Dynamics of Cortical Columns – Sensitive Decision Making

Abstract

Abstract. Based on elementary assumptions on the interconnectivity within a cortical macrocolumn we derive a differential equation system which models the mean neural activities of its minicolumns. A stability analysis shows a rich diversity of stationary points and sensitive behavior with respect to a parameter of inhibition. If this parameter is continuously changed, the system shows the same types of bifurcations as the macrocolumn model presented in [1] which is based on explicitly defined interconnectivity and spiking neurons. Due to this behavior the macrocolumn is able to make very sensitive decisions with respect to external input. The decision making process can be used to induce selforganization of receptive fields as is shown in [2].

Rapid Convergence to Feature Layer Correspondences

“…In recent neurophysiological experiments, it was shown that columns possess a fine structure of relatively disjunct subpopulations of excitatory neurons (Yoshimura et al, 2005). A model of a column with this structure was studied in Lücke and von der Malsburg (2004) and Lücke (2004), and we will base our system on an abstract dynamical formulation as suggested in Lücke (2005). This abstract formulation models the mean activity in populations of excitatory neurons.…”

“…, p k ) = ν max α { p α }, where p α denotes the activity in population or unit α of the column. Different types of inhibitory coupling were studied (see, e.g., Lücke, von der Malsburg, & Würtz, 2002;Lücke & von der Malsburg, 2004), but inhibition proportional to the maximal activity has been found to have a number of functional advantages (Lücke, 2005). Taken together, the dynamics of a column is described by the equation system…”

“…This abstract formulation models the mean activity in populations of excitatory neurons. To recapitulate the approach in Lücke (2005), consider a single population of excitatorily interconnected neurons. Through its connections, such a population can be expected to increase its activity level.…”

“…In section 2 we introduce and discuss a dynamic model of a single cortical column as formulated in Lücke (2005) and subsequently introduce the architecture of our network model, which consists of two layers of such columns. The dynamics of the layers and their principal interaction are defined and discussed in section 3.…”

What Is the Optimal Architecture for Visual Information Routing?

“…Different routing architectures require different numbers of intermediate feature-representing nodes (we will refer to them simply as nodes) and node-to-node connections (links from now on; if we mean both links and nodes, we will use the term units). Although we will not discuss in this letter how connections in a routing circuit are controlled (for this, refer to Olshausen et al 1993, andto Lücke, 2005), we assume that the maintenance of a link and its control by a neural control unit has the same cost as feature nodes (for a deviation from this assumption, see section 2.1). It is likely that cortical architectures have evolved that minimize this cost for the organism.…”