On shrinking Gradient Ricci Soliton With Nonnegative Sectional Curvature

In this paper, we prove some rigidity theorems for shrinking gradient Ricci solitons with nonnegative sectional curvature.Comment: To appear in PJ

Computation of effective elastic moduli of rocks using hierarchical homogenization

This work focuses on computing the homogenized elastic properties of rocks from 3D micro-computed-tomography (micro-CT) scanned images. The accurate computation of homogenized properties of rocks, archetypal random media, requires both resolution of intricate underlying microstructure and large field of view, resulting in huge micro-CT images. Homogenization entails solving the local elasticity problem computationally which can be prohibitively expensive for a huge image. To mitigate this problem, we use a renormalization method inspired scheme, the hierarchical homogenization method, where a large image is partitioned into smaller subimages. The individual subimages are separately homogenized using periodic boundary conditions, and then assembled into a much smaller intermediate image. The intermediate image is again homogenized, subject to the periodic boundary condition, to find the final homogenized elastic constant of the original image. An FFT-based elasticity solver is used to solve the associated periodic elasticity problem. The error in the homogenized elastic constant is empirically shown to follow a power law scaling with exponent -1 with respect to the subimage size across all five microstructures of rocks. We further show that the inclusion of surrounding materials during the homogenization of the small subimages reduces error in the final homogenized elastic moduli while still respecting the power law with the exponent of -1. This power law scaling is then exploited to determine a better approximation of the large heterogeneous microstructures based on Richardson extrapolatio

On the topology and area of higher dimensional black holes

Over the past decade there has been an increasing interest in the study of black holes, and related objects, in higher (and lower) dimensions, motivated to a large extent by developments in string theory. The aim of the present paper is to obtain higher dimensional analogues of some well known results for black holes in 3+1 dimensions. More precisely, we obtain extensions to higher dimensions of Hawking's black hole topology theorem for asymptotically flat ($\Lambda=0$) black hole spacetimes, and Gibbons' and Woolgar's genus dependent, lower entropy bound for topological black holes in asymptotically locally anti-de Sitter ($\Lambda<0$) spacetimes. In higher dimensions the genus is replaced by the so-called $\sigma$-constant, or Yamabe invariant, which is a fundamental topological invariant of smooth compact manifolds.Comment: 15 pages, Latex2e; typos corrected, a convention clarified, resulting in the simplification of certain formulas, other improvement

Recognizing topological attributes and spatiotemporal patterns in spotted seals (Phoca largha) trophic networks based on eDNA metabarcoding

Spotted seals, a protected species, face multifaceted threats to their habitat, which in turn impact the closely associated trophic networks. These threats will lead to irreversible structural variations within the ecosystem. Therefore, investigating the topological variability of trophic networks in spotted seals is important. Applying environmental DNA methods, field sample collection was conducted in 2021 during both the sea fishing moratorium period and the fishing period to decode fish diversity. Assessing the current status of fish resources by using the multivariate statistics approach. Applying dietary information establishes the spotted seals’ trophic network. Selecting 12 network indexes to analyze the spatiotemporal patterns of network topological attributes. As a result, about 51 families, and 76 genera species were identified. During the sea fishing moratorium and the fishing period, there are 12 and 18 different food resources available for spotted seals, respectively. The diversity index revealed that the FP had greater species richness and diversity than the SP. Comparatively, the Fishing period exhibited higher species richness and biodiversity, likely influenced by habitat heterogeneity and anthropogenic activities. Additionally, the topological features of networks reflected the high clustering coefficients (CC=0.35) and the proportion of omnivorous species (O≈60%), indicating that the network structure in this region tends to form higher trophic-level clustering patterns, which facilitate the formation of weaker interactions between clusters, enhancing the robustness of the network. The higher connectivity complexity index during the fishing period (SC=12.3) supported that the spotted seal’s trophic network was relatively more stable in this period. Thus, during the fishing period, it is crucial to pay more attention to the intensity of human fishing on mid-to-high trophic-level omnivorous fish resources to ensure the sustainability of these potential food resources for spotted seals. This comprehensive study achieved three key objectives: (a) utilizing eDNA to characterize fish diversity during distinct periods, (b) establishing trophic networks of spotted seals, and (c) discerning topological attributes and spatiotemporal patterns within the ecological network. Overall, this study can provide technical and data support for integrated ecological network management and propose suggestions for protecting and recovering spotted seals

Integrative analysis of the metabolome and transcriptome reveals the molecular mechanism of chlorogenic acid synthesis in peach fruit

As the most abundant phenolic acid in peach fruit, chlorogenic acid (CGA) is an important entry point for the development of natural dietary supplements and functional foods. However, the metabolic and regulation mechanisms underlying its accumulation in peach fruits remain unclear. In this study, we evaluated the composition and content of CGAs in mature fruits of 205 peach cultivars. In peach fruits, three forms of CGA (52.57%), neochlorogenic acid (NCGA, 47.13%), and cryptochlorogenic acid (CCGA, 0.30%) were identified. During the growth and development of peach fruits, the content of CGAs generally showed a trend of rising first and then decreasing. Notably, the contents of quinic acid, shikimic acid, p-coumaroyl quinic acid, and caffeoyl shikimic acid all showed similar dynamic patterns to that of CGA, which might provide the precursor material basis for the accumulation of CGA in the later stage. Moreover, CGA, lignin, and anthocyanins might have a certain correlation and these compounds work together to maintain a dynamic balance. By the comparative transcriptome analysis, 8 structural genes (Pp4CL, PpCYP98A, and PpHCT) and 15 regulatory genes (PpMYB, PpWRKY, PpERF, PpbHLH, and PpWD40) were initially screened as candidate genes of CGA biosynthesis. Our findings preliminarily analyzed the metabolic and molecular regulation mechanisms of CGA biosynthesis in peach fruit, which provided a theoretical basis for developing high-CGA content peaches in future breeding programs