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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.

In this paper, we address the flexible job-shop scheduling problem (FJSP) with release times for minimising the total weighted tardiness by learning dispatching rules from schedules. We propose a random-forest-based approach called Random Forest for Obtaining Rules for Scheduling (RANFORS) in order to extract dispatching rules from the best schedules. RANFORS consists of three phases: schedule generation, rule learning with data transformation, and rule improvement with discretisation. In the schedule generation phase, we present three solution approaches that are widely used to solve FJSPs. Based on the best schedules among them, the rule learning with data transformation phase converts them into training data with constructed attributes and generates a dispatching rule with inductive learning. Finally, the rule improvement with discretisation improves dispatching rules with a genetic algorithm by discretising continuous attributes and changing parameters for random forest with the aim of minimising the average total weighted tardiness. We conducted experiments to verify the performance of the proposed approach and the results showed that it outperforms the existing dispatching rules. Moreover, compared with the other decision-tree-based algorithms, the proposed algorithm is effective in terms of extracting scheduling insights from a set of rules. [ABSTRACT FROM AUTHOR]

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]

A statistical framework applicable to Ring-LWE was outlined by Murphy and Player (IACR eprint 2019/452). Its applicability was demonstrated with an analysis of the decryption failure probability for degree-1 and degree-2 ciphertexts in the homomorphic encryption scheme of Lyubashevsky, Peikert and Regev (IACR eprint 2013/293). In this paper, we clarify and extend results presented by Murphy and Player. Firstly, we make precise the approximation of the discretisation of a Normal random variable as a Normal random variable, as used in the encryption process of Lyubashevsky, Peikert and Regev. Secondly, we show how to extend the analysis given by Murphy and Player to degree-k ciphertexts, by precisely characterising the distribution of the noise in these ciphertexts.

When patterns to be recognised are described by features of continuous type, discretisation becomes either an optional or necessary step in the initial data pre-processing stage. Characteristics of data, distribution of data points in the input space, can significantly influence the process of transformation from real-valued into nominal attributes, and the resulting performance of classification systems employing them. If data include several separate sets, their discretisation becomes more complex, as varying numbers of intervals and different ranges can be constructed for the same variables. The paper presents research on irregularities in data distribution, observed in the context of discretisation processes. Selected discretisation methods were used and their effect on the performance of decision algorithms, induced in classical rough set approach, was investigated. The studied input space was defined by measurable style-markers, which, exploited as characteristic features, facilitate treating a task of stylometric authorship attribution as classification

When mining of input data is focused on rule induction, knowledge, discovered in exploration of existing patterns, is stored in combinations of certain conditions on attributes included in rule premises, leading to specific decisions. Through their properties, such as lengths, supports, cardinalities of rule sets, inferred rules characterise relations detected among variables. The paper presents research dedicated to analysis of these dependencies, considered in the context of various discretisation methods applied to the input data from stylometric domain. For induction of decision rules from data, Classical Rough Set Approach was employed. Next, based on rule properties, several factors were proposed and evaluated, reflecting characteristics of available condition attributes. They allowed to observe how variables and rule sets changed depending on applied discretisation algorithms. [ABSTRACT FROM AUTHOR]

When patterns to be recognised are described by features of continuous type, discretisation becomes either an optional or necessary step in the initial data pre-processing stage. Characteristics of data, distribution of data points in the input space, can significantly influence the process of transformation from real-valued into nominal attributes, and the resulting performance of classification systems employing them. If data include several separate sets, their discretisation becomes more complex, as varying numbers of intervals and different ranges can be constructed for the same variables. The paper presents research on irregularities in data distribution, observed in the context of discretisation processes. Selected discretisation methods were used and their effect on the performance of decision algorithms, induced in classical rough set approach, was investigated. The studied input space was defined by measurable style-markers, which, exploited as characteristic features, facilitate treating a task of stylometric authorship attribution as classification. [ABSTRACT FROM AUTHOR]

This paper presents a method for calculating eigenvalues lying in the gaps of the essential spectrum of matrix-valued Schrödinger operators. The technique of dissipative perturbation allows eigenvalues of interest to move up the real axis in order to achieve approximations free from spectral pollution. Some results of the behaviour of the corresponding eigenvalues are obtained. The effectiveness of this procedure is illustrated by several numerical examples. [ABSTRACT FROM AUTHOR]

