5,890 research outputs found
Unsupervised machine learning for detection of phase transitions in off-lattice systems I. Foundations
We demonstrate the utility of an unsupervised machine learning tool for the
detection of phase transitions in off-lattice systems. We focus on the
application of principal component analysis (PCA) to detect the freezing
transitions of two-dimensional hard-disk and three-dimensional hard-sphere
systems as well as liquid-gas phase separation in a patchy colloid model. As we
demonstrate, PCA autonomously discovers order-parameter-like quantities that
report on phase transitions, mitigating the need for a priori construction or
identification of a suitable order parameter--thus streamlining the routine
analysis of phase behavior. In a companion paper, we further develop the method
established here to explore the detection of phase transitions in various model
systems controlled by compositional demixing, liquid crystalline ordering, and
non-equilibrium active forces
Unsupervised machine learning for detection of phase transitions in off-lattice systems II. Applications
We outline how principal component analysis (PCA) can be applied to particle
configuration data to detect a variety of phase transitions in off-lattice
systems, both in and out of equilibrium. Specifically, we discuss its
application to study 1) the nonequilibrium random organization (RandOrg) model
that exhibits a phase transition from quiescent to steady-state behavior as a
function of density, 2) orientationally and positionally driven equilibrium
phase transitions for hard ellipses, and 3) compositionally driven demixing
transitions in the non-additive binary Widom-Rowlinson mixture
Method to Correct the Voxel Size in PRESS Localized NMR Stereoscopy
Two techniques commonly used on human magnetic resonance spectroscopy systems to obtain spectra from localized volumes in the brain are point resolved spectroscopy (PRESS) and stimulated echo acquisition mode (STEAM) spectroscopy. PRESS gives a signal twice as large as that obtained with STEAM, but suffers from longer minimum echo times. While STEAM must be used to detect species with short spin-spin relaxation times, PRESS can be used for species with longer relaxation times to give a spectrum with a better signal to noise ratio. Only STEAM was provided for the GE Omega 4.7 T small animal imager used in this laboratory. Therefore, a PRESS pulse program was written for this instrument. With the standard sequence, the sampled voxel is smaller than the prescribed voxel. A larger voxel can be prescribed to increase the sampled volume. A different approach, involving the modification of the gradient strength, has been used in this laboratory. The resulting pulse sequence, with representative profiles, is discussed
Black hole collisions from Brill-Lindquist initial data: predictions of perturbation theory
The Misner initial value solution for two momentarily stationary black holes
has been the focus of much numerical study. We report here analytic results for
an astrophysically similar initial solution, that of Brill and Lindquist (BL).
Results are given from perturbation theory for initially close holes and are
compared with available numerical results. A comparison is made of the
radiation generated from the BL and the Misner initial values, and the physical
meaning is discussed.Comment: 11 pages, revtex3.0, 5 figure
Treating random sequential addition via the replica method
While many physical processes are non-equilibrium in nature, the theory and
modeling of such phenomena lag behind theoretical treatments of equilibrium
systems. The diversity of powerful theoretical tools available to describe
equilibrium systems has inspired strategies that map non-equilibrium systems
onto equivalent equilibrium analogs so that interrogation with standard
statistical mechanical approaches is possible. In this work, we revisit the
mapping from the non-equilibrium random sequential addition process onto an
equilibrium multi-component mixture via the replica method, allowing for
theoretical predictions of non-equilibrium structural quantities. We validate
the above approach by comparing the theoretical predictions to numerical
simulations of random sequential addition.Comment: 32 pages, 3 figure
Improving Reliability of Subject-Level Resting-State fMRI Parcellation with Shrinkage Estimators
A recent interest in resting state functional magnetic resonance imaging
(rsfMRI) lies in subdividing the human brain into anatomically and functionally
distinct regions of interest. For example, brain parcellation is often used for
defining the network nodes in connectivity studies. While inference has
traditionally been performed on group-level data, there is a growing interest
in parcellating single subject data. However, this is difficult due to the low
signal-to-noise ratio of rsfMRI data, combined with typically short scan
lengths. A large number of brain parcellation approaches employ clustering,
which begins with a measure of similarity or distance between voxels. The goal
of this work is to improve the reproducibility of single-subject parcellation
using shrinkage estimators of such measures, allowing the noisy
subject-specific estimator to "borrow strength" in a principled manner from a
larger population of subjects. We present several empirical Bayes shrinkage
estimators and outline methods for shrinkage when multiple scans are not
available for each subject. We perform shrinkage on raw intervoxel correlation
estimates and use both raw and shrinkage estimates to produce parcellations by
performing clustering on the voxels. Our proposed method is agnostic to the
choice of clustering method and can be used as a pre-processing step for any
clustering algorithm. Using two datasets---a simulated dataset where the true
parcellation is known and is subject-specific and a test-retest dataset
consisting of two 7-minute rsfMRI scans from 20 subjects---we show that
parcellations produced from shrinkage correlation estimates have higher
reliability and validity than those produced from raw estimates. Application to
test-retest data shows that using shrinkage estimators increases the
reproducibility of subject-specific parcellations of the motor cortex by up to
30%.Comment: body 21 pages, 11 figure
- …