Linear Coding of non-linear Hierarchies: Revitalization of an - PowerPoint PPT Presentation

Problem P¯ an .ini’s Solution Generalization Transfer Linear Coding of non-linear Hierarchies: Revitalization of an Ancient Classification Method Wiebke Petersen Institute of Language and Information University of Düsseldorf petersew@uni-duesseldorf.de GfKl 2008 Linear Coding of non-linear Hierarchies Wiebke Petersen

Problem P¯ an .ini’s Solution Generalization Transfer The Problem: Sometimes we are forced to order things (nearly) linearly, e. g. in . . . Linear Coding of non-linear Hierarchies Wiebke Petersen

Problem P¯ an .ini’s Solution Generalization Transfer Libraries Linear Coding of non-linear Hierarchies Wiebke Petersen

Problem P¯ an .ini’s Solution Generalization Transfer Warehouses Linear Coding of non-linear Hierarchies Wiebke Petersen

Problem P¯ an .ini’s Solution Generalization Transfer Stores Linear Coding of non-linear Hierarchies Wiebke Petersen

Problem P¯ an .ini’s Solution Generalization Transfer The problem is old! Linear Coding of non-linear Hierarchies Wiebke Petersen

Problem P¯ an .ini’s Solution Generalization Transfer But more than 2 000 years ago it has been solved! P¯ an .ini’s Grammar of Sanskrit (ca. 350 BC) Sanskrit: rich morphology, complex Sandhi-system linguistics in ancient India: astram ‘science of sciences’ ś¯ astr¯ an¯ am . ś¯ oral tradition P¯ an .ini’s grammar: system of more than 4. 000 concise rules many phonological rules Linear Coding of non-linear Hierarchies Wiebke Petersen

Problem P¯ an .ini’s Solution Generalization Transfer Phonological Rules modern notation A is replaced by B if preceded by C and succeeded by D . A → B / C D example: final devoicing in German     + consonantal + consonantal  →  / − nasal − nasal ♯   + voiced − voiced Linear Coding of non-linear Hierarchies Wiebke Petersen

Problem P¯ an .ini’s Solution Generalization Transfer Phonological Rules modern notation A is replaced by B if preceded by C and succeeded by D . A → B / C D P¯ an .ini’s linear Coding A + genitive , B + nominative , C + ablative , D + locative . example . aci ( �� ) s¯ utra 6.1.77: iko yan analysis: [ ik ] gen [ yan . ] nom [ ac ] loc modern notation: [ iK ] → [ yN . ] / [ aC ] Linear Coding of non-linear Hierarchies Wiebke Petersen

Problem P¯ an .ini’s Solution Generalization Transfer praty¯ ah¯ aras 1. a i u N . 2. r l K . . ˙ 3. e o N 4. ai au C 5. h y v r T . a praty¯ ah¯ ara is a pair of a sound and a marker it denotes the continuous sequence of sounds in the interval between the sound and the marker Linear Coding of non-linear Hierarchies Wiebke Petersen

Problem P¯ an .ini’s Solution Generalization Transfer praty¯ ah¯ aras 1. a i u N . 2. r l K . . ˙ 3. e o N 4. ai au C 5. h y v r T . iK a praty¯ ah¯ ara is a pair of a sound and a marker it denotes the continuous sequence of sounds in the interval between the sound and the marker Linear Coding of non-linear Hierarchies Wiebke Petersen

Linear Coding of non-linear Hierarchies: Revitalization of an - PowerPoint PPT Presentation

Problem P an .inis Solution Generalization Transfer Linear Coding of non-linear Hierarchies: Revitalization of an Ancient Classification Method Wiebke Petersen Institute of Language and Information University of Dsseldorf

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Linear Coding of non-linear Hierarchies: Revitalization of an - PowerPoint PPT Presentation

Problem P an .inis Solution Generalization Transfer Linear Coding of non-linear Hierarchies: Revitalization of an Ancient Classification Method Wiebke Petersen Institute of Language and Information University of Dsseldorf

Lecture 11 Vector Linear Network Coding Vector Linear Network Coding Outline Fundamentals for

Linear Programming Linear Programming In a linear programming problem, there is a set of

Extending the linear model DAAG Chapters 7 and 8 Learning objectives The linear model framework

Chapter 1 What is Linear Algebra? Chapter 1 What is Linear Algebra? The study of linear

Topic 5: Non-Linear Relationships and Non-Linear Least Squares Non-linear Relationships Many

QcBits: constant-time small-key code-based cryptography Tung Chou Technische Universiteit

Linear Algebra Linear algebra has become as basic and as applicable as calculus, and

Random Linear Network Coding on Programmable Switches D. Gonalves 1 , S. Signorello 1 , F . M.

lgebra Linear e Aplicaes LINEAR EQUATIONS Start with a few examples One way of

Linear Transformations Linear Transformations 1 / 21 Linear Transformations A function T from R

Notes on the Non-linear Regression The model Non-linear regression models, like ordinary linear

Signing a Linear Subspace: Signature Schemes for Network Coding David Mandell Freeman CWI &amp;

Low Delay Random Linear Coding Over a Douglas J. Leith Stream Mohammad Karzand, Douglas J.

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GCDs &amp; linear gcd(a,b) is an integer combinations: linear combination of a and b . The

Linear dependence and independence Linear dependence 1 Definition (linear (in)dependence) Let {

Overview IAML: Linear Regression The linear model Fitting the linear model to data

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GCDs & linear gcd(a,b) is an integer combinations: linear combination of a and b . The