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Trinitary algebras
V. A. Vassiliev
https://arxiv.org/abs/2506.12865 https://arxiv.org/pdf/2506.12865…

Trinitary algebras
A {\em trinitary algebra} is any subalgebra of the space of smooth functions $f: M \to {\mathbb R}$ that is distinguished in this space by finitely many linear conditions of the form $f(x_i) = f(\tilde x_i) = f(\hat x_i)$, where $x_i, \tilde x_i,$ and $ \hat x_i $ are distinct points in $ M$, $i=1, \dots, k$, or is approximated by such subalgebras. These algebras naturally arise in the study of discriminant varieties, i.e., the spaces of singular geometric objects, in theories where the propert…

The Shield of Achilles by W. H. Auden - Poems | Academy of American Poets
https://poets.org/poem/shield-achilles

Experimental Design for Semiparametric Bandits
Seok-Jin Kim, Gi-Soo Kim, Min-hwan Oh
https://arxiv.org/abs/2506.13390 https://arxiv.o…

Experimental Design for Semiparametric Bandits
We study finite-armed semiparametric bandits, where each arm's reward combines a linear component with an unknown, potentially adversarial shift. This model strictly generalizes classical linear bandits and reflects complexities common in practice. We propose the first experimental-design approach that simultaneously offers a sharp regret bound, a PAC bound, and a best-arm identification guarantee. Our method attains the minimax regret $\tilde{O}(\sqrt{dT})$, matching the known lower bound for …

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Solving Convex-Concave Problems with $\tilde{\mathcal{O}}(\epsilon^{-4/7})$ Second-Order Oracle Complexity
Lesi Chen, Chengchang Liu, Luo Luo, Jingzhao Zhang
https://arxiv.org/abs/2506.08362

Solving Convex-Concave Problems with $\tilde{\mathcal{O}}(ε^{-4/7})$ Second-Order Oracle Complexity
Previous algorithms can solve convex-concave minimax problems $\min_{x \in \mathcal{X}} \max_{y \in \mathcal{Y}} f(x,y)$ with $\mathcal{O}(ε^{-2/3})$ second-order oracle calls using Newton-type methods. This result has been speculated to be optimal because the upper bound is achieved by a natural generalization of the optimal first-order method. In this work, we show an improved upper bound of $\tilde{\mathcal{O}}(ε^{-4/7})$ by generalizing the optimal second-order method for convex optimizat…

Faster negative length shortest paths by bootstrapping hop reducers
Yufan Huang, Peter Jin, Kent Quanrud
https://arxiv.org/abs/2506.00428 https://

Faster negative length shortest paths by bootstrapping hop reducers
The textbook algorithm for real-weighted single-source shortest paths takes $O(m n)$ time on a graph with $m$ edges and $n$ vertices. The breakthrough algorithm by Fineman [Fin24] takes $\tilde{O}(m n^{8/9})$ randomized time. The running time was subsequently improved to $\tilde{O}(mn^{4/5})$ [HJQ25]. We build on [Fin24; HJQ25] to obtain an $\tilde{O}(m n^{3/4} + m^{4/5} n)$ randomized running time. (Equivalently, $\tilde{O}(mn^{3/4})$ for $m \geq n^{5/4}$, and $\tilde{O}(m^{4/5} n)$ for $m \…

This https://arxiv.org/abs/2502.07995 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Genuine multi-entropy and holography
Is bipartite entanglement sufficient for holography? Through the analysis of the Markov gap, it is known that the answer is no. In this paper, we give a new perspective on this issue from a different angle using a multi-entropy. We define a genuine $\mathtt{q}$-partite multi-entropy from a $\mathtt{q}$-partite multi-entropy by subtracting appropriate linear combinations of $\mathtt{\tilde{q}}$-partite multi-entropies for $\mathtt{\tilde{q}} < \mathtt{q}$, in such a way that the genuine $\mathtt…

Canonical Partition Function on a Quantum Computer through Trotter Interpolation
Taozhi Guo, Gumaro Rendon, Rutuja Kshirsagar
https://arxiv.org/abs/2506.09318

