518 research outputs found
Towards Interpretable Deep Learning Models for Knowledge Tracing
As an important technique for modeling the knowledge states of learners, the
traditional knowledge tracing (KT) models have been widely used to support
intelligent tutoring systems and MOOC platforms. Driven by the fast
advancements of deep learning techniques, deep neural network has been recently
adopted to design new KT models for achieving better prediction performance.
However, the lack of interpretability of these models has painfully impeded
their practical applications, as their outputs and working mechanisms suffer
from the intransparent decision process and complex inner structures. We thus
propose to adopt the post-hoc method to tackle the interpretability issue for
deep learning based knowledge tracing (DLKT) models. Specifically, we focus on
applying the layer-wise relevance propagation (LRP) method to interpret
RNN-based DLKT model by backpropagating the relevance from the model's output
layer to its input layer. The experiment results show the feasibility using the
LRP method for interpreting the DLKT model's predictions, and partially
validate the computed relevance scores from both question level and concept
level. We believe it can be a solid step towards fully interpreting the DLKT
models and promote their practical applications in the education domain
Cooling of young stars growing by disk accretion
In the initial formation stages young stars must acquire a significant
fraction of their mass by accretion from a circumstellar disk that forms in the
center of a collapsing protostellar cloud. Throughout this period mass
accretion rates through the disk can reach 10^{-6}-10^{-5} M_Sun/yr leading to
substantial energy release in the vicinity of stellar surface. We study the
impact of irradiation of the stellar surface produced by the hot inner disk on
properties of accreting fully convective low-mass stars, and also look at
objects such as young brown dwarfs and giant planets. At high accretion rates
irradiation raises the surface temperature of the equatorial region above the
photospheric temperature T_0 that a star would have in the absence of
accretion. The high-latitude (polar) parts of the stellar surface, where disk
irradiation is weak, preserve their temperature at the level of T_0. In
strongly irradiated regions an almost isothermal outer radiative zone forms on
top of the fully convective interior, leading to the suppression of the local
internal cooling flux derived from stellar contraction (similar suppression
occurs in irradiated ``hot Jupiters''). Properties of this radiative zone
likely determine the amount of thermal energy that gets advected into the
convective interior of the star. Total intrinsic luminosity integrated over the
whole stellar surface is reduced compared to the non-accreting case, by up to a
factor of several in some systems (young brown dwarfs, stars in quasar disks,
forming giants planets), potentially leading to the retardation of stellar
contraction. Stars and brown dwarfs irradiated by their disks tend to lose
energy predominantly through their cool polar regions while young giant planets
accreting through the disk cool through their whole surface.Comment: 14 pages, 6 figures, submitted to Ap
Hydrogen Burning on Magnetar Surfaces
We compute the rate of diffusive nuclear burning for hydrogen on the surface
of a "magnetar" (Soft Gamma-Ray Repeater or Anomalous X-Ray Pulsar). We find
that hydrogen at the photosphere will be burned on an extremely rapid timescale
of hours to years, depending on composition of the underlying material.
Improving on our previous studies, we explore the effect of a maximally thick
"inert" helium layer, previously thought to slow down the burning rate. Since
hydrogen diffuses faster in helium than through heavier elements, we find this
helium buffer actually increases the burning rate for magnetars. We compute
simple analytic scalings of the burning rate with temperature and magnetic
field for a range of core temperature. We conclude that magnetar photospheres
are very unlikely to contain hydrogen. This motivates theoretical work on heavy
element atmospheres that are needed to measure effective temperature from the
observed thermal emission and constrains models of AXPs that rely on magnetar
cooling through thick light element envelopes.Comment: 4 pages, 2 figures, To be published in ApJ Letter
R-modes in Neutron Stars with Crusts: Turbulent Saturation, Spin-down, and Crust Melting
Rossby waves (r-modes) have been suggested as a means to regulate the spin
periods of young or accreting neutron stars, and also to produce observable
gravitational wave radiation. R-modes involve primarily transverse,
incompressive motions of the star's fluid core. However, neutron stars gain
crusts early in their lives: therefore, r-modes also imply shear in the fluid
beneath the crust. We examine the criterion for this shear layer to become
turbulent, and derive the rate of dissipation in the turbulent regime. Unlike
dissipation from a viscous boundary layer, turbulent energy loss is nonlinear
in mode energy and can therefore cause the mode to saturate at amplitudes
typically much less than unity. This energy loss also reappears as heat below
the crust. We study the possibility of crust melting as well as its
implications for the spin evolution of low-mass X-ray binaries. Lastly, we
identify some universal features of the spin evolution that may have
observational consequences.Comment: 12 pages, 4 figures, submitted to Ap
Seismology of the Accreting White Dwarf in GW Lib
We present a first analysis of the g-mode oscillation spectrum for the white
dwarf (WD) primary of GW Lib, a faint cataclysmic variable (CV). Stable
periodicities have been observed from this WD for a number of years, but their
interpretation as stellar pulsations has been hampered by a lack of theoretical
models appropriate to an accreting WD. Using the results of Townsley and
Bildsten, we construct accreting models for the observed effective temperature
and approximate mass of the WD in GW Lib. We compute g-mode frequencies for a
range of accreted layer masses, Macc, and long term accretion rates, . If
we assume that the observed oscillations are from l=1 g-modes, then the
observed periods are matched when M ~= 1.02 Msun, Macc ~= 0.31 x 10^-4 Msun and
~= 7.3 x 10^-11 Msun/yr. Much more sensitive observations are needed to
discover more modes, after which we will be able to more accurately measure
these parameters and constrain or measure the WD's rotation rate.Comment: 4 pages, 3 figures; uses emulateapj; Accepted by the Astrophysical
Journal Letter
Differential rotation of nonlinear r-modes
Differential rotation of r-modes is investigated within the nonlinear theory
up to second order in the mode amplitude in the case of a slowly-rotating,
Newtonian, barotropic, perfect-fluid star. We find a nonlinear extension of the
linear r-mode, which represents differential rotation that produces large scale
drifts of fluid elements along stellar latitudes. This solution includes a
piece induced by first-order quantities and another one which is a pure
second-order effect. Since the latter is stratified on cylinders, it cannot
cancel differential rotation induced by first-order quantities, which is not
stratified on cylinders. It is shown that, unlikely the situation in the
linearized theory, r-modes do not preserve vorticity of fluid elements at
second-order. It is also shown that the physical angular momentum and energy of
the perturbation are, in general, different from the corresponding canonical
quantities.Comment: 9 pages, revtex4; section III revised, comments added in Introduction
and Conclusions, references updated; to appear in Phys. Rev.
