Continued fractions and Catalan problems

We find a generating function expressed as a continued fraction that enumerates ordered trees by the number of vertices at different levels. Several Catalan problems are mapped to an ordered-tree problem and their generating functions also expressed as a continued fraction. Among these problems is the enumeration of (132)-pattern avoiding permutations that have a given number of increasing patterns of length k. This extends and illuminates a result of Robertson, Wilf and Zeilberger for the case k=3.Comment: 9 pages, 1 figur

Ultracold polarized Fermi gas at intermediate temperatures

We consider non-zero temperature properties of the polarized two-component Fermi gas. We point out that stable polarized paired states which are more stable than their phase separated counterparts with unpolarized superfluid region can exist below the critical temperature. We also solve the system behavior in a trap using the local density approximation and find gradually increasing polarization in the center of the system as the temperature is increased. However, in the strongly interacting region the central polarization increases most rapidly close to the mean-field critical temperature, which is known to be substantially higher than the critical temperature for superfluidity. This indicates that most of the phase separation occurs in the fluctuation region prior to superfluidity and that the polarization in the actual superfluid is modest.Comment: Final published versio

Composite multiple wavelength laser material and multiple wavelength laser for use therewith

A composite multiple wavelength laser material is provided and is typically constructed with a common axis of construction in the form of a rod of uniform cross-section. The rod comprises a plurality of segments of laser material bonded, e.g., diffusion bonded, to one another along the common axis. Each segment lases at a unique wavelength when excited to produce a laser emission. The segments can be made from a birefringent material doped with laser active ions. If the same birefringent host material is used for all segments, ground-state absorption losses can be reduced by terminating either end of the rod with end segments made from undoped pieces of the birefringent material

Challenges and implications of routine depression screening for depression in chronic disease and multimorbidity: a cross sectional study

<b>Background</b> Depression screening in chronic disease is advocated but its impact on routine practice is uncertain. We examine the effects of a programme of incentivised depression screening in chronic disease within a UK primary care setting.<p></p> <b>Methods and Findings</b> Cross sectional analysis of anonymised, routinely collected data (for 2008-9) from family practices in Scotland serving a population of circa 1.8 million. Patients registered in primary care with at least one of three chronic diseases, coronary heart disease, diabetes and stroke, underwent incentivised depression screening using the Hospital Anxiety and Depression Score (HADS). <p></p> 125143 patients were identified with at least one chronic disease. 10670 (8.5%) were under treatment for depression and exempt from screening. Of the remaining, HADS were recorded for 35537 (31.1%) patients. 7080 (19.9% of screened) had raised HADS (≥8); the majority had indications of mild depression with a HADS between 8 and 10. Over 6 months, 572 (8%) of those with a raised HADS (≥8) were initiated on antidepressants, while 696 (2.4%) patients with a normal HADS (<8) were also initiated on antidepressants (relative risk of antidepressant initiation with raised HADS 3.3 (CI 2.97-3.67), p value <0.0001). Of those with multimorbidity who were screened, 24.3% had a raised HADS (≥8). A raised HADS was more likely in females, socioeconomically deprived, multimorbid or younger (18-44) individuals. Females and 45-64 years old were more likely to receive antidepressants.<p></p> <b>Limitations</b> – retrospective study of routinely collected data.<p></p> <b>Conclusions </b> Despite incentivisation, only minority of patients underwent depression screening, suggesting that systematic depression screening in chronic disease can be difficult to achieve in routine practice. Targeting those at greatest risk such as the multimorbid or using simpler screening methods may be more effective. Raised HADS was associated with a higher number of new antidepressant prescriptions which has significant resource implications. The clinical benefits of such screening remain uncertain and merit investigation

Evidence of Cooper pair pumping with combined flux and voltage control

We have experimentally demonstrated pumping of Cooper pairs in a single-island mesoscopic structure. The island was connected to leads through SQUID (Superconducting Quantum Interference Device) loops. Synchronized flux and voltage signals were applied whereby the Josephson energies of the SQUIDs and the gate charge were tuned adiabatically. From the current-voltage characteristics one can see that the pumped current increases in 1e steps which is due to quasiparticle poisoning on the measurement time scale, but we argue that the transport of charge is due to Cooper pairs.Comment: 4 page

