A note on permutation regularity

The existence of a small partition of a combinatorial structure into random-like subparts, a so-called regular partition, has proven to be very useful in the study of extremal problems, and has deep algorithmic consequences. The main result in this direction is the Szemeredi Regularity Lemma in graph theory. In this note, we are concerned with regularity in permutations: we show that every permutation of a sufficiently large set has a regular partition into a small number of intervals. This refines the partition given by Cooper (2006) [10], which required an additional non-interval exceptional class. We also introduce a distance between permutations that plays an important role in the study of convergence of a permutation sequence. (C) 2011 Elsevier B.V. All rights reserved.

Image Reconstruction Using Interval Simulated Annealing in Electrical Impedance Tomography

Electrical impedance tomography (EIT) is an imaging technique that attempts to reconstruct the impedance distribution inside an object from the impedance between electrodes placed on the object surface. The EIT reconstruction problem can be approached as a nonlinear nonconvex optimization problem in which one tries to maximize the matching between a simulated impedance problem and the observed data. This nonlinear optimization problem is often ill-posed, and not very suited to methods that evaluate derivatives of the objective function. It may be approached by simulated annealing (SA), but at a large computational cost due to the expensive evaluation process of the objective function, which involves a full simulation of the impedance problem at each iteration. A variation of SA is proposed in which the objective function is evaluated only partially, while ensuring boundaries on the behavior of the modified algorithm.

Similar health benefits of endurance and high-intensity interval training in obese children

Purpose: To compare two modalities of exercise training (i.e., Endurance Training [ET] and High-Intensity Interval Training [HIT]) on health-related parameters in obese children aged between 8 and 12 years. Methods: Thirty obese children were randomly allocated into either the ET or HIT group. The ET group performed a 30 to 60-minute continuous exercise at 80% of the peak heart rate (HR). The HIT group training performed 3 to 6 sets of 60-s sprint at 100% of the peak velocity interspersed by a 3-min active recovery period at 50% of the exercise velocity. HIT sessions last similar to 70% less than ET sessions. At baseline and after 12 weeks of intervention, aerobic fitness, body composition and metabolic parameters were assessed. Results: Both the absolute (ET: 26.0%; HIT: 19.0%) and the relative VO2 peak (ET: 13.1%; HIT: 14.6%) were significantly increased in both groups after the intervention. Additionally, the total time of exercise (ET: 19.5%; HIT: 16.4%) and the peak velocity during the maximal graded cardiorespiratory test (ET: 16.9%; HIT: 13.4%) were significantly improved across interventions. Insulinemia (ET: 29.4%; HIT: 30.5%) and HOMA-index (ET: 42.8%; HIT: 37.0%) were significantly lower for both groups at POST when compared to PRE. Body mass was significantly reduced in the HIT (2.6%), but not in the ET group (1.2%). A significant reduction in BMI was observed for both groups after the intervention (ET: 3.0%; HIT: 5.0%). The responsiveness analysis revealed a very similar pattern of the most responsive variables among groups. Conclusion: HIT and ET were equally effective in improving important health related parameters in obese youth.

Effect of the rest interval duration between contractions on muscle fatigue

Background: We aimed to investigate the effect of rest interval, between successive contractions, on muscular fatigue. Methods: Eighteen subjects performed elbow flexion and extension (30 repetitions) on an isokinetic dynamometer with 80 degrees of range of motion. The flexion velocity was 120 degrees/s, while for elbow extension we used 5 different velocities (30, 75, 120, 240, 360 degrees/s), producing 5 different rest intervals (2.89, 1.28, 0.85, 0.57 and 0.54 s). Results: We observed that when the rest interval was 2.89 s there was a reduction in fatigue. On the other hand, when the rest interval was 0.54 s the fatigue was increased. Conclusions: When the resting time was lower (0.54 s) the decline of work in the flexor muscle group was higher compared with different rest interval duration.

Effect of continuous and interval exercise training on the PETCO2 response during a graded exercise test in patients with coronary artery disease

OBJECTIVE: The purpose of this study was to evaluate the following: 1) the effects of continuous exercise training and interval exercise training on the end-tidal carbon dioxide pressure (PETCO2) response during a graded exercise test in patients with coronary artery disease; and 2) the effects of exercise training modalities on the association between PETCO2 at the ventilatory anaerobic threshold (VAT) and indicators of ventilatory efficiency and cardiorespiratory fitness in patients with coronary artery disease. METHODS: Thirty-seven patients (59.7 +/- 1.7 years) with coronary artery disease were randomly divided into two groups: continuous exercise training (n = 20) and interval exercise training (n = 17). All patients performed a graded exercise test with respiratory gas analysis before and after three months of the exercise training program to determine the VAT, respiratory compensation point (RCP) and peak oxygen consumption. RESULTS: After the interventions, both groups exhibited increased cardiorespiratory fitness. Indeed, the continuous exercise and interval exercise training groups demonstrated increases in both ventilatory efficiency and PETCO2 values at VAT, RCP, and peak of exercise. Significant associations were observed in both groups: 1) continuous exercise training (PETCO(2)VAT and cardiorespiratory fitness r = 0.49; PETCO(2)VAT and ventilatory efficiency r = -0.80) and 2) interval exercise training (PETCO(2)VAT and cardiorespiratory fitness r = 0.39; PETCO(2)VAT and ventilatory efficiency r = -0.45). CONCLUSIONS: Both exercise training modalities showed similar increases in PETCO2 levels during a graded exercise test in patients with coronary artery disease, which may be associated with an improvement in ventilatory efficiency and cardiorespiratory fitness.

Chains of Infinite Order, Chains with Memory of Variable Length, and Maps of the Interval

We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we characterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval.

Influence of Alloying Elements Upon the Solidification Interval of CA6NM Cast Martensitic Stainless Steel

The influence of different Cr and C contents upon the solidification interval of ASTM A352M-06 Grade CA6NM cast martensitic stainless steel has been investigated using computational thermodynamics, and checked against DTA measurements in samples taken from 13 large cast parts, in order to identify potential sources for improvement on the part castability. Calculation results suggest, indeed, that this would be the case for C: when its content increases from 0.018 to 0.044 wt.% C (within the allowed range in the alloy specification), the solidification intervals increases from 25 to 43 K, which suggests improved castability with decreasing C contents. DTA results, however, do not support this prediction, showing a fairly constant solidification interval around 23 K for all investigated samples. The results are discussed both regarding the impact in alloy processing and the fitness of the existing databases to reproduce experimental results in these limiting cases.

Rigidity for piecewise smooth homeomorphisms on the circle

We find conditions for two piecewise 'C POT.2+V' homeomorphisms f and g of the circle to be 'C POT.1' conjugate. Besides the restrictions on the combinatorics of the maps (we assume that the maps have bounded combinatorics), and necessary conditions on the one-side derivatives of points where f and g are not differentiable, we also assume zero mean-nonlinearity for f and g.