Jonckheere-Terpstra test for nonclassical error versus log-sensitivity relationship of quantum spin network controllers

The tail of a quantum spin network in the two-sphere is a [Formula: see text]-series associated to the network. We study the existence of the head and tail functions of quantum spin networks colored by [Formula: see text]. We compute the [Formula: see text]-series for an infinite family of quantum spin networks and give the relation between the tail of these networks and the tail of the colored Jones polynomial. Finally, we show that the family of quantum spin networks under study satisfies a natural product structure.

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STATE SUM MODELS FOR TRIVALENT KNOTTED GRAPH INVARIANTS USING QUANTUM GROUP SLq(2)

Journal of Knot Theory and Its Ramifications ◽

10.1142/s021821659200015x ◽

1992 ◽

Vol 01 (03) ◽

pp. 253-278 ◽

Cited By ~ 3

Author(s):

SERGEY PIUNIKHIN

Keyword(s):

Network Theory ◽

Quantum Spin ◽

Topological Invariants ◽

Graph Invariants ◽

Spin Network ◽

Face Model ◽

Polynomial Invariants ◽

Root Of Unity ◽

State Models ◽

6J Symbols

Four approaches to construct polynomial invariants for trivalent knotted graphs in S3 are compared. The first approach is based on vertex model with R-matrices and Glebsh-Gordan coefficients, appearing in SLq(2)-representations theory, as Boltzman weights. The second approach is based on Kauffman's quantum spin network theory, the third one is based on Witten-Turaev area-coloring model (or face model) based on quantum 6j-symbols, where q is root of unity. The fourth approach is based on the same face (or area-coloring) model, but q is not root of unity. The coincidence (up to certain normalization) of topological invariants, arising from these four state models, is proved.

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Beam splitter for spin waves in quantum spin network

The European Physical Journal B ◽

10.1140/epjb/e2006-00319-2 ◽

2006 ◽

Vol 52 (3) ◽

pp. 377-381 ◽

Cited By ~ 12

Author(s):

S. Yang ◽

Z. Song ◽

C. P. Sun

Keyword(s):

Beam Splitter ◽

Spin Waves ◽

Quantum Spin ◽

Spin Network

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The relationship of the scleractinian corals to the rugose corals

Paleobiology ◽

10.1017/s0094837300025707 ◽

1980 ◽

Vol 6 (02) ◽

pp. 146-160 ◽

Cited By ~ 29

Author(s):

William A. Oliver

Keyword(s):

Critical Points ◽

Scleractinian Corals ◽

Convincing Evidence ◽

Early Triassic ◽

Rugose Corals ◽

History Of ◽

The Subject ◽

Relationship Of ◽

The Relationship ◽

Biologic Factors

The Mesozoic-Cenozoic coral Order Scleractinia has been suggested to have originated or evolved (1) by direct descent from the Paleozoic Order Rugosa or (2) by the development of a skeleton in members of one of the anemone groups that probably have existed throughout Phanerozoic time. In spite of much work on the subject, advocates of the direct descent hypothesis have failed to find convincing evidence of this relationship. Critical points are:(1) Rugosan septal insertion is serial; Scleractinian insertion is cyclic; no intermediate stages have been demonstrated. Apparent intermediates are Scleractinia having bilateral cyclic insertion or teratological Rugosa.(2) There is convincing evidence that the skeletons of many Rugosa were calcitic and none are known to be or to have been aragonitic. In contrast, the skeletons of all living Scleractinia are aragonitic and there is evidence that fossil Scleractinia were aragonitic also. The mineralogic difference is almost certainly due to intrinsic biologic factors.(3) No early Triassic corals of either group are known. This fact is not compelling (by itself) but is important in connection with points 1 and 2, because, given direct descent, both changes took place during this only stage in the history of the two groups in which there are no known corals.

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Skeletal elements of crinoid echinoderms: High-resolution structural and microanalytical results

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100074768 ◽

1983 ◽

Vol 41 ◽

pp. 194-195

Author(s):

D. F. Blake ◽

L. F. Allard ◽

D. R. Peacor

Keyword(s):

High Resolution ◽

Marine Invertebrates ◽

Sea Urchins ◽

Structural Features ◽

Sea Stars ◽

High Resolution Tem ◽

Relationship Of ◽

The Relationship ◽

Insight Into

Echinodermata is a phylum of marine invertebrates which has been extant since Cambrian time (c.a. 500 m.y. before the present). Modern examples of echinoderms include sea urchins, sea stars, and sea lilies (crinoids). The endoskeletons of echinoderms are composed of plates or ossicles (Fig. 1) which are with few exceptions, porous, single crystals of high-magnesian calcite. Despite their single crystal nature, fracture surfaces do not exhibit the near-perfect {10.4} cleavage characteristic of inorganic calcite. This paradoxical mix of biogenic and inorganic features has prompted much recent work on echinoderm skeletal crystallography. Furthermore, fossil echinoderm hard parts comprise a volumetrically significant portion of some marine limestones sequences. The ultrastructural and microchemical characterization of modern skeletal material should lend insight into: 1). The nature of the biogenic processes involved, for example, the relationship of Mg heterogeneity to morphological and structural features in modern echinoderm material, and 2). The nature of the diagenetic changes undergone by their ancient, fossilized counterparts. In this study, high resolution TEM (HRTEM), high voltage TEM (HVTEM), and STEM microanalysis are used to characterize tha ultrastructural and microchemical composition of skeletal elements of the modern crinoid Neocrinus blakei.

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Studies on Leukemogenic and Sarcomagenic Viruses

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100067777 ◽

1970 ◽

Vol 28 ◽

pp. 156-157

Author(s):

Leon Dmochowski

Keyword(s):

Electron Microscopy ◽

Electron Microscope ◽

Morphological Properties ◽

Mode Of Development ◽

Relationship Of ◽

The Relationship

Electron microscopy has proved to be an invaluable discipline in studies on the relationship of viruses to the origin of leukemia, sarcoma, and other types of tumors in animals and man. The successful cell-free transmission of leukemia and sarcoma in mice, rats, hamsters, and cats, interpreted as due to a virus or viruses, was proved to be due to a virus on the basis of electron microscope studies. These studies demonstrated that all the types of neoplasia in animals of the species examined are produced by a virus of certain characteristic morphological properties similar, if not identical, in the mode of development in all types of neoplasia in animals, as shown in Fig. 1.

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