Bothe, Thorsten; Li Wansong; Schulte, Michael; von Kopylow, Christoph; Bergmann, Ralf B.; Jueptner, Werner P. O.
2010-10-20
Exact geometric calibration of optical devices like projectors or cameras is the basis for utilizing them in quantitative metrological applications. The common state-of-the-art photogrammetric pinhole-imaging-based models with supplemental polynomial corrections fail in the presence of nonsymmetric or high-spatial-frequency distortions and in describing caustics efficiently. These problems are solved by our vision ray calibration (VRC), which is proposed in this paper. The VRC takes an optical mapping system modeled as a black box and directly delivers corresponding vision rays for each mapped pixel. The underlying model, the calibration process, and examples are visualized and reviewed, demonstrating the potential of the VRC.
NASA Astrophysics Data System (ADS)
Massiot, Cécile; Nicol, Andrew; Townend, John; McNamara, David D.; Garcia-Sellés, David; Conway, Chris E.; Archibald, Garth
2017-07-01
Permeability hosted in andesitic lava flows is dominantly controlled by fracture systems, with geometries that are often poorly constrained. This paper explores the fracture system geometry of an andesitic lava flow formed during its emplacement and cooling over gentle paleo-topography, on the active Ruapehu volcano, New Zealand. The fracture system comprises column-forming and platy fractures within the blocky interior of the lava flow, bounded by autobreccias partially observed at the base and top of the outcrop. We use a terrestrial laser scanner (TLS) dataset to extract column-forming fractures directly from the point-cloud shape over an outcrop area of ∼3090 m2. Fracture processing is validated using manual scanlines and high-resolution panoramic photographs. Column-forming fractures are either steeply or gently dipping with no preferred strike orientation. Geometric analysis of fractures derived from the TLS, in combination with virtual scanlines and trace maps, reveals that: (1) steeply dipping column-forming fracture lengths follow a scale-dependent exponential or log-normal distribution rather than a scale-independent power-law; (2) fracture intensities (combining density and size) vary throughout the blocky zone but have similar mean values up and along the lava flow; and (3) the areal fracture intensity is higher in the autobreccia than in the blocky zone. The inter-connected fracture network has a connected porosity of ∼0.5 % that promote fluid flow vertically and laterally within the blocky zone, and is partially connected to the autobreccias. Autobreccias may act either as lateral permeability connections or barriers in reservoirs, depending on burial and alteration history. A discrete fracture network model generated from these geometrical parameters yields a highly connected fracture network, consistent with outcrop observations.
Descriptive Geometry and Geometric Modeling.
ERIC Educational Resources Information Center
Adams, J. Alan
1988-01-01
Describes experiences for engineering students to develop spatial awareness and reasoning capability. Describes geometric modeling, basic geometric concepts, operations, surface modeling, and conclusions. (YP)
Vela, Javier; Cirera, Jordi; Smith, Jeremy M.; Lachicotte, Rene J.; Flaschenriem, Christine J.; Alvarez, Santiago; Holland, Patrick L.
2009-01-01
Six of the seven iron atoms in the iron-molybdenum cofactor of nitrogenase display an unusual geometry, which is distorted from the tetrahedral geometry that is most common in iron-sulfur clusters. This distortion pulls the iron along one C3 axis of the tetrahedron toward a trigonal pyramid. The trigonal pyramidal coordination geometry is rare in four-coordinate transition metal complexes. In order to document this geometry in a systematic fashion in iron(II) chemistry, we have synthesized a range of four-coordinate iron(II) complexes that vary from tetrahedral to trigonal pyramidal. Continuous shape measures are used for a quantitative comparison of the stereochemistry of the Fe atoms in the iron-molybdenum cofactor with those of the presently and previously reported model complexes, as well as with those in polynuclear iron-sulfur compounds. This understanding of the iron coordination geometry is expected to assist in the design of synthetic models for intermediates in the nitrogenase catalytic cycle. PMID:17198413
A geometric description of human intestine.
Coşkun, Ihsaniye; Yildiz, Hüseyin; Arslan, Kadri; Yildiz, Bahri
2007-01-01
Mathematical models of natural phenomena play a central role in the physical sciences. Moreover, modeling of the organs draws from some beautiful areas of mathematics, such as nonlinear dynamics, multiscale transforms and stability analysis. In this study, a geometric recognition of the separate intestine sections (duodenum, jejunum, ileum, cecum and colon) of the human is presented. The human intestine was considered a tubular shape along a special curve and two male Turkish men were used for the modeling study. The length (cm) and diameter (mm) of the intestines were measured with a digital compass and formulated. These models were compared with their original photographs. It has been concluded that the geometric modeling and experimental work were consistent. These kinds of organ modeling techniques will also profit to medical lecturers to show 3-D figures to their students.
Geometric descriptions of entangled states by auxiliary varieties
Holweck, Frederic; Luque, Jean-Gabriel; Thibon, Jean-Yves
2012-10-15
The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an open subset of an algebraic variety built by classical geometric constructions (tangent lines, secant lines) from the set of separable states. In this setting, we describe well-known classifications of multipartite entanglement such as 2 Multiplication-Sign 2 Multiplication-Sign (n+ 1), for n Greater-Than-Or-Slanted-Equal-To 1, quantum systems and a new description with the 2 Multiplication-Sign 3 Multiplication-Sign 3 quantum system. Our results complete the approach of Miyake and make stronger connections with recent work of algebraic geometers. Moreover, for the quantum systems detailed in this paper, we propose an algorithm, based on the classical theory of invariants, to decide to which subvariety of the Hilbert space a given state belongs.
A Geometric Description of Raman Fingerprints on Spinor BECs
NASA Astrophysics Data System (ADS)
Schultz, Justin T.; Hansen, Azure; Murphree, Joseph D.; Jayaseelan, Maitreyi; Bigelow, Nicholas P.
2016-05-01
We employ a geometric description of a coherent, diabatic two-photon Raman interaction as a rotation on the Bloch sphere of a spin-1/2 system. The spin state of the system is described by a point on the sphere and the time evolution is described by a trajectory of the sphere's surface. The axis of rotation is determined by properties of the optical Raman beams: the pulse area, the relative intensities, relative phase, and relative frequencies. The two-photon detuning gives fine control over the sizes and phases of the imprinted features. This interpretation allows us not only to precisely engineer complex, spatially varying spin textures, but also to characterize these textures with a form of atomic polarimetry as we demonstrate on a coreless vortex in a spinor BEC.
Geometrical description of algebraic structures: Applications to Quantum Mechanics
Carinena, J. F.; Ibort, A.; Marmo, G.; Morandi, G.
2009-05-06
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to quantum mechanics. We will concentrate our attention into quantum theories and we will show how to use in a systematic way the transition from algebraic to geometrical structures to explore their geometry, mainly its Jordan-Lie structure.
Cooper, W. James; Albertson, R Craig; Jacob, Rick E.; Westneat, Mark W.
2014-12-01
Here we present a re-description of Abudefduf luridus and reassign it to the genus Similiparma. We supplement traditional diagnoses and descriptions of this species with quantitative anatomical data collected from a family-wide geometric morphometric analysis of head morphology (44 species representing all 30 damselfish genera) and data from cranial micro-CT scans of fishes in the genus Similiparma. The use of geometric morphometric analyses (and other methods of shape analysis) permits detailed comparisons between the morphology of specific taxa and the anatomical diversity that has arisen in an entire lineage. This provides a particularly useful supplement to traditional description methods and we recommend the use of such techniques by systematists. Similiparma and its close relatives constitute a branch of the damselfish phylogenetic tree that predominantly inhabits rocky reefs in the Atlantic and Eastern Pacific, as opposed to the more commonly studied damselfishes that constitute a large portion of the ichthyofauna on all coral-reef communities.
Detection and description of geometrically transformed digital images
NASA Astrophysics Data System (ADS)
Mahdian, Babak; Saic, Stanislav
2009-02-01
Geometric transformations such as scaling or rotation are common tools employed by forgery creators. These procedures are typically based on a resampling and interpolation step. The interpolation process brings specific periodic properties into the image. In this paper, we show how to detect these properties. Our aim is to detect all possible geometric transformations in the image being investigated. Furthermore, as the proposed method, as well as other existing detectors, is sensitive to noise, we also briefly show a simple method capable of detecting image noise inconsistencies. Noise is a common tool used to conceal the traces of tampering.
A geometric description of Maxwell field in a Kerr spacetime
NASA Astrophysics Data System (ADS)
Jezierski, Jacek; Smołka, Tomasz
2016-06-01
We consider the Maxwell field in the exterior of a Kerr black hole. For this system, we propose a geometric construction of generalized Klein-Gordon equation called Fackerell-Ipser equation. Our model is based on conformal Yano-Killing tensor (CYK tensor). We present non-standard properties of CYK tensors in the Kerr spacetime which are useful in electrodynamics.
Random geometric graph description of connectedness percolation in rod systems.
Chatterjee, Avik P; Grimaldi, Claudio
2015-09-01
The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The probability that an edge (or link) connects any randomly selected pair of nodes depends upon the rod volume fraction as well as the distribution over their sizes and shapes, and also upon quantities that characterize their state of dispersion (such as the orientational distribution function). We employ the observation that contributions from closed loops of connected rods are negligible in the limit of large aspect ratios to obtain percolation thresholds that are fully equivalent to those calculated within the second-virial approximation of the connectedness Ornstein-Zernike equation. Our formulation can account for effects due to interactions between the rods, and many-body features can be partially addressed by suitable choices for the edge probabilities.
Random geometric graph description of connectedness percolation in rod systems
NASA Astrophysics Data System (ADS)
Chatterjee, Avik P.; Grimaldi, Claudio
2015-09-01
The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The probability that an edge (or link) connects any randomly selected pair of nodes depends upon the rod volume fraction as well as the distribution over their sizes and shapes, and also upon quantities that characterize their state of dispersion (such as the orientational distribution function). We employ the observation that contributions from closed loops of connected rods are negligible in the limit of large aspect ratios to obtain percolation thresholds that are fully equivalent to those calculated within the second-virial approximation of the connectedness Ornstein-Zernike equation. Our formulation can account for effects due to interactions between the rods, and many-body features can be partially addressed by suitable choices for the edge probabilities.
Application of geometric algebra for the description of polymer conformations.
Chys, Pieter
2008-03-14
In this paper a Clifford algebra-based method is applied to calculate polymer chain conformations. The approach enables the calculation of the position of an atom in space with the knowledge of the bond length (l), valence angle (theta), and rotation angle (phi) of each of the preceding bonds in the chain. Hence, the set of geometrical parameters {l(i),theta(i),phi(i)} yields all the position coordinates p(i) of the main chain atoms. Moreover, the method allows the calculation of side chain conformations and the computation of rotations of chain segments. With these features it is, in principle, possible to generate conformations of any type of chemical structure. This method is proposed as an alternative for the classical approach by matrix algebra. It is more straightforward and its final symbolic representation considerably simpler than that of matrix algebra. Approaches for realistic modeling by means of incorporation of energetic considerations can be combined with it. This article, however, is entirely focused at showing the suitable mathematical framework on which further developments and applications can be built.
Quantitative study of geometrical scaling in charm production at HERA
NASA Astrophysics Data System (ADS)
Stebel, Tomasz
2013-07-01
The method of ratios was applied to search for geometrical scaling in charm production in deep inelastic scattering. Recent combined data from the H1 and ZEUS experiments were used. Two forms of geometrical scaling were tested: an originally proposed scaling that results from the Golec-Biernat-Wusthoff model and scaling motivated by a dipole representation, which takes into account charm mass. It turns out that in both cases some residual scaling is present and charm mass inclusion improves scaling quality.
Geometrical Description in Binary Composites and Spectral Density Representation
Tuncer, Enis
2010-01-01
In this review, the dielectric permittivity of dielectric mixtures is discussed in view of the spectral density representation method. A distinct representation is derived for predicting the dielectric properties, permittivities ε, of mixtures. The presentation of the dielectric properties is based on a scaled permittivity approach, ξ=(εe-εm)(εi-εm)-1, where the subscripts e, m and i denote the dielectric permittivities of the effective, matrix and inclusion media, respectively [Tuncer, E. J. Phys.: Condens. Matter 2005, 17, L125]. This novel representation transforms the spectral density formalism to a form similar to the distribution of relaxation times method of dielectric relaxation. Consequently, I propose that any dielectric relaxation formula, i.e., the Havriliak-Negami empirical dielectric relaxation expression, can be adopted as a scaled permittivity. The presented scaled permittivity representation has potential to be improved and implemented into the existing data analyzing routines for dielectric relaxation; however, the information to extract would be the topological/morphological description in mixtures. To arrive at the description, one needs to know the dielectric properties of the constituents and the composite prior to the spectral analysis. To illustrate the strength of the representation and confirm the proposed hypothesis, the Landau-Lifshitz/Looyenga (LLL) [Looyenga, H. Physica 1965, 31, 401] expression is selected. The structural information of a mixture obeying LLL is extracted for different volume fractions of phases. Both an in-house computational tool based on the Monte Carlo method to solve inverse integral transforms and the proposed empirical scaled permittivity expression are employed to estimate the spectral density function of the LLL expression. The estimated spectral functions for mixtures with different inclusion concentration compositions show similarities; they are composed of a couple of bell-shaped distributions, with
Generalization of the geometric description of a light beam in radiometry and photometry.
Simonot, Lionel; Boulenguez, Pierre
2013-04-01
Radiometric and photometric quantities rely on a geometric description of the beam subtended by a source and a receptor. In this paper, a generalization of this description is proposed as the product of the apparent size of the source times the receptor angular extent, whatever the natures of these elements: point, line, surface, or volume. The obtained flux density per geometric extent expressions are then applied to the determination of the irradiances induced in the near field and far field by a rectilinear source represented as a point source, a line source, and a surface source.
The Appalachian Child: A Quantitative Description.
ERIC Educational Resources Information Center
Mathews, Walter M.; Stepp, Ermel, Jr.
This report presents a statistical description of the Appalachian child. The population studied were fifth, sixth and seventh grade boys and girls, in home and school environments. There is no commentary beyond a brief explanation of the meaning of each scale or measure employed. Some of the areas for which data are presented are: locus of…
Unitarity triangles and geometrical description of CP violation with Majorana neutrinos
NASA Astrophysics Data System (ADS)
Aguilar-Saavedra, J. A.; Branco, G. C.
2000-11-01
We generalize the geometrical description of CP violation in the standard model in terms of a unitarity triangle. For three left-handed Majorana neutrinos CP violation in the lepton sector is determined by three unitarity triangles. With three additional right-handed neutrinos 15 quadrangles are required to characterize CP violation. We show the relation of the unitarity polygons with physical observables.
A Quantitative Description of FBI Public Relations.
ERIC Educational Resources Information Center
Gibson, Dirk C.
1997-01-01
States that the Federal Bureau of Investigation (FBI) had the most successful media relations program of all government agencies from the 1930s to the 1980s. Uses quantitative analysis to show why those media efforts were successful. Identifies themes that typified the verbal component of FBI publicity and the broad spectrum of mass communication…
A Quantitative Description of FBI Public Relations.
ERIC Educational Resources Information Center
Gibson, Dirk C.
1997-01-01
States that the Federal Bureau of Investigation (FBI) had the most successful media relations program of all government agencies from the 1930s to the 1980s. Uses quantitative analysis to show why those media efforts were successful. Identifies themes that typified the verbal component of FBI publicity and the broad spectrum of mass communication…
Extensor mechanism of the fingers. I. A quantitative geometric study.
Garcia-Elias, M; An, K N; Berglund, L; Linscheid, R L; Cooney, W P; Chao, E Y
1991-11-01
A close-range stereophotogrammetric measurement system was used to determine the three-dimensional geometric characteristics of the extensor assembly in seven human finger specimens and five finger configurations. The numerical data obtained showed that, although changes in length of the different bundles are small, their spatial orientation varies considerably from one to another position. This information should help to improve the accuracy of models derived to understand the extensor assembly behavior in normal and pathological conditions.
A quantitative description for efficient financial markets
NASA Astrophysics Data System (ADS)
Immonen, Eero
2015-09-01
In this article we develop a control system model for describing efficient financial markets. We define the efficiency of a financial market in quantitative terms by robust asymptotic price-value equality in this model. By invoking the Internal Model Principle of robust output regulation theory we then show that under No Bubble Conditions, in the proposed model, the market is efficient if and only if the following conditions hold true: (1) the traders, as a group, can identify any mispricing in asset value (even if no one single trader can do it accurately), and (2) the traders, as a group, incorporate an internal model of the value process (again, even if no one single trader knows it). This main result of the article, which deliberately avoids the requirement for investor rationality, demonstrates, in quantitative terms, that the more transparent the markets are, the more efficient they are. An extensive example is provided to illustrate the theoretical development.
Quantitative descriptions of nonlinear gravitational galaxy clustering
NASA Astrophysics Data System (ADS)
Itoh, Makoto
1990-08-01
Results are presented on three different quantitative analyses of nonlinear gravitational galaxy clustering, including determinations of two-point correlation function, xi(r); fractal dimensions, Dq; and f(N) statistics. The analyses show that, for models with n = 1 and n = 0, the exponent of the correlation function (which has a general form xi/r/ proportional to r exp -gamma) is about 2 in the nonlinear regime. It is shown that the thermodynamic f(N), which connnects the fractal dimensions with the exponent of xi(r) can describe the distribution of galaxies in the nonlinear regime.
NASA Astrophysics Data System (ADS)
Lüdde, Hans Jürgen; Achenbach, Alexander; Kalkbrenner, Thilo; Jankowiak, Hans-Christian; Kirchner, Tom
2016-04-01
A new model to account for geometric screening corrections in an independent-atom-model description of ion-molecule collisions is introduced. The ion-molecule cross sections for net capture and net ionization are represented as weighted sums of atomic cross sections with weight factors that are determined from a geometric model of overlapping cross section areas. Results are presented for proton collisions with targets ranging from diatomic to complex polyatomic molecules. Significant improvement compared to simple additivity rule results and in general good agreement with experimental data are found. The flexibility of the approach opens up the possibility to study more detailed observables such as orientation-dependent and charge-state-correlated cross sections for a large class of complex targets ranging from biomolecules to atomic clusters.
Lambert, R K; Paré, P D; Seow, C Y
2004-02-01
Despite considerable investigation, the mechanisms underlying the functional properties of smooth muscle are poorly understood. This can be attributed, at least in part, to a lack of knowledge about the structure and organization of the contractile apparatus inside the muscle cell. Recent observations of the plasticity of smooth muscle and of morphometry of the cell have provided enough information for us to propose a quantitative, although highly simplified, model for the geometric arrangement of contractile units and their collective kinematic functions in smooth muscle, particularly airway smooth muscle. We propose that, to a considerable extent, contractile machinery restructures upon activation of the muscle and adapts to cell geometry at the time of activation. We assume that, under steady-state conditions, the geometric arrangement of contractile units and the filaments within these units determines the kinematic characteristics of the muscle. The model successfully predicts the results of experiments on airway smooth muscle plasticity relating to maximal force generation, maximal velocity of shortening, and the variation of compliance with adapted length. The model is also concordant with morphometric observations that show an increase in myosin filament density when muscle is adapted to a longer length. The model provides a framework for design of experiments to quantitatively test various aspects of smooth muscle plasticity in terms of geometric arrangement of contractile units and the muscle's mechanical properties.
NASA Astrophysics Data System (ADS)
Cormann, Mirko; Caudano, Yves
2017-07-01
We express modular and weak values of observables of three- and higher-level quantum systems in their polar form. The Majorana representation of N-level systems in terms of symmetric states of N - 1 qubits provides us with a description on the Bloch sphere. With this geometric approach, we find that modular and weak values of observables of N-level quantum systems can be factored in N - 1 contributions. Their modulus is determined by the product of N - 1 ratios involving projection probabilities between qubits, while their argument is deduced from a sum of N - 1 solid angles on the Bloch sphere. These theoretical results allow us to study the geometric origin of the quantum phase discontinuity around singularities of weak values in three-level systems. We also analyze the three-box paradox (Aharonov and Vaidman 1991 J. Phys. A: Math. Gen. 24 2315-28) from the point of view of a bipartite quantum system. In the Majorana representation of this paradox, an observer comes to opposite conclusions about the entanglement state of the particles that were successfully pre- and postselected.
Using Qualitative Metasummary to Synthesize Qualitative and Quantitative Descriptive Findings
Sandelowski, Margarete; Barroso, Julie; Voils, Corrine I.
2008-01-01
The new imperative in the health disciplines to be more methodologically inclusive has generated a growing interest in mixed research synthesis, or the integration of qualitative and quantitative research findings. Qualitative metasummary is a quantitatively oriented aggregation of qualitative findings originally developed to accommodate the distinctive features of qualitative surveys. Yet these findings are similar in form and mode of production to the descriptive findings researchers often present in addition to the results of bivariate and multivariable analyses. Qualitative metasummary, which includes the extraction, grouping, and formatting of findings, and the calculation of frequency and intensity effect sizes, can be used to produce mixed research syntheses and to conduct a posteriori analyses of the relationship between reports and findings. PMID:17243111
From information theory to quantitative description of steric effects.
Alipour, Mojtaba; Safari, Zahra
2016-07-21
Immense efforts have been made in the literature to apply the information theory descriptors for investigating the electronic structure theory of various systems. In the present study, the information theoretic quantities, such as Fisher information, Shannon entropy, Onicescu information energy, and Ghosh-Berkowitz-Parr entropy, have been used to present a quantitative description for one of the most widely used concepts in chemistry, namely the steric effects. Taking the experimental steric scales for the different compounds as benchmark sets, there are reasonable linear relationships between the experimental scales of the steric effects and theoretical values of steric energies calculated from information theory functionals. Perusing the results obtained from the information theoretic quantities with the two representations of electron density and shape function, the Shannon entropy has the best performance for the purpose. On the one hand, the usefulness of considering the contributions of functional groups steric energies and geometries, and on the other hand, dissecting the effects of both global and local information measures simultaneously have also been explored. Furthermore, the utility of the information functionals for the description of steric effects in several chemical transformations, such as electrophilic and nucleophilic reactions and host-guest chemistry, has been analyzed. The functionals of information theory correlate remarkably with the stability of systems and experimental scales. Overall, these findings show that the information theoretic quantities can be introduced as quantitative measures of steric effects and provide further evidences of the quality of information theory toward helping theoreticians and experimentalists to interpret different problems in real systems.
Light beams with general direction and polarization: Global description and geometric phase
NASA Astrophysics Data System (ADS)
Nityananda, R.; Sridhar, S.
2014-02-01
We construct the manifold describing the family of plane monochromatic light waves with all directions, polarizations, phases and intensities. A smooth description of polarization, valid over the entire sphere S2 of directions, is given through the construction of an orthogonal basis pair of complex polarization vectors for each direction; any light beam is then uniquely and smoothly specified by giving its direction and two complex amplitudes. This implies that the space of all light beams is the six dimensional manifold S2×C2∖{0}, the (untwisted) Cartesian product of a sphere and a two dimensional complex vector space minus the origin. A Hopf map (i.e. mapping the two complex amplitudes to the Stokes parameters) then leads to the four dimensional manifold S2×S2 which describes beams with all directions and polarization states. This product of two spheres can be viewed as an ordered pair of two points on a single sphere, in contrast to earlier work in which the same system was represented using Majorana's mapping of the states of a spin one quantum system to an unordered pair of points on a sphere. This is a different manifold, CP2, two dimensional complex projective space, which does not faithfully represent the full space of all directions and polarizations. Following the now-standard framework, we exhibit the fibre bundle whose total space is the set of all light beams of non-zero intensity, and base space S2×S2. We give the U(1) connection which determines the geometric phase as the line integral of a one-form along a closed curve in the total space. Bases are classified as globally smooth, global but singular, and local, with the last type of basis being defined only when the curve traversed by the system is given. Existing as well as new formulae for the geometric phase are presented in this overall framework.
Houssaye, Alexandra; Herrel, Anthony; Fabre, Anne-Claire; Cornette, Raphael
2015-01-01
The challenging complexity of biological structures has led to the development of several methods for quantitative analyses of form. Bones are shaped by the interaction of historical (phylogenetic), structural, and functional constrains. Consequently, bone shape has been investigated intensively in an evolutionary context. Geometric morphometric approaches allow the description of the shape of an object in all of its biological complexity. However, when biological objects present only few anatomical landmarks, sliding semi-landmarks may provide good descriptors of shape. The sliding procedure, mandatory for sliding semi-landmarks, requires several steps that may be time-consuming. We here compare the time required by two different software packages (‘Edgewarp’ and ‘Morpho’) for the same sliding task, and investigate potential differences in the results and biological interpretation. ‘Morpho’ is much faster than ‘Edgewarp,’ notably as a result of the greater computational power of the ‘Morpho’ software routines and the complexity of the ‘Edgewarp’ workflow. Morphospaces obtained using both software packages are similar and provide a consistent description of the biological variability. The principal differences between the two software packages are observed in areas characterized by abrupt changes in the bone topography. In summary, both software packages perform equally well in terms of the description of biological structures, yet differ in the simplicity of the workflow and time needed to perform the analyses. PMID:26618086
Botton-Divet, Léo; Houssaye, Alexandra; Herrel, Anthony; Fabre, Anne-Claire; Cornette, Raphael
2015-01-01
The challenging complexity of biological structures has led to the development of several methods for quantitative analyses of form. Bones are shaped by the interaction of historical (phylogenetic), structural, and functional constrains. Consequently, bone shape has been investigated intensively in an evolutionary context. Geometric morphometric approaches allow the description of the shape of an object in all of its biological complexity. However, when biological objects present only few anatomical landmarks, sliding semi-landmarks may provide good descriptors of shape. The sliding procedure, mandatory for sliding semi-landmarks, requires several steps that may be time-consuming. We here compare the time required by two different software packages ('Edgewarp' and 'Morpho') for the same sliding task, and investigate potential differences in the results and biological interpretation. 'Morpho' is much faster than 'Edgewarp,' notably as a result of the greater computational power of the 'Morpho' software routines and the complexity of the 'Edgewarp' workflow. Morphospaces obtained using both software packages are similar and provide a consistent description of the biological variability. The principal differences between the two software packages are observed in areas characterized by abrupt changes in the bone topography. In summary, both software packages perform equally well in terms of the description of biological structures, yet differ in the simplicity of the workflow and time needed to perform the analyses.
Quantitative descriptions of rice plant architecture and their application
Li, Xumeng; Wang, Xiaohui; Peng, Yulin; Wei, Hailin; Zhu, Xinguang; Chang, Shuoqi; Li, Ming; Li, Tao; Huang, Huang
2017-01-01
Plant architecture is an important agronomic trait, and improving plant architecture has attracted the attention of scientists for decades, particularly studies to create desirable plant architecture for high grain yields through breeding and culture practices. However, many important structural phenotypic traits still lack quantitative description and modeling on structural-functional relativity. This study defined new architecture indices (AIs) derived from the digitalized plant architecture using the virtual blade method. The influences of varieties and crop management on these indices and the influences of these indices on biomass accumulation were analyzed using field experiment data at two crop growth stages: early and late panicle initiation. The results indicated that the vertical architecture indices (LAI, PH, 90%-DRI, MDI, 90%-LI) were significantly influenced by variety, water, nitrogen management and the interaction of water and nitrogen, and compact architecture indices (H-CI, Q-CI, 90%-LI, 50%-LI) were significantly influenced by nitrogen management and the interaction of variety and water. Furthermore, there were certain trends in the influence of variety, water, and nitrogen management on AIs. Biomass accumulation has a positive linear correlation with vertical architecture indices and has a quadratic correlation with compact architecture indices, respectively. Furthermore, the combination of vertical and compact architecture indices is the indicator for evaluating the effects of plant architecture on biomass accumulation. PMID:28545144
A semi-analytical description of protein folding that incorporates detailed geometrical information.
Suzuki, Yoko; Noel, Jeffrey K; Onuchic, José N
2011-06-28
Much has been done to study the interplay between geometric and energetic effects on the protein folding energy landscape. Numerical techniques such as molecular dynamics simulations are able to maintain a precise geometrical representation of the protein. Analytical approaches, however, often focus on the energetic aspects of folding, including geometrical information only in an average way. Here, we investigate a semi-analytical expression of folding that explicitly includes geometrical effects. We consider a Hamiltonian corresponding to a Gaussian filament with structure-based interactions. The model captures local features of protein folding often averaged over by mean-field theories, for example, loop contact formation and excluded volume. We explore the thermodynamics and folding mechanisms of beta-hairpin and alpha-helical structures as functions of temperature and Q, the fraction of native contacts formed. Excluded volume is shown to be an important component of a protein Hamiltonian, since it both dominates the cooperativity of the folding transition and alters folding mechanisms. Understanding geometrical effects in analytical formulae will help illuminate the consequences of the approximations required for the study of larger proteins.
NASA Astrophysics Data System (ADS)
Wang, Quanzeng; Cheng, Wei-Chung; Suresh, Nitin; Hua, Hong
2016-05-01
With improved diagnostic capabilities and complex optical designs, endoscopic technologies are advancing. As one of the several important optical performance characteristics, geometric distortion can negatively affect size estimation and feature identification related diagnosis. Therefore, a quantitative and simple distortion evaluation method is imperative for both the endoscopic industry and the medical device regulatory agent. However, no such method is available yet. While the image correction techniques are rather mature, they heavily depend on computational power to process multidimensional image data based on complex mathematical model, i.e., difficult to understand. Some commonly used distortion evaluation methods, such as the picture height distortion (DPH) or radial distortion (DRAD), are either too simple to accurately describe the distortion or subject to the error of deriving a reference image. We developed the basic local magnification (ML) method to evaluate endoscope distortion. Based on the method, we also developed ways to calculate DPH and DRAD. The method overcomes the aforementioned limitations, has clear physical meaning in the whole field of view, and can facilitate lesion size estimation during diagnosis. Most importantly, the method can facilitate endoscopic technology to market and potentially be adopted in an international endoscope standard.
Klingenberg, Christian Peter; Leamy, Larry J; Cheverud, James M
2004-01-01
The mouse mandible has long served as a model system for complex morphological structures. Here we use new methodology based on geometric morphometrics to test the hypothesis that the mandible consists of two main modules, the alveolar region and the ascending ramus, and that this modularity is reflected in the effects of quantitative trait loci (QTL). The shape of each mandible was analyzed by the positions of 16 morphological landmarks and these data were analyzed using Procrustes analysis. Interval mapping in the F(2) generation from intercrosses of the LG/J and SM/J strains revealed 33 QTL affecting mandible shape. The QTL effects corresponded to a variety of shape changes, but ordination or a parametric bootstrap test of clustering did not reveal any distinct groups of QTL that would affect primarily one module or the other. The correlations of landmark positions between the two modules tended to be lower than the correlations between arbitrary subsets of landmarks, indicating that the modules were relatively independent of each other and confirming the hypothesized location of the boundary between them. While these results are in agreement with the hypothesis of modularity, they also underscore that modularity is a question of the relative degrees to which QTL contribute to different traits, rather than a question of discrete sets of QTL contributing to discrete sets of traits. PMID:15126408
NASA Astrophysics Data System (ADS)
Checefsky, Walter A.; Abidin, Anas Z.; Nagarajan, Mahesh B.; Bauer, Jan S.; Baum, Thomas; Wismüller, Axel
2016-03-01
The current clinical standard for measuring Bone Mineral Density (BMD) is dual X-ray absorptiometry, however more recently BMD derived from volumetric quantitative computed tomography has been shown to demonstrate a high association with spinal fracture susceptibility. In this study, we propose a method of fracture risk assessment using structural properties of trabecular bone in spinal vertebrae. Experimental data was acquired via axial multi-detector CT (MDCT) from 12 spinal vertebrae specimens using a whole-body 256-row CT scanner with a dedicated calibration phantom. Common image processing methods were used to annotate the trabecular compartment in the vertebral slices creating a circular region of interest (ROI) that excluded cortical bone for each slice. The pixels inside the ROI were converted to values indicative of BMD. High dimensional geometrical features were derived using the scaling index method (SIM) at different radii and scaling factors (SF). The mean BMD values within the ROI were then extracted and used in conjunction with a support vector machine to predict the failure load of the specimens. Prediction performance was measured using the root-mean-square error (RMSE) metric and determined that SIM combined with mean BMD features (RMSE = 0.82 +/- 0.37) outperformed MDCT-measured mean BMD (RMSE = 1.11 +/- 0.33) (p < 10-4). These results demonstrate that biomechanical strength prediction in vertebrae can be significantly improved through the use of SIM-derived texture features from trabecular bone.
Soliman, George; Yevick, David; Jessop, Paul
2014-09-01
This paper demonstrates that numerous calculations involving polarization transformations can be condensed by employing suitable geometric algebra formalism. For example, to describe polarization mode dispersion and polarization-dependent loss, both the material birefringence and differential loss enter as bivectors and can be combined into a single symmetric quantity. Their frequency and distance evolution, as well as that of the Stokes vector through an optical system, can then each be expressed as a single compact expression, in contrast to the corresponding Mueller matrix formulations. The intrinsic advantage of the geometric algebra framework is further demonstrated by presenting a simplified derivation of generalized Stokes parameters that include the electric field phase. This procedure simultaneously establishes the tensor transformation properties of these parameters.
Torres-Rivas, Francisco; Flores-Hidalgo, Manuel Alberto; Glossman-Mitnik, Daniel; Barraza-Jimenez, Diana
2015-10-01
The geometric parameters, local and global chemical reactivity parameters (such as the ionization potential, electron affinity, electronegativity, hardness, softness, chemical potential, and electrophilicity index), as well as the energy levels (HOMO/LUMO) and HOMO-LUMO energy gaps have been determined for the principal carotenoids in higher plants. DFT calculations performed using the B3LYP functional in combination with the 6-31G(d,p) (for geometric parameters) and 6-31 + G(d,p) (for energy parameters) basis sets were carried out to study these structures. The HOMO-LUMO energy gaps obtained with the TPSSh functional were compared with the corresponding energy gaps obtained with B3LYP (when both functionals were used with the 6-31 + G(d,p) basis set). Upon analyzing all of the calculated parameters of the studied molecules, both carotenes were found to be the most reactive, followed by β-cryptoxanthin, zeaxanthin, lutein, violaxanthin, and finally neoxanthin, the least reactive molecule. The results reveal that all of the carotenoids show very high coplanarity in the photochemically active region, resulting in small HOMO-LUMO energy gaps. The calculated local and global chemical reactivity parameters indicate that all of the studied molecules may be classified as soft, as they are good electron donors/acceptors, making these molecules good candidates for use in artificial photosynthetic systems.
Toward a quantitative description of the neurodynamic organizations of teams.
Stevens, Ronald H; Galloway, Trysha L
2014-01-01
The goal was to develop quantitative models of the neurodynamic organizations of teams that could be used for comparing performance within and across teams and sessions. A symbolic modeling system was developed, where raw electroencephalography (EEG) signals from dyads were first transformed into second-by-second estimates of the cognitive Workload or Engagement of each person and transformed again into symbols representing the aggregated levels of the team. The resulting neurodynamic symbol streams had a persistent structure and contained segments of differential symbol expression. The quantitative Shannon entropy changes during these periods were related to speech, performance, and team responses to task changes. The dyads in an unscripted map navigation task (Human Communication Research Centre (HCRC) Map Task (MT)) developed fluctuating dynamics for Workload and Engagement, as they established their teamwork rhythms, and these were disrupted by external changes to the task. The entropy fluctuations during these disruptions differed in frequency, magnitude, and duration, and were associated with qualitative and quantitative changes in team organization and performance. These results indicate that neurodynamic models may be reliable, sensitive, and valid indicators of the changing neurodynamics of teams around which standardized quantitative models can begin to be developed.
Anzai, Natsume; Sawai, Tadashi; Sakai, Tatsuo
2014-03-01
Famous geologist Nicolaus Steno (1638-1686) was known as a skillful anatomist in his time. His main work about anatomy is "Elementorum myologiae specimen, seu musculi descriptio geometrica". Steno introduced geometrical representation into muscle study. His purpose was to handle muscle movements in the style of Cartesian mechanical philosophy, assuming muscle fibers as the structural and functional unit of muscle. Steno modelled muscles as parallelepiped integrations of fibers. Steno thought the shortening of muscle fibers modified parallelepiped integration and its modification resulted in muscle movements. His parallelepiped model enabled the regarding of muscles as objects of physics. Steno's assumption and model built a methodological foundation of mechanistic physiology of muscle, and influenced latter 17th century thinkers, especially Borelli.
Quantitative Luminescence Imaging System description and user's manual
Stahl, K.A.; Batishko, C.R.
1988-06-01
A Quantitative Luminescence Imaging System (QLIS) was designed and constructed. The system was developed for use in imaging and quantitative analysis of very low light level chemiluminescent phenomena. The luminescent reactions are imaged via microchannel plate image intensifier coupled to a newvicon video camera. The video record of the reaction can be stored on video tape or digitally captured by an image processing system which is integral to a host computer controller. Since the particular experimental conditions for which the QLIS was designed necessitate that the chemiluminescent reaction take place in an rf flux within a waveguide, the system includes a coherent fiber optic image transfer system which allows the video hardware to be mounted externally to the rf waveguide.
Miyaji, Noriaki; Miwa, Kenta; Motegi, Kazuki; Umeda, Takuro; Wagatsuma, Kei; Fukai, Shohei; Takiguchi, Tomohiro; Terauchi, Takashi; Koizumi, Mitsuru
Several cross-calibration schemes have been proposed to produce quantitative values in bone SPECT imaging. Differences in the radionuclide sources and geometric conditions can decrease the accuracy of cross-calibration factor (CCF). The present study aimed to validate the effects of calibration schemes using different sources under various geometric conditions. Temporal variations as well as variations in acquisition counts and the shapes of (57)Co standard and (99m)Tc point sources and a (99m)Tc disk source were determined. The effects of the geometric conditions of the source-to-camera distance (SCD) and lateral distance on the CCF were investigated by moving the camera or source away from the origin. The system planar sensitivity of NEMA incorporated into a Symbia Intevo SPECT/CT device (Siemens®) was defined as reference values. The temporal variation in CCF using the (57)Co source was relatively stable within the range of 0.7% to 2.3%, whereas the (99m)Tc source ranged from 2.7% to 7.3%. In terms of source shape, the (57)Co standard point source was the most stable. Both SCD and lateral distance decreased as a function of distance from the origin. Errors in the geometric condition were higher for the (57)Co standard point source than the (99m)Tc disk source. Different calibration schemes influenced the reliability of quantitative values. The (57)Co standard point source was stable over a long period, and this helped to maintain the quality of quantitative SPECT/CT imaging data. The CCF accuracy of the (99m)Tc source decreased depending on the preparative method. The method of calibration for quantitative SPECT should be immediately standardized to eliminate uncertainty.
Stróż, Kazimierz
2011-09-01
A fixed set, that is the set of all lattice metrics corresponding to the arithmetic holohedry of a primitive lattice, is a natural tool for keeping track of the symmetry changes that may occur in a deformable lattice [Ericksen (1979). Arch. Rat. Mech. Anal. 72, 1-13; Michel (1995). Symmetry and Structural Properties of Condensed Matter, edited by T. Lulek, W. Florek & S. Walcerz. Singapore: Academic Press; Pitteri & Zanzotto (1996). Acta Cryst. A52, 830-838; and references quoted therein]. For practical applications it is desirable to limit the infinite number of arithmetic holohedries, and simplify their classification and construction of the fixed sets. A space of 480 matrices with cyclic consecutive powers, determinant 1, elements from {0, ±1} and geometric description were analyzed and offered as the framework for dealing with the symmetry of reduced lattices. This matrix space covers all arithmetic holohedries of primitive lattice descriptions related to the three shortest lattice translations in direct or reciprocal spaces, and corresponds to the unique list of 39 fixed points with integer coordinates in six-dimensional space of lattice metrics. Matrices are presented by the introduced dual symbol, which sheds some light on the lattice and its symmetry-related properties, without further digging into matrices. By the orthogonal lattice distortion the lattice group-subgroup relations are easily predicted. It was proven and exemplified that new symbols enable classification of lattice groups on an absolute basis, without metric considerations. In contrast to long established but sophisticated methods for assessing the metric symmetry of a lattice, simple filtering of the symmetry operations from the predefined set is proposed. It is concluded that the space of symmetry matrices with elements from {0, ±1} is the natural environment of lattice symmetries related to the reduced cells and that complete geometric characterization of matrices in the arithmetic
Palatini approach to Born-Infeld-Einstein theory and a geometric description of electrodynamics
NASA Astrophysics Data System (ADS)
Vollick, Dan N.
2004-03-01
The field equations associated with the Born-Infeld-Einstein action are derived using the Palatini variational technique. In this approach the metric and connection are varied independently and the Ricci tensor is generally not symmetric. For sufficiently small curvatures the resulting field equations can be divided into two sets. One set, involving the antisymmetric part of the Ricci tensor Rμν∨, consists of the field equation for a massive vector field. The other set consists of the Einstein field equations with an energy momentum tensor for the vector field plus additional corrections. In a vacuum with Rμν∨=0 the field equations are shown to be the usual Einstein vacuum equations. This extends the universality of the vacuum Einstein equations, discussed by Ferraris et al., to the Born-Infeld-Einstein action. In the simplest version of the theory there is a single coupling constant and by requiring that the Einstein field equations hold to a good approximation in neutron stars it is shown that mass of the vector field exceeds the lower bound on the mass of the photon. Thus, in this case the vector field cannot represent the electromagnetic field and would describe a new geometrical field. In a more general version in which the symmetric and antisymmetric parts of the Ricci tensor have different coupling constants it is possible to satisfy all of the observational constraints if the antisymmetric coupling is much larger than the symmetric coupling. In this case the antisymmetric part of the Ricci tensor can describe the electromagnetic field.
NASA Astrophysics Data System (ADS)
Nagarajan, Mahesh B.; Coan, Paola; Huber, Markus B.; Diemoz, Paul C.; Wismüller, Axel
2014-03-01
Current assessment of cartilage is primarily based on identification of indirect markers such as joint space narrowing and increased subchondral bone density on x-ray images. In this context, phase contrast CT imaging (PCI-CT) has recently emerged as a novel imaging technique that allows a direct examination of chondrocyte patterns and their correlation to osteoarthritis through visualization of cartilage soft tissue. This study investigates the use of topological and geometrical approaches for characterizing chondrocyte patterns in the radial zone of the knee cartilage matrix in the presence and absence of osteoarthritic damage. For this purpose, topological features derived from Minkowski Functionals and geometric features derived from the Scaling Index Method (SIM) were extracted from 842 regions of interest (ROI) annotated on PCI-CT images of healthy and osteoarthritic specimens of human patellar cartilage. The extracted features were then used in a machine learning task involving support vector regression to classify ROIs as healthy or osteoarthritic. Classification performance was evaluated using the area under the receiver operating characteristic (ROC) curve (AUC). The best classification performance was observed with high-dimensional geometrical feature vectors derived from SIM (0.95 ± 0.06) which outperformed all Minkowski Functionals (p < 0.001). These results suggest that such quantitative analysis of chondrocyte patterns in human patellar cartilage matrix involving SIM-derived geometrical features can distinguish between healthy and osteoarthritic tissue with high accuracy.
Molecular acidity: A quantitative conceptual density functional theory description.
Liu, Shubin; Schauer, Cynthia K; Pedersen, Lee G
2009-10-28
Accurate predictions of molecular acidity using ab initio and density functional approaches are still a daunting task. Using electronic and reactivity properties, one can quantitatively estimate pKa values of acids. In a recent paper [S. B. Liu and L. G. Pedersen, J. Phys. Chem. A 113, 3648 (2009)], we employed the molecular electrostatic potential (MEP) on the nucleus and the sum of valence natural atomic orbital (NAO) energies for the purpose. In this work, we reformulate these relationships on the basis of conceptual density functional theory and compare the results with those from the thermodynamic cycle method. We show that MEP and NAO properties of the dissociating proton of an acid should satisfy the same relationships with experimental pKa data. We employ 27 main groups and first to third row transition metal-water complexes as illustrative examples to numerically verify the validity of these strong linear correlations. Results also show that the accuracy of our approach and that of the conventional method through the thermodynamic cycle are statistically similar.
Quantitative Description of Medical Student Interest in Neurology and Psychiatry.
Ramos, Raddy L; Cuoco, Joshua A; Guercio, Erik; Levitan, Thomas
2016-07-01
Given the well-documented shortage of physicians in primary care and several other specialties, quantitative understanding of residency application and matching data among osteopathic and allopathic medical students has implications for predicting trends in the physician workforce. To estimate medical student interest in neurology and psychiatry based on numbers of applicants and matches to neurology and psychiatry osteopathic and allopathic residency programs. Also, to gauge students' previous academic experience with brain and cognitive sciences. The number of available postgraduate year 1 positions, applicants, and matches from graduating years 2011 through 2015 were collected from the National Matching Services Inc and the American Association of Colleges of Osteopathic Medicine for osteopathic programs and the National Resident Matching Program and the Association of American Medical Colleges for allopathic programs. To determine and compare osteopathic and allopathic medical students' interest in neurology and psychiatry, the number of positions, applicants, and matches were analyzed considering the number of total osteopathic and allopathic graduates in the given year using 2-tailed χ2 analyses with Yates correction. In addition, osteopathic and allopathic medical schools' websites were reviewed to determine whether neurology and psychiatry rotations were required. Osteopathic medical students' reported undergraduate majors were also gathered. Compared with allopathic medical students, osteopathic medical students had significantly greater interest (as measured by applicants) in neurology (χ21=11.85, P<.001) and psychiatry (χ21=39.07, P<.001), and an equal proportion of osteopathic and allopathic medical students matched in neurology and psychiatry residency programs. Approximately 6% of osteopathic vs nearly 85% of allopathic medical schools had required neurology rotations. Nearly 10% of osteopathic applicants and matriculants had undergraduate
Thangappan, Jayaraman; Wu, Sangwook; Lee, Sun-Gu
2017-04-21
A macroscopic description of a protein structure allows an understanding of the protein conformations in a more simplistic manner. Here, a new macroscopic approach that utilizes the joints of the protein secondary structures as a basic descriptor for the protein structure is proposed and applied to study the arrangement of secondary structures in helical membrane proteins. Two types of dihedral angle, Ω and λ, were defined based on the joint points of the transmembrane (TM) helices and loops, and employed to analyze 103 non-homologous membrane proteins with 3 to 14 TM helices. The Ω-λ plot, which is a distribution plot of the dihedral angles of the joint points, identified the allowed and disallowed regions of helical arrangement. Analyses of consecutive dihedral angle patterns indicated that there are preferred patterns in the helical alignment and extension of TM proteins, and helical extension pattern in TM proteins is varied as the size of TM proteins increases. Finally, we could identify some symmetric protein pairs in TM proteins under the joint-based coordinate and 3-dimensional coordinates. The joint-based approach is expected to help better understand and model the overall conformational features of complicated large-scale proteins, such as membrane proteins.
ERIC Educational Resources Information Center
Berksteiner, Earl J.
2013-01-01
The purpose of this quantitative descriptive correlational study was to determine if associations existed between middle- and early-college (MEC) principals' leadership styles, teacher motivation, and teacher satisfaction. MEC programs were programs designed to assist high school students who were not served well in a traditional setting (Middle…
ERIC Educational Resources Information Center
Rodriguez-Falces, Javier
2013-01-01
In electrophysiology studies, it is becoming increasingly common to explain experimental observations using both descriptive methods and quantitative approaches. However, some electrophysiological phenomena, such as the generation of extracellular potentials that results from the propagation of the excitation source along the muscle fiber, are…
ERIC Educational Resources Information Center
Berksteiner, Earl J.
2013-01-01
The purpose of this quantitative descriptive correlational study was to determine if associations existed between middle- and early-college (MEC) principals' leadership styles, teacher motivation, and teacher satisfaction. MEC programs were programs designed to assist high school students who were not served well in a traditional setting (Middle…
Higher Education Teachers' Descriptions of Their Own Learning: A Quantitative Perspective
ERIC Educational Resources Information Center
Töytäri, Aija; Tynjälä, Päivi; Piirainen, Arja; Ilves, Vesa
2017-01-01
In this large-scale study, higher education teachers' (n = 1028) descriptions of their own learning are examined with quantitative analyses. The study follows up an earlier qualitative study that, using a phenomenographic approach, identified four different ways in which teachers at Finnish universities of applied sciences described their own…
ERIC Educational Resources Information Center
Rodriguez-Falces, Javier
2013-01-01
In electrophysiology studies, it is becoming increasingly common to explain experimental observations using both descriptive methods and quantitative approaches. However, some electrophysiological phenomena, such as the generation of extracellular potentials that results from the propagation of the excitation source along the muscle fiber, are…
Jaferzadeh, Keyvan; Moon, Inkyu
2015-11-01
Quantitative phase information obtained by digital holographic microscopy (DHM) can provide new insight into the functions and morphology of single red blood cells (RBCs). Since the functionality of a RBC is related to its three-dimensional (3-D) shape, quantitative 3-D geometric changes induced by storage time can help hematologists realize its optimal functionality period. We quantitatively investigate RBC 3-D geometric changes in the storage lesion using DHM. Our experimental results show that the substantial geometric transformation of the biconcave-shaped RBCs to the spherocyte occurs due to RBC storage lesion. This transformation leads to progressive loss of cell surface area, surface-to-volume ratio, and functionality of RBCs. Furthermore, our quantitative analysis shows that there are significant correlations between chemical and morphological properties of RBCs.
Harvati, Katerina
2003-04-01
The temporal bone is the location of several traits thought to differentiate Neanderthals from modern humans, including some proposed Neanderthal-derived traits. Most of these, however, are difficult to measure and are usually described qualitatively. This study applied the techniques of geometric morphometrics to the complex morphology of the temporal bone, in order to quantify the differences observed between Neanderthal and modern human anatomy. Two hundred and seventy modern human crania were measured, representing 9 populations of 30 individuals each, and spanning the extremes of the modern human geographical range. Twelve Neanderthal specimens, as well as Reilingen, Kabwe, Skhul 5, Qafzeh 9, and 4 Late Paleolithic European specimens, were included in the fossil sample. The data were collected in the form of three-dimensional (3-D) landmark coordinates, and specimen configurations were superimposed using generalized Procrustes analysis. The fitted coordinates were then analyzed by an array of multivariate statistical methods, including principal components analysis, canonical variates analysis, and Mahalanobis D(2). The temporal bone landmark analysis was very successful in separating Neanderthals from modern humans. Neanderthals were separated from modern humans in both the principal components and canonical variates analyses. They were much further in Mahalanobis distances from all modern human populations than any two modern human groups were from each other. Most of the previously described temporal bone traits contributed to this separation. Copyright 2003 Wiley-Liss, Inc.
Vicini, P; Di Nicola, S; Antonini, G; De Berardinis, E; Gentile, V; De Marco, F
2016-11-01
We present the use of a modified corporoplasty, based on geometrical principles, to determine the exact site for the incision in the tunica or plaque and the exact amount of albuginea for overlaying to correct with extreme precision the different types of congenital or acquired penile curvature due to Peyronie's disease. To describe our experience with a new surgical procedure for the enhancement of penile curvature avoiding any overcorrection or undercorrection. Between March 2004 and April 2013, a total of 74 patients underwent the geometrical modified corporoplasty. All patients had congenital curvature until 90° or acquired stable penile curvature 'less' than 60°, that made sexual intercourse very difficult or impossible, normal erectile function, absence of hourglass or hinge effect. Preoperative testing included a physical examination, 3 photographs (frontal, dorsal and lateral) of penis during erection, a 10 mcg PGE1-induced erection and Doppler ultrasound, administration of the International Index of Erectile Function (IIEF-15) questionnaire. A follow-up with postoperative evaluation at 12 weeks, 12 and 24 months, included the same preoperative testing. Satisfaction rates were better assessed with the use of validated questionnaire such as the International Erectile Dysfunction Inventory of the Treatment Satisfaction (EDITS). Statistical analysis with Student's t-test was performed using commercially available, personal computer software. A total of 25 patients had congenital penile curvature with a mean deviation of 46.8° (range 40-90), another 49 patients had Peyronie's disease with a mean deviation of 58.4 (range 45-60). No major complications were reported. Postoperative correction of the curvature was achieved in all patients (100%). Neither undercorrection nor overcorrection were recorded. No significant relapse (curvature>15°) occurred in our patients. Shortening of the penis was reported by 74% but did not influence the high overall
Nielsen, S P; Xie, X; Bärenholdt, O
2001-01-01
It is well known among clinicians that Colles fracture patients may have normal projected axial bone mineral density and that bone mass is not synonymous with bone strength. The aim of this work was to investigate whether cross-sectional properties of the distal radius in female patients with recent Colles fracture differ from those of a younger group of normal women without fracture. It was hypothesized that patients with Colles fracture had petite distal radii and that cortical thinning and reduced cortical and trabecular volumetric density are dominant features of this fracture type. We used a multilayer high-precision peripheral quantitative computed tomography (pQCT) device with a long-term precision error of 0.1% for a dedicated phantom during the measurement period (152 d). Clinical measurements were made at an ultradistal site rich in trabecular bone and a less ultradistal site rich in cortical bone. The results show that the following pQCT variables were significantly reduced in the nonfractured radius of the Colles fracture cases: mean ultradistal trabecular volumetric density, mean ultradistal and distal cortical volumetric density, mean ultradistal and distal cortical thickness (p < 0.001 for all differences). The outer cortical diameter, cross-sectional bone area, and cortical bending moment of inertia were not statistically different in the two groups. Thus, it would appear that Colles fracture cases did not have petite distal radii. The results suggest that the deforming force of Colles fracture has a transaxial direction (fall on outstretched arm), resulting in a crush fracture, and that it is not a bending force. We suggest that Colles fracture occurs as a result of the combined effect of a fall on the out-stretched arm, low trabecular and cortical volumetric bone density, and reduced cortical thickness.
