A Computable Characterization of the Extrinsic Mean of Reflection Shapes and Its Asymptotic Properties

2015 ◽  
Vol 32 (01) ◽  
pp. 1540005
Author(s):  
Chao Ding ◽  
Hou-Duo Qi
Keyword(s):  
Hypothesis Test ◽  
Asymptotic Properties ◽  
Shape Space ◽  
Direct Application ◽  
Symmetric Matrices ◽  
Geometric Information ◽  
Computable Formula ◽  
Arbitrary Dimensions ◽  
Extrinsic Mean

The reflection shapes of configurations in ℜm with k landmarks consist of all the geometric information that is invariant under compositions of similarity and reflection transformations. By considering the corresponding Schoenberg embedding, we embed the reflection shape space into the Euclidean space of all (k - 1) by (k - 1) real symmetric matrices. In this paper, we provide a computable formula of the extrinsic mean of the reflection shapes in arbitrary dimensions. Moreover, the asymptotic analysis of the extrinsic mean of the reflection shapes is studied. By using the differentiability of spectral operators, we obtain a central limit theorem of the sample extrinsic mean of the reflection shapes. As a direct application, the two-example hypothesis test of the reflection shapes is also derived.

Contributions to the mechanisms of mitosis and roles of cytoplasmic microtubules from ultrastructural analyses of fungi

1978 ◽  
Vol 36 (2) ◽  
pp. 266-267
Author(s):  
I. Brent Heath
Keyword(s):  
Nuclear Envelope ◽  
Direct Application ◽  
Ultrastructural Analysis ◽  
General Interest ◽  
Research Results ◽  
Organelle Motility ◽  
Cytoplasmic Microtubules

Detailed ultrastructural analysis of fungal mitotic systems and cytoplasmic microtubules might be expected to contribute to a number of areas of general interest in addition to the direct application to the organisms of study. These areas include possibly fundamental general mechanisms of mitosis; evolution of mitosis; phylogeny of organisms; mechanisms of organelle motility and positioning; characterization of cellular aspects of microtubule properties and polymerization control features. This communication is intended to outline our current research results relating to selected parts of the above questions.Mitosis in the oomycetes Saprolegnia and Thraustotheca has been described previously. These papers described simple kinetochores and showed that the kineto- chores could probably be used as markers for the poorly defined chromosomes. Kineto- chore counts from serially sectioned prophase mitotic nuclei show that kinetochore replication precedes centriole replication to yield a single hemispherical array containing approximately the 4 n number of kinetochore microtubules diverging from the centriole associated "pocket" region of the nuclear envelope (Fig. 1).

scholarly journals Further generalization of symmetric multiplicity theory to the geometric case over a field

2021 ◽  
Vol 9 (1) ◽  
pp. 31-35
Author(s):  
Isaac Cinzori ◽  
Charles R. Johnson ◽  
Hannah Lang ◽  
Carlos M. Saiago
Keyword(s):  
Symmetric Matrices

Abstract Using the recent geometric Parter-Wiener, etc. theorem and related results, it is shown that much of the multiplicity theory developed for real symmetric matrices associated with paths and generalized stars remains valid for combinatorially symmetric matrices over a field. A characterization of generalized stars in the case of combinatorially symmetric matrices is given.

Separability criteria based on the Bloch representation of density matrices

2007 ◽  
Vol 7 (7) ◽  
pp. 624-638
Author(s):  
J. de Vicente
Keyword(s):  
Sufficient Conditions ◽  
Quantum Systems ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Pure Product ◽  
Separability Problem ◽  
Arbitrary Dimensions ◽  
Necessary And Sufficient ◽  
Bloch Representation

We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which we derive a necessary condition and sufficient conditions for separability. For a certain class of states the necessary condition and a sufficient condition turn out to be equivalent, therefore yielding a necessary and sufficient condition. The proofs of the sufficient conditions are constructive, thus providing decompositions in pure product states for the states that satisfy them. We provide examples that show the ability of these conditions to detect entanglement. In particular, the necessary condition is proved to be strong enough to detect bound entangled states.

A topological criterion for group decompositions

1988 ◽  
Vol 103 (2) ◽  
pp. 285-298 ◽  
Author(s):  
J. Hebda ◽  
P. Moylan
Keyword(s):  
Asymptotic Properties ◽  
Cartesian Product ◽  
Conformal Field Theories ◽  
De Sitter ◽  
Group Representations ◽  
Conformal Field ◽  
Connected Subgroup ◽  
Closed Connected Subgroup ◽  
Necessary And Sufficient

AbstractGiven a connected Lie group G and a closed connected subgroup H of G we prove a necessary and sufficient condition that G decomposes into the Cartesian product of H with G/H is that a similar decomposition holds for the maximal compact subgroups of G and H. Our criterion is applied to the three series of groups for which G/H is SO0(p, q)/SO0(p, q − 1), SU(q + 1, q + 1)/S[U(q + 1, q) × U(1)], and SU(q + 1, q + 1)/SL(n, ℂ) ⋊ H(n) (p, q ≥ 1), and we list the values of p and q for which G ≅ H × G/H in each of the three cases. We describe certain decompositions for some of the groups. We show the usefulness of our criterion in obtaining characterization of the space of differentiable vectors for a unitary induced group representation, and, finally, we show by example of SU(2, 2), how the asymptotic properties of certain function spaces for induced group representations are readily obtained using our results. Our results should be of interest to those working in de Sitter and conformal field theories.

scholarly journals Representation and Characterization of Nonstationary Processes by Dilation Operators and Induced Shape Space Manifolds

