a wide band equivalent source reconstruction method exploiting the stoer bulirsch algorithm with the adaptive frequency sampling conventional equivalent source reconstruction methods are only operating at a single frequency point each time however for wide band radiators their computation cost of the source reconstruction increases with the number of frequency points in this communication a wide band equivalent source reconstruction method wb srm based on the neville type stoer bulirsch sb algorithm is developed since the sb algorithm is a recursive tabular method it can perform the interpolation over a broadband using a single rational function without any singularity issue supported by the adaptive frequency sampling afs scheme the number of required sampling data is significantly reduced which leads to much better computational efficiency during the afs process three fitting models fm are considered two are triangle rules and another one is rhombus rule in this communication a bisection searching strategy is performed furthermore to achieve high order accuracy the nystrom method is implemented numerical examples are presented to validate the proposed wb srm and demonstrate its accuracy and applications

multilevel plane wave based near field far field transformation for electrically large antennas in free space or above material halfspace a recently presented fully probe corrected near field far field transformation employing plane wave expansion and diagonal translation operators enables near field far field transformation for arbitrary measurement contours and arbitrary antennas a multilevel extension inspired by the multilevel fast multipole method is presented that is suitable for the efficient transformation of electrically large antennas with a size of tens or even hundreds of wavelengths the measurement points are grouped in a multilevel fashion and translations are carried out to the box centers on the highest level only the plane waves are processed through the different levels to the measurement points using a disaggregation and anterpolation procedure resulting in a reduced overall complexity in the second part of this paper the influence of perfectly conducting ground planes and dielectric halfspaces as an approximation for ground effects in a real measurement setup is investigated as such ground reflected waves are assumed which propagate from the investigated antenna to the field probe and add to the direct wave contributions the far field conditions required for these assumptions are achieved by a source box grouping scheme by this extension ground effects are directly considered within the near field far field transformation transformation results using simulated and measured near field data are shown

application of the tikhonov regularization technique to the equivalent magnetic currents near field technique the equivalent magnetic currents method can be used to characterize radiating structures and to obtain information about the current distribution on the radiating device under test dut in order to do so the system is assumed to be linear and inversion from near field measurements can be carried out using numerical techniques such as the singular value decomposition however this approach is very sensitive to modeling and measurement errors which is a consequence of the ill conditioned nature of the inversion process here we propose to account for the ill conditioning by using a tikhonov regularization technique to perform the inversion this technique requires a regularization parameter to be set to an appropriate value and we show that a generalized cross validation approach yields adequate determination of the regularization parameter directly from the measured data the proposed method can be tailored to account for specific characteristics of the dut this point is illustrated by the estimation of the current distribution of a bidimensional radiating structure for which prior information about the orientation of radiating edges is incorporated into the inversion method

balanced parametrization of classes of linear systems canonical forms and parametrizations are presented for several sets of minimal systems of given dimension asymptotically stable systems allpass systems bounded real systems positive real systems minimum phase systems and the class of all minimal systems the approach is based on balancing techniques for these classes of systems applications of these results to hankel operators and model reduction are discussed

knowledge based antenna pattern interpolation we examine the problem of interpolating antenna radiation patterns from a small number of measurements and propose an algorithm to perform the interpolation when naive methods fail often due to multipath corruption of the pattern this algorithm exploits constraints on the antenna s underlying design to avoid ambiguities but is sufficiently general to address many different antenna types a theoretical basis for the robustness of this algorithm is developed and its performance is verified in simulation using a number of popular antenna designs and with a controlled laboratory experiment

on the nearest neighbor of the nearest neighbor in multidimensional continuous and quantized space the probability that an entity in a set of entities uniformly distributed in space is the nearest neighbor of its nearest neighbor is evaluated for generic distances in a multidimensional environment such an expression is then specialized for systems with norm based distances and for systems with quantized norm based distance examples for scalar products and sup norm are derived when applicable invariances with respect to the underlying distance and entities density are highlighted dimensionality effects are investigated

