Synchronizing Automata on Quasi Eulerian Digraph

In 1964 \v{C}ern\'{y} conjectured that each $n$-state synchronizing automaton posesses a reset word of length at most $(n-1)^2$. From the other side the best known upper bound on the reset length (minimum length of reset words) is cubic in $n$. Thus the main problem here is to prove quadratic (in $n$) upper bounds. Since 1964, this problem has been solved for few special classes of \sa. One of this result is due to Kari \cite{Ka03} for automata with Eulerian digraphs. In this paper we introduce a new approach to prove quadratic upper bounds and explain it in terms of Markov chains and Perron-Frobenius theories. Using this approach we obtain a quadratic upper bound for a generalization of Eulerian automata.Comment: 8 pages, 1 figur

Fractal Analysis of Protein Potential Energy Landscapes

The fractal properties of the total potential energy V as a function of time t are studied for a number of systems, including realistic models of proteins (PPT, BPTI and myoglobin). The fractal dimension of V(t), characterized by the exponent \gamma, is almost independent of temperature and increases with time, more slowly the larger the protein. Perhaps the most striking observation of this study is the apparent universality of the fractal dimension, which depends only weakly on the type of molecular system. We explain this behavior by assuming that fractality is caused by a self-generated dynamical noise, a consequence of intermode coupling due to anharmonicity. Global topological features of the potential energy landscape are found to have little effect on the observed fractal behavior.Comment: 17 pages, single spaced, including 12 figure

Structure of shells in complex networks

In a network, we define shell $\ell$ as the set of nodes at distance $\ell$ with respect to a given node and define $r_\ell$ as the fraction of nodes outside shell $\ell$. In a transport process, information or disease usually diffuses from a random node and reach nodes shell after shell. Thus, understanding the shell structure is crucial for the study of the transport property of networks. For a randomly connected network with given degree distribution, we derive analytically the degree distribution and average degree of the nodes residing outside shell $\ell$ as a function of $r_\ell$. Further, we find that $r_\ell$ follows an iterative functional form $r_\ell=\phi(r_{\ell-1})$, where $\phi$ is expressed in terms of the generating function of the original degree distribution of the network. Our results can explain the power-law distribution of the number of nodes $B_\ell$ found in shells with $\ell$ larger than the network diameter $d$, which is the average distance between all pairs of nodes. For real world networks the theoretical prediction of $r_\ell$ deviates from the empirical $r_\ell$. We introduce a network correlation function $c(r_\ell)\equiv r_{\ell+1}/\phi(r_\ell)$ to characterize the correlations in the network, where $r_{\ell+1}$ is the empirical value and $\phi(r_\ell)$ is the theoretical prediction. $c(r_\ell)=1$ indicates perfect agreement between empirical results and theory. We apply $c(r_\ell)$ to several model and real world networks. We find that the networks fall into two distinct classes: (i) a class of {\it poorly-connected} networks with $c(r_\ell)>1$, which have larger average distances compared with randomly connected networks with the same degree distributions; and (ii) a class of {\it well-connected} networks with $c(r_\ell)<1$

Characterization of human herpesvirus 6A/B U94 as ATPase, helicase, exonuclease and DNA-binding proteins

Human herpesvirus-6A (HHV-6A) and HHV-6B integrate their genomes into the telomeres of human chromosomes, however, the mechanisms leading to integration remain unknown. HHV-6A/B encode a protein that has been proposed to be involved in integration termed U94, an ortholog of adeno-associated virus type 2 (AAV-2) Rep68 integrase. In this report, we addressed whether purified recombinant maltose-binding protein (MBP)-U94 fusion proteins of HHV-6A/B possess biological functions compatible with viral integration. We could demonstrate that MBP-U94 efficiently binds both dsDNA and ssDNA containing telomeric repeats using gel shift assay and surface plasmon resonance. MBP-U94 is also able to hydrolyze adenosine triphosphate (ATP) to ADP, providing the energy for further catalytic activities. In addition, U94 displays a 3′ to 5′ exonuclease activity on dsDNA with a preference for 3′-recessed ends. Once the DNA strand reaches 8–10 nt in length, the enzyme dissociates it from the complementary strand. Lastly, MBP-U94 compromises the integrity of a synthetic telomeric D-loop through exonuclease attack at the 3′ end of the invading strand. The preferential DNA binding of MBP-U94 to telomeric sequences, its ability to hydrolyze ATP and its exonuclease/helicase activities suggest that U94 possesses all functions required for HHV-6A/B chromosomal integratio

