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Parametric Shape Analysis via 3Valued Logic
, 2001
"... Shape Analysis concerns the problem of determining "shape invariants"... ..."
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Cited by 660 (79 self)
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Shape Analysis concerns the problem of determining "shape invariants"...
On Projection Algorithms for Solving Convex Feasibility Problems
, 1996
"... Due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences (most notably, computerized tomography), algorithms for solving convex feasibility problems continue to receive great attention. To unify, generalize, and review some of the ..."
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Cited by 330 (44 self)
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09, 49M45, 6502, 65J05, 90C25; Secondary 26B25, 41A65, 46C99, 46N10, 47N10, 52A05, 52A41, 65F10, 65K05, 90C90, 92C55. Key words and phrases. Angle between two subspaces, averaged mapping, Cimmino's method, computerized tomography, convex feasibility problem, convex function, convex
A Test of the Efficiency of a Given Portfolio
 In Econometrica
, 1989
"... A test for the ex ante efficiency of a given portfolio of assets is analyzed. The relevant statistic has a tractable small sample distribution. Its power function is derived and used to study the sensitivity of the test to the portfolio choice and to the number of assets used to determine the ex pos ..."
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Cited by 314 (13 self)
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A test for the ex ante efficiency of a given portfolio of assets is analyzed. The relevant statistic has a tractable small sample distribution. Its power function is derived and used to study the sensitivity of the test to the portfolio choice and to the number of assets used to determine the ex post meanvariance efficient frontier. Several intuitive interpretations of the test are provided, including a simple meanstandard deviation geometric explanation. A univariate test, equivalent to our multivariatebased method, is derived, and it suggests some useful diagnostic tools which may explain why the null hypothesis is rejected. Empirical examples suggest that the multivariate approach can lead to more appropriate conclusions than those based on traditional inference which relies on a set of dependent univariate statistics.
Pfam: clans, web tools and services
 Nucleic Acids Res
, 2006
"... Pfam is a database of protein families that currently contains 7973 entries (release 18.0). A recent development in Pfam has enabled the grouping of related families into clans. Pfam clans are described in detail, together with the new associated web pages. Improvements to the range of Pfam web tool ..."
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Cited by 293 (13 self)
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Pfam is a database of protein families that currently contains 7973 entries (release 18.0). A recent development in Pfam has enabled the grouping of related families into clans. Pfam clans are described in detail, together with the new associated web pages. Improvements to the range of Pfam web tools and the first set of Pfam web services that allow programmatic access to the database and associated tools are also presented. Pfam is available on the web in the UK
Learning String Edit Distance
, 1997
"... In many applications, it is necessary to determine the similarity of two strings. A widelyused notion of string similarity is the edit distance: the minimum number of insertions, deletions, and substitutions required to transform one string into the other. In this report, we provide a stochastic mo ..."
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Cited by 248 (2 self)
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In many applications, it is necessary to determine the similarity of two strings. A widelyused notion of string similarity is the edit distance: the minimum number of insertions, deletions, and substitutions required to transform one string into the other. In this report, we provide a stochastic model for string edit distance. Our stochastic model allows us to learn a string edit distance function from a corpus of examples. We illustrate the utility of our approach by applying it to the difficult problem of learning the pronunciation of words in conversational speech. In this application, we learn a string edit distance with nearly one fifth the error rate of the untrained Levenshtein distance. Our approach is applicable to any string classification problem that may be solved using a similarity function against a database of labeled prototypes.
Languages That Capture Complexity Classes
 SIAM Journal of Computing
, 1987
"... this paper a series of languages adequate for expressing exactly those properties checkable in a series of computational complexity classes. For example, we show that a property of graphs (respectively groups, binary strings, etc.) is in polynomial time if and only if it is expressible in the first ..."
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Cited by 244 (21 self)
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this paper a series of languages adequate for expressing exactly those properties checkable in a series of computational complexity classes. For example, we show that a property of graphs (respectively groups, binary strings, etc.) is in polynomial time if and only if it is expressible in the first order language of graphs (respectively groups, binary strings, etc.) together with a least fixed point operator. As another example, a property is in logspace if and only if it is expressible in first order logic together with a deterministic transitive closure operator. The roots of our approach to complexity theory go back to 1974 when Fagin showed that the NP properties are exactly those expressible in second order existential sentences. It follows that second order logic expresses exactly those properties which are in the polynomial time hierarchy. We show that adding suitable transitive closure operators to second order logic results in languages capturing polynomial space and exponential time, respectively. The existence of such natural languages for each important complexity class sheds a new light on complexity theory. These languages reaffirm the importance of the complexity classes as much more than machine dependent issues. Furthermore a whole new approach is suggested. Upper bounds (algorithms) can be produced by expressing the property of interest in one of our languages. Lower bounds may be demonstrated by showing that such expression is impossible.
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