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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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

With the advent of computers and the information age, statistical and analytical problems have grown in terms of both size and complexity. Challenges in core domains of data storage, organisation and searching have evolved to the new research field called data mining. Text classification using various machine learning (ML) mechanisms encounters the difficulty of the high dimensionality of attributes vector. Therefore, a feature selection technique is very much required to discard irrelevant as well as noisy attributes from the feature set vector so that the ML algorithms can work efficiently. In this paper, rough set theory (RST)-based attribute selection methodology is applied to achieve text classification goal. A hybrid method based on RST is proposed for text documents classification. Further, the proposed method’s performance is evaluated on standard datasets. [ABSTRACT FROM AUTHOR]

This is an extended version of the paper presented at the 4th International Workshop NFMCP 2015 held in conjunction with ECML PKDD 2015. The initial version has been published in NFMCP 2015 conference proceedings as part of Springer Series. This paper presents a novel approach to financial times series (FTS) prediction by mapping hourly foreign exchange data to string representations and deriving simple trading strategies from them. To measure the degree of similarity in these market strings we apply familiar string kernels, bag of words and n-grams, whilst also introducing a new kernel, time-decay n-grams, that captures the temporal nature of FTS. In the process we propose a sequential Parzen windows algorithm based on discrete representations where trading decisions for each string are learned in an online manner and are thus subject to temporal fluctuations. We evaluate the strength of a number of representations using both the string version and its continuous counterpart, whilst also comparing the performance of different learning algorithms on these representations, namely support vector machines, Parzen windows and Fisher discriminant analysis. Our extensive experiments show that the simple string representation coupled with the sequential Parzen windows approach is capable of outperforming other more exotic approaches, supporting the idea that when it comes to working in high noise environments often the simplest approach is the most effective. [ABSTRACT FROM AUTHOR]

Multiple uncertainties complicate socio-economic forecasting problems, especially when relying on ill-conditioned limited data. Such problems are best addressed by grey prediction models such as Grey Verhulst Model (GVM). This paper resolves the incompatibility between GVM's estimation and prediction by taking its basic form equation as the basis of both. The resultant "Basic Form"-focused GVM (BFGVM) is also further developed to create Direct Non-equidistant BFGVM (DNBFGVM) and, in turn, DNBFGVM with Recursive simulation (DNBFGVMR). Experimental analyses comprise 19 socio-economic time series with an emphasis on Iranian population, a low-frequency non-equidistant time series with remarkable strategic importance. Promisingly, the proposed DNBFGVM and DNBFGVMR provide accurate in-sample and out-of-sample socio-economic forecasts, show highly significant improvements over the best traditional GVM, and offer cost-effective intelligent support of decision-making. Final results suggest future trends of studied socio-economic time series. Specifically, they reveal Iranian population to grow even slower than anticipated, demanding an urgent consideration of policy-makers. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a mathematical model for small deformations induced by external forces of closed surfaces that are minimisers of Helfrich-type energies. Our model is suitable for the study of deformations of cell membranes induced by the cytoskeleton. We describe the deformation of the surface as a graph over the undeformed surface. A new Lagrangian and the associated Euler-Lagrange equations for the height function of the graph are derived. This is the natural generalisation of the well-known linearisation in the Monge gauge for initially flat surfaces. We discuss energy perturbations of point constraints and point forces acting on the surface. We establish existence and uniqueness results for weak solutions on spheres and on tori. Algorithms for the computation of numerical solutions in the general setting are provided. We present numerical examples which highlight the behaviour of the surface deformations in different settings at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, the problem of robust discretisation of linear time-invariant (LTI) systems with polytopic uncertainties is introduced. More specifically, the main objective is to provide a systematic way to find an approximate discrete-time (DT) model of a continuous-time (CT) plant with uncertainties in polytopic domain. The system matrices of polytopic DT model to be found are expressed as parameter-dependent matrices which are homogeneous polynomials of arbitrary degree with respect to the uncertain variables in the simplex, and is obtained in such a way that the norm between the system matrices and the truncated power series of the exact DT model is minimised while preserving the polytopic structure of the original CT plant. The solution procedures proposed are presented in terms of single-parameter minimisation problems subject to linear matrix inequality (LMI) constraints which are numerically tractable via LMI solvers. Finally, examples are given to show the validity and effectiveness of the proposed techniques. [ABSTRACT FROM PUBLISHER]

