SMARANDACHE NUMBER RELATED TRIANGLES

Given a triangle in Euclidean geometry it is well known that there exist an infinity of triangles each of which is similar to the given one. In Section I we make certain observations on Smarandache numbers

An investigation of the motion of small particles as related to the formulation of zero gravity experiments

The nature of Brownian motion and historical theoretical investigations of the phenomemon are reviewed. The feasibility of using a laser anemometer to perform small particle experiments in an orbiting space laboratory was investigated using latex particles suspended in water in a plastic container. The optical equipment and the particle Doppler analysis processor are described. The values of the standard deviation obtained for the latex particle motion experiment were significantly large compared to corresponding velocity, therefore, their accuracy was suspect and no attempt was made to draw meaningful conclusions from the results

Noise Tolerance under Risk Minimization

In this paper we explore noise tolerant learning of classifiers. We formulate the problem as follows. We assume that there is an ${\bf unobservable}$ training set which is noise-free. The actual training set given to the learning algorithm is obtained from this ideal data set by corrupting the class label of each example. The probability that the class label of an example is corrupted is a function of the feature vector of the example. This would account for most kinds of noisy data one encounters in practice. We say that a learning method is noise tolerant if the classifiers learnt with the ideal noise-free data and with noisy data, both have the same classification accuracy on the noise-free data. In this paper we analyze the noise tolerance properties of risk minimization (under different loss functions), which is a generic method for learning classifiers. We show that risk minimization under 0-1 loss function has impressive noise tolerance properties and that under squared error loss is tolerant only to uniform noise; risk minimization under other loss functions is not noise tolerant. We conclude the paper with some discussion on implications of these theoretical results