Scalar Representation and Conjugation of Set-Valued Functions

To a function with values in the power set of a pre-ordered, separated locally convex space a family of scalarizations is given which completely characterizes the original function. A concept of a Legendre-Fenchel conjugate for set-valued functions is introduced and identified with the conjugates of the scalarizations. Using this conjugate, weak and strong duality results are proven.Comment: arXiv admin note: substantial text overlap with arXiv:1012.435

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

Forkhead Transcription Factor Fd3F Cooperates with Rfx to Regulate a Gene Expression Program for Mechanosensory Cilia Specialization

Cilia have evolved hugely diverse structures and functions to participate in a wide variety of developmental and physiological processes. Ciliary specialization requires differences in gene expression, but few transcription factors are known to regulate this, and their molecular function is unclear. Here, we show that the Drosophila Forkhead box (Fox) gene, fd3F, is required for specialization of the mechanosensory cilium of chordotonal (Ch) neurons. fd3F regulates genes for Ch-specific axonemal dyneins and TRPV ion channels, which are required for sensory transduction, and retrograde transport genes, which are required to differentiate their distinct motile and sensory ciliary zones. fd3F is reminiscent of vertebrate Foxj1, a motile cilia regulator, but fd3F regulates motility genes as part of a broader sensory regulation program. Fd3F cooperates with the pan-ciliary transcription factor, Rfx, to regulate its targets directly. This illuminates pathways involved in ciliary specialization and the molecular mechanism of transcription factors that regulate them

Scattering of Glueballs and Mesons in Compact QEDQED in 2+12+1 Dimensions

We study glueball and meson scattering in compact $QED_{2+1}$ gauge theory in a Hamiltonian formulation and on a momentum lattice. We compute ground state energy and mass, and introduce a compact lattice momentum operator for the computation of dispersion relations. Using a non-perturbative time-dependent method we compute scattering cross sections for glueballs and mesons. We compare our results with strong coupling perturbation theory.Comment: figures not included (hard copy only), LAVAL-PHY-94-05, PARKS-PHY-94-0

Drosophila TRPN( = NOMPC) Channel Localizes to the Distal End of Mechanosensory Cilia

BACKGROUND: A TRPN channel protein is essential for sensory transduction in insect mechanosensory neurons and in vertebrate hair cells. The Drosophila TRPN homolog, NOMPC, is required to generate mechanoreceptor potentials and currents in tactile bristles. NOMPC is also required, together with a TRPV channel, for transduction by chordotonal neurons of the fly's antennal ear, but the TRPN or TRPV channels have distinct roles in transduction and in regulating active antennal mechanics. The evidence suggests that NOMPC is a primary mechanotransducer channel, but its subcellular location-key for understanding its exact role in transduction-has not yet been established. METHODOLOGY/PRINCIPAL FINDINGS: Here, by immunostaining, we locate NOMPC at the tips of mechanosensory cilia in both external and chordotonal sensory neurons, as predicted for a mechanotransducer channel. In chordotonal neurons, the TRPN and TRPV channels are respectively segregated into distal and proximal ciliary zones. This zonal separation is demarcated by and requires the ciliary dilation, an intraciliary assembly of intraflagellar transport (IFT) proteins. CONCLUSIONS: Our results provide a strong evidence for NOMPC as a primary transduction channel in Drosophila mechansensory organs. The data also reveals a structural basis for the model of auditory chordotonal transduction in which the TRPN and TRPV channels play sequential roles in generating and amplifying the receptor potential, but have opposing roles in regulating active ciliary motility

Dynamic Range Compression in the Honey Bee Auditory System toward Waggle Dance Sounds

Honey bee foragers use a “waggle dance” to inform nestmates about direction and distance to locations of attractive food. The sound and air flows generated by dancer's wing and abdominal vibrations have been implicated as important cues, but the decoding mechanisms for these dance messages are poorly understood. To understand the neural mechanisms of honey bee dance communication, we analyzed the anatomy of antenna and Johnston's organ (JO) in the pedicel of the antenna, as well as the mechanical and neural response characteristics of antenna and JO to acoustic stimuli, respectively. The honey bee JO consists of about 300–320 scolopidia connected with about 48 cuticular “knobs” around the circumference of the pedicel. Each scolopidium contains bipolar sensory neurons with both type I and II cilia. The mechanical sensitivities of the antennal flagellum are specifically high in response to low but not high intensity stimuli of 265–350 Hz frequencies. The structural characteristics of antenna but not JO neurons seem to be responsible for the non-linear responses of the flagellum in contrast to mosquito and fruit fly. The honey bee flagellum is a sensitive movement detector responding to 20 nm tip displacement, which is comparable to female mosquito. Furthermore, the JO neurons have the ability to preserve both frequency and temporal information of acoustic stimuli including the “waggle dance” sound. Intriguingly, the response of JO neurons was found to be age-dependent, demonstrating that the dance communication is only possible between aged foragers. These results suggest that the matured honey bee antennae and JO neurons are best tuned to detect 250–300 Hz sound generated during “waggle dance” from the distance in a dark hive, and that sufficient responses of the JO neurons are obtained by reducing the mechanical sensitivity of the flagellum in a near-field of dancer. This nonlinear effect brings about dynamic range compression in the honey bee auditory system

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

D-Theory: Field Theory via Dimensional Reduction of Discrete Variables

A new non-perturbative approach to quantum field theory --- D-theory --- is proposed, in which continuous classical fields are replaced by discrete quantized variables which undergo dimensional reduction. The 2-d classical O(3) model emerges from the (2+1)-d quantum Heisenberg model formulated in terms of quantum spins. Dimensional reduction is demonstrated explicitly by simulating correlation lengths up to 350,000 lattice spacings using a loop cluster algorithm. In the framework of D-theory, gauge theories are formulated in terms of quantum links --- the gauge analogs of quantum spins. Quantum links are parallel transporter matrices whose elements are non-commuting operators. They can be expressed as bilinears of anticommuting fermion constituents. In quantum link models dimensional reduction to four dimensions occurs, due to the presence of a 5-d Coulomb phase, whose existence is confirmed by detailed simulations using standard lattice gauge theory. Using Shamir's variant of Kaplan's fermion proposal, in quantum link QCD quarks appear as edge states of a 5-d slab. This naturally protects their chiral symmetries without fine-tuning. The first efficient cluster algorithm for a gauge theory with a continuous gauge group is formulated for the U(1) quantum link model. Improved estimators for Wilson loops are constructed, and dimensional reduction to ordinary lattice QED is verified numerically.Comment: 15 pages, LaTeX, including 9 encapsulated postscript figures. Contribution to Lattice 97 by 5 authors, to appear in Nuclear Physics B (Proceeding Supplements). Requires psfig.tex and espcrc2.st

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