arXiv subjects

Li Liang

Publications and source records attributed to Li Liang.

At least 55 records · Page 3Linked to original sources

arXiv2024

Representations of $\mathbb{N}^{\infty}$-type combinatorial categories

In this paper we consider representations of certain combinatorial categories, including the poset $\D$ of positive integers and division, the Young lattice $\mathscr{Y}$ of partitions of finite sets, the opposite category of the orbit category $\mathscr{Z}$ of $(\mathbb{Z}, +)$ with respect to nontrivial subgroups, and the category $\mathscr{CI}$ of finite cyclic groups and injective homomorphisms. We describe explicit upper bounds for homological degrees of their representations, and deduce that finitely presented representations (resp., representations presented in finite degrees) over a field form abelian subcategories of the representation categories. We also give an explicit description for the category of sheaves over the ringed atomic site $(\mathscr{Z}, \, J_{at}, \, \underline{\mathbb{C}})$, and show that irreducible sheaves are parameterized by primitive roots of the unit.

math.RT↗

arXiv2024

Stacking-dependent ferroicity of reversed bilayer: altermagnetism or ferroelectricity

Altermagnetism, as a new branch of magnetism independent of traditional ferromagnetism and antiferromagnetism, has attracted extensive attention recently. At present, researchers have proved several kinds of three-dimensional altermagnets, but research on two-dimensional (2D) altermagnets remains elusive. Here, we propose a method for designing altermagnetism in 2D lattices: bilayer reversed stacking. This method could enable altermagnetism-type spin splitting to occur intrinsically and the spin-splitting can be controlled by crystal chirality. We also demonstrate it through a real material of bilayer PtBr$_3$ with AB' stacking order. Additionally, the combination of stacking order and slidetronics offers new opportunities for electrical writing and magnetic reading of electronic devices. In the case of AC' stacking, interlayer sliding results in reversible spontaneous polarization. This unique combination of antiferromagnetism and sliding ferroelectricity leads to polarization-controlled spin-splitting, thus enabling magnetoelectric coupling, which can be detected by magneto-optical Kerr effect even without net magnetization. Our research highlights that reversed stacking provides a platform to explore rich physical properties of magnetism, ferroelectricity, and spin-splitting.

cond-mat.mtrl-sci↗

arXiv2024

Compatible weak factorization systems and model structures

In this paper the concept of compatible weak factorization systems in general categories is introduced as a counterpart of compatible complete cotorsion pairs in abelian categories. We describe a method to construct model structures on general categories via two compatible weak factorization systems satisfying certain conditions, and hence generalize a very useful result by Gillespie for abelian model structures. As particular examples, we show that weak factorizations systems associated to some classical model structures (for example, the Kan-Quillen model structure on $\mathsf{sSet}$) satisfy these conditions.

math.CT↗

arXiv2024

Multiple types of spin textures and robust valley physics in MP$_2$X$_6$

Both spin textures and multiple valleys in the momentum space have attracted great attentions due to their versatile applications in spintronics and valleytronics. It is highly desirable to realize multiple types of spin textures in a single material and further couple the spin textures to valley degree of freedom. Here, we study electronic properties of SnP$_{2}$Se$_{6}$ monolayer by first-principles calculations. The monolayer exhibits rare Weyl-type and Ising-type spin textures at different valleys, which can be conveniently expressed by electron and hole dopings, respectively. Besides valley-contrasting spin textures, Berry-curvature-driven anomalous Hall currents and optical selectivity are found to be valley dependent as well. These valley-related properties also have generalizations to SnP$_{2}$Se$_{6}$ few-layers and other MP$_{2}$X$_{6}$. Our findings open new avenue for exploring appealing interplay between spin textures and multiple valleys, and designing advanced device paradigms based on spin and valley degrees of freedom.

cond-mat.mtrl-sci↗

arXiv2024

Constructions of Waldhausen categories via Grothendieck opfibrations

Given a Grothendieck opfibration $p: \mathcal{T} \to \mathcal{B}$, we describe a method to construct a Waldhausen category structure on the total category $\mathcal{T}$ via combining Waldhausen category structures on the fibers $\mathcal{T}_A$ for $A \in \mathrm{Ob}(\mathcal{B})$ and the basis category $\mathcal{B}$. As an application, we show that if $\mathsf{E}$ is a Waldhausen category with small coproducts such that the class of cofibrations is the left part of a weak factorization system in $\mathsf{E}$, then the representation category $\mathsf{Rep}(Q, \mathsf{coE})$ of a left rooted quiver $Q$ is a Waldhausen category, where $\mathsf{coE}$ is the subcategory of $\mathsf{E}$ whose morphisms are cofibrations.

