Missing Label Research Articles

Obtainment of internal labelling operators as broken Casimir operators by means of contractions related to reduction chains in semisimple Lie algebras

We show that the Inönü-Wigner contraction naturally associated to a reduction chain s ⊃ s′ of semisimple Lie algebras induces a decomposition of the Casimir operators into homogeneous polynomials, the terms of which can be used to obtain additional mutually commuting missing label operators for this reduction. The adjunction of these scalars that are no more invariants of the contraction allow to solve the missing label problem for those reductions where the contraction provides an insuflcient number of labelling operators.

Adaptive ontology re‐use: finding and re‐using sub‐ontologies

PurposeThe discovery of the “right” ontology or ontology part is a central ingredient for effective ontology re‐use. The purpose of this paper is to present an approach for supporting a form of adaptive re‐use of sub‐ontologies, where the ontologies are deeply integrated beyond pure referencing.Design/methodology/approachStarting from an ontology draft which reflects the intended modeling perspective, the ontology engineer can be supported by suggesting similar already existing sub‐ontologies and ways for integrating them with the existing draft ontology. This paper's approach combines syntactic, linguistic, structural and logical methods into an innovative modeling‐perspective aware solution for detecting matchings between concepts from different ontologies. This paper focuses on the discovery and matching phase of this re‐use process.FindingsOwing to the combination of techniques presented in this general approach, the work described performs in the general case as well as approaches tailored for a specific usage scenario.Research limitations/implicationsThe methods used rely on lexical information obtained from the labels of the concepts and properties in the ontologies, which makes this approach appropriate in cases where this information is available. Also, this approach can handle some missing label information.Practical implicationsOntology engineering tasks can take advantage from the proposed adaptive re‐use approach in order to re‐use existing ontologies or parts of them without introducing inconsistencies in the resulting ontology.Originality/valueThe adaptive re‐use of ontologies by finding and partially re‐using parts of existing ontological resources for building new ontologies is a new idea in the field, and the inclusion of the modeling perspective in the computation of the matches adds a new perspective that could also be exploited by other matching approaches.

Rapid Analysis of Förster Resonance Energy Transfer by Two-Color Global Fluorescence Correlation Spectroscopy: Trypsin Proteinase Reaction

In this study we introduce the combination of two-color global fluorescence correlation spectroscopy (2CG-FCS) and Förster resonance energy transfer (FRET) as a very powerful combination for monitoring biochemical reactions on the basis of single molecule events. 2CG-FCS, which is a new variation emerging from the family of fluorescence correlation spectroscopy, globally analyzes the simultaneously recorded auto- and cross-correlation data from two photon detectors monitoring the fluorescence emission of different colors. Overcoming the limitations inherent in mere auto- and cross-correlation analysis, 2CG-FCS is sensitive in resolving and quantifying fluorescent species that differ in their diffusion characteristics and/or their molecular brightness either in one or both detection channels. It is able to account for effects that have often been considered as sources of severe artifacts in two-color and FRET measurements, the most prominent artifacts comprising photobleaching, cross talk, or concentration variations in sample preparation. Because of its very high statistical accuracy, the combination of FRET and 2CG-FCS is suited for high-throughput applications such as drug screening. Employing beam scanning during data acquisition even further enhances this capability and allows measurement times of <2 s. The improved performance in monitoring a FRET sample was verified by following the protease cleavage reaction of a FRET-active peptide. The FRET-inactive subpopulation of uncleaved substrate could be correctly assigned, revealing a substantial portion of inactive or missing acceptor label. The results were compared to those obtained by two-dimensional fluorescence intensity distribution analysis.

A new matrix method for the Casimir operators of the Lie algebras and

A method is given to determine the Casimir operators of the perfect Lie algebras and the inhomogeneous Lie algebras in terms of polynomials associated with a parametrized (2N + 1) × (2N + 1)-matrix. For the inhomogeneous symplectic algebras this matrix is shown to be associated to a faithful representation. We further analyse the invariants for the extended Schrodinger algebra in (N + 1) dimensions, which arises naturally as a subalgebra of . The method is extended to other classes of Lie algebras, and some applications to the missing label problem are given.

Resolution of theGL(3) ⊃O(3) state labelling problem via theO(3)-invariant Bethe subalgebra of the twisted Yangian

The labelling of states of irreducible representations of GL(3) in an O(3) basis is well known to require the addition of a single O(3)-invariant operator, to the standard diagonalizable set of Casimir operators in the subgroup chain GL(3) ⊃ O(3) ⊃ O(2). Moreover, this 'missing label' operator must be a function of the two independent cubic and quartic invariants which can be constructed in terms of the angular momentum vector and the quadrupole tensor. It is pointed out that there is a unique (in a well-defined sense) combination of these which belongs to the O(3)-invariant Bethe subalgebra of the twisted Yangian Y(GL(3); O(3)) in the enveloping algebra of GL(3).

Representations of twisted Yangians

We study highest weight representations of certain Yangian-type ‘quantum’ algebras connected with the series B, C, D of complex classical Lie algebras. In the symplectic case, we obtain a complete parametrization of irreducible finite-dimensional representations in terms of their highest weights. We apply these results to the well-known missing label problem in the reduction sp(2n)↓sp(2n−2).

