Maximum Fidelity

The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation: Which candidate distribution provides the best fit to the observed data?, (2) Goodness-of-fit: How concordant is this distribution with the observed data?, and (3) Uncertainty: How concordant are other candidate distributions with the observed data? A simple unified approach for univariate data that addresses these traditionally distinct statistical notions is presented called "maximum fidelity". Maximum fidelity is a strict frequentist approach that is fundamentally based on model concordance with the observed data. The fidelity statistic is a general information measure based on the coordinate-independent cumulative distribution and critical yet previously neglected symmetry considerations. An approximation for the null distribution of the fidelity allows its direct conversion to absolute model concordance (p value). Fidelity maximization allows identification of the most concordant model distribution, generating a method for parameter estimation, with neighboring, less concordant distributions providing the "uncertainty" in this estimate. Maximum fidelity provides an optimal approach for parameter estimation (superior to maximum likelihood) and a generally optimal approach for goodness-of-fit assessment of arbitrary models applied to univariate data. Extensions to binary data, binned data, multidimensional data, and classical parametric and nonparametric statistical tests are described. Maximum fidelity provides a philosophically consistent, robust, and seemingly optimal foundation for statistical inference. All findings are presented in an elementary way to be immediately accessible to all researchers utilizing statistical analysis.Comment: 66 pages, 32 figures, 7 tables, submitte

Analytical model for macromolecular partitioning during yeast cell division

Background: Asymmetric cell division, whereby a parent cell generates two sibling cells with unequal content and thereby distinct fates, is central to cell differentiation, organism development and ageing. Unequal partitioning of the macromolecular content of the parent cell — which includes proteins, DNA, RNA, large proteinaceous assemblies and organelles — can be achieved by both passive (e.g. diffusion, localized retention sites) and active (e.g. motor-driven transport) processes operating in the presence of external polarity cues, internal asymmetries, spontaneous symmetry breaking, or stochastic effects. However, the quantitative contribution of different processes to the partitioning of macromolecular content is difficult to evaluate. Results: Here we developed an analytical model that allows rapid quantitative assessment of partitioning as a function of various parameters in the budding yeast Saccharomyces cerevisiae. This model exposes quantitative degeneracies among the physical parameters that govern macromolecular partitioning, and reveals regions of the solution space where diffusion is sufficient to drive asymmetric partitioning and regions where asymmetric partitioning can only be achieved through additional processes such as motor-driven transport. Application of the model to different macromolecular assemblies suggests that partitioning of protein aggregates and episomes, but not prions, is diffusion-limited in yeast, consistent with previous reports. Conclusions: In contrast to computationally intensive stochastic simulations of particular scenarios, our analytical model provides an efficient and comprehensive overview of partitioning as a function of global and macromolecule-specific parameters. Identification of quantitative degeneracies among these parameters highlights the importance of their careful measurement for a given macromolecular species in order to understand the dominant processes responsible for its observed partitioning

X-Ray Spectroscopy of Astrophysical Plasmas

We provide a qualitative review of key X–ray spectral diagnostics of astrophysical plasmas. We begin with a brief discussion of the two major types of equilibria, collisional ionization and photoionization, and then consider the behaviour of hydrogen–like, helium–like, iron L–shell and iron K–shell transitions for these separate cases. Where possible, we discuss explicit examples using high–resolution spectra acquired by the grating instruments on the Chandra and XMM–Newton observatories

New Constraint on Open Cold-Dark-Matter Models

We calculate the large-angle cross-correlation between the cosmic-microwave-background (CMB) temperature and the x-ray-background (XRB) intensity expected in an open Universe with cold dark matter (CDM) and a nearly scale-invariant spectrum of adiabatic density perturbations. Results are presented as a function of the nonrelativistic-matter density $\Omega_0$ (in units of the critical density) and the x-ray bias $b_x$ (evaluated at a redshift $z\simeq1$ in evolving-bias models) for both an open Universe and a flat cosmological-constant Universe. Recent experimental upper limits to the amplitude of this cross-correlation provide a new constraint to the $\Omega_0$-$b_x$ parameter space that open-CDM models (and the open-inflation models that produce them) must satisfy.Comment: 4 pages, LaTeX. Revised version contains additional figure that clarifies new constraint. (To appear in PRL.