linear reconstruction measure steered nearest neighbor classification framework the linear reconstruction measure lrm which determines the nearest neighbors of the query sample in all known training samples by sorting the minimum l 2 norm error linear reconstruction coefficients is introduced in this paper the intuitive interpretation and mathematical proofs are presented to reveal the efficient working mechanism of lrm through analyzing the physical meaning of coefficients and regularization items we find that lrm provides more useful information and advantages than the conventional similarity measure model which calculates the distance between two entities i e conventional point to point c ptp inspired by the advantages of lrm the linear reconstruction measure steered nearest neighbor classification framework lrm nncf is designed with eight classifiers according to different decision rules and models of lrm evaluation on several face databases and the experimental results demonstrate that these proposed classifiers can achieve greater performance than the c ptp based 1 nns and competitive recognition accuracy and robustness compared with the state of the art classifiers

extended rough set based attribute reduction in inconsistent incomplete decision systems a systematic study of attribute reduction in inconsistent incomplete decision systems iidss has not yet been performed and no complete methodology of attribute reduction has been developed for iidss to date in an iids there are various ways to handle missing values in this paper a missing attribute value may be replaced with any known value of a corresponding attribute such a missing attribute value is called a do not care condition in this way this paper establishes reduction concepts specifically for iidss mainly by extending related reduction concepts from other types of decision systems into iidss and then derives their relationships and properties with these derived properties the extended reducts are divided into two distinct types heritable reducts and nonheritable reducts and algorithms for computing them are presented using the relationships derived here the eight types of extended reducts established for iidss can be converted to five equivalent types then five discernibility function based approaches are proposed each for a particular kind of reduct each approach can find all reducts of its associated type the theoretical analysis of the proposed approaches is described in detail finally numerical experiments have shown that the proposed approaches are effective and suitable for handling both numerical and categorical attributes but that they have different application conditions the proposed approaches can provide a solution to the reduction problem for iidss

planar near field to far field transformation using an array of dipole probes a method is presented for computing far field antenna patterns from measured near field data measured by an array of planar dipole probes the method utilizes the near field data to determine some equivalent magnetic current sources over a fictitious planar surface which encompasses the antenna these currents are then used to find the far fields the near field measurement is carried out by terminating each dipole with 50 spl omega load impedances and measuring the complex voltages across the loads an electric field integral equation efie is developed to relate the measured complex voltages to the equivalent magnetic currents the mutual coupling between the array of probes and the test antenna modeled by magnetic dipoles is taken into account the method of moments with galerkin s type solution procedure is used to transform the integral equation into a matrix one the matrix equation is solved with the conjugate gradient fast fourier transformation cg fft method exploiting the block toeplitz structure of the matrix numerical results are presented for several antenna configurations to show the validity of the method

comments on application of fft and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies in the original paper ibid vol ap 34 no 5 p 635 40 1986 t k sarkar et al describe how the fast fourier transform fft and the conjugate gradient method cgm can be used to efficiently make use of the convolutional form of the electric field integral equation for straight wire antennas the commentators agree that the cgm converges more rapidly than the previously used method of steepest descent and the spectral iteration technique they also point out that experience with the dyadic green s function encountered in the two dimensional transverse electric te and three dimensional equations for dielectric bodies is not so encouraging it is found that for these cases the cgm convergence can be quite slow degrading the efficiency of the algorithm in addition the solution obtained using the pulse basis point matching method to discretize the integral equation are very inaccurate for the two dimensional te and three dimensional cases a reply to these comments from the authors of the original paper is included

planar near field to far field transformation using an equivalent magnetic current approach an alternative method is presented for computing far field antenna patterns from near field measurements the method utilizes the near field data to determine equivalent magnetic current sources over a fictitious planar surface that encompasses the antenna and these currents are used to ascertain the far fields under certain approximations the currents should produce the correct far fields in all regions in front of the antenna regardless of the geometry over which the near field measurements are made an electric field integral equation efie is developed to relate the near fields to the equivalent magnetic currents the method of moments is used to transform the integral equation into a matrix one the matrix equation is solved with the conjugate gradient method and in the case of a rectangular matrix a least squares solution for the currents is found without explicitly computing the normal form of the equation near field to far field transformation for planar scanning may be efficiently performed under certain conditions numerical results are presented for several antenna configurations

