Tootfinder

On the algebraic $K$-theory of smooth schemes over truncated Witt vectors
Xiaowen Hu
https://arxiv.org/abs/2507.12458 https://arxiv.o…

On the algebraic $K$-theory of smooth schemes over truncated Witt vectors
Using Brun's theorem relating the relative algebraic $K$-theory and the relative cyclic homology, we compute certain relative algebraic $K$-groups of a $p$-adic smooth scheme over $W_n(k)$, where $k$ is a perfect field of characteristic $p$. Inspired by this result and the work of Bloch, Esnault, and Kerz, we define the infinitesimal motivic complexes, and then show a relative Chern character isomorphism with integral coefficients in a range. This has a direct consequence on infinitesimal defor…

Dear #lazyweb,
I think I've reached the limit of #matplotlib trying to graph the forks from a #git repository. What I want to to plot the slowly growing trunk and then show the relative sizes o…

Reset Controller Analysis and Design for Unstable Linear Plants using Scaled Relative Graphs
Julius P. J. Krebbekx, Roland T\'oth, Amritam Das
https://arxiv.org/abs/2506.13518

Reset Controller Analysis and Design for Unstable Linear Plants using Scaled Relative Graphs
In technical communique, we develop a graphical design procedure for reset controllers for unstable LTI plants based on recent developments on Scaled Relative Graph analysis, yielding an $L_2$-gain performance bound. The stabilizing controller consists of a second order reset element in parallel with a proportional gain. The proposed method goes beyond existing approaches that are limited to stable systems only, providing a well-applicable approach to design problems in practice where the plant…

Im Mai 2025 erlebten große Teile Mittel- und Nordeuropas – darunter Südskandinavien, die #Ukraine und Teile Russlands – deutlich trockenere Bedingungen als im langjährigen Mittel.
#Niederschlag, #Bodenfeuchte

Mental Effort Estimation in Motion Exploration and Concept Generation Design Tasks using Inter-Band Relative Power Difference of EEG
G. Kalyan Ramana, Sumit Yempalle, Prasad S. Onkar
https://arxiv.org/abs/2508.10353

Mental Effort Estimation in Motion Exploration and Concept Generation Design Tasks using Inter-Band Relative Power Difference of EEG
Conceptual design is a cognitively complex task, especially in the engineering design of products having relative motion between components. Designers prefer sketching as a medium for conceptual design and use gestures and annotations to represent such relative motion. Literature suggests that static representations of motion in sketches may not achieve the intended functionality when realised, because it primarily depends on the designers' mental capabilities for motion simulation. Thus, it is…

Relative Error Fair Clustering in the Weak-Strong Oracle Model
Vladimir Braverman, Prathamesh Dharangutte, Shaofeng H. -C. Jiang, Hoai-An Nguyen, Chen Wang, Yubo Zhang, Samson Zhou
https://arxiv.org/abs/2506.12287

Relative Error Fair Clustering in the Weak-Strong Oracle Model
We study fair clustering problems in a setting where distance information is obtained from two sources: a strong oracle providing exact distances, but at a high cost, and a weak oracle providing potentially inaccurate distance estimates at a low cost. The goal is to produce a near-optimal fair clustering on $n$ input points with a minimum number of strong oracle queries. This models the increasingly common trade-off between accurate but expensive similarity measures (e.g., large-scale embedding…

After years of relative calm, a western Ukrainian city comes to terms with being in Russia's crosshairs: https://benborges.xyz/2025/07/10/after-years-of-relative-calm.html

Lempel-Ziv Complexity, Empirical Entropies, and Chain Rules
Neri Merhav
https://arxiv.org/abs/2506.12772 https://arxiv.org/pdf/2506.1…

Lempel-Ziv Complexity, Empirical Entropies, and Chain Rules
We derive upper and lower bounds on the overall compression ratio of the 1978 Lempel-Ziv (LZ78) algorithm, applied independently to $k$-blocks of a finite individual sequence. Both bounds are given in terms of normalized empirical entropies of the given sequence. For the bounds to be tight and meaningful, the order of the empirical entropy should be small relative to $k$ in the upper bound, but large relative to $k$ in the lower bound. Several non-trivial conclusions arise from these bounds. On…

Relative modality of elements in generalized Takiff Lie algebras
Hugo Mathevet (LMR)
https://arxiv.org/abs/2506.11562 https://arxiv.o…

Relative modality of elements in generalized Takiff Lie algebras
Given a natural number m and a Lie algebra g, the m th generalized Takiff Lie algebra of g is the Lie algebra gm\,:= g $\otimes$ C[T ]/T m+1 . For n $\ge$ m, we define the (m, n)-modality of an adjoint orbit $Ω$m in gm to be the minimum codimension of an adjoint orbit in the pullback of $Ω$m in gn. In this paper, we study this family of invariants in generalized Takiff Lie algebras associated to a quadratic Lie algebra g. We show that this family of invariants satisfies some concavity and he…

Partially rigid motions in the planar three-body problem
Richard Moeckel
https://arxiv.org/abs/2506.13570 https://arxiv.org/pdf/2506.…

Partially rigid motions in the planar three-body problem
A solution of the n-body problem in R^d is a relative equilibrium if all of the mutual distance between the bodies are constant. In other words, the bodies undergo a rigid motion. Here we investigate the possibility of partially rigid motions, where some but not all of the distances are constant. For the planar three-body problem with equal masses, we show that partially rigid motions are impossible -- if even one of the three mutual distances is constant, the motion must be a relative equilibr…

Long-time relative error analysis for linear ODEs with perturbed initial value
Stefano Maset
https://arxiv.org/abs/2507.08752 https://

Long-time relative error analysis for linear ODEs with perturbed initial value
We investigate the propagation of initial value perturbations along the solution of a linear ODE \( y'(t) = Ay(t) \). This propagation is analized using the relative error rather than the absolute error. Our focus is on the long-term behavior of this relative error, which differs significantly from that of the absolute error. Understanding this long-term behavior provides insights into the growth of the relative error over all times, not just at large times. Therefore, it represents a crucial a…

DocPolarBERT: A Pre-trained Model for Document Understanding with Relative Polar Coordinate Encoding of Layout Structures
Benno Uthayasooriyar, Antoine Ly, Franck Vermet, Caio Corro
https://arxiv.org/abs/2507.08606

DocPolarBERT: A Pre-trained Model for Document Understanding with Relative Polar Coordinate Encoding of Layout Structures
We introduce DocPolarBERT, a layout-aware BERT model for document understanding that eliminates the need for absolute 2D positional embeddings. We extend self-attention to take into account text block positions in relative polar coordinate system rather than the Cartesian one. Despite being pre-trained on a dataset more than six times smaller than the widely used IIT-CDIP corpus, DocPolarBERT achieves state-of-the-art results. These results demonstrate that a carefully designed attention mechan…

Scattering Theory in Noncanonical Phase Space: A Drift-Kinetic Collision Operator for Weakly Collisional Plasmas
Naoki Sato, Philip J. Morrison
https://arxiv.org/abs/2506.11215

Scattering Theory in Noncanonical Phase Space: A Drift-Kinetic Collision Operator for Weakly Collisional Plasmas
After developing a scattering theory for grazing collisions in general noncanonical phase spaces, we introduce a guiding center collision operator in five-dimensional phase space designed for plasma regimes characterized by long wavelengths (relative to the Larmor radius), low frequencies (relative to the cyclotron frequency), and weak collisionality (where repeated Coulomb collisions induce cumulatively small changes in particle magnetic moment). The collision operator is fully determined by t…

Relative Wavefront Errors in Continuous-Variable Quantum Communication
Nathan K. Long, John Wallis, Alex Frost, Benjamin P. Dix-Matthews, Sascha W. Schediwy, Kenneth J. Grant, Robert Malaney
https://arxiv.org/abs/2508.09491

