On solvable groups with one vanishing class size

Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh. Let G be a finite group, and let cs(G) be the set of conjugacy class sizes of G. Recalling that an element g of G is called a vanishing element if there exists an irreducible character of G taking the value 0 on g, we consider one particular subset of cs(G), namely, the set vcs(G) whose elements are the conjugacy class sizes of the vanishing elements of G. Motivated by the results inBianchi et al. (2020, J. Group Theory, 23, 79-83), we describe the class of the finite groups G such that vcs(G) consists of a single element under the assumption that G is supersolvable or G has a normal Sylow 2-subgroup (in particular, groups of odd order are covered). As a particular case, we also get a characterization of finite groups having a single vanishing conjugacy class size which is either a prime power or square-free

Low-Intensity Vibration Protects the Weight-Bearing Skeleton and Suppresses Fracture Incidence in Boys With Duchenne Muscular Dystrophy: A Prospective, Randomized, Double-Blind, Placebo-Controlled Clinical Trial

The ability of low-intensity vibration (LIV) to combat skeletal decline in Duchenne Muscular Dystrophy (DMD) was evaluated in a randomized controlled trial. Twenty DMD boys were enrolled, all ambulant and treated with glucocorticoids (mean age 7.6, height-adjusted Z-scores [HAZ] of hip bone mineral density [BMD] −2.3). Ten DMD boys were assigned to stand for 10 min/d on an active LIV platform (0.4 g at 30 Hz), while 10 stood on a placebo device. Baseline and 14-month bone mineral content (BMC) and BMD of spine, hip, and total body were measured with DXA, and trabecular bone density (TBD) of tibia with quantitative computed tomography (QCT). All children tolerated the LIV intervention well, with daily compliance averaging 78%. At 14 months, TBD in the proximal and distal tibia remained unchanged in placebo subjects (−1.0% and −0.2%), while rising 3.5% and 4.6% in LIV subjects. HAZ for hip BMD and BMC in the placebo group declined 22% and 13%, respectively, contrasting with no change from baseline (0.9% and 1.4%) in the LIV group. Fat mass in the leg increased 32% in the placebo group, contrasting with 21% in LIV subjects. Across the 14-month study, there were four incident fractures in three placebo patients (30%), with no new fractures identified in LIV subjects. Despite these encouraging results, a major limitation of the study is—despite randomized enrollment—that there was a significant difference in age between the two cohorts, with the LIV group being 2.8y older, and thus at greater severity of disease. In sum, these data suggest that noninvasive LIV can help protect the skeleton of DMD children against the disease progression, the consequences of diminished load bearing, and the complications of chronic steroid use. © 2022 The Authors. JBMR Plus published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research

A review of current induction strategies and emerging prognostic factors in the management of children and adolescents with acute lymphoblastic leukemia

Introduction: Acute lymphoblastic leukemia is the most frequent hematologic malignancy in children. Almost 95% of children potentially achieve a complete remission after the induction treatment, but over the last years, new insights in the genomic disease profile and in minimal residual disease detection techniques have led to an improvement in the prognostic stratification, identifying selected patients’ subgroups with peculiar therapeutic needs. Areas covered: According to a comprehensive search of peer-review literature performed in Pubmed, in this review we summarize the recent evidences on the induction treatment strategies comprised in the children acute lymphoblastic leukemia scenario, focusing on the role of key drugs such as corticosteroids and asparaginase and discussing the crucial significance of the genomic characterization at baseline which may drive the proper induction treatment choice. Expert opinion: Current induction strategies already produce durable remissions in a significant proportion of standard-risk children with acute lymphoblastic leukemia. A broader knowledge of the biologic features related to acute lymphoblastic leukemia subtypes with worse prognosis, and an optimization of targeted drugs now available, might lead to the achievement of long-term molecular remissions in this setting

Inversions of Levy Measures and the Relation Between Long and Short Time Behavior of Levy Processes

The inversion of a Levy measure was first introduced (under a different name) in Sato 2007. We generalize the definition and give some properties. We then use inversions to derive a relationship between weak convergence of a Levy process to an infinite variance stable distribution when time approaches zero and weak convergence of a different Levy process as time approaches infinity. This allows us to get self contained conditions for a Levy process to converge to an infinite variance stable distribution as time approaches zero. We formulate our results both for general Levy processes and for the important class of tempered stable Levy processes. For this latter class, we give detailed results in terms of their Rosinski measures

A manifestly MHV Lagrangian for N=4 Yang-Mills

We derive a manifestly MHV Lagrangian for the N=4 supersymmetric Yang-Mills theory in light-cone superspace. This is achieved by constructing a canonical redefinition which maps the N=4 superfield and its conjugate to a new pair of superfields. In terms of these new superfields the N=4 Lagrangian takes a (non-polynomial) manifestly MHV form, containing vertices involving two superfields of negative helicity and an arbitrary number of superfields of positive helicity. We also discuss constraints satisfied by the new superfields, which ensure that they describe the correct degrees of freedom in the N=4 supermultiplet. We test our derivation by showing that an expansion of our superspace Lagrangian in component fields reproduces the correct gluon MHV vertices.Comment: 37 pages, 1 figure. v2: minor changes, references adde

Biomarker Testing to Estimate Under-Reported Heavy Alcohol Consumption by Persons with HIV Initiating ART in Uganda

Alcohol affects the transmission and treatment of HIV, yet may be under-reported in resource-limited settings. We compared self-reported alcohol consumption with levels of plasma carbohydrate-deficient transferrin (%CDT), a biomarker of heavy alcohol consumption, in persons initiating antiretroviral therapy in Uganda. Almost seven percent (6.7%) of persons reporting abstaining and 10% reporting consuming 1–40 drinks in the prior month tested positive for %CDT, and actual under-report may be higher due to low sensitivity of %CDT. These results suggest likely under-report in those reporting abstaining and current drinking. Improved identification of heavy alcohol consumption is needed for research and clinical purposes

