Spatial representation regularity and brain infra slow oscillation

Following a general introduction in Chapter 1, this thesis is divided into two main parts. The first part, consisting of chapters 2 to 6, focuses on grid cells and spatial cognition. Chapter 2 provided a concise overview of the experimental results on spatial representations. Chapter 3 introduces various models that have been proposed to elucidate the formation of grid cells. In chapters 4 and 5, we investigate our model of grid pattern formation based on adaptation follow questions include grid pattern in non-planar environments like a burrow environment, grid pattern anchoring in a square environment, and grid pattern distortion in an irregular environment like a trapezoid environment. In Chapter 6, due to the increasing complexity and richness of functions attributed to grid cells being described recently, we aim to describe the basic encoding properties of grid cells with a simplified self-organized model. The second part, encompassing chapters 7 to 9, is dedicated to exploring another form of regularity representation in the brain, which is brain oscillations. Specifically, our focus lies on infra-slow oscillations with periods lasting around several hundred seconds, observed in the frontal and parietal cortex during both natural sleep and anesthesia. In Chapters 7 and 8, we performed analyses of recordings obtained during natural sleep, exploring the intricate properties of infra-slow oscillations and their interactions with oscillations at faster timescales. Transitioning to Chapter 9, we shifted our attention to analyzing recordings acquired during states of anesthesia.