Relative Wavefront Errors in Continuous-Variable Quantum Communication
When undertaking continuous-variable quantum key distribution (CV-QKD) across atmospheric channels, strong classical local oscillators (LOs) are often polarization-multiplexed with the weak quantum signals for coherent measurement at the receiver. Although the wavefronts of the quantum signal and LO are often assumed to experience the same distortion across channels, previous theoretical work has shown that they can experience differential distortions, resulting in relative wavefront errors (WF…

MonoMVSNet: Monocular Priors Guided Multi-View Stereo Network
Jianfei Jiang, Qiankun Liu, Haochen Yu, Hongyuan Liu, Liyong Wang, Jiansheng Chen, Huimin Ma
https://arxiv.org/abs/2507.11333

MonoMVSNet: Monocular Priors Guided Multi-View Stereo Network
Learning-based Multi-View Stereo (MVS) methods aim to predict depth maps for a sequence of calibrated images to recover dense point clouds. However, existing MVS methods often struggle with challenging regions, such as textureless regions and reflective surfaces, where feature matching fails. In contrast, monocular depth estimation inherently does not require feature matching, allowing it to achieve robust relative depth estimation in these regions. To bridge this gap, we propose MonoMVSNet, a …

Relative Inverse Limit Perfection of Derived Commutative Rings
Daniel Fink
https://arxiv.org/abs/2506.10626 https://arxiv.org/pdf/250…

Relative Inverse Limit Perfection of Derived Commutative Rings
We study the relative Frobenius map associated with a map of derived commutative rings over a field of positive characteristic. As part of this, we examine a relative analog of perfectness and construct a relative inverse limit perfection which, under suitable conditions on the base, serves as a right adjoint to the inclusion of relatively perfect algebras into the category of all algebras. Specializing to animated rings, we investigate relative versions of semiperfectness and F-finiteness, and…

Formal models for relative adic spaces
Dimitri Dine
https://arxiv.org/abs/2507.11073 https://arxiv.org/pdf/2507.11073

Formal models for relative adic spaces
We extend Raynaud's theory of formal models from rigid-analytic spaces over a nonarchimedean field to uniform qcqs adic spaces $X$, with no finite-type assumptions, over an arbitrary Tate affinoid base $S$. The key new ingredient is the notion of a normalized formal blow-up which takes on the role played by admissible formal blow-ups in the classical theory.

Corings, their dual rings and relative (co)Hochschild cohomology
Jonathan Lindell
https://arxiv.org/abs/2508.10668 https://arxiv.org/pdf/2508.10668

Corings, their dual rings and relative (co)Hochschild cohomology
We show for a coring which is finitely generated projective as a left module that the Cartier cohomology is isomorphic to the relative Hochschild cohomology of the right algebra. Furthermore, we show that this isomorphism lifts to the level of $B_{\infty}$-algebras of the chain complexes, by showing that the opposite $B_{\infty}$-algebra of the relative Hochschild cochains of the right algebra is isomorphic to the $B_{\infty}$-algebra of Cartier cochains. Lastly, we apply this to entwining stru…

Ultracategories via Kan extensions of relative monads
Umberto Tarantino, Joshua Wrigley
https://arxiv.org/abs/2506.09788 https://arxi…

Ultracategories via Kan extensions of relative monads
Many structured categories of interest are most naturally described as algebras for a relative monad, but turn out nonetheless to be algebras for an ordinary monad. We show that, under suitable hypotheses, the left oplax Kan extension of a relative 2-monad on categories yields a pseudomonad having the same category of colax algebras. In particular, we apply this to the study of ultracategories to recover the 'ultracompletion' pseudomonad.

Robust Planning for Autonomous Vehicles with Diffusion-Based Failure Samplers
Juanran Wang, Marc R. Schlichting, Mykel J. Kochenderfer
https://arxiv.org/abs/2507.11991

Robust Planning for Autonomous Vehicles with Diffusion-Based Failure Samplers
High-risk traffic zones such as intersections are a major cause of collisions. This study leverages deep generative models to enhance the safety of autonomous vehicles in an intersection context. We train a 1000-step denoising diffusion probabilistic model to generate collision-causing sensor noise sequences for an autonomous vehicle navigating a four-way intersection based on the current relative position and velocity of an intruder. Using the generative adversarial architecture, the 1000-step…

A characterization of the Carath\'eodory number for $H$-convexity
Vuong Bui
https://arxiv.org/abs/2507.11013 https://arxiv.org/pd…

A characterization of the Carathéodory number for $H$-convexity
We show that the Carathéodory number for $H$-convexity is the maximum of two parameters: the Helly number for $H$-convexity and the cone number of $H$. The cone number in this article is defined as the maximal number of points of $H$ in conical position with an empty positive hull relative to the remaining points. Earlier partial results by Boltyanski and Martini can provide an exact value for the Carathéodory number only when the Helly number is $1$ or $2$. We further establish connections…

Murmurations using Petersson trace formula
Chan Ieong Kuan, Didier Lesesvre
https://arxiv.org/abs/2507.11418 https://arxiv.org/pdf/25…

Murmurations using Petersson trace formula
We prove the murmuration phenomenon, which is a correlation between signs of functional equations and Fourier coefficients, in the case of modular forms in the weight aspect. We in particular improve the range of visibility of murmurations compared to previous results. This is the first approach to the murmuration phenomenon using a relative trace formula, showing its robustness.

Relative accuracy of turbulence simulations using pseudo-spectral and finite difference solvers
Akash Rodhiya, Shashwat Bhattacharya, Mahendra K Verma
https://arxiv.org/abs/2508.10808

Relative accuracy of turbulence simulations using pseudo-spectral and finite difference solvers
For a single timestep, a spectral solver is known to be more accurate than its finite-difference counterpart. However, as we show in this paper, turbulence simulations using the two methods have nearly the same accuracy. In this paper, we simulate forced hydrodynamic turbulence on a uniform 256$^3$ grid for Reynolds numbers 965, 1231, 1515, and 1994. We show that the two methods yield nearly the same evolution for the total energy and the flow profiles. In addition, the steady-state energy spec…

From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties
Gennaro Auricchio, Giovanni Brigati, Paolo Giudici, Giuseppe Toscani
https://arxiv.org/abs/2507.11387

From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties
Selecting an appropriate divergence measure is a critical aspect of machine learning, as it directly impacts model performance. Among the most widely used, we find the Kullback-Leibler (KL) divergence, originally introduced in kinetic theory as a measure of relative entropy between probability distributions. Just as in machine learning, the ability to quantify the proximity of probability distributions plays a central role in kinetic theory. In this paper, we present a comparative review of div…

FuXi-\beta: Towards a Lightweight and Fast Large-Scale Generative Recommendation Model
Yufei Ye, Wei Guo, Hao Wang, Hong Zhu, Yuyang Ye, Yong Liu, Huifeng Guo, Ruiming Tang, Defu Lian, Enhong Chen
https://arxiv.org/abs/2508.10615

FuXi-β: Towards a Lightweight and Fast Large-Scale Generative Recommendation Model
Scaling laws for autoregressive generative recommenders reveal potential for larger, more versatile systems but mean greater latency and training costs. To accelerate training and inference, we investigated the recent generative recommendation models HSTU and FuXi-$α$, identifying two efficiency bottlenecks: the indexing operations in relative temporal attention bias and the computation of the query-key attention map. Additionally, we observed that relative attention bias in self-attention mec…

Gradient-Normalized Smoothness for Optimization with Approximate Hessians
Andrei Semenov, Martin Jaggi, Nikita Doikov
https://arxiv.org/abs/2506.13710 http…

Gradient-Normalized Smoothness for Optimization with Approximate Hessians
In this work, we develop new optimization algorithms that use approximate second-order information combined with the gradient regularization technique to achieve fast global convergence rates for both convex and non-convex objectives. The key innovation of our analysis is a novel notion called Gradient-Normalized Smoothness, which characterizes the maximum radius of a ball around the current point that yields a good relative approximation of the gradient field. Our theory establishes a natural …

