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.

Methodology for studying the numerical speed of sound in finite differences schemes

The space and time discretization inherent to all FDTD schemesintroduce non-physical dispersion errors, i.e. deviations ofthe speed of sound from the theoretical value predicted bythe governing Euler differential equations. A generalmethodologyfor computing this dispersion error via straightforwardnumerical simulations of the FDTD schemes is presented.The method is shown to provide remarkable accuraciesof the order of 1/1000 in a wide variety of twodimensionalfinite difference schemes.

Policy and the Evolution of the US Economy: 1948-2002

This paper investigates the relationship between monetary policy and the changes experienced by the US economy using a small scale New-Keynesian model. The model is estimated with Bayesian techniques and the stability of policy parameter estimates and of the transmission of policy shocks examined. The model fits well the data and produces forecasts comparable or superior to those of alternative specifications. The parameters of the policy rule, the variance and the transmission of policy shocks have been remarkably stable. The parameters of the Phillips curve and of the Euler equations are varying.

Solving non-linear stochastic models by parameterizing expectations: An application to asset pricing with production

A new algorithm called the parameterized expectations approach(PEA) for solving dynamic stochastic models under rational expectationsis developed and its advantages and disadvantages are discussed. Thisalgorithm can, in principle, approximate the true equilibrium arbitrarilywell. Also, this algorithm works from the Euler equations, so that theequilibrium does not have to be cast in the form of a planner's problem.Monte--Carlo integration and the absence of grids on the state variables,cause the computation costs not to go up exponentially when the numberof state variables or the exogenous shocks in the economy increase. \\As an application we analyze an asset pricing model with endogenousproduction. We analyze its implications for time dependence of volatilityof stock returns and the term structure of interest rates. We argue thatthis model can generate hump--shaped term structures.

Rate of convergence of a particle method to the solution of the Mc Kean-Vlasov's equation

This paper studies the rate of convergence of an appropriatediscretization scheme of the solution of the Mc Kean-Vlasovequation introduced by Bossy and Talay. More specifically,we consider approximations of the distribution and of thedensity of the solution of the stochastic differentialequation associated to the Mc Kean - Vlasov equation. Thescheme adopted here is a mixed one: Euler/weakly interactingparticle system. If $n$ is the number of weakly interactingparticles and $h$ is the uniform step in the timediscretization, we prove that the rate of convergence of thedistribution functions of the approximating sequence in the $L^1(\Omega\times \Bbb R)$ norm and in the sup norm is of theorder of $\frac 1{\sqrt n} + h $, while for the densities is ofthe order $ h +\frac 1 {\sqrt {nh}}$. This result is obtainedby carefully employing techniques of Malliavin Calculus.

Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defind by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincare-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.

Performance of mechanical ventilators at the patient's home: a multicentric quality control study

Background: Quality control procedures vary considerably among the providers of equipment for home mechanical ventilation (HMV). Methods: A multicentre quality control survey of HMV was performed at the home of 300 patients included in the HMV programmes of four hospitals in Barcelona. It consisted of three steps: (1) the prescribed ventilation settings, the actual settings in the ventilator control panel, and the actual performance of the ventilator measured at home were compared; (2) the different ventilator alarms were tested; and (3) the effect of differences between the prescribed settings and the actual performance of the ventilator on non-programmed readmissions of the patient was determined. Results: Considerable differences were found between actual, set, and prescribed values of ventilator variables; these differences were similar in volume and pressure preset ventilators. The percentage of patients with a discrepancy between the prescribed and actual measured main ventilator variable (minute ventilation or inspiratory pressure) of more than 20% and 30% was 13% and 4%, respectively. The number of ventilators with built in alarms for power off, disconnection, or obstruction was 225, 280 and 157, respectively. These alarms did not work in two (0.9%), 52 (18.6%) and eight (5.1%) ventilators, respectively. The number of non-programmed hospital readmissions in the year before the study did not correlate with the index of ventilator error. Conclusions: This study illustrates the current limitations of the quality control of HMV and suggests that improvements should be made to ensure adequate ventilator settings and correct ventilator performance and ventilator alarm operation.

Analog circuit for real-time computation of respiratory mechanical impedance in sleep studies

The aim of this work was to develop a low-cost circuit for real-time analog computation of the respiratory mechanical impedance in sleep studies. The practical performance of the circuit was tested in six patients with obstructive sleep apnea. The impedance signal provided by the analog circuit was compared with the impedance calculated simultaneously with a conventional computerized system. We concluded that the low-cost analog circuit developed could be a useful tool for facilitating the real-time assessment of airway obstruction in routine sleep studies.

