Stability Estimates Research Articles

Pro+: Automated protrusion and critical shear stress estimates from 3D point clouds of gravel beds

AbstractThe dimensionless critical shear stress (τ*c) needed for the onset of sediment motion is important for a range of studies from river restoration projects to landscape evolution calculations. Many studies simply assume a τ*c value within the large range of scatter observed in gravel‐bedded rivers because direct field estimates are difficult to obtain. Informed choices of reach‐scale τ*c values could instead be obtained from force balance calculations that include particle‐scale bed structure and flow conditions. Particle‐scale bed structure is also difficult to measure, precluding wide adoption of such force‐balance τ*c values. Recent studies have demonstrated that bed grain size distributions (GSD) can be determined from detailed point clouds (e.g. using G3Point open‐source software). We build on these point cloud methods to introduce Pro+, software that estimates particle‐scale protrusion distributions and τ*c for each grain size and for the entire bed using a force‐balance model. We validated G3Point and Pro+ using two laboratory flume experiments with different grain size distributions and bed topographies. Commonly used definitions of protrusion may not produce representative τ*c distributions, and Pro+ includes new protrusion definitions to better include flow and bed structure influences on particle mobility. The combined G3Point/Pro+ provided accurate grain size, protrusion and τ*c distributions with simple GSD calibration. The largest source of error in protrusion and τ*c distributions were from incorrect grain boundaries and grain locations in G3Point, and calibration of grain software beyond comparing GSD is likely needed. Pro+ can be coupled with grain identifying software and relatively easily obtainable data to provide informed estimates of τ*c. These could replace arbitrary choices of τ*c and potentially improve channel stability and sediment transport estimates.

Stability, homogeneity and measurement uncertainty estimation of PVP-I solutions for the application on oro and nasopharynx against SARS-CoV-2

Aqueous solution containing different concentration (0.5, 0.6 and 1.0%) (w/v) of Polyvinyl pyrrolodon-Iodine (PVP-I) complex, a well-known antiseptic; is prepared and the stability and homogeneity of these solution is assessed as per the ICH Guidelines and International Harmonized Protocol respectively. The solutions were found to be sufficiently homogeneous and stable for a year at 25 °C (60%RH). Measurement uncertainty of the prepared PVP-I solutions were estimated by identifying possible sources of uncertainty using Ishikawa diagram and preparing uncertainty budget based on scope of calibration laboratory. The stable and homogenized PVP-I solution is to be used in a clinical trial for the application on oro and nasopharynx against novel SARS-CoV-2 Virus.

In Silico and Chromatographic Methods for Analysis of Biotransformation of Prospective Neuroprotective Pyrrole-Based Hydrazone in Isolated Rat Hepatocytes.

In the current study, chromatographic and in silico techniques were applied to investigate the biotransformation of ethyl 5-(4-bromophenyl)-1-(2-(2-(2-hydroxybenzylidene) hydrazinyl)-2-oxoethyl)-2-methyl-1H-pyrrole-3-carboxylate (11b) in hepatocytic media. The initial chromatographic procedure was based on the employment of the conventional octadecyl stationary phase method for estimation of the chemical stability. Subsequently, a novel and rapid chromatographic approach based on a phenyl-hexyl column was developed, aiming to separate the possible metabolites. Both methods were performed on a Dionex 3000 ThermoScientific (ACM 2, Sofia, Bulgaria) device equipped with a diode array detector set up at 272 and 279 nm for analytes detection. An acetonitrile: phosphate buffer of pH 3.5: methanol (17:30:53 v/v/v) was eluted isocratically as a mobile phase with a 1 mL/min flow rate. A preliminary purification from the biological media was achieved by protein precipitation with methanol. A validation procedure was carried out, where the method was found to correspond to all ICH (Q2) and M10 set criteria. Additionally, an in silico-based approach with the online server BioTransformer 3.0 was applied in an attempt to predict the possible metabolites of the title compound 11b. It was hypothesized that four CYP450 isoforms (1A2, 2C9, 3A4, and 2C8) were involved in the phase I metabolism, resulting in the formation of 12 metabolites. Moreover, docking studies were conducted to evaluate the formation of stable complexes between 11b and the aforementioned isoforms. The obtained data indicated three metabolites as the most probable products, two of which (M9_11b and M10_11b) were synthesized by a classical approach for verification. Finally, liquid chromatography with a mass detector was implemented for comprehensive and summarized analysis, and the obtained results revealed that the metabolism of the 11b proceeds possibly with the formation of glucuronide and glycine conjugate of M11_11b.