Normal Holonomy of Complex Hyperbolic Submanifolds
Santiago Casta\~neda Montoya, Carlos E. Olmos
https://arxiv.org/abs/2506.11323 https://

Normal Holonomy of Complex Hyperbolic Submanifolds
We prove that the restricted normal holonomy group of a Kähler submanifold of the complex hyperbolic space $\mathbb{C}H^{n}$ is always transitive, provided the index of relative nullity is zero. This contrasts with the case of $\mathbb{C}P^{n}$, where a Berger type result was proved by Console, Di Scala, and the second author. The proof is based on lifting the submanifold to the pseudo-Riemannian space $\mathbb{C}^{n,1}$ and developing new tools to handle the difficulties arising from possible…

Tides Tighten the Hycean Habitable Zone
Joseph R. Livesey, Juliette Becker, Susanna L. Widicus Weaver
https://arxiv.org/abs/2506.12651 https://

Tides Tighten the Hycean Habitable Zone
Hycean planets -- exoplanets with substantial water ice layers, deep surface oceans, and hydrogen-rich atmospheres -- are thought to be favorable environments for life. Due to a relative paucity of atmospheric greenhouse gases, hycean planets have been thought to have wider habitable zones than Earth-like planets, extending down to a few times 0.001 au for those orbiting M dwarfs. In this Letter, we reconsider the hycean habitable zone accounting for star-planet tidal interaction. We show that …

More ghost modules I
Kiyoshi Igusa
https://arxiv.org/abs/2506.12904 https://arxiv.org/pdf/2506.12904…

More ghost modules I
Ghost modules were introduced in [I3] without definitions or proofs. We also introduced stability diagrams or "relative pictures" for torsion classes and torsion-free classes for representations of Dynkin quivers. Modules which were not in the chosen class reappeared as "ghosts", in fact one missing module produced two ghosts. In this short paper, we give a precise definition of ghost modules. We give several examples and prove basis properties of ghosts and pictures for torsion and torsion-fre…

The BAO-CMB Tension and Implications for Inflation
Elisa G. M. Ferreira, Evan McDonough, Lennart Balkenhol, Renata Kallosh, Lloyd Knox, Andrei Linde
https://arxiv.org/abs/2507.12459

The BAO-CMB Tension and Implications for Inflation
The scalar spectral index $n_s$ is a powerful test of inflationary models. The tightest constraint on $n_s$ to date derives from the combination of cosmic microwave background (CMB) data with baryon acoustic oscillation (BAO) data. The resulting $n_s$ constraint is shifted significantly upward relative to the constraint from CMB alone, with the consequence that previously preferred inflationary models are seemingly disfavored by $\gtrsim 2 σ$. Here we show that this shift in $n_s$ is the combi…

Metrics on Permutation Families Defined by a Restriction Graph
Danylo Tymoshenko, Leonhard Nagel
https://arxiv.org/abs/2507.10569 https://

Metrics on Permutation Families Defined by a Restriction Graph
Understanding the metric structure of permutation families is fundamental to combinatorics and has applications in social choice theory, bioinformatics, and coding theory. We study permutation families defined by restriction graphs--oriented graphs that constrain the relative order of elements in valid permutations. For any restriction graph $G$, we determine the maximum distance achievable by two permutations under the $\ell_\infty$-metric and provide an explicit algorithm that constructs opti…

LLM-Based Config Synthesis requires Disambiguation
Rajdeep Mondal, Nikolaj Bjorner, Todd Millstein, Alan Tang, George Varghese
https://arxiv.org/abs/2507.12443

LLM-Based Config Synthesis requires Disambiguation
Beyond hallucinations, another problem in program synthesis using LLMs is ambiguity in user intent. We illustrate the ambiguity problem in a networking context for LLM-based incremental configuration synthesis of route-maps and ACLs. These structures frequently overlap in header space, making the relative priority of actions impossible for the LLM to infer without user interaction. Measurements in a large cloud identify complex ACLs with 100's of overlaps, showing ambiguity is a real problem. W…

From Brittle to Ductile and Back: Reentrant Fracture Transition in Disordered Two-Phase Solids
Subrat Senapati, Anuradha Banerjee, R Rajesh
https://arxiv.org/abs/2506.13433

From Brittle to Ductile and Back: Reentrant Fracture Transition in Disordered Two-Phase Solids
Fracture processes in multi-phase solids are inherently complex due to multiple competing mechanisms. Here, we investigate the elastic and fracture behaviour of two-phase solids, comprising a fragile phase and a tough phase using a disordered spring network model. The macroscopic response is found to depend on the failure strain mismatch, the elastic modulus ratio, as well as the relative composition of the constituent phases. As the proportion of the tough phase increases, the system undergoes…

COS-EDGES: Co-rotation and Kinematic Stratification of the Multi-Phase CGM Around Edge-On Galaxies
Glenn G. Kacprzak, Benjamin D. Oppenheimer, Nikole M. Nielsen, Antonia Fernandez-Figueroa, Michael T. Murphy, Rebecca J. Allen, Tania M. Barone, Sameer, Christopher W. Churchill, Joseph N. Burchett, Kaustubh R. Gupta, Jane C. Charlton, Caleb B. Platukis

COS-EDGES: Co-rotation and Kinematic Stratification of the Multi-Phase CGM Around Edge-On Galaxies
We present the first results from the COS-EDGES survey, targeting the kinematic connection between the ISM and multi-phase circumgalactic medium (CGM) in nine isolated, edge-on galaxies at z~0.2, each probed along its major axis by a background quasar at impact parameters of 13-38kpc. Using VLT/UVES and HST/COS quasar spectra, we analyse MgI, MgII, HI, CII, CIII, and OVI absorption relative to galaxy rotation curves from Keck/LRIS and Magellan/MagE spectra. We find that at lower $D/R_{vir}$ ($D…

Tube formula for spherically contoured random fields with subexponential marginals
Satoshi Kuriki, Evgeny Spodarev
https://arxiv.org/abs/2507.11154 https:/…

Tube formula for spherically contoured random fields with subexponential marginals
It is widely known that the tube method, or equivalently the Euler characteristic heuristic, provides a very accurate approximation for the tail probability that the supremum of a smooth Gaussian random field exceeds a threshold value $c$. The relative approximation error $Δ(c)$ is exponentially small as a function of $c$ when $c$ tends to infinity. On the other hand, little is known about non-Gaussian random fields. In this paper, we obtain the approximation error of the tube method applied…

Nine-year-old relative of Chiefs owner Clark Hunt among those dead in Texas flooding

https://www.cbssports.com/nfl/news/nine-year-old-…

Coherence monotones of quantum channels based on two generalized quantum relative entropies
Jiaorui Fan, Zhaoqi Wu, Shao-Ming Fei
https://arxiv.org/abs/2506.10810

Coherence monotones of quantum channels based on two generalized quantum relative entropies
By using the Choi-Jamiołkowski isomorphism, we propose two classes of coherence monotones of quantum channels based on the unified $(r,s)$-relative entropy and the sandwiched Rényi relative entropy. Elegant properties of the coherence monotones for quantum channels are explored. Moreover, we present the upper bounds of the coherence monotones and derive the explicit formulas of the coherence monotones for qubit unitary channels.

Relative timestamps are dumb. This is a particularly dumb example, but there's literally no way to improve it while keeping it a relative timestamp.

