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On the interior of a regular convex cone K in n-dimensional real space there exist two canonical Hessian metrics, the one generated by the logarithm of the characteristic function, and the Cheng-Yau metric. The former is associated with a self-concordant logarithmically homogeneous barrier on K, the universal barrier. It is invariant with respect to the unimodular automorphism subgroup of K and is compatible with the operation of taking product cones, but in general it does not behave well under duality. Here we introduce a barrier associated with the Cheng-Yau metric, the canonical barrier. It shares with the universal barrier the invariance, existence, and uniqueness properties and is compatible with the operation of taking product cones, but in addition is well behaved under duality. The canonical barrier can be characterized as the convex solution of the partial differential equation log det F' = 2F that tends to infinity as the argument tends to the boundary of K. Its barrier parameter does not exceed the dimension n of the cone. On homogeneous cones both barriers essentially coincide. Keywords: interior-point methods; self-concordant barriers; convex cones MSC2000 subject classification: Primary: 90C51; secondary: 90C25 OR/MS subject classification-. Primary: programming, nonlinear convex; secondary: mathematics, convexity, 1. Introduction. Self-concordant logarithmically homogeneous barriers play a paramount role in the theory of interior-point methods for solving convex conic programs. Let K ⊂ [R.sup.n] be a regular (with nonempty [...]

This paper presents a procedure for evaluating the performance of reverberation chambers, by approximating the maximum working volume in a given configuration. The evaluation of this volume is based on the geometrical and physical constraints, e.g., the ones related to the internal E-field distribution recommended by standards. The importance of the present work is related to the development of a non-canonical reverberation chamber configuration, whose excitation is carried out by transmission lines, instead of antennas plus paddles. Index Terms--Optimization, reverberation chambers, working volume.

Two algorithms are presented for computing the linear canonical transforms (LCTs) from the N samples of the input signal in ~NlogN time. Results suggest the accuracy of the proposed algorithms in efficiently realizing filtering in linear canonical transform domains.

The three popular correlation analysis, canonical correlation analysis (CCA), multivariate linear regression (MLR) and partial least squares (PLS), are discussed. The correlation spread is defined as a normalized measure of how much of the overall correlation is contained in a low-dimensional subspace.

The article develops a heuristic to explain two-dimensionalism without recourse to theses of descriptivism. This is done by using a version of David Lewis's counterpart theory instead of the standard theory of canonical descriptions.

We stress the role of nonequivalent representations of the canonical commutation relations in quantum mechanics. Such representations occur when the space accessible to the system is not simply connected. An example is the magnetic Aharonov-Bohm effect, which can be interpreted in terms of nonequivalent representations, without explicitly invoking the vector potential in the region accessible to the electrons. [DOI: 10.1119/1.2360994]

Functional data can be clustered by plugging estimated regression coefficients from individual curves into the k-means algorithm. Clustering results can differ depending on how the curves are fit to the data. Estimating curves using different sets of basis functions corresponds to different linear transformations of the data. k-means clustering is not invariant to linear transformations of the data. The optimal linear transformation for clustering will stretch the distribution so that the primary direction of variability aligns with actual differences in the clusters. It is shown that clustering the raw data will often give results similar to clustering regression coefficients obtained using an orthogonal design matrix. Clustering functional data using an [L.sup.2] metric on function space can be achieved by clustering a suitable linear transformation of the regression coefficients. An example where depressed individuals are treated with an antidepressant is used for illustration. KEY WORDS: Allometric extension; Canonical discriminant analysis; Orthogonal design matrix; Principal component analysis.

Common factors play an important role in many disciplines of social science. In economics, the factors are the common shocks that underlie the co-movements of the large number of economic time series. The question of interest is whether some observable economic variables are in fact the underlying unobserved factors. We consider statistics to determine if the observed and the latent factors are exactly the same. We also provide simple to construct statistics that indicate the extent to which the two sets of factors differ. The key to the analysis is that the space spanned by the latent factors can be consistently estimated when the sample size is large in both the cross-section and the time series dimensions. The tests are used to assess how well the so-called Fama and French factors as well as several business cycle indicators approximate the factors in portfolio and individual stock returns. Data from a large panel of macroeconomic are also analyzed. JEL classification: C2; C3; C5; G1 Keywords: Principal components; Proxies; Generated regressors; Canonical coefficients

A solution to noisy sources is to first transform the noisy observations into canonical coordinates, quantize and apply a Wiener filter in this coordinate system and then transform the result back to the original coordinates. The type of canonical coordinate system depends on the design objective.

