Tootfinder

Beating the Logarithmic Barrier for the Subadditive Maximin Share Problem
Masoud Seddighin, Saeed Seddighin
https://arxiv.org/abs/2506.05613 https://

Beating the Logarithmic Barrier for the Subadditive Maximin Share Problem
We study the problem of fair allocation of indivisible goods for subadditive agents. While constant-\textsf{MMS} bounds have been given for additive and fractionally subadditive agents, the best existential bound for the case of subadditive agents is $1/O(\log n \log \log n)$. In this work, we improve this bound to a $1/O((\log \log n)^2)$-\textsf{MMS} guarantee. To this end, we introduce new matching techniques and rounding methods for subadditive valuations that we believe are of independent …

On Saturday we spent a deal of time cleaning up the shed and whist it's not finished it's a lot closer to the way it looked some 15 years ago when I started using it.
There is still a lot to do, build another 2 bookcases and put them in the server room at the end of the shed. And then replace the blinds.
#Shed

The coordinate functions of the Heighway dragon curve
Danilo Antonio Caprio
https://arxiv.org/abs/2506.05541 https://arxiv.org/pdf/25…

The coordinate functions of the Heighway dragon curve
In this work we study properties of the coordinate functions $x_θ$ and $y_θ$ of the dragon curve associated to the angle $\fracπ{3}<θ< \frac{5π}{3}$ and we prove that the box-counting dimension of its graphs are equal to $1-\frac{\log \cosα}{\log 2} $, where $α=\frac{π-θ}{2}$.

The Impact of Event Data Partitioning on Privacy-aware Process Discovery
Jungeun Lim, Stephan A. Fahrenkrog-Petersen, Xixi Lu, Jan Mendling, Minseok Song
https://arxiv.org/abs/2507.06008

The Impact of Event Data Partitioning on Privacy-aware Process Discovery
Information systems support the execution of business processes. The event logs of these executions generally contain sensitive information about customers, patients, and employees. The corresponding privacy challenges can be addressed by anonymizing the event logs while still retaining utility for process discovery. However, trading off utility and privacy is difficult: the higher the complexity of event log, the higher the loss of utility by anonymization. In this work, we propose a pipeline …

The Fair Periodic Assignment Problem
Rolf van Lieshout, Bart van Rossum
https://arxiv.org/abs/2507.04537 https://arxiv.org/pdf/2507.0…

The Fair Periodic Assignment Problem
We study the periodic assignment problem, in which a set of periodically repeating tasks must be assigned to workers within a repeating schedule. The classical efficiency objective is to minimize the number of workers required to operate the schedule. We propose a O(n log n) algorithm to solve this problem. Next, we formalize a notion of fairness among workers, and impose that each worker performs the same work over time. We analyze the resulting trade-off between efficiency and fairness, showi…

Fourier Spectral Method for Nonlocal Equations on Bounded Domains
Ilyas Mustapha, Bacim Alali, Nathan Albin
https://arxiv.org/abs/2507.05034 https://

Fourier Spectral Method for Nonlocal Equations on Bounded Domains
This work introduces efficient and accurate spectral solvers for nonlocal equations on bounded domains. These spectral solvers exploit the fact that integration in the nonlocal formulation transforms into multiplication in Fourier space and that nonlocality is decoupled from the grid size. As a result, the computational cost is reduced to $O(N\log N)$ for an $N$-point discretization grid. Our approach extends the spectral solvers developed by Alali and Albin (2020) for periodic domains by incor…

from my link log —
Recovering control flow structures from Java bytecode without CFGs.
https://purplesyringa.moe/blog/recovering-control-flow-structures-without-cfgs/
saved 2025-06-06

Recovering control flow structures without CFGs
I’m working on a Java decompiler because I’m not satisfied with the performance of other solutions. I’ve always heard that decompiling JVM bytecode is a solved problem, but I’ve concluded that the decompilation methods used by CFR and Vineflower are hacky, inefficient, and sometimes don’t even work. The existing solutions are haphazard and inadequate compared to alternative approaches. Specifically, I have beef with the control flow extraction strategies employed by most decompilers. …