Etant donné un espace topologique $$X$$ , on désigne par $$D_d(X,n)$$ le sous-espace de $$X^n$$ formé des points de $$X^n$$ dont au moins une coordonnée se répète $$d$$ fois et par $$F^{d+1}(X,n)$$ son complémentaire dans $$X^n$$ . On étudie dans ce travail quelques propriétés topologiques et combinatoires de ces espaces. Dans le cas $$n<2d$$ , on montre que l'espace $$D_d(X,n)$$ se scinde, après une seule suspension, en un bouquet de smash produits de $$X$$ . Par ailleurs, l'étude de l'espace $$D_2(S^n,4)$$ montre que la condition $$n<2d$$ est nécessaire. Pour $$n=d+1$$ , on calcule la caractéristique d'Euler de $$F^{n-1}(X,n)$$ lorsque $$X$$ est un complexe simplicial et on détermine son anneau de cohomologie $$H^{*}(F^{n-1}(X,n))$$ quand $$X$$ est une variété fermée et orientée. [ABSTRACT FROM AUTHOR]

Design of multi‐input multi‐output (MIMO) homogeneous sliding modes (HSMs) for uncertain dynamic systems is considered. The resulting closed‐loop systems feature all well‐known standard properties of single‐input single‐output (SISO) HSM systems. Introduction of robust exact differentiators produces homogeneous output‐feedback controllers. The ultimate asymptotic accuracy of SISO HSM technique is proved to be preserved in the MIMO and SISO cases, if the discrete‐time implementation is based on the one‐step Euler integration. [ABSTRACT FROM AUTHOR]

En recherche expérimentale, les chercheurs en marketing discrétisent souvent les variables quantitatives pour tester leur caractère modérateur. Cet article pédagogique explique les limites d’une telle pratique et illustre les étapes des analyses spotlight et floodlight à conduire suivant que la variable modératrice considérée présente ou non des valeurs focales signifiantes. [ABSTRACT FROM AUTHOR]

Agricultural intensification often has complex effects on a wide range of environmental and economic values, presenting planners with challenging decisions for optimising sustainable benefits. Bayesian Belief Networks (BBNs) can be used as a decision-support tool for evaluating the influence of development scenarios across a range of values. A BBN was developed to guide decisions on water abstraction and irrigation-driven land use intensification in the Hurunui River catchment, New Zealand. The BBN examines the combined effects of different irrigation water sources and four land development scenarios, with and without a suite of on-farm mitigations, on ground and surface water quality, key socioeconomic values (i.e. farm earnings and jobs, and contribution to regional gross domestic production (GDP)) and aquatic values (i.e. salmon, birds, waterscape, contact recreation, periphyton and invertebrates). It predicts high farm earnings, jobs and regional GDP with 150% increase in irrigated area, but a range of positive and negative aquatic environmental outcomes, depending on the location of water storage dams and the application of a suite of on-farm mitigations. This BBN synthesis of a complex system enhanced the ability to include aquatic values alongside economic and social values in land-use and water resource planning and decision making, and has influenced objective setting in Hurunui planning processes. Sustainable development is enhanced by tools that predict effects on a wide range of economic, social and environmental values. We developed a computerised 'knowledge network' to predict the likely states of key values in response to development scenarios involving irrigation-driven intensification of farming, on-farm pollution control measures, and dam location. The approach has assisted catchment management planning locally and has wider potential use. [ABSTRACT FROM AUTHOR]

In this study, the authors propose two fourth‐order partial differential equations (PDEs) to inpaint the image. By analysing those anisotropic fourth‐order PDEs and comparing their diffusion images, the authors confirm they are forward diffusion or backward diffusion. A numerical algorithm is presented using a finite‐difference method and analyse the stability of discretisation. Finally, they show various experimental results and conclude that the proposed new models are better than the second‐order and third‐order PDEs, especially for weakening the blocky effects. [ABSTRACT FROM AUTHOR]

