On invariant sets in Lagrangian graphs

In this exposition, we show that a Hamiltonian is always constant on a compact invariant connected subset which lies in a Lagrangian graph provided that the Hamiltonian and the graph are smooth enough. We also provide some counterexamples for the case that the Hamiltonians are not smooth enough.Comment: 4 page

Tuning the plasmonic properties of silver nanopatterns fabricated by shadow nanosphere lithography

Regular silver (Ag) nanopatterns, from disconnected nanotriangles to well coupled triangular clusters of nanoparticles, were prepared by shadow nanosphere lithography at different incident angles θ from 0 degrees to 20 degrees with continuous azimuthal rotation. The resulting nanopatterns were consistent with predictions by numerical calculations and Monte Carlo simulations of adatoms with high diffusivity. The visible localized surface plasmon resonance of these nanopatterns was tuned by θ systematically due to the change in size, shape, and arrangement of Ag nanopatterns. These resonances were consistent with finite-difference time-domain simulations using realistic nanopatterns based upon scanning electron micrographs. Such a simple fabrication strategy can be used to optimize surface enhanced Raman scattering substrate fabrication, as well as other plasmonics based applications

Using Flow Feature to Extract Pulsatile Blood Flow from 4D Flow MRI Images

4D flow MRI images make it possible to measure pulsatile blood flow inside deforming vessel, which is critical in accurate blood flow visualization, simulation, and evaluation. Such data has great potential to overcome problems in existing work, which usually does not reflect the dynamic nature of elastic vessels and blood flows in cardiac cycles. However, the 4D flow MRI data is often low-resolution and with strong noise. Due to these challenges, few efforts have been successfully conducted to extract dynamic blood flow fields and deforming artery over cardiac cycles, especially for small artery like carotid. In this paper, a robust flow feature, particularly the mean flow intensity is used to segment blood flow regions inside vessels from 4D flow MRI images in whole cardiac cycle. To estimate this flow feature more accurately, adaptive weights are added to the raw velocity vectors based on the noise strength of MRI imaging. Then, based on this feature, target arteries are tracked in at different time steps in a cardiac cycle. This method is applied to the clinical 4D flow MRI data in neck area. Dynamic vessel walls and blood flows are effectively generated in a cardiac cycle in the relatively small carotid arteries. Good image segmentation results on 2D slices are presented, together with the visualization of 3D arteries and blood flows. Evaluation of the method was performed by clinical doctors and by checking flow volume rates in the vertebral and carotid arteries

Guidelines for reporting of statistics for clinical research in urology

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/148242/1/bju14640.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/148242/2/bju14640_am.pd

Baseline Results:The Association between Cardiovascular Risk and Preclinical Alzheimer's Disease Pathology (ASCEND) Study

BACKGROUND: The rate of AD for African Americans (AAs) is 64% higher than for non-Hispanic White Americans (Whites). It is hypothesized that poor peripheral vascular function, in combination with genetics, stress, and inflammation may directly contribute to the accumulation of AD pathologic biomarkers. These risk factors may disproportionately affect AAs. OBJECTIVE: Our objective was to determine if in a healthy middle-aged cohort at risk for AD (1) AD biomarkers in CSF differ by race, (2) peripheral vascular dysfunction and cognition are related to a higher burden of CSF AD biomarkers, and (3) these relationships differ by race. METHODS: We enrolled 82 cognitively normal, middle-aged (45 and older) adults including AAs and Whites at high risk for AD due to parental history. Study procedures included lumbar puncture, vascular ultrasound, and cognitive testing. RESULTS: While participants were in overall good health, AAs exhibited poorer indices of preclinical vascular health, including higher central SBP, central MAP, and EndoPAT AI, a marker of arterial stiffness. AAs also had significantly less cerebrospinal fluid tau burden than Whites. After polynomial regression analysis, adjusted for age, gender, education, and ApoE4 status, race significantly modified the relationship between total tau, phospho-tau, and Trails B, a marker of executive function. Small differences in tau correlated with poorer cognition in AAs. CONCLUSION: In a healthy middle-aged cohort at risk for AD, AAs had worse peripheral vascular health and worse cognition than Whites. Despite lower tau burden overall, race modified the relationship between tau and cognition, such that small differences in tau between AAs was related to worse cognition when compared to Whites

