1. R. E. Hiromoto. J. Pollard. Editorial.
2. C. Papageorgiou, Th. Laopoulos. Self-Calibration of Ultrasonic Transducers in an Intelligent Data Acquisition System.
3. S. Vazquez-Rodriguez, R. J. Duro. A Genetic Based Technique for the Determination of Power System Topological Observability.
4. S. Saukh. Incomplete Cholesky Factorization in Fixed Memory with Flexible Drop-Tolerance Strategy.
5. V. Golovko. Determining of the Lyapunov Spectrum from One-Dimensional Observations Using Neural Networks.
6. N. Kussul, A. Shelestov, A. Sidorenko, S. Skakun, V. Pasechnik. Intelligent Multi-Agent Information Security System.
7. V. Koval, V. Turchenko, V. Kochan, A. Sachenko, G. Markowsky. Smarthe License Plate Recognition System Based on Image Processing Using Neural Network.
8. A. Vechur, A. Chayka, Y. Chemodakov. The Component Method of Scene Analysis and Object Recognition.
9. S. Sengupta, B. Andriamanalimanana, S. W. Card, P. Kadam, S. Ranwadkar, K. Das, S. Parikh. Towards Data Mining Temporal Patterns for Anomaly Intrusion Detection Systems.
10. A.A. Doudkin, R.Kh. Sadykhov, M.E. Vatkin. The Algorithms of Quasi-Optimal Picture Areas Matching.
11. O. Adamiv, V. Koval, I. Turchenko. Predetermined Movement of Mobile Robot Using Neural Networks.
12. J.M. Gorriz, C. G. Puntonet, M. Salmeron, and E. Lang. Time Series Prediction Using ICA Algorithms.
13. A. Lamas and R. J. Duro. A Tool for the Automatic Design of Electronic Control Systems and Circuits for Manufacturing Plants.
14. A. Voschinin, N. Skibitski. Interval Calibration Model of Multysensor System.
15. C. Renotte, A. Vande Wouwer. Stochastic Approximation Techniques Applied to Parameter Estimation in a Biological Model.
16. L. Sragner, G. Horvath. Improved Model Order Estimation for Nonlinear Dynamic Systems.
17. L. Kejzlar, J. Fischer. Inherent Signal Preprocessing in the Line CCD Sensor.
18. I. Kalchev. DSP-Algorithms for Cardiac Symptoms Investigations.
19. G. Shilo, N. Gaponenko. Interval Methods of Assigning the Nominal Tolerances and Choosing Elements.
20. V. Hahanov, G. Krivoulya, I. Hahanova, V. Obrizan. High Performance Fault Simulation for Digital Systems.
21. Y. Nykolaychuk, N. Krutskevych, O. Zastavniy, T. Grinchyshyn. Perspective Architecture and Components of Computer Networks.
22. M. Iwase, S. Hatakeyama. Development of a Teaching Material System for the Fundamental Mathematics Education for Information, Computers and Systems Engineering.
23. P. J. A. Reusch, P. Reusch. Classification of Products and Services to Support Business Process Engineering and e-Commerce.
24. T. Wheeler, K. Vel. A Scalable Inferencing System for Civilian Terrorism Intelligence.
25. V. Shyrochin, V. Mukhin, H. Z. Bing. Users Behavior Model in Tasks of Computer Systems Security Analysis.