For several decades now, ecologists have sought to determine the shape of species' response curves and how they are distributed along unknown underlying gradients, environmental latent variables, or ordination axes. Its determination has important implications for both continuum theory and community analysis because many theories and models in community ecology assume that responses are symmetric and unimodal. This article proposes a major new technique called constrained additive ordination (CAO) that solves this problem by computing the optimal gradients and flexible response curves. It allows ecologists to see the response curves as they really are, against the dominant gradients. With one gradient, CAO is a generalization of constrained quadratic ordination (CQO; formerly called canonical Gaussian ordination or CGO). It supplants symmetric bell-shaped response curves in CQO with completely flexible smooth curves. The curves are estimated using smoothers such as the smoothing spline. Loosely speaking, CAO models are generalized additive models (GAMs) fitted to a very small number of latent variables. Being data driven rather than model driven, CAO allows the data to 'speak for itself' and does not make any of the assumptions made by canonical correspondence analysis. The new methodology is illustrated with a hunting spider data set and a New Zealand tree species data set. Key words: canonical correspondence analysis; constrained ordination; direct gradient analysis; environmental gradients; generalized additive models; latent variables; nonparametric regression; smoothing; species--environmental relationships; species-packing model; S statistical language; unimodal response curve.

A report on second-order polynomial response surfaces when expressed in their canonical forms had common features like common stationary points or common eigenvector sets is presented.

The problem of two-channel constrained least squares (CLS) filtering under various sets of constraints is considered and a general set of solutions is derived. An alternating power method is proposed to recursively compute the canonical coordinate and half-canonical coordinate mappings.

Canonical analysis is a common method for exploring and exploiting fitted quadratic response surfaces. Much attention in canonical analysis is given to identifying ridge behavior in these surfaces in order to achieve optimal response at minimum cost. However, little attention has been given to classifying the identified ridge as a stationary ridge or a rising ridge. Knowing whether a ridge is stationary or rising is critical for making decisions about how to continue the response surface exploration or for setting process parameters. This article presents two methods that allow for identification, classification and confirmation of ridge behavior. The first method is based on linear regression and though easily implemented, can be imprecise. The second method is more precise and is based on a new parameterization of the canonical form. It uses nonlinear regression techniques that are becoming increasingly accessible through software packages.

A flexible method is needed for constrained ordination on the basis of any distance or dissimilarity measure, which will display a cloud of multivariate points by reference to a specific a priori hypothesis. We suggest the use of principal coordinate analysis (PCO, metric MDS), followed by either a canonical discriminant analysis (CDA, when the hypothesis concerns groups) or a canonical correlation analysis (CCorA, when the hypothesis concerns relationships with environmental or other variables), to provide a flexible and meaningful constrained ordination of ecological species abundance data. Called 'CAP' for 'Canonical Analysis of Principal coordinates,' this method will allow a constrained ordination to be done on the basis of any distance or dissimilarity measure. We describe CAP in detail, including how it can uncover patterns that are masked in an unconstrained MDS ordination. Canonical tests using permutations are also given, and we show how the method can be used (1) to place a new observation into the canonical space using only interpoint dissimilarities, (2) to classify observations and obtain misclassification or residual errors, and (3) to correlate the original variables with patterns on canonical plots. Misclassification error or residual error is used to obtain a non-arbitrary decision concerning the appropriate dimensionality of the response data cloud (number of PCO axes) for the ensuing canonical analysis. We suggest that a CAP ordination and an unconstrained ordination, such as MDS, together will provide important information for meaningful multivariate analyses of ecological data by reference to explicit a priori hypotheses. Key words: canonical ordination; classification; community structure; distance matrix; MDS; multivariate analysis; principal coordinate analysis; species abundances; statistical methods.

Grand canonical Monte Carlo simulations in the framework of the primitive model were used to determine the mechanical stability of planar charged interfaces in the presence of various salts of multivalent counterions multivalent counterions . The influence of salt addition on the strength and the range of interionic correlations were determined.

A method for calculating the quantum canonical rate constant of chemical reactions in a many body system with the help of a short-time flux autocorrelation function combined with a maximum entropy numerical analytical continuation scheme is described. The rate constant is expressed as the time integral of real-time flux autocorrelation function.

The Boltzmann reservoir (BR) is a model constant-temperature environment that exhibits highly atypical thermodynamic behavior. Its microcanonical ensemble entropy is a linear, nonconcave function of its internal energy U, and its zero-work heat capacity is infinite. Its canonical partition function diverges because all possible energies are equally likely, so the microcanonical and canonical ensembles are not equivalent. If two BRs with the same temperature T(sub B) are put in thermal contact, either can have any fraction of the total energy; i.e., there is no unique equilibrium state. If two BRs with different temperatures are in thermal contact, the higher temperature BR gives all its energy to the other. A BR's temperature cannot be changed by a heat process but, in principle, can be altered by a work process. These and other properties that challenge conventional wisdom provide thought-provoking examples for thermal physics courses.