The matrix representations of g2. II. Representations in an su(3) basis

Irreducible representations of the real compact Lie algebra g2 are given in g2⊇ su(3) bases. A missing label is accounted for by the explicit construction of a g2⊇ su(3) basis of vector holomorphic functions. Analytical results are given for two multiplicity-free classes of irreps. It is also shown how vector coherent state (VCS) theory accommodates the decomposition of the nilpotent raising operator subalgebra of an arbitrary Lie algebra into a finite but arbitrary number of irreducible tensorial sets under transformations generated by a stability algebra.

A set of commuting missing label operators for SO(5)⊃SO(3)

The two-missing label problem for basis vectors of an SO(5) irreducible representation reduced according to the principal SO(3) subalgebra is considered. A pair of commuting Hermitian operators which are scalars with respect to the SO(3) subalgebra are explicitly constructed within the SO(5) enveloping algebra. One label generating operator is of fourth order and the other of sixth order in the SO(5) basis elements.

U(3) → R(3) integrity-basis spectroscopy

Abstract The U(3) → R(3) algebra, widely used in nuclear spectroscopy studies, is revisited. The most general form of a U(3)-preserving interaction that is rotationally invariant and of given degree in the group generators is presented. Here the full purpose and beauty of the integrity-basis concept is realized. En route to the above it is shown that the structure of the U(3) → R(3) integrity basis can be deduced from a systematic counting of defining space matrix elements of p-shell, k -body scalar operators, k = 0, 1, 2⋯. The tensorial character of the so-called “missing label” operators and, more importantly, of the operators responsible for the splitting and inversion of rotational bands is obtained by relating integrity-basis multinomials through degree four in the U(3) generators to density operators of a standard U(3) → R(3) many-body spectroscopy. The results are used to show how K -band splitting as well as an [ L ( L + 1)] 2 factor in the energy can be realized within a single representation of SU(3) by two-body interactions of the ds and higher nuclear shells. Parameter sets of model interactions associated with both normal and inverted K -band structures are given, as well as the results of a “best fit” theory for the ground and gamma bands of 24 Mg.

A pair of commuting missing label operators for G⊇[SU(2)]n

A general procedure, which can lead to a pair of commuting subgroup scalars in the enveloping algebra of a Lie group G, decomposed in [SU(2)]n, is discussed. The technique is illustrated by means of three explicit examples.

Inequivalent sets of commuting missing label operators for SU(4) ⊆SU(2) ×SU(2)

We exhibit one possible choice for the four functionally independent label operators available. We prove that they can be separated into two inequivalent, i.e., functionally independent, sets of commuting label operators, namely the set of operators Ω and Φ first considered by Moshinsky and Nagel, and the set of operators C(202) and C(022).

On bases for irreducible representations of O (3) suitable for systems with an arbitrary finite symmetry group

The problem of constructing bases for representations of the rotation group O (3) adapted to an arbitrary discrete subgroup symmetry is considered. For each discrete subgroup Γ, we construct all Γ invariant operator valued functions of the generators of O (3). These invariant operators can be used to resolve the missing label problem in the O (3) ⊆Γ reduction and also to construct the corresponding bases functions.

Number of independent missing label operators

When the bases for irreducible representations of a semisimple group are reduced according to a semisimple subgroup the number of functionally independent missing label operators available is just twice the number of missing labels. The argument presented suggests that the result holds for any Lie group.

Complete sets of commuting operators and O (3) scalars in the enveloping algebra of SU (3)

We consider the ``missing label'' problem for basis vectors of SU(3) representations in a basis corresponding to the group reduction SU(3)⊃O(3)⊃O(2). We prove that only two independent O (3) scalars exist in the enveloping algebra of S U (3), in addition to the obvious ones, namely the angular momentum L2 and the two SU(3) Casimir operators C(2) and C(3). Any one of these two operators (of third and fourth order in the generators) can be added to C(2), C(3), L2, and L3 to form a complete set of commuting operators. The eigenvalues of the third and fourth order scalars X(3) and X(4) are calculated analytically or numerically for many cases of physical interest. The methods developed in this article can be used to resolve a missing label problem for any semisimple group G, when reduced to any semisimple subgroup H.

Erratum: Actinomycin D: Its Effect on Antibody Formation in Vitro

In the report "Actinomycin D: its effect on antibody formation in vitro, by J. W. Uhr [ Science 142, 1476 (13 Dec. 1963)], there are four serious errors. The amount of 3 × 10 -7 M actinomycin D given in line 10 of paragraph 3 was 0.37 μg/ml, not 0.3 μg/ml. The missing label on the ordinate of Fig. 1 is K (antibody concentration). The compounds named in the next-to-last line of the next-to-last paragraph are uridylate and guanilate (not uridylak and guanilak). The second sentence of the last paragraph should have read: "The prompt and complete inhibition . . . suggests that this messenger can have [ not has] a half-life of less than several days."