Quantitative description of the morphology of the human palate by a mathematical equation.
Ferrario, V F; Sforza, C; Schmitz, J H; Colombo, A
1998-09-01
To derive a three-dimensional mathematical description of normal human hard tissue palatal size and shape. The maxillary dental casts of 30 adolescents free from respiratory problems, who had a complete (28 teeth) permanent sound dentition with normal occlusion, were studied. The x, y, z coordinates of several standardized palatal and dental landmarks were obtained with a computerized three-dimensional digitizer. Palatal landmarks were used to derive a mathematical equation of palatal shape in the frontal and sagittal planes. Palatal width, length, frontal and sagittal heights, and sagittal slope, as well as dental arch transverse and anteroposterior dimensions, were computed. Neither the size nor the shape of the palate was significantly influenced by gender. Only the intercanine distance was larger (p < .025) in males than in females. Data collected in the present investigation could represent a first database for the quantitative description of normal human palatal morphology in subjects with a complete permanent dentition.
Lee, Won-Joon; Wilkinson, Caroline M; Hwang, Hyeon-Shik; Lee, Sang-Mi
2015-05-01
Accuracy is the most important factor supporting the reliability of forensic facial reconstruction (FFR) comparing to the corresponding actual face. A number of methods have been employed to evaluate objective accuracy of FFR. Recently, it has been attempted that the degree of resemblance between computer-generated FFR and actual face is measured by geometric surface comparison method. In this study, three FFRs were produced employing live adult Korean subjects and three-dimensional computerized modeling software. The deviations of the facial surfaces between the FFR and the head scan CT of the corresponding subject were analyzed in reverse modeling software. The results were compared with those from a previous study which applied the same methodology as this study except average facial soft tissue depth dataset. Three FFRs of this study that applied updated dataset demonstrated lesser deviation errors between the facial surfaces of the FFR and corresponding subject than those from the previous study. The results proposed that appropriate average tissue depth data are important to increase quantitative accuracy of FFR.
Quantitative methods for three-dimensional comparison and petrographic description of chondrites
Friedrich, J.M.
2008-10-20
X-ray computed tomography can be used to generate three-dimensional (3D) volumetric representations of chondritic meteorites. One of the challenges of using collected X-ray tomographic data is the extraction of useful data for 3D petrographic analysis or description. Here, I examine computer-aided quantitative 3D texture metrics that can be used for the classification of chondritic meteorites. These quantitative techniques are extremely useful for discriminating between chondritic materials, but yield little information on the 3D morphology of chondrite components. To investigate the morphology of chondrite minerals such as Fe(Ni) metal and related sulfides, the homology descriptors known as Betti numbers, are examined. Both methodologies are illustrated with theoretical discussion and examples. Betti numbers may be valuable for examining the nature of metal-silicate structural changes within chondrites with increasing degrees of metamorphism.
NASA Astrophysics Data System (ADS)
Klump, J. F.; Huber, R.; Robertson, J.; Cox, S. J. D.; Woodcock, R.
2014-12-01
Despite the recent explosion of quantitative geological data, geology remains a fundamentally qualitative science. Numerical data only constitute a certain part of data collection in the geosciences. In many cases, geological observations are compiled as text into reports and annotations on drill cores, thin sections or drawings of outcrops. The observations are classified into concepts such as lithology, stratigraphy, geological structure, etc. These descriptions are semantically rich and are generally supported by more quantitative observations using geochemical analyses, XRD, hyperspectral scanning, etc, but the goal is geological semantics. In practice it has been difficult to bring the different observations together due to differing perception or granularity of classification in human observation, or the partial observation of only some characteristics using quantitative sensors. In the past years many geological classification schemas have been transferred into ontologies and vocabularies, formalized using RDF and OWL, and published through SPARQL endpoints. Several lithological ontologies were compiled by stratigraphy.net and published through a SPARQL endpoint. This work is complemented by the development of a Python API to integrate this vocabulary into Python-based text mining applications. The applications for the lithological vocabulary and Python API are automated semantic tagging of geochemical data and descriptions of drill cores, machine learning of geochemical compositions that are diagnostic for lithological classifications, and text mining for lithological concepts in reports and geological literature. This combination of applications can be used to identify anomalies in databases, where composition and lithological classification do not match. It can also be used to identify lithological concepts in the literature and infer quantitative values. The resulting semantic tagging opens new possibilities for linking these diverse sources of data.
Quantitative description of collagen fibre network on trabecular bone surfaces based on AFM imaging.
Hua, W-D; Chen, P-P; Xu, M-Q; Ao, Z; Liu, Y; Han, D; He, F
2016-04-01
The collagen fibre network is an important part of extracellular matrix (ECM) on trabecular bone surface. The geometry features of the network can provide us insights into its physical and physiological properties. However, previous researches have not focused on the geometry and the quantitative description of the collagen fibre network on trabecular bone surface. In this study,we developed a procedure to quantitatively describe the network and verified the validity of the procedure. The experiment proceeds as follow. Atomic force microscopy (AFM) was used to acquire submicron resolution images of the trabecular surface. Then, an image analysing procedure was built to extract important parameters, including, fibre orientation, fibre density, fibre width, fibre crossing numbers, the number of holes formed by fibre s, and the area of holes from AFM images. In order to verify the validity of the parameters extracted by image analysing methods, we adopted two other methods, which are statistical geometry model and computer simulation, to calculate those same parameters and check the consistency of the three methods' results. Statistical tests indicate that there is no significant difference between three groups. We conclude that, (a) the ECM on trabecular surface mainly consists of random collagen fibre network with oriented fibres; (b) our method based on image analysing can be used to characterize quantitative geometry features of the collagen fibre network effectively. This method may provide a basis for quantitative investigating the architecture and function of collagen fibre network.
Leader, J K; Robert Boston, J; Rudy, T E; Greco, C M; Zaki, H S; Henteleff, H B
2001-05-01
This study presents a quantitative description of temporomandibular joint (TMJ) sounds provided by a rule-based classification system based on sound classification by three dentists, who listened to and classified the sound recordings as no sound, click, coarse crepitus and fine crepitus. The sounds were recorded with microphones in the ear canal from 126 subjects during vertical opening, digitized at 15 000 Hz, and replayed using a computer sound card and speakers. The dentists' classification of a test set resulted in intra- and inter-tester j values ranging from 0.71 to 0.81 and 0.61-0.73, respectively. Pooled j values for the dentists and the dentists plus the rules were 0.67 and 0.58, respectively, which were not significantly different in terms of the sound features on which the rules were based (P = 0.13). Linear discriminant analysis showed the four TMJ sound types were significantly different (P < 0.001). The performance of the rules was equivalent to the dentists and marginally better than the linear discriminant functions (P = 0.08), establishing the validity of the quantitative descriptions they provide. The recording and rebroadcast methodology produced sounds very similar to those observed in the clinic and could be used to train clinicians in classifying TMJ sounds.
Wampler, Meredith A; Topp, Kimberly S; Miaskowski, Christine; Byl, Nancy N; Rugo, Hope S; Hamel, Kate
2007-08-01
To describe the postural control of women who received taxane chemotherapy for treatment of breast cancer using quantitative and clinically feasible measures. Prospective descriptive study. University-based comprehensive cancer center. Twenty women who completed taxane treatment for breast cancer and 20 healthy controls participated in this study. Not applicable. Two quantitative measures of postural control were used, Sensory Organization Test (SOT) and center of pressure (COP) velocities. Two clinically feasible measures of postural control were used, the Fullerton Advanced Balance Scale (FABS) and Timed Up & Go (TUG) test. Compared with healthy controls, women with breast cancer had poorer postural control on all of the outcome measures. FABS and TUG scores correlated moderately with SOT and COP scores. After taxane chemotherapy, women with breast cancer show significantly increased postural instability compared with matched controls. Clinically feasible measures of postural control correlated with quantitative tests. These results suggest that these clinical measures may be useful to screen patients to determine who may benefit from rehabilitation.
Ievlev, Anton V; Jesse, Stephen; Cochell, Thomas J; Unocic, Raymond R; Protopopescu, Vladimir A; Kalinin, Sergei V
2015-12-22
Recent advances in liquid cell (scanning) transmission electron microscopy (S)TEM has enabled in situ nanoscale investigations of controlled nanocrystal growth mechanisms. Here, we experimentally and quantitatively investigated the nucleation and growth mechanisms of Pt nanostructures from an aqueous solution of K2PtCl6. Averaged statistical, network, and local approaches have been used for the data analysis and the description of both collective particles dynamics and local growth features. In particular, interaction between neighboring particles has been revealed and attributed to reduction of the platinum concentration in the vicinity of the particle boundary. The local approach for solving the inverse problem showed that particles dynamics can be simulated by a stationary diffusional model. The obtained results are important for understanding nanocrystal formation and growth processes and for optimization of synthesis conditions.
Harden, J.W.
1982-01-01
A soil development index has been developed in order to quantitatively measure the degree of soil profile development. This index, which combines eight soil field properties with soil thickness, is designed from field descriptions of the Merced River chronosequence in central California. These eight properties are: clay films, texture plus wet consistence, rubification (color hue and chroma), structure, dry consistence, moist consistence, color value, and pH. Other properties described in the field can be added when more soils are studied. Most of the properties change systematically within the 3 m.y. age span of the Merced River chronosequence. The absence of properties on occasion does not significantly affect the index. Individual quantified field properties, as well as the integrated index, are examined and compared as functions of soil depth and age. ?? 1982.
NASA Astrophysics Data System (ADS)
Lüdde, H. J.; Achenbach, A.; Kalkbrenner, T.; Jankowiak, H. C.; Kirchner, T.
2016-09-01
Recently, we proposed to calculate electron removal cross sections for ion-molecule collisions in an independent atom model that accounts for geometric screening corrections. The correction coefficients are obtained from using a pixel counting method (PCM) for the exact calculation of the effective cross sectional area that emerges when the molecular cross section is pictured as a structure of (overlapping) atomic cross sections. This structure varies with the relative orientation of the molecule with respect to the projectile beam direction and, accordingly, orientation-independent total cross sections are obtained from averaging the pixel count over many orientations. In this contribution, we apply the PCM to proton collisions from amino acids and DNA and RNA nucleobases. The strength of the screening effect is analyzed by comparing the PCM results with Bragg additivity rule cross sections and with experimental data where available. Work supported by NSERC, Canada.
NASA Astrophysics Data System (ADS)
Yan, Yuan; Shan, Hangyong; Li, Min; Chen, Shu; Liu, Jianyu; Cheng, Yanfang; Ye, Cui; Yang, Zhilin; Lai, Xuandi; Hu, Jianqiang
2015-11-01
In this work, a hierarchical DNA-directed self-assembly strategy to construct structure-controlled Au nanoassemblies (NAs) has been demonstrated by conjugating Au nanoparticles (NPs) with internal-modified dithiol single-strand DNA (ssDNA) (Au-B-A or A-B-Au-B-A). It is found that the dithiol-ssDNA-modified Au NPs and molecule quantity of thiol-modified ssDNA grafted to Au NPs play critical roles in the assembly of geometrically controlled Au NAs. Through matching Au-DNA self-assembly units, geometrical structures of the Au NAs can be tailored from one-dimensional (1D) to quasi-2D and 2D. Au-B-A conjugates readily give 1D and quasi-2D Au NAs while 2D Au NAs can be formed by A-B-Au-B-A building blocks. Surface-enhanced Raman scattering (SERS) measurements and 3D finite-difference time domain (3D-FDTD) calculation results indicate that the geometrically controllable Au NAs have regular and linearly “hot spots”-number-depended SERS properties. For a certain number of NPs, the number of “hot spots” and accordingly enhancement factor of Au NAs can be quantitatively evaluated, which open a new avenue for quantitative analysis based on SERS technique.
Yan, Yuan; Shan, Hangyong; Li, Min; Chen, Shu; Liu, Jianyu; Cheng, Yanfang; Ye, Cui; Yang, Zhilin; Lai, Xuandi; Hu, Jianqiang
2015-11-19
In this work, a hierarchical DNA-directed self-assembly strategy to construct structure-controlled Au nanoassemblies (NAs) has been demonstrated by conjugating Au nanoparticles (NPs) with internal-modified dithiol single-strand DNA (ssDNA) (Au-B-A or A-B-Au-B-A). It is found that the dithiol-ssDNA-modified Au NPs and molecule quantity of thiol-modified ssDNA grafted to Au NPs play critical roles in the assembly of geometrically controlled Au NAs. Through matching Au-DNA self-assembly units, geometrical structures of the Au NAs can be tailored from one-dimensional (1D) to quasi-2D and 2D. Au-B-A conjugates readily give 1D and quasi-2D Au NAs while 2D Au NAs can be formed by A-B-Au-B-A building blocks. Surface-enhanced Raman scattering (SERS) measurements and 3D finite-difference time domain (3D-FDTD) calculation results indicate that the geometrically controllable Au NAs have regular and linearly "hot spots"-number-depended SERS properties. For a certain number of NPs, the number of "hot spots" and accordingly enhancement factor of Au NAs can be quantitatively evaluated, which open a new avenue for quantitative analysis based on SERS technique.
Yan, Yuan; Shan, Hangyong; Li, Min; Chen, Shu; Liu, Jianyu; Cheng, Yanfang; Ye, Cui; Yang, Zhilin; Lai, Xuandi; Hu, Jianqiang
2015-01-01
In this work, a hierarchical DNA–directed self–assembly strategy to construct structure–controlled Au nanoassemblies (NAs) has been demonstrated by conjugating Au nanoparticles (NPs) with internal–modified dithiol single-strand DNA (ssDNA) (Au–B–A or A–B–Au–B–A). It is found that the dithiol–ssDNA–modified Au NPs and molecule quantity of thiol–modified ssDNA grafted to Au NPs play critical roles in the assembly of geometrically controlled Au NAs. Through matching Au–DNA self–assembly units, geometrical structures of the Au NAs can be tailored from one–dimensional (1D) to quasi–2D and 2D. Au–B–A conjugates readily give 1D and quasi–2D Au NAs while 2D Au NAs can be formed by A–B–Au–B–A building blocks. Surface-enhanced Raman scattering (SERS) measurements and 3D finite–difference time domain (3D-FDTD) calculation results indicate that the geometrically controllable Au NAs have regular and linearly “hot spots”–number–depended SERS properties. For a certain number of NPs, the number of “hot spots” and accordingly enhancement factor of Au NAs can be quantitatively evaluated, which open a new avenue for quantitative analysis based on SERS technique. PMID:26581251
Quantitative Description of a Protein Fitness Landscape Based on Molecular Features
Meini, María-Rocío; Tomatis, Pablo E.; Weinreich, Daniel M.; Vila, Alejandro J.
2015-01-01
Understanding the driving forces behind protein evolution requires the ability to correlate the molecular impact of mutations with organismal fitness. To address this issue, we employ here metallo-β-lactamases as a model system, which are Zn(II) dependent enzymes that mediate antibiotic resistance. We present a study of all the possible evolutionary pathways leading to a metallo-β-lactamase variant optimized by directed evolution. By studying the activity, stability and Zn(II) binding capabilities of all mutants in the preferred evolutionary pathways, we show that this local fitness landscape is strongly conditioned by epistatic interactions arising from the pleiotropic effect of mutations in the different molecular features of the enzyme. Activity and stability assays in purified enzymes do not provide explanatory power. Instead, measurement of these molecular features in an environment resembling the native one provides an accurate description of the observed antibiotic resistance profile. We report that optimization of Zn(II) binding abilities of metallo-β-lactamases during evolution is more critical than stabilization of the protein to enhance fitness. A global analysis of these parameters allows us to connect genotype with fitness based on quantitative biochemical and biophysical parameters. PMID:25767204
Quantitative Description of a Protein Fitness Landscape Based on Molecular Features.
Meini, María-Rocío; Tomatis, Pablo E; Weinreich, Daniel M; Vila, Alejandro J
2015-07-01
Understanding the driving forces behind protein evolution requires the ability to correlate the molecular impact of mutations with organismal fitness. To address this issue, we employ here metallo-β-lactamases as a model system, which are Zn(II) dependent enzymes that mediate antibiotic resistance. We present a study of all the possible evolutionary pathways leading to a metallo-β-lactamase variant optimized by directed evolution. By studying the activity, stability and Zn(II) binding capabilities of all mutants in the preferred evolutionary pathways, we show that this local fitness landscape is strongly conditioned by epistatic interactions arising from the pleiotropic effect of mutations in the different molecular features of the enzyme. Activity and stability assays in purified enzymes do not provide explanatory power. Instead, measurement of these molecular features in an environment resembling the native one provides an accurate description of the observed antibiotic resistance profile. We report that optimization of Zn(II) binding abilities of metallo-β-lactamases during evolution is more critical than stabilization of the protein to enhance fitness. A global analysis of these parameters allows us to connect genotype with fitness based on quantitative biochemical and biophysical parameters.
Nagarajan, Mahesh B.; Coan, Paola; Huber, Markus B.; Diemoz, Paul C.; Wismüller, Axel
2015-01-01
Phase contrast X-ray computed tomography (PCI-CT) has attracted significant interest in recent years for its ability to provide significantly improved image contrast in low absorbing materials such as soft biological tissue. In the research context of cartilage imaging, previous studies have demonstrated the ability of PCI-CT to visualize structural details of human patellar cartilage matrix and capture changes to chondrocyte organization induced by osteoarthritis. This study evaluates the use of geometrical and topological features for volumetric characterization of such chondrocyte patterns in the presence (or absence) of osteoarthritic damage. Geometrical features derived from the scaling index method (SIM) and topological features derived from Minkowski Functionals were extracted from 1392 volumes of interest (VOI) annotated on PCI-CT images of ex vivo human patellar cartilage specimens. These features were subsequently used in a machine learning task with support vector regression to classify VOIs as healthy or osteoarthritic; classification performance was evaluated using the area under the receiver-operating characteristic (ROC) curve (AUC). Our results show that the classification performance of SIM-derived geometrical features (AUC: 0.90 ± 0.09) significantly outperform Minkowski Functionals volume (AUC: 0.54 ± 0.02), surface (AUC: 0.72 ± 0.06), mean breadth (AUC: 0.74 ± 0.06) and Euler characteristic (AUC: 0.78 ± 0.04) (p < 10−4). These results suggest that such geometrical features can provide a detailed characterization of the chondrocyte organization in the cartilage matrix in an automated manner, while also enabling classification of cartilage as healthy or osteoarthritic with high accuracy. Such features could potentially serve as diagnostic imaging markers for evaluating osteoarthritis progression and its response to different therapeutic intervention strategies. PMID:26142112
Toward a quantitative description of microscopic pathway heterogeneity in protein folding.
Gopi, Soundhararajan; Singh, Animesh; Suresh, Swaathiratna; Paul, Suvadip; Ranu, Sayan; Naganathan, Athi N
2017-08-09
How many structurally different microscopic routes are accessible to a protein molecule while folding? This has been a challenging question to address experimentally as single-molecule studies are constrained by the limited number of observed folding events while ensemble measurements, by definition, report only an average and not the distribution of the quantity under study. Atomistic simulations, on the other hand, are restricted by sampling and the inability to reproduce thermodynamic observables directly. We overcome these bottlenecks in the current work and provide a quantitative description of folding pathway heterogeneity by developing a comprehensive, scalable and yet experimentally consistent approach combining concepts from statistical mechanics, physical kinetics and graph theory. We quantify the folding pathway heterogeneity of five single-domain proteins under two thermodynamic conditions from an analysis of 100 000 folding events generated from a statistical mechanical model incorporating the detailed energetics from more than a million conformational states. The resulting microstate energetics predicts the results of protein engineering experiments, the thermodynamic stabilities of secondary-structure segments from NMR studies, and the end-to-end distance estimates from single-molecule force spectroscopy measurements. We find that a minimum of ∼3-200 microscopic routes, with a diverse ensemble of transition-path structures, are required to account for the total folding flux across the five proteins and the thermodynamic conditions. The partitioning of flux amongst the numerous pathways is shown to be subtly dependent on the experimental conditions that modulate protein stability, topological complexity and the structural resolution at which the folding events are observed. Our predictive methodology thus reveals the presence of rich ensembles of folding mechanisms that are generally invisible in experiments, reconciles the contradictory
Belka, Mariusz; Hewelt-Belka, Weronika; Sławiński, Jarosław; Bączek, Tomasz
2014-01-01
A set of 15 new sulphonamide derivatives, presenting antitumor activity have been subjected to a metabolic stability study. The results showed that besides products of biotransformation, some additional peaks occurred in chromatograms. Tandem mass spectrometry revealed the same mass and fragmentation pathway, suggesting that geometric isomerization occurred. Thus, to support this hypothesis, quantitative structure-retention relationships were applied. Human liver microsomes were used as an in vitro model of metabolism. The biotransformation reactions were tracked by liquid chromatography assay and additionally, fragmentation mass spectra were recorded. In silico molecular modeling at a semi-empirical level was conducted as a starting point for molecular descriptor calculations. A quantitative structure-retention relationship model was built applying multiple linear regression based on selected three-dimensional descriptors. The studied compounds revealed high metabolic stability, with a tendency to form hydroxylated biotransformation products. However, significant chemical instability in conditions simulating human body fluids was noticed. According to literature and MS data geometrical isomerization was suggested. The developed in sillico model was able to describe the relationship between the geometry of isomer pairs and their chromatographic retention properties, thus it supported the hypothesis that the observed pairs of peaks are most likely geometric isomers. However, extensive structural investigations are needed to fully identify isomers’ geometry. An effort to describe MS fragmentation pathways of novel chemical structures is often not enough to propose structures of potent metabolites and products of other chemical reactions that can be observed in compound solutions at early drug discovery studies. The results indicate that the relatively non-expensive and not time- and labor-consuming in sillico approach could be a good supportive tool assisting the
Karanovic, Tomislav; Djurakic, Marko; Eberhard, Stefan M
2016-03-01
Discovery of cryptic species using molecular tools has become common in many animal groups but it is rarely accompanied by morphological revision, creating ongoing problems in taxonomy and conservation. In copepods, cryptic species have been discovered in most groups where fast-evolving molecular markers were employed. In this study at Yeelirrie in Western Australia we investigate a subterranean species complex belonging to the harpacticoid genus Schizopera Sars, 1905, using both the barcoding mitochondrial COI gene and landmark-based two-dimensional geometric morphometrics. Integumental organs (sensilla and pores) are used as landmarks for the first time in any crustacean group. Complete congruence between DNA-based species delimitation and relative position of integumental organs in two independent morphological structures suggests the existence of three distinct evolutionary units. We describe two of them as new species, employing a condensed taxonomic format appropriate for cryptic species. We argue that many supposedly cryptic species might not be cryptic if researchers focus on analyzing morphological structures with multivariate tools that explicitly take into account geometry of the phenotype. A perceived supremacy of molecular methods in detecting cryptic species is in our view a consequence of disparity of investment and unexploited recent advancements in morphometrics among taxonomists. Our study shows that morphometric data alone could be used to find diagnostic morphological traits and gives hope to anyone studying small animals with a hard integument or shell, especially opening the door to assessing fossil diversity and rich museum collections. We expect that simultaneous use of molecular tools with geometry-oriented morphometrics may yield faster formal description of species. Decrypted species in this study are a good example for urgency of formal descriptions, as they display short-range endemism in small groundwater calcrete aquifers in a
ERIC Educational Resources Information Center
Marrus, Natasha; Faughn, Carley; Shuman, Jeremy; Petersen, Steve E.; Constantino, John N.; Povinelli, Daniel J.; Pruett, John R., Jr.
2011-01-01
Objective: Comparative studies of social responsiveness, an ability that is impaired in autism spectrum disorders, can inform our understanding of both autism and the cognitive architecture of social behavior. Because there is no existing quantitative measure of social responsiveness in chimpanzees, we generated a quantitative, cross-species…
ERIC Educational Resources Information Center
Marrus, Natasha; Faughn, Carley; Shuman, Jeremy; Petersen, Steve E.; Constantino, John N.; Povinelli, Daniel J.; Pruett, John R., Jr.
2011-01-01
Objective: Comparative studies of social responsiveness, an ability that is impaired in autism spectrum disorders, can inform our understanding of both autism and the cognitive architecture of social behavior. Because there is no existing quantitative measure of social responsiveness in chimpanzees, we generated a quantitative, cross-species…
Quantitative descriptions of generalized arousal, an elementary function of the vertebrate brain
Quinkert, Amy Wells; Vimal, Vivek; Weil, Zachary M.; Reeke, George N.; Schiff, Nicholas D.; Banavar, Jayanth R.; Pfaff, Donald W.
2011-01-01
We review a concept of the most primitive, fundamental function of the vertebrate CNS, generalized arousal (GA). Three independent lines of evidence indicate the existence of GA: statistical, genetic, and mechanistic. Here we ask, is this concept amenable to quantitative analysis? Answering in the affirmative, four quantitative approaches have proven useful: (i) factor analysis, (ii) information theory, (iii) deterministic chaos, and (iv) application of a Gaussian equation. It strikes us that, to date, not just one but at least four different quantitative approaches seem necessary for describing different aspects of scientific work on GA. PMID:21555568
ERIC Educational Resources Information Center
Brattin, Barbara C.
Content analysis was performed on the top six core journals for 1990 in library and information science to determine the extent of research in the field. Articles (n=186) were examined for descriptive or inferential statistics and separately for the presence of mathematical models. Results show a marked (14%) increase in research for 1990,…
Schnell, S; Mendoza, C
1997-02-21
The enzymological principles of the polymerase chain reaction (PCR) and of the quantitative competitive PCR (QC-PCR) are developed, proposing a theoretical framework that will facilitate quantification in experimental methodologies. It is demonstrated that the specificity of the QC-PCR, i.e. the ratio of the target initial velocity to that of the competitor template, remains constant not only during a particular amplification but also for increasing initial competitor concentrations. Linear fitting procedures are thus recommended that will enable a quantitative estimate of the initial target concentration. Finally, expressions for the efficiency of the PCR and QC-PCR are derived that are in agreement with previous experimental inferences.
A classification based framework for quantitative description of large-scale microarray data
Sangurdekar, Dipen P; Srienc, Friedrich; Khodursky, Arkady B
2006-01-01
Genome-wide surveys of transcription depend on gene classifications for the purpose of data interpretation. We propose a new information-theoretical-based method to: assess significance of co-expression within any gene group; quantitatively describe condition-specific gene-class activity; and systematically evaluate conditions in terms of gene-class activity. We applied this technique to describe microarray data tracking Escherichia coli transcriptional responses to more than 30 chemical and physiological perturbations. We correlated the nature and breadth of the responses with the nature of perturbation, identified gene group proxies for the perturbation classes and quantitatively compared closely related physiological conditions. PMID:16626502
A quantitative description of the Na-K-2Cl cotransporter and its conformity to experimental data.
Benjamin, B A; Johnson, E A
1997-09-01
In epithelia, the Na-K-2Cl cotransporter cooperates with other transport mechanisms to produce transepithelial NaCl transport. The reaction cycle for the Na-K-2Cl cotransporter has been established experimentally, but whether it accounts, quantitatively, for experimental findings has yet to be established. The differential equations that describe the reaction cycle were formulated, and the steady-state solutions were obtained by digital computation. Conformity between this description and the experimental data obtained from the literature was explored by automatic searches for the sets of rate constants that yielded statistical best-fits to the experimental data. Fits were obtained from renal epithelial cell lines, HeLa cells, and duck erythrocytes. Results show that the reaction cycle for the Na-K-2Cl cotransporter conforms well, quantitatively, with the experimental data.
Microscope-Quantitative Luminescence Imaging System (M-Qlis) Description and User's Manual
Stahl, K. A.
1991-10-01
A Microscope Quantitative Luminescence Imaging System (M-QLIS} has been designed and constructed. The M-QLIS is designed for use in studies of chemiluminescent phenomena associated with absorption of radio-frequency radiation. The system consists of a radio-frequency waveguide/sample holder, microscope, intensified video camera, radiometric calibration source and optics, and computer-based image processor with radiometric analysis software. The system operation, hardware, software, and radiometric procedures are described.
Puri, Ritika; Khamrui, Kaushik; Khetra, Yogesh; Malhotra, Ravinder; Devraja, H C
2016-02-01
Promising development and expansion in the market of cham-cham, a traditional Indian dairy product is expected in the coming future with the organized production of this milk product by some large dairies. The objective of this study was to document the extent of variation in sensory properties of market samples of cham-cham collected from four different locations known for their excellence in cham-cham production and to find out the attributes that govern much of variation in sensory scores of this product using quantitative descriptive analysis (QDA) and principal component analysis (PCA). QDA revealed significant (p < 0.05) difference in sensory attributes of cham-cham among the market samples. PCA identified four significant principal components that accounted for 72.4 % of the variation in the sensory data. Factor scores of each of the four principal components which primarily correspond to sweetness/shape/dryness of interior, surface appearance/surface dryness, rancid and firmness attributes specify the location of each market sample along each of the axes in 3-D graphs. These findings demonstrate the utility of quantitative descriptive analysis for identifying and measuring attributes of cham-cham that contribute most to its sensory acceptability.
Marrus, Natasha; Faughn, Carley; Shuman, Jeremy; Petersen, Steve; Constantino, John; Povinelli, Daniel; Pruett, John R.
2011-01-01
Objective Comparative studies of social responsiveness, an ability that is impaired in autistic spectrum disorders, can inform our understanding of both autism and the cognitive architecture of social behavior. Because there is no existing quantitative measure of social responsiveness in chimpanzees, we generated a quantitative, cross-species (human-chimpanzee) social responsiveness measure. Method We translated the Social Responsiveness Scale (SRS), an instrument that quantifies human social responsiveness, into an analogous instrument for chimpanzees. We then retranslated this "Chimp SRS" into a human "Cross-Species SRS" (XSRS). We evaluated three groups of chimpanzees (n=29) with the Chimp SRS and typical and autistic spectrum disorder (ASD) human children (n=20) with the XSRS. Results The Chimp SRS demonstrated strong inter-rater reliability at the three sites (ranges for individual ICCs: .534–.866 and mean ICCs: .851–.970). As has been observed in humans, exploratory principal components analysis of Chimp SRS scores supports a single factor underlying chimpanzee social responsiveness. Human subjects' XSRS scores were fully concordant with their SRS scores (r=.976, p=.001) and distinguished appropriately between typical and ASD subjects. One chimpanzee known for inappropriate social behavior displayed a significantly higher score than all other chimpanzees at its site, demonstrating the scale's ability to detect impaired social responsiveness in chimpanzees. Conclusion Our initial cross-species social responsiveness scale proved reliable and discriminated differences in social responsiveness across (in a relative sense) and within (in a more objectively quantifiable manner) humans and chimpanzees. PMID:21515200
Hsuan, Chin-Feng; Yu, Hsi-Yu; Tseng, Wei-Kung; Lin, Lung-Chun; Hsu, Kwan-Lih; Wu, Chau-Chung
2013-05-01
Ischemic mitral regurgitation (IMR) is common in ischemic heart disease and results in poor prognosis. However, the exact mechanism of IMR has not been fully elucidated. Quantitation of the mitral tetrahedron using three-dimentianl (3D) echocardiography is capable of evaluating the geometric determinants and mechanisms of IMR. Forty patients with a history of ST-elevation myocardial infarction at least 6 months earlier were studied. Parameters of mitral deformation and global left ventricular (LV) function and shape were evaluated by 2-dimensional echocardiography. The effective regurgitant orifice (ERO) of IMR was obtained by the quantitative continuous-wave Doppler technique. Three-dimensional (3D) echocardiography was applied to assess the mitral tetrahedron. Mitral valvular tenting area (P < 0.001), mitral annular area (P = 0.032), dilation of the LV in diastole, impairment of the LV ejection fraction, and volume of the spherically shaped LV in systole were greater in patients with an ERO ≥20 mm(2) than in those with an ERO <20 mm(2). In the mitral tetrahedron, only the interpapillary muscle roots distance showed a significant difference (P = 0.004). Multivariate analysis with the logistic regression model showed the systolic mitral tenting area (odds ratio [OR]: 280.49, 95% confidence interval [CI]: 4.59-1.72 × 10(4), P = 0.007) and interpapillary muscle distance (OR: 1.50, 95% CI: 1.03-2.19, P = 0.036) to be independent factors in predicting significant IMR (ERO ≥20 mm(2)). 3D echocardiography can be effectively applied in measuring the mitral tetrahedron and evaluating the mechanism of IMR. Mitral valvular tenting and interpapillary muscle distance are 2 independent factors of significant IMR. © 2013 Wiley Periodicals, Inc.
Zhang, Shuxing; Golbraikh, Alexander; Tropsha, Alexander
2009-01-01
Novel geometrical chemical descriptors have been derived based on the computational geometry of protein-ligand interfaces and Pauling atomic electronegativities (EN). Delaunay tessellation has been applied to a diverse set of 517 X-ray characterized protein-ligand complexes yielding a unique collection of interfacial nearest neighbor atomic quadruplets for each complex. Each quadruplet composition was characterized by a single descriptor calculated as the sum of the EN values for the four participating atom types. We termed these simple descriptors generated from atomic EN values and derived with the Delaunay Tessellation the ENTess descriptors and used them in the variable selection k-Nearest Neighbor quantitative structure-binding affinity relationship (QSBR) studies of 264 diverse protein-ligand complexes with known binding constants. 24 complexes with chemically dissimilar ligands were set aside as an independent validation set, and the remaining dataset of 240 complexes was divided into multiple training and test sets. The best models were characterized by the leave-one-out cross-validated correlation coefficient q2 as high as 0.66 for the training set and the correlation coefficient R2 as high as 0.83 for the test set. High predictive power of these models was confirmed independently by applying them to the validation set of 24 complexes yielding R2 as high as 0.85. We conclude that QSBR models built with the ENTess descriptors can be instrumental for predicting the binding affinity of receptor-ligand complexes. PMID:16640331
Quantitative description of ion transport via plasma membrane of yeast and small cells
Volkov, Vadim
2015-01-01
Modeling of ion transport via plasma membrane needs identification and quantitative understanding of the involved processes. Brief characterization of main ion transport systems of a yeast cell (Pma1, Ena1, TOK1, Nha1, Trk1, Trk2, non-selective cation conductance) and determining the exact number of molecules of each transporter per a typical cell allow us to predict the corresponding ion flows. In this review a comparison of ion transport in small yeast cell and several animal cell types is provided. The importance of cell volume to surface ratio is emphasized. The role of cell wall and lipid rafts is discussed in respect to required increase in spatial and temporary resolution of measurements. Conclusions are formulated to describe specific features of ion transport in a yeast cell. Potential directions of future research are outlined based on the assumptions. PMID:26113853
Quantitative description of ion transport via plasma membrane of yeast and small cells.
Volkov, Vadim
2015-01-01
Modeling of ion transport via plasma membrane needs identification and quantitative understanding of the involved processes. Brief characterization of main ion transport systems of a yeast cell (Pma1, Ena1, TOK1, Nha1, Trk1, Trk2, non-selective cation conductance) and determining the exact number of molecules of each transporter per a typical cell allow us to predict the corresponding ion flows. In this review a comparison of ion transport in small yeast cell and several animal cell types is provided. The importance of cell volume to surface ratio is emphasized. The role of cell wall and lipid rafts is discussed in respect to required increase in spatial and temporary resolution of measurements. Conclusions are formulated to describe specific features of ion transport in a yeast cell. Potential directions of future research are outlined based on the assumptions.
Marrus, Natasha; Faughn, Carley; Shuman, Jeremy; Petersen, Steve E; Constantino, John N; Povinelli, Daniel J; Pruett, John R
2011-05-01
Comparative studies of social responsiveness, an ability that is impaired in autism spectrum disorders, can inform our understanding of both autism and the cognitive architecture of social behavior. Because there is no existing quantitative measure of social responsiveness in chimpanzees, we generated a quantitative, cross-species (human-chimpanzee) social responsiveness measure. We translated the Social Responsiveness Scale (SRS), an instrument that quantifies human social responsiveness, into an analogous instrument for chimpanzees. We then retranslated this "Chimpanzee SRS" into a human "Cross-Species SRS" (XSRS). We evaluated three groups of chimpanzees (n = 29) with the Chimpanzee SRS and typical and human children with autism spectrum disorder (ASD; n = 20) with the XSRS. The Chimpanzee SRS demonstrated strong interrater reliability at the three sites (ranges for individual ICCs: 0.534 to 0.866; mean ICCs: 0.851 to 0.970). As has been observed in human beings, exploratory principal components analysis of Chimpanzee SRS scores supports a single factor underlying chimpanzee social responsiveness. Human subjects' XSRS scores were fully concordant with their SRS scores (r = 0.976, p = .001) and distinguished appropriately between typical and ASD subjects. One chimpanzee known for inappropriate social behavior displayed a significantly higher score than all other chimpanzees at its site, demonstrating the scale's ability to detect impaired social responsiveness in chimpanzees. Our initial cross-species social responsiveness scale proved reliable and discriminated differences in social responsiveness across (in a relative sense) and within (in a more objectively quantifiable manner) human beings and chimpanzees. Copyright © 2011 American Academy of Child and Adolescent Psychiatry. Published by Elsevier Inc. All rights reserved.
A geometrical model for the description of the AlN shell morphology in GaN-AlN core-shell nanowires
NASA Astrophysics Data System (ADS)
Hestroffer, Karine; Daudin, Bruno
2013-12-01
A geometrical model based on the one formulated by Foxon et al. [J. Cryst. Growth 311, 3423 (2009)] is developed to describe the morphology of AlN shells in GaN-AlN core-shell nanowires grown by plasma-assisted molecular beam epitaxy. The shell aspect ratio is studied as a function of the atomic beam flux incidence angles and of the ratio between Al and N species. The comparison between experimental data and the developed geometrical model suggests the diffusion of about 55% of Al atoms from the side walls to the top surface.
2004-01-01
A detailed study has been carried out on the dependence of folate binding on the concentration of FBP (folate-binding protein) at pH 5.0, conditions selected to prevent complications arising from the pre-existing self-association of the acceptor. In contrast with the mandatory requirement that reversible interaction of ligand with a single acceptor site should exhibit a unique, rectangular hyperbolic binding curve, results obtained by ultrafiltration for the FBP–folate system required description in terms of (i) a sigmoidal relationship between concentrations of bound and free folate and (ii) an inverse dependence of affinity on FBP concentration. These findings have been attributed to the difficulties in determining the free ligand concentration in the FBP–folate mixtures for which reaction is essentially stoichiometric. This explanation also accounts for the similar published behaviour of the FBP–folate system at neutral pH, which had been attributed erroneously to acceptor self-association, a phenomenon incompatible with the experimental findings because of its prediction of a greater affinity for folate with increasing FBP concentration. PMID:15142039
Levels of Geometric Understanding.
ERIC Educational Resources Information Center
Pegg, John; Davey, Geoff
1991-01-01
Three activities are presented to assess the level of students' geometric understanding according to van Hiele learning model. The activities--Descriptions, Minimum Properties, and Class Inclusion--are applied to the example of classifying quadrilaterals as squares, rectangles, rhombi, or parallelograms. Implications of this assessment are…
Li, X; Shiota, T; Delabays, A; Teien, D; Zhou, X; Sinclair, B; Pandian, N G; Sahn, D J
1999-12-01
This study was designed to develop and test a 3-dimensional method for direct measurement of flow convergence (FC) region surface area and for quantitating regurgitant flows with an in vitro flow system. Quantitative methods for characterizing regurgitant flow events such as flow convergence with 2-dimensional color flow Doppler imaging systems have yielded variable results and may not be accurate enough to characterize those more complex spatial events. Four differently shaped regurgitant orifices were studied: 3 flat orifices (circular, rectangular, triangular) and a nonflat one mimicking mitral valve prolapse (all 4 orifice areas = 0.24 cm(2)) in a pulsatile flow model at 8 to 9 different regurgitant flow rates (10 to 50 mL/beat). An ultrasonic flow probe and meter were connected to the flow model to provide reference flow data. Video composite data from the color Doppler flow images of the FC were reconstructed after computer-controlled 180 degrees rotational acquisition was performed. FC surface area (S cm(2)) was calculated directly without any geometric assumptions by measuring parallel sliced flow convergence arc lengths through the FC volume and multiplying each by the slice thickness (2.5 to 3.2 mm) over 5 to 8 slices and then adding them together. Peak regurgitant flow rate (milliliters per second) was calculated as the product of 3-dimensional determined S (cm(2)) multiplied by the aliasing velocity (centimeters per second) used for color Doppler imaging. For all of the 4 shaped orifices, there was an excellent relationship between actual peak flow rates and 3-dimensional FC-calculated flow rates with the direct measurement of the surface area of FC (r = 0.99, mean difference = -7.2 to -0.81 mL/s, % difference = -5% to 0%), whereas a hemielliptic method implemented with 3 axial measurements of the flow convergence zone from 2-dimensional planes underestimated actual flow rate by mean difference = -39.8 to -18.2 mL/s, % difference = -32% to -17% for any
NASA Astrophysics Data System (ADS)
Kreisel, A.; Nelson, R.; Berlijn, T.; Ku, W.; Aluru, Ramakrishna; Chi, Shun; Zhou, Haibiao; Singh, Udai Raj; Wahl, Peter; Liang, Ruixing; Hardy, Walter N.; Bonn, D. A.; Hirschfeld, P. J.; Andersen, Brian M.
2016-12-01
Since the discovery of iron-based superconductors, a number of theories have been put forward to explain the qualitative origin of pairing, but there have been few attempts to make quantitative, material-specific comparisons to experimental results. The spin-fluctuation theory of electronic pairing, based on first-principles electronic structure calculations, makes predictions for the superconducting gap. Within the same framework, the surface wave functions may also be calculated, allowing, e.g., for detailed comparisons between theoretical results and measured scanning tunneling topographs and spectra. Here we present such a comparison between theory and experiment on the Fe-based superconductor LiFeAs. Results for the homogeneous surface as well as impurity states are presented as a benchmark test of the theory. For the homogeneous system, we argue that the maxima of topographic image intensity may be located at positions above either the As or Li atoms, depending on tip height and the setpoint current of the measurement. We further report the experimental observation of transitions between As- and Li-registered lattices as functions of both tip height and setpoint bias, in agreement with this prediction. Next, we give a detailed comparison between the simulated scanning tunneling microscopy images of transition-metal defects with experiment. Finally, we discuss possible extensions of the current framework to obtain a theory with true predictive power for scanning tunneling microscopy in Fe-based systems.
Quantitative description for the growth rate of self-induced GaN nanowires
NASA Astrophysics Data System (ADS)
Consonni, V.; Dubrovskii, V. G.; Trampert, A.; Geelhaar, L.; Riechert, H.
2012-04-01
We determine with high precision the growth rate of self-induced GaN nanowires grown by molecular beam epitaxy under various conditions from scanning electron micrographs by taking into account in situ measurements of the initial incubation time, which is needed before the nanowire growth starts. In order to quantitatively describe the dependence of the growth rate on growth time, gallium flux, and growth temperature, we develop a detailed theoretical model of diffusion-induced nanowire growth specifically for the self-induced approach, i.e., without any droplet at the nanowire top. The theoretical fits are in excellent agreement with the experimental data and allow us to deduce important kinetic parameters of the self-induced GaN nanowire growth. The gallium adatom effective diffusion length on the nanowire sidewalls composed of m-plane facets is only 45 nm, which is consistent with our experimental finding that the growth rate initially decreases drastically as the contribution from the adatoms on the planar substrate surface rapidly vanishes. In contrast, the gallium adatom effective diffusion length on the amorphous silicon nitride substrate surface reaches about 100 nm. Furthermore, the nucleation energy on the nanowire sidewalls is found to be 5.44 eV and is larger than on their top facet accounting for the nanowire elongation.
Genome evolution and speciation: toward quantitative descriptions of pattern and process.
Nosil, Patrik; Feder, Jeffrey L
2013-09-01
Studies of patterns of differentiation across genomes are accumulating, yet integrative work that combines approaches and fully capitalizes on new technologies to test explicit hypotheses is still rare. Thus, debates persist about the rate, magnitude, and causes of genomic change. This special section is devoted to helping resolve these debates. The eight studies contained within demonstrate how we can begin to move away from vague metaphors toward quantitative and more precise descriptors of patterns of genetic architecture and divergence. However, a particular genomic pattern can often arise via different combinations of various processes such as selection, gene flow, recombination, mutation, genetic drift, and demographic variability. Thus, substantial challenges remain in elucidating which evolutionary processes generated observed genomic patterns. Nonetheless, the studies in this section demonstrate ways forward toward bridging pattern and process, including experimental work, genetic mapping, increased knowledge of natural history and demography, and comparative studies spanning taxa at different points in the speciation continuum. Such collective work will lead to more powerful hypothesis testing. Future work can also help better integrate the contributions of ecology, genome structure (e.g., inversions and translocations), and genetic conflict to genome evolution. © 2013 The Author(s). Evolution © 2013 The Society for the Study of Evolution.
Kreisel, A.; Nelson, R.; Berlijn, T.; Ku, W.; Aluru, Ramakrishna; Chi, Shun; Zhou, Haibiao; Singh, Udai Raj; Wahl, Peter; Liang, Ruixing; Hardy, Walter N.; Bonn, D. A.; Hirschfeld, P. J.; Andersen, Brian M.
2016-12-27
Since the discovery of iron-based superconductors, a number of theories have been put forward to explain the qualitative origin of pairing, but there have been few attempts to make quantitative, material-specific comparisons to experimental results. The spin-fluctuation theory of electronic pairing, based on first-principles electronic structure calculations, makes predictions for the superconducting gap. Within the same framework, the surface wave functions may also be calculated, allowing, e.g., for detailed comparisons between theoretical results and measured scanning tunneling topographs and spectra. We present such a comparison between theory and experiment on the Fe-based superconductor LiFeAs. Our results for the homogeneous surface as well as impurity states are presented as a benchmark test of the theory. For the homogeneous system, we argue that the maxima of topographic image intensity may be located at positions above either the As or Li atoms, depending on tip height and the setpoint current of the measurement. We further report the experimental observation of transitions between As- and Li-registered lattices as functions of both tip height and setpoint bias, in agreement with this prediction. Next, we give a detailed comparison between the simulated scanning tunneling microscopy images of transition-metal defects with experiment. Finally, we discuss possible extensions of the current framework to obtain a theory with true predictive power for scanning tunneling microscopy in Fe-based systems.
Kreisel, A.; Nelson, R.; Berlijn, T.; ...
2016-12-27
Since the discovery of iron-based superconductors, a number of theories have been put forward to explain the qualitative origin of pairing, but there have been few attempts to make quantitative, material-specific comparisons to experimental results. The spin-fluctuation theory of electronic pairing, based on first-principles electronic structure calculations, makes predictions for the superconducting gap. Within the same framework, the surface wave functions may also be calculated, allowing, e.g., for detailed comparisons between theoretical results and measured scanning tunneling topographs and spectra. We present such a comparison between theory and experiment on the Fe-based superconductor LiFeAs. Our results for the homogeneous surfacemore » as well as impurity states are presented as a benchmark test of the theory. For the homogeneous system, we argue that the maxima of topographic image intensity may be located at positions above either the As or Li atoms, depending on tip height and the setpoint current of the measurement. We further report the experimental observation of transitions between As- and Li-registered lattices as functions of both tip height and setpoint bias, in agreement with this prediction. Next, we give a detailed comparison between the simulated scanning tunneling microscopy images of transition-metal defects with experiment. Finally, we discuss possible extensions of the current framework to obtain a theory with true predictive power for scanning tunneling microscopy in Fe-based systems.« less
Quantitative description of fluid flows produced by left-right cilia in zebrafish.
Fox, Craig; Manning, M Lisa; Amack, Jeffrey D
2015-01-01
Motile cilia generate directional flows that move mucus through airways, cerebrospinal fluid through brain ventricles, and oocytes through fallopian tubes. In addition, specialized monocilia beat in a rotational pattern to create asymmetric flows that are involved in establishing the left-right (LR) body axis during embryogenesis. These monocilia, which we refer to as "left-right cilia," produce a leftward flow of extraembryonic fluid in a transient "organ of asymmetry" that directs asymmetric signaling and development of LR asymmetries in the cardiovascular system and gastrointestinal tract. The asymmetric flows are thought to establish a chemical gradient and/or activate mechanosensitive cilia to initiate calcium ion signals and a conserved Nodal (TGFβ) pathway on the left side of the embryo, but the mechanisms underlying this process remain unclear. The zebrafish organ of asymmetry, called Kupffer's vesicle, provides a useful model system for investigating LR cilia and cilia-powered fluid flows. Here, we describe methods to visualize flows in Kupffer's vesicle using fluorescent microspheres and introduce a new and freely available MATLAB particle tracking code to quantitatively describe these flows. Analysis of normal and aberrant flows indicates this approach is useful for characterizing flow properties that impact LR asymmetry and may be more broadly applicable for quantifying other cilia flows.
Kreisel, A.; Nelson, R.; Berlijn, T.; Ku, W.; Aluru, Ramakrishna; Chi, Shun; Zhou, Haibiao; Singh, Udai Raj; Wahl, Peter; Liang, Ruixing; Hardy, Walter N.; Bonn, D. A.; Hirschfeld, P. J.; Andersen, Brian M.
2016-12-27
Since the discovery of iron-based superconductors, a number of theories have been put forward to explain the qualitative origin of pairing, but there have been few attempts to make quantitative, material-specific comparisons to experimental results. The spin-fluctuation theory of electronic pairing, based on first-principles electronic structure calculations, makes predictions for the superconducting gap. Within the same framework, the surface wave functions may also be calculated, allowing, e.g., for detailed comparisons between theoretical results and measured scanning tunneling topographs and spectra. We present such a comparison between theory and experiment on the Fe-based superconductor LiFeAs. Results for the homogeneous surface as well as impurity states are presented as a benchmark test of the theory. For the homogeneous system, we argue that the maxima of topographic image intensity may be located at positions above either the As or Li atoms, depending on tip height and the setpoint current of the measurement. Furthermore, we report the experimental observation of transitions between As- and Li-registered lattices as functions of both tip height and setpoint bias, in agreement with this prediction. Then, we give a detailed comparison between the simulated scanning tunneling microscopy images of transition-metal defects with experiment. Finally, we discuss possible extensions of the current framework to obtain a theory with true predictive power for scanning tunneling microscopy in Fe-based systems.
Kreisel, A.; Nelson, R.; Berlijn, T.; ...
2016-12-27
Since the discovery of iron-based superconductors, a number of theories have been put forward to explain the qualitative origin of pairing, but there have been few attempts to make quantitative, material-specific comparisons to experimental results. The spin-fluctuation theory of electronic pairing, based on first-principles electronic structure calculations, makes predictions for the superconducting gap. Within the same framework, the surface wave functions may also be calculated, allowing, e.g., for detailed comparisons between theoretical results and measured scanning tunneling topographs and spectra. We present such a comparison between theory and experiment on the Fe-based superconductor LiFeAs. Results for the homogeneous surface asmore » well as impurity states are presented as a benchmark test of the theory. For the homogeneous system, we argue that the maxima of topographic image intensity may be located at positions above either the As or Li atoms, depending on tip height and the setpoint current of the measurement. Furthermore, we report the experimental observation of transitions between As- and Li-registered lattices as functions of both tip height and setpoint bias, in agreement with this prediction. Then, we give a detailed comparison between the simulated scanning tunneling microscopy images of transition-metal defects with experiment. Finally, we discuss possible extensions of the current framework to obtain a theory with true predictive power for scanning tunneling microscopy in Fe-based systems.« less
A quantitative description of QX222 blockade of sodium channels in squid axons.
Starmer, C. F.; Yeh, J. Z.; Tanguy, J.
