Regularity Conditions Research Articles

Counterfactual copula

This paper proposes a nonparametric estimator of the counterfactual copula of two outcome variables that would be affected by a policy intervention. The proposed estimator allows policymakers to conduct ex ante evaluations by comparing the estimated counterfactual and actual copulas as well as their corresponding association measures. Asymptotic properties of the counterfactual copula estimator are established under regularity conditions. These conditions are also used to validate the nonparametric bootstrap for inference on counterfactual quantities. Simulation results indicate that our estimation and inference procedures perform well in moderately sized samples.

[formula omitted] filtering for uncertain discrete-time singular switched positive systems with time delay and output quantization

This paper focuses on the design problem of an l1 filter for singular switched positive systems with time delay and uncertainty. In order to enhance resource efficiency and information transmission security, the quantization mechanism is introduced when designing the filter. Furthermore, sufficient conditions for causality, regularity, positivity, and exponential stability of the filtering error system are provided under the constraint of mode-dependent minimum dwell time (MDMDT). These conditions are obtained by selecting an appropriate co-positive Lyapunov function and are presented in the form of linear programming (LP). Subsequently, the disturbance attenuation performance is further analyzed, and a design methodology for the corresponding filter is outlined. Finally, a numerical example is presented to verify the validity of the theoretical results.

Note on quasi-optimal error estimates for the pressure for shear-thickening fluids

In this paper, we derive quasi-optimal a priori error estimates for the kinematic pressure for a Local Discontinuous Galerkin (LDG) approximation of steady systems of $p$-Navier--Stokes type in the case of shear-thickening, \textit{i.e.}, $p>2$, imposing a new Muckenhoupt regularity condition on the viscosity of the fluid, which is mild in the two-dimensional case but potentially restrictive in the three-dimensional case.

A numerical study on a winglet floating breakwater: Enhancing wave dissipation performance

Box-type floating breakwaters (FBs), widely used for marine protection, face challenges in their wave dissipation capabilities. Although the effectiveness of the winglet-type floating breakwater in improving wave dissipation has been recognized, the specific mechanisms involved are not fully understood. This research presents an innovative winglet breakwater design, featuring three unique winglet configurations: 4-wings, Down-wings, and Up-wings. The study examines its performance against both regular and irregular waves using the Smooth Particle Hydrodynamics (SPH) method, taking into account factors such as the wave period, FB immersion depth, and FB relative density. Numerical simulations indicate a marked enhancement in wave dissipation for the FB equipped with four winglets compared to a baseline model without winglets. The Response Amplitude Operator (RAO) amplitude for the winglet-equipped FB is notably lower, approximately half that observed in the baseline scenario. Notably, the winglet FB's performance in irregular waves outperforms that in regular wave conditions. The insights gained from the design of these winglets provide significant contributions to practical engineering applications.

Conducting viscous bodies with phase transitions: Deriving Gurtin’s postulate from the second law structure invariance

We prove that the basic structures of phase-field models for phase-transitions in non-isothermal setting can be derived all together from a unique principle requiring structure invariance of the second law of thermodynamics, written as a Clausius-Duhem inequality, under orientation-preserving diffeomorphism-based changes of observer and standard regularity conditions. We thus prove that the independent scalar balance of actions driving phase transitions does not require to be postulated, as it was in Gurtin’s 1996 proposal, rather it is a natural consequence of the invariance requirement adopted and maintains independence from constitutive choices. The approach discussed here is also a model-building framework for the dynamics of complex bodies and allows one to show that the microstructural behavior can be responsible of effects leading to wave-type heat propagation. The results indicate another role for the second law of thermodynamics, in addition to being a source of constitutive restrictions and compatibility or stability conditions.