        This special issue summarizes the recent advances in theory and applications presented at the Intelligent Data Acquisition and Advanced Computing Systems (IDAACS)’2003 biannual Workshop. IDAACS 2003 provides an excellent opportunity for scientists and engineers from around the world to meet, discuss and exchange ideas, initiate collaborations, and develop new areas of interest. The venue this year was the beautiful city of Lviv in the Ukraine and the conference and poster presentations were made in the historic and superb Palace of Scientists. Once more, the guests were regaled by the generosity and friendly atmosphere that is a hallmark of the hosts from the Institute of Computer Information Technologies of Ternopil Academy of National Economy, Ukraine. The welcoming and innovative social events enhanced the technical discussions and the event was a great success for which we are all grateful.
        The theme of the biannual Workshop acknowledges the importance of attracting scientist and engineers from around the world to participate and exchange ideas that can benefit global economics, effective manufacturing processes, delivery of advanced medical systems, environmental monitoring, sensitive and accurate instrumentation, and homeland and cyber security to name just a few areas of interest. The role of intelligent data acquisition and high-performance computing systems comprise the foundation upon which these current and future areas of application areas must ultimately rely on for successful development. The primary contribution for the IDAACS Workshop then is to provide a needed forum to gather collectively professionals from academia, industry, computer hardware manufacturers, and public and private research institutions to discuss and solve problems of interdisciplinary nature.
        The Workshop sessions were organized under the following topic areas: Advanced Instrumentation in Data Acquisition Systems; Advanced and High-Performance Computing Systems; Artificial Intelligence for Advanced Data Acquisition and Computing Systems; Advanced Mathematical Methods for Data Acquisition and High Performance Computing; Artificial Neural Networks for Advanced Data Acquisition and Computing Systems; Homeland & Cyber Security; Advanced Distributed and Virtual Instrumentation; Modelling and Data Analysis; Intelligent Instrumentation in Distributed and Virtual Systems; Industrial Signal and Image Processing; Advanced Mathematical Methods and Signal Processing; Information Computing Systems; Information Computing Systems for Education and Commercial Applications; Advance Computing Techniques in Economics and Education.
        The use of mathematical theory and techniques such as neural networks, genetic algorithms and interval logic were backed by in-depth analysis of practical Digital Signal Processing (DSP) and software. The following series of papers applied neural network techniques to solutions that ranged from dynamical systems to homeland security.
        V. Golovko: “Determining of Lyapunov Spectrum from One-Dimensional Observations Using Neural Network,” describes the evaluation of the Lyapnuvov spectrum using a one dimensional time series from an unknown dynamical system. The approach is based on the reconstruction of attractor dynamics and the application of multilayer perceptron for forecasting the next state of the dynamical system from the previous state.
        N. Kussul, A. Shelestov, A. Sidorenko, S. Skakun, and V. Pasechnik: “Intelligent Multi-Agent Security System,” proposes a multi-agent approach in developing an intelligent intrusion detection system. In order to detect anomalies in a user’s activities, an on-line multilayer feed-forward neural network is employed to learn the regularities of the user. This approach provides a basis to compare a user model to real activities that may be captured as intrusions.
        V. Koval, V. Turchenko, V. Kochan, A. Sachenko, and G. Markowsky: “The License Plate Recognition System Based on Image Processing Using Neural Network,” address an emerging area of interest in homeland security. The authors propose a smart license plate recognition system based on image fusion, neural networks, and threshold techniques. A prototype of the system is currently undergoing integration and testing as part of a sensor network.
        O. Adamiv, V. Koval, I. Turchenko: “Predetermined Movement of Mobile Robot Using Neural Networks,” looks at the problem of navigating a predetermined path in a partially or unknown environment features. The proposed system uses a video camera for viewing the predetermined direction of the robot motion and three-layer neural network with feed-forward links to adjust adaptively to the imperfections encountered during its motion.
        Laszlo Sragner, Gabor Horvath: “Improved Model Order Estimation for Nonlinear Dynamic Systems,” propose methods to estimate the order of a neural network when used in the modeling nonlinear dynamic systems. The approach taken is the application of the Lipschitz quotient. The associated drawback to this quotient approach is addressed by combining the original Lipschitz method with eh Errors in Variable approach.
        S. Vazquez-Rodriguez, R.J. Duro: “A Genetic Based Technique for the Determination of Power System Topological Observability,” applies genetic algorithms in the determination of the state of a large electric power system is proposed. A genotype-phenotype transformation scheme is developed to build a spanning tree of topological observables that represent the state of the power system.
        A. Lamas and R.J. Duro: “A Tool for the Automatic Design of Electronic Control Systems and Circuits for Manufacturing Plants,” describes a tool that applies evolutionary techniques to design automatically distributed digital circuits for the control of all elements in a manufacturing plant. The objective of this tool is to obtain the best set of controllers for the global operation of the plant; rather than, isolating the criteria of particular parameters of the electronic circuits or individual controllers.
        The application of Interval methods are presented by two papers involved with sensitivity analysis. A. Voschinin, N. Skibitski in “Interval Calibration Model of Multisensor System,” proposes an aggregate interval calibration model to overcome the drawbacks associated with the statistical approach in calibrating a single variable by m sensors of different types. In particular, the interval calibration method avoids the statistical inability to deal with non-statistical type errors and the use of available prior expert information.