Improved RNA stability estimation through Bayesian modeling reveals most Salmonella transcripts have subminute half-lives

RNA decay is a crucial mechanism for regulating gene expression in response to environmental stresses. In bacteria, RNA-binding proteins (RBPs) are known to be involved in posttranscriptional regulation, but their global impact on RNA half-lives has not been extensively studied. To shed light on the role of the major RBPs ProQ and CspC/E in maintaining RNA stability, we performed RNA sequencing of Salmonella enterica over a time course following treatment with the transcription initiation inhibitor rifampicin (RIF-seq) in the presence and absence of these RBPs. We developed a hierarchical Bayesian model that corrects for confounding factors in rifampicin RNA stability assays and enables us to identify differentially decaying transcripts transcriptome-wide. Our analysis revealed that the median RNA half-life in Salmonella in early stationary phase is less than 1 min, a third of previous estimates. We found that over half of the 500 most long-lived transcripts are bound by at least one major RBP, suggesting a general role for RBPs in shaping the transcriptome. Integrating differential stability estimates with cross-linking and immunoprecipitation followed by RNA sequencing (CLIP-seq) revealed that approximately 30% of transcripts with ProQ binding sites and more than 40% with CspC/E binding sites in coding or 3' untranslated regions decay differentially in the absence of the respective RBP. Analysis of differentially destabilized transcripts identified a role for ProQ in the oxidative stress response. Our findings provide insights into posttranscriptional regulation by ProQ and CspC/E, and the importance of RBPs in regulating gene expression.

Error estimates for finite element approximations of viscoelastic dynamics: The generalized Maxwell model

We prove error estimates for a finite element approximation of viscoelastic dynamics based on continuous Galerkin in space and time, both in energy norm and in L2 norm. The proof is based on an error representation formula using a discrete dual problem and a stability estimate involving the kinetic, elastic, and viscoelastic energies. To set up the dual error analysis and to prove the basic stability estimates, it is natural to formulate the problem as a first-order-in-time system involving evolution equations for the viscoelastic stress, the displacements, and the velocities. The equations for the viscoelastic stress can, however, be solved analytically in terms of the deviatoric strain velocity, and therefore, the viscoelastic stress can be eliminated from the system, resulting in a system for displacements and velocities.

Stabilization with unknown-input estimation for time-delayed systems using functional-observer-based feedback control design

This paper focuses on the stabilization and unknown-input estimation (UIE) problem of continuous-time delayed systems by virtue of functional-observer (FO)-based feedback controller. It allows us to estimate the unknown external variable that degrades the system performance with respect to the partially known input of the system. In particular, the unknown inputs are considered in system dynamics’s state as well as in output, which makes the addressed problem to be more applicable. In addition to that, the aim is then to design minimal order functional observer. Notably, the FO-based feedback control law is introduced for the first time and it is used to ensure the asymptotic stabilization with UIE of the proposed system. Whilst, the design and analysis of UIE and FO is based on Lyapunov stability theory and applying the inequality analysis technique, the sufficient stability conditions are established in the forms of matrix inequality. Eventually, the numerical examples with simulation results are provided to validate the practicability and efficacy of the developed control strategy.

Rational approximation of operator semigroups via the [formula omitted]-calculus

We improve the classical results by Brenner and Thomée on rational approximations of operator semigroups. In the setting of Hilbert spaces, we introduce a finer regularity scale for initial data, provide sharper stability estimates, and obtain optimal approximation rates. Moreover, we strengthen a result due to Egert-Rozendaal on subdiagonal Padé approximations of operator semigroups. Our approach is direct and based on the theory of the B- functional calculus developed recently. On the way, we elaborate a new and simple approach to construction of the B-calculus thus making the paper essentially self-contained.

