Best causal mathematical models for a nonlinear system

©2005 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.We provide new causal mathematical models of a nonlinear system S which are specifications of a nonlinear operator P/sub p/ of degree p=1,2,.... The operator P/sub p/ is determined from a special orthogonalization procedure and minimization of the mean squared difference between outputs of S and P/sub p/. As a result, these models have smallest possible associated errors in the class of such operators P/sub p/. The causality condition is implemented through the use of specific matrices called lower trapezoidal. The associated computational work is reduced by the use of the orthogonalization procedure. We provide a strict justification of the proposed approach including theorems on an explicit representatoin of the models' parameters, and theorems on the associated error representation. The possible extensions of the proposed approach and its potential applications are outlined.Anatoli Torokhti, Phil Howlett, and Charles Pearc

A philosophy for the modelling of realistic nonlinear systems

First published in Proceedings of the American Mathematical Society in volume 132, number 2, by the American Mathematical Society Copyright © 2003 American Mathematical SocietyA nonlinear dynamical system is modelled as a nonlinear mapping from a set of input signals into a corresponding set of output signals. Each signal is specified by a set of real number parameters, but such sets may be uncountably infinite. For numerical simulation of the system each signal must be represented by a finite parameter set and the mapping must be defined by a finite arithmetical process. Nevertheless the numerical simulation should be a good approximation to the mathematical model. We discuss the representation of realistic dynamical systems and establish a stable approximation theorem for numerical simulation of such systems.Phil Howlett, Anatoli Torokhti, Charles Pearc

Evaluating bulk flow estimators for CosmicFlows-4 measurements

For over a decade there have been contradictory claims in the literature about whether the local bulk flow motion of galaxies is consistent or in tension with the $\Lambda$CDM model. While it has become evident that systematics affect bulk flow measurements, systematics in the estimators have not been widely investigated. In this work, we thoroughly evaluate the performance of four estimator variants, including the Kaiser maximum likelihood estimator (MLE) and the minimum variance estimator (MVE). We find that these estimators are unbiased, however their precision may be strongly correlated with the survey geometry. Small biases in the estimators can be present leading to underestimated bulk flows, which we suspect are due to the presence of non-linear peculiar velocities. The uncertainty assigned to the bulk flows from these estimators is typically underestimated, which leads to an overestimate of the tension with $\Lambda$CDM. We estimate the bulk flow for the CosmicFlows-4 data and use mocks to ensure the uncertainties are appropriately accounted for. Using the MLE we find a bulk flow amplitude of $408\pm165 \mathrm{km s}^{-1}$ at a depth of $49\, \mathrm{Mpc} h^{-1}$, in reasonable agreement with $\Lambda$CDM. However using the MVE which can probe greater effective depths, we find an amplitude of $428\pm108 \mathrm{km s}^{-1}$ at a depth of $173\, \mathrm{Mpc} h^{-1}$, in tension with the model, having only a 0.11% probability of obtaining a larger $\chi^2$. These measurements appear directed towards the Great Attractor region where more data may be needed to resolve tensions

The accuracy of interpretation of emergency abdominal CT in adult patients who present with non-traumatic abdominal pain: results of a UK national audit.

: To evaluate major/minor discrepancy rates for provisional (initial) and addendum (supplementary senior review) emergency computed tomography (CT) reports in patients presenting with non-traumatic abdominal pain. : Ethical approval for this type of study is not required in the UK. All radiology departments with an approved lead for audit registered with the Royal College of Radiologists were invited to participate in this retrospective audit. The first 50 consecutive patients (25 surgical, 25 non-surgical) who underwent emergency abdominal CT for non-traumatic abdominal pain in 2013 were included. Statistical analyses were performed to identify organisational and report/patient-related variables that might be associated with major discrepancy. : One hundred and nine (58%) of 188 departments supplied data to the study with a total of 4,931 patients (2,568 surgical, 2,363 non-surgical). The audit standard for provisional report major discrepancy was achieved for registrars (target &lt;10%, achieved 4.6%), for on-site consultants (target &lt;5%, achieved 3.1%) and consultant addendum (target &lt;5%, achieved 2.9%). Off-site reporters failed to meet the standard target (&lt;5%, achieved 8.7% overall and 12.7% in surgical patients). The standard for patients coming to harm was not met in the surgical group (target &lt;1%, achieved 1.5%) and was narrowly missed overall (target &lt;1%, achieved 1%). : This study should be used to provide impetus to improve aspects of out-of-hours CT reporting. Clear benefits of CT interpretation/review by on-site and more senior (consultant) radiologists have been demonstrated.<br/

An Ultrastructural Analysis of the Physical Organization of Collagenous (Type I) Matrices: One Determinant of Urothelium Maintenance In Vitro

