The Merton Problem with a Drawdown Constraint on Consumption

In this paper, we work in the framework of the Merton problem but we impose a drawdown constraint on the consumption process. This means that consumption can never fall below a fixed proportion of the running maximum of past consumption. In terms of economic motivation, this constraint represents a type of habit formation where the investor is reluctant to let his standard of living fall too far from the maximum standard achieved to date. We use techniques from stochastic optimal control and duality theory to obtain our candidate value function and optimal controls, which are then verified

How the brain represents the reward value of fat in the mouth.

The palatability and pleasantness of the sensory properties of foods drive food selection and intake and may contribute to overeating and obesity. Oral fat texture can make food palatable and pleasant. To analyze its neural basis, we correlated humans’ subjective reports of the pleasantness of the texture and flavor of a high- and low-fat food with a vanilla or strawberry flavor, with neural activations measured with functional magnetic resonance imaging. Activity in the midorbitofrontal and anterior cingulate cortex was correlated with the pleasantness of oral fat texture and in nearby locations with the pleasantness of flavor. The pregenual cingulate cortex showed a supralinear response to the combination of high fat and pleasant, sweet flavor, implicating it in the convergence of fat texture and flavor to produce a representation of highly pleasant stimuli. The subjective reports of oral fattiness were correlated with activations in the midorbitofrontal cortex and ventral striatum. The lateral hypothalamus and amygdala were more strongly activated by high- versus low-fat stimuli. This discovery of which brain regions track the subjective hedonic experience of fat texture will help to unravel possible differences in the neural responses in obese versus lean people to oral fat, a driver of food intake

An accurate formula for the period of a simple pendulum oscillating beyond the small-angle regime

A simple approximation formula is derived here for the dependence of the period of a simple pendulum on amplitude that only requires a pocket calculator and furnishes an error of less than 0.25% with respect to the exact period. It is shown that this formula describes the increase of the pendulum period with amplitude better than other simple formulas found in literature. A good agreement with experimental data for a low air-resistance pendulum is also verified and it suggests, together with the current availability/precision of timers and detectors, that the proposed formula is useful for extending the pendulum experiment beyond the usual small-angle oscillations.Comment: 15 pages and 4 figures. to appear in American Journal of Physic

Probing the non-linear structure of general relativity with black hole binaries

Observations of the inspiral of massive binary black holes (BBH) in the Laser Interferometer Space Antenna (LISA) and stellar mass binary black holes in the European Gravitational-Wave Observatory (EGO) offer an unique opportunity to test the non-linear structure of general relativity. For a binary composed of two non-spinning black holes, the non-linear general relativistic effects depend only on the masses of the constituents. In a recent letter, we explored the possibility of a test to determine all the post-Newtonian coefficients in the gravitational wave-phasing. However, mutual covariances dilute the effectiveness of such a test. In this paper, we propose a more powerful test in which the various post-Newtonian coefficients in the gravitational wave phasing are systematically measured by treating three of them as independent parameters and demanding their mutual consistency. LISA (EGO) will observe BBH inspirals with a signal-to-noise ratio of more than 1000 (100) and thereby test the self-consistency of each of the nine post-Newtonian coefficients that have so-far been computed, by measuring the lower order coefficients to a relative accuracy of $\sim 10^{-5}$ (respectively, $\sim 10^{-4}$) and the higher order coefficients to a relative accuracy in the range $10^{-4}$-0.1 (respectively, $10^{-3}$-1).Comment: 5 pages, 4 figures. Revised version, accepted for publication in Phys. Rev

Generic bounds on dipolar gravitational radiation from inspiralling compact binaries

