Circulant Matrix

Let $\{a_k\}$ be a sequence of real numbers defined by an $m$th order linear homogenous recurrence relation. In this paper we obtain a determinant formula for the circulant matrix $A=circ(a_1, a_2, \cdots, a_n)$, providing a generalization of determinantal results in papers of Bozkurt \cite{Bozkurt}, Bozkurt and Tam \cite{BozkurtTam}, and Shen, et al. \cite{ShenCenHao}.

Multimedia security has been the aim point of considerable research activity because of its wide application area. The major technology to achieve copyright protection, content authentication, access control and multimedia security is watermarking which is the process of embedding data into a multimedia element such as image or audio, this embedded data can later be extracted from, or detected in the embedded element for different purposes. In this work, a blind watermarking algorithm based on SVD and circulant matrices has been presented. Every circulant matrix is associated with a matrix for which the SVD decomposition coincides with the spectral decomposition. This leads to improve the Chandra algorithm [1], our presentation will include a discussion on the data hiding capacity, watermark transparency and robustness against a wide range of common image processing attacks.

The secure transmission of any form of data over a communication medium is prime important across the globe or in research arena. Cryptography is a branch of cryptology and it provides security for data transmission between any communicating parties. The Hill cipher is one of the symmetric key substitution algorithms. Hill Cipher is vulnerable to known plaintext attack. This paper presents an enhancement to the Hill cipher by utilizing the circulant matrices. The proposed technique shares a prime circulant matrix as a secret key and we choose a non-singular matrix as a public key in such way that the determinant of the coefficient matrix is zero. Computational cost shows that the proposed technique is efficient and it thwarts all the security attacks.

Kayıt tarihi: 30 Mayıs 2008, Kabul tarihi: 20 Ekim 2008 ABSTRACT Purpose: To examine the effects of an 8-week walking program on serum lipids, circulation matrix metalloproteinase-9 and tissue inhibitor of metalloproteinase-1 in post-menopausal women. Method: Body weight, percent body fat, body mass index, estimated maximal oxygen consumption, blood lipids, matrix metalloproteinase-9, tissue inhibitor of metalloproteinase-1 concentrations were assessed and their matrix metalloproteinase-9/tissue inhibitor of metalloproteinase-1 molar ratios were calculated in exercise (n=12) and control (n=12) groups. Exercise group completed an eight-week walking program at moderate (~6.29±0.15km/h; ~62% maximum heart rate reserve) intensity. Results: Significant changes in estimated maximal oxygen consumption, systolic and diastolic blood pressures, body weight, and body mass index (p< .05) were determined in exercise group. However, there were no significant changes in the measured blood lipid...

A well known family of minimally nonideal matrices is the family of the incidence matrices of chordless odd cycles. A natural generalization of these matrices is given by the family of circulant matrices. Ideal and minimally nonideal circulant matrices have been completely identified by Cornuéjols and Novick [G. Cornuéjols, B. Novick, Ideal 0 - 1 matrices, Journal of Combinatorial Theory

Long memory models have received a significant amount of attention in the theoretical literature as they cover a wide range of applications, including economics and telecommunications. In recent years, a semiparametric estimator of the long memory parameter of stationary processes with long-range dependence, based on wavelet decomposition, has been proposed and studied by Veitch and Abry (1999) under the idealized assumption of decorrelation among wavelet coefficients. The asymptotic statistical analysis of the wavelet-based estimator has been recently complemented taking into account the correlations among wavelet coefficients, at fixed scales as well as among different scales (Bardet et al., 2000). The goal of the present article is to study the statistical properties of the wavelet-based estimator for a finite sample size and the correlation among the wavelet-based long memory estimates. The analysis is conducted by simulation, through the use of the circulant matrix method and shows that the correlation among wavelet coefficients has an impact on the moments of the wavelet-based estimator and on the correlation among the wavelet-based long memory estimates computed on non overlapping blocks of the original process.

