discretization method, to entropy-based and purity-based methods, which are supervised algorithms. We found that the performance of the Naive-Bayes algorithm signi cantly improved when features were discretized using an entropy-based method. In fact, over the 16 tested datasets, the discretized version of Naive

We introduce an integrable time-discretized version of the classical Calogero-Moser 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 Kadomtsev-Petviashvili equation, leading to a finite

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

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

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 accor-dance with (9). b) When multiple order poles are involved, the Bode method is computationally somewhat more involved than the Brune-Cewertz method extended by Mitra and Vaidyanathan [2] along with sim-plifications 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,(z-i (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)

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 hand-optimized libraries, and describes the software structure that makes our

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.

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

We introduce a framework to consider transport problems for integer-valued random variables. We introduce weighting coefficients which allow us to characterise trans-port problems in a gradient flow setting, and form the basis of our introduction of a discrete version of the Benamou–Brenier formula

We study Christoffel and Darboux transforms of discrete isothermic nets in 4-dimensional 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