Tootfinder

An EKR Theorem for the Cartesian Product of Complete Graphs
Zaphenath Joseph
https://arxiv.org/abs/2509.14291 https://arxiv.org/pdf/2509.14291

An EKR Theorem for the Cartesian Product of Complete Graphs
The Erdős--Ko--Rado theorem states that for $r \leq \frac{n}{2}$, the largest intersecting family of $r$-subsets of $[n]$ is given by fixing a common element in all subsets, which trivially ensures pairwise intersection. We investigate this property for families of independent sets in the Cartesian product of complete graphs, $K_n \times K_m$. Using a novel extension of Katona's cycle method, we prove $K_n \times K_m$ is $r$-EKR when $1 \leq r \leq \frac{\min(m,n)}{2}$, demonstrating the Holro…

🇺🇦 #NowPlaying on BBCRadio3's #InTune
Johann Strauss II, Vienna Philharmonic & Zubin Mehta:
🎵 Elektro-magnetische Polka, Op 110
#JohannStraussII #ViennaPhilharmonic #ZubinMehta
https://open.spotify.com/track/0h7vlR2ysiW62dKMi5duGz
Please 🔁 BOOST to share what you like
- your followers don't see if you ⭐ favourite a post

🇺🇦 #NowPlaying on #BBC6Music's #CerysMatthews
Howlin’ Wolf:
🎵 Moanin' At Midnight
#HowlinWolf
https://bluesmasters.bandcamp.com/track/moanin-at-midnight
https://open.spotify.com/track/67PrMvxZ2P6meTwFCQ4RQi

Modulator-free, self-testing quantum random number generator
Ana Bl\'azquez-Co\'ido, Fadri Gr\"unenfelder, Anthony Martin, Raphael Houlmann, Hugo Zbinden, Davide Rusca
https://arxiv.org/abs/2507.12346

Modulator-free, self-testing quantum random number generator
Quantum random number generators (QRNGs) use the inherent unpredictability of quantum mechanics to generate true randomness, as opposed to classical random number generators. However, ensuring the authenticity of this randomness still requires robust verification. Self-testing QRNGs address this need by enabling the validation of the randomness produced based on the observed data from the experiment while requiring few assumptions. In this work, we present a practical, self-testing QRNG designe…

The Lady is a Tramp
https://www.youtube.com/watch?v=ZPAmDULCVrU

🇺🇦 #NowPlaying on KEXP's #PositiveVibrations
Deadly Headley:
🎵 Two from Alpha
#DeadlyHeadley
https://reggaearchive.bandcamp.com/track/deadly-headley-two-from-alpha
https://open.spotify.com/track/0z62S7yPnYdcUzQeRGUk8d

Synthesizing Sun-as-a-star flare spectra from high-resolution solar observations
M. De Wilde, A. G. M. Pietrow, M. K. Druett, A. Pastor Yabar, J. Koza, I. Kontogiannis, O. Andriienko, A. Berlicki, A. R. Brunvoll, J. de la Cruz Rodr\'iguez, J. T. Faber, R. Joshi, D. Kuridze, D. N\'obrega-Siverio, L. H. M. Rouppe van der Voort, J. Ryb\'ak, E. Scullion, A. M. Silva, Z. Vashalomidze, A. Vicente Ar\'evalo, A. Wi\'sniewska, R. Yadav, T. V. Zaqarashvili, J. Zbinden, E. S. …

Synthesizing Sun-as-a-star flare spectra from high-resolution solar observations
Spatially resolved observations of the Sun and the astronomical sample size of stellar bodies are the respective key strengths of solar and stellar observations. However, the large difference in object brightness between the Sun and other stars has led to distinctly different instrumentation and methodologies between the two fields. We produce and analyze synthetic full-disk spectra derived from 19 small area field-of-view optical observations of solar flares acquired by the Swedish 1-m Solar T…

Tienduizend stappen? Zevenduizend is al genoeg voor gezondheidswinst | de Volkskrant
Hoeraaa!
https://archive.ph/0R0iS

Une bonne décision donc, eu égard au statut d'incontestable boussole qui indique le sud de O'Leary
https://www.lesoir.be/690780/article/2025-07-31/une-decision-idiote-ryanair-critique-vertement…

🇺🇦 #NowPlaying on BBCRadio3's #PrivatePassions
Richard Strauss, Los Angeles Philharmonic & Zubin Mehta:
🎵 Also sprach Zarathustra
#RichardStrauss #LosAngelesPhilharmonic #ZubinMehta