Squarepants in a Tree: Sum of Subtree Clustering and Hyperbolic Pants Decomposition

We provide efficient constant factor approximation algorithms for the problems of finding a hierarchical clustering of a point set in any metric space, minimizing the sum of minimimum spanning tree lengths within each cluster, and in the hyperbolic or Euclidean planes, minimizing the sum of cluster perimeters. Our algorithms for the hyperbolic and Euclidean planes can also be used to provide a pants decomposition, that is, a set of disjoint simple closed curves partitioning the plane minus the input points into subsets with exactly three boundary components, with approximately minimum total length. In the Euclidean case, these curves are squares; in the hyperbolic case, they combine our Euclidean square pants decomposition with our tree clustering method for general metric spaces.Comment: 22 pages, 14 figures. This version replaces the proof of what is now Lemma 5.2, as the previous proof was erroneou

A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainties

This work proposes a domain adaptive stochastic collocation approach for uncertainty quantification, suitable for effective handling of discontinuities or sharp variations in the random domain. The basic idea of the proposed methodology is to adaptively decompose the random domain into subdomains. Within each subdomain, a sparse grid interpolant is constructed using the classical Smolyak construction [S. Smolyak, Quadrature and interpo- lation formulas for tensor products of certain classes of functions, Soviet Math. Dokl. 4 (1963) 240–243], to approximate the stochastic solution locally. The adaptive strategy is governed by the hierarchical surpluses, which are computed as part of the interpolation procedure. These hierarchical surpluses then serve as an error indicator for each subdo- main, and lead to subdivision whenever it becomes greater than a threshold value. The hierarchical surpluses also provide information about the more important dimensions, and accordingly the random elements can be split along those dimensions. The proposed adaptive approach is employed to quantify the effect of uncertainty in input parameters on the performance of micro-electromechanical systems (MEMS). Specifically, we study the effect of uncertain material properties and geometrical parameters on the pull-in behavior and actuation properties of a MEMS switch. Using the adaptive approach, we resolve the pull-in instability in MEMS switches. The results from the proposed approach are verified using Monte Carlo simulations and it is demonstrated that it computes the required statistics effectively

Imaging the real space structure of the spin fluctuations in an iron-based superconductor

Spin fluctuations are a leading candidate for the pairing mechanism in high temperature superconductors, supported by the common appearance of a distinct resonance in the spin susceptibility across the cuprates, iron-based superconductors and many heavy fermion materials1. The information we have about the spin resonance comes almost exclusively from neutron scattering. Here we demonstrate that by using low-temperature scanning tunneling microscopy and spectroscopy we can characterize the spin resonance in real space. We establish that inelastic tunneling leads to the characteristic "dip-hump" feature seen in tunneling spectra in high temperature superconductors and that this feature arises from excitations of the spin fluctuations. Spatial mapping of this feature near defects allows us to probe non-local properties of the spin susceptibility and to image its real space structure.Publisher PDFPeer reviewe

On the Equivalence Between Least-Squares and Kernel Approximations in Meshless Methods

Meshless methods using least-squares approximations and kernel approximations are based on non-shifted and shifted polynomial basis, respectively. We show that, mathematically, the shifted and non-shifted polynomial basis give rise to identical interpolation functions when the nodal volumes are set to unity in kernel approximations. This result indicates that mathematically the least-squares and kernel approximations are equivalent. However, for large point distributions or for higher-order polynomial basis the numerical errors with a non-shifted approach grow quickly compared to a shifted approach, resulting in violation of consistency conditions. Hence, a shifted polynomial basis is better suited from a numerical implementation point of view. Finally, we introduce an improved finite cloud method which uses a shifted polynomial basis and a fixed-kernel approximation for construction of interpolation functions and a collocation technique for discretization of the governing equations. Numerical results indicate that the improved finite cloud method exhibits superior convergence characteristics compared to our original implementation [Aluru and Li (2001)] of the finite cloud method

Impact of Iron-site defects on Superconductivity in LiFeAs

PW acknowledges funding from the MPG-UBC center and financial support from EPSRC (EP/I031014/1).In conventional s-wave superconductors, only magnetic impurities exhibit impurity bound states, whereas for an s order parameter they can occur for both magnetic and non-magnetic impurities. Impurity bound states in superconductors can thus provide important insight into the order parameter. Here, we present a combined experimental and theoretical study of native and engineered iron-site defects in LiFeAs. Detailed comparison of tunneling spectra measured on impurities with spin fluctuation theory reveals a continuous evolution from negligible impurity bound state features for weaker scattering potential to clearly detectable states for somewhat stronger scattering potentials. All bound states for these intermediate strength potentials are pinned at or close to the gap edge of the smaller gap, a phenomenon that we explain and ascribe to multi-orbital physics.PostprintPeer reviewe

