Building upon previous works by Conlon-Ferber and Wigderson, Sawin showed a few years ago that upper bounds on the minimum density of independent sets in a K_t-free G can be used to provide lower bounds for multicolor Ramsey numbers. In this note, we observe how a further improved upper bound on this parameter directly follows from a recent spherical random geometric graph construction of Ma-Shen-Xie. As a consequence, we derive a small exponential improvement over the best known lower bounds for multicolor Ramsey numbers.
We present a renormalization-group perspective on spontaneous stochasticity in hydrodynamic turbulence, viewed through the lens of multiscale dynamical systems. Building on previously established results for a solvable multiscale Arnold's cat model, we show that spontaneous stochasticity emerges as a universal fixed point of an RG transformation acting on Markov kernels, independent of the microscopic regularization. Classical examples - including the Feigenbaum equation, the central limit theorem, and hierarchical spin models - are reinterpreted within the same framework, placing spontaneous stochasticity alongside other universality phenomena.
We investigate the behavior of the empirical neighborhood distribution of marked graphs in the framework of local weak convergence. Here we extend known results by considering uniform random graphs with given degree sequences and i.i.d. marks on half-edges and vertices. We establish a large deviation principle for such families of empirical measures. The proof builds on Bordenave and Caputo's seminal 2015 paper, and Delgosha and Anantharam's 2019 introduction of BC entropy, relying on combinatorial lemmas that allow one to construct suitable approximations of measures supported on marked trees. Possible applications of these results are in the study of interacting diffusions on top of random graphs.
This technical report presents AudioWorldSim, an open-source platform designed to generate realistic binaural audio datasets and advance research in audio-based machine learning, particularly world models. Built as a custom extension of Meta's SoundSpaces 2.0 platform, AudioWorldSim leverages their comprehensive acoustics framework, but focuses on the automatic rollout of random agent navigations, as well as implements crucial fixes to how continuous sound is composed. AudioWorldSim is made publicly available to the research community at https://github.com/Luizerko/AudioWorldSim to facilitate reproducibility.
Accurate short-term precipitation forecasts predominantly rely on dense weather-radar networks, limiting operational value in places most exposed to climate extremes. We present TUPANN (Transferable and Universal Physics-Aligned Nowcasting Network), a satellite-only model trained on GOES-16 RRQPE. Unlike most deep learning models for nowcasting, TUPANN decomposes the forecast into physically meaningful components: a variational encoder-decoder infers motion and intensity fields from recent imagery under optical-flow supervision, a lead-time-conditioned MaxViT evolves the latent state, and a differentiable advection operator reconstructs future frames. We evaluate TUPANN on both GOES-16 and IMERG data, in up to four distinct climates (Rio de Janeiro, Manaus, Miami, La Paz) at 10-180-min lead times using the CSI and HSS metrics over 4-64 mm/h thresholds. Comparisons against optical-flow, deep learning, and hybrid baselines show that TUPANN achieves the best or second-best skill in most settings, with pronounced gains at higher thresholds. Training in multiple cities further improves performance, while cross-city experiments show modest degradation and occasional gains for rare heavy-rain regimes. The model produces smooth, interpretable motion fields aligned with numerical optical flow and runs in near real time due to the low latency of GOES-16. These results indicate that physically aligned learning can provide nowcasts that are skillful, transferable, and global.
