DG Modules Research Articles

Research on visual features and identification of coal and gangue in simulated underground mine environments

ABSTRACT In underground mine environments, factors such as low light intensity, diffusion of dust particles, and coal slurry coverage interfere with coal gangue identification. To further realize coal-gangue sorting underground, we analyzed the coal-gangue visual characteristics coupled with the above factors. The analysis reveals that both smoke environments and coal slurry coverage tend to make the coal-gangue visual features more consistent. There are still differences in coal-gangue visual features under smoke environments, while coal slurry coverage leads to gangue exhibiting coal-related feature information. To improve the detection capability of coal gangue in underground environments, this study adopts a coal gangue recognition method based on the DG module and YOLOX-PSB network: Utilize the DG module to achieve dehazing and then use the YOLOX-PSB model for object detection. The proposed method was validated through ablation experiments, and the results showed that the detection accuracy reached 99.6%, with an FPS of 98. The proposed method enables real-time detection and exhibits the best robustness in complex environments, realizing reliable and efficient performance.

Insulator Defect Detection Based on ML-YOLOv5 Algorithm.

To address the challenges of balancing accuracy and speed, as well as the parameters and FLOPs in current insulator defect detection, we propose an enhanced insulator defect detection algorithm, ML-YOLOv5, based on the YOLOv5 network. The backbone module incorporates depthwise separable convolution, and the feature fusion C3 module is replaced with the improved C2f_DG module. Furthermore, we enhance the feature pyramid network (MFPN) and employ knowledge distillation using YOLOv5m as the teacher model. Experimental results demonstrate that this approach achieved a 46.9% reduction in parameter count and a 43.0% reduction in FLOPs, while maintaining an FPS of 63.6. It exhibited good accuracy and detection speed on both the CPLID and IDID datasets, making it suitable for real-time inspection of high-altitude insulator defects.

GSD-YOLOX: Lightweight and more accurate object detection models

We present an enhanced YOLOX model for vehicle detection, addressing issues of slow detection speed, high parameter counts, and complex computations. Our model significantly improves inference speed while maintaining high detection accuracy. We introduce two lightweight modules, DG and DS, to reduce model size and enhance detection speed. The DG module eliminates redundant features during feature extraction, and the DS module optimizes the performance of DG, enhancing feature extraction efficiency. We utilize the CIoU loss function for accurate bounding box regression. Additionally, we introduce the Chinese Chongqing Vehicle Detection Benchmark (CCVTDB) dataset to address dataset limitations. Our lightweight model achieves an impressive 83.36% detection accuracy on CCVTDB at 65 FPS with 4.4 million parameters. Compared to the original model, our approach improves detection speed by 30% and reduces model size by 51%, while maintaining substantial detection performance.

A coal and gangue detection method for low light and dusty environments

In practical underground production environments, low light intensity and the presence of dust can disrupt the recognition of coal and gangue. To advance the separation of coal and gangue in underground settings, this paper introduces a coal–gangue recognition approach (DG Module (DGM) + YOLOX-PSB) tailored for conditions of low light intensity and dust. To address the impact of dusty conditions, a preprocessing module (DGM) is proposed. This module employs a dark channel prior dehazing algorithm to mitigate the impact of fog on coal–gangue images. Subsequent steps include white balancing, bilateral filtering, and gamma correction to alleviate noise and distortion issues arising from the dehazing algorithm. To counteract potential drawbacks of the DGM and enhance target recognition accuracy, a polarized self-attention mechanism is integrated during the feature extraction stage to prioritize edge information of coal–gangue targets. By combining the attributes of the weighted bidirectional feature pyramid network, multiple layers of coal–gangue features are efficiently fused to achieve precise identification of coal–gangue targets. Experimental results using a custom dataset demonstrate that the enhanced algorithm outperforms YOLOv3, YOLOv5, YOLOv7-Tiny, and YOLOX, achieving a recognition accuracy of 97.6%, a frames per second rate of 99 and a good smoke concentration robustness. The proposed DGM + YOLOX-PSB serves as a valuable reference for accurate coal and gangue identification in conditions of low light intensity and dust within underground environments.

Cohomological jump loci and duality in local algebra

In this article a higher order support theory, called the cohomological jump loci, is introduced and studied for dg modules over a Koszul extension of a local dg algebra. The generality of this setting applies to dg modules over local complete intersection rings, exterior algebras and certain group algebras in prime characteristic. This family of varieties generalizes the well-studied support varieties in each of these contexts. We show that cohomological jump loci satisfy several interesting properties, including being closed under (Grothendieck) duality. The main application of this support theory is that over a local ring the homological invariants of Betti degree and complexity are preserved under duality for finitely generated modules having finite complete intersection dimension.

