Temporal network embedding framework with causal anonymous walks representations.

Many tasks in graph machine learning, such as link prediction and node classification, are typically solved using representation learning. Each node or edge in the network is encoded via an embedding. Though there exists a lot of network embeddings for static graphs, the task becomes much more complicated when the dynamic (i.e., temporal) network is analyzed. In this paper, we propose a novel approach for dynamic network representation learning based on Temporal Graph Network by using a highly custom message generating function by extracting Causal Anonymous Walks. We provide a benchmark pipeline for the evaluation of temporal network embeddings. This work provides the first comprehensive comparison framework for temporal network representation learning for graph machine learning problems involving node classification and link prediction in every available setting. The proposed model outperforms state-of-the-art baseline models. The work also justifies their difference based on evaluation in various transductive/inductive edge/node classification tasks. In addition, we show the applicability and superior performance of our model in the real-world downstream graph machine learning task provided by one of the top European banks, involving credit scoring based on transaction data.

Prescaling in a Far-from-Equilibrium Bose Gas.

Nonequilibrium conditions give rise to classes of universally evolving configurations of quantum many-body systems at nonthermal fixed points. While the fixed point and thus full scaling in space and time is generically reached at very long evolution times, we propose that systems can show prescaling much earlier in time, in particular, on experimentally accessible timescales. During the prescaling evolution, some well-measurable properties of spatial correlations already scale with the universal exponents of the fixed point while others still show scaling violations. Prescaling is characterized by the evolution obeying conservation laws associated with the remaining symmetry which also defines the universality class of the asymptotically reached nonthermal fixed point. Here, we consider N=3 species of spatially uniform three-dimensional Bose gases, with identical inter- and intraspecies interactions. During prescaling, the full U(N) symmetry of the model is broken to U(N-1) while the conserved transport, reflecting explicit and emerging symmetries, leads to the buildup of rescaling quasicondensate distributions.