14,494 research outputs found
A Fast, Semi-Automatic Brain Structure Segmentation Algorithm for Magnetic Resonance Imaging
Medical image segmentation has become an essential technique in clinical and
research-oriented applications. Because manual segmentation methods are
tedious, and fully automatic segmentation lacks the flexibility of human
intervention or correction, semi-automatic methods have become the preferred
type of medical image segmentation. We present a hybrid, semi-automatic
segmentation method in 3D that integrates both region-based and boundary-based
procedures. Our method differs from previous hybrid methods in that we perform
region-based and boundary-based approaches separately, which allows for more
efficient segmentation. A region-based technique is used to generate an initial
seed contour that roughly represents the boundary of a target brain structure,
alleviating the local minima problem in the subsequent model deformation phase.
The contour is deformed under a unique force equation independent of image
edges. Experiments on MRI data show that this method can achieve high accuracy
and efficiency primarily due to the unique seed initialization technique
Approximation of the inertial manifold for a nonlocal dynamical system
We consider inertial manifolds and their approximation for a class of partial
differential equations with a nonlocal Laplacian operator
, with . The nonlocal or fractional
Laplacian operator represents an anomalous diffusion effect. We first establish
the existence of an inertial manifold and highlight the influence of the
parameter . Then we approximate the inertial manifold when a small
normal diffusion (with ) enters
the system, and obtain the estimate for the Hausdorff semi-distance between the
inertial manifolds with and without normal diffusion.Comment: 19page
Global solutions for a nonlocal Ginzberg-Landau equation and a nonlocal Fokker-Plank equation
This work is devoted to the study of a nonlocal Ginzberg-Landau equation by
the semigroup method and a nonlocal Fokker-Plank equation by the viscosity
vanishing method. For the nonlocal Ginzberg-Landau equation, there exists a
unique global solution in the set
, for . For the
nonlocal Fokker-Plank equation, the regularity of the solution is weaker than
that of the nonlocal Ginzberg-Landau equation due to the drift term
A parameter estimator based on Smoluchowski-Kramers approximation
We devise a simplified parameter estimator for a second order stochastic
differential equation by a first order system based on the Smoluchowski-Kramers
approximation. We establish the consistency of the estimator by using
{\Gamma}-convergence theory. We further illus- trate our estimation method by
an experimentally studied movement model of a colloidal particle immersed in
water under conservative force and constant diffusion
Quantum criticality of the sub-Ohmic spin-boson model within displaced Fock states
The spin-boson model is analytically studied using displaced Fock states
(DFS) without discretization of the continuum bath. In the orthogonal displaced
Fock basis, the ground-state wavefunction can be systematically improved in a
controllable way. Interestingly, the zeroth-order DFS reproduces exactly the
well known Silbey-Harris results. In the framework of the second-order DFS, the
magnetization and the entanglement entropy are exactly calculated. It is found
that the magnetic critical exponent is converged to in the whole
sub-Ohmic bath regime , compared with that by the exactly solvable
generalized Silbey-Harris ansatz. It is strongly suggested that the system with
sub-Ohmic bath is always above its upper critical dimension, in sharp contrast
with the previous findings. This is the first evidence of the violation of the
quantum-classical Mapping for .Comment: 8 pages, 4 figure
Improved Silbey-Harris polaron ansatz for the spin-boson model
In this paper, the well-known Silbey-Harris (SH) polaron ansatz for the
spin-boson model is improved by adding orthogonal displaced Fock states. The
obtained results for the ground state in all baths converge very quickly within
finite displaced Fock states and corresponding SH results are corrected
considerably. Especially for the sub-Ohmic spin-boson model, the converging
results are obtained for 0 < s < 1/2 in the fourth-order correction and very
accurate critical coupling strengths of the quantum phase transition are
achieved. Converging magnetization in the biased spin-boson model is also
arrived at. Since the present improved SH ansatz can yield very accurate, even
almost exact results, it should have wide applications and extensions in
various spin-boson model and related fields.Comment: 9 pages, 6 figures. arXiv admin note: substantial text overlap with
arXiv:1410.099
Concise analytic solutions to the quantum Rabi model with two arbitrary qubits
Using extended coherent states, an analytical exact study has been carried
out for the quantum Rabi model (QRM) with two arbitrary qubits in a very
concise way. The -functions with determinants are generally
derived. For the same coupling constants, the simplest -function, resembling
that in the one-qubit QRM, can be obtained. Zeros of the -function yield the
whole regular spectrum. The exceptional eigenvalues, which do not belong to the
zeros of the function, are obtained in the closed form. The Dark states in
the case of the same coupling can be detected clearly in a continued-fraction
technique. The present concise solution is conceptually clear and practically
feasible to the general two-qubit QRM and therefore has many applications.Comment: 13 pages, 3 figure
Exact solvability, non-integrability, and genuine multipartite entanglement dynamics of the Dicke model
In this paper, the finite size Dicke model of arbitrary number of qubits is
solved analytically in an unified way within extended coherent states. For the
or Dicke models ( is an integer), the -function, which is
only an energy dependent determinant, is derived in a transparent
manner. The regular spectrum is completely and uniquely given by stable zeros
of the -function. The closed-form exceptional eigenvalues are also derived.
The level distribution controlled by the pole structure of the -functions
suggests non-integrability for model at any finite coupling in the sense
of recent criterion in literature. A preliminary application to the exact
dynamics of genuine multipartite entanglement in the finite Dicke model is
presented using the obtained exact solutions.Comment: 18 pages, 5 figure
Sliced Latin hypercube designs with arbitrary run sizes
Latin hypercube designs achieve optimal univariate stratifications and are
useful for computer experiments. Sliced Latin hypercube designs are Latin
hypercube designs that can be partitioned into smaller Latin hypercube designs.
In this work, we give, to the best of our knowledge, the first construction of
sliced Latin hypercube designs that allow arbitrarily chosen run sizes for the
slices. We also provide an algorithm to reduce correlations of our proposed
designs
Slow manifold and parameter estimation for a nonlocal fast-slow stochastic evolutionary system
We establish a slow manifold for a fast-slow stochastic evolutionary system
with anomalous diffusion, where both fast and slow components are influ- enced
by white noise. Furthermore, we prove the exponential tracking property for the
random slow manifold and this leads to a lower dimensional reduced sys- tem
based on the slow manifold. Also we consider parameter estimation for this
nonlocal fast-slow stochastic dynamical system, where only the slow component
is observable. In quantifying parameters in stochastic evolutionary systems,
this offers an advantage of dimension reduction
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