Prime injections and quasipolarities

Let $p$ be a prime number. Consider the injection $$\iota:\mathbb{Z}/n\mathbb{Z}\to\mathbb{Z}/pn\mathbb{Z}:x\mapsto px,$$ and the elements $e^{u}.v:=(u,v)\in \mathbb{Z}/n\mathbb{Z}\rtimes \mathbb{Z}/n\mathbb{Z}^{\times}$ and $e^{w}.r:=(w,r)\in \mathbb{Z}_{p n}\rtimes \mathbb{Z}_{p n}^{\times}$. Suppose $e^{u}.v\in \mathbb{Z}/n\mathbb{Z}\rtimes \mathbb{Z}/n\mathbb{Z}^{\times}$ is seen as an automorphism of $\mathbb{Z}/n\mathbb{Z}$ by $e^{u}.v(x)=vx+u$; then $e^{u}.v$ is a quasipolarity if it is an involution without fixed points. In this brief note give an explicit formula for the number of quasipolarites of $\mathbb{Z}/n\mathbb{Z}$ in terms of the prime decomposition of $n$, and we prove sufficient conditions such that $(e^{w}.r)\circ \iota =\iota\circ (e^{u}.v)$, where $e^{w}.r$ and $e^{u}.v$ are quasipolarities

Ultrasound guided glenohumeral injections in adhesive capsulitis

Thesis (M.A.)--Boston UniversityObjective: The objective of this thesis was to assess outcomes of glenohumeral corticosteroid injections for adhesive capsulitis. Design: The thesis was composed of two parts. First, a systematic literature review was conducted on glenohumeral corticosteroid injections on shoulder outcomes for adhesive capsulitis. Second, an original prospective study was conducted to measure the effect of ultrasound-guided injections on pain and function for adhesive capsulitis patients. Setting: All injections for the prospective injection study were conducted at Brigham and Women’s Hospital in Boston, MA. Patients: Inclusion criteria were patients receiving an ultrasound guided injection for adhesive capsulitis. 67 patients were included, 59 patients were available at first follow up, and 40 patients were available at final follow up. Methods: The literature review was conducted using the online databases PubMed (1966-present), Embase (1947-present), Web of Science (1900– present), and the Cochrane Central Register of Controlled Trials. Study criteria were limited to clinical trials that evaluated the application of corticosteroid injections, both alone and in combination with other treatment modalities, specifically for the condition of adhesive capsulitis in the shoulder. Studies involving non-corticosteroid injections or injections for conditions not specific to adhesive capsulitis were excluded. Results were limited to papers in the English language. A data table summarizing pain, function, and range of motion outcomes of each treatment was produced. A percent change from baseline was calculated to facilitate comparisons. For the injection study, the first follow-up took place after an average of 2.0 months and patients' improvement in pain and range of motion were assessed. During a final follow-up after an average of 10.4 months, patients’ pain and shoulder function scores were assessed over telephone. [TRUNCATED

Estimation of the Sensitive Volume for Gravitational-wave Source Populations Using Weighted Monte Carlo Integration

The population analysis and estimation of merger rates of compact binaries is one of the important topics in gravitational wave (GW) astronomy. The primary ingredient in these analyses is the population-averaged sensitive volume. Typically, sensitive volume, of a given search to a given simulated source population, is estimated by drawing signals from the population model and adding them to the detector data as injections. Subsequently injections, which are simulated gravitational waveforms, are searched for by the search pipelines and their signal-to-noise ratio (SNR) is determined. Sensitive volume is estimated, by using Monte-Carlo (MC) integration, from the total number of injections added to the data, the number of injections that cross a chosen threshold on SNR and the astrophysical volume in which the injections are placed. So far, only fixed population models have been used in the estimation of the merger rates. However, as the scope of population analysis broaden in terms of the methodologies and source properties considered, due to an increase in the number of observed GW signals, the procedure will need to be repeated multiple times at a large computational cost. In this letter we address the problem by performing a weighted MC integration. We show how a single set of generic injections can be weighted to estimate the sensitive volume for multiple population models; thereby greatly reducing the computational cost. The weights in this MC integral are the ratios of the output probabilities, determined by the population model and standard cosmology, and the injection probability, determined by the distribution function of the generic injections. Unlike analytical/semi-analytical methods, which usually estimate sensitive volume using single detector sensitivity, the method is accurate within statistical errors, comes at no added cost and requires minimal computational resources.Comment: 11 pages, 1 figur

Phaseolus vulgaris leuco-agglutinin immunohistochemistry. A comparison between autoradiographic and lectin tracing of neuronal efferents

The autoradiographic pattern of anterograde labeling as a result from injections with tritiated amino acids is compared to the labeling of efferents with Phaseolus vulgaris leuco-agglutinin after lectin injections in the same nucleus visualized by immunohistochemical methods. This comparison is made for efferents from the ventromedial hypothalamic nucleus to the amygdaloid body.

