Riemannian geometric approach to human arm dynamics, movement optimization, and invariance

NASA Astrophysics Data System (ADS)

Biess, Armin; Flash, Tamar; Liebermann, Dario G.

2011-03-01

We present a generally covariant formulation of human arm dynamics and optimization principles in Riemannian configuration space. We extend the one-parameter family of mean-squared-derivative (MSD) cost functionals from Euclidean to Riemannian space, and we show that they are mathematically identical to the corresponding dynamic costs when formulated in a Riemannian space equipped with the kinetic energy metric. In particular, we derive the equivalence of the minimum-jerk and minimum-torque change models in this metric space. Solutions of the one-parameter family of MSD variational problems in Riemannian space are given by (reparametrized) geodesic paths, which correspond to movements with least muscular effort. Finally, movement invariants are derived from symmetries of the Riemannian manifold. We argue that the geometrical structure imposed on the arm’s configuration space may provide insights into the emerging properties of the movements generated by the motor system.

KAM tori and whiskered invariant tori for non-autonomous systems

NASA Astrophysics Data System (ADS)

Canadell, Marta; de la Llave, Rafael

2015-08-01

We consider non-autonomous dynamical systems which converge to autonomous (or periodic) systems exponentially fast in time. Such systems appear naturally as models of many physical processes affected by external pulses. We introduce definitions of non-autonomous invariant tori and non-autonomous whiskered tori and their invariant manifolds and we prove their persistence under small perturbations, smooth dependence on parameters and several geometric properties (if the systems are Hamiltonian, the tori are Lagrangian manifolds). We note that such definitions are problematic for general time-dependent systems, but we show that they are unambiguous for systems converging exponentially fast to autonomous. The proof of persistence relies only on a standard Implicit Function Theorem in Banach spaces and it does not require that the rotations in the tori are Diophantine nor that the systems we consider preserve any geometric structure. We only require that the autonomous system preserves these objects. In particular, when the autonomous system is integrable, we obtain the persistence of tori with rational rotational. We also discuss fast and efficient algorithms for their computation. The method also applies to infinite dimensional systems which define a good evolution, e.g. PDE's. When the systems considered are Hamiltonian, we show that the time dependent invariant tori are isotropic. Hence, the invariant tori of maximal dimension are Lagrangian manifolds. We also obtain that the (un)stable manifolds of whiskered tori are Lagrangian manifolds. We also include a comparison with the more global theory developed in Blazevski and de la Llave (2011).

Tokunaga self-similarity arises naturally from time invariance

NASA Astrophysics Data System (ADS)

Kovchegov, Yevgeniy; Zaliapin, Ilya

2018-04-01

The Tokunaga condition is an algebraic rule that provides a detailed description of the branching structure in a self-similar tree. Despite a solid empirical validation and practical convenience, the Tokunaga condition lacks a theoretical justification. Such a justification is suggested in this work. We define a geometric branching process G (s ) that generates self-similar rooted trees. The main result establishes the equivalence between the invariance of G (s ) with respect to a time shift and a one-parametric version of the Tokunaga condition. In the parameter region where the process satisfies the Tokunaga condition (and hence is time invariant), G (s ) enjoys many of the symmetries observed in a critical binary Galton-Watson branching process and reproduces the latter for a particular parameter value.

A geometric formulation of Higgs Effective Field Theory. Measuring the curvature of scalar field space

DOE PAGES

Alonso, Rodrigo; Jenkins, Elizabeth E.; Manohar, Aneesh V.

2016-03-01

A geometric formulation of Higgs Effective Field Theory (HEFT) is presented. Experimental observables are given in terms of geometric invariants of the scalar sigma model sector such as the curvature of the scalar field manifold M. Here we show how the curvature can be measured experimentally via Higgs cross-sections, WLscattering, and the Sparameter. The one-loop action of HEFT is given in terms of geometric invariants of M. Moreover, the distinction between the Standard Model (SM) and HEFT is whether Mis flat or curved, and the curvature is a signal of the scale of new physics.

Killing-Yano equations with torsion, worldline actions and G-structures

NASA Astrophysics Data System (ADS)

Papadopoulos, G.

2012-06-01

We determine the geometry of the target spaces of supersymmetric non-relativistic particles with torsion and magnetic couplings, and with symmetries generated by the fundamental forms of G-structures for G = U(n), SU(n), Sp(n), Sp(n) · Sp(1), G2 and Spin(7). We find that the Killing-Yano equation, which arises as a condition for the invariance of the worldline action, does not always determine the torsion coupling uniquely in terms of the metric and fundamental forms. We show that there are several connections with skew-symmetric torsion for G = U(n), SU(n) and G2 that solve the invariance conditions. We describe all these compatible connections for each of the G-structures and explain the geometric nature of the couplings.

Improved object optimal synthetic description, modeling, learning, and discrimination by GEOGINE computational kernel

NASA Astrophysics Data System (ADS)

Fiorini, Rodolfo A.; Dacquino, Gianfranco

2005-03-01

GEOGINE (GEOmetrical enGINE), a state-of-the-art OMG (Ontological Model Generator) based on n-D Tensor Invariants for n-Dimensional shape/texture optimal synthetic representation, description and learning, was presented in previous conferences elsewhere recently. Improved computational algorithms based on the computational invariant theory of finite groups in Euclidean space and a demo application is presented. Progressive model automatic generation is discussed. GEOGINE can be used as an efficient computational kernel for fast reliable application development and delivery in advanced biomedical engineering, biometric, intelligent computing, target recognition, content image retrieval, data mining technological areas mainly. Ontology can be regarded as a logical theory accounting for the intended meaning of a formal dictionary, i.e., its ontological commitment to a particular conceptualization of the world object. According to this approach, "n-D Tensor Calculus" can be considered a "Formal Language" to reliably compute optimized "n-Dimensional Tensor Invariants" as specific object "invariant parameter and attribute words" for automated n-Dimensional shape/texture optimal synthetic object description by incremental model generation. The class of those "invariant parameter and attribute words" can be thought as a specific "Formal Vocabulary" learned from a "Generalized Formal Dictionary" of the "Computational Tensor Invariants" language. Even object chromatic attributes can be effectively and reliably computed from object geometric parameters into robust colour shape invariant characteristics. As a matter of fact, any highly sophisticated application needing effective, robust object geometric/colour invariant attribute capture and parameterization features, for reliable automated object learning and discrimination can deeply benefit from GEOGINE progressive automated model generation computational kernel performance. Main operational advantages over previous, similar approaches are: 1) Progressive Automated Invariant Model Generation, 2) Invariant Minimal Complete Description Set for computational efficiency, 3) Arbitrary Model Precision for robust object description and identification.

A geometric approach to failure detection and identification in linear systems

NASA Technical Reports Server (NTRS)

Massoumnia, M. A.

1986-01-01

Using concepts of (C,A)-invariant and unobservability (complementary observability) subspaces, a geometric formulation of the failure detection and identification filter problem is stated. Using these geometric concepts, it is shown that it is possible to design a causal linear time-invariant processor that can be used to detect and uniquely identify a component failure in a linear time-invariant system, assuming: (1) The components can fail simultaneously, and (2) The components can fail only one at a time. In addition, a geometric formulation of Beard's failure detection filter problem is stated. This new formulation completely clarifies of output separability and mutual detectability introduced by Beard and also exploits the dual relationship between a restricted version of the failure detection and identification problem and the control decoupling problem. Moreover, the frequency domain interpretation of the results is used to relate the concepts of failure sensitive observers with the generalized parity relations introduced by Chow. This interpretation unifies the various failure detection and identification concepts and design procedures.

Geometrically robust image watermarking by sector-shaped partitioning of geometric-invariant regions.

PubMed

Tian, Huawei; Zhao, Yao; Ni, Rongrong; Cao, Gang

2009-11-23

In a feature-based geometrically robust watermarking system, it is a challenging task to detect geometric-invariant regions (GIRs) which can survive a broad range of image processing operations. Instead of commonly used Harris detector or Mexican hat wavelet method, a more robust corner detector named multi-scale curvature product (MSCP) is adopted to extract salient features in this paper. Based on such features, disk-like GIRs are found, which consists of three steps. First, robust edge contours are extracted. Then, MSCP is utilized to detect the centers for GIRs. Third, the characteristic scale selection is performed to calculate the radius of each GIR. A novel sector-shaped partitioning method for the GIRs is designed, which can divide a GIR into several sector discs with the help of the most important corner (MIC). The watermark message is then embedded bit by bit in each sector by using Quantization Index Modulation (QIM). The GIRs and the divided sector discs are invariant to geometric transforms, so the watermarking method inherently has high robustness against geometric attacks. Experimental results show that the scheme has a better robustness against various image processing operations including common processing attacks, affine transforms, cropping, and random bending attack (RBA) than the previous approaches.

