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A useful strategy to examine serial correlation in panel regression models is to adopt serially correlated error terms. The random effect is also present to address the individual-specific heterogeneity. Familiar transformations can restructure the AR(1) process into a serially uncorrelated dynamic model. It may result in unfitting estimation results once the statistical inference is carried on the conditional likelihood. We discuss in the article the consequence of this action. In particular, in the case of large cross-section units and short time-sequences, we provide analytical expressions for the asymptotic bias of maximum likelihood estimates when the analyst naïvely neglects the initial conditions problem. Under several conditions, we compute the size of biases and measure the mean squared errors to illustrate this violation. We also construct a joint regression model of the initial and subsequent responses to handle the initial conditions. Then, we conduct simulation studies to determine the asymptotic behavior. [ABSTRACT FROM AUTHOR]

This study evaluated the simulation performance of mesoscale convective system (MCS)-induced precipitation, focusing on three selected cases that originated from the Yellow Sea and propagated toward the Korean Peninsula. The evaluation was conducted for the European Centre for Medium-Range Weather Forecasts (ECMWF) and National Centers for Environmental Prediction (NCEP) analysis data, as well as the simulation result using them as initial and lateral boundary conditions for the Weather Research and Forecasting model. Particularly, temperature and humidity profiles from 3D dropsonde observations from the National Center for Meteorological Science of the Korea Meteorological Administration served as validation data. Results showed that the ECMWF analysis consistently had smaller errors compared to the NCEP analysis, which exhibited a cold and dry bias in the lower levels below 850 hPa. The model, in terms of the precipitation simulations, particularly for high-intensity precipitation over the Yellow Sea, demonstrated higher accuracy when applying ECMWF analysis data as the initial condition. This advantage also positively influenced the simulation of rainfall events on the Korean Peninsula by reasonably inducing convective-favorable thermodynamic features (i.e., warm and humid lower-level atmosphere) over the Yellow Sea. In conclusion, this study provides specific information about two global analysis datasets and their impacts on MCS-induced heavy rainfall simulation by employing dropsonde observation data. Furthermore, it suggests the need to enhance the initial field for MCS-induced heavy rainfall simulation and the applicability of assimilating dropsonde data for this purpose in the future. [ABSTRACT FROM AUTHOR]

On 24 June 1994 at Fairchild Air Force Base, during practice for an air show, a low-flying B-52H aircraft banked its wings vertically and crashed. Emphasizing the activity of modeling drag and gravity, these notes examine the possibility of recovery with several models. First, with algebra, historical data lead to a model where in a free fall near Earth's surface, the distance fallen is proportional to time squared. Calculus then gives an ordinary differential equation to model free fall near Earth's surface. Second, with calculus, historical data lead to various models of drag on objects moving through air. Third, combining models of drag and gravity with Newton's Laws of Motion leads to ordinary differential equations that model free fall in air. Fourth, predictions from such models with ordinary differential equations are consistent with the aircraft crash. Further models examine the possibility of increasing engine thrust to regain the vertical component of lift. All models fit in a first course in differential equations, without requiring any computational machinery. However, numerical experiments show how uninformed use of professional software can produce rounding errors to cause the modelled aircraft to plunge to the bottom of the deepest oceans and shoot up into space. [ABSTRACT FROM AUTHOR]

In this paper, fixed-time convergent RNNs with logarithmic settling time are proposed for solving time-variant quadratic programming (QP), where the domain of attraction of the RNN models can be reasonably estimated a priori. Two novel activation functions are designed, and the exact expressions of the settling time functions for each given initial condition are given; and upper bounds of the settling times for any given initial condition can be obtained. In addition, the generic activation functions are constructed and analyzed to achieve logarithmic fixed-time settling. The RNNs based on the generic activation function are designed, which have a faster convergence rate and a fixed-time convergence property. By estimating the bound of the settling time function under given initial conditions in the bounded region, the semi-global fixed-time convergence of the RNN model is in turn established. It is shown that the predefined-time convergence of modified RNN models can be assured by adopting the inverse of the bound. Simulation results verify effectiveness of the proposed computing schemes for the time-variant QP problem solving and the repetitive motion planning of a redundant manipulator. [ABSTRACT FROM AUTHOR]

A popular way to estimate the parameters of a hidden Markov model (HMM) is direct numerical maximization (DNM) of the (log-)likelihood function. The advantages of employing the TMB [Kristensen K, Nielsen A, Berg C, et al. TMB: automatic differentiation and Laplace approximation. J Stat Softw Articles. 2016;70(5):1–21] framework in R for this purpose were illustrated recently [Bacri T, Berentsen GD, Bulla J, et al. A gentle tutorial on accelerated parameter and confidence interval estimation for hidden Markov models using template model builder. Biom J. 2022 Oct;64(7):1260–1288]. In this paper, we present extensions of these results in two directions. First, we present a practical way to obtain uncertainty estimates in form of confidence intervals (CIs) for the so-called smoothing probabilities at moderate computational and programming effort via TMB. Our approach thus permits to avoid computer-intensive bootstrap methods. By means of several examples, we illustrate patterns present for the derived CIs. Secondly, we investigate the performance of popular optimizers available in R when estimating HMMs via DNM. Hereby, our focus lies on the potential benefits of employing TMB. Investigated criteria via a number of simulation studies are convergence speed, accuracy, and the impact of (poor) initial values. Our findings suggest that all optimizers considered benefit in terms of speed from using the gradient supplied by TMB. When supplying both gradient and Hessian from TMB, the number of iterations reduces, suggesting a more efficient convergence to the maximum of the log-likelihood. Last, we briefly point out potential advantages of a hybrid approach. [ABSTRACT FROM AUTHOR]

