arXiv preprints from January 1, 2026 through September 10, 2026 — 08:16:24 EST
For a graph $G$, let $L(G)=\max\{ω(G),\lceil (|V(G)|+1)/(α_{\min}(G)+1)\rceil\}$, where $ω(G)$ is the clique number and $α_{\min}(G)$ is the minimum, over all vertices $v$, of the largest size of an independent set containing $v$. Dybizbański, Furmańczyk, and Mkrtchyan (Discrete Appl. Math. 354 (2024), 15--28) conjectured that every...
Let $Γ$ be a finite group of order $k\ge2$, and label the edges of a simple loopless $d$-regular digraph $D$ by elements of $Γ$. A directed cycle is zero-sum if the ordered product of its labels is the identity of $Γ$. We prove that a zero-sum cycle exists whenever $d\ge e^3(k-1)$. We also prove that every labelled $d$-regular digraph...
We construct an exact solution-generating correspondence between restricted ansatz sectors of quartic biadjoint scalar theory, complexified $SU(2)$ Yang--Mills theory and four-dimensional general relativity with conformally flat metrics and traceless energy-momentum. A factorised biadjoint field, a Corrigan--Fairlie--'t Hooft--Wilczek...
In this article, the cyclotomic Galois action on topological K-theory adjoined with a primitive $n$th root of unity and the famous $GL_1(\mathbf{Z}/n)$- and $GL_2(\mathbf{Z}/n)$-Galois actions on topological modular forms with $Γ_1(n)$- and $Γ(n)$-level structures are unified and generalised. This is done by defining a quotient stack...
Let $n,m$ be integers such that $n\geq 2$ and $0\leq m\leq n-2$. Let $(M^n,g)$ be a complete Riemannian manifold, and let $C_{m+1}$ be the $(m+1)$-intermediate curvature introduced by Brendle--Hirsch--Johne. We prove \[ \mathrm{Ric}\geq0,\qquad C_{m+1}\geq 1 \quad\Longrightarrow\quad \mathrm{Vol} B_R(p)\leq C(n,m)R^m, \] for...
Structure-preserving discontinuous Galerkin (DG) methods typically improve the robustness of high order simulations of real fluids. In addition to conservation, key structures include the preservation of pressure equilibrium and satisfaction of at least one entropy inequality. In this work, we investigate conservative discretizations...
By work of Enomoto, Jackson, Katerinis, and Saito from 1985, every $2$-tough graph has a $2$-factor, and this toughness bound is best possible: for every $\varepsilon>0$, there exist $(2-\varepsilon)$-tough graphs with no $2$-factor. It is natural to ask whether the latter statement remains true for triangle-free graphs. Bauer, van...
Hybrid dealiasing is an FFT-based method for computing linear convolutions of complex-valued data that reduces the cost of dealiasing by performing zero padding implicitly. We develop two new algorithms that extend hybrid dealiasing to real-valued convolutions. The first algorithm exploits conjugate symmetries in the transformed...
The Shimura curve of discriminant $D$ for $D=14, 15$ is uniformized by a subgroup of an arithmetic quadrilateral Fuchsian group $(2, 2, 2, q)$, where $q=4, 6$. We relate the generator of the ring of quaternionic modular forms on this Shimura curve to explicit Heun functions for the quadrilateral group. We also discuss how the...
For a real $f\in \mathbb{N}^\mathbb{N}$, it is in general not the case that every set which is both $Σ^1_1(f)$ and $Π^1_1(f)$ is the $f$-section of a $Δ^1_1$ set. However, there are reals $f$ for which this, in fact, does happen; we say that such a real strongly relativizes $Δ^1_1$. In this paper, we will prove that the reals which...
Let $M$ be a $\mathrm{II}_1$ factor, $N$ a tracial von Neumann algebra, and $Φ: M \rightarrow N$ a subtracial completely positive map. For an irreducible $\mathrm{II}_1$ subfactor $P \subseteq M$, we characterize when $Φ$ exhibits a flattening property under conjugation by unitaries in $P$. To be specific, we show that the failure of...
