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This article addresses the simultaneous state and unknown input estimation problem for a class of discrete time-varying complex networks (CNs) under redundant channels and dynamic event-triggered mechanisms (ETMs). The redundant channels, modeled by an array of mutually independent Bernoulli distributed stochastic variables, are exploited to enhance transmission reliability. For energy-saving purposes, a dynamic event-triggered transmission scheme is enforced to ensure that every sensor node sends its measurement to the corresponding estimator only when a certain condition holds. The primary objective of the investigation carried out is to construct a recursive estimator for both the state and the unknown input such that certain upper bounds on the estimation error covariances are first guaranteed and then minimized at each time instant in the presence of dynamic event-triggered strategies and redundant channels. By solving two series of recursive difference equations, the desired estimator gains are computed. Finally, an illustrative example is presented to show the usefulness of the developed estimator design method.

Vulnerability refers to the ability of a network to continue functioning when part of the network is either naturally damaged or targeted for attack. In this paper, the rupture degree of graphs is employed to measure the vulnerability of uniform linear hypergraphs. First, we discuss the bounds of the rupture degrees of k-uniform linear hypergraphs. Then, we give a recursive algorithm for computing the rupture degree of k-uniform hypertrees.

A coiled coil is a structural motif in proteins that consists of at least two α-helices wound around each other. For structural stabilization, these α-helices form interhelical contacts via their amino acid side chains. However, there are restrictions as to the distances along the amino acid sequence at which those contacts occur. As the spatial period of the α-helix is 3.6, the most frequent distances between hydrophobic contacts are 3, 4, and 7. Up to now, the multitude of possible decompositions of α-helices participating in coiled coils at these distances has not been explored systematically. Here, we present an algorithm that computes all non-redundant decompositions of sequence periods of hydrophobic amino acids into distances of 3, 4, and 7. Further, we examine which decompositions can be found in nature by analyzing the available data and taking a closer look at correlations between the properties of the coiled coil and its decomposition. We find that the availability of decompositions allowing for coiled-coil formation without putting too much strain on the α-helix geometry follows an oscillatory pattern in respect of period length. Our algorithm supplies the basis for exploring the possible decompositions of coiled coils of any period length.

Liberalizacijom tržišta električne energije merenje električne snage i energije u nesinusoidalnim uslovima dobilo je veliki značaj. Ta tema je još uvek predmet aktivnih rasprava, tako da ne postoji neka generalizovana teorija koja se može uzeti kao osnova za potrebe obračuna, evaluacije kvaliteta energije, detekcije izvora harmonika i kompenzacije u energetskim sistemima. Kao posledica, postojeći standardi se odnose na sinusoidalne slučajeve i ne daju definiciju reaktivne energije (i/ili snage) u nesinusoidalnim uslovima. Slično, oni ne daju specifične zahteve za tačnost i odgovarajuće uslove testiranja u prisustvu harmonijskih izobličenja. Jedini standard koji se odnosi na ovu problematiku je IEEE Std. 1459-2010 koji ne daje definiciju reaktivne snage u nesinusoidalnim uslovima. Koncept ovog IEEE standarda je baziran na razdvajanju snage na fundamentalni i nefundamentalni deo. Ovaj prilaz separacije na fundamentalni i harmonijski deo može se primeniti na najbitnije veličine i može se iskoristiti kao indikator kvaliteta. U radu je prikazana jedna efikasna algoritamska struktura za računanje električnih veličina definisanih standardom IEEE 1459-2010. Struktura se sastoji od dva dekuplovana dela. Za estimaciju spektra napona i struje korišćena je efikasna metoda bazirana na paralelnoj strukturi rezonantnih filtera sa zajedničkom povratnom vezom. U drugom delu strukture se na osnovu poznatog spektra naponskog i strujnog signala računaju komponente snage i indikatori kvaliteta na osnovu definicija datih u standardu IEEE 1459-2010. Predloženi algoritam je pogodan za primene u realnom vremenu. Realizacijom virtualnog instrumenta baziranog na PC računaru i programskom paketu LabVIEW, u cilju procene performansi algoritma, izvršene su računarske simulacije i eksperimentalna merenja i dati njihovi rezultati. This paper proposes an accurate and computationally efficient implementation of the IEEE Std. 1459-2010 for power measurements. An implementation is based on digital resonators embedded in a feedback loop. In the first algorithm stage, the unknown signal harmonic parameters are estimated. By this, the voltage and current signals are processed independently of each other. In the second algorithm stage, the unknown power components are estimated (calculated) based on estimated spectra. To demonstrate the performance of the developed algorithm, computer-simulated data and laboratory testing records are processed. Simple LabView implementation, based on the point-by-point processing feature, demonstrates techniques modest computation requirements and confirms that the proposed algorithm is suitable for real-time applications.

In recent years, many industrialfacilities have been required to install sensing system to monitor the health status of the equipment. Although the PC-based diagnosis system is a good alternative, it undoubtedly increases the hardware cost greatly, and also causes restrictions on system assembly. In some critical environments, installation of the PC-based system is not suitable because of high temperature, dust, and humidity. On the contrary, a high mobility portable smart sensor will be relatively adequate for onsite inspections. To solve this problem, we developed a low-cost embedded handheld smart sensor. Instead of using sophisticated algorithms, certain frequently used statistic indicators are considered. Nevertheless, due to the resource limitations of the embedded systems, it causes difficulty for real-time realization and therefore, the recursive architecture of the statistic indicators is derived. These statistical factors are then fed into a Gaussian classifier for online defect detection, which gives a great contribution to field operators for onsite inspections. The highly integrated hardware/software co-design of the developed device provides user-friendly and high mobility for field inspections. Finally, a practical industrial application regarding the online diagnosis of a solenoid valve actuator defect is presented to demonstrate the effectiveness of the developed embedded smart sensor.

The study of vehicular networks has attracted considerable interest in academia and the industry. In the broad area, connected vehicles and autonomous driving are technologies based on wireless data communication between vehicles or between vehicles and infrastructures. A Vehicle-to-Infrastructure (V2I) system consists of communications and computing over vehicles and related infrastructures. In such a system, wireless sensors are installed in some selected points along roads or driving areas. In autonomous driving, it is crucial for a vehicle to figure out the ideal routes by the communications between its equipped sensors and infrastructures then the vehicle is automatically moving along the routes. In this paper, we propose a Bezier curve based recursive algorithm, which effectively creates routes for vehicles through the communication between the On-Board Unit (OBU) and the Road-Side Units (RSUs). In addition, this approach generates a very low overhead. We conduct simulations to test the proposed algorithm in various situations. The experiment results demonstrate that our algorithm creates almost ideal routes.

