Showing papers in "IEEE Transactions on Circuits and Systems I-regular Papers in 2003"
TL;DR: Several new sufficient conditions for ascertaining the existence, uniqueness, and global asymptotic stability of the equilibrium point of such recurrent neural networks are obtained by using the theory of topological degree and properties of nonsingular M-matrix, and constructing suitable Lyapunov functionals.
Abstract: In this paper, the existence and uniqueness of the equilibrium point and its global asymptotic stability are discussed for a general class of recurrent neural networks with time-varying delays and Lipschitz continuous activation functions. The neural network model considered includes the delayed Hopfield neural networks, bidirectional associative memory networks, and delayed cellular neural networks as its special cases. Several new sufficient conditions for ascertaining the existence, uniqueness, and global asymptotic stability of the equilibrium point of such recurrent neural networks are obtained by using the theory of topological degree and properties of nonsingular M-matrix, and constructing suitable Lyapunov functionals. The new criteria do not require the activation functions to be differentiable, bounded or monotone nondecreasing and the connection weight matrices to be symmetric. Some stability results from previous works are extended and improved. Two illustrative examples are given to demonstrate the effectiveness of the obtained results.
526 citations
TL;DR: In this paper, a switch-capacitor (SC) circuit is integrated within a boost converter for a steep step-up of the line voltage, allowing for a boost of the input voltage to high values.
Abstract: A new circuit is proposed for a steep step-up of the line voltage. It integrates a switched-capacitor (SC) circuit within a boost converter. An SC circuit can achieve any voltage ratio, allowing for a boost of the input voltage to high values. It is unregulated to allow for a very high efficiency. The boost stage has a regulation purpose. It can operate at a relatively low duty cycle, thus avoiding diode-reverse recovery problems. The new circuit is not a cascade interconnection of the two power stages; their operation is integrated. The simplicity and robustness of the solution, the possibility of getting higher voltage ratios than cascading boost converters, without using transformers with all their problems, and the good overall efficiency are the benefits of the proposed converter.
439 citations
TL;DR: Results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov are employed, and global convergence is addressed by using a Lyapunov-like approach based on the concept of monotone trajectories of a differential inclusion.
Abstract: The paper introduces a general class of neural networks where the neuron activations are modeled by discontinuous functions. The neural networks have an additive interconnecting structure and they include as particular cases the Hopfield neural networks (HNNs), and the standard cellular neural networks (CNNs), in the limiting situation where the HNNs and CNNs possess neurons with infinite gain. Conditions are derived which ensure the existence of a unique equilibrium point, and a unique output equilibrium point, which are globally attractive for the state and the output trajectories of the neural network, respectively. These conditions, which are applicable to general nonsymmetric neural networks, are based on the concept of Lyapunov diagonally-stable neuron interconnection matrices, and they can be thought of as a generalization to the discontinuous case of previous results established for neural networks possessing smooth neuron activations. Moreover, by suitably exploiting the presence of sliding modes, entirely new conditions are obtained which ensure global convergence in finite time, where the convergence time can be easily estimated on the basis of the relevant neural-network parameters. The analysis in the paper employs results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov. In particular, global convergence is addressed by using a Lyapunov-like approach based on the concept of monotone trajectories of a differential inclusion.
428 citations
TL;DR: This paper presents a complete set of blocks implemented in the popular MATLAB SIMULINK environment, which allows designers to perform time-domain behavioral simulations of switched-capacitor sigma-delta (/spl Sigma//spl Delta/) modulators.
Abstract: This paper presents a complete set of blocks implemented in the popular MATLAB SIMULINK environment, which allows designers to perform time-domain behavioral simulations of switched-capacitor (SC) sigma-delta (/spl Sigma//spl Delta/) modulators. The proposed set of blocks takes into account most of the SC /spl Sigma//spl Delta/ modulator nonidealities, such as sampling jitter, kT/C noise, and operational amplifier parameters (white noise, finite DC gain, finite bandwidth, slew rate and saturation voltages). For each block, a description of the considered effect as well as all of the implementative details are provided. The proposed simulation environment is validated by comparing the simulated behavior with the experimental results obtained from two actual circuits, namely a second-order low-pass and a sixth-order bandpass SC /spl Sigma//spl Delta/ modulator.
