Search

This paper is concerned with the linear delayed forward–backward stochastic differential equations (D-FBSDEs). The existence of time delay leads to the infinite-dimensional problem which makes the explicit solvability more challenging. The main contribution is to propose a discretisation approach which gives the explicit solution of the D-FBSDEs and consists of the following three steps: first, we transform the continuous-time D-FBSDEs into the discrete-time form with the aid of interval partition. Second, we derive the solution of the discrete-time D-FBSDEs by applying backward iterative induction. Finally the explicit solution of the continuous-time D-FBSDEs is obtained by taking the limit to the solution of discrete-time form which is also strictly proved under continuous-time framework. The proposed approach is applicable for more general FBSDEs with delay, which would provide a complete solution to the stochastic LQ control with time delay. [ABSTRACT FROM AUTHOR]

Volcanic regions can be characterised by different unrest phenomena and secondary volcanism. Several studies link these phenomena to both magma and hydrothermal fluids. For instance, in the case of the widely studied Campi Flegrei caldera, recent literature suggests that thermo-poro-elastic (TPE) inclusion models are suitable to describe both the observed deformation and seismicity that often accompany its unrest episodes. Some recent works propose analytical solutions to model the case of a thin disc-shaped inclusion, i.e. with a thickness much smaller than its radius. As this restriction may be critical, TPE inclusion models were subsequently extended to cylindrical-shaped inclusions, with an arbitrary thickness, by representing them as a superposition of several thin disc-shaped inclusions (elements). In this paper, we demonstrate how to estimate the minimum number of elements to represent both displacement and stress fields caused by cylindrical TPE inclusions with an arbitrary aspect-ratio (thickness over radius). For aspect ratios greater than 0.3, a single element model will no longer prove suitable to represent both displacement and stress with a good accuracy. [ABSTRACT FROM AUTHOR]

Supervised discretisation is widely considered as far more advantageous than unsupervised transformation of attributes, because it helps to preserve the informative content of a variable, which is useful in classification. After discretisation, based on employed criteria, some attributes can be found irrelevant, and all their values can be represented in a discrete domain by a single interval. In consequence, such attributes are removed from considerations, and no knowledge is mined from them. The paper presents research focused on extended transformations of attribute values, thus combining supervised with unsupervised discretisation strategies. For all variables with single intervals returned from supervised algorithms, the ranges of values were transformed by unsupervised methods with varying numbers of bins. Resulting variants of the data were subjected to selected data mining techniques, and the performance of a group of classifiers was evaluated and compared. The experiments were performed on a stylometric task of authorship attribution. [ABSTRACT FROM AUTHOR]

The nature of the input features is one of the key factors indicating what kind of tools, methods, or approaches can be used in a knowledge discovery process. Depending on the characteristics of the available attributes, some techniques could lead to unsatisfactory performance or even may not proceed at all without additional preprocessing steps. The types of variables and their domains affect performance. Any changes to their form can influence it as well, or even enable some learners. On the other hand, the relevance of features for a task constitutes another element with a noticeable impact on data exploration. The importance of attributes can be estimated through the application of mechanisms belonging to the feature selection and reduction area, such as rankings. In the described research framework, the data form was conditioned on relevance by the proposed procedure of gradual discretisation controlled by a ranking of attributes. Supervised and unsupervised discretisation methods were employed to the datasets from the stylometric domain and the task of binary authorship attribution. For the selected classifiers, extensive tests were performed and they indicated many cases of enhanced prediction for partially discretised datasets. [ABSTRACT FROM AUTHOR]

