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dc.contributor.authorGrossberg, Stephenen_US
dc.contributor.authorRepin, Dmitryen_US
dc.date.accessioned2011-11-14T19:02:50Z
dc.date.available2011-11-14T19:02:50Z
dc.date.issued2001-04en_US
dc.identifier.urihttps://hdl.handle.net/2144/2282
dc.description.abstractBoth 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.en_US
dc.description.sponsorshipDefense Advanced Research Projects Agency and the Office of Naval Research (N00014-95-1-0409); National Science Foundation (IRI-97-20333)en_US
dc.language.isoen_USen_US
dc.publisherBoston University Computer Science Departmenten_US
dc.relation.ispartofseriesBU CAS/CNS Technical Reports;CAS/CNS-TR-2001-006en_US
dc.rightsCopyright 2001 Boston University. Permission to copy without fee all or part of this material is granted provided that: 1. The copies are not made or distributed for direct commercial advantage; 2. the report title, author, document number, and release date appear, and notice is given that copying is by permission of BOSTON UNIVERSITY TRUSTEES. To copy otherwise, or to republish, requires a fee and / or special permission.en_US
dc.subjectNumberen_US
dc.subjectSpatial mapen_US
dc.subjectSpeech categoryen_US
dc.subjectLearningen_US
dc.subjectPlace-value systemen_US
dc.subjectInferior parietal cortexen_US
dc.subjectWhat and Where cortical streamsen_US
dc.titleA Neural Model of How the Brain Represents and Compares Multi-Digit Numbers: Spatial and Categorical Processesen_US
dc.typeTechnical Reporten_US
dc.rights.holderBoston University Trusteesen_US


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