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Qi Zhou

Publications and source records attributed to Qi Zhou.

At least 19 recordsLinked to original sources
arXiv2026

Almost Periodic Solutions of The Cubic Defocusing Nonlinear Schrödinger Equation

This paper addresses the Cauchy problem for the cubic defocusing nonlinear Schrödinger equation (NLS) with almost periodic initial data. We prove that for small analytic quasiperiodic initial data satisfying Diophantine frequency conditions, the Cauchy problem admits a solution that is almost periodic in both space and time, and that this solution is unique among solutions locally bounded in a suitable sense. The analysis combines direct and inverse spectral theory. In the inverse spectral theory part, we prove existence, almost periodicity, and uniqueness for solutions with initial data whose associated Dirac operator has purely a.c.\ spectrum that is not too thin. This resolves novel challenges presented by the NLS hierarchy, such as an additional degree of freedom and an additional commuting flow. In the direct spectral theory part, for Dirac operators with small analytic quasiperiodic potentials with Diophantine frequency conditions, we prove pure a.c.\ spectrum, exponentially decaying spectral gaps, and spectral thickness conditions (homogeneity and Craig-type conditions).

math.AP↗
arXiv2026

Precision and resource scaling of real-time flux distortion compensation for superconducting quantum control

Real-time waveform generation supports dynamic quantum circuits without pre-storing complete waveforms for every execution path. However, long-lived distortions in flux-control lines degrade gate fidelity, requiring compensation to account for the actual pulse history. A frequency-domain inversion and time-domain fitting method is proposed for resource-efficient real-time flux distortion compensation. The method fits the reconstructed compensation impulse response with a compact hybrid infinite impulse response (IIR) and finite impulse response (FIR) filter. Look-ahead parallelization enables this filter to process synthesized waveforms at 1.2GSa/s on a field-programmable gate array (FPGA). Two-qubit cross-entropy benchmarking shows that real-time IIR filtering achieves a median controlled-Z Pauli fidelity close to the software-reference value of 99.57%. Numerical analysis and FPGA synthesis indicate approximately logarithmic growth in hardware resource use with compensation timescale. Extending compensation from microsecond to hundred-microsecond timescales increases look-up table (LUT) and digital signal processing (DSP) resource use by only about 14% and 4%, respectively, while maintaining a relative arithmetic error below $10^{-4}$. This work provides a scalable hardware foundation for high-fidelity flux control in dynamic superconducting quantum circuits.

quant-ph↗
arXiv2026

Towards Synergistic Teacher-AI Interactions with Generative Artificial Intelligence

Generative artificial intelligence (GenAI) is increasingly used in education, posing significant challenges for teachers adapting to these changes. GenAI offers unprecedented opportunities for accessibility, scalability and productivity in educational tasks. However, the automation of teaching tasks through GenAI raises concerns about reduced teacher agency, potential cognitive atrophy, and the broader deprofessionalisation of teaching. Drawing findings from prior literature on AI in Education, and refining through a recent systematic literature review, this chapter presents a conceptualisation of five levels of teacher-AI teaming: transactional, situational, operational, praxical and synergistic teaming. The framework aims to capture the nuanced dynamics of teacher-AI interactions, particularly with GenAI, that may lead to the replacement, complementarity, or augmentation of teachers' competences and professional practice. GenAI technological affordances required in supporting teaming, along with empirical studies, are discussed. Drawing on empirical observations, we outline a future vision that moves beyond individual teacher agency toward collaborative decision-making between teachers and AI, in which both agents engage in negotiation, constructive challenge, and co-reasoning that enhance each other's capabilities and enable outcomes neither could realise independently. Further discussion of socio-technical factors beyond teacher-AI teaming is also included to streamline the synergy of teachers and AI in education ethically and practically.