413 citations
TL;DR: It is shown that synchronization and desynchronization of such a complex dynamical network can be determined by the network topology and the maximum Lyapunov exponent of the individual chaotic nodes.
Abstract: We study synchronization and desynchronization of a complex network of chaotic dynamical systems, in both continuous-time and discrete-time cases. With proved synchronization conditions, we illustrate network synchronization and desynchronization processes by a prototype composing of Henon maps in a scale-free network. We show that synchronization and desynchronization of such a complex dynamical network can be determined by the network topology and the maximum Lyapunov exponent of the individual chaotic nodes.
293 citations
TL;DR: These results include several sufficient conditions for the global exponential stability of general neural networks with time-varying delays and without monotone, bounded, or continuously differentiable activation function.
Abstract: This brief presents new theoretical results on the global exponential stability of neural networks with time-varying delays and Lipschitz continuous activation functions. These results include several sufficient conditions for the global exponential stability of general neural networks with time-varying delays and without monotone, bounded, or continuously differentiable activation function. In addition to providing new criteria for neural networks with time-varying delays, these stability conditions also improve upon the existing ones with constant time delays and without time delays. Furthermore, it is convenient to estimate the exponential convergence rates of the neural networks by using the results.
252 citations
TL;DR: In this paper, three sufficient conditions for the global exponential stability of cellular neural networks with time delays are presented, which provide algebraic criteria for stability verifications and improve upon existing ones with stronger conditions.
Abstract: This brief presents three sufficient conditions for the global exponential stability of cellular neural networks with time delays. The new stability results provide algebraic criteria for stability verifications and improve upon existing ones with stronger conditions. To demonstrate the differences and features of the new stability criteria, several examples are discussed to compare the present results with the existing ones.
195 citations
TL;DR: In this paper, a sufficient condition for the existence, uniqueness, and global robust stability of the equilibrium point for Hopfield-type delayed neural networks is presented. But this condition is not applicable to the case of delay-dependent networks.
Abstract: This work presents a sufficient condition for the existence, uniqueness, and global robust stability of the equilibrium point for Hopfield-type delayed neural networks. The result imposes constraint conditions on the boundary values of the network parameters independently of the delay parameter. This result is compared with the previous results derived in the literature.
176 citations
TL;DR: Wang et al. as mentioned in this paper developed a new hidden Markov tree (HMT) for statistical texture characterization in the wavelet domain, where the joint statistics captured by HMT can also exploit the cross correlation across DWT subbands.
Abstract: Wavelet-domain hidden Markov models (HMMs), in particular, hidden Markov tree (HMT), were recently proposed and applied to image processing, where it was usually assumed that three subbands of the two-dimensional discrete wavelet transform (DWT), i.e., HL, LH, and HH, are independent. In this paper, we study wavelet-based texture analysis and synthesis using HMMs. Particularly, we develop a new HMM, called HMT-3S, for statistical texture characterization in the wavelet domain. In addition to the joint statistics captured by HMT, the new HMT-3S can also exploit the cross correlation across DWT subbands. Meanwhile, HMT-3S can be characterized by using the graphical grouping technique, and has the same tree structure as HMT. The proposed HMT-3S is applied to texture analysis, including classification and segmentation, and texture synthesis with improved performance over HMT. Specifically, for texture classification, we study four wavelet-based methods, and experimental results show that HMT-3S provides the highest percentage of correct classification of over 95% upon a set of 55 Brodatz textures. For texture segmentation, we demonstrate that more accurate texture characterization from HMT-3S allows the significant improvements in terms of both classification accuracy and boundary localization. For texture synthesis, we develop an iterative maximum likelihood-based texture synthesis algorithm which adopts HMT or HMT-3S to impose the joint statistics of the texture DWT, and it is shown that the new RMT-3S enables more visually similar results than HMT does.
166 citations
TL;DR: In this article, the problem of designing a filter for a class of fuzzy dynamical systems that guarantees that the L/sub 2/ gain from an exogenous input to a filter error is less or equal to a prescribed value and the filter is quadratically stable in a prespecified linear matrix inequality (LMI) stability region is addressed.
