How averaging individual curves transforms their shape:Mathematical analyses with application to learning and forgetting curves

This paper demonstrates how averaging over individual learning and forgetting curves gives rise to transformed averaged curves. In an earlier paper (Murre and Chessa, 2011), we already showed that averaging over exponential functions tends to give a power function. The present paper expands on the analyses with exponential functions. Also, it is shown that averaging over power functions tends to give a log power function. Moreover, a general proof is given how averaging over logarithmic functions retains that shape in a specific manner. The analyses assume that the learning rate has a specific statistical distribution, such as a beta, gamma, uniform, or half-normal distribution. Shifting these distributions to the right, so that there are no low learning rates (censoring), is analyzed as well and some general results are given. Finally, geometric averaging is analyzed, and its limits are discussed in remedying averaging artefacts.</p

On a conjectural filtration on the Chow groups of an algebraic variety Part I. The general conjectures and some examples

AbstractIn this paper we describe a conjectural filtration on the Chow groups of a projective, smooth variety. This filtration is suggested by, and based upon, Grothendieck's theory of motives provided one uses the so-called category of Chow motives. This category is constructed by using as intersection ring the full Chow ring tensored with Q.We discuss some evidence for the conjectures.Finally we mention a recent result of U. Jannsen saying that this filtration coincides with conjectral filtration of Bloch and Beilinson