Activity recognition has become a key component within smart environments that aim at providing assistive solutions for their users. Learning high level activities from low level sensor data depends on several parameters, one of which is the duration of the activities themselves. Nevertheless, directly incorporating continuous duration values into a model is a complex process and may not prove to be very qualitative. In this paper we aim at discretising activity related durations using different clustering algorithms. We explore the possibility of discretising duration data through the use of rudimentary clustering algorithms such as visual inspection to more established methods such as model based clustering. In addition, a probabilistic model is built that predicts both person and activities from the observed values of sensor sequence, time and discrete duration values. Each of the models created is compared in terms of its performance in the prediction of activities. Following analysis of the results attained it has been found that irrespective of the clustering algorithm used for duration discretisation, incorporating the duration information increases the prediction performance. Prediction accuracy was improved by almost 3% when the model was built incorporating durations. [ABSTRACT FROM AUTHOR]

Numerical integration of ODEs by standard numerical methods reduces continuous time problems to discrete time problems. Discrete time problems have intrinsic properties that are absent in continuous time problems. As a result, numerical solution of an ODE may demonstrate dynamical phenomena that are absent in the original ODE. We show that numerical integration of systems with one fast rotating phase leads to a situation of such kind: numerical solution demonstrates phenomenon of scattering on resonances that is absent in the original system. [ABSTRACT FROM AUTHOR]

Discretisation, as one of the basic data preparation techniques, has played an important role in data mining. This article introduces a new hypercube division-based (HDD) algorithm for supervised discretisation. The algorithm considers the distribution of both class and continuous attributes and the underlying correlation structure in the data set. It tries to find a minimal set of cut points, which divides the continuous attribute space into a finite number of hypercubes, and the objects within each hypercube belong to the same decision class. Finally, tests are performed on seven mix-mode data sets, and the C5.0 algorithm is used to generate classification rules from the discretised data. Compared with the other three well-known discretisation algorithms, the HDD algorithm can generate a better discretisation scheme, which improves the accuracy of classification and reduces the number of classification rules. [ABSTRACT FROM AUTHOR]

Recently, Aw and Rascle and Zhang introduced a new second-order macroscopic model, following the theoretical investigations on the Payne-Whitham second-order modelling by Daganzo. The conserved variables in this model are the density and the relative flow. The aim of this paper is to solve the Riemann problem for the Aw-Rascle-Zhang (ARZ) model for all possible initial conditions, using an extended fundamental diagram. The resolution of the Riemann problem provides the user of the model with a set of nontrivial analytical solutions; it is also a prerequisite for the construction of numerical solution schemes. Some examples are given in which analytical solutions of the Riemann problem are discussed and compared to numerical solutions. The ARZ model shows better fit to real data than the embedded Lighthill-Whitham-Richards (LWR) model for the same set of physical parameters. [ABSTRACT FROM AUTHOR]

This work is devoted to the discretisation of non linear elliptic problems on general polyhedral meshes in several space dimensions. The SUSHI scheme which was recently studied for anisotropic heterogeneous problems is applied in its full barycentric version, thus resulting into a cell centred scheme written under variational form, also known as ‘SUCCES’. We prove the existence of the approximate solution and its convergence to the weak solution of the continuous solution as the mesh size tends to 0. Numerical examples are shown for the p-Laplacian. [ABSTRACT FROM AUTHOR]

This article is concerned with the fast-lifting approach to H∞ analysis and design of sampled-data systems, and extends our preceding study on modified fast-sample/fast-hold (FSFH) approximation, in which the direct feedthrough matrix D11 from the disturbance w to the controlled output z was assumed to be zero. More precisely, this article removes this assumption and shows that a γ-independent H∞ discretisation is still possible in a nontrivial fashion by applying what we call quasi-finite-rank approximation of an infinite-rank operator and then the loop-shifting technique. As in the case of D11 = 0, the modified FSFH approach retains the feature that both the upper and lower bounds of the H∞-norm or the frequency response gain can be computed, where the gap between the upper and lower bounds can be bounded with the approximation parameter N and is independent of the discrete-time controller. This feature is significant in applying the new method especially to control system design, and this study indeed has a very close relationship to the recent progress in the study of control system analysis/design via noncausal linear periodically time-varying scaling. The significance of a key lemma pertinent to the fast-lifting approach is suggested in connection with such a relationship, and also with its application to time-delay systems. [ABSTRACT FROM AUTHOR]