The method of recursive discrete wavelet noise filtering for improving metrological characteristics of measuring instruments was investigated for the first time. Methods with a common threshold for all decomposition levels, methods without threshold with a simple zeroing of detail coefficients until the minimum mean square (RMS) error is reached, and methods with universal threshold for detail coefficients at each decomposition level were studied. Twenty different types of measurement signals from the popular PyWavelets library were analyzed. The functions of filtering methods with a common threshold were determined, for which the use of recursion reduces the filtering error from 10 to 50%. For methods without threshold and with universal threshold, the recursion does not reduces the error by multiple filtering of measurement signals. To apply the recursion to the method with a common threshold for all decomposition levels, a mathematical model based on the fundamental equations of wavelet filtering was constructed. The character of distribution of the filtering RMS error depending on the number of reversible cycles is investigated. It was summarized that for the measurement signal models under consideration, the maximum error reduction occurs between the zero cycle, in which the initial measurement signal is filtered, and the first level of recursion. Further reduction of the filtering error with increasing number of recursion cycles occurs according to the law close to hyperbolic., Впервые исследован метод рекурсивной дискретной вейвлет-фильтрации шумов для повышения метрологических характеристик средств измерений. Исследовались методы: с общим порогом для всех уровней декомпозиции; без порога с простым обнулением коэффициентов детализации до момента достижения минимальной среднеквадратической погрешности; с универсальным порогом для коэффициентов детализации на каждом уровне декомпозиции. Были исследованы двадцать различных типов измерительных сигналов из популярной библиотеки PyWavelets. Определены функции методов фильтрации с общим порогом, для которых применение рекурсии снижает погрешность фильтрации от 10 до 50%. Рекурсия не обеспечивает существенного снижения погрешности для методов без порога и с универсальным порогом. Для применения рекурсии к методу с общим порогом для всех уровней декомпозиции построена математическая модель, в основу которой положены фундаментальные уравнения вейвлет-фильтрации. Изучен характер распределения среднеквадратической погрешности фильтрации от количества реверсивных циклов., Вперше досліджено метод рекурсивної дискретної вейвлет-фільтрації шумів для підвищення метрологічних характеристик засобів вимірювання. Досліджувалися методи: із загальним порогом для всіх рівнів декомпозиції; без порога із простим обнуленням коефіцієнтів деталізації до досягнення мінімальної середньоквадратичної похибки; з універсальним порогом коефіцієнтів деталізації для кожного рівня декомпозиції. Було досліджено двадцять різних типів вимірювальних сигналів із популярної бібліотеки PyWavelets. Визначено функції методів фільтрації із загальним порогом, для яких застосування рекурсії знижує похибку фільтрації від 10 до 50%. Рекурсія не забезпечує суттєвого зниження похибки для методів без порога та з універсальним порогом. Для застосування рекурсії до методу із загальним порогом для всіх рівнів декомпозиції побудовано математичну модель, основою якої є фундаментальні рівняння вейвлет-фільтрації. Вивчено характер розподілу середньоквадратичної похибки фільтрації від кількості реверсивних циклів. Показано, що для досліджуваних моделей вимірювальних сигналів максимальне зниження похибки відбувається між нульовим циклом, у якому фільтрується вихідний вимірювальний сигнал, і першим рівнем рекурсії. Подальше зниження похибки фільтрації зі зростанням числа циклів рекурсії відбувається за законом, близьким до гіперболічного.

This paper analyzes a method to approximate the first passage time probability density function which turns to be particularly useful if only sample data are available. The method relies on a Laguerre-Gamma polynomial approximation and iteratively looks for the best degree of the polynomial such that the fitting function is a probability density function. The proposed iterative algorithm relies on simple and new recursion formulae involving first passage time moments. These moments can be computed recursively from cumulants, if they are known. In such a case, the approximated density can be used also for the maximum likelihood estimates of the parameters of the underlying stochastic process. If cumulants are not known, suitable unbiased estimators relying on k-statistics are employed. To check the feasibility of the method both in fitting the density and in estimating the parameters, the first passage time problem of a geometric Brownian motion is considered., 22 pages, 6 figures

The effective wavelet filtering of real signals is impossible without determining their shape. The shape of a real signal is related to its wavelet spectrum. For shape analysis, a continuous color wavelet spectrogram of signal level is often used. The disadvantage of continuous wavelet spectrogram is the complexity of analyzing a blurry color image. A real signal with additive noise strongly distorts the spectrogram based on continuous wavelet analysis compared to a pure signal. Therefore, the identification of a real signal by using a continuous color wavelet spectrogram is difficult. To solve this problem, for the first time, a comparative analysis of spectrograms of signals and correlation matrices is carried out. The spectrograms of signals are obtained based on continuous wavelet transformation in the form of images with areas of different colors of variable intensity. Correlation matrices are computed by using mathematical functions of the coefficients of discrete wavelet spectra.

The recursive and hierarchical structure of full rooted trees is applicable to statistical models in various fields, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is not a random variable; as such, model selection to avoid overfitting is problematic. One method to solve this problem is to assume a prior distribution on the full rooted trees. This enables the optimal model selection based on Bayes decision theory. For example, by assigning a low prior probability to a complex model, the maximum a posteriori estimator prevents the selection of the complex one. Furthermore, we can average all the models weighted by their posteriors. In this paper, we propose a probability distribution on a set of full rooted trees. Its parametric representation is suitable for calculating the properties of our distribution using recursive functions, such as the mode, expectation, and posterior distribution. Although such distributions have been proposed in previous studies, they are only applicable to specific applications. Therefore, we extract their mathematically essential components and derive new generalized methods to calculate the expectation, posterior distribution, etc.

Работа направлена на выявление проблемы исследования процесса создания цифровых арт-объектов с помощью программного кода. В 21 веке современные цифровые художники используют программный код в качестве инструмента для создания объектов искусства. Наблюдается гармоничное соединение науки, современных технологий и искусства, что подтверждается новым направлением в медийном творчестве – технологической креативностью. Целью работы является анализ нескольких сред программирования для реализации арт-объектов и создание электронного сборника. Методами исследования являются изучение методической литературы и электронных ресурсов, а также создание арт-объектов в средах программирования. Для работы были выбраны три среды: Scratch 2.0, Scribble, Beetle Blocks. Scratch 2.0 позволяет создавать аудиовизуальные композиции, Scribble дает возможность реализовывать абстрактные картины и рекурсивные изображения, в Beetle-арт создаются творческие 3D-объекты. При написании работы авторы рассмотрели языки и среды программирования на предмет возможности создания объектов искусства, а именно трехмерных объектов, художественных фонов, визуальных и аудиовизуальных композиций. Кроме того, сформировали электронный сборник с инструкциями написания алгоритмов различных макетов работ. Электронный сборник практических идей может применяться в школах и университетах для изучения алгоритмических конструкций, циклов и подпрограмм. Области науки, к которым может быть отнесена работа, – информационные технологии, компьютерное моделирование, которые входят в приоритетные направления и критические технологии развития науки, техники и технологии Российской Федерации. В результате выполнения работы авторы изучили данные по проблеме исследования, провели анализ нескольких сред программирования, сформировали электронный сборник практических идей, в котором описаны коды создания различных творческих объектов., The paper aims to identify the problem of researching the process of creating digital art objects using software code. In the 21st century, modern digital artists use software code as a tool for creating art objects. There is a harmonious combination of science, modern technology and art, which is confirmed by a new trend in media creativity technological creativity. The aim of the work is to analyze several programming environments for the implementation of art objects and the creation of an electronic collection. Methods of research are the study of methodological literature and electronic resources, as well as the creation of art objects in programming environments. For the work were chosen three environments Scratch 2.0, Scribble, and Beetle Blocks. Scratch 2.0. allows you to create audiovisual compositions, Scribble allows you to implement abstract paintings and recursive images; Beetle-art creates 3D creative objects. When writing the paper, the authors analyzed programming languages and environments for the possibility of creating art objects, namely three-dimensional objects, artistic backgrounds, visual and audiovisual compositions. In addition, they formed an electronic collection with instructions for writing algorithms for various work layouts. The electronic collection of practical ideas can be used in schools and universities to study algorithmic constructions, loops and subroutines. The field of science, to which the work can be attributed information technology, computer modeling, which are included in the priority areas and critical technologies of development of science, engineering and technology of the Russian Federation. Because of the work, the authors have studied data on the problem of research, conducted an analysis of several programming environments, and formed an electronic collection of practical ideas, which describes the codes for creating various creative objects.