Optical and Radio Properties of Extragalactic Sources Observed by the FIRST and SDSS Surveys

We discuss the optical and radio properties of 30,000 FIRST sources positionally associated with an SDSS source in 1230 deg$^2$ of sky. The majority (83%) of the FIRST sources identified with an SDSS source brighter than r=21 are optically resolved. We estimate an upper limit of 5% for the fraction of quasars with broad-band optical colors indistinguishable from those of stars. The distribution of quasars in the radio flux -- optical flux plane supports the existence of the "quasar radio-dichotomy"; 8% of all quasars with i<18.5 are radio-loud and this fraction seems independent of redshift and optical luminosity. The radio-loud quasars have a redder median color by 0.08 mag, and a 3 times larger fraction of objects with red colors. FIRST galaxies represent 5% of all SDSS galaxies with r<17.5, and 1% for r<20, and are dominated by red galaxies. Magnitude and redshift limited samples show that radio galaxies have a different optical luminosity distribution than non-radio galaxies selected by the same criteria; when galaxies are further separated by their colors, this result remains valid for both blue and red galaxies. The distributions of radio-to-optical flux ratio are similar for blue and red galaxies in redshift-limited samples; this similarity implies that the difference in their luminosity functions, and resulting selection effects, are the dominant cause for the preponderance of red radio galaxies in flux-limited samples. We confirm that the AGN-to-starburst galaxy number ratio increases with radio flux, and find that radio emission from AGNs is more concentrated than radio emission from starburst galaxies (abridged).Comment: submitted to AJ, color gif figures, PS figures available from [email protected]

XMM-Newton Reflection Grating Spectrometer Observations of Discrete Soft-X-ray Emission Features from NGC 1068

We present the first high-resolution, soft-X-ray spectrum of the prototypical Seyfert 2 galaxy, NGC 1068. This spectrum was obtained with the XMM-Newton Reflection Grating Spectrometer. Emission lines from H-like and He-like low-Z ions (from C to Si) and Fe-L-shell ions dominate the spectrum. Strong, narrow radiative recombination continua (RRC) for several ions are also present, implying that most of the observed soft-X-ray emission arises in low-temperature (few eV) plasma. This plasma is photoionized by the inferred nuclear continuum (obscured along our line of sight), as in the unified model of active galactic nuclei (AGN). We find excess emission (compared with pure recombination) in all resonance lines (np to 1s) up to the photoelectric edge, demonstrating the importance of photoexcitation as well. We introduce a simple model of a cone of plasma irradiated by the nuclear continuum; the line emission we observe along our line of sight perpendicular to the cone is produced through recombination/radiative cascade following photoionization and radiative decay following photoexcitation. A remarkably good fit is obtained to the H-like/He-like ionic line series, with inferred radial ionic column densities consistent with recent observations of warm absorbers in Seyfert 1 galaxies. Previous Chandra imaging revealed a large (extending out to 500 pc) ionization cone containing most of the X-ray flux, implying that the warm absorber in NGC 1068 is a large-scale outflow. To explain the ionic column densities, a broad, flat distribution in the logarithm of the ionization parameter ($\xi=L_X/n_e r^2$) is necessary, spanning $\log\xi=0$--3. This suggests either radially-stratified ionization zones or the existence of a broad density distribution (spanning a few orders of magnitude) at each radius.Comment: 23 pages, 16 figures, ApJ (accepted). XSPEC local model "photo" is available at http://xmm.astro.columbia.edu/research.htm

