On the Treewidth of Dynamic Graphs

Dynamic graph theory is a novel, growing area that deals with graphs that change over time and is of great utility in modelling modern wireless, mobile and dynamic environments. As a graph evolves, possibly arbitrarily, it is challenging to identify the graph properties that can be preserved over time and understand their respective computability. In this paper we are concerned with the treewidth of dynamic graphs. We focus on metatheorems, which allow the generation of a series of results based on general properties of classes of structures. In graph theory two major metatheorems on treewidth provide complexity classifications by employing structural graph measures and finite model theory. Courcelle's Theorem gives a general tractability result for problems expressible in monadic second order logic on graphs of bounded treewidth, and Frick & Grohe demonstrate a similar result for first order logic and graphs of bounded local treewidth. We extend these theorems by showing that dynamic graphs of bounded (local) treewidth where the length of time over which the graph evolves and is observed is finite and bounded can be modelled in such a way that the (local) treewidth of the underlying graph is maintained. We show the application of these results to problems in dynamic graph theory and dynamic extensions to static problems. In addition we demonstrate that certain widely used dynamic graph classes naturally have bounded local treewidth

Graph Neural Networks as the Copula Mundi between Logic and Machine Learning: A Roadmap

Combining machine learning (ML) and computational logic (CL) is hard, mostly because of the inherently- different ways they use to represent knowledge. In fact, while ML relies on fixed-size numeric repre- sentations leveraging on vectors, matrices, or tensors of real numbers, CL relies on logic terms and clauses—which are unlimited in size and structure. Graph neural networks (GNN) are a novelty in the ML world introduced for dealing with graph- structured data in a sub-symbolic way. In other words, GNN pave the way towards the application of ML to logic clauses and knowledge bases. However, there are several ways to encode logic knowledge into graphs: which is the best one heavily depends on the specific task at hand. Accordingly, in this paper, we (i) elicit a number of problems from the field of CL that may benefit from many graph-related problems where GNN has been proved effective; (ii) exemplify the application of GNN to logic theories via an end-to-end toy example, to demonstrate the many intricacies hidden behind the technique; (iii) discuss the possible future directions of the application of GNN to CL in general, pointing out opportunities and open issues

Recognizing complex faces and gaits via novel probabilistic models

In the field of computer vision, developing automated systems to recognize people under unconstrained scenarios is a partially solved problem. In unconstrained sce- narios a number of common variations and complexities such as occlusion, illumi- nation, cluttered background and so on impose vast uncertainty to the recognition process. Among the various biometrics that have been emerging recently, this dissertation focus on two of them namely face and gait recognition. Firstly we address the problem of recognizing faces with major occlusions amidst other variations such as pose, scale, expression and illumination using a novel PRObabilistic Component based Interpretation Model (PROCIM) inspired by key psychophysical principles that are closely related to reasoning under uncertainty. The model basically employs Bayesian Networks to establish, learn, interpret and exploit intrinsic similarity mappings from the face domain. Then, by incorporating e cient inference strategies, robust decisions are made for successfully recognizing faces under uncertainty. PROCIM reports improved recognition rates over recent approaches. Secondly we address the newly upcoming gait recognition problem and show that PROCIM can be easily adapted to the gait domain as well. We scienti cally de ne and formulate sub-gaits and propose a novel modular training scheme to e ciently learn subtle sub-gait characteristics from the gait domain. Our results show that the proposed model is robust to several uncertainties and yields sig- ni cant recognition performance. Apart from PROCIM, nally we show how a simple component based gait reasoning can be coherently modeled using the re- cently prominent Markov Logic Networks (MLNs) by intuitively fusing imaging, logic and graphs. We have discovered that face and gait domains exhibit interesting similarity map- pings between object entities and their components. We have proposed intuitive probabilistic methods to model these mappings to perform recognition under vari- ous uncertainty elements. Extensive experimental validations justi es the robust- ness of the proposed methods over the state-of-the-art techniques.

GOAL-DTU: Development of Distributed Intelligence for the Multi-Agent Programming Contest

We provide a brief description of the GOAL-DTU system for the agent contest, including the overall strategy and how the system is designed to apply this strategy. Our agents are implemented using the GOAL programming language. We evaluate the performance of our agents for the contest, and finally also discuss how to improve the system based on analysis of its strengths and weaknesses.Comment: 28 pages, 45 figure