Upper-bound Estimates Research Articles

Blow-up of solution to semilinear wave equations with strong damping and scattering damping

This paper is devoted to investigating the initial boundary value problem for a semilinear wave equation with strong damping and scattering damping on an exterior domain. By introducing suitable multipliers and applying the test-function technique together with an iteration method, we derive the blow-up dynamics and an upper-bound lifespan estimate of the solution to the problem with power-type nonlinearity |u|^{p}, derivative-type nonlinearity |u_{t}|^{p}, and combined type nonlinearities |u_{t}|^{p}+|u|^{q} in the scattering case, respectively. The novelty of the present paper is that we establish the upper-bound lifespan estimate of the solution to the problem with strong damping and scattering damping, which are associated with the well-known Strauss exponent and Glassey exponent.

Adaptive Output Feedback Compensation for a Class of Nonlinear Systems With Actuator and Sensor Failures

In this article, an adaptive output feedback compensation scheme is proposed for a class of uncertain nonlinear systems with a set of redundant actuators and a sensor. The sensor output is the only information available for output feedback. Both the actuators and the sensor may suffer from failures during operation and, therefore, all the system states are not available. To estimate the unmeasured states, a modified high-gain observer is designed which can not only ensure the closed-loop system stability but also improve the tracking performance. In the adaptive controller design, to overcome the complexity due to the unknown actuator and sensor failures coupled with the nonlinear functions and unknown parameters, an upper bound estimation method is adopted, which greatly simplifies the design procedure. It is proved that with the proposed scheme, the actuator and sensor failures can be compensated simultaneously, the reconfiguration can be adaptively updated without fault detection and isolation, and the real-tracking error can converge to a residual set, that is, mainly proportional to the sensor gain variation and measurement error.

Finite-time input-to-state stability of switched stochastic time-varying nonlinear systems with time delays

This article extends the finite-time input-to-state stability (FTISS) to switched stochastic time-varying nonlinear systems with time delays. By using the methods of Razumikhin theorem, comparison principle combined with average dwell-time (ADT) approach, several sufficient conditions of nonlinear switched stochastic delayed systems are analyzed to obtain ISS property in the framework of finite time. Compared with the existing results, we allow the upper bound estimation for the derivative of Lyapunov function to be time-varying, which takes both positive and negative values. Finally, an example is given to illustrate the effectiveness of the proposed results.

Interval observer‐based consensus control of discrete‐time multi‐agent systems under stealthy attacks

AbstractIn this paper, interval observer‐based consensus control is developed for multi‐agent systems with unknown input signals, sensor noises, and stealthy attack signals. Compared with the conventional robust observer, the interval observer has more relaxed preconditions for the systems, so the interval observer is more extensive. First, design an interval observer for each subsystem and linearly transform into a form that is easy to obtain the coefficient matrices of the interval observer. Then, based on the upper bound estimation of the observer, design a consensus control protocol, and the technique is used to suppress the unknown input signals. Finally, a numerical simulation example is presented to illustrate the feasibility and correctness of the developed method.

Adaptive sliding mode control of switched linear systems using disturbance observer based on the RBF neural network

This study deals with analyze of an adaptive sliding model controller for a class of switched linear systems in the context of model reference adaptive control (MRAC) using RBF neural network (RBFNN) with the aid of disturbance observer (DO). For this purpose, adaptive laws and switching rules are designed. These are constructed based on tracking error and sliding mode control, together with using time-dependent switching conceptualizations. A DO is used to estimate the external disturbance with an adaptive RBFNN which is applied to obtain the external disturbance upper bound estimation, combined with an adaptive sliding mode control (ASMC) under the identic Lyapunov stability framework. The switching rules are based on dwell time (DT) and average dwell time (ADT) switching. The ASMC updates the system dynamics so that it assures the proposed closed-loop switched linear system stability via fast switching, resulting in the form of globally uniformly ultimately bounded (GUUB) stability. The convergence of the process of updating the weights in the adaptive RBFNN and the boundedness of updated estimates of weights are satisfied. Achieving the state tracking, robustness, reducing the chattering problem and anti-disturbance performance are the main objectives. Moreover, switching rules based on the mode-dependent approaches have been developed, which can allow faster switching as compared to switching rules based on the DT and ADT. Finally, to evaluate the efficiency of the obtained theoretical results, the controller and the proposed method have been tested on the electro-hydraulic system (EHS).

