957 research outputs found
Bayesian survival modelling of university outcomes
Dropouts and delayed graduations are critical issues in higher education systems world wide. A key task in this context is to identify risk factors associated with these events, providing potential targets for mitigating policies. For this, we employ a discrete time competing risks survival model, dealing simultaneously with university outcomes and its associated temporal component. We define survival times as the duration of the student's enrolment at university and possible outcomes as graduation or two types of dropout (voluntary and involuntary), exploring the information recorded at admission time (e.g. educational level of the parents) as potential predictors. Although similar strategies have been previously implemented, we extend the previous methods by handling covariate selection within a Bayesian variable selection framework, where model uncertainty is formally addressed through Bayesian model averaging. Our methodology is general; however, here we focus on undergraduate students enrolled in three selected degree programmes of the Pontificia Universidad CatĂłlica de Chile during the period 2000â2011. Our analysis reveals interesting insights, highlighting the main covariates that influence studentsâ risk of dropout and delayed graduation
Periodic orbit bifurcations and scattering time delay fluctuations
We study fluctuations of the Wigner time delay for open (scattering) systems
which exhibit mixed dynamics in the classical limit. It is shown that in the
semiclassical limit the time delay fluctuations have a distribution that
differs markedly from those which describe fully chaotic (or strongly
disordered) systems: their moments have a power law dependence on a
semiclassical parameter, with exponents that are rational fractions. These
exponents are obtained from bifurcating periodic orbits trapped in the system.
They are universal in situations where sufficiently long orbits contribute. We
illustrate the influence of bifurcations on the time delay numerically using an
open quantum map.Comment: 9 pages, 3 figures, contribution to QMC200
Incorporating unobserved heterogeneity in Weibull survival models : a Bayesian approach
Outlying observations and other forms of unobserved heterogeneity can distort inference for survival datasets. The family of Rate Mixtures of Weibull distributions includes subject-level frailty terms as a solution to this issue. With a parametric mixing distribution assigned to the frailties, this family generates flexible hazard functions. Covariates are introduced via an Accelerated Failure Time specification for which the interpretation of the regression coefficients does not depend on the choice of mixing distribution. A weakly informative prior is proposed by combining the structure of the Jeffreys prior with a proper prior on some model parameters. This improper prior is shown to lead to a proper posterior distribution under easily satisfied conditions. By eliciting the proper component of the prior through the coefficient of variation of the survival times, prior information is matched for different mixing distributions. Posterior inference on subject-level frailty terms is exploited as a tool for outlier detection. Finally, the proposed methodology is illustrated using two real datasets, one concerning bone marrow transplants and another on cerebral palsy
Quantum baker maps with controlled-NOT coupling
The characteristic stretching and squeezing of chaotic motion is linearized
within the finite number of phase space domains which subdivide a classical
baker map. Tensor products of such maps are also chaotic, but a more
interesting generalized baker map arises if the stacking orders for the factor
maps are allowed to interact. These maps are readily quantized, in such a way
that the stacking interaction is entirely attributed to primary qubits in each
map, if each subsystem has power-of-two Hilbert space dimension. We here study
the particular example of two baker maps that interact via a controlled-not
interaction. Numerical evidence indicates that the control subspace becomes an
ideal Markovian environment for the target map in the limit of large Hilbert
space dimension.Comment: 8 page
Semiclassical approach to fidelity amplitude
The fidelity amplitude is a quantity of paramount importance in echo type
experiments. We use semiclassical theory to study the average fidelity
amplitude for quantum chaotic systems under external perturbation. We explain
analytically two extreme cases: the random dynamics limit --attained
approximately by strongly chaotic systems-- and the random perturbation limit,
which shows a Lyapunov decay. Numerical simulations help us bridge the gap
between both extreme cases.Comment: 10 pages, 9 figures. Version closest to published versio
How do wave packets spread? Time evolution on Ehrenfest time scales
We derive an extension of the standard time dependent WKB theory which can be
applied to propagate coherent states and other strongly localised states for
long times. It allows in particular to give a uniform description of the
transformation from a localised coherent state to a delocalised Lagrangian
state which takes place at the Ehrenfest time. The main new ingredient is a
metaplectic operator which is used to modify the initial state in a way that
standard time dependent WKB can then be applied for the propagation.
We give a detailed analysis of the phase space geometry underlying this
construction and use this to determine the range of validity of the new method.
Several examples are used to illustrate and test the scheme and two
applications are discussed: (i) For scattering of a wave packet on a barrier
near the critical energy we can derive uniform approximations for the
transition from reflection to transmission. (ii) A wave packet propagated along
a hyperbolic trajectory becomes a Lagrangian state associated with the unstable
manifold at the Ehrenfest time, this is illustrated with the kicked harmonic
oscillator.Comment: 30 pages, 3 figure
Model updating after interventions paradoxically introduces bias
Machine learning is increasingly being used to generate prediction models for
use in a number of real-world settings, from credit risk assessment to clinical
decision support. Recent discussions have highlighted potential problems in the
updating of a predictive score for a binary outcome when an existing predictive
score forms part of the standard workflow, driving interventions. In this
setting, the existing score induces an additional causative pathway which leads
to miscalibration when the original score is replaced. We propose a general
causal framework to describe and address this problem, and demonstrate an
equivalent formulation as a partially observed Markov decision process. We use
this model to demonstrate the impact of such `naive updating' when performed
repeatedly. Namely, we show that successive predictive scores may converge to a
point where they predict their own effect, or may eventually tend toward a
stable oscillation between two values, and we argue that neither outcome is
desirable. Furthermore, we demonstrate that even if model-fitting procedures
improve, actual performance may worsen. We complement these findings with a
discussion of several potential routes to overcome these issues.Comment: Sections of this preprint on 'Successive adjuvancy' (section 4,
theorem 2, figures 4,5, and associated discussions) were not included in the
originally submitted version of this paper due to length. This material does
not appear in the published version of this manuscript, and the reader should
be aware that these sections did not undergo peer revie
Measuring the Lyapunov exponent using quantum mechanics
We study the time evolution of two wave packets prepared at the same initial
state, but evolving under slightly different Hamiltonians. For chaotic systems,
we determine the circumstances that lead to an exponential decay with time of
the wave packet overlap function. We show that for sufficiently weak
perturbations, the exponential decay follows a Fermi golden rule, while by
making the difference between the two Hamiltonians larger, the characteristic
exponential decay time becomes the Lyapunov exponent of the classical system.
We illustrate our theoretical findings by investigating numerically the overlap
decay function of a two-dimensional dynamical system.Comment: 9 pages, 6 figure
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