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AN INTRINSIC DIFFICULTY WITH INTERPOLATION ON THE BIDISK
"... Abstract. The set of possible values (w1,..., wk) = (f(x1),..., f(xk)) arising from restricting contractive elements f from some uniform algebra A to a finite set {x1,..., xk} in the domain is called an interpolation body. When the uniform algebra is the bidisk algebra, Cole and Wermer show that t ..."
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stronger notion of “computability ” follows which will allow us to discuss the intrinsic differences between interpolation on the bidisk and interpolation on the disk.
Estimating the Intrinsic Difficulty of A Recognition Problem
 Proceedings of the 12th International Conference on Pattern Recognition
, 1994
"... We describe an experiment in estimating the Bayes error of a concrete image classification problem: a difficult, practically important, twoclass character recognition problem. The Bayes error gives the "intrinsic difficulty" of the problem since it is the minimum error achievable by any ..."
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Cited by 4 (1 self)
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We describe an experiment in estimating the Bayes error of a concrete image classification problem: a difficult, practically important, twoclass character recognition problem. The Bayes error gives the "intrinsic difficulty" of the problem since it is the minimum error achievable by any
Eliciting Student Judgments of Intrinsic Difficulty for Understanding Misconceptions
, 2011
"... in Solving Basic Mathematics Problems Developmental mathematics students are one of the most challenging groups of students to work with. This particular group of students traditionally score lower on placement exams at the community college level. They have conceptions and ideas about how to solve ..."
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in Solving Basic Mathematics Problems Developmental mathematics students are one of the most challenging groups of students to work with. This particular group of students traditionally score lower on placement exams at the community college level. They have conceptions and ideas about how to solve an arithmetic problem presented to them. Some of the conceptions lead to solution strategies that result in correct answers. However, many of the students have misconceptions of solution strategies that
Searching in metric spaces
, 2001
"... The problem of searching the elements of a set that are close to a given query element under some similarity criterion has a vast number of applications in many branches of computer science, from pattern recognition to textual and multimedia information retrieval. We are interested in the rather gen ..."
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Cited by 436 (38 self)
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presentations have been given for the same approaches. We present some basic results that explain the intrinsic difficulty of the search problem. This includes a quantitative definition of the elusive concept of “intrinsic dimensionality. ” We also present a unified
Intrinsic Difficulties in Using the DoublyInfinite Time Axis for InputOutput Control Theory.
"... We point out that the natural definitions of stability and causality in inputoutput control theory lead to certain inconsistencies when inputs and outputs are allowed to have support on the doublyinfinite timeaxis. In particular, linear timeinvariant systems with right half plane poles cannot be ..."
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Cited by 1 (1 self)
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We point out that the natural definitions of stability and causality in inputoutput control theory lead to certain inconsistencies when inputs and outputs are allowed to have support on the doublyinfinite timeaxis. In particular, linear timeinvariant systems with right half plane poles cannot be considered to be both causal and stabilizable. In contrast, there is no such conflict when the semiinfinite time axis is used.
Informationbased complexity
, 1988
"... Computational complexity studies the intrinsic difficulty of mathematically posed problems and seeks optimal means for their solutions. This is a rich and diverse field; for the purpose of this paper we present a greatly simplified picture. Computational complexity may be divided into two branches, ..."
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Cited by 307 (38 self)
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Computational complexity studies the intrinsic difficulty of mathematically posed problems and seeks optimal means for their solutions. This is a rich and diverse field; for the purpose of this paper we present a greatly simplified picture. Computational complexity may be divided into two branches
Data Clustering: 50 Years Beyond KMeans
, 2008
"... Organizing data into sensible groupings is one of the most fundamental modes of understanding and learning. As an example, a common scheme of scientific classification puts organisms into taxonomic ranks: domain, kingdom, phylum, class, etc.). Cluster analysis is the formal study of algorithms and m ..."
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Cited by 294 (7 self)
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and methods for grouping, or clustering, objects according to measured or perceived intrinsic characteristics or similarity. Cluster analysis does not use category labels that tag objects with prior identifiers, i.e., class labels. The absence of category information distinguishes data clustering
Intrinsic
, 2008
"... quantum yields and radiative lifetimes of lanthanide tris(dipicolinates)w ..."
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quantum yields and radiative lifetimes of lanthanide tris(dipicolinates)w
OneDimensional Dynamics
"... Onedimensional dynamics has developed in the last decades into a subject in its own right. Yet, many recent results are inaccessible and have never been brought together. For this reason, we have tried to give a unified account of the subject and complete proofs of many results. To show what result ..."
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Cited by 267 (10 self)
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results one might expect, the first chapter deals with the theory of circle diffeomorphisms. The remainder of the book is an attempt to develop the analogous theory in the noninvertible case, despite the intrinsic additional difficulties. In this way, we have tried to show that there is a unified theory
Beyond Independent Relevance: Methods and Evaluation Metrics for Subtopic Retrieval
 In Proceedings of SIGIR
, 2003
"... We present a nontraditional retrieval problem we call subtopic retrieval. The subtopic retrieval problem is concerned with finding documents that cover many different subtopics of a query topic. This means that the utility of a document in a ranking is dependent on other documents in the ranking, v ..."
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Cited by 217 (6 self)
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precision and recall metrics by accounting for intrinsic topic difficulty as well as redundancy in documents. We propose and systematically evaluate several methods for performing subtopic retrieval using statistical language models and a maximal marginal relevance (MMR) ranking strategy. A mixture model
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