Index theory for basic Dirac operators on Riemannian foliations

In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs.

On slicewise monotone parameterized problems and optimal proof systems for TAUT

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Hankel operators on holomorphic Hardy-Orlicz spaces

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Respiratory muscle training enhances maximal minute ventilation and forced vital capacity in adolescent athletes.

Introduction. Respiratory difficulties in athletes are common, especially in adolescents, even in the absence of exercise-induced bronchoconstriction. Immaturity of the respiratory muscles coupling at high respiratory rates could be a potential mechanism. Whether respiratory muscle training (RMT) can positively influence it is yet unknown. Goal. We investigate the effects of RMT on ventilation and performance parameters in adolescent athletes and hypothesize that RMT will enhance respiratory capacity. Methods. 12 healthy subjects (8 male, 4 female, 17±0.5 years) from a sports/study high school class, competitively involved in various sports (minimum of 10 hours per week) underwent respiratory function testing, maximal minute ventilation (MMV) measurements and a maximal treadmill incremental test with VO2max and ventilatory thresholds (VT1 and VT2) determination. They then underwent one month of RMT (4 times/week) using a eucapnic hyperventilation device, with an incremental training program. The same tests were repeated after RMT. Results. Subjects completed 14.8 sessions of RMT, with an increase in total ventilation per session of 211±29% during training. Borg scale evaluation of the RMT session was unchanged or reduced in all subjects, despite an increase in total respiratory work. No changes (p>0.05) were observed pre/post RMT in VO2max (53.4±7.5 vs 51.6±7.7 ml/kg/min), VT2 (14.4±1.4 vs 14.0±1.1 km/h) or Speed max at end of test (16.1±1.7 vs 15.8±1.7 km/h). MVV increased by 9.2% (176.7±36.9 vs 192.9±32.6 l/min, p<0.001) and FVC by 3.3% (6.70±0.75 vs 4.85±0.76 litres, p<0.05). Subjective evaluation of respiratory sensations during exercise and daily living were also improved. Conclusions. RMT improves MMV and FVC in adolescent athletes, along with important subjective respiratory benefits, although no changes are seen in treadmill maximal performance tests and VO2max measurements. RMT can be easily performed in adolescent without side effects, with a potential for improvement in training capacity and overall well-being.

Complex and real Hausdorff operators

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Moduli of smoothness and rate of a.e. convergence for some convolution operators

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Hyperthermia and maximal oxygen uptake in men and women.

To compare the effect of hyperthermia on maximal oxygen uptake (VO2max) in men and women, VO2max was measured in 11 male and 11 female runners under seven conditions involving various ambient temperatures (Ta at 50% RH) and preheating designed to manipulate the esophageal (Tes) and mean skin (Tsk) temperatures at VO2max. The conditions were: 25 degrees C, no preheating (control); 25, 35, 40, and 45 degrees C, with exercise-induced preheating by a 20-min walk at approximately 33% of control VO2max; 45 degrees C, no preheating; and 45 degrees C, with passive preheating during which Tes and Tsk were increased to the same degree as at the end of the 20-min walk at 45 degrees C. Compared to VO2max (l x min(-1)) in the control condition (4.52+/-0.46 in men, 3.01+/-0.45 in women), VO2max in men and women was reduced with exercise-induced or passive preheating and increased Ta, approximately 4% at 35 degrees C, approximately 9% at 40 degrees C and approximately 18% at 45 degrees C. Percentage reductions (7-36%) in physical performance (treadmill test time to exhaustion) were strongly related to reductions in VO2max (r=0.82-0.84). The effects of hyperthermia on VO2max and physical performance in men and women were almost identical. We conclude that men and women do not differ in their thermal responses to maximal exercise, or in the relationship of hyperthermia to reductions in VO2max and physical performance at high temperature. Data are reported as mean (SD) unless otherwise stated.

Right-left digit ratio (2D:4D) and maximal oxygen uptake.

