Ranking Of Components Research Articles

On a problem on chamber systems

It is well known that a geometry belonging to a disconnected diagram is the direct sum of geometries corresponding to the connected components of the diagram. On the other hand, chamber systems with a disconnected diagram exist which do not split as direct products of components of smaller rank. Many finite examples of this kind are discussed in Groups of Lie Type and their Geometries (CUP, 1995, pp. 185–214), but none of them is simply connected. In this article, we construct a simply connected finite example.

Software component search

An important problem in software development is to make better use of software libraries by improving the search and retrieval process, that is, by making it easier to find the few components you may want among the many you do not want. This paper suggests some ideas to improve this process: (1) Associate analgebraic specification with each software component; these specifications should include complete syntactic information, but need have onlypartial semantic information. (2) User queries consist of syntactic declarations plus results forsample executions. (3) User queries may be posed in standard programming notation, which is then automatically translated into algebraic notation. (4) Search is organized asranked multi-level filtering, where each level yields aranked set of partial matches. (5) Early stages of filtering narrow the search space by using computationally simple procedures, such as checking that the number of types is adequate. (6) Middle levels may findpartial signature matches. (7) Pre-computedcatalogues (i.e., indexes) can speed up early and middle level filtering. (8) Semantic information is used in a final filter withterm rewriting, but complete verification is not attempted. (9) The series of filters is implementedincrementally, so as to backtrack to lower ranked components in case of failure. This approach avoids the need for complex theorem proving, and does not require any knowledge of algebraic specification from the user. Moreover, it does not require either specifications or queries to be complete or even fully correct, because it yields partial matches ranked by how well they fit the query. The paper concludes with a description of some preliminary experiments and some suggestions for further experiments.

Adaptive detection using low rank approximation to a data matrix

Using an accurate formula for the error in approximating a low rank component, we calculate the performance of adaptive detection based on reduced-rank nulling. In this principal component inverse (PCI) method, one temporarily regards the interference as a strong signal to be enhanced. The resulting estimate of the interference waveform is subtracted from the observed data, and matched filtering is used to detect signal components in the residual waveform. We also present a generalized likelihood-ratio test (GLRT) for adaptively detecting a low rank signal in the presence of low rank interference. This approach leads to a test which is closely related to the PCI method and extends the PCI method to the case where strong signal components are present in the data. A major accomplishment of the work is our calculation of the statistics of the output of the matched filter for the case in which interference cancellation and signal detection are carried out on the same observed data matrix. That is, no separate data is used for adaptation. Examples are presented using both simulated data and real, active-sonar reverberation data from the ARSRP, the Acoustic Reverberation Special Research Program of the Office of Naval Research.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An efficient method for solving the eigenvalue problem for matrices having a skew‐symmetric (or skew‐Hermitian) component of low rank

AbstractIn the numerical modelling of mechanical systems, eigenvalue problems occur in connection with the evaluation of resonance frequencies, buckling modes and other more esoteric calculations. The matrices whose eigenvalues are sought sometimes have a skew‐symmetric component and the presence of this component adds significantly to the computational effort required. In many cases where there is a skew‐symmetric component, this component has a much lower rank than the symmetric component which generally has rank equal to its dimension. Examples of such cases abound in the area of rotor dynamics where the stiffness and damping matrices associated with journal bearings have significant skew‐symmetric components. The solution of the eigenvalue problem for an unsymmetric matrix takes more than twice the number of operations required for the solution of the eigenvalue problem for a symmetric matrix of the same dimension. This paper puts forward a new method for the solution of the eigenvalue problem for matrices having a skew‐symmetric component of low rank and shows that it is faster than established methods of comparable accuracy for the general unsymmetric NxN matrix if the rank of the skew‐symmetric component is less than N/7.3.

A homological criterion for reducibility of analytic spaces, with application to characterizing the theta divisor of a product of two general principally polarized abelian varieties

A closed subset of pure codimension one in an analytic space, consisting entirely of local normal crossings double points, is called an ordinary rank two double locus. We give a topologically computable upper bound on the number of connected components of an ordinary rank two double locus in a given space. This leads to criteria for global reducibility of spaces. The first is that a simply connected space with a non empty ordinary rank two double locus is always reducible. A finer criterion implies that a principally polarized abelian variety A is isomorphic to a product of two positive dimensional principally polarized abelian varieties, each with smooth theta divisor, if and only if the theta divisor of A contains a non empty ordinary rank two double locus. Analogous reducibility results apply to certain complete intersection varieties, and to divisors on such varieties.