Composite expectile estimation in partial functional linear regression model

Recent research and substantive studies have shown growing interest in expectile regression (ER) procedures. Similar to quantile regression, ER with respect to different expectile levels can provide a comprehensive picture of the conditional distribution of a response variable given predictors. This study proposes three composite-type ER estimators to improve estimation accuracy. The proposed ER estimators include the composite estimator, which minimizes the composite expectile objective function across expectiles; the weighted expectile average estimator, which takes the weighted average of expectile-specific estimators; and the weighted composite estimator, which minimizes the weighted composite expectile objective function across expectiles. Under certain regularity conditions, we derive the convergence rate of the slope function, obtain the mean squared prediction error, and establish the asymptotic normality of the slope vector. Simulations are conducted to assess the empirical performances of various estimators. An application to the analysis of capital bike share data is presented. The numerical evidence endorses our theoretical results and confirm the superiority of the composite-type ER estimators to the conventional least squares and single ER estimators.

Competitive fitness and stability of ammonium-excreting Azotobacter vinelandii strains in the soil

Non-symbiotic N2-fixation would greatly increase the versatility of N-biofertilizers for sustainable agriculture. Genetic modification of diazotrophic bacteria has successfully enhanced NH4+ release. In this study, we compared the competitive fitness of A. vinelandii mutant strains, which allowed us to analyze the burden of NH4+ release under a broad dynamic range. Long-term competition assays under regular culture conditions confirmed a large burden for NH4+ release, exclusion by the wt strain, phenotypic instability, and loss of the ability to release NH4+. In contrast, co-inoculation in mild autoclaved soil showed a much longer co-existence with the wt strain and a stable NH4+ release phenotype. All genetically modified strains increased the N content and changed its chemical speciation in the soil. This study contributes one step forward towards bridging a knowledge gap between molecular biology laboratory research and the incorporation of N from the air into the soil in a molecular species suitable for plant nutrition, a crucial requirement for developing improved bacterial inoculants for economic and environmentally sustainable agriculture.Key points• Genetic engineering for NH4+ excretion imposes a fitness burden on the culture medium• Large phenotypic instability for NH4+-excreting bacteria in culture medium• Lower fitness burden and phenotypic instability for NH4+-excreting bacteria in soil

Multivariate Universal Local Linear Kernel Estimators in Nonparametric Regression: Uniform Consistency

In this paper, for a wide class of nonparametric regression models, new local linear kernel estimators are proposed that are uniformly consistent under close-to-minimal and visual conditions on design points. These estimators are universal in the sense that their designs can be either fixed and not necessarily satisfying the traditional regularity conditions, or random, while not necessarily consisting of independent or weakly dependent random variables. With regard to the design elements, only dense filling of the regression function domain with the design points without any specification of their correlation is assumed. This study extends the dense data methodology and main results of the authors’ previous work for the case of regression functions of several variables.

Calibration of wave-induced high-frequency dynamic response and its effects on the fatigue damage of floating offshore wind turbine

There is a demand to calibrate the high-frequency dynamic responses of semi-submersible floating offshore wind turbine (FOWT) induced by the second-order sum-frequency hydrodynamic loads in the numerical model and evaluate its effects on the fatigue damage of the FOWT. A modification approach for the calibration of the high-frequency dynamic responses of FOWT is proposed. In this approach, the effects of the viscous damping and additional restoring force on the second-order sum-frequency quadratic transfer functions (QTFs) are discussed in the frequency domain. The calibrated numerical model (CNM) is obtained with the tuned viscous damping, the second-order sum-frequency QTFs, and the structural damping, based on the measured data from the FOWT model test. The CNM is proved to accurately predict the high-frequency components of the strongly nonlinear responses, namely the pitch motion and tower-top shear force, with the proper prediction of the wave-frequency responses compared with the experimental model under regular wave conditions. The CNM is further applied to predict the high-frequency dynamic responses of the OUCwind under a typical sea state for an operational condition. It is found that the high-frequency component occupies a non-negligible part of the pitch motion, and dominates the tower-top shear force. The linear model (LM) cannot predict and the uncalibrated numerical model (UCNM) underpredicts the high-frequency components of responses. Furthermore, the fatigue damage of the CNM is 14 times greater than that of the LM after a 3 h sea state with a significant wave height of 3 m and a peak period of 6 s. It follows that the large frequency and intensity make the high-frequency tower-top shear force to be a huge risk to the safe operation of the wind turbine, which should attract the industry’s concern about the wave-induced high-frequency dynamic responses for the design of FOWTs.