This report is the user’s manual for a package of MATLAB™ scripts and functions, developed for recursive prediction error identification of nonlinear state space systems. The identified state space model incorporates delay, which allows a treatment of general nonlinear networked identification, as well as of general nonlinear systems with delay. The core of the package is an implementation of two output error identification algorithms. The algorithms are based on a continuous time, structured black box state space model of a nonlinear system. The present revision adds a new algorithm, where also the output is determined via a parameterized measurement equation in the states and inputs. The software can only be run off-line, i.e. no true real time operation is possible. The algorithms are however implemented so that true on-line operation can be obtained by extraction of the main algorithmic loop. The user must then provide the real time environment. The software package contains scripts and functions that allow the user to either input live measurements or to generate test data by simulation. The scripts and functions for the setup and execution of the identification algorithms are somewhat more general than what is described in the references. The functionality for display of results include scripts for plotting of e.g. data, parameters, prediction errors, eigenvalues and the condition number of the Hessian. The estimated model obtained at the end of a run can be simulated and the model output plotted, alone or together with the data used for identification. Model validation is supported by two methods apart from the display functionality. First, a calculation of the RPEM loss function can be performed, using parameters obtained at the end of an identification run. Secondly, the accuracy as a function of the output signal amplitude can be assessed.

Статья посвящена проблемам представления знаний в виде веб-онтологий. Актуальность исследования обусловлена двумя факторами. С одной стороны, в рамках развития концепции семантического веба за последние годы создано большое число OWL-онтологий и RDF-наборов данных. С другой стороны, язык OWL имеет ряд ограничений, которые не всегда позволяют представить знания предметной области адекватно. Например, SPARQL-запросы, использующие транзитивные свойства языка OWL, могут создавать своего рода «петли» и возвращать некорректную информацию. В данной статье показано, что в некоторых случаях предпочтительно отказаться от использования транзитивности свойств в онтологии, и предложен алгоритм обхода связанных сущностей, позволяющий решить проблему «петель». В качестве примера, иллюстрирующего эту проблему, рассматривается веб-приложение «Направления подготовки высшего образования РФ». Приложение разработано на основе RDF-набора данных, который содержит информацию из официальных открытых документов Министерства образования и науки РФ за период с 2001 года до наших дней о научных специальностях, направлениях подготовки бакалавров, магистров и аспирантов, специальностях высшего образования РФ. Для установления соответствия между специальностями, действующими в РФ в разные годы, в RDF-наборе данных используется транзитивное свойство equalsTo. Хотя разработанный алгоритм сформулирован и использован в терминах конкретной предметной области для решения проблемы отдельного приложения, он достаточно универсален и может быть применен веб-разработчиками для решения проблемы транзитивности в RDF-наборах данных других предметных областей., The article focuses on the issues of knowledge representation in the form of web ontologies. The relevance of the study is due to the two factors. On the one hand, a large number of OWL ontologies and RDF datasets have been created as part of semantic web concept development in recent years. On the other hand, the OWL language has a number of limitations that do not always allow adequate representation of domain knowledge. For example, SPARQL queries that use the transitive properties of the OWL language can create some kind of "loops" and return incorrect information. This article demonstrates that in some cases it is preferable not to use the transitivity of properties in the ontology. The algorithm for traversing related entities, which enables solving the problem of “loops”, is proposed. To illustrate the issue, we use "Higher educational programs of Russian Federation" web application. This application is developed on the basis of the RDF dataset which contains information about scientific specialties, bachelor’s, master’s and postgraduate programs obtained from publicly available official documents of the Ministry of Science and Higher Education of the Russian Federation since 2001. To set up a correspondence between the fields of studies that have existed over the years in the Russian Federation, equalsTo transitive property is employed in the RDF dataset. Although the developed algorithm is formulated and used in terms of a specific domain to solve the problem of a particular application, it is quite universal and can be applied by web developers to solve the problem of transitivity in RDF datasets of other domains., МОДЕЛИРОВАНИЕ, ОПТИМИЗАЦИЯ И ИНФОРМАЦИОННЫЕ ТЕХНОЛОГИИ, Выпуск 4 (39) 2022, Pages 9-10

In a graph $G$ , two spanning trees $T_{1}$ and $T_{2}$ are rooted at the same vertex $r$ . If, for every $v \in V(G)$ , the paths from $v$ to the root $r$ in $T_{1}$ and $T_{2}$ are internally vertex-disjoint, they are called independent spanning trees (ISTs). ISTs can be applied in numerous fields, such as fault-tolerant broadcasting and secure message distribution. The ( $n$ , $k$ )-star graphs $S_{n,k}$ constitute a generalized version of the star network. The method of constructing ISTs in ( $n$ , $k$ )-star graphs remains unknown. In this paper, we propose one recursive algorithm and one parallel algorithm for constructing ISTs on ( $n$ , $k$ )-star graphs. The main ideas of the recursive algorithm are to use induction to change small trees into large trees, to use a modified breadth-first search (MBFS) traversal to create a frame for an IST, and to use a breadth-first search (BFS) traversal to connect the rest of nodes. The main ideas of the parallel algorithm are to create frames through MBFS traversals in parallel, and to use some specific rules to connect the rest of nodes in parallel. We also present validation proofs for both algorithms, and analyze the time complexities of both algorithms. The time complexity of the recursive algorithm in $S_{n,k}$ is $O\left({n\times \frac {n!}{(n-k)!}}\right)$ , where $\frac {n!}{(n-k)!}$ is the number of nodes of $S_{n,k}$ . The time complexity of the parallel algorithm can be reduced to $O\left({\frac {n!}{(n-k)!}}\right)$ if the system has $n-1$ processors computing in parallel. Both algorithms are correct with the stated time complexity values; the parallel algorithm is more efficient than the recursive algorithm.

Modifications are proposed to the recursive algorithm of combinations generation by reducing the number of non-performing recursive calls and recovering this gap through iterative processes.

In connection with the development of next-generation wireless networks based on LTE technology, demands for high-speed services are increasing leading to an exponential increase in the volume of traffic generated in mobile networks. According to the latest data from Cisco Systems, this volume will increase by 46 percent by 2021. At the same time, requirements for the level of quality of service (QoS) are increasing. The rapid growth of traffic in the conditions of providing users with a wide range of high-quality multimedia services leads to a lack of available frequency resources. This problem be-comes the main one in the development of modern wireless technologies. In this regard, cellular net-work operators offer various methods for its solution, for example, using the LAA (Licensed Assist-ed-Access) or LSA (Licensed Shared Access) systems allowing more efficient use of available frequency resources. In addition, in the framework of the implementation of various technologies to ensure the required QoS, radio resource management mechanisms (RRM) such as reducing data transmission power and interrupting users’ service can be applied. Models implementing such mechanisms can be described as queuing systems (QS) with unreliable servers. In the paper, a model of a wireless network cell is constructed, presented in the form of a QS, servers of which are in a random environment (RE). RE state can change, which is technically equivalent to a decrease or increase in the transmission pow-er. Reducing power may interrupt users’ service. Exact and approximate methods are proposed for calculating the stationary probability distribution of the model.