Stable reconstruction of anisotropic scattering objects from electromagnetic Cauchy data

ABSTRACT This paper addresses the electromagnetic inverse scattering problem of determining the location and shape of anisotropic objects from near-field Cauchy data. We investigate both cases involving the Helmholtz equation and Maxwell's equations for this inverse problem. Our study focuses on developing efficient imaging functionals that enable a fast and stable recovery of the anisotropic object. The implementation of the imaging functionals is simple and avoids the need to solve an ill-posed problem. The resolution analysis of the imaging functionals is conducted using the Green representation formula. Furthermore, we establish stability estimates for these imaging functionals when noise is present in the data. To illustrate the effectiveness of the methods, we present numerical examples showcasing their performance.

Stable determination of an impedance obstacle by a single far-field measurement

We establish sharp stability estimates of logarithmic type in determining an impedance obstacle in R2 . The obstacle is the polygonal shape and the surface impedance parameter is non-zero constant. We establish the stability results using a single far-field pattern, constituting a longstanding problem in the inverse scattering theory. This is the first stability result in the literature in determining an impedance obstacle by a single far-field measurement. The stability in simultaneously determining the obstacle and the boundary impedance is established in terms of the classical Hausdorff distance. Several technical novelties and developments in the mathematical strategy developed for establishing the aforementioned stability results exist. First, the stability analysis is conducted around a corner point in a micro-local manner. Second, our stability estimates establish explicit relationships between the obstacle’s geometric configurations and the wave field’s vanishing order at the corner point. Third, we develop novel error propagation techniques to tackle singularities of the wave field at a corner with the impedance boundary condition.

Role of Explicit Solvation in Computational Modeling of Chemical Reactions: Mechanism of Cu(I) Transfer Between Thiolate-Based Chelators in Water.

Solvation plays important roles in controlling the thermodynamic and kinetic aspects of chemical reactions. The conventional approaches to treat solvation via electronic structure methods are likely to become inadequate, when the reacting solutes have strong electrostatic and hydrogen bonding interactions with the solvent and undergo significant structural changes during the course of the reaction. In this article, we present evidence of such solvent and structural effects in the computational study of the Cu(I) transfer reaction between thiolate-based chelators dithiobutylamine (DTBA) and dithiotheritol (DTT) in water, inspired from biological copper trafficking phenomena. We propose a general solution to the problem by combining classical molecular dynamics (MD) simulations of the bulk system and static quantum chemistry calculations. The fluctuating solvation shell was estimated from MD, and energetics was assessed by averaging QM energies of a series of molecular clusters constructed from the MD snapshots. Applying this approach, we propose a reaction pathway with estimates of relative intermediate stabilities and barriers, which suggest the overall reaction to be reversible in nature and likely to go through both two and three coordinated intermediates, confirming previous studies of similar protein analogues. An interesting fact that emerged from our study was the strong indication that the rate-determining step is the deprotonation of initial thiol bound Cu(I) complex, without involving any Cu(I)-S bonds. The proposed method will lead to a better treatment of solvations, and these mechanistic insights will aid our understanding of biological copper(I) trafficking.

Consistency of the Bayes method for the inverse scattering problem

In this work, we consider the inverse scattering problem of determining an unknown refractive index from the far-field measurements using the nonparametric Bayesian approach. We use a collection of large ‘samples’, which are noisy discrete measurements taking from the scattering amplitude. We will study the frequentist property of the posterior distribution as the sample size tends to infinity. Our aim is to establish the consistency of the posterior distribution with an explicit contraction rate in terms of the sample size. We will consider two different priors on the space of parameters. The proof relies on the stability estimates of the forward and inverse problems. Due to the ill-posedness of the inverse scattering problem, the contraction rate is of a logarithmic type. We also show that such contraction rate is optimal in the statistical minimax sense.

