Exponential Mean Research Articles

Exponential Mean Modeling of Coping Strategies and Dietary Diversity During the COVID-19 Pandemic in Mozambique

The COVID-19 pandemic has brought significant socioeconomic problems to many developing countries. In Mozambique, the impacts of the pandemic were felt in different spheres of households’ livelihoods. This study contributes to the existing body of knowledge by analyzing the effects of coping strategies and other factors on households’ dietary diversity scores (HDDS). The data were collected in two non-longitudinal waves in 2021 and 2022 from 3975 households by the Food and Agriculture Organization (FAO). The instrumental Poisson regression model was used for data analysis. The results showed that across the two periods, cereals were mostly consumed (96.93%), while meats (15.75%), milk and dairy (13.99%), and eggs (9.16%) were the least consumed. There was an increment in the proportion of households that consumed between zero and four food groups. Furthermore, there were declines in the utilization of coping strategies, while depletion of savings (50.62%) and credit (45.21%) were mostly used. The instrumental variable Poisson regression results revealed that expected HDDS decreased significantly (p<0.05) with sold animals, eating elsewhere, consumption of seed stock, decreased agricultural input expenditures, and emergency begging, whereas illegal activities increased it. In addition, household incomes, crop farming, and being younger than 35 years significantly increased (p<0.05) the expected HDDS, while all regions except Gaza had significantly higher expected HDDS than Cabo Delgado. It was concluded that adopted coping mechanisms could not offset households’ food problems during the pandemic, although some regional differences existed. Therefore, initiatives to promote human nutrition in Mozambique should enhance households’ resilience to income shocks through region-specific income-promoting activities.

Soil Temperature and Moisture Forecasting Using Exponential Smoothing Method Based on Mean Absolute Percentage Error

Soil is an essential medium for almost all plants. Temperature and moisture in the soil become one of the factors that affect plant growth. Unbalanced or unfavorable soil conditions will adversely affect the plant. Therefore, soil conditions, including temperature and moisture, must be monitored to maintain plant health. Forecasting can be used to find out the soil condition in the future so that strategies can be prepared to deal with these conditions. This forecasting is carried out based on existing soil temperature and moisture data, which is then processed using the exponential smoothing method and mean absolute percentage error as a reference for the error rate or accuracy of the forecasting. The application of these methods succeeded in producing forecasting with very good overall accuracy.<em> </em>

Establishment of quadratic exponential quality gain-loss function model and design of process mean

Taking into account the fluctuation of the growth rate on the left and right sides of the classic QGLF, a quadratic exponential quality gain-loss function (QGLF) is created based on the asymmetric QGLF. The two scenarios of non-normal distribution (triangular distribution) and truncated normal distribution of quality characteristic values are optimized using the quadratic exponential quality gain-loss process mean. Through the case study approaches, the empirical validity and applicability of the quadratic exponential QGLF model are thoroughly assessed, confirming its effectiveness in improving quality management practices.

Formation control and collision avoidance of unmanned water surface vehicles in maritime environments

The formation control of a team of unmanned water surface vehicles (USVs) experiencing maritime environmental disturbances is investigated. These perturbations include water waves, ocean current, wind gusts, communication and measurement errors, and other unmodeled dynamics that are captured through stochastic noise. A distributed control scheme leveraging local communication among team members is proposed to drive the group towards a set of waypoints while simultaneously achieving a desired spatial configuration and collision avoidance. The exponential mean square convergence of the proposed control scheme is shown under a version of the Lyapunov stability theory adapted to stochastic systems. Closed form expressions are proposed to estimate model parameters from experimental data collected in operating environments. The effectiveness of the proposed formation control scheme and collision avoidance method is assessed through numerical simulations demonstrating the interplay between the control parameters and the intensity of the noise. It also highlight the crucial role of the stochastic noise in resolving potential singularities or deadlocks in the vehicles’ motion , which originate from the collision avoidance forces.

Improved exponential type mean estimators for non-response case using two concomitant variables in simple random sampling

This paper addresses new exponential estimators for population mean in case of non-response on both the study and the concomitant variables using simple random sampling. The expressions for theoretical bias and mean square error of new estimators are derived up to first-order approximation and comparisons are made with the existing estimators. The proposed estimators are observed more efficient as compared to the considered estimators in the literature. For instance, the classical [4] unbiased estimator, the estimator of [9], and other existing estimators under the explained conditions. The theoretical results are supported numerically by using real-life data sets, under the criteria of bias, mean square error, percent relative efficiency and mathematical conditions. It is also clear from the numerical results that the suggested exponential estimators performed better than the estimators in the literature.