        G. Shilo and N. Gaponenko: “Interval Methods of Assigning the Nominal Tolerances and Choosing Elements,” the use of interval mathematics is applied to the problem of assigning tolerances for the parameters of electronic devices. The authors develop methods of assigning the nominal tolerances by combining simplified interval models and the effects of changes of parameters of elements under stress.
        Homeland and cyber security is represented by four papers one of which I have discussed above in the neural network section. The papers below represent varying aspect of intrusion detection.
        S. Sengupta, B. Andriamanalimanana, S.W. Card, P. Kadam, S. Ranwadkar, K. Kas,andS.Parikh: ”Towards Data Mining Temporal Patterns for Anomaly Intrusion Detection Systems,” outlines a low-CPU-usage, low-bufferbased network-, host-, or router-centric intrusion detection system that is essentially an anomaly detector. The basic architecture is iterative where an encounter of a questionable event on it event list triggers an alert signal to the system administrator and post the event to a syslog file for further processing.
        V. Shyrochin, V. Mukhin, and Hu Zheng Bing: “Users Behavior Model in Tasks of Computer Systems Security Analysis,” describes the use of the state machine for modeling a user’s behavior as a detection tool to protect against unauthorized access.
        T. Wheeler, K. Vel: “A Scalable Inferencing System for Civilian Terrorism Intelligence,” describes information fusion within the context of its organization as graphs, the directionality of inferences, patterns matching and level of (un)certainties, etc. These characteristic features are then identified within the context of architectural realizations.
        The application of DSP are applied to new filtering methods and Line CCD sensors. The third paper describe a medical application.
        J.M. Gorriz, Carlos G. Puntonet, Moises Salmeron, and Julio Ortega: “New Method for Filtered ICA Signals Applied To Volatile Time Series,” proposes a new method for volatile time series forecasting using Independent Component Analysis (ICA) algorithms and Savitzky-Golay filtering as a preprocessing tool.
        L. Kejzlar, J. Fischer: “Inherent Signal Preprocessing in the Line CCD Sensor,” describes a new image sensor control method where they use a FIR filter mode of operation.
        I. Kalchev: “DSP-algorithms for cardiac symptoms investigations,” describes an application of digital signal processing (DSP) algorithms in advanced medical treatments has obvious implications. In this regards a DSP algorithm for ECG signal processing is presented and described. The underlying implementation is demonstrated using the MATLAB program.
        Mathematical theory and application techniques are represented in the following papers:
        S. Saukh: “Incomplete Cholesky Factorization in Fixed Memory with Flexible Drop-Tolerance Strategy,” proposes a new incomplete Cholesky factorization that is based on a two-parameter drop-tolerance strategy for the insignificant elements in the incomplete factor matrix. This two-parameter strategy has the advantage of forming the factor matrix in fixed memory.
        C.  Renotte, A. Vande Wouwer: “Stochastic Approximation Techniques Applied to Parameter Estimation in a Biological Model,” studies the optimization benefits of a simultaneous perturbation stochastic approximation (SPSA) technique that allows computing an approximation to the gradient of the objective function by performing simultaneous random perturbations in all the parameters. Two variations of the SPSA algorithms are applied to the dynamic modeling of batch animal cell cultures from sets of experimental data.
        The teaching of mathematics to undergraduates with a range of prior experience is described by
        M. Iwase, S. Hatakeyama in his paper: “Development of a Teaching Material System for the Fundamental Mathematics Education for Information, Computers and Systems Engineering,” In this paper, the authors present an integrated computer network system for the delivery of fundamental mathematical education. The educational approach relies on both a graphical approach and relevant project style lectures where students are expected to participate in demonstrating the understanding of the mathematical concepts.
        The need for a simple classification environment to support e-commerce and multinational product processing is discussed by Peter J.A. Reusch and Pascal Reusch. In “Classification of Products and Services to Support Business Process Engineering and e-Commerce,” the author discusses and proposals a new XML-based language to support a unified approach in product and service classification that has significant implications to multinational corporations and e-Commerce in general.
        The following two papers applies artificial intelligence techniques to solve problems in object recognition and picture area matching. A. Vechur, A. Chayka, Y. Chemodakov: “The Component Method of Scene Analysis and Object Recognition,” proposes a method for scene analysis and object recognition in real time. The goal of their approach is to minimize the demands on the computer resources required to achieve acceptable recognition quality. The practical importance of this work occurs in real-time, environmental decision-making. A.A. Doudkin, R.Kh. Sadykhov, and M.E. Vatkin: “The Algorithms of Quasioptimal Picture Areas Matching,” this work is motivated by the image matching problems that arise in wafer production and printed circuit board inspection. The problem of finding an optimum matching of partially overlapped picture areas is considered. The authors offer two schemes where the first restricts the areas to rectangular regions, and the second is restricted to areas with identical scale.
        The design of information computing systems are explored in two papers. V. Hahanov, G. Krivoulya, and I. Hahanova, V. Obrizan in “High Performance Fault Simulation for Digital Systems,” develops a fast fault simulation method to address the testing of large-scale digital devices that contains millions of gates. The proposed Backtracked Deductive-Parallel(BDP) fault simulation method is based on the application of Group Theory. Y. Nykolaychuk, N. Krutskevych, O. Zastavniy, T. Grinchyshyn in “Perspective Architecture and Components of Computer Networks,” analyze and design a network with added connectivity for optimal communication and computing balance.
        Finally, C. Papageorgiou, Th. Laopoulos in “Self-Calibration of Ultrasonic Transducers in an Intelligent Data Acquisition System,” presents their design of an advanced on-line automated testing and calibration technique to improve the performance and lifetime of ultrasonic transducers.
 

