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

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

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

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

White Dwarf Heating and Subsequent Cooling in Dwarf Nova Outbursts

We follow the time dependent thermal evolution of a white dwarf (WD) undergoing sudden accretion in a dwarf nova outburst, using both simulations and analytic estimates. The post-outburst lightcurve clearly separates into early times when the WD flux is high, and late times when the flux is near the quiescent level. The break between these two regimes, occurring at a time of order the outburst duration, corresponds to a thermal diffusion wave reaching the base of the freshly accreted layer. Our principal result is that long after the outburst, the fractional flux perturbation about the quiescent flux decays as a power law with time (and {\it not} as an exponential). We use this result to construct a simple fitting formula that yields estimates for both the quiescent flux and the accreted column, i.e. the total accreted mass divided by WD surface area. The WD mass is not well constrained by the late time lightcurve alone, but it can be inferred if the accreted mass is known from observations. We compare our work with the well-studied outburst of WZ Sge, finding that the cooling is well described by our model, giving an effective temperature $T_{\rm eff}=14,500 {\rm K}$ and accreted column $\Delta y\approx10^6 {\rm g cm^{-2}}$, in agreement with the modeling of Godon et al. To reconcile this accreted column with the accreted mass inferred from the bolometric accretion luminosity, a large WD mass $\gtrsim1.1M_\odot$ is needed. Our power law result is a valuable tool for making quick estimates of the outburst properties. We show that fitting the late time lightcurve with this formula yields a predicted column within 20% of that estimated from our full numerical calculations.Comment: Accepted for publication in The Astrophysical Journal, 10 pages, 8 figure

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.

Coalescing Binary Neutron Stars

Coalescing compact binaries with neutron star or black hole components provide the most promising sources of gravitational radiation for detection by the LIGO/VIRGO/GEO/TAMA laser interferometers now under construction. This fact has motivated several different theoretical studies of the inspiral and hydrodynamic merging of compact binaries. Analytic analyses of the inspiral waveforms have been performed in the Post-Newtonian approximation. Analytic and numerical treatments of the coalescence waveforms from binary neutron stars have been performed using Newtonian hydrodynamics and the quadrupole radiation approximation. Numerical simulations of coalescing black hole and neutron star binaries are also underway in full general relativity. Recent results from each of these approaches will be described and their virtues and limitations summarized.Comment: Invited Topical Review paper to appear in Classical and Quantum Gravity, 35 pages, including 5 figure

Intermittent applied mechanical loading induces subchondral bone thickening that may be intensified locally by contiguous articular cartilage lesions

Objectives: Changes in subchondral bone (SCB) and cross-talk with articular cartilage (AC) have been linked to osteoarthritis (OA). Using micro-computed tomography (micro-CT) this study: (1) examines changes in SCB architecture in a non-invasive loading mouse model in which focal AC lesions are induced selectively in the lateral femur, and (2) determines any modifications in the contralateral knee, linked to changes in gait, which might complicate use of this limb as an internal control. Methods: Right knee joints of CBA mice were loaded: once with 2weeks of habitual use (n=7), for 2weeks (n=8) or for 5weeks (n=5). Both left (contralateral) and right (loaded) knees were micro-CT scanned and the SCB and trabecular bone analysed. Gait analysis was also performed. Results: These analyses showed a significant increase in SCB thickness in the lateral compartments in joints loaded for 5weeks, which was most marked in the lateral femur; the contralateral non-loaded knee also showed transient SCB thickening (loaded once and repetitively). Epiphyseal trabecular bone BV/TV and trabecular thickness were also increased in the lateral compartments after 5 weeks of loading, and in all joint compartments in the contralateral knee. Gait analysis showed that applied loading only affected gait in the contralateral himd-limb in all groups of mice from the second week after the first loading episode. Conclusions: These data indicate a spatial link between SCB thickening and AC lesions following mechanical trauma, and the clear limitations associated with the use of contralateral joints as controls in such OA models, and perhaps in OA diagnosis

Implications of the measured parameters of PSR J1903+0327 for its progenitor neutron star

Using the intrinsic PSR J1903+0327 parameters evaluated from radio observations (mass, rotation period and dipole magnetic field deduced from the timing properties) we calculate the mass of its neutron star progenitor, M_i, at the onset of accretion. Simultaneously, we derive constraints on average accretion rate Mdot and the pre-accretion magnetic field B_i. Spin-up is modelled by accretion from a thin disk, using the magnetic-torque disk-pulsar coupling model proposed by Kluzniak and Rappaport (2007), improved for the existence of relativistic marginally-stable circular orbit. Orbital parameters in the disk are obtained using the space-time generated by a rotating neutron star in the framework of General Relativity. We employ an observationally motivated model of the surface magnetic field decay. We also seek for the imprint of the poorly known equation of state of dense matter on the spin-up tracks - three equations of state of dense matter, consistent with the existence of 2 Msun neutron star, are considered. We find that the minimum average accretion rate should be larger than 2-8 10^(-10) Msun/yr, the highest lower bound corresponding to the stiffest equation of state. We conclude that the influence of magnetic field in the "recycling" process is crucial - it leads to a significant decrease of spin-up rate and larger accreted masses, in comparison to the B=0 model. Allowed B_i-dependent values of M_i are within 1.0-1.4 Msun, i.e., much lower than an oversimplified but widely used B=0 result, where one gets M_i>1.55 Msun. Estimated initial neutron-star mass depends on the assumed dense-matter equation of state.Comment: 11 pages, 10 figures; A&A accepte

Neutron Stars in Teleparallel Gravity

In this paper we deal with neutron stars, which are described by a perfect fluid model, in the context of the teleparallel equivalent of general relativity. We use numerical simulations to find the relationship between the angular momentum of the field and the angular momentum of the source. Such a relation was established for each stable star reached by the numerical simulation once the code is fed with an equation of state, the central energy density and the ratio between polar and equatorial radii. We also find a regime where linear relation between gravitational angular momentum and moment of inertia (as well as angular velocity of the fluid) is valid. We give the spatial distribution of the gravitational energy and show that it has a linear dependence with the squared angular velocity of the source.Comment: 19 pages, 14 figures. arXiv admin note: text overlap with arXiv:1206.331