me: *low whistles*
me: "Damn, check out THOSE bollards!"
8yo: "What?"
me: "These metal things. they're nice, aren't they? No drivers parking on this sidewalk!"
8yo: *lays down on one*
8yo: "Yeah, they're good, I guess."
#SafeStreets
Gloom & Bloom III ☁️🌺
黑暗绽放 III ☁️ 🌺
📷 Zeiss IKON Super Ikonta 533/16
🎞️ Lucky SHD 400
#filmphotography #Photography #blackandwhite
Gloom & Bloom II ☁️🌺
黑暗绽放 II ☁️ 🌺
📷 Zeiss IKON Super Ikonta 533/16
🎞️ Lucky SHD 400
#filmphotography #Photography #blackandwhite
Last minute decision to go to philharmonic last night for Shostakovich. Was delighted with Miguel del Águila’s “Concierto en Tango” for cello (commissioned by BPO in 2014).
History: https://interlude.hk/the-less-classical-cello-concerto-miguel-de…
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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The #EU reached a complicated compromise on the regulation of biotech #crops last Thursday. This is a significant step, from negotiations under the Danish presidency 🇩🇰. The proposal still needs to be ratified by the Council and @…, though both were already participating to reach this stage.
There's a lot of detail of course but one key biological aspect is that varieties with the smallest, so-called NGT-1 changes would no longer be regulated under GMO rules, and would be labelled for marketing as seeds but not their products thereafter. Not so for NGT-2.
➡️ https://www.consilium.europa.eu/en/press/press-releases/2025/12/04/new-genomic-techniques-council-and-parliament-strike-deal-to-boost-the-competitiveness-and-sustainability-of-our-food-systems/
My new business cards finally came in the mail!
#photo #photography #foxwork #fox
Gloom & Bloom ☁️🌺
黑暗绽放 ☁️ 🌺
📷 Zeiss IKON Super Ikonta 533/16
🎞️ Lucky SHD 400
#filmphotography #Photography #blackandwhite