The paper is devoted to the local moment matching method and its links with the discrete version of the s-convex extremal distributions. It is well-known that the local moment matching method can produce some negative masses. Connecting the local moment matching method to the discrete s-convex extrema gives an explicit criterion that explains why (and says when) the local moment matching method gives some negative mass. [ABSTRACT FROM AUTHOR]

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper examines stochastic pairwise dependence structures in binary time series obtained from discretised versions of standard chaotic logistic maps. It is motivated by applications in communications modelling which make use of so-called chaotic binary sequences. The strength of non-linear stochastic dependence of the binary sequences is explored. In contrast to the original chaotic sequence, the binary version is non-chaotic with non-Markovian non-linear dependence, except in a special case. Marginal and joint probability distributions, and autocorrelation functions are elicited. Multivariate binary and more discretised time series from a single realisation of the logistic map are developed from the binary paradigm. Proposals for extension of the methodology to other cases of the general logistic map are developed. Finally, a brief illustration of the place of chaos-based binary processes in chaos communications is given. [ABSTRACT FROM AUTHOR]

A useful unified analysis framework is proposed for exploring the intriguing behaviors of a second-order switching control system. Complex discretization behaviors of the switching control system are explored in detail, and some intrinsic relationships between the system periodic behaviors and their associated symbolic sequences are studied. [ABSTRACT FROM AUTHOR]

An introduction to the approaches used to discretise continuous database features is given, together with a discussion of the potential benefits of such techniques. These benefits are investigated by applying discretisation algorithms to two large commercial databases; the discretisations yielded are then evaluated using a simulated annealing based data mining algorithm. The results produced suggest that dramatic reductions in problem size may be achieved, yielding improvements in the speed of the data mining algorithm. However, it is also demonstrated under certain circumstances that the discretisation produced may give an increase in problem size or allow overfitting by the data mining algorithm. Such cases, within which often only a small proportion of the database belongs to the class of interest, highlight the need both for caution when producing discretisations and for the development of more robust discretisation algorithms. [ABSTRACT FROM AUTHOR]

Copyright of Computing is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper adopts the idea of discretising continuous attributes (Fayyad and Irani 1993) and applies it to lazy learning algorithms (Aha 1990; Aha, Kibler and Albert 1991). This approach converts continuous attributes into nominal attributes at the outset. We investigate the effects of this approach on the performance of lazy learning algorithms and examine it empirically using both real-world and artificial data to characterise the benefits of discretisation in lazy learning algorithms. Specifically, we have showed that discretisation achieves an effect of noise reduction and increases lazy learning algorithms' tolerance for irrelevant continuous attributes. The proposed approach constrains the representation space in lazy learning algorithms to hyper-rectangular regions that are orthogonal to the attribute axes. Our generally better results obtained using a more restricted representation language indicate that employing a powerful representation language in a learning algorithm is not always the best choice as it can lead to a loss of accuracy. [ABSTRACT FROM AUTHOR]

This paper proposes a new statistical method of estimation and simulation for systems of stochastic differential equations. By using this method, we can easily derive a discretised process from a system of stochastic differential equations. The discretised process is tractable enough to simulate the system and to construct the likelihood which is used to estimate the coefficients of the stochastic differential equations from discrete observation. [ABSTRACT FROM AUTHOR]

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Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

