Results 31 to 40 of about 237,552 (328)

Approximation by piecewise-regular maps

, 2019
A real algebraic variety W of dimension m is said to be uniformly rational if each of its points has a Zariski open neighborhood which is biregularly isomorphic to a Zariski open subset of R^m. Let l be any nonnegative integer. We prove that every map of
Bilski, Marcin, Kucharz, Wojciech
core   +1 more source

A classification of equivariant principal bundles over nonsingular toric varieties

, 2015
We classify holomorphic as well as algebraic torus equivariant principal $G$-bundles over a nonsingular toric variety $X$, where $G$ is a complex linear algebraic group.
Biswas, Indranil, Dey, Arijit, Poddar, Mainak   +2 more
core   +1 more source

The Euclidean distance degree of an algebraic variety [PDF]

, 2013
The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low rank matrices, the Eckart-Young Theorem states that this map is given by the singular value decomposition ...
Draisma, Jan, Horobet, Emil, Ottaviani, Giorgio, Sturmfels, Bernd, Thomas, Rekha R.   +4 more
core   +2 more sources

Genome‐Wide by Lifetime Environment Interaction Studies of Brain Imaging Phenotypes

Advanced Science, EarlyView.
This study explores genome‐wide by lifetime environment interactions on brain imaging phenotypes. Gene‐environment interactions explain more phenotypic variance than main effects, pinpoint regulatory variants, and reveal exposure‐specific biological pathways.
Sijia Wang, Meiyun Wang, Peng Zhang, Jingliang Cheng, Longjiang Zhang, Wenzhen Zhu, Shijun Qiu, Zuojun Geng, Guangbin Cui, Yongqiang Yu, Weihua Liao, Xi‐Nian Zuo, Hui Zhang, Bo Gao, Xiaojun Xu, Tong Han, Zhenwei Yao, Quan Zhang, Feng Liu, Qiang Xu, Jiayuan Xu, Jilian Fu, Nana Liu, Yuan Ji, Jie Tang, Lining Guo, Mengge Liu, Xiaoxiao Xiao, Xiaoxuan Liu, Wei Li, Caihong Wang, Wei Wei, Dapeng Shi, Su Lui, Zhihan Yan, Feng Chen, Jing Zhang, Wen Shen, Yanwei Miao, Dawei Wang, Jia‐Hong Gao, Yunjun Yang, Kai Xu, Junfang Xian, Bing Zhang, Xiaochu Zhang, Zhaoxiang Ye, Le Yu, Wen Qin, Meng Liang, Chunshui Yu, the CHIMGEN Consortium   +51 more
wiley   +1 more source

EXPLORING ALGEBRAIC ANALYSIS: DEFINITIONS, INTERPRETATIONS, AND METHODOLOGIES

Cifra: Информационные технологии и телекоммуникации
For further than 200 times, the word algebraic analysis has been used to relate to a variety of motifs and methodologies. These connotations are still present moment.
Altaher A., Saba S.M., Khalid S.M., Haneen h.M.   +3 more
doaj   +1 more source

Graph Attention Neural Networks for Interpretable and Generalizable Prediction of Janus III–Vi Van Der Waals Heterostructures

Advanced Intelligent Discovery, EarlyView.
A crystal graph neural network based on the attention mechanism is proposed in this work. The model dynamically weights features through the attention mechanism, enabling precise prediction of properties of material from structural features. Here, taking Janus III–VI van der Waals heterostructures as a representative case, the properties have been ...
Yudong Shi, Zhao Zheng, Yinggan Zhang, Zhou Cui, Peng Lin, Cuilian Wen, Baisheng Sa, Zhimei Sun   +7 more
wiley   +1 more source

Dimensions of Prym varieties

International Journal of Mathematics and Mathematical Sciences, 2001
Given a tame Galois branched cover of curves π:X→Y with any finite Galois group G whose representations are rational, we compute the dimension of the (generalized) Prym variety Prymρ(X) corresponding to any irreducible representation ρ of G. This formula
Amy E. Ksir
doaj   +1 more source

Knowledgebra: An Algebraic Learning Framework for Knowledge Graph

Machine Learning and Knowledge Extraction, 2022
Knowledge graph (KG) representation learning aims to encode entities and relations into dense continuous vector spaces such that knowledge contained in a dataset could be consistently represented.
Tong Yang, Yifei Wang, Long Sha, Jan Engelbrecht, Pengyu Hong   +4 more
doaj   +1 more source

From Sheaf Cohomology to the Algebraic de Rham Theorem

, 2014
Let X be a smooth complex algebraic variety with the Zariski topology, and let Y be the underlying complex manifold with the complex topology. Grothendieck's algebraic de Rham theorem asserts that the singular cohomology of Y with complex coefficients ...
Tu, Loring W., Zein, Fouad El
core   +1 more source

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real‐World Data

Advanced Intelligent Discovery, EarlyView.
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley   +1 more source