We propose KG-ER, a conceptual schema language for knowledge graphs that describes the structure of knowledge graphs independently of their representation (relational databases, property graphs, RDF) while helping to capture the semantics of the information stored in a knowledge graph.

Shape analysis, or geometric data science, is a field dedicated to building statistical and machine learning methods able to retrieve and analyze the morphological variability in geometric structures. This is a particularly central problem in applications such as computer vision or biomedical imaging where observations often come as segmented curves, surfaces, densities or other types of complex geometric data. Various approaches have been proposed, including Riemannian and elastic shape space models [23, 41, 31, 56], topology based methods [22, 15, 20], and metric/functional matching frameworks [11, 40, 42]. These different methods have proved quite successful in tackling problems such as pairwise comparison, regression, classification or clustering for datasets of shapes. However, with the constant advances in acquisition protocols and the explosion in the size and resolution of datasets that followed, many such methods do not always scale well to recent applications that may involve databases with up to tens of thousands of subjects, each made of potentially hundreds of thousands of vertices. In view of the rapid development of new machine learning paradigms, in particular neural network models, and their impressive achievements in image processing and analysis tasks, one can reasonably expect similar tools to be able to address those challenges on geometric data. Yet, the very particular and intricate nature of shape spaces poses unique challenges when it comes to designing robust neural network models for shape analysis tasks.

SHACL (SHApe Constraint Language) is a W3C standardized constraint language for RDF graphs. In this paper, we study SHACL validation in RDF graphs under updates. We present a SHACL-based update language that can capture intuitive and realistic modifications on RDF graphs and study the problem of static validation under such updates. This problem asks to verify whether every graph that validates a SHACL specification will still do so after applying a given update sequence. More importantly, it provides a basis for further services for reasoning about evolving RDF graphs. Using a regression technique that embeds the update actions into SHACL constraints, we show that static validation under updates can be reduced to (un)satisfiability of constraints in (a minor extension of) SHACL. We analyze the computational complexity of the static validation problem for SHACL and some key fragments. Finally, we present a prototype implementation that performs static validation and other static analysis tasks on SHACL constraints and demonstrate its behavior through preliminary experiments.

Recent studies on the Shapes Constraint Language (SHACL), a W3C specification for validating RDF graphs, rely on translating the language into first-order logic in order to provide formally-grounded solutions to the validation, containment and satisfiability decision problems. Continuing on this line of research, we introduce SHACL2FOL, the first automatic tool that (i) translates SHACL documents into FOL sentences and (ii) computes the answer to the two static analysis problems of satisfiability and containment; it also allow to test the validity of a graph with respect to a set of constraints. By integrating with existing theorem provers, such as E and Vampire, the tool computes the answer to the aforementioned decision problems and outputs the corresponding first-order logic theories in the standard TPTP format. We believe this tool can contribute to further theoretical studies of SHACL, by providing an automatic first-order logic interpretation of its semantics, while also benefiting SHACL practitioners, by supplying static analysis capabilities to help the creation and management of SHACL constraints.

This paper focuses on the statistical analysis of shapes of data objects called shape graphs, a set of nodes connected by articulated curves with arbitrary shapes. A critical need here is a constrained registration of points (nodes to nodes, edges to edges) across objects. This, in turn, requires optimization over the permutation group, made challenging by differences in nodes (in terms of numbers, locations) and edges (in terms of shapes, placements, and sizes) across objects. This paper tackles this registration problem using a novel neural-network architecture and involves an unsupervised loss function developed using the elastic shape metric for curves. This architecture results in (1) state-of-the-art matching performance and (2) an order of magnitude reduction in the computational cost relative to baseline approaches. We demonstrate the effectiveness of the proposed approach using both simulated data and real-world 2D and 3D shape graphs. Code and data will be made publicly available after review to foster research.