Bound Estimate Research Articles

Lateral Shared Sliding Mode Control for Lane Keeping Assist System in Steer-by-Wire Vehicles: Theory and Experiments

The lane-keeping assistance design for steer-by-wire road vehicles is a multi-objective control problem that addresses lane tracking, improvement of driver comfort and ensuring vehicle stability. The designed architecture must be sensitive to various driver behaviors, provide assistance to drivers whenever required and ensure a smooth transition of authority between manual and automated driving modes. In this work, we propose a novel shared lane-keeping controller-based on quasi-continuous high-order sliding mode control dealing with the above challenges. The parameters of the controller are characterized by an upper bound estimate of the lateral winds force and the road curvature which acts as disturbances. Using the sharing parameter dependent on the monitored driver attribute, the authority is smoothly transitioned between various modes while accounting for driver behaviors. Experimental results on the SHERPA vehicle simulator shows the real-time implementation feasibility. Extensive results and discussions are provided to demonstrate the effectiveness and the applicability of the proposed controller.

Fekete–Szegö Problem and Second Hankel Determinant for a Class of Bi-Univalent Functions Involving Euler Polynomials

Some well-known authors have extensively used orthogonal polynomials in the framework of geometric function theory. We are motivated by the previous research that has been conducted and, in this study, we solve the Fekete–Szegö problem as well as give bound estimates for the coefficients and an upper bound estimate for the second Hankel determinant for functions in the class GΣ(v,σ) of analytical and bi-univalent functions, implicating the Euler polynomials.

Fourier Analysis and Its Application

In this article, mathematicianswill give a general summary of Fourier analysis and some of its applications. The Fourier transform will be organized in a developing order, the discrete Fourier transform, Fourier transform on the unit circle and Fourier transform on the real line. Some theorems about the convergence of Fourier series in different forms will be proved in detail. Finally, an estimation of the upper bound of Fourier transform will be discussed. Mathematicianscan prove that it is controlled by the 1-norm of the derivative of f.

Estimation of Absorbed Power Density Based on Spherical Wave Expansion to Plane Wave Expansion for Exposure Assessment at 30 GHz

The international guidelines and standard specified the area-averaged absorbed/epithelial power density (APD/EPD) as the basic restriction at frequencies above 6 GHz. Assessment methods for APD are current under the consideration of standardization organizations. In this study, we first showed the enhancement of the APD due to the antenna/body interaction using full-wave simulations. We then proposed a hybrid method combining the spherical near-field measurement and numerical simulation of the exposure dose in human body, using an equivalent source reconstructed on the total field/scattered field boundary using the spherical wave expansion to plane wave expansion. By comparing with the full-wave simulated APD at 30 GHz for various antenna arrays, the proposed method gives a rather accurate estimation of the upper bound of the area-averaged APD (with relative differences < 28%). It can be utilized as an efficient method for electromagnetic safety assessment as the need for specific measurement equipment is eliminated.

In Search of the Max Coverage Region in Road Networks

The widespread use of mobile devices has resulted in the generation of vast amounts of spatial data. The availability of such large-scale spatial data facilitates the development of data-driven approaches to address real-life problems. This paper introduces the max coverage region (MCR) problem in road networks and provides efficient solutions. Given a set of spatial objects and a coverage radius, the MCR problem aims to identify a location from the road network, so that we can reach as many spatial objects as possible within the given coverage radius from the location. This problem is fundamental to supporting many real-world applications. Given a road network and a set of sensors, this problem can be used to find the best location for a sensor maintenance station. This problem can also be applied in medical research, such as in a protein–protein interaction network, where the nodes represent proteins, the edges represent their interactions, and the weight of an edge represents confidence. We can use the MCR problem to find the set of interacting proteins with a confidence budget. We propose an efficient exact solution to solve the problem, where we reduce the MCR problem to an equivalent problem named the most overlapped interval and design an edge-level upper bound estimation method to reduce the search space. Furthermore, we propose two approximate solutions that sacrifice a little accuracy for much better efficiency. Our experimental study on real-road network datasets demonstrates the effectiveness and superiority of the proposed approaches.

Optimal blending of multiple independent prediction models.

We derive blending coefficients for the optimal blend of multiple independent prediction models with normal (Gaussian) distribution as well as the variance of the final blend. We also provide lower and upper bound estimation for the final variance and we compare these results with machine learning with counts, where only binary information (feature says yes or no only) is used for every feature and the majority of features agreeing together make the decision.

