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Ruofan Li

Publications and source records attributed to Ruofan Li.

17 recordsLinked to original sources
arXiv2026

Dimension drop for intersections of Cantor sets

Let $E\subset \mathbb{R}$ be a self-similar set generated by a homogeneous iterated function system $\Phi$ with contraction ratio $\rho\in (0,1)$. Assume that $\Phi$ satisfies the open set condition and $\dim_{\rm H}E<1$. Let $f$ be a $C^1$-diffeomorphism on $\mathbb{R}$. We prove that if $\log|f'(x)|/\log\rho\not\in\mathbb{Q}$ for every $x\in E\cap f^{-1}(E)$, then the upper Minkowski dimension of $f(E)\cap E$ is strictly less than the Hausdorff dimension of $E$. We also establish a quantitative dimension drop result when $E$ is a missing-digit set and $f$ is an affine map with rational slope satisfying a certain arithmetic condition. Based on these results and a result of Shmerkin [Ann. of Math., 2019], we obtain characterizations of $\gamma$ in various contexts such that $\overline{\dim}_{\rm M}\left((\gamma E+\alpha)\cap E\right)<\dim_{\rm H}E$ for every $\alpha\in\mathbb{R}$.

math.CA↗
arXiv2026

Non-Wieferich property of prime ideals and a conjecture of Erd\"os

Let $K$ be a number field with ring of integers $\mathcal{O}$ and $\alpha\in\mathcal{O}$. For any prime ideal $\mathfrak{p}$ of $\mathcal{O}$, we obtain its higher $\alpha$-Wieferich property, which implies a nonexistence theorem for higher Wieferich unramified prime ideals. If $\beta\in\mathcal{O}$ is relatively prime to $\alpha$ and all prime ideal factors of $(\beta)$ are unramified and have residue degree $1$, we apply our higher $\alpha$-Wieferich property to establish the asymptotic equidistribution of digits in $\beta$-adic expansions of $\alpha^n$, which is a generalization of the Dupuy-Weirich theorem. When $(\beta)$ have ramified prime ideal factors, we also obtain a result on the block complexity of $\beta$-adic expansions of $\alpha^n$.

math.NT↗
arXiv2026

Mosaic: Unlocking Long-Context Inference for Diffusion LLMs via Global Memory Planning and Dynamic Peak Taming

Diffusion-based large language models (dLLMs) have emerged as a promising paradigm, utilizing simultaneous denoising to enable global planning and iterative refinement. While these capabilities are particularly advantageous for long-context generation, deploying such models faces a prohibitive memory capacity barrier stemming from severe system inefficiencies. We identify that existing inference systems are ill-suited for this paradigm: unlike autoregressive models constrained by the cumulative KV-cache, dLLMs are bottlenecked by transient activations recomputed at every step. Furthermore, general-purpose memory reuse mechanisms lack the global visibility to adapt to dLLMs' dynamic memory peaks, which toggle between logits and FFNs. To address these mismatches, we propose Mosaic, a memory-efficient inference system that shifts from local, static management to a global, dynamic paradigm. Mosaic integrates a mask-only logits kernel to eliminate redundancy, a lazy chunking optimizer driven by an online heuristic search to adaptively mitigate dynamic peaks, and a global memory manager to resolve fragmentation via virtual addressing. Extensive evaluations demonstrate that Mosaic achieves an average 2.71$\times$ reduction in the memory peak-to-average ratio and increases the maximum inference sequence length supportable on identical hardware by 15.89-32.98$\times$. This scalability is achieved without compromising accuracy and speed, and in fact reducing latency by 4.12%-23.26%.

cs.LG↗
arXiv2025

Unusual dependence on the angle of magnetic field for the spin Hall magnetoresistance of monodomain epitaxial BiFeO3 thin films

Spin Hall magnetoresistance (SMR) measurements provide a way to probe the surface spin structure of insulating magnetic materials. Such measurements produce resistance signals of the form {$\Delta$}R {$\propto$} cos[2($\alpha$-$\alpha$$_0$)], where $\alpha$ is the angle between the current and the external in-plane magnetic field. Previous experiments on a wide range of materials have found $\alpha$$_0$ = 0$\deg$ for ferromagnets and $\alpha$$_0$ = 90$\deg$ for antiferromagnets. Here we investigate SMR in bilayers of Pt with monodomain BiFeO$_3$ multiferroic epitaxial thin films. We observe signals of the form {$\Delta$}R {$\propto$} cos[2($\alpha$-$\alpha$$_0$)] but surprisingly the angle $\alpha$$_0$ can take values very different from 90$\deg$ or 0$\deg$, with large variations from sample to sample. The aim of the paper is to report this striking departure from the expected magnetic field dependence of SMR and to encourage consideration of possible microscopic mechanisms.