math.RT↗

arXiv2024

Flat model structures and Gorenstein objects in functor categories

We construct a flat model structure on the category $_{\mathcal{Q},R}{\mathsf{Mod}}$ of additive functors from a small preadditive category $\mathcal{Q}$ satisfying certain conditions to the module category $_{R}{\mathsf{Mod}}$ over an associative ring $R$, whose homotopy category is the $\mathcal{Q}$-shaped derived category introduced by Holm and Jorgensen. Moreover, we prove that for an arbitrary associative ring $R$, an object in $_{\mathcal{Q},R}{\mathsf{Mod}}$ is Gorenstein projective (resp., Gorenstein injective, Gorenstein flat, projective coresolving Gorenstein flat) if and only if so is its value on each object of $\mathcal{Q}$, and hence improve a result by Dell'Ambrogio, Stevenson and Šťov\'ıček.

math.RT↗

arXiv2024

One-way Valley-locked waveguide with large channel achieved by all-dielectric Photonic Crystals

Nonreciprocity, which denotes the asymmetric or even unidirectional transmission of light, constitutes the cornerstone of modern photonic circuits. In the realm of photonic devices, it has been widely utilized in isolators, circulators and so on. Recent topology in artificial materials, an unprecedented degree of freedom, has been proposed to solve the effect of impurities on nonreciprocal transmission. However, in view of the bulk-edge correspondence, the spatial width of the transmission channel with uniform field distribution is quite narrow and needs further exploration. In this paper, we proposed a one-way valley-locked waveguide with a large channel in an all-dielectric photonic crystal. Quite different from the topological edge modes, the unidirectional property of our waveguide comes from the bulk modes with valley-lock, which can fully utilize the whole dimension of the structure with an efficiency of 100%. Additionally, the electrical field is uniformly distributed across the entire channel, which opens a new avenue for low-loss nonreciprocity devices.

physics.app-ph↗

arXiv2024

Few-Shot Learning for Annotation-Efficient Nucleus Instance Segmentation

Nucleus instance segmentation from histopathology images suffers from the extremely laborious and expert-dependent annotation of nucleus instances. As a promising solution to this task, annotation-efficient deep learning paradigms have recently attracted much research interest, such as weakly-/semi-supervised learning, generative adversarial learning, etc. In this paper, we propose to formulate annotation-efficient nucleus instance segmentation from the perspective of few-shot learning (FSL). Our work was motivated by that, with the prosperity of computational pathology, an increasing number of fully-annotated datasets are publicly accessible, and we hope to leverage these external datasets to assist nucleus instance segmentation on the target dataset which only has very limited annotation. To achieve this goal, we adopt the meta-learning based FSL paradigm, which however has to be tailored in two substantial aspects before adapting to our task. First, since the novel classes may be inconsistent with those of the external dataset, we extend the basic definition of few-shot instance segmentation (FSIS) to generalized few-shot instance segmentation (GFSIS). Second, to cope with the intrinsic challenges of nucleus segmentation, including touching between adjacent cells, cellular heterogeneity, etc., we further introduce a structural guidance mechanism into the GFSIS network, finally leading to a unified Structurally-Guided Generalized Few-Shot Instance Segmentation (SGFSIS) framework. Extensive experiments on a couple of publicly accessible datasets demonstrate that, SGFSIS can outperform other annotation-efficient learning baselines, including semi-supervised learning, simple transfer learning, etc., with comparable performance to fully supervised learning with less than 5% annotations.

cs.CV↗

arXiv2023

One-sided Gorenstein rings

Distinctive characteristics of Iwanaga--Gorenstein rings are typically understood through their intrinsic symmetry. We show that several of those that pertain to the Gorenstein global dimensions carry over to the one-sided situation, even without the noetherian hypothesis. Our results yield new relations among homological invariants related to the Gorenstein property, not only Gorenstein global dimensions but also the suprema of projective/injective dimensions of injective/projective modules and finitistic dimensions.

