Explicit towers of Drinfeld modular curves

We give explicit equations for the simplest towers of Drinfeld modular curves over any finite field, and observe that they coincide with the asymptotically optimal towers of curves constructed by Garcia and Stichtenoth.Comment: 10 pages. For mini-symposium on "curves over finite fields and codes" at the 3rd European Congress in Barcelona 7/2000 Revised to correct minor typographical and grammatical error

Linear independence of Gamma values in positive characteristic

We investigate the arithmetic nature of special values of Thakur's function field Gamma function at rational points. Our main result is that all linear independence relations over the field of algebraic functions are consequences of the known relations of Anderson and Thakur arising from the functional equations of the Gamma function.Comment: 51 page

Modular symbols in Iwasawa theory

This survey paper is focused on a connection between the geometry of $\mathrm{GL}_d$ and the arithmetic of $\mathrm{GL}_{d-1}$ over global fields, for integers $d \ge 2$. For $d = 2$ over $\mathbb{Q}$, there is an explicit conjecture of the third author relating the geometry of modular curves and the arithmetic of cyclotomic fields, and it is proven in many instances by the work of the first two authors. The paper is divided into three parts: in the first, we explain the conjecture of the third author and the main result of the first two authors on it. In the second, we explain an analogous conjecture and result for $d = 2$ over $\mathbb{F}_q(t)$. In the third, we pose questions for general $d$ over the rationals, imaginary quadratic fields, and global function fields.Comment: 43 page

Numerical Computations with H(div)-Finite Elements for the Brinkman Problem

The H(div)-conforming approach for the Brinkman equation is studied numerically, verifying the theoretical a priori and a posteriori analysis in previous work of the authors. Furthermore, the results are extended to cover a non-constant permeability. A hybridization technique for the problem is presented, complete with a convergence analysis and numerical verification. Finally, the numerical convergence studies are complemented with numerical examples of applications to domain decomposition and adaptive mesh refinement.Comment: Minor clarifications, added references. Reordering of some figures. To appear in Computational Geosciences, final article available at http://www.springerlink.co

Interim Results of a Multicenter Trial with the New Electronic Subretinal Implant Alpha AMS in 15 Patients Blind from Inherited Retinal Degenerations

Purpose: We assessed the safety and efficacy of a technically advanced subretinal electronic implant, RETINA IMPLANT Alpha AMS, in end stage retinal degeneration in an interim analysis of two ongoing prospective clinical trials. The purpose of this article is to describe the interim functional results (efficacy). Methods: The subretinal visual prosthesis RETINA IMPLANT Alpha AMS (Retina Implant AG, Reutlingen, Germany) was implanted in 15 blind patients with hereditary retinal degenerations at four study sites with a follow-up period of 12 months (www.clinicaltrials.gov NCT01024803 and NCT02720640). Functional outcome measures included (1) screen-based standardized 2- or 4-alternative forced-choice (AFC) tests of light perception, light localization, grating detection (basic grating acuity (BaGA) test), and Landolt C-rings; (2) gray level discrimination; (3) performance during activities of daily living (ADL-table tasks). Results: Implant-mediated light perception was observed in 13/15 patients. During the observation period implant mediated localization of visual targets was possible in 13/15 patients. Correct grating detection was achieved for spatial frequencies of 0.1 cpd (cycles per degree) in 4/15; 0.33 cpd in 3/15; 0.66 cpd in 2/15; 1.0 cpd in 2/15 and 3.3 cpd in 1/15 patients. In two patients visual acuity (VA) assessed with Landolt C- rings was 20/546 and 20/1111. Of 6 possible gray levels on average 4.6 ± 0.8 (mean ± SD, n = 10) were discerned. Improvements (power ON vs. OFF) of ADL table tasks were measured in 13/15 patients. Overall, results were stable during the observation period. Serious adverse events (SAEs) were reported in 4 patients: 2 movements of the implant, readjusted in a second surgery; 4 conjunctival erosion/dehiscence, successfully treated; 1 pain event around the coil, successfully treated; 1 partial reduction of silicone oil tamponade leading to distorted vision (silicon oil successfully refilled). The majority of adverse events (AEs) were transient and mostly of mild to moderate intensity. Conclusions: Psychophysical and subjective data show that RETINA IMPLANT Alpha AMS is reliable, well tolerated and can restore limited visual functions in blind patients with degenerations of the outer retina. Compared with the previous implant Alpha IMS, longevity of the new implant Alpha AMS has been considerably improved. Alpha AMS has meanwhile been certified as a commercially available medical device, reimbursed in Germany by the public health system

