Beyond first-order asymptotics for Cox regression

To go beyond standard first-order asymptotics for Cox regression, we develop parametric bootstrap and second-order methods. In general, computation of $P$-values beyond first order requires more model specification than is required for the likelihood function. It is problematic to specify a censoring mechanism to be taken very seriously in detail, and it appears that conditioning on censoring is not a viable alternative to that. We circumvent this matter by employing a reference censoring model, matching the extent and timing of observed censoring. Our primary proposal is a parametric bootstrap method utilizing this reference censoring model to simulate inferential repetitions of the experiment. It is shown that the most important part of improvement on first-order methods - that pertaining to fitting nuisance parameters - is insensitive to the assumed censoring model. This is supported by numerical comparisons of our proposal to parametric bootstrap methods based on usual random censoring models, which are far more unattractive to implement. As an alternative to our primary proposal, we provide a second-order method requiring less computing effort while providing more insight into the nature of improvement on first-order methods. However, the parametric bootstrap method is more transparent, and hence is our primary proposal. Indications are that first-order partial likelihood methods are usually adequate in practice, so we are not advocating routine use of the proposed methods. It is however useful to see how best to check on first-order approximations, or improve on them, when this is expressly desired.Comment: Published at http://dx.doi.org/10.3150/13-BEJ572 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Entanglement dynamics for two harmonic oscillators coupled to independent environments

We study the entanglement evolution between two harmonic oscillators having different free frequencies each leaking into an independent bath. We use an exact solution valid in the weak coupling limit and in the short time non-Markovian regime. The reservoirs are identical and characterized by an Ohmic spectral distribution with Lorents-Drude cut-off. This work is an extension of the case reported in [Phys. Rev. A 80, 062324 (2009)] where the oscillators have the same free frequency.Comment: 8 pages, 3 figures, submitted to Physica Script

Dual contribution to amplification in the mammalian inner ear

The inner ear achieves a wide dynamic range of responsiveness by mechanically amplifying weak sounds. The enormous mechanical gain reported for the mammalian cochlea, which exceeds a factor of 4,000, poses a challenge for theory. Here we show how such a large gain can result from an interaction between amplification by low-gain hair bundles and a pressure wave: hair bundles can amplify both their displacement per locally applied pressure and the pressure wave itself. A recently proposed ratchet mechanism, in which hair-bundle forces do not feed back on the pressure wave, delineates the two effects. Our analytical calculations with a WKB approximation agree with numerical solutions.Comment: 4 pages, 4 figure

Continuous-variable quantum key distribution in non-Markovian channels

We address continuous-variable quantum key distribution (QKD) in non-Markovian lossy channels and show how the non-Markovian features may be exploited to enhance security and/or to detect the presence and the position of an eavesdropper along the transmission line. In particular, we suggest a coherent-state QKD protocol which is secure against Gaussian individual attacks based on optimal 1 ->2 asymmetric cloning machines for arbitrarily low values of the overall transmission line. The scheme relies on specific non-Markovian properties, and cannot be implemented in ordinary Markovian channels characterized by uniform losses. Our results give a clear indication of the potential impact of non-Markovian effects in QKD

Quantifying non-Markovianity of continuous-variable Gaussian dynamical maps

We introduce a non-Markovianity measure for continuous-variable open quantum systems based on the idea put forward in H.-P. Breuer, that is, by quantifying the flow of information from the environment back to the open system. Instead of the trace distance we use here the fidelity to assess distinguishability of quantum states. We employ our measure to evaluate non-Markovianity of two paradigmatic Gaussian channels: the purely damping channel and the quantum Brownian motion channel with Ohmic environment. We consider different classes of Gaussian states and look for pairs of states maximizing the backflow of information. For coherent states we find simple analytical solutions, whereas for squeezed states we provide both exact numerical and approximate analytical solutions in the weak coupling limit

The Cochlear Tuning Curve

The tuning curve of the cochlea measures how large an input is required to elicit a given output level as a function of the frequency. It is a fundamental object of auditory theory, for it summarizes how to infer what a sound was on the basis of the cochlear output. A simple model is presented showing that only two elements are sufficient for establishing the cochlear tuning curve: a broadly tuned traveling wave, moving unidirectionally from high to low frequencies, and a set of mechanosensors poised at the threshold of an oscillatory (Hopf) instability. These two components suffice to generate the various frequency-response regimes which are needed for a cochlear tuning curve with a high slope

The SU(2) ⊗ U(1) Electroweak Model Based on the Nonlinearly Realized Gauge Group. II. Functional Equations and the Weak Power-Counting

In the present paper, that is the second part devoted to the construction of an electroweak model based on a nonlinear realization of the gauge group SU(2) ⊗ U(1), we study the tree-level vertex functional with all the sources necessary for the functional formulation of the relevant symmetries (Local Functional Equation, Slavnov–Taylor identity, Landau Gauge Equation) and for the symmetric removal of the divergences. The Weak Power Counting criterion is proven in the presence of the novel sources. The local invariant solutions of the functional equations are constructed in order to represent the counterterms for the one-loop subtractions. The bleaching technique is fully extended to the fermion sector. The neutral sector of the vector mesons is analyzed in detail in order to identify the physical fields for the photon and the Z boson. The identities necessary for the decoupling of the unphysical modes are fully analyzed. These latter results are crucially bound to the Landau gauge used throughout the paper.United States. Dept. of Energy (Cooperative Research Agreement DE FG02-05ER41360

Electronic phase separation near the superconductor-insulator transition of Nd1+xBa2−xCu3O7−δ thin films studied by an electric-field-induced doping effect

We report a detailed study of the transport properties of Nd(1+x)Ba(2-x)Cu(3)O(7-delta) thin films with doping changed by field effect. The data cover the whole superconducting to insulating transition and show remarkable Similarities with the effect of chemical doping in high critical temperature superconductors. The results suggest that the add-on of carriers is accompanied by an electronic phase separation, independent on the details of the doping mechanism

Essential nonlinearities in hearing

Our hearing organ, the cochlea, evidently poises itself at a Hopf bifurcation to maximize tuning and amplification. We show that in this condition several effects are expected to be generic: compression of the dynamic range, infinitely shrap tuning at zero input, and generation of combination tones. These effects are "essentially" nonlinear in that they become more marked the smaller the forcing: there is no audible sound soft enough not to evoke them. All the well-documented nonlinear aspects of hearing therefore appear to be consequences of the same underlying mechanism.Comment: 4 pages, 3 figure