arXiv subjects

Bixuan Li

Publications and source records attributed to Bixuan Li.

5 recordsLinked to original sources

arXiv2026

The Cartesian product of exact approximation sets

We determine the Hausdorff and packing dimensions of Cartesian products of one-dimensional exact approximation sets. Our main result establishes the exact-approximation counterpart of the recent product theorem of Wang and Wu (2024) for limsup approximation sets, showing that passing to the substantially smaller exact approximation sets (liminf sets) does not reduce the Hausdorff dimension of the Cartesian product. One of the key ingredients is a refinement of the well-distributed-system framework of Bandi--Ghosh--Nandi (2023) by exploiting the fine arithmetic distribution of rational points which then gives the Hausdorff dimension of the product set under a weaker convergence condition.

math.NT↗

arXiv2026

OpenAaaS: An Open Agent-as-a-Service Framework for Distributed Materials-Informatics Research

The Materials Genome Initiative catalyzed the proliferation of centralized platforms--SaaS, PaaS, and IaaS--that aggregate computational and experimental resources for accelerated materials discovery. In parallel, breakthroughs in large language models (LLMs) and autonomous agents have created powerful new reasoning capabilities for scientific research. Yet a critical "last mile" problem remains: while we possess world-class models and vast repositories of materials data, we lack the organizational infrastructure to compose these capabilities securely across institutional boundaries. The development of structural and functional materials for harsh service environments--high-temperature alloys, radiation resistant steels, corrosion-resistant coatings--remains characterized by long-term iteration, mechanistic complexity, and high domain expertise--demands that exceed both monolithic agent systems and traditional centralized platforms. To address this gap we propose OpenAaaS, an open-source hierarchical and distributed Agent-as-a-Service framework that enables organized multi-agent collaboration for intelligent materials design. OpenAaaS is built on a single foundational principle: code flows, data stays still. A Master Agent plans and decomposes complex research tasks without requiring direct access to subordinate agents' managed data and computational resources. Sub-agents, deployed as near-data execution nodes, retain full sovereignty over local datasets, proprietary algorithms, and specialized hardware. This architecture guarantees that raw data never leaves its domain of origin while enabling cross-scale, cross-domain secure integration of previously isolated materials intelligence silos. We validate the framework through two representative case studies: (i) AlphaAgent, an evidence-grounded materials literature analysis executor that achieves 4.66/5.0 on deep analytical questions against single-pass RAG baselines; and (ii) an ultra-large-scale hexa-high-entropy alloy descriptor database service that demonstrates secure near-data execution and domain-specific scientific workflows under strict data-sovereignty constraints. OpenAaaS establishes a principled pathway toward "organized research" via agent collectives, offering a scalable foundation for next-generation materials intelligent design platforms. All source code is available at https://github.com/Wolido/OpenAaaS.

cond-mat.mtrl-sci↗

arXiv2026

Skill-Contracted Agents for Evidence-Aware Materials Literature Analysis

Materials science literature analysis requires simultaneous attention to composition, processing, characterization, and property relationships, yet conventional retrieval-augmented generation pipelines struggle to reconcile heterogeneous tasks within a single retrieve-then-generate architecture. Here we present AlphaAgent, a skill-driven agent framework that decouples retrieval-based question answering from paper-level report generation through explicit skill contracts. A dedicated retrieval skill rewrites user requests into material-specific search intents, queries a curated index of more than 300,000 papers from the Journal Citation Reports Metallurgy and Metallurgical Engineering category, and reformulates queries when initial evidence is insufficient. A separate report-generation skill parses full-text PDFs to produce structured per-paper analytical reports and cross-paper summaries. In a blind evaluation on 40 materials-science questions, half of which required deep analytical reasoning, AlphaAgent substantially outperformed a baseline system matched for underlying model, document index, and retrieval scale, with the largest gains in mechanistic explanation and awareness of credibility boundaries. These results indicate that explicit task separation, refined retrieval intent, and evidence-aware generation improve large-language-model-based literature analysis for materials research.

cs.CL↗

arXiv2023

Metrical properties of the product of partial quotients with geometric mean in continued fractions

The theory of uniform Diophantine approximation concerns the study of Dirichlet improvable numbers and the metrical aspect of this theory leads to the study of the product of consecutive partial quotients in continued fractions. It is known that the dimension of the set of Dirichlet non-improvable numbers depends upon the number of partial quotients in the product string. However, one can see that the Hausdorff dimension is the same for any number of consecutive partial quotients with a constant gap. This paper is aimed at a detailed analysis on how the Hausdorff dimension changes when there is a linear gap in indices and the number of partial quotients in the product grows. More precisely, let $d\in \N_{\ge 1}, t\in\Z_{\geq 0}$ and $f(n)=dn+t$, we present the detailed Hausdorff dimension analysis of the set\begin{equation*} E_{f}(ψ):=\left\{x\in [0, 1): \sqrt[n]{a_{f(n)}(x)a_{2f(n)}(x)\cdots a_{nf(n)}(x)}\geq ψ(n) \ {\rm for \ infinitely \ many} \ n\in \N\right\}. \end{equation*} It is seen that the dimension is larger if $d$ is larger and $t$ has no contribution to the dimension.

math.NT↗

arXiv2022

A Hausdorff dimension analysis of sets with the product of consecutive vs single partial quotients in continued fractions

We present a detailed Hausdorff dimension analysis of the set of real numbers where the product of consecutive partial quotients in their continued fraction expansion grow at a certain rate but the growth of the single partial quotient is at a different rate. We consider the set \begin{equation*} \FF(Φ_1,Φ_2) \defeq \EE(Φ_1) \backslash \EE(Φ_2)=\left\{x\in[0,1): \begin{split} a_n(x)a_{n+1}(x) & \geqΦ_1(n) \text{\,\, for infinitely many } n\in\N a_{n+1}(x) & <Φ_2(n) \text{\,\, for all sufficiently large } n\in\N \end{split} \right\}, \end{equation*} where $Φ_i:\N\to(0,\infty)$ are any functions such that $\lim\limits_{n\to\infty} Φ_i(n)=\infty$. We obtain some surprising results including the situations when $\FF(Φ_1,Φ_2)$ is empty for various non-trivial choices of $Φ_i$'s. Our results contribute to the metrical theory of continued fractions by generalising several known results including the main result of [Nonlinearity, 33(6):2615--2639, 2020]. To obtain some of the results, we consider an alternate generalised set, which may be of independent interest, and calculate its Hausdorff dimension. One of the main ingredients is in the usage of the classical mass distribution principle; specifically a careful distribution of the mass on the Cantor subset by introducing a new idea of two different types of probability measures.

math.NT↗