arXiv subjects

Rui Xiong

Publications and source records attributed to Rui Xiong.

At least 19 recordsLinked to original sources

arXiv2026

Permutation Representations on Cohomology of Toric Varieties

Let $G$ be a finite group acting properly by lattice automorphisms on a complete simplicial fan $\Sigma$. An open question due to Stanley asked whether the (ungraded) representation carried by the cohomology $H^*(X_{\Sigma})$ of the associated toric variety $X_{\Sigma}$ is isomorphic to a permutation representation of $G$. We prove that Stanley's question has an affirmative answer for all smooth projective toric varieties without the properness assumption on the action. The proof is inspired by toric mirror symmetry.

math.AG↗

arXiv2026

Non-vanishing of Single, Double, and Triple Schubert Structure Constants

The Schubert vanishing problem asks whether the single Schubert coefficients $c_{u,v}^w$ are zero. In this paper, we consider the non-vanishing problems of double Schubert coefficients $c_{u,v}^w(t)$ and triple Schubert coefficients $c_{u,v}^w(t;y)$. We show that the non-vanishing of $c_{u,v}^w(t;y)$ is completely determined by the non-vanishing of single Schubert coefficients. As a byproduct, we obtain the saturation property of the triple Littlewood--Richardson coefficients $c_{\lambda,\mu}^\nu(t;y)$. Moreover, we pose a conjecture asserting that the non-vanishing of $c_{u,v}^w(t)$ is also determined by the non-vanishing of single or triple Schubert coefficients. We prove a one-side inclusion of the conjecture. For the reverse inclusion, we show that the conjecture holds for the following three cases: the Pieri case, the separated descents case, and the inverse Grassmannian case.

math.CO↗

arXiv2026

Quantized Coulomb Branches of Separated Cotangent Type and Orthosymplectic Quivers

We propose a definition of the quantized Coulomb branches of separated cotangent type, and prove that the corresponding classical construction recovers the non-cotangent Coulomb branch. We also obtain a formula for quasi-minuscule monopole operators in arbitrary cotangent type. Applying these results, we compute the monopole operators for orthosymplectic quivers and construct a homomorphism from the shifted twisted Yangian of split ADE type to the corresponding quantized Coulomb branch algebra.

math.RT↗

arXiv2026

A solution to Butler's positivity conjecture

Let $\lambda, \mu, \nu$ be distinct partitions such that $\lambda, \mu\subset \nu$ and $|\nu/\lambda|=|\nu/\mu|=1$. We prove Butler's positivity conjecture posed in 1994: the expansion of the Macdonald intersection polynomial \[ \frac{T_\lambda\widetilde{H}_\mu(X;q,t)-T_\mu\widetilde{H}_\lambda(X;q,t)}{T_\lambda-T_\mu} \] in terms of the Schur function basis has coefficients in $\mathbb{Z}_{\geq 0}[q,t]$.

math.CO↗

arXiv2026

On weight modules over truncated shifted iYangians

Truncated shifted iYangians are a family of algebras expected to quantize certain components of affine Grassmannian islices. We introduce orientifold KLRW (oKLRW) algebras associated with quivers with involution and establish their faithful polynomial representations and diagrammatic bases. We also define KLR iYangians using double reflective KLR diagrams and construct diagrammatic realizations of the iGKLO homomorphisms. For integral parameters, we introduce interval oKLRW algebras and prove an equivalence between integral weight modules over truncated shifted iYangians and nilpotent modules over the corresponding interval oKLRW algebras.

math.RT↗

arXiv2026

Anisotropic Spin Polarization and magnetic spin hall effect in Ferromagnets

Spin-dependent transport in ferromagnets underpins the development of high-density spintronic memories. Spin-dependent transport in strong spin-orbit-coupled ferromagnets exhibits a significant anisotropy. Both the overall spin polarization during charge transport and the magnetic spin Hall conductivity are found to exhibit pronounced anisotropy when the magnetization is tilted away from the crystallographic easy axis or when the electric field is rotated relative to the crystal axes. These anisotropic responses originate primarily from spin-orbit coupling, which is identified as the key driver of the large anisotropy observed in ferromagnet. Furthermore, strain tunability of the magnetic spin Hall anisotropy is demonstrated, with tensile strain progressively enhancing the oscillatory amplitude of the spin Hall conductivity. These findings establish strong spin-orbit-coupled ferromagnets as a platform for anisotropic spin-current generation and field-free spintronic devices that exploit intrinsic material anisotropy for improved performance and energy efficiency.

