Neural controlled differential equations (Neural CDEs) are a continuous-time extension of recurrent neural networks (RNNs). They are considered SOTA for modelling functions on irregular time series, outperforming other ODE benchmarks (ODE-RNN, GRU-ODE-Bayes) in offline prediction tasks. However, current implementations are not suitable to be used in online prediction tasks, severely restricting the domains of applicability of this powerful modeling framework. We identify such limitations with previous implementations and show how said limitations may be addressed, most notably to allow for online predictions. We benchmark our online Neural CDE model on three continuous monitoring tasks from the MIMIC-IV ICU database, demonstrating improved performance on two of the three tasks against state-of-the-art (SOTA) non-ODE benchmarks, and improved performance on all tasks against our ODE benchmark.

Joint work with Patrick Kidger, Lingyi Yang, and Terry Lyons.

Networks are a widely-used tool to investigate the large-scale connectivity structure in complex systems and graphons have been proposed as an infinite size limit of dense networks. The detection of communities or other meso-scale structures is a prominent topic in network science as it allows the identification of functional building blocks in complex systems. When such building blocks may be present in graphons is an open question. In this paper, we define a graphon-modularity and demonstrate that it can be maximised to detect communities in graphons. We then investigate specific synthetic graphons and show that they may show a wide range of different community structures. We also reformulate the graphon-modularity maximisation as a continuous optimisation problem and so prove the optimal community structure or lack thereof for some graphons, something that is usually not possible for networks. Furthermore, we demonstrate that estimating a graphon from network data as an intermediate step can improve the detection of communities, in comparison with exclusively maximising the modularity of the network. While the choice of graphon-estimator may strongly influence the accord between the community structure of a network and its estimated graphon, we find that there is a substantial overlap if an appropriate estimator is used. Our study demonstrates that community detection for graphons is possible and may serve as a privacy-preserving way to cluster network data.

arXiv link: https://arxiv.org/abs/2101.00503

Over the last several years, it has been shown that black hole microstate level statistics in various models of 2D gravity are encoded in wormhole amplitudes.  These statistics quantitatively agree with predictions of random matrix theory for chaotic quantum systems; this behavior is realized since the 2D theories in question are dual to matrix models.  But what about black hole microstate statistics for Einstein gravity in 3D and higher spacetime dimensions, and ultimately in non-perturbative string theory?  We will discuss progress in these directions.  In 3D, we compute a wormhole amplitude that encodes the energy level statistics of BTZ black holes.  In 4D and higher, we find analogous wormholes which appear to encode the level statistics of small black holes just above threshold.  Finally, we study analogous Euclidean wormholes in the low-energy limit of type IIB string theory; we provide evidence that they encode the level statistics of small black holes just above threshold in AdS5 x S5.  Remarkably, these wormholes appear to be stable in appropriate regimes, and dominate over brane-anti-brane nucleation processes in the computation of black hole microstate statistics.

In a broad class of gravity theories, the equations of motion for vacuum compactifications give a curvature bound on the Ricci tensor minus a multiple of the Hessian of the warping function. Using results in so-called Bakry-Émery geometry, I will show how to put rigorous general bounds on the KK scale in gravity compactifications in terms of the reduced Planck mass or the internal diameter.
If time permits, I will reexamine in this light the local behavior in type IIA for the class of supersymmetric solutions most promising for scale separation. It turns out that the local O6-plane behavior cannot be smoothed out as in other local examples; it generically turns into a formal partially smeared O4.

https://teams.microsoft.com/l/meetup-join/19%3ameeting_ZGRiMTM1ZjQtZWNi…

I will introduce the notion of moduli spaces of curves and specifically genus 0 curves. They are in general not compact, and we will discuss the most common way to compactify them. In particular, I will try to explain the construction of Mbar_{0,5}, together with how to classify the boundary, how it is related to a moduli space of tropical curves, and how to do intersection theory on this space.