166,687 research outputs found
Classification of Material Mixtures in Volume Data for Visualization and Modeling
Material classification is a key stop in creating computer graphics models and images from volume data, We present a new algorithm for identifying the distribution of different material types in volumetric datasets such as those produced with Magnetic Resonance Imaging (NMI) or Computed Tomography (CT). The algorithm assumes that voxels can contain more than one material, e.g. both muscle and fat; we wish to compute the relative proportion of each material in the voxels. Other classification methods have utilized Gaussian probability density functions to model the distribution of values within a dataset. These Gaussian basis functions work well for voxels with unmixed materials, but do not work well where the materials are mixed together. We extend this approach by deriving non-Gaussian "mixture" basis functions. We treat a voxel as a volume, not as a single point. We use the distribution of values within each voxel-sized volume to identify materials within the voxel using a probabilistic approach. The technique reduces the classification artifacts that occur along boundaries between materials. The technique is useful for making higher quality geometric models and renderings from volume data, and has the potential to make more accurate volume measurements. It also classifies noisy, low-resolution data well
Near-optimal protocols in complex nonequilibrium transformations
The development of sophisticated experimental means to control nanoscale
systems has motivated efforts to design driving protocols which minimize the
energy dissipated to the environment. Computational models are a crucial tool
in this practical challenge. We describe a general method for sampling an
ensemble of finite-time, nonequilibrium protocols biased towards a low average
dissipation. We show that this scheme can be carried out very efficiently in
several limiting cases. As an application, we sample the ensemble of
low-dissipation protocols that invert the magnetization of a 2D Ising model and
explore how the diversity of the protocols varies in response to constraints on
the average dissipation. In this example, we find that there is a large set of
protocols with average dissipation close to the optimal value, which we argue
is a general phenomenon.Comment: 6 pages and 3 figures plus 4 pages and 5 figures of supplemental
materia
Random matrices and quantum spin chains
Random matrix ensembles are introduced that respect the local tensor
structure of Hamiltonians describing a chain of distinguishable spin-half
particles with nearest-neighbour interactions. We prove a central limit theorem
for the density of states when , giving explicit bounds on
the rate of approach to the limit. Universality within a class of probability
measures and the extension to more general interaction geometries are
established. The level spacing distributions of the Gaussian Orthogonal,
Unitary and Symplectic Ensembles are observed numerically for the energy levels
in these ensembles.Comment: Updated figures, as accepted in 'Markov Processes and Related Fields'
on 3 March 201
- β¦