386 research outputs found
Additional symmetries of constrained CKP and BKP hierarchies
The additional symmetries of the constrained CKP (cCKP) and BKP (cBKP)
hierarchies are given by their actions on the Lax operators, and their actions
on the eigenfunction and adjoint eigenfunction are
presented explicitly. Furthermore, we show that acting on the space of the wave
operator, forms new centerless and
-subalgebra of centerless respectively. In
order to define above symmetry flows of the cCKP and cBKP
hierarchies, two vital operators are introduced to revise the additional
symmetry flows of the CKP and BKP hierarchies.Comment: 14 pages, accepted by SCIENCE CHINA Mathematics(2010
Iterative algorithms for total variation-like reconstructions in seismic tomography
A qualitative comparison of total variation like penalties (total variation,
Huber variant of total variation, total generalized variation, ...) is made in
the context of global seismic tomography. Both penalized and constrained
formulations of seismic recovery problems are treated. A number of simple
iterative recovery algorithms applicable to these problems are described. The
convergence speed of these algorithms is compared numerically in this setting.
For the constrained formulation a new algorithm is proposed and its convergence
is proven.Comment: 28 pages, 8 figures. Corrected sign errors in formula (25
On the performance of algorithms for the minimization of -penalized functionals
The problem of assessing the performance of algorithms used for the
minimization of an -penalized least-squares functional, for a range of
penalty parameters, is investigated. A criterion that uses the idea of
`approximation isochrones' is introduced. Five different iterative minimization
algorithms are tested and compared, as well as two warm-start strategies. Both
well-conditioned and ill-conditioned problems are used in the comparison, and
the contrast between these two categories is highlighted.Comment: 18 pages, 10 figures; v3: expanded version with an additional
synthetic test problem
Polynomials Associated with Equilibria of Affine Toda-Sutherland Systems
An affine Toda-Sutherland system is a quasi-exactly solvable multi-particle
dynamics based on an affine simple root system. It is a `cross' between two
well-known integrable multi-particle dynamics, an affine Toda molecule and a
Sutherland system. Polynomials describing the equilibrium positions of affine
Toda-Sutherland systems are determined for all affine simple root systems.Comment: 9 page
Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints
Regularization of ill-posed linear inverse problems via penalization
has been proposed for cases where the solution is known to be (almost) sparse.
One way to obtain the minimizer of such an penalized functional is via
an iterative soft-thresholding algorithm. We propose an alternative
implementation to -constraints, using a gradient method, with
projection on -balls. The corresponding algorithm uses again iterative
soft-thresholding, now with a variable thresholding parameter. We also propose
accelerated versions of this iterative method, using ingredients of the
(linear) steepest descent method. We prove convergence in norm for one of these
projected gradient methods, without and with acceleration.Comment: 24 pages, 5 figures. v2: added reference, some amendments, 27 page
Explorations of the Extended ncKP Hierarchy
A recently obtained extension (xncKP) of the Moyal-deformed KP hierarchy
(ncKP hierarchy) by a set of evolution equations in the Moyal-deformation
parameters is further explored. Formulae are derived to compute these equations
efficiently. Reductions of the xncKP hierarchy are treated, in particular to
the extended ncKdV and ncBoussinesq hierarchies. Furthermore, a good part of
the Sato formalism for the KP hierarchy is carried over to the generalized
framework. In particular, the well-known bilinear identity theorem for the KP
hierarchy, expressed in terms of the (formal) Baker-Akhiezer function, extends
to the xncKP hierarchy. Moreover, it is demonstrated that N-soliton solutions
of the ncKP equation are also solutions of the first few deformation equations.
This is shown to be related to the existence of certain families of algebraic
identities.Comment: 34 pages, correction of typos in (7.2) and (7.5
Home parenteral nutrition with an omega-3-fatty-acid-enriched MCT/LCT lipid emulsion in patients with chronic intestinal failure (the HOME study):study protocol for a randomized, controlled, multicenter, international clinical trial
BACKGROUND: Home parenteral nutrition (HPN) is a life-preserving therapy for patients with chronic intestinal failure (CIF) indicated for patients who cannot achieve their nutritional requirements by enteral intake. Intravenously administered lipid emulsions (ILEs) are an essential component of HPN, providing energy and essential fatty acids, but can become a risk factor for intestinal-failure-associated liver disease (IFALD). In HPN patients, major effort is taken in the prevention of IFALD. Novel ILEs containing a proportion of omega-3 polyunsaturated fatty acids (n-3 PUFA) could be of benefit, but the data on the use of n-3 PUFA in HPN patients are still limited. METHODS/DESIGN: The HOME study is a prospective, randomized, controlled, double-blind, multicenter, international clinical trial conducted in European hospitals that treat HPN patients. A total of 160 patients (80 per group) will be randomly assigned to receive the n-3 PUFA-enriched medium/long-chain triglyceride (MCT/LCT) ILE (Lipidem/LipoplusÂŽ 200âmg/ml, B. Braun Melsungen AG) or the MCT/LCT ILE (LipofundinÂŽ MCT/LCT/MedialipideÂŽ 20%, B. Braun Melsungen AG) for a projected period of 8 weeks. The primary endpoint is the combined change of liver function parameters (total bilirubin, aspartate transaminase and alanine transaminase) from baseline to final visit. Secondary objectives are the further evaluation of the safety and tolerability as well as the efficacy of the ILEs. DISCUSSION: Currently, there are only very few randomized controlled trials (RCTs) investigating the use of ILEs in HPN, and there are very few data at all on the use of n-3 PUFAs. The working hypothesis is that n-3 PUFA-enriched ILE is safe and well-tolerated especially with regard to liver function in patients requiring HPN. The expected outcome is to provide reliable data to support this thesis thanks to a considerable number of CIF patients, consequently to broaden the present evidence on the use of ILEs in HPN. TRIAL REGISTRATION: ClinicalTrials.gov, ID: NCT03282955. Registered on 14 September 2017
The political ontology of collaborative water governance
This article examines the various definitions of, and analytical approaches to, collaborative water governance (CWG). While the conceptâs usage has increased over the past decade, there lacks any deep engagement with the concept of the political at the heart of CWG. This article argues that contemporary approaches to CWG risk emptying the concept of its utility and coherence. Correcting this deficiency requires a focus on the social and ideational constructions of water. This will strengthen future collaborative water arrangements and enable deeper appreciation of the ways the political makes and remakes what is possible in water governance
Nanobody-aided crystallization of the transcription regulator PaaR2 from Escherichia coli O157:H7
paaR2âpaaA2âparE2 is a three-component toxinâantitoxin module found in prophage CP-993P of Escherichia coli O157:H7. Transcription regulation of this module occurs via the 123-amino-acid regulator PaaR2, which forms a large oligomeric structure. Despite appearing to be well folded, PaaR2 withstands crystallization, as does its N-terminal DNA-binding domain. Native mass spectrometry was used to screen for nanobodies that form a unique complex and stabilize the octameric structure of PaaR2. One such nanobody, Nb33, allowed crystallization of the protein. The resulting crystals belong to space group F432, with unit-cell parameter a = 317â
Ă
, diffract to 4.0â
Ă
resolution and are likely to contain four PaaR2 monomers and four nanobody monomers in the asymmetric unit. Crystals of two truncates containing the N-terminal helixâturnâhelix domain also interact with Nb33, and the corresponding co-crystals diffracted to 1.6 and 1.75â
Ă
resolution
- âŚ