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Yu Qiu

Publications and source records attributed to Yu Qiu.

At least 37 records · Page 2Linked to original sources
arXiv2025

UMC: Unified Resilient Controller for Legged Robots with Joint Malfunctions

Adaptation to unpredictable damages is crucial for autonomous legged robots, yet existing methods based on multi-policy or meta-learning frameworks face challenges like limited generalization and complex maintenance. To address this issue, we first analyze and summarize eight types of damage scenarios, including sensor failures and joint malfunctions. Then, we propose a novel, model-free, two-stage training framework, Unified Malfunction Controller (UMC), incorporating a masking mechanism to enhance damage resilience. Specifically, the model is initially trained with normal environments to ensure robust performance under standard conditions. In the second stage, we use masks to prevent the legged robot from relying on malfunctioning limbs, enabling adaptive gait and movement adjustments upon malfunction. Experimental results demonstrate that our approach improves the task completion capability by an average of 36% for the transformer and 39% for the MLP across three locomotion tasks. The source code and trained models will be made available to the public.

cs.RO↗
arXiv2025

Contractibility and total semi-stability conditions of Euclidean quivers

We study the bounded derived category $\mathcal{D}$ of an Euclidean quiver, or equivalently, that of coherent sheaves on a tame weighted projective line. We give a description of the moduli space $\mathrm{ToSS}$ of the total semi-stability conditions on $\mathcal{D}$, which implies that $\mathrm{ToSS}$ can linearly contract to any chosen non-concentrated stability condition in it. For type $\widetilde{A_{p,q}}$, this gives an alternative proof of the contractibility of the whole space of stability conditions.

math.RT↗
arXiv2025

Geometric classification of total stability spaces

We construct a geometric model for the root category $\mathcal{D}^b(Q)/[2]$ of any Dynkin diagram $Q$, which is an $h_Q$-gon $\mathbf{V}_Q$ with cores, where $h_Q$ is the Coxeter number and $\mathcal{D}^b(Q)$ is the bounded derived category associated to $Q$. As an application, we classify all spaces $\mathrm{ToSt}\mathcal{D}$ of total stability conditions on triangulated categories $\mathcal{D}$, where $\mathcal{D}$ must be of the form $\mathcal{D}^b(Q)$. More precisely, we prove that $\mathrm{ToSt}\mathcal{D}^b(Q)/[2]$ is isomorphic to a suitable moduli space of stable $h_Q$-gons of type $Q$. In particular, an $h_Q$-gon $\mathbf{V}$ of type $D_n$ is a (centrally) symmetric doubly punctured $2(n-1)$-gon. $\mathbf{V}$ is stable if it is convex and the punctures are inside the level-$(n-2)$ diagonal-gon. Another interesting case is $E_6$, where the (stable) $h_Q$-gon (dodecagon) can be realized as a pair of planar tiling pattern.

math.RT↗
arXiv2025

Fusion-stable structures on triangulated categories

Let $\mathcal{G}$ be a fusion category acting on a triangulated category $\mathcal{D}$, in the sense that $\mathcal{D}$ is a $\mathcal{G}$-module category. Our motivation example is fusion-weighted species, which is essentially Heng's construction. We study $\mathcal{G}$-stable tilting, cluster and stability structures on $\mathcal{D}$. In particular, we prove the deformation theorem for $\mathcal{G}$-stable stability conditions. A first application is that Duffield-Tumarkin's categorification of cluster exchange graphs of finite Coxeter-Dynkin type can be naturally realized as fusion-stable cluster exchange graphs. Another application is that the universal cover of the hyperplane arrangements of any finite Coxeter-Dynkin type can be realized as the space of fusion-stable stability conditions for certain ADE Dynkin quiver. This provides an alternative uniform proof of $K(π,1)$-conjecture in the finite Coxeter-Dynkin case.

