The following list of projects represents some topical ideas for applications of Empirical Modelling (EM). It is complementary to the list of project ideas that is given on the Empirical Modelling web page which should also be consulted for further background about EM and how project work in EM is typically organised and supervised. In many cases, there is scope for worthwhile projects on the specified topic that range in difficulty from modest to exceptionally challenging. A distinctive feature of EM is the way in which the precise scope, emphasis and direction of the project can be shaped as the model-building activity develops. Several of these projects, if successfully accomplished, could be the platform for a subsequent MSc-by-research.
In 1702, Leeuwenhoek - a Dutch pioneer in the use of the optical microsocope - observed what appeared to be rotating discs in small aquatic organisms. In 1831, Faraday constructed a physical model to reproduce Leeuwenhoek's observation, thus showing these 'rotating discs' to be an optical illusion. The aim of this project is to investigate how EM can be used to construct models such as Faraday's using the computer, and to look more generally at how EM can be used for empirical studies of human perception. Possible topics include: modelling of traditional optical illusions, experiments with colour, and analysis of keyboard skills.
Several recent projects have led to the development of models that relate to music. In all these projects, the manner in which sound has been generated has been somewhat ad hoc, and many different styles of representation and interface have been used. For instance, some projects have made use of sound samples that are directly accessed by the EDEN interpreter, others have exploited the tk/tcl feature for playing .wav files, some have made use of a commercial synthesiser and interfacing software. The aim of this project is to investigate ways in which the capacity for EDEN to handle sound and music can be enhanced through developing new functionality, new interfaces or new interfaces.
The task of analysing a literary text to identify features is one that lends itself to empirical study. Dr Willard McCarty, at KCL London, has been applying computer analysis to the text of Ovid's Metamorphoses (a classic Latin text). He has been using Excel in conjunction with an Access database to make a model of the text from which he can infer where features such as 'personification' occur. The purpose of this project would be to review McCarty's research and explore the extent to which EM techniques and tools might be able to emulate and hopefully (in some respects) complement or extend modelling based on Excel and Access. This might involve the development of new notations for handling text in tkeden.
The HyperFun geometric modelling language has been developed by Pasko, Adzhiev (NCCA, Bournemouth) and others [see www.hyperfun.org - NB not .com, which refers to quite another kind of fun]. HyperFun is a solid modeller based on function representation that has much greater expressive power than a traditional CSG modeller. A variant of HyperFun, called Empirical HyperFun, that incorporates some EM features, has been developed by Richard Cartwright. It would be of interest to explore ways in which HyperFun / Empirical HyperFun could be implemented in tkeden using the new parser generator, and perhaps developed for use in conjunction with Sasami.
As is illustrated by the demonstration models that were developed for the CS324 Computer Graphics module by Abhir Bhalerao prior to 2006 and by myself in 2006-7 (see the CS324 webpages for 2006-7), there is rich scope for interesting educational aids for graphics. Models can be used to animate algorithms, for instance, or to create interactive environments in which it is possible to study concepts and situations through experiment. There is rich scope for developing new models to support graphics education, and potential advantages in some aspects in the application of Empirical Modelling principles through modelling with dependency. There is potential here for model-building using a number of different approaches, possibly with a comparative study in mind. There may also be scope for working in collaboration with Dr Silvester Czanner of the Warwick Digital Laboratory, who is also developing resources to support computer graphics teaching.
One of the most successful Empirical Modelling projects has involved modelling railway operation as it was in the vicinity of the Clayton Tunnel in 1861, when a historic accident occurred. Apart from the Clayton Tunnel, numerous other railway accident scenarios have been studied from an EM perspective as examples of complex and unusual agent interaction. Several of these would provide interesting case-studies for model-building in a similar style to that illustrated in the Clayton Tunnel model. Specific details of target scenarios, for which the modelling challenges range in level of difficulty from modest to extreme, can be obtained from WMB. An accident that occurred at Abermule in mid-Wales in 1926 presents a particularly challenging exercise in modelling intelligent agent interaction, in which the interplay between the knowledge and perceptions of several human actors is particularly subtle.
