arXiv preprints from January 1, 2026 through September 21, 2026 — 00:03:48 EST
In this manuscript, we analyze the dynamics of a model in which two spin-1/2 systems are each coupled noncommutingly to a static environmental field and to a self-Hamiltonian, while also being mutually coupled through a $σ_y^{(1)}σ_y^{(2)}$ interaction. By constructing an exact solution that exploits parity symmetry, and by applying...
Dual-comb technology has emerged as an essential tool for high-precision spectroscopy, real-time ranging, and high-sensitivity sensing. Integrating dual-comb sources into a single microresonator would substantially reduce pump power, footprint, system complexity, and cost, yet this remains a significant challenge. Here, we...
Emergency management assistance programs, such as relief distribution, are essential for delivering necessary supplies to affected communities. However, these programs operate in a decentralized network of local centers that face uncertain local demand and supply dynamics, resulting in inconsistent avail- ability of local services....
The main contribution of this work is to identify model parameters for an Anion Exchange Membrane (AEM) system directly from measured operational data, enabling their use in power system studies. Due to the relatively low technology readiness level (TRL) of AEM electrolysers, only limited literature reports operational parameters...
Complex networks are often compared using selected graph-theoretical measures that capture a selected set of properties with effects ranging from local to global, such as degree, clustering or betweenness centrality. Here we introduce a structural fingerprinting framework based on graphlets: small rooted subgraphs whose distributions...
Living systems compute with chemistry by mapping environmental signals onto specific internal chemical states. Despite recent advances in molecular programming, it remains unclear which physicochemical features control the computational expressivity of chemical systems. Here we inverse-design thermodynamically consistent chemical...
Let $μ$ be a finitely supported probability measure on $\mathrm{SL}_2(\mathbb{R})$ whose support generates a Zariski-dense discrete subgroup. We prove that its stationary probability measure on $\mathbb{P}^1(\mathbb{R})$ is singular with respect to the $\mathrm{SO}(2)$-invariant probability measure. The proof compares winding...
We show that for all negative $L$-space knots and framings $n\geq2g(K)$, if a certain cobordism map between cables of $K$ is non-vanishing, then the Floer lasagna module of the knot trace of $K$ with framing $-n$ is infinite dimensional. Further, for the maps on the hat flavour of link Floer homology induced by band maps,...
Let $C$ be a connected nodal curve of genus $g$ over an algebraically closed field $k$ of characteristic zero. Let \[ A(C)=\Big(J(C), {\overline{P^{g-1}_C}}, Θ(C) \Big) \] be the stable semi-abelic pair (in the sense of Alexeev) associated with its canonical compactified Jacobian $\overline{P^{g-1}_C}$ in degree $g-1$. The canonical...
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...