Abstract: This brief addresses the problem of designing a filter for a class of fuzzy dynamical systems that guarantees that: 1) the L/sub 2/ gain from an exogenous input to a filter error is less or equal to a prescribed value and 2) the filter is quadratically stable in a prespecified linear matrix inequality (LMI) stability region. Based on an LMI approach, solutions to the problem of the H/sub /spl infin// fuzzy filtering with quadratic D stability are derived in terms of a family of LMIs. Numerical simulation examples are presented to illustrate the theory development.
161 citations
TL;DR: In this article, the problem of continuous-time Kalman filtering for a class of linear, uncertain time-lag systems with randomly jumping parameters is considered, where the parameter uncertainties are norm bounded and the transitions of the jumping parameters are governed by a finite-state Markov process.
Abstract: The problem of continuous-time Kalman filtering for a class of linear, uncertain time-lag systems with randomly jumping parameters is considered. The parameter uncertainties are norm bounded and the transitions of the jumping parameters are governed by a finite-state Markov process. We establish LMI-based sufficient conditions for stochastic stability. The conditions under which a linear delay-less state estimator guarantees that the estimation error covariance lies within a prescribed bound for all admissible uncertainties are investigated. It is established that a robust Kalman filter algorithm can be determined in terms of two Riccati equations involving scalar parameters. The developed theory is illustrated by a numerical example.
TL;DR: In this article, a new design method for two-dimensional (2-D) recursive digital filters using genetic algorithms (GAs) is examined, where the design of the 2-D filter is reduced to a constrained minimization problem the solution of which is achieved by the convergence of an appropriate GA.
Abstract: In this paper, we examine a new design method for two-dimensional (2-D) recursive digital filters using genetic algorithms (GAs). The design of the 2-D filter is reduced to a constrained minimization problem the solution of which is achieved by the convergence of an appropriate GA. Theoretical results are illustrated by a numerical example. Also, comparison with the results of some previous design methods is attempted.
TL;DR: It is proved that the existence of a set of solvable bilinear matrix inequalities suffices to guarantee the quadratic stabilization of an uncertain fuzzy system in an H/sub /spl infin// sense.
Abstract: An optimization technique is proposed to represent a class of nonlinear systems by a Takagi-Sugeno uncertain fuzzy model. Then, a robust H/sub /spl infin// quadratic stabilization problem to the uncertain fuzzy systems via static output feedback is investigated. It is proved that the existence of a set of solvable bilinear matrix inequalities (BMIs) suffices to guarantee the quadratic stabilization of an uncertain fuzzy system in an H/sub /spl infin// sense. A linear matrix inequality formulation is suggested to alleviate the difficulties of BMI that are inherited from the stabilizability problems via static output feedback control. Both continuous- and discrete-time systems are treated in a unified approach and connections to state feedback and dynamic-output feedback are addressed.
TL;DR: In this article, sufficient conditions for global exponential stability of neural networks with variable delays are obtained. But the conditions for the existence, uniqueness, and globally exponential stability are not studied.
Abstract: In this brief, the conditions ensuring existence, uniqueness, and globally exponential stability of the equilibrium point of neural networks with variable delays are studied. Applying the ideas of the vector Lyapunov function and M-matrix theory, sufficient conditions for global exponential stability of neural networks are obtained.
TL;DR: In this article, a new signal detection and estimation method based on the intermittency transition between order and chaos is developed, and the length of the laminar phase of the bifurcation is exploited to describe quantitatively the property of sensitivity dependence on the initial condition of the chaotic Duffing system.
Abstract: A new signal detection and estimation method based on the intermittency transition between order and chaos is developed. The corresponding bifurcation process for the Duffing oscillator is discussed in detail, and the length of the laminar phase of the bifurcation is exploited to describe quantitatively the property of sensitivity dependence on the initial condition of the chaotic Duffing system. Estimation and detection of weak signals are carried out through obtaining the value and the probability distribution of the laminar length.
TL;DR: Criteria on uniform equi-boundedness andEqui-Lagrange stability for impulsive systems are derived and are used to synchronize two nonidentical chaotic systems by impulsively controlling a nonautonomous second order system, which leads to the development of an induced-message scheme for communication system security.
