The Incompleteness of Theories of Games

We first state a few previously obtained results that lead to general undecidability and incompleteness theorems in axiomatized theories that range from the theory of finite sets to classical elementary analysis. Out of those results we prove several incompleteness theorems for axiomatic versions of the theory of noncooperative games with Nash equilibria; in particular, we show the existence of finite games whose equilibria cannot be proven to be computable.     

Perforant path activation modulates the induction of long-term potentiation of the schaffer collateral--hippocampal CA1 response: theoretical and experimental analyses

In one computational model of hippocampal function, the entorhinal cortical input to CA1 is hypothesized to play a key role in the ability of CA1 to decode CA3 recodings. Here, we develop a modification of this CA1 decoder hypothesis that is applicable to several computational theories of hippocampal function, and then we electrophysiologically investigate one assumption of this new hypothesis. First, using biologically realistic estimates, we calculate that CA3-induced CA1 excitation is too high and that inhibition plausibly plays a role in this CA1 decoder model. Thus motivated, we turn to a physiological demonstration to substantiate the plausibility of the proposed mechanism. Using the rat hippocampal slice, we examine an interlaminar interaction between the distal perforant path input to hippocampal CA1 stratum moleculare and the more proximal Schaffer collateral input to stratum radiatum. Perforant path activation provides sufficient inhibition to block homosynaptic long-term potentiation elicited by a suitably strong stratum radiatum input. For this interlaminar interaction to be most effective, perforant path activation must both precede and follow Schaffer collateral activation. Perforant path-evoked inhibition in CA1 can thus serve as a viable mechanism in the learned decoder theory of hippocampal CA1.     

Contextual Control in Visuospatial Perspective‐Taking Skills in Adults with Intellectual Disabilities

The aim of this study was to teach left/right (Experiment 1) and near/far (Experiment 2) discrimination with reference both to self and to another person. The procedures used involved teaching discrimination in expressive language (speaker behavior) and then testing the transfer of learning into receptive language (listener behavior). A total of six intellectually disabled adults took part in the study, four in Experiment 1 and two in Experiment 2. The results showed that the subjects learned the target behavior in expressive language and performed correctly in tests to confirm the transfer of learning to receptive language. Experiments to analyze the function of the stimuli involved in receptive language share a certain amount of common ground with research into conditional discrimination under contextual control. The procedures used in such experiments may additionally enhance the teaching of visuospatial perspective‐taking skills. Copyright © 2015 John Wiley & Sons, Ltd.     

Differences in the micromechanical properties of dendrites and interdendritic regions in superalloys

Statistical analysis of white-light interferometry (WLI) experiments performed on Ni-based single-crystal superalloys (SX) have revealed a different height distribution between the dendritic cores (DCs) and the interdendritic regions (IRs) of the polished samples. The micromechanical property difference is largely ascribed to the uneven distribution of the alloying elements. In this context, possible reasons for this difference are discussed by comparing with different experiment results obtained by previous researchers, and a proposal forecasting the hardness ratio of IRs/DCs is put forward.