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2021 ◽  
Author(s):  
Wujie Zhang ◽  
Jacqueline Gottlieb ◽  
Kenneth D Miller

When monkeys learn to group visual stimuli into arbitrary categories, lateral intraparietal area (LIP) neurons become category-selective. Surprisingly, the representations of learned categories are overwhelmingly biased: nearly all LIP neurons in a given animal prefer the same category over other behaviorally equivalent categories. We propose a model where such biased representations develop through the interplay between Hebbian plasticity and the recurrent connectivity of LIP. In this model, two separable processes of positive feedback unfold in parallel: in one, category selectivity emerges from competition between prefrontal inputs; in the other, bias develops due to lateral interactions among LIP neurons. This model reproduces the levels of category selectivity and bias observed under a variety of conditions, as well as the redevelopment of bias after monkeys learn redefined categories. It predicts that LIP receptive fields would spatially cluster by preferred category, which we experimentally confirm. In summary, our model reveals a mechanism by which LIP learns abstract representations and assigns meaning to sensory inputs.


Author(s):  
Kevin Maya ◽  
Adriana Mejía Castaño ◽  
Bernardo Uribe

We give a complete classification of pointed fusion categories over [Formula: see text] of global dimension [Formula: see text] for [Formula: see text] any odd prime. We proceed to classify the equivalence classes of pointed fusion categories of dimension [Formula: see text] and we determine which of these equivalence classes have equivalent categories of modules.


2017 ◽  
Vol 82 (4) ◽  
pp. 1181-1198 ◽  
Author(s):  
DIMITRIS TSEMENTZIS

AbstractWe characterize Morita equivalence of theories in the sense of Johnstone in terms of a new syntactic notion of a common definitional extension developed by Barrett and Halvorson for cartesian, regular, coherent, geometric and first-order theories. This provides a purely syntactic characterization of the relation between two theories that have equivalent categories of models naturally in any Grothendieck topos.


2008 ◽  
Vol 35 (1) ◽  
pp. 35-54 ◽  
Author(s):  
Marian Hickendorff ◽  
Willem J. Heiser ◽  
Cornells M. van Putten ◽  
Norman D. Verhelst

1990 ◽  
Vol 2 (2) ◽  
pp. 1-14 ◽  
Author(s):  
Laszlo Fuchs ◽  
Luigi Salce

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