Tootfinder

Incremental (k, z)-Clustering on Graphs
Emilio Cruciani, Sebastian Forster, Antonis Skarlatos
https://arxiv.org/abs/2602.08542 https://arxiv.org/pdf/2602.08542 https://arxiv.org/html/2602.08542
arXiv:2602.08542v1 Announce Type: new
Abstract: Given a weighted undirected graph, a number of clusters $k$, and an exponent $z$, the goal in the $(k, z)$-clustering problem on graphs is to select $k$ vertices as centers that minimize the sum of the distances raised to the power $z$ of each vertex to its closest center. In the dynamic setting, the graph is subject to adversarial edge updates, and the goal is to maintain explicitly an exact $(k, z)$-clustering solution in the induced shortest-path metric.
While efficient dynamic $k$-center approximation algorithms on graphs exist [Cruciani et al. SODA 2024], to the best of our knowledge, no prior work provides similar results for the dynamic $(k,z)$-clustering problem. As the main result of this paper, we develop a randomized incremental $(k, z)$-clustering algorithm that maintains with high probability a constant-factor approximation in a graph undergoing edge insertions with a total update time of $\tilde O(k m^{1 o(1)} k^{1 \frac{1}{\lambda}} m)$, where $\lambda \geq 1$ is an arbitrary fixed constant. Our incremental algorithm consists of two stages. In the first stage, we maintain a constant-factor bicriteria approximate solution of size $\tilde{O}(k)$ with a total update time of $m^{1 o(1)}$ over all adversarial edge insertions. This first stage is an intricate adaptation of the bicriteria approximation algorithm by Mettu and Plaxton [Machine Learning 2004] to incremental graphs. One of our key technical results is that the radii in their algorithm can be assumed to be non-decreasing while the approximation ratio remains constant, a property that may be of independent interest.
In the second stage, we maintain a constant-factor approximate $(k,z)$-clustering solution on a dynamic weighted instance induced by the bicriteria approximate solution. For this subproblem, we employ a dynamic spanner algorithm together with a static $(k,z)$-clustering algorithm.
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Muito importante!
@… https://ursal.zone/@dru/116199035741579701

the eveready bunny of merkle trees remains my favorite sunday times feature

Sources: Elon requires banks seeking roles in SpaceX's IPO to subscribe to Grok and advertise on X; some banks are spending tens of millions integrating Grok (Maureen Farrell/New York Times)
https://www.nytimes.com/2026/04/03/b…

Big Banks Seeking a Piece of SpaceX’s I.P.O. Must Subscribe to Elon Musk’s Grok
Mr. Musk is requiring Wall Street firms to purchase subscriptions to his A.I. chatbot if they want to advise on one of the largest initial public offerings in history.

High-Dimensional Robust Mean Estimation with Untrusted Batches
Maryam Aliakbarpour, Vladimir Braverman, Yuhan Liu, Junze Yin
https://arxiv.org/abs/2602.20698 https://arxiv.org/pdf/2602.20698 https://arxiv.org/html/2602.20698
arXiv:2602.20698v1 Announce Type: new
Abstract: We study high-dimensional mean estimation in a collaborative setting where data is contributed by $N$ users in batches of size $n$. In this environment, a learner seeks to recover the mean $\mu$ of a true distribution $P$ from a collection of sources that are both statistically heterogeneous and potentially malicious. We formalize this challenge through a double corruption landscape: an $\varepsilon$-fraction of users are entirely adversarial, while the remaining ``good'' users provide data from distributions that are related to $P$, but deviate by a proximity parameter $\alpha$.
Unlike existing work on the untrusted batch model, which typically measures this deviation via total variation distance in discrete settings, we address the continuous, high-dimensional regime under two natural variants for deviation: (1) good batches are drawn from distributions with a mean-shift of $\sqrt{\alpha}$, or (2) an $\alpha$-fraction of samples within each good batch are adversarially corrupted. In particular, the second model presents significant new challenges: in high dimensions, unlike discrete settings, even a small fraction of sample-level corruption can shift empirical means and covariances arbitrarily.
We provide two Sum-of-Squares (SoS) based algorithms to navigate this tiered corruption. Our algorithms achieve the minimax-optimal error rate $O(\sqrt{\varepsilon/n} \sqrt{d/nN} \sqrt{\alpha})$, demonstrating that while heterogeneity $\alpha$ represents an inherent statistical difficulty, the influence of adversarial users is suppressed by a factor of $1/\sqrt{n}$ due to the internal averaging afforded by the batch structure.
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Adversarial Attacks on Multimodal Large Language Models: A Comprehensive Survey
Bhavuk Jain, Sercan \"O. Ar{\i}k, Hardeo K. Thakur
https://arxiv.org/abs/2603.27918 https://…

Oooo, RNZ's NineToNoon is advertising a segment on 'open source granny flats' being developed by Prof Anthony Hōete (Ngāti Awa) at the University of Auckland at 9:35 this morning... interesting. I'll post a link to the podcast following.

"Typeface „Volvo Centum“ soll die Sicherheit beim Autofahren erhöhen"
https://www.designtagebuch.de/typeface-volvo-centum-soll-die-sicherheit-beim-autofahren-erhoehen/

Ohh heerlijk ... YouTube op mn 'Chromecast' is niet advertentievrij, maar met buitenlandse reclame (door vpn) ineens veel beter te doen.. 😅🙃

Le F-35, le talon d’Achille des alliés face Š Trump:
"En cas de conflit au Groenland, les États-Unis pourraient en effet décider de rendre les F-35 du Danemark et de leurs alliés inopérants ou presque, en suspendant les mises Š jour des données de vol. Certaines capacités, liées notamment au système d’armement, pourraient également être totalement ou partiellement inhibées."