1986-01-01
The interaction of QX222, a quaternary ammonium derivative of lidocaine, with the Na channel was studied in internally perfused squid axons under voltage-clamped conditions. A use-dependent block was observed in response to repetitive depolarizing pulses. The time constant for block development and the steady state level of the block were increased with increasing frequency of stimulation from 0.1 to 10 Hz. Use-dependent block can be viewed as a net increase in the drug incorporation into Na channels with successive pulses. That is, net drug uptake by Na channels occurs during the depolarizing phase and net drug release occurs during the interpulse interval. The observed uptake rate of use-dependent block is shown to be a linear combination of the uptake rates associated with the depolarizing and resting potentials. Also, the steady state fraction of blocked channels is shown to be a linear combination of the state-dependent blockade equilibria. Drug-channel interactions are assumed to be dependent on gated control of the diffusion path between drug pool and the interior channel binding site. Drug ingress to the binding site can be inhibited by the channel gates (receptor guarding), while drug bound to the channel may become trapped by closure of the channel gates (trapping). On the basis of these assumptions, a simple procedure is proposed for estimating apparent rate constants governing the drug-channel binding reactions for two cases of channel blockade. The estimated forward (k) and backward (1) rate constants are: 2.45 x I05 M-1 s- and 0.23 x 103 s-1, respectively, for k and I for the case when the drug is trapped by both activation and inactivation gates, and 3.58 x 105 M-l s-l and 4.15 x 10-3 S-l for the case when the drug is not trapped. While these two schemes make a similar prediction with respect to the resulting uptake rates, their prediction of the steady state level of block differs. The observed steady state level of block could quantitatively be
Place, Benjamin J; Morris, Mallory J; Phillips, Melissa M; Sander, Lane C; Rimmer, Catherine A
2014-11-14
Comprehensive, two-dimensional liquid chromatography (LC × LC) is a powerful technique for the separation of complex mixtures. Most studies using LC × LC are focused on qualitative efforts, such as increasing peak capacity. The present study examined the use of LC × LC-UV/vis for the separation and quantitation of polycyclic aromatic hydrocarbons (PAHs). More specifically, this study evaluated the impact of different peak integration approaches on the quantitative performance of the LC × LC method. For well-resolved three-dimensional peaks, parameters such as baseline definition, peak base shape, and peak width determination did not have a significant impact on accuracy and precision. For less-resolved peaks, a dropped baseline and the summation of all slices in the peak improved the accuracy and precision of the integration methods. The computational approaches to three-dimensional peak integration are provided, including fully descriptive, select slice, and summed heights integration methods, each with its own strengths and weaknesses. Overall, the integration methods presented quantify each of the PAHs within acceptable precision and accuracy ranges and have comparable performance to that of single dimension liquid chromatography.
NASA Astrophysics Data System (ADS)
Wendler, F.; Blum, P.; Thaler, H.; Nestler, B.; Okamoto, A.
2013-12-01
conducted in the limit of low Damköhler numbers explain the observed transition regime in competitive crystal growth for blocky-elongate veins. A mechanism for the initial formation of quartz needles is proposed. For virtual fractured rock samples we study the influence of fracture shape and opening aperture in the evolution of syntaxial (blocky-elongated vs. stretched) veins. In the case of calcite, the chemical variability of the growth process in real systems strongly influences the crystal growth kinetics and limits the significance of quantitative predictions. On the basis of the numerical studies and known parameter uncertainties, we give an assessment of the variabilities of sealing times and vein microstructures. References: F. Wendler, C. Mennerich and B. Nestler, J. Cryst. Growth 327 (2011), 189-201. A. Okamoto and K. Sekine, J. Struct. Geol. 33 (2011) 1764-1775. Three time steps in the sealing of a flat fracture with calcite, only liquid phase evolution is shown.
Wang, Youwei; Zhang, Wenqing; Chen, Lidong; Shi, Siqi; Liu, Jianjun
2017-01-01
Abstract Li-ion batteries are a key technology for addressing the global challenge of clean renewable energy and environment pollution. Their contemporary applications, for portable electronic devices, electric vehicles, and large-scale power grids, stimulate the development of high-performance battery materials with high energy density, high power, good safety, and long lifetime. High-throughput calculations provide a practical strategy to discover new battery materials and optimize currently known material performances. Most cathode materials screened by the previous high-throughput calculations cannot meet the requirement of practical applications because only capacity, voltage and volume change of bulk were considered. It is important to include more structure–property relationships, such as point defects, surface and interface, doping and metal-mixture and nanosize effects, in high-throughput calculations. In this review, we established quantitative description of structure–property relationships in Li-ion battery materials by the intrinsic bulk parameters, which can be applied in future high-throughput calculations to screen Li-ion battery materials. Based on these parameterized structure–property relationships, a possible high-throughput computational screening flow path is proposed to obtain high-performance battery materials. PMID:28458737
Wang, Youwei; Zhang, Wenqing; Chen, Lidong; Shi, Siqi; Liu, Jianjun
2017-01-01
Li-ion batteries are a key technology for addressing the global challenge of clean renewable energy and environment pollution. Their contemporary applications, for portable electronic devices, electric vehicles, and large-scale power grids, stimulate the development of high-performance battery materials with high energy density, high power, good safety, and long lifetime. High-throughput calculations provide a practical strategy to discover new battery materials and optimize currently known material performances. Most cathode materials screened by the previous high-throughput calculations cannot meet the requirement of practical applications because only capacity, voltage and volume change of bulk were considered. It is important to include more structure-property relationships, such as point defects, surface and interface, doping and metal-mixture and nanosize effects, in high-throughput calculations. In this review, we established quantitative description of structure-property relationships in Li-ion battery materials by the intrinsic bulk parameters, which can be applied in future high-throughput calculations to screen Li-ion battery materials. Based on these parameterized structure-property relationships, a possible high-throughput computational screening flow path is proposed to obtain high-performance battery materials.
da Silva, Paula Porrelli Moreira; Casemiro, Renata Cristina; Zillo, Rafaela Rebessi; de Camargo, Adriano Costa; Prospero, Evanilda Teresinha Perissinotto; Spoto, Marta Helena Fillet
2014-01-01
This study evaluated the effect of pasteurization followed by storage under different conditions on the sensory attributes of frozen juçara pulp using quantitative descriptive analysis (QDA). Pasteurization of packed frozen pulp was performed by its immersion in stainless steel tank containing water (80°C) for 5 min, followed by storage under refrigerated and frozen conditions. A trained sensory panel evaluated the samples (6°C) on day 1, 15, 30, 45, 60, 75, and 90. Sensory attributes were separated as follows: appearance (foamy, heterogeneous, purple, brown, oily, and creamy), aroma (sweet and fermented), taste (astringent, bitter, and sweet), and texture (oily and consistent), and compared to a reference material. In general, unpasteurized frozen pulp showed the highest score for foamy appearance, and pasteurized samples showed highest scores to creamy appearance. Pasteurized samples remained stable regarding brown color development while unpasteurized counterparts presented increase. Color is an important attribute related to the product identity. All attributes related to taste and texture remained constant during storage for all samples. Pasteurization followed by storage under frozen conditions has shown to be the best conservation method as samples submitted to such process received the best sensory evaluation, described as foamy, slightly heterogeneous, slightly bitter, and slightly astringent. PMID:25473489
Windhager, Elmar; Thaler, Katharina; Selberis-Vahl, Wilia Vasiliki; Friedl-Wörgetter, Petra; Windhager, Isabella; Zauner, Katharina
2015-01-01
The integration of psychiatric departments in general hospitals lead to an increasing demand of psychiatric consultation, which often overstrains personnel resources of short staffed psychiatric services. To provide consulting service, as it is demanded by guidelines, a multidisciplinary consulting team could be a possible solution. A retrospective descriptive analysis of all consultations made by the psychosocial consultation and liaison service at the general hospital Wels-Grieskirchen in the years 2012 and 2013. There was an increase in referrals overall of 22 % from 2012 to 2013. The largest increase was observed in the group of psychiatrists, who carried out 33.1 % of all consultations. Most consultations, 39.5 %, were done by the group of clinical psychologists, partly substituting medical attendance. Taking together both occupational groups, the expected number of consultations of at least 3 % of all admissions could be achieved. A multidisciplinary consulting team consisting of psychiatrists, psychologists, psychosomatic physicians and social workers staffed with 5.11-6.79 full-time personnel is able to provide psychosocial consultation service at a quantitative level required by international guidelines.
NASA Astrophysics Data System (ADS)
Talman, Richard
1999-10-01
Mechanics for the nonmathematician-a modern approach For physicists, mechanics is quite obviously geometric, yet the classical approach typically emphasizes abstract, mathematical formalism. Setting out to make mechanics both accessible and interesting for nonmathematicians, Richard Talman uses geometric methods to reveal qualitative aspects of the theory. He introduces concepts from differential geometry, differential forms, and tensor analysis, then applies them to areas of classical mechanics as well as other areas of physics, including optics, crystal diffraction, electromagnetism, relativity, and quantum mechanics. For easy reference, Dr. Talman treats separately Lagrangian, Hamiltonian, and Newtonian mechanics-exploring their geometric structure through vector fields, symplectic geometry, and gauge invariance respectively. Practical perturbative methods of approximation are also developed. Geometric Mechanics features illustrative examples and assumes only basic knowledge of Lagrangian mechanics. Of related interest . . . APPLIED DYNAMICS With Applications to Multibody and Mechatronic Systems Francis C. Moon A contemporary look at dynamics at an intermediate level, including nonlinear and chaotic dynamics. 1998 (0-471-13828-2) 504 pp. MATHEMATICAL PHYSICS Applied Mathematics for Scientists and Engineers Bruce Kusse and Erik Westwig A comprehensive treatment of the mathematical methods used to solve practical problems in physics and engineering. 1998 (0-471-15431-8) 680 pp.
Missen, Karen; McKenna, Lisa; Beauchamp, Alison; Larkins, Jo-Ann
2016-10-01
Evidence from the literature and anecdotally from clinical settings suggests that newly graduated nurses are not fully prepared to be independent practitioners in healthcare settings. The aim of this study was to explore perceptions of qualified nurses in relation to the practice readiness of newly registered nursing graduates and determine whether these views differ according to specific demographic characteristics, clinical settings, and geographical locations. A descriptive quantitative design was used. An online survey tool was used to assess how qualified nurses (n=201) in Victoria, Australia, rated newly graduated nurses' abilities on 51 individual clinical skills/competencies in eight key skill areas. A composite score was calculated for each skill area and a comparative analysis was undertaken on the various cohorts of participants according to their demographic and clinical characteristics using one-way ANOVA and post hoc tests. Newly graduated nurses were found to be lacking competence in two key skill areas and were rated as performing adequately in the remaining six skill areas assessed. Significant differences (p≤0.05) in performance were found according to the age of the nurse, number of years registered, the educational setting in which they undertook their nurse education, their role, and the clinical area in which they worked. There were no significant differences according to whether the nurse worked in the private or public healthcare sector. Few differences were found between nurses working in a metropolitan vs. regional/rural healthcare setting. This is the first study to quantify the scale of this problem. Our findings serve as a reference for both nurse education providers and healthcare settings in better preparing nursing graduates to be competent, safe practitioners in all clinical areas. Copyright © 2016 Elsevier Ltd. All rights reserved.
NASA Astrophysics Data System (ADS)
Coley, Alan A.; McNutt, David D.; Shoom, Andrey A.
2017-08-01
We discuss black hole spacetimes with a geometrically defined quasi-local horizon on which the curvature tensor is algebraically special relative to the alignment classification. Based on many examples and analytical results, we conjecture that a spacetime horizon is always more algebraically special (in all of the orders of specialization) than other regions of spacetime. Using recent results in invariant theory, such geometric black hole horizons can be identified by the alignment type II or D discriminant conditions in terms of scalar curvature invariants, which are not dependent on spacetime foliations. The above conjecture is, in fact, a suite of conjectures (isolated vs dynamical horizon; four vs higher dimensions; zeroth order invariants vs higher order differential invariants). However, we are particularly interested in applications in four dimensions and especially the location of a black hole in numerical computations.
Nagarajan, Mahesh B; Coan, Paola; Huber, Markus B; Diemoz, Paul C; Wismüller, Axel
2015-11-01
Phase-contrast X-ray computed tomography (PCI-CT) has attracted significant interest in recent years for its ability to provide significantly improved image contrast in low absorbing materials such as soft biological tissue. In the research context of cartilage imaging, previous studies have demonstrated the ability of PCI-CT to visualize structural details of human patellar cartilage matrix and capture changes to chondrocyte organization induced by osteoarthritis. This study evaluates the use of geometrical and topological features for volumetric characterization of such chondrocyte patterns in the presence (or absence) of osteoarthritic damage. Geometrical features derived from the scaling index method (SIM) and topological features derived from Minkowski Functionals were extracted from 1392 volumes of interest (VOI) annotated on PCI-CT images of ex vivo human patellar cartilage specimens. These features were subsequently used in a machine learning task with support vector regression to classify VOIs as healthy or osteoarthritic; classification performance was evaluated using the area under the receiver operating characteristic curve (AUC). Our results show that the classification performance of SIM-derived geometrical features (AUC: 0.90 ± 0.09) is significantly better than Minkowski Functionals volume (AUC: 0.54 ± 0.02), surface (AUC: 0.72 ± 0.06), mean breadth (AUC: 0.74 ± 0.06) and Euler characteristic (AUC: 0.78 ± 0.04) (p < 10(-4)). These results suggest that such geometrical features can provide a detailed characterization of the chondrocyte organization in the cartilage matrix in an automated manner, while also enabling classification of cartilage as healthy or osteoarthritic with high accuracy. Such features could potentially serve as diagnostic imaging markers for evaluating osteoarthritis progression and its response to different therapeutic intervention strategies.
A quantitative description of tubular system Ca2+ handling in fast‐ and slow‐twitch muscle fibres
Cully, Tanya R.; Edwards, Joshua N.; Murphy, Robyn M.
2016-01-01
Key points Current methods do not allow a quantitative description of Ca2+ movements across the tubular (t‐) system membrane without isolating the membranes from their native skeletal muscle fibre.Here we present a fluorescence‐based method that allows determination of the t‐system [Ca2+] transients and derivation of t‐system Ca2+ fluxes in mechanically skinned skeletal muscle fibres. Differences in t‐system Ca2+‐handling properties between fast‐ and slow‐twitch fibres from rat muscle are resolved for the first time using this new technique.The method can be used to study Ca2+ handling of the t‐system and allows direct comparisons of t‐system Ca2+ transients and Ca2+ fluxes between groups of fibres and fibres from different strains of animals. Abstract The tubular (t‐) system of skeletal muscle is an internalization of the plasma membrane that maintains a large Ca2+ gradient and exchanges Ca2+ between the extracellular and intracellular environments. Little is known of the Ca2+‐handling properties of the t‐system as the small Ca2+ fluxes conducted are difficult to resolve with conventional methods. To advance knowledge in this area we calibrated t‐system‐trapped rhod‐5N inside skinned fibres from rat and [Ca2+]t‐sys, allowing confocal measurements of Ca2+‐dependent changes in rhod‐5N fluorescence during rapid changes in the intracellular ionic environment to be converted to [Ca2+] transients in the t‐system ([Ca2+]t‐sys (t)). Furthermore, t‐system Ca2+‐buffering power was determined so that t‐system Ca2+ fluxes could be derived from [Ca2+]t‐sys (t). With this new approach, we show that rapid depletion of sarcoplasmic reticulum (SR) Ca2+ induced a robust store‐operated Ca2+ entry (SOCE) in fast‐ and slow‐twitch fibres, reducing [Ca2+]t‐sys to < 0.1 mm. The rapid activation of SOCE upon Ca2+ release was consistent with the presence of STIM1L in both fibre types. Abruptly introducing internal solutions with 1
Chabert, Steren; Villalobos, Manuel; Ulloa, Patricia; Salas, Rodrigo; Tejos, Cristian; San Martin, Sebastian; Pereda, Jaime
2012-03-01
Human tissues are usually studied using a series of two-dimensional visualizations of in vivo or cutout specimens. However, there is no precise anatomical description of some of the processes of human fetal development. The purpose of our study is to develop a quantitative description of the normal axial skeleton by means of high-resolution three-dimensional magnetic resonance (MR) images, collected from six normal 20-week-old human fetuses fixed in formaldehyde. Fetuses were collected after spontaneous abortion and subsequently fixed with formalin. They were imaged using a 1.5 T MR scanner with an isotropic spatial resolution of 200 µm. The correct tissue discrimination between ossified and cartilaginous bones was confirmed by comparing the images achieved by MR scans and computerized axial tomographies. The vertebral column was segmented out from each image using a specially developed semi-automatic algorithm. Vertebral body dimensions and inter-vertebral distances were larger in the lumbar region, in agreement with the beginning of the ossification process from the thoracolumbar region toward the sacral and cephalic ends. In this article, we demonstrate the feasibility of using MR images to study the ossification process in formalin-fixed fetal tissues. A quantitative description of the ossification centers of vertebral bodies and arches is presented. © 2012 John Wiley & Sons, Ltd.
Pragmatic geometric model evaluation
NASA Astrophysics Data System (ADS)
Pamer, Robert
2015-04-01
Quantification of subsurface model reliability is mathematically and technically demanding as there are many different sources of uncertainty and some of the factors can be assessed merely in a subjective way. For many practical applications in industry or risk assessment (e. g. geothermal drilling) a quantitative estimation of possible geometric variations in depth unit is preferred over relative numbers because of cost calculations for different scenarios. The talk gives an overview of several factors that affect the geometry of structural subsurface models that are based upon typical geological survey organization (GSO) data like geological maps, borehole data and conceptually driven construction of subsurface elements (e. g. fault network). Within the context of the trans-European project "GeoMol" uncertainty analysis has to be very pragmatic also because of different data rights, data policies and modelling software between the project partners. In a case study a two-step evaluation methodology for geometric subsurface model uncertainty is being developed. In a first step several models of the same volume of interest have been calculated by omitting successively more and more input data types (seismic constraints, fault network, outcrop data). The positions of the various horizon surfaces are then compared. The procedure is equivalent to comparing data of various levels of detail and therefore structural complexity. This gives a measure of the structural significance of each data set in space and as a consequence areas of geometric complexity are identified. These areas are usually very data sensitive hence geometric variability in between individual data points in these areas is higher than in areas of low structural complexity. Instead of calculating a multitude of different models by varying some input data or parameters as it is done by Monte-Carlo-simulations, the aim of the second step of the evaluation procedure (which is part of the ongoing work) is to
Ogawa, Junji; Yokota, Azusa; Araki, Takuya; Aomori, Tohru; Nakamura, Tomonori; Yamamoto, Koujirou; Koshiishi, Ichiro
2014-09-01
Gadoxetate, a magnetic resonance imaging contrast agent, is eliminated into bile. Gadoxetate geometrical isomers are chromatographically classified into two groups by differences between their ionic states (GIs-I and GIs-II; 65:35 w/w); however, the elimination mechanism of each isomer in vivo remains controversial. Thus, the contribution of carrier-mediated transport systems on the biliary elimination of gadoxetate was examined. Gadoxetate was injected intravenously into rats, and the time courses of the plasma concentrations and biliary elimination of GIs-I and GIs-II were examined by high-performance liquid chromatography techniques. The results showed that 34.7% of GIs-I (GIs-I(s); 22.6% of gadoxetate) was quickly eliminated into bile within 30 min after injection. The contents of the residual GIs-I (GIs-I(r)) and GIs-II in plasma similarly decreased according to a first-order elimination process (t1/2=23-27 min), and 64.0% of GIs-I(r) and GIs-II (49.6% of gadoxetate) was eliminated into the bile within 2 h after injection. There was no significant difference between the elimination half-lives of GIs-I(r) and GIs-II in rats. In conclusion, the geometrical isomer with specific conformation corresponding to 22.6% of gadoxetate was eliminated into bile in rats via a carrier-mediated transport system no later than 30 min after intravenous injection.
Katsube, Motoki; Yamada, Shigehito; Miyazaki, Reina; Yamaguchi, Yutaka; Makishima, Haruyuki; Takakuwa, Tetsuya; Yamamoto, Akira; Fujii, Yosuke; Morimoto, Naoki; Ito, Tsuyoshi; Imai, Hirohiko; Suzuki, Shigehiko
2017-09-01
Disturbance of the development of the nasal septum in the early prenatal period causes congenital facial anomalies characterized by a flat nose and defects of the anterior nasal spine (ANS), such as Binder phenotype. The present research aimed to assess the development of the nasal septum and the ANS with growth in the early prenatal period. Magnetic resonance images were obtained from 56 specimens. Mid-sagittal images were analyzed by using geometric morphometrics for the development of the nasal septum, and angle analysis was performed for the development of the ANS. Additionally, we calculated and visualized the ontogenetic allometry of the nasal septum. Our results showed that the nasal septum changed shape in the anteroposterior direction in smaller specimens, while it maintained an almost isometric shape in larger specimens. Furthermore, mathematical evidence revealed that the maturation periods of the shapes of the ANS and the nasal septum were around 12 and 14 weeks of gestation, respectively. The anteroposterior development of the nasal septum is specific until 14 weeks of gestation, and it is important for nasal protrusion and the development of the ANS. Therefore, the disturbance of such development could induce low nasal deformity, including Binder phenotype. © 2017 John Wiley & Sons, Ltd. © 2017 John Wiley & Sons, Ltd.
Zhou, Lixia; Zhu, Dunxue; Zhang, Shujuan; Pan, Bingcai
2015-03-01
Understanding the aggregation and deposition behavior of carbon nanotubes (CNTs) is of great significance in terms of their fate and transport in the environment. Attachment efficiency is a widely used index for well-dispersed CNT solutions. However, in natural waters, CNTs are usually heterogeneous in particle size. The attachment efficiency method is not applicable to such systems. Describing the dispersion stability of CNTs in natural aquatic systems is still a challenge. In this work, a settling curve modeling (SCM) method was developed for the description of the aggregation and deposition behavior of CNTs in aqueous solutions. The effects of water chemistry (natural organic matter, pH, and ionic strength) on the aggregation and deposition behavior of pristine and surface-functionalized multi-walled carbon nanotubes (MWCNTs) were systematically studied to evaluate the reliability of the SCM method. The results showed that, as compared to particle size and optical density, the centrifugal sedimentation rate constant (ks) from the settling curve profile is a practical, useful and reliable index for the description of heterogeneous CNT suspensions. The SCM method was successfully applied to MWCNT in three natural waters. The constituents in water, especially organic matter, determine the dispersion stability of MWCNTs in natural water bodies. Copyright © 2015. Published by Elsevier B.V.
Wang, Ziyun; Hu, P
2017-02-15
The relation between the surface structure and adsorption energy of adsorbates is of great importance in heterogeneous catalysis. Based on density functional theory calculations, we propose an explicit equation with three chemically meaningful terms, namely the bonding contribution equation, to quantitatively account for the surface structures and the adsorption energies. Successful predictions of oxygen adsorption energies on complex alloy surfaces containing up to 4 components are demonstrated, and the generality of this equation is also tested using different surface sizes and other adsorbates. This work may not only offer a powerful tool to understand the structure-adsorption relation, but may also be used to inversely design novel catalysts.
Shabelnikova, Ya. L. Yakimov, E. B.; Nikolaev, D. P.; Chukalina, M. V.
2015-06-15
A solar cell on a wafer of multicrystalline silicon containing grain boundaries was studied by the induced-current method. The sample was scanned by an electron beam and by a laser beam at two wavelengths (980 and 635 nm). The recorded induced-current maps were aligned by means of a specially developed code, that enabled to analyze the same part of the grain boundary for three types of measurements. Optimization of the residual between simulated induced-current profiles and those obtained experimentally yielded quantitative estimates of the characteristics of a sample and its defects: the diffusion length of minority carriers and recombination velocity at the grain boundary.
Godelmann, Rolf; Kost, Christian; Patz, Claus-Dieter; Ristow, Reinhard; Wachter, Helmut
2016-09-01
To examine whether NMR analysis is a suitable method for the quantitative determination of wine components, an international collaborative trial was organized to evaluate the method according to the international regulations and guidelines of the German Institute for Standardization/International Organization for Standardization, AOAC INTERNATIONAL, the International Union of Pure and Applied Chemistry, and the International Organization of Vine and Wine. Sugars such as glucose; acids such as malic, acetic, fumaric, and shikimic acids (the latter two as minor components); and sorbic acid, a preservative, were selected for the exemplary quantitative determination of substances in wine. Selection criteria for the examination of sample material included different NMR spectral signal types (singlet and multiplet), as well as the suitability of the proposed substances for manual integration at different levels of challenge (e.g., interference as a result of the necessary suppression of a water signal or the coverage of different typical wine concentration ranges for a selection of major components, minor components, and additives). To show that this method can be universally applied, NMR measurement and the method of evaluation were not strictly elucidated. Fifteen international laboratories participated in the collaborative trial and determined six parameters in 10 samples. The values, in particular the reproducibility SD (SR), were compared with the expected Horwitz SD (SH) by forming the quotient SR/SH (i.e., the HorRat value). The resulting HorRat values of most parameters were predominantly between 0.6 and 1.5, and thus of an acceptable range.
Bernardo, Vagner; Lourenço, Simone Q C; Cruz, Renato; Monteiro-Leal, Luiz H; Silva, Licínio E; Camisasca, Danielle R; Farina, Marcos; Lins, Ulysses
2009-08-01
Quantification of immunostaining is a widely used technique in pathology. Nonetheless, techniques that rely on human vision are prone to inter- and intraobserver variability, and they are tedious and time consuming. Digital image analysis (DIA), now available in a variety of platforms, improves quantification performance: however, the stability of these different DIA systems is largely unknown. Here, we describe a method to measure the reproducibility of DIA systems. In addition, we describe a new image-processing strategy for quantitative evaluation of immunostained tissue sections using DAB/hematoxylin-stained slides. This approach is based on image subtraction, using a blue low pass filter in the optical train, followed by digital contrast and brightness enhancement. Results showed that our DIA system yields stable counts, and that this method can be used to evaluate the performance of DIA systems. The new image-processing approach creates an image that aids both human visual observation and DIA systems in assessing immunostained slides, delivers a quantitative performance similar to that of bright field imaging, gives thresholds with smaller ranges, and allows the segmentation of strongly immunostained areas, all resulting in a higher probability of representing specific staining. We believe that our approach offers important advantages to immunostaining quantification in pathology.
Friedman, M H
1972-06-01
The description of corneal mechanics and transport developed in part I and used there to describe normal corneal behavior is here applied to corneas whose properties or boundary conditions are abnormal. The predicted effects of changing intraocular pressure, aqueous concentration, and tear tonicity are examined, and these compare favorably with available experimental data. The periodic variation in tear tonicity which accompanies the sleep-wake cycle prevents the cornea from achieving a true steady state, but a time-average steady state, about which corneal behavior oscillates, can be defined. The in vivo effects of endothelial dystrophy and epithelial removal are explained, and it is suggested that the epithelial sodium pump may act homeostatically to maintain corneal thickness in the face of ambient temperature variations. Part II concludes with a discussion, from the standpoint of the present theory, of the role of metabolically coupled water transport in the maintenance of the normal corneal thickness.
Representing geometrical knowledge.
Anderson, J A
1997-08-29
This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space-time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top-down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space-time. It can be used to match a prototype shape to an image, even in so called 'accidental' views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic.
Representing geometrical knowledge.
Anderson, J A
1997-01-01
This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space-time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top-down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space-time. It can be used to match a prototype shape to an image, even in so called 'accidental' views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic. PMID:9304680
NASA Astrophysics Data System (ADS)
Kumazawa, Takao; Ogata, Yosihiko
2013-12-01
The epidemic-type aftershock sequence (ETAS) model is extended for application to nonstationary seismic activity, including transient swarm activity or seismicity anomalies, in a seismogenic region. The time-dependent rates of both background seismicity and aftershock productivity in the ETAS model are optimally estimated from hypocenter data. These rates can provide quantitative evidence for abrupt or gradual changes in shear stress and/or fault strength due to aseismic transient causes such as triggering by remote earthquakes, slow slips, or fluid intrusions within the region. This extended model is applied to data sets from several seismic events including swarms that were induced by the M9.0 Tohoku-Oki earthquake of 2011.
Albrecht-Buehler, G; Lancaster, R M
1976-11-01
We suggest a method of quantitating the motile actions of surface protrusions in spreading animal cells in culture. Its basis is the determination of the percentage of freshly plated cells which produce particle-free areas around them on a gold particle-coated glass cover slip within 50 min. Studying 3T3 cells with this assay, we found that the presence of Na+, K+, Cl-, and Mg++ or Ca++ in a neutral or slightly alkaline phosphate or bicarbonate buffered solution is sufficient to support the optimal particle removal by the cells for at least 50 min. Two metabolic inhibitors, 2,4-dinitrophenol and Na-azide, inhibit the particle removal. If D-glucose is added along with the inhibitors, particle removal can be restored, whereas the addition of three glucose analogues which are generally believed to be nonmetabolizable cannot restore the activity. Serum is not required for the mechanism(s) of the motile actions of surface protrusions in spreading 3T3 cells. However, it contains components which can neutralize the inhibitory actions of bovine serum albumin and several amino acids, particularly L-cystine or L-cystein and L-methionine. Furthermore, serum codetermines which of the major surface extension, filopodia, lamellipodia, or lobopodia, is predominantly active. We found three distinct classes of extracellular conditions under which the active surface projections are predominantly either lamellipodia, (sheetlike projections), lobopodia (blebs), or filopodia (microspikes). The quantitated dependencies on temperature, pH and the inhibition by cytochalasin B or the particle removal are very similar in all three cases. Preventing the cells from anchoring themselves for 15-20 min before plating in serum-free medium seems to stimulate particle removal threefold.
NASA Astrophysics Data System (ADS)
Scudder, J. D.; Salem, C. S.
2016-12-01
A new model for solar wind electrons provides an explanation for the origin of the non-thermal core-halo-strahl-superhalo VDF ubiquitously observed in the solar wind. Such kurtotic VDF's should be as common as the gradient induced occurrence of finite parallel electric fields that enforce quasi-neutrality in astrophysical plasmas. The velocity space separatrix of coulomb runaway predicts the observed scaling of the break point energy at 1AU of the electron VDF between thermal and suprathermal components and agrees well with the tabulations of its variation with radius. SERM quantitatively reproduces: 14 year IMP archives of the fraction of supra thermal electrons and the observed variation of the supra thermal density with local (nearly asymptotic) solar wind speed; the observed inverse correlation between halo density fraction and Th/Tc; and the reported, but theoretically unusual relative slippage of the core and halo that supports the heat flux. Requirements for quasi-neutrality (in the presence of runaways) lead to a quantitative non-local specification of the required supra thermal density fraction and the lowest even Legendre order approximate VDF that is symmetric, but kurtotic in the proton rest frame. The Stokes drift of the thermals suggested by runaway physics requires a counter drift of the non-locally returning suprathermals which determine the observed heat flux and thermal force contributions and the lowest order odd Legendre dependence of the VDF. The strahl is recovered as an extreme part of the non-local suprathermals. "Direct'' runaways caused by the parallel electric field are identified as an omnipresent source for the observed sunward portion of the non-thermal VDF. The source of the super halo electrons is suggested to be mirrored runaways produced at the base of the corona with subsequent near isotropization in the interplanetary medium.
He, Hong-Gu; Vehviläinen-Julkunen, Katri; Qian, Xiao-Fang; Sapountzi-Krepia, Despina; Gong, Yuhua; Wang, Wenru
2015-05-01
This study examined Chinese fathers' feelings about their partners' delivery and views on their presence during labour and birth. A questionnaire survey was conducted with 403 fathers whose partners gave birth in one provincial hospital in China. Data were analysed by descriptive statistics, χ(2)-test and content analysis. The results indicated that more than 80% of fathers experienced feelings of pride related to fatherhood and of love towards their partners and newborns. Significant differences in fathers' feelings were found between subgroups with regard to age, education, employment, presence in the delivery room, method of birth and whether preparatory visits had been made to the hospital. The majority who answered an open-ended question on the meaning of fathers' presence in the delivery room held a positive attitude towards fathers' presence at labour and birth, as their presence could empower their partners and provide psychological support. This study indicates fathers' presence at delivery and birth is important and that younger fathers need more support. It also provides evidence for clinical practice and future interventions to improve fathers' psychological health and experiences. © 2015 Wiley Publishing Asia Pty Ltd.
Quantitative description of the lie-to-sit-to-stand-to-walk transfer by a single body-fixed sensor.
Bagalà, Fabio; Klenk, Jochen; Cappello, Angelo; Chiari, Lorenzo; Becker, Clemens; Lindemann, Ulrich
2013-07-01
Sufficient capacity and quality of performance of complex movement patterns during daily activity, such as standing up from a bed, is a prerequisite for independent living and also may be an indicator of fall risk. Until now, the transfer from lying-to-sit-to-stand-to-walk (LSSW) was investigated by functional testing, subjective rating or for activity classification of subtasks. The aim of this study was to use a single body-fixed inertial sensor to describe the complex movement of the LSSW transfer. Fifteen older patients of a geriatric rehabilitation clinic (median age 81 years) and ten young, healthy persons (median age 37 years) were instructed to stand up from bed in a continuous movement and to start walking. Data acquisition was performed using an inertial measurement unit worn on the lower back. Parameters extracted from the sensor outputs were able to correctly classify the subjects into a correct group with sensitivity and specificity between 90% and 100%. ICCs 3,1 of the descriptive parameters ranged between 0.85 and 0.95 in the cohort of older patients. The different strategies adopted to transfer from lying to standing up were estimated through an extended Kalman filter. The results obtained in this study suggest the usability of the instrumented LSSW test in clinical settings.
Quantification and description of fracture network by MRI image analysis.
Balzarini, M; Nicula, S; Mattiello, D; Aliverti, E
2001-01-01
The contribution of fractures to total porosity and their geometrical descriptions have been studied by Image Analysis applied to 1H Magnetic Resonance Imaging (MRI). Reservoirs of different lithology were acquired with MSME 2D quantitative and 3D sequences. An image analysis procedure, developed ad hoc, was then applied to these acquisitions and the petrophysical parameters computed. These parameters range from fracture porosity to fracture density.
Identifying and Fostering Higher Levels of Geometric Thinking
ERIC Educational Resources Information Center
Škrbec, Maja; Cadež, Tatjana Hodnik
2015-01-01
Pierre M. Van Hiele created five levels of geometric thinking. We decided to identify the level of geometric thinking in the students in Slovenia, aged 9 to 11 years. The majority of students (60.7%) are at the transition between the zero (visual) level and the first (descriptive) level of geometric thinking. Nearly a third (31.7%) of students is…
Identifying and Fostering Higher Levels of Geometric Thinking
ERIC Educational Resources Information Center
Škrbec, Maja; Cadež, Tatjana Hodnik
2015-01-01
Pierre M. Van Hiele created five levels of geometric thinking. We decided to identify the level of geometric thinking in the students in Slovenia, aged 9 to 11 years. The majority of students (60.7%) are at the transition between the zero (visual) level and the first (descriptive) level of geometric thinking. Nearly a third (31.7%) of students is…
Marillet, Simon; Lefranc, Marie-Paule; Boudinot, Pierre; Cazals, Frédéric
2017-01-01
Antibody–antigen complexes challenge our understanding, as analyses to date failed to unveil the key determinants of binding affinity and interaction specificity. We partially fill this gap based on novel quantitative analyses using two standardized databases, the IMGT/3Dstructure-DB and the structure affinity benchmark. First, we introduce a statistical analysis of interfaces which enables the classification of ligand types (protein, peptide, and chemical; cross-validated classification error of 9.6%) and yield binding affinity predictions of unprecedented accuracy (median absolute error of 0.878 kcal/mol). Second, we exploit the contributions made by CDRs in terms of position at the interface and atomic packing properties to show that in general, VH CDR3 and VL CDR3 make dominant contributions to the binding affinity, a fact also shown to be consistent with the enthalpy–entropy compensation associated with preconfiguration of CDR3. Our work suggests that the affinity prediction problem could be partially solved from databases of high resolution crystal structures of complexes with known affinity. PMID:28232828
Hernández-Castellano, Lorenzo E; Argüello, Anastasio; Almeida, André M; Castro, Noemí; Bendixen, Emøke
2015-01-01
Colostrum intake is a key factor for newborn ruminant survival because the placenta does not allow the transfer of immune components. Therefore, newborn ruminants depend entirely on passive immunity transfer from the mother to the neonate, through the suckling of colostrum. Understanding the importance of specific colostrum proteins has gained significant attention in recent years. However, proteomics studies of sheep colostrum and their uptake in neonate lambs has not yet been presented. The aim of this study was to describe the proteomes of sheep colostrum and lamb blood plasma, using sodium dodecyl sulfate-PAGE for protein separation and in-gel digestion, followed by liquid chromatography-tandem mass spectrometry of resulting tryptic peptides for protein identification. An isobaric tag for relative and absolute quantitation (iTRAQ)-based proteomics approach was subsequently used to provide relative quantification of how neonatal plasma protein concentrations change as an effect of colostrum intake. The results of this study describe the presence of 70 proteins in the ovine colostrum proteome. Furthermore, colostrum intake resulted in an increase of 8 proteins with important immune functions in the blood plasma of lambs. Further proteomic studies will be necessary, particularly using the selected reaction monitoring approach, to describe in detail the role of specific colostrum proteins for immune transfer to the neonate.
Lu, Lu; Hu, Yan; Huang, Xirong; Qu, Yinbo
2012-09-13
It is imperative to establish a simple, efficient, and practical method to investigate the Hofmeister effect of ionic liquids (ILs) on the behavior of proteins (enzymes). In this study, the effects of the cations and anions of different ILs in aqueous media on the structural stability of horseradish peroxidase (HRP), a model oxidoreductase, were systematically investigated using electrochemical methods. It is found that without ILs no direct electron transfer current signals of HRP appear at bare glassy carbon electrode (GCE) in phosphate buffer (pH 7.0) even after incubation and accumulation at a negative potential. In the presence of ILs, however, a current signal occurs at GCE, depending on the structure of the IL and its concentration. A linear relationship between the peak currents and the scan rates demonstrates that the direct electron transfer is a surface-confined thin-layer electrochemical process. The redox signal at GCE is from the heme of HRP. An IL has a perturbing effect on the HRP structure. The anodic peak current of HRP at GCE, the catalytic activity of HRP, and the secondary structure of HRP are well correlated. Different cations or anions at varied concentrations have different effects on the structural stability of HRP, resulting in different current signals at GCE. Thus, the anodic peak current of HRP at GCE can be used as an indicator to quantitatively characterize the effect of ILs on the structural stability of HRP. The present Hofmeister series for cations and anions is in good agreement with that reported elsewhere. To our knowledge, this is a first attempt to establish a simple and practical electrochemical method to correlate Hofmeister effects with characteristics of ions and solvents. The present investigation not only deepens our understanding of the complex electrochemical behavior of proteins in ILs media but also offers a practical guidance to designing "green" and biocompatible ILs for protein (enzyme) separation, purification
Brunskill, Jeffrey C
2010-03-01
This paper presents a study of the relationship between quantitative and qualitative descriptions of temperature. Online weather forecast narratives produced by local television forecasters were collected from affiliates in 23 cities throughout the northeastern, central and southern portions of the United States from August 2007 to July 2008. The narratives were collected to study the terminology and reference frames that local forecasters use to describe predicted temperatures for the following day. The main objectives were to explore the adjectives used to describe thermal conditions and the impact that geographical and seasonal variations in thermal conditions have on these descriptions. The results of this empirical study offer some insights into the structure of weather narratives and suggest that spatiotemporal variations in the weather impact how forecasters describe the temperature to their local audiences. In a broader sense, this investigation builds upon research in biometeorology, urban planning and linguistics that has explored the physiological and psychological factors that influence subjective assessments of thermal sensation and comfort. The results of this study provide a basis to reason about how thermal comfort is conveyed in meteorological communications and how experiential knowledge derived from daily observations of the weather influence how we think about and discuss the weather.
NASA Astrophysics Data System (ADS)
Brunskill, Jeffrey C.
2010-03-01
This paper presents a study of the relationship between quantitative and qualitative descriptions of temperature. Online weather forecast narratives produced by local television forecasters were collected from affiliates in 23 cities throughout the northeastern, central and southern portions of the United States from August 2007 to July 2008. The narratives were collected to study the terminology and reference frames that local forecasters use to describe predicted temperatures for the following day. The main objectives were to explore the adjectives used to describe thermal conditions and the impact that geographical and seasonal variations in thermal conditions have on these descriptions. The results of this empirical study offer some insights into the structure of weather narratives and suggest that spatiotemporal variations in the weather impact how forecasters describe the temperature to their local audiences. In a broader sense, this investigation builds upon research in biometeorology, urban planning and linguistics that has explored the physiological and psychological factors that influence subjective assessments of thermal sensation and comfort. The results of this study provide a basis to reason about how thermal comfort is conveyed in meteorological communications and how experiential knowledge derived from daily observations of the weather influence how we think about and discuss the weather.
NASA Astrophysics Data System (ADS)
Bueno, M.; Schulte, R.; Meylan, S.; Villagrasa, C.
2015-11-01
The aim of this study was to evaluate the influence of the geometrical detail of the DNA on nanodosimetric parameters of track structure induced by protons and alpha particles of different energies (LET values ranging from 1 to 162.5~\\text{keV}~μ {{\\text{m}}-1} ) as calculated by Geant4-DNA Monte Carlo simulations. The first geometry considered consisted of a well-structured placement of a realistic description of the DNA double helix wrapped around cylindrical histones (GeomHist) forming a 18 kbp-long chromatin fiber. In the second geometry considered, the DNA was modeled as a total of 1800 ten bp-long homogeneous cylinders (2.3 nm diameter and 3.4 nm height) placed in random positions and orientations (GeomCyl). As for GeomHist, GeomCyl contained a DNA material equivalent to 18 kbp. Geant4-DNA track structure simulations were performed and ionizations were counted in the scoring volumes. For GeomCyl, clusters were defined as the number of ionizations (ν) scored in each 10 bp-long cylinder. For GeomHist, clusters of ionizations scored in the sugar-phosphate groups of the double-helix were revealed by the DBSCAN clustering algorithm according to a proximity criteria among ionizations separated by less than 10 bp. The topology of the ionization clusters formed using GeomHist and GeomCyl geometries were compared in terms of biologically relevant nanodosimetric quantities. The discontinuous modeling of the DNA for GeomCyl led to smaller cluster sizes than for GeomHist. The continuous modeling of the DNA molecule for GeomHist allowed the merging of ionization points by the DBSCAN algorithm giving rise to larger clusters, which were not detectable within the GeomCyl geometry. Mean cluster size (m1) was found to be of the order of 10% higher for GeomHist compared to GeomCyl for LET <15~\\text{keV}~μ {{\\text{m}}-1} . For higher LETs, the difference increased with LET similarly for protons and alpha particles. Both geometries showed the same relationship
DeBeer George, S; Metz, M; Szilagyi, R K; Wang, H; Cramer, S P; Lu, Y; Tolman, W B; Hedman, B; Hodgson, K O; Solomon, E I
2001-06-20
To evaluate the importance of the electronic structure of Cu(A) to its electron-transfer (ET) function, a quantitative description of the ground-state wave function of the mixed-valence (MV) binuclear Cu(A) center engineered into Pseudomonas aeruginosa azurin has been developed, using a combination of S K-edge and Cu L-edge X-ray absorption spectroscopies (XAS). Parallel descriptions have been developed for a binuclear thiolate-bridged MV reference model complex ([(L(i)(PrdacoS)Cu)(2)](+)) and a homovalent (II,II) analogue ([L(i)(Pr2tacnS)Cu)(2)](2+), where L(i)(PrdacoS) and L(i)(Pr2tacnS) are macrocyclic ligands with attached thiolates that bridge the Cu ions. Previous studies have qualitatively defined the ground-state wave function of Cu(A) in terms of ligand field effects on the orbital orientation and the presence of a metal--metal bond. The studies presented here provide further evidence for a direct Cu--Cu interaction and, importantly, experimentally quantify the covalency of the ground-state wave function. The experimental results are further supported by DFT calculations. The nature of the ground-state wave function of Cu(A) is compared to that of the well-defined blue copper site in plastocyanin, and the importance of this wave function to the lower reorganization energy and ET function of Cu(A) is discussed. This wave function incorporates anisotropic covalency into the intra- and intermolecular ET pathways in cytochrome c oxidase. Thus, the high covalency of the Cys--Cu bond allows a path through this ligand to become competitive with a shorter His path in the intramolecular ET from Cu(A) to heme a and is particularly important for activating the intermolecular ET path from heme c to Cu(A).
Solheim, Elisabeth; Plathe, Hilde Syvertsen; Eide, Hilde
2017-09-04
Clinical skills training is an important part of nurses' education programmes. Clinical skills are complex. A common understanding of what characterizes clinical skills and learning outcomes needs to be established. The aim of the study was to develop and evaluate a new reflection and feedback tool for formative assessment. The study has a descriptive quantitative design. 129 students participated who were at the end of the first year of a Bachelor degree in nursing. After highfidelity simulation, data were collected using a questionnaire with 19 closed-ended and 2 open-ended questions. The tool stimulated peer assessment, and enabled students to be more thorough in what to assess as an observer in clinical skills. The tool provided a structure for selfassessment and made visible items that are important to be aware of in clinical skills. This article adds to simulation literature and provides a tool that is useful in enhancing peer learning, which is essential for nurses in practice. The tool has potential for enabling students to learn about reflection and developing skills for guiding others in practice after they have graduated. Copyright © 2017 Elsevier Ltd. All rights reserved.
Geometric morphology of granular materials
NASA Astrophysics Data System (ADS)
Schlei, Bernd R.; Prasad, Lakshman; Skourikhine, Alexei N.
2000-10-01
We present a new method to transform the spectral pixel information of a micrograph into an affine geometric description, which allows us to analyze the morphology of granular materials. We use spectral and pulse-coupled neural network based segmentation techniques to generate blobs, and a newly developed algorithm to extract dilated contours. A constrained Delaunay tessellation of the contour points results in a triangular mesh. This mesh is the basic ingredient of the Chodal Axis Transform, which provides a morphological decomposition of shapes. Such decomposition allows for grain separation and the efficient computation of the statistical features of granular materials.
NASA Astrophysics Data System (ADS)
Hensleigh, J.; Buscombe, D.; Wheaton, J. M.; Brasington, J.; Welcker, C. W.; Anderson, K.
2015-12-01
The increasing use of high-resolution topography (HRT) constructed from point clouds obtained from technology such as LiDAR, SoNAR, SAR, SfM and a variety of range-imaging techniques, has created a demand for custom analytical tools and software for point cloud decimation (data thinning and gridding) and spatially explicit statistical analysis of terrestrial surfaces. We will present on a number of analytical and computational tools designed to quantify surface roughness and texture, directly from point clouds in a variety of ways (using spatial- and frequency-domain statistics). TopCAT (Topographic Point Cloud Analysis Toolkit; Brasington et al., 2012) and PySESA (Python program for Spatially Explicit Spectral Analysis) both work by applying a small moving window to (x,y,z) data to calculate a suite of (spatial and spectral domain) statistics, which are then spatially-referenced on a regular (x,y) grid at a user-defined resolution. Collectively, these tools facilitate quantitative description of surfaces and may allow, for example, fully automated texture characterization and segmentation, roughness and grain size calculation, and feature detection and classification, on very large point clouds with great computational efficiency. Using tools such as these, it may be possible to detect geomorphic change in surfaces which have undergone minimal elevation difference, for example deflation surfaces which have coarsened but undergone no net elevation change, or surfaces which have eroded and accreted, leaving behind a different textural surface expression than before. The functionalities of the two toolboxes are illustrated with example high-resolution bathymetric point cloud data collected with multibeam echosounder, and topographic data collected with LiDAR.
Geometrizing the Quantum - A Toy Model
Koch, Benjamin
2009-12-15
It is shown that the equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of conformally 'curved' space-time. This shows that it is possible to formulate quantum mechanics as a purely classical geometrical theory. The results are further generalized to interactions with an external electromagnetic field.
Exploring New Geometric Worlds
ERIC Educational Resources Information Center
Nirode, Wayne
2015-01-01
When students work with a non-Euclidean distance formula, geometric objects such as circles and segment bisectors can look very different from their Euclidean counterparts. Students and even teachers can experience the thrill of creative discovery when investigating these differences among geometric worlds. In this article, the author describes a…
Exploring New Geometric Worlds
ERIC Educational Resources Information Center
Nirode, Wayne
2015-01-01
When students work with a non-Euclidean distance formula, geometric objects such as circles and segment bisectors can look very different from their Euclidean counterparts. Students and even teachers can experience the thrill of creative discovery when investigating these differences among geometric worlds. In this article, the author describes a…
The nuclear geometric Yang-Mills equation for incompressible nuclei
NASA Astrophysics Data System (ADS)
Sparks, Nicholas; Rosensteel, George
2016-09-01
The geometric Yang-Mills equation for the Bohr-Mottelson collective model provides a way of relating angular momentum degrees of freedom to the internal (Kelvin circulation) degrees of freedom. It is well known that nuclei are highly incompressible. The correct mathematical description for nuclear incompressibility involves an equation of constraint for constant volume. An alternative yet equivalent description involves treating this constraint in a purely differential geometric way. The relationship between these two seemingly different approaches is explored here.
Solitons in geometric potentials
NASA Astrophysics Data System (ADS)
Kartashov, Yaroslav V.; Szameit, Alexander; Keil, Robert; Vysloukh, Victor A.; Torner, Lluis
2011-09-01
We show that the geometrically induced potential existing in undulated slab waveguides dramatically affects the properties of solitons. In particular, whereas solitons residing in the potential maxima do not feature power thresholds and are stable, their counterparts residing in the potential minima are unstable and may exhibit a power threshold for their existence. Additionally, the geometric potential is shown to support stable multipole solitons that cannot be supported by straight waveguides. Finally, the geometric potential results in the appearance of the effective barriers that prevent transverse soliton motion.
Geometrically Induced Interactions and Bifurcations
NASA Astrophysics Data System (ADS)
Binder, Bernd
2010-01-01
In order to evaluate the proper boundary conditions in spin dynamics eventually leading to the emergence of natural and artificial solitons providing for strong interactions and potentials with monopole charges, the paper outlines a new concept referring to a curvature-invariant formalism, where superintegrability is given by a special isometric condition. Instead of referring to the spin operators and Casimir/Euler invariants as the generator of rotations, a curvature-invariant description is introduced utilizing a double Gudermann mapping function (generator of sine Gordon solitons and Mercator projection) cross-relating two angular variables, where geometric phases and rotations arise between surfaces of different curvature. Applying this stereographic projection to a superintegrable Hamiltonian can directly map linear oscillators to Kepler/Coulomb potentials and/or monopoles with Pöschl-Teller potentials and vice versa. In this sense a large scale Kepler/Coulomb (gravitational, electro-magnetic) wave dynamics with a hyperbolic metric could be mapped as a geodesic vertex flow to a local oscillator singularity (Dirac monopole) with spherical metrics and vice versa. Attracting fixed points and dynamic constraints are given by special isometries with magic precession angles. The nonlinear angular encoding directly provides for a Shannon mutual information entropy measure of the geodesic phase space flow. The emerging monopole patterns show relations to spiral Fresnel holography and Berry/Aharonov-Bohm geometric phases subject to bifurcation instabilities and singularities from phase ambiguities due to a local (entropy) overload. Neutral solitons and virtual patterns emerging and mediating in the overlap region between charged or twisted holographic patterns are visualized and directly assigned to the Berry geometric phase revealing the role of photons, neutrons, and neutrinos binding repulsive charges in Coulomb, strong and weak interaction.
Wrinkled flames and geometrical stretch
NASA Astrophysics Data System (ADS)
Denet, Bruno; Joulin, Guy
2011-07-01
Localized wrinkles of thin premixed flames subject to hydrodynamic instability and geometrical stretch of uniform intensity (S) are studied. A stretch-affected nonlinear and nonlocal equation, derived from an inhomogeneous Michelson-Sivashinsky equation, is used as a starting point, and pole decompositions are used as a tool. Analytical and numerical descriptions of isolated (centered or multicrested) wrinkles with steady shapes (in a frame) and various amplitudes are provided; their number increases rapidly with 1/S>0. A large constant S>0 weakens or suppresses all localized wrinkles (the larger the wrinkles, the easier the suppression), whereas S<0 strengthens them; oscillations of S further restrict their existence domain. Self-similar evolutions of unstable many-crested patterns are obtained. A link between stretch, nonlinearity, and instability with the cutoff size of the wrinkles in turbulent flames is suggested. Open problems are evoked.
\\overline{D3} induced geometric inflation
NASA Astrophysics Data System (ADS)
Kallosh, Renata; Linde, Andrei; Roest, Diederik; Yamada, Yusuke
2017-07-01
Effective supergravity inflationary models induced by anti-D3 brane interaction with the moduli fields in the bulk geometry have a geometric description. The Kähler function carries the complete geometric information on the theory. The non-vanishing bisectional curvature plays an important role in the construction. The new geometric formalism, with the nilpotent superfield representing the anti-D3 brane, allows a powerful generalization of the existing inflationary models based on supergravity. They can easily incorporate arbitrary values of the Hubble parameter, cosmological constant and gravitino mass. We illustrate it by providing generalized versions of polynomial chaotic inflation, T- and E-models of α-attractor type, disk merger. We also describe a multi-stage cosmological attractor regime, which we call cascade inflation.
NASA Astrophysics Data System (ADS)
Matsuzaki, F.; Yoshikawa, N.; Tanaka, M.; Fujimaki, A.; Takai, Y.
2003-10-01
Recently many single flux quantum (SFQ) logic circuits containing several thousands of Josephson junctions have been designed successfully by using digital domain simulation based on the hard ware description language (HDL). In the present HDL-based design of SFQ circuits, a structure-level HDL description has been used, where circuits are made up of basic gate cells. However, in order to analyze large-scale SFQ digital systems, such as a microprocessor, more higher-level circuit abstraction is necessary to reduce the circuit simulation time. In this paper we have investigated the way to describe functionality of the large-scale SFQ digital circuits by a behavior-level HDL description. In this method, the functionality and the timing of the circuit block is defined directly by describing their behavior by the HDL. Using this method, we can dramatically reduce the simulation time of large-scale SFQ digital circuits.
Geometric systematic prostate biopsy.