Relative Riemann-Hilbert and Newlander-Nirenberg Theorems for torsion-free analytic sheaves on maximal and homogeneous spaces
Thomas Kurbach
https://arxiv.org/abs/2506.05841

Relative Riemann-Hilbert and Newlander-Nirenberg Theorems for torsion-free analytic sheaves on maximal and homogeneous spaces
In this paper it is shown that for locally trivial complex analytic morphisms between some reduced spaces the Relative Riemann-Hilbert Theorem still holds up to torsion, i.e. tame flat relative connections on torsion-free sheaves are in 1-to-1 correspondence with torsion-free relative local systems. Subsequently, it is shown that generalised $\bar{\partial}$-operators on real analytic sheaves over complex analytic spaces can be viewed as relative complex analytic connections on the complexifica…

Multiscale transform based seismic reflectivity inversion using convolutional neural network
John Castagna (University of Houston), Oleg Portniaguine (Lumina Geophysical, Houston, Tx), Gabriel Gil (Lumina Geophysical, Houston, Tx), Arnold Oyem (Lumina Geophysical, Houston, Tx), Chen Liang (Lumina Geophysical, Houston, Tx)
https://

Multiscale transform based seismic reflectivity inversion using convolutional neural network
The Multiscale Fourier Transform of a seismic trace performs time-frequency analyses over a range of window lengths. The variation in window length captures local and global relative amplitudes between events, thereby allowing reflectivity inversion that is independent of the amplitude spectrum of the seismic wavelet. As the temporal and spatial variation of the actual seismic wavelet in seismic reflection data is poorly known, this approach has many advantages over conventional seismic reflect…

The Case against Scale: Empirical Evidence of Underperformance in Large Secondary Funds
Jitesh Gurav
https://arxiv.org/abs/2507.12436 https://

The Case against Scale: Empirical Evidence of Underperformance in Large Secondary Funds
The paper analyses the increasing popularity of large funds in the secondary private equity market, which are pegged on the perceived larger scale advantages of operational efficiency and fewer manager relationships (Reuter & Zitzewitz, 2021). However, it has been proved empirically that smaller funds perform better than the big ones in terms of their internal rates of return (IRRs). This work questions this authoritative view, providing evidence of outperformance of smaller funds relative to t…

Slope detection, taut foliations, and the relative L-space conjecture
Steven Boyer, Cameron McA. Gordon, Ying Hu
https://arxiv.org/abs/2508.06395 https://a…

Slope detection, taut foliations, and the relative L-space conjecture
The $L$-space conjecture asserts the equivalence, for prime $3$-manifolds, of three properties: not being an $L$-space ($NLS$), having a left-orderable fundamental group ($LO$), and admitting a co-orientable taut foliation ($CTF$). In this paper we introduce a relative version of the $L$-space conjecture for knot manifolds $M$, stated in terms of sets of slopes on $\partial M$ characterised (i.e. detected) by Heegaard Floer homology, left-orders, and foliations, respectively. We give a unified …

I believe I have "mild” (relative to others I've heard about) Long COVID and my symptoms include, fatigue, memory loss, loss of focus, loss of motivation, worse sleep.
It's real folks.
https://mastodon.social/@augieray/114841505817793827

Quantile Reward Policy Optimization: Alignment with Pointwise Regression and Exact Partition Functions
Simon Matrenok, Skander Moalla, Caglar Gulcehre
https://arxiv.org/abs/2507.08068 https://arxiv.org/pdf/2507.08068 https://arxiv.org/html/2507.08068
arXiv:2507.08068v1 Announce Type: new
Abstract: Aligning large language models with pointwise absolute rewards has so far required online, on-policy algorithms such as PPO and GRPO. In contrast, simpler methods that can leverage offline or off-policy data, such as DPO and REBEL, are limited to learning from preference pairs or relative signals. To bridge this gap, we introduce \emph{Quantile Reward Policy Optimization} (QRPO), which learns from pointwise absolute rewards while preserving the simplicity and offline applicability of DPO-like methods. QRPO uses quantile rewards to enable regression to the closed-form solution of the KL-regularized RL objective. This reward yields an analytically tractable partition function, removing the need for relative signals to cancel this term. Moreover, QRPO scales with increased compute to estimate quantile rewards, opening a new dimension for pre-computation scaling. Empirically, QRPO consistently achieves top performance on chat and coding evaluations -- reward model scores, AlpacaEval 2, and LeetCode -- compared to DPO, REBEL, and SimPO across diverse datasets and 8B-scale models. Finally, we find that training with robust rewards instead of converting them to preferences induces less length bias.
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Relative mirror symmetry, theta functions and the Gamma conjecture
Fenglong You
https://arxiv.org/abs/2508.06750 https://arxiv.org/pdf/2508.06750

Relative mirror symmetry, theta functions and the Gamma conjecture
Let $X$ be a Fano variety, and $D\subset X$ be an snc anticanonical divisor. We study relative mirror symmetry for the log Calabi--Yau pair $(X,D)$. (1) We prove a relative mirror theorem for snc pairs without assuming the divisors are nef. (2) We study theta functions associated with the pair $(X,D)$. (3) We introduce functions on the mirror that are obtained from the higher-degree part of the big relative quantum cohomology. As an application, we use these new ingredients in relative mirror s…

English is great, but have you tried French? They have an adjective for "relative to cod" ("morutier")! Mom always said you learn something every day.

Quantifying coherence of quantum channels based on the generalized $\alpha$-$z$-relative R\'{e}nyi entropy
Jiaorui Fan, Zhaoqi Wu, Shao-Ming Fei
https://arxiv.org/abs/2506.10796

Quantifying coherence of quantum channels based on the generalized $α$-$z$-relative Rényi entropy
By using the Choi-Jamiołkowski isomorphism, we propose a well-defined coherence measure of quantum channels based on the generalized $α$-$z$-relative Rényi entropy. In addition, we present an alternative coherence measure of quantum channels by quantifying the commutativity between the channels and the completely dephasing channels with the generalized $α$-$z$-relative Rényi entropy. Some elegant properties of the measures are illustrated in detail. Explicit formulas of these coherence mea…

A Geometric Solution to the Isoperimetric Problem and its Quantitative Inequalities
Lakshya Chaudhary
https://arxiv.org/abs/2506.12864 https://

A Geometric Solution to the Isoperimetric Problem and its Quantitative Inequalities
This paper introduces a geometric solution to the classical isoperimetric problem by analysing the area efficiency of n-sided regular polygons through a novel apothem-hypotenuse ratio framework. A new formula is derived to quantify polygonal efficiency based on apothem, hypotenuse, and perimeter, demonstrating how regular polygons approach the optimal area-enclosing efficiency of the circle as the number of sides increases. The work further presents an original formula for area lost relative to…

Some runs are trials of endurance. Tonight was less about physical or mental factors and more about overcoming environmental ones. Not really hot tonight (75°F/23.9°C) but the relative humidity was 93.5%. My point is I’m a sweaty mess and cooler seasons cannot get here soon enough.
Adding to my suffering, some animal died near one end of the track. Didn’t notice until I was underway. Every lap was an agony of decomposition. I reckon 1/3 of this run was with held breath. 🤢

Planetary waves can activate resonant drag instabilities in 3D dusty gaseous discs
Ra\'ul O. Chametla, Yasuhiro Hasegawa, Gennaro D'Angelo
https://arxiv.org/abs/2506.13592

Planetary waves can activate resonant drag instabilities in 3D dusty gaseous discs
Resonant Drag Instabilities (RDIs) in protoplanetary discs are driven by the aerodynamic back-reaction of dust on gas and occur when the relative dust-gas motion resonate with a wave mode intrinsic to the gas fluid. Axisymmetric models indicate that the RDI generates filamentary perturbations, leading to grain clumping and planetesimal formation. Motivated by these findings, we investigate the dust-gas interaction in a non-axisymmetric inviscid protoplanetary disc with an embedded low-mass plan…

Intrinsic spin distributions in multinucleon transfer reactions
Dan Dan Zhang, Dario Vretenar, Tamara Nik\v{s}i\'c, Peng Wei Zhao, Jie Meng
https://arxiv.org/abs/2507.11905

Intrinsic spin distributions in multinucleon transfer reactions
Time-dependent covariant density functional theory (TD-CDFT) combined with angular momentum projection is developed and applied to study multinucleon transfer (MNT) reactions, with a focus on the intrinsic angular momentum distributions of the final fragments. Using the illustrative reaction $^{40}$Ca + $^{208}$Pb across a range of impact parameters, we find that the MNT process generates broad distributions of intrinsic spins. These distributions arise from the conversion of relative orbital a…

The Relative Instability of Model Comparison with Cross-validation
Alexandre Bayle, Lucas Janson, Lester Mackey
https://arxiv.org/abs/2508.04409 https://ar…

The Relative Instability of Model Comparison with Cross-validation
Existing work has shown that cross-validation (CV) can be used to provide an asymptotic confidence interval for the test error of a stable machine learning algorithm, and existing stability results for many popular algorithms can be applied to derive positive instances where such confidence intervals will be valid. However, in the common setting where CV is used to compare two algorithms, it becomes necessary to consider a notion of relative stability which cannot easily be derived from existin…

"New oil and gas fields incompatible with Paris climate goals"
#Climate #ClimateChange #ParisAgreement

New oil and gas fields incompatible with Paris climate goals
Opening any new North Sea oil and gas fields is incompatible with achieving the Paris Climate Agreement goals of limiting warming to 1.5°C or holding warming to “well below 2°C” relative to preindustrial levels, finds a new report published by UCL academics.