Abstract: In this paper, criteria on uniform equi-boundedness and equi-Lagrange stability for impulsive systems are derived. These criteria are used to synchronize two nonidentical chaotic systems by impulsively controlling a nonautonomous second order system, which leads to the development of an induced-message scheme for communication system security. With the scheme, message signals are not transmitted across public channels, but induced at the receiver end. The scheme overcomes the transmission time-frame congestion in impulsive cryptosystems discussed in the literature and improves system security. Simulation results are given to demonstrate the performance of the proposed scheme.
TL;DR: In this paper, the robust L/sub 2/L/sub /spl infin// filtering problem for uncertain systems with multiple time-varying state delays is studied, where the uncertain parameters are supposed to reside in a polytope and the design of robust full-order and reduced-order filters guaranteeing a prescribed energy-to-peak noise-attenuation level for all admissible uncertainties and time delays is focused.
Abstract: This paper is concerned with the robust L/sub 2/-L/sub /spl infin// filtering problem for uncertain systems with multiple time-varying state delays. The uncertain parameters are supposed to reside in a polytope and the attention is focused on the design of robust full-order and reduced-order filters guaranteeing a prescribed energy-to-peak noise-attenuation level for all admissible uncertainties and time delays. The admissible filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities, which can be solved via efficient interior-point algorithms. Both delay-independent and dependent approaches are presented, with an example illustrating the validity of the proposed designs.
TL;DR: Using reconfigurable devices to implement emulated digital architectures provides more flexibility compared to the custom very large-scale integration designs because different Falcon architectures can be used on the same FPGA device.
Abstract: A new emulated digital multilayer cellular neural network (universal machine (CNN-UM) chip architecture called Falcon has been developed. In this brief, the main steps of the field-programmable gate array (FPGA) implementation are introduced. The main results are as follows. The CNN-UM architecture emulated on Xilinx Virtex series FPGA, three-dimensional nonlinear spatio-temporal dynamics can be implemented on this architecture. The critical parameters of the implementation in a single-layer configuration are 55 million cell update/s/processor core, or, equivalently 1 giga-operation per second (GOPS) computing performance. In the face of the high performance, the power requirements of the architecture are relatively low only /spl sim/3 W per processor core. Using reconfigurable devices to implement emulated digital architectures provides more flexibility compared to the custom very large-scale integration designs because different Falcon architectures can be used on the same FPGA device.
TL;DR: In this article, the authors presented several new chaos generators, switching piecewise-linear controllers, which can generate some new chaotic attractors with two or three merged basins of attraction from a given three-dimensional linear autonomous system within a wide range of parameter values.
Abstract: This paper presents several new chaos generators, switching piecewise-linear controllers, which can generate some new chaotic attractors with two or three merged basins of attraction from a given three-dimensional linear autonomous system within a wide range of parameter values. Based on this success, chaotic attractors with n merged basins of attraction are further generated using a formalized controller design methodology. Basic dynamical behaviors of the controlled chaotic system are then investigated via both theoretical analysis and numerical simulation. To that end, the underlying chaos-generation mechanism is further explored by analyzing the parameterization of the controlled system and the dynamics of the system orbits.
TL;DR: In this paper, a generalized circuit structure of bi-directional switched-capacitor dc/dc converters that feature voltage stepdown, voltage step-up, and power flow was presented.
Abstract: This paper presents a generalized circuit structure of bi-directional switched-capacitor dc/dc converters that feature voltage step-down, voltage step-up, and bi-directional power flow. The starting point is the derivation of two structures of single-capacitor bi-directional converter cells. Current control scheme is applied in the capacitor-charging phase, resulting in a near-constant capacitor charging current and low electromagnetic interference. A converter string is then formulated by cascading a number of converter cells, in order to meet the input and output voltage requirements and conversion efficiency. By paralleling two similar strings and operating them in the anti phase, the overall converter input current becomes continuous. A reduced-order modeling and state-space averaging technique are used to study the static and dynamic behavior of the converter. The theoretical conversion efficiency in the step-down and step-up mode, respectively, is investigated for different voltage-conversion ratios and numbers of stages. The performance of the proposed structure is experimentally verified on a 5-V/12-V prototype.
TL;DR: In this paper, a quantitative analysis of the operating characteristics of three-phase diode bridge rectifiers with AC-side reactance and constant-voltage loads is presented, where simple approximate expressions are derived for the line and output current characteristics as well as the input power factor.