Infinite flag varieties and conjugacy theorems

PubMed Central

Peterson, Dale H.; Kac, Victor G.

1983-01-01

We study the orbit of a highest-weight vector in an integrable highest-weight module of the group G associated to a Kac-Moody algebra [unk](A). We obtain applications to the geometric structure of the associated flag varieties and to the algebraic structure of [unk](A). In particular, we prove conjugacy theorems for Cartan and Borel subalgebras of [unk](A), so that the Cartan matrix A is an invariant of [unk](A). PMID:16593298

Fingerprint-Based Structure Retrieval Using Electron Density

PubMed Central

Yin, Shuangye; Dokholyan, Nikolay V.

2010-01-01

We present a computational approach that can quickly search a large protein structural database to identify structures that fit a given electron density, such as determined by cryo-electron microscopy. We use geometric invariants (fingerprints) constructed using 3D Zernike moments to describe the electron density, and reduce the problem of fitting of the structure to the electron density to simple fingerprint comparison. Using this approach, we are able to screen the entire Protein Data Bank and identify structures that fit two experimental electron densities determined by cryo-electron microscopy. PMID:21287628

Fingerprint-based structure retrieval using electron density.

PubMed

Yin, Shuangye; Dokholyan, Nikolay V

2011-03-01

We present a computational approach that can quickly search a large protein structural database to identify structures that fit a given electron density, such as determined by cryo-electron microscopy. We use geometric invariants (fingerprints) constructed using 3D Zernike moments to describe the electron density, and reduce the problem of fitting of the structure to the electron density to simple fingerprint comparison. Using this approach, we are able to screen the entire Protein Data Bank and identify structures that fit two experimental electron densities determined by cryo-electron microscopy. Copyright © 2010 Wiley-Liss, Inc.

Geometric invariance of compressible turbulent boundary layers

NASA Astrophysics Data System (ADS)

Bi, Wei-Tao; Wu, Bin; She, Zhen-Su; Hussain, Fazle

2015-11-01

A symmetry based approach is applied to analyze the mean velocity and temperature fields of compressible, flat plate turbulent boundary layers (CTBL). A Reynolds stress length scale and a turbulent heat flux length scale are identified to possess the same defect scaling law in the CTBL bulk, which is solely owing to the constraint of the wall to the geometry of the wall-attached eddies, but invariant to compressibility and wall heat transfer. This invariance is called the geometric invariance of CTBL eddies and is likely the origin of the Mach number invariance of Morkovin's hypothesis, as well as the similarity of energy and momentum transports. A closure for the turbulent transport by using the invariant lengths is attainted to predict the mean velocity and temperature profiles in the CTBL bulk- superior to the van Driest transformation and the Reynolds analogy based relations for its sound physics and higher accuracy. Additionally, our approach offers a new understanding of turbulent Prandtl number.

Geometrical eigen-subspace framework based molecular conformation representation for efficient structure recognition and comparison

NASA Astrophysics Data System (ADS)

Li, Xiao-Tian; Yang, Xiao-Bao; Zhao, Yu-Jun

2017-04-01

We have developed an extended distance matrix approach to study the molecular geometric configuration through spectral decomposition. It is shown that the positions of all atoms in the eigen-space can be specified precisely by their eigen-coordinates, while the refined atomic eigen-subspace projection array adopted in our approach is demonstrated to be a competent invariant in structure comparison. Furthermore, a visual eigen-subspace projection function (EPF) is derived to characterize the surrounding configuration of an atom naturally. A complete set of atomic EPFs constitute an intrinsic representation of molecular conformation, based on which the interatomic EPF distance and intermolecular EPF distance can be reasonably defined. Exemplified with a few cases, the intermolecular EPF distance shows exceptional rationality and efficiency in structure recognition and comparison.

Blurred image recognition by legendre moment invariants

PubMed Central

Zhang, Hui; Shu, Huazhong; Han, Guo-Niu; Coatrieux, Gouenou; Luo, Limin; Coatrieux, Jean-Louis

2010-01-01

Processing blurred images is a key problem in many image applications. Existing methods to obtain blur invariants which are invariant with respect to centrally symmetric blur are based on geometric moments or complex moments. In this paper, we propose a new method to construct a set of blur invariants using the orthogonal Legendre moments. Some important properties of Legendre moments for the blurred image are presented and proved. The performance of the proposed descriptors is evaluated with various point-spread functions and different image noises. The comparison of the present approach with previous methods in terms of pattern recognition accuracy is also provided. The experimental results show that the proposed descriptors are more robust to noise and have better discriminative power than the methods based on geometric or complex moments. PMID:19933003

Finite-time barriers to reaction front propagation

NASA Astrophysics Data System (ADS)

Locke, Rory; Mahoney, John; Mitchell, Kevin

2015-11-01

Front propagation in advection-reaction-diffusion systems gives rise to rich geometric patterns. It has been shown for time-independent and time-periodic fluid flows that invariant manifolds, termed burning invariant manifolds (BIMs), serve as one-sided dynamical barriers to the propagation of reaction front. More recently, theoretical work has suggested that one-sided barriers, termed burning Lagrangian Coherent structures (bLCSs), exist for fluid velocity data prescribed over a finite time interval, with no assumption on the time-dependence of the flow. In this presentation, we use a time-varying fluid ``wind'' in a double-vortex channel flow to demonstrate that bLCSs form the (locally) most attracting or repelling fronts.

Metrics on the relative spacecraft motion invariant manifold.

PubMed

Gurfil, P; Kholshevnikov, Konstantin V

2005-12-01

This paper establishes a methodology for obtaining the general solution to the spacecraft relative motion problem by utilizing Cartesian configuration space in conjunction with classical orbital elements. The geometry of the relative motion configuration space is analyzed, and the relative motion invariant manifold is determined. Most importantly, the geometric structure of the relative motion problem is used to derive useful metrics for quantification of the minimum, maximum, and mean distance between spacecraft for commensurable and non-commensurable mean motions. A number of analytic solutions, as well as useful examples, are provided, illustrating the calculated bounds. A few particular cases are given that yield simple solutions.

Multi-clues image retrieval based on improved color invariants

NASA Astrophysics Data System (ADS)

Liu, Liu; Li, Jian-Xun

2012-05-01

At present, image retrieval has a great progress in indexing efficiency and memory usage, which mainly benefits from the utilization of the text retrieval technology, such as the bag-of-features (BOF) model and the inverted-file structure. Meanwhile, because the robust local feature invariants are selected to establish BOF, the retrieval precision of BOF is enhanced, especially when it is applied to a large-scale database. However, these local feature invariants mainly consider the geometric variance of the objects in the images, and thus the color information of the objects fails to be made use of. Because of the development of the information technology and Internet, the majority of our retrieval objects is color images. Therefore, retrieval performance can be further improved through proper utilization of the color information. We propose an improved method through analyzing the flaw of shadow-shading quasi-invariant. The response and performance of shadow-shading quasi-invariant for the object edge with the variance of lighting are enhanced. The color descriptors of the invariant regions are extracted and integrated into BOF based on the local feature. The robustness of the algorithm and the improvement of the performance are verified in the final experiments.

Geometric integrator for simulations in the canonical ensemble

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tapias, Diego, E-mail: diego.tapias@nucleares.unam.mx; Sanders, David P., E-mail: dpsanders@ciencias.unam.mx; Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

2016-08-28

We introduce a geometric integrator for molecular dynamics simulations of physical systems in the canonical ensemble that preserves the invariant distribution in equations arising from the density dynamics algorithm, with any possible type of thermostat. Our integrator thus constitutes a unified framework that allows the study and comparison of different thermostats and of their influence on the equilibrium and non-equilibrium (thermo-)dynamic properties of a system. To show the validity and the generality of the integrator, we implement it with a second-order, time-reversible method and apply it to the simulation of a Lennard-Jones system with three different thermostats, obtaining good conservationmore » of the geometrical properties and recovering the expected thermodynamic results. Moreover, to show the advantage of our geometric integrator over a non-geometric one, we compare the results with those obtained by using the non-geometric Gear integrator, which is frequently used to perform simulations in the canonical ensemble. The non-geometric integrator induces a drift in the invariant quantity, while our integrator has no such drift, thus ensuring that the system is effectively sampling the correct ensemble.« less

Approximate Joint Diagonalization and Geometric Mean of Symmetric Positive Definite Matrices

