Georgij Kert 1923–2009

KERT: Automatic Extraction and Ranking of Topical Keyphrases from Content-Representative Document Titles

We introduce KERT (Keyphrase Extraction and Ranking by Topic), a framework for topical keyphrase generation and ranking. By shifting from the unigram-centric traditional methods of unsupervised keyphrase extraction to a phrase-centric approach, we are able to directly compare and rank phrases of different lengths. We construct a topical keyphrase ranking function which implements the four crite...

Notes on Fredholm operators

(2) If K ∈ B(X) is compact, then for all λ ∈ C \ {0}, K − λ1 is Fredholm with index zero. (3) The shift operator S± ∈ B(`p) for 1 ≤ p ≤ ∞ defined by (S±x)n = xn±1 is Fredholm with index ±1. (4) If X,Y are finite dimensional and T ∈ B(X,Y ), then by the Rank-Nullity Theorem, ind(T ) = dim(X)− dim(Y ). Lemma 3. Suppose E,F ⊆ X are closed subspaces with F finite dimensional. (1) The subspace E + F...

UNIVERSITY OF TARTU FACULTY OF SCIENCE AND TECHNOLOGY Institute of Technology Kert Pjatkin PROBABILITY DISTRIBUTION FUNCTION BASED IRIS RECOGNITION SYSTEM BOOSTED BY THE MEAN RULE

Theory and Application of a Class of Abstract Differential-Algebraic Equations

DAEs: Infinite-dimensional LTI Index-1 Case 3.1 Infinite-dimensional Linear Algebra We first collect some useful infinite-dimensional definitions and statements which will be used in this and the next section. Details and proofs of these statements can be found in standard functional analysis references such as [11], [26], [28] and [38]: Proposition 3.1. Let L(X,Y ) denote the space of bounded ...

Depth Resolved Differences After Corneal Crosslinking With and Without Epithelial Debridement Using Multimodal Imaging

Depth Resolved Differences After Corneal Crosslinking With and Without Epithelial Debridement Using Multimodal Imaging Praveena Gupta, Best Anyama, Kert Edward, Kevin Wells, Massoud Motamedi, Bernard F. Godley, and Gracie Vargas 1 Department of Ophthalmology and Visual Sciences, University of Texas Medical Branch, Galveston, TX 2 School of Medicine, University of Texas Medical Branch, Galveston...