The minimum cycle basis problem in a graph G = (V, E) is the task to construct a minimum length basis of its cycle vector space. A well-known algorithm by Horton of 1987 needs running time O(|V ||E| 2.376 ). We present a new combinatorial approach which generates minimum cycle bases in time O(max{|E| 3 , |E||V | 2 log|V |}) with a space requirement of (|E| 2 ). This method is especially suitable for large sparse graphs of electric engineering applications since there, typically, |E| is close to linear in |V |.

Abstract. Ring information is a large part of the structural topology used to identify and characterize molecular structures. It is hence of crucial importance to obtain this information for a variety of tasks in computational chemistry. Many different approaches for "ring perception", i.e., the extraction of cycles from a molecular graph, have been described. The chemistry literature on this topic, however, reports a surprisingly large number of incorrect statements about the properties of chemically relevant ring sets and, in particular, about the mutual relationships of different sets of cycles in a graph. In part these problems seem to have arisen from a sometimes rather idiosyncratic terminology for notions that are fairly standard in graph theory. In this contribution we translate the definitions of concepts such as the Smallest Set of Smallest Rings, Essential Set of Essential Rings, Extended Set of Smallest Rings, Set of Smallest Cycles at Edges, Set of Elementary Rings, K-rings, and β-rings into a more widely-used mathematical language. We then outline the basic properties of different cycle sets and provide numerous counterexamples to incorrect claims in the published literature. These counterexamples may have a serious practical impact because at least some of them are molecular graphs of well-known molecules. As a consequence, we propose a catalogue of desirable properties for chemically useful sets of rings.

Purpose Pelvic floor disorders are common and associated with pregnancy and childbirth. For restitution of pelvic floor connective tissue and thereby therapy of postpartum pelvic organ prolapse and stress urinary incontinence, the Restifem® pessary is approved. It supports the anterior vaginal wall behind the symphysis, the lateral sulci and the sacro-uterine ligaments and stabilises the connective tissue. We evaluated the compliance and applicability of Restifem® use in women postpartum in a preventive and therapeutic approach. Methods Restifem® pessary was handed out to 857 women. Six weeks after birth, they started the pessary use. After 8 weeks, 3 and 6 months postpartum, women received a questionnaire via online survey for evaluation of pessary applicability and efficacy. Results After 8 weeks, 209 women answered the questionnaire. 119 women used the pessary. Common problems were discomfort, pain and the pessary use was to circuitous. Vaginal infections were rare. After 3 months, 85 women and after 6 months, 38 women still used the pessary. 3 months postpartum, 94% of women with POP, 72% of women with UI and 66% of women with OAB stated to have an improvement of their symptoms using the pessary. 88% women without any disorder felt an improvement of stability. Conclusions Use of the Restifem® pessary in the postpartum period is feasible and accompanied with less complications. It reduces POP and UI and leads to an increased sense of stability. So, Restifem® pessary can be offered to women postpartum to improve pelvic floor dysfunction.

Ring structures in molecules belong to the most important substructures for many applications in Computational Chemistry. One typical task is to find an implicit description of the ring structure of a molecule. We present efficient algorithms for cyclic graph invariants that may serve as molecular descriptors to accelerate database searches. Another task is to construct a well‐defined set of rings of a molecular graph explicitly. We give a new algorithm for computing the set of relevant cycles of a graph. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(2), 116–131 2017

In the summer of 2020, we investigated the rate of inapparent shedding of SARS-CoV-2 in a representative sample of day care centers from Hesse, Germany, and found a low positivity rate during a period of low local community spread. To investigate the influence of a high local incidence setting, we conducted the SAFE KiDS 2 study. 577 children and 334 staff members of 47 daycare centers were tested for respiratory and gastrointestinal shedding of SARS-CoV-2, and three infections with SARS-CoV-2 in the infectious period were detected. We conclude that viral shedding occurred infrequently while the original "wild-type" variant was dominant. The more transmissible SARS-CoV-2 variant Alpha (B.1.1.7) became the dominant strain after the SAFE KiDS 2 was concluded. The SAFE KiDS 3 study investigated the impact of the Alpha variant of SARS-Co-2 on inapparent viral shedding in the day care setting. In this study, 756 children and 226 staff members from 46 day care centers provided self-collected saliva swabs, the so-called "Lollipop" swabs, which were tested by RT-PCR. In the four-week study period, none of the participants tested positive for SARS-CoV-2 RNA, demonstrating that inapparent shedding of SARS-CoV-2 in the day care setting was also rare during the dominance of the Alpha variant. The influence of the variant of concern Delta on day care centers has yet to be examined.