Chang, Doyoung; Chong, Xue; Kim, Chunwoo; Jun, Changhan; Petrisor, Doru; Han, Misop; Stoianovici, Dan
2017-04-01
The common sextant prostate biopsy schema lacks a three-dimensional (3D) geometric definition. The study objective was to determine the influence of the geometric distribution of the cores on the detection probability of prostate cancer (PCa). The detection probability of significant (>0.5 cm(3)) and insignificant (<0.2 cm(3)) tumors was quantified based on a novel 3D capsule model of the biopsy sample. The geometric distribution of the cores was optimized to maximize the probability of detecting significant cancer for various prostate sizes (20-100cm(3)), number of biopsy cores (6-40 cores) and biopsy core lengths (14-40 mm) for transrectal and transperineal biopsies. The detection of significant cancer can be improved by geometric optimization. With the current sextant biopsy, up to 20% of tumors may be missed at biopsy in a 20 cm(3) prostate due to the schema. Higher number and longer biopsy cores are required to sample with an equal detection probability in larger prostates. Higher number of cores increases both significant and insignificant tumor detection probability, but predominantly increases the detection of insignificant tumors. The study demonstrates mathematically that the geometric biopsy schema plays an important clinical role, and that increasing the number of biopsy cores is not necessarily helpful.
Geometric decompositions of collective motion.
Mischiati, Matteo; Krishnaprasad, P S
2017-04-01
Collective motion in nature is a captivating phenomenon. Revealing the underlying mechanisms, which are of biological and theoretical interest, will require empirical data, modelling and analysis techniques. Here, we contribute a geometric viewpoint, yielding a novel method of analysing movement. Snapshots of collective motion are portrayed as tangent vectors on configuration space, with length determined by the total kinetic energy. Using the geometry of fibre bundles and connections, this portrait is split into orthogonal components each tangential to a lower dimensional manifold derived from configuration space. The resulting decomposition, when interleaved with classical shape space construction, is categorized into a family of kinematic modes-including rigid translations, rigid rotations, inertia tensor transformations, expansions and compressions. Snapshots of empirical data from natural collectives can be allocated to these modes and weighted by fractions of total kinetic energy. Such quantitative measures can provide insight into the variation of the driving goals of a collective, as illustrated by applying these methods to a publicly available dataset of pigeon flocking. The geometric framework may also be profitably employed in the control of artificial systems of interacting agents such as robots.
Geometric decompositions of collective motion
NASA Astrophysics Data System (ADS)
Mischiati, Matteo; Krishnaprasad, P. S.
2017-04-01
Collective motion in nature is a captivating phenomenon. Revealing the underlying mechanisms, which are of biological and theoretical interest, will require empirical data, modelling and analysis techniques. Here, we contribute a geometric viewpoint, yielding a novel method of analysing movement. Snapshots of collective motion are portrayed as tangent vectors on configuration space, with length determined by the total kinetic energy. Using the geometry of fibre bundles and connections, this portrait is split into orthogonal components each tangential to a lower dimensional manifold derived from configuration space. The resulting decomposition, when interleaved with classical shape space construction, is categorized into a family of kinematic modes-including rigid translations, rigid rotations, inertia tensor transformations, expansions and compressions. Snapshots of empirical data from natural collectives can be allocated to these modes and weighted by fractions of total kinetic energy. Such quantitative measures can provide insight into the variation of the driving goals of a collective, as illustrated by applying these methods to a publicly available dataset of pigeon flocking. The geometric framework may also be profitably employed in the control of artificial systems of interacting agents such as robots.
Inflation from geometrical tachyons
Thomas, Steven; Ward, John
2005-10-15
We propose an alternative formulation of tachyon inflation using the geometrical tachyon arising from the time dependent motion of a BPS D3-brane in the background geometry due to k parallel NS5-branes arranged around a ring of radius R. Because of the fact that the mass of this geometrical tachyon field is {radical}(2/k) times smaller than the corresponding open-string tachyon mass, we find that the slow-roll conditions for inflation and the number of e-foldings can be satisfied in a manner that is consistent with an effective 4-dimensional model and with a perturbative string coupling. We also show that the metric perturbations produced at the end of inflation can be sufficiently small and do not lead to the inconsistencies that plague the open-string tachyon models. Finally we argue for the existence of a minimum of the geometrical tachyon potential which could give rise to a traditional reheating mechanism.
Geometrical optical illusionists.
Wade, Nicholas J
2014-01-01
Geometrical optical illusions were given this title by Oppel in 1855. Variants on such small distortions of visual space were illustrated thereafter, many of which bear the names of those who first described them. Some original forms of the geometrical optical illusions are shown together with 'perceptual portraits' of those who described them. These include: Roget, Chevreul, Fick, Zöllner, Poggendorff, Hering, Kundt, Delboeuf Mach, Helmholtz, Hermann, von Bezold, Müller-Lyer, Lipps, Thiéry, Wundt, Münsterberg, Ebbinghaus, Titchener, Ponzo, Luckiesh, Sander, Ehrenstein, Gregory, Heard, White, Shepard, and. Lingelbach. The illusions are grouped under the headings of orientation, size, the combination of size and orientation, and contrast. Early theories of illusions, before geometrical optical illusions were so named, are mentioned briefly.
Toroidal Precession as a Geometric Phase
J.W. Burby and H. Qin
2012-09-26
Toroidal precession is commonly understood as the orbit-averaged toroidal drift of guiding centers in axisymmetric and quasisymmetric configurations. We give a new, more natural description of precession as a geometric phase effect. In particular, we show that the precession angle arises as the holonomy of a guiding center's poloidal trajectory relative to a principal connection. The fact that this description is physically appropriate is borne out with new, manifestly coordinate-independent expressions for the precession angle that apply to all types of orbits in tokamaks and quasisymmetric stellarators alike. We then describe how these expressions may be fruitfully employed in numerical calculations of precession.
NASA Technical Reports Server (NTRS)
Lada, Charles J.
2004-01-01
This grant funds a research program to use infrared extinction measurements to probe the detailed structure of dark molecular cloud cores and investigate the physical conditions which give rise to star and planet formation. The goals of this program are to acquire, reduce and analyze deep infrared and molecular-line observations of a carefully selected sample of nearby dark clouds in order to determine the detailed initial conditions for star formation from quantitative measurements of the internal structure of starless cloud cores and to quantitatively investigate the evolution of such structure through the star and planet formation process.
NASA Technical Reports Server (NTRS)
Lada, Charles J.
2004-01-01
This grant funds a research program to use infrared extinction measurements to probe the detailed structure of dark molecular cloud cores and investigate the physical conditions which give rise to star and planet formation. The goals of this program are to acquire, reduce and analyze deep infrared and molecular-line observations of a carefully selected sample of nearby dark clouds in order to determine the detailed initial conditions for star formation from quantitative measurements of the internal structure of starless cloud cores and to quantitatively investigate the evolution of such structure through the star and planet formation process.
Chiral models: Geometrical aspects
NASA Astrophysics Data System (ADS)
Perelomov, A. M.
1987-02-01
Two-dimensional classical chiral models of field theory are considered, the main attention being paid on geometrical aspects of such theories. A characteristic feature of these models is that the interaction is inserted not by adding the interaction Lagrangian to the free field Lagrangian, but has a purely geometrical origin and is related to the inner curvature of the manifold. These models are in many respects analogous to non-Abelian gauge theories and as became clear recently, they are also important for the superstring theory which nowadays is the most probable candidate for a truly unified theory of all interactions including gravitation.
Time as a geometric property of space
NASA Astrophysics Data System (ADS)
Chappell, James; Hartnett, John; Iannella, Nicolangelo; Iqbal, Azhar; Abbott, Derek
2016-11-01
The proper description of time remains a key unsolved problem in science. Newton conceived of time as absolute and universal which `flows equably without relation to anything external'. In the nineteenth century, the four-dimensional algebraic structure of the quaternions developed by Hamilton, inspired him to suggest that they could provide a unified representation of space and time. With the publishing of Einstein's theory of special relativity these ideas then lead to the generally accepted Minkowski spacetime formulation in 1908. Minkowski, though, rejected the formalism of quaternions suggested by Hamilton and adopted rather an approach using four-vectors. The Minkowski framework is indeed found to provide a versatile formalism for describing the relationship between space and time in accordance with Einstein's relativistic principles, but nevertheless fails to provide more fundamental insights into the nature of time itself. In order to answer this question we begin by exploring the geometric properties of three-dimensional space that we model using Clifford geometric algebra, which is found to contain sufficient complexity to provide a natural description of spacetime. This description using Clifford algebra is found to provide a natural alternative to the Minkowski formulation as well as providing new insights into the nature of time. Our main result is that time is the scalar component of a Clifford space and can be viewed as an intrinsic geometric property of three-dimensional space without the need for the specific addition of a fourth dimension.
PREFACE: Geometrically frustrated magnetism Geometrically frustrated magnetism
NASA Astrophysics Data System (ADS)
Gardner, Jason S.
2011-04-01
Frustrated magnetism is an exciting and diverse field in condensed matter physics that has grown tremendously over the past 20 years. This special issue aims to capture some of that excitement in the field of geometrically frustrated magnets and is inspired by the 2010 Highly Frustrated Magnetism (HFM 2010) meeting in Baltimore, MD, USA. Geometric frustration is a broad phenomenon that results from an intrinsic incompatibility between some fundamental interactions and the underlying lattice geometry based on triangles and tetrahedra. Most studies have centred around the kagomé and pyrochlore based magnets but recent work has looked at other structures including the delafossite, langasites, hyper-kagomé, garnets and Laves phase materials to name a few. Personally, I hope this issue serves as a great reference to scientist both new and old to this field, and that we all continue to have fun in this very frustrated playground. Finally, I want to thank the HFM 2010 organizers and all the sponsors whose contributions were an essential part of the success of the meeting in Baltimore. Geometrically frustrated magnetism contents Spangolite: an s = 1/2 maple leaf lattice antiferromagnet? T Fennell, J O Piatek, R A Stephenson, G J Nilsen and H M Rønnow Two-dimensional magnetism and spin-size effect in the S = 1 triangular antiferromagnet NiGa2S4 Yusuke Nambu and Satoru Nakatsuji Short range ordering in the modified honeycomb lattice compound SrHo2O4 S Ghosh, H D Zhou, L Balicas, S Hill, J S Gardner, Y Qi and C R Wiebe Heavy fermion compounds on the geometrically frustrated Shastry-Sutherland lattice M S Kim and M C Aronson A neutron polarization analysis study of moment correlations in (Dy0.4Y0.6)T2 (T = Mn, Al) J R Stewart, J M Hillier, P Manuel and R Cywinski Elemental analysis and magnetism of hydronium jarosites—model kagome antiferromagnets and topological spin glasses A S Wills and W G Bisson The Herbertsmithite Hamiltonian: μSR measurements on single crystals
ERIC Educational Resources Information Center
Burgess, Claudia R.
2014-01-01
Designed for a broad audience, including educators, camp directors, afterschool coordinators, and preservice teachers, this investigation aims to help individuals experience mathematics in unconventional and exciting ways by engaging them in the physical activity of building geometric shapes using ropes. Through this engagement, the author…
ERIC Educational Resources Information Center
Smart, Julie; Marshall, Jeff
2007-01-01
Children possess a genuine curiosity for exploring the natural world around them. One third grade teacher capitalized on this inherent trait by leading her students on "A Geometric Scavenger Hunt." The four-lesson inquiry investigation described in this article integrates mathematics and science. Among the students' discoveries was the fact that…
Geometric Series via Probability
ERIC Educational Resources Information Center
Tesman, Barry
2012-01-01
Infinite series is a challenging topic in the undergraduate mathematics curriculum for many students. In fact, there is a vast literature in mathematics education research on convergence issues. One of the most important types of infinite series is the geometric series. Their beauty lies in the fact that they can be evaluated explicitly and that…
ERIC Educational Resources Information Center
Smart, Julie; Marshall, Jeff
2007-01-01
Children possess a genuine curiosity for exploring the natural world around them. One third grade teacher capitalized on this inherent trait by leading her students on "A Geometric Scavenger Hunt." The four-lesson inquiry investigation described in this article integrates mathematics and science. Among the students' discoveries was the fact that…
ERIC Educational Resources Information Center
Burgess, Claudia R.
2014-01-01
Designed for a broad audience, including educators, camp directors, afterschool coordinators, and preservice teachers, this investigation aims to help individuals experience mathematics in unconventional and exciting ways by engaging them in the physical activity of building geometric shapes using ropes. Through this engagement, the author…
NASA Technical Reports Server (NTRS)
Ives, David
1995-01-01
This paper presents a highly automated hexahedral grid generator based on extensive geometrical and solid modeling operations developed in response to a vision of a designer-driven one day turnaround CFD process which implies a designer-driven one hour grid generation process.
Morphing of geometric composites via residual swelling.
Pezzulla, Matteo; Shillig, Steven A; Nardinocchi, Paola; Holmes, Douglas P
2015-08-07
Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel, adaptive ways such as fabricating smart actuators or mimicking living tissues. Here, we present the controlled growth-like morphing of 2D sheets into 3D shapes by preparing geometric composite structures that deform by residual swelling. The morphing of these geometric composites is dictated by both swelling and geometry, with diffusion controlling the swelling-induced actuation, and geometric confinement dictating the structure's deformed shape. Building on a simple mechanical analog, we present an analytical model that quantitatively describes how the Gaussian and mean curvatures of a thin disk are affected by the interplay among geometry, mechanics, and swelling. This model is in excellent agreement with our experiments and numerics. We show that the dynamics of residual swelling is dictated by a competition between two characteristic diffusive length scales governed by geometry. Our results provide the first 2D analog of Timoshenko's classical formula for the thermal bending of bimetallic beams - our generalization explains how the Gaussian curvature of a 2D geometric composite is affected by geometry and elasticity. The understanding conferred by these results suggests that the controlled shaping of geometric composites may provide a simple complement to traditional manufacturing techniques.
The geometrical structure of quantum theory as a natural generalization of information geometry
Reginatto, Marcel
2015-01-13
Quantum mechanics has a rich geometrical structure which allows for a geometrical formulation of the theory. This formalism was introduced by Kibble and later developed by a number of other authors. The usual approach has been to start from the standard description of quantum mechanics and identify the relevant geometrical features that can be used for the reformulation of the theory. Here this procedure is inverted: the geometrical structure of quantum theory is derived from information geometry, a geometrical structure that may be considered more fundamental, and the Hilbert space of the standard formulation of quantum mechanics is constructed using geometrical quantities. This suggests that quantum theory has its roots in information geometry.
Bourdeaux, Margaret Ellis; Lawry, Lynn; Bonventre, Eugene V; Burkle, Frederick M
2010-03-01
To review the history and goals of the US Department of Defense's largest civilian assistance program, the Overseas Humanitarian, Disaster and Civic Aid Program and to describe the number, geographic regions, years, key words, countries, and types of projects carried out under this program since 2001. Using the program's central database, we reviewed all approved projects since 2001 and tabulated them by year, combatant command, country, and key word. We also reviewed the project descriptions of projects funded between January 1, 2006, and February 9, 2008, and examined how their activities varied by combatant command and year. Of the 5395 projects in the database, 2097 were funded. Projects took place in more than 90 countries, with Southern, Pacific, and Africa Command hosting the greatest number. The most common types of projects were school, health, disaster response, and water infrastructure construction, and disaster-response training. The "global war on terror" was the key word most frequently tagged to project descriptions. Project descriptions lacked stated goals as well as implementation and coordination strategies with potential partners, and did not report outcome or impact indicators. The geographic reach of the program is vast and projects take place in a wide variety of public sectors. Yet their security and civilian assistance value remains unclear given the lack of stated project goals, implementation strategies, or measures of effectiveness. To facilitate transparency and policy discussion, we recommend project proposals include hypotheses as to how they will enhance US security, their relevance to the public sector they address, and outcome and impact indicators that can assess their value and effectiveness.
CAM - Geometric systems integration
NASA Astrophysics Data System (ADS)
Dunlap, G. C.
The integration of geometric and nongeometric information for efficient use of CAM is examined. Requirements for engineering drawings requested by management are noted to involve large volumes of nongeometric data to define the materials and quantity variables which impinge on the required design, so that the actual design may be the last and smaller step in the CAM process. Geometric classification and coding are noted to offer an alpha/numeric identifier for integrating the engineering design, manufacturing, and quality assurance functions. An example is provided of a turbine gear part coding in terms of polycode and monocode displays, showing a possible covering of more than 10 trillion features. Software is stressed as the key to integration of company-wide data.
Special generalized densities and propagators: A geometric account
NASA Astrophysics Data System (ADS)
Canarutto, Daniel
2016-11-01
Starting from a short review of spaces of generalized sections of vector bundles, we give a concise systematic description, in precise geometric terms, of Leray densities, principal value densities, propagators and elementary solutions of field equations in flat spacetime. We then sketch a partly original geometric presentation of free quantum fields and show how propagators arise from their graded commutators in the boson and fermion cases.
Geometric measures of entanglement
Uyanik, K.; Turgut, S.
2010-03-15
The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three-qubit case is discussed and it is argued that the distance to the W states is a new monotone.
Geometrical deuteron stripping revisited
Neoh, Y. S.; Yap, S. L.
2014-03-05
We investigate the reality of the idea of geometrical deuteron stripping originally envisioned by Serber. By taking into account of realistic deuteron wavefunction, nuclear density, and nucleon stopping mean free path, we are able to estimate inclusive deuteron stripping cross section for deuteron energy up to before pion production. Our semiclassical model contains only one global parameter constant for all nuclei which can be approximated by Woods-Saxon or any other spherically symmetric density distribution.
NASA Technical Reports Server (NTRS)
Lada, Charles J.
2005-01-01
This grant funds a research program to use infrared extinction measurements to probe the detailed structure of dark molecular cloud cores and investigate the physical conditions which give rise to star and planet formation. The goals of this program are to acquire, reduce and analyze deep infrared and molecular-line observations of a carefully selected sample of nearby dark clouds in order to internal structure of starless cloud cores and to quantitatively investigate the evolution of such structure through the star and planet formation process. During the second year of this grant, progress toward these goals is discussed.
Perspective: Geometrically frustrated assemblies
NASA Astrophysics Data System (ADS)
Grason, Gregory M.
2016-09-01
This perspective will overview an emerging paradigm for self-organized soft materials, geometrically frustrated assemblies, where interactions between self-assembling elements (e.g., particles, macromolecules, proteins) favor local packing motifs that are incompatible with uniform global order in the assembly. This classification applies to a broad range of material assemblies including self-twisting protein filament bundles, amyloid fibers, chiral smectics and membranes, particle-coated droplets, curved protein shells, and phase-separated lipid vesicles. In assemblies, geometric frustration leads to a host of anomalous structural and thermodynamic properties, including heterogeneous and internally stressed equilibrium structures, self-limiting assembly, and topological defects in the equilibrium assembly structures. The purpose of this perspective is to (1) highlight the unifying principles and consequences of geometric frustration in soft matter assemblies; (2) classify the known distinct modes of frustration and review corresponding experimental examples; and (3) describe outstanding questions not yet addressed about the unique properties and behaviors of this broad class of systems.
Geometric diffusion of quantum trajectories.
Yang, Fan; Liu, Ren-Bao
2015-07-16
A quantum object can acquire a geometric phase (such as Berry phases and Aharonov-Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects.
Geometric diffusion of quantum trajectories
Yang, Fan; Liu, Ren-Bao
2015-01-01
A quantum object can acquire a geometric phase (such as Berry phases and Aharonov–Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects. PMID:26178745
Quantum computation using geometric algebra
NASA Astrophysics Data System (ADS)
Matzke, Douglas James
This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.
Geometric Constructions with the Computer.
ERIC Educational Resources Information Center
Chuan, Jen-chung
The computer can be used as a tool to represent and communicate geometric knowledge. With the appropriate software, a geometric diagram can be manipulated through a series of animation that offers more than one particular snapshot as shown in a traditional mathematical text. Geometric constructions with the computer enable the learner to see and…
Geometric Heat Engines Featuring Power that Grows with Efficiency.
Raz, O; Subaşı, Y; Pugatch, R
2016-04-22
Thermodynamics places a limit on the efficiency of heat engines, but not on their output power or on how the power and efficiency change with the engine's cycle time. In this Letter, we develop a geometrical description of the power and efficiency as a function of the cycle time, applicable to an important class of heat engine models. This geometrical description is used to design engine protocols that attain both the maximal power and maximal efficiency at the fast driving limit. Furthermore, using this method, we also prove that no protocol can exactly attain the Carnot efficiency at nonzero power.
Geometric Heat Engines Featuring Power that Grows with Efficiency
NASA Astrophysics Data System (ADS)
Raz, O.; Subaşı, Y.; Pugatch, R.
2016-04-01
Thermodynamics places a limit on the efficiency of heat engines, but not on their output power or on how the power and efficiency change with the engine's cycle time. In this Letter, we develop a geometrical description of the power and efficiency as a function of the cycle time, applicable to an important class of heat engine models. This geometrical description is used to design engine protocols that attain both the maximal power and maximal efficiency at the fast driving limit. Furthermore, using this method, we also prove that no protocol can exactly attain the Carnot efficiency at nonzero power.
Geometric phase in Bohmian mechanics
Chou, Chia-Chun; Wyatt, Robert E.
2010-10-15
Using the quantum kinematic approach of Mukunda and Simon, we propose a geometric phase in Bohmian mechanics. A reparametrization and gauge invariant geometric phase is derived along an arbitrary path in configuration space. The single valuedness of the wave function implies that the geometric phase along a path must be equal to an integer multiple of 2{pi}. The nonzero geometric phase indicates that we go through the branch cut of the action function from one Riemann sheet to another when we locally travel along the path. For stationary states, quantum vortices exhibiting the quantized circulation integral can be regarded as a manifestation of the geometric phase. The bound-state Aharonov-Bohm effect demonstrates that the geometric phase along a closed path contains not only the circulation integral term but also an additional term associated with the magnetic flux. In addition, it is shown that the geometric phase proposed previously from the ensemble theory is not gauge invariant.
Majstorović, Branislava M; Simić, Snezana; Milaković, Branko D; Vucović, Dragan S; Aleksić, Valentina V
2010-01-01
In anaesthesiology, economic aspects have been insufficiently studied. The aim of this paper was the assessment of rational choice of the anaesthesiological services based on the analysis of the scope, distribution, trend and cost. The costs of anaesthesiological services were counted based on "unit" prices from the Republic Health Insurance Fund. Data were analysed by methods of descriptive statistics and statistical significance was tested by Student's t-test and chi2-test. The number of general anaesthesia was higher and average time of general anaesthesia was shorter, without statistical significance (t-test, p = 0.436) during 2006 compared to the previous year. Local anaesthesia was significantly higher (chi2-test, p = 0.001) in relation to planned operation in emergency surgery. The analysis of total anaesthesiological procedures revealed that a number of procedures significantly increased in ENT and MFH surgery, and ophthalmology, while some reduction was observed in general surgery, orthopaedics and trauma surgery and cardiovascular surgery (chi2-test, p = 0.000). The number of analgesia was higher than other procedures (chi2-test, p = 0.000). The structure of the cost was 24% in neurosurgery, 16% in digestive (general) surgery,14% in gynaecology and obstetrics, 13% in cardiovascular surgery and 9% in emergency room. Anaesthesiological services costs were the highest in neurosurgery, due to the length anaesthesia, and digestive surgery due to the total number of general anaesthesia performed. It is important to implement pharmacoeconomic studies in all departments, and to separate the anaesthesia services for emergency and planned operations. Disproportions between the number of anaesthesia, surgery interventions and the number of patients in surgical departments gives reason to design relation database.
Geometric time delay interferometry
Vallisneri, Michele
2005-08-15
The space-based gravitational-wave observatory LISA, a NASA-ESA mission to be launched after 2012, will achieve its optimal sensitivity using time delay interferometry (TDI), a LISA-specific technique needed to cancel the otherwise overwhelming laser noise in the interspacecraft phase measurements. The TDI observables of the Michelson and Sagnac types have been interpreted physically as the virtual measurements of a synthesized interferometer. In this paper, I present Geometric TDI, a new and intuitive approach to extend this interpretation to all TDI observables. Unlike the standard algebraic formalism, Geometric TDI provides a combinatorial algorithm to explore exhaustively the space of second-generation TDI observables (i.e., those that cancel laser noise in LISA-like interferometers with time-dependent arm lengths). Using this algorithm, I survey the space of second-generation TDI observables of length (i.e., number of component phase measurements) up to 24, and I identify alternative, improved forms of the standard second-generation TDI observables. The alternative forms have improved high-frequency gravitational-wave sensitivity in realistic noise conditions (because they have fewer nulls in the gravitational-wave and noise response functions), and are less susceptible to instrumental gaps and glitches (because their component phase measurements span shorter time periods)
Geometric Modeling Applications Interface Program (GMAP). Volume 2. Program Description
1989-09-01
Retirement for Cause ..................................................... 3- 41 3-21 Interrelationship of GMAP Documents...M a 9 2a. ~* .E 0 4) -------- U- 00 004-4 a___ cam 0 0 Z CL cw; 3- 41 CI FTR560240001U September 1989 Initially, GMAP looked at several programs...oteInpcinPanGnrto Sub System Intgratof IBIs.tfaiithPats hinecto AMofa Syservic Rene aoressr bade fo sufaenoaiesuin fluo.ResCInteetrface inspetin. ee eainhp 3.3.21
Vulnerability Analyst’s Guide to Geometric Target Description
1992-09-01
46 5.3 Surrogacy ..............................................46 5.4 Specialized Targets......................................46 5.5...adequate representation of shielding components must be included. 5.3 Surrogacy Sometimes, so little information is available about a target that it is
Decaestecker, C; Lopes, B S; Gordower, L; Camby, I; Cras, P; Martin, J J; Kiss, R; VandenBerg, S R; Salmon, I
1997-04-01
The oligoastrocytoma, as a mixed glioma, represents a nosologic dilemma with respect to precisely defining the oligodendroglial and astroglial phenotypes that constitute the neoplastic cell lineages of these tumors. In this study, cell image analysis with Feulgen-stained nuclei was used to distinguish between oligodendroglial and astrocytic phenotypes in oligodendrogliomas and astrocytomas and then applied to mixed oligoastrocytomas. Quantitative features with respect to chromatin pattern (30 variables) and DNA ploidy (8 variables) were evaluated on Feulgen-stained nuclei in a series of 71 gliomas using computer-assisted microscopy. These included 32 oligodendrogliomas (OLG group: 24 grade II and 8 grade III tumors according to the WHO classification), 32 astrocytomas (AST group: 13 grade II and 19 grade III tumors), and 7 oligoastrocytomas (OLGAST group). Initially, image analysis with multivariate statistical analyses (Discriminant Analysis) could identify each glial tumor group. Highly significant statistical differences were obtained distinguishing the morphonuclear features of oligodendrogliomas from those of astrocytomas, regardless of their histological grade. When compared with the 7 mixed oligoastrocytomas under study, 5 exhibited DNA ploidy and chromatin pattern characteristics similar to grade II oligodendrogliomas, I to grade III oligodendrogliomas, and I to grade II astrocytomas. Using multifactorial statistical analyses (Discriminant Analysis combined with Principal Component Analysis). It was possible to quantify the proportion of "typical" glial cell phenotypes that compose grade II and III oligodendrogliomas and grade II and III astrocytomas in each mixed glioma. Cytometric image analysis may be an important adjunct to routine histopathology for the reproducible identification of neoplasms containing a mixture of oligodendroglial and astrocytic phenotypes.
Wang, W Q; Song, S Q; Li, S H; Gan, Y Y; Wu, J H; Cheng, H Y
2009-01-01
The effect of stratification on dormancy release of grape seeds crossing from the sub- to the supraoptimal range of temperatures and water contents was analysed by modified threshold models. The stratification impacted on dormancy release in three different ways: (i) dormancy was consistently released with prolonged stratification time when stratified at temperatures of <15 degrees C; (ii) at 15 degrees C and 20 degrees C, the stratification effect initially increased, and then decreased with extended time; and (iii) stratification at 25 degrees C only reduced germinable seeds. These behaviours indicated that stratification could not only release primary dormancy but also induce secondary dormancy in grape seed. The rate of dormancy release changed linearly in two phases, while induction increased exponentially with increasing temperature. The thermal time approaches effectively quantified dormancy release only at suboptimal temperature, but a quantitative method to integrate the occurrence of dormancy release and induction at the same time could describe it well at either sub- or supraoptimal temperatures. The regression with the percentage of germinable seeds versus stratification temperature or water content within both the sub- and supraoptimal range revealed how the optimal temperature (T(so)) and water content (W(so)) for stratification changed. The T(so) moved from 10.6 degrees C to 5.3 degrees C with prolonged time, while W(so) declined from >0.40 g H2O g DW(-1) at 5 degrees C to approximately 0.23 g H2O g DW(-1) at 30 degrees C. Dormancy release in grape seeds can occur across a very wide range of conditions, which has important implications for their ability to adapt to a changeable environment in the wild.
Geometric precipices in string cosmology
Kaloper, Nemanja; Watson, Scott
2008-03-15
We consider the effects of graviton multiplet fields on transitions between string gas phases. Focusing on the dilaton field, we show that it may obstruct transitions between different thermodynamic phases of the string gas, because the sign of its dimensionally reduced, T-duality invariant, part is conserved when the energy density of the Universe is positive. Thus, many interesting solutions for which this sign is positive end up in a future curvature singularity. Because of this, some of the thermodynamic phases of the usual gravitating string gases behave like superselection sectors. For example, a past-regular Hagedorn phase and an expanding Friedmann-Robertson-Walker (FRW) phase dominated by string momentum modes cannot be smoothly connected in the framework of string cosmology with positive sources. The singularity separates them like a geometric precipice in the moduli space, preventing the dynamics of the theory from bridging across. Sources which simultaneously violate the positivity of energy and null energy condition (NEC) could modify these conclusions. We provide a quantitative measure of positivity of energy and NEC violations that would be necessary for such transitions. These effects must dominate the Universe at the moment of transition, altering the standard gas pictures. At present, it is not known how to construct such sources from first principles in string theory.
Geometric and functional organization of cortical circuits.
Shepherd, Gordon M G; Stepanyants, Armen; Bureau, Ingrid; Chklovskii, Dmitri; Svoboda, Karel
2005-06-01
Can neuronal morphology predict functional synaptic circuits? In the rat barrel cortex, 'barrels' and 'septa' delineate an orderly matrix of cortical columns. Using quantitative laser scanning photostimulation we measured the strength of excitatory projections from layer 4 (L4) and L5A to L2/3 pyramidal cells in barrel- and septum-related columns. From morphological reconstructions of excitatory neurons we computed the geometric circuit predicted by axodendritic overlap. Within most individual projections, functional inputs were predicted by geometry and a single scale factor, the synaptic strength per potential synapse. This factor, however, varied between projections and, in one case, even within a projection, up to 20-fold. Relationships between geometric overlap and synaptic strength thus depend on the laminar and columnar locations of both the pre- and postsynaptic neurons, even for neurons of the same type. A large plasticity potential appears to be incorporated into these circuits, allowing for functional 'tuning' with fixed axonal and dendritic arbor geometry.
Hemodynamic characterization of geometric cerebral aneurysm templates.
Nair, Priya; Chong, Brian W; Indahlastari, Aprinda; Lindsay, James; DeJeu, David; Parthasarathy, Varsha; Ryan, Justin; Babiker, Haithem; Workman, Christopher; Gonzalez, L Fernando; Frakes, David
2016-07-26
Hemodynamics are currently considered to a lesser degree than geometry in clinical practices for evaluating cerebral aneurysm (CA) risk and planning CA treatment. This study establishes fundamental relationships between three clinically recognized CA geometric factors and four clinically relevant hemodynamic responses. The goal of the study is to develop a more combined geometric/hemodynamic basis for informing clinical decisions. Flows within eight idealized template geometries were simulated using computational fluid dynamics and measured using particle image velocimetry under both steady and pulsatile flow conditions. The geometric factor main effects were then analyzed to quantify contributions made by the geometric factors (aneurysmal dome size (DS), dome-to-neck ratio (DNR), and parent-vessel contact angle (PV-CA)) to effects on the hemodynamic responses (aneurysmal and neck-plane root-mean-square velocity magnitude (Vrms), aneurysmal wall shear stress (WSS), and cross-neck flow (CNF)). Two anatomical aneurysm models were also examined to investigate how well the idealized findings would translate to more realistic CA geometries. DNR made the greatest contributions to effects on hemodynamics including a 75.05% contribution to aneurysmal Vrms and greater than 35% contributions to all responses. DS made the next greatest contributions, including a 43.94% contribution to CNF and greater than 20% contributions to all responses. PV-CA and several factor interactions also made contributions of greater than 10%. The anatomical aneurysm models and the most similar idealized templates demonstrated consistent hemodynamic response patterns. This study demonstrates how individual geometric factors, and combinations thereof, influence CA hemodynamics. Bridging the gap between geometry and flow in this quantitative yet practical way may have potential to improve CA evaluation and treatment criteria. Agreement among results from idealized and anatomical models further
Geometrical aspects of entanglement
Leinaas, Jon Magne; Myrheim, Jan; Ovrum, Eirik
2006-07-15
We study geometrical aspects of entanglement, with the Hilbert-Schmidt norm defining the metric on the set of density matrices. We focus first on the simplest case of two two-level systems and show that a 'relativistic' formulation leads to a complete analysis of the question of separability. Our approach is based on Schmidt decomposition of density matrices for a composite system and nonunitary transformations to a standard form. The positivity of the density matrices is crucial for the method to work. A similar approach works to some extent in higher dimensions, but is a less powerful tool. We further present a numerical method for examining separability and illustrate the method by a numerical study of bound entanglement in a composite system of two three-level systems.
Goldberg, P.W.
1993-04-01
In this paper we consider the problem of learning the positions of spheres in metric spaces, given as data randomly drawn points classified according to whether they are internal or external to an unknown sphere. The particular metrics under consideration are geometrical shape metrics, and the results are intended to be applicable to the problem of learning to identify a shape from related shapes classified according to whether they resemble it visually. While it is typically NP-hard to locate a central point for a hypothesis sphere, we find that it is however often possible to obtain a non-spherical hypothesis which can accurately predict whether further random points lie within the unknown sphere. We exhibit algorithms which achieve this, and in the process indicate useful general techniques for computational learning. Finally we exhibit a natural shape metric and show that it defines a class of spheres not predictable in this sense, subject to standard cryptographic assumptions.
The relationship between strain geometry and geometrically necessary dislocations
NASA Astrophysics Data System (ADS)
Hansen, Lars; Wallis, David
2016-04-01
The kinematics of past deformations are often a primary goal in structural analyses of strained rocks. Details of the strain geometry, in particular, can help distinguish hypotheses about large-scale tectonic phenomena. Microstructural indicators of strain geometry have been heavily utilized to investigate large-scale kinematics. However, many of the existing techniques require structures for which the initial morphology is known, and those structures must undergo the same deformation as imposed macroscopically. Many deformed rocks do not exhibit such convenient features, and therefore the strain geometry is often difficult (if not impossible) to ascertain. Alternatively, crystallographic textures contain information about the strain geometry, but the influence of strain geometry can be difficult to separate from other environmental factors that might affect slip system activity and therefore the textural evolution. Here we explore the ability for geometrically necessary dislocations to record information about the deformation geometry. It is well known that crystallographic slip due to the motion of dislocations yields macroscopic plastic strain, and the mathematics are established to relate dislocation glide on multiple slip systems to the strain tensor of a crystal. This theoretical description generally assumes that dislocations propagate across the entire crystal. However, at any point during the deformation, dislocations are present that have not fully transected the crystal, existing either as free dislocations or as dislocations organized into substructures like subgrain boundaries. These dislocations can remain in the lattice after deformation if the crystal is quenched sufficiently fast, and we hypothesize that this residual dislocation population can be linked to the plastic strain geometry in a quantitative manner. To test this hypothesis, we use high-resolution electron backscatter diffraction to measure lattice curvatures in experimentally deformed
Descriptive approaches to landscape analysis
R. Burton Litton Jr.
1979-01-01
Descriptive landscape analyses include various procedures used to document visual/scenic resources. Historic and regional examples of landscape description represent desirable insight for contemporary professional inventory work. Routed and areal landscape inventories are discussed as basic tools. From them, qualitative and quantitative evaluations can be developed...
Light polarization: A geometric-algebra approach
NASA Astrophysics Data System (ADS)
Baylis, W. E.; Bonenfant, J.; Derbyshire, J.; Huschilt, J.
1993-06-01
The geometric algebra of three-dimensional space (the ``Pauli algebra'') is known to provide an efficient geometric description of electromagnetic phenomena. Here, it is applied to the three-dimensional Stokes subspace to describe the polarization of an approximately monochromatic collimated beam of electromagnetic radiation. The coherency density ρ is a real element of the algebra whose components are the four Stokes parameters: a scalar representing the total photon flux density plus a three-dimensional vector whose direction and length in the Poincaré sphere give the type and degree of polarization. The detection of the radiation and the incoherent and coherent modification of the polarization by various optical elements are calculated by algebraic multiplication which has faithful representations in 2×2 matrices. One matrix representation of ρ is the coherency matrix with which Jones and Mueller matrices are related whereas another representation is the spin density matrix. However, the calculations are simplest to perform and interpret in the algebraic form independent of any particular matrix representation. It is shown that any possible change in the Stokes parameters can be treated algebraically by a combination of attenuation, depolarization, polarization, and rotation transformations of ρ. The geometric algebra thus unifies Stokes parameters, the Poincaré sphere, Jones and Mueller matrices, and the coherency and density matrices in a single, simple formalism.
Quantification of the geometrical parameters of non-cylindrical folds
NASA Astrophysics Data System (ADS)
Zulauf, G.; Zulauf, J.; Maul, H.
2017-07-01
The geometrical parameters of natural folds are used by structural geologists to estimate finite strain and rheological properties of deformed rocks. The relation between geometry and rheology is well understood in cases of cylindrical folds, but is still limited for non-cylindrical folds, although the latter are frequent in nature. The sparsity of quantitative geometrical data of non-cylindrical folds can be explained by the small number of 3D exposures and by the lack of robust methods to quantify their geometrical parameters in 3D space. We present a new workflow, which can be used to quantify geometrical parameters of non-cylindrical folds. 3D fold geometry is described using fold wavelength, λ, arc-length, L, and amplitude, A. As most natural folds do not show ideal shapes, but are affected by various types of discontinuities, the new procedure is not fully automatic, but requires the manual selection of measuring profiles along which the geometrical parameters are constrained. The new workflow is tested using natural and experimentally produced non-cylindrical folds. The geometric parameters obtained can be used to improve our understanding of fold kinematics and fold mechanics and should assist the quantitative analysis of non-cylindrical folds present in gneiss and salt domes and in rocks containing reservoirs of hydrocarbons and minerals deposits.
Salt bridges: geometrically specific, designable interactions.
Donald, Jason E; Kulp, Daniel W; DeGrado, William F
2011-03-01
Salt bridges occur frequently in proteins, providing conformational specificity and contributing to molecular recognition and catalysis. We present a comprehensive analysis of these interactions in protein structures by surveying a large database of protein structures. Salt bridges between Asp or Glu and His, Arg, or Lys display extremely well-defined geometric preferences. Several previously observed preferences are confirmed, and others that were previously unrecognized are discovered. Salt bridges are explored for their preferences for different separations in sequence and in space, geometric preferences within proteins and at protein-protein interfaces, co-operativity in networked salt bridges, inclusion within metal-binding sites, preference for acidic electrons, apparent conformational side chain entropy reduction on formation, and degree of burial. Salt bridges occur far more frequently between residues at close than distant sequence separations, but, at close distances, there remain strong preferences for salt bridges at specific separations. Specific types of complex salt bridges, involving three or more members, are also discovered. As we observe a strong relationship between the propensity to form a salt bridge and the placement of salt-bridging residues in protein sequences, we discuss the role that salt bridges might play in kinetically influencing protein folding and thermodynamically stabilizing the native conformation. We also develop a quantitative method to select appropriate crystal structure resolution and B-factor cutoffs. Detailed knowledge of these geometric and sequence dependences should aid de novo design and prediction algorithms. Copyright © 2010 Wiley-Liss, Inc.
Geometric Reasoning in an Active-Engagement Upper-Division E&M Classroom
ERIC Educational Resources Information Center
Cerny, Leonard Thomas
2012-01-01
A combination of theoretical perspectives is used to create a rich description of student reasoning when facing a highly-geometric electricity and magnetism problem in an upper-division active-engagement physics classroom at Oregon State University. Geometric reasoning as students encounter problem situations ranging from familiar to novel is…
Geometric Reasoning in an Active-Engagement Upper-Division E&M Classroom
ERIC Educational Resources Information Center
Cerny, Leonard Thomas
2012-01-01
A combination of theoretical perspectives is used to create a rich description of student reasoning when facing a highly-geometric electricity and magnetism problem in an upper-division active-engagement physics classroom at Oregon State University. Geometric reasoning as students encounter problem situations ranging from familiar to novel is…
Geometrical method of decoupling
NASA Astrophysics Data System (ADS)
Baumgarten, C.
2012-12-01
The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries—like midplane symmetry—are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane, and (under certain circumstances) the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as, for instance, the method of Teng and Edwards. In a preceding paper, it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately, the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all conceivable cases. Hence, a systematic derivation of a more general treatment seemed advisable. In a second paper, the author suggested the use of real Dirac matrices as basic tools for coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. The decoupling of symplectic matrices which are exponentials of such Hamiltonian matrices can be deduced from this in a few steps. It is shown that this algebraic decoupling is closely related to a geometric “decoupling” by the orthogonalization of the vectors E→, B→, and P→, which were introduced with the so-called “electromechanical equivalence.” A mathematical analysis of the problem can be traced down to the task of finding a structure-preserving block diagonalization of symplectic or Hamiltonian matrices. Structure preservation means in this context that the (sequence of) transformations must be symplectic and hence canonical. When used iteratively, the decoupling
GEOMETRICAL ISOMERS OF RETINENE
Hubbard, Ruth; Gregerman, Robert I.; Wald, George
1953-01-01
Five crystalline retinenes have been isolated, which have every appearance of being cis-trans isomers of one another. They are all-trans retinene; three apparently mono-cis isomers: neoretinenes a and b and isoretinene a; and isoretinene b, an apparently di-cis isomer. The absorption spectra of these substances display the relations expected of cis-trans isomers. The main absorption band is displaced 5.5 to 7 mµ toward shorter wave lengths for each presumptive cis linkage. Some of the presumptive cis isomers also display a cis peak at 255 to 260 mµ. All five substances yield an identical blue product on mixing with antimony chloride. All of them are converted by light to what appears to be an identical mixture of stereoisomers. Heat isomerizes them very slowly; only neoretinene b exhibits large changes on heating at 70°C. for 3 hours. The various isomers have been extensively interconverted by gentle procedures, and all of them have been converted to all-trans retinene. The present theory of cis-trans isomerism in carotenoids predicts the existence of four stable isomers of retinene. Instead we seem to have five—specifically three mono-cis forms where two are expected. There is no doubt that all these substances are closely related isomers of one another. The only point in question is whether they differ in part by something other than cis-trans configuration. One possibility, as yet little supported by evidence, is that isomerization between β- and α-ionone rings may be involved. If, however, as seems more likely, all these substances are geometrical isomers of one another, some modification is needed in the present theory of configurational relationships in this class of compounds. PMID:13022935
Quantitative description and modeling of real networks
NASA Astrophysics Data System (ADS)
Capocci, Andrea; Caldarelli, Guido; de Los Rios, Paolo
2003-10-01
We present data analysis and modeling of two particular cases of study in the field of growing networks. We analyze World Wide Web data set and authorship collaboration networks in order to check the presence of correlation in the data. The results are reproduced with good agreement through a suitable modification of the standard Albert-Barabási model of network growth. In particular, intrinsic relevance of sites plays a role in determining the future degree of the vertex.
Shi, Runhua; McLarty, Jerry W
2009-10-01
In this article, we introduced basic concepts of statistics, type of distributions, and descriptive statistics. A few examples were also provided. The basic concepts presented herein are only a fraction of the concepts related to descriptive statistics. Also, there are many commonly used distributions not presented herein, such as Poisson distributions for rare events and exponential distributions, F distributions, and logistic distributions. More information can be found in many statistics books and publications.
Geometric phase shifting digital holography.
Jackin, Boaz Jessie; Narayanamurthy, C S; Yatagai, Toyohiko
2016-06-01
A new phase shifting digital holographic technique using a purely geometric phase in Michelson interferometric geometry is proposed. The geometric phase in the system does not depend upon either optical path length or wavelength, unlike dynamic phase. The amount of geometric phase generated is controllable through a rotating wave plate. The new approach has unique features and major advantages in holographic measurement of transparent and reflecting three-dimensional (3D) objects. Experimental results on surface shape measurement and imaging of 3D objects are presented using the proposed method.
Geometric Effects on Electron Cloud
Wang, L
2007-07-06
The development of an electron cloud in the vacuum chambers of high intensity positron and proton storage rings may limit the machine performances by inducing beam instabilities, beam emittance increase, beam loss, vacuum pressure increases and increased heat load on the vacuum chamber wall. The electron multipacting is a kind of geometric resonance phenomenon and thus is sensitive to the geometric parameters such as the aperture of the beam pipe, beam shape and beam bunch fill pattern, etc. This paper discusses the geometric effects on the electron cloud build-up in a beam chamber and examples are given for different beams and accelerators.
Optical traps with geometric aberrations
Roichman, Yael; Waldron, Alex; Gardel, Emily; Grier, David G
2006-05-20
We assess the influence of geometric aberrations on the in-plane performance of optical traps by studying the dynamics of trapped colloidal spheres in deliberately distorted holographic optical tweezers. The lateral stiffness of the traps turns out to be insensitive to moderate amounts of coma, astigmatism, and spherical aberration. Moreover holographic aberration correction enables us to compensate inherent shortcomings in the optical train, thereby adaptively improving its performance. We also demonstrate the effects of geometric aberrations on the intensity profiles of optical vortices, whose readily measured deformations suggest a method for rapidly estimating and correcting geometric aberrations in holographic trapping systems.
A Geometrical Version of the Maxwell-Vlasov Hamiltonian Structure
NASA Astrophysics Data System (ADS)
Vittot, Michel; Morrison, Philip
2014-10-01
We present a geometrization of the Hamiltonian approach of classical electrodynamics, via (non-canonical) Poisson structures. This relativistic Hamiltonian framework (introduced by Morrison, Marsden, Weinstein) is a field theory written in terms of differential forms, independently of the gauge potentials. This algebraic and geometric description of the Vlasov kinetics is well suited for a perturbation theory, in a strong inhomogeneous magnetic field (expansion in 1/B, with all the curvature terms...), like in magnetically confined plasmas, and in any coordinates, for instance adapted to a Tokamak (toroidal coordinates, or else...).
Geometric phase gradient and spin Hall effect of light
NASA Astrophysics Data System (ADS)
Ling, Xiaohui; Zhou, Xinxing; Qiu, Cheng-Wei
2016-10-01
The spin Hall effect (SHE) of light originates from the spin-orbit interaction, which can be explained in terms of two geometric phases: the Rytov-Vladimirskii-Berry phase and the Pancharatnam-Berry phase. Here we present a unified theoretical description of the SHE based on the two types of geometric phase gradients, and observe experimentally the SHE in structured dielectric metasurfaces induced by the PB phase. Unlike the weak real-space spin-Hall shift induced by the SRB phase occurring at interfacial reflection/refraction, the observed SHE occurs in momentum space is large enough to be measured directly.
Geometric derivations of minimal sets of sufficient multiview constraints
Thomas, Orrin H.; Oshel, Edward R.
2012-01-01
Geometric interpretations of four of the most common determinant formulations of multiview constraints are given, showing that they all enforce the same geometry and that all of the forms commonly in use in the machine vision community are a subset of a more general form. Generalising the work of Yi Ma yields a new general 2 x 2 determinant trilinear and 3 x 3 determinant quadlinear. Geometric descriptions of degenerate multiview constraints are given, showing that it is necessary, but insufficient, that the determinant equals zero. Understanding the degeneracies leads naturally into proofs for minimum sufficient sets of bilinear, trilinear and quadlinear constraints for arbitrary numbers of conjugate observations.
Guitars, Violins, and Geometric Sequences
ERIC Educational Resources Information Center
Barger, Rita; Haehl, Martha
2007-01-01
This article describes middle school mathematics activities that relate measurement, ratios, and geometric sequences to finger positions or the placement of frets on stringed musical instruments. (Contains 2 figures and 2 tables.)
Activities: Geometric Transformations. Part 2.
ERIC Educational Resources Information Center
Eddins, Susan K.; And Others
1994-01-01
Presents a lesson that connects basic transformational concepts with transformations on a Cartesian-coordinate system, culminating with the application of matrix operations to perform geometric transformations. Includes reproducible student worksheets and assessment activities. (MKR)
Geometric symmetries in light nuclei
NASA Astrophysics Data System (ADS)
Bijker, R.
2017-06-01
The algebraic cluster model is is applied to study cluster states in the nuclei12C and16O. The observed level sequences can be understood in terms of the underlying discrete symmetry that characterizes the geometrical configuration of the α-particles, i.e. an equilateral triangle for12C, and a regular tetrahedron for16O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of α-particles.
Antenna with Dielectric Having Geometric Patterns
NASA Technical Reports Server (NTRS)
Dudley, Kenneth L. (Inventor); Elliott, Holly A. (Inventor); Cravey, Robin L. (Inventor); Connell, John W. (Inventor); Ghose, Sayata (Inventor); Watson, Kent A. (Inventor); Smith, Jr., Joseph G. (Inventor)
2013-01-01
An antenna includes a ground plane, a dielectric disposed on the ground plane, and an electrically-conductive radiator disposed on the dielectric. The dielectric includes at least one layer of a first dielectric material and a second dielectric material that collectively define a dielectric geometric pattern, which may comprise a fractal geometry. The radiator defines a radiator geometric pattern, and the dielectric geometric pattern is geometrically identical, or substantially geometrically identical, to the radiator geometric pattern.
Leaf Morphology, Taxonomy and Geometric Morphometrics: A Simplified Protocol for Beginners
Viscosi, Vincenzo; Cardini, Andrea
2011-01-01
Taxonomy relies greatly on morphology to discriminate groups. Computerized geometric morphometric methods for quantitative shape analysis measure, test and visualize differences in form in a highly effective, reproducible, accurate and statistically powerful way. Plant leaves are commonly used in taxonomic analyses and are particularly suitable to landmark based geometric morphometrics. However, botanists do not yet seem to have taken advantage of this set of methods in their studies as much as zoologists have done. Using free software and an example dataset from two geographical populations of sessile oak leaves, we describe in detailed but simple terms how to: a) compute size and shape variables using Procrustes methods; b) test measurement error and the main levels of variation (population and trees) using a hierachical design; c) estimate the accuracy of group discrimination; d) repeat this estimate after controlling for the effect of size differences on shape (i.e., allometry). Measurement error was completely negligible; individual variation in leaf morphology was large and differences between trees were generally bigger than within trees; differences between the two geographic populations were small in both size and shape; despite a weak allometric trend, controlling for the effect of size on shape slighly increased discrimination accuracy. Procrustes based methods for the analysis of landmarks were highly efficient in measuring the hierarchical structure of differences in leaves and in revealing very small-scale variation. In taxonomy and many other fields of botany and biology, the application of geometric morphometrics contributes to increase scientific rigour in the description of important aspects of the phenotypic dimension of biodiversity. Easy to follow but detailed step by step example studies can promote a more extensive use of these numerical methods, as they provide an introduction to the discipline which, for many biologists, is less
Geometric aspects of Painlevé equations
NASA Astrophysics Data System (ADS)
Kajiwara, Kenji; Noumi, Masatoshi; Yamada, Yasuhiko
2017-02-01
In this paper a comprehensive review is given on the current status of achievements in the geometric aspects of the Painlevé equations, with a particular emphasis on the discrete Painlevé equations. The theory is controlled by the geometry of certain rational surfaces called the spaces of initial values, which are characterized by eight point configuration on {{{P}}}1× {{{P}}}1 and classified according to the degeneration of points. We give a systematic description of the equations and their various properties, such as affine Weyl group symmetries, hypergeometric solutions and Lax pairs under this framework, by using the language of Picard lattice and root systems. We also provide with a collection of basic data; equations, point configurations/root data, Weyl group representations, Lax pairs, and hypergeometric solutions of all possible cases.
Monolithic geometric anti-spring blades
NASA Astrophysics Data System (ADS)
Cella, G.; Sannibale, V.; DeSalvo, R.; Márka, S.; Takamori, A.
2005-03-01
In this article we investigate the principle and properties of a vertical passive seismic noise attenuator conceived for ground based gravitational wave interferometers. This mechanical attenuator based on a particular geometry of cantilever blades called monolithic geometric anti springs (MGAS) permits the design of mechanical harmonic oscillators with very low resonant frequency (below 10 mHz). Here we address the theoretical description of the mechanical device, focusing on the most important quantities for the low-frequency regime, on the distribution of internal stresses, and on the thermal stability. In order to obtain physical insight of the attenuator peculiarities, we devise some simplified models, rather than use the brute force of finite element analysis. Those models have been used to optimize the design of a seismic attenuation system prototype for LIGO advanced configurations and for the next generation of the TAMA interferometer.
