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The purpose of this paper is to revisit the recursive computation of closed-form expressions for the topological derivative of shape functionals in the context of time-harmonic acoustic waves scattering by sound-soft (Dirichlet condition), sound-hard (Neumann condition) and isotropic inclusions (transmission conditions).

The elliptic boundary value problems in the singularly perturbed domains are equivalently reduced to couples of boundary integral equations with unknown densities given by boundary traces. In the case of circular or spherical holes, the spectral Fourier and Mie series expansions of the potential operators are used to derive the first-order term in the asymptotic expansion of the boundary traces for the solution to the two- and three-dimensional perturbed problems.

As the shape gradients of shape functionals are expressed in terms of boundary integrals involving the boundary traces of the state and the associated adjoint field, then the topological gradient formulae follow readily.

The authors exhibit singular perturbation asymptotics that can be reused in the derivation of the topological gradient function in the iterated numerical solution of any shape optimization or imaging problem relying on time-harmonic acoustic waves propagation. When coupled with converging Gauss−Newton iterations for the search of optimal boundary parametrizations, it generates fully automatic algorithms.

In this paper, the authors revisit the computation of closed-form expressions of the topological indicator function for a one step imaging algorithm of two- and three-dimensional sound-soft (Dirichlet condition), sound-hard (Neumann condition) and isotropic inclusions (transmission conditions) in the free space.

From the addition theorem for translated harmonics, explicit expressions of the scattered waves by infinitesimal circular (and spherical) holes subject to an incident plane wave or a compactly supported distribution of point sources are available. Then the authors derive the first-order term in the asymptotic expansion of the Dirichlet and Neumann traces and their surface derivatives on the boundary of the singular medium perturbation.

As the shape gradient of shape functionals are expressed in terms of boundary integrals involving the boundary traces of the state and the associated adjoint field, then the topological gradient formulae follow readily.

The authors exhibit singular perturbation asymptotics that can be reused in the derivation of the topological gradient function that generates initial guesses in the iterated numerical solution of any shape optimization problem or imaging problems relying on time-harmonic acoustic wave propagation.

For kernel-based estimators, smoothness conditions ensure that the asymptotic rate at which the bias goes to zero is determined by the kernel order. In a finite sample, the leading term in the expansion of the bias may provide a poor approximation. We explore the relation between smoothness and bias and provide estimators for the degree of the smoothness and the bias. We demonstrate the existence of a linear combination of estimators whose trace of the asymptotic mean-squared error is reduced relative to the individual estimator at the optimal bandwidth. We examine the finite-sample performance of a combined estimator that minimizes the trace of the MSE of a linear combination of individual kernel estimators for a multimodal density. The combined estimator provides a robust alternative to individual estimators that protects against uncertainty about the degree of smoothness.

We examine the Stein-rule shrinkage estimator for possible improvements in estimation and forecasting when there are many predictors in a linear time series model. We consider the Stein-rule estimator of Hill and Judge (1987) that shrinks the unrestricted unbiased ordinary least squares (OLS) estimator toward a restricted biased principal component (PC) estimator. Since the Stein-rule estimator combines the OLS and PC estimators, it is a model-averaging estimator and produces a combined forecast. The conditions under which the improvement can be achieved depend on several unknown parameters that determine the degree of the Stein-rule shrinkage. We conduct Monte Carlo simulations to examine these parameter regions. The overall picture that emerges is that the Stein-rule shrinkage estimator can dominate both OLS and principal components estimators within an intermediate range of the signal-to-noise ratio. If the signal-to-noise ratio is low, the PC estimator is superior. If the signal-to-noise ratio is high, the OLS estimator is superior. In out-of-sample forecasting with AR(1) predictors, the Stein-rule shrinkage estimator can dominate both OLS and PC estimators when the predictors exhibit low persistence.

This paper seeks to contribute to the study of the relationship between savings and investment in a panel of five South Asian countries.

A number of unit root tests such as Levin, Lin, and Chu or LLC, Breitung, Im, Pesaran, and Shin or IPS, Fisher‐type tests using ADF and Fisher‐type tests using PP tests are conducted that confirm the non‐stationarity of data. Then the paper applies maximum likelihood‐based panel cointegration method to examine the relationship between savings and investment using data on investment and savings for five South Asian developing countries, namely, Bangladesh, Pakistan, India, Nepal, and Sri Lanka over the period 1973‐2007 compiled from the World Development Indicator (WDI) Database 2008 CD‐ROM.

The results obtained suggest that savings and investment are cointegrated, which implies that the Feldstein‐Horioka (F‐H) puzzle does not hold in this region. It is also found that most of these countries have maintained an international solvency condition.

This is another contribution that would enrich the existing literature on the F‐H puzzle. The paper includes data that involve the longest sample period. No other study, as of now, has employed the panel cointegration method to study the savings investment relationship in this region.

The purpose of this paper is to investigate the relationship between growth, investment and military expenditure in the case of the European Union‐15.

