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Is Incompleteness A Serious Problem?
, 2006
"... In 1931 Kurt Gödel astonished the mathematical world by showing that no finite set of axioms can suffice to capture all of mathematical truth. He did this by constructing an assertion GF about the whole numbers that manages to assert that it itself is unprovable (from a given finite set F of axioms ..."
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In 1931 Kurt Gödel astonished the mathematical world by showing that no finite set of axioms can suffice to capture all of mathematical truth. He did this by constructing an assertion GF about the whole numbers that manages to assert that it itself is unprovable (from a given finite set F of axioms using formal logic). 1 GF: “GF cannot be proved from the finite set of axioms F.” This assertion GF is therefore true if and only if it is unprovable, and the formal axiomatic system F in question either proves falsehoods (because it enables us to prove GF) or fails to prove a true assertion (because it does not enable us to prove GF). If we assume that the former situation is impossible, we conclude that F is necessarily incomplete since it does not permit us to establish the true statement GF. Either GF is provable and F proves false statements, or GF is unprovable and therefore true, and F is incomplete. Today, a century after Gödel’s birth, the full implications of this “incompleteness ” result are still quite controversial. 2 An important step forward was achieved by Alan Turing in 1936. He showed that
solving a widespread, serious problem
, 2011
"... This article cites 8 articles, 1 of which can be accessed free ..."
The broadcast storm problem in a mobile ad hoc network
 ACM Wireless Networks
, 2002
"... Broadcasting is a common operation in a network to resolve many issues. In a mobile ad hoc network (MANET) in particular, due to host mobility, such operations are expected to be executed more frequently (such as finding a route to a particular host, paging a particular host, and sending an alarm s ..."
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Cited by 1235 (15 self)
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signal). Because radio signals are likely to overlap with others in a geographical area, a straightforward broadcasting by flooding is usually very costly and will result in serious redundancy, contention, and collision, to which we refer as the broadcast storm problem. In this paper, we iden
Rank Aggregation Methods for the Web
, 2010
"... We consider the problem of combining ranking results from various sources. In the context of the Web, the main applications include building metasearch engines, combining ranking functions, selecting documents based on multiple criteria, and improving search precision through word associations. Wed ..."
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Cited by 479 (6 self)
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. Wedevelop a set of techniques for the rank aggregation problem and compare their performance to that of wellknown methods. A primary goal of our work is to design rank aggregation techniques that can effectively combat "spam," a serious problem in Web searches. Experiments show that our methods
Empirical Bayes Analysis of a Microarray Experiment
 Journal of the American Statistical Association
, 2001
"... Microarrays are a novel technology that facilitates the simultaneous measurement of thousands of gene expression levels. A typical microarray experiment can produce millions of data points, raising serious problems of data reduction, and simultaneous inference. We consider one such experiment in whi ..."
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Cited by 492 (20 self)
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Microarrays are a novel technology that facilitates the simultaneous measurement of thousands of gene expression levels. A typical microarray experiment can produce millions of data points, raising serious problems of data reduction, and simultaneous inference. We consider one such experiment
Risk and protective factors for alcohol and other drug problems in adolescence and early adulthood: Implications for substance abuse prevention
 Psychological Bulletin
, 1992
"... The authors suggest that the most promising route to effective strategies for the prevention of adolescent alcohol and other drug problems is through a riskfocused approach. This approach requires the identification of risk factors for drug abuse, identification of methods by which risk factors hav ..."
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Cited by 722 (18 self)
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, and make recommendations for research and practice. In spite of general decreases in the prevalence of the nonmedical use of most legal and illegal drugs in recent years, the abuse of alcohol and other drugs during adolescence and early adulthood remains a serious public health problem (Adams, Blanken
Reinforcement Learning I: Introduction
, 1998
"... In which we try to give a basic intuitive sense of what reinforcement learning is and how it differs and relates to other fields, e.g., supervised learning and neural networks, genetic algorithms and artificial life, control theory. Intuitively, RL is trial and error (variation and selection, search ..."
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Cited by 5597 (118 self)
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, search) plus learning (association, memory). We argue that RL is the only field that seriously addresses the special features of the problem of learning from interaction to achieve longterm goals.
A Comparison of Methods for Multiclass Support Vector Machines
 IEEE TRANS. NEURAL NETWORKS
, 2002
"... Support vector machines (SVMs) were originally designed for binary classification. How to effectively extend it for multiclass classification is still an ongoing research issue. Several methods have been proposed where typically we construct a multiclass classifier by combining several binary class ..."
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Cited by 958 (22 self)
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classifiers. Some authors also proposed methods that consider all classes at once. As it is computationally more expensive to solve multiclass problems, comparisons of these methods using largescale problems have not been seriously conducted. Especially for methods solving multiclass SVM in one step, a much
The Quickhull algorithm for convex hulls
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1996
"... The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental algo ..."
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Cited by 713 (0 self)
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is implemented with floatingpoint arithmetic, this assumption can lead to serious errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of “thick ” facets that contain all possible exact convex hulls of the input. A variation
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