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41
ILP: A Short Look Back and a Longer Look Forward
 Journal of Machine Learning Research
, 2003
"... Inductive logic programming (ILP) is built on a foundation laid by research in other areas of machine learning and computational logic. But in spite of this strong foundation, at just over 10 years of age ILP now faces a number of new challenges brought on by exciting areas of application. Research ..."
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Cited by 19 (0 self)
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Inductive logic programming (ILP) is built on a foundation laid by research in other areas of machine learning and computational logic. But in spite of this strong foundation, at just over 10 years of age ILP now faces a number of new challenges brought on by exciting areas of application. Research in other areas of machine learning and computational logic can contribute much to help ILP meet these challenges. After a brief review, the paper presents ve future research directions for ILP and points to initial approaches or results where they exist. It is hoped that the paper will motivate research workers in machine learning and computational logic to invest some time into ILP.
The Sources of Kolmogorov’s Grundbegriffe
, 2006
"... Andrei Kolmogorov’s Grundbegriffe Wahrscheinlichkeitsrechnung put probability’s modern mathematical formalism in place. It also provided a philosophy of probability—an explanation of how the formalism can be connected to the world of experience. In this article, we examine the sources of these two a ..."
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Cited by 12 (8 self)
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Andrei Kolmogorov’s Grundbegriffe Wahrscheinlichkeitsrechnung put probability’s modern mathematical formalism in place. It also provided a philosophy of probability—an explanation of how the formalism can be connected to the world of experience. In this article, we examine the sources of these two aspects of the Grundbegriffe—the work of the earlier scholars whose ideas Kolmogorov synthesized.
Small limit cycles bifurcating from fine focus points in cubic order Z2equivariant vector fields
, 2005
"... ..."
LMI approximations for cones of positive semidefinite forms
 Fachbereich Mathematik, Universität Konstanz, 78457
"... An interesting recent trend in optimization is the application of semidefinite programming techniques to new classes of optimization problems. In particular, this trend has been successful in showing that under suitable circumstances, polynomial optimization problems can be approximated via a sequen ..."
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Cited by 8 (2 self)
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An interesting recent trend in optimization is the application of semidefinite programming techniques to new classes of optimization problems. In particular, this trend has been successful in showing that under suitable circumstances, polynomial optimization problems can be approximated via a sequence of semidefinite programs. Similar ideas apply to conic optimization over the cone of copositive matrices, and to certain optimization problems involving random variables with some known moment information. We bring together several of these approximation results by studying the approximability of cones of positive semidefinite forms (homogeneous polynomials). Our approach enables us to extend the existing methodology to new approximation schemes. In particular, we derive a novel approximation to the cone of copositive forms, that is, the cone of forms that are positive semidefinite over the nonnegative orthant. The format of our construction can be extended to forms that are positive semidefinite over more general conic domains. We also construct polyhedral approximations to cones of positive semidefinite forms over a polyhedral domain. This opens the possibility of using linear programming technology in optimization problems over these cones.
Proof Theory of MartinLof Type Theory  An
 Mathematiques et Sciences Humaines, 42 année, n o 165:59 – 99
, 2004
"... We give an overview over the historic development of proof theory and the main techniques used in ordinal theoretic proof theory. We argue, that in a revised Hilbert's programme, ordinal theoretic proof theory has to be supplemented by a second step, namely the development of strong equiconsisten ..."
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Cited by 4 (2 self)
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We give an overview over the historic development of proof theory and the main techniques used in ordinal theoretic proof theory. We argue, that in a revised Hilbert's programme, ordinal theoretic proof theory has to be supplemented by a second step, namely the development of strong equiconsistent constructive theories. Then we show, how, as part of such a programme, the proof theoretic analysis of MartinLof type theory with Wtype and one microscopic universe containing only two finite sets is carried out. Then we look at the analysis of MartinLof type theory with Wtype and a universe closed under the Wtype, and consider the extension of type theory by one Mahlo universe and its prooftheoretic analysis. Finally we repeat the concept of inductiverecursive definitions, which extends the notion of inductive definitions substantially. We introduce a closed formalisation, which can be used in generic programming, and explain, what is known about its strength.