a balanced canonical form for discrete time minimal systems using characteristic maps abstract this paper presents a balanced canonical form for the class of discrete time minimal systems the main tool is to establish a bijection between the set of minimal systems and the class of minimal discrete time asymptotically stable systems of the same dimension this characteristic map is shown to preserve system equivalence and balancing the canonical form for discrete time minimal systems is then constructed by mapping the system to its discrete time asymptotically stable counterpart via the characteristic map transforming the resulting system to lyapunov balanced canonical form and returning to the original system class by means of the inverse characteristic map

reconstruction of equivalent currents distribution over arbitrary three dimensional surfaces based on integral equation algorithms a technique for the determination of the equivalent currents distribution from a known radiated field is described this inverse radiation problem is solved through an integral equation algorithm that allows the characterization of antennas of complex geometry both for near field to far field nf ff transformation purposes as well as for diagnostic tasks the algorithm is based on the representation of the radiating structure by means of a set of equivalent currents over a three dimensional 3d surface that can be fitted to the arbitrary geometry of the antenna the innovative formulation uses an integral equation involving the electric field due to the currents tangential components to the represented antenna 3d surface for that purpose both the magnetic and electric equivalent currents are considered in the integral equations regularization techniques are also introduced to improve the convergence of the proposed iterative solution the paper concludes with several results related to the practical verification of the equivalence principle and the characterization of a horn antenna

a note on double insertion deletion correcting codes by using a run length representation of sequences ways to determine suband supersequences are discussed this is then used in determining the number of sub and supersequences of a sequence after double insertions or deletions it is also used in creating subsequence supersequence books that are searched to find new double insertion deletion correcting code books with higher cardinalities than those already known

a global parametrization of symptotically stable linear systems abstract in this paper we construct a homeomorphism from the set of p m transfer functions of mcmillan degree n onto the open subspace of asymptotically stable linear systems this homeomorphism yields a one to one correspondence between 1 i canonical forms for state space equivalence of minimal systems and 2 ii canonical forms for state space equivalence of asymptotically stable minimal systems implications for the topology of various sets of asymptotically stable systems are given

nearest neighbors by neighborhood counting finding nearest neighbors is a general idea that underlies many artificial intelligence tasks including machine learning data mining natural language understanding and information retrieval this idea is explicitly used in the k nearest neighbors algorithm knn a popular classification method in this paper this idea is adopted in the development of a general methodology neighborhood counting for devising similarity functions we turn our focus from neighbors to neighborhoods a region in the data space covering the data point in question to measure the similarity between two data points we consider all neighborhoods that cover both data points we propose to use the number of such neighborhoods as a measure of similarity neighborhood can be defined for different types of data in different ways here we consider one definition of neighborhood for multivariate data and derive a formula for such similarity called neighborhood counting measure or ncm ncm was tested experimentally in the framework of knn experiments show that ncm is generally comparable to vdm and its variants the state of the art distance functions for multivariate data and at the same time is consistently better for relatively large k values additionally ncm consistently outperforms heom a mixture of euclidean and hamming distances the standard and most widely used distance function for multivariate data ncm has a computational complexity in the same order as the standard euclidean distance function and ncm is task independent and works for numerical and categorical data in a conceptually uniform way the neighborhood counting methodology is proven sound for multivariate data experimentally we hope it works for other types of data

a functional approach to lqg balancing the paper has as its theme a circle of problems related to lqg balancing with a special emphasis on the related problems of model reduction and robust stabilization the aim is to present a unified point of view to both previously described problems the unification is achieved by focusing on the study of three functions and the relationships between them and the various operators that are associated with these functions with an arbitrary transfer function g one can associate canonically two objects the conjugate inner function which is based on the nrcf and the r which is associated with the lqg controller of the function g the approach that is taken is functional emphasizing operators a balanced realization of a stable g arises as a matrix representation of the shift realization with respect to a basis made out of suitably normalized hankel singular vectors a similar result holds for lqg balanced realizations here the underlying hankel operator we study is h r where r u m v n and u v s

