6,567 research outputs found
A reinterpretation of set differential equations as differential equations in a Banach space
Set differential equations are usually formulated in terms of the Hukuhara
differential, which implies heavy restrictions for the nature of a solution. We
propose to reformulate set differential equations as ordinary differential
equations in a Banach space by identifying the convex and compact subsets of
with their support functions. Using this representation, we demonstrate
how existence and uniqueness results can be applied to set differential
equations. We provide a simple example, which can be treated in support
function representation, but not in the Hukuhara setting
Sample-efficient estimation of entanglement entropy through supervised learning
We explore a supervised machine learning approach to estimate the
entanglement entropy of multi-qubit systems from few experimental samples. We
put a particular focus on estimating both aleatoric and epistemic uncertainty
of the network's estimate and benchmark against the best known conventional
estimation algorithms. For states that are contained in the training
distribution, we observe convergence in a regime of sample sizes in which the
baseline method fails to give correct estimates, while extrapolation only seems
possible for regions close to the training regime. As a further application of
our method, highly relevant for quantum simulation experiments, we estimate the
quantum mutual information for non-unitary evolution by training our model on
different noise strengths.Comment: 5 + 1 pages, 4 figure
Lorentz Boost Networks: Autonomous Physics-Inspired Feature Engineering
We present a two-stage neural network architecture that enables a fully
autonomous and comprehensive characterization of collision events by
exclusively exploiting the four momenta of final-state particles. We refer to
the first stage of the architecture as Lorentz Boost Network (LBN). The LBN
allows the creation of particle combinations representing rest frames. The LBN
also enables the formation of further composite particles, which are then
transformed into said rest frames by Lorentz transformation. The properties of
the composite, transformed particles are compiled in the form of characteristic
variables that serve as input for a subsequent network. This second network has
to be configured for a specific analysis task such as the separation of signal
and background events. Using the example of the classification of ttH and ttbb
events, we compare the separation power of the LBN approach with that of
domain-unspecific deep neural networks (DNN). We observe leading performance
with the LBN, even though we provide the DNNs with extensive additional input
information beyond the particle four momenta. Furthermore, we demonstrate that
the LBN forms physically meaningful particle combinations and autonomously
generates suitable characteristic variables
Procalcitonin as a biomarker in equine chronic pneumopathies
Background Procalcitonin (PCT), a precursor protein of the hormone calcitonin,
is a sensitive inflammatory marker in human medicine, which is primarily used
for diagnosis of bacterial sepsis, but is also useful in diagnosis of
exacerbation of asthma and COPD. In this study, PCT was evaluated as a
potential biomarker for different chronic pneumopathies in the horse using an
equine specific ELISA in comparison to established clinical markers and
different interleukins. Sixty-four horses were classified as free of
respiratory disease, recurrent airway obstruction (RAO), inflammatory airway
disease (IAD) or chronic interstitial pneumopathy (CIP) using a scoring
system. PCT concentrations were measured in plasma (n = 17) and in the cell-
free supernatant of bronchoalveolar lavage (n = 64). PCT concentrations were
correlated to interleukins IL-1ß and IL-6 in BALF, clinical findings and BALF
cytology. Results The median PCT concentrations in plasma were increased in
respiratory disease (174.46 ng/ml, n = 7) compared to controls (13.94 ng/ml, n
= 10, P = 0.05) and correlated to PCT in BALF supernatant (rs = 0.48).
Compared to controls (5.49 ng/ml, n = 15), median PCT concentrations in BALF
supernatant correlated to the overall clinical score (rs = 0.32, P = 0.007)
and were significantly increased in RAO (13.40 ng/ml, n = 21) and IAD (16.89
ng/ml, n = 16), while no differences were found for CIP (12.02 ng/ml, n = 12).
No significant increases were found for IL-1 and IL-6 between controls and
respiratory disease in general as well as different disease groups.
Conclusions Although some correlations were found between PCT in plasma, BALF
supernatant and clinical scores, PCT in BALF does not seem to be a superior
marker compared to established clinical markers. PCT in plasma seems to be
more promising and a greater number of samples should be evaluated in further
studies
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