The tournament isomorphism problem is one of the two fundamental bottlenecks to designing better algorithms for the graph isomorphism problem. Though the problem has been investigated for more than five decades, compared to graphs, there are only very few results on the isomorphism problem of tournaments. For most classes of...
Let $G$ be an isotropic reductive group and $X$ be a projective $G$-homogeneous variety. Using results from Bialynicki-Birula, Hesselink and Iversen, Brosnan showed that if $G$ is of inner type, the motive of $X$ can be expressed as a direct sum of Tate twists of motives of projective homogeneous varieties for the anisotropic kernel...
We develop an arbitrary-degree geometry-conforming finite element (GC-FE) framework for two-dimensional elliptic boundary value and interface problems on curved domains. Using the Frenet--Serret transformation, curved-boundary and interface-fitted segments are represented exactly, while polynomials in Frenet coordinates generate...
We show that an inductive AH-system with diagonal connecting maps describes an action of the canonical AF-groupoid on the spectrum of the canonical C$^*$-diagonal, and that the canonical groupoid model is given by the transformation groupoid associated to this action. This divides the groupoid structure into two distinct aspects: the...
This paper proposes a metric approach to measuring the complexity of lotteries. Starting by observing that degenerate lotteries are the simplest choice alternatives, the complexity of a lottery is evaluated by its distance from the closest degenerate lottery. Equivalently, a lottery is complex when it is difficult to approximate it by...
AI is increasingly being used to help with AI R&D. Under certain conditions this feedback loop might be able to produce an intelligence explosion, with rapidly escalating AI capabilities. I explore the mathematics of the most explosive possibilities, with an eye to understanding what drives the dynamics. I show that singular growth...
This paper studies how information censoring enables a myopic cutoff rule in Bayesian sequential search. Under full information, Bayesian learning generally destroys the monotonicity of continuation values, preventing simple cutoff rules. We show that one-sided censoring restores monotonicity by limiting posterior fluctuations,...
This paper employs a Threshold Bayesian Vector Autoregression (TBVAR) to estimate the regime-dependent macroeconomic effects of capital regulation in Hungary. Using the Factor-based Index of Systemic Stress (FISS) as the threshold variable, the model identifies normal and stress regimes consistent with the occasionally binding...
We formulate the voter's strategic information acquisition to control the future self's action as a Bayesian persuasion problem. Our main result shows that acquiring information that is irrelevant to the voter's objective can be a \textit{worst-case optimal} solution: it can reduce the possibility that the future self is swayed by...
Academic freedom has come under growing strain worldwide. To study whether and how academics respond to political pressure, we exploit a natural experiment: the publication in early 2025 of a "blacklist" of words flagged by the U.S. government. We find that the release of this list led to a sharp reduction in the use of these flagged...
Ownership matters for the media's watchdog role. We map the ownership networks behind thousands of online news outlets in the U.S., Canada, and Europe. The networks reveal who is ultimately responsible for the news: for over half of the outlets, a single entity. The rest sit behind multi-layered structures, making responsibility hard...
We develop an axiomatic model of robust Bayesian persuasion where the sender cannot fully control the information available to the receiver. After selecting an information structure, the sender expects that more informative structures might be implemented. We model this by allowing the sender to assess each information structure under...
We develop a model of interbank networks with random liquidity shocks. Networks of dilutable debt---e.g., long-term, unsecured---facilitate efficient liquidity transfers: Shocked banks pledge interbank claims as collateral for new senior debt, diluting existing debt. Unlike with non-dilutable debt, indebtedness and connectedness are...
We develop a method for estimating and testing a single block of a macroeconomic model with heterogeneous agents, without placing assumptions on the structure of the rest of the economy. In a large class of models, individual agents' decisions depend on the macroeconomy only through their expectations of the evolution of a...