应用数学所近期发表的若干重要成果汇编

2024-01-14 | 撰稿： | 浏览:

2024-01-14 | 撰稿： | 浏览:

我院王启华研究员的论文Distributed Nonparametric Regression Imputation for Missing Response Problems with Large-scale Data被JOURNAL OF MACHINE LEARNING RESEARCH接收发表。

摘要：Nonparametric regression imputation is commonly used in missing data analysis. However, it suffers from the curse of dimension. The problem can be alleviated by the explosive sample size in the era of big data, while the large-scale data size presents some challenges in the storage of data and the calculation of estimators. These challenges make the classical nonparametric regression imputation methods no longer applicable. This motivates us to develop two distributed nonparametric regression imputation methods. One is based on kernel smoothing and the other on the sieve method. The kernel-based distributed imputation method has extremely low communication cost, and the sieve-based distributed imputation method can accommodate more local machines. The response mean estimation is considered to illustrate the proposed imputation methods. Two distributed nonparametric regression imputation estimators are proposed for the response mean, which are proved to be asymptotically normal with asymptotic variances achieving the semiparametric efficiency bound. The proposed methods are evaluated through simulation studies and illustrated in a real data analysis.

我院刘晓东研究员的论文Uniqueness and numerical scheme for spherical shell-structured sources from the far field patterns with at most two frequencies被JOURNAL OF COMPUTATIONAL PHYSICS接收发表。

摘要：It is well known that the far field patterns at finitely many frequencies are not enough to uniquely determine a general source. To establish uniqueness, we consider the acoustic scattering of spherical shell-structured sources. We show that the spherical shell-structured sources can be identified from the far field patterns with at most two frequencies. Precisely, we show that the number and the centers (i.e., locations) of the spherical shells can be uniquely determined by the far field patterns at a fixed frequency. Furthermore, the scattering strengths, the inner and outer diameters are uniquely determined by the far field patterns at two frequencies. Motivated by the uniqueness arguments, a numerical scheme is proposed for reconstructing the spherical shell -structured sources. A migration series method is designed to located the centers. The numerical simulations show that the reconstruction quality is the same as the direct sampling method. Furthermore, an iterative method is designed for computing the inner diameters and outer diameters. An important feature of the proposed iterative method is that it avoids computing any derivatives. The convergence of the iterative method is also proved. Finally, some numerical examples are presented to verify the effectiveness and robustness of the proposed numerical scheme.

我院王勇副研究员的论文Global solutions of the compressible Euler-Poisson equations with large initial data of spherical symmetry被COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS接收发表。

摘要：We are concerned with a global existence theory for finite-energy solutions of the multidimensional Euler-Poisson equations for both compressible gaseous stars and plasmas with large initial data of spherical symmetry. One of the main challenges is the strengthening of waves as they move radially inward towards the origin, especially under the self-consistent gravitational field for gaseous stars. A fundamental unsolved problem is whether the density of the global solution forms a delta measure (i.e., concentration) at the origin. To solve this problem, we develop a new approach for the construction of approximate solutions as the solutions of an appropriately formulated free boundary problem for the compressible Navier-Stokes-Poisson equations with a carefully adapted class of degenerate density-dependent viscosity terms, so that a rigorous convergence proof of the approximate solutions to the corresponding global solution of the compressible Euler-Poisson equations with large initial data of spherical symmetry can be obtained. Even though the density may blow up near the origin at a certain time, it is proved that no delta measure (i.e., concentration) in space-time is formed in the vanishing viscosity limit for the finite-energy solutions of the compressible Euler-Poisson equations for both gaseous stars and plasmas in the physical regimes under consideration.

我院王勇研究员的论文Polygenic adaptation leads to a higher reproductive fitness of native Tibetans at high altitude被CURRENT BIOLOGY接收发表。

摘要：The adaptation of Tibetans to high-altitude environments has been studied extensively. However, the direct assessment of evolutionary adaptation, i.e., the reproductive fitness of Tibetans and its genetic basis, remains elusive. Here, we conduct systematic phenotyping and genome-wide association analysis of 2,252 mother-newborn pairs of indigenous Tibetans, covering 12 reproductive traits and 76 maternal physiological traits. Compared with the lowland immigrants living at high altitudes, indigenous Tibetans show better reproductive outcomes, reflected by their lower abortion rate, higher birth weight, and better fetal development. The results of genome-wide association analyses indicate a polygenic adaptation of reproduction in Tibetans, attributed to the genomic backgrounds of both the mothers and the newborns. Furthermore, the EPAS1-edited mice display higher reproductive fitness under chronic hypoxia, mirroring the situation in Tibetans. Collectively, these results shed new light on the phenotypic pattern and the genetic mechanism of human reproductive fitness in extreme environments.

我院曹道民研究员的论文EXISTENCE OF MULTIPLE BOUNDARY VORTEXES IN PLANAR INCOMPRESSIBLE EULER FLOWS被SIAM JOURNAL ON MATHEMATICAL ANALYSIS接收发表。

摘要：For the incompressible Euler flows in planar bounded domains Omega, we prove that the vortex concentrating at the harmonic center of Omega causes the existence of vortexes with small vorticities near the boundary. These results are very different from the known results for the multivortex flows in which all the local vorticities are of the same orders.

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