PubMed Central

Congedo, Marco; Afsari, Bijan; Barachant, Alexandre; Moakher, Maher

2015-01-01

We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate joint diagonalization (AJD). Today there is a considerable interest in estimating the geometric mean of a SPD matrix set in the manifold of SPD matrices endowed with the Fisher information metric. The resulting mean has several important invariance properties and has proven very useful in diverse engineering applications such as biomedical and image data processing. While for two SPD matrices the mean has an algebraic closed form solution, for a set of more than two SPD matrices it can only be estimated by iterative algorithms. However, none of the existing iterative algorithms feature at the same time fast convergence, low computational complexity per iteration and guarantee of convergence. For this reason, recently other definitions of geometric mean based on symmetric divergence measures, such as the Bhattacharyya divergence, have been considered. The resulting means, although possibly useful in practice, do not satisfy all desirable invariance properties. In this paper we consider geometric means of covariance matrices estimated on high-dimensional time-series, assuming that the data is generated according to an instantaneous mixing model, which is very common in signal processing. We show that in these circumstances we can approximate the Fisher information geometric mean by employing an efficient AJD algorithm. Our approximation is in general much closer to the Fisher information geometric mean as compared to its competitors and verifies many invariance properties. Furthermore, convergence is guaranteed, the computational complexity is low and the convergence rate is quadratic. The accuracy of this new geometric mean approximation is demonstrated by means of simulations. PMID:25919667

Geometry of Spin and SPINc Structures in the M-Theory Partition Function

NASA Astrophysics Data System (ADS)

Sati, Hisham

We study the effects of having multiple Spin structures on the partition function of the spacetime fields in M-theory. This leads to a potential anomaly which appears in the eta invariants upon variation of the Spin structure. The main sources of such spaces are manifolds with nontrivial fundamental group, which are also important in realistic models. We extend the discussion to the Spinc case and find the phase of the partition function, and revisit the quantization condition for the C-field in this case. In type IIA string theory in 10 dimensions, the (mod 2) index of the Dirac operator is the obstruction to having a well-defined partition function. We geometrically characterize manifolds with and without such an anomaly and extend to the case of nontrivial fundamental group. The lift to KO-theory gives the α-invariant, which in general depends on the Spin structure. This reveals many interesting connections to positive scalar curvature manifolds and constructions related to the Gromov-Lawson-Rosenberg conjecture. In the 12-dimensional theory bounding M-theory, we study similar geometric questions, including choices of metrics and obtaining elements of K-theory in 10 dimensions by pushforward in K-theory on the disk fiber. We interpret the latter in terms of the families index theorem for Dirac operators on the M-theory circle and disk. This involves superconnections, eta forms, and infinite-dimensional bundles, and gives elements in Deligne cohomology in lower dimensions. We illustrate our discussion with many examples throughout.

Fractal analysis of urban catchments and their representation in semi-distributed models: imperviousness and sewer system

NASA Astrophysics Data System (ADS)

Gires, Auguste; Tchiguirinskaia, Ioulia; Schertzer, Daniel; Ochoa-Rodriguez, Susana; Willems, Patrick; Ichiba, Abdellah; Wang, Lipen; Pina, Rui; Van Assel, Johan; Bruni, Guendalina; Murla Tuyls, Damian; ten Veldhuis, Marie-Claire

2017-04-01

Land use distribution and sewer system geometry exhibit complex scale dependent patterns in urban environment. This scale dependency is even more visible in a rasterized representation where only a unique class is affected to each pixel. Such features are well grasped with fractal tools, which are based scale invariance and intrinsically designed to characterise and quantify the space filled by a geometrical set exhibiting complex and tortuous patterns. Fractal tools have been widely used in hydrology but seldom in the specific context of urban hydrology. In this paper, they are used to analyse surface and sewer data from 10 urban or peri-urban catchments located in 5 European countries in the framework of the NWE Interreg RainGain project (www.raingain.eu). The aim was to characterise urban catchment properties accounting for the complexity and inhomogeneity typical of urban water systems. Sewer system density and imperviousness (roads or buildings), represented in rasterized maps of 2 m x 2 m pixels, were analysed to quantify their fractal dimension, characteristic of scaling invariance. It appears that both sewer density and imperviousness exhibit scale invariant features that can be characterized with the help of fractal dimensions ranging from 1.6 to 2, depending on the catchment. In a given area, consistent results were found for the two geometrical features, yielding a robust and innovative way of quantifying the level of urbanization. The representation of imperviousness in operational semi-distributed hydrological models for these catchments was also investigated by computing fractal dimensions of the geometrical sets made up of the sub-catchments with coefficients of imperviousness greater than a range of thresholds. It enables to quantify how well spatial structures of imperviousness are represented in the urban hydrological models.

Geometry of the scalar sector

DOE PAGES

Alonso, Rodrigo; Jenkins, Elizabeth E.; Manohar, Aneesh V.

2016-08-17

The S-matrix of a quantum field theory is unchanged by field redefinitions, and so it only depends on geometric quantities such as the curvature of field space. Whether the Higgs multiplet transforms linearly or non-linearly under electroweak symmetry is a subtle question since one can make a coordinate change to convert a field that transforms linearly into one that transforms non-linearly. Renormalizability of the Standard Model (SM) does not depend on the choice of scalar fields or whether the scalar fields transform linearly or non-linearly under the gauge group, but only on the geometric requirement that the scalar field manifoldmore » M is flat. Standard Model Effective Field Theory (SMEFT) and Higgs Effective Field Theory (HEFT) have curved M, since they parametrize deviations from the flat SM case. We show that the HEFT Lagrangian can be written in SMEFT form if and only ifMhas a SU(2) L U(1) Y invariant fixed point. Experimental observables in HEFT depend on local geometric invariants of M such as sectional curvatures, which are of order 1/Λ 2 , where Λ is the EFT scale. We give explicit expressions for these quantities in terms of the structure constants for a general G → H symmetry breaking pattern. The one-loop radiative correction in HEFT is determined using a covariant expansion which preserves manifest invariance of M under coordinate redefinitions. The formula for the radiative correction is simple when written in terms of the curvature of M and the gauge curvature field strengths. We also extend the CCWZ formalism to non-compact groups, and generalize the HEFT curvature computation to the case of multiple singlet scalar fields.« less

Killings, duality and characteristic polynomials

NASA Astrophysics Data System (ADS)

Álvarez, Enrique; Borlaf, Javier; León, José H.

1998-03-01

In this paper the complete geometrical setting of (lowest order) abelian T-duality is explored with the help of some new geometrical tools (the reduced formalism). In particular, all invariant polynomials (the integrands of the characteristic classes) can be explicitly computed for the dual model in terms of quantities pertaining to the original one and with the help of the canonical connection whose intrinsic characterization is given. Using our formalism the physically, and T-duality invariant, relevant result that top forms are zero when there is an isometry without fixed points is easily proved. © 1998

From isosuperatoms to isosupermolecules: new concepts in cluster science

NASA Astrophysics Data System (ADS)

Liu, Liren; Li, Pai; Yuan, Lan-Feng; Cheng, Longjiu; Yang, Jinlong

2016-06-01

As an extension of the superatom concept, a new concept ``isosuperatom'' is proposed, reflecting the physical phenomenon that a superatom cluster can take multiple geometrical structures with their electronic structures topologically invariant. The icosahedral and cuboctahedral Au135+ units in the Au25(SCH2CH2Ph)18-, Au23(SC6H11)16- and Au24(SAdm)16 nanoclusters are found to be examples of this concept. Furthermore, two isosuperatoms can combine to form a supermolecule. For example, the structure of the {Ag32(DPPE)5(SC6H4CF3)24}2- nanocluster can be understood well in terms of a Ag2212+ supermolecule formed by two Ag138+ isosuperatoms. On the next level of complexity, various combinations of isosuperatoms can lead to supermolecules with different geometrical structures but similar electronic structures, i.e., ``isosupermolecules''. We take two synthesized nanoclusters Au20(PPhpy2)10Cl42+ and Au30S(StBu)18 to illustrate two Au206+ isosupermolecules. The proposed concepts of isosuperatom and isosupermolecule significantly enrich the superatom concept, give a new framework for understanding a wide range of nanoclusters, and open a new door for designing assembled materials.As an extension of the superatom concept, a new concept ``isosuperatom'' is proposed, reflecting the physical phenomenon that a superatom cluster can take multiple geometrical structures with their electronic structures topologically invariant. The icosahedral and cuboctahedral Au135+ units in the Au25(SCH2CH2Ph)18-, Au23(SC6H11)16- and Au24(SAdm)16 nanoclusters are found to be examples of this concept. Furthermore, two isosuperatoms can combine to form a supermolecule. For example, the structure of the {Ag32(DPPE)5(SC6H4CF3)24}2- nanocluster can be understood well in terms of a Ag2212+ supermolecule formed by two Ag138+ isosuperatoms. On the next level of complexity, various combinations of isosuperatoms can lead to supermolecules with different geometrical structures but similar electronic structures, i.e., ``isosupermolecules''. We take two synthesized nanoclusters Au20(PPhpy2)10Cl42+ and Au30S(StBu)18 to illustrate two Au206+ isosupermolecules. The proposed concepts of isosuperatom and isosupermolecule significantly enrich the superatom concept, give a new framework for understanding a wide range of nanoclusters, and open a new door for designing assembled materials. Electronic supplementary information (ESI) available. See DOI: 10.1039/c6nr01998f

Dain’s invariant on non-time symmetric initial data sets

NASA Astrophysics Data System (ADS)

Valiente Kroon, J. A.; Williams, J. L.

