BackgroundCorneal cross-linking is widely used to treat keratoconus. However, to date, only limited data from randomized trials support its efficacy.MethodsThe efficacy and safety of corneal cross-linking for halting progression of keratoconus were investigated in a prospective, randomized, blinded, placebo controlled, multicentre trial. Twenty-nine keratoconus patients were randomized in three trial centres. The mean age at inclusion was 28 years. Longitudinal changes in corneal refraction were assessed by linear regression. The best corrected visual acuity, surface defects and corneal inflammation were also assessed. These data were analysed with a multifactorial linear regression model.ResultsA total of 15 eyes were randomized to the treatment and 14 to the control group. Follow-up averaged 1098 days. Corneal refractive power decreased on average (+/−standard deviation) by 0.35 +/− 0.58 dioptres/year in the treatment group. The controls showed an increase of 0.11 +/− 0.61 dioptres/year. This difference was statistically significant (p = 0.02).ConclusionsOur data suggest that corneal cross-linking is an effective treatment for some patients to halt the progression of keratoconus. However, some of the treated patients still progressed, whereas some untreated controls improved. Therefore, further investigations are necessary to decide which patients require treatment and which do not.Trial registrationNCT00626717, Date of registration: February 20, 2008.

The entangled quantum state of a photon pair propagating through atmospheric turbulence suffers decay of entanglement due to the scintillation it experiences. In this paper, we investigate the robustness against this decay for different qutrit states. An infinitesimal propagation equation is used to obtain the density matrix as a function of the propagation distance and the tangle is used to quantify the entanglement between a pair of qutrits. We consider the evolution of various initial states as they propagate through turbulence. Using optimization of the parameters that define the initial state, we obtain expressions for bipartite qutrit states that retain their initial entanglement longer than the initially maximally entangled states.

The dynamics of bosons in generic multimode systems, such as Bose-Hubbard models, are not only determined by interactions among the particles, but also by their mutual indistinguishability manifested in many-particle interference. We introduce a measure of indistinguishability for Fock states of bosons whose mutual distinguishability is controlled by an internal degree of freedom. We demonstrate how this measure emerges both in the noninteracting and interacting evolution of observables. In particular, we find an unambiguous relationship between our measure and the variance of single-particle observables in the noninteracting limit. A nonvanishing interaction leads to a hierarchy of interaction-induced interference processes, such that even the expectation value of single-particle observables is influenced by the degree of indistinguishability.

Abundant evidence exists that expected utility theory does not adequately describe decision making under risk. Although prospect theory is a popular alternative, it is rarely applied in strategic situations in which risk arises through individual interactions. This study fills this research gap by incorporating prospect theory preferences into a dynamic game theoretic model. Using a large field data set from multiple online pay-per-bid auction sites, the authors empirically show that their proposed model with prospect theory preferences makes a better out-of-sample prediction than a corresponding expected utility model. Prospect theory also provides a unified explanation for two behavioral anomalies: average auctioneer revenues above current retail prices and the sunk cost fallacy. The empirical results indicate that bidders are loss averse and overweight small probabilities, such that the expected revenue of the auction exceeds the current retail price by 25.46%. The authors illustrate and empirically confirm a managerial implication for how an auctioneer can increase revenue by changing the details of the auction design.

We conceive an all-optical representation of the dynamics of two distinct types of interacting bosons in a double well by an array of evanescently coupled photonic waveguides. Many-particle interference effects are probed for various interaction strengths by changing the relative abundance of the particle species and can be readily identified by monitoring the propagation of the light intensity across the waveguide array. In particular, we show that finite inter-particle interaction strengths reduce the many-particle interference contrast by dephasing. A general description of the many-particle dynamics for arbitrary initial states is given in terms of two coupled spins by generalising the Schwinger representation to two particle species.The Schwinger representation is particularly useful under isospecific conditions, since the Hamiltonian (11) of the interacting system can then be brought into the Lipkin-Meshkov-Glick form [59,72] for the total spin J J J A B = +   ˆˆ: H J U J . 1 6 x z 2   = -W +ˆˆ( ) This prompts us to introduce the common eigenstates j m , ñ | of J 2 and J ẑ , which, with the help of the Clebsch-Gordan coefficients C m m m j j j , , , , A B A B