7,686 research outputs found
Stochastics theory of log-periodic patterns
We introduce an analytical model based on birth-death clustering processes to
help understanding the empirical log-periodic corrections to power-law scaling
and the finite-time singularity as reported in several domains including
rupture, earthquakes, world population and financial systems. In our
stochastics theory log-periodicities are a consequence of transient clusters
induced by an entropy-like term that may reflect the amount of cooperative
information carried by the state of a large system of different species. The
clustering completion rates for the system are assumed to be given by a simple
linear death process. The singularity at t_{o} is derived in terms of
birth-death clustering coefficients.Comment: LaTeX, 1 ps figure - To appear J. Phys. A: Math & Ge
Individual differences in white matter microstructure reflect variation in functional connectivity during action choice.
The relation between brain structure and function is of fundamental importance in neuroscience. Comparisons between behavioral and brain imaging measures suggest that variation in brain structure correlates with the presence of specific skills[1-3]. Behavioral measures, however, reflect the integrated function of multiple brain regions. Rather than behavior, a physiological index of function could be a more sensitive and informative measure with which to compare structural measures. Here, we test for a relationship between a physiological measure of functional connectivity between two brain areas during a simple decision making task and a measure of structural connectivity. Paired-pulse transcranial magnetic stimulation indexed functional connectivity between two regions important for action choices: premotor and motor cortex. Fractional anisotropy (FA), a marker of microstructural integrity, indexed structural connectivity. Individual differences in functional connectivity during action selection show highly specific correlations with FA in localised regions of white matter interconnecting regions including the premotor and motor cortex. Probabilistic tractography[4, 5], a technique for identifying fibre pathways from diffusion-weighted imaging (DWI), reconstructed the anatomical networks linking the component brain regions involved in making decisions. These findings demonstrate a relationship between individual differences in functional and structural connectivity within human brain networks central to action choice
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Assessing adaptive mesh refinement (AMR) in a forced shallow-water model with moisture
Two forced shallow-water flow scenarios are explored in a 2D fourth-order finite-volume dynamical core with adaptive mesh refinement (AMR) to investigate AMR’s ability to track and resolve complex evolving features. Traditional shallow-water test cases are mainly characterized by large-scale smooth flows that do not effectively test the multiscale abilities of variable-resolution and AMR models to resolve sharp gradients and small-scale flow filaments. Therefore, adding forcing mechanisms to the shallow-water system to model key atmospheric processes adds complexity and creates small-scale phenomena. These can serve as foci for dynamic grid refinement while remaining simple enough to study the numerical design of a model’s dynamical core. The first shallow-water flow scenario represents a strengthening, tropical cyclone–like, vortex that is driven by a Betts–Miller-like convection scheme. The second shallow-water test is built upon a barotropically unstable jet with an added Kessler-like warm rain scheme that leads to precipitating frontal zones. The key feature of both tests is that there is significant sensitivity to the model grid while converging (structurally) at high resolution. Both test cases are investigated for a series of uniform resolutions and a variety of AMR tagging criteria. The AMR simulations demonstrate that grid refinement can resolve local features without requiring global high-resolution meshes. However, the results are sensitive to the refinement criteria. Criteria that trigger refinement early in a simulation reproduce the uniform-resolution reference solutions most reliably. In contrast, AMR criteria that delay refinement for several days require careful tuning of the AMR thresholds to improve results compared with uniform-resolution simulations
Vortex avalanches and self organized criticality in superconducting niobium
In 1993 Tang proposed [1] that vortex avalanches should produce a self
organized critical state in superconductors, but conclusive evidence for this
has heretofore been lacking. In the present paper, we report extensive
micro-Hall probe data from the vortex dynamics in superconducting niobium,
where a broad distribution of avalanche sizes scaling as a power-law for more
than two decades is found. The measurements are combined with magneto-optical
imaging, and show that over a widely varying magnetic landscape the scaling
behaviour does not change, hence establishing that the dynamics of
superconducting vortices is a SOC phenomenon.Comment: 3 pages + 4 figures, a reference added, citation typos fixe
Anisotropic thermal expansion and magnetostriction of YNiBC single crystals
We present results of anisotropic thermal expansion and low temperature
magnetostriction measurements on YNiBC single crystals grown by high
temperature flux and floating zone techniques. Quantum oscillations of
