849 research outputs found
Functional Liftings of Vectorial Variational Problems with Laplacian Regularization
We propose a functional lifting-based convex relaxation of variational
problems with Laplacian-based second-order regularization. The approach rests
on ideas from the calibration method as well as from sublabel-accurate
continuous multilabeling approaches, and makes these approaches amenable for
variational problems with vectorial data and higher-order regularization, as is
common in image processing applications. We motivate the approach in the
function space setting and prove that, in the special case of absolute
Laplacian regularization, it encompasses the discretization-first
sublabel-accurate continuous multilabeling approach as a special case. We
present a mathematical connection between the lifted and original functional
and discuss possible interpretations of minimizers in the lifted function
space. Finally, we exemplarily apply the proposed approach to 2D image
registration problems.Comment: 12 pages, 3 figures; accepted at the conference "Scale Space and
Variational Methods" in Hofgeismar, Germany 201
Tasks for multivariate network analysis
In Chap. 1, a multivariate network was defined as having two important characteristics. First, nodes are connected to each other via links; there is topological structure. Second, being multivariate, nodes and links have attributes associated with them, with these attributes having a value. In this chapter, we describe tasks associated with multivariate networks. We consider a task to be an activity that a user wishes to accomplish by interacting with a visual representation of a multivariate network. This implies that there is user intent [13], and that the network has been presented visually. At the highest level, this intent is usually described as the goal of obtaining insight about the data being studied [6]
Combined effect of frustration and dimerization in ferrimagnetic chains and square lattice
Within the zero-temperature linear spin-wave theory we have investigated the
effect of frustration and dimerization of a Heisenberg system with alternating
spins and on one- and two-dimensional lattices. The combined
effect most visibly appears in the elementary excitation spectra. In contrast
to the ground state energy that decreases with dimerization and increases with
frustration, the excitation energies are shown to be suppressed in energy by
both dimerization and frustration. The threshold value of frustration that
signals a transition from a classical ferrimagnetic state to a spiral state,
decreases with dimerization, showing that dimerization further helps in the
phase transition. The correlation length and sublattice magnetization decrease
with both dimerization and frustration indicating the destruction of the
long-range classical ferrimagnetic. The linear spin wave theory shows that in
the case of a square lattice, dimerization initially opposes the
frustration-led transition to a spiral magnetic state, but then higher
magnitudes of lattice deformation facilitate the transition. It also shows that
the transition to spiral state is inhibited in a square lattice beyond a
certain value of dimerization.Comment: 8 pages, latex, 12 postscript figure
Comparing memory skill maintenance across the lifespan : Preservation in adults, increase in children
Specific Heat Study on a Novel Spin-Gapped System : (CH_3)_2NH_2CuCl_3
Specific heat measurements down to 120mK have been performed on a
quasi-one-dimensional spin-gapped system (CH)NHCuCl in
a magnetic field up to 8 T. This compound has a characteristic magnetization
curve which shows a gapless ground state and a plateau at 1/2 of the saturation
value. We have observed a spontaneous antiferromagnetic ordering and a
field-induced one below and above the 1/2 plateau field range, respectively.
The field versus temperature phase diagram is quite unusual and completely
different from those of the other quantum spin systems investigated so far. In
the plateau field range, a double-structure in the specific heat is observed,
reflecting the coexistence of ferromagnetic and antiferromagnetic excitations.
These behaviors are discussed on the basis of a recently proposed novel quantum
spin chain model consisting of weakly coupled ferromagnetic and
antiferromagnetic dimers.Comment: 4 pages, 3 figures, submitted to J. Phys. Soc. Jp
Spin-dependent resonant tunneling through semimetallic ErAs quantum wells
Resonant tunneling through semimetallic ErAs quantum wells embedded in GaAs
structures with AlAs barriers was recently found to exhibit an intriguing
behavior in magnetic fields which is explained in terms of tunneling selection
rules and the spin-polarized band structure including spin-orbit coupling.Comment: 4 pages, figures supplied as self-unpacking figures.uu, uses
epsfig.sty to incorporate figures in preprin
Mixed Heisenberg Chains. I. The Ground State Problem
We consider a mechanism for competing interactions in alternating Heisenberg
spin chains due to the formation of local spin-singlet pairs. The competition
of spin-1 and spin-0 states reveals hidden Ising symmetry of such alternating
chains.Comment: 7 pages, RevTeX, 4 embedded eps figures, final versio
Phase diagram and hidden order for generalized spin ladders
We investigate the phase diagram of antiferromagnetic spin ladders with
additional exchange interactions on diagonal bonds by variational and numerical
methods. These generalized spin ladders interpolate smoothly between the
chain with competing nn and nnn interactions, the chain with
alternating exchange and the antiferromagnetic chain. The Majumdar-Ghosh
ground states are formulated as matrix product states and are shown to exhibit
the same type of hidden order as the af chain. Generalized matrix product
states are used for a variational calculation of the ground state energy and
the spin and string correlation functions. Numerical (Lanczos) calculations of
the energies of the ground state and of the low-lying excited states are
performed, and compare reasonably with the variational approach. Our results
support the hypothesis that the dimer and Majumdar-Ghosh points are in the same
phase as the af chain.Comment: 23 pages, REVTEX, 7 figure
Ground State Property of an Alternating Spin Ladder Involving Two Kinds of Inter-Chain Interactions
The ground state property of the alternating spin ladder is studied in the
case that the system involves an antiferromagnetic intra-chain interaction as
well as two kinds of inter-chain interactions; one is between spins of the same
magnitude and the other is between spins with different magnitudes. The
calculation has been carried out by the exact diagonalization method. As a
consequence of the competition among interactions, the system is revealed to
show an interesting variety of phases in the ground state property. Its phase
diagram is exhibited in the parameter space of the system. We find that,
however small the total amount of the inter-chain interactions is, the
ferrimagnetic ground state becomes unstable in a certain region. In this case,
which of the ferrimagnetic and the singlet ground state to appear is determined
only by the ratio between the inter-chain interactions regardless of their
total amount. The nature of two phases appearing in the singlet region of the
phase diagram and the type of the phase transition between them are also
discussed. The results are ensured by comparing with those of obtained in other
models which are contained in our model as special limiting cases.Comment: 12 pages, 9 PostScript figure
Dominant ferromagnetism in the spin-1/2 half-twist ladder 334 compounds, Ba3Cu3In4O12 and Ba3Cu3Sc4O12
The magnetic properties of polycrystalline samples of Ba3Cu3In4O12 (In-334)
and Ba3Cu3Sc4O12 (Sc-334) are reported. Both 334 phases have a structure
derived from perovskite, with CuO4 squares interconnected to form half-twist
ladders along the c-axis. The Cu-O-Cu angles, ~ 90o, and the positive Weiss
temperatures indicate the presence of significant ferromagnetic (FM)
interactions along the Cu ladders. At low temperatures, T < 20 K, sharp
transitions in the magnetic susceptibility and heat capacity measurements
indicate three-dimensional (3D) antiferromagnetic (AFM) ordering at TN. TN is
suppressed on application of a field and a complex magnetic phase diagram with
three distinct magnetic regimes below the upper critical field can be inferred
from our measurements. The magnetic interactions are discussed in relation to a
modified spin-1/2 FM-AFM model and the 334 half-twist ladder is compared to
other 2-rung ladder spin-1/2 systems.Comment: 20 pages, 7 figure
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