Reionization Constraints on the Contribution of Primordial Compact Objects to Dark Matter
Many lines of evidence suggest that nonbaryonic dark matter constitutes
roughly 30% of the critical closure density, but the composition of this dark
matter is unknown. One class of candidates for the dark matter is compact
objects formed in the early universe, with typical masses M between 0.1 and 1
solar masses to correspond to the mass scale of objects found with microlensing
observing projects. Specific candidates of this type include black holes formed
at the epoch of the QCD phase transition, quark stars, and boson stars. Here we
show that accretion onto these objects produces substantial ionization in the
early universe, with an optical depth to Thomson scattering out to z=1100 of
approximately tau=2-4 [f_CO\epsilon_{-1}(M/Msun)]^{1/2} (H_0/65)^{-1}, where
\epsilon_{-1} is the accretion efficiency \epsilon\equiv L/{\dot M}c^2 divided
by 0.1 and f_CO is the fraction of matter in the compact objects. The current
upper limit to the scattering optical depth, based on the anisotropy of the
microwave background, is approximately 0.4. Therefore, if accretion onto these
objects is relatively efficient, they cannot be the main component of
nonbaryonic dark matter.Comment: 12 pages including one figure, uses aaspp4, submitted to Ap
Bulk viscosity in the nonlinear and anharmonic regime of strange quark matter
The bulk viscosity of cold, dense three-flavor quark matter is studied as a
function of temperature and the amplitude of density oscillations. The study is
also extended to the case of two different types of anharmonic oscillations of
density. We point several qualitative effects due to the anharmonicity,
although quantitatively they appear to be relatively small. We also find that,
in most regions of the parameter space, with the exception of the case of a
very large amplitude of density oscillations (i.e. 10% and above), nonlinear
effects and anharmonicity have a small effect on the interplay of the
nonleptonic and semileptonic processes in the bulk viscosity.Comment: 14 pages, 6 figures; v2: Appendix B is omitted, a few new discussions
added and some new references adde
Ambipolar diffusion in superfluid neutron stars
In this paper we reconsider the problem of magnetic field diffusion in
neutron star cores. We model the star as consisting of a mixture of neutrons,
protons and electrons, and allow for particle reactions and binary collisions
between species. Our analysis is in much the same spirit as that of Goldreich &
Reisenegger (1992), and we content ourselves with rough estimates of magnetic
diffusion timescales, rather than solving accurately for some particular field
geometry. However, our work improves upon previous treatments in one crucial
respect: we allow for superfluidity in the neutron star matter. We find that
the consequent mutual friction force, coupling the neutrons and charged
particles, together with the suppression of particles collisions and reactions,
drastically affect the ambipolar magnetic field diffusion timescale. In
particular, the addition of superfluidity means that it is unlikely that there
is ambipolar diffusion in magnetar cores on the timescale of the lifetimes of
these objects, contradicting an assumption often made in the modelling of the
flaring activity commonly observed in magnetars. Our work suggests that if a
decaying magnetic field is indeed the cause of magnetar activity, the field
evolution is likely to take place outside of the core, and might represent
Hall/Ohmic diffusion in the stellar crust, or else that a mechanism other than
standard ambipolar diffusion is active, e.g. flux expulsion due to the
interaction between neutron vortices and magnetic fluxtubes.Comment: Paper changed to incorporate comments from referee. To appear in
MNRA
Developing a catalogue of explainability methods to support expert and non-expert users.
Organisations face growing legal requirements and ethical responsibilities to ensure that decisions made by their intelligent systems are explainable. However, provisioning of an explanation is often application dependent, causing an extended design phase and delayed deployment. In this paper we present an explainability framework formed of a catalogue of explanation methods, allowing integration to a range of projects within a telecommunications organisation. These methods are split into low-level explanations, high-level explanations and co-created explanations. We motivate and evaluate this framework using the specific case-study of explaining the conclusions of field engineering experts to non-technical planning staff. Feedback from an iterative co-creation process and a qualitative evaluation is indicative that this is a valuable development tool for use in future company projects
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