magnetostriction were observed at low temperatures for starting at
fields significantly below (). Large irreversible,
longitudinal magnetostriction was seen in both, in-plane and along the c-axis,
directions of the applied magnetic field in the intermediate superconducting
state. Anisotropic uniaxial pressure dependencies of were evaluated using
results of zero field, thermal expansion measurements
Log-periodic route to fractal functions
Log-periodic oscillations have been found to decorate the usual power law
behavior found to describe the approach to a critical point, when the
continuous scale-invariance symmetry is partially broken into a discrete-scale
invariance (DSI) symmetry. We classify the `Weierstrass-type'' solutions of the
renormalization group equation F(x)= g(x)+(1/m)F(g x) into two classes
characterized by the amplitudes A(n) of the power law series expansion. These
two classes are separated by a novel ``critical'' point. Growth processes
(DLA), rupture, earthquake and financial crashes seem to be characterized by
oscillatory or bounded regular microscopic functions g(x) that lead to a slow
power law decay of A(n), giving strong log-periodic amplitudes. In contrast,
the regular function g(x) of statistical physics models with
``ferromagnetic''-type interactions at equibrium involves unbound logarithms of
polynomials of the control variable that lead to a fast exponential decay of
A(n) giving weak log-periodic amplitudes and smoothed observables. These two
classes of behavior can be traced back to the existence or abscence of
``antiferromagnetic'' or ``dipolar''-type interactions which, when present,
make the Green functions non-monotonous oscillatory and favor spatial modulated
patterns.Comment: Latex document of 29 pages + 20 ps figures, addition of a new
demonstration of the source of strong log-periodicity and of a justification
of the general offered classification, update of reference lis
Fiber Orientation Estimation Guided by a Deep Network
Diffusion magnetic resonance imaging (dMRI) is currently the only tool for
noninvasively imaging the brain's white matter tracts. The fiber orientation
(FO) is a key feature computed from dMRI for fiber tract reconstruction.
Because the number of FOs in a voxel is usually small, dictionary-based sparse
reconstruction has been used to estimate FOs with a relatively small number of
diffusion gradients. However, accurate FO estimation in regions with complex FO
configurations in the presence of noise can still be challenging. In this work
we explore the use of a deep network for FO estimation in a dictionary-based
framework and propose an algorithm named Fiber Orientation Reconstruction
guided by a Deep Network (FORDN). FORDN consists of two steps. First, we use a
smaller dictionary encoding coarse basis FOs to represent the diffusion
signals. To estimate the mixture fractions of the dictionary atoms (and thus
coarse FOs), a deep network is designed specifically for solving the sparse
reconstruction problem. Here, the smaller dictionary is used to reduce the
computational cost of training. Second, the coarse FOs inform the final FO
estimation, where a larger dictionary encoding dense basis FOs is used and a
weighted l1-norm regularized least squares problem is solved to encourage FOs
that are consistent with the network output. FORDN was evaluated and compared
with state-of-the-art algorithms that estimate FOs using sparse reconstruction
on simulated and real dMRI data, and the results demonstrate the benefit of
using a deep network for FO estimation.Comment: A shorter version is accepted by MICCAI 201
The effect of gas drag on the growth of protoplanets -- Analytical expressions for the accretion of small bodies in laminar disks
Planetary bodies form by accretion of smaller bodies. It has been suggested
that a very efficient way to grow protoplanets is by accreting particles of
size <<km (e.g., chondrules, boulders, or fragments of larger bodies) as they
can be kept dynamically cold. We investigate the effects of gas drag on the
impact radii and the accretion rates of these particles. As simplifying
assumptions we restrict our analysis to 2D settings, a gas drag law linear in
velocity, and a laminar disk characterized by a smooth (global) pressure
gradient that causes particles to drift in radially. These approximations,
however, enable us to cover an arbitrary large parameter space. The framework
of the circularly restricted three body problem is used to numerically
integrate particle trajectories and to derive their impact parameters. Three
accretion modes can be distinguished: hyperbolic encounters, where the 2-body
gravitational focusing enhances the impact parameter; three-body encounters,
where gas drag enhances the capture probability; and settling encounters, where
particles settle towards the protoplanet. An analysis of the observed behavior
is presented; and we provide a recipe to analytically calculate the impact
radius, which confirms the numerical findings. We apply our results to the
sweepup of fragments by a protoplanet at a distance of 5 AU. Accretion of
debris on small protoplanets (<50 km) is found to be slow, because the
fragments are distributed over a rather thick layer. However, the newly found
settling mechanism, which is characterized by much larger impact radii, becomes
relevant for protoplanets of ~10^3 km in size and provides a much faster
channel for growth.Comment: accepted for publication in Astronomy & Astrophysic
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