The main research object of this paper is to present a systematic computational procedure for computing the inverse of a generalized Vandermonde matrix. Short and rigorous proofs for the formulas of the determinant and the inverse of a generalized Vandermonde matrix are proposed. The computational cost of this method is O(n2). The proposed method can be used efficiently for hand calculation as well as for computer programming. Some examples are given for the sake of illustration. Furthermore, we present a simulation study to compare the time spent to calculate the inverse using the proposed algorithm and the inverse function in Maple.

Collaborative filtering (CF) is a recommendation technique that analyzes the behavior of various users and recommends the items preferred by users with similar preferences. However, CF methods suffer from poor recommendation accuracy when the user preference data used in the recommendation process is sparse. Data imputation can alleviate the data sparsity problem by substituting a virtual part of the missing user preferences. In this paper, we propose a k-recursive reliability-based imputation (k-RRI) that first selects data with high reliability and then recursively imputes data with additional selection while gradually lowering the reliability criterion. We also propose a new similarity measure that weights common interests and indifferences between users and items. The proposed method can overcome disregarding the importance of missing data and resolve the problem of poor data imputation of existing methods. The experimental results demonstrate that the proposed approach significantly improves recommendation accuracy compared to those resulting from the state-of-the-art methods while demanding less computational complexity.

Meta-elliptical copulas are often proposed to model dependence between the components of a random vector. They are specified by a correlation matrix and a map $g$, called density generator. While the latter correlation matrix can easily be estimated from pseudo-samples of observations, the density generator is harder to estimate, especially when it does not belong to a parametric family. We give sufficient conditions to non-parametrically identify this generator. Several nonparametric estimators of $g$ are then proposed, by M-estimation, simulation-based inference, or by an iterative procedure available in the R package ElliptCopulas. Some simulations illustrate the relevance of the latter method., Comment: 27 pages, 10 figures

International audience; We consider the problem of multiple knife-edge diffraction estimation which is a fundamental task in many wireless communication applications. So far, one of the most accurate methods for this problem is the Vogler one whose recursive implementation is efficient to reduce the high computational complexity of the direct one. However, in the original report, Vogler only presented the final result of the recursive algorithm without a rigorous mathematical proof, thus making the method difficult to understand and implement in practice. To tackle this shortcoming, we first analyze the mathematical structure of the problem and then present a formal proof of the result. To gain intuition of the proof and the key steps, we provide a simplified study case of four knife-edges. The insight from our proposed analysis and proof can be used to obtain a comprehensive interpretation, initiate a practical implementation and develop new efficient algorithms with similar structure.

Kalman filtering is a linear quadratic estimation (LQE) algorithm that uses a time series of observed data to produce estimations of unknown variables. The Kalman filter (KF) concept is widely used in applied mathematics and signal processing. In this study, we developed a methodology for estimating Gaussian errors by minimizing the symmetric loss function. Relevant applications of the kinetic models are described at the end of the manuscript.

Recently, a multiple-resonator structure was proposed as a robust and computationally efficient tool for harmonic analysis. Two trivial cases have been previously observed. The first case exhibits good out-of-band suppression and elimination of unwanted harmonics, but with a high latency. In the second case, a phase frequency response around the passband centre is zero-flat, that provides fast estimates. However, in this case, resonant peaks at the ends of the passband and high interharmonic gains cause large overshoots. In general, the basic algorithm performance requirements: selectivity and speed, are contradictory which makes it impossible to completely fulfil both of them. In this paper, the Constrained Linear Least-Squares (CLLS) optimization method is used to obtain a compromise solution. As a result, the resonant peaks in the passband are avoided and side lobes are mitigated, simultaneously minimizing the group delay in the middle of the passband. Performed simulations confirmed the effectiveness of the proposed algorithm.

The Quasi-Maximum Likelihood (QML) procedure is widely used for statistical inference due to its robustness against overdispersion. However, while there are extensive references on non-recursive QML estimation, recursive QML estimation has attracted little attention until recently. In this paper, we investigate the convergence properties of the QML procedure in a general conditionally heteroscedastic time series model, extending the classical offline optimization routines to recursive approximation. We propose an adaptive recursive estimation routine for GARCH models using the technique of Variance Targeting Estimation (VTE) to alleviate the convergence difficulties encountered in the usual QML estimation. Finally, empirical results demonstrate a favorable trade-off between the ability to adapt to time-varying estimates and stability of the estimation routine.

International audience; We first improve the known lower bound for the absolute Zhang-Zagier measure in the general case. Then we restrict our study to totally positive algebraic integers. In this case, we are able to find six points for the related spectrum. At last, we give inequalities involving the Zhang-Zagier measure, the Mahler measure and the length of such integers.

We have developed a sequential recursive Kalman Filter algorithm to filter data in the field of the non-Gaussian noise distribution to be used in measurement instruments. A special feature of the constructed Kalman Filter algorithm to filter data with the non-Gaussian noises is the absence of a need to determine a priori the statistical characteristics of noise. The applicability of the developed Kalman filtering procedure was tested by processing different distribution laws: the Cauchy, Pareto noises, normal and logistic distributions. The effectiveness of the devised filtering procedure is confirmed by applying the filter when processing experimental data with different laws of noise distribution. We have conducted approbation of the developed procedure for the Kalman filtering based on data obtained experimentally, with respect to the superposition of noise distribution laws. The a priori estimate for a filtering error when the number of iterations exceeds 30 tends to zero. The devised filtering procedure employing the Kalman filter could be used when performing the metrological certification of measuring instruments under industrial conditions. Under such circumstances, measuring information could become noisy due to various noises, including those that are not governed by the Gaussian distribution law. The filter could be used when processing data from control systems over state parameters, implemented on the principle of a magnitude threshold control. The applied aspect of the scientific result obtained implies the possibility of extending the scope of application of the classic Kalman filter in measurement instruments. This is a prerequisite for the development of a generic filtering algorithm using the Kalman filter.

This paper presents an improved approach to the recently proposed multiple-resonator-based method for the harmonic analysis that has been provided in the previous papers. Previously, two inherent particular cases have been considered. In these cases, reference points in which estimation is performed are located either in the middle or at the end of the observation interval. The first case exhibits a good noises and unwanted harmonics attenuation but possesses a large delay time. In the second case, the filters are able to form a zero-flat phase response about the operation frequency and hence able to provide instantaneous estimates, but with large overshoots caused by resonant frequencies at the edges of the passband, and the high level of the sidelobes, that also makes it susceptible to interharmonics and noise interference. The aim of this paper is to propose a compromised solution provided by the tradeoff between those opposite requirements by shifting this point along the observation interval. This way the frequency responses of the estimator are reshaped. A maximally flatness of the frequency response in the operation harmonic frequency is kept in all cases, but only locating the reference point in a fraction around the center of the observation interval provides flat-top frequency responses. The effectiveness of the proposed estimation technique is shown through simulations.

