We study multi-marginal optimal transport, a generalization of optimal transport that allows us to define discrepancies between multiple measures. It provides a framework to solve multi-task learning problems and to perform barycentric averaging. However, multi-marginal distances between multiple measures are typically challenging to compute because they require estimating a transport plan with $N^P$ variables. In this paper, we address this issue in the following way: 1) we efficiently solve the one-dimensional multi-marginal Monge-Wasserstein problem for a classical cost function in closed form, and 2) we propose a higher-dimensional multi-marginal discrepancy via slicing and study its generalized metric properties. We show that computing the sliced multi-marginal discrepancy is massively scalable for a large number of probability measures with support as large as $10^7$ samples. Our approach can be applied to solving problems such as barycentric averaging, multi-task density estimation and multi-task reinforcement learning.

The paper analyzes the parameterized complexity of evaluating Ontology Mediated Queries (OMQs) based on Guarded TGDs (GTGDs) and Unions of Conjunctive Queries (UCQs), in the setting where relational symbols might have unbounded arity and where the parameter is the size of the OMQ. It establishes exact criteria for fixed-parameter tractability (fpt) evaluation of recursively enumerable classes of such OMQs (under the widely held Exponential Time Hypothesis). One of the main technical tools introduced in the paper is an fpt-reduction from deciding parameterized uniform CSPs to parameterized OMQ evaluation. A fundamental feature of the reduction is preservation of measures which are known to be essential for classifying classes of parameterized uniform CSPs: submodular width (according to the well known result of Marx for unbounded-arity schemas) and treewidth (according to the well known result of Grohe for bounded-arity schemas). As such, the reduction can be employed to obtain hardness results for evaluation of classes of parameterized OMQs both in the unbounded and in the bounded arity case. Previously, in the case of bounded arity schemas, this has been tackled using a technique requiring full introspection into the construction employed by Grohe.

Considering the evolution of the semantic wiki engine based platforms, two main approaches could be distinguished: Ontologies for Wikis (OfW) and Wikis for Ontologies (WfO). OfW vision requires existing ontologies to be imported. Most of them use the RDF-based (Resource Description Framework) systems in conjunction with the standard SQL (Structured Query Language) database to manage and query semantic data. But, relational database is not an ideal type of storage for semantic data. A more natural data model for SMW (Semantic MediaWiki) is RDF, a data format that organizes information in graphs rather than in fixed database tables. This paper presents an ontology based architecture, which aims to implement this idea. The architecture mainly includes three layered functional architectures: Web User Interface Layer, Semantic Layer and Persistence Layer. Introduction This research study is set in an African context, where the main problem is an economic, social development and the means to achieve it. Indeed, after the failure of several development models in the recent decades, theoretical research seems to be turning to the development knowledgebased approaches (UNESCO, 2014). The place of knowledge, science and technology in the current dynamics of growth gives rise to intensify the reflection within the economic field.