math.RT↗
arXiv2024

Cumulenic sp-carbon Atomic Wires Wrapped Polymers for Supercapacitor Application

Carbon atomic wires, a linear atomic chain of sp-carbon, is theoretically predicted to have around five times higher surface area than graphene, notable charge mobilities, as well as excellent optical and thermal properties. Despite these impressive properties, the properties of sp-carbon as an electrochemical energy-storage electrode have not been reported so far. Herein, we prepare solution processed thin films of tetraphenyl[3]cumulenic sp-carbon atomic wires embedded in a polymer matrix, in which sp-carbon atomic wires feature three cumulated carbon-carbon double bonds terminated at each end by two phenyl groups. Raman and UV-visible spectroscopy are used to confirm the presence and possible degradation of sp-carbons inside the polymeric matrix. Finally, we investigate the supercapacitor performance of cumulenic sp-carbon atomic wires embedded polymer in three aqueous mediums, namely 1M Na2SO4 (neutral), 1M H2SO4 (acidic), and 6M KOH (basic). The results suggest 6M KOH is the best electrolyte to obtain high charge-storage performance of device with areal capacitance of 2.4 mF/cm2 at 20 mV/s, 85% cycle stability after 10000 charge-discharge cycles, and excellent frequency response.

physics.app-ph↗
arXiv2024

Merging Parameter Estimation and Classification Using LASSO

Soft sensing is a way to indirectly obtain information of signals for which direct sensing is difficult or prohibitively expensive. It may not \textit{a priori} be evident which sensors provide useful information about the target signal, and various operating conditions often necessitate different models. In this paper, we provide a systematic method to construct a soft sensor that can deal with these issues. We propose a single estimation criterion, where the objectives are encoded in terms of model fit, model sparsity (reducing the number of different models), and model parameter coefficient sparsity (to exclude irrelevant sensors). The proposed method is tested on real-world scenarios involving prototype vehicles, demonstrating its effectiveness.

eess.SY↗
arXiv2024

Two geometric models for graded skew-gentle algebras

In Part 1, we classify (indecomposable) objects in the perfect derived category $\mathrm{per}Λ$ of a graded skew-gentle algebra $Λ$, generalizing technique/results of Burban-Drozd and Deng to the graded setting. We also use the usual punctured marked surface $\mathbf{S}^λ$ with grading (and a full formal arc system) to give a geometric model for this classification. In Part2, we introduce a new surface $\mathbf{S}^λ_*$ with binaries from $\mathbf{S}^λ$ by replacing each puncture $P$ by a boundary component $*_P$ (called a binary) with one marked point, and composing an equivalent relation $D_{*_P}^2=\mathrm{id}$, where $D_{*_p}$ is the Dehn twist along $*_P$. Certain indecomposable objects in $\mathrm{per}Λ$ can be also classified by graded unknotted arcs on $\mathbf{S}^λ_*$. Moreover, using this new geometric model, we show that the intersections between any two unknotted arcs provide a basis of the morphisms between the corresponding arc objects, i.e. formula $\mathrm{Int}=\mathrm{dim}\mathrm{Hom}$ holds.

math.RT↗
arXiv2024

Quadratic differentials as stability conditions: collapsing subsurfaces

We introduce a new class of triangulated categories, which are Verdier quotients of three-Calabi-Yau categories from (decorated) marked surfaces, and show that its spaces of stability conditions can be identified with moduli spaces of framed quadratic differentials on Riemann surfaces with arbitrary order zeros and arbitrary higher order poles. A main tool in our proof is a comparison of two exchange graphs, obtained by tilting hearts in the quotient categories and by flipping mixed angulations associated with the quadratic differentials.

math.GT↗
arXiv2024

CatNorth: An Improved Gaia DR3 Quasar Candidate Catalog with Pan-STARRS1 and CatWISE

