Low-dimensional chaos maps learning in a model neuropil (olfactory bulb)

Quantification of a chaotic system can be made by calculating the correlation dimension (D2) of the data that the system generates (Packard et al., 1980). The D2 algorithm, however, requires stationarity of the generator, a feature that biological data rarely reflect (Mayer-Kress et al., 1988). So we developed the “point correlation dimension” (PD2), an algorithm that accurately tracks D2 in linked data of different dimensions (Carpeggiani et al., 1991). We now present a mathematical argument that, for stationary data, individual PD2s converge to D2 and we demonstrate that the algorithm rejects contributions made by bursts of noise. Data were obtained from the surface of the olfactory bulb of the conscious rabbit (64 electrodes, 640 Hz each, 1.3 sec epochs) before and after presentation of a novel or habituated odor. D2 could be calculated in only 1 of 10 novel-odor trials, whereas PD2 could be calculated in all. Both algorithms indicated that a novel odor evokes a spatially uniform dimensional increase. The PD2 uniquely exhibited the dimensional decreases that occur during inspiration and the gradients of mean dimension present during the nonstimulated control state. These control gradients remained unchanged without odor experience, but showed spatially specific PD2 increases following odor habituation. It is interpreted that, 1) the PD2 issensitive, accurate, and appropriate for dimensional assessment of biological data, 2) that during analysis of unfamiliar information a singleglobal process is transiently evoked in the neuropil, and 3) after experience multiplespatially specific processes tonically map the sites of learning. Grant Support: National Institutes of Health, HL 31164 and NS27745     

Social reinforcement of operant behavior in rats: a methodological note.

An apparatus was developed to study social reinforcement in the rat. Four Long-Evans female rats were trained to press a lever via shaping, with the reinforcer being access to a castrated male rat. Responding under a fixed-ratio schedule and in extinction was also observed. Social access was found to be an effective reinforcer. When social reinforcement was compared with food reinforcement under similar conditions of deprivation and reinforcer duration, no significant differences were observed.     

When and how communicated guilt affects contributions in public good dilemmas

Two laboratory studies investigated how groups may deal with the strong emotions that social dilemmas often elicit. A first study showed that a new group member evaluated guilt communicated by a fellow group member as more instrumental than neutral emotion feedback when the amount of required resources to obtain the public good (i.e., provision point) was perceived as difficult to obtain. A second study revealed that participants use communicated guilt to draw inferences about both past and future contributions from all fellow group members. Participants also contributed more themselves and adhered to equality more often when guilt versus no emotion was communicated, but only when the provision point was high. Expected contributions from fellow group members mediated this effect.     

Single and double alternation learning in rats: The role of set size and correction

In many experiments, rats have evidenced extreme difficulty mastering alternation patterns. In three experiments, we explored rats’ ability to learn double alternation patterns and possible reasons behind their past difficulties with such patterns. In Experiment 1, rats learned single and double alternation patterns. In the second and third experiment, we explored the role of correction and interference from stimulus set size on rats’ learning of double alternation patterns. Our results showed that rats easily learned both single and double alternation patterns and that stimulus set size had no noticeable effect on learning double alternation patterns. Findings additionally evidenced that correction played an important role in rats’ learning double alternation patterns.     

The Structure of the Ordinals and the Interpretation of ZF in Double Extension Set Theory

Andrzej Kisielewicz has proposed three systems of double extension set theory of which we have shown two to be inconsistent in an earlier paper. Kisielewicz presented an argument that the remaining system interprets ZF, which is defective: it actually shows that the surviving possibly consistent system of double extension set theory interprets ZF with Separation and Comprehension restricted to ₀ formulas. We show that this system does interpret ZF, using an analysis of the structure of the ordinals.     

Admissibility of Cut in <Emphasis Type="Italic">LC</Emphasis> with Fixed Point Combinator

The fixed point combinator (Y) is an important non-proper combinator, which is defhable from a combinatorially complete base. This combinator guarantees that recursive equations have a solution. Structurally free logics (LC) turn combinators into formulas and replace structural rules by combinatory ones. This paper introduces the fixed point and the dual fixed point combinator into structurally free logics. The admissibility of (multiple) cut in the resulting calculus is not provable by a simple adaptation of the similar proof for LC with proper combinators. The novelty of our proof—beyond proving the cut for a newly extended calculus–is that we add a fourth induction to the by-and-large Gentzen-style proof. Presented by Robert Goldblatt     

Another Paradox In Naive Set-Theory

Reasonning in naive set theory (with unlimited comprehension), we derive a paradox (a formal contradiction) which can be seen as a variant of the Burali-Forti paradox. Presented by Robert Goldblatt     

Asymmetric dominance and phantom decoy effects in games

In individual choices between alternatives x and y, the availability of a third alternative z, judged inferior to x but not to y, tends to increase preferences for x. Two experiments investigated corresponding strategic asymmetric dominance effects in games. In Experiment 1, 72 players chose strategies in six symmetric 3 × 3 games, each having one strategy dominating just one other, or in reduced 2 × 2 games constructed by deleting the dominated strategies. Asymmetrically dominated strategies, even when unavailable (phantom decoy), increased choices of the strategies that dominated them and bolstered decision confidence. In Experiment 2, 81 participants played 12 similar but asymmetric games with or without dominated strategies, and similar asymmetric dominance, phantom decoy, and confidence effects were found.