Seeing Stars: Sequences on U.S. Flag

2020 ◽  
Vol 113 (9) ◽  
pp. e24-e33
Author(s):  
Günhan Caglayan
Keyword(s):  
Pattern Growth ◽  
Algebraic Representations

Students analyze photographs of patterns and determine algebraic representations for the pattern growth.

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

A MALAY TEXT CORPUS ANALYSIS FOR SENTENCE COMPRESSION USING PATTERN-GROWTH METHOD

2016 ◽  
Vol 78 (8) ◽  
Author(s):  
Suraya Alias ◽  
Siti Khaotijah Mohammad ◽  
Gan Keng Hoon ◽  
Tan Tien Ping
Keyword(s):  
Text Summarization ◽  
Corpus Analysis ◽  
Text Corpus ◽  
Sentence Compression ◽  
Condensed Representation ◽  
Pattern Growth ◽  
Growth Method ◽  
Document Collection ◽  
Input Source ◽  
Confidence Value

A text summary extracts serves as a condensed representation of a written input source where important and salient information is kept. However, the condensed representation itself suffer in lack of semantic and coherence if the summary was produced in verbatim using the input itself. Sentence Compression is a technique where unimportant details from a sentence are eliminated by preserving the sentence’s grammar pattern. In this study, we conducted an analysis on our developed Malay Text Corpus to discover the rules and pattern on how human summarizer compresses and eliminates unimportant constituent to construct a summary. A Pattern-Growth based model named Frequent Eliminated Pattern (FASPe) is introduced to represent the text using a set of sequence adjacent words that is frequently being eliminated across the document collection. From the rules obtained, some heuristic knowledge in Sentence Compression is presented with confidence value as high as 85% - that can be used for further reference in the area of Text Summarization for Malay language.

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