We present in detail the convolutional neural network used in our previous work to detect cosmic strings in cosmic microwave background (CMB) temperature anisotropy maps. By training this neural network on numerically generated CMB temperature maps, with and without cosmic strings, the network can produce prediction maps that locate the position of the cosmic strings and provide a probabilistic estimate of the value of the string tension Gµ. Supplying noiseless simulations of CMB maps with arcmin resolution to the network resulted in the accurate determination both of string locations and string tension for sky maps having strings with string tension as low as Gµ = 5 × 10 −9 , a result from our previous work. In this work we discuss the numerical details of the code that is publicly available online. Furthermore, we show that though we trained the network with a long straight string toy model, the network performs well with realistic Nambu-Goto simulations.

We make a formal analogy between random sampling and fresh name generation. We show that quasi-Borel spaces, a model for probabilistic programming, can soundly interpret the ν-calculus, a calculus for name generation. Moreover, we prove that this semantics is fully abstract up to first-order types. This is surprising for an ‘off-the-shelf’ model, and requires a novel analysis of probability distributions on function spaces. Our tools are diverse and include descriptive set theory and normal forms for the ν-calculus.

We make a formal analogy between random sampling and fresh name generation. We show that quasi-Borel spaces, a model for probabilistic programming, can soundly interpret Stark's ν-calculus, a calculus for name generation. Moreover, we prove that this semantics is fully abstract up to first-order types. This is surprising for an 'off-the-shelf' model, and requires a novel analysis of probability distributions on function spaces. Our tools are diverse and include descriptive set theory and normal forms for the ν -calculus.