What is the probability that a random symmetric tensor is close to rank-one?

We address the general problem of estimating the probability that a real symmetric tensor is close to rank-one tensors. Using Weyl's tube formula, we turn this question into a differential geometric one involving the study of metric invariants of the real Veronese variety. More precisely, we give an explicit formula for its reach and curvature coefficients with respect to the Bombieri-Weyl metric. These results are obtained using techniques from Random Matrix theory and an explicit description of the second fundamental form of the Veronese variety in terms of GOE matrices. Our findings give a complete solution to the original problem, and in the case of rational normal curves lead to some novel asymptotic results.Comment: 25 pages. Minor changes, corrected a typo that affected some constant

New treatments for chronic obstructive pulmonary disease using ergogenic aids

Chronic obstructive pulmonary disease is currently considered a systemic disease, presenting structural and metabolic alterations that can lead to skeletal muscle dysfunction. This negatively affects the performance of respiratory and peripheral muscles, functional capacity, health-related quality of life and even survival. The decision to prescribe ergogenic aids for patients with chronic obstructive pulmonary disease is based on the fact that these drugs can avert or minimize catabolism and stimulate protein synthesis, thereby reducing the loss of muscle mass and increasing exercise tolerance. This review summarizes the available data regarding the use of anabolic steroids, creatine, L-carnitine, branched-chain amino acids and growth hormones in patients with chronic obstructive pulmonary disease. The advantage of using these ergogenic aids appears to lie in increasing lean muscle mass and inducing bioenergetic modifications. Within this context, most of the data collected deals with anabolic steroids. However, to date, the clinical benefits in terms of increased exercise tolerance and muscle strength, as well as in terms of the effect on morbidity and mortality, have not been consistently demonstrated. Dietary supplementation with substances of ergogenic potential might prove to be a valid adjuvant therapy for treating patients with advanced chronic obstructive pulmonary disease, especially those presenting loss of muscle mass or peripheral muscle weakness.A doença pulmonar obstrutiva crônica é considerada, atualmente, uma doença sistêmica, cujas alterações estruturais e metabólicas podem levar à disfunção muscular esquelética. Esta afeta negativamente o desempenho muscular respiratório e periférico, a capacidade funcional, a qualidade de vida relacionada à saúde e mesmo a sobrevida. A indicação de suplementação de substâncias ergogênicas para pacientes com doença pulmonar obstrutiva crônica baseia-se no fato de que estas drogas podem evitar, ou minimizar, o catabolismo e/ou estimular a síntese protéica, diminuindo a depleção de massa muscular e aumentando a capacidade de exercício. A presente revisão sumariza o conhecimento disponível acerca da utilização de esteróides anabolizantes, creatina, L-carnitina, aminoácidos de cadeia ramificada e hormônio de crescimento em pacientes com doença pulmonar obstrutiva crônica. A vantagem do uso dessas substâncias ergogênicas parece residir no aumento da massa magra e/ou na indução de modificações bioenergéticas. Nesse contexto, a maior experiência acumulada é com os esteróides anabolizantes. Entretanto, os benefícios clínicos em relação à melhora da capacidade de exercício e força muscular, bem como os efeitos na morbimortalidade, não foram, até a presente data, consistentemente demonstrados. A suplementação ergogênica pode vir a se constituir numa ferramenta adjuvante para o tratamento de pacientes com doença pulmonar obstrutiva crônica avançada, especialmente naqueles com depleção muscular e/ou fraqueza periférica.Universidade Federal de São Paulo (UNIFESP) Setor de Função Pulmonar e Fisiologia Clínica do ExercícioUniversidade Federal de São Paulo (UNIFESP)UNIFESP, Setor de Função Pulmonar e Fisiologia Clínica do ExercícioUNIFESPSciEL

Effects of rituximab in two patients with dysferlin-deficient muscular dystrophy

Background. The administration of rituximab (RTX) in vivo results in B-cell depletion, but evidence for multiple mechanisms of action have been reported. Surprisingly, B cell depletion produced a response in patients with polymyositis, which is characterized as a T cell-mediated autoimmune disorder with biopsy findings similar to Miyoshi myopathy (MM). Indeed, in dysferlinopathies, there is evidence of immune system involvement including the presence of muscle inflammation and a down regulation of the complement inhibitory factor, CD55. Methods. Two patients were treated with four weekly infusions of RTX 375 mg/m2. To measure the improvement in muscle strength after treatment, the isometric hand grip maximal voluntary contraction (MVC) was measured by load cell four times during treatment, and again after one year. In order to assess the reproducibility of our grip assessment, we determined the hand MVC analysis in 16 healthy subjects. Moreover, we measured the number of B cells present in patients by flow cytometric analysis during the course of treatment. Results. The analysis of B cell number during the course of treatment showed that CD20- and CD19-positive cells were depleted to 0-0.01%. The decrease in B cells was followed by an improvement in the mobility of the pelvic and shoulder girdles as shown by the MRC%. The MVC values of both patients began at values lower than normal whereas during treatment patients had improved percentage of muscle strength. The strength peak in both patients coincided with the minimum B cell values. There were no severe adverse events associated with an infusion of RTX. Conclusion. We consider the increase in muscle strength observed in both treated patients to be a consequence of their treatment with RTX. To our knowledge, these are the first cases of increased muscle strength in patients with MM. Furthermore, the results of this study indicate that B cell depletion with RTX may be useful in the treatment of patients affected by MM, suggesting a possible role for B cells in the pathophysiology of this muscle disorder

Spontaneous generation, enhanced propagation and optical imprinting of quantized vortices and dark solitons in a polariton superfluid: towards the control of quantum turbulence

In resonantly pumped polariton superfluids we recently explored a new regime based on the bistability of the polariton system to enhance the propagation of polariton fluids up to macroscopic distances. This technique together with an all-optical imprinting method allowed the generation and control of various topological excitations such as quantized vortices and dark solitons. The flexibility and scalability of the new experimental scheme opens the way to the systematic study of quantum turbulence in driven dissipative quantum fluids of light. In this article we review the basic working principles of the bistability enhanced propagation and of the imprinting technique and we discuss the main achieved results as well as the most promising future research directions.Comment: Review, 12 pages, 16 figure

MYH2 myopathy, a new case expands the clinical and pathological spectrum of the recessive form

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