56,531 research outputs found
On landmark selection and sampling in high-dimensional data analysis
In recent years, the spectral analysis of appropriately defined kernel
matrices has emerged as a principled way to extract the low-dimensional
structure often prevalent in high-dimensional data. Here we provide an
introduction to spectral methods for linear and nonlinear dimension reduction,
emphasizing ways to overcome the computational limitations currently faced by
practitioners with massive datasets. In particular, a data subsampling or
landmark selection process is often employed to construct a kernel based on
partial information, followed by an approximate spectral analysis termed the
Nystrom extension. We provide a quantitative framework to analyse this
procedure, and use it to demonstrate algorithmic performance bounds on a range
of practical approaches designed to optimize the landmark selection process. We
compare the practical implications of these bounds by way of real-world
examples drawn from the field of computer vision, whereby low-dimensional
manifold structure is shown to emerge from high-dimensional video data streams.Comment: 18 pages, 6 figures, submitted for publicatio
Multivariate side-band subtraction using probabilistic event weights
A common situation in experimental physics is to have a signal which can not
be separated from a non-interfering background through the use of any cut. In
this paper, we describe a procedure for determining, on an event-by-event
basis, a quality factor (-factor) that a given event originated from the
signal distribution. This procedure generalizes the "side-band" subtraction
method to higher dimensions without requiring the data to be divided into bins.
The -factors can then be used as event weights in subsequent analysis
procedures, allowing one to more directly access the true spectrum of the
signal.Comment: 17 pages, 9 figure
Exploring Zeptosecond Quantum Equilibration Dynamics: From Deep-Inelastic to Fusion-Fission Outcomes in Ni+Ni Reactions
Energy dissipative processes play a key role in how quantum many-body systems
dynamically evolve towards equilibrium. In closed quantum systems, such
processes are attributed to the transfer of energy from collective motion to
single-particle degrees of freedom; however, the quantum many-body dynamics of
this evolutionary process are poorly understood. To explore energy dissipative
phenomena and equilibration dynamics in one such system, an experimental
investigation of deep-inelastic and fusion-fission outcomes in the
Ni+Ni reaction has been carried out. Experimental outcomes have
been compared to theoretical predictions using Time Dependent Hartree Fock and
Time Dependent Random Phase Approximation approaches, which respectively
incorporate one-body energy dissipation and fluctuations. Excellent
quantitative agreement has been found between experiment and calculations,
indicating that microscopic models incorporating one-body dissipation and
fluctuations provide a potential tool for exploring dissipation in low-energy
heavy ion collisions.Comment: 11 pages, 9 figures, 1 table, including Supplemental Material -
Version accepted for publication in Physical Review Letter
Using generative models for handwritten digit recognition
We describe a method of recognizing handwritten digits by fitting generative models that are built from deformable B-splines with Gaussian ``ink generators'' spaced along the length of the spline. The splines are adjusted using a novel elastic matching procedure based on the Expectation Maximization (EM) algorithm that maximizes the likelihood of the model generating the data. This approach has many advantages. (1) After identifying the model most likely to have generated the data, the system not only produces a classification of the digit but also a rich description of the instantiation parameters which can yield information such as the writing style. (2) During the process of explaining the image, generative models can perform recognition driven segmentation. (3) The method involves a relatively small number of parameters and hence training is relatively easy and fast. (4) Unlike many other recognition schemes it does not rely on some form of pre-normalization of input images, but can handle arbitrary scalings, translations and a limited degree of image rotation. We have demonstrated our method of fitting models to images does not get trapped in poor local minima. The main disadvantage of the method is it requires much more computation than more standard OCR techniques
On the relationship between Bayesian error bars and the input data density
We investigate the dependence of Bayesian error bars on the distribution of data in input space. For generalized linear regression models we derive an upper bound on the error bars which shows that, in the neighbourhood of the data points, the error bars are substantially reduced from their prior values. For regions of high data density we also show that the contribution to the output variance due to the uncertainty in the weights can exhibit an approximate inverse proportionality to the probability density. Empirical results support these conclusions
DCO, DCN and ND reveal three different deuteration regimes in the disk around the Herbig Ae star HD163296
The formation pathways of deuterated species trace different regions of
protoplanetary disks and may shed light into their physical structure. We aim
to constrain the radial extent of main deuterated species; we are particularly
interested in spatially characterizing the high and low temperature pathways
for enhancing deuteration of these species. We observed the disk surrounding
the Herbig Ae star HD 163296 using ALMA in Band 6 and obtained resolved
spectral imaging data of DCO (=3-2), DCN (=3-2) and ND
(=3-2). We model the radial emission profiles of DCO, DCN and
ND, assuming their emission is optically thin, using a parametric model
of their abundances and radial excitation temperature estimates. DCO can be
described by a three-region model, with constant-abundance rings centered at 70
AU, 150 AU and 260 AU. The DCN radial profile peaks at about ~60 AU and
ND is seen in a ring at ~160 AU. Simple models of both molecules using
constant abundances reproduce the data. Assuming reasonable average excitation
temperatures for the whole disk, their disk-averaged column densities (and
deuterium fractionation ratios) are 1.6-2.6 cm
(0.04-0.07), 2.9-5.2 cm (0.02) and 1.6-2.5 cm (0.34-0.45) for DCO, DCN and ND, respectively.
Our simple best-fit models show a correlation between the radial location of
the first two rings in DCO and the DCN and ND abundance
distributions that can be interpreted as the high and low temperature
deuteration pathways regimes. The origin of the third DCO ring at 260 AU is
unknown but may be due to a local decrease of ultraviolet opacity allowing the
photodesorption of CO or due to thermal desorption of CO as a consequence of
radial drift and settlement of dust grains
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