Oscillating water column wave energy converter arrays coupled with a parabolic-wall energy concentrator in regular and irregular wave conditions

Based upon previous research on a single, high-efficiency Oscillating Water Column (OWC) wave energy capture system (Mayon et al., 2021), this work further extends the numerical investigation to the layout design and performance of the wave energy convertor (WEC) array coupled with a parabolic, energy concentrating wall in both regular and irregular incident wave conditions. A heuristic method to identify the optimal siting of the component, cylindrical OWC WECs in the array, installed in the concave opening of the wall is presented. The most advantageous location of the chambers is found to lie on a parabolic curvature line which is inset from the wall. Two separate arrays composed of three and five component OWCs are investigated in a range of regular wave conditions. The hydrodynamic power and efficiency of each chamber in each of the arrays is determined, and subsequently the aggregated array performance is established. It is found that the primary OWC chamber in the array configuration can attain approximately the same hydrodynamic power output as a single, isolated OWC chamber located the parabolic wall focus, albeit with a narrower energy capture bandwidth. The secondary and tertiary component chambers in the arrays contribute a lesser, yet still considerable quantity of hydrodynamic power to the consolidated system. The cumulative hydrodynamic efficiency of the collective arrays is less than the hydrodynamic efficiency of a single OWC chamber at the wall focus, but more efficient than an isolated OWC chamber positioned in open-sea conditions. Moreover, the hydrodynamic efficiency of the arrays exhibits better stability across the range of incident wave periods investigated, denoting that the individual component chambers in the array are efficacious at different incident wave conditions. The five chamber array is comprehensively analysed in irregular incident wave conditions. The array system is demonstrated to maintain a high power output and efficient behaviour in irregular incident wave conditions-an effect attributable to the reflecting wall influence. In summary, the five-chamber array configuration yields a higher power output and improved stability in terms of efficiency performance when compared with the three-chamber array configuration in regular waves. The array maintains this exceptional performance in irregular incident wave conditions.

Improved uniform error bounds of a Lawson-type exponential wave integrator method for the Klein-Gordon-Dirac equation

For the Klein-Gordon-Dirac equation (KGDE) with small coupling constant ε∈(0,1], we propose a Lawson-type exponential wave integrator Fourier pseudo-spectral (LEWIFP) method and establish the improved uniform error bounds in the time domain at O(1/ε). We first convert the KGDE to a coupled system and then consider LEWIFP method for the coupled system. The LEWIFP method is proved to be time symmetric which is an important structure in numerical geometric integration. Through careful and rigorous convergence analysis, we establish the error bounds O(hm+ετ2+τ0m) for the full-discretization, where m is determined by the regularity conditions. If the solution is sufficiently smooth with m sufficiently large, we obtain the errors with improved uniform bounds at O(hm+ετ2) in the long-time domain up to O(1/ε). These error bounds are much better than the classical bounds O(hm+τ2) provided by the traditional analysis for the non-Lawson-type exponential wave integrators equipped with Fourier pseudo-spectral method. Combined with the classical analysis tools such as mathematical induction and energy method, we complete our error analysis by adopting the regularity compensation oscillation (RCO) technique which controls the high frequency modes by the regularity of the solution and low frequency modes by phase cancellation. By applying the LEWIFP method to some problems, we show the numerical results to support our error bounds. In addition, the numerical results also show that the discrete mass and energy are stable in the time domain which is long enough. Finally we extend our method to the oscillatory problem.

Design comparison and effects of a chamber structure on wave dissipation

ABSTRACT Among all the ocean energy sources that have been widely studied, chamber structures such as oscillating water column (OWC) technologies are effective and low-cost methods to develop hundreds of wave power generation devices as the disadvantage is its lack of efficiency. Even if the OWC system does not perform any power generation operations, it is a wave-absorbing structure. A large part of the wave energy may be blocked by the structure’s acting chamber or could be dissipated during the interaction of the waves in the air chamber, which affects the actual power generation benefit evaluation. Nevertheless, a better wave attenuation structure may present a relatively poor design of the OWC generator chamber. A series of experiments were conducted with regular and irregular wave conditions to study the effects of energy dissipation caused by a chamber structure under varied barrier and orifice designs.

