64,657 research outputs found

    Revisting the Jordan, Minnesota Cases

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    Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

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    We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states. Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled ``spins'' which are elements of u(1,1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams.Comment: 39 pages, 1 figur

    Electroweak Breaking in Supersymmetric Models

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    We discuss the mechanism for electroweak symmetry breaking in supersymmetric versions of the standard model. After briefly reviewing the possible sources of supersymmetry breaking, we show how the required pattern of symmetry breaking can automatically result from the structure of quantum corrections in the theory. We demonstrate that this radiative breaking mechanism works well for a heavy top quark and can be combined in unified versions of the theory with excellent predictions for the running couplings of the model. (To be published in ``Perspectives in Higgs Physics'', G. Kane editor.)Comment: 47 page

    Neural Network Based Diagnosis of Breast Cancer Using the BreakHis Dataset

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    Breast cancer is the most common type of cancer in the world, and it is the second deadliest cancer for females. In the fight against breast cancer, early detection plays a large role in saving people’s lives. In this work, an image classifier is designed to diagnose breast tumors as benign or malignant. The classifier is designed with a neural network and trained on the BreakHis dataset. After creating the initial design, a variety of methods are used to try to improve the performance of the classifier. These methods include preprocessing, increasing the number of training epochs, changing network architecture, and data augmentation. Preprocessing includes changing image resolution and trying grayscale images rather than RGB. The tested network architectures include VGG16, ResNet50, and a custom structure. The final algorithm creates 50 classifier models and keeps the best one. Classifier designs are primarily judged on the classification accuracies of their best model and their median model. Designs are also judged on how consistently they produce their highest performing models. The final classifier design has a median accuracy of 93.62% and best accuracy of 96.35%. Of the 50 models generated, 46 of them performed with over 85% accuracy. The final classifier design is compared to the works of two groups of researchers who created similar classifiers for the same dataset. This will show that the classifier performs at the same level or better than the classifiers designed by other researchers. The classifier achieves similar performance to the classifier made by the first group of researchers and performs better than the classifier from the second. Finally, the learned lessons and future steps are discussed
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