22,573 research outputs found
The Total Acquisition Number of the Randomly Weighted Path
There exists a significant body of work on determining the acquisition number
of various graphs when the vertices of those graphs are each initially
assigned a unit weight. We determine properties of the acquisition number of
the path, star, complete, complete bipartite, cycle, and wheel graphs for
variations on this initial weighting scheme, with the majority of our work
focusing on the expected acquisition number of randomly weighted graphs. In
particular, we bound the expected acquisition number of the
-path when distinguishable "units" of integral weight, or chips, are
randomly distributed across its vertices between and . With
computer support, we improve it by showing that lies between
and . We then use subadditivity to show that the limiting
ratio exists, and simulations reveal more exactly what the
limiting value equals. The Hoeffding-Azuma inequality is used to prove that the
acquisition number is tightly concentrated around its expected value.
Additionally, in a different context, we offer a non-optimal acquisition
protocol algorithm for the randomly weighted path and exactly compute the
expected size of the resultant residual set.Comment: 19 page
Application of Time-Fractional Order Bloch Equation in Magnetic Resonance Fingerprinting
Magnetic resonance fingerprinting (MRF) is one novel fast quantitative
imaging framework for simultaneous quantification of multiple parameters with
pseudo-randomized acquisition patterns. The accuracy of the resulting
multi-parameters is very important for clinical applications. In this paper, we
derived signal evolutions from the anomalous relaxation using a fractional
calculus. More specifically, we utilized time-fractional order extension of the
Bloch equations to generate dictionary to provide more complex system
descriptions for MRF applications. The representative results of phantom
experiments demonstrated the good accuracy performance when applying the
time-fractional order Bloch equations to generate dictionary entries in the MRF
framework. The utility of the proposed method is also validated by in-vivo
study.Comment: Accepted at 2019 IEEE 16th International Symposium on Biomedical
Imaging (ISBI 2019
Does graph disclosure bias reduce the cost of equity?
Research on disclosure and capital markets focuses primarily on the amount of
information provided but pays little attention to the presentation format of this
information. This paper examines the impact of graph utilization and graph quality
(distortion) on the cost of equity capital, controlling for the interaction between
disclosure and graph distortion. Despite the advantages of graphs in communicating
information, our results show that graph utilization does not have a significant impact
on usersâ decisions. However we observe a significant (negative) association between
graph distortion and the exante
cost of equity. This effect though, disappears if we use
realised returns as a measure of expost
cost of equity. Moreover, we find that
disclosure and graph distortion interact so that the impact of disclosure on the cost of
capital depends on graph integrity. For low level of overall disclosure, graph distortion
reduces the exante
cost of equity. However for high level of disclosure graph distortion
increases the exante
cost of equity
Changing Bases: Multistage Optimization for Matroids and Matchings
This paper is motivated by the fact that many systems need to be maintained
continually while the underlying costs change over time. The challenge is to
continually maintain near-optimal solutions to the underlying optimization
problems, without creating too much churn in the solution itself. We model this
as a multistage combinatorial optimization problem where the input is a
sequence of cost functions (one for each time step); while we can change the
solution from step to step, we incur an additional cost for every such change.
We study the multistage matroid maintenance problem, where we need to maintain
a base of a matroid in each time step under the changing cost functions and
acquisition costs for adding new elements. The online version of this problem
generalizes online paging. E.g., given a graph, we need to maintain a spanning
tree at each step: we pay for the cost of the tree at time
, and also for the number of edges changed at
this step. Our main result is an -approximation, where is
the number of elements/edges and is the rank of the matroid. We also give
an approximation for the offline version of the problem. These
bounds hold when the acquisition costs are non-uniform, in which caseboth these
results are the best possible unless P=NP.
We also study the perfect matching version of the problem, where we must
maintain a perfect matching at each step under changing cost functions and
costs for adding new elements. Surprisingly, the hardness drastically
increases: for any constant , there is no
-approximation to the multistage matching maintenance
problem, even in the offline case
Statistical properties of acoustic emission signals from metal cutting processes
Acoustic Emission (AE) data from single point turning machining are analysed
in this paper in order to gain a greater insight of the signal statistical
properties for Tool Condition Monitoring (TCM) applications. A statistical
analysis of the time series data amplitude and root mean square (RMS) value at
various tool wear levels are performed, �nding that ageing features can
be revealed in all cases from the observed experimental histograms. In
particular, AE data amplitudes are shown to be distributed with a power-law
behaviour above a cross-over value. An analytic model for the RMS values
probability density function (pdf) is obtained resorting to the Jaynes' maximum
entropy principle (MEp); novel technique of constraining the modelling function
under few fractional moments, instead of a greater amount of ordinary moments,
leads to well-tailored functions for experimental histograms.Comment: 16 pages, 7 figure
Improved correction for the tissue fraction effect in lung PET/CT imaging
Recently, there has been an increased interest in imaging different pulmonary disorders using PET techniques. Previous work has shown, for static PET/CT, that air content in the lung influences reconstructed image values and that it is vital to correct for this 'tissue fraction effect' (TFE). In this paper, we extend this work to include the blood component and also investigate the TFE in dynamic imaging. CT imaging and PET kinetic modelling are used to determine fractional air and blood voxel volumes in six patients with idiopathic pulmonary fibrosis. These values are used to illustrate best and worst case scenarios when interpreting images without correcting for the TFE. In addition, the fractional volumes were used to determine correction factors for the SUV and the kinetic parameters. These were then applied to the patient images. The kinetic parameters K1 and Ki along with the static parameter SUV were all found to be affected by the TFE with both air and blood providing a significant contribution to the errors. Without corrections, errors range from 34-80% in the best case and 29-96% in the worst case. In the patient data, without correcting for the TFE, regions of high density (fibrosis) appeared to have a higher uptake than lower density (normal appearing tissue), however this was reversed after air and blood correction. The proposed correction methods are vital for quantitative and relative accuracy. Without these corrections, images may be misinterpreted
- âŠ