A Neural Model of How The Brain Represents and Compares Numbers

Many psychophysical experiments have shown that the representation of numbers and numerical quantities in humans and animals is related to number magnitude. A neural network model is proposed to quantitatively simulate error rates in quantification and numerical comparison tasks, and reaction times for number priming and numerical assessment and comparison tasks. Transient responses to inputs arc integrated before they activate an ordered spatial map that selectively responds to the number of events in a sequence. The dynamics of numerical comparison are encoded in activity pattern changes within this spatial map. Such changes cause a "directional comparison wave" whose properties mimic data about numerical comparison. These model mechanisms are variants of neural mechanisms that have elsewhere been used to explain data about motion perception, attention shifts, and target tracking. Thus, the present model suggests how numerical representations may have emerged as specializations of more primitive mechanisms in the cortical Where processing stream.National Science Foundation (IRI-97-20333); Defense Advanced research Projects Agency and the Office of Naval Research (N00014-95-1-0409); National Institute of Health (1-R29-DC02952-01

A Neural Model of How the Brain Represents and Compares Multi-Digit Numbers: Spatial and Categorical Processes

Both animals and humans are capable of representing and comparing numerical quantities, but only humans seem to have evolved multi-digit place-value number systems. This article develops a neural model, called the Spatial Number Network, or SpaN model, which predicts how these shared numerical capabilities are computed using a spatial representation of number quantities in the Where cortical processing stream, notably the Inferior Parietal Cortex. Multi-digit numerical representations that obey a place-value principle are proposed to arise through learned interactions between categorical language representations in the What cortical processing stream and the Where spatial representation. It is proposed that learned semantic categories that symbolize separate digits, as well as place markers like "tens," "hundreds," "thousands," etc., are associated through learning with the corresponding spatial locations of the Where representation, leading to a place-value number system as an emergent property of What-Where information fusion. The model quantitatively simulates error rates in quantification and numerical comparison tasks, and reaction times for number priming and numerical assessment and comparison tasks. In the Where cortical process, it is proposed that transient responses to inputs are integrated before they activate an ordered spatial map that selectively responds to the number of events in a sequence. Neural mechanisms are defined which give rise to an ordered spatial numerical map ordering and Weber law characteristics as emergent properties. The dynamics of numerical comparison are encoded in activity pattern changes within this spatial map. Such changes cause a "directional comparison wave" whose properties mimic data about numerical comparison. These model mechanisms are variants of neural mechanisms that have elsewhere been used to explain data about motion perception, attention shifts, and target tracking. Thus, the present model suggests how numerical representations may have emerged as specializations of more primitive mechanisms in the cortical Where processing stream. The model's What-Where interactions can explain human psychophysical data, such as error rates and reaction times, about multi-digit (base 10) numerical stimuli, and describe how such a competence can develop through learning. The SpaN model and its explanatory range arc compared with other models of numerical representation.Defense Advanced Research Projects Agency and the Office of Naval Research (N00014-95-1-0409); National Science Foundation (IRI-97-20333

Adaptive Resonance Associative Map: A Hierarchical ART System for Fast Stable Associative Learning

This paper introduces a new class of predictive ART architectures, called Adaptive Resonance Associative Map (ARAM) which performs rapid, yet stable heteroassociative learning in real time environment. ARAM can be visualized as two ART modules sharing a single recognition code layer. The unit for recruiting a recognition code is a pattern pair. Code stabilization is ensured by restricting coding to states where resonances are reached in both modules. Simulation results have shown that ARAM is capable of self-stabilizing association of arbitrary pattern pairs of arbitrary complexity appearing in arbitrary sequence by fast learning in real time environment. Due to the symmetrical network structure, associative recall can be performed in both directions.Air Force Office of Scientific Research (90-0128

Dwelling Quietly in the Rich Club: Brain Network Determinants of Slow Cortical Fluctuations

For more than a century, cerebral cartography has been driven by investigations of structural and morphological properties of the brain across spatial scales and the temporal/functional phenomena that emerge from these underlying features. The next era of brain mapping will be driven by studies that consider both of these components of brain organization simultaneously -- elucidating their interactions and dependencies. Using this guiding principle, we explored the origin of slowly fluctuating patterns of synchronization within the topological core of brain regions known as the rich club, implicated in the regulation of mood and introspection. We find that a constellation of densely interconnected regions that constitute the rich club (including the anterior insula, amygdala, and precuneus) play a central role in promoting a stable, dynamical core of spontaneous activity in the primate cortex. The slow time scales are well matched to the regulation of internal visceral states, corresponding to the somatic correlates of mood and anxiety. In contrast, the topology of the surrounding "feeder" cortical regions show unstable, rapidly fluctuating dynamics likely crucial for fast perceptual processes. We discuss these findings in relation to psychiatric disorders and the future of connectomics.Comment: 35 pages, 6 figure