Collagenous matrices, used as cell culture substrata, can be prepared from different collagen types in a variety of forms using a range of polymerization procedures. Type I collagen has been most frequently used either as dried collagen films or hydrated collagen gels. Sheets of isolated bladder urothelium, when plated onto such matrices prepared from type I collagen by different polymerization methods (eg. air-drying; NaOH; NaCl; NH3; or NH3 followed by glutaraldehyde crosslinking) demonstrate the capability of urothelial cells to attach to a variety of differently prepared matrices irrespective of polymerization procedure. In contrast, both cell proliferation and maintenance of the urothelium are markedly influenced by the polymerized form of the collagen matrix. Comparative ultrastructural (scanning and transmission electron microscopy) analysis of these matrices demonstrates dissimilarities in their physical organization. The level of filamentous, fibrillar or fibrous reaggregation of solubilized collagen molecules varies in relation to the polymerization procedure used viz, a) air dried matrices form a dense meshwork of many forms of collagen fibrils and associated filaments with an irregular surface array of coarser collagen fibres; b) matrices prepared by NaOH, NaCl and NH3 polymerization present no major differences and form a felt of interlocking collagen fibres with discrete filamentous networks associated with these fibres; and c) matrices polymerized by NH3 and crosslinked with glutaraldehyde form a dense meshwork of filaments with a more occasional distribution of fibrils associated with filaments or dense amorphous aggregates. The level of supramolecular reassemblage of solubilized collagen may be, therefore, a significant factor in determining urothelial cell growth and differentiation on collagen matrices

The clustering of the SDSS main galaxy sample - II. Mock galaxy catalogues and a measurement of the growth of structure from redshift space distortions at z=0.15

Citation: Howlett, C., Ross, A. J., Samushia, L., Percival, W. J., & Manera, M. (2015). The clustering of the SDSS main galaxy sample - II. Mock galaxy catalogues and a measurement of the growth of structure from redshift space distortions at z=0.15. Monthly Notices of the Royal Astronomical Society, 449(1), 848-866. doi:10.1093/mnras/stu2693We measure redshift space distortions in the two-point correlation function of a sample of 63 163 spectroscopically identified galaxies with z < 0.2, an epoch where there are currently only limited measurements, from the Sloan Digital Sky Survey Data Release 7 main galaxy sample (MGS). Our sample, which we denote MGS, covers 6813 deg(2) with an effective redshift z(eff) = 0.15 and is described in our companion paper (Paper I), which concentrates on baryon acoustic oscillation (BAO) measurements. In order to validate the fitting methods used in both papers, and derive errors, we create and analyse 1000 mock catalogues using a new algorithm called PICOLA to generate accurate dark matter fields. Haloes are then selected using a friends-of-friends algorithm, and populated with galaxies using a halo-occupation distribution fitted to the data. Using errors derived from these mocks, we fit a model to the monopole and quadrupole moments of the MGS correlation function. If we assume no Alcock-Paczynski (AP) effect (valid at z = 0.15 for any smooth model of the expansion history), we measure the amplitude of the velocity field, f sigma(8), at z = 0.15 to be 0.49(-0.14)(+0.15) . We also measure f sigma(8) including the AP effect. This latter measurement can be freely combined with recent cosmic microwave background results to constrain the growth index of fluctuations, gamma Assuming a background Lambda cold dark matter cosmology and combining with current BAO data, we find gamma = 0.64 +/- 0.09, which is consistent with the prediction of general relativity (gamma approximate to 0.55), though with a slight preference for higher gamma and hence models with weaker gravitational interactions

The Simple Chordate \u3cem\u3eCiona intestinalis\u3c/em\u3e Has a Reduced Complement of Genes Associated with Fanconi Anemia

Fanconi anemia (FA) is a human genetic disease characterized by congenital defects, bone marrow failure, and increased cancer risk. FA is associated with mutation in one of 24 genes. The protein products of these genes function cooperatively in the FA pathway to orchestrate the repair of DNA interstrand cross-links. Few model organisms exist for the study of FA. Seeking a model organism with a simpler version of the FA pathway, we searched the genome of the simple chordate Ciona intestinalis for homologs of the human FA-associated proteins. BLAST searches, sequence alignments, hydropathy comparisons, maximum likelihood phylogenetic analysis, and structural modeling were used to infer the likelihood of homology between C. intestinalis and human FA proteins. Our analysis indicates that C. intestinalis indeed has a simpler and potentially functional FA pathway. The C. intestinalis genome was searched for candidates for homology to 24 human FA and FA-associated proteins. Support was found for the existence of homologs for 13 of these 24 human genes in C. intestinalis. Members of each of the three commonly recognized FA gene functional groups were found. In group I, we identified homologs of FANCE, FANCL, FANCM, and UBE2T/FANCT. Both members of group II, FANCD2 and FANCI, have homologs in C. intestinalis. In group III, we found evidence for homologs of FANCJ, FANCO, FANCQ/ERCC4, FANCR/RAD51, and FANCS/BRCA1, as well as the FA-associated proteins ERCC1 and FAN1. Evidence was very weak for the existence of homologs in C. intestinalis for any other recognized FA genes. This work supports the notion that C. intestinalis, as a close relative of vertebrates, but having a much reduced complement of FA genes, offers a means of studying the function of certain FA proteins in a simpler pathway than that of vertebrate cells

N-methyl-N-alkylpyrrolidinium nonafluoro-1-butanesulfonate salts : Ionic liquid properties and plastic crystal behaviour

A series of N-methyl-N-alkylpyrrolidinium nonafluoro-1-butanesulfonate salts were synthesised and characterised. The thermophysical characteristics of this family of salts have been investigated with respect to potential use as ionic liquids and solid electrolytes. N-Methyl-N-butylpyrrolidinium nonafluoro-1-butanesulfonate (p1,4NfO) has the lowest melting point of the family, at 94 &deg;C. Electrochemical analysis of p1,4 NfO in the liquid state shows an electrochemical window of ~6 V. All compounds exhibit one or more solid&ndash;solid transitions at sub-ambient temperatures, indicating the existence of plastic crystal phases.<br /