Relative Completeness of Incorrectness Separation Logic
Yeonseok Lee, Koji Nakazawa
https://arxiv.org/abs/2508.01535 https://arxiv.org/pdf/2508.01535

Relative Completeness of Incorrectness Separation Logic
Incorrectness Separation Logic (ISL) is a proof system that is tailored specifically to resolve problems of under-approximation in programs that manipulate heaps, and it primarily focuses on bug detection. This approach is different from the over-approximation methods that are used in traditional logics such as Hoare Logic or Separation Logic. Although the soundness of ISL has been established, its completeness remains unproven. In this study, we establish relative completeness by leveraging th…

This https://arxiv.org/abs/2506.01483 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Inter-Speaker Relative Cues for Text-Guided Target Speech Extraction
We propose a novel approach that utilize inter-speaker relative cues for distinguishing target speakers and extracting their voices from mixtures. Continuous cues (e.g., temporal order, age, pitch level) are grouped by relative differences, while discrete cues (e.g., language, gender, emotion) retain their categories. Relative cues offers greater flexibility than fixed speech attribute classification, facilitating much easier expansion of text-guided target speech extraction datasets. Our exper…

Entropy production rate and time-reversibility for general jump diffusions on $\mathbb{R}^n$
Qi Zhang, Yubin Lu
https://arxiv.org/abs/2506.13135 https://…

Entropy production rate and time-reversibility for general jump diffusions on $\mathbb{R}^n$
This paper investigates the entropy production rate and time-reversibility for general jump diffusions (Lévy processes) on $\mathbb{R}^n$. We first formulate the entropy production rate and explore its associated thermodynamic relations for jump diffusions. Subsequently, we derive the entropy production rate using the relative entropy between the forward and time-reversed path measures for stationary jump diffusions via the Girsanov transform. Furthermore, we establish the equivalence among ti…

New oil and gas fields incompatible with Paris climate goals #environment

New oil and gas fields incompatible with Paris climate goals
Opening any new North Sea oil and gas fields is incompatible with achieving the Paris Climate Agreement goals of limiting warming to 1.5°C or holding warming to "well below 2°C" relative to preindustrial levels, finds a new report published by UCL academics.

A Dissipativity Framework for Constructing Scaled Graphs
Timo de Groot, Maurice heemels, Sebastiaan van den Eijnden
https://arxiv.org/abs/2507.08411 https:…

A Dissipativity Framework for Constructing Scaled Graphs
Scaled relative graphs have been originally introduced in the context of convex optimization and have recently gained attention in the control systems community for the graphical analysis of nonlinear systems. Of particular interest in stability analysis of feedback systems is the scaled graph, a special case of the scaled relative graph. In many ways, scaled graphs can be seen as a generalization of the classical Nyquist plot for linear time-invariant systems, and facilitate a powerful graphic…

Forbidden configurations for coherency
Victoria Gould, Marianne Johnson
https://arxiv.org/abs/2506.11321 https://arxiv.org/pdf/2506.1…

Forbidden configurations for coherency
Right (and left) coherency and right (and left) weak coherency are natural finitary conditions for monoids, however, determining whether a given monoid is right, or dually left, coherent turns out to be hard and disparate techniques have been developed to show that certain classes of monoids are (or are not) right coherent. We exhibit a particular configuration of elements in a monoid subsemigroup of a right (respectively, left) $E$-Ehresmann monoid, relative to the Ehresmann structure of the o…

First images of the Sun's south pole!
Solar Orbiter is the first space probe to look at the Sun's poles – and finds the magnetic field there in a state of turmoil. The Sun's magnetic field is currently undergoing a flip. During its latest flyby of the Sun at the end of March this year, the Solar Orbiter space probe had its first clear view of our star's poles. First images:

"Although police officers per capita are above the median among OECD countries, the U.S. is an outlier in having few police per homicide. [This] is explained not by police staffing levels but by high levels of bureaucratic shirking... inefficient allocation, low effort, and the avoidance of bodily harm. We show that U.S. officers are paid significantly more (in relative and absolute terms) while not being at greater risk... than their international counterparts."

Quality attributes of test cases and test suites -- importance & challenges from practitioners' perspectives
Huynh Khanh Vi Tran, Nauman bin Ali, Michael Unterkalmsteiner, J\"urgen B\"orstler, Panagiota Chatzipetrou
https://arxiv.org/abs/2507.06343

Quality attributes of test cases and test suites -- importance & challenges from practitioners' perspectives
Context: The quality of the test suites and the constituent test cases significantly impacts confidence in software testing. While research has identified several quality attributes of test cases and test suites, there is a need for a better understanding of their relative importance in practice. Objective: We investigate practitioners' perceptions regarding the relative importance of quality attributes of test cases and test suites and the challenges they face in ensuring the perceived importa…

This https://arxiv.org/abs/2309.15793 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Targeting relative risk heterogeneity with causal forests
The identification of heterogeneous treatment effects (HTE) across subgroups is of significant interest in clinical trial analysis. Several state-of-the-art HTE estimation methods, including causal forests, apply recursive partitioning for non-parametric identification of relevant covariates and interactions. However, the partitioning criterion is typically based on differences in absolute risk. This can dilute statistical power by masking variation in the relative risk, which is often a more a…

General Boosted Black Holes: A First Approximation
Rodrigo Maier
https://arxiv.org/abs/2508.09988 https://arxiv.org/pdf/2508.09988

General Boosted Black Holes: A First Approximation
In this paper we obtain an approximate solution of Einstein field equations which describes a general boosted Kerr-Newman black hole relative to a Lorentz frame at future null infinity. The boosted black hole is obtained from a general twisting metric whose boost emerges from the BMS group. Employing a standard procedure we build the electromagnetic energy-momentum tensor with the Kerr boosted metric together with its timelike Killing vector as the electromagnetic potential. We demonstrate that…

Reinforced Language Models for Sequential Decision Making
Jim Dilkes, Vahid Yazdanpanah, Sebastian Stein
https://arxiv.org/abs/2508.10839 https://arxiv.org…

Reinforced Language Models for Sequential Decision Making
Large Language Models (LLMs) show potential as sequential decision-making agents, but their application is often limited due to a reliance on large, computationally expensive models. This creates a need to improve smaller models, yet existing post-training methods are designed for single-turn interactions and cannot handle credit assignment in multi-step agentic tasks. To address this, we introduce Multi-Step Group-Relative Policy Optimization (MS-GRPO), a new algorithm for post-training LLM ag…

Uncertainty relations for unified ($\alpha$,$\beta$)-relative entropy of coherence under mutually unbiased equiangular tight frames
Baolong Cheng, Zhaoqi Wu
https://arxiv.org/abs/2506.09779

