arXiv subjects
Publications and source records attributed to Haiyan Zhu.
We give a counterexample to completeness descent from ideal cotorsion pairs to their objects. A radical-square-zero algebra on the two-cycle gives a finite-dimensional example. The construction is intrinsically non-weakly-idempotent-complete.
Low-dimensional multiferroics hold great promise for integrated magnetoelectric devices. Spin spiral state has recently been shown to induce ferroelectricity in single-layer van der Waals (vdW) material NiI2. However, how this state evolves and can be tuned towards the two-dimensional limit remain unclear. Here, we combine spin-polarized scanning tunneling microscopy, layer-by-layer film growth, and multi-scale theoretical modeling to investigate the spin spirals in NiI2 thin films. As the film thickness increases from 1 to 7 monolayers, we observed a continuous increase of spin-spiral wavelength and a rotation of wavevector from near [110] to [1-10] direction, which evidences a dimensional crossover primarily driven by enhanced interlayer exchange energy. Moreover, we find that the film wrinkles can cause deflection of the spin spiral wavevector, which is caused by local curvature induced modification of exchange interactions. Our findings establish thickness and local strain as two tuning methods for engineering non-collinear helical magnetism and accompanied electric polarization in vdW multiferroics.
In this paper, we improve the marked-vertex strategy introduced by Fu and Liang, and design the algorithm to compute all mutation paths and generator elements of cluster automorphism groups efficiently. As an application, we get generators of cluster automorphism groups of cluster algebras of finite mutation type of rank 4.
The main aim of this paper is to study chains of model structures arising from cotorsion pairs in extriangulated categories. Starting with a hereditary Hovey triple, we construct further hereditary Hovey triples whose homotopy categories are equivalent under suitable completeness assumptions, thereby refining results due to El Maaouy and Shao-Wang-Zhang. As an application, we consider objects of finite Gorenstein injective dimension with respect to a proper class of $\mathbb{E}$-triangles. Under mild set-theoretic assumptions, we obtain a chain of model structures whose homotopy categories are all triangulated equivalent to a common stable category. This recovers known results for Gorenstein injective modules and yields new examples in the derived category of a ring when the proper class is given by cohomological ghost triangles.
Postpartum hemorrhage (PPH) remains a leading cause of maternal morbidity and mortality worldwide. Oxytocin, though widely recognized for facilitating labor, is also the primary pharmacological intervention for PPH prevention. However, current dosing protocols lack personalization and fail to account for real-time physiological changes during labor. Moreover, standard dynamic treatment regime (DTR) methods cannot accommodate the continuous monitoring and adjustment. To address this, we propose a semiparametric Bayesian method for estimating an optimal treatment regime in real-time, which allows for the existence of latent individual-level variables. Specifically, random real-time DTRs are defined through interventional parameters, optimized by minimizing posterior predictive loss. We further introduce a "physician-in-the-loop" framework to align optimal strategies with clinical expertise. In an application to Consortium on Safe Labor data, the proposed method achieved consistently lower estimated blood loss than other competing methods. The learned policy recommends earlier initiation, rapid dose escalation, and more frequent titration for parturients with higher BMI, alongside increased adjustments relative to cervical dilation and the interval since the last dose change. Simulation studies demonstrate robust performance and computational efficiency, especially when unmeasured patient factors influence outcomes and covariates. Supplementary materials provides a standardized description of the materials available for reproducing the work.
Modern medical research demands specialized causal inference methods evaluating complex continuous-time dynamic treatment regimens using observational data. For instance, obtaining the causal effects of intravenous administration, a continuous process involving dynamic adjustments of the treatment dose, can guide clinicians on drug use. However, the existing causal inference frameworks in longitudinal studies typically assume that time advances in discrete time steps. Therefore, this paper proposes a new methodology to estimate the causal effects of continuous-time dynamic treatments in the presence of unmeasured confounding. Unmeasured confounding is incorporated into estimating continuous-time Marginal Structural Models from a Bayesian perspective. Simulation demonstrates that compared to existing methods, the proposed approach can provide approximately unbiased estimates for target causal parameters across three degrees of confounding. The proposed method is applied to analyze the causal relationship between the intravenous oxytocin administration process and postpartum hemorrhage, leading to meaningful results that may guide clinicians in using oxytocin.
