On averaging, reduction, and symmetry in hamiltonian systems

AbstractThe existence of periodic orbits for Hamiltonian systems at low positive energies can be deduced from the existence of nondegenerate critical points of an averaged Hamiltonian on an associated “reduced space.” Alternatively, in classical (kinetic plus potential energy) Hamiltonians the existence of such orbits can often be established by elementary geometrical arguments. The present paper unifies the two approaches by exploiting discrete symmetries, including reversing diffeomorphisms, that occur in a given system. The symmetries are used to locate the periodic orbits in the averaged Hamiltonian, and thence in the original Hamiltonian when the periodic orbits are continued under perturbations admitting the same symmetries. In applications to the Hénon-Heiles Hamiltonian, it is illustrated how “higher order” averaging can sometimes be used to overcome degeneracies encountered at first order

Modal Analysis and Coupling in Metal-Insulator-Metal Waveguides

This paper shows how to analyze plasmonic metal-insulator-metal waveguides using the full modal structure of these guides. The analysis applies to all frequencies, particularly including the near infrared and visible spectrum, and to a wide range of sizes, including nanometallic structures. We use the approach here specifically to analyze waveguide junctions. We show that the full modal structure of the metal-insulator-metal (MIM) waveguides--which consists of real and complex discrete eigenvalue spectra, as well as the continuous spectrum--forms a complete basis set. We provide the derivation of these modes using the techniques developed for Sturm-Liouville and generalized eigenvalue equations. We demonstrate the need to include all parts of the spectrum to have a complete set of basis vectors to describe scattering within MIM waveguides with the mode-matching technique. We numerically compare the mode-matching formulation with finite-difference frequency-domain analysis and find very good agreement between the two for modal scattering at symmetric MIM waveguide junctions. We touch upon the similarities between the underlying mathematical structure of the MIM waveguide and the PT symmetric quantum mechanical pseudo-Hermitian Hamiltonians. The rich set of modes that the MIM waveguide supports forms a canonical example against which other more complicated geometries can be compared. Our work here encompasses the microwave results, but extends also to waveguides with real metals even at infrared and optical frequencies.Comment: 17 pages, 13 figures, 2 tables, references expanded, typos fixed, figures slightly modifie

Developmental origin underlies evolutionary rate variation across the placental skull

The placental skull has evolved into myriad forms, from longirostrine whales to globular primates, and with a diverse array of appendages from antlers to tusks. This disparity has recently been studied from the perspective of the whole skull, but the skull is composed of numerous elements that have distinct developmental origins and varied functions. Here, we assess the evolution of the skull's major skeletal elements, decomposed into 17 individual regions. Using a high-dimensional morphometric approach for a dataset of 322 living and extinct eutherians (placental mammals and their stem relatives), we quantify patterns of variation and estimate phylogenetic, allometric and ecological signal across the skull. We further compare rates of evolution across ecological categories and ordinal-level clades and reconstruct rates of evolution along lineages and through time to assess whether developmental origin or function discriminate the evolutionary trajectories of individual cranial elements. Our results demonstrate distinct macroevolutionary patterns across cranial elements that reflect the ecological adaptations of major clades. Elements derived from neural crest show the fastest rates of evolution, but ecological signal is equally pronounced in bones derived from neural crest and paraxial mesoderm, suggesting that developmental origin may influence evolutionary tempo, but not capacity for specialisation. This article is part of the theme issue 'The mammalian skull: development, structure and function'

Genetic Analysis of Hematological Parameters in Incipient Lines of the Collaborative Cross