Spin-2 gravitational trace anomaly

The part proportional to the Euler-Poincar characteristic of the contribution of spin-2 fields to the gravitational trace anomaly is computed. It is seen to be of the same sign as all the lower-spin contributions, making anomaly cancellation impossible. Subtleties related to Weyl invariance, gauge independence, ghosts, and counting of degrees of freedom are pointed out.

Energy and structure of dilute hard- and soft-sphere gases

The energy and structure of dilute hard- and soft-sphere Bose gases are systematically studied in the framework of several many-body approaches, such as the variational correlated theory, the Bogoliubov model, and the uniform limit approximation, valid in the weak-interaction regime. When possible, the results are compared with the exact diffusion Monte Carlo ones. Jastrow-type correlation provides a good description of the systems, both hard- and soft-spheres, if the hypernetted chain energy functional is freely minimized and the resulting Euler equation is solved. The study of the soft-sphere potentials confirms the appearance of a dependence of the energy on the shape of the potential at gas paremeter values of x~0.001. For quantities other than the energy, such as the radial distribution functions and the momentum distributions, the dependence appears at any value of x. The occurrence of a maximum in the radial distribution function, in the momentum distribution, and in the excitation spectrum is a natural effect of the correlations when x increases. The asymptotic behaviors of the functions characterizing the structure of the systems are also investigated. The uniform limit approach is very easy to implement and provides a good description of the soft-sphere gas. Its reliability improves when the interaction weakens.

Ground-state properties of a dilute homogeneous Bose gas of hard disks in two dimensions

The energy and structure of a dilute hard-disks Bose gas are studied in the framework of a variational many-body approach based on a Jastrow correlated ground-state wave function. The asymptotic behaviors of the radial distribution function and the one-body density matrix are analyzed after solving the Euler equation obtained by a free minimization of the hypernetted chain energy functional. Our results show important deviations from those of the available low density expansions, already at gas parameter values x~0.001 . The condensate fraction in 2D is also computed and found generally lower than the 3D one at the same x.

Boson-boson mixtures and triplet correlations

The hypernetted-chain formalism for boson-boson mixtures described by an extended Jastrow correlated wave function is derived, taking into account elementary diagrams and triplet correlations. The energy of an ideal boson 3He-4He mixture is computed for low values of the 3He concentration. The zero-3He-concentration limit provides a 3He chemical potential in good agreement with the experimental value, when a McMillan two-body correlation factor and the Lennard-Jones potential are adopted. If the Euler equations for the two-body correlation factors are solved in presence of triplet correlations, the agreement is again improved. At the experimental 4He equilibrium density, the 3He chemical potential turns out to be -2.58 K, to be compared with the experimental value, -2.79 K.

A reduction of order two for infinite-order Lagrangians

Given a Lagrangian system depending on the position derivatives of any order, and assuming that certain conditions are satisfied, a second-order differential system is obtained such that its solutions also satisfy the Euler equations derived from the original Lagrangian. A generalization of the singular Lagrangian formalism permits a reduction of order keeping the canonical formalism in sight. Finally, the general results obtained in the first part of the paper are applied to Wheeler-Feynman electrodynamics for two charged point particles up to order 1/c4.

Analog circuit for real-time computation of respiratory mechanical impedance in sleep studies

The aim of this work was to develop a low-cost circuit for real-time analog computation of the respiratory mechanical impedance in sleep studies. The practical performance of the circuit was tested in six patients with obstructive sleep apnea. The impedance signal provided by the analog circuit was compared with the impedance calculated simultaneously with a conventional computerized system. We concluded that the low-cost analog circuit developed could be a useful tool for facilitating the real-time assessment of airway obstruction in routine sleep studies.

Chronic intestinal pseudoobstruction and ophthalmoplegia in a patient with mitochondrial myopathy

A 38 year old woman having chronic intestinal pseudoobstruction associated with mitochondrial myopathy is reported. The clinical and radiographic features suggested the diagnosis of chronic intestinal pseudoobstruction. Muscular atrophy and ophthalmoplegia led to muscle biopsy, which disclosed accumulation of normal and abnormal mitochondria ('ragged red fibres'), characteristic of mitochondrial myopathy.