The effects of degree correlations on network topologies and robustness

Complex networks have been applied to model numerous interactive nonlinear systems in the real world. Knowledge about network topology is crucial for understanding the function, performance and evolution of complex systems. In the last few years, many network metrics and models have been proposed to illuminate the network topology, dynamics and evolution. Since these network metrics and models derive from a wide range of studies, a systematic study is required to investigate the correlations between them. The present paper explores the effect of degree correlation on the other network metrics through studying an ensemble of graphs where the degree sequence (set of degrees) is fixed. We show that to some extent, the characteristic path length, clustering coefficient, modular extent and robustness of networks are directly influenced by the degree correlation.Comment: 13 pages, 6 figure

The Genomic Signature of Crop-Wild Introgression in Maize

The evolutionary significance of hybridization and subsequent introgression has long been appreciated, but evaluation of the genome-wide effects of these phenomena has only recently become possible. Crop-wild study systems represent ideal opportunities to examine evolution through hybridization. For example, maize and the conspecific wild teosinte Zea mays ssp. mexicana, (hereafter, mexicana) are known to hybridize in the fields of highland Mexico. Despite widespread evidence of gene flow, maize and mexicana maintain distinct morphologies and have done so in sympatry for thousands of years. Neither the genomic extent nor the evolutionary importance of introgression between these taxa is understood. In this study we assessed patterns of genome-wide introgression based on 39,029 single nucleotide polymorphisms genotyped in 189 individuals from nine sympatric maize-mexicana populations and reference allopatric populations. While portions of the maize and mexicana genomes were particularly resistant to introgression (notably near known cross-incompatibility and domestication loci), we detected widespread evidence for introgression in both directions of gene flow. Through further characterization of these regions and preliminary growth chamber experiments, we found evidence suggestive of the incorporation of adaptive mexicana alleles into maize during its expansion to the highlands of central Mexico. In contrast, very little evidence was found for adaptive introgression from maize to mexicana. The methods we have applied here can be replicated widely, and such analyses have the potential to greatly informing our understanding of evolution through introgressive hybridization. Crop species, due to their exceptional genomic resources and frequent histories of spread into sympatry with relatives, should be particularly influential in these studies

The Role of Dwarf Galaxy Interactions in Shaping the Magellanic System and Implications for Magellanic Irregulars

We present a novel pair of numerical models of the interaction history between the Large and Small Magellanic Clouds (LMC and SMC, respectively) and our Milky Way (MW) in light of recent high precision proper motions (Kallivayalil et al. 2006a,b). Given the new velocities, cosmological simulations of structure formation favor a scenario where the Magellanic Clouds (MCs) are currently on their first infall towards our Galaxy (Boylan-Kolchin et al. 2011, Busha et al. 2011). We illustrate here that the observed irregular morphology and internal kinematics of the MCs (in gas and stars) are naturally explained by interactions between the LMC and SMC, rather than gravitational interactions with the MW. This picture further supports a first infall scenario (Besla et a. 2007). In particular, we demonstrate that the Magellanic Stream, a band of HI gas trailing behind the MCs 150 degrees across the sky, can be accounted for by the action of LMC tides on the SMC before the system was accreted by the MW. We further demonstrate that the off-center, warped stellar bar of the LMC and its one-armed spiral, can be naturally explained by a recent direct collision with the SMC. Such structures are key morphological characteristics of a class of galaxies referred to as Magellanic Irregulars (de Vaucouleurs & Freeman 1972), the majority of which are not associated with massive spiral galaxies. We infer that dwarf-dwarf galaxy interactions are important drivers for the morphological evolution of Magellanic Irregulars and can dramatically affect the efficiency of baryon removal from dwarf galaxies via the formation of extended tidal bridges and tails. Such interactions are important not only for the evolution of dwarf galaxies but also have direct consequences for the buildup of baryons in our own MW, as LMC-mass systems are believed to be the dominant building blocks of MW-type halos.Comment: 33 pages, 21 figures, Accepted for publication in MNRAS, Dec 23 201