On quasi‐varieties of multiple valued logic models

We extend the concept of quasi‐variety of first‐order models from classical logic to multiple valued logic (MVL) and study the relationship between quasi‐varieties and existence of initial models in MVL. We define a concept of ‘Horn sentence’ in MVL and based upon our study of quasi‐varieties of MVL models we derive the existence of initial models for MVL ‘Horn theories’. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

CHILDREN'S PROPORTIONAL REASONING AND TENDENCY FOR AN ADDITIVE STRATEGY: THE ROLE OF MODELS

In this paper we report on 10 –14 year old children's strategies while solving two versions of ratio and proportion tasks: one ‘with models’ thought to facilitate proportional reasoning and one ‘without’. Rasch methodology was used to develop ‘with’ and ‘without models’ test versions which were given to a linked sample involving 673 children. We examine the pupils’ additive errors, their effect on ratio reasoning and how contingent on ‘model’ presentation this is. First, we provide a single scale on which pupils, item-difficulty and additive errors can be located. We then provide a new scale constructed from the error prone items, which we name the ‘tendency for additive strategy’. The measurement data is supported by qualitative data showing that the presence of ‘models’ can sometimes affect children's strategies, both positively and negatively but rarely makes a significant measurement difference on this, untutored, sample.     

Small worlds

Small world models are networks consisting of many local links and fewer long range ‘shortcuts’. In this paper, we consider some particular instances, and rigorously investigate the distribution of their inter‐point network distances. Our results are framed in terms of approximations, whose accuracy increases with the size of the network. We also give some insight into how the reduction in typical inter‐point distances occasioned by the presence of shortcuts is related to the dimension of the underlying space. © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 19, 54–74, 2001     

Multifractal analysis of foreign exchange data

In this paper we perform multifractal analyses of five daily Foreign Exchange (FX) rates. These techniques are currently used in turbulence to characterize scaling and intermittency. We show the multifractal nature of FX returns, and estimate the three parameters in the universal multifactal framework, which characterize all small and medium intensity fluctuations, at all scales. For large fluctuations, we address the question of hyperbolic (fat) tails of the distributions which are characterized by a fourth parameter, the tail index. We studied both the prices fluctuations and the returns, finding no systematic difference in the scaling exponents in the two cases. We discuss and compare our results with several recent studies, and show how the additive models are not compatible with data: Brownian, fractional Brownian, Lévy, Truncated Lévy and fractional Lévy models. We analyse in this framework the ARCH(1), GARCH(1,1) and HARCH (7) models, and show that their structure functions scaling exponents are undistinguishable from that of Brownian motion, which means that these models do not adequately describe the scaling properties of the statistics of the data. Our results indicate that there might exist a multiplicative ‘flux of financial information’, which conditions small‐scale statistics to large‐scale values, as an analogy with the energy flux in turbulence. Copyright © 1999 John Wiley & Sons, Ltd.     

Markov chain models for delinquency: Transition matrix estimation and forecasting

A Markov chain is a natural probability model for accounts receivable. For example, accounts that are ‘current’ this month have a probability of moving next month into ‘current’, ‘delinquent’ or ‘paid‐off’ states. If the transition matrix of the Markov chain were known, forecasts could be formed for future months for each state. This paper applies a Markov chain model to subprime loans that appear neither homogeneous nor stationary. Innovative estimation methods for the transition matrix are proposed. Bayes and empirical Bayes estimators are derived where the population is divided into segments or subpopulations whose transition matrices differ in some, but not all entries. Loan‐level models for key transition matrix entries can be constructed where loan‐level covariates capture the non‐stationarity of the transition matrix. Prediction is illustrated on a $7 billion portfolio of subprime fixed first mortgages and the forecasts show good agreement with actual balances in the delinquency states. Copyright © 2010 John Wiley & Sons, Ltd.     

Local maxima of solutions to some nonsymmetric reaction‐diffusion systems

In this study, we examine the solution profile of some reaction‐diffusion systems. The systems are derived after approximating the Arrhenius term in our system which models the sintering process and consists of two coupled equations in terms of two unknowns. The unknowns describe the temperature of the solid and the concentration of the fuel. We show the evolution over time of local temperature hot spots. The key idea is to use ‘microscopic scaling’ around the temperature hot spot at the initial time along with asymptotic analysis. We also provide some numerical results that support the efficiency of our analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

An analysis of the fourth‐order PDEs – ‘patterns’ and ‘di‐block polymers’

We analyze some fourth‐order partial differential equations that model the ‘propagation of hexagonal patterns’ and the ‘microphase separation of di‐block copolymers’. The underlying invariance properties and conservation laws of the models and related partial differential equations are studied. Copyright © 2017 John Wiley & Sons, Ltd.     