Floods are among natural disasters which cause the largest damages worldwide each year, inducing fatalities of human lives, destruction of infrastructure and economical losses. Consequently, forecasting this type of events through hydro‐meteorological models is still of great importance from a civil protection point of view since it allows to reduce hydrological risk by means of early warning systems. Nevertheless, hydrological model initialization in ungauged basins, where there is lack of direct measurements of meteorological information, is a known issue affecting the entire prediction chain. The present study evaluates the possibility of using forecasts provided by the meteorological model MOLOCH developed by CNR‐ISAC forcing the FEST‐WB hydrological model developed by Politecnico di Milano to perform discharge simulations assuming that the forecasting errors are negligible when using the first 24 h of time horizon. The study is carried out in the urban catchments of Milan city, the Seveso‐Olona‐Lambro (SOL) river basins, located in northern Italy. The main hydro‐meteorological variables are analysed by comparing the spatialized and observed meteorological data, provided by an official regional network of weather stations plus a citizen scientists' contribution with the meteorological model forecasts. Moreover, a sensitivity analysis following the well‐known one‐factor‐at‐a‐time methodology is accomplished with the aim of defining which atmospheric forcing, beyond rainfall, mostly affects flowrate forecasts. Results generally show satisfactory correspondences between forecasts and observed data for the discharge variable at daily scale, although an underestimation of precipitation, particularly for severe events in summer, is present. Therefore, using meteorological forecasts to create daily initial conditions for hydrological model, instead of ground observations, might be a reliable and valuable approach, even if some considerations should be borne in mind when coupling the two models. [ABSTRACT FROM AUTHOR]

Offshore wind farms equipped with Direct Drive Permanent Magnet Synchronous Generators (DD-PMSG) are drawing increased attention due to their advantage over other variable speed technologies. VSC-HVDC links are considered the most suitable option for transferring power to the onshore system. The integration of VSC-HVDC connected DD-PMSG based offshore wind farms into multi-machine systems is explored in this paper. A novel approach for power flow and initial condition calculations is proposed to facilitate dynamic analysis of the system. For three cases of the most commonly specified quantities of the wind farm, efficient methods have been described. The cases comprise combinations of data like the total output of the wind farm, the number of wind turbines, the wind speed, or the output of individual wind turbine, which are frequently given in literature. This approach enables the user to build the dynamic model of the system in any basic graphical dynamic modeler and numerical computational software without requiring power system toolboxes or electromagnetic transient packages. The proposed methods are highly effective for studies focusing primarily on the dynamic aspects and controls of the system. Case studies and simulations are conducted to verify the proposed technique. [ABSTRACT FROM AUTHOR]

When the universe is treated as a quantum system, it is described by a wave function. This wave function is a function not only of the matter fields, but also of spacetime. The no-boundary proposal is the idea that the wave function should be calculated by summing over geometries that have no boundary to the past, and over regular matter configurations on these geometries. Accordingly, the universe is finite, self-contained and the big bang singularity is avoided. Moreover, given a dynamical theory, the no-boundary proposal provides probabilities for various solutions of the theory. In this sense it provides a quantum theory of initial conditions. This review starts with a general overview of the framework of quantum cosmology, describing both the canonical and path integral approaches, and their interpretations. After recalling several heuristic motivations for the no-boundary proposal, its consequences are illustrated with simple examples, mainly in the context of cosmic inflation. We review how to include perturbations, assess the classicality of spacetime and how probabilities may be derived. A special emphasis is given to explicit implementations in minisuperspace, to observational consequences, and to the relationship of the no-boundary wave function with string theory. At each stage, the required analytic and numerical techniques are explained in detail, including the Picard–Lefschetz approach to oscillating integrals. [ABSTRACT FROM AUTHOR]

In this article, we describe the xttestms command, which implements the Lagrange multiplier test proposed by Magazzini and Calzolari (2020, Econometric Reviews 39: 115–134). The test verifies the validity of the initial conditions in dynamic panel-data models, which is required for consistency of the system generalized method of moments estimator. [ABSTRACT FROM AUTHOR]

In this research paper, we find the numerical solutions of fractional order scalers and coupled system of differential equations under initial conditions using shifted Legendre polynomials. By using the properties of shifted Legendre polynomials, we establish operational matrices of integration and differentiation in order to simplify our considered problems under initial conditions. In order to check the accuracy of the proposed model, some test problems are solved along with the graphical representations. For coupled system, we applied the algorithm to the Pharmacokinetic two-compartment model. As the proposed method is computer-oriented, we use therefore the MATLAB for required calculations. Numerical results are shown graphically. [ABSTRACT FROM AUTHOR]

When estimating full-body motion from experimental data, inverse kinematics followed by inverse dynamics does not guarantee dynamical consistency of the resulting motion, especially in movements where the trajectory depends heavily on the initial state, such as in free-fall. Our objective was to estimate dynamically consistent joint kinematics and kinetics of complex aerial movements. A 42-degrees-of-freedom model with 95 markers was personalised for five elite trampoline athletes performing various backward and forward twisting somersaults. Using dynamic optimisation, our algorithm estimated joint angles, velocities and torques by tracking the recorded marker positions. Kinematics, kinetics, angular and linear momenta, and marker tracking difference were compared to results of an Extended Kalman Filter (EKF) followed by inverse dynamics. Angular momentum and horizontal linear momentum were conserved throughout the estimated motion, as per free-fall dynamics. Marker tracking difference went from 17 ± 4 mm for the EKF to 36 ± 11 mm with dynamic optimisation tracking the experimental markers, and to 49 ± 9 mm with dynamic optimisation tracking EKF joint angles. Joint angles from the dynamic optimisations were similar to those of the EKF, and joint torques were smoother. This approach satisfies the dynamics of complex aerial rigid-body movements while remaining close to the experimental 3D marker dataset. [ABSTRACT FROM AUTHOR]

