Life is a die

Life are consist of uncertainty and certainty. The most functional way for people to deal with life is to try their best for certainty and to accept uncertainty. However, due to the consistently changing environment and fast increasing uncertainty, people are more and more unlikely to deal with life and its uncertainty. This project, Life-is-a-die, will express the personal thought to deal with life and release worries and fear through a poetic video. In this video, the designed metaphors, poetic story, sound effects, text, 3d elements, motions, visuals, motion, and textures will play a vital role to help people understand and learn the whole theme

Linear isometric invariants of bounded domains

We introduce two new conditions for bounded domains, namely $A^p$-completeness and boundary blow down type, and show that, for two bounded domains $D_1$ and $D_2$ that are $A^p$-complete and not of boundary blow down type, if there exists a linear isometry from $A^p(D_1)$ to $A^{p}(D_2)$ for some real number $p>0$ with $p\neq$ even integers, then $D_1$ and $D_2$ must be holomorphically equivalent, where for a domain $D$, $A^p(D)$ denotes the space of $L^p$ holomorphic functions on $D$.Comment: 14pages, comments welcome

Subsampling-Based Modified Bayesian Information Criterion for Large-Scale Stochastic Block Models

Identifying the number of communities is a fundamental problem in community detection, which has received increasing attention recently. However, rapid advances in technology have led to the emergence of large-scale networks in various disciplines, thereby making existing methods computationally infeasible. To address this challenge, we propose a novel subsampling-based modified Bayesian information criterion (SM-BIC) for identifying the number of communities in a network generated via the stochastic block model and degree-corrected stochastic block model. We first propose a node-pair subsampling method to extract an informative subnetwork from the entire network, and then we derive a purely data-driven criterion to identify the number of communities for the subnetwork. In this way, the SM-BIC can identify the number of communities based on the subsampled network instead of the entire dataset. This leads to important computational advantages over existing methods. We theoretically investigate the computational complexity and identification consistency of the SM-BIC. Furthermore, the advantages of the SM-BIC are demonstrated by extensive numerical studies

Approximation and extension of Hermitian metrics on holomorphic vector bundles over Stein manifolds

We show that a singular Hermitian metric on a holomorphic vector bundle over a Stein manifold which is negative in the sense of Griffiths (resp. Nakano) can be approximated by a sequence of smooth Hermitian metrics with the same curvature negativity. We also show that a smooth Hermitian metric on a holomorphic vector bundle over a Stein manifold restricted to a submanifold which is negative in the sense of Griffiths (resp. Nakano) can be extended to the whole bundle with the same curvature negativity.Comment: 10pages. Comments welcome

Z∗Z^*: Zero-shot Style Transfer via Attention Rearrangement

Despite the remarkable progress in image style transfer, formulating style in the context of art is inherently subjective and challenging. In contrast to existing learning/tuning methods, this study shows that vanilla diffusion models can directly extract style information and seamlessly integrate the generative prior into the content image without retraining. Specifically, we adopt dual denoising paths to represent content/style references in latent space and then guide the content image denoising process with style latent codes. We further reveal that the cross-attention mechanism in latent diffusion models tends to blend the content and style images, resulting in stylized outputs that deviate from the original content image. To overcome this limitation, we introduce a cross-attention rearrangement strategy. Through theoretical analysis and experiments, we demonstrate the effectiveness and superiority of the diffusion-based $\underline{Z}$ero-shot $\underline{S}$tyle $\underline{T}$ransfer via $\underline{A}$ttention $\underline{R}$earrangement, Z-STAR