A low digit ratio (2D:4D) and low 2D:4D in the right compared with the left hand (right-left 2D:4D) are thought to be determined by high in utero concentrations of testosterone, and are related to "masculine" traits such as aggression and performance in sports like running and rugby. Low right-left 2D:4D is also related to sensitivity to testosterone as measured by the number of cytosine-adenine-guanine triplet repeats in exon 1 of the androgen receptor gene. Here we show that low right-left 2D:4D is associated with high maximal oxygen uptake (VO2(max)), high velocity at VO2(max), and high maximum lactate concentration in a sample of teenage boys. We suggest that low right-left 2D:4D is linked to performance in some sports because it is a proxy of high sensitivity to prenatal and maybe also circulating testosterone and high VO2(max).

Folner sequences and finite operators

This article analyzes Folner sequences of projections for bounded linear operators and their relationship to the class of finite operators introduced by Williams in the 70ies. We prove that each essentially hyponormal operator has a proper Folner sequence (i.e. a Folner sequence of projections strongly converging to 1). In particular, any quasinormal, any subnormal, any hyponormal and any essentially normal operator has a proper Folner sequence. Moreover, we show that an operator is finite if and only if it has a proper Folner sequence or if it has a non-trivial finite dimensional reducing subspace. We also analyze the structure of operators which have no Folner sequence and give examples of them. For this analysis we introduce the notion of strongly non-Folner operators, which are far from finite block reducible operators, in some uniform sense, and show that this class coincides with the class of non-finite operators.

Implementació de la cerca d'un subgraf comú maximal a dos grafs mitjançant colles

La memòria que ací es presenta s'emmarca dins de l'àrea de teoria de grafs. En concret es treballa la implementació d'un algorisme per trobar el subgraf comú maximal (SCM) de dos grafs mitjançant la cerca de colles maximals (CM). L'aportació principal del projecte consisteix en, donats dos grafs qualsevol, trobar el seu graf associat per tal de poder cercar la seva colla maximal (CM). I així, utilitzant funcions existents en el llenguatge de programació, poder trobar el seu subgraf comú maximal (SCM), necessari per calcular la distància entre grafs i així determinar quan d'isomorfs són.

The equity core and the Lorenz-maximal allocations in the equal division core

In this paper, we characterize the non-emptiness of the equity core (Selten, 1978) and provide a method, easy to implement, for computing the Lorenz-maximal allocations in the equal division core (Dutta-Ray, 1991). Both results are based on a geometrical decomposition of the equity core as a finite union of polyhedrons. Keywords: Cooperative game, equity core, equal division core, Lorenz domination. JEL classification: C71

Hierachy-based methodology for producing educational contents with maximal reutilization

Computer based training or distance education are facing dramatic changes withthe advent of standardization efforts, some of them concentrating in maximal reuse.This is of paramount importance for a sustainable -cost affordable- production ofeducational materials. Reuse in itself should not be a goal, though, since manymethodological aspects might be lost. In this paper we propose two contentproduction approaches for the InterMediActor platform under a competence-basedmethodology: either a bottom-up approach where content is designed from scratchor a top-down methodology where existing material can be gradually adapted tofulfil requisites to be used with maximal flexibility into InterMediActor.

Evidence for a TCR affinity threshold delimiting maximal CD8 T cell function.

Protective adaptive immune responses rely on TCR-mediated recognition of Ag-derived peptides presented by self-MHC molecules. However, self-Ag (tumor)-specific TCRs are often of too low affinity to achieve best functionality. To precisely assess the relationship between TCR-peptide-MHC binding parameters and T cell function, we tested a panel of sequence-optimized HLA-A(*)0201/NY-ESO-1(157-165)-specific TCR variants with affinities lying within physiological boundaries to preserve antigenic specificity and avoid cross-reactivity, as well as two outliers (i.e., a very high- and a low-affinity TCR). Primary human CD8 T cells transduced with these TCRs demonstrated robust correlations between binding measurements of TCR affinity and avidity and the biological response of the T cells, such as TCR cell-surface clustering, intracellular signaling, proliferation, and target cell lysis. Strikingly, above a defined TCR-peptide-MHC affinity threshold (K(D) < approximately 5 muM), T cell function could not be further enhanced, revealing a plateau of maximal T cell function, compatible with the notion that multiple TCRs with slightly different affinities participate equally (codominantly) in immune responses. We propose that rational design of improved self-specific TCRs may not need to be optimized beyond a given affinity threshold to achieve both optimal T cell function and avoidance of the unpredictable risk of cross-reactivity.