A complete and pure sample of quasars with accurate redshifts is crucial for quasar studies and cosmology. In this paper, we present CatNorth, an improved Gaia DR3 quasar candidate catalog with more than 1.5 million sources in the 3$π$ sky built with data from Gaia, Pan-STARRS1, and CatWISE2020. The XGBoost algorithm is used to reclassify the original Gaia DR3 quasar candidates as stars, galaxies, and quasars. To construct training/validation datasets for the classification, we carefully built two different master stellar samples in addition to the spectroscopic galaxy and quasar samples. An ensemble classification model is obtained by averaging two XGBoost classifiers trained with different master stellar samples. Using a probability threshold of $p_{\mathrm{QSO\_mean}}>0.95$ in our ensemble classification model and an additional cut on the logarithmic probability density of zero proper motion, we retrieved 1,545,514 reliable quasar candidates from the parent Gaia DR3 quasar candidate catalog. We provide photometric redshifts for all candidates with an ensemble regression model. For a subset of 89,100 candidates, accurate spectroscopic redshifts are estimated with the Convolutional Neural Network from the Gaia BP/RP spectra. The CatNorth catalog has a high purity of ~ 90% while maintaining high completeness, which is an ideal sample to understand the quasar population and its statistical properties. The CatNorth catalog is used as the main source of input catalog for the LAMOST phase III quasar survey, which is expected to build a highly complete sample of bright quasars with $i < 19.5$.

astro-ph.GA↗
arXiv2023

Cluster braid groups of Coxeter-Dynkin diagrams

Cluster exchange groupoids are introduced by King-Qiu as an enhancement of cluster exchange graphs to study stability conditions and quadratic differentials. In this paper, we introduce the exchange groupoid for any finite Coxeter-Dynkin diagram $Δ$ and show that the fundamental group of which is isomorphic to the corresponding braid group associated with $Δ$.

math.CO↗
arXiv2023

Boosting Salient Object Detection with Transformer-based Asymmetric Bilateral U-Net

Existing salient object detection (SOD) methods mainly rely on U-shaped convolution neural networks (CNNs) with skip connections to combine the global contexts and local spatial details that are crucial for locating salient objects and refining object details, respectively. Despite great successes, the ability of CNNs in learning global contexts is limited. Recently, the vision transformer has achieved revolutionary progress in computer vision owing to its powerful modeling of global dependencies. However, directly applying the transformer to SOD is suboptimal because the transformer lacks the ability to learn local spatial representations. To this end, this paper explores the combination of transformers and CNNs to learn both global and local representations for SOD. We propose a transformer-based Asymmetric Bilateral U-Net (ABiU-Net). The asymmetric bilateral encoder has a transformer path and a lightweight CNN path, where the two paths communicate at each encoder stage to learn complementary global contexts and local spatial details, respectively. The asymmetric bilateral decoder also consists of two paths to process features from the transformer and CNN encoder paths, with communication at each decoder stage for decoding coarse salient object locations and fine-grained object details, respectively. Such communication between the two encoder/decoder paths enables AbiU-Net to learn complementary global and local representations, taking advantage of the natural merits of transformers and CNNs, respectively. Hence, ABiU-Net provides a new perspective for transformer-based SOD. Extensive experiments demonstrate that ABiU-Net performs favorably against previous state-of-the-art SOD methods. The code is available at https://github.com/yuqiuyuqiu/ABiU-Net.

cs.CV↗
arXiv2023

Topological model for q-deformed rational number and categorification

Let $\mathbf{D}_{3}$ be a bigraded 3-decorated disk with an arc system $\mathbf{A}$. We associate a bigraded simple closed arc $\widehatη_{\frac{r}{s}}$ on $\mathbf{D}_{3}$ to any rational number $\frac{r}{s}\in\overline{\mathbb{Q}}=\mathbb{Q}\cup\{\infty\}$. We show that the right (resp. left) $q$-deformed rational numbers associated to $\frac{r}{s}$, in the sense of Morier-Genoud-Ovsienko (resp. Bapat-Becker-Licata) can be naturally calculated by the $\mathfrak{q}$-intersection between $\widehatη_{\frac{r}{s}}$ and $\mathbf{A}$ (resp. dual arc system $\mathbf{A}^*$). The Jones polynomials of rational knots can be also given by such intersections. Moreover, the categorification of $\widehatη_{\frac{r}{s}}$ is given by the spherical object $X_{\frac{r}{s}}$ in the Calabi-Yau-$\mathbb{X}$ category of Ginzburg dga of type $A_2$. Reduce to CY-2 case, we recover result of Bapat-Becker-Licata with a slight improvement.

