A generalization of the van-der-Pol oscillator underlies active signal amplification in Drosophila hearing

The antennal hearing organs of the fruit fly Drosophila melanogaster boost their sensitivity by an active mechanical process that, analogous to the cochlear amplifier of vertebrates, resides in the motility of mechanosensory cells. This process nonlinearly improves the sensitivity of hearing and occasionally gives rise to self-sustained oscillations in the absence of sound. Time series analysis of self-sustained oscillations now unveils that the underlying dynamical system is well described by a generalization of the van-der-Pol oscillator. From the dynamic equations, the underlying amplification dynamics can explicitly be derived. According to the model, oscillations emerge from a combination of negative damping, which reflects active amplification, and a nonlinear restoring force that dictates the amplitude of the oscillations. Hence, active amplification in fly hearing seems to rely on the negative damping mechanism initially proposed for the cochlear amplifier of vertebrate

A theorem concerning twisted and untwisted partition functions in U(N) and SU(N) lattice gauge theories

In order to get a clue to understanding the volume-dependence of vortex free energy (which is defined as the ratio of the twisted against the untwisted partition function), we investigate the relation between vortex free energies defined on lattices of different sizes. An equality is derived through a simple calculation which equates a general linear combination of vortex free energies defined on a lattice to that on a smaller lattice. The couplings in the denominator and in the numerator however shows a discrepancy, and we argue that it vanishes in the thermodynamic limit. Comparison between our result and the work of Tomboulis is also presented. In the appendix we carefully examine the proof of quark confinement by Tomboulis and summarize its loopholes.Comment: 19 pages, 4 figures; v2:Clarifying comments added; v3:Appendix added, the version published in Physics Letters

Two Phases for Compact U(1) Pure Gauge Theory in Three Dimensions

We show that if actions more general than the usual simple plaquette action ($\sim F_{\mu\nu}^2$) are considered, then compact $U(1)$ {\sl pure} gauge theory in three Euclidean dimensions can have two phases. Both phases are confining phases, however in one phase the monopole condensate spontaneously `magnetizes'. For a certain range of parameters the phase transition is continuous, allowing the definition of a strong coupling continuum limit. We note that these observations have relevance to the `fictitious' gauge field theories of strongly correlated electron systems, such as those describing high-$T_c$ superconductors.Comment: 10 pages, Plain TeX, uses harvma

Gauge-ball spectrum of the four-dimensional pure U(1) gauge theory

We investigate the continuum limit of the gauge-ball spectrum in the four-dimensional pure U(1) lattice gauge theory. In the confinement phase we identify various states scaling with the correlation length exponent $\nu \simeq 0.35$. The square root of the string tension also scales with this exponent, which agrees with the non-Gaussian fixed point exponent recently found in the finite size studies of this theory. Possible scenarios for constructing a non-Gaussian continuum theory with the observed gauge-ball spectrum are discussed. The $0^{++}$ state, however, scales with a Gaussian value $\nu \simeq 0.5$. This suggests the existence of a second, Gaussian continuum limit in the confinement phase and also the presence of a light or possibly massless scalar in the non-Gaussian continuum theory. In the Coulomb phase we find evidence for a few gauge-balls, being resonances in multi-photon channels; they seem to approach the continuum limit with as yet unknown critical exponents. The maximal value of the renormalized coupling in this phase is determined and its universality confirmed.Comment: 46 pages, 12 figure

A lattice study of 3D compact QED at finite temperature

We study the deconfinement phase transition and monopole properties in the finite temperature 3D compact Abelian gauge model on the lattice. We predict the critical coupling as function of the lattice size in a simplified model to describe monopole binding. We demonstrate numerically that the monopoles are sensitive to the transition. In the deconfinement phase the monopoles appear in the form of a dilute gas of magnetic dipoles. In the confinement phase both monopole density and string tension differ from semiclassical estimates if monopole binding is neglected. However, the analysis of the monopole clusters shows that the relation between the string tension and the density of monopoles in charged clusters is in reasonable agreement with those predictions. We study the cluster structure of the vacuum in both phases of the model.Comment: 18 pages, 14 EPS figures, LaTeX uses epsfig.st

Effective Field Theories

Effective field theories encode the predictions of a quantum field theory at low energy. The effective theory has a fairly low ultraviolet cutoff. As a result, loop corrections are small, at least if the effective action contains a term which is quadratic in the fields, and physical predictions can be read straight from the effective Lagrangean. Methods will be discussed how to compute an effective low energy action from a given fundamental action, either analytically or numerically, or by a combination of both methods. Basically,the idea is to integrate out the high frequency components of fields. This requires the choice of a "blockspin",i.e. the specification of a low frequency field as a function of the fundamental fields. These blockspins will be the fields of the effective field theory. The blockspin need not be a field of the same type as one of the fundamental fields, and it may be composite. Special features of blockspins in nonabelian gauge theories will be discussed in some detail. In analytical work and in multigrid updating schemes one needs interpolation kernels \A from coarse to fine grid in addition to the averaging kernels $C$ which determines the blockspin. A neural net strategy for finding optimal kernels is presented. Numerical methods are applicable to obtain actions of effective theories on lattices of finite volume. The constraint effective potential) is of particular interest. In a Higgs model it yields the free energy, considered as a function of a gauge covariant magnetization. Its shape determines the phase structure of the theory. Its loop expansion with and without gauge fields can be used to determine finite size corrections to numerical data.Comment: 45 pages, 9 figs., preprint DESY 92-070 (figs. 3-9 added in ps format

A doublecortin containing microtubule-associated protein is implicated in mechanotransduction in Drosophila sensory cilia

Mechanoreceptors are sensory cells that transduce mechanical stimuli into electrical signals and mediate the perception of sound, touch and acceleration. Ciliated mechanoreceptors possess an elaborate microtubule cytoskeleton that facilitates the coupling of external forces to the transduction apparatus. In a screen for genes preferentially expressed in Drosophila campaniform mechanoreceptors, we identified DCX-EMAP, a unique member of the EMAP family (echinoderm–microtubule-associated proteins) that contains two doublecortin domains. DCX-EMAP localizes to the tubular body in campaniform receptors and to the ciliary dilation in chordotonal mechanoreceptors in Johnston's organ, the fly's auditory organ. Adult flies carrying a piggyBac insertion in the DCX-EMAP gene are uncoordinated and deaf and display loss of mechanosensory transduction and amplification. Electron microscopy of mutant sensilla reveals loss of electron-dense materials within the microtubule cytoskeleton in the tubular body and ciliary dilation. Our results establish a catalogue of candidate genes for Drosophila mechanosensation and show that one candidate, DCX-EMAP, is likely to be required for mechanosensory transduction and amplification

Direct gating and mechanical integrity of Drosophila auditory transducers require TRPN1

The elusive transduction channels for hearing are directly gated mechanically by the pull of gating springs. We found that the transient receptor potential (TRP) channel TRPN1 (NOMPC) is essential for this direct gating of Drosophila auditory transduction channels and that the channel-spring complex was disrupted if TRPN1 was lost. Our results identify TRPN1 as a mechanical constituent of the fly's auditory transduction complex that may act as the channel and/or gating spring

Series Expansions for three-dimensional QED

Strong-coupling series expansions are calculated for the Hamiltonian version of compact lattice electrodynamics in (2+1) dimensions, with 4-component fermions. Series are calculated for the ground-state energy per site, the chiral condensate, and the masses of `glueball' and positronium states. Comparisons are made with results obtained by other techniques.Comment: 13 figure