Article
Computer Science, Information Systems
Moises Ramos-Martinez, Christophe Corbier, Victor M. Alvarado, Guadalupe Lopez Lopez
Summary: This paper introduces a new method based on the mother-wave function for decomposing the mean Euler-Poincare characteristic of non-Gaussian random fields, suitable for processing long-term noisy physiological signals. By preprocessing and merging polynomialized signals, a real-valued non-Gaussian physiological random field is formed, studying its geometric properties and topological invariants, providing a model with a viable interpretation for different heart conditions.
Article
Statistics & Probability
Jan Rataj
Summary: The translative intersection formula of integral geometry provides an expression for the mean Euler characteristic of a stationary random closed set intersected with a fixed observation window. This result is formulated in the setting of sets with positive reach and using flag measures, which yield curvature measures as marginals. As an application, the study focuses on excursion sets of stationary random fields with C-1,C-1 realizations, such as stationary Gaussian fields, and extends known results from the literature.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2021)
Article
Mathematics, Applied
Hunter Dinkins, Andrey Smirnov
Summary: In this paper, we prove a formula that relates the equivariant Euler characteristic of K-theoretic stable envelopes to the index vertex of the cotangent bundle of the full flag variety. Our formula shows that the index vertex is the power series expansion of a rational function. This result is a consequence of the 3d mirror self-symmetry of the variety being considered.
SELECTA MATHEMATICA-NEW SERIES
(2022)
Article
Mathematics
Wangwang Yan, Jing Ba, Taihua Xu, Hualong Yu, Jinlong Shi, Bin Han
Summary: This study proposes a novel attribute selector called Beam-Influenced Selector (BIS), which enhances the stability of attribute reduction through random partition and beam strategies. Experimental results show that this selector significantly improves the stability of the derived reducts and achieves excellent performance in classification tasks.
Article
Computer Science, Interdisciplinary Applications
Xi -Yuan Yin, Kai Schneider, Jean-Christophe Nave
Summary: We propose an efficient semi-Lagrangian Characteristic Mapping (CM) method for solving the 3D incompressible Euler equations. This method discretizes the flow map associated with the velocity field to evolve advected quantities. By utilizing the properties of the Lie group of volume preserving diffeomorphisms SDiff, long-time deformations can be accurately computed from short-time submaps on coarse grids. The method extends the CM method for 2D incompressible Euler equations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Xi-Yuan Yin, Olivier Mercier, Badal Yadav, Kai Schneider, Jean-Christophe Nave
Summary: An efficient semi-Lagrangian method is proposed for solving the two-dimensional incompressible Euler equations with high precision on a coarse grid. The method achieves exponential resolution and conservation properties, demonstrated through examples like vortex merger, four-modes, and random flow problems. Comparisons with the Cauchy-Lagrangian method are also provided.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Giacomo Cherubini, Niko Laaksonen
Summary: This brief note proves an upper bound of the variance of the volume of the nodal set of arithmetic random waves on the d-dimensional torus for d >= 4, with a power saving O(E/N (1+alpha(d)-epsilon)), where alpha(d) tends to zero as d increases. This upper bound is the best possible with the current method when d >= 5 due to the proof of the l(2) -decoupling conjecture by Bourgain and Demeter.
FORUM MATHEMATICUM
(2022)
Article
Mathematics
Marc Levine
Summary: In motivic stable homotopy theory, an analog of the intrinsic normal cone of Behrend-Fantechi is constructed, and a perfect obstruction theory introduces a virtual fundamental class in E-cohomology for any motivic cohomology theory E. This also encompasses the oriented Chow groups of Barge-Morel and Fasel.
ALGEBRAIC GEOMETRY
(2021)
Article
Mathematics, Applied
Peng Li, Bao-Shan Wang, Wai-Sun Don
Summary: The research suggests that the instability effects of a sensitivity parameter in the WENO polynomial reconstruction procedure may cause the numerical scheme for Euler equations with a gravitational source term to become unbalanced. By introducing two numerical techniques, the issue is addressed to ensure the correctness and non-oscillatory nature of the FV-WENO scheme.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Hossain Chizari, Vishal Singh, Farzad Ismail
Summary: An alternative cell-vertex entropy-stable finite volume method for the system of Euler equations is presented, using signals from each triangular element to control entropy. The method includes first-order and second-order versions, where the results demonstrate its accuracy and robustness compared to the current method.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics
Michael Borinsky, Karen Vogtmann
Summary: This study investigates the relationship between the moduli space of rank n graphs, the outer automorphism group of the free group of rank n, and Kontsevich's Lie graph complex, and proves that they have the same rational cohomology. The study also shows that as n goes to infinity, the associated Euler characteristic grows rapidly, indicating a rapid growth in the total dimension of this cohomology.
ADVANCES IN MATHEMATICS
(2023)
Article
Chemistry, Multidisciplinary
Yutong Wu, Bohong Chang, Lian Wang, Hui Li, Lu Pan, Zhen Liu, Longwei Yin
Summary: This study develops a unique and efficient strategy to modulate the intrinsic dipole arrangement in perovskite films for high-performance and stable perovskite solar cells (PSCs). The reorientation of dipolar cation methylamine is triggered by a polar molecule, constructing a vertical polarization during crystallization regulation. This strategy enhances the built-in electric field, suppresses nonradiative recombination, and increases the power conversion efficiency of PSCs.
ADVANCED MATERIALS
(2023)
Article
Computer Science, Interdisciplinary Applications
Pierre Lavoie, Emmanuel Radenac, Ghislain Blanchard, Eric Laurendeau, Philippe Villedieu
Summary: Immersed boundary methods offer a simpler mesh generation approach for dealing with complex geometries; a new penalization method based on characteristic-based volume penalization is proposed, enforcing the conservation of entropy and total enthalpy in the normal direction to the wall; the new method outperforms the previous one on coarser meshes and is better at retrieving attached flows for curved geometries.
COMPUTERS & FLUIDS
(2021)
Article
Chemistry, Physical
Wenyi Du, Juan Ma, Changhu Zhou, Yongchun Yan, Peter Wriggers
Summary: This work presents a robust non-deterministic free vibration analysis for engineering structures with random field parameters using the stochastic finite element method. The uncertainty of structural material parameters is described using Gauss random field theory and the random parameters are discretized with the Karhunen-Loeve expansion method. The structural dynamic characteristics are analyzed based on the discretized random parameters and finite element method, and the probability distribution density function of the random natural frequency is estimated.
Article
Mathematics
Stanislaw Spodzieja
Summary: In this study, an elementary construction of an arbitrary differentially closed field and a universal extension of a differential field were presented using Nash function fields. Additionally, a characterization of any Archimedean ordered differentially closed field was provided in terms of Nash functions.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2021)