This paper concerns with the time-variant neural computing in a semi-global sense, taking into account initial conditions located within a region with a definitely finite radius. Both the conventional single and double power-rate RNN models are characterized and the closed-form expressions of the settling time functions are presented for given initial conditions, by which the fixed/predefined-time convergence can be assured in the semi-global sense. Despite asymptotic convergence behavior, the conventional linear RNN model is examined for comparison purposes. Modified RNN models adopt the inverse of the bound, according to the fixed-time convergence results, and the prescribed time can be an adjustable parameter. A novel two-phase RNN model with the pre-specified transition state is proposed, which has not only semi-global fixed/predefined-time stability but also a faster convergence rate than that of the conventional models. The proposed models are applied and compared, through numerical simulation, for time-variant matrix inversion, linear equation solving, and repeatable motion planning of a redundant manipulator in the presence of initial errors. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the most general exact solutions of Brans–Dicke cosmology by choosing the scale factor "a" as the new independent variable. It is shown that a set of three field equations can be reduced to a constraint equation and a first-order linear differential equation. Thus this new set of equations is solvable when one supplies one of the following pairs of functions: (ϕ (a) , ρ (a)), (ϕ (a) , V (a)) or (ϕ (a) , H (a)). A universe with a single component energy-matter density, the early universe with constant energy density and radiation and the present universe with constant energy density and matter are studied. It is seen that in all cases initial values of the universe cause ϕ 2 potential and a constant term in the Hubble function which causes an exponential expansion of the universe. The relation between cosmological constant and initial values of the universe is found. [ABSTRACT FROM AUTHOR]

Contribution: Two general rules for calculating, in the time domain, step discontinuities of voltages and currents in electric circuits, combining physical principles and basic mathematical treatment. The two general rules, resulting from a formal method of analysis, provide a straightforward way to update the states of a circuit, immediately after the occurrence of switching or impulsive excitation. Among its advantages, they can be used to simplify the numerical simulation of elaborate circuit topologies by avoiding approximate models of impulsive sources or switches. Background: In most engineering undergraduate textbooks, the effects of switching and impulsive sources on higher order electric circuits are usually studied for the particular case of linear time-invariant (LTI) circuits in the Laplace transform domain. This approach, however, can be time consuming and demands little reasoning on the physical principles of circuit operation. Moreover, it is not adequate for linear time-variant or nonlinear circuits. Intended Outcomes: Step discontinuities in electric circuits, caused by switching or impulsive sources, are identified and calculated through the method, allowing complete responses to be obtained afterward. Not only can the method be extended to linear time-variant and nonlinear circuits but it also has interesting consequences in numerical simulation of circuits. Application Design: An application exercise and a set of conceptual questions on the subject were proposed to electrical engineering students. Findings: The analysis of the educational experiment indicates that applying the method presented herein improves the students’ ability to obtain initial conditions of circuits, being a more straightforward and effective approach than using Laplace transform techniques. [ABSTRACT FROM AUTHOR]

The results of studying the influence of impact interactions on the operation of a three-electrode two-capacitor microelectromechanical transducer (MEMT) and a microgenerator based on it are presented. The operation of the microgenerator in the impact periodic mode is analyzed for two extreme cases, when the movable electrode initially comes into contact with the limiters located on the left (LWC) or right (RWC) walls of the casing. The relationship between the system parameters and the characteristics of the external driving force source, which makes it possible to evaluate the possibility of implementing a periodic impact operation, is obtained. The dependences of the average generated power of the impact microgenerator on the number of collisions and the load are calculated. It is shown that a microgenerator with a three-electrode MEMT, in the case when the movable electrode initially comes into contact with the limiters located on the LWC, develops more power than in the case when the movable electrode initially touches the limiters located on the RWC. The efficiency of the microgenerator in impact and nonimpact modes is compared. It is shown that when using the impact mode, a gain by factors of 2 to 5 in the developed power is possible with a significant decrease of 1 to 2 orders of magnitude of the optimal load resistance compared to using an equivalent impact-free mode. In general, the analysis carried out and the developed approach make it possible to significantly narrow the range of the search for the necessary system parameters at the preliminary design stage and reduce the design time. [ABSTRACT FROM AUTHOR]

Friction factor enhancements in pipe-flows subject to fixed electric fields are evaluated using the stochastic One-Dimensional Turbulence (ODT) model. To that extent, low Mach asymptotics are used to derive the leading order effects of the governing equations in electrohydrodynamic (EHD) flows considering low mobility ratios. Temporal and spatial ODT formulations are then carried out for three different Reynolds numbers (Re = 3000 , Re = 4000 and Re = 5000) at a set of electrohydrodynamic numbers in the range 0 ≤ N EHD ≤ 600. The ODT simulation results are compared to published experimental data on Darcy friction factor enhancements of Nelson et al. (1990). The results signalize the importance of the developing flow for the EHD-enhanced drag. On one hand, the ratio N EHD 2/Re2 characterizes the enhancement. On the other hand, the developing flow and the laminar-to-turbulent transition also have an important contribution to the friction factor. The ODT results presented here show that reduced order models can deliver relevant insights in otherwise numerically challenging flow simulations, therefore aiding the quantitative analysis of experimental observations in EHD flows. [ABSTRACT FROM AUTHOR]

Motivated by the analysis of behavioral data taken from an economic experiment based on the Hawk-and-Dove game, this article describes a multilevel hidden Markov model, that includes covariates, autoregression, and endogenous initial conditions under a unified framework. The data at hand are affected by multiple sources of latent heterogeneity, due to multilevel unobserved factors that operate in conjunction with observed covariates at all the levels of the data hierarchy. We fit a multilevel logistic regression model for repeated measurements of player behaviors, nested within groups of interacting players. The model integrates discrete random effects at the group level and Markovian sequences of discrete random effects at the player level. Parameters are estimated by a computationally feasible expectation-maximization algorithm. We model the probability of playing the Hawk strategy, which implies fighting aggressively for controlling an asset, and test the role played by initial possession, property, and other player-specific characteristics in driving hawkish behaviors. The results from our study suggest that crucial factors in determining hawkish behavior are both the way possession is achieved – which depends on our treatment manipulation- and possession itself. Furthermore, a clear time-dependence is observed in the data at the player level as accounted for by the Markovian random effects. [ABSTRACT FROM AUTHOR]

