Zobrazeno 1 - 10
of 5 897
pro vyhledávání: '"Lek, A."'
Autor:
Chaton, Kham Lek, Meuwly, Markus
The effect of replacing individual contributions to an empirical energy function are assessed for halogenated benzenes (X-Bz, X = H, F, Cl, Br) and chlorinated phenols (Cl-PhOH). Introducing electrostatic models based on distributed charges (MDCM) in
Externí odkaz:
http://arxiv.org/abs/2411.08831
We highlight a perhaps important but hitherto unobserved insight: The attention module in a transformer is a smoothed cubic spline. Viewed in this manner, this mysterious but critical component of a transformer becomes a natural development of an old
Externí odkaz:
http://arxiv.org/abs/2408.09624
Autor:
Lim, Lek-Heng, Ye, Ke
We derive three families of orthogonally-equivariant matrix submanifold models for the Grassmann, flag, and Stiefel manifolds respectively. These families are exhaustive -- every orthogonally-equivariant submanifold model of the lowest dimension for
Externí odkaz:
http://arxiv.org/abs/2407.13482
Autor:
Lim, Lek-Heng, Ye, Ke
We show that the flag manifold $\operatorname{Flag}(k_1,\dots, k_p, \mathbb{R}^n)$, with Grassmannian the special case $p=1$, has an $\operatorname{SO}_n(\mathbb{R})$-equivariant embedding in an Euclidean space of dimension $(n-1)(n+2)/2$, two orders
Externí odkaz:
http://arxiv.org/abs/2407.12546
We show that unconstrained quadratic optimization over a Grassmannian $\operatorname{Gr}(k,n)$ is NP-hard. Our results cover all scenarios: (i) when $k$ and $n$ are both allowed to grow; (ii) when $k$ is arbitrary but fixed; (iii) when $k$ is fixed a
Externí odkaz:
http://arxiv.org/abs/2406.19377
We show that modeling a Grassmannian as symmetric orthogonal matrices $\operatorname{Gr}(k,\mathbb{R}^n) \cong\{Q \in \mathbb{R}^{n \times n} : Q^{\scriptscriptstyle\mathsf{T}} Q = I, \; Q^{\scriptscriptstyle\mathsf{T}} = Q,\; \operatorname{tr}(Q)=2k
Externí odkaz:
http://arxiv.org/abs/2406.11821
We extend several celebrated methods in classical analysis for summing series of complex numbers to series of complex matrices. These include the summation methods of Abel, Borel, Ces\'aro, Euler, Lambert, N\"orlund, and Mittag-Leffler, which are fre
Externí odkaz:
http://arxiv.org/abs/2405.19713
Autor:
Lim, Lek-Heng, Ye, Ke
The degree of the Grassmannian with respect to the Pl\"ucker embedding is well-known. However, the Pl\"ucker embedding, while ubiquitous in pure mathematics, is almost never used in applied mathematics. In applied mathematics, the Grassmannian is usu
Externí odkaz:
http://arxiv.org/abs/2405.05128
Autor:
Yun Soo Hong, Sergiu Pasca, Wen Shi, Daniela Puiu, Nicole J. Lake, Monkol Lek, Meng Ru, Megan L. Grove, Anna Prizment, Corinne E. Joshu, Elizabeth A. Platz, Eliseo Guallar, Dan E. Arking, Lukasz P. Gondek
Publikováno v:
Nature Communications, Vol 15, Iss 1, Pp 1-15 (2024)
Abstract Clonal hematopoiesis of indeterminate potential is the primary pathogenic risk factor for myeloid neoplasms, while heteroplasmy (mutations in a subset of cellular mitochondrial DNA) is another marker of clonal expansion associated with hemat
Externí odkaz:
https://doaj.org/article/7f8586a4638e405dbde112e6a26b0a05
Autor:
Chee Wai Ku, Ruther Teo Zheng, Hong Ying Tan, Jamie Yong Qi Lim, Ling-Wei Chen, Yin Bun Cheung, Keith M. Godfrey, Jerry Kok Yen Chan, Fabian Yap, Ngee Lek, See Ling Loy
Publikováno v:
Diabetology & Metabolic Syndrome, Vol 16, Iss 1, Pp 1-11 (2024)
Abstract Background Gestational diabetes mellitus (GDM) and insulin resistance (IR) increase the risk of adverse pregnancy outcomes. We aimed to examine the relationship of interstitial glucose assessed by continuous glucose monitoring (CGM) at early
Externí odkaz:
https://doaj.org/article/762adadccbca4b2f9c3bb492413b3ef0