Beyond upper bound estimates of active site densities in heterogeneous catalysis: A note on the critical role of titrant pressure

In-situ titrations employed in the estimation of active site densities oftentimes only provide upper bound estimates, not true active site densities. Discounting unselective contributions that result in a disparity between the two requires a treatment of transient titration data more nuanced than merely integrating under the titrant breakthrough curve. Three methods for estimating site densities (and turnover frequencies) are presented in the context of ceria-catalyzed ethene hydrogenation, and their strengths and limitations discussed. Readily accessible supra-monolayer coverages of CO prevalent on ceria surfaces help bring into relief considerations relating to unselective adsorption and active site heterogeneity common, yet infrequently addressed, in the characterization of heterogeneous catalysts using in-situ titration methods.

Optimal prediction intervals for macroeconomic time series using chaos and evolutionary multi-objective optimization algorithms

In a first-of-its-kind study, this paper formulates the problem of estimating the prediction intervals (PIs) in a macroeconomic time series as a bi-objective optimization problem and solves it with three evolutionary algorithms namely, Non-dominated Sorting Genetic Algorithm (NSGA-II), Non-dominated Sorting Particle Swarm Optimization (NSPSO) and Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA-D). We also proposed modeling the chaos present in the time series as a preprocessor, which we called stage-1. Accordingly, we proposed 2-stage models, where stage-1 is followed by obtaining the optimal point prediction using NSGA-II/NSPSO/MOEA-D and using these point predictions to obtain PIs (stage-2). We then proposed a 3-stage hybrid, which is built on the 2-stage model, wherein the 3 rd stage also invokes NSGA-II/NSPSO/MOEA-D in order to estimate the PIs from the point predictions obtained in 2 nd stage by simultaneously and explicitly optimizing (i) prediction interval coverage probability (PICP) and (ii) prediction interval average width (PIAW). The proposed models yielded better results in terms of both PICP and PIAW compared to the state-of-the-art Lower Upper Bound Estimation Method (LUBE) with Gradient Descent (GD) and LUBE with long short-term memory (LSTM) network. The 3-stage models outperformed the 2-stage models with respect to PICP but showed similar performance in PIAW at the cost of running NSGA-II/NSPSO/MOEA-D second time. Overall, MOEA-D yielded best PIs in two datasets and NSGA-II outperformed the other two in the third dataset. But, in terms of hypervolume, in 2-stage MOEA-D produced most diverse solutions in two datasets, while NSGA-II was the winner in the third dataset.

Bidirectional Gated Recurrent Unit-Based Lower Upper Bound Estimation Method for Wind Power Interval Prediction

High-quality interval prediction is helpful to accurately capture the uncertainty of wind power generation and provide support to grid dispatchers and operators. As an effective and reliable prediction interval (PI) construction framework, lower upper bound estimation (LUBE) method is used in forecasting tasks. This article proposes a new data-driven PI construction method for wind power prediction based on LUBE theory and a bidirectional gated recurrent unit (GRU) neural network, which integrates a loss function based on likelihood for model training. In this framework, the bidirectional GRU acts as the core predictor, and learns the long-term dependence of wind power time series in chronological and reverse chronological order. The learned features are merged by using a fully connected layer to generate the upper and the lower bounds of the target PI. The proposed method is evaluated on a real wind farm dataset. Numerical results show the superiority of the proposed method by comparing with the traditional LUBE method, long short-term memory-based LUBE method, mean-variance estimation method, and an emerging efficient gradient descent method.

Fixed-Time Lyapunov Criteria and State-Feedback Controller Design for Stochastic Nonlinear Systems

This paper investigates the fixed-time stability theorem and state-feedback controller design for stochastic nonlinear systems. We propose an improved fixed-time Lyapunov theorem with a more rigorous and reasonable proof procedure. In particular, an important corollary is obtained, which can give a less conservative upper-bound estimate of the settling time. Based on the backstepping technique and the addition of a power integrator method, a state-feedback controller is skillfully designed for a class of stochastic nonlinear systems. It is proved that the proposed controller can render the closed-loop system fixed-time stable in probability with the help of the proposed fixed-time stability criteria. Finally, the effectiveness of the proposed controller is demonstrated by simulation examples and comparisons.

