Closure theorems with applications to entire functions with gaps

In this paper we consider questions of completeness for spaces of continuous functions on a half line which satisfy appropriate growth conditions. The results obtained have consequences in the theory of entire functions with gap power series. In particular we show that, under an appropriate gap hypothesis, the rate of growth of an entire function in the whole plane is determined by its rate of growth along any given ray

Time-weighted multi-touch attribution and channel relevance in the customer journey to online purchase

We address statistical issues in attributing revenue to marketing channels and inferring the importance of individual channels in customer journeys towards an online purchase. We describe the relevant data structures and introduce an example. We suggest an asymmetric bathtub shape as appropriate for time-weighted revenue attribution to the customer journey, provide an algorithm, and illustrate the method. We suggest a modification to this method when there is independent information available on the relative values of the channels. To infer channel importance, we employ sequential data analysis ideas and restrict to data which ends in a purchase. We propose metrics for source, intermediary, and destination channels based on twoand three-step transitions in fragments of the customer journey. We comment on the practicalities of formal hypothesis testing. We illustrate the ideas and computations using data from a major UK online retailer. Finally, we compare the revenue attributions suggested by the methods in this paper with several common attribution methods

Characterization of a reproducible model of fracture healing in mice using an open femoral osteotomy

Purpose: The classic fracture model, described by Bonnarens and Einhorn in 1984, enlists a blunt guillotine to generate a closed fracture in a pre-stabilized rodent femur. However, in less experienced hands, this technique yields considerable variability in fracture pattern and requires highly-specialized equipment. This study describes a reproducible and low-cost model of mouse fracture healing using an open femoral osteotomy. Methods: Femur fractures were produced in skeletally mature male and female mice using an open femoral osteotomy after intramedullary stabilization. Mice were recovered for up to 28 days prior to analysis with microradiographs, histomorphometry, a novel μCT methodology, and biomechanical torsion testing at weekly intervals. Results: Eight mice were excluded due to complications (8/193, 4.1%), including unacceptable fracture pattern (2/193, 1.0%). Microradiographs showed progression of the fracture site to mineralized callus by 14 days and remodelling 28 days after surgery. Histomorphometry from 14 to 28 days revealed decreased cartilage area and maintained bone area. μCT analysis demonstrated a reduction in mineral surface from 14 to 28 days, stable mineral volume, decreased strut number, and increased strut thickness. Torsion testing at 21 days showed that fractured femurs had 61% of the ultimate torque, 63% of the stiffness, and similar twist to failure when compared to unfractured contralateral femurs. Conclusions: The fracture model described herein, an open femoral osteotomy, demonstrated healing comparable to that reported using closed techniques. This simple model could be used in future research with improved reliability and reduced costs compared to the current options

Increasing thermal stress for tropical coral reefs: 1871-2017

Tropical corals live close to their upper thermal limit making them vulnerable to unusually warm summer sea temperatures. The resulting thermal stress can lead to breakdown of the coral-algal symbiosis, essential for the functioning of reefs, and cause coral bleaching. Mass coral bleaching is a modern phenomenon associated with increases in reef temperatures due to recent global warming. Widespread bleaching has typically occurred during El Nino events. We examine the historical level of stress for 100 coral reef locations with robust bleaching histories. The level of thermal stress (based on a degree heating month index, DHMI) at these locations during the 2015-2016 El Nino was unprecedented over the period 1871-2017 and exceeded that of the strong 1997-1998 El Nino. The DHMI was also 5 times the level of thermal stress associated with the 'pre-industrial', 1877-1878, El Nino. Coral reefs have, therefore, already shown their vulnerability to the modest (similar to 0.92 degrees C) global warming that has occurred to date. Estimates of future levels of thermal stress suggest that even the optimistic 1.5 degrees C Paris Agreement target is insufficient to prevent more frequent mass bleaching events for the world's reefs. Effectively, reefs of the future will not be the same as those of the past

Ultrasonic characterization of the pulmonary venous wall: echographic and histological correlation

Background: Pulmonary vein isolation with radiofrequency catheter ablation techniques is used to prevent recurrences of human atrial fibrillation. Visualization of the architecture at the venoatrial junction could be crucial for these ablative techniques. Our study assesses the potential for intravascular ultrasound to provide this information. Methods and Results: We retrieved 32 pulmonary veins from 8 patients dying from noncardiac causes. We obtained cross-sectional intravascular ultrasound (IVUS) images with a 3.2F, 30-MHz ultrasound catheter at intervals on each vein. Histological cross-sections at the intervals allowed comparisons with ultrasonic images. The pulmonary venous wall at the venoatrial junction revealed a 3-layered ultrasonic pattern. The inner echogenic layer represents both endothelium and connective tissue of the media (mean maximal thickness, 1.4±0.3 mm). The middle hypoechogenic stratum corresponds to the sleeves of left atrial myocardium surrounding the external aspect of the venous media. This layer was thickest at the venoatrial junction (mean maximal thickness, 2.6±0.8 mm) and decreased toward the lung hilum. The outer echodense layer corresponds to fibro-fatty adventitial tissue (mean maximal thickness, 2.15±0.36 mm). We found a close agreement among the IVUS and histological measurements for maximal luminal diameter (mean difference, -0.12±1.3 mm) and maximal muscular thickness (mean difference, 0.17±0.13 mm) using the Bland and Altman method. Conclusions: Our experimental study demonstrates for the first time that IVUS images of the pulmonary veins can provide information on the distal limits and thickness of the myocardial sleeves and can be a valuable tool to help accurate targeting during ablative procedures

Kondo lattice model: Unitary transformations, spin dynamics, strongly correlated charged modes, and vacuum instability

Using unitary transformations, we express the Kondo lattice Hamiltonian in terms of fermionic operators that annihilate the ground state of the interacting system and that represent the best possible approximations to the actual charged excitations. In this way, we obtain an effective Hamiltonian which, for small couplings, consists in a kinetic term for conduction electrons and holes, an RKKY-like term, and a renormalized Kondo interaction. The physical picture of the system implied by this formalism is that of a vacuum state consisting in a background of RKKY-induced spin correlations, where two kinds of elementary modes can be excited: Soft neutral modes associated with deformations of the spin liquid, which lead to very large low-temperature values of the heat capacity and magnetic susceptibility, and charged modes corresponding to the excitation of electrons and holes in the system. Using the translational and spin rotational symmetries, we construct a simple ansatz to determine the charged excitations neglecting the effects of the spin correlations. Apart from the `normal', uncorrelated states, we find strongly correlated charged modes involving soft electrons (or holes) and spin fluctuations, which strongly renormalize the low-energy charged spectrum, and whose energy becomes negative beyond a critical coupling, signaling a vacuum instability and a transition to a new phase.Comment: 35 pages, revtex 3.

Breakdown of Landau Fermi liquid properties in the 2D2D Boson-Fermion model

We study the normal state spectral properties of the fermionic excitations in the Boson-Fermion model. The fermionic single particle excitations show a flattening of the dispersion as the Fermi vector ${\bf k}_{_F}$ is approached from below, forshadowing a Bogoliubov spectrum of a superconducting ground state. The width of the quasiparticle excitations near ${\bf k}_{_F}$ increases monotonically as the temperature is lowered. In the fermionic distribution function this temperature dependence is manifest in a strong modification of $n({\bf k})$ in a small region below ${\bf k}_{_F}$, but a nearly $T$ independant $n({\bf k}_{_F})$.Comment: 10 pages, RevTeX 3.