Phase portraits of planar vector fields: computer proofs
 J. Exp. Math
, 1995
"... This paper presents an algorithm for computer verification of the global structure of structurally stable planar vector fields. Constructing analytical proofs for the qualitative properties of phase portraits has been difficult. We try to avoid this barrier by augmenting numerical computations of tr ..."
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Cited by 3 (1 self)
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This paper presents an algorithm for computer verification of the global structure of structurally stable planar vector fields. Constructing analytical proofs for the qualitative properties of phase portraits has been difficult. We try to avoid this barrier by augmenting numerical computations of trajectories of dynamical systems with error estimates that yield rigorous proofs. Our approach is one that lends itself to high precision estimates, because the proofs are broken into independent calculations whose length in floating point operations does not increase with increasing precision. The algorithm that we present is tested on a system that arises in the study of Hopf bifurcation of periodic orbits with 1:4 resonance. 1
The Complexity of Proving Chaoticity and the ChurchTuring Thesis
, 2010
"... Proving the chaoticity of some dynamical systems is equivalent to solving the hardest problems in mathematics. Conversely, one argues that it is not unconceivable that classical physical systems may “compute the hard or even the incomputable” by measuring observables which correspond to computationa ..."
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Cited by 2 (1 self)
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Proving the chaoticity of some dynamical systems is equivalent to solving the hardest problems in mathematics. Conversely, one argues that it is not unconceivable that classical physical systems may “compute the hard or even the incomputable” by measuring observables which correspond to computationally hard or even incomputable problems.
Gröbner Bases and Invariant Theory
"... This paper was Hilbert's quick answer to those of his fellow mathematicians who harshly criticized the nonconstructiveness of his first proof. The second paper contains the Nullstellensatz, the HilbertMumford criterion ..."
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This paper was Hilbert's quick answer to those of his fellow mathematicians who harshly criticized the nonconstructiveness of his first proof. The second paper contains the Nullstellensatz, the HilbertMumford criterion
Grand Challenges, Benchmarks, and TraceLab: Developing Infrastructure for the Software Traceability Research Community
"... The challenges of implementing successful and costeffective traceability have created a compelling research agenda that has addressed a broad range of traceability related issues, ranging from qualitative studies of traceability users in industry to very technical and quantitative studies. Unfortun ..."
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The challenges of implementing successful and costeffective traceability have created a compelling research agenda that has addressed a broad range of traceability related issues, ranging from qualitative studies of traceability users in industry to very technical and quantitative studies. Unfortunately, advances are hampered by the significant time and effort needed to establish a traceability research environment and to perform comparative evaluations of new results against existing baselines. In this panel we discuss ongoing efforts by members of the Center of Excellence for Software Traceability (CoEST) to define the Grand Challenges of Traceability, develop benchmarks, and to construct TraceLab, an extensible and scalable visual environment for designing and executing a broad range of traceability experiments.
On the number of attractors of Boolean automata circuits
, 2009
"... In line with elds of theoretical computer science and biology that study Boolean automata networks often seen as models of regulation networks, we present some results concerning the dynamics of networks whose underlying interaction graphs are circuits, that is Boolean automata circuits. In the cont ..."
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In line with elds of theoretical computer science and biology that study Boolean automata networks often seen as models of regulation networks, we present some results concerning the dynamics of networks whose underlying interaction graphs are circuits, that is Boolean automata circuits. In the context of biological regulation, former studies have highlighted the importance of circuits on the asymptotic dynamical behaviour of the biological networks that contain them. Our work focuses on the number of attractors of Boolean automata circuits. We prove how to obtain formally the exact value of the total number of attractors of a circuit of arbitrary size n as well as, for every positive integer p, the number of its attractors of period p depending on whether the circuit has an even or an odd number of inhibitions. As a consequence, we obtain that both numbers depend only on the parity of the number of inhibitions and not on their distribution along the circuit.