Let $(\mathcal{T}',\mathcal{T},\mathcal{T}'')$ be a recollement of triangulated categories.A complete ideal cotorsion pair in $\mathcal{T}$ induces complete ideal cotorsion pairs in $\mathcal{T}'$ and $\mathcal{T}''$. In addition, if $(\mathcal{I}, \mathcal{I}^\perp )$ and $(\mathcal{J},\mathcal{J}^\perp)$ are two complete ideal cotorsion pairs in a triangulated category, then $(\mathcal{I}\cap\mathcal{J}, \langle\mathcal{I}^\perp,\mathcal{J}^\perp\rangle)$ is also a complete ideal cotorsion pair. By this method, starting from two complete ideal cotorsion pairs in $\mathcal{T}'$ and $\mathcal{T}''$, one can induce a family of complete ideal cotorsion pairs in $\mathcal{T}$.
Given two (hereditary) complete cotorsion pairs $(\mathcal{X}_1,\mathcal{Y}_1)$ and $(\mathcal{X}_2,\mathcal{Y}_2)$ in an exact category with $\mathcal{X}_1\subseteq \mathcal{Y}_2$, we prove that $\left({\rm Smd}\langle \mathcal{X}_1,\mathcal{X}_2 \rangle,\mathcal{Y}_1\cap \mathcal{Y}_2\right)$ is also a (hereditary) complete cotorsion pair, where ${\rm Smd}\langle \mathcal{X}_1,\mathcal{X}_2 \rangle$ is the class of direct summands of extension of $\mathcal{X}_1$ and $\mathcal{X}_2$. As an application, we construct complete cotorsion pairs, such as $(^\perp\mathcal{GI}^{\leqslant n},\mathcal{GI}^{\leqslant n})$, where $\mathcal{GI}^{\leqslant n}$ is the class of modules of Gorenstein injective dimension at most $n$. And we also characterize the left orthogonal class of exact complexes of injective modules and the classes of modules with finite Gorenstein projective, Gorenstein flat, and PGF dimensions.
This paper investigates the conditions under which the centralizer algebra $S_n(c,R)$ of a matrix $ c\in M_n(R)$ is a (separable) Frobenius extension of the base algebra $R$. For an algebra $R$ over an integral domain $\mathbb{k}$, we provide necessary and sufficient conditions for $S_n(c,R)/R$ to be a (separable) Frobenius extension when $c$ is in Jordan canonical form with eigenvalues in $\mathbb{k}$. We extend this analysis to arbitrary matrices over a field and derive conditions for matrix diagonalizability through Frobenius extensions.
Ovarian tumour management has increasingly relied on multidisciplinary tumour board (MDT) deliberation to address treatment complexity and disease heterogeneity. However, most patients worldwide lack access to timely expert consensus, particularly in resource-constrained centres where MDT resources are scarce or unavailable. Here we present OMGs (Ovarian tumour Multidisciplinary intelligent aGent System), a multi-agent AI framework where domain-specific agents deliberate collaboratively to integrate multidisciplinary evidence and generate MDT-style recommendations with transparent rationales. To systematically evaluate MDT recommendation quality, we developed SPEAR (Safety, Personalization, Evidence, Actionability, Robustness) and validated OMGs across diverse clinical scenarios spanning the care continuum. In multicentre re-evaluation, OMGs achieved performance comparable to expert MDT consensus ($4.45 \pm 0.30$ versus $4.53 \pm 0.23$), with higher Evidence scores (4.57 versus 3.92). In prospective multicentre evaluation (59 patients), OMGs demonstrated high concordance with routine MDT decisions. Critically, in paired human-AI studies, OMGs most substantially enhanced clinicians' recommendations in Evidence and Robustness, the dimensions most compromised when multidisciplinary expertise is unavailable. These findings suggest that multi-agent deliberative systems can achieve performance comparable to expert MDT consensus, with potential to expand access to specialized oncology expertise in resource-limited settings.