Molecular characteristics, sources, and formation pathways of organosulfur compounds in ambient aerosol in Guangzhou, South China

Abstract. Organosulfur compounds (OrgSs), especially organosulfates, have been widely reported to be present in large quantities in particulate organic matter found in various atmospheric environments. Despite hundreds of organosulfates and their formation mechanisms being previously identified, a large fraction of OrgSs remain unexplained at the molecular level, and a better understanding of their formation pathways and critical environmental parameters is required to explain the variations in their concentrations. In this study, the abundance and molecular composition of OrgSs in fine particulate samples collected in Guangzhou were reported. The results revealed that the ratio of the annual average mass of organic sulfur to total particulate sulfur was 33 ± 12 %, and organic sulfur had positive correlations with SO2 (r=0.37, p<0.05) and oxidant (NOx + O3, r=0.40, p<0.01). A Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) analysis revealed that more than 80 % of the sulfur-containing formulas detected in the samples had the elemental composition of o/(4s+3n)≥1, indicating that they were largely in the form of oxidized organosulfates or nitrooxy organosulfates. Many OrgSs that were previously tentatively identified as having biogenic or anthropogenic origins were also present in freshly emitted aerosols derived from combustion sources. The results indicated that the formation of OrgSs through an epoxide intermediate pathway could account for up to 46 % of OrgSs from an upper bound estimation, and the oxidant levels could explain 20 % of the variation in the mass of organic sulfur. The analysis of our large dataset of FT-ICR MS results suggested that relative humidity, oxidation of biogenic volatile organic compounds via ozonolysis, and NOx-related nitrooxy organosulfate formation were the major reasons for the molecular variation of OrgSs, possibly highlighting the importance of the acid-catalyzed ring-opening of epoxides, oxidation processes, and heterogeneous reactions involving either the uptake of SO2 or the heterogeneous oxidation of particulate organosulfates into additional unrecognized OrgSs.

On a Nonlinear Fractional Langevin Equation of Two Fractional Orders with a Multiplicative Noise

We consider a stochastic nonlinear fractional Langevin equation of two fractional orders Dβ(Dα+γ)ψ(t)=λϑ(t,ψ(t))w˙(t),0<t≤1. Given some suitable conditions on the above parameters, we prove the existence and uniqueness of the mild solution to the initial value problem for the stochastic nonlinear fractional Langevin equation using Banach fixed-point theorem (Contraction mapping theorem). The upper bound estimate for the second moment of the mild solution is given, which shows exponential growth in time t at a precise rate of 3c1expc3t2(α+β)−1+c4t2α−1 on the parameters α>1 and α+β>1 for some positive constants c1,c3 and c4.

Some Upper Bounds for RKHS Approximation by Bessel Functions

A reproducing kernel Hilbert space (RKHS) approximation problem arising from learning theory is investigated. Some K-functionals and moduli of smoothness with respect to RKHSs are defined with Fourier–Bessel series and Fourier–Bessel transforms, respectively. Their equivalent relation is shown, with which the upper bound estimate for the best RKHS approximation is provided. The convergence rate is bounded with the defined modulus of smoothness, which shows that the RKHS approximation can attain the same approximation ability as that of the Fourier–Bessel series and Fourier–Bessel transform. In particular, it is shown that for a RKHS produced by the Bessel operator, the convergence rate sums up to the bound of a corresponding convolution operator approximation. The investigations show some new applications of Bessel functions. The results obtained can be used to bound the approximation error in learning theory.

A robust control scheme for synchronizing fractional order disturbed chaotic systems with uncertainty and time-varying delay

In this paper, a new method is presented for synchronization between two fractional order delayed chaotic systems, while there is uncertainty on the models and external disturbances enter the systems at the same time. The considered delay in the fractional order system is unspecified and varied with time, and of course it is present in different forms in master and slave systems. External disturbances enter the master–slave systems in a finite manner, albeit with an undetermined upper bound, and uncertainty is present in the nonlinear functions of chaotic systems. The goal of synchronizing a particular class of master–slave chaotic systems is achieved through a combination of adaptive and sliding mode techniques. The sliding mode method has been used to cover the effects of uncertainties and delay functions, and an adaptive method has been applied to ensure the stability of the proposed synchronization technique, disturbance upper bound estimation and overcoming the effects of delay variability. A practical example of the innovative method is simulated in MATLAB environment and the obtained results confirm the optimal efficiency of the proposed synchronization method.

Radiation Exposures and Compensation of Victims of French Atmospheric Nuclear Tests in Polynesia

Between 1966 and 1974, France conducted 41 atmospheric nuclear weapon tests in French Polynesia, exposing local populations to radioactive fallout. Under French law, individuals who were present at the time and later developed certain radiogenic cancers are eligible for compensation from the government—unless it is proven that they could not have received effective doses greater than 1 mSv in any given year. Using new information available from recently declassified documents, as well as atmospheric transport modeling of radioactive fallout, this article shows that upper-bound government estimates of effective doses received by the public have been underestimated by factors of 2 to 10. As a result, approximately 110,000 people, representing 90% of the French Polynesian population at the time, could have received doses greater than 1 mSv per year. Integrating updated dose estimates into the claim adjudication process would enlarge the pool of eligible claimants by a factor of 10.

