The explosion of data available in life sciences is fueling an increasing demand for expressive models and computational methods. Graph transformation is a model for dynamic systems with a large variety of applications. We introduce a novel method of the graph transformation model construction, combining generative and dynamical viewpoints to give a fully automated data-driven model inference method. The method takes the input dynamical properties, given as a "snapshot" of the dynamics encoded by explicit transitions, and constructs a compatible model. The obtained model is guaranteed to be minimal, thus framing the approach as model compression (from a set of transitions into a set of rules). The compression is permissive to a lossy case, where the constructed model is allowed to exhibit behavior outside of the input transitions, thus suggesting a completion of the input dynamics. The task of graph transformation model inference is naturally highly challenging due to the combinatorics involved. We tackle the exponential explosion by proposing a heuristically minimal translation of the task into a well-established problem, set cover, for which highly optimized solutions exist. We further showcase how our results relate to Kolmogorov complexity expressed in terms of graph transformation.

Time-series analyses has become a key instrument for the evaluation of continuously collected data in several domains such as Medicine, Physics and Statistics [Firmino et al., 2014, Box and Jenkins, 2015]. Such analysis generally involves the creation of a model (a regression function or a classifier, for instance) that usually leads to inconsistent results when built over raw data, specially if it contains chaotic behavior [Brock et al., 1992]. In order to reach more reliable results, an alternative is to study time-series trajectories in the phase space, as proposed by the area of Dynamical Systems [Ott, 2002, Alligood et al., 1996]. Besides leading to more robust models, the phase space also allows the inference of other important measures, such as the correlation dimension [Grassberger and Procaccia, 1983, Mandelbrot, 1977, Theiler, 1990, Clark, 1990, Ding et al., 1993] and the Lyapunov exponent [Sano and Sawada, 1985, Kantz and Schreiber, 2004], which support further analyses in modeling. In this context, Takens' embedding theorem [Takens, 1981] is one of the most used methods in the literature to reconstruct phase spaces from time series [Ravindra and Hagedorn, 1998]. Such method relies on two parameters known as embedding dimension m and time delay τ (see Figure 1) that, although Takens proved an arbitrary τ can be used given m is sufficiently large, the minimum-but-sufficient (from now on denoted as optimal) set of embedding parameters is desirable either to optimize phase-space computations as to better understand the analyzed phenomenon. In this context, several methods based on entropy [Han et al., 2012], fractal dimensions [Theiler, 1990] and/or nearest neighbors [Kennel et al., 1992] were proposed to guide the estimation of optimal embeddings.

The financial services sector is pouring money into artificial intelligence (AI), with banks, for example, expected to spend $5.6 billion on AI in 2019 – second only to the retail sector. Until now, the vast majority of AI projects have remained pilots, and in many cases those projects led to tech deployments without a clear business use. Simply put, it's been trendy. Most AI projects today are aimed at improving customer service efficiency and security by introducing chatbot technology, or by deploying machine-based learning to uncover trends across business lines in customer behavior and what they need. "It's about ensuring banks are able to retain the memory of a customer's journey across bank services," said Sankar Narayanan, chief practice officer at analytics service provider Fractal Analytics.

Answering conjunctive queries (CQs) over a set of facts extended with existential rules is a key problem in knowledge representation and databases. This problem can be solved using the chase (aka materialisation) algorithm; however, CQ answering is undecidable for general existential rules, so the chase is not guaranteed to terminate. Several acyclicity conditions provide sufficient conditions for chase termination. In this paper, we present two novel such conditions—model-faithful acyclicity (MFA) and model-summarising acyclicity (MSA)—that generalise many of the acyclicity conditions known so far in the literature. Materialisation provides the basis for several widely-used OWL 2 DL reasoners. In order to avoid termination problems, many of these systems handle only the OWL 2 RL profile of OWL 2 DL; furthermore, some systems go beyond OWL 2 RL, but they provide no termination guarantees. In this paper we investigate whether various acyclicity conditions can provide a principled and practical solution to these problems. On the theoretical side, we show that query answering for acyclic ontologies is of lower complexity than for general ontologies. On the practical side, we show that many of the commonly used OWL 2 DL ontologies are MSA, and that the facts obtained via materialisation are not too large. Thus, our results suggest that principled extensions to materialisationbased OWL 2 DL reasoners may be practically feasible.