2017-06-01

We extend Dain’s construction of a geometric invariant characterising static initial data sets for the vacuum Einstein field equations to situations with a non-vanishing extrinsic curvature. This invariant gives a measure of how much an initial data set with non-vanishing ADM 4-momentum deviates from stationarity. In particular, it vanishes if and only if the initial data set is stationary. Thus, the invariant provides a quantification of the amount of gravitational radiation contained in the initial data set.

BFV quantization on hermitian symmetric spaces

NASA Astrophysics Data System (ADS)

Fradkin, E. S.; Linetsky, V. Ya.

1995-02-01

Gauge-invariant BFV approach to geometric quantization is applied to the case of hermitian symmetric spaces G/ H. In particular, gauge invariant quantization on the Lobachevski plane and sphere is carried out. Due to the presence of symmetry, master equations for the first-class constraints, quantum observables and physical quantum states are exactly solvable. BFV-BRST operator defines a flat G-connection in the Fock bundle over G/ H. Physical quantum states are covariantly constant sections with respect to this connection and are shown to coincide with the generalized coherent states for the group G. Vacuum expectation values of the quantum observables commuting with the quantum first-class constraints reduce to the covariant symbols of Berezin. The gauge-invariant approach to quantization on symplectic manifolds synthesizes geometric, deformation and Berezin quantization approaches.

Canopy Spectral Invariants. Part 2; Application to Classification of Forest Types from Hyperspectral Data

NASA Technical Reports Server (NTRS)

Schull, M. A.; Knyazikhin, Y.; Xu, L.; Samanta, A.; Carmona, P. L.; Lepine, L.; Jenkins, J. P.; Ganguly, S.; Myneni, R. B.

2011-01-01

Many studies have been conducted to demonstrate the ability of hyperspectral data to discriminate plant dominant species. Most of them have employed the use of empirically based techniques, which are site specific, requires some initial training based on characteristics of known leaf and/or canopy spectra and therefore may not be extendable to operational use or adapted to changing or unknown land cover. In this paper we propose a physically based approach for separation of dominant forest type using hyperspectral data. The radiative transfer theory of canopy spectral invariants underlies the approach, which facilitates parameterization of the canopy reflectance in terms of the leaf spectral scattering and two spectrally invariant and structurally varying variables - recollision and directional escape probabilities. The methodology is based on the idea of retrieving spectrally invariant parameters from hyperspectral data first, and then relating their values to structural characteristics of three-dimensional canopy structure. Theoretical and empirical analyses of ground and airborne data acquired by Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) over two sites in New England, USA, suggest that the canopy spectral invariants convey information about canopy structure at both the macro- and micro-scales. The total escape probability (one minus recollision probability) varies as a power function with the exponent related to the number of nested hierarchical levels present in the pixel. Its base is a geometrical mean of the local total escape probabilities and accounts for the cumulative effect of canopy structure over a wide range of scales. The ratio of the directional to the total escape probability becomes independent of the number of hierarchical levels and is a function of the canopy structure at the macro-scale such as tree spatial distribution, crown shape and size, within-crown foliage density and ground cover. These properties allow for the natural separation of dominant forest classes based on the location of points on the total escape probability vs the ratio log-log plane.

A geometric approach to problems in birational geometry.

PubMed

Chi, Chen-Yu; Yau, Shing-Tung

2008-12-02

A classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces. Each of these vector spaces admits a typical metric structure which is also birationally invariant. These vector spaces so metrized will be referred to as the pseudonormed spaces of the original varieties. A fundamental question is the following: Given two mildly singular projective varieties with some of the first variety's pseudonormed spaces being isometric to the corresponding ones of the second variety's, can one construct a birational map between them that induces these isometries? In this work, a positive answer to this question is given for varieties of general type. This can be thought of as a theorem of Torelli type for birational equivalence.

Statistical evidence of anasymptotic geometric structure to the momentum transporting motions in turbulent boundary layers

NASA Astrophysics Data System (ADS)

Morrill-Winter, Caleb; Philip, Jimmy; Klewicki, Joseph

2017-03-01

The turbulence contribution to the mean flow is reflected by the motions producing the Reynolds shear stress (<-uv>) and its gradient. Recent analyses of the mean dynamical equation, along with data, evidence that these motions asymptotically exhibit self-similar geometric properties. This study discerns additional properties associated with the uv signal, with an emphasis on the magnitudes and length scales of its negative contributions. The signals analysed derive from high-resolution multi-wire hot-wire sensor data acquired in flat-plate turbulent boundary layers. Space-filling properties of the present signals are shown to reinforce previous observations, while the skewness of uv suggests a connection between the size and magnitude of the negative excursions on the inertial domain. Here, the size and length scales of the negative uv motions are shown to increase with distance from the wall, whereas their occurrences decrease. A joint analysis of the signal magnitudes and their corresponding lengths reveals that the length scales that contribute most to <-uv> are distinctly larger than the average geometric size of the negative uv motions. Co-spectra of the streamwise and wall-normal velocities, however, are shown to exhibit invariance across the inertial region when their wavelengths are normalized by the width distribution, W(y), of the scaling layer hierarchy, which renders the mean momentum equation invariant on the inertial domain.

Restoration of four-dimensional diffeomorphism covariance in canonical general relativity: An intrinsic Hamilton-Jacobi approach

NASA Astrophysics Data System (ADS)

Salisbury, Donald; Renn, Jürgen; Sundermeyer, Kurt

2016-02-01

Classical background independence is reflected in Lagrangian general relativity through covariance under the full diffeomorphism group. We show how this independence can be maintained in a Hamilton-Jacobi approach that does not accord special privilege to any geometric structure. Intrinsic space-time curvature-based coordinates grant equal status to all geometric backgrounds. They play an essential role as a starting point for inequivalent semiclassical quantizations. The scheme calls into question Wheeler’s geometrodynamical approach and the associated Wheeler-DeWitt equation in which 3-metrics are featured geometrical objects. The formalism deals with variables that are manifestly invariant under the full diffeomorphism group. Yet, perhaps paradoxically, the liberty in selecting intrinsic coordinates is precisely as broad as is the original diffeomorphism freedom. We show how various ideas from the past five decades concerning the true degrees of freedom of general relativity can be interpreted in light of this new constrained Hamiltonian description. In particular, we show how the Kuchař multi-fingered time approach can be understood as a means of introducing full four-dimensional diffeomorphism invariants. Every choice of new phase space variables yields new Einstein-Hamilton-Jacobi constraining relations, and corresponding intrinsic Schrödinger equations. We show how to implement this freedom by canonical transformation of the intrinsic Hamiltonian. We also reinterpret and rectify significant work by Dittrich on the construction of “Dirac observables.”

Binary optical filters for scale invariant pattern recognition

NASA Technical Reports Server (NTRS)

Reid, Max B.; Downie, John D.; Hine, Butler P.

1992-01-01

Binary synthetic discriminant function (BSDF) optical filters which are invariant to scale changes in the target object of more than 50 percent are demonstrated in simulation and experiment. Efficient databases of scale invariant BSDF filters can be designed which discriminate between two very similar objects at any view scaled over a factor of 2 or more. The BSDF technique has considerable advantages over other methods for achieving scale invariant object recognition, as it also allows determination of the object's scale. In addition to scale, the technique can be used to design recognition systems invariant to other geometric distortions.

Object matching using a locally affine invariant and linear programming techniques.

PubMed

Li, Hongsheng; Huang, Xiaolei; He, Lei

2013-02-01

In this paper, we introduce a new matching method based on a novel locally affine-invariant geometric constraint and linear programming techniques. To model and solve the matching problem in a linear programming formulation, all geometric constraints should be able to be exactly or approximately reformulated into a linear form. This is a major difficulty for this kind of matching algorithm. We propose a novel locally affine-invariant constraint which can be exactly linearized and requires a lot fewer auxiliary variables than other linear programming-based methods do. The key idea behind it is that each point in the template point set can be exactly represented by an affine combination of its neighboring points, whose weights can be solved easily by least squares. Errors of reconstructing each matched point using such weights are used to penalize the disagreement of geometric relationships between the template points and the matched points. The resulting overall objective function can be solved efficiently by linear programming techniques. Our experimental results on both rigid and nonrigid object matching show the effectiveness of the proposed algorithm.

