A dynamical definition of f.g. virtually free groups

We show that the class of finitely generated virtually free groups is precisely the class of demonstrable subgroups for R. Thompson's group V . The class of demonstrable groups for V consists of all groups which can embed into V with a natural dynamical behaviour in their induced actions on the Cantor space C2 := {0,1}ω. There are also connections with formal language theory, as the class of groups with context-free word problem is also the class of finitely generated virtually free groups, while R. Thompson's group V is a candidate as a universal coCF group by Lehnert's conjecture, corresponding to the class of groups with context free co-word problem (as introduced by Holt, Rees, Röver, and Thomas). Our main results answers a question of Berns-Zieze, Fry, Gillings, Hoganson, and Matthews, and separately of Bleak and Salazar-Días, and fits into the larger exploration of the class of coCF groups as it shows that all four of the known properties of the class of coCF groups hold for the set of finitely generation subgroups of V .PostprintPeer reviewe

MalStone: Towards A Benchmark for Analytics on Large Data Clouds

Developing data mining algorithms that are suitable for cloud computing platforms is currently an active area of research, as is developing cloud computing platforms appropriate for data mining. Currently, the most common benchmark for cloud computing is the Terasort (and related) benchmarks. Although the Terasort Benchmark is quite useful, it was not designed for data mining per se. In this paper, we introduce a benchmark called MalStone that is specifically designed to measure the performance of cloud computing middleware that supports the type of data intensive computing common when building data mining models. We also introduce MalGen, which is a utility for generating data on clouds that can be used with MalStone

Arbitrary precision composite pulses for NMR quantum computing

We discuss the implementation of arbitrary precision composite pulses developed using the methods of Brown et al. [Phys. Rev. A 70 (2004) 052318]. We give explicit results for pulse sequences designed to tackle both the simple case of pulse length errors and for the more complex case of off-resonance errors. The results are developed in the context of NMR quantum computation, but could be applied more widely.Comment: 16 pages elsart, no figures. In press at Journal of Magnetic resonanc

A Brief History of AGN

Astronomers knew early in the twentieth century that some galaxies have emission-line nuclei. However, even the systematic study by Seyfert (1943) was not enough to launch active galactic nuclei (AGN) as a major topic of astronomy. The advances in radio astronomy in the 1950s revealed a new universe of energetic phenomena, and inevitably led to the discovery of quasars. These discoveries demanded the attention of observers and theorists, and AGN have been a subject of intense effort ever since. Only a year after the recognition of the redshifts of 3C 273 and 3C 48 in 1963, the idea of energy production by accretion onto a black hole was advanced. However, acceptance of this idea came slowly, encouraged by the discovery of black hole X-ray sources in our Galaxy and, more recently, supermassive black holes in the center of the Milky Way and other galaxies. Many questions remain as to the formation and fueling of the hole, the geometry of the central regions, the detailed emission mechanisms, the production of jets, and other aspects. The study of AGN will remain a vigorous part of astronomy for the foreseeable future.Comment: 37 pages, no figures. Uses aaspp4.sty. To be published in Publications of the Astronomical Society of the Pacific, 1999 Jun

Calculation of absolute free energy of binding for theophylline and its analogs to RNA aptamer using nonequilibrium work values

The massively parallel computation of absolute binding free energy with a well-equilibrated system (MP-CAFEE) has been developed [H. Fujitani, Y. Tanida, M. Ito, G. Jayachandran, C. D. Snow, M. R. Shirts, E. J. Sorin, and V. S. Pande, J. Chem. Phys. ${\bf 123}$, 084108 (2005)]. As an application, we perform the binding affinity calculations of six theophylline-related ligands with RNA aptamer. Basically, our method is applicable when using many compute nodes to accelerate simulations, thus a parallel computing system is also developed. To further reduce the computational cost, the adequate non-uniform intervals of coupling constant $\lambda$, connecting two equilibrium states, namely bound and unbound, are determined. The absolute binding energies $\Delta G$ thus obtained have effective linear relation between the computed and experimental values. If the results of two other different methods are compared, thermodynamic integration (TI) and molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) by the paper of Gouda $et al$ [H. Gouda, I. D. Kuntz, D. A. Case, and P. A. Kollman, Biopolymers ${\bf 68}$, 16 (2003)], the predictive accuracy of the relative values $\Delta\Delta G$ is almost comparable to that of TI: the correlation coefficients (R) obtained are 0.99 (this work), 0.97 (TI), and 0.78 (MM-PBSA). On absolute binding energies meanwhile, a constant energy shift of $\sim$ -7 kcal/mol against the experimental values is evident. To solve this problem, several presumable reasons are investigated.Comment: 23 pages including 6 figure

CRISPR-Cas9 correction of a nonsense mutation in LCA5 rescues lebercilin expression and localization in human retinal organoids