Brownian motion represents simple diffusion random walk processes. More complex random walk processes also can occur when probability distributions describing the random jump distances and times have infinite moments. We explore the manner in which these distributions can arise and how they underlie various scaling laws that play an important role in both random and deterministic systems.

This paper presents a discussion of cointegration amongst I(2) variables and provides a synthesis of various ways I(2) cointegrated systems may be characterized and represented. Following Yoo (1986), Engle and Yoo (1991) and Salmon (1988) we use the Smith-McMillan form of a rational polynomial matrix as a unifying framework to describe the null-space structure of I(2)-cointegrated systems and show how different representations such as the autoregressive and error correction representations, the common stochastic trends representation and various triangular array decompositions, can be derived. Hence we extend the I(1) results of Hylleberg and Mizon (1989) to I(2) systems. The different representations provide different insights into distinct features of multivariate systems that may simultaneously contain several types of equilibrium behaviour that is more complex than that found with I(1) systems. We also discuss how appropriately defined state variables may ease the interpretational difficulties that may arise in polynomially cointegrated systems. Keywords: Cointegration; Smith-McMillan canonical form; Error correction; Bewley representation; Triangular decomposition; Common stochastic trends

An expression for the shift necessary to obtain a canonical m-sequence is obtained in terms of the coefficients of the primitive polynomial that generates this m-sequence. This shift for obtaining a canonical m-sequence is also directly related to the shift for obtaining the location of the span "100 ... 0" in the m-sequence. In addition, a recursion is developed for obtaining the dual basis elements of the basis expressing GF ([q.sup.m]) over GF (q). Index Terms - Canonical m-sequence, dual basis, trace recursion.

The purpose of this paper is to review the various available estimation techniques for the canonical disequilibrium model: full information maximum likelihood (FIML), pseudo maximum likelihood methods, and their simulated counterparts. The use of the latter was advocated by Laroque-Salanie (1989) when the model is analytically untractable. We provide some new asymptotic results for all of these methods and compare their behavior on finite samples using Monte Carlo simulations. It appears that FIML performs only slightly better than the second-order PML method, which in turn performs only slightly better than its simulated counterpart. Given the ease of implementation of the latter technique, these results strongly militate for its use.

Since its invention in 1988, while retaining the two basic concepts of local connectedness and analog circuit dynamics, the CNN paradigm has evolved to cover a very broad class of problems and frameworks. In this paper a tutorial summary of the various classes of CNN is presented along with a precise taxonomy. Some examples are presented to demonstrate the inherent richness of this paradigm.

Canonical discriminant functions are defined here as linear combinations that separate groups of observations, and canonical variates are defined as linear combinations associated with canonical correlations between two sets of variables. In standardized form, the coefficients in either type of canonical function provide information about the joint contribution of the variables to the canonical function. The standardized coefficients can be converted to correlations between the variables and the canonical function. These correlations generally alter the interpretation of the canonical functions. For canonical discriminant functions, the standardized coefficients are compared with the correlations, with partial t and F tests, and with rotated coefficients. For canonical variates. the discussion includes standardized coefficients, correlations between variables and the function, rotation, and redundancy analysis. Various approaches to interpretation of principal components are compared: the choice between the covariance and correlation matrices, the conversion of coefficients to correlations, the rotation of the coefficients, and the effect of special patterns in the covariance and correlation matrices.

In textbooks on multivariate statistics, the topic of multivariate analysis of variance (MANOVA) is usually presented in terms of the decomposition of the 'total sums of squares and products' matrix into the 'within' and 'between' matrices, often called the 'hypothesis' and the 'error' matrices. While this decomposition can be justified by maximum likelihood estimation and hypothesis testing under normality assumptions, better motivation is provided by a finite mixture model in which no assumptions beyond the existence of second moments are needed. We propose that the decomposition be interpreted in terms of estimates of conditional and unconditional moments, rather than a just an algebraic identity. KEY WORDS: Canonical discriminant functions; Conditional distribution; Finite mixtures; One-way MANOVA.

The fluctuations in the number of particles of the ideal gas are calculated using the canonical and the grand canonical ensembles. The two results differ by a factor which accounts for the relative size of the total volume and the subvolume where the canonical ensemble fluctuations are calculated. This factor gives a simple example of explicit finite-size effects, because it arises from considering a fixed number of particles in the canonical ensemble. Our simulation results for the isothermal compressibility of the hard disk fluid with a finite number of particles are improved by applying this correction.

We describe a simple experiment, suitable for an undergraduate laboratory, in which the collector current in a transistor is measured as a function of the base-emitter voltage at various temperatures. The experiment gives a very convincing demonstration of the canonical distribution of statistical mechanics, in which the probability of occupancy of a state of energy E is proportional to e-(super E/kT).

