A new class of multiscale lattice cell (MLC) models for spatio-temporal evolutionary image representation

Spatio-temporal evolutionary (STE) images are a class of complex dynamical systems that evolve over both space and time. With increased interest in the investigation of nonlinear complex phenomena, especially spatio-temporal behaviour governed by evolutionary laws that are dependent on both spatial and temporal dimensions, there has been an increased need to investigate model identification methods for this class of complex systems. Compared with pure temporal processes, the identification of spatio-temporal models from observed images is much more difficult and quite challenging. Starting with an assumption that there is no apriori information about the true model but only observed data are available, this study introduces a new class of multiscale lattice cell (MLC) models to represent the rules of the associated spatio-temporal evolutionary system. An application to a chemical reaction exhibiting a spatio-temporal evolutionary behaviour, is investigated to demonstrate the new modelling framework

Big Data Guided Resources Businesses – Leveraging Location Analytics and Managing Geospatial-temporal Knowledge

Location data rapidly grow with fast-changing logistics and business rules. Due to fast-growing business ventures and their diverse operations locally and globally, location-based information systems are in demand in resource industries. Data sources in these industries are spatial-temporal, with petabytes in size. Managing volumes and various data in periodic and geographic dimensions using the existing modelling methods is challenging. The current relational database models have implementation challenges, including the interpretation of data views. Multidimensional models are articulated to integrate resource databases with spatial-temporal attribute dimensions. Location and periodic attribute dimensions are incorporated into various schemas to minimise ambiguity during database operations, ensuring resource data's uniqueness and monotonic characteristics. We develop an integrated framework compatible with the multidimensional repository and implement its metadata in resource industries. The resources’ metadata with spatial-temporal attributes enables business research analysts a scope for data views’ interpretation in new geospatial knowledge domains for financial decision support

A Framework for Spatio-Temporal Data Analysis and Hypothesis Exploration

We present a general framework for pattern discovery and hypothesis exploration in spatio-temporal data sets that is based on delay-embedding. This is a remarkable method of nonlinear time-series analysis that allows the full phase-space behaviour of a system to be reconstructed from only a single observable (accessible variable). Recent extensions to the theory that focus on a probabilistic interpretation extend its scope and allow practical application to noisy, uncertain and high-dimensional systems. The framework uses these extensions to aid alignment of spatio-temporal sub-models (hypotheses) to empirical data - for example satellite images plus remote-sensing - and to explore modifications consistent with this alignment. The novel aspect of the work is a mechanism for linking global and local dynamics using a holistic spatio-temporal feedback loop. An example framework is devised for an urban based application, transit centric developments, and its utility is demonstrated with real data

Data mining as a tool for environmental scientists

Over recent years a huge library of data mining algorithms has been developed to tackle a variety of problems in fields such as medical imaging and network traffic analysis. Many of these techniques are far more flexible than more classical modelling approaches and could be usefully applied to data-rich environmental problems. Certain techniques such as Artificial Neural Networks, Clustering, Case-Based Reasoning and more recently Bayesian Decision Networks have found application in environmental modelling while other methods, for example classification and association rule extraction, have not yet been taken up on any wide scale. We propose that these and other data mining techniques could be usefully applied to difficult problems in the field. This paper introduces several data mining concepts and briefly discusses their application to environmental modelling, where data may be sparse, incomplete, or heterogenous

Foundations and modelling of dynamic networks using Dynamic Graph Neural Networks: A survey

Dynamic networks are used in a wide range of fields, including social network analysis, recommender systems, and epidemiology. Representing complex networks as structures changing over time allow network models to leverage not only structural but also temporal patterns. However, as dynamic network literature stems from diverse fields and makes use of inconsistent terminology, it is challenging to navigate. Meanwhile, graph neural networks (GNNs) have gained a lot of attention in recent years for their ability to perform well on a range of network science tasks, such as link prediction and node classification. Despite the popularity of graph neural networks and the proven benefits of dynamic network models, there has been little focus on graph neural networks for dynamic networks. To address the challenges resulting from the fact that this research crosses diverse fields as well as to survey dynamic graph neural networks, this work is split into two main parts. First, to address the ambiguity of the dynamic network terminology we establish a foundation of dynamic networks with consistent, detailed terminology and notation. Second, we present a comprehensive survey of dynamic graph neural network models using the proposed terminologyComment: 28 pages, 9 figures, 8 table

Multiscale Bone Remodelling with Spatial P Systems

Many biological phenomena are inherently multiscale, i.e. they are characterized by interactions involving different spatial and temporal scales simultaneously. Though several approaches have been proposed to provide "multilayer" models, only Complex Automata, derived from Cellular Automata, naturally embed spatial information and realize multiscaling with well-established inter-scale integration schemas. Spatial P systems, a variant of P systems in which a more geometric concept of space has been added, have several characteristics in common with Cellular Automata. We propose such a formalism as a basis to rephrase the Complex Automata multiscaling approach and, in this perspective, provide a 2-scale Spatial P system describing bone remodelling. The proposed model not only results to be highly faithful and expressive in a multiscale scenario, but also highlights the need of a deep and formal expressiveness study involving Complex Automata, Spatial P systems and other promising multiscale approaches, such as our shape-based one already resulted to be highly faithful.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

Predicting Spatio-Temporal Time Series Using Dimension Reduced Local States

We present a method for both cross estimation and iterated time series prediction of spatio temporal dynamics based on reconstructed local states, PCA dimension reduction, and local modelling using nearest neighbour methods. The effectiveness of this approach is shown for (noisy) data from a (cubic) Barkley model, the Bueno-Orovio-Cherry-Fenton model, and the Kuramoto-Sivashinsky model