Injections of mapping class groups

We construct new monomorphisms between mapping class groups of surfaces. The first family of examples injects the mapping class group of a closed surface into that of a different closed surface. The second family of examples are defined on mapping class groups of once-punctured surfaces and have quite curious behaviour. For instance, some pseudo-Anosov elements are mapped to multi-twists. Neither of these two types of phenomena were previously known to be possible although the constructions are elementary

Administration of Long-Acting Injections

Expanding the scope of pharmacy practice demonstrates that the profession has been successful at improving public health. Despite being a late adopter, New York\u27s limited experience with vaccines has improved immunization rates and lowered rates of disease. During emergencies, the 2017-2018 flu season for example, the state has turned to pharmacists to go beyond what the pharmacy practice law permits, in this case enabling immunizations in pediatric patients.1 This illustrates recognition of untapped potential within the profession to contribute to the public health. Another opportunity for pharmacists to enhance the public health is embodied in a Bill introduced in the New York State Legislature that would amend the pharmacy practice law to enable administration of long-acting injectables designed to treat mental health disorders including schizophrenia and substance use disorder ( SUD ). The goal of this paper is to review the proposed amendment, the relevant background, and to discuss the implications for patients and the pharmacy profession

Safety and efficacy of a propofol and ketamine based procedural sedation protocol in children with cerebral palsy undergoing botulinum toxin A injections.

Background Pediatric patients with cerebral palsy (CP) often undergo intramuscular botulinum toxin (BoNT‐A) injections. These injections can be painful and may require procedural sedation. An ideal sedation protocol has yet to be elucidated. Objective To investigate the safety and efficacy of a propofol and ketamine based sedation protocol in pediatric patients with cerebral palsy requiring BoNT‐A injections. Design This is a retrospective chart review of children with CP undergoing propofol and ketamine based sedation for injections with botulinum toxin A. Setting The sedations took place in a procedural sedation suite at a tertiary children’s hospital from Feb 2013 through Sept 2017. Patients 164 patients with diagnoses of cerebral palsy were included in this study. Methods An initial bolus of 0.5 mg/kg ketamine followed by a 2 mg/kg bolus of propofol was administered with supplemental boluses of propofol as needed to achieve deep sedation during the intramuscular BoNT‐A injections. Main Outcome Measurements Propofol dosages, adverse events, serious adverse events, and sedation time parameters were reviewed. Results 345 sedations were successfully performed on 164 patients. The median total dose of propofol was 4.7 mg/kg (IQR 3.5, 6.3). Adverse events were encountered in 10.1% of procedures including hypoxemia responsive to supplemental oxygen (9.6%) and transient apnea (1.4%). The mean procedure time, recovery time and total sedation time were 10, 11 and 33 minutes, respectively. With regard to patient variables, including age, weight, dose of propofol, sedation time, and Gross Motor Function Classification System classification, there was no association with increased incidence of adverse events. Conclusion Our sedation protocol of propofol and ketamine is safe and effective in children with cerebral palsy undergoing procedural sedation for intramuscular injections with BoNT‐A. The adverse events encountered appeared to be related to airway and respiratory complications secondary to musculoskeletal deformities, emphasizing the importance of airway monitoring and management in these patients

Conjugation of injections by permutations

Let X be a countably infinite set, and let f, g, and h be any three injective self-maps of X, each having at least one infinite cycle. (For instance, this holds if f, g, and h are not bijections.) We show that there are permutations a and b of X such that h=afa^{-1}bgb^{-1} if and only if |X\Xf|+|X\Xg|=|X\Xh|. We also prove a version of this statement that holds for infinite sets X that are not necessarily countable. This generalizes results of Droste and Ore about permutations.Comment: 27 pages, 4 figure