From isolated subgroups to generic permutation representations

Let $G$ be a countable group, $\operatorname{Sub}(G)$ the (compact, metric) space of all subgroups of $G$ with the Chabauty topology and $\operatorname{Is}(G) \subset \operatorname{Sub}(G)$ the collection of isolated points. We denote by $X!$ the (Polish) group of all permutations of a countable set $X$. Then the following properties are equivalent: (i) $\operatorname{Is}(G)$ is dense in $\operatorname{Sub}(G)$, (ii) $G$ admits a "generic permutation representation". Namely there exists some $\tau^* \in \operatorname{Hom}(G,X!)$ such that the collection of permutation representations $\{\phi \in \operatorname{Hom}(G,X!) \ | \ \phi {\text{is permutation isomorphic to}} \tau^*\}$ is co-meager in $\operatorname{Hom}(G,X!)$. We call groups satisfying these properties solitary. Examples of solitary groups include finitely generated LERF groups and groups with countably many subgroups.Comment: 21 page

Discitis Following Microdiskectomy: A Preliminary Report on the Role of Pre-Operative Prophylactic Antibiotics

Study Design: 83 consecutive microdiskectomies were performed and evaluated to discern the efficacy of pre-operative prophylactic antibiotics ( cefazolin and vancomycin). Objective: The objective of this preliminary report was to evaluate the amount, time of administration, effectiveness, and need of prophylactic antibiotics using our surgical results. Summary of Background Data: Previous studies have yielded conflicting results regarding the role of antibiotics in prevention and treatment of discitis , and in their ability to penetrate the intervertebral disc. Methods: 1gm of cefazolin was intravenously administered to 76 patients, 30 minutes prior to incision; 500mg of vancomycin was likewise administered to the remaining 7 patients who were allergic to cepbalosporins. No post-operative antibiotic was administered. Results: Of the 83 consecutive surgeries, no patient developed iatrogenic disci tis. The average length of follow-up was 6 months (range 1 - 23 months). Conclusions: Our results suggest that the use of cephalosporins (and glycopeptides) seems to prevent discitis when intravenously administered 30 minutes prior to surgery; that being the case, there appears to be no advantage in additional post-operative dosing. However, in light of conflicting reports and the preliminary nature of this study, conceivably there is another explanation. Perhaps there is in fact no correlation between pre-operative antibiotics and post-operative discitis

Machine Learning for Understanding and Predicting Injuries in Football

Attempts to better understand the relationship between training and competition load and injury in football are essential for helping to understand adaptation to training programmes, assessing fatigue and recovery, and minimising the risk of injury and illness. To this end, technological advancements have enabled the collection of multiple points of data for use in analysis and injury prediction. The full breadth of available data has, however, only recently begun to be explored using suitable statistical methods. Advances in automatic and interactive data analysis with the help of machine learning are now being used to better establish the intricacies of the player load and injury relationship. In this article, we examine this recent research, describing the analyses and algorithms used, reporting the key findings, and comparing model fit. To date, the vast array of variables used in analysis as proxy indicators of player load, alongside differences in approach to key aspects of data treatment—such as response to data imbalance, model fitting, and a lack of multi-season data—limit a systematic evaluation of findings and the drawing of a unified conclusion. If, however, the limitations of current studies can be addressed, machine learning has much to offer the field and could in future provide solutions to the training load and injury paradox through enhanced and systematic analysis of athlete data

The Effectiveness of a Far Lateral L5-S1 Microdiscectomy in Pain Reduction

Diagnosis of far lateral disc herniations has become more common in recent years. This study describes the surgical procedure used for L5-S1 far lateral disc herniations, shows the benefits derived from a far lateral approach and retrospectively evaluates the outcome of the surgery. Eight patients were included in the study, five females and three males. The mean age was 62 years (range, 45-77 years). VAS pain scale, OSW index and SF-36 forms were used to evaluate the surgical outcome. Both the VAS pain scale and OSW index were improved postoperatively. The SF-36 scores were significantly lower (p\u3c0.05) for the far lateral patients compared to both the low back pain population and the U.S. aged 55-64 year population

