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Engineering Preprint PDF DOI

FlexiTac: A Low-Cost, Open-Source, Scalable Tactile Sensing Solution for Robotic Systems

Binghao Huang, Yunzhu Li · 2026

We present FlexiTac, a low-cost, open-source, and scalable piezoresistive tactile sensing solution designed for robotic end-effectors. FlexiTac is a practical "plug-in" module consisting of (i) thin, …

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Mathematics Preprint PDF DOI

Stein's square function associated with the Bochner-Riesz means on M\'etivier groups and its applications

Joydwip Singh · 2026

In this paper, we study the $L^p$-boundedness of Stein's square function $\mathfrak{S}^{\alpha}(\mathcal{L})$ associated with the sub-Laplacian $\mathcal{L}$ on M\'etivier group $G$. A key aspect of o…

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Mathematics Preprint PDF DOI

Sufficient conditions for spanning $k$-trees in tough graphs

Caili Jia, Yong Lu · 2026

The toughness of a graph $G$, denoted by $\tau(G)$, is defined by $\tau(G)=$min $\{\frac{|S|}{c(G-S)}:S\subseteq V(G)$ and $c(G-S)\geq2\}$. A graph $G$ is said to be $\tau$-tough if $\tau(G)\geq \tau$…

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AI & Data Science Preprint PDF DOI

Math Education Digital Shadows for facilitating learning with LLMs: Math performance, anxiety and confidence in simulated students and AIs

Naomi Esposito, Anthony Tricarico, Luisa Porzio, Ali Aghazadeh Ardebili, Massimo Stella · 2026

To enhance LLMs' impact on math education, we need data on their mathematical prowess and biases across prompts. To fill this gap, we introduce MEDS (Math Education Digital Shadows) as a dataset mappi…

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Mathematics Preprint PDF DOI

Barriers, Barenblatt solutions and regularity of soda can domains for the heat equation and nonlinear $p$-parabolic equations

Anders Bjorn, Jana Bjorn · 2026

In this paper we study when the origin $(0,0)$ is a regular (or irregular) boundary point for the so-called soda can domains of the type \[ \Theta_{l,\theta}:= \{(x,t) \in \mathbf{R}^{n+1}: 0<-t < \th…

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AI & Data Science Preprint PDF DOI

Perturbation Probing: A Two-Pass-per-Prompt Diagnostic for FFN Behavioral Circuits in Aligned LLMs

Hongliang Liu, Tung-Ling Li, Yuhao Wu · 2026

Perturbation probing generates task-specific causal hypotheses for FFN neurons in large language models using two forward passes per prompt and no backpropagation, followed by a one-time intervention …

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AI & Data Science Preprint PDF DOI

BoostLoRA: Growing Effective Rank by Boosting Adapters

Raviteja Anantha, Nick Levato, Layne C. Price · 2026

Parameter-efficient fine-tuning (PEFT) methods face a tradeoff between adapter size and expressivity: ultra-low-parameter adapters are confined to fixed low-rank subspaces, capping performance even wi…

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AI & Data Science Preprint PDF DOI

Path-Lock Expert: Separating Reasoning Mode in Hybrid Thinking via Architecture-Level Separation

Shouren Wang, Wang Yang, Chuang Ma, Debargha Ganguly, Vikash Singh, Chaoda Song, Xinpeng Li, Xianxuan Long, Vipin Chaudhary, Xiaotian Han · 2026

Hybrid-thinking language models expose explicit think and no-think modes, but current designs do not separate them cleanly. Even in no-think mode, models often emit long and self-reflective responses,…

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Physics Preprint PDF DOI

On matrix Lax representations for (1+1)-dimensional evolutionary differential-difference equations

Sergei Igonin · 2026

Differential-difference matrix Lax representations (Lax pairs), gauge transformations, and discrete Miura-type transformations (MTs) belong to the main tools in the theory of (nonlinear) integrable di…

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Computer Science Preprint PDF DOI

What Is the Cost of Energy Monitoring? An Empirical Study on the Overhead of RAPL-Based Tools

