18,359 research outputs found
A Non-Local Structure Tensor Based Approach for Multicomponent Image Recovery Problems
Non-Local Total Variation (NLTV) has emerged as a useful tool in variational
methods for image recovery problems. In this paper, we extend the NLTV-based
regularization to multicomponent images by taking advantage of the Structure
Tensor (ST) resulting from the gradient of a multicomponent image. The proposed
approach allows us to penalize the non-local variations, jointly for the
different components, through various matrix norms with .
To facilitate the choice of the hyper-parameters, we adopt a constrained convex
optimization approach in which we minimize the data fidelity term subject to a
constraint involving the ST-NLTV regularization. The resulting convex
optimization problem is solved with a novel epigraphical projection method.
This formulation can be efficiently implemented thanks to the flexibility
offered by recent primal-dual proximal algorithms. Experiments are carried out
for multispectral and hyperspectral images. The results demonstrate the
interest of introducing a non-local structure tensor regularization and show
that the proposed approach leads to significant improvements in terms of
convergence speed over current state-of-the-art methods
A Constrained Sequential-Lamination Algorithm for the Simulation of Sub-Grid Microstructure in Martensitic Materials
We present a practical algorithm for partially relaxing multiwell energy
densities such as pertain to materials undergoing martensitic phase
transitions. The algorithm is based on sequential lamination, but the evolution
of the microstructure during a deformation process is required to satisfy a
continuity constraint, in the sense that the new microstructure should be
reachable from the preceding one by a combination of branching and pruning
operations. All microstructures generated by the algorithm are in static and
configurational equilibrium. Owing to the continuity constrained imposed upon
the microstructural evolution, the predicted material behavior may be
path-dependent and exhibit hysteresis. In cases in which there is a strict
separation of micro and macrostructural lengthscales, the proposed relaxation
algorithm may effectively be integrated into macroscopic finite-element
calculations at the subgrid level. We demonstrate this aspect of the algorithm
by means of a numerical example concerned with the indentation of an Cu-Al-Ni
shape memory alloy by a spherical indenter.Comment: 27 pages with 9 figures. To appear in: Computer Methods in Applied
Mechanics and Engineering. New version incorporates minor revisions from
revie
Deterministic Annealing and Nonlinear Assignment
For combinatorial optimization problems that can be formulated as Ising or
Potts spin systems, the Mean Field (MF) approximation yields a versatile and
simple ANN heuristic, Deterministic Annealing. For assignment problems the
situation is more complex -- the natural analog of the MF approximation lacks
the simplicity present in the Potts and Ising cases. In this article the
difficulties associated with this issue are investigated, and the options for
solving them discussed. Improvements to existing Potts-based MF-inspired
heuristics are suggested, and the possibilities for defining a proper
variational approach are scrutinized.Comment: 15 pages, 3 figure
Computing stationary free-surface shapes in microfluidics
A finite-element algorithm for computing free-surface flows driven by
arbitrary body forces is presented. The algorithm is primarily designed for the
microfluidic parameter range where (i) the Reynolds number is small and (ii)
force-driven pressure and flow fields compete with the surface tension for the
shape of a stationary free surface. The free surface shape is represented by
the boundaries of finite elements that move according to the stress applied by
the adjacent fluid. Additionally, the surface tends to minimize its free energy
and by that adapts its curvature to balance the normal stress at the surface.
The numerical approach consists of the iteration of two alternating steps: The
solution of a fluidic problem in a prescribed domain with slip boundary
conditions at the free surface and a consecutive update of the domain driven by
the previously determined pressure and velocity fields. ...Comment: Revised versio
Approximating strongly correlated spin and fermion wavefunctions with correlator product states
We explore correlator product states for the approximation of correlated
wavefunctions in arbitrary dimensions. We show that they encompass many
interesting states including Laughlin's quantum Hall wavefunction, Huse and
Elser's frustrated spin states, and Kitaev's toric code. We further establish
their relation to common families of variational wavefunctions, such as matrix
and tensor product states and resonating valence bond states. Calculations on
the Heisenberg and spinless Hubbard models show that correlator product states
capture both two-dimensional correlations (independent of system width) as well
as non-trivial fermionic correlations (without sign problems). In
one-dimensional simulations, correlator product states appear competitive with
matrix product states with a comparable number of variational parameters,
suggesting they may eventually provide a route to practically generalise the
density matrix renormalisation group to higher dimensions.Comment: Table 1 expanded, Table 2 updated, optimization method discussed,
discussions expanded in some sections, earlier work on similar wavefunctions
included in text and references, see also (arXiv:0905.3898). 5 pages, 1
figure, 2 tables, submitted to Phys. Rev.
OSQP: An Operator Splitting Solver for Quadratic Programs
We present a general-purpose solver for convex quadratic programs based on
the alternating direction method of multipliers, employing a novel operator
splitting technique that requires the solution of a quasi-definite linear
system with the same coefficient matrix at almost every iteration. Our
algorithm is very robust, placing no requirements on the problem data such as
positive definiteness of the objective function or linear independence of the
constraint functions. It can be configured to be division-free once an initial
matrix factorization is carried out, making it suitable for real-time
applications in embedded systems. In addition, our technique is the first
operator splitting method for quadratic programs able to reliably detect primal
and dual infeasible problems from the algorithm iterates. The method also
supports factorization caching and warm starting, making it particularly
efficient when solving parametrized problems arising in finance, control, and
machine learning. Our open-source C implementation OSQP has a small footprint,
is library-free, and has been extensively tested on many problem instances from
a wide variety of application areas. It is typically ten times faster than
competing interior-point methods, and sometimes much more when factorization
caching or warm start is used. OSQP has already shown a large impact with tens
of thousands of users both in academia and in large corporations
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