5,553 research outputs found
Emergent Fermi sea in a system of interacting bosons
An understanding of the possible ways in which interactions can produce
fundamentally new emergent many-body states is a central problem of condensed
matter physics. We ask if a Fermi sea can arise in a system of bosons subject
to contact interaction. Based on exact diagonalization studies and variational
wave functions, we predict that such a state is likely to occur when a system
of two-component bosons in two dimensions, interacting via a species
independent contact interaction, is exposed to a synthetic magnetic field of
strength that corresponds to a filling factor of unity. The fermions forming
the SU(2) singlet Fermi sea are bound states of bosons and quantized vortices,
formed as a result of the repulsive interaction between bosons in the lowest
Landau level
Decoding the Encoding of Functional Brain Networks: an fMRI Classification Comparison of Non-negative Matrix Factorization (NMF), Independent Component Analysis (ICA), and Sparse Coding Algorithms
Brain networks in fMRI are typically identified using spatial independent
component analysis (ICA), yet mathematical constraints such as sparse coding
and positivity both provide alternate biologically-plausible frameworks for
generating brain networks. Non-negative Matrix Factorization (NMF) would
suppress negative BOLD signal by enforcing positivity. Spatial sparse coding
algorithms ( Regularized Learning and K-SVD) would impose local
specialization and a discouragement of multitasking, where the total observed
activity in a single voxel originates from a restricted number of possible
brain networks.
The assumptions of independence, positivity, and sparsity to encode
task-related brain networks are compared; the resulting brain networks for
different constraints are used as basis functions to encode the observed
functional activity at a given time point. These encodings are decoded using
machine learning to compare both the algorithms and their assumptions, using
the time series weights to predict whether a subject is viewing a video,
listening to an audio cue, or at rest, in 304 fMRI scans from 51 subjects.
For classifying cognitive activity, the sparse coding algorithm of
Regularized Learning consistently outperformed 4 variations of ICA across
different numbers of networks and noise levels (p0.001). The NMF algorithms,
which suppressed negative BOLD signal, had the poorest accuracy. Within each
algorithm, encodings using sparser spatial networks (containing more
zero-valued voxels) had higher classification accuracy (p0.001). The success
of sparse coding algorithms may suggest that algorithms which enforce sparse
coding, discourage multitasking, and promote local specialization may capture
better the underlying source processes than those which allow inexhaustible
local processes such as ICA
Adiabatic continuity between Hofstadter and Chern insulator states
We show that the topologically nontrivial bands of Chern insulators are
adiabatic cousins of the Landau bands of Hofstadter lattices. We demonstrate
adiabatic connection also between several familiar fractional quantum Hall
states on Hofstadter lattices and the fractional Chern insulator states in
partially filled Chern bands, which implies that they are in fact different
manifestations of the same phase. This adiabatic path provides a way of
generating many more fractional Chern insulator states and helps clarify that
nonuniformity in the distribution of the Berry curvature is responsible for
weakening or altogether destroying fractional topological states
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