Solving a class of zero-sum stopping game with regime switching

This paper studies a class of zero-sum stopping game in a regime switching model. A verification theorem as a sufficient criterion for Nash equilibriums is established based on a set of variational inequalities (VIs). Under an appropriate regularity condition for solutions to the VIs, a suitable system of algebraic equations is derived via the so-called smooth-fit principle. Explicit Nash equilibrium stopping rules of threshold-type for the two players and the corresponding value function of the game in closed form are obtained. Numerical experiments are reported to demonstrate the dependence of the threshold levels on various model parameters. A reduction to the case with no regime switching is also presented as a comparison

A note on inversion of Toeplitz matrices

AbstractIt is shown that the invertibility of a Toeplitz matrix can be determined through the solvability of two standard equations. The inverse matrix can be denoted as a sum of products of circulant matrices and upper triangular Toeplitz matrices. The stability of the inversion formula for a Toeplitz matrix is also considered

Can SAM Segment Anything? When SAM Meets Camouflaged Object Detection

SAM is a segmentation model recently released by Meta AI Research and has been gaining attention quickly due to its impressive performance in generic object segmentation. However, its ability to generalize to specific scenes such as camouflaged scenes is still unknown. Camouflaged object detection (COD) involves identifying objects that are seamlessly integrated into their surroundings and has numerous practical applications in fields such as medicine, art, and agriculture. In this study, we try to ask if SAM can address the COD task and evaluate the performance of SAM on the COD benchmark by employing maximum segmentation evaluation and camouflage location evaluation. We also compare SAM's performance with 22 state-of-the-art COD methods. Our results indicate that while SAM shows promise in generic object segmentation, its performance on the COD task is limited. This presents an opportunity for further research to explore how to build a stronger SAM that may address the COD task. The results of this paper are provided in \url{https://github.com/luckybird1994/SAMCOD}