Upper-bound Estimates Research Articles

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.

Impact of plastic pollution on atmospheric carbon dioxide

Since the beginning of its large-scale production in the early 20th century, plastics have remained an important material in widespread use throughout modern society. Nevertheless, despite possessing many benefits, plastics are resistant to degradation and instead accumulate in the ocean and terrestrial sediments, thereby potentially affecting marine and terrestrial ecosystems. Plastics release CO2 throughout their entire lifecycle; during the extraction of materials used in their production, through plastic–carbon leaching in the marine and terrestrial environment, and during their different end-of-life scenarios, which include recycling, landfill, and incineration. Here, we use the University of Victoria earth system climate model to quantity the effects on atmospheric CO2 and the ocean carbon cycle by using upper-bound estimates of carbon emissions from marine plastic–carbon leaching or land-based incineration. Despite the suggestions of some, our results indicate that it has only a very minor influence and an insignificant effect on the earth's global climate system. This holds even if plastic contamination increases well beyond current levels. On the other hand, carbon emissions associated with plastic production and incineration have a greater impact on climate while still dwarfed by emissions associated with the combustion of fossil fuels (coal, oil, and natural gas) and other anthropogenic sources. Our results have important policy implications for ongoing United Nations Environment Programme Intergovernmental Negotiating Committee on Plastic Pollution negotiations.

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).

Fixed‐time control of nonlinear p‐normal systems under saturated threshold event‐triggered mechanism

SummaryIn this article, the saturated threshold event‐triggered (STET) adaptive fixed‐time control problem for a class of nonlinear ‐normal systems with external disturbances is studied. Firstly, a nonsingular fixed‐time controller is designed by adding one power integrator and a smoothing function. Compared with existing fixed‐time control schemes for nonlinear ‐normal systems, the upper bound estimation of settling time is more accurate. Second, an STET control strategy is introduced to reduce the communication burden. Moreover, the influence of external disturbances on the system is inhibited by performance. Through theoretical analysis, it is proved that all states in closed‐loop system converge to origin within a fixed‐time and the Zeno phenomenon is completely circumvented. Simulation results are finally provided to verify the effectiveness of the proposed method.

Modeling unsaturated flow in fractured rocks with scaling relationships between hydraulic parameters

Modeling unsaturated flow in fractured rocks is essential in various subsurface engineering applications, but it remains a great challenge due to the difficulties in determining the unsaturated hydraulic properties of rocks that contain various scales of fractures. It is generally accepted that the van Genuchten (VG) model can be applied to fractured rocks, provided that the hydraulic parameters could be representatively determined. In this study, scaling relationships between the VG parameters ( α and n ) and hydraulic conductivity ( K ) across 8 orders of magnitude, from 10 −10 m/s to 10 −2 m/s, were proposed by statistical analysis of data obtained from 1416 soil samples. The correlations were then generalized to predict the upper bounds of VG parameters for fractured rocks from the K data that could be obtained more easily under field conditions, and were validated against a limited set of data from cores, fractures and fractured rocks available in the literature. The upper bound estimates significantly narrow the ranges of VG parameters, and the representative values of α and n for fractured rocks at the field scale can then be determined with confidence by inverse modeling using groundwater observations in saturated zones. The proposed methodology was applied to saturated-unsaturated flow modeling in the right-bank slope at the Baihetan dam site with a continuum approach, showing that most of the flow behaviors in fractured rocks in this complex hydrogeological condition could be properly reproduced. The proposed method overcomes difficulties in suction measurement in fractured rocks with strong heterogeneity, and provides a feasible way for modeling of saturated-unsaturated flow in fractured rocks with acceptable engineering accuracy.

Estimating the spectral abscissa for switched linear systems via square coordinate transformations

AbstractSwitched linear systems are important in providing a convenient method to represent many practical systems. This paper investigates the performance analysis of switched linear systems under arbitrary switching. Computational algorithms based on square coordinate transformations are presented to obtain the least μ1 measure. Theoretical results showed that sequences of the least μ1 matrix set measure obtained by two different algorithms are convergent and the limit gives an upper bound estimation of the spectral abscissa. A numerical example is presented to show the effectiveness of the proposed method.