This https://arxiv.org/abs/2208.00676 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Pansiot-type subword complexity theorem for automorphisms of free groups
Inspired by Pansiot's work on substitutions, we prove a similar theorem for automorphisms of a free group F of finite rank: if a right-infinite word X represents an attracting fixed point of an automorphism of F, the subword complexity of X is equivalent to n, n log log n, n log n, or n^2. The proof uses combinatorial arguments analogue to Pansiot's as well as train tracks. We also define the recurrence complexity of X, and we apply it to laminations. In particular, we show that attracting lami…

This https://arxiv.org/abs/2503.20170 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Decomposing a factorial into large factors
Let $t(N)$ denote the largest number such that $N!$ can be expressed as the product of $N$ integers greater than or equal to $t(N)$. The bound $t(N)/N = 1/e-o(1)$ was apparently established in unpublished work of Erdős, Selfridge, and Straus; but the proof is lost. Here we obtain the more precise asymptotic $$ \frac{t(N)}{N} = \frac{1}{e} - \frac{c_0}{\log N} + O\left( \frac{1}{\log^{1+c} N} \right)$$ for an explicit constant $c_0 = 0.30441901\dots$ and some absolute constant $c>0$, answering …

This https://arxiv.org/abs/2504.06940 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

More-efficient Quantum Multivariate Mean Value Estimator from Generalized Grover Operator
In this work, we present an efficient algorithm for multivariate mean value estimation. Our algorithm outperforms previous work by polylog factors and nearly saturates the known lower bound. More formally, given a random vector $\vec{X}$ of dimension $d$, we find an algorithm that uses $O\left(n \log \frac{d}δ\right)$ samples to find a mean estimate that $\vec{\tildeμ}$ that differs from the true mean $\vecμ$ by $\frac{\sqrt{\text{tr } Σ}}{n}$ in $\ell^\infty$ norm and hence $\frac{\sqrt{d …

from my link log —
The first year of free-threaded Python.
https://labs.quansight.org/blog/free-threaded-one-year-recap
saved 2025-05-14

The first year of free-threaded Python
A recap of the first year of work on enabling support for the free-threaded build of CPython in community packages.

Log entry: The Matrix project proceeds apace. Dr. Forbin is continuing his work on Colossus, while Dr. Ellis and Dr. Morris continue to prep Harold Benson and Mr. Anderson for surgery...
https://www.reut…

MichelangeRoll: Sculpting Rational Distributions Exactly and Efficiently
Jui-Hsiang Shao, Hsin-Po Wang
https://arxiv.org/abs/2507.00915 https://

MichelangeRoll: Sculpting Rational Distributions Exactly and Efficiently
Simulating an arbitrary discrete distribution $D \in [0, 1]^n$ using fair coin tosses incurs trade-offs between entropy complexity and space and time complexity. Shannon's theory suggests that $H(D)$ tosses are necessary and sufficient, but does not guarantee exact distribution. Knuth and Yao showed that a decision tree consumes fewer than $H(D) + 2$ tosses for one exact sample. Drapper and Saad's recent work addresses the space and time aspect, showing that $H(D) + 2$ tosses, $O(n \log(n) \log…

Bayesian-Guided Diversity in Sequential Sampling for Recommender Systems
Hiba Bederina, Jill-J\^enn Vie
https://arxiv.org/abs/2506.21617 https://

Bayesian-Guided Diversity in Sequential Sampling for Recommender Systems
The challenge of balancing user relevance and content diversity in recommender systems is increasingly critical amid growing concerns about content homogeneity and reduced user engagement. In this work, we propose a novel framework that leverages a multi-objective, contextual sequential sampling strategy. Item selection is guided by Bayesian updates that dynamically adjust scores to optimize diversity. The reward formulation integrates multiple diversity metrics-including the log-determinant vo…

CNN-Derived Elemental Abundances of LAMOST DR10 Giants: Implications for Galactic Substructures
Haoyang Liu, Cuihua Du, Mingji Deng, Jian Zhang
https://arxiv.org/abs/2506.16135