Global weak solutions to a nonlinear equation with fourth order nonlinearities

Global weak solution for a nonlinear model with forth order nonlinearities and conserved quantities is considered. Assuming its initial value satisfies certain assumptions that are weaker than the sign condition, we derive a higher integrability estimate and an upper bound estimate about the space derivatives of its solutions and then prove that the equation has global weak solutions.

Potential Airborne Releases and Deposition of Radionuclides from the Santa Susana Field Laboratory during the Woolsey Fire.

The Santa Susana Field Laboratory (SSFL), located in southern California, is a former research facility, and past activities have resulted in residual radioactive contamination in Area IV of the Site. The Woolsey Fire burned across the site, including some of the contaminated areas, on 8-11 November 2018. Atmospheric transport modeling was performed to determine where the smoke plume went while the fire burned across the SSFL and the deposition footprint of particulates in downwind communities. Any radionuclides on vegetation and in surface soil released by the fire were assumed to follow particulate matter transport path and deposition. The predicted deposition footprint was used to guide confirmatory soil sampling at 16 locations including background. Highest offsite deposition was determined to be northeast of the Oak Park community, which is located about 6 km southwest of SSFL. Depth-profile sampling was used to evaluate whether radionuclides of SSFL origin were potentially emitted and deposited during the Woolsey Fire. If radionuclides had been deposited from the Woolsey Fire at sufficient concentrations, then they would be detected in the surface layer and would be expected to be higher within the plume footprint than outside it. An upper bound estimate of the hypothetical effective dose to a person in Oak Park based on measured radionuclide concentrations in soil and vegetation on the SSFL was less than 0.0002 mSv. The occurrence of naturally occurring radionuclides at concentrations above the established background for the SSFL was attributed to natural variability in geologic formations and not SSFL. No anthropogenic radionuclides were measured at levels above those expected from global fallout. The soil sampling confirmed that no detectable levels of SSFL-derived radionuclides migrated from SSFL at the locations sampled because of the Woolsey Fire or from past operations of the SSFL.

Laboratory modeling in laser-induced plasma to estimate the pressure in bolide wake

Aims. We study Fe and FeO emission in laser-induced plasma under reduced pressure to develop an approach for finding the conditions under which the laboratory plasma state matches the state of bolide wake plasma. Methods. To acquire spectra of laser-induced plasma, we ablated a target of Fe3O4 in a vacuum chamber using a Q-switched laser. The Boltzmann plot method and Stark broadening of the emission lines were used to estimate the plasma temperature and electron number density. The intensity ratios of two Fe I lines (544.61 nm and 558.69 nm) to the intensity of FeO orange band at 587.1 nm were calculated to compare the conditions in laser-induced plasma and bolide wake plasma. Results. Several combinations of pressure (75–150 Torr) and delay (12–15 μs) lead to the highest degree of similarity between laser-induced plasma and the Beneov bolide spectra at an altitude of 39 km. Importantly, the plasma parameters and pressure are consistent at these points. A detailed comparison of the spectra shows that the best-match conditions are 100 Torr and 15 μs. This pressure is ≈25 times higher than the ambient pressure at this altitude. Conclusions. We assume that the pressure in the bolide wake is higher than the ambient pressure by a factor of 20–30. This can be considered to be the upper bound estimate of the pressure in the bolide wake, and the developed approach would be beneficial to support the modeling of a meteoroid entry.

Application of Ramsey theory to localization of set of product states via multicopies

It is well known that any N orthogonal pure states can always be perfectly distinguished under local operation and classical communications (LOCC) if \((N-1)\) copies of the state are available (Walgate et al. Phys. Rev. Lett. 85, 4972 (2000)). It is important to reduce the number of quantum state copies that ensures the LOCC distinguishability in terms of resource saving and nonlocality strength characterization. Denote \(f_r(N)\) the least number of copies needed to LOCC distinguish any N orthogonal r-partite product states. This work will be devoted to the estimation of the upper bound of \(f_r(N)\). In fact, we first relate this problem with Ramsey theory, a branch of combinatorics dedicated to studying the conditions under which orders must appear. Subsequently, we prove \(f_2(N)\le \lceil \frac{N}{6}\rceil +2\), which is better than \(f_2(N)\le \lceil \frac{N}{4}\rceil\) obtained in Shu (Eur. Phys. J. Plus 136, 1172 (2021)) when \(N>32\). We further exhibit that for arbitrary \(\epsilon >0\), \(f_r(N)\le \lceil \epsilon N\rceil\) always holds for sufficiently large N.

$$L^{p}$$-Improving Bounds and Weighted Estimates for Maximal Functions Associated with Curvature

$$L^{p}$$-Improving Bounds and Weighted Estimates for Maximal Functions Associated with Curvature

