Identifying short motifs by means of extreme value analysis

The problem of detecting a binding site -- a substring of DNA where transcription factors attach -- on a long DNA sequence requires the recognition of a small pattern in a large background. For short binding sites, the matching probability can display large fluctuations from one putative binding site to another. Here we use a self-consistent statistical procedure that accounts correctly for the large deviations of the matching probability to predict the location of short binding sites. We apply it in two distinct situations: (a) the detection of the binding sites for three specific transcription factors on a set of 134 estrogen-regulated genes; (b) the identification, in a set of 138 possible transcription factors, of the ones binding a specific set of nine genes. In both instances, experimental findings are reproduced (when available) and the number of false positives is significantly reduced with respect to the other methods commonly employed.Comment: 6 pages, 5 figure

Distribution of hammerhead and hammerhead-like RNA motifs through the GenBank

Hammerhead ribozymes previously were found in satellite RNAs from plant viroids and in repetitive DNA from certain species of newts and schistosomes. To determine if this catalytic RNA motif has a wider distribution, we decided to scrutinize the GenBank database for RNAs that contain hammerhead or hammerhead-like motifs. The search shows a widespread distribution of this kind of RNA motif in different sequences suggesting that they might have a more general role in RNA biology. The frequency of the hammerhead motif is half of that expected from a random distribution, but this fact comes From the low CpG representation in vertebrate sequences and the bias of the GenBank for those sequences. Intriguing motifs include those found in several families of repetitive sequences, in the satellite RNA from the carrot red leaf luteovirus, in plant viruses like the spinach latent virus and the elm mottle virus, in animal viruses like the hepatitis E virus and the caprine encephalitis virus, and in mRNAs such as those coding for cytochrome P450 oxidoreductase in the rat and the hamster

Aspects of classical and quantum motion on a flux cone

Motion of a non-relativistic particle on a cone with a magnetic flux running through the cone axis (a ``flux cone'') is studied. It is expressed as the motion of a particle moving on the Euclidean plane under the action of a velocity-dependent force. Probability fluid (``quantum flow'') associated with a particular stationary state is studied close to the singularity, demonstrating non trivial Aharonov-Bohm effects. For example, it is shown that near the singularity quantum flow departs from classical flow. In the context of the hydrodynamical approach to quantum mechanics, quantum potential due to the conical singularity is determined and the way it affects quantum flow is analysed. It is shown that the winding number of classical orbits plays a role in the description of the quantum flow. Connectivity of the configuration space is also discussed.Comment: LaTeX file, 21 pages, 8 figure

Approach to Perturbative Results in the N-Delta Transition

We show that constraints from perturbative QCD calculations play a role in the nucleon to Delta(1232) electromagnetic transition even at moderate momentum transfer scales. The pQCD constraints, tied to real photoproduction data and unseparated resonance response functions, lead to explicit forms for the helicity amplitudes wherein the E2/M1 ratio remains small at moderately large momentum transfer.Comment: 4 pages, 2 figures, ReVTe

Hamiltonian structure of 2+1 dimensional gravity

A summary is given of some results and perspectives of the hamiltonian ADM approach to 2+1 dimensional gravity. After recalling the classical results for closed universes in absence of matter we go over the the case in which matter is present in the form of point spinless particles. Here the maximally slicing gauge proves most effective by relating 2+1 dimensional gravity to the Riemann- Hilbert problem. It is possible to solve the gravitational field in terms of the particle degrees of freedom thus reaching a reduced dynamics which involves only the particle positions and momenta. Such a dynamics is proven to be hamiltonian and the hamiltonian is given by the boundary term in the gravitational action. As an illustration the two body hamiltonian is used to provide the canonical quantization of the two particle system.Comment: 13 pages,2 figures,latex, Plenary talk at SIGRAV2000 Conferenc

Perturbative Renormalizations of Anyon Quantum Mechanics

In bosonic end perturbative calculations for quantum mechanical anyon systems a regularization and renormalization procedure, analogous to those used in field theory, is necessary. I examine the reliability and the physical interpretation of the most commonly used bosonic end regularization procedures. I then use the regularization procedure with the most transparent physical interpretation to derive some bosonic end perturbation theory results on anyon spectra, including a 3-anyon ground state energy.Comment: 19 pages, Plain LaTex, MIT-CTP-232

Nucleon to Delta Weak Excitation Amplitudes in the Non-relativistic Quark Model

We investigate the nucleon to Delta(1232) vector and axial vector amplitudes in the non-relativistic quark model of the Isgur-Karl variety. A particular interest is to investigate the SU(6) symmetry breaking, due to color hyperfine interaction. We compare the theoretical estimates to recent experimental investigation of the Adler amplitudes by neutrino scattering.Comment: \documentstyle[aps]{revtex}, 21pages; 11 postscript figures. Accepted for publication by Phys. Rev.

Effective Lagrangian Approach to the Theory of Eta Photoproduction in the N∗(1535)N^{*}(1535) Region

We investigate eta photoproduction in the $N^{*}(1535)$ resonance region within the effective Lagrangian approach (ELA), wherein leading contributions to the amplitude at the tree level are taken into account. These include the nucleon Born terms and the leading $t$-channel vector meson exchanges as the non-resonant pieces. In addition, we consider five resonance contributions in the $s$- and $u$- channel; besides the dominant $N^{*}(1535)$, these are: $N^{*}(1440),N^{*}(1520),N^{*}(1650)$ and $N^{*}(1710)$. The amplitudes for the $\pi^\circ$ and the $\eta$ photoproduction near threshold have significant differences, even as they share common contributions, such as those of the nucleon Born terms. Among these differences, the contribution to the $\eta$ photoproduction of the $s$-channel excitation of the $N^{*}(1535)$ is the most significant. We find the off-shell properties of the spin-3/2 resonances to be important in determining the background contributions. Fitting our effective amplitude to the available data base allows us to extract the quantity $\sqrt{\chi \Gamma_\eta} A_{1/2}/\Gamma_T$, characteristic of the photoexcitation of the $N^{*}(1535)$ resonance and its decay into the $\eta$-nucleon channel, of interest to precise tests of hadron models. At the photon point, we determine it to be $(2.2\pm 0.2)\times 10^{-1} GeV^{-1}$ from the old data base, and $(2.2\pm 0.1) \times 10^{-1} GeV^{-1}$ from a combination of old data base and new Bates data. We obtain the helicity amplitude for $N^{*}(1535)\rightarrow \gamma p$ to be $A_{1/2}=(97\pm 7)\times 10^{-3} GeV^{-1/2}$ from the old data base, and $A_{1/2}=(97\pm 6)\times 10^{-3} GeV^{-1/2}$ from the combination of the old data base and new Bates data, compared with the results of the analysis of pion photoproduction yielding $74\pm 11$, in the same units.Comment: 43 pages, RevTeX, 9 figures available upon request, to appear in Phys. Rev.