Self-consistent Calculation of Real Space Renormalization Group Flows and Effective Potentials

We show how to compute real space renormalization group flows in lattice field theory by a self-consistent method. In each step, the integration over the fluctuation field (high frequency components of the field) is performed by a saddle point method. The saddle point depends on the block-spin. Higher powers of derivatives of the field are neglected in the actions, but no polynomial approximation in the field is made. The flow preserves a simple parameterization of the action. In this paper we treat scalar field theories as an example.Comment: 52 pages, uses pstricks macro, three ps-figure

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

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

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

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

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

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

A Novel Mutation in the Upstream Open Reading Frame of the CDKN1B Gene Causes a MEN4 Phenotype

PubMed ID: 23555276This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Monopoles, confinement and deconfinement of (2+1)D compact lattice QED in external fields

The compact Abelian model in three space--time dimensions is studied in the presence of external electromagnetic fields at finite temperatures. We show that the deconfinement phase transition is independent on the strength of the external fields. This result is in agreement with our observation that the external fields create small--size magnetic dipoles from the vacuum which do not influence the confining properties of the model. Contrary to the deconfinement phase, the internal field in the direction of the applied external field is attenuated in the confinement phase, this screening becomes stronger with decreasing temperature.Comment: 22 pages, 24 EPS figures, LaTeX uses epsfig.st