Quasi-Maximum Likelihood (QML) procedures are theoretically appealing and widely used for statistical inference. While there are extensive references on QML estimation in batch settings, the QML estimation in streaming settings has attracted little attention until recently. An investigation of the convergence properties of the QML procedure in a general conditionally heteroscedastic time series model is conducted, and the classical batch optimization routines extended to the framework of streaming and large-scale problems. An adaptive recursive estimation routine for GARCH models named AdaVol is presented. The AdaVol procedure relies on stochastic approximations combined with the technique of Variance Targeting Estimation (VTE). This recursive method has computationally efficient properties, while VTE alleviates some convergence difficulties encountered by the usual QML estimation due to a lack of convexity. Empirical results demonstrate a favorable trade-off between AdaVol's stability and the ability to adapt to time-varying estimates for real-life data.

International audience; Let α be a nonzero algebraic integer of degree d whose all conjugates α 1 = α, α 2 ,. .. , α d lie in a sector | arg z| ≤ θ, 0 ≤ θ ≤ 90 •. We define the N-measure of α by N(α) = d i=1 (|α i |+1/|α i |) and the absolute N-measure of α by ν(α) = N(α) 1/ deg(α). Firstly, we consider the case θ = 0. We prove that N(α) ∈ N and that, if α is a reciprocal algebraic integer, N(α) is a square. Then, we study the set N of the quantities ν(α). We prove that there exists a number l such that N is dense in (l, ∞). Finally, using the method of auxiliary functions, we find the seven smallest points of N in (2, l). In case of 0 < θ ≤ 90 • , we compute the greatest lower bound c(θ) of the absolute N-measure of α, for α belonging to eight subintervals of ]0, θ[. Among these subintervals, two are complete. These computations are also done by using auxiliary functions. The polynomials involved in the auxiliary functions are found by our recursive algorithm.

As crucial rotary components of high-speed trains, wheel treads in realistic operation environment usually suffer severe cyclic shocks, which damage the health status and ultimately cause safety risks. Timely and precise health prognosis based on vibration signals is an effective technology to mitigate such risks. In this work, a new parameter-related Wiener process model is proposed to capture multiple uncertainties existed in on-site prognosis of wheel treads. The proposed model establishes a quantitative relationship between degradation rate and variations, and integrates uncertainties via heterogeneity analysis of both criterions. A maximum-likelihood-based method is presented to initialize the unknown model parameters, followed by a recursive update algorithm with fully utilization of historical lifetime information. An investigation of real-world wheel tread signals demonstrates the superiority of the proposed model in accuracy improvement.

A scattering (S-) parameter method has been proposed for electromagnetic property extraction of a target layer within metal-backed inhomogeneous metamaterial (MM) structures. It relies on recursive S-parameters for two different polarizations (parallel and perpendicular). Two different algorithms depending on the value of the incidence angles were proposed to add flexibility to our method. The algorithms were first validated by a metal-backed quasi-one-port method applicable only for one-layer (homogeneous) samples. Then, they were applied to extract electromagnetic properties of the split-ring-resonator-wire MM slab of a metal-backed two-layer inhomogeneous structure and the Omega MM slab of a metal-backed four-layer inhomogeneous structure, and extracted properties by our algorithms were compared with those retrieved by different methods applicable for homogeneous samples only. The accuracy of our method was also examined when there was some noise in S-parameters, when there was a misalignment in incidence angles, and a when large value of iteration number was used.

В связи с развитием телекоммуникационных беспроводных сетей последующих поколений, в частности сетей на базе технологии LTE, повышается спрос на высокоскоростные услуги, а также увеличивается число их пользователей. Это приводит к экспоненциальному росту объема передаваемого в мобильных сетях трафика. Согласно последним данным ведущих участников телекоммуникационного рынка, таких как, например, компания Cisco Systems, объем трафика, генерируемого в современных мобильных сетях, увеличится на 46 процентов в период с 2016 по 2021 года. В то же время повышаются требования к уровню качества обслуживания пользователей. Стремительный рост трафика в условиях предоставления пользователям мобильных сетей широкого спектра высококачественных мультимедийных услуг приводит к нехватке доступного частотного диапазона. Данная проблема становится главной в развитии современных технологий беспроводной связи. В связи с этим операторы сотовых сетей предлагают различные методы ее решения, например, применение системы LAA (англ. Licensed Assisted-Access) или LSA (англ. Licensed Shared Access). Эти системы позволяют более эффективно использовать имеющиеся частотные ресурсы. Помимо этого, в рамках реализации различных технологий для обеспечения требуемого уровня качества обслуживания пользователей могут быть применены такие механизмы управления радиоресурсами, как снижение мощности передачи данных и прерывание обслуживания пользователей. Модели реализующие такие механизмы могут быть описаны в виде систем массового обслуживания (СМО) с ненадежными приборами. В работе построена модель соты беспроводнои сети, представленная в виде СМО, приборы которои находятся в случаинои среде. Состояние случайной среды может изменяться, что с технической точки зрения эквивалентно уменьшению или увеличению мощности передачи сигнала. Снижение мощности может привести к прерыванию обслуживания пользователей. Предложены точный и приближенный методы для расчета стационарного распределения вероятностей состояний модели., In connection with the development of next-generation wireless networks based on LTE technology, demands for high-speed services are increasing leading to an exponential increase in the volume of traffic generated in mobile networks. According to the latest data from Cisco Systems, this volume will increase by 46 percent by 2021. At the same time, requirements for the level of quality of service (QoS) are increasing. The rapid growth of traffic in the conditions of providing users with a wide range of high-quality multimedia services leads to a lack of available frequency resources. This problem becomes the main one in the development of modern wireless technologies. In this regard, cellular network operators offer various methods for its solution, for example, using the LAA (Licensed Assisted-Access) or LSA (Licensed Shared Access) systems allowing more efficient use of available frequency resources. In addition, in the framework of the implementation of various technologies to ensure the required QoS, radio resource management mechanisms (RRM) such as reducing data transmission power and interrupting users service can be applied. Models implementing such mechanisms can be described as queuing systems (QS) with unreliable servers. In the paper, a model of a wireless network cell is constructed, presented in the form of a QS, servers of which are in a random environment (RE). RE state can change, which is technically equivalent to a decrease or increase in the transmission power. Reducing power may interrupt users service. Exact and approximate methods are proposed for calculating the stationary probability distribution of the model., №3 (2020)

We consider intervals of the form $\left [ \frac {r}{s}, u \right ] $, where $r,s$ are positive integers with gcd($r,s$)=1 and $u$ is a real number, or of the form $[0, \smash {(\sqrt {a}{-}\sqrt {b})^2} ]$, where $a,b$ are positive integers. Thanks to a lemma of Chudnovsky, we give first a lower bound of the integer transfinite diameter of such intervals. Then, using the method of explicit auxiliary functions and our recursive algorithm, we explain how to get an upper bound for this quantity. We finish with some numerical examples. Secondly, we prove inequalities on the integer transfinite diameter of Farey intervals, i.e., intervals of the type $\bigl [ \frac {a}{q}, \frac {b}{s} \bigr ] $, where $|as-bq|=1$.

In this work, we give a lower bound and an upper bound for the trace of a Salem number whose Mahler measure is less than 1.3. We use the method of explicit auxiliary functions combined with the recursive algorithm developed in [F3].