Geometric Observers for Dynamically Evolving Curves
Niethammer, Marc; Vela, Patricio A.; Tannenbaum, Allen
2009-01-01
This paper proposes a deterministic observer design for visual tracking based on nonparametric implicit (level-set) curve descriptions. The observer is continuous discrete with continuous-time system dynamics and discrete-time measurements. Its state-space consists of an estimated curve position augmented by additional states (e.g., velocities) associated with every point on the estimated curve. Multiple simulation models are proposed for state prediction. Measurements are performed through standard static segmentation algorithms and optical-flow computations. Special emphasis is given to the geometric formulation of the overall dynamical system. The discrete-time measurements lead to the problem of geometric curve interpolation and the discrete-time filtering of quantities propagated along with the estimated curve. Interpolation and filtering are intimately linked to the correspondence problem between curves. Correspondences are established by a Laplace-equation approach. The proposed scheme is implemented completely implicitly (by Eulerian numerical solutions of transport equations) and thus naturally allows for topological changes and subpixel accuracy on the computational grid. PMID:18421113
Gaussian geometric discord in terms of Hellinger distance
Suciu, Serban Isar, Aurelian
2015-12-07
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we address the quantification of general non-classical correlations in Gaussian states of continuous variable systems from a geometric perspective. We give a description of the Gaussian geometric discord by using the Hellinger distance as a measure for quantum correlations between two non-interacting non-resonant bosonic modes embedded in a thermal environment. We evaluate the Gaussian geometric discord by taking two-mode squeezed thermal states as initial states of the system and show that it has finite values between 0 and 1 and that it decays asymptotically to zero in time under the effect of the thermal bath.
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.
Arrieta, Jorge; Cartwright, Julyan H E; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2015-01-01
Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach
Arrieta, Jorge; Cartwright, Julyan H. E.; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2015-01-01
Mixing fluid in a container at low Reynolds number— in an inertialess environment—is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the “belly phase,” peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing. PMID:26154384
ERIC Educational Resources Information Center
Beller, Charley
2013-01-01
The study of definite descriptions has been a central part of research in linguistics and philosophy of language since Russell's seminal work "On Denoting" (Russell 1905). In that work Russell quickly dispatches analyses of denoting expressions with forms like "no man," "some man," "a man," and "every…
ERIC Educational Resources Information Center
Beller, Charley
2013-01-01
The study of definite descriptions has been a central part of research in linguistics and philosophy of language since Russell's seminal work "On Denoting" (Russell 1905). In that work Russell quickly dispatches analyses of denoting expressions with forms like "no man," "some man," "a man," and "every…
Geometric incompatibility in a fault system.
Gabrielov, A; Keilis-Borok, V; Jackson, D D
1996-01-01
Interdependence between geometry of a fault system, its kinematics, and seismicity is investigated. Quantitative measure is introduced for inconsistency between a fixed configuration of faults and the slip rates on each fault. This measure, named geometric incompatibility (G), depicts summarily the instability near the fault junctions: their divergence or convergence ("unlocking" or "locking up") and accumulation of stress and deformations. Accordingly, the changes in G are connected with dynamics of seismicity. Apart from geometric incompatibility, we consider deviation K from well-known Saint Venant condition of kinematic compatibility. This deviation depicts summarily unaccounted stress and strain accumulation in the region and/or internal inconsistencies in a reconstruction of block- and fault system (its geometry and movements). The estimates of G and K provide a useful tool for bringing together the data on different types of movement in a fault system. An analog of Stokes formula is found that allows determination of the total values of G and K in a region from the data on its boundary. The phenomenon of geometric incompatibility implies that nucleation of strong earthquakes is to large extent controlled by processes near fault junctions. The junctions that have been locked up may act as transient asperities, and unlocked junctions may act as transient weakest links. Tentative estimates of K and G are made for each end of the Big Bend of the San Andreas fault system in Southern California. Recent strong earthquakes Landers (1992, M = 7.3) and Northridge (1994, M = 6.7) both reduced K but had opposite impact on G: Landers unlocked the area, whereas Northridge locked it up again. Images Fig. 1 Fig. 2 PMID:11607673
Geometrically nonlinear behavior of piezoelectric laminated plates
NASA Astrophysics Data System (ADS)
Rabinovitch, Oded
2005-08-01
The geometrically nonlinear behavior of piezo-laminated plates actuated with isotropic or anisotropic piezoelectric layers is analytically investigated. The analytical model is derived using the variational principle of virtual work along with the lamination and plate theories, the von Karman large displacement and moderate rotation kinematic relations, and the anisotropic piezoelectric constitutive laws. A solution strategy that combines the approach of the method of lines, the advantages of the finite element concept, and the variational formulation is developed. This approach yields a set of nonlinear ordinary differential equations with nonlinear boundary conditions, which are solved using the multiple-shooting method. Convergence and verification of the model are examined through comparison with linear and nonlinear results of other approximation methods. The nonlinear response of two active plate structures is investigated numerically. The first plate is actuated in bending using monolithic piezoceramic layers and the second one is actuated in twist using macro-fiber composites. The results quantitatively reveal the complicated in-plane stress state associated with the piezoelectric actuation and the geometrically nonlinear coupling of the in-plane and out-of-plane responses of the plate. The influence of the nonlinear effects ranges from significant stiffening in certain combinations of electrical loads and boundary conditions to amplifications of the induced deflections in others. The paper closes with a summary and conclusions.
Geometric similarity between protein-RNA interfaces.
Zhou, Peng; Zou, Jianwei; Tian, Feifei; Shang, Zhicai
2009-12-01
A new method is described to measure the geometric similarity between protein-RNA interfaces quantitatively. The method is based on a procedure that dissects the interface geometry in terms of the spatial relationships between individual amino acid nucleotide pairs. Using this technique, we performed an all-on-all comparison of 586 protein-RNA interfaces deposited in the current Protein Data Bank, as the result, an interface-interface similarity score matrix was obtained. Based upon this matrix, hierarchical clustering was carried out which yielded a complete clustering tree for the 586 protein-RNA interfaces. By investigating the organizing behavior of the clustering tree and the SCOP classification of protein partners in complexes, a geometrically nonredundant, diverse data set (representative data set) consisting of 45 distinct protein-RNA interfaces was extracted for the purpose of studying protein-RNA interactions, RNA regulations, and drug design. We classified protein-RNA interfaces into three types. In type I, the families and interface structural classes of the protein partners, as well as the interface geometries are all similar. In type II, the interface geometries and the interface structural classes are similar, whereas the protein families are different. In type III, only the interface geometries are similar but the protein families and the interface structural classes are distinct. Furthermore, we also show two new RNA recognition themes derived from the representative data set.
Geometric scalar theory of gravity
Novello, M.; Bittencourt, E.; Goulart, E.; Salim, J.M.; Toniato, J.D.; Moschella, U. E-mail: eduhsb@cbpf.br E-mail: egoulart@cbpf.br E-mail: toniato@cbpf.br
2013-06-01
We present a geometric scalar theory of gravity. Our proposal will be described using the ''background field method'' introduced by Gupta, Feynman, Deser and others as a field theory formulation of general relativity. We analyze previous criticisms against scalar gravity and show how the present proposal avoids these difficulties. This concerns not only the theoretical complaints but also those related to observations. In particular, we show that the widespread belief of the conjecture that the source of scalar gravity must be the trace of the energy-momentum tensor — which is one of the main difficulties to couple gravity with electromagnetic phenomenon in previous models — does not apply to our geometric scalar theory. From the very beginning this is not a special relativistic scalar gravity. The adjective ''geometric'' pinpoints its similarity with general relativity: this is a metric theory of gravity. Some consequences of this new scalar theory are explored.
Guiding light via geometric phases
NASA Astrophysics Data System (ADS)
Slussarenko, Sergei; Alberucci, Alessandro; Jisha, Chandroth P.; Piccirillo, Bruno; Santamato, Enrico; Assanto, Gaetano; Marrucci, Lorenzo
2016-09-01
All known methods for transverse confinement and guidance of light rely on modification of the refractive index, that is, on the scalar properties of electromagnetic radiation. Here, we disclose the concept of a dielectric waveguide that exploits vectorial spin-orbit interactions of light and the resulting geometric phases. The approach relies on the use of anisotropic media with an optic axis that lies orthogonal to the propagation direction but is spatially modulated, so that the refractive index remains constant everywhere. A spin-controlled cumulative phase distortion is imposed on the beam, balancing diffraction for a specific polarization. As well as theoretical analysis, we present an experimental demonstration of the guidance using a series of discrete geometric-phase lenses made from liquid crystal. Our findings show that geometric phases may determine the optical guiding behaviour well beyond a Rayleigh length, paving the way to a new class of photonic devices. The concept is applicable to the whole electromagnetic spectrum.
Geometrical modelling of textile reinforcements
NASA Technical Reports Server (NTRS)
Pastore, Christopher M.; Birger, Alexander B.; Clyburn, Eugene
1995-01-01
The mechanical properties of textile composites are dictated by the arrangement of yarns contained with the material. Thus to develop a comprehensive understanding of the performance of these materials, it is necessary to develop a geometrical model of the fabric structure. This task is quite complex, as the fabric is made form highly flexible yarn systems which experience a certain degree of compressability. Furthermore there are tremendous forces acting on the fabric during densification typically resulting in yarn displacement and misorientation. The objective of this work is to develop a methodology for characterizing the geometry of yarns within a fabric structure including experimental techniques for evaluating these models. Furthermore, some applications of these geometric results to mechanical prediction models are demonstrated. Although more costly than its predecessors, the present analysis is based on the detailed architecture developed by one of the authors and his colleagues and accounts for many of the geometric complexities that other analyses ignore.
Dual geometric-gauge field aspects of gravity
Huei Peng; Wang, K.
1992-07-01
We propose that the geometric and standard gauge field aspects of gravity are equally essential for a complete description of gravity and can be reconciled. We show that this dualism of gravity resolves the dimensional Newtonian constant problem in both quantum gravity and unification schemes involving gravity (i.e., the Newtonian constant is no longer the coupling constant in the gauge aspect of gravity) and reveals the profound similarity between gravity and other fields. 23 refs., 3 tabs.
Nonlinear Geometric Effects in Bioinspired Multistable Structures
NASA Astrophysics Data System (ADS)
Chen, Zi; Guo, Qiaohang; Chu, Kevin; Shillig, Steven; Li, Chi; Chen, Wenzhe; Taber, Larry; Holmes, Douglas
2013-03-01
Nature features many thin shell structures with spontaneous curvatures, where mechanical instabilities play important roles in the morphogenesis and functioning of the organisms. However, the large deformation and instability phenomena of shells due to geometric nonlinearity, which often arise in morphogenesis and nanofabrication, remain incompletely understood. Here, we create spontaneously curved shapes with pre-strains in tabletop experiments, and study their instabilities with a minimal theory based on linear elasticity. The development of such theoretical and experimental approaches will promote quantitative understanding of the morphogenesis of growing soft tissues, and meet the emergent needs of designing stretchable electronics, artificial muscles and bio-inspired robots. Zi Chen and Qiaohang Guo contributed equally. This work was supported by National Science Foundation of China (No. 11102040), American Academy of Mechanics Founder's Award, and Society in Science - Branco Weiss fellowship, administered by ETH.
Dietary Ecology of Murinae (Muridae, Rodentia): A Geometric Morphometric Approach
Gómez Cano, Ana Rosa; Hernández Fernández, Manuel; Álvarez-Sierra, M. Ángeles
2013-01-01
Murine rodents represent a highly diverse group, which displays great ecological versatility. In the present paper we analyse the relationship between dental morphology, on one hand, using geometric morphometrics based upon the outline of first upper molar and the dietary preference of extant murine genera, on the other. This ecomorphological study of extant murine rodents demonstrates that dietary groups can be distinguished with the use of a quantitative geometric morphometric approach based on first upper molar outline. A discriminant analysis of the geometric morphometric variables of the first upper molars enables us to infer the dietary preferences of extinct murine genera from the Iberian Peninsula. Most of the extinct genera were omnivore; only Stephanomys showed a pattern of dental morphology alike that of the herbivore genera. PMID:24236090
Rendón-Macías, Mario Enrique; Villasís-Keever, Miguel Ángel; Miranda-Novales, María Guadalupe
2016-01-01
Descriptive statistics is the branch of statistics that gives recommendations on how to summarize clearly and simply research data in tables, figures, charts, or graphs. Before performing a descriptive analysis it is paramount to summarize its goal or goals, and to identify the measurement scales of the different variables recorded in the study. Tables or charts aim to provide timely information on the results of an investigation. The graphs show trends and can be histograms, pie charts, "box and whiskers" plots, line graphs, or scatter plots. Images serve as examples to reinforce concepts or facts. The choice of a chart, graph, or image must be based on the study objectives. Usually it is not recommended to use more than seven in an article, also depending on its length.
Geometric scaling as traveling waves.
Munier, S; Peschanski, R
2003-12-05
We show the relevance of the nonlinear Fisher and Kolmogorov-Petrovsky-Piscounov (KPP) equation to the problem of high energy evolution of the QCD amplitudes. We explain how the traveling wave solutions of this equation are related to geometric scaling, a phenomenon observed in deep-inelastic scattering experiments. Geometric scaling is for the first time shown to result from an exact solution of nonlinear QCD evolution equations. Using general results on the KPP equation, we compute the velocity of the wave front, which gives the full high energy dependence of the saturation scale.
Supersymmetric chiral models: Geometrical aspects
NASA Astrophysics Data System (ADS)
Perelomov, A. M.
1989-03-01
We consider classical supersymmetric chiral models of field theory and focus our attention on the geometrical aspects of such theories. A characteristic feature of such models is that the interaction is not introduced by adding the interaction Lagrangian to the free field Lagrangian, but has a purely geometrical origin and is related to the inner curvature of the target manifold. In many aspects these models are analogous to gauge theories and, as became clear recently, they are also important for superstring theory, which nowadays is the most probable candidate for a truly unified theory of all interactions including gravitation.
NASA Astrophysics Data System (ADS)
Strekalov, D. V.; Shih, Y. H.
1997-10-01
An advanced wave model is applied to a two-photon interference experiment to show that the observed interference effect is due to the geometrical phase of a two-photon state produced in spontaneous parametric down-conversion. The polarization state of the signal-idler pair is changed adiabatically so that the ``loop'' on the Poincaré sphere is opened in the signal channel and closed in the idler channel. Therefore, we observed an essentially nonlocal geometrical phase, shared by the entangled photon pair, or a biphoton.
Geometrical Optics of Dense Aerosols
Hay, Michael J.; Valeo, Ernest J.; Fisch, Nathaniel J.
2013-04-24
Assembling a free-standing, sharp-edged slab of homogeneous material that is much denser than gas, but much more rare ed than a solid, is an outstanding technological challenge. The solution may lie in focusing a dense aerosol to assume this geometry. However, whereas the geometrical optics of dilute aerosols is a well-developed fi eld, the dense aerosol limit is mostly unexplored. Yet controlling the geometrical optics of dense aerosols is necessary in preparing such a material slab. Focusing dense aerosols is shown here to be possible, but the nite particle density reduces the eff ective Stokes number of the flow, a critical result for controlled focusing. __________________________________________________
Geometric phases in astigmatic optical modes of arbitrary order
Habraken, Steven J. M.; Nienhuis, Gerard
2010-08-15
The transverse spatial structure of a paraxial beam of light is fully characterized by a set of parameters that vary only slowly under free propagation. They specify bosonic ladder operators that connect modes of different orders, in analogy to the ladder operators connecting harmonic-oscillator wave functions. The parameter spaces underlying sets of higher-order modes are isomorphic to the parameter space of the ladder operators. We study the geometry of this space and the geometric phase that arises from it. This phase constitutes the ultimate generalization of the Gouy phase in paraxial wave optics. It reduces to the ordinary Gouy phase and the geometric phase of nonastigmatic optical modes with orbital angular momentum in limiting cases. We briefly discuss the well-known analogy between geometric phases and the Aharonov-Bohm effect, which provides some complementary insights into the geometric nature and origin of the generalized Gouy phase shift. Our method also applies to the quantum-mechanical description of wave packets. It allows for obtaining complete sets of normalized solutions of the Schroedinger equation. Cyclic transformations of such wave packets give rise to a phase shift, which has a geometric interpretation in terms of the other degrees of freedom involved.
Platonic Symmetry and Geometric Thinking
ERIC Educational Resources Information Center
Zsombor-Murray, Paul
2007-01-01
Cubic symmetry is used to build the other four Platonic solids and some formalism from classical geometry is introduced. Initially, the approach is via geometric construction, e.g., the "golden ratio" is necessary to construct an icosahedron with pentagonal faces. Then conventional elementary vector algebra is used to extract quantitative…
Celestial mechanics with geometric algebra
NASA Technical Reports Server (NTRS)
Hestenes, D.
1983-01-01
Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.
Geometric Quantum Noise of Spin
NASA Astrophysics Data System (ADS)
Shnirman, Alexander; Gefen, Yuval; Saha, Arijit; Burmistrov, Igor S.; Kiselev, Mikhail N.; Altland, Alexander
2015-05-01
The presence of geometric phases is known to affect the dynamics of the systems involved. Here, we consider a quantum degree of freedom, moving in a dissipative environment, whose dynamics is described by a Langevin equation with quantum noise. We show that geometric phases enter the stochastic noise terms. Specifically, we consider small ferromagnetic particles (nanomagnets) or quantum dots close to Stoner instability, and investigate the dynamics of the total magnetization in the presence of tunneling coupling to the metallic leads. We generalize the Ambegaokar-Eckern-Schön effective action and the corresponding semiclassical equations of motion from the U(1) case of the charge degree of freedom to the SU(2) case of the magnetization. The Langevin forces (torques) in these equations are strongly influenced by the geometric phase. As a first but nontrivial application, we predict low temperature quantum diffusion of the magnetization on the Bloch sphere, which is governed by the geometric phase. We propose a protocol for experimental observation of this phenomenon.
Celestial mechanics with geometric algebra
NASA Technical Reports Server (NTRS)
Hestenes, D.
1983-01-01
Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.
Vergence, Vision, and Geometric Optics
ERIC Educational Resources Information Center
Keating, Michael P.
1975-01-01
Provides a definition of vergence in terms of the curvature of the wave fronts, and gives examples to illustrate the advantages of this approach. The vergence treatment of geometrical optics provides both conceptual and algebraic advantages, particularly for the life science student, over the traditional object distance-image distance-focal length…
Platonic Symmetry and Geometric Thinking
ERIC Educational Resources Information Center
Zsombor-Murray, Paul
2007-01-01
Cubic symmetry is used to build the other four Platonic solids and some formalism from classical geometry is introduced. Initially, the approach is via geometric construction, e.g., the "golden ratio" is necessary to construct an icosahedron with pentagonal faces. Then conventional elementary vector algebra is used to extract quantitative…
The geometric oblateness of Uranus
NASA Technical Reports Server (NTRS)
Franklin, F. A.; Avis, C. C.; Colombo, G.; Shapiro, I. I.
1980-01-01
The paper considers photographs of Uranus obtained by the Stratoscope II balloon-borne telescope in 1970. These data have been redigitized and reanalyzed, and the geometric oblateness of Uranus was determined from the isophotes near the limb using an expression in terms of the equatorial and polar radii.
Multiscale geometric modeling of macromolecules II: Lagrangian representation
Feng, Xin; Xia, Kelin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei
2013-01-01
Geometric modeling of biomolecules plays an essential role in the conceptualization of biolmolecular structure, function, dynamics and transport. Qualitatively, geometric modeling offers a basis for molecular visualization, which is crucial for the understanding of molecular structure and interactions. Quantitatively, geometric modeling bridges the gap between molecular information, such as that from X-ray, NMR and cryo-EM, and theoretical/mathematical models, such as molecular dynamics, the Poisson-Boltzmann equation and the Nernst-Planck equation. In this work, we present a family of variational multiscale geometric models for macromolecular systems. Our models are able to combine multiresolution geometric modeling with multiscale electrostatic modeling in a unified variational framework. We discuss a suite of techniques for molecular surface generation, molecular surface meshing, molecular volumetric meshing, and the estimation of Hadwiger’s functionals. Emphasis is given to the multiresolution representations of biomolecules and the associated multiscale electrostatic analyses as well as multiresolution curvature characterizations. The resulting fine resolution representations of a biomolecular system enable the detailed analysis of solvent-solute interaction, and ion channel dynamics, while our coarse resolution representations highlight the compatibility of protein-ligand bindings and possibility of protein-protein interactions. PMID:23813599
Linear patterning of mesenchymal condensations is modulated by geometric constraints.
Klumpers, Darinka D; Mao, Angelo S; Smit, Theo H; Mooney, David J
2014-06-06
The development of the vertebral column starts with the formation of a linear array of mesenchymal condensations, forming the blueprint for the eventual alternating pattern of bone and cartilage. Despite growing insight into the molecular mechanisms of morphogenesis, the impact of the physical aspects of the environment is not well understood. We hypothesized that geometric boundary conditions may play a pivotal role in the linear patterning of condensations, as neighbouring tissues provide physical constraints to the cell population. To study the process of condensation and the patterning thereof under tightly controlled geometric constraints, we developed a novel in vitro model that combines micropatterning with the established micromass assay. The spacing and alignment of condensations changed with the width of the cell adhesive patterns, a phenomenon that could not be explained by cell availability alone. Moreover, the extent of chondrogenic commitment was increased on substrates with tighter geometric constraints. When the in vivo pattern of condensations was investigated in the developing vertebral column of chicken embryos, the measurements closely fit into the quantitative relation between geometric constraints and inter-condensation distance found in vitro. Together, these findings suggest a potential role of geometric constraints in skeletal patterning in a cellular process of self-organization.
Geometrical Phases in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Christian, Joy Julius
In quantum mechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantum mechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a
The verdict geometric quality library.
Knupp, Patrick Michael; Ernst, C.D. (Elemental Technologies, Inc., American Fork, UT); Thompson, David C.; Stimpson, C.J.; Pebay, Philippe Pierre
2006-03-01
Verdict is a collection of subroutines for evaluating the geometric qualities of triangles, quadrilaterals, tetrahedra, and hexahedra using a variety of metrics. A metric is a real number assigned to one of these shapes depending on its particular vertex coordinates. These metrics are used to evaluate the input to finite element, finite volume, boundary element, and other types of solvers that approximate the solution to partial differential equations defined over regions of space. The geometric qualities of these regions is usually strongly tied to the accuracy these solvers are able to obtain in their approximations. The subroutines are written in C++ and have a simple C interface. Each metric may be evaluated individually or in combination. When multiple metrics are evaluated at once, they share common calculations to lower the cost of the evaluation.
Geometrical modelling of textile reinforcements
NASA Technical Reports Server (NTRS)
Pastore, Christopher M.; Birger, Alexander B.; Clyburn, Eugene
1995-01-01
The mechanical properties of textile composites are dictated by the arrangement of yarns contained within the material. Thus, to develop a comprehensive understanding of the performance of these materials, it is necessary to develop a geometrical model of the fabric structure. This task is quite complex, as the fabric is made from highly flexible yarn systems which experience a certain degree of compressibility. Furthermore there are tremendous forces acting on the fabric during densification typically resulting in yarn displacement and misorientation. The objective of this work is to develop a methodology for characterizing the geometry of yarns within a fabric structure including experimental techniques for evaluating these models. Furthermore, some applications of these geometric results to mechanical property predictions models are demonstrated.
Geometric Landau-Zener interferometry.
Gasparinetti, S; Solinas, P; Pekola, J P
2011-11-11
We propose a new type of interferometry, based on geometric phases accumulated by a periodically driven two-level system undergoing multiple Landau-Zener transitions. As a specific example, we study its implementation in a superconducting charge pump. We find that interference patterns appear as a function of the pumping frequency and the phase bias, and clearly manifest themselves in the pumped charge. We also show that the effects described should persist in the presence of realistic decoherence.
Geometrical interpretation of optical absorption
Monzon, J. J.; Barriuso, A. G.; Sanchez-Soto, L. L.; Montesinos-Amilibia, J. M.
2011-08-15
We reinterpret the transfer matrix for an absorbing system in very simple geometrical terms. In appropriate variables, the system appears as performing a Lorentz transformation in a (1 + 3)-dimensional space. Using homogeneous coordinates, we map that action on the unit sphere, which is at the realm of the Klein model of hyperbolic geometry. The effects of absorption appear then as a loxodromic transformation, that is, a rhumb line crossing all the meridians at the same angle.
Polar metals by geometric design
NASA Astrophysics Data System (ADS)
Kim, T. H.; Puggioni, D.; Yuan, Y.; Xie, L.; Zhou, H.; Campbell, N.; Ryan, P. J.; Choi, Y.; Kim, J.-W.; Patzner, J. R.; Ryu, S.; Podkaminer, J. P.; Irwin, J.; Ma, Y.; Fennie, C. J.; Rzchowski, M. S.; Pan, X. Q.; Gopalan, V.; Rondinelli, J. M.; Eom, C. B.
2016-05-01
Gauss’s law dictates that the net electric field inside a conductor in electrostatic equilibrium is zero by effective charge screening; free carriers within a metal eliminate internal dipoles that may arise owing to asymmetric charge distributions. Quantum physics supports this view, demonstrating that delocalized electrons make a static macroscopic polarization, an ill-defined quantity in metals—it is exceedingly unusual to find a polar metal that exhibits long-range ordered dipoles owing to cooperative atomic displacements aligned from dipolar interactions as in insulating phases. Here we describe the quantum mechanical design and experimental realization of room-temperature polar metals in thin-film ANiO3 perovskite nickelates using a strategy based on atomic-scale control of inversion-preserving (centric) displacements. We predict with ab initio calculations that cooperative polar A cation displacements are geometrically stabilized with a non-equilibrium amplitude and tilt pattern of the corner-connected NiO6 octahedra—the structural signatures of perovskites—owing to geometric constraints imposed by the underlying substrate. Heteroepitaxial thin-films grown on LaAlO3 (111) substrates fulfil the design principles. We achieve both a conducting polar monoclinic oxide that is inaccessible in compositionally identical films grown on (001) substrates, and observe a hidden, previously unreported, non-equilibrium structure in thin-film geometries. We expect that the geometric stabilization approach will provide novel avenues for realizing new multifunctional materials with unusual coexisting properties.
Polar Metals by Geometric Design
Kim, T. H.; Puggioni, D.; Yuan, Y.; Xie, L.; Zhou, H.; Campbell, N.; Ryan, P. J.; Choi, Y.; Kim, J. -W.; Patzner, J. R.; Ryu, S.; Podkaminer, J. P.; Irwin, J.; Ma, Y.; Fennie, C. J.; Rzchowski, M. S.; Pan, X. Q.; Gopalan, V.; Rondinelli, J. M.; Eom, C. B.
2016-05-05
Gauss's law dictates that the net electric field inside a conductor in electrostatic equilibrium is zero by effective charge screening; free carriers within a metal eliminate internal dipoles that may arise owing to asymmetric charge distributions(1). Quantum physics supports this view(2), demonstrating that delocalized electrons make a static macroscopic polarization, an ill-defined quantity in metals(3)-it is exceedingly unusual to find a polar metal that exhibits long-range ordered dipoles owing to cooperative atomic displacements aligned from dipolar interactions as in insulating phases(4). Here we describe the quantum mechanical design and experimental realization of room-temperature polar metals in thin-film ANiO(3) perovskite nickelates using a strategy based on atomic-scale control of inversion-preserving (centric) displacements(5). We predict with ab initio calculations that cooperative polar A cation displacements are geometrically stabilized with a non-equilibrium amplitude and tilt pattern of the corner-connected NiO6 octahedra-the structural signatures of perovskites-owing to geometric constraints imposed by the underlying substrate. Heteroepitaxial thin-films grown on LaAlO3 (111) substrates fulfil the design principles. We achieve both a conducting polar monoclinic oxide that is inaccessible in compositionally identical films grown on (001) substrates, and observe a hidden, previously unreported(6-10), non-equilibrium structure in thin-film geometries. We expect that the geometric stabilization approach will provide novel avenues for realizing new multifunctional materials with unusual coexisting properties.
Serth, J; Panitz, F; Herrmann, H; Alves, J
1998-10-01
Competitive PCR is a frequently used technique for quantitation of DNA and mRNA. However, the application of the most favourable homologous mutated competitors is impeded by the formation of heteroduplex molecules which complicates the data evaluation and may lead to quantitation errors. Moreover, in most cases a single quantitation of an unknown sample requires multiple competitive reactions for identification of the equivalence point. In the present study, a highly efficient and reliable method as well as the underlying theoretical model is described. The mathematical solutions of this model provide the basis for single-tube quantitation using a homologous mutated competitor. For quantitation of Human Papilloma Virus 16-DNA, it is shown that single tube quantitations using simple PAGE separation and video evaluation for signal analysis permit linear detection within more than two orders of magnitude. In addition, repeated single-tube competitive PCRs exhibited good precision (average standard deviation 5%), even if carried out as nested high cycle PCR for quantitation of low abundant sequences (intraassay sensitivity <2 x 10(2) copies). This evaluation method can be applied to any DNA separation and detection method which is capable of resolving the heteroduplex fraction from both homoduplex molecules.
NASA Astrophysics Data System (ADS)
Ford, David; Huntsman, Steven
2006-06-01
Thermodynamics (in concert with its sister discipline, statistical physics) can be regarded as a data reduction scheme based on partitioning a total system into a subsystem and a bath that weakly interact with each other. Whereas conventionally, the systems investigated require this form of data reduction in order to facilitate prediction, a different problem also occurs, in the context of communication networks, markets, etc. Such “empirically accessible” systems typically overwhelm observers with the sort of information that in the case of (say) a gas is effectively unobtainable. What is required for such complex interacting systems is not prediction (this may be impossible when humans besides the observer are responsible for the interactions) but rather, description as a route to understanding. Still, the need for a thermodynamical data reduction scheme remains. In this paper, we show how an empirical temperature can be computed for finite, empirically accessible systems, and further outline how this construction allows the age-old science of thermodynamics to be fruitfully applied to them.
Generalized geometrically convex functions and inequalities.
Noor, Muhammad Aslam; Noor, Khalida Inayat; Safdar, Farhat
2017-01-01
In this paper, we introduce and study a new class of generalized functions, called generalized geometrically convex functions. We establish several basic inequalities related to generalized geometrically convex functions. We also derive several new inequalities of the Hermite-Hadamard type for generalized geometrically convex functions. Several special cases are discussed, which can be deduced from our main results.
In-flight Geometric Calibration Plan
NASA Technical Reports Server (NTRS)
Jovanovic, V.
2000-01-01
This MISR in-flight Geometric Calibration (IGC) Plan describes the concept, development strategy and operational design to be used for geometric calibration of the instrument and for producing the Geometric Calibration Dataset (GCD) which is required as an input to the L1B2 standard processing.
Development of a Geometric Spatial Visualization Tool
ERIC Educational Resources Information Center
Ganesh, Bibi; Wilhelm, Jennifer; Sherrod, Sonya
2009-01-01
This paper documents the development of the Geometric Spatial Assessment. We detail the development of this instrument which was designed to identify middle school students' strategies and advancement in understanding of four geometric concept domains (geometric spatial visualization, spatial projection, cardinal directions, and periodic patterns)…
Geometrical Visualisation--Epistemic and Emotional
ERIC Educational Resources Information Center
Rodd, Melissa
2010-01-01
A well-documented experience of students of elementary Euclidean geometry is "seeing" a geometric result and being sure about its truth; this sort of experience gives rise to the notion of geometrical visualisation that is developed here. In this essay a philosophical argument for the epistemic potential of geometrical visualisation is reviewed,…
Development of a Geometric Spatial Visualization Tool
ERIC Educational Resources Information Center
Ganesh, Bibi; Wilhelm, Jennifer; Sherrod, Sonya
2009-01-01
This paper documents the development of the Geometric Spatial Assessment. We detail the development of this instrument which was designed to identify middle school students' strategies and advancement in understanding of four geometric concept domains (geometric spatial visualization, spatial projection, cardinal directions, and periodic patterns)…
A Geometric Crescent Model for Black Hole Images
NASA Astrophysics Data System (ADS)
Kamruddin, Ayman Bin; Dexter, J.
2013-01-01
The Event Horizon Telescope (EHT), a global very long baseline interferometry array operating at millimeter wavelengths, is spatially resolving the immediate environment of black holes for the first time. The current observations of the Galactic center black hole, Sagittarius A* (Sgr A*), have been interpreted in terms of unmotivated geometric models (e.g., a symmetric Gaussian) or detailed calculations involving accretion onto a black hole. The latter are subject to large systematic uncertainties. Motivated by relativistic effects around black holes, we propose a geometric crescent model for black hole images. We show that this simple model provides an excellent statistical description of the existing EHT data of Sgr A*, superior to the Gaussian. It also closely matches physically predicted models, bridging accretion theory and observation. Based on our results, we make predictions for future observations for the accessibility of the black hole shadow, direct evidence for a black hole event horizon.
Remarks on the geometric quantization of Landau levels
NASA Astrophysics Data System (ADS)
Galasso, Andrea; Spera, Mauro
2016-08-01
In this note, we resume the geometric quantization approach to the motion of a charged particle on a plane, subject to a constant magnetic field perpendicular to the latter, by showing directly that it gives rise to a completely integrable system to which we may apply holomorphic geometric quantization. In addition, we present a variant employing a suitable vertical polarization and we also make contact with Bott’s quantization, enforcing the property “quantization commutes with reduction”, which is known to hold under quite general conditions. We also provide an interpretation of translational symmetry breaking in terms of coherent states and index theory. Finally, we give a representation theoretic description of the lowest Landau level via the use of an S1-equivariant Dirac operator.
The geometrical properties researching of surface quality by membership function
NASA Astrophysics Data System (ADS)
Yang, Yufen
2008-12-01
The main content of assessing the machined surface quality of machine components is the geometrical properties of surface quality. The geometrical properties of the two assessing parameters of identical surface quality (surface roughness and surface waviness) exist in the identical substance and there are certain blend and fuzziness, what's more, there is not the concept of the value to describe its varying blend degree, there are, so far, still not practicable methods and measuring tools to separate surface roughness and waviness completely. In contrast, the paper is based on the membership function of fuzzy mathematics to research the geometrical properties of surface roughness and waviness. This method completely broke the traditional one that only adopts numerical values to separate surface roughness and waviness. It can not only directly separate the two assessing parameters from actual surface, measure the actual values of parameters that meet the assessing quality and obtain the actual probability of the blend compositions between the two, but also entirely evaluate the geometrical properties of the actual surface quality, moreover, there will be a quantitative evaluation for the authenticity and reliability of the measured values from measuring systems and instruments.
Geometrical Determinants of Neuronal Actin Waves
Tomba, Caterina; Braïni, Céline; Bugnicourt, Ghislain; Cohen, Floriane; Friedrich, Benjamin M.; Gov, Nir S.; Villard, Catherine
2017-01-01
Hippocampal neurons produce in their early stages of growth propagative, actin-rich dynamical structures called actin waves. The directional motion of actin waves from the soma to the tip of neuronal extensions has been associated with net forward growth, and ultimately with the specification of neurites into axon and dendrites. Here, geometrical cues are used to control actin wave dynamics by constraining neurons on adhesive stripes of various widths. A key observable, the average time between the production of consecutive actin waves, or mean inter-wave interval (IWI), was identified. It scales with the neurite width, and more precisely with the width of the proximal segment close to the soma. In addition, the IWI is independent of the total number of neurites. These two results suggest a mechanistic model of actin wave production, by which the material conveyed by actin waves is assembled in the soma until it reaches the threshold leading to the initiation and propagation of a new actin wave. Based on these observations, we formulate a predictive theoretical description of actin wave-driven neuronal growth and polarization, which consistently accounts for different sets of experiments. PMID:28424590
Geometric Exponents of Dilute Loop Models
NASA Astrophysics Data System (ADS)
Provencher, Guillaume; Saint-Aubin, Yvan; Pearce, Paul A.; Rasmussen, Jørgen
2012-04-01
The fractal dimensions of the hull, the external perimeter and of the red bonds are measured through Monte Carlo simulations for dilute minimal models, and compared with predictions from conformal field theory and SLE methods. The dilute models used are those first introduced by Nienhuis. Their loop fugacity is β=-2 \\cos(π/bar{kappa}) where the parameter bar{kappa} is linked to their description through conformal loop ensembles. It is also linked to conformal field theories through their central charges c(bar{kappa})=13-6(bar{kappa}+bar{kappa}^{-1}) and, for the minimal models of interest here, bar{kappa}=p/p' where p and p' are two coprime integers. The geometric exponents of the hull and external perimeter are studied for the pairs ( p, p')=(1,1),(2,3),(3,4),(4,5),(5,6),(5,7), and that of the red bonds for ( p, p')=(3,4). Monte Carlo upgrades are proposed for these models as well as several techniques to improve their speeds. The measured fractal dimensions are obtained by extrapolation on the lattice size H, V→∞. The extrapolating curves have large slopes; despite these, the measured dimensions coincide with theoretical predictions up to three or four digits. In some cases, the theoretical values lie slightly outside the confidence intervals; explanations of these small discrepancies are proposed.
Evolution: geometrical and dynamical aspects.
Freguglia, Paolo; Bazzani, Armando
2003-01-01
We develop a possible axiomatic approach to the evolution theory that has been previously discussed in Freguglia [2002]. The axioms synthesize the fundamental ideas of evolution theory and allow a geometrical and dynamical interpretation of the generation law. Using the axioms we derive a simple reaction-diffusion model which introduces the species as self-organized stationary distribution of a finite population and simulates the evolution of a phenotypic character under the effect of an external perturbing action. The dynamical properties of the model are briefly presented using numerical simulations.
NASA Astrophysics Data System (ADS)
Pittman, T. B.; Strekalov, D. V.; Klyshko, D. N.; Rubin, M. H.; Sergienko, A. V.; Shih, Y. H.
1996-04-01
We report two-photon correlation experiments using spontaneous parametric down-conversion under a severe manipulation of the input pump field. Considering the case of passing the laser beam through a focusing lens before the down-conversion crystal, theoretical calculations and a series of imaging experiments demonstrate two-photon geometric optics effects. In particular, the imaging in coincidence counts of an aperture placed in one of the down-conversion beams is found to be the analog of a simple spherical mirror system, which displays a ``vacuum dispersion'' effect in that the object and image distances are wavelength weighted.
Graphene with geometrically induced vorticity.
Pachos, Jiannis K; Stone, Michael; Temme, Kristan
2008-04-18
At half filling, the electronic structure of graphene can be modeled by a pair of free two-dimensional Dirac fermions. We explicitly demonstrate that in the presence of a geometrically induced gauge field an everywhere-real Kekulé modulation of the hopping matrix elements can correspond to a nonreal Higgs field with nontrivial vorticity. This provides a natural setting for fractionally charged vortices with localized zero modes. For fullerenelike molecules we employ the index theorem to demonstrate the existence of six low-lying states that do not depend strongly on the Kekulé-induced mass gap.
Geometric Theory of Hinged Devices
NASA Astrophysics Data System (ADS)
Kovalev, M. D.
1995-02-01
This article contains results connected with engineering mechanics. Among them are: a theorem "on the nonuniqueness of a statically determinable truss", a classification of hinged mechanisms and their schemes, and an example of a hinged mechanism with variable number of degrees of freedom. The study of general geometric properties is based on the concept, introduced here, of an abstract hinged device in Rd. This concept formalizes a well-known approach in the theory of mechanisms. The formalization gives rise to a number of interesting mathematical questions.
Geometric methods in quantum computation
NASA Astrophysics Data System (ADS)
Zhang, Jun
Recent advances in the physical sciences and engineering have created great hopes for new computational paradigms and substrates. One such new approach is the quantum computer, which holds the promise of enhanced computational power. Analogous to the way a classical computer is built from electrical circuits containing wires and logic gates, a quantum computer is built from quantum circuits containing quantum wires and elementary quantum gates to transport and manipulate quantum information. Therefore, design of quantum gates and quantum circuits is a prerequisite for any real application of quantum computation. In this dissertation we apply geometric control methods from differential geometry and Lie group representation theory to analyze the properties of quantum gates and to design optimal quantum circuits. Using the Cartan decomposition and the Weyl group, we show that the geometric structure of nonlocal two-qubit gates is a 3-Torus. After further reducing the symmetry, the geometric representation of nonlocal gates is seen to be conveniently visualized as a tetrahedron. Each point in this tetrahedron except on the base corresponds to a different equivalent class of nonlocal gates. This geometric representation is one of the cornerstones for the discussion on quantum computation in this dissertation. We investigate the properties of those two-qubit operations that can generate maximal entanglement. It is an astonishing finding that if we randomly choose a two-qubit operation, the probability that we obtain a perfect entangler is exactly one half. We prove that given a two-body interaction Hamiltonian, it is always possible to explicitly construct a quantum circuit for exact simulation of any arbitrary nonlocal two-qubit gate by turning on the two-body interaction for at most three times, together with at most four local gates. We also provide an analytic approach to construct a universal quantum circuit from any entangling gate supplemented with local gates
Geometric reasoning and spatial understanding
Binford, T.O.
1982-01-01
Progress has been made on extensions to ACRONYM which include: representation and reasoning with time, events, and sequences; collaboration with MIT to develop geometric learning: representation of function, and reasoning between structure and function. A new ribbon finder for ACRONYM is under construction. Work in figure/ground separation is underway as a basis for the ribbon finder. Preliminary results are shown in grouping operations to determine regularities in images. A stereo system has been completed which combines edge-based stereo matching with surface interpolation utilizing correspondence of gray levels. Design of a new stereo vision system is underway.
Moving walls and geometric phases
NASA Astrophysics Data System (ADS)
Facchi, Paolo; Garnero, Giancarlo; Marmo, Giuseppe; Samuel, Joseph
2016-09-01
We unveil the existence of a non-trivial Berry phase associated to the dynamics of a quantum particle in a one dimensional box with moving walls. It is shown that a suitable choice of boundary conditions has to be made in order to preserve unitarity. For these boundary conditions we compute explicitly the geometric phase two-form on the parameter space. The unboundedness of the Hamiltonian describing the system leads to a natural prescription of renormalization for divergent contributions arising from the boundary.
Geometrization of Classical Wave Fields
NASA Astrophysics Data System (ADS)
Olkhov, Oleg A.
2007-12-01
Geometrical interpretation of quantum physics is suggested. It is shown that the Dirac equation for free quantum particles can be considered as a relation describing propagation of the space topological defect with wave and corpuscular properties. This explains all "strange" properties of quantum formalism: appearance of probabilities, absence of the particles trajectories, unremovable influence of the measurement procedure, instantaneous nonlocal correlation in EPR-experiments. The same interpretation is suggested for the Maxwell equations for free electromagnetic waves. This interpretation explains independence of light velocity on the source movement.
Science, art and geometrical imagination
NASA Astrophysics Data System (ADS)
Luminet, Jean-Pierre
2011-06-01
From the geocentric, closed world model of Antiquity to the wraparound universe models of relativistic cosmology, the parallel history of space representations in science and art illustrates the fundamental rôle of geometric imagination in innovative findings. Through the analysis of works of various artists and scientists like Plato, Dürer, Kepler, Escher, Grisey or the author, it is shown how the process of creation in science and in the arts rests on aesthetical principles such as symmetry, regular polyhedra, laws of harmonic proportion, tessellations, group theory, etc., as well as on beauty, conciseness and an emotional approach of the world.
Geometric analysis of wing sections
NASA Technical Reports Server (NTRS)
Chang, I.-CHUNG; Torres, Francisco J.; Tung, Chee
1995-01-01
This paper describes a new geometric analysis procedure for wing sections. This procedure is based on the normal mode analysis for continuous functions. A set of special shape functions is introduced to represent the geometry of the wing section. The generators of the NACA 4-digit airfoils were included in this set of shape functions. It is found that the supercritical wing section, Korn airfoil, could be well represented by a set of ten shape functions. Preliminary results showed that the number of parameters to define a wing section could be greatly reduced to about ten. Hence, the present research clearly advances the airfoil design technology by reducing the number of design variables.
SQCD Vacua and Geometrical Engineering
Tatar, Radu; Wetenhall, Ben
2008-11-23
We consider the geometrical engineering constructions for the N = 1 SQCD vacua. After one T-duality, these geometries with wrapped D5 branes become N = 1 brane configurations with NS-branes and D4-branes. After performing a flop, the geometries contain branes, antibranes and branes wrapped on non-holomorphic cycles. The various tachyon condensations between pairs of wrapped D5 branes and anti-D5 branes together with deformations of the cycles give rise to a variety of supersymmetric and metastable non-supersymmetric vacua.
Measurement error in geometric morphometrics.
Fruciano, Carmelo
2016-06-01
Geometric morphometrics-a set of methods for the statistical analysis of shape once saluted as a revolutionary advancement in the analysis of morphology -is now mature and routinely used in ecology and evolution. However, a factor often disregarded in empirical studies is the presence and the extent of measurement error. This is potentially a very serious issue because random measurement error can inflate the amount of variance and, since many statistical analyses are based on the amount of "explained" relative to "residual" variance, can result in loss of statistical power. On the other hand, systematic bias can affect statistical analyses by biasing the results (i.e. variation due to bias is incorporated in the analysis and treated as biologically-meaningful variation). Here, I briefly review common sources of error in geometric morphometrics. I then review the most commonly used methods to measure and account for both random and non-random measurement error, providing a worked example using a real dataset.
Image coding with geometric wavelets.
Alani, Dror; Averbuch, Amir; Dekel, Shai
2007-01-01
This paper describes a new and efficient method for low bit-rate image coding which is based on recent development in the theory of multivariate nonlinear piecewise polynomial approximation. It combines a binary space partition scheme with geometric wavelet (GW) tree approximation so as to efficiently capture curve singularities and provide a sparse representation of the image. The GW method successfully competes with state-of-the-art wavelet methods such as the EZW, SPIHT, and EBCOT algorithms. We report a gain of about 0.4 dB over the SPIHT and EBCOT algorithms at the bit-rate 0.0625 bits-per-pixels (bpp). It also outperforms other recent methods that are based on "sparse geometric representation." For example, we report a gain of 0.27 dB over the Bandelets algorithm at 0.1 bpp. Although the algorithm is computationally intensive, its time complexity can be significantely reduced by collecting a "global" GW n-term approximation to the image from a collection of GW trees, each constructed separately over tiles of the image.
Geometric effects in tomographic reconstruction
Barnes, F.L.; Azevedo, S.G.; Martz, H.E. Jr.; Roberson, G.P.; Schneberk, D.J.; Skeate, M.F.
1990-01-08
In x-ray and ion-beam computerized tomography, there are a number of reconstruction effects, manifested as artifacts, that can be attributed to the geometry of the experimental setup and of the object being scanned. In this work, we will examine four geometric effects that are common to first-and third-generation (parallel beam, 180 degree) computerized tomography (CT) scanners and suggest solutions for each problem. The geometric effects focused on in this paper are: X-pattern'' artifacts (believed to be caused by several errors), edge-generated ringing artifacts (due to improper choice of the reconstruction filter and cutoff frequency), circular-ring artifacts (caused by employing uncalibrated detectors), and tuning-fork artifacts (generated by an incorrectly specified center-of-rotation). Examples of four effects are presented. The X-pattern and edge-generated ringing artifacts are presented with actual experimental data introducing the artifact. given the source of the artifact, we present simulated data designed to replicate the artifact. Finally, we suggest ways to reduce or completely remove these artifacts. The circular-ring and tuning-fork artifacts are introduced with actual experimental data as well, while digital signal processing solutions are employed to remove the artifacts from the data. 15 refs., 12 figs.
NPP VIIRS Geometric Performance Status
NASA Technical Reports Server (NTRS)
Lin, Guoqing; Wolfe, Robert E.; Nishihama, Masahiro
2011-01-01
Visible Infrared Imager Radiometer Suite (VIIRS) instrument on-board the National Polar-orbiting Operational Environmental Satellite System (NPOESS) Preparatory Project (NPP) satellite is scheduled for launch in October, 2011. It is to provide satellite measured radiance/reflectance data for both weather and climate applications. Along with radiometric calibration, geometric characterization and calibration of Sensor Data Records (SDRs) are crucial to the VIIRS Environmental Data Record (EDR) algorithms and products which are used in numerical weather prediction (NWP). The instrument geometric performance includes: 1) sensor (detector) spatial response, parameterized by the dynamic field of view (DFOV) in the scan direction and instantaneous FOV (IFOV) in the track direction, modulation transfer function (MTF) for the 17 moderate resolution bands (M-bands), and horizontal spatial resolution (HSR) for the five imagery bands (I-bands); 2) matrices of band-to-band co-registration (BBR) from the corresponding detectors in all band pairs; and 3) pointing knowledge and stability characteristics that includes scan plane tilt, scan rate and scan start position variations, and thermally induced variations in pointing with respect to orbital position. They have been calibrated and characterized through ground testing under ambient and thermal vacuum conditions, numerical modeling and analysis. This paper summarizes the results, which are in general compliance with specifications, along with anomaly investigations, and describes paths forward for characterizing on-orbit BBR and spatial response, and for improving instrument on-orbit performance in pointing and geolocation.
Geometrical interpretation for the outer SU(3) outer multiplicity label
NASA Technical Reports Server (NTRS)
Draayer, Jerry P.; Troltenier, D.
1995-01-01
A geometrical interpretation for the outer multiplicity rho that occurs in a reduction of the product of two SU(3) representations, (lambda(sub pi), mu(sub pi)) x (lambda(sub nu), mu(sub nu)) approaches sigma(sub rho)(lambda, mu)(sub rho), is introduced. This coupling of proton (pi) and neutron (nu) representations arises, for example, in both boson and fermion descriptions of heavy deformed nuclei. Attributing a geometry to the coupling raises the possibility of introducing a simple interaction that provides a physically meaningful way for distinguishing multiple occurrences of (lambda, mu) values that can arise in such products.
Quantitative Pedagogy: A Digital Two Player Game to Examine Communicative Competence
Lopez-Rosenfeld, Matías; Carrillo, Facundo; Garbulsky, Gerry; Fernandez Slezak, Diego; Sigman, Mariano
2015-01-01
Inner concepts are much richer than the words that describe them. Our general objective is to inquire what are the best procedures to communicate conceptual knowledge. We construct a simplified and controlled setup emulating important variables of pedagogy amenable to quantitative analysis. To this aim, we designed a game inspired in Chinese Whispers, to investigate which attributes of a description affect its capacity to faithfully convey an image. This is a two player game: an emitter and a receiver. The emitter was shown a simple geometric figure and was asked to describe it in words. He was informed that this description would be passed to the receiver who had to replicate the drawing from this description. We capitalized on vast data obtained from an android app to quantify the effect of different aspects of a description on communication precision. We show that descriptions more effectively communicate an image when they are coherent and when they are procedural. Instead, the creativity, the use of metaphors and the use of mathematical concepts do not affect its fidelity. PMID:26554833
Quantitative Pedagogy: A Digital Two Player Game to Examine Communicative Competence.
Lopez-Rosenfeld, Matías; Carrillo, Facundo; Garbulsky, Gerry; Fernandez Slezak, Diego; Sigman, Mariano
2015-01-01
Inner concepts are much richer than the words that describe them. Our general objective is to inquire what are the best procedures to communicate conceptual knowledge. We construct a simplified and controlled setup emulating important variables of pedagogy amenable to quantitative analysis. To this aim, we designed a game inspired in Chinese Whispers, to investigate which attributes of a description affect its capacity to faithfully convey an image. This is a two player game: an emitter and a receiver. The emitter was shown a simple geometric figure and was asked to describe it in words. He was informed that this description would be passed to the receiver who had to replicate the drawing from this description. We capitalized on vast data obtained from an android app to quantify the effect of different aspects of a description on communication precision. We show that descriptions more effectively communicate an image when they are coherent and when they are procedural. Instead, the creativity, the use of metaphors and the use of mathematical concepts do not affect its fidelity.
Geometric asymmetry driven Janus micromotors.
Zhao, Guanjia; Pumera, Martin
2014-10-07
The production and application of nano-/micromotors is of great importance. In order for the motors to work, asymmetry in their chemical composition or physical geometry must be present if no external asymmetric field is applied. In this paper, we present a "coconut" micromotor made of platinum through the partial or complete etching of the silica templates. It was shown that although both the inner and outer surfaces are made of the same material (Pt), motion of the structure can be observed as the convex surface is capable of generating oxygen bubbles. This finding shows that not only the chemical asymmetry of the micromotor, but also its geometric asymmetry can lead to fast propulsion of the motor. Moreover, a considerably higher velocity can be seen for partially etched coconut structures than the velocities of Janus or fully etched, shell-like motors. These findings will have great importance on the design of future micromotors.
Geometric solitons of Hamiltonian flows on manifolds
Song, Chong; Sun, Xiaowei; Wang, Youde
2013-12-15
It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.
Dualities and geometrical invariants for static and spherically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Seidel, Paola Terezinha; Cabral, Luís Antonio
2016-04-01
In this work, we consider spinless particles in curved spacetime and symmetries related to extended isometries. We search for solutions of a generalized Killing equation whose structure entails a general class of Killing tensors. The conserved quantities along particle’s geodesic are associated with a dual description of the spacetime metric. In the Hamiltonian formalism, some conserved quantities generate a dual description of the metric. The Killing tensors belonging to the conserved objects imply in a nontrivial class of dual metrics even for a Schwarzschild metric in the original spacetime. From these metrics, we construct geometrical invariants for classes of dual spacetimes to explore their singularity structure. A nontrivial singularity behavior is obtained in the dual sector.