On the derived Lusztig correspondence

Abstract Let G be a connected reductive group, T a maximal torus of G, N the normalizer of T and $W=N/T$ the Weyl group of G. Let ${\mathfrak {g}}$ and ${\mathfrak {t}}$ be the Lie algebras of G and T. The affine variety $\mathfrak {car}={\mathfrak {t}}/\!/W$ of semisimple G-orbits of ${\mathfrak {g}}$ has a natural stratification $$ \begin{align*} \mathfrak{car}=\coprod_{\lambda}\mathfrak{car}_{\lambda} \end{align*} $$ indexed by the set of G-conjugacy classes of Levi subgroups: the open stratum is the set of regular semisimple orbits and the closed stratum is the set of central orbits. In [17], Rider considered the triangulated subcategory $D_{\mathrm {c}}^{\mathrm {b}}([{\mathfrak {g}}_{\mathrm {nil}}/G])^{\mathrm {Spr}}$ of $D_{\mathrm {c}}^{\mathrm {b}}([{\mathfrak {g}}_{\mathrm {nil}}/G])$ generated by the direct summand of the Springer sheaf. She proved that it is equivalent to the derived category of finitely generated dg modules over the smash product algebra ${\overline {\mathbb {Q}}_{\ell }}[W]\# H^{\bullet }_G(G/B)$ where $H^{\bullet }_G(G/B)$ is the G-equivariant cohomology of the flag variety. Notice that the later derived category is $D_{\mathrm {c}}^{\mathrm {b}}(\mathrm {B}(N))$ where $\mathrm {B}(N)=[\mathrm {Spec}(k)/N]$ is the classifying stack of N-torsors. The aim of this paper is to understand geometrically and generalise Rider’s equivalence of categories: For each $\lambda $ we construct a cohomological correspondence inducing an equivalence of categories between $D_{\mathrm {c}}^{\mathrm {b}}([{\mathfrak {t}}_{\lambda }/N])$ and $D_{\mathrm {c}}^{\mathrm {b}}([{\mathfrak {g}}_{\lambda }/G])^{\mathrm {Spr}}$ .

English

In this paper we show that every object in the dg category of relative singularities Sing$(B,\underline{f})$ associated to a pair $(B,\underline{f})$, where $B$ is a ring and $\underline{f}\in B^n$, is equivalent to a retract of a $K(B,\underline{f})$-dg module concentrated in $n+1$ degrees. When $n=1$, we show that Orlov's comparison theorem, which relates the dg category of relative singularities and that of matrix factorizations of an LG-model, holds true without any regularity assumption on the potential.

The theory of j-operators with application to (weak) liftings of DG modules

A major part of this paper is devoted to an in-depth study of j-operators and their properties. This study enables us to obtain several results on liftings and weak liftings of DG modules along simple extensions of DG algebras and unify the proofs of the existing results obtained by the authors on these subjects. Finally, we provide a new characterization of the (weak) lifting property of DG modules along simple extensions of DG algebras.

A braid group action on a p-DG homotopy category

We construct a categorical braid group action on a homotopy category of p-DG modules of a deformed Webster algebra.

Hopf algebras arising from dg manifolds

Let (M,Q) be a dg manifold. The space of vector fields with shifted degrees (X(M)[−1],LQ) is a Lie algebra object in the homology category H((CM∞,Q)−mod) of dg modules over (M,Q), the Atiyah class αM being its Lie bracket. The triple (X(M)[−1],LQ; αM) is also a Lie algebra object in the Gabriel-Zisman homotopy category Π((CM∞,Q)−mod). In this paper, we describe the universal enveloping algebra of (X(M)[−1],LQ;αM) and prove that it is a Hopf algebra object in Π((CM∞,Q)−mod). As an application, we study Fedosov dg Lie algebroids and recover a result of Stiénon, Xu, and the second author on the Hopf algebra arising from a Lie pair.

Cohomological supports over derived complete intersections and local rings

A theory of cohomological support for pairs of DG modules over a Koszul complex is investigated. These specialize to the support varieties of Avramov and Buchweitz defined over a complete intersection ring, as well as support varieties over an exterior algebra. The main objects of study are certain DG modules over a polynomial ring; these determine the aforementioned cohomological supports and are shown to encode (co)homological information about pairs of DG modules over a Koszul complex. The perspective in this article leads to new proofs of well-known results for pairs of complexes over a complete intersection. Furthermore, these cohomological supports are used to define a support theory for pairs of objects in the derived category of an arbitrary commutative noetherian local ring. Finally, we calculate several examples; one of which answers a question of D. Jorgensen in the negative.