Multi-model ensemble successfully predicted atmospheric methane consumption in soils across the complex landscape

Multi-model ensemble successfully predicted atmospheric methane consumption in soils across the complex landscape

Synchronization conditions for stochastic landslide chain model with delayed coupling

We examine the conditions for synchronization of landslide stochastic chain model with delayed coupling. Firstly, a new chain model for landslide dynamics is proposed, with the included effect of delayed coupling and background noise. The model is of the microscopic type, where the state of each block in the chain is influenced by the previous state of the same block and its neighbors as well as by noise. Secondly, we examine the stochastic synchronization of such a system of stochastic delay-differential equations. A sufficient condition for the exponential mean square stability of the synchronization is obtained. The sufficient condition indicates that the uni-directional asymmetric coupling induces the synchronization much more efficiently than the bi-directionally symmetric one. From the practical viewpoint, the results obtained confirm that different parts of the large unstable slope could exhibit synchronized activity under certain conditions, which indicates their possible larger influence on the structures (and generation of corresponding deformation) compared to the individual effect of unsynchronized activities.

Models and numerical methods for XVA pricing under mean reversion spreads in a multicurrency framework

In this article we make some new relevant contributions to the computation of total valuation adjustments (XVA) for financial derivatives involving several currencies. From the modelling point of view, for the credit spreads we consider the more realistic exponential Vasicek and CIR positive mean reversion processes. Moreover, the derivative is partially collateralized in cash in a foreign currency and the collateral value is a percentage of the derivative prices. Under this modelling assumptions and using appropriate dynamic hedging methodologies, we obtain formulations in terms of linear and nonlinear partial differential equations, which are solved with Lagrange-Galerkin methods in low dimension. For higher dimensions, we use the Monte Carlo techniques for the equivalent formulations in terms of expectations. These techniques include a multilevel Picard iteration method for the nonlinear case. Finally, the methodologies are applied to several European options with different payoffs and the numerical results are discussed.

Resilient adaptive event‐triggered synchronization control of piecewise‐homogeneous Markov jump delayed neural networks under aperiodic DoS attacks

SummaryUnder the aperiodic Denial‐of‐service (DoS) attacks, this paper studies the resilient adaptive event‐triggered synchronization control problem for a class of Piecewise‐Homogeneous Uncertain Markov Jump Neural Networks (PHUMJNNs) with time‐varying delays. First of all, a new way of carving DoS attacks is given from the defenders' perspective, that is, aperiodic DoS attacks based on fixed detection periods. Then, under such attacks, a new Resilient Adaptive Event‐triggered Communication (RAETC) is designed between sensor and controller, which has a threshold function based on the net change rate and is real‐time updated depending on the present sampling state. Next, a single functional is used in the construction of the Lyapunov‐Krasovskii functional, while a new looped functional is introduced that makes full use of the state information of the current instant , the trigger instant and the next trigger instant . Based on the constructed single functional, under the framework of the input delay method and the linear matrix inequality technique, the exponential mean square stabilization criterion of the error system is obtained, which makes the master system and the slave system synchronized. In the end, three simulation examples are used to illustrate the validity of the obtained results.

A better one stage multiple comparison procedure of several treatment mean lifetimes with the control for exponential distributions under heteroscedasticity

In this article, we present a new one-stage multiple comparison procedure for exponential mean lifetimes with the control under heteroscedasticity including one-sided and two-sided confidence intervals by improving the coverage probability and average confidence length compared with the old one. Users can use these simultaneous confidence intervals to identify better-than-the-control, worse-than-the-control and not-much-different-from-the-control products in agriculture, stock market, pharmaceutical industries in terms of the mean lifetimes. In the end, one example is used to demonstrate the proposed procedure.

Fuzzy correlational analysis for dynamic consolidation of virtual machines in cloud computing environment