Chromatin Profiles of Chromosomally Integrated Human Herpesvirus-6A

Human herpesvirus-6A (HHV-6A) and 6B (HHV-6B) are two closely related betaherpesviruses that are associated with various diseases including seizures and encephalitis. The HHV-6A/B genomes have been shown to be present in an integrated state in the telomeres of latently infected cells. In addition, integration of HHV-6A/B in germ cells has resulted in individuals harboring this inherited chromosomally integrated HHV-6A/B (iciHHV-6) in every cell of their body. Until now, the viral transcriptome and the epigenetic modifications that contribute to the silencing of the integrated virus genome remain elusive. In the current study, we used a patient-derived iciHHV-6A cell line to assess the global viral gene expression profile by RNA-seq, and the chromatin profiles by MNase-seq and ChIP-seq analyses. In addition, we investigated an in vitro generated cell line (293-HHV-6A) that expresses GFP upon the addition of agents commonly used to induce herpesvirus reactivation such as TPA. No viral gene expression including miRNAs was detected from the HHV-6A genomes, indicating that the integrated virus is transcriptionally silent. Intriguingly, upon stimulation of the 293-HHV-6A cell line with TPA, only foreign promoters in the virus genome were activated, while all HHV-6A promoters remained completely silenced. The transcriptional silencing of latent HHV-6A was further supported by MNase-seq results, which demonstrate that the latent viral genome resides in a highly condensed nucleosome-associated state. We further explored the enrichment profiles of histone modifications via ChIP-seq analysis. Our results indicated that the HHV-6 genome is modestly enriched with the repressive histone marks H3K9me3/H3K27me3 and does not possess the active histone modifications H3K27ac/H3K4me3. Overall, these results indicate that HHV-6 genomes reside in a condensed chromatin state, providing insight into the epigenetic mechanisms associated with the silencing of the integrated HHV-6A genome

Alien Registration- Dubuc, Gilberte B. (Auburn, Androscoggin County)

https://digitalmaine.com/alien_docs/31135/thumbnail.jp

Elastic Scattering by Deterministic and Random Fractals: Self-Affinity of the Diffraction Spectrum

The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the Cantor set and Sierpinski carpet as special cases. Also randomized versions of these fractals are treated. The general result is that the diffraction intensities obey a strict recursion relation, and become self-affine in the limit of large iteration number, with a self-affinity exponent related directly to the fractal dimension of the scattering object. Applications include neutron scattering, x-rays, optical diffraction, magnetic resonance imaging, electron diffraction, and He scattering, which all display the same universal scaling.Comment: 20 pages, 11 figures. Phys. Rev. E, in press. More info available at http://www.fh.huji.ac.il/~dani

Dynamical chaos and power spectra in toy models of heteropolymers and proteins

The dynamical chaos in Lennard-Jones toy models of heteropolymers is studied by molecular dynamics simulations. It is shown that two nearby trajectories quickly diverge from each other if the heteropolymer corresponds to a random sequence. For good folders, on the other hand, two nearby trajectories may initially move apart but eventually they come together. Thus good folders are intrinsically non-chaotic. A choice of a distance of the initial conformation from the native state affects the way in which a separation between the twin trajectories behaves in time. This observation allows one to determine the size of a folding funnel in good folders. We study the energy landscapes of the toy models by determining the power spectra and fractal characteristics of the dependence of the potential energy on time. For good folders, folding and unfolding trajectories have distinctly different correlated behaviors at low frequencies.Comment: 8 pages, 9 EPS figures, Phys. Rev. E (in press

Discovery of the Optical Transient of the Gamma Ray Burst 990308

The optical transient of the faint Gamma Ray Burst 990308 was detected by the QUEST camera on the Venezuelan 1-m Schmidt telescope starting 3.28 hours after the burst. Our photometry gives $V = 18.32 \pm 0.07$, $R = 18.14 \pm 0.06$, $B = 18.65 \pm 0.23$, and $R = 18.22 \pm 0.05$ for times ranging from 3.28 to 3.47 hours after the burst. The colors correspond to a spectral slope of close to $f_{\nu} \propto \nu^{1/3}$. Within the standard synchrotron fireball model, this requires that the external medium be less dense than $10^{4} cm^{-3}$, the electrons contain $> 20$ of the shock energy, and the magnetic field energy must be less than 24% of the energy in the electrons for normal interstellar or circumstellar densities. We also report upper limits of $V > 12.0$ at 132 s (with LOTIS), $V > 13.4$ from 132-1029s (with LOTIS), $V > 15.3$ at 28.2 min (with Super-LOTIS), and a 8.5 GHz flux of $< 114 \mu Jy$ at 110 days (with the Very Large Array). WIYN 3.5-m and Keck 10-m telescopes reveal this location to be empty of any host galaxy to $R > 25.7$ and $K > 23.3$. The lack of a host galaxy likely implies that it is either substantially subluminous or more distant than a red shift of $\sim 1.2$.Comment: ApJ Lett submitted, 5 pages, 2 figures, no space for 12 coauthor

Surface Studies of Calcium Oxalate Dihydrate Single Crystals During Dissolution in the Presence of Urine

Single crystals of Calcium Oxalate Dihydrate (COD) were grown from solution under controlled release of the reacting ions. Dissolution of COD was studied at different pH levels and in different dilutions of urine. The descriptors of the contour were determined during dissolution of COD using a quantitative morphological technique. The shape parameters and surface ruggedness were determined from Fourier and fractal analysis. The results obtained give quantitative information on the dissolution kinetics and the surface geometry of COD crystals in normal and diluted urine. Dissolution inhibition and morphological changes of COD crystals during dissolution were attributed to selective adsorption of urine non-ionic macromolecules on the crystal stepped surface. Surface etching of COD was found to depend on urine dilution and time of incubation. The data obtained suggest that the geometric structure of the surface is likely to be a potential factor in understanding crystal aggregation in stone formation