In this paper we introduce a new concept, that of hybrid base, which is a maximal circuitless and... more In this paper we introduce a new concept, that of hybrid base, which is a maximal circuitless and cutsetless subset of a graph. Although this concept of simultaneous circuitlessness and cutsetlessness has been used in proofs of some theorems in so called hybrid graph theory, it has not received much attention. Only largest circuitless and cutsetless subsets (hybrid bases of maximum cardinality) have been recognised as important and then only as an auxiliary notion. In contrast to maximally circuitless subsets (trees) or to maximally cutsetless subsets (cotrees), hybrid bases are not of the same cardinality. This fact, although seemingly an "imperfection is the cause of rich structure which we describe in this paper through several propositions. The concept of hybrid bases is related to several important notions in hybrid orientated graph theory. For example, it is related to maximally distant pairs of trees, to complementary pairs of trees, to perfect trees and to topological d...
Considers the following question: when do the regular parts of state variables of an LTI system r... more Considers the following question: when do the regular parts of state variables of an LTI system remain continuous functions, regardless of the presence of a singular part in the inputs. A simple test, which gives an answer to the above question, before solving this system, is presented.
In this paper, two-parameter families of periodic current waveforms for class-F and inverse class... more In this paper, two-parameter families of periodic current waveforms for class-F and inverse class-F power amplifiers (PAs) are considered. These waveforms are obtained by truncating cosine waveforms composed of dc component and fundamental and either second(k=2)or third(k=3)harmonic. In each period, waveforms are truncated to become zero outside of a prescribed interval (so-called conduction angle). The considered families of waveforms include both discontinuous and continuous waveforms. Fourier series expansion of truncated waveform contains an infinite number of harmonics, although a number of harmonics may be missing. Taking into account common assumptions that for class-F PA the third(n=3)harmonic is missing in current waveform and for inverse class-F PA the second(n=2)harmonic is missing in current waveform, we consider the following four cases: (i)n=k=3,(ii)n=3,k=2,(iii)n=k=2,and (iv)n=2,k=3.We show that, in each of these cases, current waveform enabling maximal efficiency (op...
1991 Ieee International Sympoisum on Circuits and Systems, 1991
A new property of m-dimensional resistive n-ports, dual to the concept of reciprocity, is present... more A new property of m-dimensional resistive n-ports, dual to the concept of reciprocity, is presented and investigated in detail. This concept, which is called coreciprocity, is formulated as a commutativity property of constitutive relations by means of Poisson's brackets. It implies the condition m>or=n, as opposed to reciprocity, which implies m<or=n. For example the norator is coreciprocal while the nullator is reciprocal. In the case of regular resistive n-ports, the reciprocity and coreciprocity of resistive n-ports coincide.<<ETX>>
This article briefly surveys the concepts of conflict sets and non-negative trigonometric polynom... more This article briefly surveys the concepts of conflict sets and non-negative trigonometric polynomials. In the parametric space of nonnegative trigonometric polynomials, these two concepts are related via an extremal problem of finding maximal amplitude of fundamental harmonic providing that trigonometric polynomial is non-negative. In power amplifier analysis, this extremal problem coincides with the problem of finding maximum attainable efficiencies of finite harmonic class-C and class-F power amplifiers.
In this paper a universal reconfigurable computing architecture for hardware implementation of ho... more In this paper a universal reconfigurable computing architecture for hardware implementation of homogeneous and heterogeneous ensemble classifiers composed from decision trees (DTs), artificial neur...
Various classes of nonnegative waveforms containing dc component, fundamental andkthharmonick≥2, ... more Various classes of nonnegative waveforms containing dc component, fundamental andkthharmonick≥2, which proved to be of interest in waveform modelling for power amplifier (PA) design, are considered in this paper. In optimization of PA efficiency, nonnegative waveforms with maximal amplitude of fundamental harmonic and those with maximal coefficient of cosine term of fundamental harmonic (optimal waveforms) play an important role. Optimal waveforms have multiple global minima and this fact closely relates the problem of optimization of PA efficiency to the concept of conflict set. There is also keen interest in finding descriptions for various classes of suboptimal waveforms, such as nonnegative waveforms with at least one zero, nonnegative waveforms with maximal amplitude of fundamental harmonic for prescribed amplitude ofkthharmonic, nonnegative waveforms with maximal coefficient of cosine part of fundamental harmonic for prescribed coefficients ofkthharmonic, and nonnegative cosin...