lqg balancing for continuous time infinite dimensional systems in this paper we study the existence of linear quadratic gaussian lqg balanced realizations for continuous time infinite dimensional systems lqg balanced realizations are those for which the optimal cost operator for the system and its dual system are equal and diagonal the class of systems we consider is that of distributional resolvent linear systems which includes well posed linear systems as a subclass we prove the existence of lqg balanced realizations under a finite cost condition for both the system and its dual system we also show that an lqg balanced realization of a well posed transfer function is well posed we further show that approximately controllable and observable lqg balanced realizations are unique up to a unitary state space transformation finally we show that the spectrum of the product of the optimal cost operator of a system and its dual system is independent of the particular realization our method of proof shows the connections with coprime factorizations lyapunov balanced realizations and discrete time systems the main reason for studying lqg balanced realizations is that truncated lqg balanced realizations provide a good approximation of the original system we show that under certain conditions this is also true in the infinite dimensional case by proving an error bound in the gap metric

neighborhood rough set based heterogeneous feature subset selection feature subset selection is viewed as an important preprocessing step for pattern recognition machine learning and data mining most of researches are focused on dealing with homogeneous feature selection namely numerical or categorical features in this paper we introduce a neighborhood rough set model to deal with the problem of heterogeneous feature subset selection as the classical rough set model can just be used to evaluate categorical features we generalize this model with neighborhood relations and introduce a neighborhood rough set model the proposed model will degrade to the classical one if we specify the size of neighborhood zero the neighborhood model is used to reduce numerical and categorical features by assigning different thresholds for different kinds of attributes in this model the sizes of the neighborhood lower and upper approximations of decisions reflect the discriminating capability of feature subsets the size of lower approximation is computed as the dependency between decision and condition attributes we use the neighborhood dependency to evaluate the significance of a subset of heterogeneous features and construct forward feature subset selection algorithms the proposed algorithms are compared with some classical techniques experimental results show that the neighborhood model based method is more flexible to deal with heterogeneous data

complexity for finite factors of infinite sequences abstract we define several notions of language complexity for finite words and use them to define and compute some new complexity functions for infinite sequences in particular they give a new characterization of sturmian sequences and discriminate between sturmian sequences with bounded or unbounded partial quotients

on the state complexity of closures and interiors of regular languages with subwords and superwords the downward and upward closures of a regular language l are obtained by collecting all the subwords and superwords of its elements respectively the downward and upward interiors of l are obtained dually by collecting words having all their subwords and superwords in l respectively we provide lower and upper bounds on the size of the smallest automata recognizing these closures and interiors we also consider the computational complexity of decision problems for closures of regular languages

feature selection based on neighborhood discrimination index feature selection is viewed as an important preprocessing step for pattern recognition machine learning and data mining neighborhood is one of the most important concepts in classification learning and can be used to distinguish samples with different decisions in this paper a neighborhood discrimination index is proposed to characterize the distinguishing information of a neighborhood relation it reflects the distinguishing ability of a feature subset the proposed discrimination index is computed by considering the cardinality of a neighborhood relation rather than neighborhood similarity classes variants of the discrimination index including joint discrimination index conditional discrimination index and mutual discrimination index are introduced to compute the change of distinguishing information caused by the combination of multiple feature subsets they have the similar properties as shannon entropy and its variants a parameter named neighborhood radius is introduced in these discrimination measures to address the analysis of real valued data based on the proposed discrimination measures the significance measure of a candidate feature is defined and a greedy forward algorithm for feature selection is designed data sets selected from public data sources are used to compare the proposed algorithm with existing algorithms the experimental results confirm that the discrimination index based algorithm yields superior performance compared to other classical algorithms