        The rapid growth of powerful single-chip microcomputers for monitoring and data acquisition applications permits nowadays the design of advanced measuring systems. The work reported here is presenting an advanced on-line monitoring configuration in order to improve the performance and extend the lifetime of ultrasonic transducers by applying an automated testing and calibration technique. The operation of this instrumentation system is based on the fast measurement of frequency and amplitude, performed by the proposed configuration. The combination of this information with the time of flight of each pulse-train is then used to derive practically all characteristics of ultrasonic transducers. Due to its low cost and small size, the system can be used either for characterization and classification of transducers, or as a self-testing and automated calibration section within any high performance ultrasonic system.

        In this paper we have addressed the problem of observability of power systems from the point of view of topological observability and using genetic algorithms for its determination. The objective is to find a way to determine if a system is observable by establishing if a spanning tree of the system that verifies certain properties with regards to the use of available measurements can be obtained. To this end we have developed a genotype-phenotype transformation scheme for genetic algorithms that permits using very simple genetic operators over integer based chromosomes which after a building process can become very complex trees. The procedure was successfully applied to standard benchmark systems and we present some results for one of them.

        We propose an incomplete Cholesky factorization for the solution of large positive definite systems of equations and for the solution of large-scale trust region sub-problems. The factorization is based on the two-parameter (m,p)– drop-tolerance strategy for insignificant elements in the incomplete factor matrix. The factorization proposed essentially reduces the negative processes of irregular distribution and accumulation of errors in factor matrix and provides the optimal rate of memory filling with essential nonzero elements. On the contrary to the known p– retain and t– drop-tolerance strategies, the (m,p)– strategy allows to form the factor matrix in fixed memory.

        This paper discusses the neural network approach for computing of Lyapunov spectrum using one dimensional time series from unknown dynamical system. Such an approach is based on the reconstruction of attractor dynamics and applying of multilayer perceptron (MLP) for forecasting the next state of dynamical system from the previous one. It allows for evaluating the Lyapunov spectrum of unknown dynamical system accurately and efficiently only by using one observation. The results of experiments are discussed.

        It is proposed an agent approach for creation of intelligent intrusion detection system. The system allows detecting known type of attacks and anomalies in user activity and computer system behavior. The system includes different types of intelligent agents. The most important one is user agent based on neural network model of user behavior. Proposed approach is verified by experiments in real intranet of Institute of Physics and Technologies of National Technical University of Ukraine "Kiev Polytechnic Institute.

        This paper describes the Smart Vehicle Screening System, which can be installed into a tollbooth for automated recognition of vehicle license plate information using a photograph of a vehicle. An automated system could then be implemented to control the payment of fees, parking areas, highways, bridges or tunnels, etc. There are considered an approach to identify vehicle through recognizing of it license plate using image fusion, neural networks and threshold techniques as well as some experimental results to recognize the license plate successfully.