Tourism Demand Interval Forecasting Amid COVID-19: A Hybrid Model With a Modified Multi-Objective Optimization Algorithm

A hybrid tourism demand interval forecasting system is proposed consisting of two parts: the construction of forecasting interval based on lower and upper bound estimates, and the forecasting interval adjustment based on an optimized reduction coefficient. Coronavirus factors are added as input variables to improve forecasting performance. A new multi-objective optimization algorithm is proposed to construct a feature selection method, optimize the forecasting model, and estimate the optimal reduction coefficient. The results of the experiments show that the proposed system has a powerful interval forecasting ability, which provides crucial guidance for balancing the recovery of the tourism industry and the control of the epidemic spread during the COVID-19 pandemic, and contributes to contingency planning for tourism practitioners and managers.

Model and upper–lower bound estimation scheme for portfolio optimisation considering uncertain investment time horizon

In this paper, we study the portfolio selection problem considering the uncertain investment time horizon. We employ the Period Value at Risk (PVaR) to characterise the risk in the special cases and establish a fundamental mixed integer linear programming (MILP) model to obtain the optimal portfolio solutions. Identifying that the symmetric property of PVaR can significantly reduce the computation burden of the CPLEX solver, an enhanced MILP model is proposed. To verify the quality of obtained solutions, we also develop fast lower and upper bound estimation schemes respectively. Using the real-world data sets from NYSE and NASDAQ stock markets, numerical results are provided to show the efficiency of the enhanced model.

Global weak solutions of nonlinear rotation-Camassa-Holm model

&lt;abstract&gt;&lt;p&gt;A nonlinear rotation-Camassa-Holm equation, physically depicting the motion of equatorial water waves and having the Coriolis effect, is investigated. Using the viscous approximation tool, we obtain an upper bound estimate about the space derivative of the viscous solution and a high order integrable estimate about the time-space variables. Utilizing these two estimates, we prove that there exist $ H^1(\mathbb{R}) $ global weak solutions to the rotation-Camassa-Holm model.&lt;/p&gt;&lt;/abstract&gt;

On the distribution of adjacent zeros of solutions to first-order neutral differential equations

The purpose of this paper is to study the distribution of zeros of solutions to a first-order neutral differential equation of the form \begin{equation*} \left[x(t) + p(t) x(t-\tau)\right]' + q(t) x(t-\sigma) = 0, \quad t \geq t_0, \end{equation*} where $p\in C([t_0,\infty),[0,\infty))$, $q \in C([t_0,\infty),(0,\infty))$, $\tau,\sigma>0$, and $\sigma>\tau$. We obtain new upper bound estimates for the distance between consecutive zeros of solutions, which improve upon many of the previously known ones. The results are formulated so that they can be generalized without much effort to equations for which the distribution of zeros problem is related to the study of this property for a first-order delay differential inequality. The strength of our results is demonstrated viatwo illustrative examples.

Estimating the Impact of New Health Price Transparency Policies.

This analysis investigates and scores the impact of new health price transparency rules. Using a set of novel data sources, we estimate substantial savings are possible following the implementation of the insurer price transparency rule. Specifically, we estimate annual savings to consumers, employers, and insurers by 2025, assuming a robust set of tools to allow consumers to purchase medical services. We matched claims with 70 HHS defined shoppable services by CPT and DRG codes and replaced them with an estimated median commercial allowed payment multiplied by a reduced cost of 40% based on estimates found from literature for the difference in cost between negotiated and cash payment for medical services. We consider 40% to be an upper bound estimate of the potential savings based on existing literature. Several databases are used to estimate the potential benefits of insurer price transparency. Two different all-payer claim databases were used, representing the entire insured population in the US. For this analysis, only the private insurer commercial population was examined, comprised of over 200 million covered lives as of 2021. The estimated impact of price transparency will vary significantly by region and income level. The national upper bound estimate is $80.7 billion. The national lower bound estimate is $17.6 billion. For the upper bound, the region with the most significant impact in the US will be the Midwest, with $20 billion in potential savings and an 8% reduction in medical expenditure. The region with the lowest impact will be the South, with only a 5.8% reduction. Concerning income, those at lower levels of income will have the most significant impact with a -7.4% (<100% Federal Poverty Level) to -7.5% (100%-137% Federal Poverty Level) impact. Overall, the total impact could be a 6.9% reduction for the whole privately insured population in the United States. In summary, a unique set of national data resources were used to estimate the cost savings impact medical price transparency. This analysis suggests price transparency for shoppable services may yields significant savings between $17.6 to $80.7 billion by 2025. Consumers may have strong incentives to shop with the rise in the use of high deductibles, health plans, and health savings accounts. How these potential saving are to be shared by consumers, employers and health plans has yet to be determined.