The impact of different initial conditions in non-adiabatic trajectory surface hopping dynamics within a hybrid quantum mechanical/molecular mechanics scheme is investigated. The influence of a quantum sampling, based on a Wigner distribution, a fully thermal sampling, based on classical molecular dynamics, and a quantum sampled system, but thermally equilibrated with the environment, is investigated on the relaxation dynamics of solvated fulvene after light irradiation. We find that the decay from the first singlet excited state to the ground state shows high dependency on the initial condition and simulation parameters. The three sampling methods lead to different distributions of initial geometries and momenta, which then affect the fate of the excited state dynamics. We evaluated both the effect of sampling geometries and momenta, analysing how the ultrafast decay of fulvene changes accordingly. The results are expected to be of interest to decide how to initialize non-adiabatic dynamics in the presence of the environment. This article is part of the theme issue 'Chemistry without the Born–Oppenheimer approximation'. [ABSTRACT FROM AUTHOR]

In this paper, some myths associated to the initial condition problem are studied and demystified. It is shown that the initial conditions provided by the one-sided Laplace transform are not those required for Riemann-Liouville and Caputo derivatives. The problem is studied and solved with generality as well as applied to continuous-time fractional autoregressive-moving average systems. [ABSTRACT FROM AUTHOR]

Methane/air is a widely used fuel. The effects of equivalent ratio (0.8–1.2) and initial pressure (1.0 atm–1.2 atm) on the flame propagation process and explosion overpressure of methane/air premixed gas were studied using a high-speed camera and pressure sensor in a rectangular closed container. Four flame modes in the late propagation stage are distinguished according to the different modes of secondary cup movement. The flame propagation velocity and structure evolution are analyzed by defining the characteristic times. The relationship between the flame structure evolution and the growth of flame propagation velocity and explosion overpressure is revealed. The results show that, in lean combustion, the maximum flame propagation velocity increases with initial pressure increase, and the explosion overpressure fluctuates more significantly. However, the opposite is true with fuel-rich combustion. The interaction between pressure waves and flame fronts can enhance the growth of explosion overpressure in fuel-rich combustion but can inhibit the growth in lean combustion. This work can provide more data support and reference for the application prospect and safe application of methane. • Different growth modes of overpressure and flame propagation velocity are analyzed. • The four types of flame structure after distorted tulip flames are distinguished. • The effects of flame instability on flame propagation are analyzed. [ABSTRACT FROM AUTHOR]

We investigate the influence of uncertain data on solutions to initial boundary value problems with well posed boundary conditions. Uncertainty in the forcing function, initial conditions and boundary conditions are considered and we quantify their relative influence for short and long time calculations. For short time calculations, uncertainty in the initial data dominates. As time grows, the influence of initial data vanishes exponentially fast. For longer time calculations, the uncertainty in the forcing function and boundary data dominate, as they grow in time. Errors due to the forcing function grow faster (linearly in time) than the ones due to the boundary data (grow as the square root of time). Roughly speaking, the results indicate that for short time calculations, the initial conditions are the most important, but for longer time calculations, focus should be on the forcing function and boundary conditions. The findings are especially important when similar mathematical and numerical techniques are used for both short and long times. Our qualitative results can guide more quantitative investigations where details of the uncertain data are known. [ABSTRACT FROM AUTHOR]

Advances in our understanding of the origin, evolution, and structure of the universe have long been driven by cosmological perturbation theory, model building, and effective field theory. In this review, numerical relativity is introduced as a powerful new complementary tool for fundamental cosmology. To illustrate its power, applications of numerical relativity are discussed to studying the robustness of slow contraction and inflation in homogenizing, isotropizing, and flattening the universe beginning from generic unsmooth initial conditions. In particular, it is described how recent numerical relativity studies of slow contraction have revealed a novel, non-linear smoothing mechanism based on ultralocality that challenges the conventional view on what is required to explain the large-scale homogeneity and isotropy of the observable universe. [ABSTRACT FROM AUTHOR]

In this article, we propose a method to solve the time‐fractional hyperbolic heat equation. We first formulate a boundary value problem for the standard hyperbolic heat equation in a finite domain and provide an analytical solution by means of separation of variables and Fourier series. Then, we consider the same boundary value problem for the fractional hyperbolic heat equation. The fractional problem is solved using three different definitions of the fractional derivative: the Caputo fractional derivative and two recently defined alternative versions of this derivative, the Caputo–Fabrizio and the Atangana–Baleanu. A closed form of the solution is provided for each case. Finally, we compare the solutions of the fractional and the standard problem and show numerically that the solution of the standard hyperbolic heat equation can be retrieved from the solution of the fractional equation in the limit γ→2, where γ represents the exponent of the fractional derivative. [ABSTRACT FROM AUTHOR]

In this article, we focus on a class of singular linear systems of fractional differential equations with given nonconsistent initial conditions (IC). Because the nonconsistency of the IC can not lead to a unique solution for the singular system, we use two optimization techniques to provide an optimal solution for the system. We use two optimization techniques to provide the optimal solution for the system because a unique solution for the singular system cannot be obtained due to the non‐consistency of the IC. These two optimization techniques involve perturbations to the non‐consistent IC, specifically, an l2 perturbation (which seeks an optimal solution for the system in terms of least squares), and a second‐order optimization technique at an l1 minimum perturbation, (which includes an appropriate smoothing). Numerical examples are given to justify our theory. We use the Caputo (C) fractional derivative and two recently defined alternative versions of this derivative, the Caputo‐Fabrizio (CF) and the Atangana‐Baleanu (AB) fractional derivative. [ABSTRACT FROM AUTHOR]

