The Experts below are selected from a list of 48 Experts worldwide ranked by ideXlab platform

Zekeriya Uykan - One of the best experts on this subject based on the ideXlab platform.

  • Discrete-Time Autonomous Linear Networks
    1
    Co-Authors: Zekeriya Uykan
    Abstract:

    In this letter, we improve the results in [5] by relaxing the symmetry assumption and also taking the noise term into account. The author examines two discrete-time autonomous linear systems whose motivation comes from a neural network point of view in [5]. Here, we examine the following discretetime autonomous linear system: x(k+1) = Ax(k)+b where A is any real square Matrix with linearly independent eigenvectors whose largest eigenvalue is real and its norm is larger than 1, and vector b is constant. Using the same “SIR ” (“Signal”-to-“Interference”-Ratio) concept as in [4] and [5], we show that the ultimate “SIR ” is equal to aii, i = 1, 2,...,N, where N is the number of states, aii λmax−aii is the diagonal Elements of Matrix A, and λmax is the (single or multiple) eigenvalue with maximum norm

Hideki Tanemura - One of the best experts on this subject based on the ideXlab platform.

  • infinite systems of noncolliding generalized meanders and riemann liouville differintegrals
    Probability Theory and Related Fields, 2007
    Co-Authors: Makoto Katori, Hideki Tanemura
    Abstract:

    Yor’s generalized meander is a temporally inhomogeneous modification of the 2(ν + 1)-dimensional Bessel process with ν > − 1, in which the inhomogeneity is indexed by \(\kappa \in [0, 2(\nu+1))\). We introduce the noncolliding particle systems of the generalized meanders and prove that they are Pfaffian processes, in the sense that any multitime correlation function is given by a Pfaffian. In the infinite particle limit, we show that the Elements of Matrix kernels of the obtained infinite Pfaffian processes are generally expressed by the Riemann–Liouville differintegrals of functions comprising the Bessel functions Jν used in the fractional calculus, where orders of differintegration are determined by ν − κ. As special cases of the two parameters (ν, κ), the present infinite systems include the quaternion determinantal processes studied by Forrester, Nagao and Honner and by Nagao, which exhibit the temporal transitions between the universality classes of random Matrix theory.

  • infinite systems of non colliding generalized meanders and riemann liouville differintegrals
    arXiv: Probability, 2005
    Co-Authors: Makoto Katori, Hideki Tanemura
    Abstract:

    Yor's generalized meander is a temporally inhomogeneous modification of the $2(\nu+1)$-dimensional Bessel process with $\nu > -1$, in which the inhomogeneity is indexed by $\kappa \in [0, 2(\nu+1))$. We introduce the non-colliding particle systems of the generalized meanders and prove that they are the Pfaffian processes, in the sense that any multitime correlation function is given by a Pfaffian. In the infinite particle limit, we show that the Elements of Matrix kernels of the obtained infinite Pfaffian processes are generally expressed by the Riemann-Liouville differintegrals of functions comprising the Bessel functions $J_{\nu}$ used in the fractional calculus, where orders of differintegration are determined by $\nu-\kappa$. As special cases of the two parameters $(\nu, \kappa)$, the present infinite systems include the quaternion determinantal processes studied by Forrester, Nagao and Honner and by Nagao, which exhibit the temporal transitions between the universality classes of random Matrix theory.

Uykan Zekeriya - One of the best experts on this subject based on the ideXlab platform.

  • On the SIRs (Signal-to-Interference-Ratio) in Discrete-Time Autonomous Linear Networks
    'Institute of Electrical and Electronics Engineers (IEEE)', 2009
    Co-Authors: Uykan Zekeriya
    Abstract:

