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Li Liang

Publications and source records attributed to Li Liang.

At least 73 records · Page 4Linked to original sources

RestainNet: a self-supervised digital re-stainer for stain normalization

Color inconsistency is an inevitable challenge in computational pathology, which generally happens because of stain intensity variations or sections scanned by different scanners. It harms the pathological image analysis methods, especially the learning-based models. A series of approaches have been proposed for stain normalization. However, most of them are lack flexibility in practice. In this paper, we formulated stain normalization as a digital re-staining process and proposed a self-supervised learning model, which is called RestainNet. Our network is regarded as a digital restainer which learns how to re-stain an unstained (grayscale) image. Two digital stains, Hematoxylin (H) and Eosin (E) were extracted from the original image by Beer-Lambert's Law. We proposed a staining loss to maintain the correctness of stain intensity during the restaining process. Thanks to the self-supervised nature, paired training samples are no longer necessary, which demonstrates great flexibility in practical usage. Our RestainNet outperforms existing approaches and achieves state-of-the-art performance with regard to color correctness and structure preservation. We further conducted experiments on the segmentation and classification tasks and the proposed RestainNet achieved outstanding performance compared with SOTA methods. The self-supervised design allows the network to learn any staining style with no extra effort.

eess.IV↗

A study of Tate homology via the approximation theory with applications to the depth formula

In this paper we are concerned with absolute, relative and Tate Tor modules. In the first part of the paper we generalize a result of Avramov and Martsinkovsky by using the Auslander-Buchweitz approximation theory, and obtain a new exact sequence connecting absolute Tor modules with relative and Tate Tor modules. In the second part of the paper we consider a depth equality, called the depth formula, which has been initially introduced by Auslander and developed further by Huneke and Wiegand. As an application of our main result, we generalize a result of Yassemi and give a new sufficient condition implying the depth formula to hold for modules of finite Gorenstein and finite injective dimension.

math.AC↗

PDBL: Improving Histopathological Tissue Classification with Plug-and-Play Pyramidal Deep-Broad Learning

Histopathological tissue classification is a fundamental task in pathomics cancer research. Precisely differentiating different tissue types is a benefit for the downstream researches, like cancer diagnosis, prognosis and etc. Existing works mostly leverage the popular classification backbones in computer vision to achieve histopathological tissue classification. In this paper, we proposed a super lightweight plug-and-play module, named Pyramidal Deep-Broad Learning (PDBL), for any well-trained classification backbone to further improve the classification performance without a re-training burden. We mimic how pathologists observe pathology slides in different magnifications and construct an image pyramid for the input image in order to obtain the pyramidal contextual information. For each level in the pyramid, we extract the multi-scale deep-broad features by our proposed Deep-Broad block (DB-block). We equipped PDBL in three popular classification backbones, ShuffLeNetV2, EfficientNetb0, and ResNet50 to evaluate the effectiveness and efficiency of our proposed module on two datasets (Kather Multiclass Dataset and the LC25000 Dataset). Experimental results demonstrate the proposed PDBL can steadily improve the tissue-level classification performance for any CNN backbones, especially for the lightweight models when given a small among of training samples (less than 10%), which greatly saves the computational time and annotation efforts.

eess.IV↗

Completeness of the induced cotorsion pairs in functor categories

This paper focuses on a question raised by Holm and Jørgensen, who asked if the induced cotorsion pairs $(Φ({\sf X}),Φ({\sf X})^{\perp})$ and $(^{\perp}Ψ({\sf Y}),Ψ({\sf Y}))$ in $\mathrm{Rep}(Q,{\sf{A}})$ -- the category of all $\sf{A}$-valued representations of a quiver $Q$ -- are complete whenever $(\sf X,\sf Y)$ is a complete cotorsion pair in an abelian category $\sf{A}$ satisfying some mild conditions. Recently, Odabaşı gave an affirmative answer if the quiver $Q$ is rooted and the cotorsion pair $(\sf X,\sf Y)$ is further hereditary. In this paper, we improve Odabaşı's work by removing the hereditary assumption on the cotorsion pair. As an application, we show under certain mild conditions that if a subcategory $\sf L$, which is not necessarily closed under direct summands, of $\sf A$ is special precovering (resp., preenveloping), then $Φ(\sf L)$ (resp., $Ψ(\sf L)$) is special precovering (resp., preenveloping) in $\mathrm{Rep}(Q,{\sf{A}})$.

