2,756 research outputs found
Knowing what you know in brain segmentation using Bayesian deep neural networks
In this paper, we describe a Bayesian deep neural network (DNN) for
predicting FreeSurfer segmentations of structural MRI volumes, in minutes
rather than hours. The network was trained and evaluated on a large dataset (n
= 11,480), obtained by combining data from more than a hundred different sites,
and also evaluated on another completely held-out dataset (n = 418). The
network was trained using a novel spike-and-slab dropout-based variational
inference approach. We show that, on these datasets, the proposed Bayesian DNN
outperforms previously proposed methods, in terms of the similarity between the
segmentation predictions and the FreeSurfer labels, and the usefulness of the
estimate uncertainty of these predictions. In particular, we demonstrated that
the prediction uncertainty of this network at each voxel is a good indicator of
whether the network has made an error and that the uncertainty across the whole
brain can predict the manual quality control ratings of a scan. The proposed
Bayesian DNN method should be applicable to any new network architecture for
addressing the segmentation problem.Comment: Submitted to Frontiers in Neuroinformatic
Rectangular Wilson Loops at Large N
This work is about pure Yang-Mills theory in four Euclidean dimensions with
gauge group SU(N). We study rectangular smeared Wilson loops on the lattice at
large N and relatively close to the large-N transition point in their
eigenvalue density. We show that the string tension can be extracted from these
loops but their dependence on shape differs from the asymptotic prediction of
effective string theory.Comment: 47 pages, 21 figures, 8 table
On the Inability of Markov Models to Capture Criticality in Human Mobility
We examine the non-Markovian nature of human mobility by exposing the
inability of Markov models to capture criticality in human mobility. In
particular, the assumed Markovian nature of mobility was used to establish a
theoretical upper bound on the predictability of human mobility (expressed as a
minimum error probability limit), based on temporally correlated entropy. Since
its inception, this bound has been widely used and empirically validated using
Markov chains. We show that recurrent-neural architectures can achieve
significantly higher predictability, surpassing this widely used upper bound.
In order to explain this anomaly, we shed light on several underlying
assumptions in previous research works that has resulted in this bias. By
evaluating the mobility predictability on real-world datasets, we show that
human mobility exhibits scale-invariant long-range correlations, bearing
similarity to a power-law decay. This is in contrast to the initial assumption
that human mobility follows an exponential decay. This assumption of
exponential decay coupled with Lempel-Ziv compression in computing Fano's
inequality has led to an inaccurate estimation of the predictability upper
bound. We show that this approach inflates the entropy, consequently lowering
the upper bound on human mobility predictability. We finally highlight that
this approach tends to overlook long-range correlations in human mobility. This
explains why recurrent-neural architectures that are designed to handle
long-range structural correlations surpass the previously computed upper bound
on mobility predictability
Infinite N phase transitions in continuum Wilson loop operators
We define smoothed Wilson loop operators on a four dimensional lattice and
check numerically that they have a finite and nontrivial continuum limit. The
continuum operators maintain their character as unitary matrices and undergo a
phase transition at infinite N reflected by the eigenvalue distribution closing
a gap in its spectrum when the defining smooth loop is dilated from a small
size to a large one. If this large N phase transition belongs to a solvable
universality class one might be able to calculate analytically the string
tension in terms of the perturbative Lambda-parameter. This would be achieved
by matching instanton results for small loops to the relevant large-N-universal
function which, in turn, would be matched for large loops to an effective
string theory. Similarities between our findings and known analytical results
in two dimensional space-time indicate that the phase transitions we found only
affect the eigenvalue distribution, but the traces of finite powers of the
Wilson loop operators stay smooth under scaling.Comment: 31 pages, 9 figures, typos and references corrected, minor
clarifications adde
Active Mean Fields for Probabilistic Image Segmentation: Connections with Chan-Vese and Rudin-Osher-Fatemi Models
Segmentation is a fundamental task for extracting semantically meaningful
regions from an image. The goal of segmentation algorithms is to accurately
assign object labels to each image location. However, image-noise, shortcomings
of algorithms, and image ambiguities cause uncertainty in label assignment.
Estimating the uncertainty in label assignment is important in multiple
application domains, such as segmenting tumors from medical images for
radiation treatment planning. One way to estimate these uncertainties is
through the computation of posteriors of Bayesian models, which is
computationally prohibitive for many practical applications. On the other hand,
most computationally efficient methods fail to estimate label uncertainty. We
therefore propose in this paper the Active Mean Fields (AMF) approach, a
technique based on Bayesian modeling that uses a mean-field approximation to
efficiently compute a segmentation and its corresponding uncertainty. Based on
a variational formulation, the resulting convex model combines any
label-likelihood measure with a prior on the length of the segmentation
boundary. A specific implementation of that model is the Chan-Vese segmentation
model (CV), in which the binary segmentation task is defined by a Gaussian
likelihood and a prior regularizing the length of the segmentation boundary.
Furthermore, the Euler-Lagrange equations derived from the AMF model are
equivalent to those of the popular Rudin-Osher-Fatemi (ROF) model for image
denoising. Solutions to the AMF model can thus be implemented by directly
utilizing highly-efficient ROF solvers on log-likelihood ratio fields. We
qualitatively assess the approach on synthetic data as well as on real natural
and medical images. For a quantitative evaluation, we apply our approach to the
icgbench dataset
Exposing strangeness: projections for kaon electromagnetic form factors
A continuum approach to the kaon and pion bound-state problems is used to
reveal their electromagnetic structure. For both systems, when used with parton
distribution amplitudes appropriate to the scale of the experiment, Standard
Model hard-scattering formulae are accurate to within 25% at momentum transfers
GeV. There are measurable differences between the
distribution of strange and normal matter within the kaons, e.g. the ratio of
their separate contributions reaches a peak value of at GeV. Its subsequent -evolution is accurately described by the hard
scattering formulae. Projections for kaon and pion form factors at timelike
momenta beyond the resonance region are also presented. These results and
projections should prove useful in planning next-generation experiments.Comment: 7 pages, 4 figure
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