This paper is concerned with the minimum variance filtering problem for a class of time-varying systems with both additive and multiplicative stochastic noises through a sensor network with a given topology. The measurements collected via the sensor network are subject to stochastic sensor gain degradation, and the gain degradation phenomenon for each individual sensor occurs in a random way governed by a random variable distributed over the interval [0, 1]. The purpose of the addressed problem is to design a distributed filter for each sensor such that the overall estimation error variance is minimized at each time step via a novel recursive algorithm. By solving a set of Riccati-like matrix equations, the parameters of the desired filters are calculated recursively. The performance of the designed filters is analyzed in terms of the boundedness and monotonicity. Specifically, sufficient conditions are obtained under which the estimation error is exponentially bounded in mean square. Moreover, the monotonicity property for the error variance with respect to the sensor gain degradation is thoroughly discussed. Numerical simulations are exploited to illustrate the effectiveness of the proposed filtering algorithm and the performance of the developed filter. This work was supported by the National Natural Science Foundation of China under Grants 61490701, 61210012, 61290324, 61473163, 61522309, and 61273156; in part by the Tsinghua University Initiative Scientific Research Program; and in part by the Jiangsu Provincial Key Laboratory of E-business at Nanjing University of Finance and Economics of China under Grant JSEB201301; and in part by the Research Fund for the Taishan Scholar Project of Shandong Province of China.

A stochastic convergence analysis of the parameter vector estimation obtained by the recursive successive over-relaxation (RSOR) algorithm is performed in mean sense and mean-square sense. Also, excess of mean-square error and misadjustment analysis of the RSOR algorithm is presented. These results are verified by ensemble-averaged computer simulations. Furthermore, the performance of the RSOR algorithm is examined using a system identification example and compared with other widely used adaptive algorithms. Computer simulations show that the RSOR algorithm has better convergence rate than the widely used gradient-based algorithms and gives comparable results obtained by the recursive least-squares RLS algorithm.

This paper proposes a safety stock calculation function based on their distribution properties and create a guideline for the stock status optimization problem. The motivation for this paper originates the cooperation with a drilling tools company, Epiroc Drilling tools AB. The safety stock calculation divides all items into three distribution and design the safety stock for each types separately considering the influence of service level value and lead time. During the process of guideline design, complicated production chain framework is taken into account through recursive algorithm. The stock status combination which can give the minimum storage cost is the optimal guideline for stock item and non-stock item. The time for approximating the global minimum through exhaustive search is remarkably reduced due to the application of Parallel programming and statistical model.

Thanks to our recursive algorithm developed in [Trace of totally positive algebraic integers and integer transfinite diameter, Math. Comp. 78(266) (2009) 1119–1125], we prove that, if [Formula: see text] is a totally positive algebraic integer of degree [Formula: see text] with minimum conjugate [Formula: see text] then, with a finite number of explicit exceptions, [Formula: see text]

International audience; Firstly, we consider intervals of the form r s , u where r, s are positive integers with gcd(r, s)=1 and u is a real number, or of the form [0, (√ a− √ b) 2 ] where a, b are positive integers. Thanks to a lemma of Chudnovsky, we give first a lower bound of the integer transfinite diameter of such intervals. Then, using the method of explicit auxiliary functions and our recursive algorithm, we explain how to get an upper bound for this quantity. We finish with some numerical examples. Secondly, we prove inequalities on the integer transfinite diameter of Farey intervals, i.e., intervals of the type a q , b s where |as − bq| = 1.

We have developed a sequential recursive Kalman Filter algorithm to filter data in the field of the non-Gaussian noise distribution to be used in measurement instruments. A special feature of the constructed Kalman Filter algorithm to filter data with the non-Gaussian noises is the absence of a need to determine a priori the statistical characteristics of noise.The applicability of the developed Kalman filtering procedure was tested by processing different distribution laws: the Cauchy, Pareto noises, normal and logistic distributions. The effectiveness of the devised filtering procedure is confirmed by applying the filter when processing experimental data with different laws of noise distribution. We have conducted approbation of the developed procedure for the Kalman filtering based on data obtained experimentally, with respect to the superposition of noise distribution laws. The a priori estimate for a filtering error when the number of iterations exceeds 30 tends to zero.The devised filtering procedure employing the Kalman filter could be used when performing the metrological certification of measuring instruments under industrial conditions. Under such circumstances, measuring information could become noisy due to various noises, including those that are not governed by the Gaussian distribution law. The filter could be used when processing data from control systems over state parameters, implemented on the principle of a magnitude threshold control.The applied aspect of the scientific result obtained implies the possibility of extending the scope of application of the classic Kalman filter in measurement instruments. This is a prerequisite for the development of a generic filtering algorithm using the Kalman filter., Разработан последовательный рекурсивный алгоритм Фильтра Калмана для фильтрации данных в области шумов отличных от гауссовского распределения для использования в измерительной технике. Отличительной чертой разработанного алгоритма Фильтра Калмана для фильтрации данных с неаусовскими шумами является отсутствие необходимости априорного определения статистических характеристик шума.Была проверена работоспособность разработанной методики фильтрации Калмана путем обработки различных законов распределения: шумов Коши, Парето, нормального и логистического распределений. Эффективность разработанной методики фильтрации подтверждается путем применения фильтра при обработке экспериментальных данных с различными законами распределения шумов. Проведена апробация разработанной методики фильтрации Калмана для данных полученных экспериментально с учетом суперпозиции законов распределения шумов. Априорная оценка ошибки фильтрации при количестве итераций больше 30 стремится к нулю.Разработанная методика фильтрации с использованием фильтра Калмана может быть использована при проведении метрологической аттестации средств измерений в условиях предприятия. В этой ситуации возможно зашумление измерительной информации различными шумами, в том числе и не подчиняющимися закону распределения Гаусса. Фильтр может быть использован при обработке данных систем контроля параметров состояния, реализуемых по принципу порогового контроля величины.Прикладным аспектом использования полученного научного результата есть возможность расширения области применения классического фильтра Калмана в измерительной технике. Это составляет предпосылки для разработки универсального алгоритма фильтрации с использованием фильтра Калмана, Розроблено послідовний рекурсивний алгоритм фільтра Калмана для фільтрації даних в області шумів відмінних від гаусовського розподілу для використання у вимірювальній техніці. Відмінною рисою розробленого алгоритму фільтра Калмана для фільтрації даних з негаусовськими шумами є відсутність необхідності апріорного визначення статистичних характеристик шуму.Була перевірена працездатність розробленої методики фільтрації Калмана шляхом обробки різних законів розподілу: шумів Коші, Парето, нормального і логістичного розподілів. Ефективність розробленої методики фільтрації підтверджується шляхом застосування фільтра при обробці експериментальних даних з різними законами розподілу шумів. Проведено апробацію розробленої методики фільтрації Калмана для даних, отриманих експериментально з урахуванням суперпозиції законів розподілу шумів. Апріорна оцінка помилки фільтрації при кількості ітерацій більше 30 прагне до нуля.Розроблена методика фільтрації з використанням фільтра Калмана може бути використана при проведенні метрологічної атестації засобів вимірювальної техніки в умовах підприємства. В цій ситуації можливе зашумлення вимірювальної інформації різними шумами, в тому числі і тими, що не підкоряються закону розподілу Гауса. Фільтр може бути використаний при обробці даних систем контролю параметрів стану, що реалізуються за принципом порогового контролю величини.Прикладним аспектом використання отриманого наукового результату є можливість розширення області застосування класичного фільтра Калмана в вимірювальній техніці. Це становить передумови для розробки універсального алгоритму фільтрації з використанням фільтра Калмана

A recursive algorithm is proposed to accurately extract the electromagnetic parameters of isotropic/bianisotropic metamaterial (MM) slabs of inhomogeneous structures. The algorithm is based on the recursive calculations of measured/ simulated forward and backward scattering (S-) parameters from previously extracted wave impedances and refractive indices of each homogeneous layer (except the analyzed intermediate layer) by a suitable retrieval method. There are two main advantages of our proposed method over existing extraction algorithms. First, it could retrieve the electromagnetic parameters of both isotropic and bianisotropic MM slabs. Second, it is applicable for electromagnetic parameter extraction of inhomogeneous structures. For validation of our method and assessing its accuracy over existing extraction methods, we used the simulation results of various inhomogeneous structures constructed by different isotropic/bianisotropic MM slabs (split-ring-resonator (SRR), SRR-wire, omega, and omega-wire). For completeness, the effects of noise present in S-parameters and iterative error (by increasing the value of iteration numbers) are examined to test the robustness of the proposed algorithm. © 1963-2012 IEEE.

