Chaos on compact manifolds: Differentiable synchronizations beyond the Takens theorem.

This paper shows that a large class of fading memory state-space systems driven by discrete-time observations of dynamical systems defined on compact manifolds always yields continuously differentiable synchronizations. This general result provides a powerful tool for the representation, reconstruction, and forecasting of chaotic attractors. It also improves previous statements in the literature for differentiable generalized synchronizations, whose existence was so far guaranteed for a restricted family of systems and was detected using Hölder exponent-based criteria.

The ventilation of buildings and other mitigating measures for COVID-19: a focus on wintertime.

The year 2020 has seen the emergence of a global pandemic as a result of the disease COVID-19. This report reviews knowledge of the transmission of COVID-19 indoors, examines the evidence for mitigating measures, and considers the implications for wintertime with a focus on ventilation.

Embedding and approximation theorems for echo state networks.

Echo State Networks (ESNs) are a class of single-layer recurrent neural networks that have enjoyed recent attention. In this paper we prove that a suitable ESN, trained on a series of measurements of an invertible dynamical system, induces a C1 map from the dynamical system's phase space to the ESN's reservoir space. We call this the Echo State Map. We then prove that the Echo State Map is generically an embedding with positive probability. Under additional mild assumptions, we further conjecture that the Echo State Map is almost surely an embedding. For sufficiently large, and specially structured, but still randomly generated ESNs, we prove that there exists a linear readout layer that allows the ESN to predict the next observation of a dynamical system arbitrarily well. Consequently, if the dynamical system under observation is structurally stable then the trained ESN will exhibit dynamics that are topologically conjugate to the future behaviour of the observed dynamical system. Our theoretical results connect the theory of ESNs to the delay-embedding literature for dynamical systems, and are supported by numerical evidence from simulations of the traditional Lorenz equations. The simulations confirm that, from a one dimensional observation function, an ESN can accurately infer a range of geometric and topological features of the dynamics such as the eigenvalues of equilibrium points, Lyapunov exponents and homology groups.

A hidden Markov model for describing turbostratic disorder applied to carbon blacks and graphene.

A mathematical framework is presented to represent turbostratic disorder in materials like carbon blacks, smectites and twisted n-layer graphene. In particular, the set of all possible disordered layers, including rotated, shifted and curved layers, forms a stochastic sequence governed by a hidden Markov model. The probability distribution over the set of layer types is treated as an element of a Hilbert space and, using the tools of Fourier analysis and functional analysis, expressions are developed for the scattering cross sections of a broad class of disordered materials.

A threat in the computer: the race implicit association test as a stereotype threat experience.

Three experiments test whether the threat of appearing racist leads White participants to perform worse on the race Implicit Association Test (IAT) and whether self-affirmation can protect from this threat. Experiments 1 and 2 suggest that White participants show a stereotype threat effect when completing the race IAT, leading to stronger pro-White scores when the test is believed to be diagnostic of racism. This effect increases for domain-identified (highly motivated to control prejudice) participants (Experiment 2). In Experiment 3, self-affirmation inoculates participants against stereotype threat while taking the race IAT. These findings have methodological implications for use of the race IAT and theoretical implications concerning the malleability of automatic prejudice and the potential interpersonal effects of the fear of appearing racist.