U(1)-invariant membranes: The geometric formulation, Abel, and pendulum differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zheltukhin, A. A.; Fysikum, AlbaNova, Stockholm University, 106 91 Stockholm; NORDITA, Roslagstullsbacken 23, 106 91 Stockholm

The geometric approach to study the dynamics of U(1)-invariant membranes is developed. The approach reveals an important role of the Abel nonlinear differential equation of the first type with variable coefficients depending on time and one of the membrane extendedness parameters. The general solution of the Abel equation is constructed. Exact solutions of the whole system of membrane equations in the D=5 Minkowski space-time are found and classified. It is shown that if the radial component of the membrane world vector is only time dependent, then the dynamics is described by the pendulum equation.

General N=2 supersymmetric quantum mechanical model: Supervariable approach to its off-shell nilpotent symmetries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krishna, S., E-mail: skrishna.bhu@gmail.com; Shukla, A., E-mail: ashukla038@gmail.com; Malik, R.P., E-mail: rpmalik1995@gmail.com

2014-12-15

Using the supersymmetric (SUSY) invariant restrictions on the (anti-)chiral supervariables, we derive the off-shell nilpotent symmetries of the general one (0+1)-dimensional N=2 SUSY quantum mechanical (QM) model which is considered on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables θ and θ-bar with θ{sup 2}=(θ-bar){sup 2}=0,θ(θ-bar)+(θ-bar)θ=0). We provide the geometrical meanings to the two SUSY transformations of our present theory which are valid for any arbitrary type of superpotential. We express the conserved charges and Lagrangian of the theory in terms of the supervariables (that are obtained after the application of SUSYmore » invariant restrictions) and provide the geometrical interpretation for the nilpotency property and SUSY invariance of the Lagrangian for the general N=2 SUSY quantum theory. We also comment on the mathematical interpretation of the above symmetry transformations. - Highlights: • A novel method has been proposed for the derivation of N=2 SUSY transformations. • General N=2 SUSY quantum mechanical (QM) model with a general superpotential, is considered. • The above SUSY QM model is generalized onto a (1, 2)-dimensional supermanifold. • SUSY invariant restrictions are imposed on the (anti-)chiral supervariables. • Geometrical meaning of the nilpotency property is provided.« less

Hall viscosity and electromagnetic response of electrons in graphene

NASA Astrophysics Data System (ADS)

Sherafati, Mohammad; Principi, Alessandro; Vignale, Giovanni

The Hall viscosity is a dissipationless component of the viscosity tensor of an electron liquid with broken time- reversal symmetry, such as a two-dimensional electron gas (2DEG) in the quantum Hall state. Similar to the Hall conductivity, the Hall viscosity is an anomalous transport coefficient; however, while the former is connected with the current response, the latter stems from the stress response to a geometric deformation. For a Galilean-invariant system such as 2DEG, the current density is indeed the generator of the geometric deformation: therefore a connection between the Hall connectivity and viscosity is expected and by now well established. In the case of graphene, a non-Galilean-invariant system, the existence of such a connection is far from obvious, as the current operator is essentially different from the momentum operator. In this talk, I will first present our results of the geometric Hall viscosity of electrons in single-layer graphene. Then, from the expansion of the nonlocal Hall conductivity for small wave vectors, I demonstrate that, in spite of the lack of Galilean invariance, an effective mass can be defined such that the relationship between the Hall conductivity and the viscosity retains the form it has in Galilean-invariant systems, not only for a large number of occupied Landau levels, but also, with very high accuracy, for the undoped system.

Detection and analysis of diamond fingerprinting feature and its application

NASA Astrophysics Data System (ADS)

Li, Xin; Huang, Guoliang; Li, Qiang; Chen, Shengyi

2011-01-01

Before becoming a jewelry diamonds need to be carved artistically with some special geometric features as the structure of the polyhedron. There are subtle differences in the structure of this polyhedron in each diamond. With the spatial frequency spectrum analysis of diamond surface structure, we can obtain the diamond fingerprint information which represents the "Diamond ID" and has good specificity. Based on the optical Fourier Transform spatial spectrum analysis, the fingerprinting identification of surface structure of diamond in spatial frequency domain was studied in this paper. We constructed both the completely coherent diamond fingerprinting detection system illuminated by laser and the partially coherent diamond fingerprinting detection system illuminated by led, and analyzed the effect of the coherence of light source to the diamond fingerprinting feature. We studied rotation invariance and translation invariance of the diamond fingerprinting and verified the feasibility of real-time and accurate identification of diamond fingerprint. With the profit of this work, we can provide customs, jewelers and consumers with a real-time and reliable diamonds identification instrument, which will curb diamond smuggling, theft and other crimes, and ensure the healthy development of the diamond industry.

Magnetic solutions in Einstein-massive gravity with linear and nonlinear fields

NASA Astrophysics Data System (ADS)

Hendi, Seyed Hossein; Panah, Behzad Eslam; Panahiyan, Shahram; Momennia, Mehrab

2018-06-01

The solutions of U(1) gauge-gravity coupling is one of the interesting models for analyzing the semi-classical nature of spacetime. In this regard, different well-known singular and nonsingular solutions have been taken into account. The paper at hand investigates the geometrical properties of the magnetic solutions by considering Maxwell and power Maxwell invariant (PMI) nonlinear electromagnetic fields in the context of massive gravity. These solutions are free of curvature singularity, but have a conic one which leads to presence of deficit/surplus angle. The emphasize is on modifications that these generalizations impose on deficit angle which determine the total geometrical structure of the solutions, hence, physical/gravitational properties. It will be shown that depending on the background spacetime [being anti de Sitter (AdS) or de Sitter (dS)], these generalizations present different effects and modify the total structure of the solutions differently.

Littelmann path model for geometric crystals, Whittaker functions on Lie groups and Brownian motion

NASA Astrophysics Data System (ADS)

Chhaibi, Reda

2013-02-01

Generally speaking, this thesis focuses on the interplay between the representations of Lie groups and probability theory. It subdivides into essentially three parts. In a first rather algebraic part, we construct a path model for geometric crystals in the sense of Berenstein and Kazhdan, for complex semi-simple Lie groups. We will mainly describe the algebraic structure, its natural morphisms and parameterizations. The theory of total positivity will play a particularly important role. Then, we anticipate on the probabilistic part by exhibiting a canonical measure on geometric crystals. It uses as ingredients the superpotential for the flag manifold and a measure invariant under the crystal actions. The image measure under the weight map plays the role of Duistermaat-Heckman measure. Its Laplace transform defines Whittaker functions, providing an interesting formula for all Lie groups. Then it appears clearly that Whittaker functions are to geometric crystals, what characters are to combinatorial crystals. The Littlewood-Richardson rule is also exposed. Finally we present the probabilistic approach that allows to find the canonical measure. It is based on the fundamental idea that the Wiener measure will induce the adequate measure on the algebraic structures through the path model. In the last chapter, we show how our geometric model degenerates to the continuous classical Littelmann path model and thus recover known results. For example, the canonical measure on a geometric crystal of highest weight degenerates into a uniform measure on a polytope, and recovers the parameterizations of continuous crystals.

Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time

NASA Astrophysics Data System (ADS)

Duval, C.; Gibbons, G. W.; Horvathy, P. A.; Zhang, P. M.

2014-04-01

The Carroll group was originally introduced by Lévy-Leblond (1965 Ann. Inst. Henri Poincaré 3 1) by considering the contraction of the Poincaré group as c → 0. In this paper an alternative definition, based on the geometric properties of a non-Minkowskian, non-Galilean but nevertheless boost-invariant, spacetime structure is proposed. A ‘duality’ with the Galilean limit c → ∞ is established. Our theory is illustrated by Carrollian electromagnetism.

Geometrically controlled evolution of four-qubit states

NASA Astrophysics Data System (ADS)

Duy, Hoang Ngoc; Heydari, Hoshang

2011-03-01

In this paper the evolution of some states of four qubits in [1] under global bipartite unitary operation and controlled by local unitary operation using four-tangle [2] and the geometric invariants [3] is investigated. Particularly the entanglement distribution and properties of these four-qubit states are studied.

