30,576 research outputs found
Griffiths phases and localization in hierarchical modular networks
We study variants of hierarchical modular network models suggested by Kaiser
and Hilgetag [Frontiers in Neuroinformatics, 4 (2010) 8] to model functional
brain connectivity, using extensive simulations and quenched mean-field theory
(QMF), focusing on structures with a connection probability that decays
exponentially with the level index. Such networks can be embedded in
two-dimensional Euclidean space. We explore the dynamic behavior of the contact
process (CP) and threshold models on networks of this kind, including
hierarchical trees. While in the small-world networks originally proposed to
model brain connectivity, the topological heterogeneities are not strong enough
to induce deviations from mean-field behavior, we show that a Griffiths phase
can emerge under reduced connection probabilities, approaching the percolation
threshold. In this case the topological dimension of the networks is finite,
and extended regions of bursty, power-law dynamics are observed. Localization
in the steady state is also shown via QMF. We investigate the effects of link
asymmetry and coupling disorder, and show that localization can occur even in
small-world networks with high connectivity in case of link disorder.Comment: 18 pages, 20 figures, accepted version in Scientific Report
Twisted Split Fermions
The observed flavor structure of the standard model arises naturally in
"split fermion" models which localize fermions at different places in an extra
dimension. It has, until now, been assumed that the bulk masses for such
fermions can be chosen to be flavor diagonal simultaneously at every point in
the extra dimension, with all the flavor violation coming from the Yukawa
couplings to the Higgs. We consider the more natural possibility in which the
bulk masses cannot be simultaneously diagonalized, that is, that they are
twisted in flavor space. We show that, in general, this does not disturb the
natural generation of hierarchies in the flavor parameters. Moreover, it is
conceivable that all the flavor mixing and CP-violation in the standard model
may come only from twisting, with the five-dimensional Yukawa couplings taken
to be universal.Comment: 15 pages, 1 figur
Localization Length Exponent, Critical Conductance Distribution and Multifractality in Hierarchical Network Models for the Quantum Hall Effect
We study hierarchical network models which have recently been introduced to
approximate the Chalker-Coddington model for the integer quantum Hall effect
(A.G. Galstyan and M.E. Raikh, PRB 56 1422 (1997); Arovas et al., PRB 56, 4751
(1997)). The hierarchical structure is due to a recursive method starting from
a finite elementary cell. The localization-delocalization transition occurring
in these models is displayed in the flow of the conductance distribution under
increasing system size. We numerically determine this flow, calculate the
critical conductance distribution, the critical exponent of the localization
length, and the multifractal exponents of critical eigenstates.Comment: 6 pages REVTeX, 9 postscript figures and 1 postscript tabl
Intensity-based elastic registration incorporating anisotropic landmark errors and rotational information
Purpose: Thin-plate splines (TPS) represent an effective tool for estimating the deformation that warps one set of landmarks to another based on the physical equivalent of thin metal sheets. In the original formulation, data used to estimate the deformation field are restricted to landmark locations only and thus does not allow to incorporate information about the rotation of the image around the landmark. It furthermore assumes that landmark positions are known exactly which is not the case in real world applications. These localization inaccuracies are propagated to the entire deformation field as each landmark has a global influence. We propose to use a TPS approximation method that incorporates anisotropic landmark errors and rotational information and integrate it into a hierarchical elastic registration framework (HERA). The improvement of the registration performance has been evaluated. Methods: The proposed TPS approximation scheme integrates anisotropic landmark errors with rotational information of the landmarks. The anisotropic landmark errors are represented by their covariance matrices estimated directly from the image data as a minimal stochastic localization error, i.e. the Cramér-Rao bound. The rotational attribute of each landmark is characterized by an additional angular landmark, thus doubling the number of landmarks in the TPS model. This allows the TPS approximation to better cope up with local deformations. Results: We integrated the proposed TPS approach into the HERA registration framework and applied it to register 161 image pairs from a digital mammogram database. Experiments showed that the mean squared error using the proposed TPS approximation was superior to pure TPS interpolation. On artificially deformed breast images HERA, with the proposed TPS approximation, performed significantly better than the state-of-the-art registration method presented by Rueckert. Conclusion: The TPS approximation approach proposed in this publication allows to incorporate anisotropic landmark errors as well as rotational information. The integration of the method into an intensity-based hierarchical non-rigid registration framework is straightforward and improved the registration quality significantl
