Smooth, identifiable supermodels of discrete DAG models with latent variables

We provide a parameterization of the discrete nested Markov model, which is a supermodel that approximates DAG models (Bayesian network models) with latent variables. Such models are widely used in causal inference and machine learning. We explicitly evaluate their dimension, show that they are curved exponential families of distributions, and fit them to data. The parameterization avoids the irregularities and unidentifiability of latent variable models. The parameters used are all fully identifiable and causally-interpretable quantities.Comment: 30 page

Highly eccentric inspirals into a black hole

We model the inspiral of a compact stellar-mass object into a massive nonrotating black hole including all dissipative and conservative first-order-in-the-mass-ratio effects on the orbital motion. The techniques we develop allow inspirals with initial eccentricities as high as $e\sim0.8$ and initial separations as large as $p\sim 50$ to be evolved through many thousands of orbits up to the onset of the plunge into the black hole. The inspiral is computed using an osculating elements scheme driven by a hybridized self-force model, which combines Lorenz-gauge self-force results with highly accurate flux data from a Regge-Wheeler-Zerilli code. The high accuracy of our hybrid self-force model allows the orbital phase of the inspirals to be tracked to within $\sim0.1$ radians or better. The difference between self-force models and inspirals computed in the radiative approximation is quantified.Comment: Updated to reflect published versio

Evolution of small-mass-ratio binaries with a spinning secondary

We calculate the evolution and gravitational-wave emission of a spinning compact object inspiraling into a substantially more massive (non-rotating) black hole. We extend our previous model for a non-spinning binary [Phys. Rev. D 93, 064024] to include the Mathisson-Papapetrou-Dixon spin-curvature force. For spin-aligned binaries we calculate the dephasing of the inspiral and associated waveforms relative to models that do not include spin-curvature effects. We find this dephasing can be either positive or negative depending on the initial separation of the binary. For binaries in which the spin and orbital angular momentum are not parallel, the orbital plane precesses and we use a more general osculating element prescription to compute inspirals.Comment: 17 pages, 6 figure

Comptonisation of Cosmic Microwave Background Photons in Dwarf Spheroidal Galaxies

We present theoretical modelling of the electron distribution produced by annihilating neutralino dark matter in dwarf spheroidal galaxies (dSphs). In particular, we follow up the idea of Colafrancesco (2004) and find that such electrons distort the cosmic microwave background (CMB) by the Sunyaev-Zeldovich effect. For an assumed neutralino mass of 10 GeV and beam size of 1'', the SZ temperature decrement is of the order of nano-Kelvin for dSph models with a soft core. By contrast, it is of the order of micro-Kelvin for the strongly cusped dSph models favoured by some cosmological simulations. Although this is out of reach of current instruments, it may well be detectable by future mm telescopes, such as ALMA. We also show that the upscattered CMB photons have energies within reach of upcoming X-ray observatories, but that the flux of such photons is too small to be detectable soon. Nonetheless, we conclude that searching for the dark matter induced Sunyaev-Zeldovich effect is a promising way of constraining the dark distribution in dSphs, especially if the particles are light.Comment: 10 pages, 5 figures, MNRAS, in pres