1,013 research outputs found
Regularization of Linear Ill-posed Problems by the Augmented Lagrangian Method and Variational Inequalities
We study the application of the Augmented Lagrangian Method to the solution
of linear ill-posed problems. Previously, linear convergence rates with respect
to the Bregman distance have been derived under the classical assumption of a
standard source condition. Using the method of variational inequalities, we
extend these results in this paper to convergence rates of lower order, both
for the case of an a priori parameter choice and an a posteriori choice based
on Morozov's discrepancy principle. In addition, our approach allows the
derivation of convergence rates with respect to distance measures different
from the Bregman distance. As a particular application, we consider sparsity
promoting regularization, where we derive a range of convergence rates with
respect to the norm under the assumption of restricted injectivity in
conjunction with generalized source conditions of H\"older type
Solvent contribution to the stability of a physical gel characterized by quasi-elastic neutron scattering
The dynamics of a physical gel, namely the Low Molecular Mass Organic Gelator
{\textit Methyl-4,6-O-benzylidene- -D-mannopyranoside (-manno)}
in water and toluene are probed by neutron scattering. Using high gelator
concentrations, we were able to determine, on a timescale from a few ps to 1
ns, the number of solvent molecules that are immobilised by the rigid network
formed by the gelators. We found that only few toluene molecules per gelator
participate to the network which is formed by hydrogen bonding between the
gelators' sugar moieties. In water, however, the interactions leading to the
gel formations are weaker, involving dipolar, hydrophobic or
interactions and hydrogen bonds are formed between the gelators and the
surrounding water. Therefore, around 10 to 14 water molecules per gelator are
immobilised by the presence of the network. This study shows that neutron
scattering can give valuable information about the behaviour of solvent
confined in a molecular gel.Comment: Langmuir (2015
Nonlinear Hydrodynamics of a Hard Sphere Fluid Near the Glass Transition
We conduct a numerical study of the dynamic behavior of a dense hard sphere
fluid by deriving and integrating a set of Langevin equations. The statics of
the system is described by a free energy functional of the
Ramakrishnan-Yussouff form. We find that the system exhibits glassy behavior as
evidenced through stretched exponential decay and two-stage relaxation of the
density correlation function. The characteristic times grow with increasing
density according to the Vogel-Fulcher law. The wavenumber dependence of the
kinetics is extensively explored. The connection of our results with
experiment, mode coupling theory, and molecular dynamics results is discussed.Comment: 34 Pages, Plain TeX, 12 PostScript Figures (not included, available
on request
Planar Graph Coloring with Forbidden Subgraphs: Why Trees and Paths Are Dangerous
We consider the problem of coloring a planar graph with the minimum number of colors such that each color class avoids one or more forbidden graphs as subgraphs. We perform a detailed study of the computational complexity of this problem.
We present a complete picture for the case with a single forbidden connected (induced or non-induced) subgraph. The 2-coloring problem is NP-hard if the forbidden subgraph is a tree with at least two edges, and it is polynomially solvable in all other cases. The 3-coloring problem is NP-hard if the forbidden subgraph is a path, and it is polynomially solvable in all other cases. We also derive results for several forbidden sets of cycles
A combined first and second order variational approach for image reconstruction
In this paper we study a variational problem in the space of functions of
bounded Hessian. Our model constitutes a straightforward higher-order extension
of the well known ROF functional (total variation minimisation) to which we add
a non-smooth second order regulariser. It combines convex functions of the
total variation and the total variation of the first derivatives. In what
follows, we prove existence and uniqueness of minimisers of the combined model
and present the numerical solution of the corresponding discretised problem by
employing the split Bregman method. The paper is furnished with applications of
our model to image denoising, deblurring as well as image inpainting. The
obtained numerical results are compared with results obtained from total
generalised variation (TGV), infimal convolution and Euler's elastica, three
other state of the art higher-order models. The numerical discussion confirms
that the proposed higher-order model competes with models of its kind in
avoiding the creation of undesirable artifacts and blocky-like structures in
the reconstructed images -- a known disadvantage of the ROF model -- while
being simple and efficiently numerically solvable.Comment: 34 pages, 89 figure
Re-Inventing Adherence: Toward a Patient-Centered Model of Care for Drug-Resistant Tuberculosis and HIV
BACKGROUND—Despite renewed focus on molecular tuberculosis (TB) diagnostics and new antimycobacterial agents, treatment outcomes for patients co-infected with drug-resistant TB and human immunodeficiency virus (HIV) remain dismal, in part due to lack of focus on medication adherence as part of a patient-centered continuum of care.