In this article, an analytical concept and hardware verification of the time-varying infinite impulse response narrow multiband-stop filter with nonzero initial conditions are presented. The time variability of the filter parameters and nonzero initial conditions are introduced to the filter structure in order to reduce its transient response. Such a filter can be very useful in various measurement systems. In particular, short transient filters are very desirable for processing signals whose initial part is of great importance. In this article, the algorithm for finding the length of the initial conditions vector is presented. As an example, the proposed IIR multinotch filter is used for removing power-line interferences from the ECG signal. Computer simulations, hardware verification, and performance indices demonstrate that the proposed time-varying IIR multinotch filter with nonzero initial conditions possesses much better properties than the traditional time-invariant filter with zero initial conditions. [ABSTRACT FROM AUTHOR]

Summary: The scope of this research is a problem of parameters identification of a linear time‐invariant plant, which (1) input signal is not frequency‐rich, (2) is subjected to initial conditions and external disturbances. The memory regressor extension (MRE) scheme, in which a specially derived differential equation is used as a filter, is applied to solve the above‐stated problem. Such a filter allows us to obtain a bounded regressor value, for which a condition of the initial excitation (IE) is met. Using the MRE scheme, the recursive least‐squares method with the forgetting factor is used to derive an adaptation law. The following properties have been proved for the proposed approach. If the IE condition is met, then: (1) the parameter error of identification is bounded and converges to zero exponentially (if there are no external disturbances) or to a set (in the case of them) with an adjustable rate, (2) the parameters adaptation rate is a finite value. The above‐mentioned properties are mathematically proved and demonstrated via simulation experiments. [ABSTRACT FROM AUTHOR]

Common criteria used for measuring performance of vibrating systems have one thing in common: they do not depend on initial conditions of the system. In some cases it is assumed that the system has zero initial conditions, or some kind of averaging is used to get rid of initial conditions. The aim of this paper is to initiate rigorous study of the dependence of vibrating systems on initial conditions in the setting of optimal damping problems. We show that, based on the type of initial conditions, especially on the ratio of potential and kinetic energy of the initial conditions, the vibrating system will have quite different behavior and correspondingly the optimal damping coefficients will be quite different. More precisely, for single degree of freedom systems and the initial conditions with mostly potential energy, the optimal damping coefficient will be in the under-damped regime, while in the case of the predominant kinetic energy the optimal damping coefficient will be in the over-damped regime. In fact, in the case of pure kinetic initial energy, the optimal damping coefficient is + ∞ ! Qualitatively, we found the same behavior in multi degree of freedom systems with mass proportional damping. We also introduce a new method for determining the optimal damping of vibrating systems, which takes into account the peculiarities of initial conditions and the fact that, although in theory these systems asymptotically approach equilibrium and never reach it exactly, in nature and in experiments they effectively reach equilibrium in some finite time. • Optimal damping strongly depends on initial conditions. • For a purely kinetic initial energy, the optimal damping is infinite. • New method for determination of optimal damping is presented. [ABSTRACT FROM AUTHOR]

This paper presents designs of fixed-time zeroing neural networks (FxZNNs) for solving time-variant convex optimization problems, especially arising from repetitive motion planning of redundant manipulators. Through introducing the transition state, the bound estimation for settling time of the FxZNN models with double power-rate activation functions is carried out, and it is shown that the computing accuracy improvement can be made dramatically, in comparison to the models with the transition state being one. Novel two-phase FxZNN models with the pre-specified transition state are designed and analyzed in detail. The closed-form settling time functions are presented for each given initial condition, and the upper bounds on settling time are established in the presence of arbitrary initial conditions. The semi-global FxZNNs are designed to take account of initial conditions within the region with a specified radius. In addition, the modified FxZNN models assure predefined-time convergence also in the semi-global sense. The theoretical results demonstrate the flexibility and efficiency of the transition state introduced in the activation functions. The proposed FxZNNs are applied and compared with the existing models for solving a time-variant optimization problem and the repetitive motion planning of a redundant manipulator with initial errors, and numerical results are presented to verify effectiveness of the proposed FxZNN models. • Performance enhancement by two-phase ZNN models with a transition state. • The closed-form settling time functions presented for each initial condition. • The bound estimations on the settling time functions for comparison. • The semi-global ZNNs accounting for finite initial conditions. • Solving the time-variant optimization and the robotic motion planning. [ABSTRACT FROM AUTHOR]

This article deals with some existence results for some classes of Caputo-Fabrizio implicit fractional differential equations in b-metric spaces with initial conditions. The results are based on some fixed point theorems. We illustrate our results by some examples in the last section. [ABSTRACT FROM AUTHOR]

This paper presents a simplified analytical model within numerical results to determine the thermal balance of Earth-Air Heat Exchanger (EAHE). The EAHE is a device which uses the principle of soil thermal inertia used for ventilation in buildings. It has three sections: a vertical section at the entrance, an horizontal section in the area of soil thermal inertia and a vertical section at the exit, also considered as area in soil thermal inertia. The assessment for the heat algebrical gain at the vertical section of air entrance in the EAHE is established. In this study, the initial conditions of the problem are obtained and the temperature equation specified model is solved analytically, by considering that the vertical part of an EAHE or a vertical EAHE is under periodic fluctuations in both ambient air temperature and soil temperature. The model can predict the air temperature variation along vertical and horizontal section of the tube for any hour of the day and can be used for a vertical EAHE. It can also determine the daily or annualy mean and amplitude of the total cooling or heating effect of the tube. Numerical results are graphically presented, discussed and compared to experimental datas. • Analytical model to evaluate performance of the vertical part of an EAHE is proposed. • EAHE under fluctuations in both ambient air temperature and soil temperature. • Analytical determination of the initial conditions of temperature inside the EAHE. • The temperature of the air flowing in the EAHE determined analytically. • The vertical part of an EAHE impacts considerably on the whole system. [ABSTRACT FROM AUTHOR]

