Word Length Perturbations in Certain Symmetric Presentations of Dihedral Groups

Given a finite group with a generating subset there is a well-established notion of length for a group element given in terms of its minimal length expression as a product of elements from the generating set. Recently, certain quantities called $\lambda_{1}$ and $\lambda_{2}$ have been defined that allow for a precise measure of how stable a group is under certain types of small perturbations in the generating expressions for the elements of the group. These quantities provide a means to measure differences among all possible paths in a Cayley graph for a group, establish a group theoretic analog for the notion of stability in nonlinear dynamical systems, and play an important role in the application of groups to computational genomics. In this paper, we further expose the fundamental properties of $\lambda_{1}$ and $\lambda_{2}$ by establishing their bounds when the underlying group is a dihedral group. An essential step in our approach is to completely characterize so-called symmetric presentations of the dihedral groups, providing insight into the manner in which $\lambda_{1}$ and $\lambda_{2}$ interact with finite group presentations. This is of interest independent of the study of the quantities $\lambda_{1},\; \lambda_{2}$. Finally, we discuss several conjectures and open questions for future consideration

Oral malodor in Special Care Patients: current knowledge

Epidemiological studies report that about 50% of the population may have oral malodor with a strong social and psychological impact in their daily life. When intra-oral causes are excluded, referral to an appropriate medical specialist is paramount for management and treatment of extra-oral causes. The intra-oral causes of halitosis are highly common, and the dentist is the central clinician to diagnose and treat them. Pseudohalitosis or halitophobia may occur and an early identification of these conditions by the dentist is important in order to avoid unnecessary dental treatments for patients who need psychological or psychiatric therapy. The organoleptic technique is still considered the most reliable examination method to diagnose genuine halitosis. Special needs patients are more prone than others to have oral malodor because of concurrent systemic or metabolic diseases, and medications. The present report reviews halitosis, its implications, and the management in special care dentistry

Crowdsourcing Linked Data on listening experiences through reuse and enhancement of library data

Research has approached the practice of musical reception in a multitude of ways, such as the analysis of professional critique, sales figures and psychological processes activated by the act of listening. Studies in the Humanities, on the other hand, have been hindered by the lack of structured evidence of actual experiences of listening as reported by the listeners themselves, a concern that was voiced since the early Web era. It was however assumed that such evidence existed, albeit in pure textual form, but could not be leveraged until it was digitised and aggregated. The Listening Experience Database (LED) responds to this research need by providing a centralised hub for evidence of listening in the literature. Not only does LED support search and reuse across nearly 10,000 records, but it also provides machine-readable structured data of the knowledge around the contexts of listening. To take advantage of the mass of formal knowledge that already exists on the Web concerning these contexts, the entire framework adopts Linked Data principles and technologies. This also allows LED to directly reuse open data from the British Library for the source documentation that is already published. Reused data are re-published as open data with enhancements obtained by expanding over the model of the original data, such as the partitioning of published books and collections into individual stand-alone documents. The database was populated through crowdsourcing and seamlessly incorporates data reuse from the very early data entry phases. As the sources of the evidence often contain vague, fragmentary of uncertain information, facilities were put in place to generate structured data out of such fuzziness. Alongside elaborating on these functionalities, this article provides insights into the most recent features of the latest instalment of the dataset and portal, such as the interlinking with the MusicBrainz database, the relaxation of geographical input constraints through text mining, and the plotting of key locations in an interactive geographical browser

Higher-order Laguerre-Gauss interferometry for gravitational-wave detectors with in situ mirror defects compensation