Uncertainty relations for unified ($α$,$β$)-relative entropy of coherence under mutually unbiased equiangular tight frames
Uncertainty relations based on quantum coherence is an important problem in quantum information science. We discuss uncertainty relations for averaged unified ($α$,$β$)-relative entropy of coherence under mutually unbiased equiangular tight frames, and derive an interesting result for different parameters. As consequences, we obtain corresponding results under mutually unbiased bases, equiangular tight frames or based on Tsallis $α$- relative entropies and Rényi-$α$ relative entropies. We …

Improving LLM Reasoning for Vulnerability Detection via Group Relative Policy Optimization
Marco Simoni, Aleksandar Fontana, Giulio Rossolini, Andrea Saracino
https://arxiv.org/abs/2507.03051

Improving LLM Reasoning for Vulnerability Detection via Group Relative Policy Optimization
Improving and understanding the training dynamics and reasoning of Large Language Models (LLMs) has become essential for their deployment in AI-based security tools, such as software vulnerability detection. In this work, we present an extensive study aimed at advancing recent RL-based finetuning techniques for LLMs in the context of vulnerability detection. We start by highlighting key limitations of commonly adopted LLMs, such as their tendency to over-predict certain types of vulnerabiliti…

Updated Mutual Inclination Measurement for 14 Her b and c
Guang-Yao Xiao, Fabo Feng
https://arxiv.org/abs/2506.13580 https://arxiv.or…

Updated Mutual Inclination Measurement for 14 Her b and c
The mutual inclination $ψ$ between orbits within multi-planetary systems is difficult to measure directly. Through a joint analysis of RVs, Hipparcos-Gaia absolute astrometry and relative astrometry of JWST, \citet{Bardalez2025} recently found two possible values of $ψ_{bc}={32_{-15.1}^{+13.6}}^{\circ}$ and $ψ_{bc}={145.0_{-11.1}^{+15.8}}^{\circ}$ for the nearby, non-transit planet system, 14\,Her. By incorporating additional astrometry from Gaia second data release (DR2), we have further co…

Combinatorial relative algebraic $K$-theory
Jane Turner
https://arxiv.org/abs/2506.09905 https://arxiv.org/pdf/2506.09905

Combinatorial relative algebraic $K$-theory
In a preprint released in 2016, Daniel Grayson introduces a conjectural presentation of the (higher) relative algebraic $K$-groups using purely combinatorial means. In this paper, we will show that this presentation is isomorphic to the classically defined higher relative algebraic $K$-groups, and provide some reasons to believe the conjecture posed in this 2016 preprint to be true.

Equivariant Filter for Relative Attitude and Target Angular Velocity Estimation
Gil Serrano, Bruno J. Guerreiro, Pedro Louren\c{c}o, Rita Cunha
https://arxiv.org/abs/2506.06016

Equivariant Filter for Relative Attitude and Target Angular Velocity Estimation
Accurate estimation of the relative attitude and angular velocity between two rigid bodies is fundamental in aerospace applications such as spacecraft rendezvous and docking. In these scenarios, a chaser vehicle must determine the orientation and angular velocity of a target object using onboard sensors. This work addresses the challenge of designing an Equivariant Filter (EqF) that can reliably estimate both the relative attitude and the target angular velocity using noisy observations of two …

ReNiL: Relative Neural Inertial Locator with Any-Scale Bayesian Inference
Kaixuan Wu (School of Computer Science, Wuhan University, Wuhan, China, School of Cyber Science and Engineering, Wuhan University, Wuhan, China), Yuanzhuo Xu (School of Computer Science, Wuhan University, Wuhan, China), Zejun Zhang (University of Southern California, Los Angeles, United States), Weiping Zhu (School of Computer Science, Wuhan University, Wuhan, China), Steve Drew (Department of Electrical and Soft…

ReNiL: Relative Neural Inertial Locator with Any-Scale Bayesian Inference
Pedestrian inertial localization is key for mobile and IoT services because it provides infrastructure-free positioning. Yet most learning-based methods depend on fixed sliding-window integration, struggle to adapt to diverse motion scales and cadences, and yield inconsistent uncertainty, limiting real-world use. We present ReNiL, a Bayesian deep-learning framework for accurate, efficient, and uncertainty-aware pedestrian localization. ReNiL introduces Inertial Positioning Demand Points (IPDPs)…

Uncertainty and entropies of classical channels
Takla Nateeboon
https://arxiv.org/abs/2507.12310 https://arxiv.org/pdf/2507.12310

Uncertainty and entropies of classical channels
In this thesis, I studied a mathematical development to define and quantify the uncertainty inherent in classical channels. This thesis starts with the introduction and background on how to formally think about uncertainty in the domain of classical states. The concept of probability vector majorization and its variants, relative majorization and conditional majorization, are reviewed. This thesis introduces three conceptually distinct approaches to formalize the notion of uncertainty inherent …

Relative Income and Gender Norms: Evidence from Latin America
Ercio Mu\~noz, Dario Sansone, Jo\~ao Tampellini
https://arxiv.org/abs/2508.08166 https://arxi…

Relative Income and Gender Norms: Evidence from Latin America
Using data from over 500,000 dual-earner households in Mexico, we provide evidence of discontinuities in the distribution of relative income within households in Latin America. Similar to high-income countries, we observe a sharp drop at the 50% threshold, where the wife earns more than the husband, but the discontinuity is up to five times larger and has increased over time. These patterns are robust to excluding equal earners, self-employed individuals, or couples in the same occupation/indus…

On Relative Ordered Tur\'an Density
Dylan King, Bernard Lidick\'y, Minghui Ouyang, Florian Pfender, Runze Wang, Zimu Xiang
https://arxiv.org/abs/2508.05515 https://

On Relative Ordered Turán Density
For an ordered graph $F$, denote the Turán density by $\vecπ(F)$. The relative Turán density, denoted by $ρ(F)$, is the supremum over $α\in [0,1]$ such that every ordered graph $G$ contains an $F$-free subgraph $G'$ with $e(G') \geq αe(G)$. Reiher, Rödl, Sales and Schacht showed that $ρ(P) = \vecπ(P)/2$ and $ρ(K) = \vecπ(K)$ for any ascending path $P$ or clique $K$. They asked if there are any ordered graphs $F$ with $\vecπ(F)/2 < ρ(F) < \vecπ(F)$. We answer this question in the a…

Making Qwen3 Think in Korean with Reinforcement Learning
Jungyup Lee, Jemin Kim, Sang Park, SeungJae Lee
https://arxiv.org/abs/2508.10355 https://arxiv.org…

Making Qwen3 Think in Korean with Reinforcement Learning
We present a two-stage fine-tuning approach to make the large language model Qwen3 14B "think" natively in Korean. In the first stage, supervised fine-tuning (SFT) on a high-quality Korean reasoning dataset establishes a strong foundation in Korean logical reasoning, yielding notable improvements in Korean-language tasks and even some gains in general reasoning ability. In the second stage, we employ reinforcement learning with a customized Group Relative Policy Optimization (GRPO) algorithm to…

Horizontal Descent, Immersions, Unramified Morphisms, Submersions, \'Etale Morphisms and the Relative Cotangent Sequence in Tangent Categories
Jean-Simon Pacaud Lemay, Geoff Vooys
https://arxiv.org/abs/2506.07874

Horizontal Descent, Immersions, Unramified Morphisms, Submersions, Étale Morphisms and the Relative Cotangent Sequence in Tangent Categories
In this paper we provide a deep and systematic study of the classes of what it means to be an immersion, a submersion, a local diffeomorphism, and unramified in a tangent category. We also give a systematic study of the ways in which these classes of morphisms interact, the properties they have, and give very explicit and concrete characterizations of how each class of maps appear in algebraic geometry, in differential geometry, in the theory of semirings, and in the theory of Cartesian differe…

On singular limits of relative entropies
Feng Xu
https://arxiv.org/abs/2508.03271 https://arxiv.org/pdf/2508.03271

On singular limits of relative entropies
In this paper we generalize a key result relating singular limits of certain relative entropies with index in the setting of conformal nets, which has played an important role recently in the mathematical theory of relative entropies in the context of Conformal Field Theory.