Maximum displacement prediction of composite floor system under falling impact

Analytical and numerical investigations on the maximum displacement of the steel-concrete composite floor system subjected to falling impact are presented in this paper. Explicit formulae are established to compute the floor maximum displacement under impacts with different kinetic energy transfer ratios. Parametric analyses are conducted to study the influence of impactor mass, impact height, floor longitudinal span, floor thickness, rebar diameter, beam depth, and coefficient of restitution on the maximum displacement of floor. Associated practical recommendations are also proposed for determining the maximum displacement of floor under falling impact. It is found that in fully elastic impact, the maximum displacement is highly sensitive to the impact height, whereas in fully plastic impact, the value is significantly affected by the impactor mass. The upper-bound estimation of the displacement can be achieved by using fully elastic impact model. However, fully plastic impact model should be adopted when the impactor mass increases to more than 30 % of the total mass of the floor.

CTNI-10. RANDOMIZED PIVOTAL STUDY OF BLOOD-BRAIN BARRIER (BBB) DISRUPTION USING EXABLATE MODEL 4000 WITH STANDARD OF CARE (SOC) THERAPY IN NON-SMALL CELL LUNG CANCER (NSCLC) BRAIN METASTASES: LIMITLESS TRIAL

Abstract BACKGROUND NSCLC is the most common cause of brain metastases. The Exablate focused ultrasound with circulating microbubble resonators uses the concept of real-time imaging to treat small target spots focusing energy through the skull in noninvasive manner, thereby disrupting the BBB. There is preclinical evidence of synergy of FUS-mediated BBB with immunotherapy beyond improved drug delivery due to BBB disruption (BBBD). METHODS LIMITLESS is a prospective, multi-center, randomized, two-arm, controlled, pivotal clinical trial to evaluate the safety and efficacy of additional targeted BBB disruption using Exablate Model 4000 for the treatment of NSCLC brain metastases in subjects who are undergoing planned pembrolizumab monotherapy compared to Pembrolizumab alone in 2:1 randomization. The inclusion criteria include age ≥ 18 years, KPS ≥ 70, NSCLC (EGFR and ALK negative) with up to 3 brain metastases, one of which meets the RANO-BM criteria for measurable Disease (1 cm x 1 cm) with normal organ function. The primary endpoint is to test superiority of Exablate BBBD targeted to their brain metastases over the standard of care without Exablate BBBD as determined by Objective Response Rate (ORR) based on RANO- BM by 6 months. The secondary endpoints include best objective response rate and time to response for brain metastases by treatment arm. Other end points include progression-free survival (PFS), overall survival (OS), Intracranial and extracranial PFS, quality of life assessments. The Bayesian design statistical analysis will assume superior ORR of 60% in Exablate group compared to 30% in SOC group for a total sample size of 96 subjects (64 subjects in Exablate and 32 in SOC) for 80% power using a two-sided Pearson's Chi-Square test with alpha = 0.05. For the upper-bound estimate ORR of 45% in Exablate group and 30% in SOC group will need 369 subjects (246 subjects in Exablate and 123 in SOC).

A new direct acyclic graph task scheduling method for heterogeneous Multi-Core processors

At present, the traditional methods of calculating the worst response time upper bounds for direct acyclic graph (DAG) task scheduling on heterogeneous multi-core platforms suffer from problems such as nonself-sustainability, too many blocking nodes, and excessive estimation of the overhead time required for task scheduling, all of which cause response time upper bound estimates to be far too pessimistic. We propose to reconstruct the DAG graph by adding execution edges in order to eliminate blocking nodes. The specific method is to first use triples to represent each node of the DAG task graph, then to select blocking nodes according to the priority rules with which we add execution edges graph to reconstruct it, and finally to remove the blocking nodes again and repeat the process until all blocking nodes have been eliminated. Our experiments show that the worst response time upper bound from this method can achieve a 20% improvement in accuracy compared to the traditional methods for calculating the worst response time upper bound.