This theoretical research in fuzzy correlation analysis integrates data uncertainty analysis by measuring the strength of the linear relationship restricted to two fuzzy sets. As the relevant contribution to this research area, this paper presents the axiomatic definition of the n-dimensional generalized fuzzy correlation coefficient (nGCC), assigning to n input fuzzy sets an output value in the interval [−1,1]. Thus, the properties of general overlap functions and fuzzy negations are studied, discussing binary non-normed restricted dissimilarity functions, and the n-dimensional non-normed conjunctive functions. This study provides new methods for the n-dimensional generalized fuzzy correlation coefficient analysis, regarding their applications in solving multi-criteria and decision-making problems founded on fuzzy logic extensions. The n-dimensional non-normed conjunctive aggregation functions are also introduced, as range domain extensions from [0,1] to [−1.1], covering the interpretation of negative to positive variable associations. The proposal correlation analysis promotes a better evaluation and data selection even when more than one algorithm is applied to evaluate the reduction methods in the defuzzification process based on Interval-valued Fuzzy Logic. We also investigate the relevance to determine a reliable result from the fuzzy inference system based on the nGCC methodology. This correlation methodology applied to the Interval Fuzzy Load Balancing for Cloud Computing (Int-FLBCC) model contributes as a flexible approach for virtual machines dynamic consolidation enabling improvements in resource usage and power efficiency, improving the computational system’s energy efficiency. So, the nGCC methodology extends the Int-FLBCC model by adding other degrees of reliability to the results obtained with diverse evaluations through n-dimensional generalized fuzzy correlation coefficient expressions, exploring average aggregations as arithmetic and exponential means and the median operator.

Simple approaches to nonlinear difference-in-differences with panel data

Summary I derive simple, flexible strategies for difference-in-differences settings where the nature of the response variable may warrant a nonlinear model. I allow for general staggered interventions, with and without covariates. Under an index version of parallel trends, I show that average treatment effects on the treated (ATTs) are identified for each cohort and calendar time period in which a cohort was subjected to the intervention. The pooled quasi-maximum likelihood estimators in the linear exponential family extend pooled ordinary least squares estimation of linear models. By using the conditional mean associated with the canonical link function, imputation and pooling across the entire sample produce identical estimates. Generally, pooled estimation results in very simple computation of the ATTs and their standard errors. The leading cases are a logit functional form for binary and fractional outcomes—combined with the Bernoulli quasi-log likelihood (QLL)—and an exponential mean combined with the Poisson QLL.

Lyapunov Characterizations of Exponential Mean Square Input-to-State Stability for Discrete-Time Markovian Switching Nonlinear Systems

Lyapunov Characterizations of Exponential Mean Square Input-to-State Stability for Discrete-Time Markovian Switching Nonlinear Systems

Comparison of the several two-parameter exponential distributed group means in the presence of outliers

The two-parameter exponential distribution is often used to model the lifetime of a product. The comparison of the mean lifetimes of several products is a main concern in reliability applications. In this study, the performance of the methods to compare the mean lifetimes of several products based on generalized p-value, parametric bootstrap, and fiducial approach are compared in the presence of outliers. The results of Monte-Carlo simulations clearly indicate that there is no uniformly powerful test. The parametric bootstrap test is superior to the others except in the case of the lower number of groups and the presence of outliers. An illustrative example of testing the equality lifetimes of a component is given to perform the proposed tests. The considered tests are implemented in an R package doex.

Domain-Aware Adaptive Logarithmic Transformation

Tone mapping (TM) aims to display high dynamic range scenes on media with limited visual information reproduction. Logarithmic transformation is a widely used preprocessing method in TM algorithms. However, the conventional logarithmic transformation does not take the difference in image properties into account, nor does it consider tone mapping algorithms, which are designed based on the luminance or gradient-domain features. There will be problems such as oversaturation and loss of details. Based on the analysis of existing preprocessing methods, this paper proposes a domain-aware adaptive logarithmic transformation AdaLogT as a preprocessing method for TM algorithms. We introduce the parameter p and construct different objective functions for different domains TM algorithms to determine the optimal parameter values adaptively. Specifically, for luminance-domain algorithms, we use image exposure and histogram features to construct objective function; while for gradient-domain algorithms, we introduce texture-aware exponential mean local variance (EMLV) to build objective function. Finally, we propose a joint domain-aware logarithmic preprocessing method for deep-neural-network-based TM algorithms. The experimental results show that the novel preprocessing method AdaLogT endows each domain algorithm with wider scene adaptability and improves the performance in terms of visual effects and objective evaluations, the subjective and objective index scores of the tone mapping quality index improved by 6.04% and 5.90% on average for the algorithms.