In this article recent progress in the development of molecules exhibiting Thermally Activated Delayed Fluorescence (TADF) is discussed with a particular focus upon their application as emitters in highly efficient organic light emitting diodes (OLEDs). The key aspects controlling the desirable functional properties, e. g. fast intersystem crossing, high radiative rate and unity quantum yield, are introduced with a particular focus upon the competition between the key requirements needed to achieve high performance OLEDs. The design rules required for organic and metal organic materials are discussed, and the correlation between them outlined. Recent progress towards understanding the influence of the interaction between a molecule and its environment are explained as is the role of the mechanism for excited state formation in OLEDs. Finally, all of these aspects are combined to discuss the ability to implement high level design rules for achieving higher quality materials for commercial applications. This article highlights the significant progress that has been made in recent years, but also outlines the significant challenges which persist to achieve a full understanding of the TADF mechanism and improve the stability and performance of these materials. [ABSTRACT FROM AUTHOR]

In this paper, it is shown that in many cases, science can predict the future. Based on the available information of the real system, the scientific method for future prediction is to develop a virtual model with similar response to the real system. The classical models are usually presented with a set of linear / nonlinear, ordinary / partial differential equations. The necessary and sufficient condition for future prediction is given by three axioms; A model with accurate description of the real system, perfect knowledge of the initial conditions, and perfect knowledge of present and future values of inputs to the system. In reality, none of these conditions are perfectly realizable and each axiom has some uncertainties. The failure in future prediction is exactly due to these uncertainties. The model description as the major axiom is always accompanied with uncertainty and although, there is no way to vanish it, there are different methods to reduce it. Soft computing is one of the recent approaches in the past few decades, not only used for modeling of systems in the field of engineering systems, but also used in the field of human sciences such as economy, management and social sciences. [ABSTRACT FROM AUTHOR]

The ricochet behaviour of the air–water trans-media vehicle (AWTMV) during water-entry crossing was experimentally investigated. Three types of small-scale AWTMV including cone, ogive, and flat nose were used in the test. The underwater trajectory, velocity, and inclination angle of projectiles during the ricochet process were obtained using a high-speed camera. The angle change of the AWTMV and the ratio of the residual velocity are introduced. Based on this result, the relationship between the ricochet responses and initial conditions was derived. The results of this study show that (1) a small incident angle and great velocity make the occurrence of ricochet behaviour easier, (2) the stability of the trajectory of projectiles with cone, ogive, and flat nose weakened in turn at the same initial conditions, (3) the angle change and the ratio of the residual velocity are linear functions of the incident angle and velocity. [ABSTRACT FROM AUTHOR]

A specific class of nonlinear systems, admitting finite-duration attractors (FDAs), is introduced in this paper, and used for consensus of multiagent systems (MASs). The advantage is that one can obtain a closed-form solution for the settling time function of the presented nonlinear systems. Such a system exhibits a two-phase convergence process, and its settling time function takes values over a finite duration. However, the duration width changes with respect to the initial condition. The FDA-based consensus protocol is shown to make the MAS undertaken achieve finite-duration convergence. With illustrative examples, the perfect consensus property is verified for MASs with or without a leader agent. [ABSTRACT FROM AUTHOR]

Focusing on the role of initial condition uncertainty, we use WRF initial perturbation ensemble forecasts to investigate the uncertainty in intensity forecasts of Tropical Cyclone (TC) Rammasun (1409), which is the strongest TC to have made landfall in China during the past 50 years. Forecast results indicate that initial condition uncertainty leads to TC forecast uncertainty, particularly for TC intensity. This uncertainty increases with forecast time, with a more rapid and significant increase after 24 h. The predicted TC develops slowly before 24 h, and at this stage the TC in the member forecasting the strongest final TC is not the strongest among all members. However, after 24 h, the TC in this member strengthens much more than that the TC in other members. The variations in convective instability, precipitation, surface upward heat flux, and surface upward water vapor flux show similar characteristics to the variation in TC intensity, and there is a strong correlation between TC intensity and both the surface upward heat flux and the surface upward water vapor flux. The initial condition differences that result in the maximum intensity difference are smaller than the errors in the analysis system. Differences in initial humidity, and to a lesser extent initial temperature differences, at the surface and at lower heights are the key factors leading to differences in the forecasted TC intensity. These differences in initial humidity and temperature relate to both the overall values and distribution of these parameters. [ABSTRACT FROM AUTHOR]

We propose a new framework for testing the "mean stationarity" assumption in dynamic panel data models, required for the consistency of the system GMM estimator. In our set up the assumption is obtained as a parametric restriction in an extended set of moment conditions, allowing the use of a LM test to check its validity. Our framework provides a ranking in terms of power of the analyzed test statistics, in which our approach exhibits better power than the difference-in-Sargan/Hansen test that compares system GMM and difference GMM, that is, on its turn, more powerful than the Sargan/Hansen test based on the system GMM moment conditions. [ABSTRACT FROM AUTHOR]

• M-systems appear after applying the Möbius transform to the pencil of a system of differential equations. • We provide a link between the solutions of a singular linear system and the solutions of its corresponding M-systems. • By using the invariants of the initial system we obtain information (existence, uniqueness of solutions) for the M-systems. • This enables us to construct explicit solutions of each M-system, without resorting to further processes of computation. The main objective of this article is to provide a link between the solutions of an initial value problem of a linear singular system of differential equations and the solutions of its proper M-systems, i.e., systems that appear after applying the generalized Möbius transform to the pencil of the original singular system (prime system). Firstly, we prove that by using the pencil of the prime system we can study the existence and uniqueness of solutions of its proper M-systems. Moreover these solutions can be explicitly represented without resorting to any further processes of computations. Finally, numerical examples are given to illustrate our theory. [ABSTRACT FROM AUTHOR]

In this study, a new observer for a class of non‐linear single input/single output systems is proposed. This observer is based on a modulating function with time/output dependent coordinates transformation which transforms the original system into a like‐type observer canonical form. In the new coordinates, the initial conditions are annihilated. This property permits to construct a fast convergent deadbeat observer activated after an time delay chosen in order to avoid the singularity of the transformation at the initial time t=t0. The finite‐time convergence of the observer is established, i.e. it is shown that the estimation error is bounded in finite time. The proposed observer is used in an output feedback controller design. Using the already established results on the output feedback stabilisation of non‐linear input‐affine systems, the separation principle is addressed here and the authors show that output feedback controller guarantees under certain conditions the stability of the closed‐loop system. Two numerical examples are given to illustrate the effectiveness of the proposed observer‐based output feedback controller. [ABSTRACT FROM AUTHOR]