math.RA↗

arXiv2023

Stable functors and cohomology theory in abelian categories

In this paper, we first introduce stable functors with respect to a preenveloping/precovering subcategory and investigate some of their properties. Using that we then introduce and study a relative complete cohomology theory in abelian categories. Some properties of the cohomology including vanishing are given. As applications, we give some characterizations of objects of finite homological dimensions including the flat dimension, cotorsion dimension, Gorenstein injective/flat dimension and projectively coresolved Gorenstein flat dimension.

math.RA↗

arXiv2023

Tunable Magnetism and Valleys in VSiZ$_3$ monolayers

Two-dimensional magnetism and valleys have recently emerged as two significant research areas, with intriguing properties and practical uses in advanced information technology. Considering the importance of these two areas and their couplings, controllable creations of both the magnetism and valley polarization are highly sought after. Based on first-principles calculations, we propose a new class of two-dimensional monolayers with a chemical formula of MAZ$_3$, which is viewed as a 2H-MZ$_2$ trilayer passivated by the A-Z bilayer on its one side. Taking VSiN$_3$ as an example, the MAZ$_3$ monolayers are found to exhibit tunable magnetism and valleys. For the intrinsic VSiN$_3$ monolayer, it is a non-magnetic semiconductor, with multiple degenerate valleys and trigonal warping near $K_\pm$ points in the band structure. Besides, the bands have spin splittings owing to the spin-orbit coupling. Under a moderate carrier doping, the monolayer becomes a Stoner ferromagnet, which enhances the spin splittings of the valence band and generates valley splittings. Moreover, the Berry curvature is valley contrasting, leading to distinct valley-spin related anomalous Hall currents as the doping concentration increases. Our work opens up new way to modulate the spin splittings and valley splittings via electric means, and provides opportunities for exploring advanced spintronic and valleytronic devices.

cond-mat.mtrl-sci↗

arXiv2023

Representations over diagrams of abelian categories I: Global structure and homological objects

Representations over diagrams of abelian categories unify quite a few notions appearing widely in literature such as representations of categories, presheaves of modules over categories, representations of species, etc. In this series of papers we study them systematically, characterizing special homological objects in representation category and constructing various structures (such as model structures and Wandhuasen category strcutres) on it. In the first paper we investigate the Grothendieck structure of the representation category, describe important functors and adjunction relations between them, and characterize special homological objects. These results lay a foundation for our future works.

math.RT↗

arXiv2023

Rethinking Mitosis Detection: Towards Diverse Data and Feature Representation

Mitosis detection is one of the fundamental tasks in computational pathology, which is extremely challenging due to the heterogeneity of mitotic cell. Most of the current studies solve the heterogeneity in the technical aspect by increasing the model complexity. However, lacking consideration of the biological knowledge and the complex model design may lead to the overfitting problem while limited the generalizability of the detection model. In this paper, we systematically study the morphological appearances in different mitotic phases as well as the ambiguous non-mitotic cells and identify that balancing the data and feature diversity can achieve better generalizability. Based on this observation, we propose a novel generalizable framework (MitDet) for mitosis detection. The data diversity is considered by the proposed diversity-guided sample balancing (DGSB). And the feature diversity is preserved by inter- and intra- class feature diversity-preserved module (InCDP). Stain enhancement (SE) module is introduced to enhance the domain-relevant diversity of both data and features simultaneously. Extensive experiments have demonstrated that our proposed model outperforms all the SOTA approaches in several popular mitosis detection datasets in both internal and external test sets using minimal annotation efforts with point annotations only. Comprehensive ablation studies have also proven the effectiveness of the rethinking of data and feature diversity balancing. By analyzing the results quantitatively and qualitatively, we believe that our proposed model not only achieves SOTA performance but also might inspire the future studies in new perspectives. Source code is at https://github.com/Onehour0108/MitDet.

cs.CV↗

arXiv2023

Magnetically and electrically controllable valley splittings in MXene monolayers

The modulation of the valley structure in two-dimensional valley materials is vital in the field of valleytronics. The multiferroicity provides possibility for multiple modulations of the valley, including the magnetic and electric means. Based on the first-principle calculations, we study the valley properties and associated manipulations of multiferroic Co$_2$CF$_2$ monolayers with different stacking patterns. Our calculations show that the Co$_2$CF$_2$ monolayer in the H$^{\prime}$ phase is a ferrovalley material, with sizable valley splittings. By rotating the magnetization direction, the valley splittings can be tuned for both the magnitude and sign. The electric field, driving the reversal of the electric polarization, can also change the magnitude of the valley splittings. Besides, a metastable T$^{\prime}$ phase exhibits valley splittings as well, of which the magnitude and sign can be simultaneously controlled by applied magnetic and electric fields. These findings offer a practical way for realizing highly tunable valleys by multiferroic couplings.