Designing information to improve welfare in matching markets

In matching markets, objects are allocated to agents without monetary transfers, based on agents’ preferences. However, agents may not have enough information to determine their preferences over the objects precisely. How should a benevolent planner optimally reveal information to maximize social welfare in this context? I show that when agents are symmetric and there are just two options, letting each agent know his rank in the realized distribution of preferences – but not his actual preferences – always improves social welfare over providing no information. When there are more objects, this rank-based information policy generalizes to the Object Recommendation (OR) Signal, which consists of simply recommending each agent to pick his socially-optimal choice. Under a mild regularity condition, I show that, when agents’ a priori relative preferences over the objects are “not too strong”, the OR Signal, used together with any standard ordinal mechanism, not only maximizes welfare, but achieves the unconstrained social optimum — formalizing the intuition that when people do not have strong opinions over several options, it is easy to sway them.

Weak approximation of Schrödinger–Föllmer diffusion

We consider the weak convergence of the Euler–Maruyama approximation for Schrödinger–Föllmer diffusions, which are solutions of Schrödinger bridge problems and can be used for sampling from given distributions. We show that the distribution of the terminal random variable of the time-discretized process weakly converges to the target one under mild regularity conditions.

Bayesian equilibrium: From local to global

We study Bayesian games with a continuum of states which partition into a continuum of components, each of which is common knowledge, such that equilibria exist on each component. A canonical case is when each agent’s information consists of both public and private information, and conditional on each possible public signal, equilibria exist. We show that under some regularity conditions on the partition, measurable Bayesian equilibria exist for the game in its entirety. The results extend to pure equilibria, as well as to non-compact state-dependent action sets, uncommon priors, and non-bounded payoffs; the results also apply to several notions of approximate equilibria.

Variance-Reduced Stochastic Optimization for Efficient Inference of Hidden Markov Models

Hidden Markov models (HMMs) are popular models to identify a finite number of latent states from sequential data. However, fitting them to large datasets can be computationally demanding because most likelihood maximization techniques require iterating through the entire underlying dataset for every parameter update. We propose a novel optimization algorithm that updates the parameters of an HMM without iterating through the entire dataset. Namely, we combine a partial E step with variance-reduced stochastic optimization within the M step. We prove the algorithm converges under certain regularity conditions. We test our algorithm empirically using a simulation study as well as a case study of kinematic data collected using suction-cup attached biologgers from eight northern resident killer whales (Orcinus orca) off the western coast of Canada. In both, our algorithm converges in fewer epochs, with less computation time, and to regions of higher likelihood compared to standard numerical optimization techniques. Our algorithm allows practitioners to fit complicated HMMs to large time-series datasets more efficiently than existing baselines. Supplemental materials are available online.

In Vitro Hypoxia/Reoxygenation Induces Mitochondrial Cardiolipin Remodeling in Human Kidney Cells.

Renal ischemia/reperfusion is a serious condition that not only causes acute kidney injury, a severe clinical syndrome with high mortality, but is also an inevitable part of kidney transplantation or other kidney surgeries. Alterations of oxygen levels during ischemia/reperfusion, namely hypoxia/reoxygenation, disrupt mitochondrial metabolism and induce structural changes that lead to cell death. A signature mitochondrial phospholipid, cardiolipin, with many vital roles in mitochondrial homeostasis, is one of the key players in hypoxia/reoxygenation-induced mitochondrial damage. In this study, we analyze the effect of hypoxia/reoxygenation on human renal proximal tubule epithelial cell (RPTEC) cardiolipins, as well as their metabolism and mitochondrial functions. RPTEC cells were placed in a hypoxic chamber with a 2% oxygen atmosphere for 24 h to induce hypoxia; then, they were replaced back into regular growth conditions for 24 h of reoxygenation. Surprisingly, after 24 h, hypoxia cardiolipin levels substantially increased and remained higher than control levels after 24 h of reoxygenation. This was explained by significantly elevated levels of cardiolipin synthase and lysocardiolipin acyltransferase 1 (LCLAT1) gene expression and protein levels. Meanwhile, hypoxia/reoxygenation decreased ADP-dependent mitochondrial respiration rates and oxidative phosphorylation capacity and increased reactive oxygen species generation. Our findings suggest that hypoxia/reoxygenation induces cardiolipin remodeling in response to reduced mitochondrial oxidative phosphorylation in a way that protects mitochondrial function.

