O(n^{4/3})$
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Mutation-dependent responses to sleep and exercise in clonal haematopoiesis
Abstract Clonal haematopoiesis (CH) activates inflammation and increases the risk of atherosclerosis1,2. Whether lifestyle alters CH clone expansion or the phenotypic programming of CH mutant cells, thereby affecting atherosclerosis, is unknown. Here, in humans and mice and across mutations in Jak2, Tet2, Trp53 and Dnmt3a, we demonstrate mutation-dependent responses to sleep and exercise in CH and show that mutant cells are uniquely sensitive to lifestyle.
Derivative Informed Learning of Exchange-Correlation Functionals
arXiv:2606.04279v1 Announce Type: new Abstract: Machine-learned (ML) exchange-correlation (XC) functionals aim to replace human-designed density functional approximations by learning directly from reference data, but they still do not consistently outperform traditional $\mathcal{O}(N^4)$-scaling hybrid functionals. We study a hybrid-distillation setting in which $\mathcal{O}(N^3)$-scaling ML-XC functionals are trained to reproduce B3LYP/def2-SVP targets. We introduce Derivative Informed...
Scalable Derivative Gaussian Processes via Exact Gradient Reduction
Announce Type: cross Abstract: Gradient observations can substantially improve Gaussian process (GP) surrogates, particularly in high-dimensional settings where function evaluations are expensive. However, exact inference with $n$ function values and $n$ full gradients in $d$ dimensions scales cubically in the joint state size, imposing an intractable $\mathcal{O}(n^3 d^3)$ computational bottleneck.
An Efficient Genus Algorithm Based on Graph Rotations
arXiv:2411.07347v5 Announce Type: replace Abstract: We study the problem of determining the minimal genus of a simple finite connected graph. We present an algorithm which, for an arbitrary graph $G$ with $n$ vertices and $m$ edges, determines the orientable genus of $G$ in $O(n(4^m/n)^{n/t})$ steps where $t$ is the girth of $G$. This algorithm avoids difficulties that many other genus algorithms have with handling bridge placements which is a well-known issue. The algorithm has a number of...
Removing bottlenecks in the recognition of small $(k,\ell)$-graph classes
arXiv:2510.17665v2 Announce Type: replace Abstract: A graph is a $(k,\ell)$-graph if its vertex set can be partitioned into $k$ independent sets and $\ell$ cliques. This family simultaneously generalizes split, bipartite, and co-bipartite graphs. While the recognition problem is NP-complete whenever $k\geq 3$ or $\ell\geq 3$, the remaining small cases are polynomial-time solvable.
SIRT7 regulates dosage compensation and safeguards the female X chromosome
Abstract Sirtuins are deacetylases implicated in stress responses and longevity in mammals1,2. Although their differential impact on disease for the two sexes has been noted3,4,5,6,7, the underlying reasons are unclear. Here, using Sirt7 as a model in mice, we examine the mechanisms leading to sex differences and find that Sirt7−/− female mice have decreased fitness throughout their lifespan.
On the Duke--Erd\H{o}s--R\"odl Problem at the One-Third Threshold
Announce Type: cross Abstract: Let $G$ be an $n$-vertex graph with $e(G)\ge n^2/ k$. We prove a self-contained internal short-cycle core theorem at the threshold $k\le n^{1/3}$: the graph $G$ contains a subgraph $H_6$ with $\Omega(n^2/ k^3)$ edges in which every two distinct edges lie together on a cycle of length at most $6$ contained in $H_6$, and a subgraph $H_8$ with $\Omega(n^2/k^2)$ edges in which every two distinct edges lie together on a cycle of length at most $8$ contained in...
Tree-Guided Identify-Then-Exploit: A Unified Framework of Best Arm Identification and Regret Minimization for Dueling Bandits
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Deterministic Distance Approximation in MPC via Improved Hitting Sets
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Lean 4 Machine-Verified Proof of P = NP via the Pedigree Polytope Membership Problem
arXiv:2606.03194v1 Announce Type: new Abstract: The Membership Problem for Pedigree Polytope (M3P) asks, given $X\in\mathbb{Q}^{\binom{n}{3}}$, whether $X\in\mathrm{conv}(P_n)$, where $P_n$ is the set of all pedigrees. A pedigree is a structured encoding of a Hamiltonian cycle construction in $K_n$. We establish that M3P is solvable in strongly polynomial time via a recursively constructed layered network $(N_k, R_k, \mu)$ and a multicommodity flow problem MCF$(k)$. The necessary and...