Hematological parameters, including red and white blood cell counts and hemoglobin concentration, are widely used clinical indicators of health and disease. These traits are tightly regulated in healthy individuals and are under genetic control. Mutations in key genes that affect hematological parameters have important phenotypic consequences, including multiple variants that affect susceptibility to malarial disease. However, most variation in hematological traits is continuous and is presumably influenced by multiple loci and variants with small phenotypic effects. We used a newly developed mouse resource population, the Collaborative Cross (CC), to identify genetic determinants of hematological parameters. We surveyed the eight founder strains of the CC and performed a mapping study using 131 incipient lines of the CC. Genome scans identified quantitative trait loci for several hematological parameters, including mean red cell volume (Chr 7 and Chr 14), white blood cell count (Chr 18), percent neutrophils/lymphocytes (Chr 11), and monocyte number (Chr 1). We used evolutionary principles and unique bioinformatics resources to reduce the size of candidate intervals and to view functional variation in the context of phylogeny. Many quantitative trait loci regions could be narrowed sufficiently to identify a small number of promising candidate genes. This approach not only expands our knowledge about hematological traits but also demonstrates the unique ability of the CC to elucidate the genetic architecture of complex traits

Developmental origin underlies evolutionary rate variation across the placental skull

The placental skull has evolved into myriad forms, from longirostrine whales to globular primates, and with a diverse array of appendages from antlers to tusks. This disparity has recently been studied from the perspective of the whole skull, but the skull is composed of numerous elements that have distinct developmental origins and varied functions. Here, we assess the evolution of the skull's major skeletal elements, decomposed into 17 individual regions. Using a high-dimensional morphometric approach for a dataset of 322 living and extinct eutherians (placental mammals and their stem relatives), we quantify patterns of variation and estimate phylogenetic, allometric and ecological signal across the skull. We further compare rates of evolution across ecological categories and ordinal-level clades and reconstruct rates of evolution along lineages and through time to assess whether developmental origin or function discriminate the evolutionary trajectories of individual cranial elements. Our results demonstrate distinct macroevolutionary patterns across cranial elements that reflect the ecological adaptations of major clades. Elements derived from neural crest show the fastest rates of evolution, but ecological signal is equally pronounced in bones derived from neural crest and paraxial mesoderm, suggesting that developmental origin may influence evolutionary tempo, but not capacity for specialisation. This article is part of the theme issue 'The mammalian skull: development, structure and function'

Double quantum dot with integrated charge sensor based on Ge/Si heterostructure nanowires

Coupled electron spins in semiconductor double quantum dots hold promise as the basis for solid-state qubits. To date, most experiments have used III-V materials, in which coherence is limited by hyperfine interactions. Ge/Si heterostructure nanowires seem ideally suited to overcome this limitation: the predominance of spin-zero nuclei suppresses the hyperfine interaction and chemical synthesis creates a clean and defect-free system with highly controllable properties. Here we present a top gate-defined double quantum dot based on Ge/Si heterostructure nanowires with fully tunable coupling between the dots and to the leads. We also demonstrate a novel approach to charge sensing in a one-dimensional nanostructure by capacitively coupling the double dot to a single dot on an adjacent nanowire. The double quantum dot and integrated charge sensor serve as an essential building block required to form a solid-state spin qubit free of nuclear spin.Comment: Related work at http://marcuslab.harvard.edu and http://cmliris.harvard.ed

Teaching tobacco dependence treatment and counseling skills during medical school: rationale and design of the Medical Students helping patients Quit tobacco (MSQuit) group randomized controlled trial

INTRODUCTION: Physician-delivered tobacco treatment using the 5As is clinically recommended, yet its use has been limited. Lack of adequate training and confidence to provide tobacco treatment is cited as leading reasons for limited 5A use. Tobacco dependence treatment training while in medical school is recommended, but is minimally provided. The MSQuit trial (Medical Students helping patients Quit tobacco) aims to determine if a multi-modal and theoretically-guided tobacco educational intervention will improve tobacco dependence treatment skills (i.e. 5As) among medical students. METHODS/DESIGN: 10 U.S. medical schools were pair-matched and randomized in a group-randomized controlled trial to evaluate whether a multi-modal educational (MME) intervention compared to traditional education (TE) will improve observed tobacco treatment skills. MME is primarily composed of TE approaches (i.e. didactics) plus a 1st year web-based course and preceptor-facilitated training during a 3rd year clerkship rotation. The primary outcome measure is an objective score on an Objective Structured Clinical Examination (OSCE) tobacco-counseling smoking case among 3rd year medical students from schools who implemented the MME or TE. DISCUSSION: MSQuit is the first randomized to evaluate whether a tobacco treatment educational intervention implemented during medical school will improve medical students\u27 tobacco treatment skills. We hypothesize that the MME intervention will better prepare students in tobacco dependence treatment as measured by the OSCE. If a comprehensive tobacco treatment educational learning approach is effective, while also feasible and acceptable to implement, then medical schools may substantially influence skill development and use of the 5As among future physicians. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved

The Persistence of Cool Galactic Winds in High Stellar Mass Galaxies Between z~1.4 and ~1

We present an analysis of the MgII 2796, 2803 and FeII 2586, 2600 absorption line profiles in coadded spectra of 468 galaxies at 0.7 < z < 1.5. The galaxy sample, drawn from the Team Keck Treasury Redshift Survey of the GOODS-N field, has a range in stellar mass (M_*) comparable to that of the sample at z~1.4 analyzed in a similar manner by Weiner et al. (2009; W09), but extends to lower redshifts and has specific star formation rates which are lower by ~0.6 dex. We identify outflows of cool gas from the Doppler shift of the MgII absorption lines and find that the equivalent width (EW) of absorption due to outflowing gas increases on average with M_* and star formation rate (SFR). We attribute the large EWs measured in spectra of the more massive, higher-SFR galaxies to optically thick absorbing clouds having large velocity widths. The outflows have hydrogen column densities N(H) > 10^19.3 cm^-2, and extend to velocities of ~500 km/s. While galaxies with SFR > 10 Msun/yr host strong outflows in both this and the W09 sample, we do not detect outflows in lower-SFR (i.e., log M_*/Msun < 10.5) galaxies at lower redshifts. Using a simple galaxy evolution model which assumes exponentially declining SFRs, we infer that strong outflows persist in galaxies with log M_*/Msun > 10.5 as they age between z=1.4 and z~1, presumably because of their high absolute SFRs. Finally, using high resolution HST/ACS imaging in tandem with our spectral analysis, we find evidence for a weak trend (at 1 sigma significance) of increasing outflow absorption strength with increasing galaxy SFR surface density.Comment: Submitted to ApJ. 25 pages, 19 figures, Figure 2 reduced in resolution. Uses emulateapj forma

Altered growth characteristics of skin fibroblasts from wild-derived mice, and genetic loci regulating fibroblast clone size

Mouse fibroblast senescence in vitro is an important model for the study of aging at cellular level. However, common laboratory mouse strains may have lost some important allele variations related to aging processes. In this study, growth in vitro of tail skin fibroblasts (TSFs) derived from a wild-derived stock, Pohnpei (Pohn) mice, differed from growth of control C57BL/6 J (B6) TSFs. Pohn TSFs exhibited higher proliferative ability, fewer apoptotic cells, decreased expression of Cip1 , smaller surface areas, fewer cells positive for senescence associated-β-galactosidase (SA-β-gal) and greater resistance to H 2 O 2 -induced SA-β-gal staining and Cip1 expression. These data suggest that TSFs from Pohn mice resist cellular senescence-like changes. Using large clone ratio (LCR) as the phenotype, a quantitative trait locus (QTL) analysis in a Pohn/B6 backcross population found four QTLs for LCR: Fcs1 on Chr 3 at 55 cm; Fcs2 on Chr X at 50 cm; Fcs3 on Chr 4 at 51 cm and Fcs4 on Chr 10 at 25 cm. Together, these four QTLs explain 26.1% of the variations in LCRs in the N2 population. These are the first QTLs reported that regulate fibroblast growth. Glutathione S transferase mu ( GST-mu ) genes are overrepresented in the 95% confidence interval of Fcs1 , and Pohn TSFs have higher H 2 O 2 -induced GST-mu 4 , 5 and 7 mRNA levels than B6 TSFs. These enzymes may protect Pohn TSFs from oxidation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71416/1/j.1474-9726.2006.00208.x.pd