Subgroup discovery (SD) is an exploratory pattern mining paradigm that comes into its own when dealing with large real-world data, which typically involves many attributes, of a mixture of data types. Essential is the ability to deal with numeric attributes, whether they concern the target (a regression setting) or the description attributes (by which subgroups are identified). Various specific algorithms have been proposed in the literature for both cases, but a systematic review of the available options is missing. This paper presents a generic framework that can be instantiated in various ways in order to create different strategies for dealing with numeric data. The bulk of the work in this paper describes an experimental comparison of a considerable range of numeric strategies in SD, where these strategies are organised according to four central dimensions. These experiments are furthermore repeated for both the classification task (target is nominal) and regression task (target is numeric), and the strategies are compared based on the quality of the top subgroup, and the quality and redundancy of the top-k result set. Results of three search strategies are compared: traditional beam search, complete search, and a variant of diverse subgroup set discovery called cover-based subgroup selection. Although there are various subtleties in the outcome of the experiments, the following general conclusions can be drawn: it is often best to determine numeric thresholds dynamically (locally), in a fine-grained manner, with binary splits, while considering multiple candidate thresholds per attribute. [ABSTRACT FROM AUTHOR]

A statistical framework applicable to Ring-LWE was outlined by Murphy and Player (IACR eprint 2019/452). Its applicability was demonstrated with an analysis of the decryption failure probability for degree-1 and degree-2 ciphertexts in the homomorphic encryption scheme of Lyubashevsky, Peikert and Regev (IACR eprint 2013/293). In this paper, we clarify and extend results presented by Murphy and Player. Firstly, we make precise the approximation of the discretisation of a Normal random variable as a Normal random variable, as used in the encryption process of Lyubashevsky, Peikert and Regev. Secondly, we show how to extend the analysis given by Murphy and Player to degree-k ciphertexts, by precisely characterising the distribution of the noise in these ciphertexts. [ABSTRACT FROM AUTHOR]

Discretisation often constitutes a part of initial data preparation stage. It translates continuous domain of features into granular, by assigning a number of intervals to represent attributes' values by nominal categories. Typically all real-valued features are subjected to transformations, regardless of their characteristics. The paper presents research on discretisation executed with a discerning approach. To all available attributes, feature selection mechanisms were employed, in the form of rankings that order variables based on their importance. Exploiting this discovered knowledge on attributes, discretisation was then driven by a ranking, and either highest or lowest ranking features were selected for transformation. The influence of selective discretisation on the performance of classification systems was studied for three popular inducers. The procedure was employed in the field of stylometry, and a task of authorship recognition, considered as a binary classification with balanced classes. The experiments show that discretisation based on importance of features can lead to better performance than in the case of transformations applied to all attributes. [ABSTRACT FROM AUTHOR]

We present a simple model for describing the dynamics of the interaction between a homogeneous population or society, and the natural resources and reserves that the society needs for its survival. The model is formulated in terms of ordinary differential equations, which are subsequently discretised, the discrete system providing a natural integrator for the continuous one. An ultradiscrete, generalised cellular automaton-like, model is also derived. The dynamics of our simple, three-component, model are particularly rich exhibiting either a route to a steady state or an oscillating, limit cycle-type regime or to a collapse. While these dynamical behaviours depend strongly on the choice of the details of the model, the important conclusion is that a collapse or near collapse, leading to the disappearance of the population or to a complete transfiguration of its societal model, is indeed possible. [ABSTRACT FROM AUTHOR]

We study the principal component analysis based approach introduced by Reisinger and Wittum (2007) and the comonotonic approach considered by Hanbali and Linders (2019) for the approximation of American basket option values via multidimensional partial differential complementarity problems (PDCPs). Both approximation approaches require the solution of just a limited number of low-dimensional PDCPs. It is demonstrated by ample numerical experiments that they define approximations that lie close to each other. Next, an efficient discretisation of the pertinent PDCPs is presented that leads to a favourable convergence behaviour.

