Comparing mixing times on sparse random graphs

It is natural to expect that nonbacktracking random walk will mix faster than simple random walks, but so far this has only been proved in regular graphs. To analyze typical irregular graphs, let $G$ be a random graph on $n$ vertices with minimum degree 3 and a degree distribution that has exponential tails. We determine the precise worst-case mixing time for simple random walk on $G$, and show that, with high probability, it exhibits cutoff at time $\mathbf{h}^{-1} \log n$, where $\mathbf{h}$ is the asymptotic entropy for simple random walk on a Galton--Watson tree that approximates $G$ locally. (Previously this was only known for typical starting points.) Furthermore, we show that this asymptotic mixing time is strictly larger than the mixing time of nonbacktracking walk, via a delicate comparison of entropies on the Galton-Watson tree

Navigating Cultural Chasms: Exploring and Unlocking the Cultural POV of Text-To-Image Models

Text-To-Image (TTI) models, such as DALL-E and StableDiffusion, have demonstrated remarkable prompt-based image generation capabilities. Multilingual encoders may have a substantial impact on the cultural agency of these models, as language is a conduit of culture. In this study, we explore the cultural perception embedded in TTI models by characterizing culture across three hierarchical tiers: cultural dimensions, cultural domains, and cultural concepts. Based on this ontology, we derive prompt templates to unlock the cultural knowledge in TTI models, and propose a comprehensive suite of evaluation techniques, including intrinsic evaluations using the CLIP space, extrinsic evaluations with a Visual-Question-Answer (VQA) model and human assessments, to evaluate the cultural content of TTI-generated images. To bolster our research, we introduce the CulText2I dataset, derived from four diverse TTI models and spanning ten languages. Our experiments provide insights regarding Do, What, Which and How research questions about the nature of cultural encoding in TTI models, paving the way for cross-cultural applications of these models

Magnetic Monopole Noise

Magnetic monopoles are hypothetical elementary particles exhibiting quantized magnetic charge $m_0=\pm(h/\mu_0e)$ and quantized magnetic flux $\Phi_0=\pm h/e$. A classic proposal for detecting such magnetic charges is to measure the quantized jump in magnetic flux $\Phi$ threading the loop of a superconducting quantum interference device (SQUID) when a monopole passes through it. Naturally, with the theoretical discovery that a plasma of emergent magnetic charges should exist in several lanthanide-pyrochlore magnetic insulators, including Dy$_2$Ti$_2$O$_7$, this SQUID technique was proposed for their direct detection. Experimentally, this has proven extremely challenging because of the high number density, and the generation-recombination (GR) fluctuations, of the monopole plasma. Recently, however, theoretical advances have allowed the spectral density of magnetic-flux noise $S_{\Phi}(\omega,T)$ due to GR fluctuations of $\pm m_*$ magnetic charge pairs to be determined. These theories present a sequence of strikingly clear predictions for the magnetic-flux noise signature of emergent magnetic monopoles. Here we report development of a high-sensitivity, SQUID based flux-noise spectrometer, and consequent measurements of the frequency and temperature dependence of $S_{\Phi}(\omega,T)$ for Dy$_2$Ti$_2$O$_7$ samples. Virtually all the elements of $S_{\Phi}(\omega,T)$ predicted for a magnetic monopole plasma, including the existence of intense magnetization noise and its characteristic frequency and temperature dependence, are detected directly. Moreover, comparisons of simulated and measured correlation functions $C_{\Phi}(t)$ of the magnetic-flux noise $\Phi(t)$ imply that the motion of magnetic charges is strongly correlated because traversal of the same trajectory by two magnetic charges of same sign is forbidden