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Zhicheng Feng

Publications and source records attributed to Zhicheng Feng.

At least 19 recordsLinked to original sources

A reduction theorem for the blockwise Navarro Alperin weight conjecture via H-triples

The Galois Alperin weight (GAW) conjecture has been reduced to the inductive GAW condition for simple groups. We proceed in two steps to refine this reduction. First, we propose the blockwise Galois Alperin weight (BGAW) conjecture and define its associated inductive BGAW condition. Second, assuming the inductive GAW (respectively, BGAW) condition for simple groups, we establish a stronger version of the GAW (respectively, BGAW) conjecture in terms of central (respectively, block) isomorphism of H-triples.

math.GR

A reduction theorem for the Navarro Alperin weight conjecture

The Alperin weight conjecture has been reduced to simple groups by Navarro and Tiep. In this paper, we investigate the Navarro Alperin weight conjecture, which includes Galois automorphisms and group automorphisms in comparison with the original version, and give a reduction to simple groups. As an application, we prove the conjecture for the finite groups with abelian Sylow 2-subgroups.

math.RT

Generic weights for finite reductive groups

This paper is motivated by the study of Alperin's weight conjecture in the representation theory of finite groups. We generalize the notion of $e$-cuspidality in the $e$-Harish-Chandra theory of finite reductive groups, and define generic weights in non-defining characteristic. We show that the generic weights play an analogous role as the weights defined by Alperin in the investigation of the inductive Alperin weight condition for simple groups of Lie type at most good primes. We hope that our approach will constitute a step towards an eventual proof of Alperin's weight conjecture.

math.RT

Image-Goal Navigation Using Refined Feature Guidance and Scene Graph Enhancement

In this paper, we introduce a novel image-goal navigation approach, named RFSG. Our focus lies in leveraging the fine-grained connections between goals, observations, and the environment within limited image data, all the while keeping the navigation architecture simple and lightweight. To this end, we propose the spatial-channel attention mechanism, enabling the network to learn the importance of multi-dimensional features to fuse the goal and observation features. In addition, a selfdistillation mechanism is incorporated to further enhance the feature representation capabilities. Given that the navigation task needs surrounding environmental information for more efficient navigation, we propose an image scene graph to establish feature associations at both the image and object levels, effectively encoding the surrounding scene information. Crossscene performance validation was conducted on the Gibson and HM3D datasets, and the proposed method achieved stateof-the-art results among mainstream methods, with a speed of up to 53.5 frames per second on an RTX3080. This contributes to the realization of end-to-end image-goal navigation in realworld scenarios. The implementation and model of our method have been released at: https://github.com/nubot-nudt/RFSG.

cs.RO

Alperin's bound and normal Sylow subgroups

Let $G$ be a finite group, $p$ a prime number and $P$ a Sylow $p$-subgroup of $G$. Recently, G. Malle, G. Navarro, and P. H. Tiep conjectured that the number of $p$-Brauer characters of $G$ coincides with that of the normaliser ${\bf N}_G(P)$ if and only if $P$ is normal in $G$. We reduce this conjecture to a question about finite simple groups and prove it for the prime $p = 2$. As a by-product of our work, we prove a reduction theorem for the blockwise version of Alperin's lower bound on $p$-Brauer characters and prove it for $2$-blocks of maximal defect. This improves recent results obtained by Malle, Navarro, and Tiep.

math.RT

Character triples and weights

We define a new relation between character triples and prove some Clifford theory properties for weights in terms of character triples.

math.RT

Radical subgroups of finite reductive groups

Radical subgroups play an important role in both finite group theory and representation theory. This is the first of a series of papers of ours in classifying radical $p$-subgroups of finite reductive groups and in verifying the inductive blockwise Alperin weight condition for them, contributing to the program of proving the Alperin weight conjecture by verifying its inductive condition for finite simple groups. In this paper we present a uniform method for classifying radical subgroups of finite reductive groups. As applications, we investigate the inductive blockwise Alperin weight condition for classical groups, as well as groups of type $F_4$.

math.RT

FedFTN: Personalized Federated Learning with Deep Feature Transformation Network for Multi-institutional Low-count PET Denoising

Low-count PET is an efficient way to reduce radiation exposure and acquisition time, but the reconstructed images often suffer from low signal-to-noise ratio (SNR), thus affecting diagnosis and other downstream tasks. Recent advances in deep learning have shown great potential in improving low-count PET image quality, but acquiring a large, centralized, and diverse dataset from multiple institutions for training a robust model is difficult due to privacy and security concerns of patient data. Moreover, low-count PET data at different institutions may have different data distribution, thus requiring personalized models. While previous federated learning (FL) algorithms enable multi-institution collaborative training without the need of aggregating local data, addressing the large domain shift in the application of multi-institutional low-count PET denoising remains a challenge and is still highly under-explored. In this work, we propose FedFTN, a personalized federated learning strategy that addresses these challenges. FedFTN uses a local deep feature transformation network (FTN) to modulate the feature outputs of a globally shared denoising network, enabling personalized low-count PET denoising for each institution. During the federated learning process, only the denoising network's weights are communicated and aggregated, while the FTN remains at the local institutions for feature transformation. We evaluated our method using a large-scale dataset of multi-institutional low-count PET imaging data from three medical centers located across three continents, and showed that FedFTN provides high-quality low-count PET images, outperforming previous baseline FL reconstruction methods across all low-count levels at all three institutions.