International Experts Rank Critical Outdoor Leadership Concerns and Components

International Experts Rank Critical Outdoor Leadership Concerns and Components

Modeling adaptive biological systems

During the evolution of many systems found in nature, both the system composition and the interactions between components will vary. Equating the dimension with the number of different components, a system which adds or deletes components belongs to a class of dynamical systems with a finite dimensional phase space of variable dimension. We present two models of biochemical systems with a variable phase space, a model of autocatalytic reaction networks in the prebiotic soup and a model of the idiotypic network of the immune system. Each model contains characteristic meta-dynamical rules for constructing equations of motion from component properties. The simulation of each model occurs on two levels. On one level, the equations of motion are integrated to determine the state of each component. On a second level, algorithms which approximate physical processes in the real system are employed to change the equations of motion. Models with meta-dynamical rules possess several advantages for the study of evolving systems. First, there are no explicit fitness functions to determine how the components of the model rank in terms of survivability. The success of any component is a function of its relationship to the rest of the system. A second advantage is that since the phase space representation of the system is always finite but continually changing, we can explore a potentially infinite phase space which would otherwise be inaccessible with finite computer resources. Third, the enlarged capacity of systems with meta-dynamics for variation allows us to conduct true evolution experiments. The modeling methods presented here can be applied to many real biological systems. In the two studies we present, we are investigating two apparent properties of adaptive networks. With the simulation of the prebiotic soup, we are most interested in how a chemical reaction network might emerge from an initial state of relative disorder. With the study of the immune system, we study the self-regulation of the network including its ability to distinguish between species which are part of the network and those which are not.

The structure of Jahn–Teller surfaces

In chemical applications of the Jahn–Teller effect, the shape of the adiabatic potential near the instability point is of primary importance. The present article examines this shape, both in the usual representation in the space of the nuclear configurations and in the less current projective representation in the space of the electronic functions. The general structural aspects of these representations are viewed as the results of a symmetry breaking process, starting at the continuous invariance group of the degenerate coupling limit, and ending with the finite point group of the representation space. The various vibronic coupling mechanisms involved in this process are characterized by irreducible tensor functions of the full orthogonal groups. The leading tensorial rank of the unequal linear coupling mechanism is shown to be four, while the bilinear coupling mechanism also involves an irreducible component of the sixth rank. This tensorial analysis provides a grouptheoretical foundation for the recently formulated epikernel principle, which predicts the location of extremal points on a Jahn–Teller surface.

Rapid analysis of coal blends by diffuse reflectance FT-i.r. spectrometry

A method is described for the rapid analysis of coal blends by the treatment of diffuse reflectance Fourier transform infrared (FT-i.r.) spectral data with the computer program CIRCOM (Computerized Infra Red Characterization Of Materials). CIRCOM uses factor analysis of the FT-i.r. spectra of a calibration set of samples of known blend proportions to reduce the data set, followed by multiple linear regression to derive correlation equations for the blend components. These correlation equations can then be used to estimate the blend proportions for unknown samples similar to those in the calibration set. The method was demonstrated with a calibration set of synthetic blends of four Australian coals used in the coking blend at the BHP Newcastle Steelworks. The standard deviation of the calibration for Metropolitan coal, the high rank component of the blend, was 0.68 wt %. Four months after calibration, the correlation for wt % Metropolitan coal was tested with a further 35 blend samples. Good agreement was found and the RMS difference between actual and estimated results was 1.78 wt %. After calibration, the method is fast and sample preparation is simple.

The relative importance of identity status interview components: replication and extension

The present study partially replicates and extends the work of Rogow et al. (1983) in probing the relative importance of Ego Identity Status Interview components for both sexes. Eighty female and sixty male students attending a New Zealand university were given the Ego Identity Status Interview with identity components of occupation, religion, politics, and sex role beliefs presented in counterbalanced order. Subjects were then asked to rank components in order of importance to their sense of identity and additional identity contents were explored through open-ended questions. This investigation revealed few sex differences in terms of number of content areas having a common rating, hit rates between single or paired content areas and overall identity ratings, rank order for importance of identity contents, or reported areas of additional identity concerns. In support of Rogow findings, this study suggests that identity not be viewed as a unitary structure and encourages the reporting of both component and overall identity status ratings to allow a more comprehensive means of researching the identity formation process. In general, the identity status approach provides a useful model for clinical research of ego synthesis in late adolescence.

An absolute polarization monitor for odd rank components of a polarized spin 3/2 beam

A polarimeter for 7Li odd rank polarizations is discussed. The ideas presented are applicable to any spin 3/2 polarized particle.