Singular Spectrum and Recent Results on Hierarchical Operators
We use trace class scattering theory to exclude the possibility of absolutely
continuous spectrum in a large class of self-adjoint operators with an
underlying hierarchical structure and provide applications to certain random
hierarchical operators and matrices. We proceed to contrast the localizing
effect of the hierarchical structure in the deterministic setting with previous
results and conjectures in the random setting. Furthermore, we survey stronger
localization statements truly exploiting the disorder for the hierarchical
Anderson model and report recent results concerning the spectral statistics of
the ultrametric random matrix ensemble
Flexible Multi-layer Sparse Approximations of Matrices and Applications
The computational cost of many signal processing and machine learning
techniques is often dominated by the cost of applying certain linear operators
to high-dimensional vectors. This paper introduces an algorithm aimed at
reducing the complexity of applying linear operators in high dimension by
approximately factorizing the corresponding matrix into few sparse factors. The
approach relies on recent advances in non-convex optimization. It is first
explained and analyzed in details and then demonstrated experimentally on
various problems including dictionary learning for image denoising, and the
approximation of large matrices arising in inverse problems
Multimodal Hierarchical Dirichlet Process-based Active Perception
In this paper, we propose an active perception method for recognizing object
categories based on the multimodal hierarchical Dirichlet process (MHDP). The
MHDP enables a robot to form object categories using multimodal information,
e.g., visual, auditory, and haptic information, which can be observed by
performing actions on an object. However, performing many actions on a target
object requires a long time. In a real-time scenario, i.e., when the time is
limited, the robot has to determine the set of actions that is most effective
for recognizing a target object. We propose an MHDP-based active perception
method that uses the information gain (IG) maximization criterion and lazy
greedy algorithm. We show that the IG maximization criterion is optimal in the
sense that the criterion is equivalent to a minimization of the expected
Kullback--Leibler divergence between a final recognition state and the
recognition state after the next set of actions. However, a straightforward
calculation of IG is practically impossible. Therefore, we derive an efficient
Monte Carlo approximation method for IG by making use of a property of the
MHDP. We also show that the IG has submodular and non-decreasing properties as
a set function because of the structure of the graphical model of the MHDP.
Therefore, the IG maximization problem is reduced to a submodular maximization
problem. This means that greedy and lazy greedy algorithms are effective and
have a theoretical justification for their performance. We conducted an
experiment using an upper-torso humanoid robot and a second one using synthetic
data. The experimental results show that the method enables the robot to select
a set of actions that allow it to recognize target objects quickly and
accurately. The results support our theoretical outcomes.Comment: submitte
A subdivision-based implementation of non-uniform local refinement with THB-splines
Paper accepted for 15th IMA International Conference on Mathematics on Surfaces, 2017. Abstract: Local refinement of spline basis functions is an important process for spline approximation and local feature modelling in computer aided design (CAD). This paper develops an efficient local refinement method for non-uniform and general degree THB-splines(Truncated hierarchical B-splines). A non-uniform subdivision algorithm is improved to efficiently subdivide a single non-uniform B-spline basis function. The subdivision scheme is then applied to locally hierarchically refine non-uniform B-spline basis functions. The refined basis functions are non-uniform and satisfy the properties of linear independence, partition of unity and are locally supported. The refined basis functions are suitable for spline approximation and numerical analysis. The implementation makes it possible for hierarchical approximation to use the same non-uniform B-spline basis functions as existing modelling tools have used. The improved subdivision algorithm is faster than classic knot insertion. The non-uniform THB-spline approximation is shown to be more accurate than uniform low degree hierarchical local refinement when applied to two classical approximation problems
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