Spectral properties of the two-dimensional Schrödinger Hamiltonian with various solvable confinements in the presence of a central point perturbation

We study three solvable two-dimensional systems perturbed by a point interaction centered at the origin. The unperturbed systems are the isotropic harmonic oscillator, a square pyramidal potential and a combination thereof. We study the spectrum of the perturbed systems. We show that, while most eigenvalues are not affected by the point perturbation, a few of them are strongly perturbed. We show that for some values of one parameter, these perturbed eigenvalues may take lower values than the immediately lower eigenvalue, so that level crossings occur. These level crossings are studied in some detail

'Structure-from-Motion' photogrammetry: A low-cost, effective tool for geoscience applications

High-resolution topographic surveying is traditionally associated with high capital and logistical costs, so that data acquisition is often passed on to specialist third party organisations. The high costs of data collection are, for many applications in the earth sciences, exacerbated by the remoteness and inaccessibility of many field sites, rendering cheaper, more portable surveying platforms (i.e. terrestrial laser scanning or GPS) impractical. This paper outlines a revolutionary, low-cost, user-friendly photogrammetric technique for obtaining high-resolution datasets at a range of scales, termed ‘Structure-from-Motion’ (SfM). Traditional softcopy photogrammetric methods require the 3-D location and pose of the camera(s), or the 3-D location of ground control points to be known to facilitate scene triangulation and reconstruction. In contrast, the SfM method solves the camera pose and scene geometry simultaneously and automatically, using a highly redundant bundle adjustment based on matching features in multiple overlapping, offset images. A comprehensive introduction to the technique is presented, followed by an outline of the methods used to create high-resolution digital elevation models (DEMs) from extensive photosets obtained using a consumer-grade digital camera. As an initial appraisal of the technique, an SfM-derived DEM is compared directly with a similar model obtained using terrestrial laser scanning. This intercomparison reveals that decimetre-scale vertical accuracy can be achieved using SfM even for sites with complex topography and a range of land-covers. Example applications of SfM are presented for three contrasting landforms across a range of scales including; an exposed rocky coastal cliff; a breached moraine-dam complex; and a glacially-sculpted bedrock ridge. The SfM technique represents a major advancement in the field of photogrammetry for geoscience applications. Our results and experiences indicate SfM is an inexpensive, effective, and flexible approach to capturing complex topography

Quantum Heisenberg Chain with Long-Range Ferromagnetic Interactions at Low Temperature

A modified spin-wave theory is applied to the one-dimensional quantum Heisenberg model with long-range ferromagnetic interactions. Low-temperature properties of this model are investigated. The susceptibility and the specific heat are calculated; the relation between their behaviors and strength of the long-range interactions is obtained. This model includes both the Haldane-Shastry model and the nearest-neighbor Heisenberg model; the corresponding results in this paper are in agreement with the solutions of both the models. It is shown that there exists an ordering transition in the region where the model has longer-range interactions than the HS model. The critical temperature is estimated.Comment: 17 pages(LaTeX REVTeX), 1 figure appended (PostScript), Technical Report of ISSP A-274

Hand classification of fMRI ICA noise components

We present a practical "how-to" guide to help determine whether single-subject fMRI independent components (ICs) characterise structured noise or not. Manual identification of signal and noise after ICA decomposition is required for efficient data denoising: to train supervised algorithms, to check the results of unsupervised ones or to manually clean the data. In this paper we describe the main spatial and temporal features of ICs and provide general guidelines on how to evaluate these. Examples of signal and noise components are provided from a wide range of datasets (3T data, including examples from the UK Biobank and the Human Connectome Project, and 7T data), together with practical guidelines for their identification. Finally, we discuss how the data quality, data type and preprocessing can influence the characteristics of the ICs and present examples of particularly challenging datasets