Various alternative theories of gravity predict dipolar gravitational radiation in addition to quadrupolar radiation. We show that gravitational wave (GW) observations of inspiralling compact binaries can put interesting constraints on the strengths of the dipole modes of GW polarizations. We put forward a physically motivated gravitational waveform for dipole modes, in the Fourier domain, in terms of two parameters: one which captures the relative amplitude of the dipole mode with respect to the quadrupole mode ($\alpha$) and the other a dipole term in the phase ($\beta$). We then use this two parameter representation to discuss typical bounds on their values using GW measurements. We obtain the expected bounds on the amplitude parameter $\alpha$ and the phase parameter $\beta$ for Advanced LIGO (AdvLIGO) and Einstein Telescope (ET) noise power spectral densities using Fisher information matrix. AdvLIGO and ET may at best bound $\alpha$ to an accuracy of $\sim10^{-2}$ and $\sim10^{-3}$ and $\beta$ to an accuracy of $\sim10^{-5}$ and $\sim10^{-6}$ respectively.Comment: Matches with the published versio

Pseudo-Landau levels of Bogoliubov quasiparticles in strained nodal superconductors

Motivated by theory and experiments on strain induced pseudo-Landau levels (LLs) of Dirac fermions in graphene and topological materials, we consider its extension for Bogoliubov quasiparticles (QPs) in a nodal superconductor (SC). We show, using an effective low energy description and numerical lattice calculations for a d-wave SC, that a spatial variation of the electronic hopping amplitude or a spatially varying s-wave pairing component can act as a pseudo-magnetic field for the Bogoliubov QPs, leading to the formation of pseudo-LLs. We propose realizations of this phenomenon in the cuprate SCs, via strain engineering in films or nanowires, or s-wave proximity coupling in the vicinity of a nematic instability, and discuss its signatures in tunneling experiments.Comment: 13 pages, 5 figs (added refs

Formulation and characterization of an apigenin-phospholipid phytosome (APLC) for improved solubility, in vivo bioavailability, and antioxidant potential

The apigenin-phospholipid phytosome (APLC) was developed to improve the aqueous solubility, dissolution, in vivo bioavailability, and antioxidant activity of apigenin. The APLC synthesis was guided by a full factorial design strategy, incorporating specific formulation and process variables to deliver an optimized product. The design-optimized formulation was assayed for aqueous solubility, in vitro dissolution, pharmacokinetics, and antioxidant activity. The pharmacological evaluation was carried out by assessing its effects on carbon tetrachloride-induced elevation of liver function marker enzymes in a rat model. The antioxidant activity was assessed by studying its effects on the liver antioxidant marker enzymes. The developed model was validated using the design-optimized levels of formulation and process variables. The physical-chemical characterization confirmed the formation of phytosomes. The optimized formulation demonstrated over 36-fold higher aqueous solubility of apigenin, compared to that of pure apigenin. The formulation also exhibited a significantly higher rate and extent of apigenin release in dissolution studies. The pharmacokinetic analysis revealed a significant enhancement in the oral bioavailability of apigenin from the prepared formulation, compared to pure apigenin. The liver function tests indicated that the prepared phytosome showed a significantly improved restoration of all carbon tetrachloride-elevated rat liver function marker enzymes. The prepared formulation also exhibited antioxidant potential by significantly increasing the levels of glutathione, superoxide dismutase, catalase, and decreasing the levels of lipid peroxidase. The study shows that phospholipid-based phytosome is a promising and viable strategy for improving the delivery of apigenin and similar phytoconstituents with low aqueous solubility

Inspiralling compact binaries in quasi-elliptical orbits: The complete third post-Newtonian energy flux

The instantaneous contributions to the 3PN gravitational wave luminosity from the inspiral phase of a binary system of compact objects moving in a quasi elliptical orbit is computed using the multipolar post-Minkowskian wave generation formalism. The necessary inputs for this calculation include the 3PN accurate mass quadrupole moment for general orbits and the mass octupole and current quadrupole moments at 2PN. Using the recently obtained 3PN quasi-Keplerian representation of elliptical orbits the flux is averaged over the binary's orbit. Supplementing this by the important hereditary contributions arising from tails, tails-of-tails and tails squared terms calculated in a previous paper, the complete 3PN energy flux is obtained. The final result presented in this paper would be needed for the construction of ready-to-use templates for binaries moving on non-circular orbits, a plausible class of sources not only for the space based detectors like LISA but also for the ground based ones.Comment: 40 pages. Minor changes in text throughout. Minor typos in Eqs. (3.3b), (7.7f), (8.19d) and (8.20) corrected. Matches the published versio