Fil: Ortíz, Guillermo P. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura; Argentina. Fil: Mochán, W Luis. Universidad Nacional Autónoma de México. Instituto de Ciencias Físicas; México. Keller’s theorem relates the components of the macroscopic dielectric response of a binary twodimensional composite system with those of the reciprocal system obtained by interchanging its components. We present a derivation of the theorem that, unlike previous ones, does not employ the common assumption that the response function relates an irrotational to a solenoidal field and that is valid for dispersive and dissipative anisotropic systems. We show that the usual statement of Keller’s theorem in terms of the conductivity is strictly valid only at zero frequency and we obtain a new generalization for finite frequencies. We develop applications of the theorem to the study of the optical properties of systems such as superlattices, 2D isotropic and anisotropic metamaterials and random media, to test the accuracy of theories and computational schemes, and to increase the accuracy of approximate calculations.

In this paper, a modified and improved approach to the recently proposed multiple-resonator-based observer structure for harmonic estimation has been proposed. In the previous papers, two inherent particular cases have been considered. In the first case, estimation is performed in the point located in the middle of the observation interval, and exhibits good noises and unwanted harmonics attenuation but possesses a large response delay. In the second case, the estimation point is at the end of the observation window. In this case, the filters are able to form a zero-flat phase response about the operation frequency and hence able to provide instantaneous estimates, but with large overshoots caused by resonant frequencies at the edges of the pass band, and the high level of the sidelobs. In this paper, the estimation point is shifted along the observation interval reshaping frequency responses to tradeoff between those opposite requirements. The effectiveness of the proposed algorithm is shown through simulations.

This paper studies the parameter identification problems for multivariable output-error-like systems with colored noises. Based on the hierarchical identification principle, the original system is decomposed into several subsystems. However, each subsystem contains the same parameter vector, which leads to redundant computation. By taking the average of the parameter estimation vectors of each subsystem, a partially-coupled subsystem recursive generalized extended least squares (PC-S-RGELS) algorithm is presented to cut down the redundant parameter estimates. Furthermore, a partially-coupled recursive generalized extended least squares (PC-RGELS) algorithm is presented to further reduce the computational cost and the redundant estimates by using the coupling identification concept. Finally, an example indicates the effectiveness of the derived algorithms.

The learning of recursive algorithms in computer programming is problematic, because its execution and resolution is not natural to the thinking way people are trained and used to since young. As with other topics in algorithms, we use metaphors to make parallels between the abstract and the concrete to help in understanding the operation of recursive algorithms. However, the classic metaphors employed in this area, such as calculating factorial recursively and Towers of Hanoi game, may just confuse more or be insufficient. In this work, we produced a computer game to assist students in computer courses in learning recursive algorithms. It was designed to have regular video game characteristics, with narrative and classical gameplay elements, commonly found in this kind of product. Aiding to education occurs through metaphorization, or in other words, through experiences provided by game situations that refer to recursive algorithms. To this end, we designed and imbued in the game four valid metaphors related to the theory, and other minor references to the subject.

This report is the user's manual for a package of MATLAB™ scripts and functions, developed for recursive prediction error identification of nonlinear state space systems. The identified state space model incorporates delay, which allows a treatment of general nonlinear networked identification, as well as of general nonlinear systems with delay. The core of the package is an implementation of an output error identification algorithm. The algorithm is based on a continuous time, structured black box state space model of a nonlinear system. The software can only be run off-line, i.e. no true real time operation is possible. The algorithms are however implemented so that true on-line operation can be obtained by extraction of the main algorithmic loop. The user must then provide the real time environment. The software package contains scripts and functions that allow the user to either input live measurements or to generate test data by simulation. The scripts and functions for the setup and execution of the identification algorithms are somewhat more general than what is described in the references. The functionality for display of results include scripts for plotting of e.g. data, parameters, prediction errors, eigenvalues and the condition number of the Hessian. The estimated model obtained at the end of a run can be simulated and the model output plotted, alone or together with the data used for identification. Model validation is supported by two methods apart from the display functionality. First, a calculation of the RPEM loss function can be performed, using parameters obtained at the end of an identification run. Secondly, the accuracy as a function of the output signal amplitude can be assessed.

Suprathreshold stochastic resonance (SSR) is a distinct form of stochastic resonance, which occurs in multilevel parallel threshold arrays with no requirements on signal strength. In the generic SSR model, an optimal weighted decoding scheme shows its superiority in minimizing the mean square error (MSE). In this study, we extend the proposed optimal weighted decoding scheme to more general input characteristics by combining a Kalman filter and a least mean square (LMS) recursive algorithm, wherein the weighted coefficients can be adaptively adjusted so as to minimize the MSE without complete knowledge of input statistics. We demonstrate that the optimal weighted decoding scheme based on the Kalman–LMS recursive algorithm is able to robustly decode the outputs from the system in which SSR is observed, even for complex situations where the signal and noise vary over time. Refereed/Peer-reviewed

This paper aims to simplify the continuity conditions of Bezier curves. For this purpose, a special family of Bezier curves with three parameters, to be called adjustable Bezier curves, is constructed. They have the same structure as the quartic Bezier curves. The newly constructed curves possess some of the basic properties of Bezier curves, such as the convex hull property, symmetry, geometric invariance, etc., and they have shape adjustability. Moreover, under the geometric continuity of order 1 ( G 1 ) conditions of the usual Bezier curves, the adjustable Bezier curves can reach geometric continuity of order k ( G k ); here, k is one of the parameters of the newly constructed curves. The recursive evaluation algorithm of the new curves is provided. We also discuss how to construct the adjustable Bezier curves with a given tangent polygon. Numerical examples illustrate the correctness and validity of the proposed method.