Canonical Partition Function on a Quantum Computer through Trotter Interpolation
In this work, we present a Gibbs state observable estimation algorithm based on Trotter interpolation, which reaches a state-of-the-art quantum computational cost of $ \tilde{O}(β\log{1/ε})$. Our approach saves $\log(Γ)$ ancilla qubits compared with the qubitization-based methods for Hamiltonian with $Γ$ stages. To provide a robust assessment of our approach, we benchmark our results against state-of-the-art methodology using the SYK model as a testbed. Our method provides an efficient alte…

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This https://arxiv.org/abs/2504.18292 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Large time cumulants of the KPZ equation on an interval
We consider the Kardar-Parisi-Zhang equation on the interval $[0,L]$ with Neumann type boundary conditions and boundary parameters $u,v$. We show that the $k$-th order cumulant of the height behaves as $c_k(L,u,v)\, t$ in the large time limit $t \to +\infty$, and we compute the coefficients $c_k(L,u,v)$. We obtain an expression for the upper tail large deviation function of the height. We also consider the limit of large $L$, with $u=\tilde u/\sqrt{L}$, $u=\tilde v/\sqrt{L}$, which should give …

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This https://arxiv.org/abs/2504.05655 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Multi-bubble solutions for the Dirichlet problem of the $H$-system with higher degree
We consider a Dirichlet problem of the $H$-system \begin{equation*} \begin{cases} Δv = 2v_x\wedge v_y ~& \text{ in }\mathcal{D},\\ v=\varepsilon \tilde g ~& \text{ on }\partial{\mathcal{D}}, \end{cases} \end{equation*} where $\mathcal D\subset \mathbb{R}^2$ is the unit disk, $v:\mathcal D\to \mathbb{R}^3$, and $\tilde g:\partial \mathcal D\to \mathbb{R}^3$ is a given smooth map. As $\varepsilon\to 0^+$, we construct multi-bubble solutions concentrating at distinct points, taking around each po…

Kierkegaard on Nonconformity, the Individual vs. the Crowd, and the Power of the Minority – The Marginalian
https://www.themarginalian.org/2014/11/26/kierkegaard-individual-crowd-conformity-minority/

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Faster MPC Algorithms for Approximate Allocation in Uniformly Sparse Graphs
Jakub {\L}\k{a}cki, Slobodan Mitrovi\'c, Srikkanth Ramachandran, Wen-Horng Sheu
https://arxiv.org/abs/2506.04524

Faster MPC Algorithms for Approximate Allocation in Uniformly Sparse Graphs
We study the allocation problem in the Massively Parallel Computation (MPC) model. This problem is a special case of $b$-matching, in which the input is a bipartite graph with capacities greater than $1$ in only one part of the bipartition. We give a $(1+ε)$ approximate algorithm for the problem, which runs in $\tilde{O}(\sqrt{\log λ})$ MPC rounds, using sublinear space per machine and $\tilde{O}(λn)$ total space, where $λ$ is the arboricity of the input graph. Our result is obtained by pro…

Twisted associative algebras associated to vertex algebras
Shun Xu
https://arxiv.org/abs/2506.01321 https://arxiv.org/pdf/2506.01321

Twisted associative algebras associated to vertex algebras
Let $V$ be a vertex algebra and $g$ an automorphism of $V$ of order $T$. We construct a sequence of associative algebras $\tilde{A}_{g,n}(V )$ for any $n\in(1/T)\mathbb{N}$, which are not depend on the conformal structure of $V$. We show that for a vertex operator algebra, $g$-rationality, $g$-regularity, and twisted fusion rules are independent of the choice of the conformal vector.

