Learning and reasoning with graph data

Reasoning about graphs, and learning from graph data is a field of artificial intelligence that has recently received much attention in the machine learning areas of graph representation learning and graph neural networks. Graphs are also the underlying structures of interest in a wide range of more traditional fields ranging from logic-oriented knowledge representation and reasoning to graph kernels and statistical relational learning. In this review we outline a broad map and inventory of the field of learning and reasoning with graphs that spans the spectrum from reasoning in the form of logical deduction to learning node embeddings. To obtain a unified perspective on such a diverse landscape we introduce a simple and general semantic concept of a model that covers logic knowledge bases, graph neural networks, kernel support vector machines, and many other types of frameworks. Still at a high semantic level, we survey common strategies for model specification using probabilistic factorization and standard feature construction techniques. Based on this semantic foundation we introduce a taxonomy of reasoning tasks that casts problems ranging from transductive link prediction to asymptotic analysis of random graph models as queries of different complexities for a given model. Similarly, we express learning in different frameworks and settings in terms of a common statistical maximum likelihood principle. Overall, this review aims to provide a coherent conceptual framework that provides a basis for further theoretical analyses of respective strengths and limitations of different approaches to handling graph data, and that facilitates combination and integration of different modeling paradigms

Freshwater transport in the coupled ocean-atmosphere system: a passive ocean

Conservation of water demands that meridional ocean and atmosphere freshwater transports (FWT) are of equal magnitude but opposite in direction. This suggests that the atmospheric FWT and its associated latent heat (LH) transport could be thought of as a \textquotedblleft coupled ocean/atmosphere mode\textquotedblright. But what is the true nature of this coupling? Is the ocean passive or active? Here we analyze a series of simulations with a coupled ocean-atmosphere-sea ice model employing highly idealized geometries but with markedly different coupled climates and patterns of ocean circulation. Exploiting streamfunctions in specific humidity coordinates for the atmosphere and salt coordinates for the ocean to represent FWT in their respective medium, we find that atmospheric FWT/LH transport is essentially independent of the ocean state. Ocean circulation and salinity distribution adjust to achieve a return freshwater pathway demanded of them by the atmosphere. So, although ocean and atmosphere FWTs are indeed coupled by mass conservation, the ocean is a passive component acting as a reservoir of freshwater

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Vlasov moment flows and geodesics on the Jacobi group

By using the moment algebra of the Vlasov kinetic equation, we characterize the integrable Bloch-Iserles system on symmetric matrices (arXiv:math-ph/0512093) as a geodesic flow on the Jacobi group. We analyze the corresponding Lie-Poisson structure by presenting a momentum map, which both untangles the bracket structure and produces particle-type solutions that are inherited from the Vlasov-like interpretation. Moreover, we show how the Vlasov moments associated to Bloch-Iserles dynamics correspond to particular subgroup inclusions into a group central extension (first discovered in arXiv:math/0410100), which in turn underlies Vlasov kinetic theory. In the most general case of Bloch-Iserles dynamics, a generalization of the Jacobi group also emerges naturally.Comment: 45 page

Climate at high-obliquity

The question of climate at high obliquity is raised in the context of both exoplanet studies (e.g. habitability) and paleoclimates studies (evidence for low-latitude glaciation during the Neoproterozoic and the ”Snowball Earth” hypothesis). States of high obliquity, φ, are distinctive in that, for φ ≥54◦, the poles receive more solar radiation in the annual mean than the Equator, opposite to the present day situation. In addition, the seasonal cycle of insolation is extreme, with the poles alternatively “facing” the sun and sheltering in the dark for months. The novelty of our approach is to consider the role of a dynamical ocean in controlling the surface climate at high obliquity, which in turn requires understanding of the surface winds patterns when temperature gradients are reversed. To address these questions, a coupled ocean-atmosphere-sea ice GCM configured on an aquaplanet is employed. Except for the absence of topography and modified obliquity, the set-up is Earth-like. Two large obliquities φ, 54◦ and 90◦, are compared to today’s Earth value, φ=23.5◦. Three key results emerge at high obliquity: 1) despite reversed temper- ature gradients, mid-latitudes surface winds are westerly and trade winds exist at the equator (as for φ=23.5◦) although the westerlies are confined to the summer hemisphere, 2) a habitable planet is possible with mid-latitude temperatures in the range 300-280 K and 3) a stable climate state with an ice cap limited to the equatorial region is unlikely. We clarify the dynamics behind these features (notably by an analysis of the potential vorticity structure and conditions for baroclinic instability of the atmosphere). Interestingly, we find that the absence of a stable partially glaciated state is critically linked to the absence of ocean heat transport during winter, a feature ultimately traced back to the high seasonality of baroclinic instability conditions in the atmosphere