arXiv subjects

Ang Xiao

Publications and source records attributed to Ang Xiao.

4 recordsLinked to original sources

arXiv2026

On Lattice Tilings by Symmetric Limited Magnitude Error Balls: Q-polynomials and Ideal Characterization

In this paper, we study the lattice tilings of $\mathbb{Z}^n$ by the symmetric limited magnitude error balls $\mathcal{B}(n,t,k,k)$, which play a crucial role in flash memory applications. Using generating functions and complete Bell polynomials, we derive an explicit formula for the $r$-th Q-polynomial associated with $\mathcal{B}(n,t,k,k)$. Then, an ideal-theoretic characterization of the lattice tiling condition is developed: for an odd prime $p$ dividing $|\mathcal{B}(n,t,k,k)|$ exactly once, a lattice tiling would force a certain polynomial to lie outside a certain ideal of $\mathbb{F}_p[Y_1,\dots,Y_{\frac{p-1}{2}}]$. Applying this criterion yields congruence conditions on the dimension $n$ that rule out lattice tilings; for $2\le t\le10$ and $1\le k\le10$, a systematic Maple computation over all primes $3\le p\le29$ excludes, on average, $35.65\%$ of all dimensions, with a maximum of $76.69\%$. Finally, we obtain two infinite families of parameters $(n,t,k)$ for which no lattice tiling exists: no lattice tiling exists if $k\equiv4\pmod9$ and the base-$3$ addition of $t$ and $n-1-t$ produces exactly one carry; and no lattice tiling of $\mathbb{Z}^n$ by $\mathcal{B}(n,n-1,k,k)$ exists if $k\equiv8\pmod9$ and $n\equiv2,4\pmod6$. Their sizes are also estimated.

math.CO↗

arXiv2026

On the Lattice Tilings by Lee Balls: Q-Polynomials, Group-Ring Equations, and a Decision Algorithm

More than 50 years ago, Golomb and Welch conjectured that no tilings of $\mathbb{Z}^n$ by Lee balls of radius $r$ exist for $n \geq 3$ and $r \geq 2$. This conjecture remains open even under the additional assumption that the tiling is a lattice tiling. In general, there are two known effective approaches to the lattice case which are based on symmetric polynomials and on the arithmetic of group-ring equations, respectively. In this paper, we develop both approaches. First, we determine all coefficients of the Q-polynomials associated with Lee balls; previously, only leading coefficients and certain special cases were known. Second, for arbitrary radii, we give necessary and sufficient conditions for the existence of lattice tilings by Lee balls in terms of group-ring equations, extending earlier results for radii $r=2$ and $3$. We then derive new necessary conditions for such tilings. For every radius $3\le r\le 50$, we prove that the set of dimensions for which no lattice tiling exists has positive density in $\mathbb{Z}^+$. We also give an algorithm that combines the available necessary conditions and apply it to all pairs $(n,r)$ for which the corresponding Lee ball of radius $r$ and dimension $n$ has size less than $2^{30}$. Among these $1{,}358$ pairs, the combined method excludes $1{,}356$, leaving only $(n,r)=(35,3)$ and $(805,3)$.

math.CO↗

arXiv2026

AQVolt26: High-Temperature r$^2$SCAN Halide Dataset for Universal ML Potentials and Solid-State Batteries

The demand for safe, high-energy-density batteries has spotlighted halide solid-state electrolytes, which offer the potential for enhanced ionic mobility, electrochemical stability, and interfacial deformability. Accelerating their discovery requires extensive molecular dynamics, which has been increasingly enabled by universal machine learning interatomic potentials trained on foundational datasets. However, the dynamic softness of halides poses a stringent test of whether general-purpose models can reliably replace first-principles calculations under the highly distorted, elevated-temperature regimes necessary to probe ion transport. Here, we present AQVolt26, a dataset of 322,656 r$^2$SCAN single-point calculations for lithium halides, generated via high-temperature configurational sampling across $\sim$5K structures. We demonstrate that foundational datasets provide a strong baseline for stable halide chemistries and transfer local forces well, however absolute energy predictions degrade in distorted higher-temperature regimes. Co-training with AQVolt26 resolves this blind spot. Furthermore, incorporating Materials Project relaxation data improves near-equilibrium performance but degrades extreme-strain robustness without enhancing high-temperature force accuracy. These results demonstrate that domain-specific configurational sampling is essential for the reliable dynamic screening of halide electrolytes. Furthermore, our findings suggest that while foundational models provide a robust base, they are most effective for dynamically soft solid-state chemistries when augmented with targeted, high-temperature data. Finally, we show that near-equilibrium relaxation data serves as a task-specific complement rather than a universally beneficial addition.

cond-mat.mtrl-sci↗

arXiv2025

Early-Cycle Internal Impedance Enables ML-Based Battery Cycle Life Predictions Across Manufacturers

Predicting the end-of-life (EOL) of lithium-ion batteries across different manufacturers presents significant challenges due to variations in electrode materials, manufacturing processes, cell formats, and a lack of generally available data. Methods that construct features solely on voltage-capacity profile data typically fail to generalize across cell chemistries. This study introduces a methodology that combines traditional voltage-capacity features with Direct Current Internal Resistance (DCIR) measurements, enabling more accurate and generalizable EOL predictions. The use of early-cycle DCIR data captures critical degradation mechanisms related to internal resistance growth, enhancing model robustness. Models are shown to successfully predict the number of cycles to EOL for unseen manufacturers of varied electrode composition with a mean absolute error (MAE) of 150 cycles. This cross-manufacturer generalizability reduces the need for extensive new data collection and retraining, enabling manufacturers to optimize new battery designs using existing datasets. Additionally, a novel DCIR-compatible dataset is released as part of ongoing efforts to enrich the growing ecosystem of cycling data and accelerate battery materials development.

cs.LG↗