Abstract: This work presents a quantitative analysis of the operating characteristics of three-phase diode bridge rectifiers with AC-side reactance and constant-voltage loads. We focus on the case where the AC-side currents vary continuously (continuous AC-side conduction mode). This operating mode is of particular importance in alternators and generators, for example. Simple approximate expressions are derived for the line and output current characteristics as well as the input power factor. Expressions describing the necessary operating conditions for continuous AC-side conduction are also developed. The derived analytical expressions are applied to practical examples and both simulations and experimental results are utilized to validate the analytical results. It is shown that the derived expressions are far more accurate than calculations based on traditional constant-current models.
TL;DR: The new Chinese remainder theorem introduced recently has been employed to exploit the special properties of the proposed moduli set where modulo corrections are done without resorting to the costly and time consuming modulo operations.
Abstract: The inherent properties of carry-free operations, parallelism and fault-tolerance have made the residue number system a promising candidate for high-speed arithmetic and specialized high-precision digital signal-processing applications. However, the reverse conversion from the residues to the weighted binary number has long been the performance bottleneck, particularly when the number of moduli set increases beyond 3. In this paper, we present an elegant residue-to-binary conversion algorithm for a new 4-moduli set {2/sup n/ $1, 2/sup n/, 2/sup n/ + 1, 2/sup 2n/ + 1}. The new Chinese remainder theorem introduced recently has been employed to exploit the special properties of the proposed moduli set where modulo corrections are done without resorting to the costly and time consuming modulo operations. The resulting architecture is notably simple and can be realized in hardware with only bit reorientation and one multioperand modular adder. The new reverse converter has superior area-time complexity in comparison with the reverse converters for several other 4-moduli sets.
TL;DR: In this article, a strategy for the design of source-coupled logic (SCL) gates both with and without an output buffer is proposed, and closed-form design equations to size bias currents and transistor aspect ratios to meet assigned specifications are derived from a simple SCL gate analytical delay model.
Abstract: In this paper, a strategy for the design of source-coupled logic (SCL) gates both with and without an output buffer is proposed. Closed-form design equations to size bias currents and transistor aspect ratios to meet assigned specifications are derived from a simple SCL gate analytical delay model, shown to be sufficiently accurate by extensive simulations. The design criteria proposed are simple and provide the designer with a more profound understanding of the tradeoff between delay and power consumption. More specifically, design criteria are derived to consciously manage this tradeoff in practical design cases, i.e., when either high performance or an optimum balance with power dissipation is needed. Therefore, the strategy proposed is useful right from the early design phases, and avoids tedious simulation iterations.
TL;DR: In this article, a design procedure for the class-E amplifier with a nonlinear shunt capacitance is presented, and simulation of the designed class-e amplifier is performed to verify the design equations that ensure zero-voltage-switching operation.
Abstract: Comparison of various parameters of the class-E amplifier with nonlinear and linear shunt capacitance is given. A concept of an equivalent linear shunt capacitance is introduced. The following parameters are compared for the amplifiers with nonlinear and linear shunt capacitance at the duty cycle D=0.5: series reactance, peak switch voltage, and power capability. A design procedure for the class-E amplifier with a nonlinear shunt capacitance is presented. Simulation of the designed class-E amplifier is performed to verify the design equations that ensure zero-voltage-switching operation.
TL;DR: A class of chaos-based pseudorandom bit generators is constructed and simple arguments are given to explain the unpredictability of the generators.
Abstract: Different possibilities of using chaotic maps as pseudorandom number generators are discussed. A class of chaos-based pseudorandom bit generators is constructed. We give simple arguments to explain the unpredictability of the generators.
TL;DR: In this paper, generalized first integrals are used to characterize the most destabilizing nonlinearity and to explicitly construct a Lyapunov function that yields an easily verifiable, necessary and sufficient condition for absolute stability of second-order systems.
Abstract: We consider the problem of absolute stability of linear feedback systems in which the control is a sector-bounded time-varying nonlinearity. Absolute stability entails not only the characterization of the "most destabilizing" nonlinearity, but also determining the parametric value of the nonlinearity that yields instability of the feedback system. The problem was first formulated in the 1940s, however, finding easily verifiable necessary and sufficient conditions for absolute stability remained an open problem all along. Recently, the problem gained renewed interest in the context of stability of hybrid dynamical systems, since solving the absolute stability problem implies stability analysis of switched linear systems. In this paper, we introduce the concept of generalized first integrals and use it to characterize the "most destabilizing" nonlinearity and to explicitly construct a Lyapunov function that yields an easily verifiable, necessary and sufficient condition for absolute stability of second-order systems.