Enhancing PHGMS performance for recovery of ultra-fine ilmenite from tailings

In southwest China, the Panzhihua area annually produces about 80 million tons of tailings with a TiO<sub>2</sub> grade of around 5.0%, which causes serious waste of titanium resources as well as environmental and safety issues. The ilmenite contained in these tailings is ultra-fine in size, so it is difficult to recover under the regular operating conditions of pulsating high gradient magnetic separation (PHGMS). In this study, an SLon-100 PHGMS separator was applied to concentrate an ultra-fine titanium tailing under a wide range of operating conditions. The experimental results indicated that a combination of high pulsating frequency, large pulsating stroke, and low feed velocity was favorable for the highly efficient recovery of ultra-fine ilmenite from the tailings. The TiO<sub>2</sub> grade in the optimal concentrate was enhanced from 4.33% to 13.64%, at a recovery of 66.55% and an enrichment ratio of 3.15 through a one-stage PHGMS process. The size analysis of the optimal concentrate showed that the TiO<sub>2</sub> recovery in -25+18 µm and -18+10 µm fractions exceeded 70%. To further understand this PHGMS performance, the optimal ultra-fine ilmenite and larger-size ilmenite concentration conditions were compared. This study provides a valuable reference in the PHGMS operation for recovering ultra-fine weakly magnetic minerals, including ilmenite.

Black bounces in conformal Killing gravity

In this work, we analyse black bounce solutions in the recently proposed “Conformal Killing gravity” (CKG), by coupling the theory to nonlinear electrodynamics (NLED) and scalar fields. The original motivation of the theory was essentially to fulfill specific criteria that are absent in existing gravitational theories, namely, to obtain the cosmological constant as an integration constant, derive the energy–momentum conservation law as a consequence of the gravitational field equations, rather than assuming it, and not necessarily considering conformally flat metrics as vacuum solutions. In this work, we extend the static and spherically symmetric solutions obtained in the literature, and explore the possibility of black bounces in CKG, coupled to NLED and scalar fields. We find novel NLED Lagrangian densities and scalar potentials, and extend the class of black bounce solutions found in the literature. Furthermore, within black bounce geometries, we find generalizations of the Bardeen-type and Simpson–Visser geometries and explore the regularity conditions of the solutions.

Influence of vegetation on heavy metal Cr release process from bottom sediment under unidirectional flows and regular waves

As human activities become more intensive, a substantial number of heavy metals are discharged into estuarine or wetland environments. Due to the poor degradability, heavy metals are prone to adsorption and deposition on suspended particles in bottom sediments. Subsequently, under the influence of disturbances, there is a potential for their re-release, causing secondary pollution. To investigate the release process of the heavy metal Cr from sediment, laboratory experiments were conducted under both unidirectional flow and regular wave conditions. At the initial stage, the temporal trends of particulate (CrP) and dissolved (CrD) Chromium concentrations were both characterized by initial increments followed by stabilization and continuous escalation. Vertically, the stable concentrations of CrP and CrD increased with the presence of vegetation and the enhancement of hydrodynamics. The Elovich equation, pseudo-second-order kinetic equation, Double constant equation (Freundlich model), and parabolic diffusion equation were employed to predict the release process of CrD from bottom sediment. The Elovich equation proved most suitable for describing the release process of CrD, with an R2 exceeding 0.9. In order to assess the influence of vegetation on the Cr release process, the Stem-Reynolds were introduced to modify the Elovich equation. The final maximum error was 12 % (excluding the initial stage), which was much lower than that using the original Elovich equation (maximum error of 32 %). The study findings provide practical support for estuarine and wetland managers to formulate effective heavy metal management measures, which contribute to the conservation and sustainable management of aquatic ecosystems.