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Pin Liu

Publications and source records attributed to Pin Liu.

13 recordsLinked to original sources
arXiv2026

Geometric models for endomorphism algebras of tilting modules over gentle algebras

This paper investigates tilting modules over gentle algebras and their endomorphism algebras within the framework of marked surfaces and tilings introduced by Baur and Sim\~{o}es. Faithful dissections of a tiling are shown to correspond to tilting modules. For a faithful dissection, we define an auxiliary algebra and prove that it is isomorphic to the endomorphism algebra of the corresponding tilting module. We also construct a new tiling realizing this endomorphism algebra and introduce a flip preserving tilting modules.

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arXiv2025

Intersection vectors over skew-tilings

We prove that under a mild condition, a multiset of tagged permissible arcs over a skew-tiling is uniquely determined by its intersection vector. As an application, it is proved that -- up to isomorphism -- different $\tau$-rigid modules over a skew-gentle algebra $A$ arising from a skew-triple $(Q,Sp,I)$ have different dimension vectors if and only if $(Q,I)$ has no minimal oriented cycle of even-length with full zero relations. This generalizes a recent work of Fu-Geng for gentle algebras.

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arXiv2024

On $\tau$-tilting graphs for quasi-silted algebras

We prove that the $\tau$-tilting graph of any quasi-silted algebra is connected and has the reachable-in-face property. Our approach utilizes $\tau$-reduction and wall and chamber structures. In particular, we observe a sufficient condition on the wall and chamber structure under which the connectivity of $\tau$-tilting graphs is preserved under taking quotients of algebras. As an immediate consequence, the connectivity of $\tau$-tilting graphs is also established for several new classes of algebras.

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arXiv2023

FRAD: Front-Running Attacks Detection on Ethereum using Ternary Classification Model

With the evolution of blockchain technology, the issue of transaction security, particularly on platforms like Ethereum, has become increasingly critical. Front-running attacks, a unique form of security threat, pose significant challenges to the integrity of blockchain transactions. In these attack scenarios, malicious actors monitor other users' transaction activities, then strategically submit their own transactions with higher fees. This ensures their transactions are executed before the monitored transactions are included in the block. The primary objective of this paper is to delve into a comprehensive classification of transactions associated with front-running attacks, which aims to equip developers with specific strategies to counter each type of attack. To achieve this, we introduce a novel detection method named FRAD (Front-Running Attacks Detection on Ethereum using Ternary Classification Model). This method is specifically tailored for transactions within decentralized applications (DApps) on Ethereum, enabling accurate classification of front-running attacks involving transaction displacement, insertion, and suppression. Our experimental validation reveals that the Multilayer Perceptron (MLP) classifier offers the best performance in detecting front-running attacks, achieving an impressive accuracy rate of 84.59% and F1-score of 84.60%.

cs.CR↗
arXiv2022

Deep Contrastive One-Class Time Series Anomaly Detection

The accumulation of time-series data and the absence of labels make time-series Anomaly Detection (AD) a self-supervised deep learning task. Single-normality-assumption-based methods, which reveal only a certain aspect of the whole normality, are incapable of tasks involved with a large number of anomalies. Specifically, Contrastive Learning (CL) methods distance negative pairs, many of which consist of both normal samples, thus reducing the AD performance. Existing multi-normality-assumption-based methods are usually two-staged, firstly pre-training through certain tasks whose target may differ from AD, limiting their performance. To overcome the shortcomings, a deep Contrastive One-Class Anomaly detection method of time series (COCA) is proposed by authors, following the normality assumptions of CL and one-class classification. It treats the original and reconstructed representations as the positive pair of negative-sample-free CL, namely "sequence contrast". Next, invariance terms and variance terms compose a contrastive one-class loss function in which the loss of the assumptions is optimized by invariance terms simultaneously and the "hypersphere collapse" is prevented by variance terms. In addition, extensive experiments on two real-world time-series datasets show the superior performance of the proposed method achieves state-of-the-art.

cs.LG↗
arXiv2021

On support $\tau$-tilting graphs of gentle algebras

Let $A$ be a finite-dimensional gentle algebra over an algebraically closed field. We investigate the combinatorial properties of support $\tau$-tilting graph of $A$. In particular, it is proved that the support $\tau$-tilting graph of $A$ is connected and has the so-called reachable-in-face property. This property was conjectured by Fomin and Zelevinsky for exchange graphs of cluster algebras which was recently confirmed by Cao and Li.