OBJECTIVE—To review current barriers to drug-resistant TB-HIV treatment and propose an alternative model to conventional approaches to treatment support.
DISCUSSION—Current national TB control programs rely heavily on directly observed therapy (DOT) as the centerpiece of treatment delivery and adherence support. Medication adherence and care for drug-resistant TB-HIV could be improved by fully implementing team-based patient-centered care, empowering patients through counseling and support, maintaining a rights-based approach while acknowledging the responsibility of health care systems in providing comprehensive care, and prioritizing critical research gaps.
CONCLUSION—It is time to re-invent our understanding of adherence in drug-resistant TB and HIV by focusing attention on the complex clinical, behavioral, social, and structural needs of affected patients and communities
Simulations of galactic dynamos
We review our current understanding of galactic dynamo theory, paying
particular attention to numerical simulations both of the mean-field equations
and the original three-dimensional equations relevant to describing the
magnetic field evolution for a turbulent flow. We emphasize the theoretical
difficulties in explaining non-axisymmetric magnetic fields in galaxies and
discuss the observational basis for such results in terms of rotation measure
analysis. Next, we discuss nonlinear theory, the role of magnetic helicity
conservation and magnetic helicity fluxes. This leads to the possibility that
galactic magnetic fields may be bi-helical, with opposite signs of helicity and
large and small length scales. We discuss their observational signatures and
close by discussing the possibilities of explaining the origin of primordial
magnetic fields.Comment: 28 pages, 15 figure, to appear in Lecture Notes in Physics "Magnetic
fields in diffuse media", Eds. E. de Gouveia Dal Pino and A. Lazaria
Narrowing the gap between eye care needs and service provision: the service-training nexus
<p>Abstract</p> <p>Background</p> <p>The provision of eye care in the developing world has been constrained by the limited number of trained personnel and by professional cultures. The use of personnel with specific but limited training as members of multidisciplinary teams has become increasingly important as health systems seek to extract better value from their investments in personnel. Greater positive action is required to secure more efficient allocation of roles and resources. The supply of professional health workers is a factor of the training system, so it stands to reason that more cost-effective, flexible and available education methods are needed. This paper presents a highly flexible competencies-based multiple entry and exit training system that matches and adapts training to the prevailing population and service needs and demands, while lifting overall standards over time and highlighting the areas of potential benefit.</p> <p>Methods</p> <p>Literature surveys and interviews in five continents were carried out. Based on this and the author's own experience, a encies-based multiple entry and exit scheme for eye care in a developing country was derived, modeled and critically reviewed by interested parties in one country.</p> <p>Results</p> <p>The scheme was shown to be highly cost-effective and readily adaptable to the anticipated eye care needs of the population. Eye care players in one selected country have commented favourably on the scheme.</p> <p>Conclusion</p> <p>The underlying principles used to derive this model can be applied to many eye care systems in many developing countries. The model can be used in other disciplines with similar constructs to eye care.</p
Current status of turbulent dynamo theory: From large-scale to small-scale dynamos
Several recent advances in turbulent dynamo theory are reviewed. High
resolution simulations of small-scale and large-scale dynamo action in periodic
domains are compared with each other and contrasted with similar results at low
magnetic Prandtl numbers. It is argued that all the different cases show
similarities at intermediate length scales. On the other hand, in the presence
of helicity of the turbulence, power develops on large scales, which is not
present in non-helical small-scale turbulent dynamos. At small length scales,
differences occur in connection with the dissipation cutoff scales associated
with the respective value of the magnetic Prandtl number. These differences are
found to be independent of whether or not there is large-scale dynamo action.
However, large-scale dynamos in homogeneous systems are shown to suffer from
resistive slow-down even at intermediate length scales. The results from
simulations are connected to mean field theory and its applications. Recent
work on helicity fluxes to alleviate large-scale dynamo quenching, shear
dynamos, nonlocal effects and magnetic structures from strong density
stratification are highlighted. Several insights which arise from analytic
considerations of small-scale dynamos are discussed.Comment: 36 pages, 11 figures, Spa. Sci. Rev., submitted to the special issue
"Magnetism in the Universe" (ed. A. Balogh
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