11,086 research outputs found
Disorder-Induced Stabilization of the Pseudogap in Strongly Correlated Systems
The interplay of strong interaction and strong disorder, as contained in the
Anderson-Hubbard model, is addressed using two non-perturbative numerical
methods: the Lanczos algorithm in the grand canonical ensemble at zero
temperature and Quantum Monte Carlo. We find distinctive evidence for a
zero-energy anomaly which is robust upon variation of doping, disorder and
interaction strength. Its similarities to, and differences from, pseudogap
formation in other contexts, including perturbative treatments of interactions
and disorder, classical theories of localized charges, and in the clean Hubbard
model, are discussed.Comment: 4.2 pages, 4 figure
Spectral Embedding Norm: Looking Deep into the Spectrum of the Graph Laplacian
The extraction of clusters from a dataset which includes multiple clusters
and a significant background component is a non-trivial task of practical
importance. In image analysis this manifests for example in anomaly detection
and target detection. The traditional spectral clustering algorithm, which
relies on the leading eigenvectors to detect clusters, fails in such
cases. In this paper we propose the {\it spectral embedding norm} which sums
the squared values of the first normalized eigenvectors, where can be
significantly larger than . We prove that this quantity can be used to
separate clusters from the background in unbalanced settings, including extreme
cases such as outlier detection. The performance of the algorithm is not
sensitive to the choice of , and we demonstrate its application on synthetic
and real-world remote sensing and neuroimaging datasets
Cluster analysis of multiple planetary flow regimes
A modified cluster analysis method was developed to identify spatial patterns of planetary flow regimes, and to study transitions between them. This method was applied first to a simple deterministic model and second to Northern Hemisphere (NH) 500 mb data. The dynamical model is governed by the fully-nonlinear, equivalent-barotropic vorticity equation on the sphere. Clusters of point in the model's phase space are associated with either a few persistent or with many transient events. Two stationary clusters have patterns similar to unstable stationary model solutions, zonal, or blocked. Transient clusters of wave trains serve as way stations between the stationary ones. For the NH data, cluster analysis was performed in the subspace of the first seven empirical orthogonal functions (EOFs). Stationary clusters are found in the low-frequency band of more than 10 days, and transient clusters in the bandpass frequency window between 2.5 and 6 days. In the low-frequency band three pairs of clusters determine, respectively, EOFs 1, 2, and 3. They exhibit well-known regional features, such as blocking, the Pacific/North American (PNA) pattern and wave trains. Both model and low-pass data show strong bimodality. Clusters in the bandpass window show wave-train patterns in the two jet exit regions. They are related, as in the model, to transitions between stationary clusters
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