arXiv subjects

Daniel Garcia

Publications and source records attributed to Daniel Garcia.

9 recordsLinked to original sources

arXiv2026

Small graphs without power-of-two cycles: a lower bound of 24, a correction to a construction of Exoo, and explicit bounds for f(k)

The Erdos-Gyarfas conjecture states that every graph with minimum degree at least 3 contains a cycle whose length is a power of two. We prove by a SAT-based exhaustive search, certified by DRAT proofs, that every graph with minimum degree at least 3 on at most 23 vertices contains a cycle of length 4 or a cycle of length 8; consequently any counterexample has at least 24 vertices, improving the previously published bound of 16, and the smallest graph of minimum degree 3 with no 4-cycle and no 8-cycle has exactly 24 vertices. We show that the lemma underlying Exoo's 450-vertex construction for the bound f(5) at most 450 is false: the Tutte-Coxeter graph contains 8-cycles alternating between outer and chord edges, and the graph as specified contains 32-cycles. We repair the construction and verify the corrected graph, so the bound stands. We also give an exact window calculus for vertex-replacement constructions, prove that f(k) is at most 15 times the order of the smallest known cubic graph of girth 2 to the power (k-2) plus 1 for all k at least 4 (in particular f(6) is at most 32640, the first bound for f(6)), and show that Exoo's 78-vertex witness for f(4) at most 78 is optimal among gadget designs on bases with at most 12 vertices. All graphs, scripts and certificates are archived at doi:10.5281/zenodo.22180583.

math.CO↗

arXiv2026

SOMA-SQL: Resolving Multi-Source Ambiguity in NL-to-SQL via Synthetic Log and Execution Probing

Natural language interfaces to databases aim to translate user questions into executable SQL, yet remain brittle in real-world settings where questions are underspecified and schemas are large and ambiguous. Ambiguity across user questions, database schemas, and model interpretations are central failure modes in NL2SQL, leading to misaligned intent, incorrect schema grounding, and erroneous SQL generation. Existing approaches rely on human clarification or treat ambiguity as a schema representation problem, but these do not scale nor resolve ambiguity autonomously. We propose SOMA-SQL to automatically resolve ambiguity via targeted synthetic query log and ambiguity-driven probing. SOMA-SQL constructs synthetic query log to ground schema interpretation and guide candidate SQL generation; it then executes targeted probing queries, driven by a structured ambiguity taxonomy and candidate disagreements, to produce disambiguation evidence for final SQL selection and repair. This active approach to ambiguity discovery and resolution generalizes across unseen schemas and query distributions without human-in-the-loop. Experiments on six public benchmarks demonstrate that SOMA-SQL improves execution accuracy by 13.0% on average over state-of-the-art baselines, with gains of up to 16.7% on ambiguous questions.

cs.CL↗

arXiv2026

Verification and Validation (V&V)-in-the-Loop for RISC-V Design: The Holistic Vision of BZL

The Barcelona Zetascale Lab (BZL) project aims to strengthening Europe's capacity in the design and manufacture of RISC-V based high-performance computing chips. In this context, we present a holistic pre-silicon verification and validation (V&V) methodology targeting highly robust RISC-V chip designs. This paper provides an overview of BZL's V&V approach, which integrates three complementary platforms: (1) a UVM-based verification environment to thoroughly validate RTL functionality; (2) an FPGA-based validation platform that enables system-level pre-silicon hardware-software RTL validation; and (3) a CI/CD flow that continuously automates build, deployment, and tests across these domains. By embedding these platforms into an industrial-grade V&V loop and exploiting large-scale CPU and FPGA hardware infrastructures, the BZL project enables continuous evolution of reliable hardware development and software integration. We believe that the BZL's V&V flow represents a robust and scalable foundation for ensuring the pre-silicon functional correctness and system level validation of RISC-V chip designs, and can serve as a key enabler for strategic initiatives in Europe, such as EPI and DARE, and beyond.

cs.AR↗

arXiv2026

LAPIS: Lightweight API Specification for Intelligent Systems

Large Language Models (LLMs) increasingly serve as consumers of API specifications, whether for code generation, autonomous agent interaction, or API-assisted reasoning. The de facto standard for API description, OpenAPI, was designed for documentation tools and code generators, resulting in substantial token overhead when used as LLM context. We present LAPIS (Lightweight API Specification for Intelligent Systems), a domain-specific format optimized for LLM consumption that preserves the semantic information necessary for API reasoning while minimizing token usage. Through empirical evaluation against five real-world production API specifications including GitHub (1,080 endpoints), Twilio (197 endpoints), DigitalOcean (545 endpoints), Petstore, and HTTPBin we demonstrate an average token reduction of 85.5% compared to OpenAPI YAML and 88.6% compared to OpenAPI JSON, measured with the cl100k_base tokenizer. LAPIS introduces domain-specific structural innovations, including centralized error definitions, webhook trigger conditions, structured rate limit descriptions, and operation flow declarations information that OpenAPI either duplicates redundantly or cannot represent at all. The format is fully convertible from OpenAPI 3.x via an automated converter, requires no special parser for LLM consumption, and is released as an open specification under CC BY 4.0.

cs.SE↗

arXiv2025

ToolScope: Enhancing LLM Agent Tool Use through Tool Merging and Context-Aware Filtering