2011-06-17
validation before prototyping. This serialized optimization process provides critical CAE support for NVH assessment to the designer during the...requiring a comprehensive geometric description. They can be used to optimize the architecture layout of a vehicle, conduct iterative design studies...Once the concept vehicle model meets the minimum requirements, detailed models should be developed for localized optimization and final design
Gaussian geometric discord of two-mode systems in a thermal environment
Suciu, Serban Isar, Aurelian
2014-11-24
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the Gaussian geometric discord for a system consisting of two non-interacting non-resonant bosonic modes embedded in a thermal environment. We take as initial state of the system a two-mode squeezed thermal state and describe the time evolution of the Gaussian geometric discord under the influence of the thermal bath. By tracing the distance between the state of the considered subsystem and the closest classical-quantum Gaussian state we evaluate the Gaussian geometric discord for all times and temperatures. The geometric discord has finite values between 0 and 1 and decreases asymptotically to zero at large times and temperatures with oscillations on the time axis.
A geometric crescent model for black hole images
NASA Astrophysics Data System (ADS)
Kamruddin, Ayman Bin; Dexter, Jason
2013-09-01
The Event Horizon Telescope (EHT), a global very long baseline interferometry array operating at millimetre wavelengths, is spatially resolving the immediate environments of black holes for the first time. The current observations of the Galactic centre black hole, Sagittarius A* (Sgr A*), and M87 have been interpreted in terms of either geometric models (e.g. a symmetric Gaussian) or detailed calculations of the appearance of black hole accretion flows. The former are not physically motivated, while the latter are subject to large systematic uncertainties. Motivated by the dominant relativistic effects of Doppler beaming and gravitational lensing in many calculations, we propose a geometric crescent model for black hole images. We show that this simple model provides an excellent statistical description of the existing EHT data of Sgr A* and M87, superior to other geometric models for Sgr A*. It also qualitatively matches physically predicted models, bridging accretion theory and observation. Based on our results, we make predictions for the detectability of the black hole shadow, a signature of strong gravity, in future observations.
A geometric rationale for invariance, covariance and constitutive relations
NASA Astrophysics Data System (ADS)
Romano, Giovanni; Barretta, Raffaele; Diaco, Marina
2017-09-01
There are, in each branch of science, statements which, expressed in ambiguous or even incorrect but seemingly friendly manner, were repeated for a long time and eventually became diffusely accepted. Objectivity of physical fields and of their time rates and frame indifference of constitutive relations are among such notions. A geometric reflection on the description of frame changes as spacetime automorphisms, on induced push-pull transformations and on proper physico-mathematical definitions of material, spatial and spacetime tensor fields and of their time-derivatives along the motion, is here carried out with the aim of pointing out essential notions and of unveiling false claims. Theoretical and computational aspects of nonlinear continuum mechanics, and especially those pertaining to constitutive relations, involving material fields and their time rates, gain decisive conceptual and operative improvement from a proper geometric treatment. Outcomes of the geometric analysis are frame covariance of spacetime velocity, material stretching and material spin. A univocal and frame-covariant tool for evaluation of time rates of material fields is provided by the uc(Lie) derivative along the motion. The postulate of frame covariance of material fields is assessed to be a natural physical requirement which cannot interfere with the formulation of constitutive laws, with claims of the contrary stemming from an improper imposition of equality in place of equivalence.
Geometric, Kinematic and Radiometric Aspects of Image-Based Measurements
NASA Technical Reports Server (NTRS)
Liu, Tianshu
2002-01-01
This paper discusses theoretical foundations of quantitative image-based measurements for extracting and reconstructing geometric, kinematic and dynamic properties of observed objects. New results are obtained by using a combination of methods in perspective geometry, differential geometry. radiometry, kinematics and dynamics. Specific topics include perspective projection transformation. perspective developable conical surface, perspective projection under surface constraint, perspective invariants, the point correspondence problem. motion fields of curves and surfaces. and motion equations of image intensity. The methods given in this paper arc useful for determining morphology and motion fields of deformable bodies such as elastic bodies. viscoelastic mediums and fluids.
A geometric model of defensive peripersonal space.
Bufacchi, R J; Liang, M; Griffin, L D; Iannetti, G D
2016-01-01
Potentially harmful stimuli occurring within the defensive peripersonal space (DPPS), a protective area surrounding the body, elicit stronger defensive reactions. The spatial features of the DPPS are poorly defined and limited to descriptive estimates of its extent along a single dimension. Here we postulated a family of geometric models of the DPPS, to address two important questions with respect to its spatial features: What is its fine-grained topography? How does the nervous system represent the body area to be defended? As a measure of the DPPS, we used the strength of the defensive blink reflex elicited by electrical stimulation of the hand (hand-blink reflex, HBR), which is reliably modulated by the position of the stimulated hand in egocentric coordinates. We tested the goodness of fit of the postulated models to HBR data from six experiments in which we systematically explored the HBR modulation by hand position in both head-centered and body-centered coordinates. The best-fitting model indicated that 1) the nervous system's representation of the body area defended by the HBR can be approximated by a half-ellipsoid centered on the face and 2) the DPPS extending from this area has the shape of a bubble elongated along the vertical axis. Finally, the empirical observation that the HBR is modulated by hand position in head-centered coordinates indicates that the DPPS is anchored to the face. The modeling approach described in this article can be generalized to describe the spatial modulation of any defensive response. Copyright © 2016 the American Physiological Society.
NASA Technical Reports Server (NTRS)
Meyer, Peter; Green, Robert O.; Chrien, Thomas G.
1993-01-01
Remotely sensed data are affected by system (sensor and platform), and scene related effects. For quantitative investigations the spectral, radiometric characteristics of the system and scene have to be known. The relevant effects and their possible influence on an image have to be specifically determined for every remote sensing system and adequate description parameters need to be updated and reported on a regular basis as they are carried out, e.g., for the AVIRIS system. It is evident that the strength of the influence of similar effects in very dependent on the accessibility of auxiliary information about such sensor systems. Degradation in a spaceborne system can normally be just reported and cannot be corrected. In contrast, an airborne sensor can be evaluated, maintained and improved periodically. Such maintenance efforts are particularly important because airborne systems are exposed to extreme and changing environments. These include tens of takeoffs and landing each year as well as extreme changes in temperature and humidity on the tarmac and in flight. For the AVIRIS system there are environmental stresses such as changes in temperature, air pressure, humidity, vibration of the platform or scene-related reasons like atmospheric conditions, and topography. The information contained in the auxiliary files included with the AVIRIS data can be used to assess these effects and compensate for them. In addition the spectral, radiometer and geometric calibration data contained in the auxiliary file are required for quantitative analysis of the data. The paper describes tools to access the auxiliary information that characterizes the AVIRIS system. These tools allow the examination of parameters that may impact the quality of the measured AVIRIS image. An example of the use of this auxiliary data was carried out with regard to a parametric geocoding approach. Emphasis is placed on the reported auxiliary information that describes the geometric character of the
Geometric asymmetry driven Janus micromotors
NASA Astrophysics Data System (ADS)
Zhao, Guanjia; Pumera, Martin
2014-09-01
The production and application of nano-/micromotors is of great importance. In order for the motors to work, asymmetry in their chemical composition or physical geometry must be present if no external asymmetric field is applied. In this paper, we present a ``coconut'' micromotor made of platinum through the partial or complete etching of the silica templates. It was shown that although both the inner and outer surfaces are made of the same material (Pt), motion of the structure can be observed as the convex surface is capable of generating oxygen bubbles. This finding shows that not only the chemical asymmetry of the micromotor, but also its geometric asymmetry can lead to fast propulsion of the motor. Moreover, a considerably higher velocity can be seen for partially etched coconut structures than the velocities of Janus or fully etched, shell-like motors. These findings will have great importance on the design of future micromotors.The production and application of nano-/micromotors is of great importance. In order for the motors to work, asymmetry in their chemical composition or physical geometry must be present if no external asymmetric field is applied. In this paper, we present a ``coconut'' micromotor made of platinum through the partial or complete etching of the silica templates. It was shown that although both the inner and outer surfaces are made of the same material (Pt), motion of the structure can be observed as the convex surface is capable of generating oxygen bubbles. This finding shows that not only the chemical asymmetry of the micromotor, but also its geometric asymmetry can lead to fast propulsion of the motor. Moreover, a considerably higher velocity can be seen for partially etched coconut structures than the velocities of Janus or fully etched, shell-like motors. These findings will have great importance on the design of future micromotors. Electronic supplementary information (ESI) available: Additional SEM images, data analysis, Videos S
Geometric Quantization and Foliation Reduction
NASA Astrophysics Data System (ADS)
Skerritt, Paul
A standard question in the study of geometric quantization is whether symplectic reduction interacts nicely with the quantized theory, and in particular whether "quantization commutes with reduction." Guillemin and Sternberg first proposed this question, and answered it in the affirmative for the case of a free action of a compact Lie group on a compact Kahler manifold. Subsequent work has focused mainly on extending their proof to non-free actions and non-Kahler manifolds. For realistic physical examples, however, it is desirable to have a proof which also applies to non-compact symplectic manifolds. In this thesis we give a proof of the quantization-reduction problem for general symplectic manifolds. This is accomplished by working in a particular wavefunction representation, associated with a polarization that is in some sense compatible with reduction. While the polarized sections described by Guillemin and Sternberg are nonzero on a dense subset of the Kahler manifold, the ones considered here are distributional, having support only on regions of the phase space associated with certain quantized, or "admissible", values of momentum. We first propose a reduction procedure for the prequantum geometric structures that "covers" symplectic reduction, and demonstrate how both symplectic and prequantum reduction can be viewed as examples of foliation reduction. Consistency of prequantum reduction imposes the above-mentioned admissibility conditions on the quantized momenta, which can be seen as analogues of the Bohr-Wilson-Sommerfeld conditions for completely integrable systems. We then describe our reduction-compatible polarization, and demonstrate a one-to-one correspondence between polarized sections on the unreduced and reduced spaces. Finally, we describe a factorization of the reduced prequantum bundle, suggested by the structure of the underlying reduced symplectic manifold. This in turn induces a factorization of the space of polarized sections that agrees
Multiple representation approach to geometric model construction from range data
NASA Astrophysics Data System (ADS)
Koivunen, Visa; Vezien, Jean-Marc; Bajcsy, Ruzena
1995-04-01
A method is presented for constructing geometric design data from noisy 3-D sensor measurements of physical parts. In early processing phase, RLTS regression filters stemming from robust estimation theory are used for separating the desired part of the signal in contaminated sensor data from undesired part. Strategies for producing a complete 3-D data set from partial views are studied. Surface triangulation, NURBS, and superellipsoids are employed in model construction to be able to represent efficiently polygonal shapes, free form surfaces and standard primitive solids. Multiple representations are used because there is no single representation that would be most appropriate in all situations. The size of the required control point mesh for spline description is estimated using a surface characterization process. Surfaces of arbitrary topology are modeled using triangulation and trimmed NURBS. A user given tolerance value is driving refinement of the obtained surface model. The resulting model description is a procedural CAD model which can convey structural information in addition to low level geometric primitives. The model is translated to IGES standard product data exchange format to enable data sharing with other processes in concurrent engineering environment. Preliminary results on view registration and integration using simulated data are shown. Examples of model construction using both real and simulated data are also given.
Geometric Phase Generated Optical Illusion.
Yue, Fuyong; Zang, Xiaofei; Wen, Dandan; Li, Zile; Zhang, Chunmei; Liu, Huigang; Gerardot, Brian D; Wang, Wei; Zheng, Guoxing; Chen, Xianzhong
2017-09-12
An optical illusion, such as "Rubin's vase", is caused by the information gathered by the eye, which is processed in the brain to give a perception that does not tally with a physical measurement of the stimulus source. Metasurfaces are metamaterials of reduced dimensionality which have opened up new avenues for flat optics. The recent advancement in spin-controlled metasurface holograms has attracted considerate attention, providing a new method to realize optical illusions. We propose and experimentally demonstrate a metasurface device to generate an optical illusion. The metasurface device is designed to display two asymmetrically distributed off-axis images of "Rubin faces" with high fidelity, high efficiency and broadband operation that are interchangeable by controlling the helicity of the incident light. Upon the illumination of a linearly polarized light beam, the optical illusion of a 'vase' is perceived. Our result provides an intuitive demonstration of the figure-ground distinction that our brains make during the visual perception. The alliance between geometric metasurface and the optical illusion opens a pathway for new applications related to encryption, optical patterning, and information processing.
Geometric reasoning about assembly tools
Wilson, R.H.
1997-01-01
Planning for assembly requires reasoning about various tools used by humans, robots, or other automation to manipulate, attach, and test parts and subassemblies. This paper presents a general framework to represent and reason about geometric accessibility issues for a wide variety of such assembly tools. Central to the framework is a use volume encoding a minimum space that must be free in an assembly state to apply a given tool, and placement constraints on where that volume must be placed relative to the parts on which the tool acts. Determining whether a tool can be applied in a given assembly state is then reduced to an instance of the FINDPLACE problem. In addition, the author presents more efficient methods to integrate the framework into assembly planning. For tools that are applied either before or after their target parts are mated, one method pre-processes a single tool application for all possible states of assembly of a product in polynomial time, reducing all later state-tool queries to evaluations of a simple expression. For tools applied after their target parts are mated, a complementary method guarantees polynomial-time assembly planning. The author presents a wide variety of tools that can be described adequately using the approach, and surveys tool catalogs to determine coverage of standard tools. Finally, the author describes an implementation of the approach in an assembly planning system and experiments with a library of over one hundred manual and robotic tools and several complex assemblies.
Geometrical aspects of quantum spaces
Ho, Pei -Ming
1996-05-11
Various geometrical aspects of quantum spaces are presented showing the possibility of building physics on quantum spaces. In the first chapter the authors give the motivations for studying noncommutative geometry and also review the definition of a Hopf algebra and some general features of the differential geometry on quantum groups and quantum planes. In Chapter 2 and Chapter 3 the noncommutative version of differential calculus, integration and complex structure are established for the quantum sphere S_{1}^{2} and the quantum complex projective space CP{sub q}(N), on which there are quantum group symmetries that are represented nonlinearly, and are respected by all the aforementioned structures. The braiding of S_{q}^{2} and CP_{q}(N) is also described. In Chapter 4 the quantum projective geometry over the quantum projective space CP_{q}(N) is developed. Collinearity conditions, coplanarity conditions, intersections and anharmonic ratios is described. In Chapter 5 an algebraic formulation of Reimannian geometry on quantum spaces is presented where Riemannian metric, distance, Laplacian, connection, and curvature have their quantum counterparts. This attempt is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space. The quantum group of general coordinate transformations on some quantum spaces is also given.
Generalized Geometric Quantum Speed Limits
NASA Astrophysics Data System (ADS)
Pires, Diego Paiva; Cianciaruso, Marco; Céleri, Lucas C.; Adesso, Gerardo; Soares-Pinto, Diogo O.
2016-04-01
The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.
Geometric Reasoning for Automated Planning
NASA Technical Reports Server (NTRS)
Clement, Bradley J.; Knight, Russell L.; Broderick, Daniel
2012-01-01
An important aspect of mission planning for NASA s operation of the International Space Station is the allocation and management of space for supplies and equipment. The Stowage, Configuration Analysis, and Operations Planning teams collaborate to perform the bulk of that planning. A Geometric Reasoning Engine is developed in a way that can be shared by the teams to optimize item placement in the context of crew planning. The ISS crew spends (at the time of this writing) a third or more of their time moving supplies and equipment around. Better logistical support and optimized packing could make a significant impact on operational efficiency of the ISS. Currently, computational geometry and motion planning do not focus specifically on the optimized orientation and placement of 3D objects based on multiple distance and containment preferences and constraints. The software performs reasoning about the manipulation of 3D solid models in order to maximize an objective function based on distance. It optimizes for 3D orientation and placement. Spatial placement optimization is a general problem and can be applied to object packing or asset relocation.
Geometric aspects of ordering phenomena
NASA Astrophysics Data System (ADS)
Cugliandolo, Leticia F.
2017-01-01
A macroscopic system prepared in a disordered phase and quenched across a second-order phase transition into an ordered phase undergoes a coarsening process whereby it orders locally in one of the equilibrium states. The study of the evolution of the morphology of the ordered structures in two dimensions has recently unveiled two interesting and generic features. On the one hand, the dynamics first approach a critical percolating state via the growth of a new lengthscale and satisfying scaling properties with respect to it. The time needed to reach the critical percolating state diverges with the system size, though more weakly than the equilibration time. On the other hand, once the critical percolating structures established, the geometrical and statistical properties at larger scales than the one established by the usual dynamic growing length remain the ones of critical percolation. These observations are common to different microscopic dynamics (single spin flip, local and non-local spin exchange, voter) in pure or weakly disordered systems. We discuss these results and we refer to the relevant publications for details. xml:lang="fr"
Parameterization of a Geometric Flow Implicit Solvation Model
Thomas, Dennis G.; Chun, Jaehun; Chen, Zhan; Wei, Guowei; Baker, Nathan A.
2012-01-01
Implicit solvent models are popular for their high computational efficiency and simplicity over explicit solvent models and are extensively used for computing molecular solvation properties. The accuracy of implicit solvent models depends on the geometric description of the solute-solvent interface and the solvent dielectric profile that is defined near the surface of the solute molecule. Typically, it is assumed that the dielectric profile is spatially homogeneous in the bulk solvent medium and varies sharply across the solute-solvent interface. However, the specific form of this profile is often described by ad hoc geometric models rather than physical solute-solvent interactions. Hence, it is of significant interest to improve the accuracy of these implicit solvent models by more realistically defining the solute-solvent boundary within a continuum setting. Recently, a differential geometry-based geometric flow solvation model was developed, in which the polar and nonpolar free energies are coupled through a characteristic function that describes a smooth dielectric interface profile across the solvent–solute boundary in a thermodynamically self-consistent fashion. The main parameters of the model are the solute/solvent dielectric coefficients, solvent pressure on the solute, microscopic surface tension, solvent density, and molecular force-field parameters. In this work, we investigate how changes in the pressure, surface tension, solute dielectric coefficient, and choice of different force-field charge and radii parameters affect the prediction accuracy for hydration free energies of 17 small organic molecules based on the geometric flow solvation model. The results of our study provide insights on the parameterization, accuracy, and predictive power of this new implicit solvent model. PMID:23212974
A Framework for Analyzing Geometric Pattern Tasks
ERIC Educational Resources Information Center
Friel, Susan N.; Markworth, Kimberly A.
2009-01-01
Teachers can use geometric patterns to promote students' understanding of functional relationships. In this article, the authors first look at a problem-solving process that supports the use of figural reasoning to explore and interpret geometric pattern tasks and generalize function rules. Second, the authors discuss a framework for…
The geometric semantics of algebraic quantum mechanics.
Cruz Morales, John Alexander; Zilber, Boris
2015-08-06
In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.
Parabolas: Connection between Algebraic and Geometrical Representations
ERIC Educational Resources Information Center
Shriki, Atara
2011-01-01
A parabola is an interesting curve. What makes it interesting at the secondary school level is the fact that this curve is presented in both its contexts: algebraic and geometric. Being one of Apollonius' conic sections, the parabola is basically a geometric entity. It is, however, typically known for its algebraic characteristics, in particular…
Second-quantized formulation of geometric phases
Deguchi, Shinichi; Fujikawa, Kazuo
2005-07-15
The level crossing problem and associated geometric terms are neatly formulated by the second-quantized formulation. This formulation exhibits a hidden local gauge symmetry related to the arbitrariness of the phase choice of the complete orthonormal basis set. By using this second-quantized formulation, which does not assume adiabatic approximation, a convenient exact formula for the geometric terms including off-diagonal geometric terms is derived. The analysis of geometric phases is then reduced to a simple diagonalization of the Hamiltonian, and it is analyzed both in the operator and path-integral formulations. If one diagonalizes the geometric terms in the infinitesimal neighborhood of level crossing, the geometric phases become trivial (and thus no monopole singularity) for arbitrarily large but finite time interval T. The integrability of Schroedinger equation and the appearance of the seemingly nonintegrable phases are thus consistent. The topological proof of the Longuet-Higgins' phase-change rule, for example, fails in the practical Born-Oppenheimer approximation where a large but finite ratio of two time scales is involved and T is identified with the period of the slower system. The difference and similarity between the geometric phases associated with level crossing and the exact topological object such as the Aharonov-Bohm phase become clear in the present formulation. A crucial difference between the quantum anomaly and the geometric phases is also noted.
Some technical issues in geometric modeling
Peterson, D.P.
1983-01-01
The full impact of CAD/CAM will not be felt until geometric modeling systems support dimensioning and tolerancing, have sophisticated user interfaces, and are capable of routinely handling many representation conversions. The attainment of these capabilities requires a joint effort among users, implementors, and theoreticians of geometric modeling.
Geometrical splitting and reduction of Feynman diagrams
NASA Astrophysics Data System (ADS)
Davydychev, Andrei I.
2016-10-01
A geometrical approach to the calculation of N-point Feynman diagrams is reviewed. It is shown that the geometrical splitting yields useful connections between Feynman integrals with different momenta and masses. It is demonstrated how these results can be used to reduce the number of variables in the occurring functions.
Geometric Growing Patterns: What's the Rule?
ERIC Educational Resources Information Center
Hourigan, Mairéad; Leavy, Aisling
2015-01-01
While within a geometric repeating pattern, there is an identifiable core which is made up of objects that repeat in a predictable manner, a geometric growing pattern (also called visual or pictorial growing patterns in other curricula) "is a pattern that is made from a sequence of figures [or objects] that change from one term to the next in…
Early Sex Differences in Weighting Geometric Cues
ERIC Educational Resources Information Center
Lourenco, Stella F.; Addy, Dede; Huttenlocher, Janellen; Fabian, Lydia
2011-01-01
When geometric and non-geometric information are both available for specifying location, men have been shown to rely more heavily on geometry compared to women. To shed insight on the nature and developmental origins of this sex difference, we examined how 18- to 24-month-olds represented the geometry of a surrounding (rectangular) space when…
Geometric Growing Patterns: What's the Rule?
ERIC Educational Resources Information Center
Hourigan, Mairéad; Leavy, Aisling
2015-01-01
While within a geometric repeating pattern, there is an identifiable core which is made up of objects that repeat in a predictable manner, a geometric growing pattern (also called visual or pictorial growing patterns in other curricula) "is a pattern that is made from a sequence of figures [or objects] that change from one term to the next in…
Geometric Derivation of Radial Acceleration Magnitude.
ERIC Educational Resources Information Center
Kraft, David W.; Motz, Lloyd
1995-01-01
Standard treatments of uniform circular motion generally employ a combination of geometric and kinematic arguments to obtain the magnitude of radial acceleration. Presents a novel approach to the geometric portion of the derivation that uses the property that vectors can be translated parallel to themselves. (JRH)
Early Sex Differences in Weighting Geometric Cues
ERIC Educational Resources Information Center
Lourenco, Stella F.; Addy, Dede; Huttenlocher, Janellen; Fabian, Lydia
2011-01-01
When geometric and non-geometric information are both available for specifying location, men have been shown to rely more heavily on geometry compared to women. To shed insight on the nature and developmental origins of this sex difference, we examined how 18- to 24-month-olds represented the geometry of a surrounding (rectangular) space when…
Plate Wave Transmission/reflection at Geometric Obstructions: Experiment
NASA Astrophysics Data System (ADS)
Reusser, R. S.; Chimenti, D. E.; Holland, S. D.; Roberts, R. A.
2010-02-01
This paper reports on the experimental examination of the transmission and reflection characteristics of arbitrarily shaped geometric obstructions in problems of plate wave propagation, such as joints, stiffeners, thickness transitions, and bends. The motivation for this work is noise source location in structures, the specific application being the location of air leaks in spacecraft skins, funded by NASA. In this work, it has been demonstrated that leaks can be located at a distance using array-based sensors which determine direction of signal propagation at the sensor location. The limiting factor in practice is the influence of geometric obstructions between the leak and sensor. This work reports a quantitative examination of the transmission properties of various obstructions such as stiffening ribs. Surface motions arising from a distance source are recorded over a local array of spatial positions using a scanned laser vibrometer. Spatial Fourier analysis is then applied to determine the individual contributions of the constituent mode types to the measured signals. Transmission properties of intervening geometric obstructions are determined by comparison to unobstructed signals. Comparisons to theoretical predictions of transmission characteristics will be presented for selected cases.
Geometric Hamiltonian quantum mechanics and applications
NASA Astrophysics Data System (ADS)
Pastorello, Davide
2016-08-01
Adopting a geometric point of view on Quantum Mechanics is an intriguing idea since, we know that geometric methods are very powerful in Classical Mechanics then, we can try to use them to study quantum systems. In this paper, we summarize the construction of a general prescription to set up a well-defined and self-consistent geometric Hamiltonian formulation of finite-dimensional quantum theories, where phase space is given by the Hilbert projective space (as Kähler manifold), in the spirit of celebrated works of Kibble, Ashtekar and others. Within geometric Hamiltonian formulation quantum observables are represented by phase space functions, quantum states are described by Liouville densities (phase space probability densities), and Schrödinger dynamics is induced by a Hamiltonian flow on the projective space. We construct the star-product of this phase space formulation and some applications of geometric picture are discussed.
Geometric entanglement in the Laughlin wave function
NASA Astrophysics Data System (ADS)
Zhang, Jiang-Min; Liu, Yu
2017-08-01
We study numerically the geometric entanglement in the Laughlin wave function, which is of great importance in condensed matter physics. The Slater determinant having the largest overlap with the Laughlin wave function is constructed by an iterative algorithm. The logarithm of the overlap, which is a geometric quantity, is then taken as a geometric measure of entanglement. It is found that the geometric entanglement is a linear function of the number of electrons to a good extent. This is especially the case for the lowest Laughlin wave function, namely the one with filling factor of 1/3. Surprisingly, the linear behavior extends well down to the smallest possible value of the electron number, namely, N = 2. The constant term does not agree with the expected topological entropy. In view of previous works, our result indicates that the relation between geometric entanglement and topological entropy is very subtle.
Mobility in geometrically confined membranes.
Domanov, Yegor A; Aimon, Sophie; Toombes, Gilman E S; Renner, Marianne; Quemeneur, François; Triller, Antoine; Turner, Matthew S; Bassereau, Patricia
2011-08-02
Lipid and protein lateral mobility is essential for biological function. Our theoretical understanding of this mobility can be traced to the seminal work of Saffman and Delbrück, who predicted a logarithmic dependence of the protein diffusion coefficient (i) on the inverse of the size of the protein and (ii) on the "membrane size" for membranes of finite size [Saffman P, Delbrück M (1975) Proc Natl Acad Sci USA 72:3111-3113]. Although the experimental proof of the first prediction is a matter of debate, the second has not previously been thought to be experimentally accessible. Here, we construct just such a geometrically confined membrane by forming lipid bilayer nanotubes of controlled radii connected to giant liposomes. We followed the diffusion of individual molecules in the tubular membrane using single particle tracking of quantum dots coupled to lipids or voltage-gated potassium channels KvAP, while changing the membrane tube radius from approximately 250 to 10 nm. We found that both lipid and protein diffusion was slower in tubular membranes with smaller radii. The protein diffusion coefficient decreased as much as 5-fold compared to diffusion on the effectively flat membrane of the giant liposomes. Both lipid and protein diffusion data are consistent with the predictions of a hydrodynamic theory that extends the work of Saffman and Delbrück to cylindrical geometries. This study therefore provides strong experimental support for the ubiquitous Saffman-Delbrück theory and elucidates the role of membrane geometry and size in regulating lateral diffusion.
Mobility in geometrically confined membranes
Domanov, Yegor A.; Aimon, Sophie; Toombes, Gilman E. S.; Renner, Marianne; Quemeneur, François; Triller, Antoine; Turner, Matthew S.; Bassereau, Patricia
2011-01-01
Lipid and protein lateral mobility is essential for biological function. Our theoretical understanding of this mobility can be traced to the seminal work of Saffman and Delbrück, who predicted a logarithmic dependence of the protein diffusion coefficient (i) on the inverse of the size of the protein and (ii) on the “membrane size” for membranes of finite size [Saffman P, Delbrück M (1975) Proc Natl Acad Sci USA 72:3111—3113]. Although the experimental proof of the first prediction is a matter of debate, the second has not previously been thought to be experimentally accessible. Here, we construct just such a geometrically confined membrane by forming lipid bilayer nanotubes of controlled radii connected to giant liposomes. We followed the diffusion of individual molecules in the tubular membrane using single particle tracking of quantum dots coupled to lipids or voltage-gated potassium channels KvAP, while changing the membrane tube radius from approximately 250 to 10 nm. We found that both lipid and protein diffusion was slower in tubular membranes with smaller radii. The protein diffusion coefficient decreased as much as 5-fold compared to diffusion on the effectively flat membrane of the giant liposomes. Both lipid and protein diffusion data are consistent with the predictions of a hydrodynamic theory that extends the work of Saffman and Delbrück to cylindrical geometries. This study therefore provides strong experimental support for the ubiquitous Saffman–Delbrück theory and elucidates the role of membrane geometry and size in regulating lateral diffusion. PMID:21768336
Students' Geometrical Perception on a Task-Based Dynamic Geometry Platform
ERIC Educational Resources Information Center
Leung, Allen; Lee, Arthur Man Sang
2013-01-01
This paper describes a task-based dynamic geometry platform that is able to record student responses in a collective fashion to pre-designed dragging tasks. The platform provides a new type of data and opens up a quantitative dimension to interpret students' geometrical perception in dynamic geometry environments. The platform is capable of…
Analyser-based phase contrast image reconstruction using geometrical optics.
Kitchen, M J; Pavlov, K M; Siu, K K W; Menk, R H; Tromba, G; Lewis, R A
2007-07-21
Analyser-based phase contrast imaging can provide radiographs of exceptional contrast at high resolution (<100 microm), whilst quantitative phase and attenuation information can be extracted using just two images when the approximations of geometrical optics are satisfied. Analytical phase retrieval can be performed by fitting the analyser rocking curve with a symmetric Pearson type VII function. The Pearson VII function provided at least a 10% better fit to experimentally measured rocking curves than linear or Gaussian functions. A test phantom, a hollow nylon cylinder, was imaged at 20 keV using a Si(1 1 1) analyser at the ELETTRA synchrotron radiation facility. Our phase retrieval method yielded a more accurate object reconstruction than methods based on a linear fit to the rocking curve. Where reconstructions failed to map expected values, calculations of the Takagi number permitted distinction between the violation of the geometrical optics conditions and the failure of curve fitting procedures. The need for synchronized object/detector translation stages was removed by using a large, divergent beam and imaging the object in segments. Our image acquisition and reconstruction procedure enables quantitative phase retrieval for systems with a divergent source and accounts for imperfections in the analyser.
On geometric factors for neutral particle analyzers.
Stagner, L; Heidbrink, W W
2014-11-01
Neutral particle analyzers (NPA) detect neutralized energetic particles that escape from plasmas. Geometric factors relate the counting rate of the detectors to the intensity of the particle source. Accurate geometric factors enable quick simulation of geometric effects without the need to resort to slower Monte Carlo methods. Previously derived expressions [G. R. Thomas and D. M. Willis, "Analytical derivation of the geometric factor of a particle detector having circular or rectangular geometry," J. Phys. E: Sci. Instrum. 5(3), 260 (1972); J. D. Sullivan, "Geometric factor and directional response of single and multi-element particle telescopes," Nucl. Instrum. Methods 95(1), 5-11 (1971)] for the geometric factor implicitly assume that the particle source is very far away from the detector (far-field); this excludes applications close to the detector (near-field). The far-field assumption does not hold in most fusion applications of NPA detectors. We derive, from probability theory, a generalized framework for deriving geometric factors that are valid for both near and far-field applications as well as for non-isotropic sources and nonlinear particle trajectories.
Conceptual aspects of geometric quantum computation
NASA Astrophysics Data System (ADS)
Sjöqvist, Erik; Azimi Mousolou, Vahid; Canali, Carlo M.
2016-10-01
Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic evolution, controlled by slowly changing parameters, this form of quantum computation can as well be realized at high speed by using nonadiabatic schemes. Recent advances in quantum gate technology have allowed for experimental demonstrations of different types of geometric gates in adiabatic and nonadiabatic evolution. Here, we address some conceptual issues that arise in the realizations of geometric gates. We examine the appearance of dynamical phases in quantum evolution and point out that not all dynamical phases need to be compensated for in geometric quantum computation. We delineate the relation between Abelian and non-Abelian geometric gates and find an explicit physical example where the two types of gates coincide. We identify differences and similarities between adiabatic and nonadiabatic realizations of quantum computation based on non-Abelian geometric phases.
On geometric factors for neutral particle analyzers
NASA Astrophysics Data System (ADS)
Stagner, L.; Heidbrink, W. W.
2014-11-01
Neutral particle analyzers (NPA) detect neutralized energetic particles that escape from plasmas. Geometric factors relate the counting rate of the detectors to the intensity of the particle source. Accurate geometric factors enable quick simulation of geometric effects without the need to resort to slower Monte Carlo methods. Previously derived expressions [G. R. Thomas and D. M. Willis, "Analytical derivation of the geometric factor of a particle detector having circular or rectangular geometry," J. Phys. E: Sci. Instrum. 5(3), 260 (1972); J. D. Sullivan, "Geometric factor and directional response of single and multi-element particle telescopes," Nucl. Instrum. Methods 95(1), 5-11 (1971)] for the geometric factor implicitly assume that the particle source is very far away from the detector (far-field); this excludes applications close to the detector (near-field). The far-field assumption does not hold in most fusion applications of NPA detectors. We derive, from probability theory, a generalized framework for deriving geometric factors that are valid for both near and far-field applications as well as for non-isotropic sources and nonlinear particle trajectories.
On geometric factors for neutral particle analyzers
Stagner, L.; Heidbrink, W. W.
2014-11-15
Neutral particle analyzers (NPA) detect neutralized energetic particles that escape from plasmas. Geometric factors relate the counting rate of the detectors to the intensity of the particle source. Accurate geometric factors enable quick simulation of geometric effects without the need to resort to slower Monte Carlo methods. Previously derived expressions [G. R. Thomas and D. M. Willis, “Analytical derivation of the geometric factor of a particle detector having circular or rectangular geometry,” J. Phys. E: Sci. Instrum. 5(3), 260 (1972); J. D. Sullivan, “Geometric factor and directional response of single and multi-element particle telescopes,” Nucl. Instrum. Methods 95(1), 5–11 (1971)] for the geometric factor implicitly assume that the particle source is very far away from the detector (far-field); this excludes applications close to the detector (near-field). The far-field assumption does not hold in most fusion applications of NPA detectors. We derive, from probability theory, a generalized framework for deriving geometric factors that are valid for both near and far-field applications as well as for non-isotropic sources and nonlinear particle trajectories.
Geometric Gyrokinetic Theory for Edge Plasma
Qin, H; Cohen, R H; Nevins, W M; Xu, X Q
2007-01-18
It turns out that gyrokinetic theory can be geometrically formulated as special cases of a geometrically generalized Vlasov-Maxwell system. It is proposed that the phase space of the spacetime is a 7-dimensional fiber bundle P over the 4-dimensional spacetime M, and that a Poincare-Cartan-Einstein 1-form {gamma} on the 7-dimensional phase space determines particles worldlines in the phase space. Through Liouville 6-form {Omega} and fiber integral, the 1-form {gamma} also uniquely defines a geometrically generalized Vlasov-Maxwell system as a field theory for the collective electromagnetic field. The geometric gyrokinetic theory is then developed as a special case of the geometrically generalized Vlasov-Maxwell system. In its most general form, gyrokinetic theory is about a symmetry, called gyro-symmetry, for magnetized plasmas, and the 1-form {gamma} again uniquely defines the gyro-symmetry. The objective is to decouple the gyro-phase dynamics from the rest of particle dynamics by finding the gyro-symmetry in {gamma}. Compared with other methods of deriving the gyrokinetic equations, the advantage of the geometric approach is that it allows any approximation based on mathematical simplification or physical intuition to be made at the 1-form level, and yet the field theories still have the desirable exact conservation properties such as phase space volume conservation and energy-momentum conservation if the 1-form does not depend on the spacetime coordinate explicitly. A set of generalized gyrokinetic equations valid for the edge plasmas is then derived using this geometric method. This formalism allows large-amplitude, time-dependent background electromagnetic fields to be developed fully nonlinearly in addition to small-amplitude, short-wavelength electromagnetic perturbations. The fact that we adopted the geometric method in the present study does not necessarily imply that the major results reported here can not be achieved using classical methods. What the
The promise of geometric morphometrics.
Richtsmeier, Joan T; DeLeon, Valerie Burke; Lele, Subhash R
2002-01-01
Nontraditional or geometric morphometric methods have found wide application in the biological sciences, especially in anthropology, a field with a strong history of measurement of biological form. Controversy has arisen over which method is the "best" for quantifying the morphological difference between forms and for making proper statistical statements about the detected differences. This paper explains that many of these arguments are superfluous to the real issues that need to be understood by those wishing to apply morphometric methods to biological data. Validity, the ability of a method to find the correct answer, is rarely discussed and often ignored. We explain why demonstration of validity is a necessary step in the evaluation of methods used in morphometrics. Focusing specifically on landmark data, we discuss the concepts of size and shape, and reiterate that since no unique definition of size exists, shape can only be recognized with reference to a chosen surrogate for size. We explain why only a limited class of information related to the morphology of an object can be known when landmark data are used. This observation has genuine consequences, as certain morphometric methods are based on models that require specific assumptions, some of which exceed what can be known from landmark data. We show that orientation of an object with reference to other objects in a sample can never be known, because this information is not included in landmark data. Consequently, a descriptor of form difference that contains information on orientation is flawed because that information does not arise from evidence within the data, but instead is a product of a chosen orientation scheme. To illustrate these points, we apply superimposition, deformation, and linear distance-based morphometric methods to the analysis of a simulated data set for which the true differences are known. This analysis demonstrates the relative efficacy of various methods to reveal the true
NASA Astrophysics Data System (ADS)
Duerr, Fabian; Meuret, Youri; Thienpont, Hugo
2010-05-01
Scaling down the dimensions of concentrating photovoltaic systems based on plane Fresnel lenses has several promising advantages. By conserving a designed concentration ratio and reducing the aperture size of the lens, the working distance decreases as well. This provides thinner modules and the dimensions of the used solar cells can be scaled down to the millimeter range. An important benefit of this miniaturization process is the avoidance of technically demanding cooling. In this work the design of a plane Fresnel lens is introduced and the basic limitations concerning the achievable concentration ratio are investigated based on geometrical optics. However, accompanied by the down scaling of the prism dimensions, pure ray tracing based on the geometrical optics approximation may no longer be valid for the determination of the concentration ratio. In terms of micro-structured Fresnel lenses for solar concentration, only a qualitative description of this limit - typically a rule of thumb - is provided in the literature. For this reason a quantitative investigation of the influence of the prisms' down scaling and thus the appearing wave optical effects on the obtained concentration ratio is presented. In a final step the introduced monochromatic investigations are extended to a polychromatic analysis. This allows for the prediction of the influence of miniaturization on the effective concentration ratio for a given spectrum and thus the adequate size of the receiver. A better quantitative understanding of the impact of diffraction in micro-structured Fresnel lenses might help to optimize the design of several applications in nonimaging optics.
Numerical procedure to determine geometric view factors for surfaces occluded by cylinders
NASA Technical Reports Server (NTRS)
Sawyer, P. L.
1978-01-01
A numerical procedure was developed to determine geometric view factors between connected infinite strips occluded by any number of infinite circular cylinders. The procedure requires a two-dimensional cross-sectional model of the configuration of interest. The two-dimensional model consists of a convex polygon enclosing any number of circles. Each side of the polygon represents one strip, and each circle represents a circular cylinder. A description and listing of a computer program based on this procedure are included in this report. The program calculates geometric view factors between individual strips and between individual strips and the collection of occluding cylinders.
Polyakov, Felix
2017-02-01
Neuroscientific studies of drawing-like movements usually analyze neural representation of either geometric (e.g., direction, shape) or temporal (e.g., speed) parameters of trajectories rather than trajectory's representation as a whole. This work is about identifying geometric building blocks of movements by unifying different empirically supported mathematical descriptions that characterize relationship between geometric and temporal aspects of biological motion. Movement primitives supposedly facilitate the efficiency of movements' representation in the brain and comply with such criteria for biological movements as kinematic smoothness and geometric constraint. The minimum-jerk model formalizes criterion for trajectories' maximal smoothness of order 3. I derive a class of differential equations obeyed by movement paths whose nth-order maximally smooth trajectories accumulate path measurement with constant rate. Constant rate of accumulating equi-affine arc complies with the 2/3 power-law model. Candidate primitive shapes identified as equations' solutions for arcs in different geometries in plane and in space are presented. Connection between geometric invariance, motion smoothness, compositionality and performance of the compromised motor control system is proposed within single invariance-smoothness framework. The derived class of differential equations is a novel tool for discovering candidates for geometric movement primitives.
Stereo Orthogonal Axonometric Perspective for the Teaching of Descriptive Geometry
ERIC Educational Resources Information Center
Méxas, José Geraldo Franco; Guedes, Karla Bastos; Tavares, Ronaldo da Silva
2015-01-01
Purpose: The purpose of this paper is to present the development of a software for stereo visualization of geometric solids, applied to the teaching/learning of Descriptive Geometry. Design/methodology/approach: The paper presents the traditional method commonly used in computer graphic stereoscopic vision (implemented in C language) and the…
Stereo Orthogonal Axonometric Perspective for the Teaching of Descriptive Geometry
ERIC Educational Resources Information Center
Méxas, José Geraldo Franco; Guedes, Karla Bastos; Tavares, Ronaldo da Silva
2015-01-01
Purpose: The purpose of this paper is to present the development of a software for stereo visualization of geometric solids, applied to the teaching/learning of Descriptive Geometry. Design/methodology/approach: The paper presents the traditional method commonly used in computer graphic stereoscopic vision (implemented in C language) and the…
NASA Astrophysics Data System (ADS)
Le Pape, Olivier; Chauvet, Florence; Mahévas, Stéphanie; Lazure, Pascal; Guérault, Daniel; Désaunay, Yves
2003-11-01
This study describes the spatial distribution of young-of-the-year sole based on autumnal beam trawl surveys conducted in the Bay of Biscay (France) during a 15-y period. Previous studies showed that habitat suitability for juvenile sole varies according to physical factors such as bathymetry, sediment structure and river plume influence. These factors, which are known exhaustively for the entire Bay of Biscay from static maps (bathymetry and granulometry) or temporal maps based on a hydrodynamic model (the river plume), were used as descriptors in a generalised linear model of habitat suitability in order to characterise the distribution of juvenile 0-group sole according to delta distribution. This model was used to identify the habitats in which juvenile 0-group sole are concentrated. The respective areas of these habitats were determined from a Geographic Information System (GIS), and their respective contribution to the sole population in the Bay of Biscay was calculated in terms of the estimated number of young fish (GIS area×density derived from the model). Despite the great variability of survey data, this quantitative approach emphasises the highly important role of restricted shallow, muddy estuarine areas as nursery grounds of sole in the Bay of Biscay and demonstrates the relation between interannual variations of nursery habitat capacity (with respect to estuarine extent) and sole recruitment.
Tomlinson, A; Coupland, R E
1990-01-01
The innervation of the adrenal medulla has been investigated in normal Wistar rats from birth to old age and ultrastructural findings compared with biochemical markers of the cholinergic innervation of the adrenal gland and catecholamine storage. Morphological evidence of the immaturity of the innervation during the first postnatal week is provided and using quantitative morphometry the innervation of chromaffin cells is shown to reach a mean total of 5.4 synapses per chromaffin cell during the period 26 days to 12 weeks of age. The variation in contents of synaptic profiles is discussed in the light of recent work that demonstrates a major sensory as well as visceral efferent innervation of the gland. Adrenal medullary neurons usually occur in closely packed groups, intimately associated with Schwann cells. Axodendritic and axosomatic synapses on these neurons are described and the likely origin of axonal processes innervating the neurons discussed. In old age the density of innervation remains the same as in young adult animals even though the medulla shows evidence of hyperplasia and hypertrophy of individual chromaffin cells. Images Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 Fig. 8 Fig. 9 Fig. 10 Fig. 11 Fig. 12 Fig. 13 Fig. 14 Fig. 15 Fig. 16 Fig. 17 Fig. 18 Fig. 19 Fig. 20 Fig. 21 Fig. 22 Fig. 23 Fig. 24 Fig. 25 PMID:2384334
The perception of geometrical structure from congruence
NASA Technical Reports Server (NTRS)
Lappin, Joseph S.; Wason, Thomas D.
1989-01-01
The principle function of vision is to measure the environment. As demonstrated by the coordination of motor actions with the positions and trajectories of moving objects in cluttered environments and by rapid recognition of solid objects in varying contexts from changing perspectives, vision provides real-time information about the geometrical structure and location of environmental objects and events. The geometric information provided by 2-D spatial displays is examined. It is proposed that the geometry of this information is best understood not within the traditional framework of perspective trigonometry, but in terms of the structure of qualitative relations defined by congruences among intrinsic geometric relations in images of surfaces. The basic concepts of this geometrical theory are outlined.
Geometric vector potentials from nonadiabatic spin dynamics
NASA Astrophysics Data System (ADS)
Baltanás, J. P.; Saarikoski, H.; Reynoso, A. A.; Frustaglia, D.
2017-07-01
We propose a theoretical framework that captures the geometric vector potential emerging from the nonadiabatic spin dynamics of itinerant carriers subject to arbitrary magnetic textures. Our approach results in a series of constraints on the geometric potential and the nonadiabatic geometric phase associated with it. These constraints play a decisive role when studying, e.g., the geometric spin phase gathered by conducting electrons in ring interferometers under the action of in-plane magnetic textures, allowing a simple characterization of the topological transition recently reported by Saarikoski et al. [H. Saarikoski, J. E. Vázquez-Lozano, J. P. Baltanás, F. Nagasawa, J. Nitta, and D. Frustaglia, Phys. Rev. B 91, 241406(R) (2015), 10.1103/PhysRevB.91.241406].
Heat transfer in geometrically similar cylinders
NASA Technical Reports Server (NTRS)
Riekert, P; Held, A
1941-01-01
The power and heat-stress conditions of geometrically similar engines are discussed. The advantages accruing from smaller cylinder dimensions are higher specific horsepower, lower weight per horsepower, lower piston temperature, and less frontal area, with reduced detonation tendency.
Geometric symmetries in superfluid vortex dynamics
Kozik, Evgeny; Svistunov, Boris
2010-10-01
Dynamics of quantized vortex lines in a superfluid feature symmetries associated with the geometric character of the complex-valued field, w(z)=x(z)+iy(z), describing the instant shape of the line. Along with a natural set of Noether's constants of motion, which - apart from their rather specific expressions in terms of w(z) - are nothing but components of the total linear and angular momenta of the fluid, the geometric symmetry brings about crucial consequences for kinetics of distortion waves on the vortex lines, the Kelvin waves. It is the geometric symmetry that renders Kelvin-wave cascade local in the wave-number space. Similar considerations apply to other systems with purely geometric degrees of freedom.
Hidden geometric correlations in real multiplex networks
NASA Astrophysics Data System (ADS)
Kleineberg, Kaj-Kolja; Boguñá, Marián; Ángeles Serrano, M.; Papadopoulos, Fragkiskos
2016-11-01
Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are not random combinations of single network layers. Instead, they are organized in specific ways dictated by hidden geometric correlations between the layers. We find that these correlations are significant in different real multiplexes, and form a key framework for answering many important questions. Specifically, we show that these geometric correlations facilitate the definition and detection of multidimensional communities, which are sets of nodes that are simultaneously similar in multiple layers. They also enable accurate trans-layer link prediction, meaning that connections in one layer can be predicted by observing the hidden geometric space of another layer. And they allow efficient targeted navigation in the multilayer system using only local knowledge, outperforming navigation in the single layers only if the geometric correlations are sufficiently strong.
Concepts and Figures in Geometric Reasoning.
ERIC Educational Resources Information Center
Fischbein, Efraim; Nachlieli, Talli
1998-01-01
Opens with the theoretical construct of figural concepts. Argues that geometrical figures are characterized by both conceptual and sensorial properties. Investigates the effects of interaction between conceptual and figural components. Contains 19 references. (DDR)
The Geometric Grids of the Hieratic Numeral.
NASA Astrophysics Data System (ADS)
Aboulfotouh, Hossam M. K.
The paper discusses the geometrical designs of the hieratic numeral signs. It shows the regular-grid-patterns of squares upon which, the shapes of the already decoded hieratic numeral-signs, have been designed. Also, it shows the design of some hieratic numeral signs, based on subdividing the circle; and the hieratic signs of modular notation. It might reveal the basic geometrical level of understanding of anonymous ancient Egyptians who designed them some four thousand years ago.
Geometric sigma model of the Universe
NASA Astrophysics Data System (ADS)
Vasilić, Milovan
2017-05-01
The purpose of this work is to demonstrate how an arbitrarily chosen background of the Universe can be made a solution of a simple geometric sigma model. Geometric sigma models are purely geometric theories in which spacetime coordinates are seen as scalar fields coupled to gravity. Although they look like ordinary sigma models, they have the peculiarity that their complete matter content can be gauged away. The remaining geometric theory possesses a background solution that is predefined in the process of constructing the theory. The fact that background configuration is specified in advance is another peculiarity of geometric sigma models. In this paper, I construct geometric sigma models based on different background geometries of the Universe. Whatever background geometry is chosen, the dynamics of its small perturbations is shown to have a generic classical stability. This way, any freely chosen background metric is made a stable solution of a simple model. Three particular models of the Universe are considered as examples of how this is done in practice. Supported by Serbian Ministry of Education, Science and Technological Development (171031)
Geometric crossovers for multiway graph partitioning.
Moraglio, Alberto; Kim, Yong-Hyuk; Yoon, Yourim; Moon, Byung-Ro
2007-01-01
Geometric crossover is a representation-independent generalization of the traditional crossover defined using the distance of the solution space. By choosing a distance firmly rooted in the syntax of the solution representation as a basis for geometric crossover, one can design new crossovers for any representation. Using a distance tailored to the problem at hand, the formal definition of geometric crossover allows us to design new problem-specific crossovers that embed problem-knowledge in the search. The standard encoding for multiway graph partitioning is highly redundant: each solution has a number of representations, one for each way of labeling the represented partition. Traditional crossover does not perform well on redundant encodings. We propose a new geometric crossover for graph partitioning based on a labeling-independent distance that filters out the redundancy of the encoding. A correlation analysis of the fitness landscape based on this distance shows that it is well suited to graph partitioning. A second difficulty with designing a crossover for multiway graph partitioning is that of feasibility: in general recombining feasible partitions does not lead to feasible offspring partitions. We design a new geometric crossover for permutations with repetitions that naturally suits partition problems and we test it on the graph partitioning problem. We then combine it with the labeling-independent crossover and obtain a much superior geometric crossover inheriting both advantages.
Geometric sensitivity of ClearPET™ Neuro
NASA Astrophysics Data System (ADS)
Gundlich, Brigitte; Weber, Simone
2007-02-01
ClearPET™ Neuro is a small-animal positron emission tomography (PET) scanner dedicated to brain studies on rats and primates. The design of ClearPET™ Neuro leads to a specific geometric sensitivity, characterized by inhomogeneous and, depending on the measurement setup, even incomplete data. With respect to reconstruction techniques, homogeneous and complete data sets are a 'must' for analytical reconstruction methods, whereas iterative methods take the geometrical sensitivity into account during the reconstruction process. Nevertheless, here a homogeneous geometric sensitivity over the field of view is highly desirable. Therefore, this contribution aims at studying the impact of different scanner geometries and measurement setups on the geometric sensitivity. A data set of coincident events is computed for certain settings that contains each possible crystal combination once. The lines of response are rebinned into normalizing sinograms and backprojected into sensitivity images. Both, normalizing sinograms and sensitivity images mirror the geometric sensitivity and therefore, provide information which setting enables most complete and homogeneous data sets. An optimal measurement setup and scanner geometry in terms of homogeneous geometric sensitivity is found by analyzing the sensitivity images.
Graphene geometric diodes for terahertz rectennas
NASA Astrophysics Data System (ADS)
Zhu, Zixu; Joshi, Saumil; Grover, Sachit; Moddel, Garret
2013-05-01
We demonstrate a new thin-film graphene diode called a geometric diode that relies on geometric asymmetry to provide rectification at 28 THz. The geometric diode is coupled to an optical antenna to form a rectenna that rectifies incoming radiation. This is the first reported graphene-based antenna-coupled diode working at 28 THz, and potentially at optical frequencies. The planar structure of the geometric diode provides a low RC time constant, on the order of 10-15 s, required for operation at optical frequencies, and a low impedance for efficient power transfer from the antenna. Fabricated geometric diodes show asymmetric current-voltage characteristics consistent with Monte Carlo simulations for the devices. Rectennas employing the geometric diode coupled to metal and graphene antennas rectify 10.6 µm radiation, corresponding to an operating frequency of 28 THz. The graphene bowtie antenna is the first demonstrated functional antenna made using graphene. Its response indicates that graphene is a suitable terahertz resonator material. Applications for this terahertz diode include terahertz-wave and optical detection, ultra-high-speed electronics and optical power conversion.