cs.CY↗
arXiv2026

Equidistribution of saddle periodic points for Hénon-like maps

We prove that under a natural assumption on the dynamical degrees, the saddle periodic points of a Hénon-like map in any dimension equidistribute with respect to the equilibrium measure. Our work is a generalization of the results of Bedford-Lyubich-Smillie, Dujardin, and Dinh-Sibony along with improvements of their techniques. We also investigate some fine properties of Green currents associated with the map.

math.DS↗
arXiv2026

Monotonicity, global symplectification and the stability of Dry Ten Martini Problem

We prove that, for every irrational frequency and every analytic Type I potential, each supercritical spectral energy satisfying the gap-labelling condition is an endpoint of an open spectral gap. This establishes the conjecture of Ge--Jitomirskaya--You \cite{GJY,You} in the supercritical regime. Consequently, the ``all gaps open'' property of the supercritical almost Mathieu operator persists under sufficiently small analytic perturbations. The main ingredient is a global symplectification of the center bundle that preserves quantitative monotonicity. This allows us to study gap opening through the center dynamics of the dual long-range operator, which has no natural Schrödinger form. We first establish the result for trigonometric polynomial potentials and then pass to general analytic potentials by controlling the dependence on the truncation dimension. The proof combines a discrete Hellmann--Feynman identity, dimension-free Aubry duality in weighted analytic norms, and a quantitative cone argument based on pre-monotonicity. These estimates ensure that the gaps survive in the analytic limit. Our results establish analytic stability of the Dry Ten Martini Problem in the supercritical regime and give a partial answer to a question of M. Shamis on the persistence of periodic spectral gaps.

math.DS↗
arXiv2026

Canonical analytic realizations of hyperbolic determinantal processes

Krishnapur asked whether the invariant hyperbolic determinantal point processes on the disk admit a random analytic zero-set interpretation at noninteger parameters. We construct such a realization for every positive real parameter as the full compact-open limit in distribution of normalized finite Blaschke products. The zeros determine the modulus and normalized analytic shape, leaving one independent uniform phase. We prove exact Möbius covariance and classify all realizations with this covariance and square-integrable logarithmic modulus at the origin: they are precisely independent positive random multiples of the canonical function. Within this covariant class, matching the canonical logarithmic mean and variance uniquely determines the canonical function law. The family is weakly continuous in the parameter and agrees at positive integers with determinants of matrix-valued Gaussian power series. An explicit Barnes $G$-function Mellin transform determines the basepoint normalization.

math.PR↗
arXiv2026

The Local Embedding Problem for Hardy Spaces of Dirichlet Series

We solve the local embedding problem for Hardy spaces of Dirichlet series, which is a dimension-free trace problem asking whether the global $\mathscr{H}^p$-norm controls local $L^p$-mass on the critical line $\operatorname{Re}s=1/2$. More precisely, for every $2<p<\infty$, there exists a constant $C_p<\infty$ such that every Dirichlet polynomial $P$ satisfies $$ \sup_{θ\in\mathbb{R}}\int_θ^{θ+1}\left|P\left(\frac12+it\right)\right|^p\,\mathrm{d}t\le C_p\left\lVert P\right\rVert_{\mathscr{H}^p}^{p}, $$ with $C_p$ independent of the number and choice of prime variables on which $P$ depends. Before the present work, the embedding was known at $p=2$ and, by taking integer powers, at the even exponents $p=2k$; it had been conjectured that these exhaust the finite positive cases above $2$. Together with the known failure for $0<p<2$, our theorem gives the sharp finite-exponent classification: the local embedding property holds exactly for $p\ge2$. Thus, the true threshold is $p=2$, rather than even integrality. The proof passes to the dual exponent $q=p/(p-1)\in(1,2)$, where an exact frequency decomposition isolates a single resonant Euler-product term. A covariance-preserving replacement of the shared prime factors reduces the resulting fractional-moment estimate to a log-correlated Gaussian field, and a critical branching-random-walk bound supplies the required multiscale decay. A finite-cyclic square-function estimate assembles the resonant scales, and Hardy-quotient duality converts the resulting vector-valued bound into the critical-line trace. For $1\le p<\infty$, known equivalences give the same sharp threshold in several classical problems, including the conformally invariant half-plane embedding, the reverse local Carleson-measure transfer, and boundedness of all characteristic-zero Gordon--Hedenmalm composition operators.

