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Supervised and unsupervised discretization of continuous features
 in A. Prieditis & S. Russell, eds, Machine Learning: Proceedings of the Twelfth International Conference
, 1995
"... Many supervised machine learning algorithms require a discrete feature space. In this paper, we review previous work on continuous feature discretization, identify de ning characteristics of the methods, and conduct an empirical evaluation of several methods. We compare binning, an unsupervised dis ..."
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Cited by 540 (11 self)
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discretization method, to entropybased and puritybased methods, which are supervised algorithms. We found that the performance of the NaiveBayes algorithm signi cantly improved when features were discretized using an entropybased method. In fact, over the 16 tested datasets, the discretized version of Naive
A time discretized version of the Calogero–Moser model
 In: Proc. Int. Workshop Symmetries and Integrability of
, 1994
"... We introduce an integrable timediscretized version of the classical CalogeroMoser model, which goes to the original model in a continuum limit. This discrete model is obtained from pole solutions of a discretized version of the KadomtsevPetviashvili equation, leading to a finitedimensional sympl ..."
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Cited by 7 (1 self)
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We introduce an integrable timediscretized version of the classical CalogeroMoser model, which goes to the original model in a continuum limit. This discrete model is obtained from pole solutions of a discretized version of the KadomtsevPetviashvili equation, leading to a finite
Discrete versions of the BeckmanQuarles theorem
 Aequationes Math
"... Abstract. Let F ⊆ R denote the field of numbers which are constructible by means of ruler and compass. We prove that: (1) if x, y ∈ R n (n> 1) and x − y  is an algebraic number then there exists a finite set Sxy ⊆ R n containing x and y such that each map from Sxy to R n preserving all unit dis ..."
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Cited by 6 (4 self)
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Abstract. Let F ⊆ R denote the field of numbers which are constructible by means of ruler and compass. We prove that: (1) if x, y ∈ R n (n> 1) and x − y  is an algebraic number then there exists a finite set Sxy ⊆ R n containing x and y such that each map from Sxy to R n preserving all unit distances preserves the distance between x and y; if x, y ∈ F n then we can choose Sxy ⊆ F n, (2) only algebraic distances x − y  have the property from item (1), (3) if X1, X2,..., Xm ∈ R n (n> 1) lie on some affine hyperplane then there exists a finite set L(X1, X2,..., Xm) ⊆ R n containing X1, X2,..., Xm such that each map from L(X1, X2,..., Xm) to R n preserving all unit distances preserves the property that X1, X2,..., Xm lie on some affine hyperplane, (4) if J, K, L, M ∈ R n (n> 1) and JK  = LM (JK  < LM) then there exists a finite set CJKLM ⊆ Rn containing J, K, L, M such that any map f: CJKLM → Rn that preserves unit distance satisfies f(J)f(K)  = f(L)f(M)  (f(J)f(K)  < f(L)f(M)). Let F ⊆ R denote the field of numbers which are constructible by means
Discrete versions of continuous isoperimetric problems
 J. Differ. Equations Appl
, 1998
"... Dedicated to Gerry Ladas in appreciation of his contributions to the subject area of difference equations. Discrete isoperimetric variational problems which model single and double integral isoperimetric problems are formulated and some multiplier rules are derived. For quadratic functionals, the Eu ..."
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Cited by 2 (0 self)
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Dedicated to Gerry Ladas in appreciation of his contributions to the subject area of difference equations. Discrete isoperimetric variational problems which model single and double integral isoperimetric problems are formulated and some multiplier rules are derived. For quadratic functionals
Iv. DISCRETE VERSION OF THE BODE PROCEDURE
"... a) Let us first consider the case where all p o l e s of H(z) are simple. It can be shown that HR(z) in (3) can be expanded in the following form: where k i can be evaluated from The required transfer function H(z) is then identified as an expression which only requires the calculation of { k i} in ..."