Stability estimate for an inverse stochastic parabolic problem of determining unknown time-varying boundary *

Stochastic parabolic equations are widely used to model many random phenomena in natural sciences, such as the temperature distribution in a noisy medium, the dynamics of a chemical reaction in a noisy environment, or the evolution of the density of bacteria population. In many cases, the equation may involve an unknown moving boundary which could represent a change of phase, a reaction front, or an unknown population. In this paper, we focus on an inverse problem with the goal is to determine an unknown moving boundary based on data observed in a specific interior subdomain for the stochastic parabolic equation. The uniqueness of the solution of this problem is proved, and furthermore a stability estimate of log type is derived. This allows us, theoretically, to track and to monitor the behavior of the unknown boundary from observation in an arbitrary interior domain. The primary tool is a new Carleman estimate for stochastic parabolic equations. As a byproduct, we obtain a quantitative unique continuation property for stochastic parabolic equations.

Estimation of stability of lifting equipment during excavation of pits in cramped conditions

Estimation of stability of lifting equipment during excavation of pits in cramped conditions

Stability estimates for semigroups in the Banach case

Stability estimates for semigroups in the Banach case

Analysis of the boundary conditions for the ultraweak-local discontinuous Galerkin method of time-dependent linear fourth-order problems

In this paper, we study the ultraweak-local discontinuous Galerkin (UWLDG) method for time-dependent linear fourth-order problems with four types of boundary conditions. In one dimension and two dimensions, stability and optimal error estimates of order k + 1 k+1 are derived for the UWLDG scheme with polynomials of degree at most k k ( k ≥ 1 k\ge 1 ) for solving initial-boundary value problems. The main difficulties are the design of suitable penalty terms at the boundary for numerical fluxes and the construction of projections. More precisely, in two dimensions with the Dirichlet boundary condition, an elaborate projection of the exact boundary condition is proposed as the boundary flux, which, in combination with some proper penalty terms, leads to the stability and optimal error estimates. For other three types of boundary conditions, optimal error estimates can also be proved for fluxes without any penalty terms when special projections are designed to match different boundary conditions. Numerical experiments are presented to confirm the sharpness of theoretical results.

The dimension reduction method of two-grid Crank–Nicolson mixed finite element solution coefficient vectors for nonlinear fourth-order reaction diffusion equation with temporal fractional derivative

Herein, we mainly resort to a proper orthogonal decomposition (POD) to study the dimension reduction of unknown solution coefficient vectors in the two-grid Crank–Nicolson mixed finite element (CNMFE) (TGCNMFE) method for the nonlinear fourth-order reaction diffusion equation with temporal fractional derivative and establish a new reduced-dimension extrapolated TGCNMFE (RDETGCNMFE) method. For this purpose, we firstly retrospect the TGCNMFE method for the nonlinear fourth-order reaction diffusion equation and provide the existence, unconditional stability, and error estimates of the TGCNMFE solutions. Thereafter, we use the POD method to reduce the dimensionality of the unknown TGCNMFE solution coefficient vectors of the nonlinear fourth-order reaction diffusion equation and develop the new RDETGCNMFE method, and use matrix analysis to analyze the existence, unconditional stability, and errors of the RDETGCNMFE solutions. Finally, we perform numerical experiments to verify our theoretical results and show the advantages of the RDETGCNMFE method. It is worth noting that the RDETGCNMFE method herein is completely distinguished from the existing ones. Hence, the work in this paper is brand-new.