    In this letter, we improve the results in [5] by relaxing the symmetry assumption and also taking the noise term into account. The author examines two discrete-time autonomous linear systems whose motivation comes from a neural network point of view in [5]. Here, we examine the following discrete-time autonomous linear system: ${\mathbf x}(k+1) = {\mathbf A} {\mathbf x}(k) + {\mathbf b}$ where ${\mathbf A}$ is any real square Matrix with linearly independent eigenvectors whose largest eigenvalue is real and its norm is larger than 1, and vector ${\mathbf b}$ is constant. Using the same "SIR" ("Signal"-to-"Interference"-Ratio) concept as in [4] and [5], we show that the ultimate "SIR" is equal to $\frac{a_{ii}}{\lambda_{max} - a_{ii}}$, $i=1, 2, >..., N$, where $N$ is the number of states, $a_{ii}$ is the diagonal Elements of Matrix ${\bf A}$, and $\lambda_{max}$ is the (single or multiple) eigenvalue with maximum norm.Comment: 10 pages, 2 figures, has been submitted in March 2009 to IEEE International Conference on Artificial Neural Networks (ICANN) 2009, Cypru

Makoto Katori - One of the best experts on this subject based on the ideXlab platform.

  • infinite systems of noncolliding generalized meanders and riemann liouville differintegrals
    Probability Theory and Related Fields, 2007
    Co-Authors: Makoto Katori, Hideki Tanemura
    Abstract:

    Yor’s generalized meander is a temporally inhomogeneous modification of the 2(ν + 1)-dimensional Bessel process with ν > − 1, in which the inhomogeneity is indexed by \(\kappa \in [0, 2(\nu+1))\). We introduce the noncolliding particle systems of the generalized meanders and prove that they are Pfaffian processes, in the sense that any multitime correlation function is given by a Pfaffian. In the infinite particle limit, we show that the Elements of Matrix kernels of the obtained infinite Pfaffian processes are generally expressed by the Riemann–Liouville differintegrals of functions comprising the Bessel functions Jν used in the fractional calculus, where orders of differintegration are determined by ν − κ. As special cases of the two parameters (ν, κ), the present infinite systems include the quaternion determinantal processes studied by Forrester, Nagao and Honner and by Nagao, which exhibit the temporal transitions between the universality classes of random Matrix theory.

  • infinite systems of non colliding generalized meanders and riemann liouville differintegrals
    arXiv: Probability, 2005
    Co-Authors: Makoto Katori, Hideki Tanemura
    Abstract:

    Yor's generalized meander is a temporally inhomogeneous modification of the $2(\nu+1)$-dimensional Bessel process with $\nu > -1$, in which the inhomogeneity is indexed by $\kappa \in [0, 2(\nu+1))$. We introduce the non-colliding particle systems of the generalized meanders and prove that they are the Pfaffian processes, in the sense that any multitime correlation function is given by a Pfaffian. In the infinite particle limit, we show that the Elements of Matrix kernels of the obtained infinite Pfaffian processes are generally expressed by the Riemann-Liouville differintegrals of functions comprising the Bessel functions $J_{\nu}$ used in the fractional calculus, where orders of differintegration are determined by $\nu-\kappa$. As special cases of the two parameters $(\nu, \kappa)$, the present infinite systems include the quaternion determinantal processes studied by Forrester, Nagao and Honner and by Nagao, which exhibit the temporal transitions between the universality classes of random Matrix theory.

Waleed Abd El Maguid Ahmed - One of the best experts on this subject based on the ideXlab platform.

  • Hermite-Gaussian-like eigenvectors of the DFT Matrix generated by the eigenanalysis of an almost tridiagonal Matrix
    2005 IEEE International Symposium on Circuits and Systems, 2005
    Co-Authors: Magdy Tawfik Hanna, Nabila Philip Attalla Seif, Waleed Abd El Maguid Ahmed
    Abstract:

    The development of the discrete fractional Fourier transform (DFRFT) necessitates having orthonormal eigenvectors for the DFT Matrix, F. The objective of having the DFRFT approximate its continuous counterpart can be met if the eigenvectors of F approximate samples of the Hermite-Gaussian functions. Orthonormal Hermite-Gaussian-like eigenvectors for F are rigorously derived by a detailed analysis of an almost tridiagonal Matrix, S, which commutes with F. By an appropriate similarity transformation, S is reduced to a 2/spl times/2 block diagonal form and the Elements of the two exactly tridiagonal matrices forming the two diagonal blocks are explicitly derived in terms of the Elements of Matrix S.