In this paper, rigorous analytical derivation of the coefficients of optimal current waveform for... more In this paper, rigorous analytical derivation of the coefficients of optimal current waveform for class-F power amplifier (PA) up to fourth harmonic (dc, 1st, 2nd and 4th harmonic) is presented. The coefficients of the optimal current waveform along with related maximum attainable efficiency are provided in closed form. The results obtained are also of interest for the inverse class-F, in the case when optimal voltage waveform consists of dc, 1st, 2nd and 4th harmonic.
This paper proposes universal coarse-grained reconfigurable computing architecture for hardware i... more This paper proposes universal coarse-grained reconfigurable computing architecture for hardware implementation of decision trees (DTs), artificial neural networks (ANNs), and support vector machines (SVMs), suitable for both field programmable gate arrays (FPGA) and application specific integrated circuits (ASICs) implementation. Using this universal architecture, two versions of DTs (functional DT and axis-parallel DT), two versions of SVMs (with polynomial and radial kernel) and two versions of ANNs (multi layer perceptron ANN and radial basis ANN) machine learning classifiers, have been implemented in FPGA. Experimental results, based on 18 benchmark datasets of standard UCI machine learning repository database, show that FPGA implementation provides significant improvement (1–2 orders of magnitude) in the average instance classification time, in comparison with software implementations based on R project.
ABSTRACT In this paper an algorithm for construction of neural networks from decision trees is pr... more ABSTRACT In this paper an algorithm for construction of neural networks from decision trees is presented. First decision tree is constructed using some standard algorithm, then equivalent set of rules is extracted from that tree. Neural network is than formed using that set of rules. This neural network is than used as a basis for further learning that will improve the classification performance on the given problem. Using this algorithm neural network structure and initial set of weight values can be quickly estimated, eliminating extensive experiments that are currently needed to find these parameters.
In this paper we introduce a new concept, that of hybrid base, which is a maximal circuitless and... more In this paper we introduce a new concept, that of hybrid base, which is a maximal circuitless and cutsetless subset of a graph. Although this concept of simultaneous circuitlessness and cutsetlessness has been used in proofs of some theorems in so called hybrid graph theory, it has not received much attention. Only largest circuitless and cutsetless subsets (hybrid bases of maximum cardinality) have been recognised as important and then only as an auxiliary notion. In contrast to maximally circuitless subsets (trees) or to maximally cutsetless subsets (cotrees), hybrid bases are not of the same cardinality. This fact, although seemingly an "imperfection is the cause of rich structure which we describe in this paper through several propositions. The concept of hybrid bases is related to several important notions in hybrid orientated graph theory. For example, it is related to maximally distant pairs of trees, to complementary pairs of trees, to perfect trees and to topological d...
Considers the following question: when do the regular parts of state variables of an LTI system r... more Considers the following question: when do the regular parts of state variables of an LTI system remain continuous functions, regardless of the presence of a singular part in the inputs. A simple test, which gives an answer to the above question, before solving this system, is presented.
In this paper, two-parameter families of periodic current waveforms for class-F and inverse class... more In this paper, two-parameter families of periodic current waveforms for class-F and inverse class-F power amplifiers (PAs) are considered. These waveforms are obtained by truncating cosine waveforms composed of dc component and fundamental and either second(k=2)or third(k=3)harmonic. In each period, waveforms are truncated to become zero outside of a prescribed interval (so-called conduction angle). The considered families of waveforms include both discontinuous and continuous waveforms. Fourier series expansion of truncated waveform contains an infinite number of harmonics, although a number of harmonics may be missing. Taking into account common assumptions that for class-F PA the third(n=3)harmonic is missing in current waveform and for inverse class-F PA the second(n=2)harmonic is missing in current waveform, we consider the following four cases: (i)n=k=3,(ii)n=3,k=2,(iii)n=k=2,and (iv)n=2,k=3.We show that, in each of these cases, current waveform enabling maximal efficiency (op...