Large language model (LLM) agents rely on external tools to solve complex tasks, but real-world toolsets often contain redundant tools with overlapping names and descriptions, introducing ambiguity and reducing selection accuracy. LLMs also face strict input context limits, preventing efficient consideration of large toolsets. To address these challenges, we propose ToolScope, which includes: (1) ToolScopeMerger with Auto-Correction to automatically audit and fix tool merges, reducing redundancy, and (2) ToolScopeRetriever to rank and select only the most relevant tools for each query, compressing toolsets to fit within context limits without sacrificing accuracy. Evaluations on three state-of-the-art LLMs and three open-source tool-use benchmarks show gains of 8.38% to 38.6% in tool selection accuracy, demonstrating ToolScope's effectiveness in enhancing LLM tool use.

cs.CL↗

arXiv2022

Frequency dependence of near-surface oceanic kinetic energy from drifter observations and global high-resolution models

The geographical variability, frequency content, and vertical structure of near-surface oceanic kinetic energy (KE) are important for air-sea interaction, marine ecosystems, operational oceanography, pollutant tracking, and interpreting remotely sensed velocity measurements. Here, KE in high-resolution global simulations (HYbrid Coordinate Ocean Model; HYCOM, and Massachusetts Institute of Technology general circulation model; MITgcm), at the sea surface (0 m) and 15 m, are respectively compared with KE from undrogued and drogued surface drifters. Global maps and zonal averages are computed for low-frequency ($<$ 0.5 cpd), near-inertial, diurnal, and semi-diurnal bands. Both models exhibit low-frequency equatorial KE that is low relative to drifter values. HYCOM near-inertial KE is higher than in MITgcm, and closer to drifter values, probably due to more frequently updated atmospheric forcing. HYCOM semi-diurnal KE is lower than in MITgcm, and closer to drifter values, likely due to inclusion of a parameterized topographic internal wave drag. A concurrent tidal harmonic analysis in the diurnal band demonstrates that much of the diurnal flow is non-tidal. We compute a simple proxy of near-surface vertical structure, the ratio of 0 m KE to 0 m KE plus 15 m KE in model outputs, and undrogued KE to undrogued KE plus drogued KE in drifter observations. Over most latitudes and frequency bands, model ratios track the drifter ratios to within error bars. Values of this ratio demonstrate significant vertical structure in all frequency bands except the semidiurnal band. Latitudinal dependence in the ratio is greatest in diurnal and low-frequency bands.

physics.ao-ph↗

arXiv2021

Performance of Refined Isogeometric Analysis in Solving Quadratic Eigenvalue Problems

Certain applications that analyze damping effects require the solution of quadratic eigenvalue problems (QEPs). We use refined isogeometric analysis (rIGA) to solve quadratic eigenproblems. rIGA discretization, while conserving desirable properties of maximum-continuity isogeometric analysis (IGA), reduces the interconnection between degrees of freedom by adding low-continuity basis functions. This connectivity reduction in rIGA's algebraic system results in faster matrix LU factorizations when using multifrontal direct solvers. We compare computational costs of rIGA versus those of IGA when employing Krylov eigensolvers to solve quadratic eigenproblems arising in 2D vector-valued multifield problems. For large problem sizes, the eigencomputation cost is governed by the cost of LU factorization, followed by costs of several matrix-vector and vector-vector multiplications, which correspond to Krylov projections. We minimize the computational cost by introducing C^0 and C^1 separators at specific element interfaces for our rIGA generalizations of the curl-conforming Nedelec and divergence-conforming Raviart-Thomas finite elements. Let p be the polynomial degree of basis functions; the LU factorization is up to O((p-1)^2) times faster when using rIGA compared to IGA in the asymptotic regime. Thus, rIGA theoretically improves the total eigencomputation cost by O((p-1)^2) for sufficiently large problem sizes. Yet, in practical cases of moderate-size eigenproblems, the improvement rate deteriorates as the number of computed eigenvalues increases because of multiple matrix-vector and vector-vector operations. Our numerical tests show that rIGA accelerates the solution of quadratic eigensystems by O(p-1) for moderately sized problems when we seek to compute a reasonable number of eigenvalues.

math.NA↗

arXiv2020

Database Generation for Deep Learning Inversion of 2.5D Borehole Electromagnetic Measurements using Refined Isogeometric Analysis

Borehole resistivity measurements are routinely inverted in real-time during geosteering operations. The inversion process can be efficiently performed with the help of advanced artificial intelligence algorithms such as deep learning. These methods require a large dataset that relates multiple earth models with the corresponding borehole resistivity measurements. In here, we propose to use an advanced numerical method --refined isogeometric analysis (rIGA)-- to perform rapid and accurate 2.5D simulations and generate databases when considering arbitrary 2D earth models. Numerical results show that we can generate a meaningful synthetic database composed of 100,000 earth models with the corresponding measurements in 56 hours using a workstation equipped with two CPUs.

math.NA↗

arXiv2012

Fused Azulenes: Possible Organic Multiferroics

We present compelling theoretical results showing that fused azulene molecules are strong candidates for exhibiting room temperature multiferroic behavior, i.e., having both, ferroelectric and ferromagnetic properties. If this is experimentally proved, these systems will be the first organic multiferroic materials with important potential applications.

cond-mat.str-el↗