Mathematical Analysis of Some Typical Problems in Geodesy by Means of Computer Algebra

There are many complicated and fussy mathematical analysis processes in geodesy, such as the power series expansions of the ellipsoid’s eccentricity, high order derivation of complex and implicit functions, operation of trigonometric function, expansions of special functions and integral transformation. Taking some typical mathematical analysis processes in geodesy as research objects, the computer algebra analysis are systematically carried out to bread, deep and detailed extent with the help of computer algebra analysis method and the powerful ability of mathematical analysis of computer algebra system. The forward and inverse expansions of the meridian arc in geometric geodesy, the nonsingular expressions of singular integration in physical geodesy and the series expansions of direct transformations between three anomalies in satellite geodesy are established, which have more concise form, stricter theory basis and higher accuracy compared to traditional ones. The breakthrough and innovation of some mathematical analysis problems in the special field of geodesy are realized, which will further enrich and perfect the theoretical system of geodesy

Controllable Generation with Text-to-Image Diffusion Models: A Survey

In the rapidly advancing realm of visual generation, diffusion models have revolutionized the landscape, marking a significant shift in capabilities with their impressive text-guided generative functions. However, relying solely on text for conditioning these models does not fully cater to the varied and complex requirements of different applications and scenarios. Acknowledging this shortfall, a variety of studies aim to control pre-trained text-to-image (T2I) models to support novel conditions. In this survey, we undertake a thorough review of the literature on controllable generation with T2I diffusion models, covering both the theoretical foundations and practical advancements in this domain. Our review begins with a brief introduction to the basics of denoising diffusion probabilistic models (DDPMs) and widely used T2I diffusion models. We then reveal the controlling mechanisms of diffusion models, theoretically analyzing how novel conditions are introduced into the denoising process for conditional generation. Additionally, we offer a detailed overview of research in this area, organizing it into distinct categories from the condition perspective: generation with specific conditions, generation with multiple conditions, and universal controllable generation. For an exhaustive list of the controllable generation literature surveyed, please refer to our curated repository at \url{https://github.com/PRIV-Creation/Awesome-Controllable-T2I-Diffusion-Models}.Comment: A collection of resources on controllable generation with text-to-image diffusion models: https://github.com/PRIV-Creation/Awesome-Controllable-T2I-Diffusion-Model