Hurricane Leslie (2018) was a non-tropical system that lasted for a long time undergoing several transitions between tropical and extratropical states. Its trajectory was highly uncertain and difficult to predict. Here the extratropical transition of Leslie is simulated using the Model for Prediction Across Scales (MPAS) with two different sets of initial conditions (IC): the operational analysis of the Integrate Forecast System (IFS) and the Global Forecast System (GFS). Discrepancies in Leslie position are found in the IC patterns, and in the intensity and amplitude of the dorsal-trough system in which Leslie is found. Differences are identified both in the geopotential height at 300 hPa and the geopotential thickness. Potential temperature in the dynamic tropopause shows a broader, more intense trough displaced western when using the IC-IFS. The IC-IFS simulation shows lesser trajectory errors but wind speed overestimation than the IC-GFS one. The complex situation of the extratropical transition, where Leslie interacts with a trough, increases the uncertainty associated with the intensification process. The disparities observed in the simulations are attributed to inaccuracies in generating the ICs. Both ICs generate different atmospheric configurations when propagated in time. Results suggest that during an extratropical transition in a highly baroclinic atmosphere, the IFS model's data assimilation method produced a more precise analysis than GFS due to the greater number of observations assimilated by the IFS, the greater spatial resolution of the model and the continuous adjustment of the simulations with the field of observations. [Display omitted] • Simulation of the Leslie extratropical transition with the global model MPAS. • Simulation differences from initial conditions of IFS and GFS models. • Evolution of the extratropical transition and interaction with the ridge-trough system. • Importance of generating initial conditions for modeling extratropical transitions. [ABSTRACT FROM AUTHOR]

We investigate a cosmological model in which dark energy, represented by a quintessential scalar field, is coupled to a dark-matter perfect fluid in the spatially flat Friedmann–Robertson–Walker Universe. This allows an energy exchange in the dark sector which could happen both at early times before recombination era or at late times. We use the coupling function Q = γ ρ d m φ ̇ which is induced by conformal transforming scalar-tensor and f (R) gravity theories to Einstein frame. It is argued that there is a connection between this coupling function and Q ∝ ρ d m H. A dynamical analysis is used to show that there are early- and late-time attracting solutions for which the system evolves for a wide range of initial conditions. These attractors generalize the scaling solutions which have been already found in the non-interacting case. [ABSTRACT FROM AUTHOR]

Contributions to climate uncertainty in the modeling of the near surface temperature of the ocean come from several sources: the knowledge of the initial state of the atmosphere, the inadequacy of a model to include or correctly represent all aspects of the dynamics, the uncertain knowledge of the initial state of the ocean and small-scale (or internal, "weather") noise. This paper concentrates on the latter uncertainty, the uncertainty in the knowledge of the initial field, resulting in a map of the uncertainty of the near surface temperature field. To make the full estimate of this uncertainty, the outcomes from a relatively small, 30 member, ensemble were expanded using statistical emulators. The uncertainty varies in space and decreases in time. There are broad areas of similar uncertainty, consistent with uncertainties in the initial conditions and the variability in local processes. After 10 years, the average spatial uncertainty calculated from this expanded data set gives a range of +/− 0.4 ∘ C with 95% of the spatial areas having an uncertainty of less than +/− 0.9 ∘ C. When compared to other estimates of similar metrics, the map represents a lower bound on the uncertainty because this first experiment examines the ocean/ice system in isolation from feedbacks that occur between the atmosphere and the ocean. This uncertainty also does not include any contribution from the lack of knowledge about how a future state of the air/ocean system will be forced by changes in greenhouse gases. [ABSTRACT FROM AUTHOR]

Decomposition is a common tool for the synthesis of many physical systems. It is also used for analyzing large-scale systems which are then known as tearing and reconstruction. On the other hand, commutativity of cascade-connected systems has gained a great deal of interest, and its possible benefits have been pointed out on the literature. In this paper, the necessary and sufficient conditions for decomposition of any third-order linear time-varying system as a commutative pair of first- and second-order systems of which parameters are also explicitly expressed, are investigated. Further, additional requirements in case of nonzero initial conditions are derived. This paper highlights the direct formulas for realization of any third-order linear time-varying systems as a series (cascade) connection of first- and second-order subsystems. This series connection is commutative so that it is independent from the sequence of subsystems in the connection. Hence, the convenient sequence can be decided by considering the overall performance of the system when the sensitivity, disturbance, and robustness effects are considered. Realization covers transient responses as well as steady-state responses. [ABSTRACT FROM AUTHOR]

The sensitivity of ensemble simulations of deep convective events in the southeastern United States to initial‐condition (IC) errors is examined by imposing idealized moisture perturbations at small and large scales. Four severe weather events are considered, ranging from a springtime frontal system to convection driven almost exclusively by daytime heating. Events with strong synoptic‐scale forcing were insensitive to the scale of IC errors, but weakly forced events exhibited greater sensitivity to small‐scale than large‐scale IC errors. Additional ensemble simulations of idealized convective systems suggest that the greater sensitivity to small‐scale IC errors of the weakly forced cases arises from their higher sensitivity to the strength and location of the first convective elements. Ensemble spread and predictability are characterized by two measures: the ratio of the perturbation kinetic energy (KE) about the ensemble mean to the background KE and the neighborhood‐based fractions skill score (FSS) of hourly precipitation with respect to that in an unperturbed reference simulation. For simulations of both observed events and idealized convective systems, the FSS appears to be a more discriminating indicator of differences in predictability between different convective events. [ABSTRACT FROM AUTHOR]