Glaucoma Detection in Retinal Fundus Images Based on Deep Transfer Learning and Fuzzy Aggregation Operators

The early diagnosis of the glaucoma disease in the eye is crucial to avoid vision loss. This paper proposes an efficient computer-aided detection (CAD) system for diagnosing glaucoma based on fundus images, deep transfer learning and fuzzy aggregation operators. Specifically, the proposed CAD system includes three stages: (1) Detection of the region of interest of the optic disc using an efficient deep learning network, (2) Classification of images based on different pre-trained deep convolutional neural networks and support vector machines, and (3) Use of fuzzy aggregation operators to fuse the predictions of glaucoma classifiers. We used three popular yet robust aggregators: ordered weighted averaging (OWA) operator, weighted power mean (WPM), and exponential mean (EXM). We assessed the efficacy of the proposed glaucoma CAD system on three public datasets: DRISHTI-GS1, RIM-ONE, and REFUGE. The proposed conjunctive OWA aggregation method (Conj-OWA) achieves the best glaucoma classification results. Specifically, it achieves accuracy values of 90.2%, 97.8%, and 94.3% and area under the curve (AUC) values of 95.3%, 99.8%, and 96.2%, respectively, on DRISHTI-GS1, RIM-ONE, and REFUGE databases.

Constraining Bedrock Groundwater Residence Times in a Mountain System With Environmental Tracer Observations and Bayesian Uncertainty Quantification

AbstractGroundwater residence time distributions provide fundamental insights on the hydrological processes within watersheds. Yet, observations that can constrain groundwater residence times over broad timescales remain scarce in mountain catchment studies. We use environmental tracers (CFC‐12, SF6, 3H, and 4He) to investigate groundwater residence times along a hillslope in the East River Watershed, Colorado, USA. We develop a Bayesian inference framework that applies a Markov‐chain Monte Carlo (MCMC) approach to estimate noble gas recharge temperature, elevation, and excess‐air parameters and the resulting environmental tracer concentrations. MCMC is then used to propagate the environmental tracer uncertainties to estimates of groundwater mean residence times inferred with lumped parameter models. All samples contain 3H, CFC‐12, and SF6 in addition to terrigenic 4He, suggesting a mixture of water characterized by modern and premodern residence times. 4He exponential mean residence times range from hundreds of years at the upslope well to thousands of years at the toe‐slope well assuming average crustal production rates. We find that binary mixing residence time distributions with separate young and old mixing fractions are needed to predict the 4He, CFC‐12, SF6, and 3H observations, supporting the importance of flow path mixing in this bedrock system. Our findings that the fractured bedrock hosts groundwater with a mixture of residence times ranging from decades to millennia suggest variable recharge dynamics and flow path mixing along the hillslope and highlight the importance of characterizing groundwater systems with observations that are sensitive to transport over a broad range of residence times.

Stability analysis for time-varying positive systems with stochastic impulses

AbstractThis article addresses the stochastically exponential stability and mean stability of positive time-varying systems with stochastic impulses. The term ‘stochastic impulse’ means the randomness of impulsive densities or intensities. More specifically, the impulsive maps are not unique and the impulsive intensities are independent random variables with different distributions. The occurrence instants of impulses are restricted by several different processes, e.g. a mode-dependent average impulsive interval, a Markov chain, a Poisson process and a renewal process. Using a time-varying copositive Lyapunov function and stochastic analysis theory, several stochastic stability conditions are given. Finally, an example with four cases is presented to show the effectiveness of the proposed results.

Some existence results for elliptic systems with exponential nonlinearities and convection terms in dimension two

In this paper, we establish the existence of solutions to a class of elliptic systems. The nonlinearities include exponential growth terms and convection terms. The exponential growth term means it could be critical growth at $\infty$. The Trudinger-Moser inequality is used to deal with it. The convection term means it involves the gradient of unknown function. The strong convergence of sequences is employed to overcome the difficulties caused by convection terms. The variational methods are invalid and the Galerkin method and an approximation scheme are applied to obtain four different solutions. Our results supplements those from \cite{Araujo2018}.

Fault-Tolerant Periodic Event-Triggered Consensus Under Communication Delay and Multiple Attacks

This article proposes a resilient strategy for leaderless and leader–following consensus in general linear multiagent systems under simultaneous presence of false data injection and denial-of-service (DoS) attacks. To save energy, local control updates and communication between the neighboring agents are based on a distributed periodic event-triggered scheme. Sufficient conditions to guarantee the exponential mean square bounded consensus are derived as linear matrix inequality (LMI) conditions obtained from some delay-dependent Lyapunov–Krasovskii functionals. The proposed design framework computes the required consensus control gain based on a desired level of resilience to DoS. The guaranteed level of resilience in our proposed LMI-based method is less conservative (more realistic) compared to the existing analytical solutions. Two physical constraints, namely nonuniform time-varying communication delay and actuator faults, are also included in the problem formulation to enhance the practicability of the proposed solution. Simulations results demonstrate the effectiveness of the proposed framework in the presence of the considered cyberthreats and physical constraints.