The molecular hallmarks of primary and secondary vitreoretinal lymphoma

Vitreoretinal lymphoma (VRL) is a rare subtype of diffuse large B-cell lymphoma (DLBCL) considered a variant of primary central nervous system lymphoma (PCNSL). Diagnosis of VRL requires examination of vitreous fluid, but cytologic differentiation from uveitis remains difficult. Due to its rarity and difficulty in obtaining diagnostic material, little is known about the genetic profile of VRL. The aim of our study was to investigate the mutational profile of a large series of primary and secondary VRL. Targeted next generation sequencing using a custom panel containing the most frequent mutations in PCNSL was performed on 34 vitrectomy samples of 31 patients with VRL and negative controls with uveitis. In a subset of cases, genome-wide copy number alterations (CNA) were assessed using the Oncoscan platform. Mutations in MYD88 (74%), PIM1 (71%), CD79B (55%), IGLL5 (52%), TBL1XR1 (48%), ETV6 (45%) and 9p21/CDKN2A deletions (85%) were the most common alterations, with similar frequencies in primary (15), synchronous (3) or secondary (13) VRL. This mutational spectrum is similar to MYD88mut/CD79Bmut (MCD or cluster 5) DLBCL with activation of Toll-like and B-cell receptor pathways and CDKN2A loss, confirming their close relationship. Oncoscan analysis demonstrated a high number of CNAs (mean 18.6/case). Negative controls lacked mutations or CNAs. Using cell free DNA of vitreous fluid supernatant, mutations present in cellular DNA were reliably detected in all examined cases. Mutational analysis is a highly sensitive and specific tool for the diagnosis of VRL and can also be applied successfully to cell free DNA derived from the vitreous.Copyright © 2021 American Society of Hematology

Corrigendum: A MALDI-TOF MS library for rapid identification of human commensal gut bacteria from the class; Clostridia

[This corrects the article DOI: 10.3389/fmicb.2023.1104707.]

A MALDI-TOF MS library for rapid identification of human commensal gut bacteria from the class Clostridia

INTRODUCTION: Microbial isolates from culture can be identified using 16S or whole-genome sequencing which generates substantial costs and requires time and expertise. Protein fingerprinting via Matrix-assisted Laser Desorption Ionization-time of flight mass spectrometry (MALDI-TOF MS) is widely used for rapid bacterial identification in routine diagnostics but shows a poor performance and resolution on commensal bacteria due to currently limited database entries. The aim of this study was to develop a MALDI-TOF MS plugin database (CLOSTRI-TOF) allowing for rapid identification of non-pathogenic human commensal gastrointestinal bacteria. METHODS: We constructed a database containing mass spectral profiles (MSP) from 142 bacterial strains representing 47 species and 21 genera within the class Clostridia. Each strain-specific MSP was constructed using >20 raw spectra measured on a microflex Biotyper system (Bruker-Daltonics) from two independent cultures. RESULTS: For validation, we used 58 sequence-confirmed strains and the CLOSTRI-TOF database successfully identified 98 and 93% of the strains, respectively, in two independent laboratories. Next, we applied the database to 326 isolates from stool of healthy Swiss volunteers and identified 264 (82%) of all isolates (compared to 170 (52.1%) with the Bruker-Daltonics library alone), thus classifying 60% of the formerly unknown isolates. DISCUSSION: We describe a new open-source MSP database for fast and accurate identification of the Clostridia class from the human gut microbiota. CLOSTRI-TOF expands the number of species which can be rapidly identified by MALDI-TOF MS