CNN-Derived Elemental Abundances of LAMOST DR10 Giants: Implications for Galactic Substructures
Stellar parameters and abundances provide crucial insights into stellar and Galactic evolution studies. In this work, we developed a convolutional neural network (CNN) to estimate stellar parameters: effective temperature ($T_{\text{eff}}$), surface gravity (log $g$) and metallicity (both [Fe/H] and [M/H]) as well as six $α$-elements (C, N, O, Mg, Si, Ca) and [$α$/M]. We selected giant stars with \( 3500 \, \text{K} < T_{\text{eff}} < 5500 \, \text{K} \) and \( 0 \, \text{dex} < \log g < 3.6 …

from my link log —
Making emacs tramp go brrrr.
https://coredumped.dev/2025/06/18/making-tramp-go-brrrr./
saved 2025-06-23

Affine invariant interacting Langevin dynamics in Markov chain importance sampling for rare event estimation
Jason Beh, J\'er\^ome Morio, Florian Simatos, Simon Weissmann
https://arxiv.org/abs/2506.20185

Affine invariant interacting Langevin dynamics in Markov chain importance sampling for rare event estimation
This work considers the framework of Markov chain importance sampling~(MCIS), in which one employs a Markov chain Monte Carlo~(MCMC) scheme to sample particles approaching the optimal distribution for importance sampling, prior to estimating the quantity of interest through importance sampling. In rare event estimation, the optimal distribution admits a non-differentiable log-density, thus gradient-based MCMC can only target a smooth approximation of the optimal density. We propose a new gradie…

On Fine-Grained Distinct Element Estimation
Ilias Diakonikolas, Daniel M. Kane, Jasper C. H. Lee, Thanasis Pittas, David P. Woodruff, Samson Zhou
https://arxiv.org/abs/2506.22608 …

On Fine-Grained Distinct Element Estimation
We study the problem of distributed distinct element estimation, where $α$ servers each receive a subset of a universe $[n]$ and aim to compute a $(1+\varepsilon)$-approximation to the number of distinct elements using minimal communication. While prior work establishes a worst-case bound of $Θ\left(α\log n+\fracα{\varepsilon^2}\right)$ bits, these results rely on assumptions that may not hold in practice. We introduce a new parameterization based on the number $C = \fracβ{\varepsilon^2}$ …

A valuative approach to the anticanonical minimal model program
Sung Rak Choi, Sungwook Jang, Donghyeon Kim, Dae-Won Lee
https://arxiv.org/abs/2506.13637 h…

A valuative approach to the anticanonical minimal model program
In this paper, we show that the log canonical threshold of a potentially klt triple can be computed by a quasi-monomial valuation. The notion of potential triples provides a larger and more flexible framework to work with than that of generalized pairs. Our main result can be considered as an extension to the result of Xu on klt pairs. As an application of the main result, we show that we can run the MMP on any potentially klt triples and $-(K_X+Δ)$-MMP on the potentially klt pairs.

from my link log —
ECFiber: building a fibre-to-the-premises network in rural Vermont.
https://blog.apnic.net/2021/02/18/building-your-own-fibre-to-premises-network/
saved 2021-02-18

Building your own Fibre-to-Premises Network: The ECFiber Story | APNIC Blog
How to build and operate a FTTH network when existing infrastructure, topography, and low population all work against the need for fast Internet

Refuting Perfect Matchings in Spectral Expanders is Hard
Ari Biswas, Rajko Nenadov
https://arxiv.org/abs/2506.07700 https://arxiv.org…

Refuting Perfect Matchings in Spectral Expanders is Hard
This work studies the complexity of refuting the existence of a perfect matching in spectral expanders with an odd number of vertices, in the Polynomial Calculus (PC) and Sum of Squares (SoS) proof system. Austrin and Risse [SODA, 2021] showed that refuting perfect matchings in sparse $d$-regular \emph{random} graphs, in the above proof systems, with high probability requires proofs with degree $Ω(n/\log n)$. We extend their result by showing the same lower bound holds for \emph{all} $d$-regul…

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…

from my link log —
Rewriting the Ruby parser.
https://railsatscale.com/2023-06-12-rewriting-the-ruby-parser/
saved 2024-12-26

