Empirical Likelihood Confidence Bands in Density Estimation

Abstract

Empirical likelihood methods are developed for constructing confidence bands in problems of nonparametric density estimation. These techniques have an advantage over more conventional methods in that the shape of the bands is determined solely by the data. We show how to construct an empirical likelihood functional, rather than a function, and contour it to produce the confidence bands. Analogs of Wilks's theorem are established in this infinite-parameter setting and may be used to select the appropriate contour. An alternative calibration, based on the bootstrap, is also suggested. Large-sample theory is developed to show that the bands have asymptotically correct coverage, and a numerical example is presented to demonstrate the technique. Comparisons are made with the use of bootstrap replications to choose both the shape and size of the bands.     

Nonparametric Approach to Analysis of Space-Time Data on Earthquake Occurrences

Abstract

As an alternative to traditional, parametric approaches, we suggest nonparametric methods for analyzing spatial and temporal data on earthquake occurrences. Nonparametric techniques are particularly adaptive to anomalous behavior in the data and provide a new way of accessing a variety of different types of information about the way in which both intensity and magnitude of events evolve in time. They can be employed to estimate the spatial trajectory of event clusters as a function of time, and to define quiescent and active periods. The latter application suggests new approaches to forecasting high magnitude events. Our methods are founded on multivariate techniques for curve and surface estimation, particularly in contexts where curves or surfaces are unbounded at points or along lines.     

Millisecond time-scale folding and unfolding of DNA hairpins using rapid-mixing stopped-flow kinetics

We report stopped-flow kinetics experiments to study the folding and unfolding of 5 base-pair stem and 21 nucleotide polythymidine loop DNA hairpins over various concentrations of NaCl. The reactions occurred on a time scale of milliseconds, considerably longer than the microsecond time scale suggested by previous kinetics studies of similar-sized hairpins. In comparison to a recent fluorescence correlation spectroscopy study (J. Am. Chem. Soc. 2006, 128, 1240-1249), we suggest the microsecond time-scale reactions are due to intermediate states and the millisecond time-scale reactions reported here are due to the formation of the fully folded DNA hairpin. These results support our view that DNA hairpin folding occurs via a minimum three-state mechanism.     

Input-dependent induction of oligonucleotide structural motifs for performing molecular logic

The K(+)-H(+)-triggered structural conversion of multiple nucleic acid helices involving duplexes, triplexes, G-quadruplexes, and i-motifs is studied by gel electrophoresis, circular dichroism, and thermal denaturation. We employ the structural interconversions for perfoming molecular logic operations, as verified by fluorimetry and colorimetry. Short G-rich and C-rich cDNA and RNA single strands are hybridized to produce four A-form and B-form duplexes. Addition of K(+) triggers the unwinding of the duplexes by inducing the folding of G-rich strands into DNA- or RNA G-quadruplex mono- and multimers, respectively. We found a decrease in pH to have different consequences on the resulting structural output, depending on whether the C-rich strand is DNA or RNA: while the protonated C-rich DNA strand folds into at least two isomers of a stable i-motif structure, the protonated C-rich RNA strand binds a DNA/RNA hybrid duplex to form a Y·RY parallel triplex. When using K(+) and H(+) as external stimuli, or inputs, and the induced G-quadruplexes as reporters, these structural interconversions of nucleic acid helices can be employed for performing logic-gate operations. The signaling mode for detecting these conversions relies on complex formation between DNA or RNA G-quadruplexes (G4) and the cofactor hemin. The G4/hemin complexes catalyze the H(2)O(2)-mediated oxidation of peroxidase substrates, resulting in a fluorescence or color change. Depending on the nature of the respective peroxidase substrate, distinct output signals can be generated, allowing one to operate multiple logic gates such as NOR, INH, or AND.     

Projective relatedness and conformal flatness

This paper discusses the connection between projective relatedness and conformal flatness for 4-dimensional manifolds admitting a metric of signature (+,+,+,+) or (+,+,+,−). It is shown that if one of the manifolds is conformally flat and not of the most general holonomy type for that signature then, in general, the connections of the manifolds involved are the same and the second manifold is also conformally flat. Counterexamples are provided which place limitations on the potential strengthening of the results.     

