25,305 research outputs found
Atmospheric contaminant sensor. Book 2: Appendices
Appendices containing equipment specifications and performance test data of the atmospheric contaminant sensor for submarines are presented
Sedentary behaviors and adiposity in young people: causality and conceptual model
Research on sedentary behavior and adiposity in youth dates back to the 1980s. Sedentary behaviors, usually screen time, can be associated with adiposity. Although the association usually is small but significant, the field is complex, and results are dependent on what sedentary behaviors are assessed and may be mediated and moderated by other behaviors
Strong convergence rates of probabilistic integrators for ordinary differential equations
Probabilistic integration of a continuous dynamical system is a way of
systematically introducing model error, at scales no larger than errors
introduced by standard numerical discretisation, in order to enable thorough
exploration of possible responses of the system to inputs. It is thus a
potentially useful approach in a number of applications such as forward
uncertainty quantification, inverse problems, and data assimilation. We extend
the convergence analysis of probabilistic integrators for deterministic
ordinary differential equations, as proposed by Conrad et al.\ (\textit{Stat.\
Comput.}, 2017), to establish mean-square convergence in the uniform norm on
discrete- or continuous-time solutions under relaxed regularity assumptions on
the driving vector fields and their induced flows. Specifically, we show that
randomised high-order integrators for globally Lipschitz flows and randomised
Euler integrators for dissipative vector fields with polynomially-bounded local
Lipschitz constants all have the same mean-square convergence rate as their
deterministic counterparts, provided that the variance of the integration noise
is not of higher order than the corresponding deterministic integrator. These
and similar results are proven for probabilistic integrators where the random
perturbations may be state-dependent, non-Gaussian, or non-centred random
variables.Comment: 25 page
Analysis of the 3DVAR Filter for the Partially Observed Lorenz '63 Model
The problem of effectively combining data with a mathematical model
constitutes a major challenge in applied mathematics. It is particular
challenging for high-dimensional dynamical systems where data is received
sequentially in time and the objective is to estimate the system state in an
on-line fashion; this situation arises, for example, in weather forecasting.
The sequential particle filter is then impractical and ad hoc filters, which
employ some form of Gaussian approximation, are widely used. Prototypical of
these ad hoc filters is the 3DVAR method. The goal of this paper is to analyze
the 3DVAR method, using the Lorenz '63 model to exemplify the key ideas. The
situation where the data is partial and noisy is studied, and both discrete
time and continuous time data streams are considered. The theory demonstrates
how the widely used technique of variance inflation acts to stabilize the
filter, and hence leads to asymptotic accuracy
Displaying 3D images: algorithms for single-image random-dot
A new, simple, and symmetric algorithm can be implemented that results in higher levels of detail in solid objects than previously possible with autostereograms. In a stereoscope, an optical instrument similar to binoculars, each eye views a different picture and thereby receives the specific image that would have arisen naturally. An early suggestion for a color stereo computer display involved a rotating filter wheel held in front of the eyes. In contrast, this article describes a method for viewing on paper or on an ordinary computer screen without special equipment, although it is limited to the display of 3D monochromatic objects. (The image can be colored, say, for artistic reasons, but the method we describe does not allow colors to be allocated in a way that corresponds to an arbitrary coloring of the solid object depicted.) The image can easily be constructed by computer from any 3D scene or solid object description
Calibrating the Galaxy Halo - Black Hole Relation Based on the Clustering of Quasars
The observed number counts of quasars may be explained either by long-lived
activity within rare massive hosts, or by short-lived activity within smaller,
more common hosts. It has been argued that quasar lifetimes may therefore be
inferred from their clustering length, which determines the typical mass of the
quasar host. Here we point out that the relationship between the mass of the
black-hole and the circular velocity of its host dark-matter halo is more
fundamental to the determination of the clustering length. In particular, the
clustering length observed in the 2dF quasar redshift survey is consistent with
the galactic halo - black-hole relation observed in local galaxies, provided
that quasars shine at ~10-100% of their Eddington luminosity. The slow
evolution of the clustering length with redshift inferred in the 2dF quasar
survey favors a black-hole mass whose redshift-independent scaling is with halo
circular velocity, rather than halo mass. These results are independent from
observations of the number counts of bright quasars which may be used to
determine the quasar lifetime and its dependence on redshift. We show that if
quasar activity results from galaxy mergers, then the number counts of quasars
imply an episodic quasar lifetime that is set by the dynamical time of the host
galaxy rather than by the Salpeter time. Our results imply that as the redshift
increases, the central black-holes comprise a larger fraction of their host
galaxy mass and the quasar lifetime gets shorter.Comment: 10 pages, 5 figures. Submitted to Ap
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