Disentangling Cerebellar and Parietal Contributions to Gait and Body Schema: A Repetitive Transcranial Magnetic Stimulation Study

The overlap between motor and cognitive signs resulting from posterior parietal cortex (PPC) and cerebellar lesions can mask their relative contribution in the sensorimotor integration process. This study aimed to identify distinguishing motor and cognitive features to disentangle PPC and cerebellar involvement in two sensorimotor-related functions: gait and body schema representation. Thirty healthy volunteers were enrolled and randomly assigned to PPC or cerebellar stimulation. Sham stimulation and 1 Hz-repetitive-Transcranial-Magnetic-Stimulation were delivered over P3 or cerebellum before a balance and a walking distance estimation task. Each trial was repeated with eyes open (EO) and closed (EC). Eight inertial measurement units recorded spatiotemporal and kinematic variables of gait. Instability increased in both groups after real stimulation: PPC inhibition resulted in increased instability in EC conditions, as evidenced by increased ellipse area and range of movement in medio-lateral and anterior–posterior (ROMap) directions. Cerebellar inhibition affected both EC (increased ROMap) and EO stability (greater displacement of the center of mass). Inhibitory stimulation (EC vs. EO) affected also gait spatiotemporal variability, with a high variability of ankle and knee angles plus different patterns in the two groups (cerebellar vs parietal). Lastly, PPC group overestimates distances after real stimulation (EC condition) compared to the cerebellar group. Stability, gait variability, and distance estimation parameters may be useful clinical parameters to disentangle cerebellar and PPC sensorimotor integration deficits. Clinical differential diagnosis efficiency can benefit from this methodological approach.

A simple estimation method of grid‐forming inverter inertia based on rate of change of frequency

AbstractInertia is the core index of the estimation of power system frequency stability; a simple estimation method of grid‐forming inverter inertia based on the rate of change of frequency (RoCoF) is proposed in this paper. The method records and fits the active power curve by applying RoCoF to obtain the value of the grid‐forming inverter inertia, and it is simpler and higher accuracy compared to existing methods. In addition, the inertia and damping are analysed to support the system, and the relationship equation between the grid frequency slope change and the output active power is derived. Considering the theoretical analyses and influencing factors, the inertia and damping are obtained by using the method of function fitting. The test steps show the simplicity of the proposed test method. Finally, the effectiveness of the proposed method is verified in MATLAB/Simulation and two 1.575‐MW parallel grid‐forming electrochemical energy storage power plants.

Estimation of slope stability using ensemble-based hybrid machine learning approaches

Mining is one of the most daunting occupations gain the sector since it entails risk at any point in the operation. In its operation, the main focus is on slope stability. To avoid slope failures, work should be performed in line with both the regulations and the safety criteria. Slope stability is essential in mining activities owing to slope failure putting productivity and safety at risk. Prediction of slope failure is difficult because of the complexity of traditional engineering techniques. Through study, recent technologies have helped mining companies predict slope problems quickly and effectively. In this current research, an ensemble of machine learning intelligence algorithms was used to estimate and assess the Factor of Safety (FOS). In Ostapal Chromicte Mine, India, 79 experimental and failure slope occurrences were tracked to gather in-the-moment field data. The available data were split into training and testing sets at random to build algorithms. The five influenced factors such as the unit weight, the friction angle, the cohesiveness, the mining depth, as well as the slope angle used as input variables to estimate the FOS. Selected machine learning techniques such as Multiple Linear Regression (MLR), Decision Tree, Random Forest (RF), eXtreme Gradient Boosting (XGBoost) and ensemble hybrid model combining eXtreme Gradient Boosting and Random Forest (XGBoost-RF) were developed to evaluate the FOS. The validity and efficiency of created models can be evaluated using standard evaluation parameters such as coefficient of determination (R2), root mean square error (RMSE), mean square error (MSE), normalized root mean square error (NRMSE), mean absolute percentage error (MAPE) and mean absolute deviation (MAD). The most precise model to assess the FOS across all models was discovered to be the XGBOOST-RF ensemble model, which had a high R2 of 0.931, MSE of 0.009, NRMSE of 0.069, MAD of 0.037, MAPE of 3.581 and an RMSE of 0.098.

Stabilization and Energy Consumption Estimation of Discontinuous Fuzzy Inertial CGNNs via Saturation Function Approach

Stabilization and Energy Consumption Estimation of Discontinuous Fuzzy Inertial CGNNs via Saturation Function Approach