Domination in graphs is well known and has been an extensively researched branch of graph theory. Since the variation over time is one of the important properties of real-world networks, we study the influence of time on the domination problem. In this paper, we introduce the domination over time problem, including time delay on arcs. Then, an optimal solution to its discretisation is obtained, which is the solution of the original problem. [ABSTRACT FROM AUTHOR]

This paper is focused on the double-grid integration with interpolation-projection (DoGIP), which is a novel matrix-free discretisation method of variational formulations introduced for Fourier–Galerkin approximation. Here, it is described as a more general approach with an application to the finite element method (FEM) on simplexes. The approach is based on treating the trial and a test function in variational formulation together, which leads to the decomposition of a linear system into interpolation and (block) diagonal matrices. It usually leads to reduced memory demands, especially for higher-order basis functions, but with higher computational requirements. The numerical examples are studied here for two variational formulations: weighted projection and scalar elliptic problem modelling, e.g. diffusion or stationary heat transfer. This paper also opens a room for further investigation, which is discussed in the conclusion. [ABSTRACT FROM AUTHOR]

• The contact surface of the object with the friction force fields is discretised. • Friction forces of discrete elements are described by luGre and MSC Adams models. • Two state variables of the luGre model are assigned to each discrete element. • Discrete element transition between friction zones, does not cause Stribeck effect. • If external force increases rapidly the force breaking the static friction decreases. The paper presents a model of the angular positioning process of cuboidal objects with the use the system of two oblique friction forces fields created by conveyor belts. In this model, the contact surface of the object with conveyors was divided into discrete elements. To describe the reaction of the frictional forces of discrete elements in the plane motion, the models of LuGre, MSC Adams with or without the Stribeck effect were used. Numerical tests show that due to the implementation of the positioning process at high sliding velocities, the object transition between the friction fields does not cause appearing the Stribeck effect. The disappearance of this effect is caused by disclosure of nonlinear phenomena, break-away force and stick-slip, which cause a drop in the friction limit force value, when the external force breaking the static friction builds up at high velocity. In addition, based on the analyses of numerical test results, determined recommended parameters of the conveyor belts motion, allowing to minimize the value of the final rotation angle of the object after passing through a system of two oblique friction force fields. [ABSTRACT FROM AUTHOR]

The paper presents research on unsupervised and supervised discretisation of input data used in execution of stylometric tasks of authorship attribution. Basing on numeric characterisation of writing styles, recognition of authorship is performed by decision rules, as their transparent structure enhances understanding of discovered knowledge. The performance of rule classifiers, constructed in rough set approach, is studied in the context of a strategy employed for resolving conflicts. It is also contrasted with that of other selected inducers. [ABSTRACT FROM AUTHOR]

Aufnahmesysteme wie Kameras oder Augen zerlegen das Bild in kleinere Bereiche wie Pixel oder Sehzellen um die Weiterverarbeitung zu ermöglichen. Technische Lösungen benutzen hierfür rechteckige Formen, biologische hingegen sechseckige. Deren Vorteile wurden in verschiedenen früheren, meist theoretischen Arbeiten zwar gezeigt, aber mangels hexagonbasierter Aufnahmesysteme kaum umfassender untersucht. Mit der vorgestellten, softwaregestützten Lösung wird dies weitgehend behoben und weiterführende Evaluationen ermöglicht. Erste Ergebnisse zeigen bereits eine bessere Darstellung runder Kanten mit weniger Treppenstufenartefakten bei sechseckbasierten Bildern als bei rechteckbasierten. Image acquisition systems like cameras or eyes disassemble the image into smaller elements like pixels or visual cells to realize further processing. For this purpose, technical solutions use rectangle shaped pixel but biological solutions use hexagonal shapes. Advantages of the second are known from theoretical studies but hard to compare because of the missing of native hexagon based cameras. As a consequence, nearly no more comprehensive studies were executed. The proposed software-based solution solve this widely and allow further, more extensive evaluations. First results show better quality of round edges and lesser artefacts in the hexagon based images over the rectangle based images. [ABSTRACT FROM AUTHOR]

• A practical chiller FD method of based on discrete Bayesian network is proposed. • Making no assumptions concerning the distribution of the input features. • Quickly determine the parameters of BN without experts' knowledge. • Has strong robustness and generality in practical applications of FD. • Chiller faults can be diagnosed effectively. On site application of the fault diagnosis (FD) techniques is beneficial to reduce energy use and to extend life of the equipment. Considering the following aspects, a practical chiller FD method is proposed by introducing discretization to Bayesian network (BN) in this study. Firstly, most real-world domains involve continuous variables which are not easy to handle, and the gaussian hypothesis is not always realistic. Secondly, BN is easier to be dealt with discrete variables, but the traditional discrete FD method based on chiller experts is time-consuming and inefficient. The proposed method makes no assumptions concerning the distribution of the input features, and can quickly determine the parameters of BN without experts, thus it is more efficient and has strong robustness in practical applications of FD. Using the experimental data from ASHRAE RP-1043 to evaluate the proposed method, the results show that the proposed method is very effective for chiller FD. [ABSTRACT FROM AUTHOR]