Resolution of independently titrating spectral components of the ultraviolet circular dichroism of subtilisin enzymes by matrix rank analysis

The ultraviolet circular dichroism of di-isopropylphophoryl-subtilisins Carlsberg and Novo (EC 3.4.21.14) has been examined as a function of pH. The CD of these enzymes below 260 nm is invariant over the pH interval 4 to 12, below or above which spectral changes occur suggesting a transition to a random coil form. Above pH 8 contributions due to the ionization of tyrosyl residues appear in the CD above 260 nm as bands shifted to longer wavelengths. Three independently titratable components, obtained by matrix rank analysis, account for the observed CD spectral changes above 260 nm of Dip-subtilisin Carlsberg in the pH interval 8 to 12. By contrast, two components were derived for the Novo enzyme. The identities of the matrix rank component were surmised from their apparent p K 1 values. One component of both subtilisin enzymes corresponds to the CD of the “buried” or irreversibly titratable tyrosyl residues of the enzyme. The other matrix rank components correspond to the CD of the “exposed’ or freely ionizable tyrosyl residues. These residues are optically active only in the ionized state. Two types of “expressed” tyrosyl residues, arising because of differing sensitivity to the ionization of the “partially buried” or abnormally titrating tyrosyl residues, are evident in Dip-subtilisin Carlsberg. A pH-induced local conformational change in this enzyme is proposed to account for this behavior. The “partially buried” tyrosyl residues of both subtilisins appear to be devoid of optical activity in either the tyrosyl or tyrosylate form.

COMPONENTS OF YIELD OF RECOVERABLE SUGAR IN RANDOM AND IMPROVED SUGARBEET POPULATIONS

Path coefficient analyses indicated that the components of recoverable sugar yield rank differently in relative importance in improved populations of sugarbeet (Beta vulgaris L.) than in relatively unimproved populations. Root weight was a more important yield component than sucrose percentage and over twice as important as purity in unselected populations. Root weight and sucrose percentage contributed about equally in improved populations, but the importance of both to recoverable sugar was substantially greater than in the unselected population. Purity was about twice as important a component in the improved population as it was in the unselected population. Results suggest that the emphasis of breeding programs will need to change with changes in the genetic structure of the improved population. Because of the lack of negative indirect effects in the commercial population, the association of recoverable sugar and sucrose percent was nearly twice as high as compared to the relatively unimproved random hybrid population.

Influence of Piezoelectricity and Axial Distortions on the Electric Field Effect in Paramagnetic Resonance of3d5Ions in SeveralAII−BVICompounds

New results are presented concerning ${\mathrm{Cr}}^{+}$ in ZnS, ${\mathrm{Mn}}^{++}$ in ZnSe, and ${\mathrm{Mn}}^{++}$ in ZnO. The contribution of the piezoelectric deformations has been studied in detail. We show that it is equal to $\frac{1}{15}$ of the experimental value in the case of ZnS: ${\mathrm{Mn}}^{++}$ (sphalerite). We also show that in the cases of ${\mathrm{Mn}}^{++}$ in wurtzite and zincite, the axial terms induced by the electric field are caused primarily by the components of rank four of the crystal potential.

Collisional depolarization of light alkali atoms excited to their lowest 2P levels

Transition matrix elements connecting the Zeeman sublevels of the lowest p doublets in light alkali atoms have been derived using methods of steady-state collision theory. The matrix elements generally consist of two parts which, under rotations of the quantization axis with respect to the scattering plane, behave like components of a first rank and a second rank tensor, respectively. Only the second rank tensor components lead to the selection rule j, mJ↔j, −mj, whereas the first rank tensor components do not. The latter can be ascribed to a formal interaction term which is proportional to the inner product of the orbital angular momenta of the valence electron and the colliding atoms, respectively, thus accounting for molecular coupling phenomena during the collision. Finally, the transition matrix elements are used to calculate the depolarizing cross sections from the van der Waals potential.

