genetic algorithms for modelling and optimisation genetic algorithms gas are a heuristic search and optimisation technique inspired by natural evolution they have been successfully applied to a wide range of real world problems of significant complexity this paper is intended as an introduction to gas aimed at immunologists and mathematicians interested in immunology we describe how to construct a ga and the main strands of ga theory before speculatively identifying possible applications of gas to the study of immunology an illustrative example of using a ga for a medical optimal control problem is provided the paper also includes a brief account of the related area of artificial immune systems

eigenvalues of rank one perturbations of unstructured matrices abstract let a be a fixed complex matrix and let u v be two vectors the eigenvalues of matrices a uv r form a system of intersecting curves the dependence of the intersections on the vectors u v is studied

similarity vs unitary similarity and perturbation analysis of sign characteristics complex and real indefinite inner products for selfadjoint and unitary matrices with respect to indefinite inner products on finite dimensional complex or real vector spaces the unitary similarity relation is studied in contrast to the similarity relation the number of unitary similarity classes in a similarity class of such matrices is identified it is proved that under sufficiently small perturbations similarity of selfadjoint or unitary with respect to an indefinite inner product matrices implies unitary similarity estimates are given for the sizes of perturbation that guarantee this property canonical forms and sign characteristics play a key role in the proofs a perturbation analysis is developed of the sign characteristics in the real case under sufficiently small structure preserving perturbations of both selfadjoint or unitary matrices and of the indefinite inner product

the change of the jordan structure under one row perturbations we study the variation of the jordan structure of a complex square matrix when we make small perturbations on the elements of one row

eigenvalue perturbation theory of classes of structured matrices under generic structured rank one perturbations abstract udy the perturbation theory of structured matrices under structured rank one perturbations and then focus on several classes of complex matrices generic jordan structures of perturbed matrices are identified it is shown that the perturbation behavior of the jordan structures in the case of singular j hamiltonian matrices is substantially different from the corresponding theory for unstructured generic rank one perturbation as it has been studied in 18 28 30 31 thus a generic structured perturbation would not be generic if considered as an unstructured perturbation in other settings of structured matrices the generic perturbation behavior of the jordan structures within the confines imposed by the structure follows the pattern of that of unstructured perturbations

optimization of ldpc codes for modulation and detection in layered multi antenna architectures in this paper we first perform the density evolution of ldpc codes in layered multi antenna architectures using bit interleaved coded modulation and detection based on successive decoding and interference cancellation the noise thresholds of ldpc codes are shown to be achieved within 1 2 db of the capacity for these architectures we then present a rate allocation method which optimizes the performance of a layered architecture and find good degree distributions for ldpc codes with the rates allocated by our method simulation results show that the performance for an optimized layered architecture is better by 4 db than that for the layered architecture using ldpc codes with the same rate in all layers

analysis of sum product decoding of low density parity check codes using a gaussian approximation density evolution is an algorithm for computing the capacity of low density parity check ldpc codes under message passing decoding for memoryless binary input continuous output additive white gaussian noise awgn channels and sum product decoders we use a gaussian approximation for message densities under density evolution to simplify the analysis of the decoding algorithm we convert the infinite dimensional problem of iteratively calculating message densities which is needed to find the exact threshold to a one dimensional problem of updating the means of the gaussian densities this simplification not only allows us to calculate the threshold quickly and to understand the behavior of the decoder better but also makes it easier to design good irregular ldpc codes for awgn channels for various regular ldpc codes we have examined thresholds can be estimated within 0 1 db of the exact value for rates between 0 5 and 0 9 codes designed using the gaussian approximation perform within 0 02 db of the best performing codes found so far by using density evolution when the maximum variable degree is 10 we show that by using the gaussian approximation we can visualize the sum product decoding algorithm we also show that the optimization of degree distributions can be understood and done graphically using the visualization

generic complete eigenstructures for sets of matrix polynomials with bounded rank and degree abstract the set pol d r m n of m n complex matrix polynomials of grade d and normal rank at most r in a complex d 1 m n dimensional space is studied for r 1 min m n 1 we show that pol d r m n is the union of the closures of the r d 1 sets of matrix polynomials with rank r degree exactly d and explicitly described complete eigenstructures in addition for the full rank rectangular polynomials i e r min m n and m n we show that pol d r m n coincides with the closure of a single set of the polynomials with rank r degree exactly d and the described complete eigenstructure these complete eigenstructures correspond to generic m n matrix polynomials of grade d and rank at most r

