Berry-Esseen bounds for nonlinear statistics, and asymptotic relative efficiency between correlation statistics

Four papers, written in collaboration with the author’s graduate school advisor, are presented. In the first paper, uniform and non-uniform Berry-Esseen (BE) bounds on the convergence to normality of a general class of nonlinear statistics are provided; novel applications to specific statistics, including the non-central Student’s, Pearson’s, and the non-central Hotelling’s, are also stated. In the second paper, a BE bound on the rate of convergence of the F-statistic used in testing hypotheses from a general linear model is given. The third paper considers the asymptotic relative efficiency (ARE) between the Pearson, Spearman, and Kendall correlation statistics; conditions sufficient to ensure that the Spearman and Kendall statistics are equally (asymptotically) efficient are provided, and several models are considered which illustrate the use of such conditions. Lastly, the fourth paper proves that, in the bivariate normal model, the ARE between any of these correlation statistics possesses certain monotonicity properties; quadratic lower and upper bounds on the ARE are stated as direct applications of such monotonicity patterns.

Leg ischemia: assessment with MR angiography and spectroscopy

PURPOSE: To prospectively determine reproducibility of magnetic resonance (MR) angiography and MR spectroscopy of deoxymyoglobin in assessment of collateral vessels and tissue perfusion in patients with critical limb ischemia (CLI) and to follow changes in patients undergoing intramuscular vascular endothelial growth factor (pVEGF)-C gene therapy, percutaneous transluminal angioplasty, supervised exercise training, or no therapy. MATERIALS AND METHODS: Study and gene therapy protocols were approved, and all patients gave written informed consent. To determine repeatability and reproducibility, seven patients underwent MR angiography and five underwent MR spectroscopy. The techniques were used to judge disease progress in 12 other patients with or without therapy: MR angiography to help determine change in visualization of collateral vessels and MR spectroscopy to help assess change in perfusion at proximal and distal calf levels. MR angiographic results were subjectively analyzed by three blinded readers. Intraobserver variability was expressed as 95% confidence interval (CI) (n=7); interobserver variability, as kappa statistic (n=15). Reexamination variability of MR spectroscopy was given as 95% CI for subsequent recovery times, and correlation with disease extent was calculated with Kendall taub rank correlation. Fisher-Yates test was used to correlate changes with pressure measurements and clinical course. RESULTS: Intraobserver and interobserver concordance was sensitive for detection of collateral vessels. Intraobserver agreement was 85.7% (95% CI: 42.1%, 99.6%). Interobserver agreement was high for small collateral vessels (kappa=0.74, P <.001) and fair for large collateral vessels (kappa=0.36, P=.002). MR spectroscopy was reproducible (95% CI: +/-26 seconds for proximal, +/-21 seconds for distal) and showed a correlation with disease extent (proximal calf, taub=0.84, P <.001; distal calf, taub=0.68, P=.04). Small collateral vessels increased over time (P=.04) but did not correlate with pressure measurements and clinical course. Recovery time correlated with clinical course (proximal calf, P=.03; distal calf, P=.005). CONCLUSION: MR angiography and MR spectroscopy of deoxymyoglobin can help document changes in visualization of collateral vessels and tissue perfusion in patients with CLI.

A Donor-Acceptor Tetrathiafulvalene Ligand Complexed to Iron(II): Synthesis, Electrochemistry, and Spectroscopy of Fe(phen)(2)(TTF-dppz)(PF6)(2)

The synthesis and photophysical properties of the complex Fe(phen)(2)(TTF-dppz)(2+) (TTF-dppz = 4',5'-bis-(propylthio)tetrathiafulvenylidipyrido3,2-a:2',3'-c-phenazine, phen = 1,10-phenanthroline) are described. In this complex, excitation into the metal ligand charge transfer bands results in the population of a high-spin state of iron(II), with a decay lifetime of approximately 1.5 ns, in dichloromethane, at room temperature. An intraligand charge transfer state can also be obtained and has a lifetime of 38 ps. A mechanism for the different states reached is proposed based on transient absorption spectroscopy.

First order mem-circuits: modeling, nonlinear oscillations and bifurcations

This paper presents a theoretical framework intended to accommodate circuit devices described by characteristics involving more than two fundamental variables. This framework is motivated by the recent appearance of a variety of so-called mem-devices in circuit theory, and makes it possible to model the coexistence of memory effects of different nature in a single device. With a compact formalism, this setting accounts for classical devices and also for circuit elements which do not admit a two-variable description. Fully nonlinear characteristics are allowed for all devices, driving the analysis beyond the framework of Chua and Di Ventra We classify these fully nonlinear circuit elements in terms of the variables involved in their constitutive relations and the notions of the differential- and the state-order of a device. We extend the notion of a topologically degenerate configuration to this broader context, and characterize the differential-algebraic index of nodal models of such circuits. Additionally, we explore certain dynamical features of mem-circuits involving manifolds of non-isolated equilibria. Related bifurcation phenomena are explored for a family of nonlinear oscillators based on mem-devices.