Traditional claim estimation in general insurance works with accident year cohorts and development patterns. For the impending International Financial Reporting Standard (IFRS) 17 Insurance Contracts and often for reinsurance purposes, claim estimates must be split by contract year. This paper proposes to add contract year as a cohort classifier and to adjust the development patterns accordingly. To this end, we use the continuous time models of Hesselager and Norberg. Having contract year as an additional cohort classifier, display of claim estimates by contract year and/or accident year becomes a simple matter of summation across the appropriate dimensions. The continuous time model also enables us to derive mutually consistent development patterns for discrete time intervals of different length, such as years and quarters. In addition to delivering consistent development patterns in discrete time, continuous time modelling offers the advantage of requiring only a fixed number of model parameters. Although most of the derivations in this paper are explained in terms of claim numbers, the mechanics can also be applied to claim payments. [ABSTRACT FROM AUTHOR]

Supervised discretisation is widely considered as far more advantageous than unsupervised transformation of attributes, because it helps to preserve the informative content of a variable, which is useful in classification. After discretisation, based on employed criteria, some attributes can be found irrelevant, and all their values can be represented in a discrete domain by a single interval. In consequence, such attributes are removed from considerations, and no knowledge is mined from them. The paper presents research focused on extended transformations of attribute values, thus combining supervised with unsupervised discretisation strategies. For all variables with single intervals returned from supervised algorithms, the ranges of values were transformed by unsupervised methods with varying numbers of bins. Resulting variants of the data were subjected to selected data mining techniques, and the performance of a group of classifiers was evaluated and compared. The experiments were performed on a stylometric task of authorship attribution.

Decision reducts and rules belong to forms used for the representation of knowledge learnt from input data while using a rough set approach in the exploration stage. As with any patterns that capture properties of data, the size is considered as the most important indicator of their quality, as a more general and concise description allows for improved understanding and simplified interpretation. The size of a reduct is given by its cardinality, and for a rule it is a number of included conditions, both referred to as lengths. These lengths undergo transformations along with data transformations, so such processing as discretisation leads to changed characteristics of existing patterns and through them also reducts and rules. The paper presents research with contributions in the observations focused on the influence of supervised and unsupervised discretisation on properties of attributes, induced decision reducts, and rules, offering a deeper insight into relations among them. [ABSTRACT FROM AUTHOR]

Control-based continuation (CBC) is an experimental method that can reveal stable and unstable dynamics of physical systems. It extends the path-following principles of numerical continuation to experiments and provides systematic dynamical analyses without the need for mathematical modelling. CBC has seen considerable success in studying the bifurcation structure of mechanical systems. Nevertheless, the method is not practical for studying relaxation oscillations. Large numbers of Fourier modes are required to describe them, and the length of the experiment significantly increases when many Fourier modes are used, as the system must be run to convergence many times. Furthermore, relaxation oscillations often arise in autonomous systems, for which an appropriate phase constraint is required. To overcome these challenges, we introduce an adaptive B-spline discretisation that can produce a parsimonious description of responses that would otherwise require many Fourier modes. We couple this to a novel phase constraint that phase-locks control target and solution phase. Results are demonstrated on simulations of a slow-fast synthetic gene network and an Oregonator model. Our methods extend CBC to a much broader range of systems than have been studied so far, opening up a range of novel experimental opportunities on slow-fast systems. [ABSTRACT FROM AUTHOR]

Summary: Permutation entropy (PE) is an ordinal‐based non‐parametric complexity measure for studying the temporal dependence structure in a linear or non‐linear time series. Based on the PE, we propose a new measure, namely permutation dependence (PD), to quantify the strength of the temporal dependence in a univariate time series and remedy the major drawbacks of PE. We demonstrate that the PE and PD are viable and useful alternatives to conventional temporal dependence measures, such as the autocorrelation function (ACF) and mutual information (MI). Compared to the ACF, the PE and PD are not restricted in detecting the linear or quasi‐linear serial correlation in an autoregression model. Instead, they can be viewed as non‐parametric and non‐linear alternatives since they do not require any prior knowledge or assumptions about the underlying structure. Compared to MI estimated by k‐nearest neighbour, PE and PD show added sensitivity to structures of relatively weak strength. We compare the finite‐sample performance of the PE and PD with the ACF and the MI estimated by k‐nearest neighbour in a number of simulation studies to showcase their respective strengths and weaknesses. Moreover, their performance under non‐stationarity is also investigated. Using high‐frequency EUR/USD exchange rate returns data, we apply the PE and PD to study the temporal dependence structure in intraday foreign exchange. [ABSTRACT FROM AUTHOR]

