Rational equivalence theory on arbitrary noetherian schemes

1990 ◽  
pp. 256-297 ◽  
Author(s):  
Anders Thorup
Keyword(s):  
Rational Equivalence ◽  
Equivalence Theory

Invariants of rational equivalence

2000 ◽  
Vol 41 (2) ◽  
pp. 357-361 ◽  
Author(s):  
A. G. Pinus
Keyword(s):  
Rational Equivalence

Pieri’S Formula Via Explicit Rational Equivalence

1997 ◽  
Vol 49 (6) ◽  
pp. 1281-1298 ◽  
Author(s):  
Frank Sottile
Keyword(s):  
Combinatorial Proof ◽  
Geometric Proof ◽  
Intersection Product ◽  
Rational Equivalence ◽  
Schubert Cycles

AbstractPieri’s formula describes the intersection product of a Schubert cycle by a special Schubert cycle on a Grassmannian. We present a new geometric proof, exhibiting an explicit chain of rational equivalences from a suitable sum of distinct Schubert cycles to the intersection of a Schubert cycle with a special Schubert cycle. The geometry of these rational equivalences indicates a link to a combinatorial proof of Pieri’s formula using Schensted insertion.

scholarly journals Equivalence Projective Simulation as a Framework for Modeling Formation of Stimulus Equivalence Classes

2020 ◽  
Vol 32 (5) ◽  
pp. 912-968 ◽  
Author(s):  
Asieh Abolpour Mofrad ◽  
Anis Yazidi ◽  
Hugo L. Hammer ◽  
Erik Arntzen
Keyword(s):  
Stimulus Equivalence ◽  
Human Subjects ◽  
Network Models ◽  
Equivalence Classes ◽  
Equivalence Relations ◽  
Learning Context ◽  
Neural Network Models ◽  
Equivalence Theory ◽  
Hypothetical Experiment ◽  
Theory Research

Stimulus equivalence (SE) and projective simulation (PS) study complex behavior, the former in human subjects and the latter in artificial agents. We apply the PS learning framework for modeling the formation of equivalence classes. For this purpose, we first modify the PS model to accommodate imitating the emergence of equivalence relations. Later, we formulate the SE formation through the matching-to-sample (MTS) procedure. The proposed version of PS model, called the equivalence projective simulation (EPS) model, is able to act within a varying action set and derive new relations without receiving feedback from the environment. To the best of our knowledge, it is the first time that the field of equivalence theory in behavior analysis has been linked to an artificial agent in a machine learning context. This model has many advantages over existing neural network models. Briefly, our EPS model is not a black box model, but rather a model with the capability of easy interpretation and flexibility for further modifications. To validate the model, some experimental results performed by prominent behavior analysts are simulated. The results confirm that the EPS model is able to reliably simulate and replicate the same behavior as real experiments in various settings, including formation of equivalence relations in typical participants, nonformation of equivalence relations in language-disabled children, and nodal effect in a linear series with nodal distance five. Moreover, through a hypothetical experiment, we discuss the possibility of applying EPS in further equivalence theory research.

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