The algebraic study of formal languages shows thatω-rational languages are exactly the sets recognizable by finite ω-semigroups. Within this framework, we provide a construction of the algebraic counterpart of the Wagner hierarchy. We adopt a hierarchical game approach, by translating the Wadge theory from the ω-rational language to the ω-semigroup context. More precisely, we first define a red...

The Rescorla-Wagner model has been the most influential theory of associative learning to emerge from the study of animal behavior over the last 25 years. Recently, equivalence to this model has become a benchmark in assessing connectionist models, with such equivalence often achieved by incorporating the Widrow-Hoff delta rule. This article presents the Rescorla-Wagner model's basic assumption...

The purpose of this note is to attract attention to the following conjecture (metastable r-fold Whitney trick) by clarifying its status as not having a complete proof, in the sense described in the paper. Assume that D = D1 ⊔ . . . ⊔ Dr is disjoint union of r disks of dimension s, f : D → B a proper PL map such that f∂D1∩. . .∩f∂Dr = ∅, rd ≥ (r+1)s+3 and d ≥ s+ 3. If the map f r : ∂(D1 × . . .×...

Despite the fact that only 21 fluorinated molecules are known to be biosynthesized, it is notable that about 20–25% of all modern pharmaceuticals and agrochemicals incorporate at least one fluorine atom. Nevertheless, the practice of introducing fluorine atoms into bioactive compounds is rather recent, as the first synthetic fluorinated drug, namely 5-fluorouracil, was synthesized as late as in...

The Rescorla–Wagner model has been a leading theory of animal causal induction for nearly 30 years, and human causal induction for the past 15 years. Recent theories (especially Psychol. Rev. 104 (1997) 367) have provided alternative explanations of how people draw causal conclusions from covariational data. However, theoretical attempts to compare the Rescorla–Wagner model with more recent mod...