L'article décrit les méthodes numériques introduites dans le programme de simulation du comportement électrique des circuits appelé eldo. Un algorithme de relaxation en une étape appelé osr y remplace la méthode classique de Newton pour résoudre les schémas implicites à grand nombre de variables qui résultent de la discrétisation des équations. Il est comparé à d'autres algorithmes. Un algorithme dérivé permet la résolution de très grands systèmes linéaires, donc l'inversion des matrices de grande taille. On peut traiter ainsi des circuits contenant des milliers de variables et de transistors en des temps acceptables. This article describes the original numerical methods introduced in a new circuit simulator named eldo. Its basic algorithm named osr (onestep relaxation) replaces the classical Newton method to solve the implicit schemes with large number of variables. A derived algorithm from osr allows the resolution of very large linear systems, eldo is able to simulate circuits containing 10 000 variables and 15 000 transistors. [ABSTRACT FROM AUTHOR]

Après avoir montré comment est obtenue l'équation intégrale du champ électrique pour les problèmes à une et deux dimensions, l'auteur indique la procédure employée pour la résolution. Cette procédure est basée sur l'emploi de la méthode des moments et a conduit à l'élaboration d'algorithmes programmés sur ordinateur dont les limites d'application sont précisées. Les résultats présentés sont relatifs à l'examen de quelques cas canoniques. The author is studying the electric field integral equation in the time domain for one and two dimensional surfaces respectively. The equations are solved with the moment method. The algorithms are presented. Special attention is given to their differences and limitations. A few results are presented for canonical cases. [ABSTRACT FROM AUTHOR]

A partir de l'équation des ondes et compte tenu des conditions aux limites du problème, les auteurs développent une équation intégrale de Fredholm de 2 espèce dans laquelle intervient le temps. La forme particulière de cette équation intégrale se prête parfaitement à une méthode d'approximation numérique qui permet d'obtenir la solution sous la forme d'une densité de simple couche répartie sur la surface de l'obstacle. Connaissant cette densité, en tous points et à chaque instant, on peut calculer la réponse spatiotemporelle de la cible considérée. La méthode décrite est tout à fait générale et peut s'appliquer à des cibles de forme géométrique plus ou moins complexe. Une application numérique a été envisagée pour le cas particulier d'une sphère parfaitement réfléchissante afin de bénéficier de certaines simplifications, et a fait apparaître une bonne concordance avec des résultats obtenus par des méthodes classiques. From the wave equation and the use of boundary conditions of the problem we have developped an integral equation which is time dependant. The particular form of this integral equation is well suited to a numerical approximation method which gives the solution as a single boundary layer. If one knows this boundary layer for all space and for all time, one can calculate the spacetime response of the target under investigation. The method is a very general one and can be applied to targets of arbitrary shape. To check the efficiency of the algorithm a computation has been done in the particular case of a perfectly reflecting sphere. Results are in good agreement with classical ones reported in the littérature. [ABSTRACT FROM AUTHOR]

Les auteurs procèdent à une étude critique de la méthode des lignes de transmission (TLM) afin de l'appliquer à une étude dynamique des microcircuits en hyperfréquence. D'importantes améliorations portant sur l'initialisation du processus dynamique, la rapidité et la précision du calcul sur ordinateur et le traitement du signal temporel obtenu sont proposées. La méthode étant dynamique, l'utilisation des symétries géométriques et électriques, et le choix des impulsions d'excitation permettent un premier filtrage sélectif de l'information à transmettre. L'utilisation de la transformation de Fourier rapide et la simplification du processus de calcul permettent un gain en temps et en précision. Enfin le traitement du signal temporel obtenu par convolution avec diverses fenêtres autorise une meilleure lecture des spectres de réponse en fréquence. A critical study of the transmissionlinematrix method has been carried out by the authors to apply it for a dynamical study of the microwaves microcircuits. As a consequence of this critical study the authors suggest important improvements on the following three points: the dynamical process initialization, the rapidity and precision of computer calculation, the treatment of the resulting time signal. The method being a dynamical one, a first selecting filtering of the information to be transmitted is performed by using the geometrical and electrical symetries. A fast Fourier transform and a simplification of the computation procedure give a gain in time and precision. At last a better reading of the frequency response spectra is obtained by treating with various windows of convolution the resulting time signal. [ABSTRACT FROM AUTHOR]