Action-gradient-minimizing pseudo-orbits and almost-invariant tori

Transport in near-integrable, but partially chaotic, $1 1/2$ degree-of-freedom Hamiltonian systems is blocked by invariant tori and is reduced at \emph{almost}-invariant tori, both associated with the invariant tori of a neighboring integrable system. "Almost invariant" tori with rational rotation number can be defined using continuous families of periodic \emph{pseudo-orbits} to foliate the surfaces, while irrational-rotation-number tori can be defined by nesting with sequences of such rational tori. Three definitions of "pseudo-orbit," \emph{action-gradient--minimizing} (AGMin), \emph{quadratic-flux-minimizing} (QFMin) and \emph{ghost} orbits, based on variants of Hamilton's Principle, use different strategies to extremize the action as closely as possible. Equivalent Lagrangian (configuration-space action) and Hamiltonian (phase-space action) formulations, and a new approach to visualizing action-minimizing and minimax orbits based on AGMin pseudo-orbits, are presented.Comment: Accepted for publication in a special issue of Communications in Nonlinear Science and Numerical Simulation (CNSNS) entitled "The mathematical structure of fluids and plasmas : a volume dedicated to the 60th birthday of Phil Morrison

Exceptional collections and D-branes probing toric singularities

We demonstrate that a strongly exceptional collection on a singular toric surface can be used to derive the gauge theory on a stack of D3-branes probing the Calabi-Yau singularity caused by the surface shrinking to zero size. A strongly exceptional collection, i.e., an ordered set of sheaves satisfying special mapping properties, gives a convenient basis of D-branes. We find such collections and analyze the gauge theories for weighted projective spaces, and many of the Y^{p,q} and L^{p,q,r} spaces. In particular, we prove the strong exceptionality for all p in the Y^{p,p-1} case, and similarly for the Y^{p,p-2r} case.Comment: 49 pages, 6 figures; v2 refs added; v3 published versio

Systematic model behavior of adsorption on flat surfaces

A low density film on a flat surface is described by an expansion involving the first four virial coefficients. The first coefficient (alone) yields the Henry's law regime, while the next three correct for the effects of interactions. The results permit exploration of the idea of universal adsorption behavior, which is compared with experimental data for a number of systems

Identification of novel miRNAs involved in cardiac repair following infarction in fetal and adolescent sheep hearts

Aims:Animal models have been used to show that there are critical molecular mechanisms that can be activated to induce myocardial repair at specific times in development. For example, specific miRNAs are critical for regulating the response to myocardial infarction (MI) and improving the response to injury. Manipulating these miRNAs in small animal models provides beneficial effects post-MI; however it is not known if these miRNAs are regulated similarly in large mammals. Studying a large animal where the timing of heart development in relation to birth is similar to humans may provide insights to better understand the capacity to repair a developing mammalian heart and its application to the adult heart. Methods:We used a sheep model of MI that included permanent ligation of the left anterior descending (LAD) coronary artery. Surgery was performed on fetuses (at 105 days gestation when all cardiomyocytes are mononucleated and proliferative) and adolescent sheep (at 6 months of age when all cardiomyocytes contribute to heart growth by hypertrophy). A microarray was utilized to determine the expression of known miRNAs within the damaged and undamaged tissue regions in fetal and adolescent hearts after MI. Results:73 miRNAs were up-regulated and 58 miRNAs were down-regulated significantly within the fetal infarct compared to remote cardiac samples. From adolescent hearts 69 non-redundant miRNAs were up-regulated and 63 miRNAs were down-regulated significantly in the infarct area compared to remote samples. Opposite differential expression profiles of 10 miRNAs within tissue regions (Infarct area, Border zone and Remote area of the left ventricle) occurred between the fetuses and adolescent sheep. These included miR-558 and miR-1538, which when suppressed using LNA anti-miRNAs in cell culture, increased cardiomyoblast proliferation. Conclusion:There were significant differences in miRNA responses in fetal and adolescent sheep hearts following a MI, suggesting that the modulation of novel miRNA expression may have therapeutic potential, by promoting proliferation or repair in a damaged heart.Mitchell C. Lock, Ross L. Tellam, Jack R. T. Darby, Jia Yin Soo, Doug A. Brooks, Mike Seed ... et al

Long-lived oscillons from asymmetric bubbles

The possibility that extremely long-lived, time-dependent, and localized field configurations (``oscillons'') arise during the collapse of asymmetrical bubbles in 2+1 dimensional phi^4 models is investigated. It is found that oscillons can develop from a large spectrum of elliptically deformed bubbles. Moreover, we provide numerical evidence that such oscillons are: a) circularly symmetric; and b) linearly stable against small arbitrary radial and angular perturbations. The latter is based on a dynamical approach designed to investigate the stability of nonintegrable time-dependent configurations that is capable of probing slowly-growing instabilities not seen through the usual ``spectral'' method.Comment: RevTeX 4, 9 pages, 11 figures. Revised version with a new approach to stability. Accepted to Phys. Rev.