math.FA↗
arXiv2026

Attractors and Late Time Asymptotics in a Generalized Relativistic Second Order Spin Hydrodynamics

We investigate the attractor of spin density in relativistic spin hydrodynamics using Zubarev's non-equilibrium statistical operator formalism in the spin probe limit. We derive the (0+1)D Bjorken flow equations and the associated attractor equation while retaining second order gradient corrections in the relevant relaxation constitutive equations including couplings associated with nonlinear response and nonlocal memory effects. We analyze the early time fixed point structure and analytically determine the early time attractor solution, thereby clarifying branch selection and the role of different dynamical corrections. We find that source-like driving terms modify the leading correction to the attractor solution without changing the fixed point structure, whereas self feedback terms involving the rotational stress tensor modify the dominant balance and modify the early time fixed point structure. We further analyze the late time asymptotics in the conformal limit and show that the newly added terms modify the algebraic prefactor and logarithmic phase shift, while leaving the leading late time decay unchanged. These results provide a unified picture of early time attractor and late time asymptotics in the conformal limit.

hep-ph↗
arXiv2026

Spectral bipartiteness in generalized odd graphs of diameter three

For a graph $G$ of order $n$, put $σ(G)=(λ_1(G)+λ_n(G))/n$. We determine the first three largest values of this invariant among nonbipartite distance-regular graphs of diameter three and odd girth at least seven. The unique maximizer is the folded $7$-cube, with value $1/32$; the unique second maximizer is the Odd graph $O_4$, with value $1/35$; and the unique third maximizer is $C_7$, with value $2(1-\cos(π/7))/7$. More precisely, every other graph in the class satisfies $σ(G)<1/36$. This answers Problem~11 of Abiad, Taranchuk and van Veluw in \emph{Electronic Journal of Combinatorics} 33(2) (2026), P2.31. The proof combines established local multiplicity and odd-moment bounds: the condition $σ(G)\geq1/36$ forces the valency to be at most $182$. An exhaustive certificate using only integer and rational arithmetic then leaves three intersection arrays. The complete certificate is publicly available, and neither a classification of generalized odd graphs nor the $Q$-polynomial property is assumed. The odd-girth theorem gives the same extremal conclusions for connected $\{C_3,C_5\}$-free graphs with at most four distinct adjacency eigenvalues, without assuming regularity.

math.CO↗
arXiv2026

A Functional Central Limit Theorem for Window Counts of Hardy--Szegő Zeros

The Hardy--Szegő zero process, investigated in the disk by Peres and Virág through the independent identically distributed Gaussian analytic function, is a canonical conformally invariant determinantal point process. This paper studies its upper half-plane realization. Although conformally equivalent to the disk model, this realization has its own natural geometry: real-translation invariance turns the process into a stationary object along the boundary and makes long horizontal windows the natural observables. For every admissible height window, we prove a Donsker-type functional central limit theorem for the centered zero counts in expanding horizontal windows, with an explicit intensity and variance depending on the height window. The proof is based on factorial cumulants and Brillinger mixing. The main technical input is a family of all-order integrability estimates for reduced cumulant densities, obtained by exploiting the determinantal cycle structure before integrating over the height variables. As further consequences, we derive an explicit covariance density, an asymptotic variance formula, and a macroscopic Gaussian white-noise limit for linear statistics.

math.PR↗
arXiv2026

Relocation of compact sets in $\mathbb{R}^n$ by diffeomorphisms and linear separability of datasets in $\mathbb{R}^n$

