arXiv preprints from January 1, 2026 through September 20, 2026 — 16:54:49 EST
Sorting By Transpositions (SBT) seeks the minimum number of transpositions required to sort a permutation $π$ on $n$ symbols into the identity $ι$. Let $N=n+1$. A cyclic-target pair $(ω,β)$ consists of an even permutation $ω$ and an $N$-cycle $β$ such that $ρ=ωβ$ is also an $N$-cycle. An SBT instance is the special case $(\barι...
Let G be a non-trivial finite subgroup of SL_2(C) and let p : X \to C^2/G be the minimal resolution. We prove the C^*-equivariant Cohomological Crepant Resolution Conjecture for the ADE orbifold [C^2/G]. More precisely, after specializing the quantum parameters at suitable roots of unity, we prove that the Bryan-Gholampour...
In this work we propose a new existence theorem for numerical flux functions for supercritical fluids that are pressure-equilibrium preserving (PEP). In particular, we characterize the existence of consistent numerical flux functions that satisfy an algebraic PEP property. Our theory links the existence of PEP schemes to geometric...
Kemeny's constant quantifies the expected time for a random walk to reach a randomly chosen vertex, capturing global properties of a Markov chain. We develop a matrix-analytic framework for bounding Kemeny's constant of a finite connected weighted graph using degree-weighted compressions of the normalized adjacency matrix, pinching...
We consider a possible approach to the Lindelöf hypothesis for Dirichlet $L$-functions. It is based on a special form of the functional equation for the corresponding theta functions. To estimate $L_χ(0.5+it)$ we need to solve certain systems of linear equations. The entries to the corresponding matrices are formed by the summands to...
We bound the difference between two stochastic Volterra processes with identical Lipschitz coefficients but different kernels. For non-convolution kernels, we establish estimates in $C^0([0,T];L^p(Ω))$, $p\geq 2$, and for convolution kernels in $L^p(Ω;L^q(0,T))$, $q \in [1,p]$, and $C^β([0,T];L^p(Ω))$, $L^p(Ω;C^β([0,T]))$, where the...
Explicit computations of generic infinitesimal Newton--Okounkov bodies are difficult even for varieties with simple product structure. We give an explicit formula in arbitrary dimension for positive-degree external tensor products on products of smooth projective curves. Writing $d^\downarrow=(d_1^\downarrow,\ldots,d_n^\downarrow)$...
Balogh, Bollobás and Narayanan conjectured that among all finite simple $r$-uniform $d$-regular hypergraphs, the number of weak independent sets is maximized by a natural quasi-bipartite construction $H_{r,d}$. We give three types of evidence for this conjecture. For every fixed $r$, we prove the conjectured asymptotic exponential...
We show that the universal rigid monoidal category on one object has an abelian envelope. Since it was proven by Coulembier-Etingof-Ostrik-Pauwels (2023) that this category cannot have an abelian envelope with the quotient property, this disproves the conjecture in [op.cit.] saying that every abelian envelope has the quotient...
Let $n \geq 5$. We prove that the helical maximal operator is bounded on $L^p(\mathbb{R}^n)$ for some $p<2n-4$. This improves the previously known range $p>2n-4$ obtained by Gan-Maldague-Oh. As observed by Beltran-Hickman, the exponent $2n-4$ is the natural limit of the standard local smoothing method.
The (massless) sinh-Gordon model is defined in terms of a continuum massless Gaussian free field perturbed by a cosh interaction. For the hierarchical version of the model, we prove existence of the infinite volume limit, a uniform log-Sobolev inequality, and a mass gap. Our results hold for all $b^2 \in (0,1)$ and simplify for...
A random unitary quantum circuit is expected to be incompressible for exponentially long times. We show that the constant-error circuit complexity of a random unitary circuit grows almost linearly with time as $Ω(T/\log T)$. The bound holds for all $2\leq T\leq 4^n$ where $n$ is the system size, and involves no other $n$-dependence....
Uncertainty estimation for Vision-Language-Navigation (VLN) models is a critical task since it can help identify ambiguous and unreliable predictions, enabling agents to make safer navigation decisions. As one of the most advanced uncertainty estimation frameworks, conformal prediction (CP) offers a promising approach for uncertainty...
LLM assistants are widely used for daily social advice, yet evaluating their social reasoning in such consultation settings remains challenging since (i) it requires setups where the assistant learns about social situations from subjective user narratives, and (ii) social properties, such as others' intentions, typically lack...
Unauthorized hardware replacement can preserve a wireless device's logical identity while altering its physical implementation, posing a challenge to hardware integrity verification. Spatio-frequency polarization fingerprints (SFPFs) capture device-dependent responses across multiple frequencies and directions, but their frequency and...
We introduce LimiX-2, a new model in the LimiX family, developed through model and data scaling guided by our previously established scaling laws. LimiX-2 adopts the Contextual Mechanism Networks (CMNs) paradigm and is pretrained with Context-Conditional Masked Modeling (CCMM). CMNs shifts the organizing principle of in-context...
A \emph{linear sketch} is a randomized linear mapping of a vector $v$ to a lower dimensional sketch vector, designed to preserve relevant information about $v$. We consider sketches of vectors $v \in Z^u$ (for $u \in N$), designed for exact recovery of $v$ from its sketch. Concretely, our \emph{Stuffed IBLT} is a linear sketch...
Visual data communication in digital media is increasingly characterized by short attention spans and snapshot-based viewing, often employing line charts to convey trends and patterns. Among all visual elements, titles are crucial ones that can shape how viewers interpret visual information and form chart takeaways. In this study, we...
This study asks whether training-time motion-prior regularization can improve insertion success when a diffusion policy is learned from only 15 demonstrations. Minimum jerk discourages abrupt changes in predicted translational acceleration; speed-curvature regularization instead couples movement speed to path geometry. These are...
Modern large-scale machine learning tasks often require multiple workers, devices, CPUs, or GPUs to compute stochastic gradients in parallel and asynchronously to train model weights. Theoretical results typically distinguish between two settings: (i) the homogeneous setting, where all workers have access to the same data...
Despite the rapid uptake of black-box object detectors in marine mammal research and monitoring, explainability techniques are rarely integrated into conservation workflows. Furthermore, most classification-oriented explainability tools are ill-suited to detection tasks involving imagery of social organisms or those with colonial life...
Capable open-weight models make local coding and reasoning attractive, but their context and execution state strain laptop memory. We present JustFit, an MLX-based inference runtime that combines KVExec for compressed KV execution, PhaseSwap for component residency, and StateTrans for state-preserving serving transitions. These...
Multi-agent systems split a task across a tree of agents and justify the split with folklore: smaller contexts, cleaner separation, parallelism. We ask what the split does to how much of what the leaves discover reaches the root. Model a decomposition as a tree in which an agent handed $b$ items keeps any one with probability $r(b)$....
Robot swarms, by virtue of their decentralised architecture, are a natural tool for scalable, robust modelling of spatial fields, such as water temperature, wind velocity, or terrain elevation. However, existing methods rely on external positioning systems that allow each robot to determine its own position in space. Here, we...
Table understanding is a core task in document intelligence, encompassing two key subtasks: table reconstruction and table visual question answering (TabVQA). While recent approaches predominantly rely on vision- language models (VLMs) operating on table images, we propose a more scalable and effective alternative based on structured...