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arXiv2018

Relative rigid objects in triangulated categories

Let $\mathcal{T}$ be a Krull-Schmidt, Hom-finite triangulated category with suspension functor $[1]$. Let $R$ be a basic rigid object, $\Gamma$ the endomorphism algebra of $R$, and $\operatorname{\mathsf{pr}}(R)\subseteq \mathcal{T}$ the subcategory of objects finitely presented by $R$. We investigate the relative rigid objects, \ie $R[1]$-rigid objects of $\mathcal{T}$. Our main results show that the $R[1]$-rigid objects in $\operatorname{\mathsf{pr}}(R)$ are in bijection with $\tau$-rigid $\Gamma$-modules, and the maximal $R[1]$-rigid objects with respect to $\operatorname{\mathsf{pr}}(R)$ are in bijection with support $\tau$-tilting $\Gamma$-modules. We also show that various previously known bijections involving support $\tau$-tilting modules are recovered under respective assumptions.

math.RA↗
arXiv2018

Cluster algebras arising from cluster tubes II: the Caldero-Chapoton map

We continue our investigation on cluster algebras arising from cluster tubes. Let $\mathcal{C}$ be a cluster tube of rank $n+1$. For an arbitrary basic maximal rigid object $T$ of $\mathcal{C}$, one may associate a skew-symmetrizable integer matrix $B_T$ and hence a cluster algebra $\mathcal{A}(B_T)$ to $T$. We define an analogue Caldero-Chapoton map $\mathbb{X}_M^T$ for each indecomposable rigid object $M\in \mathcal{C}$ and prove that $\mathbb{X}_?^T$ yields a bijection between the indecomposable rigid objects of $\mathcal{C}$ and the cluster variables of the cluster algebra $\mathcal{A}(B_T)$. The construction of the Caldero-Chapoton map involves Grassmanians of locally free submodules over the endomorphism algebra of $T$. We also show that there is a non-trivial $\mathbb{C}^{\times}$-action on the Grassmanians of locally free submodules, which is of independent interest.

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arXiv2017

Cluster algebras arising from cluster tubes I: integer vectors

We study cluster algebras arising from cluster tubes. We obtain categorical interpretations for $g$-vectors, $c$-vectors and denominator vectors for cluster algebras of type $\mathrm{C}$ with respect to arbitrary initial seeds. In particular, a denominator theorem has been proved, which enables us to establish the linearly independence of denominator vectors of cluster variables from the same cluster for cluster algebras of type $\mathrm{A}\mathrm{B}\mathrm{C}$. This strengthens the link between cluster tubes and cluster algebras of type $\mathrm{C}$ initiated by Buan, Marsh and Vatne.

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arXiv2013

Tilting objects on tubular weighted projective lines: a cluster tilting approach

Using cluster tilting theory, we investigate tilting objects in the stable category of vector bundles on a weighted projective line of weight type $(2, 2, 2, 2)$. More precisely, a tilting object consisting of rank-two bundles is constructed via cluster tilting mutation. Moreover, the cluster tilting approach also provides a new method to classify the endomorphism algebras of tilting objects in the category of coherent sheaves and the associated bounded derived category.

math.RT↗
arXiv2008

Lifting to cluster-tilting objects in higher cluster categories

In this note, we consider the $d$-cluster-tilted algebras, the endomorphism algebras of $d$-cluster-tilting objects in $d$-cluster categories. We show that a tilting module over such an algebra lifts to a $d$-cluster-tilting object in this $d$-cluster category.

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