Lyapunov exponent and natural invariant density determination of chaotic maps: An iterative maximum entropy ansatz

We apply the maximum entropy principle to construct the natural invariant density and Lyapunov exponent of one-dimensional chaotic maps. Using a novel function reconstruction technique that is based on the solution of Hausdorff moment problem via maximizing Shannon entropy, we estimate the invariant density and the Lyapunov exponent of nonlinear maps in one-dimension from a knowledge of finite number of moments. The accuracy and the stability of the algorithm are illustrated by comparing our results to a number of nonlinear maps for which the exact analytical results are available. Furthermore, we also consider a very complex example for which no exact analytical result for invariant density is available. A comparison of our results to those available in the literature is also discussed.Comment: 16 pages including 6 figure

An investigation of the RWPE prostate derived family of cell lines using FTIR spectroscopy

Interest in developing robust, quicker and easier diagnostic tests for cancer has lead to an increased use of Fourier transform infrared (FTIR) spectroscopy to meet that need. In this study we present the use of different experimental modes of infrared spectroscopy to investigate the RWPE human prostate epithelial cell line family which are derived from the same source but differ in their mode of transformation and their mode of invasive phenotype. Importantly, analysis of the infrared spectra obtained using different experimental modes of infrared spectroscopy produces similar results. The RWPE family of cell lines can be separated into groups based upon the method of cell transformation rather than the resulting invasiveness/aggressiveness of the cell line. The study also demonstrates the possibility of using a genetic algorithm as a possible standardised pre-processing step and raises the important question of the usefulness of cell lines to create a biochemical model of prostate cancer progression

Nanostructure of cellulose microfibrils in spruce wood

The structure of cellulose microfibrils in wood is not known in detail, despite the abundance of cellulose in woody biomass and its importance for biology, energy, and engineering. The structure of the microfibrils of spruce wood cellulose was investigated using a range of spectroscopic methods coupled to small-angle neutron and wide-angle X-ray scattering. The scattering data were consistent with 24-chain microfibrils and favored a “rectangular” model with both hydrophobic and hydrophilic surfaces exposed. Disorder in chain packing and hydrogen bonding was shown to increase outwards from the microfibril center. The extent of disorder blurred the distinction between the I alpha and I beta allomorphs. Chains at the surface were distinct in conformation, with high levels of conformational disorder at C-6, less intramolecular hydrogen bonding and more outward-directed hydrogen bonding. Axial disorder could be explained in terms of twisting of the microfibrils, with implications for their biosynthesis

A Hopf laboratory for symmetric functions

An analysis of symmetric function theory is given from the perspective of the underlying Hopf and bi-algebraic structures. These are presented explicitly in terms of standard symmetric function operations. Particular attention is focussed on Laplace pairing, Sweedler cohomology for 1- and 2-cochains, and twisted products (Rota cliffordizations) induced by branching operators in the symmetric function context. The latter are shown to include the algebras of symmetric functions of orthogonal and symplectic type. A commentary on related issues in the combinatorial approach to quantum field theory is given.Comment: 29 pages, LaTeX, uses amsmat

Modelling the orientation of accretion disks in quasars using H-alpha emission

Infrared spectroscopy of the H-alpha emission lines of a sub-sample of 19 high-redshift (0.8 < z < 2.3) Molonglo quasars, selected at 408 MHz, is presented. These emission lines are fitted with composite models of broad and narrow emission, which include combinations of classical broad-line regions of fast-moving gas clouds lying outside the quasar nucleus, and/or a theoretical model of emission from an optically-thick, flattened, rotating accretion disk. All bar one of the nineteen sources are found to have emission consistent with the presence of an optically-emitting accretion disk, with the exception appearing to display complex emission including at least three broad components. Ten of the quasars have strong Bayesian evidence for broad-line emission arising from an accretion disk together with a standard broad-line region, selected in preference to a model with two simple broad lines. Thus the best explanation for the complexity required to fit the broad H-alpha lines in this sample is optical emission from an accretion disk in addition to a region of fast-moving clouds. We derive estimates of the angle between the rotation axis of the accretion disk and the line of sight. A weak correlation is found between the accretion disk angle and the logarithm of the low-frequency radio luminosity. This is direct, albeit tenuous, evidence for the receding torus model. Velocity shifts of the broad H-alpha components are analysed and the results found to be consistent with a two-component model comprising one single-peaked broad line emitted at the same redshift as the narrow lines, and emission from an accretion disk which appears to be preferentially redshifted with respect to the narrow lines for high-redshift sources and blueshifted relative to the narrow lines for low-redshift sources.Comment: The definitive version is available at www.blackwell-synergy.com. 36 pages, 21 figures, 13 tables. Replaced to fix A4/US letter paper size confusio

Electrical Material Property Measurements using a Free-Field, Ultra-Wideband System [Dielectric Measurements]

We present nondestructive measurements of material properties using TEM horn antennas and an ultra-wideband measurement system. Time-domain gating and genetic algorithms are used to process the data and extract the dielectric properties of the material under test

A gauge model for quantum mechanics on a stratified space

In the Hamiltonian approach on a single spatial plaquette, we construct a quantum (lattice) gauge theory which incorporates the classical singularities. The reduced phase space is a stratified K\"ahler space, and we make explicit the requisite singular holomorphic quantization procedure on this space. On the quantum level, this procedure furnishes a costratified Hilbert space, that is, a Hilbert space together with a system which consists of the subspaces associated with the strata of the reduced phase space and of the corresponding orthoprojectors. The costratified Hilbert space structure reflects the stratification of the reduced phase space. For the special case where the structure group is $\mathrm{SU}(2)$, we discuss the tunneling probabilities between the strata, determine the energy eigenstates and study the corresponding expectation values of the orthoprojectors onto the subspaces associated with the strata in the strong and weak coupling approximations.Comment: 38 pages, 9 figures. Changes: comments on the heat kernel and coherent states have been adde