A non-stationary model is shown, formed by the 1D hyperbolic differential equation, which is commonly used in practice for wave propagation of rivers and channels. As an upstream boundary condition, a function that depends on time has been taken, representing the variation of the water levels in the channel. Downstream, the wave equation with first derivatives in space and time is taken as the boundary condition, thus ensuring that there is no reflection of the wave in that boundary. Numerical algorithms obtained from the application of the Finite Differences Method and the Finite Element Method are formulated and the calculation algorithms are compared with an analytical solution showing good results. [ABSTRACT FROM AUTHOR]

Landscape evolution models (LEMs) are dependent on their initial conditions (ICs). Commonly, LEMs use a horizontal surface with randomized perturbations as their IC and tend toward a steady state under constant forcing. The initial and steady state topographies are inherently linked, but they bear no obvious resemblance to each other. Here we reveal a connection by adding a shallow sinusoidal channel to the IC. This channel transforms into a deep canyon at steady state. Hence, the general behavior of LEMs is to indefinitely preserve topographic features from their ICs. Then we test whether experimental landscapes exhibit a similar behavior. In our experiments, we use the same sinusoidal signal, but find that it is ultimately erased. We believe that the culprit reorganizing processes are lateral channel migration and spatiotemporal variability in incision. Our results imply that LEMs are missing fundamental mechanisms and that long‐term preservation of ICs in erosional environments is unlikely. Plain Language Summary: Researchers use computer simulations and sandbox experiments to model how mountains develop over geologic time. The computer models are aptly named landscape evolution models. These models predict that rivers and mountains remain static on the landscape over long periods of time, but the experiments imply that they fluctuate endlessly. In this paper, we compare the landscape evolution models to landscape experiments and hypothesize that the reason they differ in their behavior is because the models are missing key processes that describe how rivers erode. Key Points: Numerical landscape evolution models preserve topographic signals from initial conditions indefinitelyExperimental landscapes frequently reorganize their drainage networks and destroy past topographic signalsIn the experiments, we suggest that lateral channel migration and autogenic knickpoints are the drivers of drainage network reorganization [ABSTRACT FROM AUTHOR]

We propose a class of prior distributions that discipline the long-run behavior of vector autoregressions (VARs). These priors can be naturally elicited using economic theory, which provides guidance on the joint dynamics of macroeconomic time series in the long run. Our priors for the long run are conjugate, and can thus be easily implemented using dummy observations and combined with other popular priors. In VARs with standard macroeconomic variables, a prior based on the long-run predictions of a wide class of theoretical models yields substantial improvements in the forecasting performance. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

It is proven that the transitivity property of commutativity is always valid for second-order linear time-varying analog systems whether their initial states are zero or not. Throughout the study, it is assumed that the subsystems considered cannot be obtained from each other by any feed-forward and feedback structure. The results are well validated by MATLAB simulations. [ABSTRACT FROM AUTHOR]

Radiative forcing from volcanic aerosol impacts surface temperatures; however, the background climate state also affects the response. A key question thus concerns whether constraining forcing estimates is more important than constraining initial conditions for accurate simulation and attribution of posteruption climate anomalies. Here we test whether different realistic volcanic forcing magnitudes for the 1815 Tambora eruption yield distinguishable ensemble surface temperature responses. We perform a cluster analysis on a superensemble of climate simulations including three 30‐member ensembles using the same set of initial conditions but different volcanic forcings based on uncertainty estimates. Results clarify how forcing uncertainties can overwhelm initial‐condition spread in boreal summer due to strong direct radiative impact, while the effect of initial conditions predominate in winter, when dynamics contribute to large ensemble spread. In our setup, current uncertainties affecting reconstruction‐simulation comparisons prevent conclusions about the magnitude of the Tambora eruption and its relation to the "year without summer." Plain Language Summary: Strong volcanic eruptions are a major natural forcing of climate, and there is increasing awareness of their importance for understanding and prediction of climate. Much of our current understanding is based on past eruptions for which there is no direct observation and that are therefore subject to substantial uncertainties regarding the eruption characteristics, the associated volcanic forcing, and the climatic response. With these premises, our study tackles the question of whether, for a past or analogously future eruption, it is more important to constrain the uncertainty in the volcanic forcing it generates rather than the initial climate conditions upon which it occurs, in order to obtain robust information about the associated climate responses. We use the 1815 eruption of Mount Tambora as a test case. We demonstrate that the climatic effects of initial condition uncertainties can overwhelm those of forcing uncertainties especially in winter and at the regional scale. We show how the European "year without a summer" seen in climate reconstructions is compatible with very different combinations of forcing magnitude and initial conditions. Key Points: The 1815 Tambora eruption is used to demonstrate how initial conditions affect the simulation of posteruption climate anomaliesForcing uncertainties can overwhelm initial‐condition spread in boreal summer, while the effect of initial conditions predominate in winterCurrent initial‐condition uncertainties hamper inferences on magnitude of the Tambora eruption in relation to the "year without summer" [ABSTRACT FROM AUTHOR]

Abstract Disentangling the effect of initial conditions and medium properties is an open question in the field of relativistic heavy-ion collisions. We argue that, while one can study the impact of initial inhomogeneities by varying their size, it is important to maintain the global properties fixed. We present a method to do this. We show that many observables are insensitive to the the hot spot sizes, including integrated v n , scaled distributions of v n , symmetric cumulants, event-plane correlations, and differential v n (p T). We find however that the factorization breaking ratio r n and sub-leading component in a Principal Component Analysis are more sensitive to the initial granularity and can be used to probe short-scale features of the initial density. [ABSTRACT FROM AUTHOR]

Abstract We overview the current status and recent developments on initial conditions in ultra-relativistic nucleus-nucleus collisions. Specifically, we look at the progress in understanding the role of sub-nucleonic fluctuations in large and small collision systems. Next, we review the current ideas of going beyond boost invariant initial conditions and introducing physically motivated rapidity fluctuations at RHIC and LHC energies. Finally, we discuss the time evolution of initial stages and the matching between different descriptions of the QGP. [ABSTRACT FROM AUTHOR]