cond-mat.mtrl-sci↗
arXiv2025

A Grid-Forming HVDC Series Tapping Converter Using Extended Techniques of Flex-LCC

This paper discusses an extension technology for the previously proposed Flexible Line-Commutated Converter (Flex LCC) [1]. The proposed extension involves modifying the arm internal-electromotive-force control, redesigning the main-circuit parameters, and integrating a low-power coordination strategy. As a result, the Flex-LCC transforms from a grid-forming (GFM) voltage source converter (VSC) based on series-connected LCC and FBMMC into a novel GFM HVDC series tapping converter, referred to as the Extended Flex-LCC (EFLCC). The EFLCC provides dc characteristics resembling those of current source converters (CSCs) and ac characteristics resembling those of GFM VSCs. This makes it easier to integrate relatively small renewable energy sources (RESs) that operate in islanded or weak-grid supported conditions with an existing LCC-HVDC. Meanwhile, the EFLCC distinguishes itself by requiring fewer full-controlled switches and less energy storage, resulting in lower losses and costs compared to the FBMMC HVDC series tap solution. In particular, the reduced capacity requirement and the wide allowable range of valve-side ac voltages in the FBMMC part facilitate the matching of current-carrying capacities between full-controlled switches and thyristors. The application scenario, system-level analysis, implementation, converter-level operation, and comparison of the EFLCC are presented in detail in this paper. The theoretical analysis is confirmed by experimental and simulation results.

eess.SY↗
arXiv2025

Exploiting the Hidden Capacity of MMC Through Accurate Quantification of Modulation Indices

The modular multilevel converter (MMC) has become increasingly important in voltage-source converter-based high-voltage direct current (VSC-HVDC) systems. Direct and indirect modulation are widely used as mainstream modulation techniques in MMCs. However, due to the challenge of quantitatively evaluating the operation of different modulation schemes, the academic and industrial communities still hold differing opinions on their performance. To address this controversy, this paper employs the state-of-the-art computational methods and quantitative metrics to compare the performance among different modulation schemes. The findings indicate that direct modulation offers superior modulation potential for MMCs, highlighting its higher ac voltage output capability and broader linear PQ operation region. Conversely, indirect modulation is disadvantaged in linear modulation, which indicates inferior output voltage capability. Furthermore, this paper delves into the conditions whereby direct and indirect modulation techniques become equivalent in steady-state. The study findings suggest that the modulation capability of direct modulation is the same as that of indirect modulation in steady-state when additional controls, including closed-loop capacitor voltage control and circulating current suppression control (CCSC), are simultaneously active. Simulation and experiments verify the correctness and validity.

eess.SY↗
arXiv2024

Multiplicative Diophantine approximation with restricted denominators

Let $\{a_n\}_{n\in\mathbb{N}}$, $\{b_n\}_{n\in \mathbb{N}}$ be two infinite subsets of positive integers and $\psi:\mathbb{N}\to \mathbb{R}_{>0}$ be a positive function. We completely determine the Hausdorff dimensions of the set of all points $(x,y)\in [0,1]^2$ which satisfy $\|a_nx\|\|b_ny\|<\psi(n)$ infinitely often, and the set of all $x\in [0,1]$ satisfying $\|a_nx\|\|b_nx\|<\psi(n)$ infinitely often. This is based on establishing general convergence results for Hausdorff measures of these two sets. We also obtain some results on the set of all $x\in [0,1]$ such that $\max\{\|a_nx\|, \|b_nx\|\}<\psi(n)$ infinitely often.

math.NT↗
arXiv2024

A Methodology for Power Dispatch Based on Traction Station Clusters in the Flexible Traction Power Supply System

The flexible traction power supply system (FTPSS) eliminates the neutral zone but leads to increased complexity in power flow coordinated control and power mismatch. To address these challenges, the methodology for power dispatch (PD) based on traction station clusters (TSCs) in FTPSS is proposed, in which each TSC with a consistent structure performs independent local phase angle control. First, to simplify the PD problem of TSCs, the system is transformed into an equivalent model with constant topology, resulting in it can be solved by univariate numerical optimization with higher computational performance. Next, the calculation method of the feasible phase angle domain under strict and relaxed power circulation constraints are described, respectively, which ensures that power circulation can be either eliminated or precisely controlled. Finally, the PD method with three unique modes for uncertain train loads is introduced to enhance power flow flexibility: specified power distribution coefficients between traction substations (TSs), constant output power of TSs, and maximum consumption of renewable resources within TSs. In the experimental section, the performance of the TSC methodology for PD is verified through detailed train operation scenarios.