1991 Ieee International Sympoisum on Circuits and Systems, 1991
A new property of m-dimensional resistive n-ports, dual to the concept of reciprocity, is present... more A new property of m-dimensional resistive n-ports, dual to the concept of reciprocity, is presented and investigated in detail. This concept, which is called coreciprocity, is formulated as a commutativity property of constitutive relations by means of Poisson's brackets. It implies the condition m>or=n, as opposed to reciprocity, which implies m<or=n. For example the norator is coreciprocal while the nullator is reciprocal. In the case of regular resistive n-ports, the reciprocity and coreciprocity of resistive n-ports coincide.<<ETX>>
This article briefly surveys the concepts of conflict sets and non-negative trigonometric polynom... more This article briefly surveys the concepts of conflict sets and non-negative trigonometric polynomials. In the parametric space of nonnegative trigonometric polynomials, these two concepts are related via an extremal problem of finding maximal amplitude of fundamental harmonic providing that trigonometric polynomial is non-negative. In power amplifier analysis, this extremal problem coincides with the problem of finding maximum attainable efficiencies of finite harmonic class-C and class-F power amplifiers.
In this paper a universal reconfigurable computing architecture for hardware implementation of ho... more In this paper a universal reconfigurable computing architecture for hardware implementation of homogeneous and heterogeneous ensemble classifiers composed from decision trees (DTs), artificial neur...
Various classes of nonnegative waveforms containing dc component, fundamental andkthharmonick≥2, ... more Various classes of nonnegative waveforms containing dc component, fundamental andkthharmonick≥2, which proved to be of interest in waveform modelling for power amplifier (PA) design, are considered in this paper. In optimization of PA efficiency, nonnegative waveforms with maximal amplitude of fundamental harmonic and those with maximal coefficient of cosine term of fundamental harmonic (optimal waveforms) play an important role. Optimal waveforms have multiple global minima and this fact closely relates the problem of optimization of PA efficiency to the concept of conflict set. There is also keen interest in finding descriptions for various classes of suboptimal waveforms, such as nonnegative waveforms with at least one zero, nonnegative waveforms with maximal amplitude of fundamental harmonic for prescribed amplitude ofkthharmonic, nonnegative waveforms with maximal coefficient of cosine part of fundamental harmonic for prescribed coefficients ofkthharmonic, and nonnegative cosin...
In this paper, rigorous analytical derivation of the coefficients of optimal current waveform for... more In this paper, rigorous analytical derivation of the coefficients of optimal current waveform for class-F power amplifier (PA) up to fourth harmonic (dc, 1st, 2nd and 4th harmonic) is presented. The coefficients of the optimal current waveform along with related maximum attainable efficiency are provided in closed form. The results obtained are also of interest for the inverse class-F, in the case when optimal voltage waveform consists of dc, 1st, 2nd and 4th harmonic.
This paper proposes universal coarse-grained reconfigurable computing architecture for hardware i... more This paper proposes universal coarse-grained reconfigurable computing architecture for hardware implementation of decision trees (DTs), artificial neural networks (ANNs), and support vector machines (SVMs), suitable for both field programmable gate arrays (FPGA) and application specific integrated circuits (ASICs) implementation. Using this universal architecture, two versions of DTs (functional DT and axis-parallel DT), two versions of SVMs (with polynomial and radial kernel) and two versions of ANNs (multi layer perceptron ANN and radial basis ANN) machine learning classifiers, have been implemented in FPGA. Experimental results, based on 18 benchmark datasets of standard UCI machine learning repository database, show that FPGA implementation provides significant improvement (1–2 orders of magnitude) in the average instance classification time, in comparison with software implementations based on R project.
ABSTRACT In this paper an algorithm for construction of neural networks from decision trees is pr... more ABSTRACT In this paper an algorithm for construction of neural networks from decision trees is presented. First decision tree is constructed using some standard algorithm, then equivalent set of rules is extracted from that tree. Neural network is than formed using that set of rules. This neural network is than used as a basis for further learning that will improve the classification performance on the given problem. Using this algorithm neural network structure and initial set of weight values can be quickly estimated, eliminating extensive experiments that are currently needed to find these parameters.
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