Restricted Boltzmann Machines for Quantum States with Non-Abelian or Anyonic Symmetries.

Although artificial neural networks have recently been proven to provide a promising new framework for constructing quantum many-body wave functions, the parametrization of a quantum wave function with non-abelian symmetries in terms of a Boltzmann machine inherently leads to biased results due to the basis dependence. We demonstrate that this problem can be overcome by sampling in the basis of irreducible representations instead of spins, for which the corresponding ansatz respects the non-abelian symmetries of the system. We apply our methodology to find the ground states of the one-dimensional antiferromagnetic Heisenberg (AFH) model with spin-1/2 and spin-1 degrees of freedom, and obtain a substantially higher accuracy than when using the s_{z} basis as an input to the neural network. The proposed ansatz can target excited states, which is illustrated by calculating the energy gap of the AFH model. We also generalize the framework to the case of anyonic spin chains.

Network control by a constrained external agent as a continuous optimization problem.

Social science studies dealing with control in networks typically resort to heuristics or solely describing the control distribution. Optimal policies, however, require interventions that optimize control over a socioeconomic network subject to real-world constraints. We integrate optimisation tools from deep-learning with network science into a framework that is able to optimize such interventions in real-world networks. We demonstrate the framework in the context of corporate control, where it allows to characterize the vulnerability of strategically important corporate networks to sensitive takeovers, an important contemporaneous policy challenge. The framework produces insights that are relevant for governing real-world socioeconomic networks, and opens up new research avenues for improving our understanding and control of such complex systems.

Noise robustness of persistent homology on greyscale images, across filtrations and signatures.

Topological data analysis is a recent and fast growing field that approaches the analysis of datasets using techniques from (algebraic) topology. Its main tool, persistent homology (PH), has seen a notable increase in applications in the last decade. Often cited as the most favourable property of PH and the main reason for practical success are the stability theorems that give theoretical results about noise robustness, since real data is typically contaminated with noise or measurement errors. However, little attention has been paid to what these stability theorems mean in practice. To gain some insight into this question, we evaluate the noise robustness of PH on the MNIST dataset of greyscale images. More precisely, we investigate to what extent PH changes under typical forms of image noise, and quantify the loss of performance in classifying the MNIST handwritten digits when noise is added to the data. The results show that the sensitivity to noise of PH is influenced by the choice of filtrations and persistence signatures (respectively the input and output of PH), and in particular, that PH features are often not robust to noise in a classification task.

Combined frequency-tagging EEG and eye-tracking measures provide no support for the "excess mouth/diminished eye attention" hypothesis in autism.

BACKGROUND: Scanning faces is important for social interactions. Difficulty with the social use of eye contact constitutes one of the clinical symptoms of autism spectrum disorder (ASD). It has been suggested that individuals with ASD look less at the eyes and more at the mouth than typically developing (TD) individuals, possibly due to gaze aversion or gaze indifference. However, eye-tracking evidence for this hypothesis is mixed. While gaze patterns convey information about overt orienting processes, it is unclear how this is manifested at the neural level and how relative covert attention to the eyes and mouth of faces might be affected in ASD. METHODS: We used frequency-tagging EEG in combination with eye tracking, while participants watched fast flickering faces for 1-min stimulation sequences. The upper and lower halves of the faces were presented at 6 Hz and 7.5 Hz or vice versa in different stimulation sequences, allowing to objectively disentangle the neural saliency of the eyes versus mouth region of a perceived face. We tested 21 boys with ASD (8-12 years old) and 21 TD control boys, matched for age and IQ. RESULTS: Both groups looked longer at the eyes than the mouth, without any group difference in relative fixation duration to these features. TD boys looked significantly more to the nose, while the ASD boys looked more outside the face. EEG neural saliency data partly followed this pattern: neural responses to the upper or lower face half were not different between groups, but in the TD group, neural responses to the lower face halves were larger than responses to the upper part. Face exploration dynamics showed that TD individuals mostly maintained fixations within the same facial region, whereas individuals with ASD switched more often between the face parts. LIMITATIONS: Replication in large and independent samples may be needed to validate exploratory results. CONCLUSIONS: Combined eye-tracking and frequency-tagged neural responses show no support for the excess mouth/diminished eye gaze hypothesis in ASD. The more exploratory face scanning style observed in ASD might be related to their increased feature-based face processing style.