A distributed storage MLCS algorithm with time efficient upper bound and precise lower bound

Finding the longest common subsequence of multiple sequences (i.e., the MLCS problem) is a key issue in data mining, such as pattern recognition of bio-sequences (e.g., DNA and protein sequences), diagnosis of diseases, and deciphering human genetic codes. The length of the longest common subsequence is often used to measure the similarity between sequences. Current state-of-the-art algorithms for the MLCS problem often transform the problem into finding the longest path in a directed acyclic graph (DAG); however, their fatal flaw is that the time cost or constructed DAG is too large. Aiming at solving the problem of the existing algorithms, this paper proposes a time-efficient upper bound estimation method that can estimate the upper bound for the length of any path through a node in much less time, and then proposes an adaptive lower bound estimation strategy that can estimate the more precise lower bound for the length of the longest common subsequences. This study also describes a distributed storage scheme that stores most parts of the DAG in external devices and only a few parts in memory. A comparison with several state-of-the-art algorithms in the experiments indicates that the proposed algorithm is more efficient and effective.

A Novel Fixed-Time Protocol for First-Order Consensus Tracking With Disturbance Rejection

This technical note studies fixed-time consensus tracking with disturbance rejection for first-order multiagent systems. The communication topology among the leader and followers contains a directed spanning tree. The control input to the leader is time-varying and unknown to the followers, except that its upper bound is known <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> . A novel fixed-time protocol is devised based on discontinuous and nonlinear control. A fixed-time stability analysis for consensus tracking with disturbance rejection is completed as a one-step control process using nonsmooth analysis. An upper bound estimate for the settling time, independent of the initial conditions, is aesthetically pleasing, in comparison to previous results derived based on two-step control design technique using sliding modes. Finally, a numeric example confirms the theoretical results.

Upper and Lower Bound Estimates of Inequality of Opportunity: A Cross‐National Comparison for Europe

I provide lower and upper bound estimates of inequality of opportunity (IOp) for 32 European countries, between 2005 and 2019. Lower bound estimates use machine learning methods to address sampling variability. Upper bound estimates use longitudinal data to capture all‐time invariant factors. Across all years and countries, lower bound estimates of IOp account from 6 percent to 60 percent of total income inequality, while upper bound estimates account from 20 percent to almost all income inequality. On average, upper bound IOp saw a slight decrease in the aftermath of the Great Recession, recovering and stabilizing at around 80 percent of total inequality in the second half of the 2010s. Lower bound estimates for 2005, 2011, and 2019 show a similar pattern. My findings suggest that lower and upper bound estimates complement each other, corroborating information and compensating each other's weaknesses, highlighting the relevance of a bounded estimate of IOp.

Comparison of the simulated seismic behavior of small- and large-scale cripple walls: PEER-CEA Project test programs

As part of the Pacific Earthquake Engineering Research Center (PEER)-California Earthquake Authority (CEA) project, experimental programs were performed at UC San Diego and UC Berkeley, with the former focusing on small-component testing and the latter focusing on large-component testing. During the small-component testing program, a suite of 28 cripple wall-only specimens was tested under quasi-static reverse cyclic lateral loading with variations in exterior finishes, retrofit condition, cripple wall height, anchorage condition, boundary conditions, vertical load, and loading protocol. In the large-component testing program, cripple wall-first story specimens, load path connections, and combined materials in occupied stories were tested. The more easily performed small-component specimens facilitate comparison with the large-component specimens to allow the assessment of their potential to emulate large-scale specimen behavior, with a particular interest in cross-comparing their global hysteresis and physical damage evolution. This cross-comparison among small- and large-scale specimen test results is intended to offer best practices for the future design of cripple wall seismic retrofits in residential housing, with a particular interest in: (1) supporting the realistic design of small-component specimens that may capture the response of large-component specimens and (2) to qualitatively determine where the small-component tests fall in the range of lower- to upper-bound estimation of strength and deformation capacity for the purposes of numerical modeling. Data from both test programs were utilized in the PEER-CEA project to assist with validating numerical modeling tools, which in turn were used to generate seismic loss models capable of quantifying the reduction of loss achieved by applying state-of-practice retrofit methods as identified in FEMA P-1100 Vulnerability-Base Seismic Assessment and Retrofit of One- and Two-Family Dwellings. The objective of this article is to present an overview of the small- and large-component testing programs and key results pertaining to exterior finishes, boundary conditions, the FEMA P-1100 retrofit, and cripple wall height.

