On the zero set of G-equivariant maps

Let $G$ be a finite group acting on vector spaces $V$ and $W$ and consider a smooth $G$-equivariant mapping $f:V\to W$. This paper addresses the question of the zero set near a zero $x$ of $f$ with isotropy subgroup $G$. It is known from results of Bierstone and Field on $G$-transversality theory that the zero set in a neighborhood of $x$ is a stratified set. The purpose of this paper is to partially determine the structure of the stratified set near $x$ using only information from the representations $V$ and $W$. We define an index $s(\Sigma)$ for isotropy subgroups $\Sigma$ of $G$ which is the difference of the dimension of the fixed point subspace of $\Sigma$ in $V$ and $W$. Our main result states that if $V$ contains a subspace $G$-isomorphic to $W$, then for every maximal isotropy subgroup $\Sigma$ satisfying $s(\Sigma)>s(G)$, the zero set of $f$ near $x$ contains a smooth manifold of zeros with isotropy subgroup $\Sigma$ of dimension $s(\Sigma)$. We also present a systematic method to study the zero sets for group representations $V$ and $W$ which do not satisfy the conditions of our main theorem. The paper contains many examples and raises several questions concerning the computation of zero sets of equivariant maps. These results have application to the bifurcation theory of $G$-reversible equivariant vector fields

Deformation of geometry and bifurcation of vortex rings

We construct a smooth family of Hamiltonian systems, together with a family of group symmetries and momentum maps, for the dynamics of point vortices on surfaces parametrized by the curvature of the surface. Equivariant bifurcations in this family are characterized, whence the stability of the Thomson heptagon is deduced without recourse to the Birkhoff normal form, which has hitherto been a necessary tool.Comment: 26 page

Piecewise smooth systems near a co-dimension 2 discontinuity manifold: can one say what should happen?

We consider a piecewise smooth system in the neighborhood of a co-dimension 2 discontinuity manifold $\Sigma$. Within the class of Filippov solutions, if $\Sigma$ is attractive, one should expect solution trajectories to slide on $\Sigma$. It is well known, however, that the classical Filippov convexification methodology is ambiguous on $\Sigma$. The situation is further complicated by the possibility that, regardless of how sliding on $\Sigma$ is taking place, during sliding motion a trajectory encounters so-called generic first order exit points, where $\Sigma$ ceases to be attractive. In this work, we attempt to understand what behavior one should expect of a solution trajectory near $\Sigma$ when $\Sigma$ is attractive, what to expect when $\Sigma$ ceases to be attractive (at least, at generic exit points), and finally we also contrast and compare the behavior of some regularizations proposed in the literature. Through analysis and experiments we will confirm some known facts, and provide some important insight: (i) when $\Sigma$ is attractive, a solution trajectory indeed does remain near $\Sigma$, viz. sliding on $\Sigma$ is an appropriate idealization (of course, in general, one cannot predict which sliding vector field should be selected); (ii) when $\Sigma$ loses attractivity (at first order exit conditions), a typical solution trajectory leaves a neighborhood of $\Sigma$; (iii) there is no obvious way to regularize the system so that the regularized trajectory will remain near $\Sigma$ as long as $\Sigma$ is attractive, and so that it will be leaving (a neighborhood of) $\Sigma$ when $\Sigma$ looses attractivity. We reach the above conclusions by considering exclusively the given piecewise smooth system, without superimposing any assumption on what kind of dynamics near $\Sigma$ (or sliding motion on $\Sigma$) should have been taking place.Comment: 19 figure

Optimal stent design for high bleeding risk patients: Evidence from a network meta-analysis

