Tootfinder

New pre-print out (and submitted to JFP): "niFite semPurtatoni" (Finite permutations in Agda). We study a first-order representation of finite permutations: every value of this type represents a bijection by construction (1st image). An interesting part is composition — finding a definition that's structurally recursive at all takes some care (2nd image: an example, plus the key lemma that `skip` and `pinch` are approximate inverses). Inversion, and the classical Lehmer-code &q…

#footpathFriday , I'm back! here with a beautiful path that we walked last year in the #schwarzwald .
#eineSpurWilder

This is the 1st time I’ve given a fleeting thought to creating an Insta account.
I need more coffee. @… https://circumstances.run/@davidgerard

I can't stress enough how awesome #Immich is. I've installed other photo gallery stuff before, and this is the first time I've ever not only been happy with it, but actively impressed by the features. It all Just Works, the web interface and android app are a consistent experience, and..it's just good.
Next up, getting my wife off of Google Photos.

✅ Weekly errands done (our trailer was quite packed this time)
✅ Physical exercise after an office day
✅ Avoided afterwork traffic jams
✅ Fresh air
✅ Saved fuel / car cost
✅ Got some Interested looks from ppl around 😀
If you wonder if buying such a trailer pays off. I would say: absolutely!
Especially the exercise is priceless!
#cycling

WEHCO sells Chattanooga Times Free Press to family with interests in logistics media. Circ is down to 12,000. Population of the area is 595,000.
#media #newspapers

Toward a mechanistic understanding of inference in visual cortex and diffusion models
Zeyu Yun, Alexander Belsten, Dasheng Bi, Zahra Kadkhodaie, Yubei Chen, Bruno A. Olshausen
https://arxiv.org/abs/2607.15693 https://arxiv.org/pdf/2607.15693 https://arxiv.org/html/2607.15693
arXiv:2607.15693v1 Announce Type: new
Abstract: We describe a model of perceptual inference in primary visual cortex (V1) equivalent to a minimal diffusion model whose function can be readily understood from its parameters. The model is based on sparse coding with a non-factorial prior over latent variables in the form of an unconstrained, pairwise interaction matrix, extending standard sparse coding inference to a general recurrent dynamical system. We efficiently train these recurrent dynamics using a denoising score-matching objective and implicit differentiation. After training on natural images, the learned interaction matrix mirrors the structure of horizontal connections in superficial layers of V1 that link neurons of similar orientation tuning. This model exhibits exceptionally good denoising performance, restoring image features such as extended contours amid extreme visual ambiguity, nearly matching the behavior of standard, black-box diffusion architectures in generalization regime. Owing to the model's simplicity, the network's Jacobian can be decomposed directly in terms of the interaction matrix between latent variables, revealing mechanistically how the recurrent dynamics assign high probability over a continuous family of natural structural deformations. Intriguingly, within this circuit, a large fraction of latent variables learn to disconnect from visual input altogether, essentially forming a hierarchical representation that appears to enforce global consistency among image features. Together, the model and results bridge two distinct domains: for neuroscience, it generates concrete, testable hypotheses regarding functional connectivity in recurrent neural circuits during perceptual inference tasks; for machine learning, it elucidates the internal mechanisms learned by diffusion models that allow them to generate infinitely many novel images from a finite training set.
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@… I might have run into a bug in #BSSG. I have assigned image in the frontmatter, and they render on the first page and on the single post page, but fail to render from page 2 onward.
For example,

Frame of Preference | Thought Outlet
Das Internet of Enthusiasts hat wieder zugeschlagen: In wundervoller Kleinarbeit hat Marcin Wichary zusammengestragen, was sich in 40 Jahren Macintosh bei den Systemeinstellungen geändert hat. Da der