Relocation of compact sets in an $n$-dimensional manifold by self-diffeomorphism is of its own interest as well as significant potential applications to data classification in data science. This paper presents a theory for relocating a finite number of compact sets in $\mathbb{R}^n$ to be relocated to arbitrary target domains in $\mathbb{R}^n$ by diffeomorphisms of $\mathbb{R}^n$. Furthermore, we prove that for any such collection, there exists a differentiable embedding into $\mathbb{R}^{n+1}$ such that their images become linearly separable. As applications of the established theory, we show that a finite number of compact datasets in $\mathbb{R}^n$ can be made linearly separable by width-$n$ deep neural networks (DNNs) with Leaky-ReLU, ELU, or SELU activation functions, under a mild condition. In addition, we show that any finite number of mutually disjoint compact datasets in $\mathbb{R}^n$ can be made linearly separable in $\mathbb{R}^{n+1}$ by a width-$(n+1)$ DNN.

cs.LG↗
arXiv2026

Power convexity of the torsion function on horo-convex domains in hyperbolic space

In this paper, we study the torsion problem on bounded, smooth, strictly horo-convex domains in hyperbolic space. We prove that if the diameter of the domain is sufficiently small, then $-\sqrt{u}$ is strictly convex, where $u$ denotes the torsion function. The main ingredients of our proof are the constant rank theorem, a boundary convexity estimate, and a deformation argument for the domain. We also show that the exponent $1/2$ is optimal, even among strictly horo-convex domains of arbitrarily small diameter.

math.AP↗
arXiv2026

RBMD 2.0: Random batch molecular dynamics package for large-scale simulations on multi-GPU architectures

Large-scale molecular dynamics simulations of particle systems on multi-GPU architectures are often constrained by the computational and communication costs of nonbonded force evaluation. We present RBMD 2.0, a major new release of the random batch molecular dynamics package designed for cross-node multi-GPU simulations of large-scale systems. It combines the improved random batch Ewald method with three-dimensional domain decomposition and ghost-particle communication to accelerate multi-GPU nonbonded force evaluation, while the DTK CUDA framework facilitates portability across heterogeneous accelerator architectures. Numerical experiments on multiple benchmark systems demonstrate both the accuracy and efficiency of simulations with RBMD 2.0. For simulations involving up to hundreds of millions of particles across multiple accelerator devices, one achieves speedups ranging from severalfold to approximately two orders of magnitude in nonbonded force evaluation while exhibiting over $97.5\%$ weak-scaling behavior. These results demonstrate the promising nature of RBMD 2.0 as a computational engine for future exascale molecular dynamics simulations.

physics.comp-ph↗
arXiv2026

Projective Origin of the Spin Hydrodynamic Attractor and Its Resurgent repeller

We investigate the projective and resurgent structure of a spin hydrodynamic attractor in Bjorken expansion. We show that the nonlinear spin attractor family is determined by the projective classes of the two dimensional linear solution space, with the attractor and repeller corresponding to two distinguished projective directions and the linear modes ratio generating the full one-parameter transseries tower. We identify the attractor and repeller as complete global solution branches associated with the two distinguished projective directions of the underlying linear solution space. Using the projective transseries structure, we show analytically that the data of repeller are encoded in the Borel-Stokes structure of the attractor expansion. These results provide an explicit analytic realization of resurgence relations that are often extracted through high order expansions and numerical Borel analysis, and yield a unified description of the attractor, the repeller, and their Borel-Stokes connection in minimal causal spin hydrodynamics.