Variation in per capita interaction strength: Thresholds due to nonlinear dynamics and nonequilibrium conditions

I measured the strength of interaction between a marine herbivore and its growing resource over a realistic range of absolute and relative abundances. The herbivores (hermit crabs: Pagurus spp.) have slow and/or weak functional and numerical responses to epiphytic diatoms (Isthmia nervosa), which show logistic growth in the absence of consumers. By isolating this interaction in containers in the field, I mimicked many of the physical and biological variables characteristic of the intertidal while controlling the densities of focal species. The per capita effects of consumers on the population dynamics of their resource (i.e., interaction strength) were defined by using the relationship between hermit crab density and proportional change in the resource. When this relationship is fit by a Weibull function, a single parameter distinguishes constant interaction strength from one that varies as a function of density. Constant interaction strength causes the proportion of diatoms to fall linearly or proportionally as hermit crab density increases whereas per capita effects that increase with density cause an accelerating decline. Although many mathematical models of species interactions assume linear dynamics and invariant parameters, at least near equilibrium, the per capita effects of hermit crabs on diatoms varied substantially, apparently crossing a threshold from weak to strong when consumption exceeded resource production. This threshold separates a domain of coexistence from one of local extinction of the resource. Such thresholds may help explain trophic cascades, resource compensation, and context-dependent interaction strengths, while indicating a way to predict trophic effects, despite nonlinearities, as a function of vital rates.

Magnetic resonance microscopy and spectroscopy reveal kinetics of cryoprotectant permeation in a multicompartmental biological system.

Successful cryopreservation of most multicompartmental biological systems has not been achieved. One prerequisite for success is quantitative information on cryoprotectant permeation into and amongst the compartments. This report describes direct measurements of cryoprotectant permeation into a multicompartmental system using chemical shift selective magnetic resonance (MR) microscopy and MR spectroscopy. We used the developing zebrafish embryo as a model for studying these complex systems because these embryos are composed of two membrane-limited compartments: (i) a large yolk (surrounded by the yolk syncytial layer) and (ii) differentiating blastoderm cells (each surrounded by a plasma membrane). MR images of the spatial distribution of three cryoprotectants (dimethyl sulfoxide, propylene glycol, and methanol) demonstrated that methanol permeated the entire embryo within 15 min. In contrast, the other cryoprotectants exhibited little or no permeation over 2.5 h. MR spectroscopy and microinjections of cryoprotectants into the yolk inferred that the yolk syncytial layer plays a critical role in limiting the permeation of some cryoprotectants throughout the embryo. This study demonstrates the power of MR technology combined with micromanipulation for elucidating key physiological factors in cryobiology.

FR Cnc revisited: photometry, polarimetry and spectroscopy

This paper is part of a multiwavelength study aimed at using complementary photometric, polarimetric and spectroscopic data to achieve an understanding of the activity process in late-type stars. Here, we present the study of FR Cnc, a young, active and spotted star. We performed analysis of All Sky Automated Survey 3 (ASAS-3) data for the years 2002–08 and amended the value of the rotational period to be 0.826518 d. The amplitude of photometric variations decreased abruptly in the year 2005, while the mean brightness remained the same, which was interpreted as a quick redistribution of spots. BVR_C and I_C broad-band photometric calibration was performed for 166 stars in FR Cnc vicinity. The photometry at Terskol Observatory shows two brightening episodes, one of which occurred at the same phase as the flare of 2006 November 23. Polarimetric BVR observations indicate the probable presence of a supplementary source of polarization. We monitored FR Cnc spectroscopically during the years 2004–08. We concluded that the radial velocity changes cannot be explained by the binary nature of FR Cnc. We determined the spectral type of FR Cnc as K7V. Calculated galactic space-velocity components (U, V, W) indicate that FR Cnc belongs to the young disc population and might also belong to the IC 2391 moving group. Based on Li Iλ6707.8 measurement, we estimated the age of FR Cnc to be between 10 and 120 Myr. Doppler tomography was applied to create a starspot image of FR Cnc. We optimized the goodness of fit to the deconvolved profiles for axial inclination, equivalent width and v sin i, finding v sin  i=46.2 km s^−1 and i= 55°. We also generated a syntheticV-band light curve based on Doppler imaging that makes simultaneous use of spectroscopic and photometric data. This synthetic light curve displays the same morphology and amplitude as the observed one. The starspot distribution of FR Cnc is also of interest since it is one of the latest spectral types to have been imaged. No polar spot was detected on FR Cnc.

Pulse phase-coherent timing and spectroscopy of CXOU J164710.2−45521 outbursts

We present a long-term phase-coherent timing analysis and pulse-phase resolved spectroscopy for the two outbursts observed from the transient anomalous X-ray pulsar CXOU J164710.2−455216. For the first outburst we used 11 Chandra and XMM–Newton observations between 2006 September and 2009 August, the longest baseline yet for this source. We obtain a coherent timing solution with P = 10.61065583(4) s, Ṗ = 9.72(1) × 10−13 s s−1 and P̈ = –1.05(5) × 10−20 s s−2. Under the standard assumptions this implies a surface dipolar magnetic field of ∼1014 G, confirming this source as a standard B magnetar. We also study the evolution of the pulse profile (shape, intensity and pulsed fraction) as a function of time and energy. Using the phase-coherent timing solution we perform a phase-resolved spectroscopy analysis, following the spectral evolution of pulse-phase features, which hints at the physical processes taking place on the star. The results are discussed from the perspective of magnetothermal evolution models and the untwisting magnetosphere model. Finally, we present similar analysis for the second, less intense, 2011 outburst. For the timing analysis we used Swift data together with 2 XMM–Newton and Chandra pointings. The results inferred for both outbursts are compared and briefly discussed in a more general framework.

Optics and lasers : a compilation /

Cover title.

Magnetic field measurement and spectroscopy in multipole fields /

"February 1965."