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In this paper, we propose a new approach to deformable image registration that captures sliding motions. The large deformation diffeomorphic metric mapping (LDDMM) registration method faces challenges in representing sliding motion since it per construction generates smooth warps. To address this issue, we extend LDDMM by incorporating both zeroth- and first-order momenta with a nondifferentiable kernel. This allows us to represent both discontinuous deformation at switching boundaries and diffeomorphic deformation in homogeneous regions. We provide a mathematical analysis of the proposed deformation model from the viewpoint of discontinuous systems. To evaluate our approach, we conduct experiments on both artificial images and the publicly available DIR-Lab 4DCT dataset. Results show the effectiveness of our approach in capturing plausible sliding motion. [ABSTRACT FROM AUTHOR]

Phages are ubiquitous in nature, but many essential factors of host-phage biology have not yet been integrated into mathematical models. In this paper, we investigate a spatial phage-bacteria model to describe the propagation of phages and bacteria in different types of nutrient media. Unlike existing models, we construct a more realistic reaction-diffusion model that incorporates inoculum and bacterial growth and movement, then rigorous mathematical analysis is challenging. We study traveling wave solutions and obtain complete information about the existence and nonexistence of nontrivial traveling wave solutions. The threshold conditions for the existence and nonexistence of traveling wave solutions are obtained by using Schauder's fixed point theorem, limiting argument, and one-sided Laplace transform. Considering different propagation media, we extend the existence of traveling wave solutions from liquid nutrition model to agar model. Moreover, in the absence of bacterial mortality, we obtain the existence of a new traveling wave solution describing phage invasion. We attempt to explain the occurrence of co-transport by the existence and nonexistence of traveling waves, and screen out the key parameters affecting the co-transport of phages and bacteria according to the definition of critical wave speed. Finally, we provide numerical simulations to verify the theoretical results and reveal the effects of key parameters on the propagation of phages and bacteria. [ABSTRACT FROM AUTHOR]