Rewriting the Ruby parser
At Shopify, we have spent the last year writing a new Ruby parser, which we’ve called YARP (Yet Another Ruby Parser). As of the date of this post, YARP can parse a semantically equivalent syntax tree to Ruby 3.3 on every Ruby file in Shopify’s main codebase, GitHub’s main codebase, CRuby, and the 100 most popular gems downloaded from rubygems.org. We recently got approval to merge this work into CRuby, and are very excited to share our work with the community. This post will take you thro…

Fast Ramanujan--type Series for Logarithms. Part II
Jorge Zuniga
https://arxiv.org/abs/2506.10321 https://arxiv.org/pdf/2506.10321

Fast Ramanujan--type Series for Logarithms. Part II
This work extends the results of the preprint Ramanujan type Series for Logarithms, Part I, arXiv:2506.08245, which introduced single hypergeometric type identities for the efficient computing of $\log(p)$, where $p\in\mathbb{Z}_{>1}$. We present novel formulas for arctangents and methods for a very fast multiseries evaluation of logarithms. Building upon a $\mathcal{O}((p-1)^{6})$ Ramanujan type series asymptotic approximation for $\log(p)$ as $p\rightarrow1$, formulas for computing $n$ simult…

Geometric Jensen-Shannon Divergence Between Gaussian Measures On Hilbert Space
Minh Ha Quang, Frank Nielsen
https://arxiv.org/abs/2506.10494 https://

Geometric Jensen-Shannon Divergence Between Gaussian Measures On Hilbert Space
This work studies the Geometric Jensen-Shannon divergence, based on the notion of geometric mean of probability measures, in the setting of Gaussian measures on an infinite-dimensional Hilbert space. On the set of all Gaussian measures equivalent to a fixed one, we present a closed form expression for this divergence that directly generalizes the finite-dimensional version. Using the notion of Log-Determinant divergences between positive definite unitized trace class operators, we then define a…

Parallel batch queries on dynamic trees: algorithms and experiments
Humza Ikram, Andrew Brady, Daniel Anderson, Guy Blelloch
https://arxiv.org/abs/2506.16477

Parallel batch queries on dynamic trees: algorithms and experiments
Dynamic tree data structures maintain a forest while supporting insertion and deletion of edges and a broad set of queries in $O(\log n)$ time per operation. Such data structures are at the core of many modern algorithms. Recent work has extended dynamic trees so as to support batches of updates or queries so as to run in parallel, and these batch parallel dynamic trees are now used in several parallel algorithms. In this work we describe improvements to batch parallel dynamic trees, describe a…

from my link log —
Dependent types at work in Agda.
https://www.cse.chalmers.se/~peterd/papers/DependentTypesAtWork.pdf
saved 2025-05-21

Memory cost of quantum contextuality with Pauli observables
Stefan Trandafir, Colm Kelleher, Ad\'an Cabello
https://arxiv.org/abs/2506.06869 https://…

Memory cost of quantum contextuality with Pauli observables
Classically simulating the quantum contextual correlations produced by sequences of ideal measurements of compatible observables requires the measured system to have an internal memory. Computing the minimum amount of memory needed is, in general, challenging. Here, building upon the work of Kleinmann et al. [New J. Phys. 13, 113011 (2011)], we prove that the memory cost for simulating the contextuality produced by the $10$ three-qubit observables of Mermin's pentagram is only $\log_2(5) \appro…

String Matching with a Dynamic Pattern
Bruno Monteiro, Vinicius dos Santos
https://arxiv.org/abs/2506.11318 https://arxiv.org/pdf/250…

String Matching with a Dynamic Pattern
In this work, we tackle a natural variation of the String Matching Problem on the case of a dynamic pattern, that is, given a static text $T$ and a pattern $P$, we want to support character additions and deletions to the pattern, and after each operation compute how many times it occurs in the text. We show a simple and practical algorithm using Suffix Arrays that achieves $\mathcal O(\log |T|)$ update time, after $\mathcal O(|T|)$ preprocess time. We show how to extend our …