Mutations in the lebercilin-encoding gene LCA5 cause one of the most severe forms of Leber congenital amaurosis, an early-onset retinal disease that results in severe visual impairment. Here, we report on the generation of a patient-specific cellular model to study LCA5-associated retinal disease. CRISPR-Cas9 technology was used to correct a homozygous nonsense variant in LCA5 (c.835C>T; p.Q279∗) in patient-derived induced pluripotent stem cells (iPSCs). The absence of off-target editing in gene-corrected (isogenic) control iPSCs was demonstrated by whole-genome sequencing. We differentiated the patient, gene-corrected, and unrelated control iPSCs into three-dimensional retina-like cells, so-called retinal organoids. We observed opsin and rhodopsin mislocalization to the outer nuclear layer in patient-derived but not in the gene-corrected or unrelated control organoids. We also confirmed the rescue of lebercilin expression and localization along the ciliary axoneme within the gene-corrected organoids. Here, we show the potential of combining precise single-nucleotide gene editing with the iPSC-derived retinal organoid system for the generation of a cellular model of early-onset retinal disease

Entanglement of electrons in interacting molecules

Quantum entanglement is a concept commonly used with reference to the existence of certain correlations in quantum systems that have no classical interpretation. It is a useful resource to enhance the mutual information of memory channels or to accelerate some quantum processes as, for example, the factorization in Shor's Algorithm. Moreover, entanglement is a physical observable directly measured by the von Neumann entropy of the system. We have used this concept in order to give a physical meaning to the electron correlation energy in systems of interacting electrons. The electronic correlation is not directly observable, since it is defined as the difference between the exact ground state energy of the many--electrons Schroedinger equation and the Hartree--Fock energy. We have calculated the correlation energy and compared with the entanglement, as functions of the nucleus--nucleus separation using, for the hydrogen molecule, the Configuration Interaction method. Then, in the same spirit, we have analyzed a dimer of ethylene, which represents the simplest organic conjugate system, changing the relative orientation and distance of the molecules, in order to obtain the configuration corresponding to maximum entanglement.Comment: 15 pages, 7 figures, standard late

Accretion Properties of A Sample of Hard X-ray (<60keV) Selected Seyfert 1 Galaxies

We examine the accretion properties in a sample of 42 hard (3-60keV) X-ray selected nearby broad-line AGNs. The energy range in the sample is harder than that usually used in the similar previous studies. These AGNs are mainly complied from the RXTE All Sky Survey (XSS), and complemented by the released INTEGRAL AGN catalog. The black hole masses, bolometric luminosities of AGN, and Eddington ratios are derived from their optical spectra in terms of the broad H$\beta$ emission line. The tight correlation between the hard X-ray (3-20keV) and bolometric/line luminosity is well identified in our sample. Also identified is a strong inverse Baldwin relationship of the H$\beta$ emission line. In addition, all these hard X-ray AGNs are biased toward luminous objects with high Eddington ratio (mostly between 0.01 to 0.1) and low column density ($<10^{22} \mathrm{cm^{-2}}$), which is most likely due to the selection effect of the surveys. The hard X-ray luminosity is consequently found to be strongly correlated with the black hole mass. We believe the sample completeness will be improved in the next few years by the ongoing Swift and INTEGRAL missions, and by the next advanced missions, such as NuSTAR, Simbol-X, and NeXT. Finally, the correlation between RFe (=optical FeII/H$\beta$) and disk temperature as assessed by $T\propto (L/L_{\mathrm{Edd}})M_{\mathrm{BH}}^{-1}$ leads us to suggest that the strength of the FeII emission is mainly determined by the shape of the ionizing spectrum.Comment: 28 pages, 7 figures, 2 tables, accepted by A

New Chiral Phases of Superfluid 3He Stabilized by Anisotropic Silica Aerogel

A rich variety of Fermi systems condense by forming bound pairs, including high temperature [1] and heavy fermion [2] superconductors, Sr2RuO4 [3], cold atomic gases [4], and superfluid 3He [5]. Some of these form exotic quantum states having non-zero orbital angular momentum. We have discovered, in the case of 3He, that anisotropic disorder, engineered from highly porous silica aerogel, stabilizes a chiral superfluid state that otherwise would not exist. Additionally, we find that the chiral axis of this state can be uniquely oriented with the application of a magnetic field perpendicular to the aerogel anisotropy axis. At suffciently low temperature we observe a sharp transition from a uniformly oriented chiral state to a disordered structure consistent with locally ordered domains, contrary to expectations for a superfluid glass phase [6].Comment: 6 pages, 4 figure, and Supplementary Informatio

Investigating the thermodynamics of small biosystems with optical tweezers

We present two examples of how single-molecule experimental techniques applied to biological systems can give insight into problems within the scope of equilibrium and nonequilibrium mesoscopic thermodynamics. The first example is the mapping of the free energy landscape of a macromolecule, the second the experimental verification of Crooks' fluctuation theorem. In both cases the experimental setup comprises optical tweezers and DNA molecules.Comment: 6 pages, 9 figures, Proceedings of the conference Frontiers of Quantum and Mesoscopic Thermodynamics, Prague 200