Circulant graphs C_n(R) and C_n(S) are said to be Adam's isomorphic if there exist some a∈ℤ_n^* such that S = aR. Vilfred defined Type-2 isomorphism, a new type of isomorphism different from Adam's isomorphism, on circulant graphs of order n with respect to r, (n, r) > 1 and r,n∈ℕ and we obtained such families of graphs for r = 2,3,5,7 and n∈ℕ. In this paper, we obtain more general cases, families of Type-2 isomorphic circulant graphs of order np^3 with respect to r = p, and derive abelian groups on these isomorphic graphs where p is a prime number and n∈ℕ. Theorems <ref> and <ref> are the main results. Using Theorem <ref>, a list of abelian groups on Type-2 isomorphic circulant graphs of order np^3 are given in the annexure for p = 3,5,7,11 and n = 1 to 5 and also for p = 13 and n = 1 to 3.

Singular Spectrum Analysis (SSA) is a nonparametric tecnique for signal extraction in time series based on principal components. However, it requires the intervention of the analyst to identify the frequencies associated to the extracted principal components. We propose a new variant of SSA, Circulant SSA (CSSA) that automatically makes this association. We also prove the validity of CSSA for the nonstationary case. Through several sets of simulations, we show the good properties of our approach: it is reliable, fast, automatic and produces strongly separable elementary components by frequency. Finally, we apply Circulant SSA to the Industrial Production Index of six countries. We use it to deseasonalize the series and to illustrate that it also reproduces a cycle in accordance to the dated recessions from the OECD.

Singular Spectrum Analysis (SSA) is a nonparametric tecnique for signal extraction in time series based on principal components. However, it requires the intervention of the analyst to identify the frequencies associated to the extracted principal components. We propose a new variant of SSA, Circulant SSA (CSSA) that automatically makes this association. We also prove the validity of CSSA for the nonstationary case. Through several sets of simulations, we show the good properties of our approach: it is reliable, fast, automatic and produces strongly separable elementary components by frequency. Finally, we apply Circulant SSA to the Industrial Production Index of six countries. We use it to deseasonalize the series and to illustrate that it also reproduces a cycle in accordance to the dated recessions from the OECD.

Algorithms for the minimal polynomial and the inverse of a level-n(r1, r2,…,rn)-block circulant matrix over any field are presented by means of the algorithm for the Gröbner basis for the ideal of the polynomial ring over the field, and two algorithms for the inverse of a level-n(r1,r2,…,rn)-block circulant matrix over a quaternion division algebra are given, which can be realized by CoCoA 4.0, an algebraic system, over the field of rational numbers or the field of residue classes of modulo a prime number.

This paper develops properties of recurrence sequences defined from circulant matrices obtained from the characteristic polynomial of the Pell–Padovan sequence. The study of these sequences modulo m yields cyclic groups and semigroups from the generating matrices. Finally, we obtain the lengths of the periods of the extended sequences in the extended triangle groups E(2, n, 2), E(2, 2, n) and E(n, 2, 2) for n ≥ 3 as applications of the results obtained.

In this work, given a positive definite matrix , we introduce a class of matrices related to which is obtained by suitably combining projections of its powers onto algebras of matrices simultaneously diagonalized by a unitary transform. After a detailed theoretical study of some spectral properties of the matrices of this class-which suggests their use as regularizing preconditioners-, we prove that such matrices can be cheaply computed when the matrix has Toeplitz structure. We provide numerical evidence of the advantages coming from the employment of the proposed preconditioners when used in regularizing procedures.