algorithms for subsequence combinatorics a subsequence is obtained from a string by deleting any number of characters thus in contrast to a substring a subsequence is not necessarily a contiguous part of the string counting subsequences under various constraints has become relevant to biological sequence analysis to machine learning to coding theory to the analysis of categorical time series in the social sciences and to the theory of word complexity we present theorems that lead to efficient dynamic programming algorithms to count 1 distinct subsequences in a string 2 distinct common subsequences of two strings 3 matching joint embeddings in two strings 4 distinct subsequences with a given minimum span and 5 sequences generated by a string allowing characters to come in runs of a length that is bounded from above

concordance and consensus this paper deals with the measurement of concordance and the construction of consensus in preference data either in the form of preference rankings or in the form of response distributions with likert items we propose a set of axioms of concordance in preference orderings and a new class of concordance measures the measures outperform classic measures like kendall s t and w and spearman s r in sensitivity and apply to large sets of orderings instead of just to pairs of orderings for sets of n orderings of n items we present very efficient and flexible algorithms that have a time complexity of only o nn 2 remarkably the algorithms also allow for fast calculation of all longest common subsequences of the full set of orderings we experimentally demonstrate the performance of the algorithms a new and simple measure for assessing concordance on likert items is proposed

the bayes decision rule induced similarity measures this paper first shows that the popular whitened cosine similarity measure is related to the bayes decision rule under specific assumptions and then presents two new similarity measures the prm whitened cosine pwc similarity measure and the within class whitened cosine wwc similarity measure experiments on face recognition using the face recognition grand challenge frgc version 2 database show the effectiveness of the new measures

multilevel fast multipole accelerated inverse equivalent current method employing rao wilton glisson discretization of electric and magnetic surface currents the radiation of any object in a homogeneous environment can be described by a set of equivalent sources different types of equivalent sources are feasible and all of them have their own benefits equivalent current methods are especially advantageous for irregular measurement grids of arbitrary shape and if a priori information about the object shall be used also they can immediately provide diagnostic information about the object in this paper a very flexible equivalent current method is presented which has been derived from a general purpose boundary integral equation solver as such the method works with arbitrary triangular surface meshes and rao wilton glisson basis functions where electric and or magnetic surface current densities can be assumed high efficiency is achieved since the multilevel fast multipole method has been adapted to speed up the inverse solution process results obtained from simulations and measurements are presented where large scale problems with dimensions up to 75 wavelengths are considered

versatile string kernels this paper proposes a class of string kernels that can handle a variety of subsequence based features slight adaptations of the basic algorithm allow for weighing subsequence lengths restricting or soft penalizing gap size character weighing and soft matching of characters an easy extension of the kernels allows for comparing run length encoded strings with a time complexity that is independent of the length of the original strings such kernels have applications in image processing computational biology in demography and in comparing partial rankings

about neighborhood counting measure metric and minimum risk metric in a 2006 tpami paper wang proposed the neighborhood counting measure a similarity measure for the k nn algorithm in his paper wang mentioned the minimum risk metric mrm an early distance measure based on the minimization of the risk of misclassification wang did not compare ncm to mrm because of its allegedly excessive computational load in this comment paper we complete the comparison that was missing in wang s paper and from our empirical evaluation we show that mrm outperforms ncm and that its running time is not prohibitive as wang suggested

neighborhood counting measure and minimum risk metric the neighborhood counting measure is a similarity measure based on the counting of all common neighborhoods in a data space the minimum risk metric mrm is a distance measure based on the minimization of the risk of misclassification the paper by argentini and blanzieri refutes a remark about the time complexity of mrm and presents an experimental comparison of mrm and ncm this paper is a response to the paper by argentini and blanzieri the original remark is clarified by a combination of theoretical analysis of different implementations of mrm and experimental comparison of mrm and ncm using straightforward implementations of the two measures

