Set Of Continuous Variables Research Articles

Phylogenetic Applications of the Minimum Contradiction Approach on Continuous Characters

We describe the conditions under which a set of continuous variables or characters can be described as an X-tree or a split network. A distance matrix corresponds exactly to a split network or a valued X-tree if, after ordering of the taxa, the variables values can be embedded into a function with at most a local maximum and a local minimum, and crossing any horizontal line at most twice. In real applications, the order of the taxa best satisfying the above conditions can be obtained using the Minimum Contradiction method. This approach is applied to 2 sets of continuous characters. The first set corresponds to craniofacial landmarks in Hominids. The contradiction matrix is used to identify possible tree structures and some alternatives when they exist. We explain how to discover the main structuring characters in a tree. The second set consists of a sample of 100 galaxies. In that second example one shows how to discretize the continuous variables describing physical properties of the galaxies without disrupting the underlying tree structure.

Quantum Communication with Continuous Variables

Many quantum communication schemes rely on the resource of entanglement. For example, quantum teleportation is the transfer of arbitrary quantum states through a classical communication channel using shared entanglement. Entanglement, however, is in general not easy to produce on demand. The bottom line of this work is that a particular kind of entanglement, namely that based on continuous quantum variables, can be created relatively easily. Only squeezers and beam splitters are required to entangle arbitrarily many electromagnetic modes. Similarly, other relevant operations in quantum communication protocols become feasible in the continuous-variable setting. For instance, measurements in the maximally entangled basis of arbitrarily many modes can be accomplished via linear optics and efficient homodyne detections. In the first two chapters, some basics of quantum optics and quantum information theory are presented. These results are then needed in Chapter III, where we characterize continuous-variable entanglement and show how to make it. The members of a family of multi-mode states are found to be truly multi-party entangled with respect to all their modes. These states also violate multi-party inequalities imposed by local realism, as we demonstrate for some members of the family. Further, we discuss how to measure and verify multi-party continuous-variable entanglement. Various quantum communication protocols based on the continuous-variable entangled states are discussed and developed in Chapter IV. These include the teleportation of entanglement (entanglement swapping) as a test for genuine quantum teleportation. It is shown how to optimize the performance of continuous-variable entanglement swapping. We highlight the similarities and differences between continuous-variable entanglement swapping and entanglement swapping with discrete variables. Chapter IV also contains a few remarks on quantum dense coding, quantum error correction, and entanglement distillation with continuous variables, and in addition a review of quantum cryptographic schemes based on continuous variables. Finally, in Chapter V, we consider a multi-party generalization of quantum teleportation. This so-called telecloning means that arbitrary quantum states are transferred not only to a single receiver, but to several. However, due to the quantum mechanical no-cloning theorem, arbitrary quantum states cannot be perfectly copied. We present a protocol that enables telecloning of arbitrary coherent states with the optimal quality allowed by quantum theory. The entangled states needed in this scheme are again producible with squeezed light and beam splitters. Although the telecloning scheme may also be used for "local'' cloning of coherent states, we show that cloning coherent states locally can be achieved in an optimal fashion without entanglement. It only requires a phase-insensitive amplifier and beam splitters.

CANCOR: A general least-squares program for univariate and multivariate analysis of variance and covariance

Many psychologists conceive of canonical correlation as a statistical technique that relates two sets of continuous variables; whether one set is deemed the "predictor set" and the other the "criterion set" is often arbitrary. Psychologists are now aware of the applicability of least-squares or regression methods to conventional experimental designs, with the independent variables serving as predictors and the dependent measures as criteria. Cohen (1968), for example, points out that, if one constructs dummy variables (+1, 0, -1) representing each between-cell degree of freedom in an experimental design and regresses the dependent measure upon these predictors, then a multiple regression analog to univariate analysis of variance (ANOVA) is achieved. If, in addition to the discrete design predictors, the researcher includes one or more continuous variables in the predictor set, then a univariate analysis of covariance (ANCOVA) can be accomplished. Leastsquares techniques are also applicable to designs involving multiple dependent measures (Woodward & Overall, 1975). Just as multiple correlation is the least-squares analog to univariate ANOVA and ANCOVA, canonical correlation is the analog to multivariate analysis of variance (MANOVA) and covariance (MANCOVA) (Knapp, 1978). SinceANOVA is simplya special case of multiple regression (i.e., one which employs discrete design predictors), which in turn is a special case of canonical correlation (Le., one which has only one criterion), canonical correlation seems to be the most general of these techniques, the closest approximation to the general linear model. Insofar as a canonical correlation analysis is concerned, the only factors that distinguish the various techniques are the number of criteria and whether the predictors are continuous, discrete, or mixed. In sum, canonical correlation can be used to perform any univariate or multivariate analysis of variance, covariance, or regression. Although there are several canonical correlation programs available [e.g., SPSS's CANCORR (Nie, Hull,

INVARIANCE OF THE GUTTMAN QUASI‐SIMPLEX LINEAR MODEL UNDER SELECTION

The paper contains a proof that the Guttman additive quasi‐simplex model is invariant under selection of examinees when a set of continuous variables each having different error of measurement is ordered on the simplex continuum in terms of either increasing or decreasing magnitudes of ‘complexity’ provided that selection is based on those measures which are less variable than each of the measures of the remaining set. When variables with highest ‘complexity’ ranks constitute the basis of selection, then such an invariance breaks down. The significance of the problem is discussed in the context of personnel selection. In addition, many implications of the results are stated which hold good for various multivariate statistical techniques.