        The main aim of this work is to propose method that allows some machine to determine surrounding objects. It is important that algorithm must use small computer resources so that machine could work in real time. To improve segmentation on natural images, it is necessary to combine multiple features effectively. Our experimental results are consistent with the theoretical analysis.

        A reasonably light-weight host and net-centric Network IDS architecture model is indicated. The model is anomaly based on a state-driven notion of “anomaly”. Therefore, the relevant distribution function need not remain constant; it could migrate from states to states without any a priori warning so long as its residency time at a next steady state is sufficiently long to make valid observations there. Only those intrusion events (basically DOS and DDOS variety) capable of triggering anomalous streams of attacks/response both near and/or far of target monitoring point(s) are considered at the first level of detection. At the next level of detection, the filtered states could be fine-combed in a batch mode to mine unacceptable strings of commands or known attack signatures.

        Using common matching quality criteria the problem of optimum matching of partially overlapped picture areas is considered. Two schemes of algorithms are proposed for quasi-optimal solution of the problem with following restrictions: the areas are rectangular and have an identical scale. In the first scheme local criterion is used to estimate a quads of frames located in square matrix. In the second scheme is used the special distance function based on neighbor picture matching criterion. The algorithms are realized in program system of layout metallization restoring of integrated circuits.

        This paper describes the experimental results of neural networks application for mobile robot control on predetermined trajectory of the road.Theret is considered the formation process of training sets for neural network, their structure and simulating features. Researches have showed robust mobile robot movement on different parts of the road.

        In this paper we propose a new method for volatile time series forecasting using Independent Component Analysis (ICA) algorithms and Savitzky-Golay filtering as preprocessing tools. The preprocessed data will be introduce in a based radial basis functions (RBF) Artificial Neural Network (ANN) and the prediction result will be compared with the one we get without these preprocessing tools or the classical Principal Component Analysis (PCA) tool.

        In this paper we have developed a tool for automatically designing distributed digital circuits for the control of all the elements in a manufacturing plant. These circuits can be implemented as traditional boards or programmed into the controllers of the machinery present. The tool is based on evolutionary techniques and provides a way to obtain the best set of controllers for the different elements in the plant using as evaluating criteria parameters related to the global operation of the plant and not to particular parameters of the electronic circuits or individual controllers. These parameters may be productivity, cost, or any other ratio having to do with the real operation of the bussiness. In this work we have extended the evolutionary methodologies in order to be able to design, at the complete system level, combinations of low level systems (digital electronic circuits) without any direct specification of their input/output relationships but rather taking into account the plant they are going to be working in and the high level constraints imposed on the whole system.
        The resulting tool has been tested in a real kitchen furniture manufacturing plant using as test bench the lacquering line within the plant.

        Problem of multisensor system calibration is of great importance in a number of applications. Most often the problem is solving by means of statistical methods using data of calibration controlled experiment. However, in many cases uncertainty and inaccuracy of experimental data more reasonably to express not in terms of random errors but in terms of known bounded absolute errors. For this case based on the introduced definition of “interval readings” interval calibration model is suggested. Within interval paradigm all calibration subproblems are reasonably solved including sensor sensitivity test, most accurate sensors subset selection and aggregate estimation of measurable variable uncertainty interval. There are given a numerical examples.

        Simultaneous perturbation stochastic approximation (SPSA) is a class of optimization algorithms which compute an approximation of the gradient and/or the Hessian of the objective function by varying all the elements of the parameter vector simultaneously and therefore, require only a few objective function evaluations to obtain first or second-order information. Consequently, these algorithms are particularly well suited to problems involving a large number of design parameters. In this study, their potentialities are assessed in the context of nonlinear system identification. To this end, a challenging modeling application is considered, i.e. dynamic modeling of batch animal cell cultures from sets of experimental data. The performance of the optimization algorithms are discussed in terms of efficiency, accuracy and ease of use.

        In system modeling the choice of proper model structure is an essential task. Model structure is defined if both the model class and the size of the model within this class are determined. In dynamic system modeling model size is mainly determined by model order. The paper deals with the question of model order estimation when neural networks are used for modeling nonlinear dynamic systems. One of the possible ways of estimating the order of a neural model is the application of Lipschitz quotient. Although it is easy to use this method, its main drawback is the high sensitivity to noisy data. The paper proposes a new way to reduce the effect of noise. The idea of the proposed method is to combine the original Lipschitz method and the Errors In Variables (EIV) approach. The paper presents the details of the proposed combined method and gives the results of an extensive experimental study.

