Searcharxiv⌕ Search

arXiv subjects

Jian He

Publications and source records attributed to Jian He.

At least 55 records · Page 3Linked to original sources

Hereditary $n$-exangulated categories

Herschend-Liu-Nakaoka introduced the concept of $n$-exangulated categories as higher-dimensional analogues of extriangulated categories defined by Nakaoka-Palu. The class of $n$-exangulated categories contains $n$-exact categories and $(n+2)$-angulated categories as specific examples. In this article, we introduce the notion of hereditary $n$-exangulated categories, which generalize hereditary extriangulated categories. We provide two classes of hereditary $n$-exangulated categories through closed subfunctors. Additionally, we define the concept of $0$-Auslander $n$-exangulated categories and discuss the circumstances under which these two classes of hereditary $n$-exangulated categories become $0$-Auslander.

math.RT↗

A dimension reduction approach for loss valuation in credit risk modelling

This paper addresses the ``curse of dimensionality'' in the loss valuation of credit risk models. A dimension reduction methodology based on the Bayesian filter and smoother is proposed. This methodology is designed to achieve a fast and accurate loss valuation algorithm in credit risk modelling, but it can also be extended to valuation models of other risk types. The proposed methodology is generic, robust and can easily be implemented. Moreover, the accuracy of the proposed methodology in the estimation of expected loss and value-at-risk is illustrated by numerical experiments. The results suggest that, compared to the currently most used PCA approach, the proposed methodology provides more accurate estimation of expected loss and value-at-risk of a loss distribution.

cs.CE↗

Cotorsion pairs in comma categories

Let A and B be abelian categories with enough projective and injective objects, and T : A-B a left exact additive functor. Then one has a comma category (B*T). It is shown that If T : A-B is X-exact, then (*X, X) is a (hereditary) cotorsion pair in A and (*Y, Y)) is a (hereditary) cotorsion pair in B if and only if ((*X, Y ), ) is a (hereditary) cotorsion pair in (B*T) and X and Y are closed under extensions. Furthermore, we characterize when special preenveloping classes in abelian categories A and B can induce special preenveloping classes in (B*T).

math.CT↗

Semi-abelian categories arising from pseudo cluster tilting subcategories

The notion of a pseudo cluster tilting subcategory $\mathcal X$ in an extriangulated category $\mathcal C$ is defined in this article. We prove that the quotient category $\mathcal C/\mathcal X$, obtained by factoring an extriangulated category by a pseudo cluster tilting subcategory, is a semi-abelian category. Furthermore, we also show that the quotient category $\mathcal C/\mathcal X$ is an abelian category if and only if certain self-orthogonal conditions are satisfied. As an application, these results generalize the work of Xu and Zheng in the exact category.

math.RT↗

Unleashing the Strengths of Unlabeled Data in Pan-cancer Abdominal Organ Quantification: the FLARE22 Challenge

Quantitative organ assessment is an essential step in automated abdominal disease diagnosis and treatment planning. Artificial intelligence (AI) has shown great potential to automatize this process. However, most existing AI algorithms rely on many expert annotations and lack a comprehensive evaluation of accuracy and efficiency in real-world multinational settings. To overcome these limitations, we organized the FLARE 2022 Challenge, the largest abdominal organ analysis challenge to date, to benchmark fast, low-resource, accurate, annotation-efficient, and generalized AI algorithms. We constructed an intercontinental and multinational dataset from more than 50 medical groups, including Computed Tomography (CT) scans with different races, diseases, phases, and manufacturers. We independently validated that a set of AI algorithms achieved a median Dice Similarity Coefficient (DSC) of 90.0\% by using 50 labeled scans and 2000 unlabeled scans, which can significantly reduce annotation requirements. The best-performing algorithms successfully generalized to holdout external validation sets, achieving a median DSC of 89.5\%, 90.9\%, and 88.3\% on North American, European, and Asian cohorts, respectively. They also enabled automatic extraction of key organ biology features, which was labor-intensive with traditional manual measurements. This opens the potential to use unlabeled data to boost performance and alleviate annotation shortages for modern AI models.

eess.IV↗

Newton saw the truth -- on the nature of fluid flow and viscous interaction

The viscous interaction of fluid is understood as the response to deformation, which is proportional to the strain rate. This model has gradually become the standard since Stokes, and has become the basis of the classical flow theory, namely the Navier-Stokes (N-S) equations. However, it has never been accurately verified in the curved laminar flow. Here, a distinctive unambiguous simple experiment is designed to falsify the viscosity model of deformation, and instead a new model is proposed, that is, the viscous friction originates from the slip of fluid layering at molecular scale. Though Newton contributed the initial idea of slip viscosity, the new model cannot be formulated without the help of modern differential geometry. From the new model, the analytical solution of laminar Taylor-Couette (T-C) flow between two concentric cylinders can reproduce the result of the ideal experiment proposed by Newton as the outer cylinder being infinite, which was once considered a mistake of Newton. A significant difference with the solution of the N-S equations when the outer cylinder is relatively large can be used to distinguish the viscosity models, even for the simplest case with both cylinders rotating with the same angular velocity. The accurate measurement data by the LDA support the slip model, and the consequent flow theory inevitably leads to a new vision in turbulence research.