Image similarity in medical images

Recent experiments have indicated a strong influence of the substrate grain orientation on the self-ordering in anodic porous alumina. Anodic porous alumina with straight pore channels grown in a stable, self-ordered manner is formed on (001) oriented Al grain, while disordered porous pattern is formed on (101) oriented Al grain with tilted pore channels growing in an unstable manner. In this work, numerical simulation of the pore growth process is carried out to understand this phenomenon. The rate-determining step of the oxide growth is assumed to be the Cabrera-Mott barrier at the oxide/electrolyte (o/e) interface, while the substrate is assumed to determine the ratio β between the ionization and oxidation reactions at the metal/oxide (m/o) interface. By numerically solving the electric field inside a growing porous alumina during anodization, the migration rates of the ions and hence the evolution of the o/e and m/o interfaces are computed. The simulated results show that pore growth is more stable when β is higher. A higher β corresponds to more Al ionized and migrating away from the m/o interface rather than being oxidized, and hence a higher retained O:Al ratio in the oxide. Experimentally measured oxygen content in the self-ordered porous alumina on (001) Al is indeed found to be about 3% higher than that in the disordered alumina on (101) Al, in agreement with the theoretical prediction. The results, therefore, suggest that ionization on (001) Al substrate is relatively easier than on (101) Al, and this leads to the more stable growth of the pore channels on (001) Al

Tear fluid biomarkers in ocular and systemic disease: potential use for predictive, preventive and personalised medicine

In the field of predictive, preventive and personalised medicine, researchers are keen to identify novel and reliable ways to predict and diagnose disease, as well as to monitor patient response to therapeutic agents. In the last decade alone, the sensitivity of profiling technologies has undergone huge improvements in detection sensitivity, thus allowing quantification of minute samples, for example body fluids that were previously difficult to assay. As a consequence, there has been a huge increase in tear fluid investigation, predominantly in the field of ocular surface disease. As tears are a more accessible and less complex body fluid (than serum or plasma) and sampling is much less invasive, research is starting to focus on how disease processes affect the proteomic, lipidomic and metabolomic composition of the tear film. By determining compositional changes to tear profiles, crucial pathways in disease progression may be identified, allowing for more predictive and personalised therapy of the individual. This article will provide an overview of the various putative tear fluid biomarkers that have been identified to date, ranging from ocular surface disease and retinopathies to cancer and multiple sclerosis. Putative tear fluid biomarkers of ocular disorders, as well as the more recent field of systemic disease biomarkers, will be shown

Novel Mannich bases bearing pyrazolone moiety. Synthesis, characterization and electrochemical studies

The present investigation describes a series of new {4-[3-Methyl-5-oxo-4-(4|-substituted phenyl hydrazono)-4,5-dihydro-pyrazol-1-yl]-phenoxy}-acetic acid (2-oxo-1-piperidine-1-ylmethyl-1,2-dihydro–indol-3-ylidene)-hydrazides synthesized by the Mannich reaction of {4-[3-Methyl-5-oxo-4-(4|-substituted phenyl hydrazono)-4,5-dihydro-pyrazol-1-yl]-phenoxy}-acetic acid (2-oxo-1,2-dihydro-indol-3-ylidene)-hydrazide with aqueous formaldehyde and a solution of piperidine in dimethylformamide. These novel Mannich bases were characterized by elemental analysis, IR, 1H NMR and mass spectral data. Electrochemical behavior of these compounds were studied by two techniques namely polarography and cyclic voltammetry. The results from both the techniques were compared and the reduction mechanism in acidic as well as basic medium was proposed

Optimality regions and fluctuations for Bernoulli last passage models

We study the sequence alignment problem and its independent version,the discrete Hammersley process with an exploration penalty. We obtain rigorous upper bounds for the number of optimality regions in both models near the soft edge.At zero penalty the independent model becomes an exactly solvable model and we identify cases for which the law of the last passage time converges to a Tracy-Widom law

Quasiharmonic models for the calculation of thermodynamic properties of crystalline silicon under strain,

Quasiharmonic models with Tersoff ͓Phys. Rev. B 38, 9902 ͑1988͔͒ interatomic potential are used to study the thermodynamic properties of crystalline silicon. It is shown that, compared to the molecular dynamics simulation data, the reciprocal space quasiharmonic model accurately predicts the thermal properties for temperatures up to 800 K. For higher temperatures, anharmonic effects become significant. With a significantly higher computational cost, the results from the real space quasiharmonic model approach the results from the reciprocal space quasiharmonic model as the number of atoms increases. The local quasiharmonic model does not accurately describe the thermal properties as it neglects the vibrational coupling of the atoms. We also investigate the effect of the strain on the thermodynamic properties. The variation of the thermodynamic properties with temperature under a tension, compression, and a shear deformation state is computed