a global best artificial bee colony algorithm for global optimization the artificial bee colony abc algorithm is a relatively new optimization technique which has been shown to be competitive to other population based algorithms however there is still an insufficiency in the abc algorithm regarding its solution search equation which is good at exploration but poor at exploitation inspired by differential evolution de we propose a modified abc algorithm denoted as abc best which is based on that each bee searches only around the best solution of the previous iteration in order to improve the exploitation in addition to enhance the global convergence when producing the initial population and scout bees both chaotic systems and opposition based learning method are employed experiments are conducted on a set of 26 benchmark functions the results demonstrate good performance of abc best in solving complex numerical optimization problems when compared with two abc based algorithms

rank two perturbations of matrices and operators and operator model for t transformation of probability measures abstract rank two parametric perturbations of operators and matrices are studied in various settings in the finite dimensional case the formula for a characteristic polynomial is derived and the large parameter asymptotics of the spectrum is computed the large parameter asymptotics of a rank one perturbation of singular values and condition number are discussed as well in the operator case the formula for a rank two transformation of the spectral measure is derived and it appears to be the t transformation of a probability measure studied previously in the free probability context new transformation of measures is studied and several examples are presented

comparison of different metaheuristic algorithms based on intercriteria analysis abstract in this paper intercriteria analysis icra based on the apparatus of the index matrices and the intuitionistic fuzzy sets is performed for a model parameters identification using different pure and hybrid metaheuristic techniques as a case study a non linear e coli mc4110 fed batch cultivation process model is considered series of cultivation model identification procedures using metaheuristics as genetic algorithms ga ant colony optimization aco firefly algorithm fa and simulated annealing sa are done the results are compared with the once obtained by applied hybrid algorithms aco ga aco fa and ga aco further the icra is used to explore the existing relations and dependences of defined cultivation model parameters namely m a x k s and y x s and considered metaheuristic algorithms outcomes e g computation time t and objective function value j applying icra on the obtained average results of model parameters estimates t and j some relations between the defined criteria are established the presented results show some dependences relating to the physical meaning of the considered model parameters and to stochastic nature of the applied in this paper metaheuristic techniques

a hybrid quantum inspired harmony search algorithm for 0 1 optimization problems this paper presents a new hybrid natural algorithm based on harmony search algorithm hsa and quantum computing qc the main features of the proposed algorithm called quantum inspired harmony search algorithm qihsa is the integration of quantum representation scheme in the basic harmony search algorithm that allows applying successfully some quantum inspired operators like measurement and interference this hybridization between quantum inspired computing and harmony search algorithm has led to an efficient hybrid framework which achieves better balance between the exploration of hs algorithm and the exploitation capabilities of the quantum inspired computing experiments on knapsack problems show the effectiveness of the proposed framework and its ability to achieve good quality solutions

analysis of spectral variation and some inequalities a geometric method based on a decomposition of the space of complex matrices is employed to study the variation of the spectrum of a matrix when adapted to special cases this leads to some classical inequalities as well as some new ones as an example of the latter we show that if u v are unitary matrices and k is a skew hermitian matrix such that uv exp k then for every unitary invariant norm the distance between the eigenvalues of v and those of vis bounded by k this generalises two earlier results which used particular unitary invariant norms

the effect of finite rank perturbations on jordan chains of linear operators abstract a general result on the structure and dimension of the root subspaces of a linear operator under finite rank perturbations is proved the increase of dimension from the kernel of the n th power to the kernel of the n 1 th power of the perturbed operator differs from the increase of dimension of the kernels of the corresponding powers of the unperturbed operator by at most the rank of the perturbation this bound is sharp

changing the spectrum of an operator by perturbation abstract we discuss the following problem how can the spectrum a of a linear operator a be changed upon perturbation of a with a one dimensional operator k in particular we study this question for normal self adjoint and unitary operators

