9 research outputs found
Generalizability of machine learning models in predicting patient deterioration
Predicting patient deterioration in an Intensive Care Unit (ICU) effectively is a critical health care task serving patient health and resource allocation. At times, the task may be highly complex for a physician, yet high-stakes and time-critical decisions need to be made based on it. In this work, we investigate the ability of a set of machine learning models to algorithimically predict future occurrence of in hospital death based on Electronic Health Record (EHR) data of ICU-patients. For one, we will assess the generalizability of the models. We do this by evaluating the models on hospitals the data of which has not been considered when training the models. For another, we consider the case in which we have access to some EHR data for the patients treated at a hospital of interest. In this setting, we assess how EHR data from other hospitals can be used in the optimal way to improve the prediction accuracy. This study is important for the deployment and integration of such predictive models in practice, e.g., for real-time algorithmic deterioration prediction for clinical decision support.
In order to address these questions, we use the eICU collaborative research database, which is a database containing EHRs of patients treated at a heterogeneous collection of hospitals in the United States. In this work, we use the patient demographics, vital signs and Glasgow coma score as the predictors. We devise and describe three computational experiments to test the generalization in different ways. The used models are the random forest, gradient boosted trees and long short-term memory network. In our first experiment concerning the generalization, we show that, with the chosen limited set of predictors, the models generalize reasonably across hospitals but that only a small data mismatch is observed. Moreover, with this setting, our second experiment shows that the model performance does not significantly improve when increasing the heterogeneity of the training set. Given these observations, our third experiment shows tha
The Kadanoff-Baym approach to spectral properties of the Holstein dimer
We present a Kadanoff-Baym formalism to study time-dependent phenomena for
systems of interacting electrons and phonons in the framework of many-body
perturbation theory. The formalism takes correctly into account effects of the
initial preparation of an equilibrium state and allows for an explicit time-
dependence of both the electronic and phononic degrees of freedom. The method
is applied to investigate the charge neutral and non-neutral excitation
spectra of a homogeneous, two-site, two-electron Holstein model. This is an
extension of a previous study of the ground state properties in the Hartree
(H), partially self-consistent Born (Gd) and fully self-consistent Born (GD)
approximations published in Säkkinen et al. [J. Chem. Phys. 143, 234101
(2015)]. Here, the homogeneous ground state solution is shown to become
unstable for a sufficiently strong interaction while a symmetry-broken ground
state solution is shown to be stable in the Hartree approximation. Signatures
of this instability are observed for the partially self-consistent Born
approximation but are not found for the fully self-consistent Born
approximation. By understanding the stability properties, we are able to study
the linear response regime by calculating the density-density response
function by time-propagation. This amounts to a solution of the Bethe-Salpeter
equation with a sophisticated kernel. The results indicate that none of the
approximations is able to describe the response function during or beyond the
bipolaronic crossover for the parameters investigated. Overall, we provide an
extensive discussion on when the approximations are valid and how they fail to
describe the studied exact properties of the chosen model system
Ground state properties of the Holstein dimer
We study ground-state properties of a two-site, two-electron Holstein model
describing two molecules coupled indirectly via electron-phonon interaction by
using both exact diagonalization and self-consistent diagrammatic many-body
perturbation theory. The Hartree and self-consistent Born approximations used
in the present work are studied at different levels of self-consistency. The
governing equations are shown to exhibit multiple solutions when the electron-
phonon interaction is sufficiently strong, whereas at smaller interactions,
only a single solution is found. The additional solutions at larger electron-
phonon couplings correspond to symmetry-broken states with inhomogeneous
electron densities. A comparison to exact results indicates that this symmetry
breaking is strongly correlated with the formation of a bipolaron state in
which the two electrons prefer to reside on the same molecule. The results
further show that the Hartree and partially self-consistent Born solutions
obtained by enforcing symmetry do not compare well with exact energetics,
while the fully self-consistent Born approximation improves the qualitative
and quantitative agreement with exact results in the same symmetric case. This
together with a presented natural occupation number analysis supports the
conclusion that the fully self-consistent approximation describes partially
the bipolaron crossover. These results contribute to better understanding how
these approximations cope with the strong localizing effect of the electron-
phonon interaction
Many-body Green's function theory for electron-phonon interactions: the Kadanoff-Baym approach to spectral properties of the Holstein dimer
We present a Kadanoff-Baym formalism to study time-dependent phenomena for
systems of interacting electrons and phonons in the framework of many-body
perturbation theory. The formalism takes correctly into account effects of the
initial preparation of an equilibrium state, and allows for an explicit
time-dependence of both the electronic and phononic degrees of freedom. The
method is applied to investigate the charge neutral and non-neutral excitation
spectra of a homogeneous, two-site, two-electron Holstein model. This is an
extension of a previous study of the ground state properties in the Hartree
(H), partially self-consistent Born (Gd) and fully self-consistent Born (GD)
approximations published in Ref. [arXiv:1403.2968]. We show that choosing a
homogeneous ground state solution leads to unstable dynamics for a sufficiently
strong interaction, and that allowing a symmetry-broken state prevents this.