Mortality levels vary by benefit amount, and a common simplification is to group by non-overlapping ranges of varying widths. However, this ignores the continuous nature of benefit amounts and leads to discretisation error, i.e. heterogeneity within benefit ranges and step jumps at range boundaries. Another drawback of discretisation is that fitted parameters are not easily extrapolated to values outside the range of the experience data. To address these shortcomings it is often better to model mortality continuously by benefit amount. In this paper we present a method of modelling mortality levels continuously by a financial covariate such as pension size. We split the task into (i) a transform function to address the presence of extreme benefit amounts in actuarial data sets, and (ii) a response function to model mortality. Using as few as two parameters, the method avoids discretisation error and extrapolates to amounts outside the range covered by the calibrating data set. We illustrate the method by applying it to seven international data sets of pensioners and annuitants. [ABSTRACT FROM AUTHOR]

TRNSYS is a standard tool recently used to model and simulate greenhouse energy demand and utilisation using building energy simulation (BES). Previously, a single thermal point was used for validation, ignoring the distribution of greenhouse climate parameters, especially the temperature. Temperature variation often leads to thermal stratification, prompting researchers to propose volume discretisation in dynamic greenhouse simulations. In this context, the effect of envelope characterisation on the accuracy of the discretised TRNSYS BES model was developed to determine the best BES model under a free-floating regime. The combination of the number of layers [double (D) and single (S)], geometry mode [3D and manual (M)], and layer type [massless (M) and no glazing window (W)], led to the development of five models: D_3D_M, D_3D_W, D_M_M, S_3D_W, and S_M_M. The simulation was performed in a standard radiation mode, and the output parameters were temperature and relative humidity (RH). R2 and the root square mean error (RSME) were used to check the fitness and degree of deviation, respectively, to validate the models. Analysis of variance (ANOVA) was employed to investigate the significant differences among the models, whereas contour plots were used to compare the distribution pattern between the significant models and experimental data. Validation of the models showed that the obtained R2 values ranged from 0.86 to 0.95, and the RSME values for the temperature were between 2.64°C and 3.91°C. These values were 0.91-0.93 and 19.72%-30.32% for RH. The ANOVA (P<0.05) result exhibited significant differences between the S-scenario models and experimental central points in temperature and RH. However, the D- and S-layer scenarios with a 3D geometry and massless layer showed similar distribution with their corresponding experimental greenhouses. Hence, 3D_M was regarded as the best combination in the discretised BES model. [ABSTRACT FROM AUTHOR]

This study proposed a generalised and concise model consisting of spring-slider elements to characterise the nonlinear bending moment-rotation relationship of semi-rigid steel beam-to-column joints. First, the density function of the constitutive model was constructed based on the rotational characteristics of the joints. Second, the mathematical expression for the moment-rotation relationship of the constitutive model was derived. A method was developed to identify the parameters. Finally, after a discretisation method of the model was derived based on the strategy of evenly divided stiffness, the discrete model was applied to the numerical simulation of the rotation of the semi-rigid steel beam-to-column joints. It is observed that the proposed model accurately describes the rotation behaviour of semi-rigid connections in the entire rotation domain while reducing the degrees of freedom of the contact interfaces to improve the computing efficiency. There are six parameters in the model with a clear physical definition, which can be directly identified through macroscopic experiments. A high level of accuracy can be achieved by numerically calculating a discrete model using only five Jenkins elements. • A constitutive model for in-plane rotation behaviour of a semi-rigid joint is proposed. • Parameter identification procedures of the model are provided. • The discretization strategy based on the stiffness equation of the proposed model is derived. • The model is embedded in the finite element software for numerical simulation of semi-rigid joints. [ABSTRACT FROM AUTHOR]