NASA Astrophysics Data System (ADS)
Zhao, P. Z.; Xu, G. F.; Tong, D. M.
2016-12-01
Nonadiabatic geometric quantum computation in decoherence-free subspaces has received increasing attention due to the merits of its high-speed implementation and robustness against both control errors and decoherence. However, all the previous schemes in this direction have been based on the conventional geometric phases, of which the dynamical phases need to be removed. In this paper, we put forward a scheme of nonadiabatic geometric quantum computation in decoherence-free subspaces based on unconventional geometric phases, of which the dynamical phases do not need to be removed. Specifically, by using three physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of geometric gates nonadiabatically and unconventionally. Our scheme not only maintains all the merits of nonadiabatic geometric quantum computation in decoherence-free subspaces, but also avoids the additional operations required in the conventional schemes to cancel the dynamical phases.
Geometrical optimization for strictly localized structures
NASA Astrophysics Data System (ADS)
Mo, Yirong
2003-07-01
Recently we proposed the block localized wavefunction (BLW) approach which takes the advantages of valence bond theory and molecular orbital theory and defines the wavefunctions for resonance structures based on the assumption that all electrons and orbitals are partitioned into a few subgroups. In this work, we implement the geometrical optimization of the BLW method based on the algorithm proposed by Gianinetti and coworkers. Thus, we can study the conjugation effect on not only the molecular stability, but also the molecular geometry. With this capability, the π conjugation effect in trans-polyenes C2nH2n+2 (n=2-5) as well as in formamide and its analogs are studied by optimizing their delocalized and strictly localized forms with the 6-31G(d) and 6-311+G(d,p) basis sets. Although it has been well presumed that the π resonance shortens the single bonds and lengthens the double bonds with the delocalization of π electrons across the whole line in polyenes, our optimization of the strictly localized structures quantitatively shows that when the conjugation effect is "turned off," the double bond lengths will be identical to the CC bond length in ethylene and the single Csp2-Csp2 bond length will be about 1.513-1.517 Å. In agreement with the classical Hückel theory, the resonance energies in polyenes are approximately in proportion to the number of double bonds. Similarly, resonance is responsible not only for the planarity of formamide, thioformamide, and selenoformamide, but also for the lengthening of the CX (X=O,S,Se) double bond and the shortening of the CN bonds. Although it is assumed that the CX bond polarization decreases in the order of O>S>Se, the π electronic delocalization increases in the opposite order, i.e., formamide
Watson, Roger
2015-04-01
This article describes the basic tenets of quantitative research. The concepts of dependent and independent variables are addressed and the concept of measurement and its associated issues, such as error, reliability and validity, are explored. Experiments and surveys – the principal research designs in quantitative research – are described and key features explained. The importance of the double-blind randomised controlled trial is emphasised, alongside the importance of longitudinal surveys, as opposed to cross-sectional surveys. Essential features of data storage are covered, with an emphasis on safe, anonymous storage. Finally, the article explores the analysis of quantitative data, considering what may be analysed and the main uses of statistics in analysis.
Geometric principles in the assembly of α-helical bundles.
Pratap, J V; Luisi, B F; Calladine, C R
2013-06-28
α-Helical coiled coils are usually stabilized by hydrophobic interfaces between the two constituent α-helices, in the form of 'knobs-into-holes' packing of non-polar residues arranged in repeating heptad patterns. Here we examine the corresponding 'hydrophobic cores' that stabilize bundles of four α-helices. In particular, we study three different kinds of bundle, involving four α-helices of identical sequence: two pack in a parallel and one in an anti-parallel orientation. We point out that the simplest way of understanding the packing of these 4-helix bundles is to use Crick's original idea that the helices are held together by 'hydrophobic stripes', which are readily visualized on the cylindrical surface lattice of the α-helices; and that the 'helix-crossing angle'--which determines, in particular, whether supercoiling is left- or right-handed--is fixed by the slope of the lattice lines that contain the hydrophobic residues. In our three examples the constituent α-helices have hydrophobic repeat patterns of 7, 11 and 4 residues, respectively; and we associate the different overall conformations with 'knobs-into-holes' packing along the 7-, 11- and 4-start lines, respectively, of the cylindrical surface lattices of the constituent α-helices. For the first two examples, all four interfaces between adjacent helices are geometrically equivalent; but in the third, one of the four interfaces differs significantly from the others. We provide a geometrical explanation for this non-equivalence in terms of two different but equivalent ways of assembling this bundle, which may possibly constitute a bistable molecular 'switch' with a coaxial throw of about 12 Å. The geometrical ideas that we deploy in this paper provide the simplest and clearest description of the structure of helical bundles. In an appendix, we describe briefly a computer program that we have devised in order to search for 'knobs-into-holes' packing between α-helices in proteins.
NASA Astrophysics Data System (ADS)
Shock, Everett L.; Holland, Melanie E.
2007-12-01
A framework is proposed for a quantitative approach to studying habitability. Considerations of environmental supply and organismal demand of energy lead to the conclusions that power units are most appropriate and that the units for habitability become watts per organism. Extreme and plush environments are revealed to be on a habitability continuum, and extreme environments can be quantified as those where power supply only barely exceeds demand. Strategies for laboratory and field experiments are outlined that would quantify power supplies, power demands, and habitability. An example involving a comparison of various metabolisms pursued by halophiles is shown to be well on the way to a quantitative habitability analysis.
Schaffner, M
1990-01-01
The skill of writing job descriptions begins with an understanding of the advantages, as well as the basic elements, of a well written description. The end result should be approved and updated as needed. Having a better understanding of this process makes writing the job description a challenge rather than a chore.
Geometric algebra and information geometry for quantum computational software
NASA Astrophysics Data System (ADS)
Cafaro, Carlo
2017-03-01
The art of quantum algorithm design is highly nontrivial. Grover's search algorithm constitutes a masterpiece of quantum computational software. In this article, we use methods of geometric algebra (GA) and information geometry (IG) to enhance the algebraic efficiency and the geometrical significance of the digital and analog representations of Grover's algorithm, respectively. Specifically, GA is used to describe the Grover iterate and the discretized iterative procedure that exploits quantum interference to amplify the probability amplitude of the target-state before measuring the query register. The transition from digital to analog descriptions occurs via Stone's theorem which relates the (unitary) Grover iterate to a suitable (Hermitian) Hamiltonian that controls Schrodinger's quantum mechanical evolution of a quantum state towards the target state. Once the discrete-to-continuos transition is completed, IG is used to interpret Grover's iterative procedure as a geodesic path on the manifold of the parametric density operators of pure quantum states constructed from the continuous approximation of the parametric quantum output state in Grover's algorithm. Finally, we discuss the dissipationless nature of quantum computing, recover the quadratic speedup relation, and identify the superfluity of the Walsh-Hadamard operation from an IG perspective with emphasis on statistical mechanical considerations.
D-brane superpotentials: Geometric and worldsheet approaches
NASA Astrophysics Data System (ADS)
Baumgartl, Marco; Brunner, Ilka; Soroush, Masoud
2011-02-01
From the worldsheet perspective, the superpotential on a D-brane wrapping internal cycles of a Calabi-Yau manifold is given as a generating functional for disk correlation functions. On the other hand, from the geometric point of view, D-brane superpotentials are captured by certain chain integrals. In this work, we explicitly show for branes wrapping internal two-cycles how these two different approaches are related. More specifically, from the worldsheet point of view, D-branes at the Landau-Ginzburg point have a convenient description in terms of matrix factorizations. We use a formula derived by Kapustin and Li to explicitly evaluate disk correlators for families of D2-branes. On the geometry side, we then construct a three-chain whose period gives rise to the effective superpotential and show that the two expressions coincide. Finally, as an explicit example, we choose a particular compact Calabi-Yau hypersurface and compute the effective D2-brane superpotential in different branches of the open moduli space, in both geometric and worldsheet approaches.
Abstract: In toxicology, the role of quantitative assessment of brain morphology can be understood in the context of two types of treatment-related alterations. One type of alteration is specifically associated with treatment and is not observed in control animals. Measurement ...
Abstract: In toxicology, the role of quantitative assessment of brain morphology can be understood in the context of two types of treatment-related alterations. One type of alteration is specifically associated with treatment and is not observed in control animals. Measurement ...
Geometric Modeling Using Both Active And Passive Sensing
NASA Astrophysics Data System (ADS)
Wang, Y. F.; Aggarwal, J. K.
1989-01-01
In this paper, we introduce a new algorithm for modeling the structure of 3-D objects from multiple viewing directions using an integration of active and passive sensing. Construction of the structural description of a 3-D object is composed of two stages: (i) The surface orientation and partial structure are first inferred from a set of single views, and (ii) the visible surface structures inferred from different viewpoints are integrated to complete the description of the 3-D object. In the first stage, an active stripe coding technique is used for recovering visible surface orientation and partial structure. In the second stage, an iterative construction/refinement scheme is used which exploits both passive and active sensing for representing the object surfaces. The active sensing technique projects spatially modulated light patterns to encode the object surfaces for analysis. The visible surface orientation is inferred using a constraint satisfaction process based upon the observed orientation of the projected patterns. The visible surface structure is recovered by integrating a dense orientation map. For multiple view integration, the bounding volume description of the imaged object is first constructed using multiple occluding contours which are acquired through passive sensing. The bounding volume description is then refined using the partial surface structures inferred from active sensing. The final surface structure is recorded in a data structure where the surface contours in a set of parallel planar cross sections are stored. The system construction is inexpensive and the algorithms introduced are adaptive, versatile and suitable for applications in dynamic environments. We expect this approach to be widely applicable in the field of robotics, geometric modeling and factory automation.
Quantitative Radiological Diagnosis Of The Temporomandibular Joint
NASA Astrophysics Data System (ADS)
Jordan, Steven L.; Heffez, Leslie B.
1989-05-01
Recent impressive technological advances in imaging techniques for the human temporomandibular (tm) joint, and in enabling geometric algorithms have outpaced diagnostic analyses. The authors present a basis for systematic quantitative diagnoses that exploit the imaging advancements. A reference line, coordinate system, and transformations are described that are appropriate for tomography of the tm joint. These yield radiographic measurements (disk displacement) and observations (beaking of radiopaque dye and disk shape) that refine diagnostic classifications of anterior displacement of the condylar disk. The relevance of these techniques has been clinically confirmed. Additional geometric invariants and procedures are proposed for future clinical verification.
Geometric Hypergraph Learning for Visual Tracking.
Du, Dawei; Qi, Honggang; Wen, Longyin; Tian, Qi; Huang, Qingming; Lyu, Siwei
2016-11-18
Graph-based representation is widely used in visual tracking field by finding correct correspondences between target parts in different frames. However, most graph-based trackers consider pairwise geometric relations between local parts. They do not make full use of the target's intrinsic structure, thereby making the representation easily disturbed by errors in pairwise affinities when large deformation or occlusion occurs. In this paper, we propose a geometric hypergraph learning-based tracking method, which fully exploits high-order geometric relations among multiple correspondences of parts in different frames. Then visual tracking is formulated as the mode-seeking problem on the hypergraph in which vertices represent correspondence hypotheses and hyperedges describe high-order geometric relations among correspondences. Besides, a confidence-aware sampling method is developed to select representative vertices and hyperedges to construct the geometric hypergraph for more robustness and scalability. The experiments are carried out on three challenging datasets (VOT2014, OTB100, and Deform-SOT) to demonstrate that our method performs favorably against other existing trackers.
Geometric modeling of pelvic organs with thickness
NASA Astrophysics Data System (ADS)
Bay, T.; Chen, Z.-W.; Raffin, R.; Daniel, M.; Joli, P.; Feng, Z.-Q.; Bellemare, M.-E.
2012-03-01
Physiological changes in the spatial configuration of the internal organs in the abdomen can induce different disorders that need surgery. Following the complexity of the surgical procedure, mechanical simulations are necessary but the in vivo factor makes complicate the study of pelvic organs. In order to determine a realistic behavior of these organs, an accurate geometric model associated with a physical modeling is therefore required. Our approach is integrated in the partnership between a geometric and physical module. The Geometric Modeling seeks to build a continuous geometric model: from a dataset of 3D points provided by a Segmentation step, surfaces are created through a B-spline fitting process. An energy function is built to measure the bidirectional distance between surface and data. This energy is minimized with an alternate iterative Hoschek-like method. A thickness is added with an offset formulation, and the geometric model is finally exported in a hexahedral mesh. Afterward, the Physical Modeling tries to calculate the properties of the soft tissues to simulate the organs displacements. The physical parameters attached to the data are determined with a feedback loop between finite-elements deformations and ground-truth acquisition (dynamic MRI).
Geometric phases in self-induced transparency
Sen, T; Milovich, J
1991-05-01
We consider the geometric phases arising in the lossless propagation of light pulses through a medium composed of near resonant two-level atoms. A reformulation of the coupled Maxwell-Schroedinger equations allows us to construct conservation laws in a general context. There exist periodic solutions of these equations which lead to the possibility of cyclical evolution of the state vector and the appearance of a geometric phase. We first show that if the ground state is the initial state of the system, then it acquires a geometric phase after the passage of the soliton pulses of McCall and Hahn. More generally if the initial state is a superposition of the two levels, continuous pulse trains can propagate without appreciable loss. We also find in this case that the state vector develops a geometric phase provided the parameters take on the particular values required for cyclical evolution. In both cases we exhibit the geometric character of the calculated phases by showing that they equal half the solid angle subtended by a closed curve traced by the Bloch, vector on the Bloch sphere. We verify a recent assertion of Anandan and Aharonov that the energy uncertainty in the state is directly related to the speed at which the tip of the Bloch vector moves along the curve on the Bloch sphere (or in more general terms the energy uncertainty is related to the speed in the projective Hilbert space).
Rational and efficient geometric definition of pharmacophores is essential for the patent process.
Guérin, Georges-Alexandre; Pratuangdejkul, Jaturong; Alemany, Monica; Launay, Jean-Marie; Manivet, Philippe
2006-11-01
The geometric description of pharmacophores suffers from approximations. No consensus has been clearly established, despite the increasing interest in using pharmacophores in drug design and in patent applications. We therefore propose an original definition of a pharmacophore using spherical coordinates. These coordinates give a precise description of each point using three parameters: distance to a geometric origin and two angles. If necessary, these parameters can be easily and rapidly converted to cartesian coordinates. Our method can guarantee, to the patent applicant, the safe protection of his intellectual property by both improving markedly the readability of a pharmacophore definition and bringing, to the person who is skilled in the art, enough information to understand easily the essence of the invention.
NASA Technical Reports Server (NTRS)
Parse, Joseph B.; Wert, J. A.
1991-01-01
Inhomogeneities in the spatial distribution of second phase particles in engineering materials are known to affect certain mechanical properties. Progress in this area has been hampered by the lack of a convenient method for quantitative description of the spatial distribution of the second phase. This study intends to develop a broadly applicable method for the quantitative analysis and description of the spatial distribution of second phase particles. The method was designed to operate on a desktop computer. The Dirichlet tessellation technique (geometrical method for dividing an area containing an array of points into a set of polygons uniquely associated with the individual particles) was selected as the basis of an analysis technique implemented on a PC. This technique is being applied to the production of Al sheet by PM processing methods; vacuum hot pressing, forging, and rolling. The effect of varying hot working parameters on the spatial distribution of aluminum oxide particles in consolidated sheet is being studied. Changes in distributions of properties such as through-thickness near-neighbor distance correlate with hot-working reduction.
Young Children's Understanding of Geometric Shapes: The Role of Geometric Models
ERIC Educational Resources Information Center
Elia, Iliada; Gagatsis, Athanasios; Kyriakides, Leonidas
2003-01-01
In this paper, we explore the role of polygonal shapes as geometrical models in teaching mathematics, so as to elicit and interpret children's geometric conceptions and understanding about shapes. Primary pupils were asked to draw a stairway of figures (triangles, squares and rectangles) each one bigger than the preceding one. Pupils use two…
Accurate geometric calibration in stepping-table digital subtraction angiography.
Schmidt, M A; Nayak, S L; Belli, A-M; Britten, A J
2007-10-01
Accurate measurements of vessel dimensions are desirable in many clinical applications. This work uses the known relative motion between X-ray source and the patient in stepping-table digital subtraction angiography (DSA) to provide an accurate geometric calibration for quantitative measurements. The method results in a calibration factor that converts the size of the object measured in pixels on the image to its size in millimetres. The main sources of error relate to: (i) the assessment of relative displacement of a structure in a series of images; (ii) patient motion throughout data acquisition; and (iii) image distortion. Error was evaluated both with a test object consisting of a large grid of ball bearings (2x2 cm spaced) and, in vivo, in five renal DSA examinations performed with identical catheters of known diameter. The calibration factor was calculated with 0.1% accuracy for the test object and at least 2% accuracy in vivo, even with breath holding and pulsatile motion. This demonstrates that the calculation of the calibration factor can be very accurate, and that the method we propose is capable of the submillimetre accuracy required for clinical studies if used in conjunction with an accurate measurement of the vessel size in pixels. In conclusion, accurate geometric measurements can be performed in stepping-table DSA, without the need for external reference objects.
Geometric estimation method for x-ray digital intraoral tomosynthesis
NASA Astrophysics Data System (ADS)
Li, Liang; Yang, Yao; Chen, Zhiqiang
2016-06-01
It is essential for accurate image reconstruction to obtain a set of parameters that describes the x-ray scanning geometry. A geometric estimation method is presented for x-ray digital intraoral tomosynthesis (DIT) in which the detector remains stationary while the x-ray source rotates. The main idea is to estimate the three-dimensional (3-D) coordinates of each shot position using at least two small opaque balls adhering to the detector surface as the positioning markers. From the radiographs containing these balls, the position of each x-ray focal spot can be calculated independently relative to the detector center no matter what kind of scanning trajectory is used. A 3-D phantom which roughly simulates DIT was designed to evaluate the performance of this method both quantitatively and qualitatively in the sense of mean square error and structural similarity. Results are also presented for real data acquired with a DIT experimental system. These results prove the validity of this geometric estimation method.
Geometric complexity is increased in in vitro activated platelets.
Bianciardi, Giorgio
2015-06-01
This article investigates the use of computerized fractal analysis for objective characterization of the complexity of platelets in vitro stimulated by low level thrombin (0.02 U mL(-1) ), collected from healthy individuals and observed by means of transmission electron microscopy. Platelet boundaries were extracted by means of automatically image analysis. Local fractal dimension was evaluated by the box-counting technique (measure of geometric complexity of the platelet outline). The results showed that the platelet boundary is fractal when observed by transmission electron microscopy and that, after an in vitro platelet activation test, the shape of platelets present increased geometric complexity in comparison to the no stimulated platelets (P < 0.001), with 100% correct classification. Computerized fractal analysis of platelet shape by transmission electron microscopy can provide accurate, quantitative, data to study platelet activation. The results may play important roles in the evaluation of the platelets status in pathological conditions, like as atherosclerosis and diabetes mellitus, where in in vivo activated platelets have been described.
Geometric uncertainty relation for mixed quantum states
Andersson, Ole Heydari, Hoshang
2014-04-15
In this paper we use symplectic reduction in an Uhlmann bundle to construct a principal fiber bundle over a general space of unitarily equivalent mixed quantum states. The bundle, which generalizes the Hopf bundle for pure states, gives in a canonical way rise to a Riemannian metric and a symplectic structure on the base space. With these we derive a geometric uncertainty relation for observables acting on quantum systems in mixed states. We also give a geometric proof of the classical Robertson-Schrödinger uncertainty relation, and we compare the two. They turn out not to be equivalent, because of the multiple dimensions of the gauge group for general mixed states. We give examples of observables for which the geometric relation provides a stronger estimate than that of Robertson and Schrödinger, and vice versa.
Quantum criticality driven by geometrical frustration
NASA Astrophysics Data System (ADS)
Gegenwart, Philipp; Tokiwa, Y.; Stingl, C.; Takabatake, T.
2015-03-01
Geometrical frustration describes situations where interactions are incompatible with the lattice geometry and stabilizes exotic phases such as spin liquids which cannot be classified by conventional order parameter theory and display emergent excitations. Whether geometrical frustration of magnetic moments in metals can induce unconventional quantum critical points is an active area of research. We focus on the heavy-fermion metal CeRhSn with twodimensional triangular configuration of the Kondo ion. Low-temperature thermodynamic experiments prove zero-field quantum criticality. A striking anisotropy of the linear thermal expansion, displaying critical and non-critical behavior along and perpendicular to the basal plane, respectively, is ascribed to the effect of strong geometrical frustration. We further find evidence of fluctuating local 4f moments, implying a novel quantum critical spin liquid state with fractionalized quasiparticles.
Quantification of Osteon Morphology Using Geometric Histomorphometrics.
Dillon, Scott; Cunningham, Craig; Felts, Paul
2016-03-01
Many histological methods in forensic anthropology utilize combinations of traditional histomorphometric parameters which may not accurately describe the morphology of microstructural features. Here, we report the novel application of a geometric morphometric method suitable when considering structures without anatomically homologous landmarks for the quantification of complete secondary osteon size and morphology. The method is tested for its suitability in the measurement of intact secondary osteons using osteons digitized from transverse femoral diaphyseal sections prepared from two human individuals. The results of methodological testing demonstrate the efficacy of the technique when applied to intact secondary osteons. In providing accurate characterization of micromorphology within the robust mathematical framework of geometric morphometrics, this method may surpass traditional histomorphometric variables currently employed in forensic research and practice. A preliminary study of the intersectional histomorphometric variation within the femoral diaphysis is made using this geometric histomorphometric method to demonstrate its potential. © 2015 American Academy of Forensic Sciences.
Geometric spin echo under zero field
Sekiguchi, Yuhei; Komura, Yusuke; Mishima, Shota; Tanaka, Touta; Niikura, Naeko; Kosaka, Hideo
2016-01-01
Spin echo is a fundamental tool for quantum registers and biomedical imaging. It is believed that a strong magnetic field is needed for the spin echo to provide long memory and high resolution, since a degenerate spin cannot be controlled or addressed under a zero magnetic field. While a degenerate spin is never subject to dynamic control, it is still subject to geometric control. Here we show the spin echo of a degenerate spin subsystem, which is geometrically controlled via a mediating state split by the crystal field, in a nitrogen vacancy centre in diamond. The demonstration reveals that the degenerate spin is protected by inherent symmetry breaking called zero-field splitting. The geometric spin echo under zero field provides an ideal way to maintain the coherence without any dynamics, thus opening the way to pseudo-static quantum random access memory and non-invasive biosensors. PMID:27193936
Overview on METEOSAT geometrical image data processing
NASA Technical Reports Server (NTRS)
Diekmann, Frank J.
1994-01-01
Digital Images acquired from the geostationary METEOSAT satellites are processed and disseminated at ESA's European Space Operations Centre in Darmstadt, Germany. Their scientific value is mainly dependent on their radiometric quality and geometric stability. This paper will give an overview on the image processing activities performed at ESOC, concentrating on the geometrical restoration and quality evaluation. The performance of the rectification process for the various satellites over the past years will be presented and the impacts of external events as for instance the Pinatubo eruption in 1991 will be explained. Special developments both in hard and software, necessary to cope with demanding tasks as new image resampling or to correct for spacecraft anomalies, are presented as well. The rotating lens of MET-5 causing severe geometrical image distortions is an example for the latter.
MM Algorithms for Geometric and Signomial Programming.
Lange, Kenneth; Zhou, Hua
2014-02-01
This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates.
The geometric phase controls ultracold chemistry
Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
2015-07-30
In this study, the geometric phase is shown to control the outcome of an ultracold chemical reaction. The control is a direct consequence of the sign change on the interference term between two scattering pathways (direct and looping), which contribute to the reactive collision process in the presence of a conical intersection (point of degeneracy between two Born–Oppenheimer electronic potential energy surfaces). The unique properties of the ultracold energy regime lead to an effective quantization of the scattering phase shift enabling maximum constructive or destructive interference between the two pathways. By taking the O + OH → H + O_{2} reaction as an illustrative example, it is shown that inclusion of the geometric phase modifies ultracold reaction rates by nearly two orders of magnitude. Interesting experimental control possibilities include the application of external electric and magnetic fields that might be used to exploit the geometric phase effect reported here and experimentally switch on or off the reactivity.
Spectral statistics of random geometric graphs
NASA Astrophysics Data System (ADS)
Dettmann, C. P.; Georgiou, O.; Knight, G.
2017-04-01
We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short-range correlations in the level spacings of the spectrum via the nearest-neighbour and next-nearest-neighbour spacing distribution and long-range correlations via the spectral rigidity Δ3 statistic. These correlations in the level spacings give information about localisation of eigenvectors, level of community structure and the level of randomness within the networks. We find a parameter-dependent transition between Poisson and Gaussian orthogonal ensemble statistics. That is the spectral statistics of spatial random geometric graphs fits the universality of random matrix theory found in other models such as Erdős-Rényi, Barabási-Albert and Watts-Strogatz random graphs.
The Geometric Phase of Stock Trading.
Altafini, Claudio
2016-01-01
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote.
The Geometric Phase of Stock Trading
2016-01-01
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote. PMID:27556642
The geometric phase controls ultracold chemistry
Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
2015-01-01
The geometric phase is shown to control the outcome of an ultracold chemical reaction. The control is a direct consequence of the sign change on the interference term between two scattering pathways (direct and looping), which contribute to the reactive collision process in the presence of a conical intersection (point of degeneracy between two Born–Oppenheimer electronic potential energy surfaces). The unique properties of the ultracold energy regime lead to an effective quantization of the scattering phase shift enabling maximum constructive or destructive interference between the two pathways. By taking the O+OH→H+O2 reaction as an illustrative example, it is shown that inclusion of the geometric phase modifies ultracold reaction rates by nearly two orders of magnitude. Interesting experimental control possibilities include the application of external electric and magnetic fields that might be used to exploit the geometric phase effect reported here and experimentally switch on or off the reactivity. PMID:26224326
MM Algorithms for Geometric and Signomial Programming
Lange, Kenneth; Zhou, Hua
2013-01-01
This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates. PMID:24634545
Geometric spin echo under zero field
NASA Astrophysics Data System (ADS)
Sekiguchi, Yuhei; Komura, Yusuke; Mishima, Shota; Tanaka, Touta; Niikura, Naeko; Kosaka, Hideo
2016-05-01
Spin echo is a fundamental tool for quantum registers and biomedical imaging. It is believed that a strong magnetic field is needed for the spin echo to provide long memory and high resolution, since a degenerate spin cannot be controlled or addressed under a zero magnetic field. While a degenerate spin is never subject to dynamic control, it is still subject to geometric control. Here we show the spin echo of a degenerate spin subsystem, which is geometrically controlled via a mediating state split by the crystal field, in a nitrogen vacancy centre in diamond. The demonstration reveals that the degenerate spin is protected by inherent symmetry breaking called zero-field splitting. The geometric spin echo under zero field provides an ideal way to maintain the coherence without any dynamics, thus opening the way to pseudo-static quantum random access memory and non-invasive biosensors.
A Toolbox for Geometric Grain Boundary Characterization
NASA Astrophysics Data System (ADS)
Glowinski, Krzysztof; Morawiec, Adam
Properties of polycrystalline materials are affected by grain boundary networks. The most basic aspect of boundary analysis is boundary geometry. This paper describes a package of computer programs for geometric boundary characterization based on macroscopic boundary parameters. The program allows for determination whether a boundary can be classified as near-tilt, -twist, -symmetric et cetera. Since calculations on experimental, i.e., error affected data are assumed, the program also provides distances to the nearest geometrically characteristic boundaries. The software has a number of other functions helpful in grain boundary analysis. One of them is the determination of planes of all characteristic boundaries for a given misorientation. The resulting diagrams of geometrically characteristic boundaries can be linked to experimentally determined grain boundary distributions. In computations, all symmetrically equivalent representations of boundaries are taken into account. Cubic and hexagonal holohedral crystal symmetries are allowed.
Connexions for the nuclear geometrical collective model
NASA Astrophysics Data System (ADS)
Rosensteel, G.; Sparks, N.
2015-11-01
The Bohr-Mottelson-Frankfurt model of nuclear rotations and quadrupole vibrations is a foundational model in nuclear structure physics. The model, also called the geometrical collective model or simply GCM(3), has two hidden mathematical structures, one group theoretic and the other differential geometric. Although the group structure has been understood for some time, the geometric structure is a new feature that this paper investigates in some detail. Using the de Rham Laplacian \\triangle =\\star d \\star d for the kinetic energy extends significantly the physical scope of the GCM(3) model. This Laplacian contains a ‘magnetic’ term due to the connexion between base manifold rotational and fibre vortex degrees of freedom. When the connexion specializes to irrotational flow, the Laplacian reduces to the Bohr-Mottelson kinetic energy operator.
Geometric inequalities in spherically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Csukás, Károly Z.
2017-07-01
In geometric inequalities ADM mass plays more fundamental role than the concept of quasi-local mass. This paper is to demonstrate that using the quasi-local mass some new insights can be acquired. In spherically symmetric spacetimes the Misner-Sharp mass and the concept of the Kodama vector field provides an ideal setting to the investigations of geometric inequalities. We applying the proposed new techniques to investigate the spacetimes containing black hole or cosmological horizons but we shall also apply them in context of normal bodies. Most of the previous investigations applied only the quasi-local charges and the area. Our main point is to include the quasi-local mass in the corresponding geometrical inequalities. This way we recover some known relations but new inequalities are also derived.
Dynamics of zonal flows: failure of wave-kinetic theory, and new geometrical optics approximations
NASA Astrophysics Data System (ADS)
Parker, Jeffrey B.
2016-12-01
The self-organisation of turbulence into regular zonal flows can be fruitfully investigated with quasi-linear methods and statistical descriptions. A wave-kinetic equation that assumes asymptotically large-scale zonal flows leads to ultraviolet divergence. From an exact description of quasi-linear dynamics emerges two better geometrical optics approximations. These involve not only the mean flow shear but also the second and third derivative of the mean flow. One approximation takes the form of a new wave-kinetic equation, but is only valid when the zonal flow is quasi-static and wave action is conserved.
Extracting dimensional geometric parameters from B-spline surface models of aircraft
NASA Technical Reports Server (NTRS)
Jayaram, U.; Myklebust, Arvid; Gelhausen, P.
1992-01-01
Research that creates techniques to automatically obtain dimensional geometric parameters from the nonuniform B-spline surface description of an object is presented. These techniques have been implemented successfully in the aircraft design software, ACSYNT, a computer-aided design system for conceptual aircraft design created at Virginia Tech and NASA Ames. The techniques created and implemented in this research are also of significance to general-purpose design.
The effect of photometric and geometric context on photometric and geometric lightness effects.
Lee, Thomas Y; Brainard, David H
2014-01-24
We measured the lightness of probe tabs embedded at different orientations in various contextual images presented on a computer-controlled stereo display. Two background context planes met along a horizontal roof-like ridge. Each plane was a graphic rendering of a set of achromatic surfaces with the simulated illumination for each plane controlled independently. Photometric context was varied by changing the difference in simulated illumination intensity between the two background planes. Geometric context was varied by changing the angle between them. We parsed the data into separate photometric effects and geometric effects. For fixed geometry, varying photometric context led to linear changes in both the photometric and geometric effects. Varying geometric context did not produce a statistically reliable change in either the photometric or geometric effects.
The effect of photometric and geometric context on photometric and geometric lightness effects
Lee, Thomas Y.; Brainard, David H.
2014-01-01
We measured the lightness of probe tabs embedded at different orientations in various contextual images presented on a computer-controlled stereo display. Two background context planes met along a horizontal roof-like ridge. Each plane was a graphic rendering of a set of achromatic surfaces with the simulated illumination for each plane controlled independently. Photometric context was varied by changing the difference in simulated illumination intensity between the two background planes. Geometric context was varied by changing the angle between them. We parsed the data into separate photometric effects and geometric effects. For fixed geometry, varying photometric context led to linear changes in both the photometric and geometric effects. Varying geometric context did not produce a statistically reliable change in either the photometric or geometric effects. PMID:24464163
Studying developmental variation with Geometric Morphometric Image Analysis (GMIA).
Mayer, Christine; Metscher, Brian D; Müller, Gerd B; Mitteroecker, Philipp
2014-01-01
The ways in which embryo development can vary across individuals of a population determine how genetic variation translates into adult phenotypic variation. The study of developmental variation has been hampered by the lack of quantitative methods for the joint analysis of embryo shape and the spatial distribution of cellular activity within the developing embryo geometry. By drawing from the strength of geometric morphometrics and pixel/voxel-based image analysis, we present a new approach for the biometric analysis of two-dimensional and three-dimensional embryonic images. Well-differentiated structures are described in terms of their shape, whereas structures with diffuse boundaries, such as emerging cell condensations or molecular gradients, are described as spatial patterns of intensities. We applied this approach to microscopic images of the tail fins of larval and juvenile rainbow trout. Inter-individual variation of shape and cell density was found highly spatially structured across the tail fin and temporally dynamic throughout the investigated period.
Control of chaos in excitable physiological systems: A geometric analysis.
Christini, David J.; Collins, James J.
1997-12-01
Model-independent chaos control techniques are inherently well-suited for the control of physiological systems for which quantitative system models are unavailable. The proportional perturbation feedback (PPF) control paradigm, which uses electrical stimulation to perturb directly the controlled system variable (e.g., the interbeat or interspike interval), was developed for excitable physiological systems that do not have an easily accessible system parameter. We develop the stable manifold placement (SMP) technique, a PPF-type technique which is simpler and more robust than the original PPF control algorithm. We use the SMP technique to control a simple geometric model of a chaotic system in the neighborhood of an unstable periodic orbit (UPO). We show that while the SMP technique can control a chaotic system that has UPO dynamics which are characterized by one stable manifold and one unstable manifold, the success of the SMP technique is sensitive to UPO parameter estimation errors. (c) 1997 American Institute of Physics.
Primary School Teacher Candidates' Geometric Habits of Mind
ERIC Educational Resources Information Center
Köse, Nilu¨fer Y.; Tanisli, Dilek
2014-01-01
Geometric habits of mind are productive ways of thinking that support learning and using geometric concepts. Identifying primary school teacher candidates' geometric habits of mind is important as they affect the development of their future students' geometric thinking. Therefore, this study attempts to determine primary school teachers' geometric…
Geometric Computation of Human Gyrification Indexes from Magnetic Resonance Images
2009-04-01
GEOMETRIC COMPUTATION OF HUMAN GYRIFICATION INDEXES FROM MAGNETIC RESONANCE IMAGES By Shu Su Tonya White Marcus Schmidt Chiu-Yen Kao and Guillermo...00-2009 to 00-00-2009 4. TITLE AND SUBTITLE Geometric Computation of Human Gyrification Indexes from Magnetic Resonance Images 5a. CONTRACT NUMBER... Geometric Computation of Gyrification Indexes Chiu-Yen Kao 1 Geometric Computation of Human Gyrification
Orlando, Ron
2010-01-01
The ability to quantitatively determine changes is an essential component of comparative glycomics. Multiple strategies are available by which this can be accomplished. These include label-free approaches and strategies where an isotopic label is incorporated into the glycans prior to analysis. The focus of this chapter is to describe each of these approaches while providing insight into their strengths and weaknesses, so that glycomic investigators can make an educated choice of the strategy that is best suited for their particular application.
Local Geometrical Machinery for Complexity and Control
NASA Astrophysics Data System (ADS)
Ivancevic, Vladimir G.; Reid, Darryn J.
2015-11-01
In this Chapter, we present local geometrical machinery for studying complexity and control, consisting of dynamics on Kähler manifolds, which combine three geometrical structures-Riemannian, symplectic and complex (Hermitian)-in a mutually compatible way. In other words, every Kähler manifold is simultaneously Riemannian, symplectic and complex (Hermitian). It is well known that Riemannian manifolds represent the stage on which Lagrangian dynamics is set, symplectic manifolds represent the stage for Hamiltonian dynamics, and complex (Hermitian) varieties comprise the stage for quantum dynamics. Therefore, Kähler manifolds represent the richest dynamical stage available where Lagrangian, Hamiltonian, and quantum dynamics all dance together.
The geometric phase in quantum physics
Bohm, A.
1993-03-01
After an explanatory introduction, a quantum system in a classical time-dependent environment is discussed; an example is a magnetic moment in a classical magnetic field. At first, the general abelian case is discussed in the adiabatic approximation. Then the geometric phase for nonadiabatic change of the environment (Anandan--Aharonov phase) is introduced, and after that general cyclic (nonadiabatic) evolution is discussed. The mathematics of fiber bundles is introduced, and some of its results are used to describe the relation between the adiabatic Berry phase and the geometric phase for general cyclic evolution of a pure state. The discussion is restricted to the abelian, U(1) phase.
Geometric Integration of Weakly Dissipative Systems
NASA Astrophysics Data System (ADS)
Modin, K.; Führer, C.; Soöderlind, G.
2009-09-01
Some problems in mechanics, e.g. in bearing simulation, contain subsystems that are conservative as well as weakly dissipative subsystems. Our experience is that geometric integration methods are often superior for such systems, as long as the dissipation is weak. Here we develop adaptive methods for dissipative perturbations of Hamiltonian systems. The methods are "geometric" in the sense that the form of the dissipative perturbation is preserved. The methods are linearly explicit, i.e., they require the solution of a linear subsystem. We sketch an analysis in terms of backward error analysis and numerical comparisons with a conventional RK method of the same order is given.
Classical light beams and geometric phases.
Mukunda, N; Chaturvedi, S; Simon, R
2014-06-01
We present a study of geometric phases in classical wave and polarization optics using the basic mathematical framework of quantum mechanics. Important physical situations taken from scalar wave optics, pure polarization optics, and the behavior of polarization in the eikonal or ray limit of Maxwell's equations in a transparent medium are considered. The case of a beam of light whose propagation direction and polarization state are both subject to change is dealt with, attention being paid to the validity of Maxwell's equations at all stages. Global topological aspects of the space of all propagation directions are discussed using elementary group theoretical ideas, and the effects on geometric phases are elucidated.
Geometric accuracy in airborne SAR images
NASA Technical Reports Server (NTRS)
Blacknell, D.; Quegan, S.; Ward, I. A.; Freeman, A.; Finley, I. P.
1989-01-01
Uncorrected across-track motions of a synthetic aperture radar (SAR) platform can cause both a severe loss of azimuthal positioning accuracy in, and defocusing of, the resultant SAR image. It is shown how the results of an autofocus procedure can be incorporated in the azimuth processing to produce a fully focused image that is geometrically accurate in azimuth. Range positioning accuracy is also discussed, leading to a comprehensive treatment of all aspects of geometric accuracy. The system considered is an X-band SAR.
Model-based vision using geometric hashing
NASA Astrophysics Data System (ADS)
Akerman, Alexander, III; Patton, Ronald
1991-04-01
The Geometric Hashing technique developed by the NYU Courant Institute has been applied to various automatic target recognition applications. In particular, I-MATH has extended the hashing algorithm to perform automatic target recognition ofsynthetic aperture radar (SAR) imagery. For this application, the hashing is performed upon the geometric locations of dominant scatterers. In addition to being a robust model-based matching algorithm -- invariant under translation, scale, and 3D rotations of the target -- hashing is of particular utility because it can still perform effective matching when the target is partially obscured. Moreover, hashing is very amenable to a SIMD parallel processing architecture, and thus potentially realtime implementable.
Quantum gates and their coexisting geometric phases
Wu Lianao; Bishop, C. Allen; Byrd, Mark S.
2011-08-15
Geometric phases arise naturally in a variety of quantum systems with observable consequences. They also arise in quantum computations when dressed states are used in gating operations. Here we show how they arise in these gating operations and how one may take advantage of the dressed states producing them. Specifically, we show that for a given, but arbitrary Hamiltonian, and at an arbitrary time {tau}, there always exists a set of dressed states such that a given gate operation can be performed by the Hamiltonian up to a phase {phi}. The phase is a sum of a dynamical phase and a geometric phase. We illustrate the dressed phase for several systems.
Methods of geometrical integration in accelerator physics
NASA Astrophysics Data System (ADS)
Andrianov, S. N.
2016-12-01
In the paper we consider a method of geometric integration for a long evolution of the particle beam in cyclic accelerators, based on the matrix representation of the operator of particles evolution. This method allows us to calculate the corresponding beam evolution in terms of two-dimensional matrices including for nonlinear effects. The ideology of the geometric integration introduces in appropriate computational algorithms amendments which are necessary for preserving the qualitative properties of maps presented in the form of the truncated series generated by the operator of evolution. This formalism extends both on polarized and intense beams. Examples of practical applications are described.
Geometric-phase atom optics and interferometry
NASA Astrophysics Data System (ADS)
Zygelman, B.
2015-10-01
We illustrate how geometric gauge forces and topological phase effects emerge in atomic and molecular systems without employing assumptions that rely on adiabaticity. We show how geometric magnetism may be harnessed to engineer novel quantum devices including a velocity sieve, a component in mass spectrometers, for neutral atoms. We introduce and outline a possible experimental setup that demonstrates topological interferometry for neutral spin-1/2 systems. For that two-level system, we study the transition from Abelian to non-Abelian behavior and explore its relation to the molecular Aharonov-Bohm effect.
Quantitative Literacy: Geosciences and Beyond
NASA Astrophysics Data System (ADS)
Richardson, R. M.; McCallum, W. G.
2002-12-01
Quantitative literacy seems like such a natural for the geosciences, right? The field has gone from its origin as a largely descriptive discipline to one where it is hard to imagine failing to bring a full range of mathematical tools to the solution of geological problems. Although there are many definitions of quantitative literacy, we have proposed one that is analogous to the UNESCO definition of conventional literacy: "A quantitatively literate person is one who, with understanding, can both read and represent quantitative information arising in his or her everyday life." Central to this definition is the concept that a curriculum for quantitative literacy must go beyond the basic ability to "read and write" mathematics and develop conceptual understanding. It is also critical that a curriculum for quantitative literacy be engaged with a context, be it everyday life, humanities, geoscience or other sciences, business, engineering, or technology. Thus, our definition works both within and outside the sciences. What role do geoscience faculty have in helping students become quantitatively literate? Is it our role, or that of the mathematicians? How does quantitative literacy vary between different scientific and engineering fields? Or between science and nonscience fields? We will argue that successful quantitative literacy curricula must be an across-the-curriculum responsibility. We will share examples of how quantitative literacy can be developed within a geoscience curriculum, beginning with introductory classes for nonmajors (using the Mauna Loa CO2 data set) through graduate courses in inverse theory (using singular value decomposition). We will highlight six approaches to across-the curriculum efforts from national models: collaboration between mathematics and other faculty; gateway testing; intensive instructional support; workshops for nonmathematics faculty; quantitative reasoning requirement; and individual initiative by nonmathematics faculty.
Quantitation of signal transduction.
Krauss, S; Brand, M D
2000-12-01
Conventional qualitative approaches to signal transduction provide powerful ways to explore the architecture and function of signaling pathways. However, at the level of the complete system, they do not fully depict the interactions between signaling and metabolic pathways and fail to give a manageable overview of the complexity that is often a feature of cellular signal transduction. Here, we introduce a quantitative experimental approach to signal transduction that helps to overcome these difficulties. We present a quantitative analysis of signal transduction during early mitogen stimulation of lymphocytes, with steady-state respiration rate as a convenient marker of metabolic stimulation. First, by inhibiting various key signaling pathways, we measure their relative importance in regulating respiration. About 80% of the input signal is conveyed via identifiable routes: 50% through pathways sensitive to inhibitors of protein kinase C and MAP kinase and 30% through pathways sensitive to an inhibitor of calcineurin. Second, we quantify how each of these pathways differentially stimulates functional units of reactions that produce and consume a key intermediate in respiration: the mitochondrial membrane potential. Both the PKC and calcineurin routes stimulate consumption more strongly than production, whereas the unidentified signaling routes stimulate production more than consumption, leading to no change in membrane potential despite increased respiration rate. The approach allows a quantitative description of the relative importance of signal transduction pathways and the routes by which they activate a specific cellular process. It should be widely applicable.
NASA Astrophysics Data System (ADS)
Heller, Marc Andre; Ikeda, Noriaki; Watamura, Satoshi
2017-02-01
We give a systematic derivation of the local expressions of the NS H-flux, geometric F- as well as non-geometric Q- and R-fluxes in terms of bivector β- and two-form B-potentials including vielbeins. They are obtained using a supergeometric method on QP-manifolds by twist of the standard Courant algebroid on the generalized tangent space without flux. Bianchi identities of the fluxes are easily deduced. We extend the discussion to the case of the double space and present a formulation of T-duality in terms of canonical transformations between graded symplectic manifolds. Thus, we find a unified description of geometric as well as non-geometric fluxes and T-duality transformations in double field theory. Finally, the construction is compared to the formerly introduced Poisson Courant algebroid, a Courant algebroid on a Poisson manifold, as a model for R-flux.
Multimedia content description framework
NASA Technical Reports Server (NTRS)
Bergman, Lawrence David (Inventor); Kim, Michelle Yoonk Yung (Inventor); Li, Chung-Sheng (Inventor); Mohan, Rakesh (Inventor); Smith, John Richard (Inventor)
2003-01-01
A framework is provided for describing multimedia content and a system in which a plurality of multimedia storage devices employing the content description methods of the present invention can interoperate. In accordance with one form of the present invention, the content description framework is a description scheme (DS) for describing streams or aggregations of multimedia objects, which may comprise audio, images, video, text, time series, and various other modalities. This description scheme can accommodate an essentially limitless number of descriptors in terms of features, semantics or metadata, and facilitate content-based search, index, and retrieval, among other capabilities, for both streamed or aggregated multimedia objects.
Impossible Geometric Constructions: A Calculus Writing Project
ERIC Educational Resources Information Center
Awtrey, Chad
2013-01-01
This article discusses a writing project that offers students the opportunity to solve one of the most famous geometric problems of Greek antiquity; namely, the impossibility of trisecting the angle [pi]/3. Along the way, students study the history of Greek geometry problems as well as the life and achievements of Carl Friedrich Gauss. Included is…
Geometric interpretations for resonances of plasmonic nanoparticles
Liu, Wei; Oulton, Rupert F.; Kivshar, Yuri S.
2015-01-01
The field of plasmonics can be roughly categorized into two branches: surface plasmon polaritons (SPPs) propagating in waveguides and localized surface plasmons (LSPs) supported by scattering particles. Investigations along these two directions usually employ different approaches, resulting in more or less a dogma that the two branches progress almost independently of each other, with few interactions. Here in this work we interpret LSPs from a Bohr model based geometric perspective relying on SPPs, thus establishing a connection between these two sub-fields. Besides the clear explanations of conventional scattering features of plasmonic nanoparticles, based on this geometric model we further demonstrate other anomalous scattering features (higher order modes supported at lower frequencies, and blueshift of the resonance with increasing particle sizes) and multiple electric resonances of the same order supported at different frequencies, which have been revealed to originate from backward SPP modes and multiple dispersion bands supported in the corresponding plasmonic waveguides, respectively. Inspired by this geometric model, it is also shown that, through solely geometric tuning, the absorption of each LSP resonance can be maximized to reach the single channel absorption limit, provided that the scattering and absorption rates are tuned to be equal. PMID:26173797
Calculation of Geometric Dilution of Precision
NASA Astrophysics Data System (ADS)
Zhu, Jijie
1992-07-01
In this short communication, a very simple closed-form formula for the calculation of the Geometric Dilution of Precision (GDOP) in Global Positioning System (GPS) navigation and in Global Navigation Satellite System (GLONASS) navigation is presented, which requires less than 40 multiplications.
Global Geometric Properties of Martian Impact Craters
NASA Technical Reports Server (NTRS)
Garvin, J. B.; Sakimoto, S. E. H.; Frawley, J. J.; Schnetzler, C.
2002-01-01
We present impact crater geometric properties for more than 5000 fresh martian features using high resolution Mars Orbiter Laser Altimeter digital elevation models and topographic profiles. We discuss global results and significant regional variations. Additional information is contained in the original extended abstract.
Geometric Mean--What Does It Mean?
ERIC Educational Resources Information Center
Kalder, Robin S.
2012-01-01
The National Council of Teachers of Mathematics and numerous mathematics educators promote the combination of conceptual understanding and procedural learning in the successful instruction of mathematics. Despite this, when geometric mean is taught in a typical American geometry class, it is taught as a process only despite the many connections…
Geometric Transformations in Middle School Mathematics Textbooks
ERIC Educational Resources Information Center
Zorin, Barbara
2011-01-01
This study analyzed treatment of geometric transformations in presently available middle grades (6, 7, 8) student mathematics textbooks. Fourteen textbooks from four widely used textbook series were evaluated: two mainline publisher series, Pearson (Prentice Hall) and Glencoe (Math Connects); one National Science Foundation (NSF) funded curriculum…
Reinforcing Geometric Properties with Shapedoku Puzzles
ERIC Educational Resources Information Center
Wanko, Jeffrey J.; Nickell, Jennifer V.
2013-01-01
Shapedoku is a new type of puzzle that combines logic and spatial reasoning with understanding of basic geometric concepts such as slope, parallelism, perpendicularity, and properties of shapes. Shapedoku can be solved by individuals and, as demonstrated here, can form the basis of a review for geometry students as they create their own. In this…
Geometrical interpretation and architecture selection of MLP.
Xiang, Cheng; Ding, Shenqiang Q; Lee, Tong Heng
2005-01-01
A geometrical interpretation of the multilayer perceptron (MLP) is suggested in this paper. Some general guidelines for selecting the architecture of the MLP, i.e., the number of the hidden neurons and the hidden layers, are proposed based upon this interpretation and the controversial issue of whether four-layered MLP is superior to the three-layered MLP is also carefully examined.
Geometric Determinants of Human Spatial Memory
ERIC Educational Resources Information Center
Hartley, Tom; Trinkler, Iris; Burgess, Neil
2004-01-01
Geometric alterations to the boundaries of a virtual environment were used to investigate the representations underlying human spatial memory. Subjects encountered a cue object in a simple rectangular enclosure, with distant landmarks for orientation. After a brief delay, during which they were removed from the arena, subjects were returned to it…
Rejuvenating Allen's Arc with the Geometric Mean.
ERIC Educational Resources Information Center
Phillips, William A.
1994-01-01
Contends that, despite ongoing criticism, Allen's arc elasticity formula remains entrenched in the microeconomics principles curriculum. Reviews the evolution and continuing scrutiny of the formula. Argues that the use of the geometric mean offers pedagogical advantages over the traditional arithmetic mean approach. (CFR)
Geometric Probability and the Areas of Leaves
ERIC Educational Resources Information Center
Hoiberg, Karen Bush; Sharp, Janet; Hodgson, Ted; Colbert, Jim
2005-01-01
This article describes how a group of fifth-grade mathematics students measured irregularly shaped objects using geometric probability theory. After learning how to apply a ratio procedure to find the areas of familiar shapes, students extended the strategy for use with irregularly shaped objects, in this case, leaves. (Contains 2 tables and 8…
More Meaning from the Geometric Mean.
ERIC Educational Resources Information Center
Dorner, Bryan C.
2003-01-01
Provides classroom suggestions for combining numerical, algebraic, and geometric techniques with the understanding of a simple method for computing square roots. Historical origins of the method illustrate the debt owed to ancient minds living in what are now India, Pakistan, Iraq, and Egypt. (Author/NB)
Geometrical Factors in the Perception of Sacredness.
Costa, Marco; Bonetti, Leonardo
2016-06-28
Geometrical and environmental factors in the perception of sacredness, dominance, and attractiveness were assessed by 137 participants in five tests. In the first test, a two-alternative forced-choice paradigm was used to test the perception of sacredness, dominance, and attractiveness in geometrical figures differing in shape, verticality, size, and symmetry. Verticality, symmetry, and convexity were found to be important factors in the perception of sacredness. In the second test, participants had to mark the point inside geometrical surfaces that was perceived as most sacred, dominant, and attractive. The top and the center areas were associated with sacredness, dominance, and attractiveness. In the third test, peaks and elevated regions in landscapes were evaluated as more sacred, dominant, and attractive than valley regions. In the fourth test, three figures sharing the same area but differing in horizontal and vertical orientation were evaluated on eight scales. The vertical figure was evaluated as more sacred, dominant, and attractive than the horizontal figure. The fifth test demonstrated the significant role of space seclusion and inaccessibility in the perception of sacredness. Geometrical factors in the perception of sacredness, dominance, and attractiveness were largely overlapping.
Deformable Subreflector Computed by Geometric Optics
NASA Technical Reports Server (NTRS)
Williams, W. F.
1986-01-01
Distorted antenna surfaces forced to produce a uniform wave front. SUBFORMING employs geometric optics in determining subreflector coordinates to match main reflector surface with known distortions. Antenna with distorted paraboloidal reflecting surface forced to produce uniform wave front by using a Cassegrainian geometry with path-length-compensating subreflector. Program written in FORTRAN V for batch execution.
How Do Young Children Learn Geometric Concepts.
ERIC Educational Resources Information Center
Ohe, Pia
Twenty children (ages 5 and 6) from each of seven cultural groups (Caucasian, Black, Jewish, Puerto Rican, Chinese, Korean-American and native Korean) were given a copying task of 21 geometric shapes to test the cultural invariancy of Piaget's topological-projective-Euclidean concept acquisition sequence. All subjects were either middle or lower…
More Meaning from the Geometric Mean.
ERIC Educational Resources Information Center
Dorner, Bryan C.