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a) Let us first consider the case where all p o l e s of H(z) are simple. It can be shown that HR(z) in (3) can be expanded in the following form: where k i can be evaluated from The required transfer function H(z) is then identified as an expression which only requires the calculation of { k i} in accordance with (9). b) When multiple order poles are involved, the Bode method is computationally somewhat more involved than the BruneCewertz method extended by Mitra and Vaidyanathan [2] along with simplifications thereof recently proposed by Dutta Roy [6]. However, for the sake of completeness, we note the following steps. The "partial fraction expansion " of HR(z) takes the form k i, + kyrj,)(z ' pi) +... + k,(z ' +c i (z l pi)" (11) where the pole at pi is of multiplicity ri and H(z) is deduced therefrom as + 2 c ki, + kicri,)(Z p;) + * * + k,(zi (I pi) ri V. EXAMPLE We consider the same example as in [2]. HR(e ' ) 17 8cos2w '&+, 1 +cos w + cos2w D ( z) = 17 4(Z2 + z ~ ) = 17 8C2(u/2)
The design and implementation of FFTW3
 PROCEEDINGS OF THE IEEE
, 2005
"... FFTW is an implementation of the discrete Fourier transform (DFT) that adapts to the hardware in order to maximize performance. This paper shows that such an approach can yield an implementation that is competitive with handoptimized libraries, and describes the software structure that makes our cu ..."
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Cited by 726 (3 self)
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FFTW is an implementation of the discrete Fourier transform (DFT) that adapts to the hardware in order to maximize performance. This paper shows that such an approach can yield an implementation that is competitive with handoptimized libraries, and describes the software structure that makes our
GOLOG: A Logic Programming Language for Dynamic Domains
, 1994
"... This paper proposes a new logic programming language called GOLOG whose interpreter automatically maintains an explicit representation of the dynamic world being modeled, on the basis of user supplied axioms about the preconditions and effects of actions and the initial state of the world. This allo ..."
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Cited by 628 (74 self)
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for applications in high level control of robots and industrial processes, intelligent software agents, discrete event simulation, etc. It is based on a formal theory of action specified in an extended version of the situation calculus. A prototype implementation in Prolog has been developed.
The particel swarm: Explosion, stability, and convergence in a multidimensional complex space
 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTION
"... The particle swarm is an algorithm for finding optimal regions of complex search spaces through interaction of individuals in a population of particles. Though the algorithm, which is based on a metaphor of social interaction, has been shown to perform well, researchers have not adequately explained ..."
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Cited by 852 (10 self)
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explained how it works. Further, traditional versions of the algorithm have had some dynamical properties that were not considered to be desirable, notably the particles’ velocities needed to be limited in order to control their trajectories. The present paper analyzes the particle’s trajectory as it moves
Discrete versions of the transport equation and the SheppOlkin conjecture
 In submission, see arXiv:1303.3381
, 2013
"... We introduce a framework to consider transport problems for integervalued random variables. We introduce weighting coefficients which allow us to characterise transport problems in a gradient flow setting, and form the basis of our introduction of a discrete version of the Benamou–Brenier formula. ..."
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Cited by 1 (1 self)
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We introduce a framework to consider transport problems for integervalued random variables. We introduce weighting coefficients which allow us to characterise transport problems in a gradient flow setting, and form the basis of our introduction of a discrete version of the Benamou–Brenier formula
A discrete version of the Darboux transform for isothermic surfaces
, 2008
"... We study Christoffel and Darboux transforms of discrete isothermic nets in 4dimensional Euclidean space: definitions and basic properties are derived. Analogies with the smooth case are discussed and a definition for discrete Ribaucour congruences is given. Surfaces of constant mean curvature are s ..."
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Cited by 33 (13 self)
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We study Christoffel and Darboux transforms of discrete isothermic nets in 4dimensional Euclidean space: definitions and basic properties are derived. Analogies with the smooth case are discussed and a definition for discrete Ribaucour congruences is given. Surfaces of constant mean curvature
Results 1  10
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