An updated analysis of two classes of f(R) theories of gravity

The observed accelerated cosmic expansion can be a signature of fourth\,-\,order gravity theories, where the acceleration of the Universe is a consequence of departures from Einstein General Relativity, rather than the sign of the existence of a fluid with negative pressure. In the fourth\,-\,order gravity theories, the gravity Lagrangian is described by an analytic function $f(R)$ of the scalar curvature $R$ subject to the demanding conditions that no detectable deviations from standard GR is observed on the Solar System scale. Here we consider two classes of $f(R)$ theories able to pass Solar System tests and investigate their viability on cosmological scales. To this end, we fit the theories to a large dataset including the combined Hubble diagram of Type Ia Supernovae and Gamma Ray Bursts, the Hubble parameter $H(z)$ data from passively evolving red galaxies, Baryon Acoustic Oscillations extracted from the seventh data release of the Sloan Digital Sky Survey (SDSS) and the distance priors from the Wilkinson Microwave Anisotropy Probe seven years (WMAP7) data. We find that both classes of $f(R)$ fit very well this large dataset with the present\,-\,day values of the matter density, Hubble constant and deceleration parameter in agreement with previous estimates; however, the strong degeneracy among the $f(R)$ parameters prevents us from strongly constraining their values. We also derive the growth factor $g = d\ln{\delta}/d\ln{a}$, with $\delta = \delta \rho_M/\rho_M$ the matter density perturbation, and show that it can still be well approximated by $g(z) \propto \Omega_M(z)^{\gamma}$. We finally constrain $\gamma$ (on some representative scales) and investigate its redshift dependence to see whether future data can discriminate between these classes of $f(R)$ theories and standard dark energy models.Comment: 27 pages, 5 figures, 1 table, accepted for publication on JCAP. Note that this paper updates and supersedes preprint arXiv:0907.468

Interior Optima and the Inada Conditions

We present a new proof of the interiority of the policy function based on the Inada conditions. It is based on supporting properties of concave functions.growth model ; Inada conditions ; policy function

Monetary Equilibrium and the Differentiability of the Value Function

In this study we offer a new approach to proving the differentiability of the value function, which complements and extends the literature on dynamic programming. This result is then applied to the analysis of equilibrium in the recent class of monetary economies developed in [13]. For this type of environments we demonstrate that the value function is differentiable and this guarantees that the marginal value of money balances is well defined.value function ; optimal plans ; money

Green synthesis of vanillin: Pervaporation and dialysis for process intensification in a membrane reactor

In the present work, two different membrane processes (pervaporation and dialysis) are compared in view of their utilization in a membrane reactor, where vanillin, which is probably the most important aroma of the food industry, is synthesized in a green and sustainable way. The utilized precursor (ferulic acid, which is possibly a natural product from agricultural wastes) is partially oxidized (photocatalytically or biologically) and the product is continuously recovered from the reacting solution by the membrane process to avoid its degradation. It is observed that pervaporation is much more selective towards vanillin than dialysis, but the permeate flux of dialysis is much higher. Furthermore, dialysis can work also at lower temperatures and can be used to continuously restore the consumed substrate into the reacting mixture. A mathematical model of the integrated process (reaction combined with membrane separation) reproduces quite satisfactorily the experimental results and can be used for the analysis and the design of the process

Mass - concentration relation and weak lensing peak counts

The statistics of peaks in weak lensing convergence maps is a promising tool to investigate both the properties of dark matter haloes and constrain the cosmological parameters. We study how the number of detectable peaks and its scaling with redshift depend upon the cluster dark matter halo profiles and use peak statistics to constrain the parameters of the mass - concentration (MC) relation. We investigate which constraints the Euclid mission can set on the MC coefficients also taking into account degeneracies with the cosmological parameters. To this end, we first estimate the number of peaks and its redshift distribution for different MC relations. We find that the steeper the mass dependence and the larger the normalisation, the higher is the number of detectable clusters, with the total number of peaks changing up to $40\%$ depending on the MC relation. We then perform a Fisher matrix forecast of the errors on the MC relation parameters as well as cosmological parameters. We find that peak number counts detected by Euclid can determine the normalization $A_v$, the mass $B_v$ and redshift $C_v$ slopes and intrinsic scatter $\sigma_v$ of the MC relation to an unprecedented accuracy being $\sigma(A_v)/A_v = 1\%$, $\sigma(B_v)/B_v = 4\%$, $\sigma(C_v)/C_v = 9\%$, $\sigma(\sigma_v)/\sigma_v = 1\%$ if all cosmological parameters are assumed to be known. Should we relax this severe assumption, constraints are degraded, but remarkably good results can be restored setting only some of the parameters or combining peak counts with Planck data. This precision can give insight on competing scenarios of structure formation and evolution and on the role of baryons in cluster assembling. Alternatively, for a fixed MC relation, future peaks counts can perform as well as current BAO and SNeIa when combined with Planck.Comment: 14 pages, 8 figures, accepted for publication on Astronomy & Astrophysic

Monetary Equilibrium and the Differentiability of the Value Function

In this study we offer a new approach to proving the differentiability of the value function, which complements and extends the literature on dynamic programming. This result is then applied to the analysis of equilibrium in the recent class of monetary economies developed in [Lagos, R., Wright, R., 2005. A unified framework for monetary theory and policy analysis. journal of Political Economy 113, 463-484]. For this type of environments we demonstrate that the value function is differentiable and this guarantees that the marginal value of money balances is well defined

GazeDrone: Mobile Eye-Based Interaction in Public Space Without Augmenting the User

Gaze interaction holds a lot of promise for seamless human-computer interaction. At the same time, current wearable mobile eye trackers require user augmentation that negatively impacts natural user behavior while remote trackers require users to position themselves within a confined tracking range. We present GazeDrone, the first system that combines a camera-equipped aerial drone with a computational method to detect sidelong glances for spontaneous (calibration-free) gaze-based interaction with surrounding pervasive systems (e.g., public displays). GazeDrone does not require augmenting each user with on-body sensors and allows interaction from arbitrary positions, even while moving. We demonstrate that drone-supported gaze interaction is feasible and accurate for certain movement types. It is well-perceived by users, in particular while interacting from a fixed position as well as while moving orthogonally or diagonally to a display. We present design implications and discuss opportunities and challenges for drone-supported gaze interaction in public