In the shotgun assembly problem for a graph, we are given the empirical profile for rooted neighborhoods of depth $r$ (up to isomorphism) for some $r\geq 1$ and we wish to recover the underlying graph up to isomorphism. When the underlying graph is an Erd\H{o}s-R\'enyi $\mathcal G(n, \frac{\lambda}{n})$, we show that the shotgun assembly threshold $r_* \approx \frac{ \log n}{\log (\lambda^2 \gamma_\lambda)^{-1}}$ where $\gamma_\lambda$ is the probability for two independent Poisson-Galton-Watson trees with parameter $\lambda$ to be rooted isomorphic with each other. Our result sharpens a constant factor in a previous work by Mossel and Ross (2019) and thus solves a question therein.
Performance indicators to measure the operating res ults of a business, which could improve business pe rformance, has positive significance to the promotion of enter prise development. The ownership structure is the b asis of the survival and development of listed companies, how t o optimize the shareholding structure in order to i mprove corporate performance has been a problem of listed companies. This article taking the related data of 57 listed companies in the year of 2008 to 2011 as subjects, analyzes the performance and its driving factors fo r empirical research. According to empirical analysis results, the first shareholders' shareholding ratio, company size, profitability and corporate performance do a signif icantly positive side on the performance; the secon d to the tenth largest shareholders and executives shareholding ra tio, leverage levels and capital expenditures do a negative side.
The saddle point (van Hove singularity) exhibits a divergent density of states in 2D systems, leading to fascinating phenomena like strong correlations and unconventional superconductivity, yet it is seldom observed in 3D systems. In this work, we have found two types of 3D higher-order saddle points (HOSPs) in emerging 3D kagome metals, YbCo$_6$Ge$_6$ and MgCo$_6$Ge$_6$. Both HOSPs exhibit a singularity in their density of states, which is significantly enhanced compared to the ordinary saddle point. The HOSP near the Fermi energy generates a flat band extending a large area in the Brillouin zone, potentially amplifying the correlation effect and fostering electronic instabilities. Two types of HOSPs exhibit distinct robustness upon element substitution and lattice distortions in these kagome compounds. Our work paves the way for engineering exotic band structures, such as saddle points and flat bands, and exploring interesting phenomena in Co-based kagome materials.
Electrical generation and transduction of polarized electron spins in semiconductors (SCs) are of central interest in spintronics and quantum information science. While spin generation in SCs is frequently realized via electrical injection from a ferromagnet (FM), there are significant advantages in nonmagnetic pathways of creating spin polarization. One such pathway exploits the interplay of electron spin with chirality in electronic structures or real space. Here, utilizing chirality-induced spin selectivity (CISS), the efficient creation of spin accumulation in n-doped GaAs via electric current injection from a normal metal (Au) electrode through a self-assembled monolayer (SAM) of chiral molecules (α-helix l-polyalanine, AHPA-L), is demonstrated. The resulting spin polarization is detected as a Hanle effect in the n-GaAs, which is found to obey a distinct universal scaling with temperature and bias current consistent with chirality-induced spin accumulation. The experiment constitutes a definitive observation of CISS in a fully nonmagnetic device structure and demonstration of its ability to generate spin accumulation in a conventional SC. The results thus place key constraints on the physical mechanism of CISS and present a new scheme for magnet-free SC spintronics.
In the shotgun assembly problem for a graph, we are given the empirical profile for rooted neighborhoods of depth $r$ (up to isomorphism) for some $r\geq 1$ and we wish to recover the underlying graph up to isomorphism. When the underlying graph is an Erdős–Rényi $\mathcal G\left({n, \frac {\lambda }{n}}\right)$ , we show that the shotgun assembly threshold $r_{*}$ satisfies that $r_{*} \approx \frac { \log n}{\log (\lambda ^{2} \gamma _{\lambda})^{-1}}$ where $\gamma _{\lambda} $ is the probability for two independent Poisson–Galton–Watson trees with parameter $\lambda $ to be rooted isomorphic with each other. Our result sharpens a constant factor in a previous work by Mossel and Ross (2019) and thus solves a question therein.
The exploration of magnetic topological states is instrumental in exploring axion electrodynamics and intriguing transport phenomena, such as the quantum anomalous Hall effect. Here, we predict that the recently-synthesized material Eu$_{3}$In$_{2}$As$_{4}$ exhibits as both an axion insulator and a 3D Stiefel-Whitney insulator with an altermagnetic order. When spins align in the $ab$ plane, we find an unpinned surface Dirac cone on the $ab$ plane and chiral hinge states along the $c$ direction, where hinge states can generate a half-quantized surface anomalous Hall effect on the $ac$ and $bc$ facets. When spins align along $c$, we observe a mirror-protected topological crystalline insulator. Furthermore, the ferromagnetic phase, in which spins are aligned in the same direction by an external in-plane magnetic field, presents an ideal Weyl semimetal with a single pair of type-I Weyl points and no extra Fermi pocket. Our work predicts rich topological states tuned by magnetic structures in Eu$_{3}$In$_{2}$As$_{4}$, supporting the further study of the topological transport and Majorana fermions in proximity to a superconductor.
'/%3e%3cuse xlink:href='%23a' transform='rotate(23.036 .093 25.536)'/%3e%3cuse xlink:href='%23a' transform='rotate(45.87 1.273 16.18)'/%3e%3cuse xlink:href='%23a' transform='rotate(69.945 .996 12.078)'/%3e%3cuse xlink:href='%23a' transform='rotate(20.66 -19.689 31.932)'/%3e%3c/svg%3e)