Minimal basilar membrane motion in low-frequency hearing

Low-frequency hearing is critically important for speech and music perception, but no mechanical measurements have previously been available from inner ears with intact low-frequency parts. These regions of the cochlea may function in ways different from the extensively studied high-frequency regions, where the sensory outer hair cells produce force that greatly increases the sound-evoked vibrations of the basilar membrane. We used laser interferometry in vitro and optical coherence tomography in vivo to study the low-frequency part of the guinea pig cochlea, and found that sound stimulation caused motion of a minimal portion of the basilar membrane. Outside the region of peak movement, an exponential decline in motion amplitude occurred across the basilar membrane. The moving region had different dependence on stimulus frequency than the vibrations measured near the mechanosensitive stereocilia. This behavior differs substantially from the behavior found in the extensively studied high-frequency regions of the cochlea

Is Quantum Mechanics Compatible with an Entirely Deterministic Universe?

A b s t r a c t It will be argued that 1) the Bell inequalities are not equivalent with those inequalities derived by Pitowsky and others that indicate the Kolmogorovity of a probability model, 2) the original Bell inequalities are irrelevant to both the question of whether or not quantum mechanics is a Kolmogorovian theory as well as the problem of determinism, whereas 3) the Pitowsky type inequalities are not violated by quantum mechanics, hence 4) quantum mechanics is a Kolmogorovian probability theory, therefore, 5) it is compatible with an entirely deterministic universe.Comment: 15 pages, (compressed and uuencoded) Postscript (188 kb), preprint 94/0

Angular momentum effects in Michelson-Morley type experiments

The effect of the angular momentum density of a gravitational source on the times of flight of light rays in an interferometer is analyzed. The calculation is made imagining that the interferometer is at the equator of the gravity source and, as long as possible, the metric, provided it is stationary and axisymmetric, is not approximated. Finally, in order to evaluate the size of the effect in the case of the Earth a weak field approximation is introduced. For laboratory scales and non-geodesic paths the correction turns out to be comparable with the sensitivity expected in gravitational waves interferometric detectors, whereas it drops under the threshold of detectability when using free (geodesic) light rays.Comment: 12 pages, LaTeX; more about the detection technique, references added; accepted for publication in GR

Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model

Cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity, see e.g. B. Kerr, M. A. Riley, M. W. Feldman and B. J. M. Bohannan [Nature {\bf 418}, 171 (2002)] and B. Kirkup and M. A. Riley [Nature {\bf 428}, 412 (2004)]. Through analytical methods supported by numerical simulations, we address this issue by studying the properties of a paradigmatic non-spatial three-species stochastic system, namely the `rock-paper-scissors' or cyclic Lotka-Volterra model. While the deterministic approach (rate equations) predicts the coexistence of the species resulting in regular (yet neutrally stable) oscillations of the population densities, we demonstrate that fluctuations arising in the system with a \emph{finite number of agents} drastically alter this picture and are responsible for extinction: After long enough time, two of the three species die out. As main findings we provide analytic estimates and numerical computation of the extinction probability at a given time. We also discuss the implications of our results for a broad class of competing population systems.Comment: 12 pages, 9 figures, minor correction

How to determine a quantum state by measurements: The Pauli problem for a particle with arbitrary potential

The problem of reconstructing a pure quantum state ¿¿> from measurable quantities is considered for a particle moving in a one-dimensional potential V(x). Suppose that the position probability distribution ¿¿(x,t)¿2 has been measured at time t, and let it have M nodes. It is shown that after measuring the time evolved distribution at a short-time interval ¿t later, ¿¿(x,t+¿t)¿2, the set of wave functions compatible with these distributions is given by a smooth manifold M in Hilbert space. The manifold M is isomorphic to an M-dimensional torus, TM. Finally, M additional expectation values of appropriately chosen nonlocal operators fix the quantum state uniquely. The method used here is the analog of an approach that has been applied successfully to the corresponding problem for a spin system

The edge of neutral evolution in social dilemmas

The functioning of animal as well as human societies fundamentally relies on cooperation. Yet, defection is often favorable for the selfish individual, and social dilemmas arise. Selection by individuals' fitness, usually the basic driving force of evolution, quickly eliminates cooperators. However, evolution is also governed by fluctuations that can be of greater importance than fitness differences, and can render evolution effectively neutral. Here, we investigate the effects of selection versus fluctuations in social dilemmas. By studying the mean extinction times of cooperators and defectors, a variable sensitive to fluctuations, we are able to identify and quantify an emerging 'edge of neutral evolution' that delineates regimes of neutral and Darwinian evolution. Our results reveal that cooperation is significantly maintained in the neutral regimes. In contrast, the classical predictions of evolutionary game theory, where defectors beat cooperators, are recovered in the Darwinian regimes. Our studies demonstrate that fluctuations can provide a surprisingly simple way to partly resolve social dilemmas. Our methods are generally applicable to estimate the role of random drift in evolutionary dynamics.Comment: 17 pages, 4 figure

On the complementarity of the quadrature observables

In this paper we investigate the coupling properties of pairs of quadrature observables, showing that, apart from the Weyl relation, they share the same coupling properties as the position-momentum pair. In particular, they are complementary. We determine the marginal observables of a covariant phase space observable with respect to an arbitrary rotated reference frame, and observe that these marginal observables are unsharp quadrature observables. The related distributions constitute the Radon tranform of a phase space distribution of the covariant phase space observable. Since the quadrature distributions are the Radon transform of the Wigner function of a state, we also exhibit the relation between the quadrature observables and the tomography observable, and show how to construct the phase space observable from the quadrature observables. Finally, we give a method to measure together with a single measurement scheme any complementary pair of quadrature observables.Comment: Dedicated to Peter Mittelstaedt in honour of his eightieth birthda

Pauli problem for a spin of arbitrary length: A simple method to determine its wave function

The problem of determining a pure state vector from measurements is investigated for a quantum spin of arbitrary length. Generically, only a finite number of wave functions is compatible with the intensities of the spin components in two different spatial directions, measured by a Stern-Gerlach apparatus. The remaining ambiguity can be resolved by one additional well-defined measurement. This method combines efficiency with simplicity: only a small number of quantities have to be measured and the experimental setup is elementary. Other approaches to determine state vectors from measurements, also known as the ‘‘Pauli problem,’’ are reviewed for both spin and particle systems