Twisted magnetic van der Waals (vdW) materials offer a promising route for multiferroic engineering, yet modeling large-scale moiré superlattices remains challenging. Leveraging a newly developed SpinGNN++ framework that effectively handles spin-lattice coupled systems, we develop a comprehensive interatomic machine learning (ML) potential and apply it to twisted bilayer NiI2 (TBN). Structural relaxation introduces moiré-periodic "bumps" that modulate the interlayer spacing by about 0.55~Å and in-plane ionic shifts up to 0.48~Å. Concurrently, our ML potential, which faithfully captures all key spin interactions, produces reliable magnetic configurations; combined with the generalized KNB mechanism, it yields accurate spin-driven polarization. For twist angles 1.89^{\circ} \leq θ\leq 2.45^{\circ}, both mechanisms become prominent, yielding rich polarization textures that combine ionic out-of-plane dipoles with purely electronic in-plane domains. In the rigid (unrelaxed) bilayer, skyrmions are absent; lattice relaxation is essential for generating polar-magnetic topologies. In contrast, near θ \approx 60^{\circ}, stacking-dependent ferroelectric displacements dominate, giving rise to polar meron-antimeron networks. These results reveal cooperative ionic and spin-driven ferroelectricity in TBN, positioning twisted vdW magnets as adaptable platforms for tunable multiferroic devices.
Magnetic excitations are important quantum phenomena in magnetic systems and have been widely studied in individual magnetic atoms and molecules as well as their assembled structures over the past few decades. Using scanning tunneling microscopy/spectroscopy (STM/S) combined with density functional theory (DFT) and the state-of-the-art ab initio wavefunction calculations, we investigated the properties of a novel dual-core Cr2Br6 molecule, which consists of two Cr ions coupled via superexchange through a single near-90° Cr-Br-Cr scissors bond. Under zero magnetic field, we observed a Fano peak with multi-steps through STS. When an external magnetic field is applied, some steps exhibit additional splitting, while others change little. We find that the Cr2Br6, exhibits a spin-degenerate ground state, and the complex peak splitting arises from the coexistence of vibrational and magnetic excitations in the molecule. Our results reveal rich quantum spin behavior in a well-defined two-core magnetic trihalide complex at the atomic scale, offering not only a minimal model for superexchange-coupled multi-spin quantum excitations but also a possible foundational unit for future molecule-based quantum functionalities.
Let $\mathcal{A}$ be a Frobenius category and $ω$ the full subcategory consisting of projective objects. The relations between special precovering (resp., precovering) ideals in $\mathcal{A}$ and special precovering (resp., preenveloping) ideals in the stable category $\mathcal{A}/ω$ are explored. In combination with a result due to Breaz and Modoi, we conclude that every precovering or preenveloping ideal $\mathcal{I}$ in $\mathcal{A}$ with $1_{X}\in{\mathcal{I}}$ for any $X\inω$ is special. As a consequence, it is proved that an ideal cotorsion pair $(\mathcal{I},\mathcal{J})$ in $\mathcal{A}$ is complete if and only if $\mathcal{I}$ is precovering if and only if $\mathcal{J}$ is preenveloping. This leads to an ideal version of the Bongartz-Eklof-Trlifaj Lemma in $\mathcal{A}/ω$, which states that an ideal cotorsion pair in $\mathcal{A}/ω$ generated by a set of morphisms is complete. As another consequence, we provide some partial answers to the question about the completeness of cotorsion pairs posed by Fu, Guil Asensio, Herzog and Torrecillas.
Let $\mathcal{I}$ and $\mathcal{J}$ be object ideals in an exact category $(\mathcal{A}; \mathcal{E})$. It is proved that $(\mathcal{I},\mathcal{J})$ is a perfect ideal cotorsion pair if and only if $({\rm Ob}(\mathcal{I}),{\rm Ob}(\mathcal{J}))$ is a perfect cotorsion pair, where ${\rm Ob}(\mathcal{I})$ and ${\rm Ob}(\mathcal{J})$ is the objects of $\mathcal{I}$ and $\mathcal{J}$, respectively. If in addition $(\mathcal{A}; \mathcal{E})$ has enough projective objects and injective objects, and $\mathcal{J}$ is enveloping, then $(\mathcal{I},\mathcal{J})$ is a complete ideal cotorsion pair if and only if $({\rm Ob}(\mathcal{I}),{\rm Ob}(\mathcal{J}))$ is a complete cotorsion pair. This gives a partial answer to the question posed by Fu, Guil Asensio, Herzog and Torrecillas. Moreover, for any object ideal $\mathcal{I}$ in the category of left $R$-modules, it is proved that $\mathcal{I}$ satisfies Enochs Conjecture if and only if ${\rm Ob}(\mathcal{I})$ satisfies Enochs Conjecture. Applications are given to projective morphisms and ideal cotorsion pairs $(\mathcal{I},\mathcal{J})$ of object ideals under certain conditions.
