A new functional role for lateral inhibition in the striatum: Pavlovian conditioning

The striatum has long been implicated in reinforcement learning and has been suggested by several neurophysiological studies as the substrate for encoding the reward value of stimuli. Reward prediction error (RPE) has been used in several basal ganglia models as the underlying learning signal, which leads to Pavlovian conditioning abilities that can be simulated by the Rescorla-Wagner model.

Lateral inhibition between striatal projection neurons was once thought to have a winner-take-all function, useful in selecting between possible actions. However, it has been noted that the necessary reciprocal connections for this interpretation are too few, and the relative strength of these synaptic connections is weak. Still, modeling studies show that lateral inhibition does have an overall suppression effect on striatal activity and may play an important role in striatal processing. 

Neurophysiological recordings show task-relevant ensembles of responsive neurons at specific points in a behavioral paradigm (Barnes et al., 2005), which appear to be induced by lateral inhibition (see Ponzi and Wickens, 2010). We have developed a similarly responding, RPE-based model of the striatum by incorporating lateral inhibition. Model neurons are assigned to either the direct or the indirect pathway but lateral connections occur within and between these groups, leading to competition between both the individual neurons and their pathways. We successfully applied this model to the simulation of Pavlovian phenomena beyond those of the Rescorla-Wagner model, including negative patterning, unovershadowing, and external inhibition

Generalization of the concepts of seniority number and ionicity

We present generalized versions of the concepts of seniority number and ionicity. These generalized numbers count respectively the partially occupied and fully occupied shells for any partition of the orbital space into shells. The Hermitian operators whose eigenspaces correspond to wave functions of definite generalized seniority or ionicity values are introduced. The generalized seniority numbers (GSNs) afford to establish refined hierarchies of configuration interaction (CI) spaces within those of fixed ordinary seniority. Such a hierarchy is illustrated on the buckminsterfullerene molecule

Garbled Elections

Majority rules are frequently used to decide whether or not a public good should be provided, but will typically fail to achieve an efficient provision. We provide a worst-case analysis of the majority rule with an optimally chosen majority threshold, assuming that voters have independent private valuations and are exante symmetric (provision cost shares are included in the valuations). We show that if the population is large it can happen that the optimal majority rule is essentially no better than a random provision of the public good. But the optimal majority rule is worst-case asymptotically efficient in the large-population limit if (i) the voters’ expected valuation is bounded away from 0, and (ii) an absolute bound for valuations is known