The Stern-Gerlach Experiment Revisited

The Stern-Gerlach-Experiment (SGE) of 1922 is a seminal benchmark experiment of quantum physics providing evidence for several fundamental properties of quantum systems. Based on today's knowledge we illustrate the different benchmark results of the SGE for the development of modern quantum physics and chemistry. The SGE provided the first direct experimental evidence for angular momentum quantization in the quantum world and thus also for the existence of directional quantization of all angular momenta in the process of measurement. It measured for the first time a ground state property of an atom, it produced for the first time a `spin-polarized' atomic beam, it almost revealed the electron spin. The SGE was the first fully successful molecular beam experiment with high momentum-resolution by beam measurements in vacuum. This technique provided a new kinematic microscope with which inner atomic or nuclear properties could be investigated. The original SGE is described together with early attempts by Einstein, Ehrenfest, Heisenberg, and others to understand directional quantization in the SGE. Heisenberg's and Einstein's proposals of an improved multi-stage SGE are presented. The first realization of these proposals by Stern, Phipps, Frisch and Segr\`e is described. The set-up suggested by Einstein can be considered an anticipation of a Rabi-apparatus. Recent theoretical work is mentioned in which the directional quantization process and possible interference effects of the two different spin states are investigated. In full agreement with the results of the new quantum theory directional quantization appears as a general and universal feature of quantum measurements. One experimental example for such directional quantization in scattering processes is shown. Last not least, the early history of the `almost' discovery of the electron spin in the SGE is revisited.Comment: 50pp, 17 fig

Applying Biclustering To Perform Collaborative Filtering

Collaborative filtering (CF) is a method to perform automated suggestions for a user based on the opinion of other users with similar interest. Most of the CF algorithms do not take into account the existent duality between users and items, considering only the similarities between users or only the similarities between items. In this paper we propose a novel methodology for the CF capable of dealing with this situation. By proposing an immune-inspired biclustering technique to carry out clustering of rows and columns at the same time, our algorithm is able to group similarities between users and items. In order to evaluate the proposed methodology, we have applied it to MovieLens dataset which contains user's ratings to a large set of movies. The results indicate that our proposal is able to provide useful recommendations for the users, outperforming other methodologies for CF reported in the literature. © 2007 IEEE.421426Agrawal, R., Gehrke, J., Gunopulus, D., Raghavan, P., Automatic subspace clustering of high dimensional data for data mining applications (1998) Proc. of the ACM/SIGMOD Int. Conference on Management of Data, pp. 94-105Cheng, Y., Church, G.M., Biclustering of expression data (2000) Proc. of the 8th Int. Conf. on Int. Systems for Molecular Biology, pp. 93-103de Castro, L.N., Von Zuben, F.J., (2001) aiNet: An Artificial Immune Network for Data Analysis, pp. 231-259. , Data Mining: A Heuristic Approachde França, F.O., Bezerra, G., Von Zuben, F.J., New Perspectives for the Biclustering Problem (2006) IEEE Congress on Evolutionary Computation, pp. 2768-2775Dhillon, I.S., Co-clustering documents and words using bipartite spectral graph partitioning (2001) Proc. of the 7th Int. Conf. on Knowledge Discovery and Data Mining, pp. 269-274Goldberg, D., Nichols, D., Brian, M., Terry, D., Using collaborative filtering to weave an information tapestry (1992) ACM Communications, 35, pp. 61-70Gomes, L.C.T., de Sousa, J.S., Bezerra, G.B., de Castro, L.N., Von Zuben, F.J., (2003) Copt-aiNet and the Gene Ordering Problem, 3 (2), pp. 27-33. , Information Technology MagazineHaixun, W., Wei, W., Jiong, Y., Yu, P.S., Clustering by pattern similarity in large data sets (2002) Proc. of the 2002 ACM SIGMOD Int. Conference on Management of Data, pp. 394-405Hartigan, J. A, Direct clustering of a data matrix. Journal of the American Statistical Association (JASA), 1972, 67, no. 337, pp. 123-129Moscato, P., Berretta, R., Mendes, A., A New Memetic Algorithm for Ordering Datasets: Applications in Microarray Analysis (2005) Proc. of the 6th Metaheuristics Int. Conference, pp. 695-700. , Austria, AugustResnick, P., Iacovou, N., Suchak, M., Bergstrom, P., Riedl, J., Grouplens: An open architecture for collaborative filtering on netnews (1994) In Proc. of the Computer Supported Collaborative Work Conference, pp. 175-186Segal, E., Taskar, B., Gasch, A., Friedman, N., Koller, D., Rich probabilistic models for gene expression (2001) In Bioinformatics, 17 (SUPPL. 1), pp. S243-S252Sheng, Q., Moreau, Y., De Moor, B., Biclustering micrarray data by Gibbs sampling (2003) Bioinformatics, 19 (SUPPL. 2), pp. 196-205Symeonidis, P., Nanopoulos, A., Papadopoulos, A., Manolopoulos, Y., Nearest-Biclusters Collaborative Filtering (2006) Proc. of the WebKDD - Workshop held in conjuction with KDDTang, C., Zhang, L., Zhang, I., Ramanathan, M., Interrelated two-way clustering: An unsupervised approach for gene expression data analysis (2001) Proc. of the 2nd IEEE Int. Symposium on Bioinformatics and Bioengineering, pp. 41-48Yu, K., Schwaighofer, A., Tresp, V., Xu, X., Kriegel, H.-P., Probabilistic Memory-based Collaborative Filtering (2004) In IEEE Transactions on Knowledge and Data Engineering, pp. 56-5