scholarly journals Algebraic Representations for Volumetric Frame Fields

2020 ◽  
Vol 39 (2) ◽  
pp. 1-17 ◽  
Author(s):  
David Palmer ◽  
David Bommes ◽  
Justin Solomon
Keyword(s):  
Algebraic Representations

scholarly journals TOPOLOGICAL NOETHERIANITY FOR ALGEBRAIC REPRESENTATIONS OF INFINITE RANK CLASSICAL GROUPS

2021 ◽  
Author(s):  
R. H. EGGERMONT ◽  
A. SNOWDEN
Keyword(s):  
Classical Groups ◽  
Infinite Rank ◽  
Polynomial Representations ◽  
Algebraic Representations

AbstractDraisma recently proved that polynomial representations of GL∞ are topologically noetherian. We generalize this result to algebraic representations of infinite rank classical groups.

scholarly journals On Polymorphic Sessions and Functions

2021 ◽  
Vol 43 (2) ◽  
pp. 1-55
Author(s):  
Bernardo Toninho ◽  
Nobuko Yoshida
Keyword(s):  
Natural Deduction ◽  
Sequent Calculus ◽  
Linear Logic ◽  
Linear Formulation ◽  
Session Types ◽  
Logical Foundation ◽  
Π Calculus ◽  
Soundness And Completeness ◽  
System F ◽  
Algebraic Representations

This work exploits the logical foundation of session types to determine what kind of type discipline for the Λ-calculus can exactly capture, and is captured by, Λ-calculus behaviours. Leveraging the proof theoretic content of the soundness and completeness of sequent calculus and natural deduction presentations of linear logic, we develop the first mutually inverse and fully abstract processes-as-functions and functions-as-processes encodings between a polymorphic session π-calculus and a linear formulation of System F. We are then able to derive results of the session calculus from the theory of the Λ-calculus: (1) we obtain a characterisation of inductive and coinductive session types via their algebraic representations in System F; and (2) we extend our results to account for value and process passing, entailing strong normalisation.

Evidence from cognitive neuroscience for the role of graphical and algebraic representations in understanding function

ZDM ◽  
2010 ◽  
Vol 42 (6) ◽  
pp. 607-619 ◽  
Author(s):  
Michael O. J. Thomas ◽  
Anna J. Wilson ◽  
Michael C. Corballis ◽  
Vanessa K. Lim ◽  
Caroline Yoon
Keyword(s):  
Cognitive Neuroscience ◽  
Algebraic Representations ◽  
Understanding Function

Probabilistic Feature Attention as an Alternative to Variables in Phonotactic Learning

2021 ◽  
pp. 1-56
Author(s):  
Brandon Prickett
Keyword(s):  
Experimental Work ◽  
Experimental Results ◽  
Phonological Acquisition ◽  
Novel Approach ◽  
Free Model ◽  
Cast Doubt ◽  
Feature Attention ◽  
Phonotactic Learning ◽  
Past Experimental Work ◽  
Algebraic Representations

Abstract Since Halle (1962), explicit algebraic variables (often called alpha notation) have been commonplace in phonological theory. However, Hayes and Wilson (2008) proposed a variable-free model of phonotactic learning, sparking a debate about whether such algebraic representations are necessary to capture human phonological acquisition. While past experimental work has found evidence that suggested a need for variables in models of phonology (Berent et al. 2012, Moreton 2012, Gallagher 2013), this paper presents a novel mechanism, Probabilistic Feature Attention (PFA), that allows a variable-free model of phonotactics to predict a number of these phenomena. Additionally, experimental results involving phonological generalization that cannot be explained by variables are captured by this novel approach. These results cast doubt on whether variables are necessary to capture human-like phonotactic learning and provide a useful alternative to such representations.

Quick Reads: Searching for Pythagorean Triples

2012 ◽  
Vol 18 (3) ◽  
pp. 140-143
Author(s):  
Natalya Vinogradova
Keyword(s):  
Pythagorean Triples ◽  
Algebraic Representations

This method emphasizes the strong connections between geometric and algebraic representations.

Finite-dimensional algebraic representations of the infinite phylon group

1992 ◽  
Vol 28 (3) ◽  
pp. 219-252 ◽  
Author(s):  
O. E. Barndorff-Nielsen ◽  
P. Bl�sild ◽  
A. L. Carey ◽  
P. E. Jupp ◽  
M. Mora ◽  
...  
Keyword(s):  
Finite Dimensional ◽  
Algebraic Representations

scholarly journals Super-rigidity and non-linearity for lattices in products

2019 ◽  
Vol 156 (1) ◽  
pp. 158-178
Author(s):  
Uri Bader ◽  
Alex Furman
Keyword(s):  
Rigidity Result ◽  
Products Of Groups ◽  
Algebraic Representations

We prove a super-rigidity result for algebraic representations over complete fields of irreducible lattices in products of groups and lattices with dense commensurator groups. We derive criteria for the non-linearity of such groups.

Reciprocal Mappings: The Neglected Transformations

1997 ◽  
Vol 90 (4) ◽  
pp. 322-327
Author(s):  
James R. Metz ◽  
Joseph T. Zilliox
Keyword(s):  
School Mathematics ◽  
Conceptual Foundation ◽  
Evaluation Standards ◽  
Algebraic Representations

The ability to make connections between graphs and algebraic representations is necessary for a strong conceptual foundation for understanding functions. According to the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989, 146),

scholarly journals Algebraic Verification Method for SEREs Properties via Groebner Bases Approaches

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ning Zhou ◽  
Jinzhao Wu ◽  
Xinyan Gao
Keyword(s):  
Algebraic Approach ◽  
Digital Systems ◽  
Groebner Bases ◽  
Symbolic Simulation ◽  
Verification Method ◽  
Symbolic Representations ◽  
Temporal Properties ◽  
Verification Methods ◽  
Algorithm Framework ◽  
Algebraic Representations

This work presents an efficient solution using computer algebra system to perform linear temporal properties verification for synchronous digital systems. The method is essentially based on both Groebner bases approaches and symbolic simulation. A mechanism for constructing canonical polynomial set based symbolic representations for both circuit descriptions and assertions is studied. We then present a complete checking algorithm framework based on these algebraic representations by using Groebner bases. The computational experience result in this work shows that the algebraic approach is a quite competitive checking method and will be a useful supplement to the existent verification methods based on simulation.

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