Objective. To determine the best stent design for high bleeding risk (HBR) patients. Background. Polymer-free (PF) drug eluting stent (DES) devices have a proven benefit over bare-metal stent (BMS) devices in previous trials. It is unknown, however, whether polymer-based (PB)-DES devices are as safe as PF-DES devices. Methods. A network meta-analysis including all randomized controlled trials (RCTs) that compared different stent technology in HBR patients with a 1-month course of dual-antiplatelet therapy (DAPT) was performed. The main efficacy outcome was major adverse cardiac event (MACE) rate, defined as the composite of all-cause mortality, myocardial infarction (MI), and target-lesion revascularization (TLR). Secondary efficacy events included all-cause and cardiac mortality, MI, stroke, TLR, and target-vessel revascularization (TVR). Safety outcomes included all bleeding, major bleeding, and stent thrombosis (ST). Results. A total of 4 RCTs with 6456 patients were included. PF-DES and PB-DES yielded a reduced rate of MACE, MI, TLR, and TVR events compared with BMS (all P<.05). ST events were reduced in PB-DES compared with BMS (P=.01). No differences were found in all-cause death, cardiac death, or stroke events in PF-DES and PB-DES compared with BMS. Furthermore, no differences were found between PF-DES and PB-DES regarding any of the outcomes. Conclusion. DES devices were associated with lower MACE and TVR rates compared with BMS, whereas there were no statistical differences in other efficacy endpoints. Also, PB-DES were associated with fewer ST events compared with BMS. There were no statistical differences between PB-DES and PF-DES with regard to any of the endpoints. t 2021 HMP Comm Personal Use Onl

The moderating role of transformational leadership on HR practices in M&A integration

Scant research exists examining the effect of HRM practices on employee behavior in M&A integration and the role that leaders play within this. This paper develops a conceptual framework that focuses on the moderating role of transformational leadership on the achievement of human integration and organizational identification in M&A integration. We argue that communication, employee involvement, teamwork, and training and development have a positive effect on employee behavior and their identification with the newly formed organization. Moreover, we argue that transformational leadership behaviors will moderate the implementation of HRM practices in M&As, leading to positive employee behavior and employee identification in the new organization. We suggest that further research is necessary to test propositions of the present study in order to achieve finer-grained understanding of the role of transformational leadership on the achievement of human integration and organizational identification in M&A integration

Does anticholinergics drug burden relate to global neuro-disability outcome measures and length of hospital stay?

Primary objective: To assess the relationship between disability, length of stay (LOS) and anticholinergic burden (ACB) with people following acquired brain or spinal cord injury. Research design: A retrospective case note review assessed total rehabilitation unit admission. Methods and procedures: Assessment of 52 consecutive patients with acquired brain/spinal injury and neuropathy in an in-patient neuro-rehabilitation unit of a UK university hospital. Data analysed included: Northwick Park Dependency Score (NPDS), Rehabilitation complexity Scale (RCS), Functional Independence Measure and Functional Assessment Measure FIM-FAM (UK version 2.2), LOS and ACB. Outcome was different in RCS, NPDS and FIM-FAM between admission and discharge. Main outcomes and results: A positive change was reported in ACB results in a positive change in NPDS, with no significant effect on FIM-FAM, either Motor or Cognitive, or on the RCS. Change in ACB correlated to the length of hospital stay (regression correlation = −6.64; SE = 3.89). There was a significant harmful impact of increase in ACB score during hospital stay, from low to high ACB on NPDS (OR = 9.65; 95% CI = 1.36–68.64) and FIM-FAM Total scores (OR = 0.03; 95% CI = 0.002–0.35). Conclusions: There was a statistically significant correlation of ACB and neuro-disability measures and LOS amongst this patient cohort

Bilateral ischemic optic neuropathy after transurethral prostatic resection: a case report

BACKGROUND: Nonarteritic ischemic optic neuropathy affects the anterior portion of the optic nerve and is characterized by sudden, painless visual loss. The affected eye has a relative afferent pupillary defect. The typical funduscopic appearance includes optic disc edema, with associated nerve fiber layer hemorrhage. Risk factors include advanced age, systemic hypertension, nocturnal hypotension, diabetes mellitus, and a small cup-to-disc ratio. Bilateral presentation is rare. Postoperative optic neuropathy has been associated with nonocular surgery; risk factors include a combination of prolonged surgical times, acute systemic hypotension, anemia due to blood loss, or prone positioning. We report for the first time a patient with bilateral, simultaneous anterior ischemic optic neuropathy after elective transurethral prostatic resection. CASE PRESENTATION: A 66-year old man underwent surgery for benign prostatic hyperplasia. The preoperative blood pressure was 140/85 mmHg, hemoglobin 15.9 g/dL, and hematocrit 48.6%. Two hours postoperatively, the blood pressure, hemoglobin, and hematocrit dropped dramatically. One day later, transient horizontal diplopia developed. Funduscopy showed a congenitally small cup-to-disc ratio without papillary edema. Other ocular findings were unremarkable. By 4 days postoperatively, sudden and painless amaurosis bilaterally developed when the patient awoke with nausea and vomiting. Visual acuity was no light perception bilaterally. The optic discs were swollen with small hemorrhages. Scans of the head and orbits and electrolyte levels were normal. There were no responses on visual evoked potentials bilaterally. The blood pressure was 90/50 mm Hg, the hemoglobin 7.0 g/dL, and the hematocrit 22.9%, necessitating infusion of three units of packed red blood cells. The blood pressure, hematocrit, and hemoglobin increased to normal levels. Three months later the visual acuity remained no light perception. The pupils were unreactive and there was marked optic disc atrophy bilaterally. CONCLUSION: Bilateral and simultaneous acute ischemic optic neuropathy may be a rare but devastating surgical complication. The combination of anemia and hypotension may increase the risk of anterior ischemic optic neuropathy postoperatively after transurethral prostatic resection