Deep reinforcement learning based energy storage management strategy considering prediction intervals of wind power

Wind power generation combined with energy storage is able to maintain energy balance and realize stable operation. This article proposes a data-driven energy storage management strategy considering the prediction intervals of wind power. Firstly, a power interval prediction model is established based on long-short term memory and lower and upper bound estimation (LUBE) to quantify the uncertainty of wind power, which solves the issue that traditional LUBE cannot adopt gradient descent method. Secondly, the energy storage management is transformed into Markov decision process and solved by deep reinforcement learning. The state space, action space and reward function of the interaction between agent and environment are established, and the value function is approximated through the deep Q network. Then, according to the real-time state, such as wind power, power prediction intervals, local load, dynamic electricity price and state of charge, the proposed strategy can make the charge/discharge schedule automatically. Finally, the effectiveness and superiority of the proposed energy storage management strategy are verified based on real wind farm dataset. The proportion of wrong decisions is zero, and daily transaction cost and wear cost of energy storage management system decrease significantly.

Resilient fixed-time synchronization of neural networks under DoS attacks

In this paper, the fixed-time synchronization of neural networks (NNs) with denial-of-service (DoS) attacks is investigated. A switching system with a stable subsystem and an unstable subsystem is utilized to describe the error dynamic behaviours between the master and slave NNs with DoS attacks. By virtue of the comparison principle, a novel fixed-time stability lemma for the switching system is established. The estimation of upper bound of setting time is provided. We further apply this lemma to investigate the resilient fixed-time synchronization of NNs subject to DoS attacks. By designing an appropriate controller, some sufficient criteria are proposed to guarantee the synchronization within a prearranged fixed time. The effects of DoS attacks on the settling time are discussed as well. Two numerical examples are given to show the effectiveness of main results and a potential application in the secure communication is provided.

Heat kernel estimates for general symmetric pure jump Dirichlet forms

In this paper, we consider the following symmetric non-local Dirichlet forms of pure jump type on metric measure space $(M,d,\mu)$: $$\mathcal{E}(f,g)=\int_{M\times M} (f(x)-f(y))(g(x)-g(y))\,J(dx,dy),$$ where $J(dx,dy)$ is a symmetric Radon measure on $M\times M\setminus {\rm diag}$ that may have different scalings for small jumps and large jumps. Under general volume doubling condition on $(M,d,\mu)$ and some mild quantitative assumptions on $J(dx, dy)$ that are allowed to have light tails of polynomial decay at infinity, we establish stability results for two-sided heat kernel estimates as well as heat kernel upper bound estimates in terms of jumping kernel bounds, the cut-off Sobolev inequalities, and the Faber-Krahn inequalities (resp. the Poincar\'e inequalities). We also give stable characterizations of the corresponding parabolic Harnack inequalities.

Adaptive robust asymptotic tracking control of nonaffine nonlinear systems

AbstractThis article investigates the barrier lyapunov function‐based adaptive robust control scheme for nonaffine nonlinear systems with unknown system dynamics. First, the nonaffine system is converted into affine system via a combination of first‐order filter and coordinate transformation, then a high‐gain observer is utilized to reconstruct the immeasurable states of the derived affine system. Second, a robust integral of the sign of the error (RISE) is incorporated into the control design to reject the unknown dynamics. Third, a barrier lyapunov function based design method is used to ensure that the input vector to the parameter estimation remain within a predefined region. Then, an adaptive robust control scheme with only one adaptive parameter by using the upper bound estimation is developed. Finally, numerical simulations validate the efficacy of the developed control scheme.