How Does the Cerebral Cortex Work? Developement, Learning, Attention, and 3D Vision by Laminar Circuits of Visual Cortex

A key goal of behavioral and cognitive neuroscience is to link brain mechanisms to behavioral functions. The present article describes recent progress towards explaining how the visual cortex sees. Visual cortex, like many parts of perceptual and cognitive neocortex, is organized into six main layers of cells, as well as characteristic sub-lamina. Here it is proposed how these layered circuits help to realize the processes of developement, learning, perceptual grouping, attention, and 3D vision through a combination of bottom-up, horizontal, and top-down interactions. A key theme is that the mechanisms which enable developement and learning to occur in a stable way imply properties of adult behavior. These results thus begin to unify three fields: infant cortical developement, adult cortical neurophysiology and anatomy, and adult visual perception. The identified cortical mechanisms promise to generalize to explain how other perceptual and cognitive processes work.Air Force Office of Scientific Research (F49620-01-1-0397); Office of Naval Research (N00014-01-1-0624

Form Perception

National Science Foundation (SBE-0354378); Office of Naval Research (N00014-01-1-0624

Seeing Numbers

In 1890 William James listed several “elementary mental categories” that he postulated as having a natural origin. Among them, alongside the ideas of time and space, he also listed the idea of number. A symptomatic feature of Informatics as well as Cognitive Science today is the tendency not to talk so much about ideas as about their representations, either in the computer or in the brain. Taking up somewhat different perspective I will discuss the way natural numbers, viewed as counts of real or imagined objects, may be experienced phenomenally. I put forth even some speculative ideas about mental number processing by numerical savants

The Complexity of Recognizing Geometric Hypergraphs

As set systems, hypergraphs are omnipresent and have various representations ranging from Euler and Venn diagrams to contact representations. In a geometric representation of a hypergraph $H=(V,E)$, each vertex $v\in V$ is associated with a point $p_v\in \mathbb{R}^d$ and each hyperedge $e\in E$ is associated with a connected set $s_e\subset \mathbb{R}^d$ such that $\{p_v\mid v\in V\}\cap s_e=\{p_v\mid v\in e\}$ for all $e\in E$. We say that a given hypergraph $H$ is representable by some (infinite) family $F$ of sets in $\mathbb{R}^d$, if there exist $P\subset \mathbb{R}^d$ and $S \subseteq F$ such that $(P,S)$ is a geometric representation of $H$. For a family F, we define RECOGNITION(F) as the problem to determine if a given hypergraph is representable by F. It is known that the RECOGNITION problem is $\exists\mathbb{R}$-hard for halfspaces in $\mathbb{R}^d$. We study the families of translates of balls and ellipsoids in $\mathbb{R}^d$, as well as of other convex sets, and show that their RECOGNITION problems are also $\exists\mathbb{R}$-complete. This means that these recognition problems are equivalent to deciding whether a multivariate system of polynomial equations with integer coefficients has a real solution.Comment: Appears in the Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023) 17 pages, 11 figure

Object representation and recognition

One of the primary functions of the human visual system is object recognition, an ability that allows us to relate the visual stimuli falling on our retinas to our knowledge of the world. For example, object recognition allows you to use knowledge of what an apple looks like to find it in the supermarket, to use knowledge of what a shark looks like to swim in th