Effect of LSD on visually evoked responses to color in visualizer and non-visualizer subjects

1. 1. The visually evoked responses (VERs) to color of visualizer subjects evidenced a significant degree of color specific characteristics and selective alteration in color specificity after LSD. The changes were somewhat more pronounced in the amplitude domain. Configuration of the VER to white and red were consistently different from those to blue or green. Visualizers also reported enhanced visual perception after LSD. 2. 2. In non-visualizer subjects the VERs to all color conditions except to red were virtually identical. Following LSD, early components of all 3 color VERs, most noticeably for red and green, were changed in configuration, all changes being in the latency domain. 3. 3. Maximal amplitudes occurred in the VERs to white while counting the flashes in both subject groups. After LSD this was unchanged in visualizers but was markedly attenuated in responses of the non-visualizers. 4. 4. A technique for ranking components of a complexly organized set of responses was used which permitted extraction of critical data from a complex of intercurrent intra- and inter-subject variation. The technique isolated patterns of response by which changes over time could be conveniently compared within and between subject groups, and as these were affected by the experimental condition. This proved useful in isolating significant differences in a multi-dimensional system in which the external stimuli, light and LSD, were both contained within reasonable physiologic and pharmacologic limits.

Spin polarization. Part. I—Rest frame polarization states

The restrictions imposed by space-time reflection symmetries on the maximum number of real parameters determining a coherent as well as an incoherent mixture of positive-mass one-particle spin states are considered. The decomposition of the rest frame spin-density operator into multipole components is used extensively. A relation expressing the polarization multipole operator components of arbitrary rank in terms of the first-rank operator components has been derived. The maximum number of measurements necessary to specify a spindensity operator exhibiting discrete space-time symmetries and the corresponding restrictions on the multipole expansions which are invariant under these symmetry operations are obtained. For some discrete space-time symmetries there exist no nontrivial half-integral spin states. Massless particles and massive particles in arbitrary Lorentz frames as well as relativistic spin polarization for multiparticle states will be dealt with in a future communication which is now under preparation.

The contribution of the magnetization to the after-effect in iron

In recent experiments on the after-effect of the magnetostriction in α-iron due to the diffusion of interstitial carbon or nitrogen, it was observed that the magnetic contribution to the after-effect is opposite in sign to the mechanical contribution. It was also found that the magnetic contribution to the free energy, D, differs more radically between carbon and nitrogen than the mechanical contribution, ϵ. We show that the energy D is related to changes of the second rank component of the electrostatic interaction energy of the interstitial impurity with the iron atoms. These are caused by distortions of the 3 d electron clouds of the iron atoms by the magnetization. By also relating the energy ϵ to changes of the zero-th rank component of the electrostatic interaction energy, caused by anisotropic magnetostrictive strains, we are able to understand why the energy ϵ for carbon and nitrogen is proportional to their ionic radii whereas the energy D differs more radically. The opposite signs of the energies D and ϵ, imply that the magnetization, through spin-orbit interaction energy of the 3 d iron electrons, favors states with prolate charge distributions over those with oblate charge distributions.

Linear Electric Shifts in the Paramagnetic Resonance ofAl2O3: Cr and MgO: Cr

It is shown that the spin Hamiltonian for ${\mathrm{Cr}}^{3+}$ ions in the ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ lattice has to be augmented by a term $\ensuremath{\Sigma}{i}^{}\ensuremath{\Sigma}{j\ensuremath{\le}k}^{}\frac{1}{2}{R}_{\mathrm{ijk}}{E}_{i}({S}_{j}{S}_{k}+{S}_{k}{S}_{j})$ in the presence of an externally applied electric field E. The five independent components of the third rank $R$ tensor appropriate to the point symmetry ${C}_{3}$ of the ${\mathrm{Cr}}^{3+}$ sites have been determined experimentally. In units of Mc/sec per kV/cm the results for one site are ${R}_{111}=\ensuremath{-}0.020$, ${R}_{222}=0.073$, ${R}_{333}=0.179$, ${R}_{123}=0.04$, and ${R}_{113}=0.09$. The ${\mathrm{Cr}}^{3+}$ site in the unit cell related by inversion symmetry has all signs reversed. The two other sites which are related to this pair by a reflection in the $y$ plane have the signs of ${R}_{222}$ and ${R}_{123}$ reversed. These results are related to the known crystal structure. Their agreement with a theoretical calculation based on a partially covalent bonding orbital in the Cr${\mathrm{O}}_{6}^{\ensuremath{-}9}$ complex is satisfactory, whereas a point-charge model of the crystal field cannot account for the spin Hamiltonian. The electric field effect for the ${\mathrm{Cr}}^{3+}$ sites with an associated vacancy in the MgO lattice, was shown to be less than 1 Mc/sec for $E={10}^{5}$ V/cm, in agreement with the covalent theory. Verification of the Kramers degeneracy in the presence of the crystalline field components of odd parity resulted in setting an upper bound on the permanent electric dipole moment of the electron of 1.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$ cm times $e$.