arXiv subjects

Ruiyao Liu

Publications and source records attributed to Ruiyao Liu.

5 recordsLinked to original sources

arXiv2026

MathGen: Revealing the Illusion of Mathematical Competence through Text-to-Image Generation

Modern generative models have demonstrated the ability to solve challenging mathematical problems. In many real-world settings, however, mathematical solutions must be expressed visually through diagrams, plots, geometric constructions, and structured symbolic layouts, where correctness depends on precise visual composition. This naturally raises the question of whether generative models can still do so when the answer must be rendered visually rather than written in text? To study this problem, we introduce MathGen, a rigorous benchmark of 420 problems spanning seven core domains, including 350 Clean-Scene problems and 70 paired Open-Scene problems. Each problem is evaluated under a Script-as-a-Judge protocol with problem-specific verification criteria implemented through reusable executable scripts for deterministic and reproducible evaluation. Experiments on representative open-source and proprietary text-to-image models show that mathematical fidelity remains a major bottleneck: even the best closed-source model reaches only 53.7% overall accuracy, while open-source models achieve just 1--11%, often near 0% on structured tasks, particularly those requiring precise geometric and functional rendering. Overall, current T2I models remain far from reliable at even elementary mathematical visual generation.

cs.CV↗

arXiv2025

DNA Nanostructures Characterized via Dual Nanopore Resensing

DNA nanotechnology uses predictable interactions of nucleic acids to precisely engineer complex nanostructures. Characterizing these self-assembled structures at the single-structure level is crucial for validating their design and functionality. Nanopore sensing is a promising technique for this purpose as it is label-free, solution-based and high-throughput. Here, we present a device that incorporates dynamic feedback to control the translocation of DNA origami structures through and between two nanopores. We observe multiple translocations of the same molecule through the two distinct nanopores as well as measure its time-of-flight between the pores. We use machine learning classification methods in tandem with classical analysis of dwell-time/blockade distributions to analyze the complex multi-translocation events generated by different nanostructures. With this approach, we demonstrate the ability to distinguish DNA nanostructures of different lengths and/or small structural differences, all of which are difficult to detect using conventional, single-nanopore sensing. In addition, we develop a finite element diffusion model of the time-of-flight process and estimate nanostructure size. This work establishes the dual nanopore device as a powerful tool for DNA nanostructure characterization.

physics.bio-ph↗

arXiv2025

Patterning programmable spin arrays on DNA origami for quantum technologies

The controlled assembly of solid-state spins with nanoscale spatial precision is an outstanding challenge for quantum technology. Here, we combine DNA-based patterning with nitrogen-vacancy (NV) ensemble quantum sensors in diamond to form and sense programmable 2D arrays of spins. We use DNA origami to control the spacing of chelated Gd$^{3+}$ spins, as verified by the observed linear relationship between proximal NVs' relaxation rate, $1/T_1$, and the engineered number of Gd$^{3+}$ spins per origami unit. We further show that DNA origami provides a robust way of functionalizing the diamond surface with spins as it preserves the charge state and spin coherence of proximal, shallow NV centers. Our work enables the formation and interrogation of ordered, strongly interacting spin networks with applications in quantum sensing and quantum simulation. We quantitatively discuss the prospects of entanglement-enhanced metrology and high-throughput proteomics.

quant-ph↗

arXiv2025

PAnDA: Rethinking Metric Differential Privacy Optimization at Scale with Anchor-Based Approximation

Metric Differential Privacy (mDP) extends the local differential privacy (LDP) framework to metric spaces, enabling more nuanced privacy protection for data such as geo-locations. However, existing mDP optimization methods, particularly those based on linear programming (LP), face scalability challenges due to the quadratic growth in decision variables. In this paper, we propose Perturbation via Anchor-based Distributed Approximation (PAnDA), a scalable two-phase framework for optimizing metric differential privacy (mDP). To reduce computational overhead, PAnDA allows each user to select a small set of anchor records, enabling the server to solve a compact linear program over a reduced domain. We introduce three anchor selection strategies, exponential decay (PAnDA-e), power-law decay (PAnDA-p), and logistic decay (PAnDA-l), and establish theoretical guarantees under a relaxed privacy notion called probabilistic mDP (PmDP). Experiments on real-world geo-location datasets demonstrate that PAnDA scales to secret domains with up to 5,000 records, two times larger than prior LP-based methods, while providing theoretical guarantees for both privacy and utility.

cs.CR↗

arXiv2024

Time-Efficient Locally Relevant Geo-Location Privacy Protection

Geo-obfuscation serves as a location privacy protection mechanism (LPPM), enabling mobile users to share obfuscated locations with servers, rather than their exact locations. This method can protect users' location privacy when data breaches occur on the server side since the obfuscation process is irreversible. To reduce the utility loss caused by data obfuscation, linear programming (LP) is widely employed, which, however, might suffer from a polynomial explosion of decision variables, rendering it impractical in largescale geo-obfuscation applications. In this paper, we propose a new LPPM, called Locally Relevant Geo-obfuscation (LR-Geo), to optimize geo-obfuscation using LP in a time-efficient manner. This is achieved by confining the geo-obfuscation calculation for each user exclusively to the locally relevant (LR) locations to the user's actual location. Given the potential risk of LR locations disclosing a user's actual whereabouts, we enable users to compute the LP coefficients locally and upload them only to the server, rather than the LR locations. The server then solves the LP problem based on the received coefficients. Furthermore, we refine the LP framework by incorporating an exponential obfuscation mechanism to guarantee the indistinguishability of obfuscation distribution across multiple users. Based on the constraint structure of the LP formulation, we apply Benders' decomposition to further enhance computational efficiency. Our theoretical analysis confirms that, despite the geo-obfuscation being calculated independently for each user, it still meets geo-indistinguishability constraints across multiple users with high probability. Finally, the experimental results based on a real-world dataset demonstrate that LR-Geo outperforms existing geo-obfuscation methods in computational time, data utility, and privacy preservation.

cs.CR↗