math.RT↗
arXiv2023

q-Stability conditions on Calabi-Yau-X categories

We introduce $q$-stability conditions $(σ,s)$ on Calabi-Yau-$\mathbb{X}$ categories $\mathcal{D}_\mathbb{X}$, where $σ$ is a stability condition on $\mathcal{D}_\mathbb{X}$ and $s$ a complex number. We prove the corresponding deformation theorem, that $\operatorname{QStab}_s\mathcal{D}_\mathbb{X}$ is a complex manifold of dimension $n$ for fixed $s$, where $n$ is the rank of the Grotendieck group of $\mathcal{D}_\mathbb{X}$ over $\mathbb{Z}[q^{\pm 1}]$. When $s=N$ is an integer, we show that the $q$-stability conditions can be identified with the stability conditions on $\mathcal{D}_N$, provided the orbit category $\mathcal{D}_N=\mathcal{D}_\mathbb{X}/[\mathbb{X}-N]$ is well defined. To attack the questions on existence and deformation along $s$ direction, we introduce the inducing method. Sufficient and necessary conditions are given, for a stability condition on an $\mathbb{X}$-baric heart (that is, an usual triangulated category) of $\mathcal{D}_\mathbb{X}$ to induce $q$-stability conditions on $\mathcal{D}_\mathbb{X}$. As a consequence, we show that the space $\operatorname{QStab}^\oplus\mathcal{D}_\mathbb{X}$ of (induced) open $q$-stability conditions is a complex manifold of dimension $n+1$. Our motivating examples for $\mathcal{D}_\mathbb{X}$ are coming from Calabi-Yau-$\mathbb{X}$ completions of dg algebras. In the case of smooth projective varieties, the $\mathbb{C}^*$-equivariant coherent sheaves on canonical bundles provide the Calabi-Yau-$\mathbb{X}$ categories. Another application is that we show the prefect derived categories can be realized as cluster-$\mathbb{X}$ categories for acyclic quivers.

math.AG↗
arXiv2022

Radio jet-ISM interaction and positive radio-mechanical feedback in Abell 1795

We present XSHOOTER observations with previous ALMA, MUSE and $HST$ observations to study the nature of radio-jet triggered star formation and the interaction of radio jets with the interstellar medium in the brightest cluster galaxy (BCG) in the Abell 1795 cluster. Using $HST$ UV data we determined an ongoing star formation rate of 9.3 M$_\odot$ yr$^{-1}$. The star formation follows the global Kennicutt-Schmidt law, however, it has a low efficiency compared to circumnuclear starbursts in nearby galaxies with an average depletion time of $\sim$1 Gyr. The star formation and molecular gas are offset by $\sim1$ kpc indicating that stars have decoupled from the gas. We detected an arc of high linewidth in ionized gas where electron densities are elevated by a factor of $\sim$4 suggesting a shock front driven by radio jets or peculiar motion of the BCG. An analysis of nebular emission line flux ratios suggests that the gas is predominantly ionized by star formation with a small contribution from shocks. We also calculated the velocity structure function (VSF) of the ionized and molecular gases using velocity maps to characterize turbulent motion in the gas. The ionized gas VSF suggests that the radio jets are driving supersonic turbulence in the gas. Thus radio jets can not only heat the atmosphere on large scales and may quench star formation on longer timescales while triggering star formation in positive feedback on short timescales of a few million years.