On the appropriate feature for general SAR image registration

NASA Astrophysics Data System (ADS)

Li, Dong; Zhang, Yunhua

2012-09-01

An investigation to the appropriate feature for SAR image registration is conducted. The commonly-used features such as tie points, Harris corner, the scale invariant feature transform (SIFT), and the speeded up robust feature (SURF) are comprehensively evaluated in terms of several criteria such as the geometrical invariance of feature, the extraction speed, the localization accuracy, the geometrical invariance of descriptor, the matching speed, the robustness to decorrelation, and the flexibility to image speckling. It is shown that SURF outperforms others. It is particularly indicated that SURF has good flexibility to image speckling because the Fast-Hessian detector of SURF has a potential relation with the refined Lee filter. It is recommended to perform SURF on the oversampled image with unaltered sampling step so as to improve the subpixel registration accuracy and speckle immunity. Thus SURF is more appropriate and competent for general SAR image registration.

The Scaling Group of the 1-D Invisicid Euler Equations

NASA Astrophysics Data System (ADS)

Schmidt, Emma; Ramsey, Scott; Boyd, Zachary; Baty, Roy

2017-11-01

The one dimensional (1-D) compressible Euler equations in non-ideal media support scale invariant solutions under a variety of initial conditions. Famous scale invariant solutions include the Noh, Sedov, Guderley, and collapsing cavity hydrodynamic test problems. We unify many classical scale invariant solutions under a single scaling group analysis. The scaling symmetry group generator provides a framework for determining all scale invariant solutions emitted by the 1-D Euler equations for arbitrary geometry, initial conditions, and equation of state. We approach the Euler equations from a geometric standpoint, and conduct scaling analyses for a broad class of materials.

Self-similarity in the inertial region of wall turbulence.

PubMed

Klewicki, J; Philip, J; Marusic, I; Chauhan, K; Morrill-Winter, C

2014-12-01

The inverse of the von Kármán constant κ is the leading coefficient in the equation describing the logarithmic mean velocity profile in wall bounded turbulent flows. Klewicki [J. Fluid Mech. 718, 596 (2013)] connects the asymptotic value of κ with an emerging condition of dynamic self-similarity on an interior inertial domain that contains a geometrically self-similar hierarchy of scaling layers. A number of properties associated with the asymptotic value of κ are revealed. This is accomplished using a framework that retains connection to invariance properties admitted by the mean statement of dynamics. The development leads toward, but terminates short of, analytically determining a value for κ. It is shown that if adjacent layers on the hierarchy (or their adjacent positions) adhere to the same self-similarity that is analytically shown to exist between any given layer and its position, then κ≡Φ(-2)=0.381966..., where Φ=(1+√5)/2 is the golden ratio. A number of measures, derived specifically from an analysis of the mean momentum equation, are subsequently used to empirically explore the veracity and implications of κ=Φ(-2). Consistent with the differential transformations underlying an invariant form admitted by the governing mean equation, it is demonstrated that the value of κ arises from two geometric features associated with the inertial turbulent motions responsible for momentum transport. One nominally pertains to the shape of the relevant motions as quantified by their area coverage in any given wall-parallel plane, and the other pertains to the changing size of these motions in the wall-normal direction. In accord with self-similar mean dynamics, these two features remain invariant across the inertial domain. Data from direct numerical simulations and higher Reynolds number experiments are presented and discussed relative to the self-similar geometric structure indicated by the analysis, and in particular the special form of self-similarity shown to correspond to κ=Φ(-2).

A New Approach to Identify Optimal Properties of Shunting Elements for Maximum Damping of Structural Vibration Using Piezoelectric Patches

NASA Technical Reports Server (NTRS)

Park, Junhong; Palumbo, Daniel L.

2004-01-01

The use of shunted piezoelectric patches in reducing vibration and sound radiation of structures has several advantages over passive viscoelastic elements, e.g., lower weight with increased controllability. The performance of the piezoelectric patches depends on the shunting electronics that are designed to dissipate vibration energy through a resistive element. In past efforts most of the proposed tuning methods were based on modal properties of the structure. In these cases, the tuning applies only to one mode of interest and maximum tuning is limited to invariant points when based on den Hartog's invariant points concept. In this study, a design method based on the wave propagation approach is proposed. Optimal tuning is investigated depending on the dynamic and geometric properties that include effects from boundary conditions and position of the shunted piezoelectric patch relative to the structure. Active filters are proposed as shunting electronics to implement the tuning criteria. The developed tuning methods resulted in superior capabilities in minimizing structural vibration and noise radiation compared to other tuning methods. The tuned circuits are relatively insensitive to changes in modal properties and boundary conditions, and can applied to frequency ranges in which multiple modes have effects.

Spectral-Spatial Scale Invariant Feature Transform for Hyperspectral Images.

PubMed

Al-Khafaji, Suhad Lateef; Jun Zhou; Zia, Ali; Liew, Alan Wee-Chung

2018-02-01

Spectral-spatial feature extraction is an important task in hyperspectral image processing. In this paper we propose a novel method to extract distinctive invariant features from hyperspectral images for registration of hyperspectral images with different spectral conditions. Spectral condition means images are captured with different incident lights, viewing angles, or using different hyperspectral cameras. In addition, spectral condition includes images of objects with the same shape but different materials. This method, which is named spectral-spatial scale invariant feature transform (SS-SIFT), explores both spectral and spatial dimensions simultaneously to extract spectral and geometric transformation invariant features. Similar to the classic SIFT algorithm, SS-SIFT consists of keypoint detection and descriptor construction steps. Keypoints are extracted from spectral-spatial scale space and are detected from extrema after 3D difference of Gaussian is applied to the data cube. Two descriptors are proposed for each keypoint by exploring the distribution of spectral-spatial gradient magnitude in its local 3D neighborhood. The effectiveness of the SS-SIFT approach is validated on images collected in different light conditions, different geometric projections, and using two hyperspectral cameras with different spectral wavelength ranges and resolutions. The experimental results show that our method generates robust invariant features for spectral-spatial image matching.

Combined invariants to similarity transformation and to blur using orthogonal Zernike moments

PubMed Central

Beijing, Chen; Shu, Huazhong; Zhang, Hui; Coatrieux, Gouenou; Luo, Limin; Coatrieux, Jean-Louis

2011-01-01

The derivation of moment invariants has been extensively investigated in the past decades. In this paper, we construct a set of invariants derived from Zernike moments which is simultaneously invariant to similarity transformation and to convolution with circularly symmetric point spread function (PSF). Two main contributions are provided: the theoretical framework for deriving the Zernike moments of a blurred image and the way to construct the combined geometric-blur invariants. The performance of the proposed descriptors is evaluated with various PSFs and similarity transformations. The comparison of the proposed method with the existing ones is also provided in terms of pattern recognition accuracy, template matching and robustness to noise. Experimental results show that the proposed descriptors perform on the overall better. PMID:20679028

Mapping the Geometric Evolution of Protein Folding Motor.

PubMed

Jerath, Gaurav; Hazam, Prakash Kishore; Shekhar, Shashi; Ramakrishnan, Vibin

2016-01-01

Polypeptide chain has an invariant main-chain and a variant side-chain sequence. How the side-chain sequence determines fold in terms of its chemical constitution has been scrutinized extensively and verified periodically. However, a focussed investigation on the directive effect of side-chain geometry may provide important insights supplementing existing algorithms in mapping the geometrical evolution of protein chains and its structural preferences. Geometrically, folding of protein structure may be envisaged as the evolution of its geometric variables: ϕ, and ψ dihedral angles of polypeptide main-chain directed by χ1, and χ2 of side chain. In this work, protein molecule is metaphorically modelled as a machine with 4 rotors ϕ, ψ, χ1 and χ2, with its evolution to the functional fold is directed by combinations of its rotor directions. We observe that differential rotor motions lead to different secondary structure formations and the combinatorial pattern is unique and consistent for particular secondary structure type. Further, we found that combination of rotor geometries of each amino acid is unique which partly explains how different amino acid sequence combinations have unique structural evolution and functional adaptation. Quantification of these amino acid rotor preferences, resulted in the generation of 3 substitution matrices, which later on plugged in the BLAST tool, for evaluating their efficiency in aligning sequences. We have employed BLOSUM62 and PAM30 as standard for primary evaluation. Generation of substitution matrices is a logical extension of the conceptual framework we attempted to build during the development of this work. Optimization of matrices following the conventional routines and possible application with biologically relevant data sets are beyond the scope of this manuscript, though it is a part of the larger project design.

Invariant submanifold for series arrays of Josephson junctions.

PubMed

Marvel, Seth A; Strogatz, Steven H

2009-03-01

We study the nonlinear dynamics of series arrays of Josephson junctions in the large-N limit, where N is the number of junctions in the array. The junctions are assumed to be identical, overdamped, driven by a constant bias current, and globally coupled through a common load. Previous simulations of such arrays revealed that their dynamics are remarkably simple, hinting at the presence of some hidden symmetry or other structure. These observations were later explained by the discovery of N-3 constants of motion, the choice of which confines the resulting flow in phase space to a low-dimensional invariant manifold. Here we show that the dimensionality can be reduced further by restricting attention to a special family of states recently identified by Ott and Antonsen. In geometric terms, the Ott-Antonsen ansatz corresponds to an invariant submanifold of dimension one less than that found earlier. We derive and analyze the flow on this submanifold for two special cases: an array with purely resistive loading and another with resistive-inductive-capacitive loading. Our results recover (and in some instances improve) earlier findings based on linearization arguments.