TL;DR: In this article, a modified phasor transformation is proposed that converts a frequency-modulated signal into an equivalent time-varying PHASOR model of the LCC resonant ballast, which explicitly models the effect of the frequency modulation on the envelopes of the outputs and facilitates ac analysis of the ballast in addition to envelope transient simulation, and is verified through comparison of experimental and simulation results.
Abstract: This paper presents analytical tools aimed at improving and simplifying the development of frequency-controlled dimming electronic ballasts. A modified phasor transformation is proposed that converts a frequency-modulated signal into an equivalent time-varying phasor. The proposed transformation is applied to develop a complete small-signal phasor model of the LCC resonant ballast, which explicitly models the effect of the frequency modulation on the envelopes of the outputs. A Spice-compatible implementation of the model is presented that facilitates ac analysis of the ballast in addition to envelope transient simulation, and is verified through comparison of experimental and simulation results. A closed-form solution of the control-to-output current transfer function for the ballast-resistor system is presented, along with key observations of the pole locations and low-frequency gain that facilitate simple and intuitive compensator design. The effects of lamp dynamics on the controller design are discussed, followed by a design example for the feedback controller.
TL;DR: In this paper, a new method for deriving an equation for the oscillation frequency of a ring oscillator is proposed, which is general enough to be used for a variety of types of delay stages.
Abstract: A new method for deriving an equation for the oscillation frequency of a ring oscillator is proposed. The method is general enough to be used for a variety of types of delay stages. Furthermore, it provides a framework to include various parasitic and secondary effects. The method is used to derive an equation for a common ring oscillator topology. The validity of the method and the resulting equation have been verified through simulation. The oscillation frequencies predicted by the proposed method are more accurate than existing equations and account for more secondary effects.
TL;DR: In order to represent 8-, 16-, 32-, and 64-bit binary numbers, the moduli set {2/sup n/,2/Sup n/+1,2/ Sup n/-1} provides the fastest R/B converter and requires the smallest area.
Abstract: In this paper, a detailed study on the four three-moduli sets reported in the literature is carried out from the point of view of the hardware complexity and speed of their residue-to-binary (R/B) converters. First, a new formulation of the Chinese remainder theorem is proposed that reduces the size of the modulo operation. Then, the proposed formulation is applied to derive, in a simple and unified manner, R/B conversion algorithms for three of the sets. Further, using this formulation, a new algorithm along with two corresponding R/B converters for the fourth set is proposed; one of these converters is area efficient while the other is speed efficient. Next, the best R/B converter(s) for each of the sets is chosen based on the hardware complexity and/or speed. These converters are implemented for 8, 16, 32, and 64-bit dynamic ranges, using CMOS VLSI technology. Based on a post-layout performance evaluation for the VLSI implementations of the chosen converters, it is shown that in order to represent 8-, 16-, 32-, and 64-bit binary numbers, the moduli set {2/sup n/,2/sup n/+1,2/sup n/-1} provides the fastest R/B converter and requires the smallest area.
TL;DR: A relatively new statistical test that may be applied to determine whether an observed time series is inconsistent with a specific class of dynamical systems is reviewed and the application of surrogate methods to the residuals of nonlinear models is equivalent to fitting that model subject to an information theoretic model selection criteria.
Abstract: We review a relatively new statistical test that may be applied to determine whether an observed time series is inconsistent with a specific class of dynamical systems. These surrogate data methods may test an observed time series against the hypotheses of: i) independent and identically distributed noise; ii) linearly filtered noise; and iii) a monotonic nonlinear transformation of linearly filtered noise. A recently suggested fourth algorithm for testing the hypothesis of a periodic orbit with uncorrelated noise is also described. We propose several novel applications of these methods for various engineering problems, including: identifying a deterministic (message) signal in a noisy time series; and separating deterministic and stochastic components. When employed to separate deterministic and noise components, we show that the application of surrogate methods to the residuals of nonlinear models is equivalent to fitting that model subject to an information theoretic model selection criteria.