2003-01-01
Provides classroom suggestions for combining numerical, algebraic, and geometric techniques with the understanding of a simple method for computing square roots. Historical origins of the method illustrate the debt owed to ancient minds living in what are now India, Pakistan, Iraq, and Egypt. (Author/NB)
Geometric Models for Collaborative Search and Filtering
ERIC Educational Resources Information Center
Bitton, Ephrat
2011-01-01
This dissertation explores the use of geometric and graphical models for a variety of information search and filtering applications. These models serve to provide an intuitive understanding of the problem domains and as well as computational efficiencies to our solution approaches. We begin by considering a search and rescue scenario where both…
Modern Geometric Algebra: A (Very Incomplete!) Survey
ERIC Educational Resources Information Center
Suzuki, Jeff
2009-01-01
Geometric algebra is based on two simple ideas. First, the area of a rectangle is equal to the product of the lengths of its sides. Second, if a figure is broken apart into several pieces, the sum of the areas of the pieces equals the area of the original figure. Remarkably, these two ideas provide an elegant way to introduce, connect, and…
If Only Clairaut Had Dynamic Geometric Tools
ERIC Educational Resources Information Center
Chang, Hyewon; Reys, Barbara J.
2013-01-01
Geometry is a major area of study in middle school mathematics, yet middle school and secondary students have difficulty learning important geometric concepts. This article considers Alexis-Claude Clairaut's approach that emphasizes engaging student curiosity about key ideas and theorems instead of directly teaching theorems before their…
Estimation on Geometric Measure of Quantum Coherence
NASA Astrophysics Data System (ADS)
Zhang, Hai-Jun; Chen, Bin; Li, Ming; Fei, Shao-Ming; Long, Gui-Lu
2017-02-01
We study the geometric measure of quantum coherence recently proposed in [Phys. Rev. Lett. 115, 020403 (2015)]. Both lower and upper bounds of this measure are provided. These bounds are shown to be tight for a class of important coherent states -- maximally coherent mixed states. The trade-off relation between quantum coherence and mixedness for this measure is also discussed.
A Geometric Approach to Fair Division
ERIC Educational Resources Information Center
Barbanel, Julius
2010-01-01
We wish to divide a cake among some collection of people (who may have very different notions of the comparative value of pieces of cake) in a way that is both "fair" and "efficient." We explore the meaning of these terms, introduce two geometric tools to aid our analysis, and present a proof (due to Dietrich Weller) that establishes the existence…
Integral representation for geometric optics solutions
NASA Astrophysics Data System (ADS)
Hazak, G.; Bernstein, I. B.; Smith, T. M.
1983-03-01
An integral representation of the geometric optics solutions for the field of dressed particles in inhomogeneous plasma is derived. The representation is a natural generalization of the Fourier integral used for homogeneous systems. The set of plane waves is replaced by a complete orthogonal set of 'quasi-plane waves' which in practice may be constructed by using the existing ray tracing codes.
Geometric Interpretations of Some Psychophysical Results.
ERIC Educational Resources Information Center
Levine, Michael V.
A theory of psychophysics is discussed that enlarges the classical theory in three general ways: (1) the multidimensional nature of perception is made explicit; (2) the transformations of the theory are interpreted geometrically; and (3) attributes are distinguished from sensations and only partially ordered. It is shown that, with the enlarged…
Plato alleges that God forever geometrizes
NASA Astrophysics Data System (ADS)
Ne'Eman, Yuval
1996-05-01
Since 1961, the experimental exploration at the fundamental level of physical reality has surprised physists by revealing to them a highly geometric scenery. Like Einstein's (classical) theory of gravity, the “standard model,” describing the strong, weak, and electromagnetic interaction, testifies in favor of Plato's reported allegation.
An underlying geometrical manifold for Hamiltonian mechanics
NASA Astrophysics Data System (ADS)
Horwitz, L. P.; Yahalom, A.; Levitan, J.; Lewkowicz, M.
2017-02-01
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture), that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamiltonian-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical picture and establish a correspondence which provides a basis for understanding how the instability in the geometrical picture is manifested in the instability of the the original Hamiltonian motion.
Geometric Transformations in Middle School Mathematics Textbooks
ERIC Educational Resources Information Center
Zorin, Barbara
2011-01-01
This study analyzed treatment of geometric transformations in presently available middle grades (6, 7, 8) student mathematics textbooks. Fourteen textbooks from four widely used textbook series were evaluated: two mainline publisher series, Pearson (Prentice Hall) and Glencoe (Math Connects); one National Science Foundation (NSF) funded curriculum…
On Arithmetic-Geometric-Mean Polynomials
ERIC Educational Resources Information Center
Griffiths, Martin; MacHale, Des
2017-01-01
We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…
On Arithmetic-Geometric-Mean Polynomials
ERIC Educational Resources Information Center
Griffiths, Martin; MacHale, Des
2017-01-01
We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…
Modern Geometric Algebra: A (Very Incomplete!) Survey
ERIC Educational Resources Information Center
Suzuki, Jeff
2009-01-01
Geometric algebra is based on two simple ideas. First, the area of a rectangle is equal to the product of the lengths of its sides. Second, if a figure is broken apart into several pieces, the sum of the areas of the pieces equals the area of the original figure. Remarkably, these two ideas provide an elegant way to introduce, connect, and…
Using geometric algebra to study optical aberrations
Hanlon, J.; Ziock, H.
1997-05-01
This paper uses Geometric Algebra (GA) to study vector aberrations in optical systems with square and round pupils. GA is a new way to produce the classical optical aberration spot diagrams on the Gaussian image plane and surfaces near the Gaussian image plane. Spot diagrams of the third, fifth and seventh order aberrations for square and round pupils are developed to illustrate the theory.
A Geometric Approach to Fair Division
ERIC Educational Resources Information Center
Barbanel, Julius
2010-01-01
We wish to divide a cake among some collection of people (who may have very different notions of the comparative value of pieces of cake) in a way that is both "fair" and "efficient." We explore the meaning of these terms, introduce two geometric tools to aid our analysis, and present a proof (due to Dietrich Weller) that establishes the existence…
Impossible Geometric Constructions: A Calculus Writing Project
ERIC Educational Resources Information Center
Awtrey, Chad
2013-01-01
This article discusses a writing project that offers students the opportunity to solve one of the most famous geometric problems of Greek antiquity; namely, the impossibility of trisecting the angle [pi]/3. Along the way, students study the history of Greek geometry problems as well as the life and achievements of Carl Friedrich Gauss. Included is…
Geometric Representations for Discrete Fourier Transforms
NASA Technical Reports Server (NTRS)
Cambell, C. W.
1986-01-01
Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.
Reflections on representing non-geometric data
NASA Technical Reports Server (NTRS)
Emnett, R. F.; Shu, H. H.
1984-01-01
The American National Standard Y14.26M-1981 on Digital Representation for Communication of Product Definition Data includes an introduction, three sections corresponding to IGES (Initial Graphics Exchange Specification) Version 1.0, and Section 5, which is a constructive, relational, language based representation for geometric and topological entitles.
Geometric Models for Collaborative Search and Filtering
ERIC Educational Resources Information Center
Bitton, Ephrat
2011-01-01
This dissertation explores the use of geometric and graphical models for a variety of information search and filtering applications. These models serve to provide an intuitive understanding of the problem domains and as well as computational efficiencies to our solution approaches. We begin by considering a search and rescue scenario where both…
Quantification and correction of geometric distortions in low-field MRI
NASA Astrophysics Data System (ADS)
Parra Robles, Juan M.; Dominguez, William; Gonzalez, Evelio R.; Berdellans, Ilse
1999-05-01
Geometric distortions are one of the most important degrading factors in MRI. They usually do not greatly affect the clinical relevance of images, but their correction is indispensable for lesion volume measurements, radiotherapy and surgical planning. In this work, the main sources of geometric distortion in Cuban low-field MRI systems are studied. Geometric distortion models and correction algorithms are tested by means of computer simulation using theoretical distributions of the magnetic fields. The real distributions are determined from images of a grid phantom. Calculated static field distributions showed that the system magnetic center is shifted, relative to magnet geometric center. Quantitative measurements provided inhomogeneity values (93 ppm in a spherical region of diameter 256 mm) larger than calibration data (65 ppm) obtained 15 months ago. The shim settings must be readjusted. The temporal behavior of static field was also studied. The magnet heating produces a slow time variation in static field intensity, but field error distribution proved to be stable. In the images, geometric distortions increase with increasing distance from image center and ranged from -6 to 7 mm. The implemented correction procedure reduced distortions from maximally 7 mm to the order of pixel resolution (0.8 - 1 mm).
A GEOMETRICAL HEIGHT SCALE FOR SUNSPOT PENUMBRAE
Puschmann, K. G.; Ruiz Cobo, B.; MartInez Pillet, V. E-mail: brc@iac.e
2010-09-10
Inversions of spectropolarimetric observations of penumbral filaments deliver the stratification of different physical quantities in an optical depth scale. However, without establishing a geometrical height scale, their three-dimensional geometrical structure cannot be derived. This is crucial in understanding the correct spatial variation of physical properties in the penumbral atmosphere and to provide insights into the mechanism capable of explaining the observed penumbral brightness. The aim of this work is to determine a global geometrical height scale in the penumbra by minimizing the divergence of the magnetic field vector and the deviations from static equilibrium as imposed by a force balance equation that includes pressure gradients, gravity, and the Lorentz force. Optical depth models are derived from the inversion of spectropolarimetric data of an active region observed with the Solar Optical Telescope on board the Hinode satellite. We use a genetic algorithm to determine the boundary condition for the inference of geometrical heights. The retrieved geometrical height scale permits the evaluation of the Wilson depression at each pixel and the correlation of physical quantities at each height. Our results fit into the uncombed penumbral scenario, i.e., a penumbra composed of flux tubes with channeled mass flow and with a weaker and more horizontal magnetic field as compared with the background field. The ascending material is hotter and denser than their surroundings. We do not find evidence of overturning convection or field-free regions in the inner penumbral area analyzed. The penumbral brightness can be explained by the energy transfer of the ascending mass carried by the Evershed flow, if the physical quantities below z = -75 km are extrapolated from the results of the inversion.
Quantitative Description of Selected West German Terrain for Ground Mobility
1970-04-01
condition: circle appropriate terms.) Q Not obviously used by man or domestic animals . C 2. Obviously used by man or domestic arimals. a. Cropland...vineyrards, tree plantations). Type c. Area grazed by do:iestic animals d. Hayfields (not currently being grazed) e. Orchards, vineyards, tree plantat-ons...31 8 )-36 9 36-45’ 10 4’ 5 5842 ’ ESTR ICTED AREA - ..... 58 40 624 abzent 1step heiir, class ranges used when water depth is ’ 3 £t ,-t ep hei
Dual Enrollment in a Rural Environment: A Descriptive Quantitative Study
ERIC Educational Resources Information Center
Dodge, Mary Beth
2012-01-01
Dual enrollment is a federally funded program that offers high school students the opportunity to earn both high school and postsecondary credits for the same course. While the phenomenon of concurrent enrollment in postsecondary and college educational programs is not new, political support and public funding has drawn focus to the policies of…
Quantitative representation and description of intravoxel fiber complexity in HARDI
NASA Astrophysics Data System (ADS)
Sun, Chang-yu; Chu, Chun-yu; Liu, Wan-yu; Hsu, Edward W.; Korenberg, Julie R.; Zhu, Yue-min
2015-11-01
Diffusion tensor imaging and high angular resolution diffusion imaging are often used to analyze the fiber complexity of tissues. In these imaging techniques, the most commonly calculated metric is anisotropy, such as fractional anisotropy (FA), generalized anisotropy (GA), and generalized fractional anisotropy (GFA). The basic idea underlying these metrics is to compute the deviation from free or spherical diffusion. However, in many cases, the question is not really to know whether it concerns spherical diffusion. Instead, the main concern is to describe and quantify fiber complexity such as fiber crossing in a voxel. In this context, it would be more direct and effective to compute the deviation from a single fiber bundle instead of a sphere. We propose a new metric, called PEAM (PEAnut Metric), which is based on computing the deviation of orientation diffusion functions (ODFs) from a single fiber bundle ODF represented by a peanut. As an example, the proposed PEAM metric is used to classify intravoxel fiber configurations. The results on simulated data, physical phantom data and real brain data consistently showed that the proposed PEAM provides greater accuracy than FA, GA and GFA and enables parallel and complex fibers to be better distinguished.
A Survey of Quantitative Descriptions of Molecular Structure
Guha, Rajarshi; Willighagen, Egon
2013-01-01
Numerical characterization of molecular structure is a first step in many computational analysis of chemical structure data. These numerical representations, termed descriptors, come in many forms, ranging from simple atom counts and invariants of the molecular graph to distribution of properties, such as charge, across a molecular surface. In this article we first present a broad categorization of descriptors and then describe applications and toolkits that can be employed to evaluate them. We highlight a number of issues surrounding molecular descriptor calculations such as versioning and reproducibility and describe how some toolkits have attempted to address these problems. PMID:23110530
Quantitative Description of Monthly Ionospheric Variability in the IRI Model
NASA Astrophysics Data System (ADS)
Bilitza, D.
2004-12-01
The International Reference Ionosphere (IRI) model provides an empirical specification of the ionospheric climatology at the level of monthly averages. Operational use of the IRI model often requires an estimate of the monthly variability, so that an operator not only knows the expected monthly average value of an ionospheric parameter but also the expected variation around this monthly average. A special IRI Task Force Activity at the International Center for Theoretical Physics (ICTP) in Trieste, Italy has worked on this modeling goal during the last few years using ionosonde data from many stations worldwide focusing primarily on the electron density in the region below the F peak. Other IRI team members have looked at the variability at different heights and have studied the variability seen for the plasma temperatures. We will report on the status and progress of this activity and will discuss the different parameter used for describing ionospheric variability (mean, median, standard deviation, quartiles, deciles) and the planned model implementation. First results will be reported based on the ICTP meetings and the 2003 IRI Workshop in Grahamstown, South Africa.
Quantitative description of realistic wealth distributions by kinetic trading models
NASA Astrophysics Data System (ADS)
Lammoglia, Nelson; Muñoz, Víctor; Rogan, José; Toledo, Benjamín; Zarama, Roberto; Valdivia, Juan Alejandro
2008-10-01
Data on wealth distributions in trading markets show a power law behavior x-(1+α) at the high end, where, in general, α is greater than 1 (Pareto’s law). Models based on kinetic theory, where a set of interacting agents trade money, yield power law tails if agents are assigned a saving propensity. In this paper we are solving the inverse problem, that is, in finding the saving propensity distribution which yields a given wealth distribution for all wealth ranges. This is done explicitly for two recently published and comprehensive wealth datasets.
QUANTITATIVE SOIL DESCRIPTIONS FOR ECOREGIONS OF THE UNITED STATES
Researchers have defined ecological regions of the United States based on patterns in the coincidence of terrestrial, aquatic, abiotic and biotic characteristics that are associated with spatial differences in ecosystems. Ecoregions potentially facilitate regional research, monit...
A survey of quantitative descriptions of molecular structure.
Guha, Rajarshi; Willighagen, Egon
2012-01-01
Numerical characterization of molecular structure is a first step in many computational analysis of chemical structure data. These numerical representations, termed descriptors, come in many forms, ranging from simple atom counts and invariants of the molecular graph to distribution of properties, such as charge, across a molecular surface. In this article we first present a broad categorization of descriptors and then describe applications and toolkits that can be employed to evaluate them. We highlight a number of issues surrounding molecular descriptor calculations such as versioning and reproducibility and describe how some toolkits have attempted to address these problems.
Descriptive Metadata: Emerging Standards.
ERIC Educational Resources Information Center
Ahronheim, Judith R.
1998-01-01
Discusses metadata, digital resources, cross-disciplinary activity, and standards. Highlights include Standard Generalized Markup Language (SGML); Extensible Markup Language (XML); Dublin Core; Resource Description Framework (RDF); Text Encoding Initiative (TEI); Encoded Archival Description (EAD); art and cultural-heritage metadata initiatives;…
Physics 3204. Course Description.
ERIC Educational Resources Information Center
Newfoundland and Labrador Dept. of Education.
A description of the physics 3204 course in Newfoundland and Labrador is provided. The description includes: (1) statement of purpose, including general objectives of science education; (2) a list of six course objectives; (3) course content for units on sound, light, optical instruments, electrostatics, current electricity, Michael Faraday and…
Descriptive Metadata: Emerging Standards.
ERIC Educational Resources Information Center
Ahronheim, Judith R.
1998-01-01
Discusses metadata, digital resources, cross-disciplinary activity, and standards. Highlights include Standard Generalized Markup Language (SGML); Extensible Markup Language (XML); Dublin Core; Resource Description Framework (RDF); Text Encoding Initiative (TEI); Encoded Archival Description (EAD); art and cultural-heritage metadata initiatives;…
Physics 3204. Course Description.
ERIC Educational Resources Information Center
Newfoundland and Labrador Dept. of Education.
A description of the physics 3204 course in Newfoundland and Labrador is provided. The description includes: (1) statement of purpose, including general objectives of science education; (2) a list of six course objectives; (3) course content for units on sound, light, optical instruments, electrostatics, current electricity, Michael Faraday and…
Descriptive models for single-jet sluicing of sludge waste
Erian, F.F.; Mahoney, L.A.; Terrones, G.
1997-12-01
Mobilization of sludge waste stored in underground storage tanks can be achieved safely and reliably by sluicing. In the project discussed in this report, the waste in Hanford single-shell Tank 241-C-106 will be mobilized by sluicing, retrieved by a slurry retrieval pump, and transferred via an 1800-ft slurry pipeline to Tank 241-AY-102. A sluicing strategy must be developed that ensures efficient use of the deployed configuration of the sluicing system: the nozzle(s) and the retrieval pump(s). Given a sluicing system configuration in a particular tank, it is desirable to prescribe the sequential locations at which the sludge will be mobilized and retrieved and the rate at which these mobilization and retrieval processes take place. In addition, it is necessary to know whether the retrieved waste slurry meets the requirements for cross-site slurry transport. Some of the physical phenomena that take place during mobilization and retrieval and certain aspects of the sluicing process are described in this report. First, a mathematical model gives (1) an idealized geometrical representation of where, within the confines of a storage tank containing a certain amount of settled waste, sludge can be removed and mobilized; and (2) a quantitative measure of the amount of sludge that can be removed during a sluicing campaign. A model describing an idealized water jet issuing from a circular nozzle located at a given height above a flat surface is also presented in this report. This dynamic water-jet model provides the basis for improving the geometrical sluicing model presented next. In this model the authors assume that the water jet follows a straight trajectory toward a target point on a flat surface. However, the water jet does not follow a straight line in the actual tank, and using the true trajectory will allow a more accurate estimate of the amount of disturbed material. Also, the authors hope that developing accurate force and pressure fields will lead to a better
Geometrical attenuation, frequency dependence of Q, and the absorption band problem
NASA Astrophysics Data System (ADS)
Morozov, Igor B.
2008-10-01
A geometrical attenuation model is proposed as an alternative to the conventional frequency-dependent attenuation law Q(f) = Q0(f/f0)η. The new model provides a straightforward differentiation between the geometrical and effective attenuation (Qe) which incorporates the intrinsic attenuation and small-scale scattering. Unlike the (Q0, η) description, the inversion procedure uses only the spectral amplitude data and does not rely on elaborate theoretical models or restrictive assumptions. Data from over 40 reported studies were transformed to the new parametrization. The levels of geometrical attenuation strongly correlate with crustal tectonic types and decrease with tectonic age. The corrected values of Qe are frequency-independent and generally significantly higher than Q0 and show no significant correlation with tectonic age. Several case studies were revisited in detail, with significant changes in the interpretations. The absorption-band and the `10-Hz transition' are not found in the corrected Qe data, and therefore, these phenomena are interpreted as related to geometrical attenuation. The absorption band could correspond to changes in the dominant mode content of the wavefield as the frequency changes from about 0.1 to 100 Hz. Alternatively, it could also be a pure artefact related to the power-law Q(f) paradigm above. The explicit separation of the geometrical and intrinsic attenuation achieves three goals: (1) it provides an unambiguous, assumption- and model-free description of attenuation, (2) it allows relating the observations to the basic physics and geology and (3) it simplifies the interpretation because of reduced emphasis on the apparent Q(f) dependence. The model also agrees remarkably well with the initial attempts for finite-difference short-period coda waveform modelling. Because of its consistency and direct link to the observations, the approach should also help in building robust and transportable coda magnitudes and in seismic
Araujo; Araujo
2000-09-01
The understanding of contact line fluctuations in heterogeneous systems of controlled wettability is relevant to many industrial processes. Despite its importance, it is poorly understood. Here, we present results on an experimental study of fluid displacement on modified Hele-Shaw cells with surface defects as heterogeneities. The system wettability is controlled by defect surface coverage. Three different surface coverage regimes were studied. For each one, the morphology and deformation energy of the displacement front is determined. The width front is described in terms of two exponents, the roughness exponent (alpha) and the one that describes its growth (beta). In all cases, it is found that the width increases logarithmically in time up to a characteristic value, where a crossover to a saturation behavior is observed. The crossover time is a function of the surface coverage. For low coverage 0.51
Towards standardized assessment of endoscope optical performance: geometric distortion
NASA Astrophysics Data System (ADS)
Wang, Quanzeng; Desai, Viraj N.; Ngo, Ying Z.; Cheng, Wei-Chung; Pfefer, Joshua
2013-12-01
Technological advances in endoscopes, such as capsule, ultrathin and disposable devices, promise significant improvements in safety, clinical effectiveness and patient acceptance. Unfortunately, the industry lacks test methods for preclinical evaluation of key optical performance characteristics (OPCs) of endoscopic devices that are quantitative, objective and well-validated. As a result, it is difficult for researchers and developers to compare image quality and evaluate equivalence to, or improvement upon, prior technologies. While endoscope OPCs include resolution, field of view, and depth of field, among others, our focus in this paper is geometric image distortion. We reviewed specific test methods for distortion and then developed an objective, quantitative test method based on well-defined experimental and data processing steps to evaluate radial distortion in the full field of view of an endoscopic imaging system. Our measurements and analyses showed that a second-degree polynomial equation could well describe the radial distortion curve of a traditional endoscope. The distortion evaluation method was effective for correcting the image and can be used to explain other widely accepted evaluation methods such as picture height distortion. Development of consensus standards based on promising test methods for image quality assessment, such as the method studied here, will facilitate clinical implementation of innovative endoscopic devices.
Towards quantitative assessment of calciphylaxis
NASA Astrophysics Data System (ADS)
Deserno, Thomas M.; Sárándi, István.; Jose, Abin; Haak, Daniel; Jonas, Stephan; Specht, Paula; Brandenburg, Vincent
2014-03-01
Calciphylaxis is a rare disease that has devastating conditions associated with high morbidity and mortality. Calciphylaxis is characterized by systemic medial calcification of the arteries yielding necrotic skin ulcerations. In this paper, we aim at supporting the installation of multi-center registries for calciphylaxis, which includes a photographic documentation of skin necrosis. However, photographs acquired in different centers under different conditions using different equipment and photographers cannot be compared quantitatively. For normalization, we use a simple color pad that is placed into the field of view, segmented from the image, and its color fields are analyzed. In total, 24 colors are printed on that scale. A least-squares approach is used to determine the affine color transform. Furthermore, the card allows scale normalization. We provide a case study for qualitative assessment. In addition, the method is evaluated quantitatively using 10 images of two sets of different captures of the same necrosis. The variability of quantitative measurements based on free hand photography is assessed regarding geometric and color distortions before and after our simple calibration procedure. Using automated image processing, the standard deviation of measurements is significantly reduced. The coefficients of variations yield 5-20% and 2-10% for geometry and color, respectively. Hence, quantitative assessment of calciphylaxis becomes practicable and will impact a better understanding of this rare but fatal disease.
Reshaping Plant Biology: Qualitative and Quantitative Descriptors for Plant Morphology
Balduzzi, Mathilde; Binder, Brad M.; Bucksch, Alexander; Chang, Cynthia; Hong, Lilan; Iyer-Pascuzzi, Anjali S.; Pradal, Christophe; Sparks, Erin E.
2017-01-01
An emerging challenge in plant biology is to develop qualitative and quantitative measures to describe the appearance of plants through the integration of mathematics and biology. A major hurdle in developing these metrics is finding common terminology across fields. In this review, we define approaches for analyzing plant geometry, topology, and shape, and provide examples for how these terms have been and can be applied to plants. In leaf morphological quantifications both geometry and shape have been used to gain insight into leaf function and evolution. For the analysis of cell growth and expansion, we highlight the utility of geometric descriptors for understanding sepal and hypocotyl development. For branched structures, we describe how topology has been applied to quantify root system architecture to lend insight into root function. Lastly, we discuss the importance of using morphological descriptors in ecology to assess how communities interact, function, and respond within different environments. This review aims to provide a basic description of the mathematical principles underlying morphological quantifications. PMID:28217137
Reshaping Plant Biology: Qualitative and Quantitative Descriptors for Plant Morphology.
Balduzzi, Mathilde; Binder, Brad M; Bucksch, Alexander; Chang, Cynthia; Hong, Lilan; Iyer-Pascuzzi, Anjali S; Pradal, Christophe; Sparks, Erin E
2017-01-01
An emerging challenge in plant biology is to develop qualitative and quantitative measures to describe the appearance of plants through the integration of mathematics and biology. A major hurdle in developing these metrics is finding common terminology across fields. In this review, we define approaches for analyzing plant geometry, topology, and shape, and provide examples for how these terms have been and can be applied to plants. In leaf morphological quantifications both geometry and shape have been used to gain insight into leaf function and evolution. For the analysis of cell growth and expansion, we highlight the utility of geometric descriptors for understanding sepal and hypocotyl development. For branched structures, we describe how topology has been applied to quantify root system architecture to lend insight into root function. Lastly, we discuss the importance of using morphological descriptors in ecology to assess how communities interact, function, and respond within different environments. This review aims to provide a basic description of the mathematical principles underlying morphological quantifications.
NASA Astrophysics Data System (ADS)
Zhevlakov, A. P.; Zatsepina, M. E.; Kirillovskii, V. K.
2014-06-01
The principles of transformation of a Foucault shadowgram into a quantitative map of wave-front deformation based on creation of a system of isophotes are unveiled. The presented studies and their results prove that there is a high degree of correspondence between a Foucault shadowgram and the geometrical model of a shear interferogram with respect to displaying wave-front deformations.
ERIC Educational Resources Information Center
Ertekin, E.; Solak, S.; Yazici, E.
2010-01-01
The aim of this study is to identify the effects of formalism in teaching on primary and secondary school mathematics teacher trainees' algebraic and geometric interpretations of the notions of linear dependency/independency. Quantitative research methods are drawn in order to determine differences in success levels between algebraic and geometric…
Geometric stability of topological lattice phases
Jackson, T. S.; Möller, Gunnar; Roy, Rahul
2015-01-01
The fractional quantum Hall (FQH) effect illustrates the range of novel phenomena which can arise in a topologically ordered state in the presence of strong interactions. The possibility of realizing FQH-like phases in models with strong lattice effects has attracted intense interest as a more experimentally accessible venue for FQH phenomena which calls for more theoretical attention. Here we investigate the physical relevance of previously derived geometric conditions which quantify deviations from the Landau level physics of the FQHE. We conduct extensive numerical many-body simulations on several lattice models, obtaining new theoretical results in the process, and find remarkable correlation between these conditions and the many-body gap. These results indicate which physical factors are most relevant for the stability of FQH-like phases, a paradigm we refer to as the geometric stability hypothesis, and provide easily implementable guidelines for obtaining robust FQH-like phases in numerical or real-world experiments. PMID:26530311
Superatoms: Electronic and Geometric Effects on Reactivity.
Reber, Arthur C; Khanna, Shiv N
2017-02-21
The relative role of electronic and geometric effects on the stability of clusters has been a contentious topic for quite some time, with the focus on electronic structure generally gaining the upper hand. In this Account, we hope to demonstrate that both electronic shell filling and geometric shell filling are necessary concepts for an intuitive understanding of the reactivity of metal clusters. This work will focus on the reactivity of aluminum based clusters, although these concepts may be applied to clusters of different metals and ligand protected clusters. First we highlight the importance of electronic shell closure in the stability of metallic clusters. Quantum confinement in small compact metal clusters results in the bunching of quantum states that are reminiscent of the electronic shells in atoms. Clusters with closed electronic shells and large HOMO-LUMO (highest occupied molecular orbital-lowest unoccupied molecular orbital) gaps have enhanced stability and reduced reactivity with O2 due to the need for the cluster to accommodate the spin of molecular oxygen during activation of the molecule. To intuitively understand the reactivity of clusters with protic species such as water and methanol, geometric effects are needed. Clusters with unsymmetrical structures and defects usually result in uneven charge distribution over the surface of the cluster, forming active sites. To reduce reactivity, these sites must be quenched. These concepts can also be applied to ligand protected clusters. Clusters with ligands that are balanced across the cluster are less reactive, while clusters with unbalanced ligands can result in induced active sites. Adatoms on the surface of a cluster that are bound to a ligand result in an activated adatom that reacts readily with protic species, offering a mechanism by which the defects will be etched off returning the cluster to a closed geometric shell. The goal of this Account is to argue that both geometric and electronic shell
Topological minimally entangled states via geometric measure
NASA Astrophysics Data System (ADS)
Buerschaper, Oliver; García-Saez, Artur; Orús, Román; Wei, Tzu-Chieh
2014-11-01
Here we show how the Minimally Entangled States (MES) of a 2d system with topological order can be identified using the geometric measure of entanglement. We show this by minimizing this measure for the doubled semion, doubled Fibonacci and toric code models on a torus with non-trivial topological partitions. Our calculations are done either quasi-exactly for small system sizes, or using the tensor network approach in Orús et al (arXiv:1406.0585) for large sizes. As a byproduct of our methods, we see that the minimisation of the geometric entanglement can also determine the number of Abelian quasiparticle excitations in a given model. The results in this paper provide a very efficient and accurate way of extracting the full topological information of a 2d quantum lattice model from the multipartite entanglement structure of its ground states.
Small-on-large geometric anelasticity
NASA Astrophysics Data System (ADS)
Sadik, Souhayl; Yavari, Arash
2016-11-01
In this paper, we are concerned with finding exact solutions for the stress fields of nonlinear solids with non-symmetric distributions of defects (or more generally finite eigenstrains) that are small perturbations of symmetric distributions of defects with known exact solutions. In the language of geometric mechanics, this corresponds to finding a deformation that is a result of a perturbation of the metric of the Riemannian material manifold. We present a general framework that can be used for a systematic analysis of this class of anelasticity problems. This geometric formulation can be thought of as a material analogue of the classical small-on-large theory in nonlinear elasticity. We use the present small-on-large anelasticity theory to find exact solutions for the stress fields of some non-symmetric distributions of screw dislocations in incompressible isotropic solids.
Color fringe projection profilometry using geometric constraints
NASA Astrophysics Data System (ADS)
Cheng, Teng; Du, Qingyu; Jiang, Yaxi
2017-09-01
A recently proposed phase unwrapping method using geometric constraints performs well without requiring additional camera, more patterns or global search. The major limitation of this technique is the confined measurement depth range (MDR) within 2π in phase domain. To enlarge the MDR, this paper proposes using color fringes for three-dimensional (3D) shape measurement. Each six fringe periods encoded with six different colors are treated as one group. The local order within one group can be identified with reference to the color distribution. Then the phase wrapped period-by-period is converted into the phase wrapped group-by-group. The geometric constraints of the fringe projection system are used to determine the group order. Such that the MDR is extended from 2π to 12π by six times. Experiment results demonstrate the success of the proposed method to measure two isolated objects with large MDR.
The bouncing ball through a geometrical series
NASA Astrophysics Data System (ADS)
Flores, Sergio; Alfaro, Luis L.; Chavez, Juan E.; Bastarrachea, Aztlan; Hurtado, Jazmin
2008-10-01
The mathematical representation of the physical situation related to a bouncing ball on the floor is an important understanding difficulty for most of the students during the introductory mechanics and mathematics courses. The research group named Physics and mathematics in context from the University of Ciudad Juarez is concerned about the versatility in the change from a mathematical representation to the own physical context of any problem under a traditional instruction. In this case, the main idea is the association of the physical properties of the bouncing ball situation to the nearest mathematical model based on a geometrical series. The proposal of the cognitive development is based on a geometrical series that shows the time the ball takes to stop. In addition, we show the behavior of the ratio of the consecutive heights during the motion.
Universal geometrical scaling of the elliptic flow
NASA Astrophysics Data System (ADS)
Andrés, C.; Dias de Deus, J.; Moscoso, A.; Pajares, C.; Salgado, Carlos A.
2015-03-01
The presence of scaling variables in experimental observables provide very valuable indications of the dynamics underlying a given physical process. In the last years, the search for geometric scaling, that is the presence of a scaling variable which encodes all geometrical information of the collision as well as other external quantities as the total energy, has been very active. This is motivated, in part, for being one of the genuine predictions of the Color Glass Condensate formalism for saturation of partonic densities. Here we extend these previous findings to the case of experimental data on elliptic flow. We find an excellent scaling for all centralities and energies, from RHIC to LHC, with a simple generalization of the scaling previously found for other observables and systems. Interestingly, the case of the photons, difficult to reconcile in most formalisms, nicely fit the scaling curve. We discuss on the possible interpretations of this finding in terms of initial or final state effects.
Geometric Mechanics of Periodic Pleated Origami
NASA Astrophysics Data System (ADS)
Wei, Z. Y.; Guo, Z. V.; Dudte, L.; Liang, H. Y.; Mahadevan, L.
2013-05-01
Origami structures are mechanical metamaterials with properties that arise almost exclusively from the geometry of the constituent folds and the constraint of piecewise isometric deformations. Here we characterize the geometry and planar and nonplanar effective elastic response of a simple periodically folded Miura-ori structure, which is composed of identical unit cells of mountain and valley folds with four-coordinated ridges, defined completely by two angles and two lengths. We show that the in-plane and out-of-plane Poisson’s ratios are equal in magnitude, but opposite in sign, independent of material properties. Furthermore, we show that effective bending stiffness of the unit cell is singular, allowing us to characterize the two-dimensional deformation of a plate in terms of a one-dimensional theory. Finally, we solve the inverse design problem of determining the geometric parameters for the optimal geometric and mechanical response of these extreme structures.
Geometric mechanics of periodic pleated origami.
Wei, Z Y; Guo, Z V; Dudte, L; Liang, H Y; Mahadevan, L
2013-05-24
Origami structures are mechanical metamaterials with properties that arise almost exclusively from the geometry of the constituent folds and the constraint of piecewise isometric deformations. Here we characterize the geometry and planar and nonplanar effective elastic response of a simple periodically folded Miura-ori structure, which is composed of identical unit cells of mountain and valley folds with four-coordinated ridges, defined completely by two angles and two lengths. We show that the in-plane and out-of-plane Poisson's ratios are equal in magnitude, but opposite in sign, independent of material properties. Furthermore, we show that effective bending stiffness of the unit cell is singular, allowing us to characterize the two-dimensional deformation of a plate in terms of a one-dimensional theory. Finally, we solve the inverse design problem of determining the geometric parameters for the optimal geometric and mechanical response of these extreme structures.
Perspective Pose Estimation with Geometric Algebra
NASA Astrophysics Data System (ADS)
Gebken, Christian; Sommer, Gerald
2008-09-01
A novel method which entirely resides inside conformal geometric algebra (CGA) is presented estimating the pose of a camera from one image of a known object. At first, subproblems covering only three feature points are solved and globally assessed. The object model is accordingly pruned and rigidly fitted to corresponding projection rays by evaluating a succinct CGA expression which emerged from a purely geometric approach. It results a set of 3-point poses each given by a motor. These spinor elements of CGA embody rigid body motions from the manifold SE(3). The poses are then to be averaged according to their quality. This is the second aspect of this work as the respective motors do not come from a linear space and averaging must be carried out appropriately. For this purpose, a technique called weighted intrinsic mean is used.
Geometric modeling for computer aided design
NASA Technical Reports Server (NTRS)
Schwing, James L.
1993-01-01
Over the past several years, it has been the primary goal of this grant to design and implement software to be used in the conceptual design of aerospace vehicles. The work carried out under this grant was performed jointly with members of the Vehicle Analysis Branch (VAB) of NASA LaRC, Computer Sciences Corp., and Vigyan Corp. This has resulted in the development of several packages and design studies. Primary among these are the interactive geometric modeling tool, the Solid Modeling Aerospace Research Tool (smart), and the integration and execution tools provided by the Environment for Application Software Integration and Execution (EASIE). In addition, it is the purpose of the personnel of this grant to provide consultation in the areas of structural design, algorithm development, and software development and implementation, particularly in the areas of computer aided design, geometric surface representation, and parallel algorithms.
a Modular Geometric Model for Underwater Photogrammetry
NASA Astrophysics Data System (ADS)
Maas, H.-G.
2015-04-01
Underwater applications of photogrammetric measurement techniques usually need to deal with multimedia photogrammetry aspects, which are characterized by the necessity of handling optical rays that are broken at interfaces between optical media with different refrative indices according to Snell's Law. This so-called multimedia geometry has to be incorporated into geometric models in order to achieve correct measurement results. The paper shows a flexible yet strict geometric model for the handling of refraction effects on the optical path, which can be implemented as a module into photogrammetric standard tools such as spatial resection, spatial intersection, bundle adjustment or epipolar line computation. The module is especially well suited for applications, where an object in water is observed by cameras in air through one or more plane parallel glass interfaces, as it allows for some simplifications here.
Descriptions of stony meteorites
NASA Technical Reports Server (NTRS)
Score, R.; King, T. V. V.; Schwarz, C. M.; Reid, A. M.; Mason, B.
1982-01-01
The individual specimens, arranged by class are described. Within the chondrites, the specimens are grouped according to the Van Schmus-Wood classification, and the descriptions follow the order of increasing petrographic type. The original weight of the specimen is given to the nearest gram (nearest 0.1 gram for specimens weighing less than 100 grams). Material on al characterized meteorites collected together with descriptions of some meteorites is included. Specimens weighing less than 100 grams are listed without descriptions, unless they show distinctive features.
Geometric Factors in Target Positioning and Tracking
2009-07-01
used in active management of distributed sensor resources and sensor path planning. Keywords: Ranging & Bearing-Only Sensors, Geometry, LOS, GDOP ... GDOP ) A scalar value that characterizes the position solution is the geometrical dilution of precision ( GDOP ) defined as [4, 13]: ))((traceGDOP 11...HRHT (14a) ))((trace 1−= HHT when R = I (14b) For the case with two ranging sensors, the GDOP can be written as: )(sin GDOP 21 2 2 2 2 1
Geometrical product specifications. Datums and coordinate systems
NASA Astrophysics Data System (ADS)
Glukhov, V. I.; Ivleva, I. A.; Zlatkina, O. Y.
2017-06-01
The work is devoted to the relevant topic such as the technical products quality improvement due to the geometrical specifications accuracy. The research purpose is to ensure the quality indicators on the basis of the systematic approach to the values normalization and geometrical specifications accuracy in the workpiece coordinate systems in the process of design. To achieve the goal two tasks are completed such as the datum features classification according to the number of linear and angular freedom degrees constraints, called the datums informativeness, and the rectangular coordinate systems identification, materialized by workpiece datums sets. The datum features informativeness characterizes the datums functional purpose to limit product workpiece linear and angular degrees of freedom. The datum features informativeness numerically coincides with the kinematic pairs classes and couplings in mechanics. The datum features informativeness identifies the coordinate system without the location redundancy. Each coordinate plane of a rectangular coordinate system has different informativeness 3 + 2 + 1. Each coordinate axis also has different informativeness 4+2+Θ (zero). It is possible to establish the associated workpiece position with three linear and three angular coordinates relative to two axes with the informativeness 4 and 2. is higher, the more informativeness of the coordinate axis or a coordinate plane is, the higher is the linear and angular coordinates accuracy, the coordinate being plotted along the coordinate axis or plane. The systematic approach to the geometrical products specifications positioning in coordinate systems is the scientific basis for a natural transition to the functional dimensions of features position - coordinating dimensions and the size of the features form - feature dimensions of two measures: linear and angular ones. The products technical quality improving is possible due to the coordinate systems introduction materialized by
Multiphase flow in geometrically simple fracture intersections
Basagaoglu, H.; Meakin, P.; Green, C.T.; Mathew, M.; ,
2006-01-01
A two-dimensional lattice Boltzmann (LB) model with fluid-fluid and solid-fluid interaction potentials was used to study gravity-driven flow in geometrically simple fracture intersections. Simulated scenarios included fluid dripping from a fracture aperture, two-phase flow through intersecting fractures and thin-film flow on smooth and undulating solid surfaces. Qualitative comparisons with recently published experimental findings indicate that for these scenarios the LB model captured the underlying physics reasonably well.
Chirality: a relational geometric-physical property.
Gerlach, Hans
2013-11-01
The definition of the term chirality by Lord Kelvin in 1893 and 1904 is analyzed by taking crystallography at that time into account. This shows clearly that chirality is a relational geometric-physical property, i.e., two relations between isometric objects are possible: homochiral or heterochiral. In scientific articles the relational term chirality is often mistaken for the two valued measure for the individual (absolute) sense of chirality, an arbitrary attributive term.
Geometric Phases in Sensing and Control
2003-01-01
this idea with an equal-sided, spring-jointed, four-bar mechanism and then apply the technique to a vibrating ring gyroscope. In physical systems the...Douglas Sparks of Delco Au- tomotive Systems ) . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.4 Equal-Sided Four-Bar Mechanism ...Landsberg in [48, 49]. Many researchers have investigated the role of the geometric phase in mechan - ical systems . In problems of this type, changes
Geometric continuum regularization of quantum field theory
Halpern, M.B. . Dept. of Physics)
1989-11-08
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.
Ergodicity breaking in geometric Brownian motion.
Peters, O; Klein, W
2013-03-08
Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by nonergodicity, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time average. A common tactic for bringing time averages closer to ensemble averages is diversification. In this Letter, we study the effects of diversification using the concept of ergodicity breaking.
Evolutionary Optimization of a Geometrically Refined Truss
NASA Technical Reports Server (NTRS)
Hull, P. V.; Tinker, M. L.; Dozier, G. V.
2007-01-01
Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection, and stress on a benchmark cantilever truss problem. Predominantly traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This Technical Publication (TP) presents a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation: genetic algorithms and differential evolution to successfully optimize a benchmark structural optimization problem. A nontraditional solution to the benchmark problem is presented in this TP, specifically a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization toolset.
A Geometric Theory of Nonlinear Morphoelastic Shells
NASA Astrophysics Data System (ADS)
Sadik, Souhayl; Angoshtari, Arzhang; Goriely, Alain; Yavari, Arash
2016-08-01
Many thin three-dimensional elastic bodies can be reduced to elastic shells: two-dimensional elastic bodies whose reference shape is not necessarily flat. More generally, morphoelastic shells are elastic shells that can remodel and grow in time. These idealized objects are suitable models for many physical, engineering, and biological systems. Here, we formulate a general geometric theory of nonlinear morphoelastic shells that describes both the evolution of the body shape, viewed as an orientable surface, as well as its intrinsic material properties such as its reference curvatures. In this geometric theory, bulk growth is modeled using an evolving referential configuration for the shell, the so-called material manifold. Geometric quantities attached to the surface, such as the first and second fundamental forms, are obtained from the metric of the three-dimensional body and its evolution. The governing dynamical equations for the body are obtained from variational consideration by assuming that both fundamental forms on the material manifold are dynamical variables in a Lagrangian field theory. In the case where growth can be modeled by a Rayleigh potential, we also obtain the governing equations for growth in the form of kinetic equations coupling the evolution of the first and the second fundamental forms with the state of stress of the shell. We apply these ideas to obtain stress-free growth fields of a planar sheet, the time evolution of a morphoelastic circular cylindrical shell subject to time-dependent internal pressure, and the residual stress of a morphoelastic planar circular shell.
The geometric and the atomic world views
Bohr, Aage; Mottelson, Ben R.; Ulfbeck, Ole
2008-01-01
The atomic world view is based on the notion that matter is built of elementary constituents called atoms, and quantum mechanics was created in the pursuit of this view with probabilistic events caused by atomic particles. This conception involves unresolved ambiguities linked to the notion of an elementary quantum of action. The resolution of these problems in quantum mechanics requires a new, geometric, world view, which recognizes the occurrence of events, clicks in counters, coming without a cause, referred to as fortuitous. The possibility of a rational theory of probabilities for such events is based on the assignment to the individual click of a proper value of an element of (flat) space–time symmetry. Thereby, the distributions of uncaused clicks can be endowed with a geometric content in terms of the irreducible representations of space–time symmetry. Through fortuity, space–time invariance itself thus acquires a hitherto unrecognized role. Departing from the norms of physical theory, the uncaused click is not a measurement of something, and the reality mirrored in the distributions is the geometry of space time itself, and not a property of an imagined object. The geometric world view involves only the dimensions of space and time, and the absence of an irreducible dimension of mass is seen as the result of the discovery of new physical phenomena. Accordingly Planck's constant has no place in fundamental theory and is seen as a relic of dimensions that have become superfluous.
The geometric phase controls ultracold chemistry
Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
2015-07-30
In this study, the geometric phase is shown to control the outcome of an ultracold chemical reaction. The control is a direct consequence of the sign change on the interference term between two scattering pathways (direct and looping), which contribute to the reactive collision process in the presence of a conical intersection (point of degeneracy between two Born–Oppenheimer electronic potential energy surfaces). The unique properties of the ultracold energy regime lead to an effective quantization of the scattering phase shift enabling maximum constructive or destructive interference between the two pathways. By taking the O + OH → H + O2more » reaction as an illustrative example, it is shown that inclusion of the geometric phase modifies ultracold reaction rates by nearly two orders of magnitude. Interesting experimental control possibilities include the application of external electric and magnetic fields that might be used to exploit the geometric phase effect reported here and experimentally switch on or off the reactivity.« less
Facades structure detection by geometric moment
NASA Astrophysics Data System (ADS)
Jiang, Diqiong; Chen, Hui; Song, Rui; Meng, Lei
2017-06-01
This paper proposes a novel method for extracting facades structure from real-world pictures by using local geometric moment. Compared with existing methods, the proposed method has advantages of easy-to-implement, low computational cost, and robustness to noises, such as uneven illumination, shadow, and shade from other objects. Besides, our method is faster and has a lower space complexity, making it feasible for mobile devices and the situation where real-time data processing is required. Specifically, a facades structure modal is first proposed to support the use of our special noise reduction method, which is based on a self-adapt local threshold with Gaussian weighted average for image binarization processing and the feature of the facades structure. Next, we divide the picture of the building into many individual areas, each of which represents a door or a window in the picture. Subsequently we calculate the geometric moment and centroid for each individual area, for identifying those collinear ones based on the feature vectors, each of which is thereafter replaced with a line. Finally, we comprehensively analyze all the geometric moment and centroid to find out the facades structure of the building. We compare our result with other methods and especially report the result from the pictures taken in bad environmental conditions. Our system is designed for two application, i.e, the reconstruction of facades based on higher resolution ground-based on imagery, and the positional system based on recognize the urban building.
Geometric simulation of structures containing rigid units
NASA Astrophysics Data System (ADS)
Wells, Stephen
2005-03-01
Much insight into the behaviour of the framework silicates can be obtained from the Rigid Unit model. I review results from geometric analyses [1] of framework structures, quantifying the significance of rigid unit motion in thermal disorder and in defect accomodation, and from a method of simulation [2,3] based on a whole-body `geometric potential' rather than on interatomic potentials. I show the application of the geometric potential to the symmetry-constrained generation of hypothetical zeolite frameworks [4], and to the rapid generation of protein conformations using insights from rigid cluster decomposition [5]. 1. Wells, Dove and Tucker, Journal of Applied Crystallography, 37:536--544 (2004). 2. G.D. Gatta and S.A. Wells, Phys. Chem. Min. 31:1--10 (2004). 3. A. Sartbaeva, S. A. Wells, S. A. T. Redfern, J. Phys.: Condens. Matter 16, 8173 (2004) 4. M. M. J. Treacy, I. Rivin, E. Balkovsky, K. H. Randall and M. D. Foster, Micropor. Mesopor. Mater. 74, 121-132 (2004). 5. M.F. Thorpe, Ming Lei, A.J. Rader, Donald J. Jacobs, and Leslie A. Kuhn, Journal of Molecular Graphics and Modelling 19, 1:60 - 69, (2001).
Geometrical families of mechanically stable granular packings
NASA Astrophysics Data System (ADS)
Gao, Guo-Jie; Blawzdziewicz, Jerzy; O'Hern, Corey S.
2009-12-01
We enumerate and classify nearly all of the possible mechanically stable (MS) packings of bidipserse mixtures of frictionless disks in small sheared systems. We find that MS packings form continuous geometrical families, where each family is defined by its particular network of particle contacts. We also monitor the dynamics of MS packings along geometrical families by applying quasistatic simple shear strain at zero pressure. For small numbers of particles (N<16) , we find that the dynamics is deterministic and highly contracting. That is, if the system is initialized in a MS packing at a given shear strain, it will quickly lock into a periodic orbit at subsequent shear strain, and therefore sample only a very small fraction of the possible MS packings in steady state. In studies with N>16 , we observe an increase in the period and random splittings of the trajectories caused by bifurcations in configuration space. We argue that the ratio of the splitting and contraction rates in large systems will determine the distribution of MS-packing geometrical families visited in steady state. This work is part of our long-term research program to develop a master-equation formalism to describe macroscopic slowly driven granular systems in terms of collections of small subsystems.
Geometric Deep Learning: Going beyond Euclidean data
NASA Astrophysics Data System (ADS)
Bronstein, Michael M.; Bruna, Joan; LeCun, Yann; Szlam, Arthur; Vandergheynst, Pierre
2017-07-01
Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field.
Landsat-5 bumper-mode geometric correction
Storey, J.C.; Choate, Michael J.
2004-01-01
The Landsat-5 Thematic Mapper (TM) scan mirror was switched from its primary operating mode to a backup mode in early 2002 in order to overcome internal synchronization problems arising from long-term wear of the scan mirror mechanism. The backup bumper mode of operation removes the constraints on scan start and stop angles enforced in the primary scan angle monitor operating mode, requiring additional geometric calibration effort to monitor the active scan angles. It also eliminates scan timing telemetry used to correct the TM scan geometry. These differences require changes to the geometric correction algorithms used to process TM data. A mathematical model of the scan mirror's behavior when operating in bumper mode was developed. This model includes a set of key timing parameters that characterize the time-varying behavior of the scan mirror bumpers. To simplify the implementation of the bumper-mode model, the bumper timing parameters were recast in terms of the calibration and telemetry data items used to process normal TM imagery. The resulting geometric performance, evaluated over 18 months of bumper-mode operations, though slightly reduced from that achievable in the primary operating mode, is still within the Landsat specifications when the data are processed with the most up-to-date calibration parameters.
Geometric Morphometrics of Rodent Sperm Head Shape
Varea Sánchez, María; Bastir, Markus; Roldan, Eduardo R. S.
2013-01-01
Mammalian spermatozoa, particularly those of rodent species, are extremely complex cells and differ greatly in form and dimensions. Thus, characterization of sperm size and, particularly, sperm shape represents a major challenge. No consensus exists on a method to objectively assess size and shape of spermatozoa. In this study we apply the principles of geometric morphometrics to analyze rodent sperm head morphology and compare them with two traditional morphometry methods, that is, measurements of linear dimensions and dimensions-derived parameters calculated using formulae employed in sperm morphometry assessments. Our results show that geometric morphometrics clearly identifies shape differences among rodent spermatozoa. It is also capable of discriminating between size and shape and to analyze these two variables separately. Thus, it provides an accurate method to assess sperm head shape. Furthermore, it can identify which sperm morphology traits differ between species, such as the protrusion or retraction of the base of the head, the orientation and relative position of the site of flagellum insertion, the degree of curvature of the hook, and other distinct anatomical features and appendices. We envisage that the use of geometric morphometrics may have a major impact on future studies focused on the characterization of sperm head formation, diversity of sperm head shape among species (and underlying evolutionary forces), the effects of reprotoxicants on changes in cell shape, and phenotyping of genetically-modified individuals. PMID:24312234
Algebraic and geometric spread in finite frames
NASA Astrophysics Data System (ADS)
King, Emily J.
2015-08-01
When searching for finite unit norm tight frames (FUNTFs) of M vectors in FN which yield robust representations, one is concerned with finding frames consisting of frame vectors which are in some sense as spread apart as possible. Algebraic spread and geometric spread are the two most commonly used measures of spread. A frame with optimal algebraic spread is called full spark and is such that any subcollection of N frame vectors is a basis for FN. A Grassmannian frame is a FUNTF which satisfies the Grassmannian packing problem; that is, the frame vectors are optimally geometrically spread given fixed M and N. A particular example of a Grassmannian frame is an equiangular frame, which is such that the absolute value of all inner products of distinct vectors is equal. The relationship between these two types of optimal spread is complicated. The folk knowledge for many years was that equiangular frames were full spark; however, this is now known not to hold for an infinite class of equiangular frames. The exact relationship between these types of spread will be further explored in this talk, as well as Plücker coordinates and coherence, which are measures of how much a frame misses being optimally algebraically or geometrically spread.