eess.IV

Anisotropic Interfacial Force Field for Interfaces of Water with Hexagonal Boron Nitride

This study introduces an anisotropic interfacial potential that provides an accurate description of the van der Waals (vdW) interactions between water and hexagonal boron nitride (h-BN) at their interface. Benchmarked against the strongly constrained and appropriately normed (SCAN) functional, the developed force field demonstrates remarkable consistency with reference data sets, including binding energy curves and sliding potential energy surfaces for various configurations involving a water molecule adsorbed atop the h-BN surface. These findings highlight the significant improvement achieved by the developed force field in empirically describing the anisotropic vdW interactions of the water/h-BN heterointerfaces. Utilizing this anisotropic force field, molecular dynamics simulations demonstrate that atomically-flat pristine h-BN exhibits inherent hydrophobicity. However, when atomic-step surface roughness is introduced, the wettability of h-BN undergoes a significant change, leading to a hydrophilic nature. The calculated water contact angle (WCA) for the roughened h-BN surface is approximately 64°, which closely aligns with experimental WCA values ranging from 52° to 67°. These findings indicate the high probability of the presence of atomic steps on the surfaces of experimental h-BN samples, emphasizing the need for further experimental verification. The development of the anisotropic interfacial force field for accurately describing interactions at the water/h-BN heterointerfaces is a significant advancement in accurately simulating the wettability of two-dimensional (2D) materials, offering a reliable tool for studying the dynamic and transport properties of water at these interfaces, with implications for materials science and nanotechnology.

physics.chem-ph

Morita equivalences and the inductive blockwise Alperin weight condition for type $\mathsf A$

As a step to establish the blockwise Alperin weight conjecture for all finite groups, we verify the inductive blockwise Alperin weight condition introduced by Navarro--Tiep and Späth for simple groups of Lie type $\mathsf A$, split or twisted. Key to the proofs is to reduce the verification of the inductive condition to the isolated (that means unipotent) blocks, using the Jordan decomposition for blocks of finite reductive groups given by Bonnafé, Dat and Rouquier.

math.RT

Unitriangular basic sets, Brauer characters and coprime actions

We show that the decomposition matrix of a given group $G$ is unitriangular, whenever $G$ has a normal subgroup $N$ such that the decomposition matrix of $N$ is unitriangular, $G/N$ is abelian and certain characters of $N$ extend to their stabilizer in $G$. Using the recent result by Brunat--Dudas--Taylor establishing that unipotent blocks have a unitriangular decomposition matrix, this allows us to prove that blocks of groups of quasi-simple groups of Lie type have a unitriangular decomposition matrix, whenever they are related via Bonnafé--Dat--Rouquier's equivalence to a unipotent block. This is then applied to study the action of automorphisms on Brauer characters of finite quasi-simple groups. We use it to verify the so-called {\it inductive Brauer--Glaubermann condition}, that aims to establish a Glauberman correspondence for Brauer characters, given a coprime action.

math.RT

Registry-Dependent Potential for interfaces of water with graphene

An anisotropic interlayer potential that can accurately describe the van der Waals interaction of the water-graphene interface is presented. The force field is benchmarked against the many-body dispersion-corrected density functional theory. The parameterization of ILP yields good agreement with the reference dataset of binding energy curves and sliding potential energy surfaces for various configurations of a water molecule deposited on monolayer graphene, indicating the developed force field enhancing significantly the accuracy in the empirical description of water-graphene interfacial interactions. The water contact angles of monolayer and multilayer graphene extracted from molecular dynamics simulations based on this force field are close to the experimental measurements and predict the hydrophilic nature of graphene. The theoretical approach proposed in this work can be easily extended to mimic the van der Waals interactions between water molecules and various two-dimensional layered materials for studying their wetting properties.

physics.chem-ph

Jordan decomposition for weights and the blockwise Alperin weight conjecture

The Alperin weight conjecture was reduced to simple groups by the work of Navarro, Tiep and Späth. To prove Alperin weight conjecture, it suffices to show that all finite non-abelian simple groups are BAW-good. We reduce the verification of the inductive conditons for groups of Lie type in non-defining characteristic to quasi-isolated blocks.

math.RT

On the inductive blockwise Alperin weight condition for type $\mathsf A$

In this paper we prove the blockwise Alperin weight conjecture for finite special linear and unitary groups, for finite groups with abelian Sylow $3$-subgroups, and verify the inductive blockwise Alperin weight condition for certain cases of groups of type $\mathsf A$. We also give a classification for the 2-blocks of special linear and unitary groups.

math.RT

Inductive blockwise Alperin weight condition for type B and odd primes

By the reduction theorems of Navarro--Tiep and Späth, a way to prove the Alperin weight conjecture and its blockwise version is to verify the co-called inductive Alperin weight condition and inductive blockwise Alperin weight condition for all finie simple groups respectively. In this paper, we establish the inductive blockwise Alperin weight condition for simple groups of type $\mathsf B$ and odd primes, using a criterion given by Brough and Späth recently.

math.RT

The inductive blockwise Alperin weight condition for type $\mathsf C$ and the prime $2$

We establish the inductive blockwise Alperin weight condition for simple groups of Lie type $\mathsf C$ and the bad prime $2$. As a main step, we derive a labelling set for the irreducible $2$-Brauer characters of the finite symplectic groups Sp$_{2n}(q)$ (with odd $q$), together with the action of automorphisms. As a further important ingredient we prove a Jordan decomposition for weights.

math.RT