astro-ph.GA↗
arXiv2022

Frobenius morphisms and stability conditions

We generalize Deng-Du's folding argument, for the bounded derived category $\mathcal{D}(Q)$ of an acyclic quiver $Q$, to the finite dimensional derived category $\mathcal{D}(ΓQ)$ of the Ginzburg algebra $ΓQ$ associated to $Q$. We show that the $F$-stable category of $\mathcal{D}(ΓQ)$ is equivalent to the finite dimensional derived category $\mathcal{D}(Γ\mathbb{S})$ of the Ginzburg algebra $Γ\mathbb{S}$ associated to the species $\mathbb{S}$, which is folded from $Q$. If $(Q,\mathbb{S})$ is of Dynkin type, we prove that $\operatorname{Stab}\mathcal{D}(\mathbb{S})$ (resp. the principal component $\operatorname{Stab}^\circ\mathcal{D}(Γ\mathbb{S})$) of the space of the stability conditions of $\mathcal{D}(\mathbb{S})$ (resp. $\mathcal{D}(Γ\mathbb{S})$) is canonically isomorphic to $\operatorname{FStab}\mathcal{D}(Q)$ (resp. the principal component $\operatorname{FStab}^\circ\mathcal{D}(ΓQ)$) of the space of $F$-stable stability conditions of $\mathcal{D}(Q)$ (resp. $\mathcal{D}(ΓQ)$). There are two applications. One is for the space $\operatorname{NStab}\mathcal{D}(ΓQ)$ of numerical stability conditions in $\operatorname{Stab}^\circ\mathcal{D}(ΓQ)$. We show that $\operatorname{NStab}\mathcal{D}(ΓQ)$ consists of $\operatorname{Br} Q/\operatorname{Br} \mathbb{S}$ many connected components, each of which is isomorphic to $\operatorname{Stab}^\circ\mathcal{D}(Γ\mathbb{S})$, for $(Q,\mathbb{S})$ is of type $(A_3, B_2)$ or $(D_4, G_2)$. The other is that we relate the $F$-stable stability conditions to the Gepner type stability conditions.

math.RT↗
arXiv2022

Global dimension function on stability conditions and Gepner equations

We study the global dimension function $\operatorname{gldim}\colon\operatorname{Aut}\backslash\operatorname{Stab}\mathcal{D}/\mathbb{C}\to\mathbb{R}_{\ge0}$ on a quotient of the space of Bridgeland stability conditions on a triangulated category $\mathcal{D}$ as well as Toda's Gepner equatio $Φ(σ)=s\cdotσ$ for some $σ\in\operatorname{Stab}\mathcal{D}$ and $(Φ,s)\in\operatorname{Aut}\mathcal{D}\times\mathbb{C}$. For the bounded derived category $\mathcal{D}^b(\mathbf{k} Q)$ of a Dynkin quiver $Q$, we show that there is a unique minimal point $σ_G$ of $\operatorname{gldim}$ (up to the $\mathbb{C}$-action), with value $1-2/h$, which is the solution of the Gepner equation $τ(σ)=(-2/h)\cdotσ$. Here $τ$ is the Auslander-Reiten functor and $h$ is the Coxeter number. This solution $σ_G$ was constructed by Kajiura-Saito-Takahashi. We also show that for an acyclic non-Dynkin quiver $Q$, the minimal value of $\operatorname{gldim}$ is $1$. Our philosophy is that the infimum of $\operatorname{gldim}$ on $\operatorname{Stab}\mathcal{D}$ is the global dimension for the triangulated category $\mathcal{D}$. We explain how this notion could shed light on the contractibility conjecture of the space of stability conditions.

math.RT↗
arXiv2022

Contractibility of space of stability conditions on the projective plane via global dimension function

We compute the global dimension function $\mathrm{gldim}$ on the principal component $\mathrm{Stab}^†(\mathbb{P}^2)$ of the space of Bridgeland stability conditions on $\mathbb{P}^2$. It admits $2$ as the minimum value and the preimage $\mathrm{gldim}^{-1}(2)$ is contained in the closure $\bar{\mathrm{Stab}^{\mathrm{Geo}}(\mathbb{P}^2)}$ of the subspace consisting of geometric stability conditions. We show that $\mathrm{gldim}^{-1}[2,x)$ contracts to $\mathrm{gldim}^{-1}(2)$ for any real number $x\geq 2$ and that $\mathrm{gldim}^{-1}(2)$ is contractible.

math.AG↗