4,963 research outputs found
Geodesic boundary value problems with symmetry
This paper shows how left and right actions of Lie groups on a manifold may
be used to complement one another in a variational reformulation of optimal
control problems equivalently as geodesic boundary value problems with
symmetry. We prove an equivalence theorem to this effect and illustrate it with
several examples. In finite-dimensions, we discuss geodesic flows on the Lie
groups SO(3) and SE(3) under the left and right actions of their respective Lie
algebras. In an infinite-dimensional example, we discuss optimal
large-deformation matching of one closed curve to another embedded in the same
plane. In the curve-matching example, the manifold \Emb(S^1, \mathbb{R}^2)
comprises the space of closed curves embedded in the plane
. The diffeomorphic left action \Diff(\mathbb{R}^2) deforms the
curve by a smooth invertible time-dependent transformation of the coordinate
system in which it is embedded, while leaving the parameterisation of the curve
invariant. The diffeomorphic right action \Diff(S^1) corresponds to a smooth
invertible reparameterisation of the domain coordinates of the curve. As
we show, this right action unlocks an important degree of freedom for
geodesically matching the curve shapes using an equivalent fixed boundary value
problem, without being constrained to match corresponding points along the
template and target curves at the endpoint in time.Comment: First version -- comments welcome
Operational LANDSAT remote sensing system development
The reduction of $121.6 million dollars from NOAA's LANDSAT development program for FY 1982, and the shortened time period for transferring remote sensing technology to the private sector resulted in changes in the Agency's plans for managing the operational system. Proposed legislation for congressional consideration or enactment to establish conditions under which this private sector transfer will occur, and the expected gradual rise in the price of data products are discussed. No money exists for capital investment and none is projected for investing in an operational data handling system for the LANDSAT D satellite. Candidates knowledgeable of various aspects of the needs and uses of remote sensing are urged to consider participation in NOAA's advisory committee
Embedded discontinuous Galerkin transport schemes with localised limiters
Motivated by finite element spaces used for representation of temperature in
the compatible finite element approach for numerical weather prediction, we
introduce locally bounded transport schemes for (partially-)continuous finite
element spaces. The underlying high-order transport scheme is constructed by
injecting the partially-continuous field into an embedding discontinuous finite
element space, applying a stable upwind discontinuous Galerkin (DG) scheme, and
projecting back into the partially-continuous space; we call this an embedded
DG scheme. We prove that this scheme is stable in L2 provided that the
underlying upwind DG scheme is. We then provide a framework for applying
limiters for embedded DG transport schemes. Standard DG limiters are applied
during the underlying DG scheme. We introduce a new localised form of
element-based flux-correction which we apply to limiting the projection back
into the partially-continuous space, so that the whole transport scheme is
bounded. We provide details in the specific case of tensor-product finite
element spaces on wedge elements that are discontinuous P1/Q1 in the horizontal
and continuous P2 in the vertical. The framework is illustrated with numerical
tests
Designing a multi-hop regular virtual topology for ultrafast optical packet switching : node placement optimisation and/or dilation minimisation?
This paper studies the design of multi-hop regular virtual topologies to facilitate optical packet switching in networks with arbitrary physical topologies. The inputs to the virtual topology design problem are the physical topology, the traffic matrix and the regular topology. In this paper, this problem is tackled directly and also by decomposition into two sub-problems. The first sub-problem, dilation minimisation, uses only the physical topology and the virtual topology as optimisation inputs. The second sub-problem considers the traffic matrix and virtual topology as optimisation inputs. The solutions of these two sub-problems are compared with each other and against the results obtained when the global problem is optimised (using all three possible input parameters) for a variety of traffic scenarios. This gives insight into the key question of whether the physical topology or the traffic matrix is the more important parameter when designing a regular virtual topology for optical packet switching. Regardless of the approach taken the problem is intractable and hence heuristics must be used to find (near) optimal solutions in reasonable time. Five different optimisation heuristics, using different artificial intelligence techniques, are employed in this paper. The results obtained by the heuristics for the three alternative design approaches are compared under a variety of traffic scenarios. An important conclusion of this paper is that the traffic matrix plays a less significant role than is conventionally assumed, and only a marginal penalty is incurred by disregarding it in several of the traffic cases considered
Singular solutions, momentum maps and computational anatomy
This paper describes the variational formulation of template matching
problems of computational anatomy (CA); introduces the EPDiff evolution
equation in the context of an analogy between CA and fluid dynamics; discusses
the singular solutions for the EPDiff equation and explains why these singular
solutions exist (singular momentum map). Then it draws the consequences of
EPDiff for outline matching problem in CA and gives numerical examples
The Square Root Depth Wave Equations
We introduce a set of coupled equations for multilayer water waves that
removes the ill-posedness of the multilayer Green-Naghdi (MGN) equations in the
presence of shear. The new well-posed equations are Hamiltonian and in the
absence of imposed background shear they retain the same travelling wave
solutions as MGN. We call the new model the Square Root Depth equations, from
the modified form of their kinetic energy of vertical motion. Our numerical
results show how the Square Root Depth equations model the effects of
multilayer wave propagation and interaction, with and without shear.Comment: 10 pages, 5 figure
Bioengineering Lantibiotics for Therapeutic Success
peer-reviewedSeveral examples of highly modified antimicrobial peptides have been described.
While many such peptides are non-ribosomally synthesized, ribosomally synthesized
equivalents are being discovered with increased frequency. Of the latter group, the
lantibiotics continue to attract most attention. In the present review, we discuss the
implementation of in vivo and in vitro engineering systems to alter, and even enhance,
the antimicrobial activity, antibacterial spectrum and physico-chemical properties,
including heat stability, solubility, diffusion and protease resistance, of these compounds.
Additionally, we discuss the potential applications of these lantibiotics for use as
therapeutics.DF,CH,PC,RR are supported by the Irish Government under the National Development Plan, through a Science Foundation Ireland (SFI) Technology and Innovation Development Award
(TIDA14/TIDA/2286) to DF, a SFI Investigator awards to CH and RR (10/IN.1/B3027),SFI-PIfunding(11/PI/1137) to PDC and the Alimentary Pharmabiotic Centre under Grant Number SFI/12/RC/2273
The Microbiota and Health Promoting Characteristics of the Fermented Beverage Kefir
peer-reviewedKefir is a complex fermented dairy product created through the symbiotic fermentation of milk by lactic acid bacteria and yeasts contained within an exopolysaccharide and protein complex called a kefir grain. As with other fermented dairy products, kefir has been associated with a range of health benefits such as cholesterol metabolism and angiotensin-converting enzyme (ACE) inhibition, antimicrobial activity, tumor suppression, increased speed of wound healing, and modulation of the immune system including the alleviation of allergy and asthma. These reports have led to increased interest in kefir as a focus of research and as a potential probiotic-containing product. Here, we review those studies with a particular emphasis on the microbial composition and the health benefits of the product, as well as discussing the further development of kefir as an important probiotic product.The authors are funded through the Teagasc Walsh Fellowship Scheme(2014025)and internal Teagasc funding(RMIS6486). BW is supported by the Canada Research Chairs Program and research in the Cotter laboratory is funded by SFI through the PI award “Obesibiotics”(11/PI/1137)and in the form of a center grant (APC Microbiome Institute Grant Number SFI/12/RC/2273)
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