An explicit conductor formula for GLn×GL1{\rm GL}_n \times {\rm GL}_1

We prove an explicit formula for the conductor of an irreducible, admissible representation of ${\rm GL}_n(F)$ twisted by a character of $F^{\times}$ where the field $F$ is local and non-archimedean. As a consequence, we quantify the number of character twists of such a representation of fixed conductor

A proof of the refined Gan--Gross--Prasad conjecture for non-endoscopic Yoshida lifts

We prove a precise formula relating the Bessel period of certain automorphic forms on ${\rm GSp}_{4}(\mathbb{A}_{F})$ to a central $L$-value. This is a special case of the refined Gan--Gross--Prasad conjecture for the groups $({\rm SO}_{5},{\rm SO}_{2})$ as set out by Ichino--Ikeda and Liu. This conjecture is deep and hard to prove in full generality; in this paper we succeed in proving the conjecture for forms lifted, via automorphic induction, from ${\rm GL}_{2}(\mathbb{A}_{E})$ where $E$ is a quadratic extension of $F$. The case where $E=F\times F$ has been previously dealt with by Liu.Comment: 38 pages in Forum Mathematicum (2016

Periodontal Health of Anterior Teeth with Two Types of Fixed Retainers

Introduction: Fixed retainers for anterior teeth have become a popular method for maintaining the position and function of teeth after orthodontic treatment. Various retainer designs, wire sizes and types have been used over the years. One problem with fixed retainers is that they complicate oral hygiene and therefore might negatively affect the periodontal tissues if left in place for long periods of time. Purpose: The purpose of this study is to compare the periodontal health of maxillary and mandibular anterior teeth retained with two different types of fixed retainers. Methods: Male and female subjects who had been in continuous orthodontic fixed retention for between 2-4 years were recruited from a single, private orthodontic practice in southwestern British Columbia. The periodontal health of the anterior teeth of 39 subjects with a wave retainer and 35 subjects with a straight retainer between the ages of 13-22 were evaluated. Pocket probing depths, bleeding on probing, plaque index, calculus index, recession and gingival crevicular fluid volume were recorded and compared to determine if there was any significant difference between the two groups. Additionally, a ten-question oral hygiene survey to assess each subject\u27s oral hygiene habits was given to each subject at the time of data collection. Results: The Independent Samples Median Test and Mann-Whitney U test indicated that there was no statistically significant difference between the groups regarding plaque index, gingival crevicular fluid volume, calculus index and pocket probing depths. The Mann-Whitney U test indicated that there was no statistically significant difference in recession and bleeding on probing between the groups. The Mann-Whitney U test indicated a statistically significant difference in the reported frequency of flossing (P =0.006) and ease of flossing (P =0.000), with the wave retainer group reporting flossing more frequently and with greater ease. Using the Mann-Whitney U test there was no significant difference between the groups for reported frequency of brushing and comfort of retainer. Conclusion: Under the conditions of this study, no difference was found in the periodontal health of anterior teeth retained with a straight or wave retainer for a period of 2-4 years following orthodontic treatment. Subjects reported an increase in frequency and ease of flossing for the fixed wave retainer compared to those with a straight retainer

Innovative regenerative medicines in the EU : a better future in evidence?

Background Despite a steady stream of headlines suggesting they will transform the future of healthcare, high-tech regenerative medicines have, to date, been quite inaccessible to patients; only eight have been granted an EU marketing licence in the last seven years. Here, we outline some of the historical reasons for this paucity of licensed innovative regenerative medicines. We discuss the challenges to be overcome to expedite the development of this complex and rapidly changing area of medicine, together with possible reasons to be more optimistic for the future. Discussion Several factors have contributed to the scarcity of cutting-edge regenerative medicines in clinical practice. These include the great expense and difficulties involved in planning how individual therapies will be developed, manufactured to commercial levels, and ultimately successfully delivered to patients. Specific challenges also exist when evaluating the safety, efficacy and cost-effectiveness of these therapies. Furthermore, many treatments are used without a licence from the EMA - under “Hospital Exemption” from the EC legislation. For products which are licensed, alternative financing approaches by healthcare providers may be needed, since many therapies will have significant up-front costs but uncertain benefits and harms in the long-term. However, increasing political interest and more flexible mechanisms for licensing and paying for therapies are now evident. These could be key to the future growth and development of regenerative medicine in clinical practice. Conclusions Recent developments in regulatory processes, coupled with increasing political interest may offer some hope for improvements to the long and often difficult routes from laboratory to marketplace for leading-edge cell or tissue therapies. Collaboration between publicly-funded researchers and the pharmaceutical industry could be key to the future development of regenerative medicine in clinical practice; such collaborations might also offer a possible antidote to the innovation crisis in the pharmaceutical industry