לוח שנה משולב

Convex hull of a set of points in two dimensions roughly describes the shape of the set. In this talk, I will discuss the statistical properties of the convex hull for two stochastic processes in two dimensions: (i) a set of n independent planar Brownian paths (ii) a branching Brownian motion with death. We show how to compute exactly the mean perimeter and the mean area of the convex hull in these two problems. The first problem has application in estimating the home range of an animal population of size n, while the second will be used to estimate the spatial extent of the outbreak of animal epidemics. Our result also makes an interesting connection between random geometry and extreme value statistics.

Traditional models of memory dissociate memory from processes. Such tendency is rooted in the analogy between computers’ architecture and the brain, which dissociate the central processing units from the memory units. Based on such conceptualization, many empirical studies focus on simple delay periods in which memory has to be actively maintained but not processed and cases in which the integration between past and present information is undesirable. However, such models are not applicable to the majority of real life processes in which the past and present converge continuously in the processes of incoming information. Based on empirical data we outline a new framework for process-memory that resists the tendency to separate memory from process. We argue that cortical areas, ranging from early sensory areas to high order areas, has the capacity to accumulate information over time. Memory is intrinsic to each and any neural circuit, and is essential for its ability to process information. Furthermore, our data suggest that the process-memory timescale increases from early sensory areas to high order areas. Our hypothesis, that each brain area accumulates information over its preferred timescale, suggests that memories of the recent past are not stored in a few localized working memory buffers, but rather are distributed in an organized hierarchical topography throughout the nervous system. The “work of memory” is performed in virtually every neural circuit, and attentional systems modulate this ongoing processing in accordance with rule- or goal-related constraints.