Statistical Properties of Lorenz-like Flows, Recent Developments and Perspectives

NASA Astrophysics Data System (ADS)

Araujo, Vitor; Galatolo, Stefano; Pacifico, Maria José

We comment on the mathematical results about the statistical behavior of Lorenz equations and its attractor, and more generally on the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be surprisingly difficult. It is remarkable that a rigorous proof of the existence of the Lorenz attractor was presented only around the year 2000 with a computer-assisted proof together with an extension of the hyperbolic theory developed to encompass attractors robustly containing equilibria. We present some of the main results on the statistical behavior of such systems. We show that for attractors of three-dimensional flows, robust chaotic behavior is equivalent to the existence of certain hyperbolic structures, known as singular-hyperbolicity. These structures, in turn, are associated with the existence of physical measures: in low dimensions, robust chaotic behavior for flows ensures the existence of a physical measure. We then give more details on recent results on the dynamics of singular-hyperbolic (Lorenz-like) attractors: (1) there exists an invariant foliation whose leaves are forward contracted by the flow (and further properties which are useful to understand the statistical properties of the dynamics); (2) there exists a positive Lyapunov exponent at every orbit; (3) there is a unique physical measure whose support is the whole attractor and which is the equilibrium state with respect to the center-unstable Jacobian; (4) this measure is exact dimensional; (5) the induced measure on a suitable family of cross-sections has exponential decay of correlations for Lipschitz observables with respect to a suitable Poincaré return time map; (6) the hitting time associated to Lorenz-like attractors satisfy a logarithm law; (7) the geometric Lorenz flow satisfies the Almost Sure Invariance Principle (ASIP) and the Central Limit Theorem (CLT); (8) the rate of decay of large deviations for the volume measure on the ergodic basin of a geometric Lorenz attractor is exponential; (9) a class of geometric Lorenz flows exhibits robust exponential decay of correlations; (10) all geometric Lorenz flows are rapidly mixing and their time-1 map satisfies both ASIP and CLT.

A novel image registration approach via combining local features and geometric invariants

PubMed Central

Lu, Yan; Gao, Kun; Zhang, Tinghua; Xu, Tingfa

2018-01-01

Image registration is widely used in many fields, but the adaptability of the existing methods is limited. This work proposes a novel image registration method with high precision for various complex applications. In this framework, the registration problem is divided into two stages. First, we detect and describe scale-invariant feature points using modified computer vision-oriented fast and rotated brief (ORB) algorithm, and a simple method to increase the performance of feature points matching is proposed. Second, we develop a new local constraint of rough selection according to the feature distances. Evidence shows that the existing matching techniques based on image features are insufficient for the images with sparse image details. Then, we propose a novel matching algorithm via geometric constraints, and establish local feature descriptions based on geometric invariances for the selected feature points. Subsequently, a new price function is constructed to evaluate the similarities between points and obtain exact matching pairs. Finally, we employ the progressive sample consensus method to remove wrong matches and calculate the space transform parameters. Experimental results on various complex image datasets verify that the proposed method is more robust and significantly reduces the rate of false matches while retaining more high-quality feature points. PMID:29293595

Discretization independence implies non-locality in 4D discrete quantum gravity

NASA Astrophysics Data System (ADS)

Dittrich, Bianca; Kamiński, Wojciech; Steinhaus, Sebastian

2014-12-01

The 4D Regge action is invariant under 5-1 and 4-2 Pachner moves, which define a subset of (local) changes of the triangulation. Given this fact, one might hope to find a local path integral measure that makes the quantum theory invariant under these moves and hence makes the theory partially triangulation invariant. We show that such a local invariant path integral measure does not exist for the 4D linearized Regge theory. To this end we uncover an interesting geometric interpretation for the Hessian of the 4D Regge action. This geometric interpretation will allow us to prove that the determinant of the Hessian of the 4D Regge action does not factorize over four-simplices or subsimplices. It furthermore allows us to determine configurations where this Hessian vanishes, which only appears to be the case in degenerate backgrounds or if one allows for different orientations of the simplices. We suggest a non-local measure factor that absorbs the non-local part of the determinant of the Hessian under 5-1 moves as well as a local measure factor that is preserved for very special configurations.

Lie group model neuromorphic geometric engine for real-time terrain reconstruction from stereoscopic aerial photos

NASA Astrophysics Data System (ADS)

Tsao, Thomas R.; Tsao, Doris

1997-04-01

In the 1980's, neurobiologist suggested a simple mechanism in primate visual cortex for maintaining a stable and invariant representation of a moving object. The receptive field of visual neurons has real-time transforms in response to motion, to maintain a stable representation. When the visual stimulus is changed due to motion, the geometric transform of the stimulus triggers a dual transform of the receptive field. This dual transform in the receptive fields compensates geometric variation in the stimulus. This process can be modelled using a Lie group method. The massive array of affine parameter sensing circuits will function as a smart sensor tightly coupled to the passive imaging sensor (retina). Neural geometric engine is a neuromorphic computing device simulating our Lie group model of spatial perception of primate's primal visual cortex. We have developed the computer simulation and experimented on realistic and synthetic image data, and performed a preliminary research of using analog VLSI technology for implementation of the neural geometric engine. We have benchmark tested on DMA's terrain data with their result and have built an analog integrated circuit to verify the computational structure of the engine. When fully implemented on ANALOG VLSI chip, we will be able to accurately reconstruct a 3D terrain surface in real-time from stereoscopic imagery.

Implementing quantum Ricci curvature

NASA Astrophysics Data System (ADS)

Klitgaard, N.; Loll, R.

2018-05-01

Quantum Ricci curvature has been introduced recently as a new, geometric observable characterizing the curvature properties of metric spaces, without the need for a smooth structure. Besides coordinate invariance, its key features are scalability, computability, and robustness. We demonstrate that these properties continue to hold in the context of nonperturbative quantum gravity, by evaluating the quantum Ricci curvature numerically in two-dimensional Euclidean quantum gravity, defined in terms of dynamical triangulations. Despite the well-known, highly nonclassical properties of the underlying quantum geometry, its Ricci curvature can be matched well to that of a five-dimensional round sphere.

Coherent multiscale image processing using dual-tree quaternion wavelets.

PubMed

Chan, Wai Lam; Choi, Hyeokho; Baraniuk, Richard G

2008-07-01

The dual-tree quaternion wavelet transform (QWT) is a new multiscale analysis tool for geometric image features. The QWT is a near shift-invariant tight frame representation whose coefficients sport a magnitude and three phases: two phases encode local image shifts while the third contains image texture information. The QWT is based on an alternative theory for the 2-D Hilbert transform and can be computed using a dual-tree filter bank with linear computational complexity. To demonstrate the properties of the QWT's coherent magnitude/phase representation, we develop an efficient and accurate procedure for estimating the local geometrical structure of an image. We also develop a new multiscale algorithm for estimating the disparity between a pair of images that is promising for image registration and flow estimation applications. The algorithm features multiscale phase unwrapping, linear complexity, and sub-pixel estimation accuracy.

BFV approach to geometric quantization

NASA Astrophysics Data System (ADS)

Fradkin, E. S.; Linetsky, V. Ya.

1994-12-01

A gauge-invariant approach to geometric quantization is developed. It yields a complete quantum description for dynamical systems with non-trivial geometry and topology of the phase space. The method is a global version of the gauge-invariant approach to quantization of second-class constraints developed by Batalin, Fradkin and Fradkina (BFF). Physical quantum states and quantum observables are respectively described by covariantly constant sections of the Fock bundle and the bundle of hermitian operators over the phase space with a flat connection defined by the nilpotent BVF-BRST operator. Perturbative calculation of the first non-trivial quantum correction to the Poisson brackets leads to the Chevalley cocycle known in deformation quantization. Consistency conditions lead to a topological quantization condition with metaplectic anomaly.

Quantum entanglement properties of geometrical and topological quantum gates

NASA Astrophysics Data System (ADS)

Sezer, Hasan Cavit; Duy, Hoang Ngoc; Heydari, Hoshang

2011-03-01

In this paper we will investigate the action of holonomic and topological quantum gates on different classes of four qubit states. In particular, we review the construction of holonomic quantum gate based on geometric phase and topological quantum gate based on braid group. Then, we investigate the entanglement properties of three different classes of four-qubit states based on geometric invariants. The result shows that entanglement properties of the two most generic classes of four-qubit states can be controlled by holonomic and topological quantum gate..