near field to near far field transformation for arbitrary near field geometry utilizing an equivalent electric current and mom presented here is a method for computing near and far field patterns of an antenna from its near field measurements taken over an arbitrarily shaped geometry this method utilizes near field data to determine an equivalent electric current source over a fictitious surface which encompasses the antenna this electric current once determined can be used to ascertain the near and the far field this method demonstrates the concept of analytic continuity i e once the value of the electric field is known for one region in space from a theoretical perspective its value for any other region can be extrapolated it is shown that the equivalent electric current produces the correct fields in the regions in front of the antenna regardless of the geometry over which the near field measurements are made in this approach the measured data need not satisfy the nyquist sampling criteria an electric field integral equation is developed to relate the near field to the equivalent electric current a moment method procedure is employed to solve the integral equation by transforming it into a matrix equation a least squares solution via singular value decomposition is used to solve the matrix equation computations with both synthetic and experimental data where the near field of several antenna configurations are measured over various geometrical surfaces illustrate the accuracy of this method

on the differentiable manifold of fixed order stable linear systems abstract it is shown that the real analytic differentiable manifold of time invariant linear dynamical systems of fixed mcmillan degree n with m dimensional inputs and m dimensional outputs is real analytically diffeomorphic to the submanifold of i o stable i e asymptotically stable systems this generalizes results of helmke ober and hanzon about the topology of such manifolds similar results hold for the corresponding state bundles and their associated principal bundles this implies in fact that there is a one to one correspondence between smooth local canonical forms for finite dimensional linear systems of fixed order and for finite dimensional i o stable linear systems of fixed order

on a class of finite step iterative methods conjugate directions for the solution of an operator equation arising in electromagnetics a class of finite step iterative methods for the solution of linear operator equations is presented specifically the basic principles of the method of conjugate directions are developed gaussian elimination and the method of conjugate gradients are then presented as two special cases with an arbitrary initial guess the method of conjugate gradient always converges to the solution in at most n iterations where n is the number of independent eigenvalues for the operator in the finite dimensional space in which the problem is being solved the conjugate gradient method requires much less storage sim 5n than the conventional matrix methods sim n 2 in the solution of problems of higher complexity also after each iteration the quality of the solution is known in the conjugate gradient method the conjugate gradient method is also superior to the spectral iterative method as the latter does not always converge and it doubles the complexity of a given problem unnecessarily four versions of the conjugate gradient method are presented in detail and numerical results for a thin wire scatterer are given to illustrate various properties of each version

antenna generalized scattering matrix in terms of equivalent infinitesimal dipoles application to finite array problems a full wave antenna modeling method by means of elementary sources described in terms of colocalized infinitesimal dipoles is presented in this paper the procedure provides a generalized scattering matrix gsm in terms of equivalent infinitesimal dipoles from the gsm of the antenna by using rotation and translation of spherical modes the number of equivalent infinitesimal dipoles and their positions are optimized by using a genetic algorithm the application to the full wave analysis of arrays is also presented providing very accurate results even when the minimum spheres of the antennas in the array environment overlap considerably which cannot be solved by the direct coupling of generalized scattering matrices in terms of spherical waves some examples of antenna modeling and their application to the analysis of arrays of antennas on a metallic plane will be shown

linear quadratic gaussian balancing for discrete time infinite dimensional linear systems in this paper we study the existence of linear quadratic gaussian lqg balanced realizations for discrete time infinite dimensional systems lqg balanced realizations are those for which the smallest nonnegative self adjoint solutions of the control and filter riccati equations are equal we show that the control filter riccati equation has a nonnegative self adjoint solution if and only if the system is output input stabilizable our main result is that the transfer function of a discrete time linear system has an approximately controllable and observable lqg balanced realization iff it has an input and output stabilizable realization the corresponding control and filter riccati equations have unique nonnegative self adjoint solutions moreover approximately controllable and observable lqg balanced realizations are unique up to a unitary state space transformation finally we show that the spectrum of the product of the smallest nonnegative self adjoint solutions of the control and filter riccati equations is independent of the particular realization