Summary: In spite of the abundance of clustering techniques and algorithms, clustering mixed interval (continuous) and categorical (nominal and/or ordinal) scale data remain a challenging problem. In order to identify the most effective approaches for clustering mixed‐type data, we use both theoretical and empirical analyses to present a critical review of the strengths and weaknesses of the methods identified in the literature. Guidelines on approaches to use under different scenarios are provided, along with potential directions for future research. [ABSTRACT FROM AUTHOR]

A general analysis is made by homotopy perturbation method while taking the advantages of the initial guess, appearance of the embedding parameter, different choices of the linear operator to the approximated solution to the non-linear Schrodinger equation. We are not dependent upon the Adomian polynomials and find the linear forms of the components without these calculations. The discretised forms of the nonlinear Schrodinger equation allow us whether to apply any numerical technique on the discritisation forms or proceed for perturbation solution of the problem. The discretised forms obtained by constructed homotopy provide the linear parts of the components of the solution series and hence a new discretised form is obtained. The general discretised form for the NLSE allows us to choose any initial guess and the solution in the closed form.

Contemporary innovations in structural form-finding and fabrication techniques are leading to design of freeform masonry architecture. These new forms create new challenges in laying out tessellation patterns, especially if structural, fabrication and construction requirements as well as aesthetical considerations are taken into account. Addressing these challenges, we review historic stone-cutting strategies and their geometric principles, forming the base for the development of two new discretisation approaches for given thrust surfaces, allowing for various degrees of user control. First, we introduce a tessellation approach based on primal, anisotropic triangular meshes and their dual counterparts. Second, an alternative tessellation approach based on transverse cutting curves is presented. Using a simple set of geometric rules, both methods enable the design of rigid, staggered bonds with locally force-flow aligned block configurations to avoid sliding failures. For this research, the tessellation design of the Armadillo Vault, an unreinforced, dry-assembled, cut-stone stone shell, served as a case study to demonstrate the feasibility of our methods in the context of a full-scale architectural project. [ABSTRACT FROM AUTHOR]

This study focuses on a fuzzy generalised predictive control method for a fractional‐order hydro‐turbine regulating system (HTRS). Based on the Grünwald–Letnikov (G–L) definition of fractional calculus and discretisation, the fractional‐order hydraulic servo system is transformed into the standard controlled autoregressive integrating moving average (CARMA) model. With the help of fuzzy linearisation theory, the fuzzy predictive model of the integer‐order part of the HTRS is presented. Furthermore, by using the fourth‐order Runge–Kutta algorithm, the obtained fuzzy predictive model can be easily transformed into the CARMA model. Then, based on the overall CARMA model and the generalised predictive control theory, a novel nonlinear fuzzy generalised predictive controller is designed for the fractional‐order HTRS. Finally, numerical simulations are implemented to verify the validity and superiority of the proposed method. It also provides a reference for relevant hydropower systems. [ABSTRACT FROM AUTHOR]

Building energy simulations have found widespread use as decision-making tools for determining design and retrofitting actions. Despite their popularity, there exists a well-reported issue regarding the numerical treatment of structural thermal-storage components in these models. The optimal means of discretising multi-layer structures is complicated by the different thermo-physical properties, material configurations and boundary conditions encountered within building energy models. This paper addresses this information gap by proposing a methodology that can be universally applied to all multi-layer structures, ensuring accurate predictions while avoiding excessive computational cost. Governing dimensionless quantities of Biot and Fourier numbers are utilised within the discretisation process, making the methodology equally applicable to all materials. The presented methodology also accounts for the configuration of materials within multi-layer structures when assigning discretisation levels, leading to nodes being distributed in accordance with expected thermal gradients. The proposed discretisation methodology has been examined for a number of boundary conditions and wall types with excellent prediction accuracy achieved throughout. Additionally, the utility of resistance-only layers has been explored as a means of increasing computational efficiency. This highlighted the importance of considering both layer position and local thermal properties when simulating multi-layer structures. [ABSTRACT FROM AUTHOR]