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Construct Weak Ranking Functions for Learning Linear Ranking Function
2011Many Learning to Rank models, which apply machine learning techniques to fuse weak ranking functions and enhance ranking performances, have been proposed for web search. However, most of the existing approaches only apply the Min --- Max normalization method to construct the weak ranking functions without considering the differences among the ranking ...
Guichun Hua +4 more
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Ranks of differentiable functions
Mathematika, 1986The purpose of this paper is to define and study a natural rank function which associates to each differentiable function (say on the interval [0,1]) a countable ordinal number, which measures the complexity of its derivative. Functions with continuous derivatives have the smallest possible rank 1, a function like \(x^ 2 \sin (x^{-1})\) has rank 2, etc.
Kechris, Alexander S., Woodin, W. Hugh
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2015
The four ranking functions were introduced to T-SQL by Microsoft in 2005. Three of the functions, ROW_NUMBER, RANK, and DENSE_RANK, assign a sequential number to each row in a query's results. The fourth ranking function, NTILE, divides the rows by assigning a bucket number to the each row in the results.
Kathi Kellenberger, Clayton Groom
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The four ranking functions were introduced to T-SQL by Microsoft in 2005. Three of the functions, ROW_NUMBER, RANK, and DENSE_RANK, assign a sequential number to each row in a query's results. The fourth ranking function, NTILE, divides the rows by assigning a bucket number to the each row in the results.
Kathi Kellenberger, Clayton Groom
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Order, 2005
The authors describe the correspondence between closure operators \(\text{cl}: D \to D\) and \(\land\)-subsemilattices \(L \subseteq D\) where \(D\) is a lattice of finite height. They investigate what type of number-valued function \(D \to N\) induces a \(\land\)-subsemilattice \(L\) and, conversely, what type of function \(D \to N\) is induced by ...
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The authors describe the correspondence between closure operators \(\text{cl}: D \to D\) and \(\land\)-subsemilattices \(L \subseteq D\) where \(D\) is a lattice of finite height. They investigate what type of number-valued function \(D \to N\) induces a \(\land\)-subsemilattice \(L\) and, conversely, what type of function \(D \to N\) is induced by ...
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2023
This thesis addresses a significant problem in numerous scientific fields - the challenge of determining whether two sets of data are statistically identical, a procedure known as a two-sample homogeneity test. Various methods, including well-known parametric tests like t-tests and analysis of variance (ANOVA), have been employed for two-sample ...
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This thesis addresses a significant problem in numerous scientific fields - the challenge of determining whether two sets of data are statistically identical, a procedure known as a two-sample homogeneity test. Various methods, including well-known parametric tests like t-tests and analysis of variance (ANOVA), have been employed for two-sample ...
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Ranking Functions over Labelings
2018We study rankings over labelings as a generalization of traditional labeling-based semantics in abstract argumentation. Our approach is an alternative to recent developments on rankings over arguments. The formal basis is a qualitative abstraction of probability theory called ranking theory. We propose a fundamental property, called SCC stratification,
Rienstra Tjitze, Thimm Matthias
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1984
Let X be a reduced irreducible complex space and K(X) be the field of meromorphic functions on X. A subfield A of K(X) is called rank complete or analytically closed in K(X) if it has the following property: Let {f1,..,fk} be a system of elements of A and f∈ K(X) a meromorphic function analytically dependent on {f1,..,fk}, then f ∈ A.
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Let X be a reduced irreducible complex space and K(X) be the field of meromorphic functions on X. A subfield A of K(X) is called rank complete or analytically closed in K(X) if it has the following property: Let {f1,..,fk} be a system of elements of A and f∈ K(X) a meromorphic function analytically dependent on {f1,..,fk}, then f ∈ A.
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Ranking functions for size-change termination
ACM Transactions on Programming Languages and Systems, 2009This article explains how to construct a ranking function for any program that is proved terminating by size-change analysis . The “principle of size-change termination” for a first-order functional language with well-ordered data is intuitive: A program terminates on all inputs, if
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Rotationally Invariant Rank 1 Convex Functions
Applied Mathematics & Optimization, 2001The author deals with functions defined on the set \(M^{n\times n}\) of all \(n\) by \(n\) real matrices. If such a function \(f\) is rotationally invariant with respect to the proper orthogonal group, then it has a representation \(\widetilde{f}\) through the signed singular values of the matrix argument \(A\in M^{n\times n}\).
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Piecewise-Defined Ranking Functions
2013We present the design and implementation of an abstract domain for proving program termination by abstract interpretation. The domain automatically synthesizes piecewise-defined ranking functions and infers sufficient conditions for program termination.
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