eess.SY↗
arXiv2024

On $\beta$-adic expansions of powers of algebraic integer omitting a digit

Let $\alpha, \beta$ be two relatively prime algebraic integers in a number field $K$ and $N$ be a positive integer. We show that the number of $n\in\{1,2,\dots,N\}$ such that the $\beta$-adic expansion of $\alpha^n$ omits a given digit is less than $C_1 N^{\sigma(\beta)}$, where $\sigma(\beta):=\frac{\log(|N(\beta)|-1)}{\log|N(\beta)|}$ and $C_1$ is an absolute constant, if all prime ideal factors of $\beta$ are unramified and their norms are integer primes.

math.NT↗
arXiv2023

Uniform Diophantine approximation with restricted denominators

Let $b\geq2$ be an integer and $A=(a_{n})_{n=1}^{\infty}$ be a strictly increasing subsequence of positive integers with $\eta:=\limsup\limits_{n\to\infty}\frac{a_{n+1}}{a_{n}}<+\infty$. For each irrational real number $\xi$, we denote by $\hat{v}_{b,A}(\xi)$ the supremum of the real numbers $\hat{v}$ for which, for every sufficiently large integer $N$, the equation $\|b^{a_n}\xi\|<(b^{a_N})^{-\hat{v}}$ has a solution $n$ with $1\leq n\leq N$. For every $\hat{v}\in[0,\eta]$, let $\hat{\mathcal{V}}_{b,A}(\hat{v})$ ($\hat{\mathcal{V}}_{b,A}^{\ast}(\hat{v})$) be the set of all real numbers $\xi$ such that $\hat{v}_{b,A}(\xi)\geq\hat{v}$ ($\hat{v}_{b,A}(\xi)=\hat{v}$) respectively. In this paper, we give some results of the Hausdorfff dimensions of $\hat{\mathcal{V}}_{b,A}(\hat{v})$ and $\hat{\mathcal{V}}_{b,A}^{\ast}(\hat{v})$. When $\eta=1$, we prove that the Hausdorfff dimensions of $\hat{\mathcal{V}}_{b,A}(\hat{v})$ and $\hat{\mathcal{V}}_{b,A}^{\ast}(\hat{v})$ are equal to $\left(\frac{1-\hat{v}}{1+\hat{v}}\right)^{2}$ for any $\hat{v}\in[0,1]$. When $\eta>1$ and $\lim_{n\to\infty}\frac{a_{n+1}}{a_{n}}$ exists, we show that the Hausdorfff dimension of $\hat{\mathcal{V}}_{b,A}(\hat{v})$ is strictly less than $\left(\frac{\eta-\hat{v}}{\eta+\hat{v}}\right)^{2}$ for some $\hat{v}$, which is different with the case $\eta=1$, and we give a lower bound of the Hausdorfff dimensions of $\hat{\mathcal{V}}_{b,A}(\hat{v})$ and $\hat{\mathcal{V}}_{b,A}^{\ast}(\hat{v})$ for any $\hat{v}\in[0,\eta]$. Furthermore, we show that this lower bound can be reached for some $\hat{v}$.

math.NT↗
arXiv2023

Zero-full law for well approximable sets in missing digit sets

Let $b \geq 3$ be an integer and $C(b,D)$ be the set of real numbers in $[0,1]$ whose base $b$ expansion only consists of digits in a set $D \subseteq \{0,...,b-1\}$. We study how close can numbers in $C(b,D)$ be approximated by rational numbers with denominators being powers of some integer $t$ and obtain a zero-full law for its Hausdorff measure in several circumstances. When $b$ and $t$ are multiplicatively dependent, our results correct an error of Levesley, Salp and Velani (Math. Ann., 338:97-118, 2007) and generalize their theorem. When $b$ and $t$ are multiplicatively independent but have the same prime divisors, we obtain a partial result on the Hausdorff measure and bounds for the Hausdorff dimension, which are close to the multiplicatively dependent case. Based on these results, several conjectures are proposed.

math.NT↗
arXiv2022

Nanoscale three-dimensional magnetic sensing with a probabilistic nanomagnet driven by spin-orbit torque

