arXiv preprints from January 1, 2026 through September 19, 2026 — 05:32:01 EST
Transaction costs can make or break a trading strategy, particularly in relative-value trading of commodity and macro markets, where edges are a few basis points. Price impact is a central component of transaction cost. Price impact models usually include self-impact (a trade in a contract moves that contract's price) but omit two...
Let a finite population of n labelled examples carry a class-weighted loss, with pi*n in a rare positive class weighted by N0/N1. We study estimation of total risk from a subsample K << n under designs allocating K0 and K1 draws to the two strata. We derive the exact finite-population variance of the weighted risk estimator under...
We prove a necessary and sufficient condition for an abstract polyhedron $Π$ to be realized as a right-angled, ideal polyhedron in hyperbolic space.
For $2 \times 2$ matrices $A_1,\dots,A_k$, write $[A_1,\dots,A_k]$ for the left-normed iterated commutator $[\dots[[A_1,A_2],A_3],\dots,A_k]$, and $I_k$ for the ideal, in the $3k$-variable reduced-coordinate polynomial ring $R_k$, cutting out its vanishing locus. We prove, for every $k \geq 2$ over any field of characteristic $\neq...
We determine, up to a factor of $2^{o(k)}$, the number of $k$-sets $A \subset \{1, \ldots, n\}$ such that $|A + A| \leq m$, where $k = Θ(\log n)$ and $m \leq k^{1 + α}$, for small $α> 0$, answering a question of Green and Morris.
We prove a weak-type $(1,1)$ estimate for the centered Hardy--Littlewood maximal function with respect to Euclidean balls with dimensional dependence $O(\sqrt{n} \log n)$. This improves the order of growth in the classical $O(n)$ estimate of Stein and Strömberg. The proof goes through a pointwise bound of the Hardy--Littlewood maximal...
Arithmetic terms are fixed finite compositions of additions, multiplications, subtractions, divisions with remainder and integer exponentiations. An arithmetic term in natural numbers $A$, $B$, $n$, obtained by refining the general method of the second author (arXiv:2608.22049) for elliptic curves in Weierstraß normal form, counts the...
McDuff and Segal proved homological stability for unordered configuration spaces of connected manifolds with non-empty boundary. Later, Church proved representation stability for ordered configuration spaces on compact manifolds. These stability patterns extend to surface braid groups and pure surface braid groups, respectively,...
Klaja and Ransford exhibited a complex unital Banach algebra in which the exponential spectra of \(ab\) and \(ba\) differ away from zero, and asked whether this can occur in an algebra of bounded operators. We answer their question affirmatively. For a Bourgain--Delbaen space \(X\) obtained from Motakis' construction with Calkin...
We study finite-sample valid tests of the one-sided mean hypothesis $H_0:μ\leq 1$ against $H_1:μ>1$ for nonnegative random variables. To do so, we develop a leave-one-out dual certificate framework, where certain pointwise inequalities imply p-value validity under the conditional mean null $\mathbb{E}[X_i\mid\mathbf{X}_{-i}]\leq 1$,...
A subtraction game is played on a heap of tokens. The players take turns removing s tokens for some s in a fixed set S of positive integers, and the player who cannot move loses. The sequence of Sprague-Grundy values of such a game is eventually periodic. We ask when it is purely periodic, meaning periodic from the very start, for the...
In this note we study a two-regime representation of a loss random variable under quadratic error. For a finite law we compute exactly the change of the optimal risk when one atom crosses the cut. This turns the problem into a convexity question in cumulative-mass coordinates. On an equally spaced support, log-concavity gives this...
Data-Driven Computational Mechanics (DDCM) replaces traditional phenomenological constitutive models by directly reformulating boundary-value problems in terms of local material state data obtained from experiments or fine-scale simulations. Standard DDCM formulations, only enforcing equilibrium and compatibility, do not inherently...
We construct a framework for higher order unbounded rough drivers defined by rough paths over vector fields. This allows us to consider a purely Eulerian perspective for rough transport equations where the driving rough path vector field is allowed to have temporal $\mathfrak{p}$-variation for any $\mathfrak{p} \in (1,\infty)$. We use...
The Koebe-Andreev-Thurston theorem assigns a 3-dimensional hyperbolic reflection group to each combinatorial polyhedron. A natural question is: which of them are arithmetic? In 2016, Kontorovich-Nakamura conjectured that all arithmetic reflection groups obtained in this way are commensurable to those obtained from the tetrahedron,...
We prove that if a real-valued function $f\in L^1$ on the complex unit circle has a gap of width at least $π$ in its essential range, then $\exp(\widetilde f)$ is not integrable, where $\widetilde f$ is the conjugate function. More generally, the exponential function can be replaced by any nonnegative convex function $Y$ satisfying $$...
We consider collisions of simple random walks on comb graphs $\mathrm{Comb}(\mathbb{Z},H)$, which are obtained by attaching vertical segments of the form $[0,H_x] \cap \mathbb{Z}$ to any point $x$ of the integer axis. For $\mathrm{Comb}(\mathbb{Z},H)$ with profile $H_x(x) = |x| \log^γ(|x| \vee 1)$, we show that two independent simple...
We study multiplicative inequalities among the coefficients of Lorentzian polynomials through the notion of \emph{bounded ratios}. Our main result completely characterizes the cone of bounded ratios for Lorentzian polynomials of degree $n$ in $k$ variables. This dual characterization is expressed in terms of equivalence classes of...
For a finite set $S$ of positive integers, put $K(S):=-\min_{x\in\mathbb T}\sum_{s\in S}\cos(2πsx)$. Bedert recently proved the uniform lower bound $K(S)\geq |S|^{1/5-o(1)}$. We remove the subpolynomial loss and prove that $K(S)\geq c|S|^{1/5}$ for an absolute constant $c>0$. The proof combines two estimates from Bedert's argument...
Consider $n$ independent random vectors sampled from uniform distribution on $(p-1)$-dimensional unit sphere. This paper investigates the limiting joint distribution for the minimum and the maximum values of their pairwise angles. It proves that the minimum and the maximum angles are asymptotically independent when both $n$ and $p$...
In the uniform sparsest cut problem we are asked to find a vertex set that cuts few edges relative to the number of vertex pairs it separates. The Goemans-Linial SDP coupled with the Arora-Rao-Vazirani rounding gives an $\mathcal{O}(\sqrt{\log n})$ approximation on arbitrary graphs on $n$ vertices. We study this relaxation on finite...
The purpose of this work is twofold. In the first part, we consider layered mixed matrices introduced by Murota, relate them to existing notions in combinatorial commutative algebra, and investigate the irreducibility of their determinants. Furthermore, for a layered mixed matrix in combinatorial canonical form, we determine the...
Tree-child networks are a useful class of binary phylogenetic networks. The Pons--Batle identity (Pons and Batle, \textit{Scientific Reports}, 2021) states that the number $a_{n,k}$ of tree-child networks with $k$ reticulations on $n$ taxa satisfies \[ a_{n,k}=(n-k+1)a_{n,k-1} +\frac{n(2n+k-3)}{n-k}a_{n-1,k}. \] In this paper, we...
We study the population dynamics of a predator-prey system with two types in each species. Within a species, predator or prey, dynamics are described by a neutral competitive Lotka-Volterra model, i.e., birth, death and competition parameters are equal for both types. Additionally, we assume that the intra- and inter-type competition...
We introduce a fully stochastic, non-Markovian SIRS-type epidemic model that incorporates varying infectivity, waning immunity and a pulse vaccination strategy that may not confer permanent immunity. The model is constructed at the individual level, where each person is characterized by random infectivity and susceptibility functions,...