The use of higher-order Laguerre-Gauss modes has been proposed to decrease the influence of thermal noise in future generation gravitational-wave interferometric detectors. The main obstacle for their implementation is the degeneracy of modes with same order, which highly increases the requirements on the mirror defects, beyond the state-of-the-art polishing and coating techniques. In order to increase the mirror surface quality, it is also possible to act in situ, using a thermal source, sent on the mirrors after a proper shaping. In this paper we present the results obtained on a tabletop Fabry-Pérot Michelson interferometer illuminated with a LG_(3,3) mode. We show how an incoherent light source can reduce the astigmatism of one of the mirrors, increasing the quality of the beam in one of the Fabry-Pérot cavities and then the contrast of the interferometer. The system has the potential to reduce more complex defects and also to be used in future gravitational-wave detectors using conventional Gaussian beams

Surgical site infection after caesarean section. Space for post-discharge surveillance improvements and reliable comparisons

Surgical site infections (SSI) after caesarean section (CS) represent a substantial health system concern. Surveying SSI has been associated with a reduction in SSI incidence. We report the findings of three (2008, 2011 and 2013) regional active SSI surveillances after CS in community hospital of the Latium region determining the incidence of SSI. Each CS was surveyed for SSI occurrence by trained staff up to 30 post-operative days, and association of SSI with relevant characteristics was assessed using binomial logistic regression. A total of 3,685 CS were included in the study. A complete 30 day post-operation follow-up was achieved in over 94% of procedures. Overall 145 SSI were observed (3.9% cumulative incidence) of which 131 (90.3%) were superficial and 14 (9.7%) complex (deep or organ/space) SSI; overall 129 SSI (of which 89.9% superficial) were diagnosed post-discharge. Only higher NNIS score was significantly associated with SSI occurrence in the regression analysis. Our work provides the first regional data on CS-associated SSI incidence, highlighting the need for a post-discharge surveillance which should assure 30 days post-operation to not miss data on complex SSI, as well as being less labour intensive

Reconstruction of the gravitational wave signal h(t)h(t) during the Virgo science runs and independent validation with a photon calibrator

The Virgo detector is a kilometer-scale interferometer for gravitational wave detection located near Pisa (Italy). About 13 months of data were accumulated during four science runs (VSR1, VSR2, VSR3 and VSR4) between May 2007 and September 2011, with increasing sensitivity. In this paper, the method used to reconstruct, in the range 10 Hz-10 kHz, the gravitational wave strain time series $h(t)$ from the detector signals is described. The standard consistency checks of the reconstruction are discussed and used to estimate the systematic uncertainties of the $h(t)$ signal as a function of frequency. Finally, an independent setup, the photon calibrator, is described and used to validate the reconstructed $h(t)$ signal and the associated uncertainties. The uncertainties of the $h(t)$ time series are estimated to be 8% in amplitude. The uncertainty of the phase of $h(t)$ is 50 mrad at 10 Hz with a frequency dependence following a delay of 8 $\mu$s at high frequency. A bias lower than $4\,\mathrm{\mu s}$ and depending on the sky direction of the GW is also present.Comment: 35 pages, 16 figures. Accepted by CQ

Search for Eccentric Binary Black Hole Mergers with Advanced LIGO and Advanced Virgo during Their First and Second Observing Runs

When formed through dynamical interactions, stellar-mass binary black holes (BBHs) may retain eccentric orbits (e > 0.1 at 10 Hz) detectable by ground-based gravitational-wave detectors. Eccentricity can therefore be used to differentiate dynamically formed binaries from isolated BBH mergers. Current template-based gravitational-wave searches do not use waveform models associated with eccentric orbits, rendering the search less efficient for eccentric binary systems. Here we present the results of a search for BBH mergers that inspiral in eccentric orbits using data from the first and second observing runs (O1 and O2) of Advanced LIGO and Advanced Virgo. We carried out the search with the coherent WaveBurst algorithm, which uses minimal assumptions on the signal morphology and does not rely on binary waveform templates. We show that it is sensitive to binary mergers with a detection range that is weakly dependent on eccentricity for all bound systems. Our search did not identify any new binary merger candidates. We interpret these results in light of eccentric binary formation models. We rule out formation channels with rates ⪆100 Gpc-3 yr-1 for e > 0.1, assuming a black hole mass spectrum with a power-law index ≲2