A thermofield-double model of Uhlmann anholonomy
P\'eter L\'evay, Csaba Velich
https://arxiv.org/abs/2507.12071 https://arxiv…

A thermofield-double model of Uhlmann anholonomy
A simple parametrized family of quantum systems consisting of two entangled subsystems, dubbed left and right ones, both of them featuring N qubits is considered in the thermofield double formalism. We assume that the system evolves in a purely geometric manner based on the parallel transport condition due to Uhlmann. We explore the different interpretations of this evolution relative to observers either coupled to the left or to the right subsystems. The Uhlmann condition breaks the symmetry b…

Onboard Dual Quaternion Guidance for Rocket Landing
Abhinav G. Kamath, Javier A. Doll, Purnanand Elango, Taewan Kim, Skye Mceowen, Yue Yu, Taylor P. Reynolds, Gavin F. Mendeck, John M. Carson III, Mehran Mesbahi, Beh\c{c}et A\c{c}{\i}kme\c{s}e
https://arxiv.org/abs/2508.10439

Onboard Dual Quaternion Guidance for Rocket Landing
The dual quaternion guidance (DQG) algorithm was selected as the candidate 6-DoF powered-descent guidance algorithm for NASA's Safe and Precise Landing -- Integrated Capabilities Evolution (SPLICE) project. DQG is capable of handling state-triggered constraints that are of utmost importance in terms of enabling technologies such as terrain relative navigation. In this work, we develop a custom solver for DQG to enable onboard implementation for future rocket landing missions. We describe the de…

Algebraic Mapping Class Group Rigidity
Seong Youn Kim
https://arxiv.org/abs/2508.09421 https://arxiv.org/pdf/2508.09421

Algebraic Mapping Class Group Rigidity
Let $g, n \geq 0$ and $Σ= Σ_{g, n}$ be a connected oriented surface of genus $g$ with $n$ punctures. The $\mathrm{SL}_2$-character variety of $Σ$ has a rigid relative automorphism group, whose elements fix each monodromies along punctures, and is a finite extension of the mapping class group. The exceptional isomorphism between the $\mathrm{SL}(2, \mathbb{C})$-character variety and moduli of points on complex $3$-sphere provides a new description of the mapping class group of certain $Σ$.

On relative cuspidality
Nadir Matringe
https://arxiv.org/abs/2506.08393 https://arxiv.org/pdf/2506.08393

On relative cuspidality
Let $(\mathbb{G},\mathbb{H})$ be a symmetric pair of reductive groups over a $p$-adic field with $p\neq 2$, attached to the involution $θ$. Under the assumption that there exists a maximally $θ$-split torus in $\mathbb{G}$, which is anisotropic modulo its intersection with the split component of $\mathbb{G}$, we extend Beuzart-Plessis' proof of existence of cuspidal representations, and prove that $\mathbb{G}(F)$ admits strongly relatively cuspidal representations. This confirms expectations …

Orientation of galaxy spins relative to filaments of the large-scale structure of the Universe
A. V. Antipova, D. I. Makarov, N. Libeskind, E. Tempel
https://arxiv.org/abs/2507.07334

Orientation of galaxy spins relative to filaments of the large-scale structure of the Universe
The theory of galaxy formation posits a clear correlation between the spin of galaxies and the orientation of the elements of the large-scale structure of the Universe, particularly cosmic filaments. A substantial number of observational and modelling studies have been undertaken with the aim of identifying the dependence of spin orientation on the components of the large-scale structure. However, the findings of these studies remain contradictory. In this paper, we present an analysis of the o…

Conditions for Large-Sample Majorization of Pairs of Flat States in Terms of $\alpha$-$z$ Relative Entropies
Frits Verhagen, Marco Tomamichel, Erkka Haapasalo
https://arxiv.org/abs/2507.07520

Conditions for Large-Sample Majorization of Pairs of Flat States in Terms of $α$-$z$ Relative Entropies
In this work, we offer the first operational interpretation of the $α$-$z$ relative entropies, which were introduced by Jakšić {\it et al.} \cite{Jaksic2012} and Audenaert and Datta \cite{Audenaert_Datta_2015}, where the $α$ and $z$ parameters are truly independent from each other. Namely, we show that these relative entropies appear in the conditions for large-sample or catalytic relative majorization of pairs of flat states and certain generalizations of them. Additionally, the optimal ra…

TGRPO :Fine-tuning Vision-Language-Action Model via Trajectory-wise Group Relative Policy Optimization
Zengjue Chen, Runliang Niu, He Kong, Qi Wang
https://arxiv.org/abs/2506.08440

TGRPO :Fine-tuning Vision-Language-Action Model via Trajectory-wise Group Relative Policy Optimization
Recent advances in Vision-Language-Action (VLA) model have demonstrated strong generalization capabilities across diverse scenes, tasks, and robotic platforms when pretrained at large-scale datasets. However, these models still require task-specific fine-tuning in novel environments, a process that relies almost exclusively on supervised fine-tuning (SFT) using static trajectory datasets. Such approaches neither allow robot to interact with environment nor do they leverage feedback from live ex…

A Dual Quaternion Control Law for Formation Control of Multiple 3-D Rigid Bodies
Chunfeng Cui, Liqun Qi, Hao Chen, Xiangke Wang
https://arxiv.org/abs/2508.10519 https://

A Dual Quaternion Control Law for Formation Control of Multiple 3-D Rigid Bodies
This paper studies the integrated position and attitude control problem for multi-agent systems of 3D rigid bodies. While the state-of-the-art method in [Olfati-Saber and Murray, 2004] established the theoretical foundation for rigid-body formation control, it requires all agents to asymptotically converge to identical positions and attitudes, limiting its applicability in scenarios where distinct desired relative configurations must be maintained. In this paper, we develop a novel dual-quatern…

Cohomologies and linear deformations of relative Rota-Baxter operators on (pre-)Jacobi-Jordan algebras
Nabil Oro Djibril, Sylvain Attan
https://arxiv.org/abs/2508.03096 https://…

Cohomologies and linear deformations of relative Rota-Baxter operators on (pre-)Jacobi-Jordan algebras
Some results on (pre-)Jacobi-Jordan algebras and their representations are proved. Moreover, the notion of matched pairs and relative Rota-Baxter operators on these algebras are introduced and studied. The cohomology theory of relative Rota-Baxter operators on (pre)-Jacobi-Jordan algebras is introduced. We use the cohomological approach to study linear deformations of relative Rota-Baxter operators. In particular, the notion of Nijenhuis elements is introduced to characterize trivial linear def…

CueLearner: Bootstrapping and local policy adaptation from relative feedback
Giulio Schiavi, Andrei Cramariuc, Lionel Ott, Roland Siegwart
https://arxiv.org/abs/2507.04730

CueLearner: Bootstrapping and local policy adaptation from relative feedback
Human guidance has emerged as a powerful tool for enhancing reinforcement learning (RL). However, conventional forms of guidance such as demonstrations or binary scalar feedback can be challenging to collect or have low information content, motivating the exploration of other forms of human input. Among these, relative feedback (i.e., feedback on how to improve an action, such as "more to the left") offers a good balance between usability and information richness. Previous research has shown th…

Finer control on relative sizes of iterated sumsets
Jacob Fox, Noah Kravitz, Shengtong Zhang
https://arxiv.org/abs/2506.05691 https://

Finer control on relative sizes of iterated sumsets
Inspired by recent questions of Nathanson, we show that for any infinite abelian group $G$ and any integers $m_1, \ldots, m_H$, there exist finite subsets $A,B \subseteq G$ such that $|hA|-|hB|=m_h$ for each $1 \leq h \leq H$. We also raise, and begin to address, questions about the smallest possible cardinalities and diameters of such sets $A,B$.