Type-II multiferroicity, where electric polarization is induced by specific spin patterns, is crucial in fundamental physics and advanced spintronics. However, the spin model and magnetoelectric coupling mechanisms in prototypical type-II multiferroic CuFeO$_2$ and Al-doped CuFeO$_2$ remain unclear. Here, by considering both spin and alloy degrees of freedom, we develop a magnetic cluster expansion method, which considers all symmetry allowed interactions. Applying such method, we not only obtain realistic spin model that can correctly reproduce observations for both CuFeO$_2$ and CuFe$_{1-x}$Al$_x$O$_2$, but also revisit well-known theories of the original spin-current (SC) model and $p$-$d$ hybridization model. Specifically, we find that (i) a previously overlooked biquadratic interaction is critical to reproduce the $\uparrow\uparrow\downarrow\downarrow$ ground state and excited states of CuFeO$_2$; (ii) the combination of absent biquadratic interaction and increased magnetic frustration around Al dopants stabilizes the proper screw state; and (iii) it is the generalized spin-current (GSC) model that can correctly characterize the multiferroicity of CuFeO$_2$. These findings have broader implications for understanding novel magnetoelectric couplings in, e.g., monolayer multiferroic NiI$_2$.
Coordination engineering was employed to optimize the coordination environment of the Zr atom anchored on the porphyrins (PP). Five promising ZrPP-A candidates as electrocatalysts for nitrogen reduction reaction (NRR) were identified through a four-step screening strategy. First-principles calculations were utilized to evaluate the performance of the candidate electrocatalysts for NRR. A comprehensive search for reaction pathways revealed that NRR reactions with these selected catalysts tend to follow a hybrid pathway. It is found that orbital hybridization and charge transfer between Zr and its coordination atoms, as well as between ZrPP-A and the adsorbed N2 ensured the stability and high catalytic activity of these selected ZrPP-A. Zr plays a crucial role in coordinating charge transfer during the NRR process. Simultaneously, the coordinating atoms and the PP moiety jointly provide additional charge transfers to or from the adsorbate. An asymmetric coordination environment results in an asymmetric charge distribution of the substrate, causing the adsorbed polarized N2 molecule oriented toward the asymmetric charge aggregation region. Our work underscores the importance of considering not only the single-atom catalyst itself but also its coordination environment for the rational design of efficient catalysts.
In this paper, we first provide an explicit procedure to glue together hereditary exact model structures for the recollement of exact categories. To that end, we use the notion of cotorsion pairs and we investigate the gluing of complete hereditary cotorsion pairs along the recollement of exact categories. Moreover, we study liftings of recollements of hereditary exact model structures to recollements of their associated homotopy categories. This leads to a new method to produce recollements of triangulated categories. Applications are given to contraderived categories, projective stable derived categories and stable categories of Gorenstein injective modules over an upper triangular matrix ring.
Let $\mathcal{C}$ be a triangulated category. We first introduce the notion of balanced pairs in $\mathcal{C}$, and then establish the bijective correspondence between balanced pairs and proper classes $ξ$ with enough $ξ$-projectives and enough $ξ$-injectives. Assume that $ξ:=ξ_{\mathcal{X}}=ξ^{\mathcal{Y}}$ is the proper class induced by a balanced pair $(\mathcal{X},\mathcal{Y})$. We prove that $(\mathcal{C}, \mathbb{E}_ξ, \mathfrak{s}_ξ)$ is an extriangulated category. Moreover, it is proved that $(\mathcal{C}, \mathbb{E}_ξ, \mathfrak{s}_ξ)$ is a triangulated category if and only if $\mathcal{X}=\mathcal{Y}=0$; and that $(\mathcal{C}, \mathbb{E}_ξ, \mathfrak{s}_ξ)$ is an exact category if and only if $\mathcal{X}=\mathcal{Y}=\mathcal{C}$. As an application, we produce a large variety of examples of extriangulated categories which are neither exact nor triangulated.