Formal Modeling of Connectionism using Concurrency Theory, an Approach Based on Automata and Model Checking

This paper illustrates a framework for applying formal methods techniques, which are symbolic in nature, to specifying and verifying neural networks, which are sub-symbolic in nature. The paper describes a communicating automata [Bowman & Gomez, 2006] model of neural networks. We also implement the model using timed automata [Alur & Dill, 1994] and then undertake a verification of these models using the model checker Uppaal [Pettersson, 2000] in order to evaluate the performance of learning algorithms. This paper also presents discussion of a number of broad issues concerning cognitive neuroscience and the debate as to whether symbolic processing or connectionism is a suitable representation of cognitive systems. Additionally, the issue of integrating symbolic techniques, such as formal methods, with complex neural networks is discussed. We then argue that symbolic verifications may give theoretically well-founded ways to evaluate and justify neural learning systems in the field of both theoretical research and real world applications

Comparing knowledge sources for nominal anaphora resolution

We compare two ways of obtaining lexical knowledge for antecedent selection in other-anaphora and definite noun phrase coreference. Specifically, we compare an algorithm that relies on links encoded in the manually created lexical hierarchy WordNet and an algorithm that mines corpora by means of shallow lexico-semantic patterns. As corpora we use the British National Corpus (BNC), as well as the Web, which has not been previously used for this task. Our results show that (a) the knowledge encoded in WordNet is often insufficient, especially for anaphor-antecedent relations that exploit subjective or context-dependent knowledge; (b) for other-anaphora, the Web-based method outperforms the WordNet-based method; (c) for definite NP coreference, the Web-based method yields results comparable to those obtained using WordNet over the whole dataset and outperforms the WordNet-based method on subsets of the dataset; (d) in both case studies, the BNC-based method is worse than the other methods because of data sparseness. Thus, in our studies, the Web-based method alleviated the lexical knowledge gap often encountered in anaphora resolution, and handled examples with context-dependent relations between anaphor and antecedent. Because it is inexpensive and needs no hand-modelling of lexical knowledge, it is a promising knowledge source to integrate in anaphora resolution systems

Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which uni¯es the qualita- tive, stochastic and continuous paradigms. Each perspective adds its con- tribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how quali- tative descriptions are abstractions over stochastic or continuous descrip- tions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks