The Dual Frequency Anisotropic Magneto-Optical Trap

The cloud of cold atoms produced by a Magneto-Optical Trap is known to exhibit instabilities. We examine in this paper in which limits it could be possible to realize an experimental trap similar to the configurations studied theoretically, i.e. mainly traps where one direction is privileged. We study the static behavior of an anisotropic trap, where anisotropy results essentially from the use of two different laser frequencies for the arms of the trap. Such a trap has very surprising behaviors, in particular the cloud disappears for some laser frequencies, while it exists for smaller and larger frequencies. A model is build to explain these behaviors. We show in particular that, to reproduce the experimental observations, the model has to take into account the cross saturation effects. Moreover, the couplings between the different directions cannot be neglected

Phase-space description of the magneto-optical trap

An exhaustive kinetic model for the atoms in a 1D Magneto-Optical Trap is derived, without any approximations. It is shown that the atomic density is described by a Vlasov-Fokker-Planck equation, coupled with two simple differential equations describing the trap beam propagation. The analogy of such a system with plasmas is discussed. This set of equations is then simplified through some approximations, and it is shown that corrective terms have to be added to the models usually used in this context

A Degeneracy Framework for Scalable Graph Autoencoders

In this paper, we present a general framework to scale graph autoencoders (AE) and graph variational autoencoders (VAE). This framework leverages graph degeneracy concepts to train models only from a dense subset of nodes instead of using the entire graph. Together with a simple yet effective propagation mechanism, our approach significantly improves scalability and training speed while preserving performance. We evaluate and discuss our method on several variants of existing graph AE and VAE, providing the first application of these models to large graphs with up to millions of nodes and edges. We achieve empirically competitive results w.r.t. several popular scalable node embedding methods, which emphasizes the relevance of pursuing further research towards more scalable graph AE and VAE.Comment: International Joint Conference on Artificial Intelligence (IJCAI 2019

Gravity-Inspired Graph Autoencoders for Directed Link Prediction

Graph autoencoders (AE) and variational autoencoders (VAE) recently emerged as powerful node embedding methods. In particular, graph AE and VAE were successfully leveraged to tackle the challenging link prediction problem, aiming at figuring out whether some pairs of nodes from a graph are connected by unobserved edges. However, these models focus on undirected graphs and therefore ignore the potential direction of the link, which is limiting for numerous real-life applications. In this paper, we extend the graph AE and VAE frameworks to address link prediction in directed graphs. We present a new gravity-inspired decoder scheme that can effectively reconstruct directed graphs from a node embedding. We empirically evaluate our method on three different directed link prediction tasks, for which standard graph AE and VAE perform poorly. We achieve competitive results on three real-world graphs, outperforming several popular baselines.Comment: ACM International Conference on Information and Knowledge Management (CIKM 2019

Of Spiky SVDs and Music Recommendation

The truncated singular value decomposition is a widely used methodology in music recommendation for direct similar-item retrieval or embedding musical items for downstream tasks. This paper investigates a curious effect that we show naturally occurring on many recommendation datasets: spiking formations in the embedding space. We first propose a metric to quantify this spiking organization's strength, then mathematically prove its origin tied to underlying communities of items of varying internal popularity. With this new-found theoretical understanding, we finally open the topic with an industrial use case of estimating how music embeddings' top-k similar items will change over time under the addition of data.Comment: Accepted for RecSys 2023 (Singapour, 18-22 September