A new discrete element method is developed to study the dynamic movement of a flexible fibers in interaction. The fiber model is represented by a chain of rigid bodies connected together by joints. This work is about the 3-D dynamic modeling of a dynamic of fibers using recursive algorithms based on the Newton-Euler equations of the articulated body system and irregular dynamic contact models which is adapted to fiber model. The direct dynamic model gives the joint accelerations as a function of the joint positions, velocities and accelerations. This method guarantees a facility of implementation, fast resolutions and high numerical stability and has a good convergence rate. Dry Fiber Placement project managed by IRT Jules Verne (French Institute in Research and Technology in Advanced Manufacturing Technologies for Composite, Metallic and Hybrid Structures). Industrial and academic partners of this project; Respectively Airbus Group Innovation, AIRBUS OPERATIONS, STELIA Aerospace, COMPOSE Tools, GeM, ICA, CNRS/IRRCyN and ECN.; Le comportement mécanique d’un fil de carbone en compression transverse est caractérisé par des déplacements relatifs importants entre fibres, ce qui lui confère un comportement fortement non-linéairelié aux contacts inter-fibres. Le caractère multi-échelle de la structure fibreuse rend problématique lacaractérisation du comportement mécanique du fil de carbone utilisé dans le procédé de placement defibres sèches automatisé. La complexité de la modélisation mécanique de ce milieu fibreux à l’échelledes fibres est due au fait que la forte non-linéarité mécanique dépend en grande partie de la configurationgéométrique des fibres, des interactions de contact-frottement entre elles et le contexte dynamique de la dépose. Le couplage fort entre chargements et modes de déformation dans les différentes directions et l’évolution de la microstructure, qu’il est bien difficile d’appréhender, accentuent fortement la complexité de la modélisation d’une telle structure fibreuse. Le travail de la thèse s’inscrit dans le cadre de l’optimisation du moyen de dépose robotisé de fils secs avec une source de chaleur par laser. Afin de comprendre le comportement thermo-mécanique du fil au cours de la dépose, un modèle dynamique a été développé pour simuler un milieux fibreux en interaction. Le but est de pouvoir prédire le réarrangement des fibres dans un fil sous sollicitation, ainsi que l’évolution des points de contact entre fibres. Ce travail est une première étape vers l’objectif final qui est de définir les paramètres procédés par rapport à la nature des fils secs déposés permettant d’obtenir une préforme de bonne qualité avec une vitesse de dépose élevée.

A new discrete element method is developed to study the dynamic movement of a flexible fibers in interaction. The fiber model is represented by a chain of rigid bodies connected together by joints. This work is about the 3-D dynamic modeling of a dynamic of fibers using recursive algorithms based on the Newton-Euler equations of the articulated body system and irregular dynamic contact models which is adapted to fiber model. The direct dynamic model gives the joint accelerations as a function of the joint positions, velocities and accelerations. This method guarantees a facility of implementation, fast resolutions and high numerical stability and has a good convergence rate. Dry Fiber Placement project managed by IRT Jules Verne (French Institute in Research and Technology in Advanced Manufacturing Technologies for Composite, Metallic and Hybrid Structures). Industrial and academic partners of this project; Respectively Airbus Group Innovation, AIRBUS OPERATIONS, STELIA Aerospace, COMPOSE Tools, GeM, ICA, CNRS/IRRCyN and ECN.; Le comportement mécanique d’un fil de carbone en compression transverse est caractérisé par des déplacements relatifs importants entre fibres, ce qui lui confère un comportement fortement non-linéairelié aux contacts inter-fibres. Le caractère multi-échelle de la structure fibreuse rend problématique lacaractérisation du comportement mécanique du fil de carbone utilisé dans le procédé de placement defibres sèches automatisé. La complexité de la modélisation mécanique de ce milieu fibreux à l’échelledes fibres est due au fait que la forte non-linéarité mécanique dépend en grande partie de la configurationgéométrique des fibres, des interactions de contact-frottement entre elles et le contexte dynamique de la dépose. Le couplage fort entre chargements et modes de déformation dans les différentes directions et l’évolution de la microstructure, qu’il est bien difficile d’appréhender, accentuent fortement la complexité de la modélisation d’une telle structure fibreuse. Le travail de la thèse s’inscrit dans le cadre de l’optimisation du moyen de dépose robotisé de fils secs avec une source de chaleur par laser. Afin de comprendre le comportement thermo-mécanique du fil au cours de la dépose, un modèle dynamique a été développé pour simuler un milieux fibreux en interaction. Le but est de pouvoir prédire le réarrangement des fibres dans un fil sous sollicitation, ainsi que l’évolution des points de contact entre fibres. Ce travail est une première étape vers l’objectif final qui est de définir les paramètres procédés par rapport à la nature des fils secs déposés permettant d’obtenir une préforme de bonne qualité avec une vitesse de dépose élevée.

Introduction. Broad application for monitoring and control of surrounding space is found by sensor networks. For the passive location of radio sources (RS) in the sensor networks uses the method of RSS (received signal strength). It brings together a group of procedures, the hallmark of which is the application to determine the location of RS of the measured strength values of a received signal. In the known RSS algorithms received on the basis of the least squares method, the error of measurement of the ranges, calculated on the measured values of power isn't considered. At the same time definitions of location of RS is performed after receipt of the measurements from all sensors.Statement of the problem. It is believed that during the propagation of the signal from RS to sensor network, its coordinates don’t change. It is required to synthesize an algorithm which after formation of entry conditions on the basis of measurements of power of signals from three sensors, allowed to specify recurrently location of RS in process of receipt of measurements from other sensors in which the error of measurement of power is considered.The main part. The vector of the estimated parameters includes coordinates of position of a RS on the plane. The recurrent algorithm of estimation is received on the basis of the extended Kalman filter and belongs to the class of quasi-optimal algorithms with Gaussian approximation of a posteriori density of probability. The initial vector of an assessment of coordinates of RS and correlation matrix of an error of assessment are defined on the basis of the method of least squares in the presence of three measurements of the signal power.Analysis of the effectiveness of the algorithm. The analysis of efficiency of recurrent algorithm and its comparison with the known algorithms are carried out by means of statistical modeling. Sensor network includes eight sensors. The RS settles down on a circle with a radius of 600 m. Comparison of precision characteristics of the considered algorithms with the lower bound of Rao-Cramer is carried out.Conclusions. The algorithm is developed belongs to the class of RSS algorithms, which after formation of initial conditions on the basis of measurements of power of signals from three sensors, allows recurrently clarify the location of RS in process of receipt of measurements from other sensors. For the considered example, the values of the circular MSD of an error of assessment of location of RS the developed algorithm is close to potentially achievable values of circular MSD of lower limit of the Cramer-Rao, and less than those of known algorithms on 36-44.4 %. The received algorithm can be also easily extended to a case of a trajectory filtration of a RS at which parameters of his movement are estimated., С использованием математического аппарата расширенного фильтра Калмана разработан рекуррентный алгоритм определения местоположения источников радиоизлучения (ИРИ) в сенсорной сети на основе измеренных значений мощности принятых сигналов. Начальные вектор оценки координат ИРИ и корреляционная матрица ошибки оценки определяются на основе метода наименьших квадратов при наличии трех измерений мощности сигналов. С помощью статистического моделирования выполнен сравнительный анализ точностных характеристик полученного алгоритма с известными RSS-алгоритмами, а также с нижней границей Рао-Крамера., З використанням математичного апарату розширеного фільтра Калмана розроблений рекурентний алгоритм визначення місця розташування джерел радіовипромінювання (ДРВ) в сенсорної мережі на основі виміряних значень потужності прийнятих сигналів. Початкові вектор оцінки координат ДРВ і кореляційна матриця помилки оцінки визначаються на основі методу найменших квадратів при наявності трьох вимірів потужностей сигналів. За допомогою статистичного моделювання виконано порівняльний аналіз точностних характеристик отриманого алгоритму з відомими RSS-алгоритмами, а також з нижньою межею Рао-Крамера.