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In this work, we investigate the regularized solutions and their finite element solutions to the inverse source problems governed by partial differential equations, and establish the stochastic convergence and optimal finite element…
The Subtractive Optimally Localized Averages (SOLA) method, developed and extensively used in helioseismology, is applied to artificial data to obtain measures of the sound speed inside a solar-type star. In contrast to inversion methods…
This paper presents a comprehensive exploration of the theoretical properties inherent in the Adaptive Lasso and the Transfer Lasso. The Adaptive Lasso, a well-established method, employs regularization divided by initial estimators and is…
Unlike in terrestrial cellular networks, certain frequency bands for low-earth orbit (LEO) satellite systems have thus far been allocated on a non-exclusive basis. In this context, systems that launch their satellites earlier (referred to…
Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence…
We discuss a new method to solve in a semianalytical way the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NLO order in the x-space. The method allows to construct an evolution operator expressed in form of a rapidly…
This paper investigates an analytical model for low-earth orbit (LEO) multi-satellite downlink non-orthogonal multiple access (NOMA) networks. The satellites transmit data to multiple NOMA user terminals (UTs), each employing successive…
In spite of planetary resonances being a common dynamical mechanism acting on planetary systems, no general model exists for describing their properties, particularly for commensurabilities of any order and arbitrary values of the…
Mega low earth orbit (LEO) satellite constellation is promising in achieving global coverage with high capacity. However, forwarding packets in mega constellation faces long end-to-end delay caused by multi-hop routing and high-complexity…
We present here results of stellar evolution calculations that include the latest advances in radiative opacities and neutrino cooling, and discuss on the basis of these models how the internal stellar structure responds to mass-loss from…
The majority of machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, given samples provided in a streaming fashion, we define a general stochastic Newton algorithm and its…
In this article, we present a new approach to averaging in non-Hamiltonian systems with periodic forcing. The results here do not depend on the existence of a small parameter. In fact, we show that our averaging method fits into an…
In this paper, we propose a novel solution for non-convex problems of multiple variables, especially for those typically solved by an alternating minimization (AM) strategy that splits the original optimization problem into a set of…
Recently, $L_1$ regularization have been attracted extensive attention and successfully applied in mean-variance portfolio selection for promoting out-of-sample properties and decreasing transaction costs. However, $L_1$ regularization…
Linear discriminant analysis (LDA) is a widely used technique for data classification. The method offers adequate performance in many classification problems, but it becomes inefficient when the data covariance matrix is ill-conditioned.…
In this two-part paper, we propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints. The algorithm solves a sequence of (separable) strongly convex problems and…
Due to their low latency, high capacity, and seamless worldwide coverage, low Earth orbit (LEO) satellites are essential to the equal access network. Stochastic geometry (SG) is an appropriate method for such a large and irregular system.…
We present different regularizations and numerical methods for the nonlinear Schr\"odinger equation with singular nonlinearity (sNLSE) including the regularized Lie-Trotter time-splitting (LTTS) methods and regularized Lawson-type…
Small corrections in the argument of the latitude can be used to improve the accuracy of the SGP4 orbit propagator. These corrections have been obtained by applying the hybrid methodology for orbit propagation to SGP4, therefore yielding a…
The proliferation of low-earth-orbit (LEO) satellite networks leads to the generation of vast volumes of remote sensing data which is traditionally transferred to the ground server for centralized processing, raising privacy and bandwidth…