cond-mat.mes-hall↗

arXiv2026

Equivariant Schubert Calculus for Inverse Grassmannian Permutations

We give a Graham-positive expansion for the product of two double Schubert polynomials indexed by two inverse Grassmannian permutations. Surprisingly, the nonzero structure constants are double Schubert polynomials in two disjoint sets of equivariant variables. We also give a positive expansion for the product of two single Schubert polynomials indexed by a $321$-avoiding permutation (e.g., a Grassmannian permutation) and an inverse Grassmannian permutation. Unexpectedly, the nonzero structure constants are Edelman--Greene coefficients.

math.CO↗

arXiv2026

BCIJelly: An integrated ecosystem for brain-computer interface research

Brain-computer interface (BCI) research relies on multistage computational pipelines, yet progress remains constrained by fragmented data formats, heterogeneous decoder implementations and hardware-specific deployment toolchains, and researchers lack an integrated workflow. Here, we fill this gap with BCIJelly, a unified computational ecosystem that integrates 18 curated BCI datasets, 15 benchmark decoders and an algorithmic library of 80 reusable modules, an automated architecture search (AAS) procedure, and hardware-aware deployment through the toChip pipeline within a single Python framework. AAS constructs task-specific decoders without manual architecture design. It is further extended into a closed-loop mode guided by a large language model (LLM), which uses task specifications, module descriptions and search history to support multitask and cross-species decoding. The toChip pipeline compiles trained decoders for execution on neuromorphic chips, enabling energy-efficient deployment for BCI systems. An accompanying visualization software provides a graphical interface to the full workflow, making BCIJelly accessible without programming. We validate BCIJelly across five BCI paradigms (motor, visual, speech, emotion and auditory) with recordings from humans, macaques and mice, and single-task, multitask and cross-species decoding settings. BCIJelly establishes a unified and extensible infrastructure that bridges decoder development and hardware-aware deployment for BCI research.

cs.HC↗

arXiv2026

UniBCI: Towards a Unified Pretrained Model for Invasive Brain-Computer Interfaces

Modeling invasive neural spike data is fundamental to advancing high-performance brain-computer interfaces (BCIs). However, existing approaches face critical challenges, including limited-scale heterogeneous data, cross-domain distribution shift, and the intrinsic spatiotemporal complexity of invasive neural signals. In this work, we propose UniBCI, a unified pretrained model for invasive Brain-Computer Interfaces. The model integrates three key components: (1) a context-conditioned spatio-temporal tokenization (CST) scheme that embeds neural signals together with metadata into a shared representation space; (2) a hierarchical Interval-Area Attention (IAA) mechanism that captures patterns of spike dynamics in slots via linear attention and locality dependencies via sliding-window attention; and (3) a scalable self-supervised masked signals reconstruction objective for learning generalizable neural representations from large-scale unlabeled data. We construct a pretraining corpus spanning multiple species, subjects, brain regions, and behavioral experiment paradigms. These heterogeneous recordings are standardize via our proposed unified normalization and tokenization. Comprehensive experiments demonstrate that UniBCI achieves SOTA performance across diverse downstream tasks while improving generalization. Moreover, the model achieves a strong balance between accuracy and efficiency, with fewer trainable parameters and lower inference latency. These results suggest that UniBCI provides a practical step toward general-purpose neural foundation models, enabling robust, scalable, and transferable representation learning for invasive neural data. The code for this paper is available at: https://anonymous.4open.science/r/UniBCI-C805.

cs.NE↗

arXiv2026

Nearly Complete Charge--Spin Conversion via Strain-Eliminated Fermi Pockets in $d$-Wave Altermagnets

Ideal $d$-wave altermagnets with nearly orthogonal flat Fermi surfaces enable complete spin-channel separation and 100% theoretical charge--spin conversion efficiency (CSE). The metallic altermagnet $\mathrm{KV_2Se_2O}$ exemplifies this, but realistic samples host residual elliptical Fermi pockets that enhance charge conductivity while suppressing spin conductivity, drastically reducing CSE. Here we show that in-plane equibiaxial tensile strain systematically eliminates these parasitic pockets, restoring the flat-band geometry. Our first-principles calculations reveal that CSE increases monotonically with strain, reaching a record $\sim$96% at 4% strain. An effective tight-binding model confirms that pocket suppression, governed by reduced next-nearest-neighbor hoppings, is the dominant mechanism. We further identify an unconventional out-of-plane spin current component with CSE $\sim$55% at optimal orientations, enabling field-free perpendicular magnetization switching. Moreover, the same strain-driven removal of parasitic pockets yields giant TMR enhancement in $\mathrm{KV_2Se_2O}$-based magnetic tunnel junctions, from $10^{5}%$ to $10^{9}%$, and the giant TMR persists over a wide energy window near the Fermi level. These findings establish strain engineering as a clean, widely applicable strategy to maximize CSE and magnetoresistance in $d$-wave altermagnets, and provide predictive descriptors for screening high-efficiency spintronic materials.

cond-mat.mtrl-sci↗

arXiv2026

Motivic Chern Classes of Open Projected Richardson Varieties and of Affine Schubert Cells

The open projected Richardson varieties are images of the open Richardson varieties of the complete flag variety under the canonical projection to the partial flag variety. Our main result compares the Segre motivic Chern (SMC) classes of the open projected Richardson varieties with those of the affine Schubert cells by pushing or pulling these classes to the affine Grassmannian. The main method is the recursive relation determined by the Demazure--Lusztig operators. As another application of this recursive relation, we relate the localization of the SMC classes to the twisted Kazhdan--Lusztig R-polynomials. In the case of Grassmannians, the open projected Richardson varieties are known as the open positroid varieties. We give a combinatorial formula for the SMC classes of these varieties.

math.AG↗

arXiv2025

Enhancing Circuit Fidelity in Transmon Qubit Rings via Operation Duration Tuning under Strong Connectivity Noise

Superconducting transmon qubits are a promising platform for quantum computation, yet they face significant fidelity degradation due to connectivity noise, particularly in the intermediate coupling regime where noise levels are substantial. While prior works suggest that high fidelity requires operating in regimes with strongly suppressed noise, maintaining such conditions under practical experimental constraints remains challenging. To address this, we investigate quantum gate operations in fully connected transmon rings, examining both SWAP and general circuits. Our study reveals that fidelity can be significantly enhanced by tuning gate operation durations, with local maxima emerging even under strong noise conditions. These fidelity enhancements occur consistently across different qubit numbers and operation types, and for specific initial states -- particularly those with favorable symmetry or entanglement properties -- the achieved fidelities approach quantum error correction thresholds. Furthermore, we develop a supervised machine learning model that accurately predicts the optimal operation durations for new devices, enabling efficient optimization without extensive experimental simulations. These results provide a pathway toward robust quantum circuit design in noisy experimental environments.

quant-ph↗

arXiv2025

Bumpless Pipe Dream Fragments -- Equivariant Geometry of Clans

In this paper, we establish a new geometric setting for bumpless pipe dreams and double Schubert polynomials. Building on the notion of bumpless pipe dream fragments, we define clan polynomials as their weight generating functions. It turns out that clan polynomials arise naturally in the equivariant geometry of ($GL_p\times GL_q$)-orbits over the flag variety $Fl_{p+q}$ parametrized by $(p,q)$-clans. Furthermore, we show that the coefficients in the equivariant Schubert expansion of the fundamental classes of ($GL_p\times GL_q$)-orbit closures are exactly clan polynomials, which resolves an open problem posed by Wyser and Yong.

