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 $S^1$ embedded in the plane $\mathbb{R}^2$. 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 $S^1$ 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

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)

A study of immiscibility in the carbonates from the metamorphic rocks of southeastern Vermont

This problem is an attempt to correlate grade of metamorphism (normally assumed to be temperature dependent) with the shape and dimensions of a solid miscibility gap. Such a correlation might permit mapping of a continuously variable function of metamorphism. The system, calcite and dolomite-ankerite, was chosen for study because of its relative simplicity. Samples of quartz-carbonate granulite were collected from the Waits River formation in southeastern Vermont through a range of metamorphic grades. Refractive index, molecular volume, manganese content, and density were determined for the carbonates of four of these samples. These values are plotted on a compositional diagram to show the proportions of the miscibility gap for different grades of metamorphism. No measurable narrowing of the gap is demonstrated. A progressive increase with metamorphic grade in the refractive indices of calcite and ankerite was noted, and an attempt is made to explain it. Other unpredicted relations are mentioned, and a promising single crystal X-ray technique is described. Recommendations are made for further study of this problem --Abstract, page 1