The paper uses fixed panel models, random coefficient models and a trivariate VAR model to examine empirically the relationship between these three macroeconomic variables.

The results obtained and reported herein show a significant positive effect of the growth rate on the share of military expenditure and on the share of investment. However, on the whole, the findings do not seem to point to any consistent quantitative relation between defence spending and either growth or investment. Thus, they appear to be in line with the findings of other studies.

The economic effects of military spending have drawn considerable attention. Demand side effects on capacity utilisation are one possible channel through which the economy can be positively affected by such expenditure. On the other hand however, reduced investment and capital stock have been reported as a possible negative economic impact of defence outlays that can more than offset any growth inducing effective demand stimulation. The paper attempts a simultaneous assessment of the impact of defence expenditure on both growth and investment for the EU‐15, something that has not been tried before.

We provide a new characterization of the equality of two positive-definite matrices A and B, and we use this to propose several new computationally convenient statistical tests for the equality of two unknown positive-definite matrices. Our primary focus is on testing the information matrix equality (e.g. White, 1982, 1994). We characterize the asymptotic behavior of our new trace-determinant information matrix test statistics under the null and the alternative and investigate their finite-sample performance for a variety of models: linear regression, exponential duration, probit, and Tobit. The parametric bootstrap suggested by Horowitz (1994) delivers critical values that provide admirable level behavior, even in samples as small as n = 50. Our new tests often have better power than the parametric-bootstrap version of the traditional IMT; when they do not, they nevertheless perform respectably.

Many investigations are going on in monitoring, contact tracing, predicting and diagnosing the COVID-19 disease and many virologists are urgently seeking to create a vaccine as early as possible. Even though there is no specific treatment for the pandemic disease, the world is now struggling to control the spread by implementing the lockdown worldwide and giving awareness to the people to wear masks and use sanitizers. The new technologies, including the Internet of things (IoT), are gaining global attention towards the increasing technical support in health-care systems, particularly in predicting, detecting, preventing and monitoring of most of the infectious diseases. Similarly, it also helps in fighting against COVID-19 by monitoring, contract tracing and detecting the COVID-19 pandemic by connection with the IoT-based smart solutions. IoT is the interconnected Web of smart devices, sensors, actuators and data, which are collected in the raw form and transmitted through the internet. The purpose of this paper is to propose the concept to detect and monitor the asymptotic patients using IoT-based sensors.

In recent days, the surge of the COVID-19 contagion has infected all over the world and it has ruined our day-to-day life. The extraordinary eruption of this pandemic virus placed the World Health Organization (WHO) in a hazardous position. The impact of this contagious virus and scarcity among the people has forced the world to get into complete lockdown, as the number of laboratory-confirmed cases is increasing in millions all over the world as per the records of the government.

COVID-19 patients are either symptomatic or asymptotic. Symptomatic patients have symptoms such as fever, cough and difficulty in breathing. But patients are also asymptotic, which is very difficult to detect and monitor by isolating them.

Asymptotic patients are very hazardous because without knowing that they are infected, they might spread the infection to others, also asymptotic patients might be having very serious lung damage. So, earlier prediction and monitoring of asymptotic patients are mandatory to save their life and prevent them from spreading.

In the context of Dynamic Factor Models, we compare point and interval estimates of the underlying unobserved factors extracted using small- and big-data procedures. Our paper differs from previous works in the related literature in several ways. First, we focus on factor extraction rather than on prediction of a given variable in the system. Second, the comparisons are carried out by implementing the procedures considered to the same data. Third, we are interested not only on point estimates but also on confidence intervals for the factors. Based on a simulated system and the macroeconomic data set popularized by Stock and Watson (2012), we show that, for a given procedure, factor estimates based on different cross-sectional dimensions are highly correlated. On the other hand, given the cross-sectional dimension, the maximum likelihood Kalman filter and smoother factor estimates are highly correlated with those obtained using hybrid procedures. The PC estimates are somehow less correlated. Finally, the PC intervals based on asymptotic approximations are unrealistically tiny.

It is widely documented that while contemporaneous spot and forward financial prices trace each other extremely closely, their difference is often highly persistent and the conventional cointegration tests may suggest lack of cointegration. This chapter studies the possibility of having cointegrated errors that are characterized simultaneously by high persistence (near-unit root behavior) and very small (near zero) variance. The proposed dual parameterization induces the cointegration error process to be stochastically bounded which prevents the variables in the cointegrating system from drifting apart over a reasonably long horizon. More specifically, this chapter develops the appropriate asymptotic theory (rate of convergence and asymptotic distribution) for the estimators in unconditional and conditional vector error correction models (VECM) when the error correction term is parameterized as a dampened near-unit root process (local-to-unity process with local-to-zero variance). The important differences in the limiting behavior of the estimators and their implications for empirical analysis are discussed. Simulation results and an empirical analysis of the forward premium regressions are also provided.