Evaluation of the EQ-5D-5L, EQ-VAS stand-alone component and Oxford knee score in the Australian knee arthroplasty population utilising minimally important difference, concurrent validity, predictive validity and responsiveness

Published online: 10 May 2023Purpose: To evaluate the Oxford Knee Score (OKS), EQ-5D-5L utility index and EQ-5D visual analogue scale (EQ-VAS) for health-related quality of life outcome measurement in patients undergoing elective total knee arthroplasty (TKA) surgery. Methods: In this prospective multi-centre study, the OKS and EQ-5D-5L index scores were collected preoperatively, six weeks (6w) and six months (6 m) following TKA. The OKS, EQ-VAS and EQ-5D-5L index were evaluated for minimally important difference (MID), concurrent validity, predictive validity (Spearman's Rho of predicted and observed values from a generalised linear regression model (GLM)), responsiveness (effect size (ES) and standard response mean (SRM)). The MID for the individual patient was determined utilising two approaches; distribution-based and anchor-based. Results: 533 patients were analysed. The EQ-5D-5L utility index showed good concurrent validity with the OKS (r = 0.72 preoperatively, 0.65 at 6w and 0.69 at 6 m). Predictive validity for the EQ-5D-5L index was lower than OKS when regressed. Responsiveness was large for all fields at 6w for the EQ-5D-5L and OKS (EQ-5D-5L ES 0.87, SRM 0.84; OKS ES 1.35, SRM 1.05) and 6 m (EQ-5D-5L index ES 1.31, SRM 0.95; OKS ES 1.69, SRM 1.59). The EQ-VAS returned poorer results, at 6w an ES of 0.37 (small) and SRM of 0.36 (small). At 6 m, the EQ-VAS had an ES of 0.59 (moderate) and SRM of 0.47 (small). It, however, had similar predictive validity to the OKS, and better than the EQ-5D-5L index. MID determined using anchor approach, was shown that for OKS at 6 weeks it was 8.84 ± 9.28 and at 6 months 13.37 ± 9.89. For the EQ-5D-5L index at 6 weeks MID was 0.23 ± 0.39, and at 6 months 0.26 ± 0.36. Conclusions: The EQ-5D-5L index score and the OKS demonstrate good concurrent validity. The EQ-5D-5L index demonstrated lower predictive validity at 6w, and 6 m than the OKS, and both PROMs had adequate responsiveness. The EQ-VAS had poorer responsiveness but better predictive validity than the EQ-5D-5L index. This article includes MID estimates for the Australian knee arthroplasty population.D-Yin Lin, Tim Soon Cheok, Billingsley Kaambwa, Anthony J. Samson, Craig Morrison, Teik Chan, Hidde M. Kroon and Ruurd L. Jaarsm

Spacetime singularity resolution by M-theory fivebranes: calibrated geometry, Anti-de Sitter solutions and special holonomy metrics

The supergravity description of various configurations of supersymmetric M-fivebranes wrapped on calibrated cycles of special holonomy manifolds is studied. The description is provided by solutions of eleven-dimensional supergravity which interpolate smoothly between a special holonomy manifold and an event horizon with Anti-de Sitter geometry. For known examples of Anti-de Sitter solutions, the associated special holonomy metric is derived. One explicit Anti-de Sitter solution of M-theory is so treated for fivebranes wrapping each of the following cycles: K\"{a}hler cycles in Calabi-Yau two-, three- and four-folds; special lagrangian cycles in three- and four-folds; associative three- and co-associative four-cycles in $G_2$ manifolds; complex lagrangian four-cycles in $Sp(2)$ manifolds; and Cayley four-cycles in $Spin(7)$ manifolds. In each case, the associated special holonomy metric is singular, and is a hyperbolic analogue of a known metric. The analogous known metrics are respectively: Eguchi-Hanson, the resolved conifold and the four-fold resolved conifold; the deformed conifold, and the Stenzel four-fold metric; the Bryant-Salamon-Gibbons-Page-Pope $G_2$ metrics on an $\mathbb{R}^4$ bundle over $S^3$, and an $\mathbb{R}^3$ bundle over $S^4$ or $\mathbb{CP}^2$; the Calabi hyper-K\"{a}hler metric on $T^*\mathbb{CP}^2$; and the Bryant-Salamon-Gibbons-Page-Pope $Spin(7)$ metric on an $\mathbb{R}^4$ bundle over $S^4$. By the AdS/CFT correspondence, a conformal field theory is associated to each of the new singular special holonomy metrics, and defines the quantum gravitational physics of the resolution of their singularities.Comment: 1+52 page

The Vlasov limit and its fluctuations for a system of particles which interact by means of a wave field

In two recent publications [Commun. PDE, vol.22, p.307--335 (1997), Commun. Math. Phys., vol.203, p.1--19 (1999)], A. Komech, M. Kunze and H. Spohn studied the joint dynamics of a classical point particle and a wave type generalization of the Newtonian gravity potential, coupled in a regularized way. In the present paper the many-body dynamics of this model is studied. The Vlasov continuum limit is obtained in form equivalent to a weak law of large numbers. We also establish a central limit theorem for the fluctuations around this limit.Comment: 68 pages. Smaller corrections: two inequalities in sections 3 and two inequalities in section 4, and definition of a Banach space in appendix A1. Presentation of LLN and CLT in section 4.3 improved. Notation improve