        This paper is devoted to the description and practical verification of a new line CCD sensor control method. This method is used for inherent signal preprocessing or processing in line CCD sensor. This new method is suitable for movement compensation, one-frame filtration or two-frame filtration. Because of the similarity between a Non-Recursive Digital Filter with Finite Impulse Response (NRDF FIR) and the new mode we named it FIR mode. Conclusions and hints applicable for operation of line CCD sensor in FIR mode are also included in this paper.

        The achievements of the advanced medicine are not possible without the use of technical sciences. The aspiration for perfect instrumentation and for high precision of the technical systems for analysis of cardiac activity are still a challenge to engineers. The invention of more effective and with better quality indexes systems will permit a fast diagnostics, therefore a better medical treatment.
        In the present paper the main cardiac-vessel symptoms are described and an possible algorithm for program assurance of *P-system for cardiac investigations is proposed. The system is based on ADU 824 type of microprocessor, but the programs are compiled in MATLAB 4.2 environment.

        The procedure of assigning the nominal tolerances is offered. The interval-structure models are used. The influence of exposures is taken into account. The maximum relative volume of tolerances is ensured. The possibility of selecting elements is taken into account.

        Fast backttraced deductive-parallel fault simulation method oriented on processing of complex digital devices containing hundreds of thousand equivalent gates is offered. Data structures and algorithms for method realization are described.

        This article is about using perspective architecture and components of computer networks will permit to increase productivity and reliability of the specialized computer networks not at the expense of escalating elements of system.

        Recently, in especially private college in Japan, dispersion of students’ educational achievement is distinguished, and fundamental educations for freshmen become more important. The education materials, which raise the level of low-achievement students and interest other students simultaneously, are required. Then in this paper, we present a teaching material system and project-style education of fundamental mathematics for freshmen, which was demonstrated in our department. It is highlighted that using this system we assign each student each data composing a project, so that we succeed in not only improving education effect but also constructing the decentralized data-making/acquisition system with students.

        Decades ago individual approaches to classify products and services had been introduced within companies to unify products and to reduce stocks and costs. Other approaches had been introduced to support international trade and tariff systems. Today new approaches are introduced to support e-commerce and improve business processes. All these approaches are different in the way how to classify, what to classify, and what results to get – and the language they use. The harmonization of all these approaches is very difficult. But especially companies that want to take part in B2B-business need bridges between the different approaches
        In this paper we first present a new XML-based system to remove the language barrier within classification systems and to improve data exchange.
        In the second part we present an implementation of classification systems based on topic maps according to the XTM standard to implement single classification systems and establish mappings between corresponding classes of different classification systems.

        This paper describes an approach to developing a scalable intelligence inferencing system for civilian terrorism intelligence. There is an obvious need for such a system in light of failures in the intelligence community leading to the September 11th attacks. It is intended as a supplement to human intelligence analysis; while intelligence analysts are good at what they do, it’s hard to see what information is important and integrate it. Information and inferences don’t always flow up the chain of command and don’t always get to where they are needed. Automated assistance can aid intelligence analysts, and managers helping to prevent other tragedies from occurring.
        The work explored an approach to automate (or provide assistance for) information fusion which effectively makes inferences over huge amounts of information and number of events using a scalable architecture. It is based on number of technical thought patterns: (1)evolutionary development of a system; (2)the use of layered inference graphs and tree based interpretations of them; (3) combining top-down with bottom-up inference; (4) and pattern matching with (un)certainty and importance calculations; (5)explanation based user interaction; and (6)using spatio-temporal localization, extrapolation/simulation and parallelism to raise inferencing performance to acceptable levels.

        Security of computer systems of various purpose and the appropriate information technologies appreciably depends on tools of user identification and authentication, and also on tools of the analysis of their behavior and behavior of their programs during reception of access to those or other information resources. This article is devoted to a substantiation of a method of use of a known formalism – state machine for modeling users behavior and to testing of protection tools on detection of attempts of the non-authorized access to information resources, including at early stages of preparation for such actions.