Hepatozoon canis in hunting dogs from Southern Italy: distribution and risk factors

Hepatozoon canis is a hemoprotozoan organism that infects domestic and wild carnivores throughout much of Europe. The parasite is mainly transmitted through the ingestion of infected ticks containing mature oocysts. The aims of the present survey were to determine the prevalence of H. canis in hunting dogs living in Southern Italy and to assess potential infection risk factors. DNA extracted from whole blood samples, collected from 1433 apparently healthy dogs living in the Napoli, Avellino, and Salerno provinces of Campania region (Southern Italy), was tested by a quantitative real-time polymerase chain reaction (qPCR) assay to amplify H. canis. Furthermore, the investigated dog population was also screened by qPCR for the presence of Ehrlichia canis, a major tick-borne pathogen in Southern Italy, in order to assess possible co-infections. Two hundred dogs were H. canis PCR-positive, resulting in an overall prevalence of 14.0% (CI 12.2–15.9). Breed category (P < 0.0001), hair coat length (P = 0.015), and province of residence (P < 0.0001) represented significant risk factors for H. canis infection. The presence ofH. canis DNA was also significantly associated with E. canis PCR positivity (P < 0.0001). Hunting dogs in Campania region (Southern Italy) are frequently exposed to H. canis, and the infection is potentially associated with close contact with wildlife. Further studies are needed to assess the pathogenic potential of H. canis, as well as the epidemiological relationships between hunting dogs and wild animal populations sharing the same habitats in Southern Italy

Full Geant4 and FLUKA Simulations of an e-LINAC for its Use in Particle Detectors Performance Tests

In this work we present the results of full Geant4 and FLUKA simulations and comparison with dosimetry data of an electron LINAC of St. Maria Hospital located in Terni, Italy. The facility is being used primarily for radiotherapy and the goal of present study is the detailed investigation of electron beam parameters to evaluate the possibility to use the e-LINAC (during time slots when it is not used for radiotherapy) to test the performance of detector systems in particular those designed to operate in space. The critical beam parameters are electron energy, profile and flux available at the surface of device to be tested. The present work aims to extract these parameters from dosimetry calibration data available at the e-LINAC. The electron energy ranges is from 4 MeV to 20 MeV. The dose measurements have been performed by using an Advanced Markus Chamber which has a small sensitive volume.Comment: 10 pages, 10 figures, 2 table

Analysis of symmetries in models of multi-strain infections

In mathematical studies of the dynamics of multi-strain diseases caused by antigenically diverse pathogens, there is a substantial interest in analytical insights. Using the example of a generic model of multi-strain diseases with cross-immunity between strains, we show that a significant understanding of the stability of steady states and possible dynamical behaviours can be achieved when the symmetry of interactions between strains is taken into account. Techniques of equivariant bifurcation theory allow one to identify the type of possible symmetry-breaking Hopf bifurcation, as well as to classify different periodic solutions in terms of their spatial and temporal symmetries. The approach is also illustrated on other models of multi-strain diseases, where the same methodology provides a systematic understanding of bifurcation scenarios and periodic behaviours. The results of the analysis are quite generic, and have wider implications for understanding the dynamics of a large class of models of multi-strain diseases