Jeremy Diamond, Vincenzo Stoico · 2026

The Running Average Power Limit (RAPL) interface is widely used to estimate software energy consumption via CPU and DRAM counters, but tool design differences and high-frequency polling can introduce …

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AI & Data Science Preprint PDF DOI

PAINT: Partial-Solution Adaptive Interpolated Training for Self-Distilled Reasoners

Zhiquan Tan, Yinrong Hong · 2026

Improving large language model (LLM) reasoning requires supervision that is both aligned with the model's own test-time states and informative at the token level. Reinforcement learning with verifiabl…

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Mathematics Preprint PDF DOI

Non-uniqueness for the stochastic incompressible Euler equations with a passive tracer

Ashish Bawalia, Zdzis{l}aw Brzezniak, Manil T. Mohan · 2026

In this work we investigate the phenomenon of pathwise non-uniqueness for the stochastic incompressible Euler equations with a passive tracer on the whole Euclidean space. The stochastic perturbations…

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Mathematics Preprint PDF DOI

Geometric structure of singular free boundary points for the logarithmic obstacle problem

Lili Du, Xu Tang, Yi Zhou · 2026

In the previous work [Interfaces Free Bound., 19, 351--369, 2017], de Queiroz and Shahgholian established the optimal $C^{1,\log}_{\mathrm{loc}}$ regularity of solutions for the obstacle problem with …

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Mathematics Preprint PDF DOI

On a conjecture of distance spectral extremal problems

Hongzhang Chen, Jianxi Li, Yongtao Li · 2026

Brualdi and Hoffman proposed a well-known problem of determining the graph with maximum adjacency spectral radius among all graphs with given size $m$. Early work by Friedland and Stanley addressed so…

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Mathematics Preprint PDF DOI

The Expiring Coupon Collector: Sliding-Window Surjection Flux and Rare-Entry Laws

Christopher D. Long · 2026

We study the coupon collector with deterministic expiration: one coupon is drawn at each time, and each coupon remains active for exactly $M$ draws. Completion occurs when all $n$ coupon types are sim…

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Biology & Life Sciences Preprint PDF DOI

The Curse of Black Sigatoka: A Backward Bifurcation Perspective

Bernard Asamoah Afful, Luis F. Gordillo · 2026

Black Sigatoka disease (BSD), also known as black leaf streak disease, is an airborne fungal infection caused by \textit{Pseudocercospora fijiensis} that severely impacts global banana and plantain pr…

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Physics Preprint PDF DOI

(Super-)renormalizable hairy meronic black holes

Luis Aviles, Borja Diez · 2026

We construct an analytical black hole solution in the Einstein-Maxwell-Yang-Mills theory with a conformally coupled scalar field in four dimensions, which generalizes the charged Mart\'inez-Troncoso-Z…

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Physics Preprint PDF DOI

Long-time asymptotics of the Newell equation on the line

Deng-Shan Wang, Yingmin Yang · 2026

In 1978, A. C. Newell [SIAM J. Appl. Math. 35(4) (1978) 650-664] proposed an exactly solvable model called Newell equation, which simulates the investigation of significant interaction mechanism betwe…

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Mathematics Preprint PDF DOI

Boundary epsilon regularity for incompressible Navier--Stokes equations via weak-strong uniqueness

Siran Li · 2026

We show that finite-energy weak solutions to the incompressible Navier--Stokes equations on a three-dimensional bounded smooth domain are regular up to the boundary, provided that the $L^4_tL^4_x$-nor…

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AI & Data Science Preprint PDF DOI

From Insight to Action: A Novel Framework for Interpretability-Guided Data Selection in Large Language Models

Ling Shi, Xinwei Wu, Xiaohu Zhao, Hao Wang, Heng Liu, Yangyang Liu, Linlong Xu, Longyue Wang, Deyi Xiong, Weihua Luo · 2026

While mechanistic interpretability tools like Sparse Autoencoders (SAEs) can uncover meaningful features within Large Language Models (LLMs), a critical gap remains in transforming these insights into…

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