Robust Dynamic Pricing Over Infinite Horizon in The Presence of Model Uncertainty( 2* Journal)

This paper studies a problem of dynamic pricing faced by a retailer with limited inventory, uncertain about the demand rate model, aiming to maximize expected discounted revenue over an infinite time horizon. The retailer doubts his demand model which is generated by historical data and views it as an approximation. Uncertainty in the demand rate model is represented by a notion of generalized relative entropy process, and the robust pricing problem is formulated as a two-player zero-sum stochastic differential game. The pricing policy is obtained through the Hamilton-Jacobi-Isaacs (HJI) equation. The existence and uniqueness of the solution of the HJI equation is shown and a verification theorem is proved to show that the solution of the HJI equation is indeed the value function of the pricing problem. The results are illustrated by an example with exponential nominal demand rate.

Quantum Discord Bounds the Amount of Distributed Entanglement

The ability to distribute quantum entanglement is a prerequisite for many fundamental tests of quantum theory and numerous quantum information protocols. Two distant parties can increase the amount of entanglement between them by means of quantum communication encoded in a carrier that is sent from one party to the other. Intriguingly, entanglement can be increased even when the exchanged carrier is not entangled with the parties. However, in light of the defining property of entanglement stating that it cannot increase under classical communication, the carrier must be quantum. Here we show that, in general, the increase of relative entropy of entanglement between two remote parties is bounded by the amount of nonclassical correlations of the carrier with the parties as quantified by the relative entropy of discord. We study implications of this bound, provide new examples of entanglement distribution via unentangled states, and put further limits on this phenomenon.

Wavelet entropy of Doppler ultrasound blood velocity flow waveforms distinguishes nitric oxide-modulated states

Wavelet entropy assesses the degree of order or disorder in signals and presents this complex information in a simple metric. Relative wavelet entropy assesses the similarity between the spectral distributions of two signals, again in a simple metric. Wavelet entropy is therefore potentially a very attractive tool for waveform analysis. The ability of this method to track the effects of pharmacologic modulation of vascular function on Doppler blood velocity waveforms was assessed. Waveforms were captured from ophthalmic arteries of 10 healthy subjects at baseline, after the administration of glyceryl trinitrate (GTN) and after two doses of N(G)-nitro-L-arginine-methyl ester (L-NAME) to produce vasodilation and vasoconstriction, respectively. Wavelet entropy had a tendency to decrease from baseline in response to GTN, but significantly increased after the administration of L-NAME (mean: 1.60 ± 0.07 after 0.25 mg/kg and 1.72 ± 0.13 after 0.5 mg/kg vs. 1.50 ± 0.10 at baseline, p < 0.05). Relative wavelet entropy had a spectral distribution from increasing doses of L-NAME comparable to baseline, 0.07 ± 0.04 and 0.08 ± 0.03, respectively, whereas GTN had the most dissimilar spectral distribution compared with baseline (0.17 ± 0.08, p = 0.002). Wavelet entropy can detect subtle changes in Doppler blood velocity waveform structure in response to nitric-oxide-mediated changes in arteriolar smooth muscle tone.

Modelling relative motion to facilitate intra-limb coordination

The importance of relative motion information when modelling a novel motor skill was examined. Participants were assigned to one of four groups. Groups 1 and 2 viewed demonstrations of a skilled cricket bowler presented in either video or point light format. Group 3 observed a single point of light pertaining to the wrist of the skilled bowler only. Participants in Group 4 did not receive a demonstration and acted as controls. During 60 acquisition trials, participants in the demonstration groups viewed a model five times before each 10-trial block. Retention was examined the following day. Intra-limb coordination was assessed for the right elbow relative to the wrist in comparison to the model. The demonstration groups showed greater concordance with the model than the control group. However, the wrist group performed less like the model than the point light and video groups, who did not differ from each other. These effects were maintained in retention. Relative motion information aided the acquisition of intra-limb coordination, while making this information more salient (through point lights) provided no additional benefit. The motion of the models bowling arm was replicated more closely than the non-bowling arm, suggesting that information from the end-effector is prioritized during observation for later reproduction.