with ownership, is where the main contribution of the study lies. The study has implications for managing the marketing mix as we know it. It asserts that not all the 4Ps of the marketing mix are important in crisis times.

The difference of smoker’s topography has been found to be a function of sex, personality, nicotine yield, cigarette type (i.e., flavored versus non-flavored) ethnicity and etc. We evaluated the puffing behaviors of Korean smokers and its association with smoking-related biomarker levels. A sample of 300 participants was randomly recruited from metropolitan areas, South Korea. Topography measures during a 24-hour period were obtained using a CReSS pocket device. Korean male smokers smoked two puffs less per cigarette, compared to female smokers [15.0 (13.0–19.0) vs. 17.5 (15.0–21.0) as median (Interquartile range)], but had a significantly larger puff volume [62.7 (52.7–75.5) mL vs. 53.5 (42.0–64.2) mL); p = 0.012]. The interpuff interval was similar between men and women [8.9 (6.5–11.2) s vs. 8.3 (6.2–11.0) s; p = 0.122] but much shorter than other study results. A dose-response association (p = 0.0011) was observed between daily total puff volumes and urinary cotinine concentrations, after controlling for sex, age, household income level, nicotine addiction level. Understanding of the difference of topography measures, especially, larger puff volume and shorter interpuff interval of Korean smokers may help to overcome potential underestimation of internal dose of hazardous substitutes of smoking or corresponding its health effect.

Bipolar neutrosophic set is an important extension of bipolar fuzzy set. This set is a hybridization of bipolar fuzzy set and neutrosophic set. Every element of a bipolar neutrosophic set consists of three independent positive membership functions and three independent negative membership functions. In this paper, we develop cross entropy measures of bipolar neutrosophic sets and prove its properties. We also define cross entropy measures of interval bipolar neutrosophic sets and prove its properties. Thereafter, we develop two novel multi-attribute decision making methods based on the proposed cross entropy measures. In the decision making framework, we calculate the weighted cross entropy measures between each alternative and the ideal alternative to rank the alternatives and choose the best one. We solve two illustrative examples of multi-attribute decision making problems and compare the obtained result with the results of other existing methods to show the applicability and effectiveness of the developed method. In the end, the main conclusion and future scope of research are summarized.

The paper investigates some similarity measures in interval bipolar neutrosophic environment for multi-attribute decision making problems. At first, we define Hamming and Euclidean distances measures between interval bipolar neutrosophic sets and establish their basic properties. We also propose two similarity measures based on the Hamming and Euclidean distance functions. Using maximum and minimum operators, we define new similarity measures and prove their basic properties. Using the proposed similarity measures, we propose a novel multi attribute decision making strategy in interval bipolar neutrosophic set environment. Lastly, we solve an illustrative example of multi attribute decision making and present comparison analysis to show the feasibility, applicability and effectiveness of the proposed strategy.

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]}.

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]}.

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]}.

Water resource management and flood forecasting are crucial societal and financial stakes requiring reliable predictions of flow parameters (depth, velocity), the accuracy of which is often limited by uncertainties in hydrodynamic numerical models. In this study, we assess the effect of two uncertainty sources, namely breach characteristics induced by overtopping and the roughness coefficient, on water elevations and inundation extent. A two-dimensional (2D) hydraulic solver was applied in a Monte Carlo integration framework to a reach of the Loire river (France) including about 300 physical parameters. Inundation hazard maps for different flood scenarios allowed highlighting the impact of the breach development chronology. A special attention was paid to proposing a relevant sensitivity analysis to exam the factors influencing the depth and extent of flooding. The spatial analysis of vulnerability area induced by a levee breach width exhibits that, with increasing the flood discharge, the rise of the parameter influence is accompanied by a more localized spatial effect. This argues for a local analysis to allow a clear understanding of the flood hazard. The physical interpretation, highlighted by a global sensitivity analysis, showed precisely the dependence of the flood simulation on the main factors studied, i.e. the roughness coefficients and the characteristics of the breaches.

The optimal timing for actively discontinuing immune checkpoint inhibitor therapy in long-term responders with recurrent/metastatic head and neck squamous cell carcinoma (R/M HNSCC) remains unresolved. We conducted a retrospective study of 246 patients with R/M HNSCC treated with nivolumab to determine the optimal timing to actively discontinue nivolumab therapy. We examined the point at which progression-free survival (PFS) plateaued in all cases. We compared the prognosis of 19 (7.7%) ongoing cases and 227 (92.3%) discontinued cases and analyzed treatment duration and treatment-free interval (TFI). The 6-year overall survival was 11.8% (median, 12.1), and the 6-year PFS was 15.3% (median, 3.0). The PFS curve remained stable for 3 years. The median duration of nivolumab treatment was 2.9 months (range, 0.03–81.9): Ongoing group, 41.8 (5.6–81.9); Decision group, 36.8 (4.0–70.1); Toxicity group, 30.6 (2.8–64.8); and progressive disease group, 2.0 (0.03–42.9). TFI in the Decision group was 15.1 months (0.6–61.6) and 30.6 months (2.8–64.8) in the Toxicity group. Limited number of long-term responders in R/M HNSCC cases treated with nivolumab exists. Given that PFS plateaued at 3 years, we propose that the optimal duration of treatment for this subset of patients is 3 years.