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 717 ◽  
Author(s):  
Maël Dugast ◽  
Guillaume Bouleux ◽  
Eric Marcon
Keyword(s):  
Lie Group ◽  
Correlation Coefficients ◽  
Shape Space ◽  
Rotation Matrices ◽  
Dilation Matrix ◽  
Naimark Dilation ◽  
Periodically Correlated Processes ◽  
New Vision

We proposed in this work the introduction of a new vision of stochastic processes through geometry induced by dilation. The dilation matrices of a given process are obtained by a composition of rotation matrices built in with respect to partial correlation coefficients. Particularly interesting is the fact that the obtention of dilation matrices is regardless of the stationarity of the underlying process. When the process is stationary, only one dilation matrix is obtained and it corresponds therefore to Naimark dilation. When the process is nonstationary, a set of dilation matrices is obtained. They correspond to Kolmogorov decomposition. In this work, the nonstationary class of periodically correlated processes was of interest. The underlying periodicity of correlation coefficients is then transmitted to the set of dilation matrices. Because this set lives on the Lie group of rotation matrices, we can see them as points of a closed curve on the Lie group. Geometrical aspects can then be investigated through the shape of the obtained curves, and to give a complete insight into the space of curves, a metric and the derived geodesic equations are provided. The general results are adapted to the more specific case where the base manifold is the Lie group of rotation matrices, and because the metric in the space of curve naturally extends to the space of shapes; this enables a comparison between curves’ shapes and allows then the classification of random processes’ measures.

scholarly journals EXTENSION OF THE OLKIN AND RUBIN CHARACTERIZATION TO THE WISHART DISTRIBUTION ON HOMOGENEOUS CONES

2011 ◽  
Vol 14 (04) ◽  
pp. 591-611 ◽  
Author(s):  
I. BOUTOURIA ◽  
A. HASSAIRI ◽  
H. MASSAM
Keyword(s):  
Wishart Distribution ◽  
Symmetric Cone ◽  
Symmetric Matrices ◽  
Riesz Distribution ◽  
Homogeneous Cones ◽  
Homogeneous Cone

The Wishart distribution on a homogeneous cone is a generalization of the Riesz distribution on a symmetric cone which corresponds to a given graph. The paper extends to this distribution, the famous Olkin and Rubin characterization of the ordinary Wishart distribution on symmetric matrices.

Transformations preserving the Lyapunov exponents

2018 ◽  
Vol 20 (04) ◽  
pp. 1750027 ◽  
Author(s):  
Luis Barreira ◽  
Claudia Valls
Keyword(s):  
Lyapunov Exponents ◽  
Asymptotic Properties ◽  
Regular Sequence ◽  
Complete Characterization ◽  
Block Form ◽  
The Family ◽  
Coordinate Changes ◽  
Invertible Matrices ◽  
Finite Exponent

We give a complete characterization of the existence of Lyapunov coordinate changes bringing an invertible sequence of matrices to one in block form. In other words, we give a criterion for the block-trivialization of a nonautonomous dynamics with discrete time while preserving the asymptotic properties of the dynamics. We provide two nontrivial applications of this criterion: we show that any Lyapunov regular sequence of invertible matrices can be transformed by a Lyapunov coordinate change into a constant diagonal sequence; and we show that the family of all coordinate changes preserving simultaneously the Lyapunov exponents of all sequences of invertible matrices (with finite exponent) coincides with the family of Lyapunov coordinate changes.

scholarly journals A SPECTRAL CHARACTERIZATION OF OPERATORS

2016 ◽  
Vol 102 (3) ◽  
pp. 369-391 ◽  
Author(s):  
SATISH K. PANDEY ◽  
VERN I. PAULSEN
Keyword(s):  
Banach Space ◽  
Hilbert Spaces ◽  
Real Banach Space ◽  
Closed Subspace ◽  
Characterization Theorem ◽  
Positive Operators ◽  
Spectral Characterization ◽  
Proper Cone ◽  
Arbitrary Dimensions

We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless, we prove that the intersection of these operators with the positive operators forms a proper cone in the real Banach space of hermitian operators.

The Steady-State and Decay Characteristics of Protein Tryptophan Fluorescence from Algae

1988 ◽  
Vol 42 (8) ◽  
pp. 1405-1412 ◽  
Author(s):  
M. Baek ◽  
W. H. Nelson ◽  
P. E. Hargraves ◽  
J. F. Tanguay ◽  
S. L. Suib
Keyword(s):  
Steady State ◽  
Tryptophan Fluorescence ◽  
Fluorescence Decay ◽  
Direct Application ◽  
Fluorescence Lifetimes ◽  
Bacterial Protein ◽  
Steady State Fluorescence ◽  
Tryptophan Residues ◽  
Rapid Characterization

The intrinsic steady-state fluorescence due to tryptophan has been obtained from monospecific cultures of fourteen plankton algae of various genera. Fluorescence decay profiles of protein tryptophan residues were obtained for eight marine plankton algae. Each organism exhibits a strong maximum in its emission spectrum at 320–340 nm when excited at 290 nm. Iodide quenching and denaturization experiments with 8 M urea provide strong evidence for the assignment of the 320–340 nm fluorescence to protein tryptophan. Most importantly, the decay of this bacterial protein tryptophan fluorescence has been described. The observation that characteristic protein-tryptophan fluorescence lifetimes have been obtained for each organism suggests that measurements of fluorescence lifetimes may be helpful in the rapid characterization of algae. Direct application will likely be found in combination with the measurement of other luminescence parameters.

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