Proof-theoretical studies on the bounded functional interpretation

Tese de doutoramento, Matemática (Álgebra Lógica e Fundamentos), 2009, Universidade de Lisboa, Faculdade de CiênciasThis dissertation studies the bounded functional interpretation of Ferreira and Oliva. The work follows two different directions. We start by focusing on the generalization of the bounded functional interpretation to second-order arithmetic (a.k.a. analysis). This is accomplished via bar recursion, a well-founded form of recursion. We carry out explicitly the bounded functional interpretation of the (non-intuitionistic) law of the double negation shift with bar recursive functionals of finite type. As a consequence, we show that full numerical comprehension has bounded functional interpretation in the classical case. In the other direction, we extend the bounded functional interpretation with new base types, representing an abstract class of normed spaces. Some studies on the representation of the real numbers are carried out, as it is useful to have a representation which meshes well with the notion of majorizability. A majorizability theorem holds. We carry out the extension of the bounded functional interpretation to new base types and prove a soundness theorem with characteristic principles similar to the numerical case. We also extend the classical direct bounded functional interpretation of Peano arithmetic to new base types and prove the corresponding soundness theorem. The characteristic principles are also similar to the ones in the numerical case. In the classical setting, these prove that linear operators are automatically bounded and that Cauchy sequences (with a modulus of Cauchyness) of elements of the new base type do converge. Relying on the characteristic principles (and on a special form of choice), a logical version of the Baire category theorem of functional analysis is proved. As a consequence, we also prove logical versions of the Banach-Steinhaus and the open mapping theorems.Programa Operacional Ciência e Inovação 2010 (POCI 2010) e FS

Effects of a multidisciplinary program on autonomic modulation in overweight or obese children and adolescents

Purpose: this study evaluated the effects of a multidisciplinary program on autonomic modulation in overweight or obese children and adolescents. Methods: fi fteen individuals with 10,93±2,28 years were submitted to autonomic evaluation using heart rate variability before and after a program based on physical exercises for three months, three times a week, 60 minutes per session and psychological and nutritional counseling. Data was analyzed using the paired t-test or Wilcoxon test and the level of signifi cance was set at P < 0.05. Results: multidisciplinary program was able to promote benefi ts in autonomic modulation observed thought temporal (SDNN: 39,96 ± 10,33 x 49,44 ± 12,31; p = 0,019; rMSSD: 28,97 ± 11,50 x 37,26 ± 11,17; p = 0,018), spectral (LFnu: 64,49 ± 12,21 x 56,74 ± 11,18; p = 0,014; HFnu: 35,50 ± 12,21 x 43,25 ± 11,18; p = 0,014) and geometrical (SD1: 20,51 ± 8,13 x 26,36 ± 7,90; p = 0,018 SD2: 52,31 ± 13,04 x 64,58 ± 16,33; p = 0,031) indices in overweigh and obese children and adolescents. Also, after the intervention there was a reduction on resting heart rate (88,53 ± 9,24 x 83,09 ± 7,93; p = 0,023) and there were changes in the classifi cation of overweigh 26,67% x 46,66% and obesity 73,33% x 53,33%, although not significant changes in body mass index. Conclusions: exercise program together with nutritional and psychological counseling is able to promote benefi ts in autonomic modulation in children and adolescents who are overweight or obese

Relevant aspects of golden retriever muscular dystrophy for the study of Duchenne muscular dystrophy in humans

ABSTRACT: Golden Retriever muscular dystrophy (GRMD) is the most representative model for studying Duchenne muscular dystrophy (DMD) in humans, owing its phenotypic expression. DMD is a recessive disorder linked to the X chromosome in which the loss of dystrophin induces progressive weakness and degeneration of the skeletal and cardiac muscles, which lead to replacement by connective and adipose tissues. Onset of clinical signs occurs between 2 and 5 years of age, and many patients die from heart or respiratory failure. The main studies concerning dystrophic Golden Retrievers (DGR) sought to elucidate the pathophysiology of the disease and its clinical implications to develop therapies and alternative treatments to improve the quality of life and increase longevity of DMD patients. This review presents an overview of relevant contributions of the DGR model for elucidating DMD in humans

Verbal and visual stimulation effects on rectus femoris and biceps femoris muscles during isometric and concentric

Background: Coactivation may be both desirable (injury prevention) or undesirable (strength measurement). In this context, different styles of muscle strength stimulus have being investigated. In this study we evaluated the effects of verbal and visual stimulation on rectus femoris and biceps femoris muscles contraction during isometric and concentric. Methods: We investigated 13 men (age =23.1 ± 3.8 years old; body mass =75.6 ± 9.1 kg; height =1.8 ± 0.07 m). We used the isokinetic dynamometer BIODEX device and an electromyographic (EMG) system. We evaluated the maximum isometric and isokinetic knee extension and flexion at 60°/s. The following conditions were evaluated: without visual nor verbal command (control); verbal command; visual command and; verbal and visual command. In relation to the concentric contraction, the volunteers performed five reciprocal and continuous contractions at 60°/s. With respect to isometric contractions it was made three contractions of five seconds for flexion and extension in a period of one minute. Results: We found that the peak torque during isometric flexion was higher in the subjects in the VVC condition (p > 0.05). In relation to muscle coactivation, the subjects presented higher values at the control condition (p > 0.05). Conclusion: We suggest that this type of stimulus is effective for the lower limbs