The dtkeden environment is a distributed modelling tool that has been applied in a variety of applications. It allows communication between a server and clients in a variety of different modes that reflect different perspectives from which a concurrent system can be viewed. The documentation of dtkeden still leaves a lot to be desired however, and this (coupled with the time and inconvenience involved in setting up and testing distributed models) makes it difficult to confirm that its behaviour conforms to its specification. This project would be aimed at consolidating our understanding of dtkeden and improving its usability. For instance, it would be useful to provide exemplars for each of the different modes of interaction in dtkeden, and to ensure that these are fully documented and illustrated. Issues such as the potential for changing modes of interaction might also be explored. Better documentation and fuller exploration of existing distributed models might also be undertaken. Finally, if it proved practical within the scope of the project, improvements to the dtkeden tool might be ventured.
Monotone boolean functions (MBFs) are defined by propositional formulae that use only 'and' and 'or'. There is a strong connection between such MBFs and the study of finite distributive lattices (of which the subsets of a finite set ordered by inclusion are simple but atypical examples). MBFs in N variables when ordered by implication define the free distributive lattice on N generators FDL(N). The lattice FDL(4), has 168 elements - it was first drawn by John Buckle, a research student here at Warwick, about 15 years ago. An alternative representation for such MBFs is given by the integer valued mappings from permutations of {1,2,3,4} into the set {1,2,3,4} that can be characterised as combinatorially piecewise-linear maps. The aim of this project would be to construct a comprehensive set of models to illustrate the connection between these different representations for MBFs for N=4, and to test a conjecture that could be helpful in understanding the complexity of such functions. It would also give scope for further investigation of related combinatorial structures that are as yet relatively little explored.
Geometric models of regular and semi-regular solids were constructed using Sasami by Helen Birch in her final year project 2000-1. It would be good to complement these models with Cayley diagrams to represent the associated symmetry groups of these solids, and (amongst other things) to create the appropriate dependencies between elements of the symmetry group and configurations of the solids. There are some interesting possibilities here for teaching materials that could be applied at a school mathematics level (e.g. illustrating features of the classification of regular solids, and recreational mathematics associated with them), in university mathematics (as an introduction to elementary group theory and generators and relations) and in graphics and geometric transformations (matrix algebra). This project can draw on several existing EM models, and has rich potential for extension in many directions.
The aim of this project is to consolidate upon several possible extensions of the EDEN environment that have been developed by research students over recent years. The focus of such an extension might be on giving richer support to model-building or to the analysis, documentation and evaluation of models.
By way of illustration, a Dependency Modelling Tool (DMT) was developed by Allan Wong for displaying definitive scripts as combinatorial graphs. Each node of the graph represents an observable, and each edge a dependency associated with that observable. The DMT is written in Java, and can process Eden definitions. It has some automatic layout features, but direct involvement of the user in the graph layout turns out to be one of the most useful modes of application in practice. At present, processing an Eden script or script fragment using Wong's DMT involves exporting it to a file and importing this to the DMT.
One objective, partially addressed by a simple prototype developed by Antony Harfield, would be to create a DMT tool that is fully integrated within the EDEN environment. It is possible that such a tool could use DoNaLD in its underlying representation, thereby creating new potential for referencing groups of definitions, and possibly laying them out dynamically. This might also lead to editing tools that allow subscripts to be extracted for independent experiment and/or re-use. Such a tool could build on prototype extensions of EDEN that include: an EDDI table representation of the Eden symboltable such as has been partially developed by J-P Dupont, Karl King's Virtual Symbol Table and Antony Harfield's presentation environment.
The development of the SQL-EDDI environment is one example of how it has proved possible to create special-purpose software to support an undergraduate module. A challenging project would explore the possibility of developing an environment based on similar principles that could assist the study of concurrent processes. A research objective here would be to try to use the concurrency model that is implicit in a definitive script (whereby certain groups of definitions can be update in parallel without interference, and all update by dependency maintenance is viewed as synchronised) to give support for models of CCS and CSP. There are many simpler variants of such a project (such as building tools to interpret or give visual support for use CCS or CSP alone) that might be sufficient for a third-year project.
Previous work has led to the development of models that were effectively used for timetabling in real application in connection with the scheduling of third-year oral presentations some years ago. The aim of this project is to revisit the timetabling theme exploiting new features of EDEN (such as the introduction of the GEL notation and the AOP) that can be used to improve the interface to timetabling models. Re-engineering the original Temposcope model is one possible theme, but alternative scheduling applications may also be usefully investigated.