physics.flu-dyn↗

Adaptive Scheduling for Edge-Assisted DNN Serving

Deep neural networks (DNNs) have been widely used in various video analytic tasks. These tasks demand real-time responses. Due to the limited processing power on mobile devices, a common way to support such real-time analytics is to offload the processing to an edge server. This paper examines how to speed up the edge server DNN processing for multiple clients. In particular, we observe batching multiple DNN requests significantly speeds up the processing time. Based on this observation, we first design a novel scheduling algorithm to exploit the batching benefits of all requests that run the same DNN. This is compelling since there are only a handful of DNNs and many requests tend to use the same DNN. Our algorithms are general and can support different objectives, such as minimizing the completion time or maximizing the on-time ratio. We then extend our algorithm to handle requests that use different DNNs with or without shared layers. Finally, we develop a collaborative approach to further improve performance by adaptively processing some of the requests or portions of the requests locally at the clients. This is especially useful when the network and/or server is congested. Our implementation shows the effectiveness of our approach under different request distributions (e.g., Poisson, Pareto, and Constant inter-arrivals).

cs.NI↗

Idempotent completion of certain $n$-exangulated categories

It was shown recently that an $n$-extension closed subcategory $\mathscr A$ of a Krull-Schmidt $(n+2)$-angulated category has a natural structure of an $n$-exangulated category. In this article, we prove that its idempotent completion $\widetilde{\mathscr A}$ admits an $n$-exangulated structure. It is not only a generalization of the main result of Lin, but also gives an $n$-exangulated category which is neither $n$-exact nor $(n+2)$-angulated in general.

math.RT↗

Two results of $n$-exangulated categories

$n$-exangulated categories were introduced by Herschend-Liu-Nakaoka which are a simultaneous generalization of $n$-exact categories and $(n+2)$-angulated categories. This paper consists of two results on $n$-exangulated categories: (1) we give an equivalent characterization of the axiom (EA2); (2) we provide a new way to construct a closed subfunctor of an $n$-exangulated category.

math.RT↗

Localization of n-exangulated categories

Nakaoka-Ogawa-Sakai considered the localization of an extriangulated category. This construction unified the Serre quotient of abelian categories and the Verdier quotient of triangulated categories. Recently, Herschend-Liu-Nakaoka defined $n$-exangulated categories as a higher dimensional analogue of extriangulated categories. Let $\mathcal C$ be an $n$-exangulated category and $\mathcal{F}$ be a multiplicative system satisfying mild assumption. In this article, we give a necessary and sufficient condition for the localization of $\mathcal C$ be an $n$-exangulated category. This way gives a new class of $n$-exangulated categories which are neither $n$-exact nor $(n+2)$-angulated in general. Moreover, our result also generalizes work by Nakaoka-Ogawa-Sakai.

math.RT↗

Auslander-Reiten-Serre duality for n-exangulated categories

Let $(\mathscr{C},\mathbb{E},\mathfrak{s})$ be an Ext-finite, Krull-Schmidt and $k$-linear $n$-exangulated category with $k$ a commutative artinian ring. In this note, we prove that $\mathscr{C}$ has Auslander-Reiten-Serre duality if and only if $\mathscr{C}$ has Auslander-Reiten $n$-exangles. Moreover, we also give an equivalent condition for the existence of Serre duality (which is a special type of Auslander-Reiten-Serre duality). Finally, assume further that $\mathscr{C}$ has Auslander-Reiten-Serre duality. We exploit a bijection triangle, which involves the restricted Auslander bijection and the Auslander-Reiten-Serre duality.

math.RT↗

Higher Auslander-Reiten sequences via morphisms determined by objects

Let $(\mathscr{C},\mathbb{E},\mathfrak{s})$ be an ${\rm Ext}$-finite, Krull-Schmidt and $k$-linear $n$-exangulated category with $k$ a commutative artinian ring. In this note, we define two additive subcategories $\mathscr{C}_r$ and $\mathscr{C}_l$ of $\mathscr{C}$ in terms of the representable functors from the stable category of $\mathscr{C}$ to the category of finitely generated $k$-modules. Moreover, we show that there exists an equivalence between the stable categories of these two full subcategories. Finally, we give some equivalent characterizations on the existence of Auslander-Reiten $n$-exangles via determined morphisms. These results unify and extend their works by Jiao-Le for exact categories, Zhao-Tan-Huang for extriangulated categories, Xie-Liu-Yang for $n$-abelian categories.

math.RT↗

On the existence of Auslander-Reiten $n$-exangles in $n$-exangulated categories

Let $\mathscr{C}$ be an $n$-exangulated category. In this note, we show that if $\mathscr{C}$ is locally finite, then $\mathscr{C}$ has Auslander-Reiten $n$-exangles. This unifies and extends results of Xiao-Zhu, Zhu-Zhuang, Zhou and Xie-Lu-Wang for triangulated, extriangulated, $(n+2)$-angulated and $n$-abelian categories, respectively.

math.RT↗

$n$-exact categories arising from $n$-exangulated categories

Let $\mathscr{C}$ be a Krull-Schmidt $n$-exangulated category and $\mathscr{A}$ be an $n$-extension closed subcategory of $\mathscr{C}$. Then $\mathscr{A}$ inherits the $n$-exangulated structure from the given $n$-exangulated category in a natural way. This construction gives $n$-exangulated categories which are not $n$-exact categories in the sense of Jasso nor $(n+2)$-angulated categories in the sense of Geiss-Keller-Oppermann in general. Furthermore, we also give a sufficient condition on when an $n$-exangulated category $\mathscr{A}$ is an $n$-exact category. These results generalize work by Klapproth and Zhou.

math.RT↗

Balanced pairs and recollements in extriangulated categories with negative first extensions

A notion of balanced pairs in an extriangulated category with a negative first extension is defined in this article. We prove that there exists a bijective correspondence between balanced pairs and proper classes $ξ$ with enough $ξ$-projectives and enough $ξ$-injectives. It can be regarded as a simultaneous generalization of Fu-Hu-Zhang-Zhu and Wang-Li-Huang. Besides, we show that if $(\mathcal A ,\mathcal B,\mathcal C)$ is a recollement of extriangulated categories, then balanced pairs in $\mathcal B$ can induce balanced pairs in $\mathcal A$ and $\mathcal C$ under natural assumptions. As a application, this result gengralizes a result by Fu-Hu-Yao in abelian categories. Moreover, it highlights a new phenomena when it applied to triangulated categories.

math.RT↗

From right (n+2)-angulated categories to n-exangulated categories

The notion of right semi-equivalence in a right $(n+2)$-angulated category is defined in this article. Let $\mathscr C$ be an $n$-exangulated category and $\mathscr X$ is a strongly covariantly finite subcategory of $\mathscr C$. We prove that the standard right $(n+2)$-angulated category $\mathscr C/\mathscr X$ is right semi-equivalence under a natural assumption. As an application, we show that a right $(n+2)$-angulated category has an $n$-exangulated structure if and only if the suspension functor is right semi-equivalence. Besides, we also prove that an $n$-exangulated category $\mathscr C$ has the structure of a right $(n+2)$-angulated category with right semi-equivalence if and only if for any object $X\in\mathscr C$, the morphism $X\to 0$ is a trivial inflation.

math.RT↗

AbdomenCT-1K: Is Abdominal Organ Segmentation A Solved Problem?

With the unprecedented developments in deep learning, automatic segmentation of main abdominal organs seems to be a solved problem as state-of-the-art (SOTA) methods have achieved comparable results with inter-rater variability on many benchmark datasets. However, most of the existing abdominal datasets only contain single-center, single-phase, single-vendor, or single-disease cases, and it is unclear whether the excellent performance can generalize on diverse datasets. This paper presents a large and diverse abdominal CT organ segmentation dataset, termed AbdomenCT-1K, with more than 1000 (1K) CT scans from 12 medical centers, including multi-phase, multi-vendor, and multi-disease cases. Furthermore, we conduct a large-scale study for liver, kidney, spleen, and pancreas segmentation and reveal the unsolved segmentation problems of the SOTA methods, such as the limited generalization ability on distinct medical centers, phases, and unseen diseases. To advance the unsolved problems, we further build four organ segmentation benchmarks for fully supervised, semi-supervised, weakly supervised, and continual learning, which are currently challenging and active research topics. Accordingly, we develop a simple and effective method for each benchmark, which can be used as out-of-the-box methods and strong baselines. We believe the AbdomenCT-1K dataset will promote future in-depth research towards clinical applicable abdominal organ segmentation methods. The datasets, codes, and trained models are publicly available at https://github.com/JunMa11/AbdomenCT-1K.

cs.CV↗

Torsion pairs and recollements of extriangulated categories

In this article, we prove that if $(\mathcal A ,\mathcal B,\mathcal C)$ is a recollement of extriangulated categories, then torsion pairs in $\mathcal A$ and $\mathcal C$ can induce torsion pairs in $\mathcal B$, and the converse holds under natural assumptions. Besides, we give mild conditions on a cluster tilting subcategory on the middle category of a recollement of extriangulated categories, for the corresponding abelian quotients to form a recollement of abelian categories.

math.RT↗