Scalar Invariants of surfaces in conformal 3-sphere via Minkowski spacetime

For a surface in 3-sphere, by identifying the conformal round 3-sphere as the projectivized positive light cone in Minkowski 5-spacetime, we use the conformal Gauss map and the conformal transform to construct the associate homogeneous 4-surface in Minkowski 5-spacetime. We then derive the local fundamental theorem for a surface in conformal round 3-sphere from that of the associate 4-surface in Minkowski 5-spacetime. More importantly, following the idea of Fefferman and Graham, we construct local scalar invariants for a surface in conformal round 3-sphere. One distinct feature of our construction is to link the classic work of Blaschke to the works of Bryan and Fefferman-Graham.Comment: 37 page

3DSAM-adapter: Holistic Adaptation of SAM from 2D to 3D for Promptable Medical Image Segmentation

Despite that the segment anything model (SAM) achieved impressive results on general-purpose semantic segmentation with strong generalization ability on daily images, its demonstrated performance on medical image segmentation is less precise and not stable, especially when dealing with tumor segmentation tasks that involve objects of small sizes, irregular shapes, and low contrast. Notably, the original SAM architecture is designed for 2D natural images, therefore would not be able to extract the 3D spatial information from volumetric medical data effectively. In this paper, we propose a novel adaptation method for transferring SAM from 2D to 3D for promptable medical image segmentation. Through a holistically designed scheme for architecture modification, we transfer the SAM to support volumetric inputs while retaining the majority of its pre-trained parameters for reuse. The fine-tuning process is conducted in a parameter-efficient manner, wherein most of the pre-trained parameters remain frozen, and only a few lightweight spatial adapters are introduced and tuned. Regardless of the domain gap between natural and medical data and the disparity in the spatial arrangement between 2D and 3D, the transformer trained on natural images can effectively capture the spatial patterns present in volumetric medical images with only lightweight adaptations. We conduct experiments on four open-source tumor segmentation datasets, and with a single click prompt, our model can outperform domain state-of-the-art medical image segmentation models on 3 out of 4 tasks, specifically by 8.25%, 29.87%, and 10.11% for kidney tumor, pancreas tumor, colon cancer segmentation, and achieve similar performance for liver tumor segmentation. We also compare our adaptation method with existing popular adapters, and observed significant performance improvement on most datasets.Comment: 14 pages, 6 figures, 5 table

Roadmap on commercialization of metal halide perovskite photovoltaics

Perovskite solar cells (PSCs) represent one of the most promising emerging photovoltaic technologies due to their high power conversion efficiency. However, despite the huge progress made not only in terms of the efficiency achieved, but also fundamental understanding of the relevant physics of the devices and issues which affect their efficiency and stability, there are still unresolved problems and obstacles on the path toward commercialization of this promising technology. In this roadmap, we aim to provide a concise and up to date summary of outstanding issues and challenges, and the progress made toward addressing these issues. While the format of this article is not meant to be a comprehensive review of the topic, it provides a collection of the viewpoints of the experts in the field, which covers a broad range of topics related to PSC commercialization, including those relevant for manufacturing (scaling up, different types of devices), operation and stability (various factors), and environmental issues (in particular the use of lead). We hope that the article will provide a useful resource for researchers in the field and that it will facilitate discussions and move forward toward addressing the outstanding challenges in this fast-developing field

Scalar conformal invariants of hypersurfaces

For a hypersurface in a conformal manifold, by following the idea of Fefferman and Graham's work, we use the conformal Gauss map and the conformal transform to construct the associate hypersurface in the ambient space. By evaluations of scalar Riemannian invariants of associate hypersurface, we find out a way to construct and collect scalar conformal invariants of the given hypersurface. This method provides chances for searching higher order partial differential equations which are similar like the Willmore equation

Scalar conformal invariants of hypersurfaces

For a hypersurface in a conformal manifold, by following the idea of Fefferman and Graham's work, we use the conformal Gauss map and the conformal transform to construct the associate hypersurface in the ambient space. By evaluations of scalar Riemannian invariants of associate hypersurface, we find out a way to construct and collect scalar conformal invariants of the given hypersurface. This method provides chances for searching higher order partial differential equations which are similar like the Willmore equation

Scalar invariants of surfaces in the conformal 3-sphere via Minkowski spacetime

For a surface in 3-sphere, by identifying the conformal round 3-sphere as the projectivized positive light cone in Minkowski 5-spacetime, we use the conformal Gauss map and the conformal transform to construct the associate homogeneous 4-surface in Minkowski 5-spacetime. We then derive the local fundamental theorem for a surface in conformal round 3-sphere from that of the associate 4-surface in Minkowski 5-spacetime. More importantly, following the idea of Fefferman and Graham, we construct local scalar invariants for a surface in conformal round 3-sphere. One distinct feature of our construction is to link the classic work of Blaschke to the works of Bryan and Fefferman-Graham

Geodesics on the Moduli Space of Oriented Circles in S-3

NNSFC [10771005]; Fundamental Research Funds for the Central Universities [2010121007]Let Q(3) be the moduli space of oriented circles in the three dimensional unit sphere S-3. Given a natural complex structure such space becomes a three dimensional complex manifold, with a Mobius invariant Hermitian metric h of type (2, 1). Up to Mobius transformations, all geodesics with respect to the Lorentz metric g = Re(h) on Q(3) are determined to form a one-parameter family of circles on a helicoid in a space form R-3,H-3 or S-3, resp. We show also that any two oriented circles in S-3 are connected by countably infinitely many geodesics in Q(3)

Fabrication of TiO2 nanoparticles/nanorod composite arrays via a two-step method for efficient dye-sensitized solar cells

TiO2 nanoparticles/nanorod composite arrays were prepared on the F-doped tin oxide (FTO) substrate through a two-step method of hydrothermal and d.c. magnetron sputtering. The microstructure and optical properties of the samples were characterized respectively by means of X-ray diffraction (XRD), field-emission scanning electron microscopy (FESEM) and UV–vis spectrometer. The results showed that the TiO2 composite nanorod arrays possess the nature of high surface area for more dye molecule absorption and the strong light scattering effects. The dye sensitized solar cells (DSSCs) based on TiO2 composite nanorod arrays exhibited a 80% improvement in the overall energy conversion efficiency compared with the pure TiO2 nanorod arrays photoanode