Three-dimensional tunnel face stability considering slurry pressure transfer mechanisms

In slurry-shield tunneling, the bentonite slurry tends to infiltrate into the soil skeleton ahead of the tunnel face, causing a forward seepage flow associated with excess pore pressures in the ground. Both the slurry infiltration and the forward seepage flow significantly impact the tunnel face stability. In the present paper, a kinematic approach of limit analysis with the classical three-dimensional discretized rotational failure mechanism is employed to assess the face stability of a slurry-shield-driven tunnel. Three situations of slurry infiltrations that influence the face pressure transfer mechanisms were considered: a full filter cake, a penetration zone, and pure groundwater flow without a filter cake or a penetration zone. The pore pressure distributions surrounding the tunnel face were firstly obtained using numerical calculations. Afterward, the incorporation of numerically obtained pore pressure distributions into the work rate calculations allows considering a three-dimensional forward seepage flow ahead of the tunnel face, which provides a rigorous upper-bound estimation to the tunnel face safety factor determined by the strength reduction technique. The proposed method is validated by comparing the calculated results with those provided by previously published literature. The effects of excess slurry pressures, hydraulic conditions, pressure drop coefficients, and soil shear strength were investigated. Several design charts are given for practical application.

Stochastic approximation of lamplighter metrics

We observe that embeddings into random metrics can be fruitfully used to study the L 1 $L_1$ -embeddability of lamplighter graphs or groups, and more generally lamplighter metric spaces. Once this connection has been established, several new upper bound estimates on the L 1 $L_1$ -distortion of lamplighter metrics follow from known related estimates about stochastic embeddings into dominating tree-metrics. For instance, every lamplighter metric on an n $n$ -point metric space embeds bi-Lipschitzly into L 1 $L_1$ with distortion O ( log n ) $O(\log n)$ . In particular, for every finite group G $G$ the lamplighter group H = Z 2 ≀ G $H=\mathbb {Z}_2\wr G$ bi-Lipschitzly embeds into L 1 $L_1$ with distortion O ( log log | H | ) $O(\log \log |H|)$ . In the case where the ground space in the lamplighter construction is a graph with some topological restrictions, better distortion estimates can be achieved. Finally, we discuss how a coarse embedding into L 1 $L_1$ of the lamplighter group over the d $d$ -dimensional infinite lattice Z d $\mathbb {Z}^d$ can be constructed from bi-Lipschitz embeddings of the lamplighter graphs over finite d $d$ -dimensional grids, and we include a remark on Lipschitz free spaces over finite metric spaces.

Prevalence of amyotrophic lateral sclerosis in the United States using established and novel methodologies, 2017

Objective:To estimate the prevalence of amyotrophic lateral sclerosis (ALS) in the United States for 2017 using data from the National ALS Registry (Registry) as well as capture–recapture methodology to account for under-ascertainment. Established in 2010, the Registry collects and examines data on ALS patients in the US to better describe the epidemiology of ALS (i.e. risk factor exposures, demographics). Methods: The Registry compiled data from national administrative databases (from the Centers for Medicare and Medicaid Services, the Veterans Health Administration, and the Veterans Benefits Administration) and a voluntary enrollment data through a web portal (www.cdc.gov/als). To estimate the number of missing cases, capture–recapture methodology was utilized. Results: The Registry conservatively identified 17,800 adult persons (lower-bound estimate) who met the Registry definition of ALS for an age-adjusted prevalence of 5.5 per 100,000 US population. Using capture–recapture methodology, we obtained a “mean case count” of 24,821 ALS cases (prevalence of 7.7 per 100,000 U.S. population) and estimated the upper-bound estimate to be 31,843 cases (prevalence of 9.9 per 100,000 U.S. population). The pattern of patient characteristics (e.g. age, sex, and race/ethnicity) remained unchanged from previous Registry reports. Overall, ALS was most common among whites, males, and persons aged 60–69 years. The age groups with the lowest number of cases were persons aged 18–39 years. Males had a higher prevalence than females overall and across all data sources. Conclusions: Existing Registry methodology, along with capture-recapture methodology, are being used to better describe the epidemiology and demographics of ALS in the US.

