Analytic continuation from Minkowski space to (2, 2) split signature spacetime has proven to be a powerful tool for the study of scattering amplitudes. Here we show that, under this continuation, null infinity becomes the product of a null interval with a celestial torus (replacing the celestial sphere) and has only one connected component. Spacelike and timelike infinity are time-periodic quotients of AdS3. These three components of infinity combine to an S3 represented as a toric fibration over the interval. Privileged scattering states of scalars organize into SL(2, ℝ)L×SL(2, ℝ)R conformal primary wave functions and their descendants with real integral or half-integral conformal weights, giving the normally continuous scattering problem a discrete character.

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We study the conformal bootstrap constraints for 3D conformal field theories with a Z 2 or parity symmetry, assuming a single relevant scalar operator that is invariant under the symmetry. When there is additionally a single relevant odd scalar σ, we map out the allowed space of dimensions and three-point couplings of such "Ising-like" CFTs. If we allow a second relevant odd scalar σ , we identify a feature in the allowed space compatible with 3D N = 1 superconformal symmetry and conjecture that it corresponds to the minimal N = 1 supersymmetric extension of the Ising CFT. This model has appeared in previous numerical bootstrap studies, as well as in proposals for emergent supersymmetry on the boundaries of topological phases of matter. Adding further constraints from 3D N = 1 superconformal symmetry, we isolate this theory and use the numerical bootstrap to compute the leading scaling dimensions ∆ σ = ∆ − 1 = .58444(22) and three-point couplings λ σσ = 1.0721(2) and λ = 1.67(1). We additionally place bounds on the central charge and use the extremal functional method to estimate the dimensions of the next several operators in the spectrum. Based on our results we observe the possible exact relation λ /λ σσ = tan(1).

In this note we report an improved determination of the scaling dimensions and OPE coefficients of the minimal supersymmetric extension of the 3d Ising model using the conformal bootstrap. We also show how this data can be used as input to the Lorentzian inversion formula, finding good agreement between analytic calculations and numerical extremal spectra once mixing effects are resolved.

Task-trained artificial recurrent neural networks (RNNs) provide a computational modeling framework of increasing interest and application in computational, systems, and cognitive neuroscience. RNNs can be trained, using deep learning methods, to perform cognitive tasks used in animal and human experiments, and can be studied to investigate potential neural representations and circuit mechanisms underlying cognitive computations and behavior. Widespread application of these approaches within neuroscience has been limited by technical barriers in use of deep learning software packages to train network models. Here we introduce PsychRNN, an accessible, flexible, and extensible Python package for training RNNs on cognitive tasks. Our package is designed for accessibility, for researchers to define tasks and train RNN models using only Python and NumPy without requiring knowledge of deep learning software. The training backend is based on TensorFlow and is readily extensible for researchers with TensorFlow knowledge to develop projects with additional customization. PsychRNN implements a number of specialized features to support applications in systems and cognitive neuroscience. Users can impose neurobiologically relevant constraints on synaptic connectivity patterns. Furthermore, specification of cognitive tasks has a modular structure, which facilitates parametric variation of task demands to examine their impact on model solutions. PsychRNN also enables task shaping during training, or curriculum learning, in which tasks are adjusted in closed-loop based on performance. Shaping is ubiquitous in training of animals in cognitive tasks, and PsychRNN allows investigation of how shaping trajectories impact learning and model solutions. Overall, the PsychRNN framework facilitates application of trained RNNs in neuroscience research.