Euclid: Quick Data Release (Q1) -- Exploring the detailed visual morphology of galaxies in clusters
Mas-Buitrago, Kruk, O'Ryan, Nardone, La Marca, Awad, Baes, Fossati, G\'eron, Ghaffari, Girardi, Lintott, Sorce, Altieri, Durret, Pettorino, Irureta-Goyena, Simmons, Reerink, S\'anchez, Knapen, Shankar, Duran-Camacho, P\'erez-Mart\'inez, Walmsley, Auricchio, Baccigalupi, Baldi, Bardelli, Battaglia, Biviano, Bolzonella, Bonchi, Branchini, Brescia, Brinchmann, Camera, Ca\~nas-Herrera, Capobianco, Carbone, Carretero, Castellano, Castignani, Cavuoti, Cimatti, Colodro-Conde, Congedo, Conselice, Conversi, Copin, Costille, Courbin, Courtois, Cropper, Degaudenzi, De Lucia, Dole, Dubath, Dupac, Dusini, Ealet, Fabricius, Farina, Farinelli, Ferriol, Fosalba, Fotopoulou, Frailis, Franceschi, Fumana, Galeotta, George, Gillis, Giocoli, G\'omez-Alvarez, Gracia-Carpio, Grazian, Grupp, Gwyn, Holmes, Hook, Hormuth, Hornstrup, Huertas-Company, Jahnke, Jhabvala, Joachimi, Kermiche, Kiessling, Kubik, K\"ummel, Kunz, Kurki-Suonio, Le Brun, Ligori, Lilje, Lindholm, Lloro, Mainetti, Mansutti, Marggraf, Martinelli, Martinet, Marulli, Massey, Maurogordato, Medinaceli, Melchior, Meneghetti, Merlin, Meylan, Mora, Moresco, Moscardini, Munari, Neissner, Niemi, Nightingale, Padilla, Paltani, Pasian, Pedersen, Percival, Pezzotta, Pires, Polenta, Poncet, Popa, Pozzetti, Raison, Renzi, Rhodes, Riccio, Romelli, Roncarelli, Rusholme, Saglia, Sakr, S\'anchez, Sapone, Sartoris, Schneider, Schrabback, Scodeggio, Secroun, Sihvola, Simon, Sirignano, Sirri, Tallada-Cresp\'{i}, Taylor, Teplitz, Tereno, Tessore, Toft, Toledo-Moreo, Torradeflot, Tutusaus, Valiviita, Vassallo, Kleijn, Veropalumbo, Wang, Weller, Zacchei, Zamorani, Zerbi, Zucca, Macias-Perez, Sereno
https://arxiv.org/abs/2609.08962 https://arxiv.org/pdf/2609.08962 https://arxiv.org/html/2609.08962
arXiv:2609.08962v1 Announce Type: new
Abstract: Galaxy clusters provide unique laboratories for studying environmental effects on galaxy evolution. The morphology--density ($T$--$\Sigma$) and morphology--cluster-centric radius ($T$--$R$) relations trace how galaxy morphology is influenced by the environment, but previous studies at intermediate redshifts have been limited in both sample size and radial coverage. We use the Euclid Quick Data Release 1 (Q1) visual morphology catalogue to measure the $T$--$\Sigma$ and $T$--$R$ relations for smooth, featured-or-disc, and barred galaxies in known clusters at $0.2\leq z\leq 0.5$, extending this analysis to large cluster-centric distances ($3 R_{500c}$) and studying their dependence on stellar mass. Using photometric redshifts and stellar masses provided by Euclid, we identify 1754 cluster members within $1.5 R_{500c}$, distributed across 71 clusters. We classify the identified galaxies as smooth, featured-or-disc, or barred using the predicted vote fractions provided by the Zoobot deep learning foundation model in the Q1 visual morphology catalogue. We confirm the $T$--$\Sigma$ relation in all the stellar mass ranges studied, with a stronger influence of the cluster environment on galaxy morphology in the densest parts of the cluster and closer to the cluster centre. Beyond $1.5 R_{500c}$, the morphological segregation weakens, with featured-or-disc galaxies overtaking smooth galaxies at the lowest densities, consistent with the growing contribution of field interlopers in the cluster outskirts. For barred galaxies, we find a tentative decline of the bar fraction toward lower densities that is most pronounced for the most massive galaxies. In conclusion, our results show that the cluster environment drives a progressive transformation of galaxy morphology, with the loss of disc structure becoming more pronounced towards the cluster core, where environmental processes act most efficiently.
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