7,680 research outputs found
Extracting fetal heart beats from maternal abdominal recordings: Selection of the optimal principal components
This study presents a systematic comparison of different approaches to the automated selection of the principal components (PC) which optimise the detection of maternal and fetal heart beats from non-invasive maternal abdominal recordings. A public database of 75 4-channel non-invasive maternal abdominal recordings was used for training the algorithm. Four methods were developed and assessed to determine the optimal PC: (1) power spectral distribution, (2) root mean square, (3) sample entropy, and (4) QRS template. The sensitivity of the performance of the algorithm to large-amplitude noise removal (by wavelet de-noising) and maternal beat cancellation methods were also assessed. The accuracy of maternal and fetal beat detection was assessed against reference annotations and quantified using the detection accuracy score F1 [2*PPV*Se / (PPV + Se)], sensitivity (Se), and positive predictive value (PPV). The best performing implementation was assessed on a test dataset of 100 recordings and the agreement between the computed and the reference fetal heart rate (fHR) and fetal RR (fRR) time series quantified. The best performance for detecting maternal beats (F1 99.3%, Se 99.0%, PPV 99.7%) was obtained when using the QRS template method to select the optimal maternal PC and applying wavelet de-noising. The best performance for detecting fetal beats (F1 89.8%, Se 89.3%, PPV 90.5%) was obtained when the optimal fetal PC was selected using the sample entropy method and utilising a fixed-length time window for the cancellation of the maternal beats. The performance on the test dataset was 142.7 beats2/min2 for fHR and 19.9 ms for fRR, ranking respectively 14 and 17 (out of 29) when compared to the other algorithms presented at the Physionet Challenge 2013
Quantum Generative Adversarial Networks for Learning and Loading Random Distributions
Quantum algorithms have the potential to outperform their classical
counterparts in a variety of tasks. The realization of the advantage often
requires the ability to load classical data efficiently into quantum states.
However, the best known methods require gates to
load an exact representation of a generic data structure into an -qubit
state. This scaling can easily predominate the complexity of a quantum
algorithm and, thereby, impair potential quantum advantage. Our work presents a
hybrid quantum-classical algorithm for efficient, approximate quantum state
loading. More precisely, we use quantum Generative Adversarial Networks (qGANs)
to facilitate efficient learning and loading of generic probability
distributions -- implicitly given by data samples -- into quantum states.
Through the interplay of a quantum channel, such as a variational quantum
circuit, and a classical neural network, the qGAN can learn a representation of
the probability distribution underlying the data samples and load it into a
quantum state. The loading requires
gates and can, thus, enable the
use of potentially advantageous quantum algorithms, such as Quantum Amplitude
Estimation. We implement the qGAN distribution learning and loading method with
Qiskit and test it using a quantum simulation as well as actual quantum
processors provided by the IBM Q Experience. Furthermore, we employ quantum
simulation to demonstrate the use of the trained quantum channel in a quantum
finance application.Comment: 14 pages, 13 figure
The path inference filter: model-based low-latency map matching of probe vehicle data
We consider the problem of reconstructing vehicle trajectories from sparse
sequences of GPS points, for which the sampling interval is between 10 seconds
and 2 minutes. We introduce a new class of algorithms, called altogether path
inference filter (PIF), that maps GPS data in real time, for a variety of
trade-offs and scenarios, and with a high throughput. Numerous prior approaches
in map-matching can be shown to be special cases of the path inference filter
presented in this article. We present an efficient procedure for automatically
training the filter on new data, with or without ground truth observations. The
framework is evaluated on a large San Francisco taxi dataset and is shown to
improve upon the current state of the art. This filter also provides insights
about driving patterns of drivers. The path inference filter has been deployed
at an industrial scale inside the Mobile Millennium traffic information system,
and is used to map fleets of data in San Francisco, Sacramento, Stockholm and
Porto.Comment: Preprint, 23 pages and 23 figure
Optimal estimation of entanglement
Entanglement does not correspond to any observable and its evaluation always
corresponds to an estimation procedure where the amount of entanglement is
inferred from the measurements of one or more proper observables. Here we
address optimal estimation of entanglement in the framework of local quantum
estimation theory and derive the optimal observable in terms of the symmetric
logarithmic derivative. We evaluate the quantum Fisher information and, in
turn, the ultimate bound to precision for several families of bipartite states,
either for qubits or continuous variable systems, and for different measures of
entanglement. We found that for discrete variables, entanglement may be
efficiently estimated when it is large, whereas the estimation of weakly
entangled states is an inherently inefficient procedure. For continuous
variable Gaussian systems the effectiveness of entanglement estimation strongly
depends on the chosen entanglement measure. Our analysis makes an important
point of principle and may be relevant in the design of quantum information
protocols based on the entanglement content of quantum states.Comment: 9 pages, 2 figures, v2: minor correction
Convergence of Smoothed Empirical Measures with Applications to Entropy Estimation
This paper studies convergence of empirical measures smoothed by a Gaussian
kernel. Specifically, consider approximating , for
, by
, where is the empirical measure,
under different statistical distances. The convergence is examined in terms of
the Wasserstein distance, total variation (TV), Kullback-Leibler (KL)
divergence, and -divergence. We show that the approximation error under
the TV distance and 1-Wasserstein distance () converges at rate
in remarkable contrast to a typical
rate for unsmoothed (and ). For the
KL divergence, squared 2-Wasserstein distance (), and
-divergence, the convergence rate is , but only if
achieves finite input-output mutual information across the additive
white Gaussian noise channel. If the latter condition is not met, the rate
changes to for the KL divergence and , while
the -divergence becomes infinite - a curious dichotomy. As a main
application we consider estimating the differential entropy
in the high-dimensional regime. The distribution
is unknown but i.i.d samples from it are available. We first show that
any good estimator of must have sample complexity
that is exponential in . Using the empirical approximation results we then
show that the absolute-error risk of the plug-in estimator converges at the
parametric rate , thus establishing the minimax
rate-optimality of the plug-in. Numerical results that demonstrate a
significant empirical superiority of the plug-in approach to general-purpose
differential entropy estimators are provided.Comment: arXiv admin note: substantial text overlap with arXiv:1810.1158
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