Frequency discrimination under conditions of comodulation masking release (L)

Masked detection thresholds can often be improved by introducing coherent masker amplitude modulation across frequency, a phenomenon referred to as comodulation masking release (CMR). While CMR can be large for detection, it is smaller for supra-threshold tasks, such as intensity discrimination. In this experiment, frequency discrimination for a 1000-Hz tone near threshold was found to be poorer in an amplitude-modulated than a steady bandpass noise. These results parallel previous findings for intensity discrimination. Although this study examined the relatively simple task of frequency discrimination, the results may have implications for more complex tasks, such as speech recognition in fluctuating noise.     

Relative Equilibria of the (1+N)-Vortex Problem

We examine existence and stability of relative equilibria of the n-vortex problem specialized to the case where N vortices have small and equal circulation and one vortex has large circulation. As the small circulation tends to zero, the weak vortices tend to a circle centered on the strong vortex. A special potential function of this limiting problem can be used to characterize orbits and stability. Whenever a critical point of this function is nondegenerate, we prove that the orbit can be continued via the Implicit Function Theorem, and its linear stability is determined by the eigenvalues of the Hessian matrix of the potential. For N≥3 there are at least three distinct families of critical points associated to the limiting problem. Assuming nondegeneracy, one of these families continues to a linearly stable class of relative equilibria with small and large circulation of the same sign. This class becomes unstable as the small circulation passes through zero and changes sign. Another family of critical points which is always nondegenerate continues to a configuration with small vortices arranged in an N-gon about the strong central vortex. This class of relative equilibria is linearly unstable regardless of the sign of the small circulation when N≥4. Numerical results suggest that the third family of critical points of the limiting problem also continues to a linearly unstable class of solutions of the full problem independent of the sign of the small circulation. Thus there is evidence that linearly stable relative equilibria exist when the large and small circulation strengths are of the same sign, but that no such solutions exist when they have opposite signs. The results of this paper are in contrast to those of the analogous celestial mechanics problem, for which the N-gon is the only relative equilibrium for N sufficiently large, and is linearly stable if and only if N≥7.     

DDLm: A New Dictionary Definition Language

A previous paper [Spadaccini and Hall J. Chem. Inf. Model. doi:10.1021/ci300074v] details extensions to the STAR File [Hall J. Chem. Inf. Comput. Sci.1991, 31, 326-333] syntax that will improve the exchange and archiving of electronic data. This paper describes a dictionary definition language (DDLm) for defining STAR File data items in a domain dictionary. A dictionary that defines the ontology and vocabulary of a discipline is built with DDLm, which is itself implemented in STAR, and is extensible and machine parsable. The DDLm is semantically rich and highly specific; provides strong data typing, data enumerations, and ranges; enables relationship keys between data items; and uses imbedded methods written in dREL [Spadaccini et al. J. Chem. Inf. Model. doi:10.1021/ci300076w] for data validation and evaluation and for refining data definitions. It promotes the modular definition of the discipline ontology and reuse through the ability to import definitions from other local and remote dictionaries, thus encouraging the sharing of data dictionaries within and across domains.     

Analysis and interpretation of the first monochromatic X‐ray tomography data collected at the Australian Synchrotron Imaging and Medical beamline

The first monochromatic X‐ray tomography experiments conducted at the Imaging and Medical beamline of the Australian Synchrotron are reported. The sample was a phantom comprising nylon line, Al wire and finer Cu wire twisted together. Data sets were collected at four different X‐ray energies. In order to quantitatively account for the experimental values obtained for the Hounsfield (or CT) number, it was necessary to consider various issues including the point‐spread function for the X‐ray imaging system and harmonic contamination of the X‐ray beam. The analysis and interpretation of the data includes detailed considerations of the resolution and efficiency of the CCD detector, calculations of the X‐ray spectrum prior to monochromatization, allowance for the response of the double‐crystal Si monochromator used (via X‐ray dynamical theory), as well as a thorough assessment of the role of X‐ray phase‐contrast effects. Computer simulations relating to the tomography experiments also provide valuable insights into these important issues. It was found that a significant discrepancy between theory and experiment for the Cu wire could be largely resolved in terms of the effect of the point‐spread function. The findings of this study are important in respect of any attempts to extract quantitative information from X‐ray tomography data, across a wide range of disciplines, including materials and life sciences.