The paper is devoted to the problem of designing matrix regulators for a special class of multivariable feedback control systems called circulant systems. The exposition is based on the characteristic transfer function method, which allows reducing the investigation of N - dimensional multivariable control system to investigation of N fictitious one-dimensional systems. An analytical formula for elements of circulant matrix regulators is derived. Դիտարկվում է հետադարձ կապով բազմաչափ կառավարման համակարգերի հատուկ դասի, այսպես կոչված, ցիրկուլյանտ համակարգերի մատրիցային կարգավորիչների նախագծման խնդիրը: Ներկայացվածը կատարված է բնութագրիչ փոխանցման ֆունկցիաների մեթոդով, որը թույլ է տալիս N –չափանի փոխադարձ կապերով կառավարման համակարգերի հետազոտումը հանգեցնել մեկ մուտքով և ելքով N հատ երևակայական համակարգերի հետազոտման: Դուրս է բերված անալիտիկ բանաձև` ցիրկուլյանտ մատրիցային կարգավորիչի տարրերի որոշման համար: Рассматривается задача проектирования матричных регуляторов для специального клас...

Circulant graphs $C_n(R)$ and $C_n(S)$ are said to be \emph{Adam's isomorphic} if there exist some $a\in \mathbb{Z}_n^*$ such that $S = a R$ under arithmetic reflexive modulo $n$. Vilfred defined a new type of isomorphism, Type-2 isomorphism, different from Adam's isomorphism, on circulant graphs of order $n$ with respect to $r$, $\gcd(n, r)$ $>$ 1 and $r,n\in\mathbb{N}$ and we obtained such families of graphs for $r$ = 2,3,5,7 and $n\in\mathbb{N}$. In this paper, we obtain more general families of Type-2 isomorphic circulant graphs of order $np^3$ with respect to $r = p$, and abelian groups on these isomorphic graphs where $p$ is a prime number and $n\in\mathbb{N}$. Theorems \ref{d2} and \ref{d4} are the main results. Using Theorem \ref{d4}, a list of abelian groups on Type-2 isomorphic circulant graphs of order $np^3$ are given in the Annexure for $p$ = 3,5,7,11 and $n$ = 1 to 5 and also for $p$ = 13 and $n$ = 1 to 3.

Gestational hypertension (GH) is dangerous to both mother and child. Arterial invasiveness and growth are dependent on successful extracellular matrix (ECM) breakdown, which may be abnormal in GH. We hypothesized abnormalities in circulating matrix metalloproteinase-9 (MMP-9) and tissue inhibitors of metalloproteinases-1 and -2 (TIMP-1 and TIMP-2, respectively) in patients with GH, when compared with normotensive women with normal pregnancies and healthy nonpregnant control subjects. Plasma MMP-9, TIMP-1, and TIMP-2 were measured by ELISA in 23 women with GH, 30 normotensive pregnant women, and 28 nonpregnant women who were matched for age, gestational age, and parity. Levels of circulating MMP-9, TIMP-1 and TIMP-2, and the MMP-9/TIMP-1 and MMP-9/TIMP-2 ratios were significantly different among the three groups (P = .026, P = .006, P = .007, P = .001 and P = .008 respectively). Within the GH group, MMP-9 and the MMP-9/TIMP-1 ratio correlated negatively with age (r = -0.581, P = .004...

In this work, we consider the model of Cellular Neural Network (CNN) introduced by Chua and Yang in 1988, but with the cloning templates !-periodic in time. By imposing periodic boundary conditions the matrices involved in the system become circulant and !-periodic. We show some results on the controllability of the linear model using a Theorem by Brunovsky for the case of linear and !-periodic system. Also we use this approach in im- age detection, specifically foreground, background and contours of figures in dierent scales of grey.

Purpose: To examine the effects of an 8-week walking program on serum lipids, circulation matrix metalloproteinase-9 and tissue inhibitor of metalloproteinase-1 in post-menopausal women. Method: Body weight, percent body fat, body mass index, estimated maximal oxygen con- sumption, blood lipids, matrix metalloproteinase-9, tissue inhibitor of metalloproteinase-1 concentrations were assessed and their matrix metalloproteinase-9/tissue inhibitor of me- talloproteinase-1 molar ratios were