Early decrements in bone density after completion of neoadjuvant chemotherapy in pediatric bone sarcoma patients

<p>Abstract</p> <p>Background</p> <p>Bone mineral density (BMD) accrual during childhood and adolescence is important for attaining peak bone mass. BMD decrements have been reported in survivors of childhood bone sarcomas. However, little is known about the onset and development of bone loss during cancer treatment. The objective of this cross-sectional study was to evaluate BMD in newly diagnosed Ewing's and osteosarcoma patients by means of dual-energy x-ray absorptiometry (DXA) after completion of neoadjuvant chemotherapy.</p> <p>Methods</p> <p>DXA measurements of the lumbar spine (L2-4), both femora and calcanei were performed perioperatively in 46 children and adolescents (mean age: 14.3 years, range: 8.6-21.5 years). Mean <it>Z</it>-scores, areal BMD (g/cm²), calculated volumetric BMD (g/cm³) and bone mineral content (BMC, g) were determined.</p> <p>Results</p> <p>Lumbar spine mean Z-score was -0.14 (95% CI: -0.46 to 0.18), areal BMD was 1.016 g/cm²(95% CI: 0.950 to 1.082) and volumetric BMD was 0.330 g/cm³(95% CI: 0.314 to 0.347) which is comparable to healthy peers. For patients with a lower extremity tumor (n = 36), the difference between the affected and non-affected femoral neck was 12.1% (95% CI: -16.3 to -7.9) in areal BMD. The reduction of BMD was more pronounced in the calcaneus with a difference between the affected and contralateral side of 21.7% (95% CI: -29.3 to -14.0) for areal BMD. Furthermore, significant correlations for femoral and calcaneal DXA measurements were found with Spearman-rho coefficients ranging from ρ = 0.55 to ρ = 0.80.</p> <p>Conclusions</p> <p>The tumor disease located in the lower extremity in combination with offloading recommendations induced diminished BMD values, indicating local osteopenia conditions. However, the results revealed no significant decrements of lumbar spine BMD in pediatric sarcoma patients after completion of neoadjuvant chemotherapy. Nevertheless, it has to be taken into account that bone tumor patients may experience BMD decrements or secondary osteoporosis in later life. Furthermore, the peripheral assessment of BMD in the calcaneus via DXA is a feasible approach to quantify bone loss in the lower extremity in bone sarcoma patients and may serve as an alternative procedure, when the established assessment of femoral BMD is not practicable due to endoprosthetic replacements.</p

Bone and body composition analyzed by Dual-energy X-ray Absorptiometry (DXA) in clinical and nutritional evaluation of young patients with Cystic Fibrosis: a cross-sectional study

<p>Abstract</p> <p>Background</p> <p>the improved general therapy has led to reduced morbidity and mortality from Cystic Fibrosis (CF), and bone status may have a potentially greater clinical impact.</p> <p>We investigated the correlation between the severity of the clinical condition, bone status and body composition parameters, in a group of children and young adults with CF.</p> <p>Methods</p> <p>we measured lumbar spine bone density and total body composition by dual energy x-ray absorptiometry (DXA) in 82 consecutive CF patients (42 males; median age: 13 years - range: 5-30). Eighty-two healthy subjects, matched for age, gender, height and pubertal stage were recruited as a control group.</p> <p>Results</p> <p>37 patients (45.1%) had a normal bone mineral density (BMD). A BMD reduction were observed in 45 (54.8%) patients. Lumbar spine Z score was positively related to Body Mass Index (BMI) and a higher Shwachman-Kulczycki score, and negatively related to Crispin-Norman score. A positive and significant correlation was also observed between lumbar spine Z score and total body composition.</p> <p>Conclusion</p> <p>a significant BMD reduction can be present early in CF children and adolescents. A careful follow up of bone status is required starting in childhood.</p

The S-Matrix in Twistor Space

The simplicity and hidden symmetries of (Super) Yang-Mills and (Super)Gravity scattering amplitudes suggest the existence of a "weak-weak" dual formulation in which these structures are made manifest at the expense of manifest locality. We suggest that this dual description lives in (2,2) signature and is naturally formulated in twistor space. We recast the BCFW recursion relations in an on-shell form that begs to be transformed into twistor space. Our twistor transformation is inspired by Witten's, but differs in treating twistor and dual twistor variables more equally. In these variables the three and four-point amplitudes are amazingly simple; the BCFW relations are represented by diagrammatic rules that precisely define the "twistor diagrams" of Andrew Hodges. The "Hodges diagrams" for Yang-Mills theory are disks and not trees; they reveal striking connections between amplitudes and suggest a new form for them in momentum space. We also obtain a twistorial formulation of gravity. All tree amplitudes can be combined into an "S-Matrix" functional which is the natural holographic observable in asymptotically flat space; the BCFW formula turns into a quadratic equation for this "S-Matrix", providing a holographic description of N=4 SYM and N=8 Supergravity at tree level. We explore loop amplitudes in (2,2) signature and twistor space, beginning with a discussion of IR behavior. We find that the natural pole prescription renders the amplitudes well-defined and free of IR divergences. Loop amplitudes vanish for generic momenta, and in twistor space are even simpler than their tree-level counterparts! This further supports the idea that there exists a sharply defined object corresponding to the S-Matrix in (2,2) signature, computed by a dual theory naturally living in twistor space.Comment: V1: 46 pages + 23 figures. Less telegraphic abstract in the body of the paper. V2: 49 pages + 24 figures. Largely expanded set of references included. Some diagrammatic clarifications added, minor typo fixe