X. Rong Li's article 'Canonical transform for tracking with kinematic models' underscored the stability and convergence of the Kalman filter to a steady state with a constant filter increase. Moreover, a Kalman filter with the steady-state gain can be used from the initial stages of implementation. This approach appeared suboptimal because a standard Kalman filter can be an optimal filter since it accounts for both the variance and the individual measurements.

A simple integrable lowest weight module of a quantized enveloping algebra is used to design a canonical basis in the tensor product of a simple integrable highest weight module. The extraordinary stability of this canonical basis makes it simultaneously compatible with several natural subspaces of the tensor product. A canonical basis of an altered version of the quantized enveloping algebra is developed.

It is shown in this note that a linear second-order system with arbitrary damping cannot be reduced to Hessenberg-triangular form by means of orthogonal transformations. However, it is also shown that such an orthogonal reduction is always possible for the modal damping commonly assumed for models of flexible structures. In fact, it is shown that modally damped models can be orthogonally reduced to a new triangular second-order Schur form.

The origin and linear progress history of financial economics as told by economists like Jovanovic is presented. It is shown that the canonical history of financial economics was created during the 1960s with a view to support theoretical viewpoints that led the mainstream community of scientists to view financial economics as a science.

Canonical extensions provide an algebraic formulation that can be applied in the setting of partially ordered algebras. Canonical extensions are used to give a uniform treatment of completeness of relational semantics for various sub structural logics with implications as the residual of fusion.

The algebra of finite rank operators as imaginaries inside a Hilbert space are interpreted. Results proved that the Hilbert space enlarged with these imaginaries had built-in canonical bases.

The problem of the electromagnetic (EM) wave diffraction by canonical image type slotted structures is studied by the methods of perturbation theory applied to analytical operator valued functions. Fundamental (scattering) frequencies, obtained in the form of expansions in powers of a small parameter (slotwidth), are shown to have negative imaginary parts. Explicit representations for scattered fields are obtained both in the resonant and nonresonant cases, and the amplitude and phase distributions are calculated. Index Terms--Image-type structures, operator-valued functions.

Recent empirical studies show that the squares of high-frequency stock returns are long-range dependent and can be modeled as fractionally integrated processes, using, for example, long-memory stochastic volatility models. Are [...]

We consider the problem of constructing and transmitting the prelude for Huffman coding. With careful organization of the required operations and an appropriate representation for the prelude, it is possible to make semistatic coding efficient even when S, the size of the source alphabet, is of the same magnitude as m, the length of the message being coded. The proposed structures are of direct relevance in applications that mimic one-pass operation through the use of semistatic compression on a block-by-block basis. Index Terms--Adaptive coding, canonical code, Huffman code, minimum-redundancy code, prefix code.

In this paper a novel method of generating canonic sinusoidal oscillators with two operational transconductance amplifiers (OTA's), two grounded capacitors (GC's), and a small number of resistors is introduced. Noninteracting control of the frequency of oscillation (FO) and the condition of oscillation (CO) are realized with the transconductance parameters of the two OTA's respectively. Bandpass (BP) and lowpass (LP) filter functions can also be realized with the same topologies. The independent tuning of the natural frequency [[Omega].sub.o] and [[Omega].sub.o]/Q of most filters can be realized without changing the topologies. Index Terms--Analog, Boolean method, filter, oscillator, OTA.

ABSTRACT: Environmental education researchers have done little to identify the relationship between attitude toward science and attitude toward the environment. In this study attitudinal measures on science and the environment [...]

It is well known that the ordinary least squares estimator of X[beta] in the general linear model Ey = X[beta], cov y =[[sigma].sup.2.V], can be the best linear unbiased estimator even if V is not a multiple of the identity matrix. This article presents, in a historical perspective, the development of the several conditions for the ordinary least squares estimator to be best linear unbiased. Various characterizations of these conditions, using generalized inverse and orthogonal projectors, along with several examples, are also given. In addition, a complete set of references is provided.

This paper presents a new iterative equalization algorithm that maximizes capacity for discrete multitone (DMT) systems. The research modifies a previously proposed criterion and applies an appropriate transformation to map the objective function and the constraint set into a canonical region. The resulting constraint set exhibits an identifiable geometric characteristic. Using the gradient projection method in conjunction with projection onto convex sets (POCS) provides us with an iterative search algorithm that facilitates the gradient descent method. We also generalize the approach to two important subclasses of equalizers, namely linear phase and unit tap filters. We also derive a fundamental limit on the performance of the proposed approach. In comparison with the previous methods, the proposed equalization algorithm is less computationally complex and more geometrically intuitive. Simulation experiments confirm the validity of the proposed method for equalization of DMT systems. Index Terms--Capacity maximization, convex optimization, discrete multitone systems, multicarrier systems, optimum equalization, projection onto convex set.