Farmer demand for certified legume seeds and the viability of farmer seed enterprises: Evidence from Myanmar

Legume seed systems in many developing countries are characterized by low availability of certified seeds because the private sector is often absent, and the public sector has limited capacity to produce such seeds. Farmer seed enterprises (FSEs) are therefore increasingly promoted as alternative suppliers of certified and in some instances, quality declared and truthfully labelled seeds. In this study, we assess the commercial viability of FSEs that produce chickpea and green gram certified seeds by comparing average seed production cost, inclusive of opportunity costs and expected profits, with consumers’ willingness to pay (WTP) price. The cost of seed production data come from a survey of 63 FSEs and the data on WTP are from the Becker, DeGroot, Marschak (BDM) bidding experiments conducted with 512 farmers from the Central Dry Zone of Myanmar. We find that the post-harvest storage cost during the 7–8 months between harvest and the next planting season contributes significantly to the total cost of producing seeds. Forty-seven percent of chickpea farmers and 53% of green gram farmers were willing to pay equal to or higher than the average minimum cost of producing certified seeds. which is as an upper bound estimate of potential market share for FSEs’ certified seeds. This potential customer base of FSEs can be further increased by reducing the cost, especially post-harvest and labor costs. What role government, private companies, and NGOs could play in reducing the cost and increasing the demand for certified seed are important policy research questions discussed in the paper.

Stochastic Fixed-Time Tracking Control for the Chaotic Multi-Agent-Based Supply Chain Networks with Nonlinear Communication

The multi-agent-based supply chain network is a dynamic system consisting of multiple subchains connected by information flows, material flows and capital flow, etc. The consensus of multi-agent systems is often applied to the cooperation between subchains and inventory management in supply chain networks. Considering the ubiquitous external disturbances, this paper mainly considers the fixed-time consensus of a stochastic three-echelon multi-agent-based supply chain system. A nonlinear feedback fixed-time control protocol is constructed for ensuring the consensus of the considered supply chain network. Using the stability theory of stochastic differential equations, sufficient conditions for the fixed-time consensus and the upper bound estimation of the settling time are obtained. Finally, the validity of the control protocol and the correctness of the theoretical analysis are revealed by numerical simulation.

Area and Spectrum Estimates for Stable Minimal Surfaces

This paper mainly concerns the area growth and bottom spectrum of complete stable minimal surfaces in a three-dimensional manifold with scalar curvature bounded from below. When the ambient manifold is the Euclidean space, by an elementary argument, it is shown directly from the stability inequality that the area of such minimal surfaces grows exactly as the Euclidean plane. Consequently, such minimal surfaces must be flat, a well-known result due to Fisher-Colbrie and Schoen as well as do Carmo and Peng. In the case of general ambient manifold, explicit area growth estimate is also derived. For the bottom spectrum, a self-contained argument involving positive Green’s function is provided for its upper bound estimates. The argument extends to stable minimal hypersurfaces in a complete manifold of dimension up to six with sectional curvature bounded from below.

Where forest may not return in the western United States

Droughts that are hotter, more frequent, and last longer; pest outbreaks that are more extensive and more common; and fires that are more frequent, more extensive, and perhaps more severe have raised concern that forests in the western United States may not return once disturbed by one or more of these agents. Numerous field-based studies have been undertaken to better understand forest response to these changing disturbance regimes. Meta-analyses of these studies provide broad guidelines on the biotic and abiotic factors that hinder forest recovery, but study-to-study differences in methods and objectives do not support estimation of the total extent of potentially impaired forest succession. In this research, we provide an estimate of the area of potentially impaired forest succession. The estimate was derived from modeling of an 18-year land cover and Normalized Difference Vegetation Index (NDVI) time series supported by an extensive ancillary dataset. We estimate an upper bound of approximately 3470 km2 of disturbed forest that may not return or reattain prior composition and structure. Based on the data used, fire appears to be the main disturbance agent of impaired forest succession, although climatic factors cannot be discounted. The numerous field studies routinely cite distal seed sources as a factor that hinders forest recovery, and we estimate that 20 % of the upper bound estimate has no forest cover within a 4.4-ha neighborhood. Our upper bound estimate is about 0.5 % of the 2001 mapped extent of western United States forests. The estimate is cognizant of measurement and modeling uncertainties (i.e., upper bound) and uncertainties related to successional rates and trajectories (i.e., potential).