A lifting problem for DG modules

Let B=A〈X|dX=t〉 be an extended DG algebra by the adjunction of a variable of positive even degree n, and let N be a semi-free DG B-module that is assumed to be bounded below as a graded module. We prove in this paper that N is liftable to A if ExtBn+1(N,N)=0. Furthermore such a lifting is unique up to DG isomorphisms if ExtBn(N,N)=0.

Cohen-Macaulay differential graded modules and negative Calabi-Yau configurations

In this paper, we introduce the class of Cohen-Macaulay (=CM) dg (=differential graded) modules over Gorenstein dg algebras and study their basic properties. We show that the category of CM dg modules forms a Frobenius extriangulated category, in the sense of Nakaoka and Palu, and it admits almost split extensions. We also study representation-finite d-self-injective dg algebras A in detail for some positive integer d. In particular, we classify the Auslander-Reiten (=AR) quivers of CMA for a large class of d-self-injective dg algebras A in terms of (−d)-Calabi-Yau (=CY) configurations, which are Riedtmann's configurations for the case d=1. For any given (−d)-CY configuration C, we show there exists a d-self-injective dg algebra A, such that the AR quiver of CMA is given by C. For type An, by using a bijection between (−d)-CY configurations and certain purely combinatorial objects which we call maximal d-Brauer relations given by Coelho Simões, we construct such A through a Brauer tree dg algebra.

Partial silting objects and smashing subcategories

We study smashing subcategories of a triangulated category with coproducts via silting theory. Our main result states that for derived categories of dg modules over a non-positive differential graded ring, every compactly generated localising subcategory is generated by a partial silting object. In particular, every such smashing subcategory admits a silting t-structure.

Equivariant isomorphisms of Ext and Tor modules

In this article we establish equivariant isomorphisms of Ext and Tor modules over different relative complete intersections. More precisely, for a commutative ring Q, this paper investigates how ExtQ/(f)⁎(M,N) and Tor⁎Q/(f)(M,N) change when one varies f among all Koszul-regular sequences of a fixed length such that fM=0 and fN=0. Of notable interest is how the theory of perturbations is used to establish isomorphisms of certain DG modules.

Motives for an elliptic curve

In this paper we describe the rigid tensor triangulated subcategory of Voevodsky’s triangulated category of motives generated by the motive of an elliptic curve as a derived category of dg modules over a commutative differential graded algebra in the category of representations over some reductive group.

Derived localisation of algebras and modules

For any dg algebra A, not necessarily commutative, and a subset S in H(A), the homology of A, we construct its derived localisation LS(A) together with a map A→LS(A), well-defined in the homotopy category of dg algebras, which possesses a universal property, similar to that of the ordinary localisation, but formulated in homotopy invariant terms. Even if A is an ordinary ring, LS(A) may have non-trivial homology. Unlike the commutative case, the localisation functor does not commute, in general, with homology but instead there is a spectral sequence relating H(LS(A)) and LS(H(A)); this spectral sequence collapses when, e.g. S is an Ore set or when A is a free ring.We prove that LS(A) could also be regarded as a Bousfield localisation of A viewed as a left or right dg module over itself. Combined with the results of Dwyer–Kan on simplicial localisation, this leads to a simple and conceptual proof of the topological group completion theorem. Further applications include algebraic K-theory, cyclic and Hochschild homology, strictification of homotopy unital algebras, idempotent ideals, the stable homology of various mapping class groups and Kontsevich's graph homology.

Derived categories of graded gentle one-cycle algebras

Let A be a graded algebra. It is shown that the derived category of dg modules over A (viewed as a dg algebra with trivial differential) is a triangulated hull of a certain orbit category of the derived category of graded A-modules. This is applied to study derived categories of graded gentle one-cycle algebras.

Semidualizing DG modules over tensor products

We study the existence of nontrivial semidualizing DG modules over tensor products of DG algebras over a field. In particular, this gives a lower bound on the number of semidualizing DG modules over the tensor product.

Ghost length, cone length and complete level of DG modules

In this paper, we introduce a new numerical invariant complete level for a DG module over a local chain DG algebra and give a characterization of it in terms of ghost length. We also study some of its upper bounds. The cone length of a DG module is an invariant closely related with the invariant level. We discover some important results on it.