Applying multi-criteria optimisation to develop cognitive models

A scientific theory is developed by modelling empirical data in a range of domains. The goal of developing a theory is to optimise the fit of the theory to as many experimental settings as possible, whilst retaining some qualitative properties such as `parsimony' or `comprehensibility'. We formalise the task of developing theories of human cognition as a problem in multi-criteria optimisation. There are many challenges in this task, including the representation of competing theories, coordinating the fit with multiple experiments, and bringing together competing results to provide suitable theories. Experiments demonstrate the development of a theory of categorisation, using multiple optimisation criteria in genetic algorithms to locate pareto-optimal sets

Ecosystem-Oriented Distributed Evolutionary Computing

We create a novel optimisation technique inspired by natural ecosystems, where the optimisation works at two levels: a first optimisation, migration of genes which are distributed in a peer-to-peer network, operating continuously in time; this process feeds a second optimisation based on evolutionary computing that operates locally on single peers and is aimed at finding solutions to satisfy locally relevant constraints. We consider from the domain of computer science distributed evolutionary computing, with the relevant theory from the domain of theoretical biology, including the fields of evolutionary and ecological theory, the topological structure of ecosystems, and evolutionary processes within distributed environments. We then define ecosystem- oriented distributed evolutionary computing, imbibed with the properties of self-organisation, scalability and sustainability from natural ecosystems, including a novel form of distributed evolu- tionary computing. Finally, we conclude with a discussion of the apparent compromises resulting from the hybrid model created, such as the network topology.Comment: 8 pages, 5 figures. arXiv admin note: text overlap with arXiv:1112.0204, arXiv:0712.4159, arXiv:0712.4153, arXiv:0712.4102, arXiv:0910.067

Idempotent structures in optimization

Consider the set A = R ∪ {+∞} with the binary operations o1 = max and o2 = + and denote by An the set of vectors v = (v1,...,vn) with entries in A. Let the generalised sum u o1 v of two vectors denote the vector with entries uj o1 vj , and the product a o2 v of an element a ∈ A and a vector v ∈ An denote the vector with the entries a o2 vj . With these operations, the set An provides the simplest example of an idempotent semimodule. The study of idempotent semimodules and their morphisms is the subject of idempotent linear algebra, which has been developing for about 40 years already as a useful tool in a number of problems of discrete optimisation. Idempotent analysis studies infinite dimensional idempotent semimodules and is aimed at the applications to the optimisations problems with general (not necessarily finite) state spaces. We review here the main facts of idempotent analysis and its major areas of applications in optimisation theory, namely in multicriteria optimisation, in turnpike theory and mathematical economics, in the theory of generalised solutions of the Hamilton-Jacobi Bellman (HJB) equation, in the theory of games and controlled Marcov processes, in financial mathematics

State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners

Applications of Finite Model Theory: Optimisation Problems, Hybrid Modal Logics and Games.

There exists an interesting relationships between two seemingly distinct fields: logic from the field of Model Theory, which deals with the truth of statements about discrete structures; and Computational Complexity, which deals with the classification of problems by how much of a particular computer resource is required in order to compute a solution. This relationship is known as Descriptive Complexity and it is the primary application of the tools from Model Theory when they are restricted to the finite; this restriction is commonly called Finite Model Theory. In this thesis, we investigate the extension of the results of Descriptive Complexity from classes of decision problems to classes of optimisation problems. When dealing with decision problems the natural mapping from true and false in logic to yes and no instances of a problem is used but when dealing with optimisation problems, other features of a logic need to be used. We investigate what these features are and provide results in the form of logical frameworks that can be used for describing optimisation problems in particular classes, building on the existing research into this area. Another application of Finite Model Theory that this thesis investigates is the relative expressiveness of various fragments of an extension of modal logic called hybrid modal logic. This is achieved through taking the Ehrenfeucht-Fraïssé game from Model Theory and modifying it so that it can be applied to hybrid modal logic. Then, by developing winning strategies for the players in the game, results are obtained that show strict hierarchies of expressiveness for fragments of hybrid modal logic that are generated by varying the quantifier depth and the number of proposition and nominal symbols available

Some of the Unanswered Questions in Finance

A very dynamic development of finance in the last 50 years is inter alia probably due to experiments and innovations in this field. Previously, theoretical base could not explain and predict movements especially in volatile times. The new finance appeared 50 years ago (portfolio theory, CAPM, the efficient market theory, M&M theorem) and made substantial progress in understanding movements in globalised and internationalised financial markets. However, many questions remain open. The author tries to put emphasis on some of these questions, perfectly aware that these are not the only ones. Unresolved questions are related to company's aims, project's risks, degree of port-folio optimisation, importance of liquidity, dividend policy, as well as factors that deter-mine M&A. As the new finance is not able to predict and explain volatile movements, a question that should be posed is whether it is appropriate to add some non-economic factors as the behaviourist theory suggests. Although the behaviourist theory is an important part of new finance, it is unfortunately the only theory able to explain movements in volatile times. In conclusion, many questions still remain unanswered and wait for appropriate theoretical explanations.New Finance, Operational leverage, Risk, Portfolio optimisation, Rating agencies, Efficient market hypothesis, Quality of liquidity, Behaviorist theory

Structure determination from powder data : Mogul and CASTEP

When solving the crystal structure of complex molecules from powder data, accurately locating the global minimum can be challenging, particularly where the number of internal degrees of freedom is large. The program Mogul provides a convenient means to access typical torsion angle ranges for fragments related to the molecule of interest. The impact that the application of modal torsion angle constraints has on the structure determination process of two structure solution attempts using DASH is presented. Once solved, accurate refinement of a molecular structure against powder data can also present challenges. Geometry optimisation using density functional theory in CASTEP is shown to be an effective means to locate hydrogen atom positions reliably and return a more accurate description of molecular conformation and intermolecular interactions than global optimisation and Rietveld refinement alone

Financial Applications of Random Matrix Theory: a short review

We discuss the applications of Random Matrix Theory in the context of financial markets and econometric models, a topic about which a considerable number of papers have been devoted to in the last decade. This mini-review is intended to guide the reader through various theoretical results (the Marcenko-Pastur spectrum and its various generalisations, random SVD, free matrices, largest eigenvalue statistics, etc.) as well as some concrete applications to portfolio optimisation and out-of-sample risk estimation.Comment: To appear in the "Handbook on Random Matrix Theory", Oxford University Pres

Recent developments in the tmLQCD software suite

We present an overview of recent developments in the tmLQCD software suite. We summarise the features of the code, including actions and operators implemented. In particular, we discuss the optimisation efforts for modern architectures using the Blue Gene/Q system as an example.Comment: presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German