Uncovering cis Regulatory Codes Using Synthetic Promoter Shuffling

Revealing the spectrum of combinatorial regulation of transcription at individual promoters is essential for understanding the complex structure of biological networks. However, the computations represented by the integration of various molecular signals at complex promoters are difficult to decipher in the absence of simple cis regulatory codes. Here we synthetically shuffle the regulatory architecture — operator sequences binding activators and repressors — of a canonical bacterial promoter. The resulting library of complex promoters allows for rapid exploration of promoter encoded logic regulation. Among all possible logic functions, NOR and ANDN promoter encoded logics predominate. A simple transcriptional cis regulatory code determines both logics, establishing a straightforward map between promoter structure and logic phenotype. The regulatory code is determined solely by the type of transcriptional regulation combinations: two repressors generate a NOR: NOT (a OR b) whereas a repressor and an activator generate an ANDN: a AND NOT b. Three-input versions of both logics, having an additional repressor as an input, are also present in the library. The resulting complex promoters cover a wide dynamic range of transcriptional strengths. Synthetic promoter shuffling represents a fast and efficient method for exploring the spectrum of complex regulatory functions that can be encoded by complex promoters. From an engineering point of view, synthetic promoter shuffling enables the experimental testing of the functional properties of complex promoters that cannot necessarily be inferred ab initio from the known properties of the individual genetic components. Synthetic promoter shuffling may provide a useful experimental tool for studying naturally occurring promoter shuffling

Direct Search for Dark Matter - Striking the Balance - and the Future

Weakly Interacting Massive Particles (WIMPs) are among the main candidates for the relic dark matter (DM). The idea of the direct DM detection relies on elastic spin-dependent (SD) and spin-independent (SI) interaction of WIMPs with target nuclei. In this review paper the relevant formulae for WIMP event rate calculations are collected. For estimations of the WIMP-proton and WIMP-neutron SD and SI cross sections the effective low-energy minimal supersymmetric standard model is used. The traditional one-coupling-dominance approach for evaluation of the exclusion curves is described. Further, the mixed spin-scalar coupling approach is discussed. It is demonstrated, taking the high-spin Ge-73 dark matter experiment HDMS as an example, how one can drastically improve the sensitivity of the exclusion curves within the mixed spin-scalar coupling approach, as well as due to a new procedure of background subtraction from the measured spectrum. A general discussion on the information obtained from exclusion curves is given. The necessity of clear WIMP direct detection signatures for a solution of the dark matter problem, is pointed out.Comment: LaTeX, 49 pages, 14 figures, 185 reference

Can a Dusty Warm Absorber Model Reproduce the Soft X-ray Spectra of MCG-6-30-15 and Mrk 766?

XMM-Newton RGS spectra of MCG-6-30-15 and Mrk 766 exhibit complex discrete structure, which was interpreted in a paper by Branduardi-Raymont et al. (2001) as evidence for the existence of relativistically broadened Lyman alpha emission from carbon, nitrogen, and oxygen, produced in the inner-most regions of an accretion disk around a Kerr black hole. This suggestion was subsequently criticized in a paper by Lee et al. (2001), who argued that for MCG-6-30-15, the Chandra HETG spectrum, which is partially overlapping the RGS in spectral coverage, is adequately fit by a dusty warm absorber model, with no relativistic line emission. We present a reanalysis of the original RGS data sets in terms of the Lee et al. (2001) model, and demonstrate that spectral models consisting of a smooth continuum with ionized and dust absorption alone cannot reproduce the RGS spectra of both objects. The original relativistic line model with warm absorption proposed by Branduardi-Raymont et al. (2001) provides a superior fit to the RGS data, both in the overall shape of the spectrum and in the discrete absorption lines. Limits on the amount of X-ray absorption by dust particles are discussed. We also discuss a possible theoretical interpretation for the putative relativistic Lyman alpha line emission in terms of the photoionized surface layers of the inner regions of an accretion disk.Comment: Replaced with accepted version. To appear in ApJ; tentatively scheduled for the v596 Oct. 10, 2003 issu