Postoperative Infection Rates with Instrumented Lumbar Fusion: A Retrospective Review of 129 Consecutive Cases

Introduction: The use of internal fixation devices in spinal surgery is common to achieve reduction, maintain alignment, and stabilize the spine while fusion occurs. Infection rates of less than 2% (0-2%) were reported in the late 1960\u27s without the use of instrumentation. Reported rates of infection following instrumented fusion are generally around 6% (range 0-11% ). The purpose of this study was to retrospectively review the incidence of postoperative infection following instrumented spinal fusion to determine if infection rates related to patient type and surgical procedure. Methods: A retrospective review was conducted of 129 consecutive cases of instrumented lumbar spinal fusion. Three patients were eliminated from the study: two due to preoperative spinal infections, and a third patient expired from unrelated disease. All instrumented fusion cases were eligible for this study regardless of level or technique used. Results: Of the 126 instrumented cases there were no superficial infections, and one (0.8%) deep infection. The infection was completely resolved and did not prevent solid fusion with good alignment. The patient was a smoker and received autograft bone. Discussion: The results of this review revealed substantially lower rates of postoperative infection following instrumented fusion than has been previously reported in the literature. No superficial and one (0.8%) deep infection was identified. Due to the low infection rates, no statistically significant conclusions could be made

The Chattanooga Procedure: A New Technique Used for Anterior Multi-level Cervical Fusions

STUDY DESIGN: A preliminary assessment of anterior cervical fusion performed with interbody cage and DOC plate. OBJECTIVES: To describe and evaluate the efficacy and safety of the Chattanooga Procedure , a modified technique in achieving anterior cervical fusion. SUMMARY OF BACKGROUND DATA: Anterior cervical fusion with interbody bone graft and anterior plating is connnonly performed. Unfortunately, the plate has been reported to shield the graft from loading thus reducing fusion rates. The use of interbody fusion cages has been effective in the lumbar spine and has gained acceptance in the cervical spine. METHODS:. Twenty-five patients received The Chattanooga Procedure between 7/24/98 and 4/8/99. All patients had anterior discectomies and carpectomies, placement of a Harms cage packed with carpectomy bone, and application ofDePuy-Acromed DOC. Fusion was defined by radiographic evidence of trabecular bone bridging across the Harms cage. CT scans were performed on twelve randomly chosen patients to verify fusion. No external bracing was used except a soft collar as needed. Pre- and post-operative pain and functional capacity data were collected and statistically analyzed using paired t-tests. RESULTS: There were no cases of pseudoarthrosis, major neurological, vascular, or wound complications. Only one case of unresolved dysphasia was noted. The average operative time (11 0 minutes) was comparable to standard instrumented multi-level anterior cervical fusion surgeries. The average estimated blood loss was 113 ml (range, 50-750 ml). Both visual analog pain scale and Oswestry functional capacity data were significantly improved post-operatively (p\u3c 0.01). DISCUSSION: Advantages of the Chattanooga Procedure include immediate stability, support, elimination of donor site pain to iliac crest bone autograft, and a decrease in pseudoarthrosis by dividing the fusion surfaces by half. Concerns regarding this technique include an increased risk for dysphasia due to the DOC\u27s high profile. Pseudoarthrosis or instrumentation migration could also become problematic since the removal of the Harms cage could be difficult if necessary

Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

We show that scattering amplitudes in planar N = 4 Super Yang-Mills in multi-Regge kinematics can naturally be expressed in terms of single-valued iterated integrals on the moduli space of Riemann spheres with marked points. As a consequence, scattering amplitudes in this limit can be expressed as convolutions that can easily be computed using Stokes' theorem. We apply this framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove that at L loops all MHV amplitudes are determined by amplitudes with up to L + 4 external legs. We also investigate non-MHV amplitudes, and we show that they can be obtained by convoluting the MHV results with a certain helicity flip kernel. We classify all leading singularities that appear at LLA in the Regge limit for arbitrary helicity configurations and any number of external legs. Finally, we use our new framework to obtain explicit analytic results at LLA for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to eight external legs and four loops.Comment: 104 pages, six awesome figures and ancillary files containing the results in Mathematica forma