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.

Abstract: Droughts are complex and gradually evolving conditions of extreme water deficits which can compromise livelihoods and ecological integrity, especially in fragile arid and semi-arid regions that depend on rainfed farming, such as Kitui West in south-eastern Kenya. Against the background of low ground-station density, 10 gridded rainfall products and four gridded temperature products were used to generate an ensemble of 40 calculations of the Standardized Precipitation Evapotranspiration Index (SPEI) to assess uncertainties in the onset, duration and magnitude of past droughts. These uncertainties were driven more by variations between the rainfall products than variations between the temperature products. Remaining ambiguities in drought occurrence could be resolved by complementing the quantitative analysis with ground-based information from key informants engaged in disaster relief, effectively formulating an ensemble approach to SPEI-based drought identification to aid decision making. The reported trend towards drier conditions in Eastern Africa was confirmed for Kitui West by the majority of data products, whereas the rainfall effect on the increasingly dry conditions was more subtle than annual and seasonal declines and greater annual variation, which warrants further investigation. Nevertheless, the effects of increasing droughts are already felt on the ground and warrant decisive action.

Background: Despite the tremendous effort in hamstring injury prevention, injury rates in soccer remain elevated. Hypothesis: Hamstring and hip/pelvic isometric strength imbalances may increase the likelihood of hamstring strain injury (HSI) occurrence amongst soccer players.Study design: Case-control study.Methods: In 120 male soccer players (mean age: 20.0 +/- 6.96 years) pre-season maximum isometric strength of the hip adductors, abductors, flexors, and knee flexors were measured, and strength ratios were calculated. Previous injury and anthropometric data were registered. Injury data were collected following the FIFA/UEFA consensus. A multivariate and Machine learning-based Logistic Regression model was employed to estimate the likelihood of players sustaining a hamstring injury.Results: 21 players sustained 32 hamstring injuries. Players with higher abduction strength in the dominant leg had an 18.5% lower risk of sustaining a hamstring injury (OR = 0.818, CI 95% = [(0.695-0.964]). No other significant contributor variables were found to be significant predictors of hamstring injury in the player group (p> 0.05).Conclusion: Isometric strength of the abductor muscles in the dominant limb had a significant association with hamstring injury.Clinical relevance: Our findings indicate the utilization of hip strength measurements as an integral component of the pre-season screening assessment, thereby affirming prior research on the correlation between lumbo-pelvic stability and incidence of hamstring injuries. Consequently, clinicians should contemplate incorporating hip strengthening exercises into regular training sessions, rehabilitation programs, and injury prevention protocols especially indicated when lower hip strength levels are observed.

This study investigated the impact of six high-intensity interval training (HIIT) running sessions at 1% or 10% slope on various physiological and performance parameters in 25 men. The partic-ipants underwent assessments of VO2max, time to exhaustion at 1% slope (TLim1%), and time to exhaustion at 10% slope (TLim10%) in the initial three visits. They were then randomly assigned to control (CON), HIIT at 1% slope (GT1%), or HIIT at 10% slope (GT10%) groups. Over three weeks, participants performed six HIIT sessions with equalized workload based on their indi-vidual maximal oxygen uptake (vVO2max). The sessions comprised 50% of TLim, with a 1:1 ratio of exercise to recovery at 50% vVO2max. Results indicated significant improvements in VO2max and peak velocity (VPeak) after HIIT at both slopes. Heart rate (HR) behavior differed between sessions for GT1%, while no significant differences were observed for GT10%. Rating of perceived exertion (RPE) significantly reduced for GT1% after the third session, with a similar trend for GT10%. In summary, six sessions of 1% or 10% slope HIIT effectively enhanced VO2max and VPeak, but there was no improvement in TLim performance, suggesting no adaptive transfer between training groups.

In the paper the new, fractional order, state space model of a heat transfer in a one- 1 dimensional metallic rod is addressed. The fractional orders of derivative along space and time 2 are not exactly known and they are described by intervals. The proposed model is the interval 3 expanding of the state space fractional model of the one dimensional heat transfer. It is expected to 4 better describe the reality because interval order of each real process is hard to estimate. Elementary 5 properties of the proposed model are analysed. Theoretical results are experimentally validated using 6 data from real experimental laboratory system.