59 research outputs found
Relationship between Nichols braided Lie algebras and Nichols algebras
We establish the relationship among Nichols algebras, Nichols braided Lie
algebras and Nichols Lie algebras. We prove two results: (i) Nichols algebra
is finite-dimensional if and only if Nichols braided Lie
algebra is finite-dimensional if there does not exist any
-infinity element in ; (ii) Nichols Lie algebra is infinite dimensional if is infinite. We give the sufficient
conditions for Nichols braided Lie algebra to be a homomorphic
image of a braided Lie algebra generated by with defining relations.Comment: LeTex 18 pages, need JOLT-macros to compile. To appear in Journal of
Lie Theor
On Nichols (braided) Lie algebras
We prove {\rm (i)} Nichols algebra of vector space is
finite-dimensional if and only if Nichols braided Lie algebra
is finite-dimensional; {\rm (ii)} If the rank of connected is and
is an arithmetic root system, then and {\rm (iii)} if is an arithmetic
root system and there does not exist any -infinity element with for any , then if and
only if there exists , which is twisting equivalent to , such that Furthermore we give an estimation of
dimensions of Nichols Lie algebras and two examples of Lie algebras which do
not have maximal solvable ideals.Comment: 29 Pages; Substantially revised version; To appear in International
Journal of Mathematic
Structures of Nichols (braided) Lie algebras of diagonal type
Let be a braided vector space of diagonal type. Let ,
and be the Nichols algebra, Nichols Lie
algebra and Nichols braided Lie algebra over , respectively. We show that a
monomial belongs to if and only if that this monomial is
connected. We obtain the basis for of arithmetic root systems
and the dimension for of finite Cartan type. We give the
sufficient and necessary conditions for and . We obtain an explicit basis of
over quantum linear space with .Comment: 23 pages. Version to appear in Journal of Lie Theor
Validation of Reference Genes for RT-qPCR Studies of Gene Expression in Preharvest and Postharvest Longan Fruits under Different Experimental Conditions
Reverse transcription quantitative PCR (RT-qPCR), a sensitive technique for quantifying gene expression, relies on stable reference gene(s) for data normalization. Although a few studies have been conducted on reference gene validation in fruit trees, none have been done on preharvest and postharvest longan fruits. In this study, 12 candidate reference genes, namely, CYP, RPL, GAPDH, TUA, TUB, Fe-SOD, Mn-SOD, Cu/Zn-SOD, 18SrRNA, Actin, Histone H3 and EF-1a, were selected. Expression stability of these genes in 150 longan samples was evaluated and analyzed using geNorm and NormFinder algorithms. Preharvest samples consisted of seven experimental sets, including different developmental stages, organs, hormone stimuli (NAA, 2,4-D and ethephon) and abiotic stresses (bagging and girdling with defoliation). Postharvest samples consisted of different temperature treatments (4 and 22 °C) and varieties. Our findings indicate that appropriate reference gene(s) should be picked for each experimental condition. Our data further showed that the commonly used reference gene Actin does not exhibit stable expression across experimental conditions in longan. Expression levels of the DlACO gene, which is a key gene involved in regulating fruit abscission under girdling with defoliation treatment, was evaluated to validate our findings. In conclusion, our data provide a useful framework for choice of suitable reference genes across different experimental conditions for RT-qPCR analysis of preharvest and postharvest longan fruits
3D Instances as 1D Kernels
We introduce a 3D instance representation, termed instance kernels, where
instances are represented by one-dimensional vectors that encode the semantic,
positional, and shape information of 3D instances. We show that instance
kernels enable easy mask inference by simply scanning kernels over the entire
scenes, avoiding the heavy reliance on proposals or heuristic clustering
algorithms in standard 3D instance segmentation pipelines. The idea of instance
kernel is inspired by recent success of dynamic convolutions in 2D/3D instance
segmentation. However, we find it non-trivial to represent 3D instances due to
the disordered and unstructured nature of point cloud data, e.g., poor instance
localization can significantly degrade instance representation. To remedy this,
we construct a novel 3D instance encoding paradigm. First, potential instance
centroids are localized as candidates. Then, a candidate merging scheme is
devised to simultaneously aggregate duplicated candidates and collect context
around the merged centroids to form the instance kernels. Once instance kernels
are available, instance masks can be reconstructed via dynamic convolutions
whose weights are conditioned on instance kernels. The whole pipeline is
instantiated with a dynamic kernel network (DKNet). Results show that DKNet
outperforms the state of the arts on both ScanNetV2 and S3DIS datasets with
better instance localization. Code is available:
https://github.com/W1zheng/DKNet.Comment: Appearing in ECCV, 202
DoF-NeRF: Depth-of-Field Meets Neural Radiance Fields
Neural Radiance Field (NeRF) and its variants have exhibited great success on
representing 3D scenes and synthesizing photo-realistic novel views. However,
they are generally based on the pinhole camera model and assume all-in-focus
inputs. This limits their applicability as images captured from the real world
often have finite depth-of-field (DoF). To mitigate this issue, we introduce
DoF-NeRF, a novel neural rendering approach that can deal with shallow DoF
inputs and can simulate DoF effect. In particular, it extends NeRF to simulate
the aperture of lens following the principles of geometric optics. Such a
physical guarantee allows DoF-NeRF to operate views with different focus
configurations. Benefiting from explicit aperture modeling, DoF-NeRF also
enables direct manipulation of DoF effect by adjusting virtual aperture and
focus parameters. It is plug-and-play and can be inserted into NeRF-based
frameworks. Experiments on synthetic and real-world datasets show that,
DoF-NeRF not only performs comparably with NeRF in the all-in-focus setting,
but also can synthesize all-in-focus novel views conditioned on shallow DoF
inputs. An interesting application of DoF-NeRF to DoF rendering is also
demonstrated. The source code will be made available at
https://github.com/zijinwuzijin/DoF-NeRF.Comment: Accepted by ACMMM 202
Architecture engineering of carbonaceous anodes for high‐rate potassium‐ion batteries
The limited lithium resource in earth's crust has stimulated the pursuit of alternative energy storage technologies to lithium‐ion battery. Potassium‐ion batteries (KIBs) are regarded as a kind of promising candidate for large‐scale energy storage owing to the high abundance and low cost of potassium resources. Nevertheless, further development and wide application of KIBs are still challenged by several obstacles, one of which is their fast capacity deterioration at high rates. A considerable amount of effort has recently been devoted to address this problem by developing advanced carbonaceous anode materials with diverse structures and morphologies. This review presents and highlights how the architecture engineering of carbonaceous anode materials gives rise to high‐rate performances for KIBs, and also the beneficial conceptions are consciously extracted from the recent progress. Particularly, basic insights into the recent engineering strategies, structural innovation, and the related advances of carbonaceous anodes for high‐rate KIBs are under specific concerns. Based on the achievements attained so far, a perspective on the foregoing, and proposed possible directions, and avenues for designing high‐rate anodes, are presented finally
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