On Dynamic Generalized Linear Models with Applications

In this paper we combine the idea of ‘power steady model’, ‘discount factor’ and ‘power prior’, for a general class of filter model, more specifically within a class of dynamic generalized linear models (DGLM). We show an optimality property for our proposed method and present the particle filter algorithm for DGLM as an alternative to Markov chain Monte Carlo method. We also present two applications; one on dynamic Poisson models for hurricane count data in Atlantic ocean and the another on the dynamic Poisson regression model for longitudinal count data.     

Extended utility and DEA models without explicit input

In this paper, we discuss the relationship between multi-attribute utility theory and data envelopment analysis (DEA) models without explicit inputs (DEA-WEI), including dual models and some theoretical analysis of DEA-WEI models. We then propose generic DEA-WEI models with quadratic utility terms. Finally, we provide illustrative examples to show that DEA-WEI with suitable quadratic utility terms are able to reflect some value judgments that the standard DEA models cannot.     

A Simple Approach for Multi‐fidelity Experimentation Applied to Financial Engineering

In practical applications, information about the accuracy or ‘fidelity’ of alternative surrogate systems may be ambiguous and difficult to determine. To address this problem, we propose to treat surrogate system fidelity level as a categorical factor in optimal response surface design. To design the associated experiments, we apply the Expected Integrated Mean Squared Error optimal design criterion, which takes into account both variance and bias errors. The performance of the proposed design was compared using three test cases to four types of alternatives using the Empirical Integrated Squared Error. Because of its ability to foster relatively accurate predictions, the proposed design is recommended in fidelity experimental design, particularly when the experimenters lack sufficient information about the fidelity levels of surrogate systems. The method was applied to the case of intraday trading optimization in which data were collected from the Taiwan Futures Exchange. We also calculated the implied volatility from the Merton's Jump‐diffusion model via the fast Fourier transform algorithm with three different models of varying fidelity levels. Copyright © 2014 John Wiley & Sons, Ltd.     

Data mining feature selection for credit scoring models

The features used may have an important effect on the performance of credit scoring models. The process of choosing the best set of features for credit scoring models is usually unsystematic and dominated by somewhat arbitrary trial. This paper presents an empirical study of four machine learning feature selection methods. These methods provide an automatic data mining technique for reducing the feature space. The study illustrates how four feature selection methods—‘ReliefF’, ‘Correlation-based’, ‘Consistency-based’ and ‘Wrapper’ algorithms help to improve three aspects of the performance of scoring models: model simplicity, model speed and model accuracy. The experiments are conducted on real data sets using four classification algorithms—‘model tree (M5)’, ‘neural network (multi-layer perceptron with back-propagation)’, ‘logistic regression’, and ‘k-nearest-neighbours’.     

Strong negation in intuitionistic style sequent systems for residuated lattices

We study the sequent system mentioned in the author's work 18 as CyInFL with ‘intuitionistic’ sequents. We explore the connection between this system and symmetric constructive logic of Zaslavsky 40 and develop an algebraic semantics for both of them. In contrast to the previous work, we prove the strong completeness theorem for CyInFL with ‘intuitionistic’ sequents and all of its basic variants, including variants with contraction. We also show how the defined classes of structures are related to cyclic involutive FL‐algebras and Nelson FL_ew‐algebras. In particular, we prove the definitional equivalence of symmetric constructive FL_ewc‐algebras (algebraic models of symmetric constructive logic) and Nelson FL_ew‐algebras (algebras introduced by Spinks and Veroff 33 , 34 as the termwise equivalent definition of Nelson algebras). Because of the strong completeness theorem that covers all basic variants of CyInFL with ‘intuitionistic’ sequents, we rename this sequent system to symmetric constructive full Lambek calculus (). We verify the decidability of this system and its basic variants, as we did in the case of their distributive cousins 18 . As a consequence we obtain that the corresponding theories of (distributive and nondistributive) symmetric constructive FL‐algebras are decidable.     

Interactive markovian models of ‘progressive’ trends

Non‐linear Markovian models are investigated for a developing society stratified in terms of literacy or some other sociocultural attribute and characterized by two opposing features: a) progressive trends which forbid upper to lower state intergeneration transitions, and b) fertility differential in favour of lower states. The progressive trends in the models arise due to ‘attraction’ of the higher states. Two different limits are considered: one in which all upward transitions are permitted (Maximal Attractor Model) and the other in which only one‐step transitions are allowed (Adjacent Attractor Model). The nature of the critical points of the two models is examined analytically and/or numerically as appropriate to the case in question. In the first model, the society converges to the highest state in due course despite the fertility differential. The three‐state and four‐state cases of the models are considered in some detail. The main interesting result concerns the Adjacent Attractor Model. For the three‐state case, numerical computation reveals this model society locked in an endless cyclic pattern of evolution despite the existence of a progressive trend.     