nucl-th↗
arXiv2026

Two Regularity Problems on Analytic Tent Spaces

We study two regularity problems on Hardy-type analytic tent spaces $\mathcal{AT}^p_{q,α}$ on the unit disk: fractional integration and randomization of Taylor coefficients. For fractional integration, we characterize completely the boundedness and compactness of the Hadamard, Flett, and Riemann--Liouville operators between analytic tent spaces, and obtain parallel results for analytic Triebel--Lizorkin spaces. In particular, the case $t=0$ yields a complete solution to the corresponding embedding problem for analytic tent spaces. For randomization, we characterize completely when the random Taylor series $\mathcal{R}f$ belongs almost surely to an analytic tent space whenever $f\in \mathcal{AT}^p_{q,α}$, and we also obtain the Triebel--Lizorkin counterpart. As part of the proof, we identify the random symbol space associated with $\mathcal{AT}^p_{q,α}$ and solve the embedding problem from analytic tent spaces into mixed norm spaces. These results extend classical theorems of Hardy--Littlewood and Littlewood, as well as their later analogues for Bergman and mixed norm spaces.

math.FA↗
arXiv2026

Minimum Block Width for Universal Approximation by Residual Neural Networks with Inner Width One

In this paper, we study the universal approximation property of residual neural networks. For input and output dimensions $d_x$ and $d_y$, and LeakyReLU, ReLU, ReLU-like activation functions, the upper and lower bounds of the minimum block width are established. To achieve $L^p$ approximation $(1\leq p <+\infty)$ on any compact set, we show that the exact minimum block width is $\max\{d_x,d_y\}$ when each residual branch has inner width 1. Furthermore, we show that residual neural networks with block width $\min\{d_x+d_y, \max\{2d_x+1,d_y\}\}$ can achieve uniform approximation on any compact set under the constraint that each residual branch has inner width 1. Besides, for any activation function family, we prove that there exist functions that cannot be approximated by residual neural networks with block width less than $\max\{d_x, d_y\}$, both in the $L^p$ sense and the uniform sense, regardless of inner width. Consequently, for LeakyReLU, ReLU, ReLU-like activation functions and $d_y\geq 2d_x+1$, the exact minimum block width for uniform approximation is $d_y$ when each residual branch has inner width 1.

cs.LG↗
arXiv2026

OpsLLM: Construction of Large Language Model for Software Operations with Multi-stage Learning

In the field of software operations, Large Language Models (LLMs) have attracted increasing attention. However, existing research has not yet achieved efficient and effective endto-end intelligent operations due to low-quality data, fragmented knowledge and insufficient learning. To explore the potential of LLMs in software operations, we propose OpsLLM, a domainspecific LLM that supports both knowledge-based question answering (QA) and root cause analysis (RCA). Moreover, we disclose the detailed workflow for building LLMs specifically in the software operations domain. First, a Human-in-the-Loop mechanism is introduced to curate high-quality data from a large collection of operational data and construct a fine-tuning dataset. Then, based on the data, supervised fine-tuning is conducted to achieve a base model. Furthermore, we introduce a domain process reward model (DPRM) during the reinforcement learning stage to optimize the accuracy and reliability of the fine-tuned model on RCA tasks. Experimental results on the tasks with diverse difficulties demonstrate that OpsLLMs effectively learns and aligns with the operational domain knowledge infused, outperforming existing open-source and closed-source LLMs in accuracy with improvements of 0.2%~11.9% on QA tasks and 8.5%~70.3% on RCA tasks, while exhibiting strong transferability. Moreover, we will open-source three versions of OpsLLM with 7B, 14B and 32B parameters, along with a 15K fine-tuning dataset.

cs.LG↗
arXiv2026

The Ultimate Ishii-Pastur Theorem for Whole-Line Ergodic Block Jacobi Operators

We establish an ultimate Ishii-Pastur theorem for whole-line ergodic block Jacobi operators. We prove that, for almost every realization, the restriction of a maximal spectral measure to the region where the smallest nonnegative Lyapunov exponent is strictly positive is carried by a Borel set of zero capacity. In the scalar case, this settles the whole-line problem formulated by Damanik and Fillman \cite[Problem~4.7.18]{Damanik-Fillman-book}.

math.SP↗