Galaxies in Southern Bright Star Fields I. Near-infrared imaging

As a prerequisite for cosmological studies using adaptive optics techniques, we have begun to identify and characterize faint sources in the vicinity of bright stars at high Galactic latitudes. The initial phase of this work has been a program of K_s imaging conducted with SOFI at the ESO NTT. From observations of 42 southern fields evenly divided between the spring and autumn skies, we have identified 391 additional stars and 1589 galaxies lying at separations 60" from candidate guide stars in the magnitude range 9.0 R 12.4. When analyzed as a "discrete deep field" with 131 arcmin^2 area, our dataset gives galaxy number counts that agree with those derived previously over the range 16 K_s 20.5. This consistency indicates that in the aggregate, our fields should be suitable for future statistical studies. We provide our source catalogue as a resource for users of large telescopes in the southern hemisphere.Comment: 10 pages, 7 figures, accepted by A&A; Table 3 is available at http://www.rzg.mpg.de/~ajb/data.html pending upload to CD

A deep / wide 1-2 GHz snapshot survey of SDSS Stripe 82 using the Karl G. Jansky Very Large Array in a compact hybrid configuration

This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society. © 2016 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.We have used the Karl G. Jansky Very Large Array to image ~100 sq. deg. of SDSS Stripe 82 at 1-2 GHz. The survey consists of 1,026 snapshot observations of 2.5 minutes duration, using the hybrid CnB configuration. The survey has good sensitivity to diffuse, low surface brightness structures and extended radio emission, making it highly synergistic with existing 1.4 GHz radio observations of the region. The principal data products are continuum images, with 16 x 10 arcsecond resolution, and a catalogue containing 11,782 point and Gaussian components resulting from fits to the thresholded Stokes-I brightness distribution, forming approximately 8,948 unique radio sources. The typical effective 1{\sigma} noise level is 88 {\mu}Jy / beam. Spectral index estimates are included, as derived from the 1 GHz of instantaneous bandwidth. Astrometric and photometric accuracy are in excellent agreement with existing narrowband observations. A large-scale simulation is used to investigate clean bias, which we extend into the spectral domain. Clean bias remains an issue for snapshot surveys with the VLA, affecting our total intensity measurements at the ~1{\sigma} level. Statistical spectral index measurements are in good agreement with existing measurements derived from matching separate surveys at two frequencies. At flux densities below ~35{\sigma} the median in-band spectral index measurements begin to exhibit a bias towards flatness that is dependent on both flux density and the intrinsic spectral index. In-band spectral curvature measurements are likely to be unreliable for all but the very brightest components. Image products and catalogues are publicly available via an FTP server.Peer reviewedFinal Published versio

Modification and preservation of environmental signals in speleothems

Speleothems are primarily studied in order to generate archives of climatic change and results have led to significant advances in identifying and dating major shifts in the climate system. However, the climatological meaning of many speleothem records cannot be interpreted unequivocally; this is particularly so for more subtle shifts and shorter time periods, but the use of multiple proxies and improving understanding of formation mechanisms offers a clear way forward. An explicit description of speleothem records as time series draws attention to the nature and importance of the signal filtering processes by which the weather, the seasons and longer-term climatic and other environmental fluctuations become encoded in speleothems. We distinguish five sources of variation that influence speleothem geochemistry: atmospheric, vegetation/soil, karstic aquifer, primary speleothem crystal growth and secondary alteration and give specific examples of their influence. The direct role of climate diminishes progressively through these five factors. \ud \ud We identify and review a number of processes identified in recent and current work that bear significantly on the conventional interpretation of speleothem records, for example: \ud \ud 1) speleothem geochemistry can vary seasonally and hence a research need is to establish the proportion of growth attributable to different seasons and whether this varies over time. \ud \ud 2) whereas there has traditionally been a focus on monthly mean Ã�´18O data of atmospheric moisture, current work emphasizes the importance of understanding the synoptic processes that lead to characteristic isotope signals, since changing relative abundance of different weather types might 1Corresponding author, fax +44(0)1214145528, E-mail: [email protected] control their variation on the longer-term. \ud \ud 3) the ecosystem and soil zone overlying the cave fundamentally imprint the carbon and trace element signals and can show characteristic variations with time. \ud \ud 4) new modelling on aquifer plumbing allows quantification of the effects of aquifer mixing. \ud \ud 5) recent work has emphasized the importance and seasonal variability of CO2-degassing leading to calcite precipitation upflow of a depositional site on carbon isotope and trace element composition of speleothems. \ud \ud 6) Although much is known about the chemical partitioning between water and stalagmites, variability in relation to crystal growth mechanisms and kinetics is a research frontier. \ud \ud 7) Aragonite is susceptible to conversion to calcite with major loss of chemical information, but the controls on the rate of this process are obscure. \ud \ud Analytical factors are critical to generate high-resolution speleothem records. A variety of methods of trace element analysis are available, but standardization is a common problem with the most rapid methods. New stable isotope data on Irish stalagmite CC3 compares rapid laser-ablation techniques with the conventional analysis of micromilled powders and ion microprobe methods. A high degree of comparability between techniques for Ã�´18O is found on the mm-cm scale, but a previously described high-amplitude oxygen isotope excursion around 8.3 ka is identified as an analytical artefact related to fractionation of the laser-analysis associated with sample cracking. High-frequency variability of not less than 0.5o/oo may be an inherent feature of speleothem Ã�´18O records