Factors shaping mathematics lecturers’ service teaching in different departments

In this article we focus on university lecturers’ approaches to the service teaching and factors that influence their approaches. We present data obtained from the interviews with 19 mathematics and three physics lecturers along with the observations of two mathematics lecturers’ calculus courses. The findings show that lecturers’ approaches to teaching the same topic vary across departments; that is, they consciously privilege different aspects of mathematics, set different questions on examinations and follow different textbooks while teaching in different departments. We discuss factors influencing lecturers’ decision of what (mathematics) to teach in different departments and offer educational implications for service mathematics teaching in terms of students’ mathematical needs and the role of mathematics for client students.     

Direct versus indirect credit scoring classifications

We introduce a new approach to assigning bank account holders to ‘good’ or ‘bad’ classes based on their future behaviour. Traditional methods simply treat the classes as qualitatively distinct, and seek to predict them directly, using statistical techniques such as logistic regression or discriminant analysis based on application data or observations of previous behaviour. We note, however, that the ‘good’ and ‘bad’ classes are defined in terms of variables such as the amount overdrawn at the time at which the classification is required. This permits an alternative, ‘indirect’, form of classification model in which, first, the variables defining the classes are predicted, for example using regression, and then the class membership is derived deterministically from these predicted values. We compare traditional direct methods with these new indirect methods using both real bank data and simulated data. The new methods appear to perform very similarly to the traditional methods, and we discuss why this might be. Finally, we note that the indirect methods also have certain other advantages over the traditional direct methods.     

A combinatorial theory of minimal social situations

A minimal social situation is a game‐like situation in which there are two actors, each of them has two possible actions, and both evaluate the outcomes of their joint actions in terms of two categories (say, ‘success’ and ‘failure'). By fixing actors and actions and varying ‘payoffs’ the set of 256 ‘configurations’ is obtained. This set decomposes into 43 ‘structural forms’, or equivalence classes with respect to the relation of isomorphism defined on it. This main theorem and other results concerning related configurations (minimal decision situations) are derived in this paper by means of certain tools of group theory. Some extensions to larger structures are proved in the Appendix. In the introductory section after a brief explanation of the meaning given to the terms ‘structure’ and ‘isomorphism’ in mathematics (Bourbaki) it is shown how these terms can be used to formalize the concept of ‘social form’.     

Real estate price estimation in French cities using geocoding and machine learning

This paper reviews real estate price estimation in France, a market that has received little attention. We compare seven popular machine learning techniques by proposing a different approach that quantifies the relevance of location features in real estate price estimation with high and fine levels of granularity. We take advantage of a newly available open dataset provided by the French government that contains 5 years of historical data of real estate transactions. At a high level of granularity, we obtain important differences regarding the models’ prediction powers between cities with medium and high standards of living (precision differences beyond 70% in some cases). At a low level of granularity, we use geocoding to add precise geographical location features to the machine learning algorithm inputs. We obtain important improvements regarding the models’ forecasting powers relative to models trained without these features (improvements beyond 50% for some forecasting error measures). Our results also reveal that neural networks and random forest techniques particularly outperform other methods when geocoding features are not accounted for, while random forest, adaboost and gradient boosting perform well when geocoding features are considered. For identifying opportunities in the real estate market through real estate price prediction, our results can be of particular interest. They can also serve as a basis for price assessment in revenue management for durable and non-replenishable products such as real estate.

     

Measuring ecological efficiency with data envelopment analysis (DEA)

The measurement of ecological efficiency provides some important information for the companies’ environmental management. Ecological efficiency is usually measured by comparing environmental performance indicators. Data envelopment analysis (DEA) shows a high potential to support such comparisons, as no explicit weights are needed to aggregate the indicators. In general, DEA assumes that inputs and outputs are ‘goods’, but from an ecological perspective also ‘bads’ have to be considered. In the literature, ‘bads’ are treated in different and sometimes arbitrarily chosen ways. This article aims at the systematic derivation of ecologically extended DEA models. Starting from the assumptions of DEA in production theory and activity analysis, a generalisation of basic DEA models is derived by incorporating a multi-dimensional value function f. Extended preference structures can be considered by different specifications of f, e.g. specifications for ecologically motivated applications of DEA.     

The Logic of Analogy

How should a scientist argue when the data are insufficient to allow him to reason by classical or statistical models? After all, in most real world situations - in business or in war - that is the unhappy norm. In such cases the ordinary man instinctively argues by analogy, as Leibniz long ago showed; indeed if time presses, there is no alternative. The trouble, however, is that if we then include such arguments in our scientific reasoning, then, as we all know, this can lead to false conclusions. To escape from this dilemma, is there any alternative logical basis from which we can start our reasoning? What is proposed here is that instead of the well tried three valued logic of true, false or probable, we should adopt the three valued logic of true, false or possible. A rational system for analogue arguments can then be developed by these means, and with it the advantages brought by the use of symbols and so on. Such a method, however, includes many necessary changes as to how to structure our problems and how to apply new criteria; and it is some of these changes that are outlined in this note. For instance, it outlines the meaning of ‘causal relationships’ in analogue arguments, as well as how to define ‘rational choice’ in terms of analogue propositions. The advantage throughout is that this allows us to argue with less rather than more data.