341 research outputs found

    Dynamical theory of dense groups of galaxies

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    It is well known that galaxies associate in groups and clusters. Perhaps 40% of all galaxies are found in groups of 4 to 20 galaxies (e.g., Tully 1987). Although most groups appear to be so loose that the galaxy interactions within them ought to be insignificant, the apparently densest groups, known as compact groups appear so dense when seen in projection onto the plane of the sky that their members often overlap. These groups thus appear as dense as the cores of rich clusters. The most popular catalog of compact groups, compiled by Hickson (1982), includes isolation among its selection critera. Therefore, in comparison with the cores of rich clusters, Hickson's compact groups (HCGs) appear to be the densest isolated regions in the Universe (in galaxies per unit volume), and thus provide in principle a clean laboratory for studying the competition of very strong gravitational interactions. The $64,000 question here is then: Are compact groups really bound systems as dense as they appear? If dense groups indeed exist, then one expects that each of the dynamical processes leading to the interaction of their member galaxies should be greatly enhanced. This leads us to the questions: How stable are dense groups? How do they form? And the related question, fascinating to any theorist: What dynamical processes predominate in dense groups of galaxies? If HCGs are not bound dense systems, but instead 1D change alignments (Mamon 1986, 1987; Walke & Mamon 1989) or 3D transient cores (Rose 1979) within larger looser systems of galaxies, then the relevant question is: How frequent are chance configurations within loose groups? Here, the author answers these last four questions after comparing in some detail the methods used and the results obtained in the different studies of dense groups

    Applications of hidden Markov models in financial modelling

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    This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University.Various models driven by a hidden Markov chain in discrete or continuous time are developed to capture the stylised features of market variables whose levels or values constitute as the underliers of financial derivative contracts or investment portfolios. Since the parameters are switching regimes, the changes and developments in the economy as soon as they arise are readily reflected in these models. The change of probability measure technique and the EM algorithm are fundamental techniques utilised in the optimal parameter estimation. Recursive adaptive filters for the state of the Markov chain and other auxiliary processes related to the Markov chain are derived which in turn yield self-tuning dynamic financial models. A hidden Markov model (HMM)-based modelling set-up for commodity prices is developed and the predictability of the gold market under this setting is examined. An Ornstein-Uhlenbeck (OU) model with HMM parameters is proposed and under this set-up, we address two statistical inference issues: the sensitivity of the model to small changes in parameter estimates and the selection of the optimal number of states. The extended OU model is implemented on a data set of 30-day Canadian T-bill yields. An exponential of a Markov-switching OU process plus a compound Poisson process is put forward as a model for the evolution of electricity spot prices. Using a data set compiled by Nord Pool, we illustrate the vast improvements gained in incorporating regimes in the model. A multivariate HMM is employed as a framework in providing the solutions of two asset allocation problems; one involves the mean-variance utility function and the other entails the CVaR constraint. Finally, the valuation of credit default swaps highlights the important considerations necessitated by pricing in a regime-switching environment. Certain numerical schemes are applied to obtain approximations for the default probabilities and swap rates.Brunel Research Initiative and Enterprise Fund (BRIEF) and European Union (Marie Curie Fellowship

    A partially linearized sigma point filter for latent state estimation in nonlinear time series models

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    A new technique for the latent state estimation of a wide class of nonlinear time series models is proposed. In particular, we develop a partially linearized sigma point filter in which random samples of possible state values are generated at the prediction step using an exact moment matching algorithm and then a linear programming-based procedure is used in the update step of the state estimation. The effectiveness of the new ¯ltering procedure is assessed via a simulation example that deals with a highly nonlinear, multivariate time series representing an interest rate process

    Temperature-Tolerant COLD-PCR Eliminates Temperature Stringency and Enables Robust Mutation Enrichment.

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    BACKGROUND: Low-level mutations in clinical tumor samples often reside below mutation detection limits, thus leading to false negatives that may impact clinical diagnosis and patient management. COLD-PCR (coamplification at lower denaturation temperature PCR) is a technology that magnifies unknown mutations during PCR, thus enabling downstream mutation detection. However, a practical difficulty in applying COLD-PCR has been the requirement for strict control of the denaturation temperature for a given sequence, to within ±0.3 °C. This requirement precludes simultaneous mutation enrichment in sequences of substantially different melting temperature (T(m)) and limits the technique to a single sequence at a time. We present a temperature-tolerant (TT) approach (TT-COLD-PCR) that reduces this obstacle. METHODS: We describe thermocycling programs featuring a gradual increase of the denaturation temperature during COLD-PCR. This approach enabled enrichment of mutations when the cycling achieves the appropriate critical denaturation temperature of each DNA amplicon that is being amplified. Validation was provided for KRAS (v-Ki-ras2 Kirsten rat sarcoma viral oncogene homolog) and TP53 (tumor protein p53) exons 6-9 by use of dilutions of mutated DNA, clinical cancer samples, and plasma-circulating DNA. RESULTS: A single thermocycling program with a denaturation-temperature window of 2.5-3.0 °C enriches mutations in all DNA amplicons simultaneously, despite their different T(m)s. Mutation enrichments of 6-9-fold were obtained with TT-full-COLD-PCR. Higher mutation enrichments were obtained for the other 2 forms of COLD-PCR, fast-COLD-PCR, and ice-COLD-PCR. CONCLUSIONS: Low-level mutations in diverse amplicons with different T(m)s can be mutation enriched via TT-COLD-PCR provided that their T(m)s fall within the denaturation-temperature window applied during amplification. This approach enables simultaneous enrichment of mutations in several amplicons and increases significantly the versatility of COLD-PCR

    VizieR Online Data Catalog: FLAIR II spectroscopy of DENIS samples (Mamon+, 2001)

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    As a pilot survey for the forthcoming 6dF Galaxy Redshift Survey, spectroscopy of galaxies selected in the 1.2 micron J waveband with the DENIS imaging survey was performed at the UKST using the FLAIR II multi-object spectroscope. Sixty-nine galaxy redshifts were obtained in a high galactic latitude field and an additional 12 redshifts in a low galactic latitude (b=-17{deg}), obscured field. This spectroscopic follow-up of NIR selected galaxies illustrates the feasibility of obtaining redshifts with optical spectra on galaxies selected at much longer wavelengths. It validated a very preliminary algorithm for star/galaxy separation for high galactic latitude DENIS objects, with 99% reliability for J<13.9. The FLAIR II redshifts are in excellent agreement with those, previously published, of 20 common galaxies. However, the FLAIR II redshift determinations presented here required substantially longer integration times to achieve 90% completeness than expected from previous optical surveys at comparable depth. This is mainly due to a degradation in overall fibre throughput due to known problems with ageing of the prism- cement-fibre interface with exposure to UV light. In comparison to our high galactic latitude field, our low latitude (high extinction) field required 2.5 times more exposure time for less than 50% of successful redshift measurements. Among the J<=13.9 galaxies with measured redshifts, only 37+/-6% display emission lines, in comparison with 60% of emission line galaxies in optical samples of comparable depth. These galaxies are, on average, half a magnitude bluer in B-J than galaxies of the same luminosity without emission fines. We confirm a previous optically-based result that the fraction of galaxies with emission lines increases rapidly with decreasing galaxy luminosity. The J band luminosity function is estimated. Our high latitude field displays a concentration of galaxies at cz~=38000km/s suggesting a possible supercluster. A radial velocity is reported for a galaxy lying near the projected centre of the Abell 1434 cluster of galaxies, for which no cluster redshift is currently available. (2 data files)

    A new algorithm for latent state estimation in nonlinear time series models

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    We consider the problem of optimal state estimation for a wide class of nonlinear time series models. A modified sigma point filter is proposed, which uses a new procedure for generating sigma points. Unlike the existing sigma point generation methodologies in engineering where negative probability weights may occur, we develop an algorithm capable of generating sample points that always form a valid probability distribution while still allowing the user to sample using a random number generator. The effectiveness of the new filtering procedure is assessed through simulation examples

    A linear algebraic method for pricing temporary life annuities and insurance policies

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    We recast the valuation of annuities and life insurance contracts under mortality and interest rates, both of which are stochastic, as a problem of solving a system of linear equations with random perturbations. A sequence of uniform approximations is developed which allows for fast and accurate computation of expected values. Our reformulation of the valuation problem provides a general framework which can be employed to find insurance premiums and annuity values covering a wide class of stochastic models for mortality and interest rate processes. The proposed approach provides a computationally efficient alternative to Monte Carlo based valuation in pricing mortality-linked contingent claims
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