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21 Apr 2010: tn, tj tn], where D4 = 12 μ2(K)f ′′(xj ) D1;. • ... tn = o(n1/6).Then. P(f̂h(x. tj ) < f̂h,τ. ) ( tf ′(xj ) D4n1/2h5/2{R(K)fτ 2D3,j D2}1/2).

24 Mar 2010: Maximum likelihood estimation of a multidimensional log-concave density. Madeleine Cule and Richard Samworth†University of Cambridge, UK. and Michael StewartUniversity of Sydney, Australia. Summary. Let X1,. , Xn be independent and identically

19 Nov 2010: Let T := Tj = {ti (j )} = 2j Z, j Z, be a bi-infinite sequence of equally spaced knots,ti := ti (j ). A function S is a spline of order r , or ... Nj,k,r (x) := Nk,r (2j x) = N0,r (2j x k).By the Curry–Schoenberg theorem, any S Sr (Tj ) can be uniquely

31 Mar 2010: Then xK is a Markovprocess with transition rates. xK Tj,j1xK at rate νxKj K,j = 0, 1,. ... C 1. xK Tj,j1xK at rate jxKj K,j = 1, 2,.

7 Jun 2010: The noise in the output can be assessed by comparing thepredicted values (yj ) of the output against those measured(tj ), for example,. ... ED. j. (tj yj )2. (4). Fig. 3 Variations in the test and training errors as a function of model complexity, for

7 Jun 2010: COMPLEX MECHANICAL. PROPERTIES OF STEEL. Radu Calin Dimitriu. Department of Materials Science and Metallurgy. University of Cambridge. Churchill College. A dissertation submitted for thedegree of Doctor of Philosophy. at the University of

7 Jun 2010: 2 and 4). Thenoise in the output can be assessed by comparing thepredicted values yj of the output using this well fittednetwork, against those measured tj, for example,. ... ED!X. j. tj{yj 2. (1). ED should be expected to increase if important

7 Jun 2010: E =. j. (tj yj)2 (3). where yj is a predicted value and tj the target value; to calculate this error we normalised the outputto be in the range 0.5.

7 Jun 2010: The overall error in the neural network model, ED, is calculated by comparing the predicted values yj of the output against those measured tj!

7 Jun 2010: tj The measured value. xj Input variables in neural networks. wi Weights in neural networks. ... predicted values yj of the output against those measured value tj:.