sharp eigenvalue estimates for rank one perturbations of nonnegative operators in krein spaces abstract let a and b be selfadjoint operators in a krein space and assume that the resolvent difference of a and b is of rank one in the case that a is nonnegative and i is an open interval such that a i consists of isolated eigenvalues we prove sharp estimates on the number and multiplicities of eigenvalues of b in i the general result is illustrated with eigenvalue estimates for singular indefinite sturm liouville problems

perturbation theory of selfadjoint matrices and sign characteristics under generic structured rank one perturbations abstract for selfadjoint matrices in an indefinite inner product possible canonical forms are identified that arise when the matrix is subjected to a selfadjoint generic rank one perturbation genericity is understood in the sense of algebraic geometry special attention is paid to the perturbation behavior of the sign characteristic typically under such a perturbation for every given eigenvalue the largest jordan block of the eigenvalue is destroyed and in case the eigenvalue is real all other jordan blocks keep their sign characteristic the new eigenvalues i e those eigenvalues of the perturbed matrix that are not eigenvalues of the original matrix are typically simple and in some cases information is provided about their sign characteristic if the new eigenvalue is real the main results are proved by using the well known canonical forms of selfadjoint matrices in an indefinite inner product a version of the brunovsky canonical form and on general results concerning rank one perturbations obtained

scheduling for an adaptive number of iterations in turbo equalizers combined with ldpc decoders a new scheduling to reduce the complexity of a turbo equalizer te combined with a low density parity check ldpc decoder is proposed simple metrics and criteria for the proposed scheduling are derived from its convergence behavior the te with the proposed scheduling monitors the status of its iterative process and determines whether additional equalization is needed or not based on the decision it adjusts performing equalization and reduces the execution number of equalization consequently this leads to lowering the overall complexity of the te numerical results show that the proposed scheduling has lower complexity than conventional schedulings while they have almost the same performance

canonical forms for hermitian matrix pairs under strict equivalence and congruence after a brief historical review and an account of the canonical forms attributed to jordan and kronecker a systematic development is made of the simultaneous reduction of pairs of quadratic forms over the complex numbers and over the reals these reductions are by strict equivalence and by congruence and essentially complete proofs are presented some closely related results which can be derived from the canonical forms are also included they concern simultaneous diagonalization a new criterion for the existence of positive definite linear combinations of a pair of hermitian matrices and the canonical structures of matrices which are self adjoint in an indefinite inner product

lipschitz stability of canonical jordan bases of h selfadjoint matrices under structure preserving perturbations in this paper we study jordan structure preserving perturbations of matrices selfadjoint in the indefinite inner product the main result of the paper is lipschitz stability of the corresponding affiliation matrices the result can be reformulated as lipschitz stability under small perturbations of canonical jordan bases i e eigenvectors and generalized eigenvectors enjoying a certain flipped orthonormality relation of matrices selfadjoint in the indefinite inner product the proof relies upon the analysis of small perturbations of invariant subspaces where the size of a permutation of an invariant subspace is measured using the concepts of a gap and of a semigap

a singular m matrix perturbed by a nonnegative rank one matrix has positive principal minors is it d stable abstract the positive stability and d stability of singular m matrices perturbed by non trivial nonnegative rank one perturbations is investigated in special cases positive stability or d stability can be established in full generality this is not the case as illustrated by a counterexample however matrices of the mentioned form are shown to be p matrices

generic rank one perturbations of structured regular matrix pencils abstract classes of regular structured matrix pencils are examined with respect to their spectral behavior under a certain type of structure preserving rank 1 perturbations the observed effects are as follows on the one hand generically the largest jordan block at each eigenvalue gets destroyed or becomes of size one under a rank 1 perturbation depending on that eigenvalue occurring in the perturbating pencil or not on the other hand certain jordan blocks of t alternating matrix pencils occur in pairs so that in some cases the largest block cannot just be destroyed or shrunk to size one without violating the pairing thus the largest remaining jordan block will typically increase in size by one in these cases finally these results are shown to carry over to the classes of palindromic and symmetric matrix pencils

zeros of nonpositive type of generalized nevanlinna functions with one negative square abstract a generalized nevanlinna function q z with one negative square has precisely one generalized zero of nonpositive type in the closed extended upper halfplane the fractional linear transformation defined by q z q z 1 q z r is a generalized nevanlinna function with one negative square its generalized zero of nonpositive type as a function of defines a path in the closed upper halfplane various properties of this path are studied in detail