math.CO↗

arXiv2025

High-Efficiency Nonrelativistic Charge-Spin Conversion in X-Type Antiferromagnets

Antiferromagnetic materials with spin splitting have attracted considerable attention for their symmetry-enabled anisotropic spin textures that sustain a zero net magnetization, thereby facilitating efficient spin-current generation. In this work, the highly efficient generation of nonrelativistic spin currents is demonstrated to be facilitated by the distinctive Fermi surface geometry of X-type collinear antiferromagnets. As a prototype conducting X-type antiferromagnet, the Fermi surface of $\beta-\mathrm{Fe_2PO_5}$ exhibits a distinct $d$-wave altermagnetic characteristic, which compresses into a nearly X-shaped configuration. This results in highly efficient spin currents, achieving a charge-spin conversion efficiency of up to 90\%. Moreover, the spin current polarization is controlled by the orientation of the N\'eel vector. When the N\'eel vector tilts to the out-of-plane direction, an in-plane injected charge current can generate a special spin current component with both spin polarization and propagation along the out-of-plane direction, whose charge-spin conversion efficiency substantially exceeds that of known ferromagnets, altermagnets, noncollinear antiferromagnets, and low-symmetry materials. The highly efficient charge-spin conversion in X-type antiferromagnets provides a novel and highly effective spin source system for the development of low-power spintronic devices.

cond-mat.mtrl-sci↗

arXiv2025

Quivers with Involutions and Shifted Twisted Yangians via Coulomb Branches

To a quiver with involution, we study the Coulomb branch of the 3d $\mathcal{N} = 4$ involution-fixed part of the quiver gauge theory. We show that there is an algebra homomorphism from the corresponding shifted twisted Yangian to the quantized Coulomb branch algebra. This gives a new instance of 3D mirror symmetries.

math.RT↗

arXiv2025

Combinatorial Aspects of Elliptic Schubert Calculus

The main goal of this paper is to extend two fundamental combinatorial results in Schubert calculus on flag manifolds from equivariant cohomology and $K$-theory to equivariant elliptic cohomology. The foundations of elliptic Schubert calculus were laid in a few relatively recent papers by Rim\'anyi, Weber, and Kumar. They include the recursive construction of elliptic Schubert classes via generalizations of the cohomology and $K$-theory push-pull operators and the study of the corresponding Demazure algebra. We derive a Billey-type formula for the localization of elliptic Schubert classes (for partial flag manifolds of arbitrary type) and a pipe dream model for their polynomial representatives in the case of type $A$ flag manifolds. The latter extends the pipe dream model for double Schubert and Grothendieck polynomials. We also study the degeneration of elliptic Schubert classes to $K$-theory, which recovers the corresponding classical formulas.

math.CO↗

arXiv2025

Quantum Schubert calculus for smooth Schubert divisors of $F\ell_n$

We propose to study the quantum Schubert calculus for Schubert varieties, and investigate the smooth Schubert divisors X of the complete flag variety Fl_n. We provide a Borel-type ring presentation of the quantum cohomology of X. We derive the quantum Chevalley formula for X by geometric arguments. We also show that the quantum Schubert polynomials for X are the same as that for Fl_n introduced by Fomin, Gelfand and Postnikov.

math.AG↗

arXiv2025

A-D-E diagrams, Hodge--Tate hyperplane sections and semisimple quantum cohomology

It is known that the semisimplicity of quantum cohomology implies the vanishing of off-diagonal Hodge numbers (Hodge--Tateness). We investigate which hyperplane sections of homogeneous varieties possess either of the two properties. We provide a new efficient criterion for non-semisimplicity of the small quantum cohomology ring of Fano manifolds that depends only on the Fano index and Betti numbers. We construct a bijection between Dynkin diagrams of types A, D or E, and complex Grassmannians with Hodge-Tate smooth hyperplane sections. By applying our criteria and using monodromy action, we completely characterize the semisimplicity of the small quantum cohomology of smooth hyperplane sections in the case of complex Grassmannians, and verify a conjecture of Benedetti and Perrin in the case of (co)adjoint Grassmannians.

math.AG↗