Many applications in geosciences require solving inverse problems to estimate the state of a physical system. Data assimilation provides a strong framework to do so when the system is partially observed and its underlying dynamics are known to some extent. In the variational flavor, it can be seen as an optimal control problem where initial conditions are the control parameters. Such problems are often ill-posed, regularization may be needed using explicit prior knowledge to enforce a satisfying solution. In this work, we propose to use a deep prior, a neural architecture that generates potential solutions and acts as implicit regularization. The architecture is trained in a fully-unsupervised manner using the variational data assimilation cost so that gradients are backpropagated through the dynamical model and then through the neural network. To demonstrate its use, we set a twin experiment using a shallow-water toy model, where we test various variational assimilation algorithms on an ocean-like circulation estimation.

Researchers of time series cross-sectional data regularly face the change-point problem, which requires them to discern between significant parametric shifts that can be deemed structural changes and minor parametric shifts that must be considered noise. In this paper, we develop a general Bayesian method for change-point detection in high-dimensional data and present its application in the context of the fixed-effect model. Our proposed method, hidden Markov Bayesian bridge model, jointly estimates high-dimensional regime-specific parameters and hidden regime transitions in a unified way. We apply our method to Alvarez, Garrett, and Lange’s (1991, American Political Science Review 85, 539–556) study of the relationship between government partisanship and economic growth and Allee and Scalera’s (2012, International Organization 66, 243–276) study of membership effects in international organizations. In both applications, we found that the proposed method successfully identify substantively meaningful temporal heterogeneity in parameters of regression models.

In this paper, we concern with a backward problem for a nonlinear time fractional wave equation in a bounded domain. By applying the properties of Mittag-Leffler functions and the method of eigenvalue expansion, we establish some results about the existence and uniqueness of the mild solutions of the proposed problem based on the compact technique. Due to the ill-posedness of backward problem in the sense of Hadamard, a general filter regularization method is utilized to approximate the solution and further we prove the convergence rate for the regularized solutions.

In shape-from-focus (SFF) methods, a single focus measure is used to compute the focus volume. However, it seems that a single focus measure operator is not capable of computing accurate focus values for the images of diverse types of object shapes. Furthermore, most of the SFF methods try to improve the depth map without considering any additional structural or prior information. Consequently, the extracted shape of the object might lack important details. In this work, we address these problems and suggest a method in which depth hypotheses are combined for a more accurate 3D shape through 3D weighted least squares. First, depth hypotheses are obtained by applying a number of focus operators. Then, structural prior or guidance volume is extracted from the focus measure volumes. Finally, a 3D weighted least squares optimization technique is applied to the depth hypothesis volume, where weights are computed from the guidance volume. Thus, by inducing structural prior, an improved resultant depth map is obtained. The proposed method was tested using various image sequences of synthetic and microscopic real objects. Experimental results and comparative analysis demonstrated the effectiveness of the proposed method.

Wavelet theory is known to be a powerful tool for compressing and processing time series or images. It consists in projecting a signal on an orthonormal basis of functions that are chosen in order to provide a sparse representation of the data. The first part of this article focuses on smoothing mortality curves by wavelets shrinkage. A chi-square test and a penalized likelihood approach are applied to determine the optimal degree of smoothing. The second part of this article is devoted to mortality forecasting. Wavelet coefficients exhibit clear trends for the Belgian population from 1965 to 2015, they are easy to forecast resulting in predicted future mortality rates. The wavelet-based approach is then compared with some popular actuarial models of Lee–Carter type estimated fitted to Belgian, UK, and US populations. The wavelet model outperforms all of them.

We show that several machine learning estimators, including square-root least absolute shrinkage and selection and regularized logistic regression, can be represented as solutions to distributionally robust optimization problems. The associated uncertainty regions are based on suitably defined Wasserstein distances. Hence, our representations allow us to view regularization as a result of introducing an artificial adversary that perturbs the empirical distribution to account for out-of-sample effects in loss estimation. In addition, we introduce RWPI (robust Wasserstein profile inference), a novel inference methodology which extends the use of methods inspired by empirical likelihood to the setting of optimal transport costs (of which Wasserstein distances are a particular case). We use RWPI to show how to optimally select the size of uncertainty regions, and as a consequence we are able to choose regularization parameters for these machine learning estimators without the use of cross validation. Numerical experiments are also given to validate our theoretical findings.

To deal with the growing migrant crisis in North Africa, several states have considered granting amnesty to foreign displaced persons (both economic migrants and potential refugees) who have entered their territories clandestinely. Morocco has taken the lead in this policy approach, launching two successful amnesty campaigns in 2014 and 2017 that regularized the status of approximately 40,000 displaced persons in total. While policymakers in many North African states increasingly see this policy as a viable solution, it is less understood how ordinary citizens view such regularization policies. Hence, this article inquires: under what conditions do ordinary native citizens support regularizing clandestine migrants and refugees? Further, what factors correlate with either higher or lower levels of public support for (or opposition to) regularization campaigns? Drawing on an original representative public opinion poll from Morocco's Casablanca-Settat region completed in 2017, this article finds that more than 59 percent of native citizens of Morocco support these regularization campaigns. Particularly, Moroccans who were wealthier, female, and ethnic minorities (black Moroccans) endorsed regularization more strongly. By contrast, Moroccans opposed regularization when they had concerns about whether displaced persons hurt the economy, undermine cultural traditions, and reduce stability.

In Venter and Şahin (2017), the author's name appeared incorrectly as “ŞULE ŞAHÎN”.

The author's name should appear as “ŞULE ŞAHİN”.

The original article has been corrected to rectify this error.

We study the numerical identification of an unknown portion of the boundary on which either the Dirichlet or the Neumann condition is provided from the knowledge of Cauchy data on the remaining, accessible and known part of the boundary of a two-dimensional domain, for problems governed by Helmholtz-type equations. This inverse geometric problem is solved using the plane waves method (PWM) in conjunction with the Tikhonov regularization method. The value for the regularization parameter is chosen according to Hansen's L-curve criterion. The stability, convergence, accuracy and efficiency of the proposed method are investigated by considering several examples.