math.RT↗

Higher-order topological phases in tunable $C_3$-symmetric photonic crystals

We demonstrate that multiple higher-order topological transitions can be triggered via the continuous change of the geometry in kagome photonic crystals composed of three dielectric rods. By tuning a single geometry parameter, the photonic corner and edge states emerge or disappear with the higher-order topological transitions. Two distinct higher-order topological insulator phases and a normal insulator phase are revealed. Their topological indices are obtained from symmetry representations. A photonic analog of fractional corner charge is introduced to distinguish the two higher-order topological insulator phases. Our predictions can be readily realized and verified in configurable dielectric photonic crystals.

physics.optics↗

Extending Implicit Discourse Relation Recognition to the PDTB-3

The PDTB-3 contains many more Implicit discourse relations than the previous PDTB-2. This is in part because implicit relations have now been annotated within sentences as well as between them. In addition, some now co-occur with explicit discourse relations, instead of standing on their own. Here we show that while this can complicate the problem of identifying the location of implicit discourse relations, it can in turn simplify the problem of identifying their senses. We present data to support this claim, as well as methods that can serve as a non-trivial baseline for future state-of-the-art recognizers for implicit discourse relations.

cs.CL↗

A refinement of Gorenstein flat dimension via the flat--cotorsion theory

We introduce a refinement of the Gorenstein flat dimension for complexes over an associative ring--the Gorenstein flat-cotorsion dimension--and prove that it, unlike the Gorenstein flat dimension, behaves as one expects of a homological dimension without extra assumptions on the ring. Crucially, we show that it coincides with the Gorenstein flat dimension for complexes where the latter is finite, and for complexes over right coherent rings--the setting where the Gorenstein flat dimension is known to behave as expected.

math.RA↗

Homology theories and Gorenstein dimensions for complexes

In this paper, we first study the Gorenstein projective/flat dimension of complexes of modules. The relation between the Gorenstein projective/flat dimension for complexes and that for modules are investigated. Then we study Tate, stable and unbounded homology for complexes of modules. In the case of module arguments, we get some results that improve the known results.

math.RA↗

Gorenstein flat representations of left rooted quivers

We study Gorenstein flat objects in the category ${\sf Rep}(Q,R)$ of representations of a left rooted quiver $Q$ with values in ${\sf Mod}(R)$, the category of all left $R$-modules, where $R$ is an arbitrary associative ring. We show that a representation $X$ in ${\sf Rep}(Q,R)$ is Gorenstein flat if and only if for each vertex $i$ the canonical homomorphism $φ_i^X: \oplus_{a:j\to i}X(j)\to X(i)$ is injective, and the left $R$-modules $X(i)$ and ${\rm Coker}φ_i^X$ are Gorenstein flat. As an application of this result, we show that there is a hereditary abelian model structure on ${\sf Rep}(Q,R)$ whose cofibrant objects are precisely the Gorenstein flat representations, fibrant objects are precisely the cotorsion representations, and trivial objects are precisely the representations with values in the right orthogonal category of all projectively coresolved Gorenstein flat left $R$-modules.

math.RA↗

Relative global dimensions and stable homotopy categories

In this paper we study the finiteness of global Gorenstein AC-homological dimensions for rings, and answer the questions posed by Becerril, Mendoza, Pérez and Santiago. As an application, we show that any left (or right) coherent and left Gorenstein ring has a projective and injective stable homotopy category, which improves the known result by Beligiannis.