Detection of vector magnetic fields at nanoscale dimensions is critical in applications ranging from basic material science, to medical diagnostic. Meanwhile, an all-electric operation is of great significance for achieving a simple and compact sensing system. Here, we propose and experimentally demonstrate a simple approach to sensing a vector magnetic field at nanoscale dimensions, by monitoring a probabilistic nanomagnet's transition probability from a metastable state, excited by a driving current due to SOT, to a settled state. We achieve sensitivities for Hx, Hy, and Hz of 1.02%/Oe, 1.09%/Oe and 3.43%/Oe, respectively, with a 200 x 200 nm^2 nanomagnet. The minimum detectable field is dependent on the driving pulse events N, and is expected to be as low as 1 uT if N = 3 x 10^6.

cond-mat.mtrl-sci↗
arXiv2022

A puzzling insensitivity of magnon spin diffusion to the presence of 180$^\circ$ domain walls in a ferrimagnetic insulator

We present room-temperature measurements of magnon spin diffusion in epitaxial ferrimagnetic insulator MgAl$_{0.5}$Fe$_{1.5}$O$_{4}$ (MAFO) thin films near zero applied magnetic field where the sample forms a multi-domain state. Due to a weak uniaxial magnetic anisotropy, the domains are separated primarily by 180$^\circ$ domain walls. We find, surprisingly, that the presence of the domain walls has very little effect on the spin diffusion -- nonlocal spin transport signals in the multi-domain state retain at least 95% of the maximum signal strength measured for the spatially-uniform magnetic state, over distances at least five times the typical domain size. This result is in conflict with simple models of interactions between magnons and static domain walls, which predict that the spin polarization carried by the magnons reverses upon passage through a 180$^\circ$ domain wall.

cond-mat.mtrl-sci↗
arXiv2022

Rational numbers in $\times b$-invariant sets

Let $b \geq 2$ be an integer and $S$ be a finite non-empty set of primes not containing divisors of $b$. For any non-dense set $A \subset [0,1)$ such that $A \cap \mathbb{Q}$ is invariant under $\times b$ operation, we prove the finiteness of rational numbers in $A$ whose denominators can only be divided by primes in $S$. A quantitative result on the largest prime divisors of the denominators of rational numbers in $A$ is also obtained.

math.NT↗
arXiv2021

Anisotropic Magnon Spin Transport in Ultra-thin Spinel Ferrite Thin Films -- Evidence for Anisotropy in Exchange Stiffness

We report measurements of magnon spin transport in a spinel ferrite, magnesium aluminum ferrite $\mathrm{MgAl_{0.5}Fe_{1.5}O_4}$ (MAFO), which has a substantial in-plane four-fold magnetic anisotropy. We observe spin diffusion lengths $> 0.8$ $\mathrm{\mu m}$ at room temperature in 6 nm films, with spin diffusion length 30% longer along the easy axes compared to the hard axes. The sign of this difference is opposite to the effects just of anisotropy in the magnetic energy for a uniform magnetic state. We suggest instead that accounting for anisotropy in exchange stiffness is necessary to explain these results.

cond-mat.mtrl-sci↗
arXiv2019

Layer-dependent spin-orbit torques generated by the centrosymmetric transition metal dichalcogenide $β$-MoTe$_2$

Single-crystal materials with sufficiently low crystal symmetry and strong spin-orbit interactions can be used to generate novel forms of spin-orbit torques on adjacent ferromagnets, such as the out-of-plane antidamping torque previously observed in WTe$_2$/ferromagnet heterostructures. Here, we present measurements of spin-orbit torques produced by the low-symmetry material $β$-MoTe$_2$, which unlike WTe$_2$ retains bulk inversion symmetry. We measure spin-orbit torques on $β$-MoTe$_2$/Permalloy heterostructures using spin-torque ferromagnetic resonance as a function of crystallographic alignment and MoTe$_2$ thickness down to the monolayer limit. We observe an out-of-plane antidamping torque with a spin torque conductivity as strong as 1/3 of that of WTe$_2$, demonstrating that the breaking of bulk inversion symmetry in the spin-generation material is not a necessary requirement for producing an out-of-plane antidamping torque. We also measure an unexpected dependence on the thickness of the $β$-MoTe$_2$ -- the out-of-plane antidamping torque is present in MoTe$_2$/Permalloy heterostructures when the $β$-MoTe$_2$ is a monolayer or trilayer thick, but goes to zero for devices with bilayer $β$-MoTe$_2$.

cond-mat.mes-hall↗