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Approximating 1-in-3 SAT by linearly ordered hypergraph 3-colouring is NP-hard
Andrei Krokhin, Danny Vagnozzi
https://arxiv.org/abs/2508.14606 https://arxi…

Approximating 1-in-3 SAT by linearly ordered hypergraph 3-colouring is NP-hard
Given a satisfiable instance of 1-in-3 SAT, it is NP-hard to find a satisfying assignment for it, but it may be possible to efficiently find a solution subject to a weaker (not necessarily Boolean) predicate than `1-in-3'. There is a folklore conjecture predicting which choices of weaker predicates lead to tractability and for which the task remains \NP-hard. One specific predicate, corresponding to the problem of linearly ordered $3$-colouring of 3-uniform hypergraphs, has been mentioned in se…

Linear Equations in the Ring of $\mathcal{S}\left(\mathcal{A}\right)$-Linearly Correlated Fuzzy Numbers
Beatriz Laiate, Peter Sussner
https://arxiv.org/abs/2508.14900 https://…

Linear Equations in the Ring of $\mathcal{S}\left(\mathcal{A}\right)$-Linearly Correlated Fuzzy Numbers
This paper investigates the solutions of a family of certain linear fuzzy arithmetic equations that involve fuzzy numbers belonging to certain finite-dimensional vector spaces of $\mathbb{R}_{\mathcal{F}}$, called $\mathcal{S}\left(\mathcal{A}\right)$-linearly correlated fuzzy numbers. Here, $\A$ stands for a strongly linearly independent (SLI) set of fuzzy numbers. The arithmetic operations in the aforementioned linear equations are the sum in the vector space $\Sc(\A)$ and the so-called $ψ$-…

1/2 order convergence rate of Euler-type methods for time-changed stochastic differential equations with super-linearly growing drift and diffusion coefficients
Yuanling Niu, Shuai Wang, Ying Zhang
https://arxiv.org/abs/2507.14562

1/2 order convergence rate of Euler-type methods for time-changed stochastic differential equations with super-linearly growing drift and diffusion coefficients
This paper investigates the convergence rates of two Euler-type methods for a class of time-changed stochastic differential equations with super-linearly growing drift and diffusion coefficients. Building upon existing research, we adapt the backward Euler method to time-changed stochastic differential equations where both coefficients exhibit super-linear growth and introduce an explicit counterpart, the projected Euler method. It is shown that both methods achieve the optimal strong convergen…

Linearly-polarized few-cycle pulses drive carrier envelope phase-sensitive coherent magnetization injection
Ofer Neufeld
https://arxiv.org/abs/2507.15490 h…

Linearly-polarized few-cycle pulses drive carrier envelope phase-sensitive coherent magnetization injection
Circularly-polarized light is well-known to induce, or flip the direction of, magnetization in solids. At its heart, this arises from time-reversal symmetry breaking by the vector potential, causing inverse-Faraday or analogous physical effects. We show here that very short few-cycle pulses can cause similar phenomena even when they are linearly-polarized and off-resonant. We analyze the new effect with ab-initio calculations and demonstrate that it similarly arises due to broken time-reversal …

On the convergence rate in the central limit theorem for linearly extended negative quadrant dependent random variables and its applications
Mohamed Kaber El Alem, Zohra Guessoum, Abdelkader Tatachak, Ourida Sadki
https://arxiv.org/abs/2509.15353

On the convergence rate in the central limit theorem for linearly extended negative quadrant dependent random variables and its applications
In this paper, we establish the convergence rate in central limit theorem (CLT) for linearly extended negative quadrant dependent (LENQD) random variables (rv's). Under some weak conditions, the rate of normal approximation is shown as $O(n^{-1/9})$. As an application, the convergence rate in CLT of the wavelet estimator for the nonparametric regression model with LENQD errors is presented as $O(n^{-1/9})$. The performance of the main results is illustrated through a simulation study based on a…

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Language models' activations linearly encode training-order recency
Dmitrii Krasheninnikov, Richard E. Turner, David Krueger
https://arxiv.org/abs/2509.14223 https://…

Language models' activations linearly encode training-order recency
We show that language models' activations linearly encode when information was learned during training. Our setup involves creating a model with a known training order by sequentially fine-tuning Llama-3.2-1B on six disjoint but otherwise similar datasets about named entities. We find that the average activations of test samples for the six training datasets encode the training order: when projected into a 2D subspace, these centroids are arranged exactly in the order of training and lie on a s…

Observed Control -- Linearly Scalable Nonlinear Model Predictive Control with Adaptive Horizons
Eugene T. Hamzezadeh, Andrew J. Petruska
https://arxiv.org/abs/2508.13339 https:/…

Observed Control -- Linearly Scalable Nonlinear Model Predictive Control with Adaptive Horizons
This work highlights the duality between state estimation methods and model predictive control. A predictive controller, observed control, is presented that uses this duality to efficiently compute control actions with linear time-horizon length scalability. The proposed algorithms provide exceptional computational efficiency, adaptive time horizon lengths, and early optimization termination criteria. The use of Kalman smoothers as the backend optimization framework provides for a straightforwa…

SPIRiT Regularization: Parallel MRI with a Combination of Sensitivity Encoding and Linear Predictability
Nicholas Dwork, Alex McManus, Stephen Becker, Gennifer T. Smith
https://arxiv.org/abs/2508.15132

SPIRiT Regularization: Parallel MRI with a Combination of Sensitivity Encoding and Linear Predictability
Accelerated Magnetic Resonance Imaging (MRI) permits high quality images from fewer samples that can be collected with a faster scan. Two established methods for accelerating MRI include parallel imaging and compressed sensing. Two types of parallel imaging include linear predictability, which assumes that the Fourier samples are linearly related, and sensitivity encoding, which incorporates a priori knowledge of the sensitivity maps. In this work, we combine compressed sensing with both types …

Filtered Instantons and the Concordance of Satellites
Ivan So
https://arxiv.org/abs/2507.14350 https://arxiv.org/pdf/2507.14350

Filtered Instantons and the Concordance of Satellites
In \cite{NST23}, Nozaki-Sato-Taniguchi defined a family of invariants $ r_s $ for integer homology spheres with filtered instanton homology \cite{FS92}. Coupling these with techniques in classical knot theory, we produce some results in the knot concordance group, including criteria for a family of satellite knots to be linearly independent and the independence of what we call the Whitehead $ n $-ble $ P_n $.