Upper-Bound Error Estimates for Double Phase Obstacle Problems with Clarke’s Subdifferential

The main goal of this article is to investigate upper-bound error estimates (also called error bounds) for a class of double phase obstacle problems. We first recall double phase implicit obstacle problems involving Clarke’s subdifferential given by Zeng et al. [Calc. Var. Partial Differential Equations 59 (2020): 176]. Then, based on regularized gap functions introduced by Yamashita and Fukushima, we establish some regularized gap functions for the double phase obstacle problem. Finally, using the properties of Clarke’s subdifferential and double phase operators, the upper-bound error estimates for such double phase obstacle problems in terms of regularized gap functions are provided.

Measuring timely geographical access to surgical care in India: a geospatial modelling study

BackgroundIn 2015, the Lancet Commission on Global Surgery proposed timely access to surgical care facilities as an indicator of preparedness in surgical systems. Since then, several African and South American countries have mapped the population coverage for their surgical facilities. However, these estimates are missing for India, despite its large population, geographical scope, and sociodemographic diversity. We conducted a nationwide analysis of timely access to surgical care in India and point to rural–urban disparities. MethodsWe extracted a nationwide dataset of 20 802 geolocated surgical care facilities from the IndoHealMap project. We obtained accessibility motorised friction surface raster data cropped for India from the Malaria Atlas Project Explorer. We calculated the travel times from each grid cell (equivalent to 1 km2) in India to its nearest surgical facility under the optimal speed estimation by means of the Djikstra least-cost algorithm. District-level and state-level rural and urban populations were estimated through raster-based analysis via data from WorldPop, Urban-Rural Catchment Areas, and GADM version 3.6. The primary endpoint of the analysis was the proportion of population within 2 h of their nearest surgical care facility at national, state, and district levels. Wilcoxon tests adjusted for multiple comparisons (Holm-Bonferroni correction) were used to investigate rural-urban differences at a 5% significance level. FindingsThe motorised travel-times distribution is highly right-skewed, depicting that a large number of areas in India were within 2 h of their nearest surgical facility. At the national level, 99·2% of the rural population had timely access to surgical care facilities, compared with 99·8% of the urban population. However, less than 80% of the rural population in the northern and northeast regions had timely access to care. The rural regions had a significantly smaller proportion of residents with timely access to surgical care compared with their and urban counterparts at the district level (n=1299, effect size=0·57; p<0·001) and state level (n=71, effect size=0·51; p<0·001) analyses. InterpretationOur findings should be considered upper-bound estimates for geographical access because they assume readily available motorised transport and optimal travel speeds, which might not always be the case. These first-ever estimates can inform India's National Surgical, Obstetric, and Anesthesia Plan and which locations should be focused on for upcoming surgical facilities. FundingNo funding to declare.

Preliminary cost variance modeling to compare autologous intraovarian platelet-rich plasma vs. standard hormone replacement therapy for menopause management

Menopause symptoms and hormone replacement therapy (HRT) are among the most common reasons patients seek gynecological advice. Although at least half of all women in developed countries will use HRT during their lifetime, the treatment is not without risk and guidance on HRT is mixed. Greater awareness of HRT risks from extended use has piqued interest in safer options. Menopause reversal with autologous ovarian platelet-rich plasma (OPRP) has brought this restorative approach forward for consideration, but appropriateness and cost-effectiveness require examination. HRT and OPRP data from USA were projected to compare cumulative 1yr patient costs using stochastic Monte Carlo modeling. Mean ± SD cost-to-patient for HRT including initial consult plus pharmacy refills was estimated at about $576 ± 246/yr. While OPRP included no pharmacy component, an estimated 4 visits over 1yr for OPRP maintenance entailed ultrasound, phlebotomy/sample processing, surgery equipment, and incubation/laboratory expense, yielding mean ± SD cost for OPRP at $8,710 ± 4,911/yr ( P < 0.0001 vs. HRT, by T-test). Upper-bound estimates for annual HRT and OPRP costs were $1,341 and $22,232, respectively. While HRT and OPRP may have similar efficacy and safety for menopause therapy, they diverge sharply in cost-effectiveness. Most patients would likely find OPRP too complex, invasive, and expensive to be competitive vs. HRT. Although OPRP is an interesting and cautiously useful technique for selected menopause patients reluctant to use HRT, repurposing this infertility treatment for wider use appears inefficient compared to standard HRT options that are currently marketed.