Performance Analysis of Hybrid 5G-GNSS Localization

\ua9 2018 IEEE. We consider a novel positioning solution combining millimeter wave (mmW) 5G and Global Navigation Satellite System (GNSS) technologies. The study is carried out theoretically by deriving the Fisher Information Matrix (FIM) of a combined 5G-GNSS positioning system and, subsequently, the position, rotation and clock-bias error lower bounds. We pursue a two-step approach, namely, computing first the FIM for the channel parameters, and then transforming it into the FIM of the position, rotation and clock-bias. The analysis shows advantages of the hybrid positioning in terms of i) localization accuracy, ii) coverage, iii) precise rotation estimation and iv) clock-error estimation. In other words, we demonstrate that a tight coupling of the two technologies can provide mutual benefits

A route towards stable homochiral topological textures in A-type antiferromagnets

Topologically protected whirling magnetic textures could emerge as data carriers in next-generation post-Moore computing. Such textures are abundantly observed in ferromagnets (FMs); however, their antiferromagnetic (AFM) counterparts are expected to be even more relevant for device applications, as they promise ultra-fast, deflection-free dynamics whilst being robust against external fields. Unfortunately, they have remained elusive, hence identifying materials hosting such textures is key to developing this technology. Here, we present comprehensive micromagnetic and analytical models investigating topological textures in the broad material class of A-type antiferromagnets, specifically focusing on the prototypical case of $\alpha \text{-Fe}_2 \text{O}_3$,an emerging candidate for AFM spintronics. By exploiting a symmetry breaking interfacial Dzyaloshinskii-Moriya interaction (iDMI), it is possible to stabilize a wide topological family, including AFM (anti)merons and bimerons and the hitherto undiscovered AFM skyrmions. Whilst iDMI enforces homochirality and improves the stability of these textures, the widely tunable anisotropy and exchange interactions enable unprecedented control of their core dimensions. We then present a unifying framework to model the scaling of texture sizes based on a simple dimensional analysis. As the parameters required to host and tune homochiral AFM textures may be obtained by rational materials design of $\alpha \text{-Fe}_2 \text{O}_3$, it could emerge as a promising platform to initiate AFM topological spintronics.Comment: 17 pages, 9 figures. Submitted to Physical Review

Assessment of the accuracy of 3D printed teeth by various 3D printers in forensic odontology

Additive manufacturing technology has benefited many sectors, and its use in forensic sciences has opened up a variety of new opportunities for analysing and exhibiting forensic materials. However, to perform analytical procedures on 3D printed bones and teeth in forensic odontology, the metric and morphological precision of the printed replicas must first be validated. To address this, the present study was undertaken using 12 extracted human teeth that were 3D printed using five different techniques. Manual measurements and a digital mesh comparison were used to evaluate the metric precision of all samples. The findings showed that the printed replicas were accurate to within 0.5 mm of the actual teeth. It was suggested that Digital Light Processing (DLP) prints be used for potential forensic odontology applications based on measurements, digital comparison, and ease of use

Novel Solution for Multi-connectivity 5G-mmW Positioning

\ua9 2018 IEEE. The forthcoming fifth generation (5G) systems with high beamforming gain antenna units, millimeter-wave (mmWave) frequency bands together with massive Multiple Input Multiple Output (MIMO) techniques are key components for accurate positioning methods. In this paper, we propose the positioning technique that is relying on the sparsity in the MIMO-OFDM channel in time and spatial domains, together with effective beamforming methods. We will study the proposed solution in a multi-connectivity context, which has been considered so far for the purpose of improving the user equipment (UE) communication data rate. We utilize the multi-connectivity for positioning, in order to improve robustness to measurement errors and increase positioning service continuity. In particular, we show that when a UE that has connectivity to more base stations, the total power and delay needed for positioning can be reduced