Beyond Uniform Criteria: Scenario-Adaptive Multi-Dimensional Jailbreak Evaluation
Lai Jiang, Yuekang Li, Xiaohan Zhang, Youtao Ding, Li Pan
https://arxiv.org/abs/2508.06194 http…

Beyond Uniform Criteria: Scenario-Adaptive Multi-Dimensional Jailbreak Evaluation
Precise jailbreak evaluation is vital for LLM red teaming and jailbreak research. Current approaches employ binary classification ( e.g., string matching, toxic text classifiers, LLM-driven methods), yielding only "yes/no" labels without quantifying harm intensity. Existing multi-dimensional frameworks ( e.g., Security Violation, Relative Truthfulness, Informativeness) apply uniform evaluation criteria across scenarios, resulting in scenario-specific mismatches--for instance, "Relative Truthful…

Two imaginarity monotones induced by unified $(\alpha,\beta)$-relative entropy
Chuanfa Wu, Zhaoqi Wu
https://arxiv.org/abs/2506.09799 https://

Two imaginarity monotones induced by unified $(α,β)$-relative entropy
Complex numbers play a pivotal role in both mathematics and physics, particularly in quantum mechanics, and are extensively utilized to depict the behavior of microscopic particles. Recognizing the significance of complex numbers, a framework of imaginarity resource theory has recently been established. In this work, we propose two types of imaginarity monotones induced by the unified $(α,β)$-relative entropy and investigate their properties. Moreover, we give explicit examples to illustrate …

(BAA)-branes from higher Teichm\"uller theory
Eric Y. Chen, Enya Hsiao, Mengxue Yang
https://arxiv.org/abs/2508.09562 https://arxiv.org/pdf/2508.09562…

(BAA)-branes from higher Teichmüller theory
Interpreting certain holomorphic Lagrangians that arise from the relative Langlands program, we construct moduli stacks underlying the generalized Slodowy categories of Collier--Sanders and $G^\mathbf{R}$-Higgs bundles over a Riemann surface. Furthermore, we extend the Cayley correspondence of Bradlow--Collier--García-Prada--Gothen--Oliveira to a morphism of Lagrangians over the Hitchin moduli stack, and initiate the study of its hyperholomorphic mirror partner under $S$-duality.

Existence of Solutions and Relative Regularity Conditions for Polynomial Vector Optimization Problems
Danyang Liu
https://arxiv.org/abs/2508.04991 https://…

Existence of Solutions and Relative Regularity Conditions for Polynomial Vector Optimization Problems
In this paper, we establish the existence of the efficient solutions for polynomial vector optimization problems on a nonempty closed constraint set without any convexity and compactness assumptions. We first introduce the relative regularity conditions for vector optimization problems whose objective functions are a vector polynomial and investigate their properties and characterizations. Moreover, we establish relationships between the relative regularity conditions, Palais-Smale condition, w…

MGPRL: Distributed Multi-Gaussian Processes for Wi-Fi-based Multi-Robot Relative Localization in Large Indoor Environments
Sai Krishna Ghanta, Ramviyas Parasuraman
https://arxiv.org/abs/2506.23514

MGPRL: Distributed Multi-Gaussian Processes for Wi-Fi-based Multi-Robot Relative Localization in Large Indoor Environments
Relative localization is a crucial capability for multi-robot systems operating in GPS-denied environments. Existing approaches for multi-robot relative localization often depend on costly or short-range sensors like cameras and LiDARs. Consequently, these approaches face challenges such as high computational overhead (e.g., map merging) and difficulties in disjoint environments. To address this limitation, this paper introduces MGPRL, a novel distributed framework for multi-robot relative loca…

Empirical and computer-aided robustness analysis of long-step and accelerated methods in smooth convex optimization
Pierre Vernimmen, Fran\c{c}ois Glineur
https://arxiv.org/abs/2506.09730

Empirical and computer-aided robustness analysis of long-step and accelerated methods in smooth convex optimization
This work assesses both empirically and theoretically, using the performance estimation methodology, how robust different first-order optimization methods are when subject to relative inexactness in their gradient computations. Relative inexactness occurs, for example, when compressing the gradient using fewer bits of information, which happens when dealing with large-scale problems on GPUs. Three major families of methods are analyzed: constant step gradient descent, long-step methods, and acc…

General base change for relative Du Bois complexes
Caleb Ji, S\'andor Kov\'acs
https://arxiv.org/abs/2508.02848 https://arxiv.org/pdf/2508.02848

General base change for relative Du Bois complexes
A partial answer is given to a question raised by Kovács and Taji in arxiv:2307.07192, namely that the relative Du Bois complex of a family parametrized by a non-singular curve commutes with base change to a general point on the base. It is also shown that this property usually fails for special points.

Train Long, Think Short: Curriculum Learning for Efficient Reasoning
Hasan Abed Al Kader Hammoud, Kumail Alhamoud, Abed Hammoud, Elie Bou-Zeid, Marzyeh Ghassemi, Bernard Ghanem
https://arxiv.org/abs/2508.08940

Train Long, Think Short: Curriculum Learning for Efficient Reasoning
Recent work on enhancing the reasoning abilities of large language models (LLMs) has introduced explicit length control as a means of constraining computational cost while preserving accuracy. However, existing approaches rely on fixed-length training budgets, which do not take advantage of the natural progression from exploration to compression during learning. In this work, we propose a curriculum learning strategy for length-controlled reasoning using Group Relative Policy Optimization (GRPO…

A Novel Feedforward Youla Parameterization Method for Avoiding Local Minima in Stereo Image Based Visual Servoing Control
Rongfei Li, Francis Assadian
https://arxiv.org/abs/2506.10252

A Novel Feedforward Youla Parameterization Method for Avoiding Local Minima in Stereo Image Based Visual Servoing Control
In robot navigation and manipulation, accurately determining the camera's pose relative to the environment is crucial for effective task execution. In this paper, we systematically prove that this problem corresponds to the Perspective-3-Point (P3P) formulation, where exactly three known 3D points and their corresponding 2D image projections are used to estimate the pose of a stereo camera. In image-based visual servoing (IBVS) control, the system becomes overdetermined, as the 6 degrees of fre…

Interpreting quantum reference frame transformations through a simple example
Esteban Castro-Ruiz, Thomas D. Galley, Leon Loveridge
https://arxiv.org/abs/2508.09540 https://

Interpreting quantum reference frame transformations through a simple example
Quantum reference frame transformations have been proposed to provide a means by which to translate descriptions of quantum systems relative to each other. At present, there are several differing frameworks for describing quantum reference frames, with concomitantly different transformation rules. Here, we investigate a simple example of three qubit systems with $\mathbb{Z}_2$ symmetry in order to analyze physical and conceptual distinctions between three contemporary approaches to quantum refe…

Strong converse rate for asymptotic hypothesis testing in type III
Nicholas Laracuente, Marius Junge
https://arxiv.org/abs/2507.07989 https://

Strong converse rate for asymptotic hypothesis testing in type III
We extend from the hyperfinite setting to general von Neumann algebras Mosonyi and Ogawa's (2015) and Mosonyi and Hiai's (2023) results showing the operational interpretation of sandwiched relative Rényi entropy in the strong converse of hypothesis testing. The specific task is to distinguish between two quantum states given many copies. We use a reduction method of Haagerup, Junge, and Xu (2010) to approximate relative entropy inequalities in an arbitrary von Neumann algebra by those in finit…

Additivity of quantum relative entropies as a single-copy criterion
Salman Beigi, Roberto Rubboli, Marco Tomamichel
https://arxiv.org/abs/2507.05696 https:…

Additivity of quantum relative entropies as a single-copy criterion
The fundamental goal of information theory is to characterize complex operational tasks using efficiently computable information quantities, Shannon's capacity formula being the prime example of this. However, many tasks in quantum information can only be characterized by regularized entropic measures that are often not known to be computable and for which efficient approximations are scarce. It is thus of fundamental importance to understand when regularization is not needed, opening the door …