The instability is caused by the bifurcation of the ground state and understood
physically to be connected with the bipolaronic crossover of the exact system.
This mean-field instability persists in the partially self-consistent Born
approximation but is not found for the fully self-consistent Born
approximation. By understanding the stability properties, we are able to study
the linear response regime by calculating the density-density response function
by time-propagation. This functions amounts to a solution of the Bethe-Salpeter
equation with a sophisticated kernel. The results indicate that none of the
approximations is able to describe the response function during or beyond the
bipolaronic crossover for the parameters investigated. Overall, we provide an
extensive discussion on when the approximations are valid, and how they fail to
describe the studied exact properties of the chosen model system.Comment: 12 figure
Application of time-dependent many-body perturbation theory to excitation spectra of selected finite model systems
In this thesis, an approximate method introduced to solve time-dependent many-body problems
known as time-dependent many-body perturbation theory is studied. Many-body perturbation theory
for interacting electrons and phonons is reviewed. In particular, the electron propagator G and an
unconventional two-component phonon propagator, which satisfy coupled integral Dyson equations,
are introduced. In practice, the associated integral kernels known as the electron Σ and phonon
self-energies need to be approximated. The conserving approximations known as the Hartree (-Fock)
and the first and second Born approximations, which respect the continuity equation between the
electron density and current, are considered in this work.
Time-dependent systems of interest are studied in this thesis by using the integro-differential forms
of the Dyson equations referred to as the Kadanoff-Baym Equations (KBE). The Kadanoff-Baym
equations are introduced for the electron and phonon propagators unconventionally as coupled firstorder integro-differential equations. It is reviewed how these equations are solved numerically by
describing an integration rule, a class of practical methods and a parallel implementation of the
numerical method. In addition, documentation of how the Kadanoff-Baym equations allow to solve
the Bethe-Salpeter Equation (BSE) with the kernel δΣ/δG for the density response function, is
provided.
In two of the enclosed publications, we benchmarked observables obtained by using the Hartree and
partially and fully self-consistent Born approximations against numerically exact results for the two-
site, two-electron Holstein model. In this model, the two electrons which are constrained to move
between two lattice sites interact indirectly via the electron-phonon coupling. It was observed that
only the fully self-consistent Born approximation could cope qualitatively correctly with the competition between the delocalizing and localizing effects of the kinetic and interaction energies. For the
other two approximations, spurious bifurcative symmetry breaking with an associated unbounded
density response was observed. Nevertheless, also the self-consistent Born approximation was concluded to fail in describing the bipolaronic behavior of the true system. In the third publication,
we benchmarked the Hartree-Fock and second Born approximations against an exact method for
the few-site Hubbard and Pariser-Parr-Pople models in which the underlying lattice is inert and the
electrons interact amongst themselves directly. It was found that the second Born approximation is
capable of describing the so-called correlation induced doubly-excited states. This is not possible for
time-local approximations such as Hartree-Fock.
In addition to the qualitative results, which highlight successes of the applied simple self-energy approximations, the approximate and exact results were also compared on a more quantitative level. It
is the quantitative and qualitative results combined which are used in this thesis to assess the quality
of the many-body approximations used, with the aim to better understand when these methods are
predictive
Phononic heat transport in the transient regime: An analytic solution
We investigate the time-resolved quantum transport properties of phonons in arbitrary harmonic systems
connected to phonon baths at different temperatures. We obtain a closed analytic expression of the time-dependent
one-particle reduced density matrix by explicitly solving the equations of motion for the nonequilibrium Green’s
function. This is achieved through a well-controlled approximation of the frequency-dependent bath self-energy.
Our result allows for exploring transient oscillations and relaxation times of local heat currents, and correctly
reduces to an earlier known result in the steady-state limit. We apply the formalism to atomic chains, and
benchmark the validity of the approximation against full numerical solutions of the bosonic Kadanoff-Baym
equations for the Green’s function. We find good agreement between the analytic and numerical solutions for
weak contacts and baths with a wide energy dispersion. We further analyze relaxation times from low to high
temperature gradients.peerReviewe