attribute reduction for heterogeneous data based on the combination of classical and fuzzy rough set models attribute reduction with rough sets aims to delete superfluous condition attributes from a decision system by considering the inconsistency between condition attributes and the decision labels however heterogeneous condition attributes including symbolic and real valued ones always coexist for most decision systems and different types of attributes induce different kinds of granular structures the existing rough set models do not have explicit mechanisms to address different kinds of granular structures reasonably and effectively in this paper we aim to perform attribute reduction for decision systems with symbolic and real valued condition attributes by composing classical rough set and fuzzy rough set models we first define a discernibility relation for every symbolic and real valued condition attribute to characterize its discernible ability related to the decision labels with these discernibility relations we can develop a dependence function to measure the inconsistency between heterogeneous condition attributes and decision labels and attribute reduction aims to keep this dependence function with a small perturbation the proposed attribute reduction deals with heterogeneous condition attributes from the viewpoint of discernible ability and can consider the mutual effects between two types of attributes without preprocessing into single typed ones an algorithm to find reducts is developed and experiments are performed to demonstrate that the proposed idea is effective

source identification in time domain electromagnetics in this paper we introduce two numerical methods to get an electric source that gives a specified electromagnetic field some time after the source starts emitting the first one is called the time reversal method trm and originates from acoustics and the second one is called linear combination of configuration fields lccf and consists in constructing and solving a linear problem in order to find a possible required source in this paper we show on 1d and 2d examples that the last method gives lower relative errors when compared with the time reversal method

feature selection in mixed data feature selection in the data with different types of feature values i e the heterogeneous or mixed data is especially of practical importance because such types of data sets widely exist in real world the key issue for feature selection in mixed data is how to properly deal with different types of the features or attributes in the data set motivated by the fuzzy rough set theory which allows different fuzzy relations to be defined for different types of attributes to measure the similarity between objects and in view of the effectiveness of entropy to measure information uncertainty we propose in this paper a fuzzy rough set based information entropy for feature selection in a mixed data set it is proved that the newly defined entropy meets the common requirement of monotonicity and can equivalently characterize the existing attribute reductions in the fuzzy rough set theory then a feature selection algorithm is formulated based on the proposed entropy and a filter wrapper method is suggested to select the best feature subset in terms of classification accuracy an extensive numerical experiment is further conducted to assess the performance of the feature selection method and the results are satisfactory highlightsa novel fuzzy rough set based information entropy is constructed for mixed data the proposed entropy can equivalently characterize the existing attribute reductions in the fuzzy rough set theory a feature selection algorithm is formulated based on the proposed entropy a filter wrapper method is suggested to select a best feature subset

efficient near field far field transformation for nonredundant sampling representation on arbitrary surfaces in near field antenna measurements a nonredundant sampling representation on arbitrary surfaces in near field antenna measurements together with a direct near field far field transformation is described the utilized sampling criterion depends on the electrical size of the antenna under test aut along with the separation between the aut and the measurement surface the minimum number of samples required is directly linked with the number of unknowns in the linear system of equations derived considering spherical expansion of radiated aut fields equivalent plane wave sources are used to represent the aut fields plane wave translations can be directly performed for any arbitrary measurement grid with the same efficiency thus nonredundant sampling representations can be utilized on any scan surface in contrast other fast field transformation techniques would lose their efficiency the proposed sampling is applied to near field measurements and synthetic data using a variety of antennas and the results are compared to the case of standard sampling remarkable decrease in the number of measurement points is observed with a negligible change in the accuracy of the transformed pattern thereby greatly reducing the measurement time and the computational effort

on the combinatorics of finite words in this paper we consider a combinatorial method for the analysis of finite words recently introduced in colosimo and de luca special factors in biological strings preprint 97 42 dipt matematica univ di roma for the study of biological macromolecules the method is based on the analysis of right special factors of a given word a factor u of a word w is special if there exist at least two occurrences of the factor u in w followed on the right by two distinct letters we show that in the combinatorics of finite words two parameters play an essential role the first denoted by r represents the minimal integer such that there do not exist special factors of w of length r the second that we denote by k is the minimal length of a factor of w which cannot be extended on the right in a factor of w some new results are proved in particular a new characterization in terms of special factors and of r and k is given for the set per of all words w having two periods p and q which are coprimes and such that w p q 2