How Israel’s Operation Rising Lion Dismantled Iran from Within: A Case Study in the Art of Deception | Hudson Institute
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This https://arxiv.org/abs/2504.15816 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Toward optimal-scaling DFT: stochastic Hartree theory in the thermodynamic and complete basis set limits at arbitrary temperature
We present the first mathematical analysis of stochastic density functional theory (DFT) in the context of the Hartree approximation. We motivate our analysis via the notion of nearly-optimal or $\tilde{O}(n)$ scaling with respect to the number $n$ of computational degrees of freedom, independent of the number of electrons, in both the thermodynamic and complete basis set limits. Indeed, the promise of such scaling is the primary motivation for stochastic DFT relative to conventional orbital-ba…

This https://arxiv.org/abs/2111.14528 has been replaced.
link: https://scholar.google.com/scholar?q=a

Reconstruction and interpolation of manifolds II: Inverse problems with partial data for distances observations and for the heat kernel
We consider how a closed Riemannian manifold $M$ and its metric tensor $g$ can be approximately reconstructed from local distance measurements. Moreover, we consider an inverse problem of determining $(M,g)$ from limited knowledge on the heat kernel. In the part 1 of the paper, we considered the approximate construction of a smooth manifold in the case when one is given the noisy distances $\tilde d(x,y)=d(x,y)+\varepsilon_{x,y}$ for all points $x,y\in X$, where $X$ is a $δ$-dense subset of $M…

Live: Speaking on Trump, Musk, and America’s Moral Moment on the Senate ...
https://youtube.com/live/v2utlMxAwtE?si=PayAFx-Mx2YFPoB0

This https://arxiv.org/abs/1911.02653 has been replaced.
link: https://scholar.google.com/scholar?q=a

Analysis of Two-variable Recurrence Relations with Application to Parameterized Approximations
In this paper we introduce randomized branching as a tool for parameterized approximation and develop the mathematical machinery for its analysis. Our algorithms improve the best known running times of parameterized approximation algorithms for Vertex Cover and $3$-Hitting Set for a wide range of approximation ratios. One notable example is a simple parameterized random $1.5$-approximation algorithm for Vertex Cover, whose running time of $\tilde{O}(1.01657^k)$ substantially improves the best k…

This https://arxiv.org/abs/2306.14853 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Near-Optimal Nonconvex-Strongly-Convex Bilevel Optimization with Fully First-Order Oracles
In this work, we consider bilevel optimization when the lower-level problem is strongly convex. Recent works show that with a Hessian-vector product (HVP) oracle, one can provably find an $ε$-stationary point within ${\mathcal{O}}(ε^{-2})$ oracle calls. However, the HVP oracle may be inaccessible or expensive in practice. Kwon et al. (ICML 2023) addressed this issue by proposing a first-order method that can achieve the same goal at a slower rate of $\tilde{\mathcal{O}}(ε^{-3})$. In this pap…

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Introducing Marginalian Editions: Extraordinary Forgotten Books Brought Back to Life – The Marginalian
https://www.themarginalian.org/2025/04/24/introducing-marginalian-editions/

A 0.51-Approximation of Maximum Matching in Sublinear $n^{1.5}$ Time
Sepideh Mahabadi, Mohammad Roghani, Jakub Tarnawski
https://arxiv.org/abs/2506.01669 h…

A 0.51-Approximation of Maximum Matching in Sublinear $n^{1.5}$ Time
We study the problem of estimating the size of a maximum matching in sublinear time. The problem has been studied extensively in the literature and various algorithms and lower bounds are known for it. Our result is a $0.5109$-approximation algorithm with a running time of $\tilde{O}(n\sqrt{n})$. All previous algorithms either provide only a marginal improvement (e.g., $2^{-280}$) over the $0.5$-approximation that arises from estimating a \emph{maximal} matching, or have a running time that i…

Nearly-Linear Time Private Hypothesis Selection with the Optimal Approximation Factor
Maryam Aliakbarpour, Zhan Shi, Ria Stevens, Vincent X. Wang
https://arxiv.org/abs/2506.01162 …

Nearly-Linear Time Private Hypothesis Selection with the Optimal Approximation Factor
Estimating the density of a distribution from its samples is a fundamental problem in statistics. Hypothesis selection addresses the setting where, in addition to a sample set, we are given $n$ candidate distributions -- referred to as hypotheses -- and the goal is to determine which one best describes the underlying data distribution. This problem is known to be solvable very efficiently, requiring roughly $O(\log n)$ samples and running in $\tilde{O}(n)$ time. The quality of the output is mea…

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