math.RA↗

The role of interstitial hydrogen in SrCoO$_{2.5}$ antiferromagnetic insulator

Hydrogen exhibits qualitatively different charge states depending on the host material, as nicely explained by the state-of-the-art impurity-state calculation. Motivated by a recent experiment [Nature 546, 124 (2017)], we show that the complex oxide SrCoO$_{2.5}$ represents an interesting example, in which the interstitial H appears as a deep-level center according to the commonly-used transition level calculation, but no bound electron can be found around the impurity. Via a combination of charge difference analysis, density of states projection and constraint magnetization calculation, it turns out that the H-doped electron is spontaneously trapped by a nonunique Co ion and is fully spin-polarized by the onsite Hund's rule coupling. Consequently, the doped system remains insulating, whereas the antiferromagnetic exchange is slightly perturbed locally.

cond-mat.mtrl-sci↗

Vanishing of stable homology with respect to a semidualizing module

We investigate stable homology of modules over a commutative noetherian ring $R$ with respect to a semidualzing module $C$, and give some vanishing results that improve/extend the known results. As a consequence, we show that the balance of the theory forces $C$ to be trivial and $R$ to be Gorenstein.

math.AC↗

Vanishing of relative homology and depth of tensor products

For finitely generated modules $M$ and $N$ over a Gorenstein local ring $R$, one has $depth M + depth N= depth(M\otimes N) +depth R$, i.e., the depth formula holds, if $M$ and $N$ are Tor-independent and Tate homology $\hat{Tor}_{i}^{R}(M,N)$ vanishes for all $i\in\mathbb{Z}$. We establish the same conclusion under weaker hypotheses: if $M$ and $N$ are $\mathcal{G}$-relative Tor-independent, then the vanishing of $\hat{Tor}_{i}^{R}(M,N)$ for all $i\le 0$ is enough for the depth formula to hold. We also analyze the depth of tensor products of modules and obtain a necessary condition for the depth formula in terms of $\mathcal{G}$-relative homology.

math.AC↗

Gorenstein dimensions of unbounded complexes and faithfully flat change of base (With an appendix by Driss Bennis)

For a commutative ring R and a faithfully flat R-algebra S we prove, under mild extra assumptions, that an R-module M is Gorenstein flat if and only if the left S-module S\otimes M is Gorenstein flat, and that an R-module N is Gorenstein injective if and only if it is cotorsion and the left S-module Hom(S,N) is Gorenstein injective. We apply these results to the study of Gorenstein homological dimensions of unbounded complexes. In particular, we prove two theorems on stability of these dimensions under faithfully flat (co-)base change.

math.AC↗

Parameter estimation for linear control valve with hysteresis

The problem of estimating parameters of linear control valve with hysteresis is considered. The hysteretic behavior of control valve is formulated as a switched linear model. An indicator vector, which shows the switching epochs of switched linear model, is explored by subspace decomposition on measurements. With the help of indicator vector, the noisy measurements are classified into separate groups, each corresponding to up-stroke and down-stroke of control valve respectively. The least squares technique is adopted to estimate the parameters of control valve. It is shown that the proposed technique exactly estimates the parameters and switching epochs in absence of noise and exhibits dominant advantage in noisy case.

eess.SY↗

Stable homology over associative rings

We analyze stable homology over associative rings and obtain results over Artin algebras and commutative noetherian rings. Our study develops similarly for these classes; for simplicity we only discuss the latter here. Stable homology is a broad generalization of Tate homology. Vanishing of stable homology detects classes of rings---among them Gorenstein rings, the original domain of Tate homology. Closely related to gorensteinness of rings is Auslander's G-dimension for modules. We show that vanishing of stable homology detects modules of finite G-dimension. This is the first characterization of such modules in terms of vanishing of (co)homology alone. Stable homology, like absolute homology, Tor, is a theory in two variables. It can be computed from a flat resolution of one module together with an injective resolution of the other. This betrays that stable homology is not balanced in the way Tor is balanced. In fact, we prove that a ring is Gorenstein if and only if stable homology is balanced.

math.RA↗

Complete Homology over associative rings

We compare two generalizations of Tate homology: stable homology and the J-completion of Tor, also known as complete homology. For finitely generated modules, we show that the two theories agree over Artin algebras and over commutative noetherian rings that are Gorenstein, or local and complete.

math.RA↗