cond-mat.mtrl-sci↗

arXiv2022

Probing complex stacking in a layered material via electron-nuclear quadrupolar coupling

For layered materials, the interlayer stacking is a critical degree of freedom tuning electronic properties, while its microscopic characterization faces great challenges. The transition-metal dichalcogenide 1T-TaS$_2$ represents a novel example, in which the stacking pattern is not only enriched by the spontaneous occurrence of the intralayer charge density wave, but also recognized as a key to understand the nature of the low-temperature insulating phase. We exploit the $^{33}\rm{S}$ nuclei in a 1T-TaS$_2$ single crystal as sensitive probes of the local stacking pattern via quadrupolar coupling to the electron density distribution nearby, by combining nuclear magnetic resonance (NMR) measurements with the state-of-the-art first-principles electric-field gradient calculations. The applicability of our proposal is analyzed through temperature, magnetic-field, and angle dependent NMR spectra. Systematic simulations of a single 1T-TaS$_2$ layer, bilayers with different stacking patterns, and typical stacking orders in three-dimensional (3D) structures unravel distinct NMR characteristics. Particularly, one 3D structure achieves a quantitative agreement with the experimental spectrum, which clearly rationalizes the coexistence of two types of interfacial environments. Our method may find general applications in the studies of layered materials.

cond-mat.mtrl-sci↗

arXiv2022

Hybrid topological photonic crystals

Photonic topological phases offering unprecedented manipulation of electromagnetic waves have attracted much research interest which, however, have been mostly restricted to a single band gap. Here, we report on the experimental discovery of hybrid topological photonic crystals which host simultaneously quantum anomalous Hall and valley Hall phases in different photonic band gaps. The underlying hybrid topological phase manifests itself in the edge responses as the coexistence of the chiral edge states and valley Hall edge states in different frequency ranges. We experimentally verify such an emergent phenomenon and show that such a feature enables novel multiplexing of photon transport in the edge channels. Our study reveals a situation with coexisting topology of distinct nature in a single photonic system that may enable frequency-dependent filtering and manipulation of topological edge photons.

cond-mat.mes-hall↗

arXiv2022

Valley and spin splittings in a valley-layer-locked monolayer via atomic adsorption

To date, a number of valley materials have been discovered with the spin-valley or valley-layer couplings. It is highly desirable to realize the interplay of more electronic degrees of freedom in a valley material. Based on the first-principles calculations, we demonstrate the valley and spin degeneracy liftings in the band structure of a TiSiCO monolayer, with the help of the selective expression of the layer pseudospin via atomic adsorption. The introduction of the transition-metal adatoms provides an effective electric field and magnetic proximity effect, giving rise to the valley and spin splittings. These splittings can be further tuned by applying an external electric field. According to the modified band structure, various interlayer excitons with different combinations of spins and electric dipoles are selectively created, under the optical field of appropriate frequencies. The tunable spin and valley splittings in atom adsorbed TiSiCO monolayer offer opportunities for exploring the interactions between spin, valley and layer pseudospin, and designing advanced optoelectronic devices.

cond-mat.mtrl-sci↗

arXiv2022

Tunable valley and spin splittings in $\rm VSi_2N_4$ bilayer

The control and manipulation of the valley and spin degrees of freedom have received great interests in fundamental studies and advanced information technologies. Compared with magnetic means, it is highly desirable to realize more energy-efficient electric control of valley and spin. Using the first-principles calculations, we demonstrate tunable valley and spin degeneracy splittings in $\rm VSi_2N_4$ bilayers, with the aid of the layered structure and associated electric control. Depending on different interlayer magnetic couplings and stacking orders, the $\rm VSi_2N_4$ bilayers exhibit a variety of combinations of valley and spin degeneracies. Under the action of a vertical electric field, the degeneracy splittings become highly tunable for both the sign and magnitude. As a result, a series of anomalous Hall currents can be selectively realized with varied indices of valley and spin. These intriguing features offer a practical way for designing energy-efficient devices based on the couplings between multiple electronic degrees of freedom.

cond-mat.mtrl-sci↗