Braided Categories of Endomorphisms as Invariants for Local Quantum Field Theories

NASA Astrophysics Data System (ADS)

Giorgetti, Luca; Rehren, Karl-Henning

2018-01-01

We want to establish the "braided action" (defined in the paper) of the DHR category on a universal environment algebra as a complete invariant for completely rational chiral conformal quantum field theories. The environment algebra can either be a single local algebra, or the quasilocal algebra, both of which are model-independent up to isomorphism. The DHR category as an abstract structure is captured by finitely many data (superselection sectors, fusion, and braiding), whereas its braided action encodes the full dynamical information that distinguishes models with isomorphic DHR categories. We show some geometric properties of the "duality pairing" between local algebras and the DHR category that are valid in general (completely rational) chiral CFTs. Under some additional assumptions whose status remains to be settled, the braided action of its DHR category completely classifies a (prime) CFT. The approach does not refer to the vacuum representation, or the knowledge of the vacuum state.

Noniterative computation of infimum in H(infinity) optimisation for plants with invariant zeros on the j(omega)-axis

NASA Technical Reports Server (NTRS)

Chen, B. M.; Saber, A.

1993-01-01

A simple and noniterative procedure for the computation of the exact value of the infimum in the singular H(infinity)-optimization problem is presented, as a continuation of our earlier work. Our problem formulation is general and we do not place any restrictions in the finite and infinite zero structures of the system, and the direct feedthrough terms between the control input and the controlled output variables and between the disturbance input and the measurement output variables. Our method is applicable to a class of singular H(infinity)-optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output satisfy certain geometric conditions. In particular, the paper extends the result of earlier work by allowing these two transfer functions to have invariant zeros on the j(omega) axis.

Multiscale unfolding of real networks by geometric renormalization

NASA Astrophysics Data System (ADS)

García-Pérez, Guillermo; Boguñá, Marián; Serrano, M. Ángeles

2018-06-01

Symmetries in physical theories denote invariance under some transformation, such as self-similarity under a change of scale. The renormalization group provides a powerful framework to study these symmetries, leading to a better understanding of the universal properties of phase transitions. However, the small-world property of complex networks complicates application of the renormalization group by introducing correlations between coexisting scales. Here, we provide a framework for the investigation of complex networks at different resolutions. The approach is based on geometric representations, which have been shown to sustain network navigability and to reveal the mechanisms that govern network structure and evolution. We define a geometric renormalization group for networks by embedding them into an underlying hidden metric space. We find that real scale-free networks show geometric scaling under this renormalization group transformation. We unfold the networks in a self-similar multilayer shell that distinguishes the coexisting scales and their interactions. This in turn offers a basis for exploring critical phenomena and universality in complex networks. It also affords us immediate practical applications, including high-fidelity smaller-scale replicas of large networks and a multiscale navigation protocol in hyperbolic space, which betters those on single layers.

On the Convergence of an Implicitly Restarted Arnoldi Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lehoucq, Richard B.

We show that Sorensen's [35] implicitly restarted Arnoldi method (including its block extension) is simultaneous iteration with an implicit projection step to accelerate convergence to the invariant subspace of interest. By using the geometric convergence theory for simultaneous iteration due to Watkins and Elsner [43], we prove that an implicitly restarted Arnoldi method can achieve a super-linear rate of convergence to the dominant invariant subspace of a matrix. Moreover, we show how an IRAM computes a nested sequence of approximations for the partial Schur decomposition associated with the dominant invariant subspace of a matrix.

Conformal invariance and the metrication of the fundamental forces

NASA Astrophysics Data System (ADS)

Mannheim, Philip D.

2016-07-01

We revisit Weyl’s metrication (geometrization) of electromagnetism. We show that by making Weyl’s proposed geometric connection be pure imaginary, not only are we able to metricate electromagnetism, an underlying local conformal invariance makes the geometry be strictly Riemannian and prevents observational gravity from being complex. Via torsion, we achieve an analogous metrication for axial-vector fields. We generalize our procedure to Yang-Mills theories, and achieve a metrication of all the fundamental forces. Only in the gravity sector does our approach differ from the standard picture of fundamental forces, with our approach requiring that standard Einstein gravity be replaced by conformal gravity. We show that quantum conformal gravity is a consistent and unitary quantum gravitational theory, one that, unlike string theory, only requires four spacetime dimensions.

Koszul information geometry and Souriau Lie group thermodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barbaresco, Frédéric, E-mail: frederic.barbaresco@thalesgroup.com

The François Massieu 1869 idea to derive some mechanical and thermal properties of physical systems from 'Characteristic Functions', was developed by Gibbs and Duhem in thermodynamics with the concept of potentials, and introduced by Poincaré in probability. This paper deals with generalization of this Characteristic Function concept by Jean-Louis Koszul in Mathematics and by Jean-Marie Souriau in Statistical Physics. The Koszul-Vinberg Characteristic Function (KVCF) on convex cones will be presented as cornerstone of 'Information Geometry' theory, defining Koszul Entropy as Legendre transform of minus the logarithm of KVCF, and Fisher Information Metrics as hessian of these dual functions, invariant bymore » their automorphisms. In parallel, Souriau has extended the Characteristic Function in Statistical Physics looking for other kinds of invariances through co-adjoint action of a group on its momentum space, defining physical observables like energy, heat and momentum as pure geometrical objects. In covariant Souriau model, Gibbs equilibriums states are indexed by a geometric parameter, the Geometric (Planck) Temperature, with values in the Lie algebra of the dynamical Galileo/Poincaré groups, interpreted as a space-time vector, giving to the metric tensor a null Lie derivative. Fisher Information metric appears as the opposite of the derivative of Mean 'Moment map' by geometric temperature, equivalent to a Geometric Capacity or Specific Heat. These elements has been developed by author in [10][11].« less

The recognition of graphical patterns invariant to geometrical transformation of the models

NASA Astrophysics Data System (ADS)

Ileană, Ioan; Rotar, Corina; Muntean, Maria; Ceuca, Emilian

2010-11-01

In case that a pattern recognition system is used for images recognition (in robot vision, handwritten recognition etc.), the system must have the capacity to identify an object indifferently of its size or position in the image. The problem of the invariance of recognition can be approached in some fundamental modes. One may apply the similarity criterion used in associative recall. The original pattern is replaced by a mathematical transform that assures some invariance (e.g. the value of two-dimensional Fourier transformation is translation invariant, the value of Mellin transformation is scale invariant). In a different approach the original pattern is represented through a set of features, each of them being coded indifferently of the position, orientation or position of the pattern. Generally speaking, it is easy to obtain invariance in relation with one transformation group, but is difficult to obtain simultaneous invariance at rotation, translation and scale. In this paper we analyze some methods to achieve invariant recognition of images, particularly for digit images. A great number of experiments are due and the conclusions are underplayed in the paper.

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.

Novel symmetries in an interacting 𝒩 = 2 supersymmetric quantum mechanical model

NASA Astrophysics Data System (ADS)

Krishna, S.; Shukla, D.; Malik, R. P.

2016-07-01

In this paper, we demonstrate the existence of a set of novel discrete symmetry transformations in the case of an interacting 𝒩 = 2 supersymmetric quantum mechanical model of a system of an electron moving on a sphere in the background of a magnetic monopole and establish its interpretation in the language of differential geometry. These discrete symmetries are, over and above, the usual three continuous symmetries of the theory which together provide the physical realizations of the de Rham cohomological operators of differential geometry. We derive the nilpotent 𝒩 = 2 SUSY transformations by exploiting our idea of supervariable approach and provide geometrical meaning to these transformations in the language of Grassmannian translational generators on a (1, 2)-dimensional supermanifold on which our 𝒩 = 2 SUSY quantum mechanical model is generalized. We express the conserved supercharges and the invariance of the Lagrangian in terms of the supervariables (obtained after the imposition of the SUSY invariant restrictions) and provide the geometrical meaning to (i) the nilpotency property of the 𝒩 = 2 supercharges, and (ii) the SUSY invariance of the Lagrangian of our 𝒩 = 2 SUSY theory.

Soft phononic crystals with deformation-independent band gaps

PubMed Central

2017-01-01

Soft phononic crystals have the advantages over their stiff counterparts of being flexible and reconfigurable. Normally, the band gaps of soft phononic crystals will be modified after deformation due to both geometric and constitutive nonlinearity. Indeed these are important properties that can be exploited to tune the dynamic properties of the material. However, in some instances, it may be that one wishes to deform the medium while retaining the band gap structure. A special class of soft phononic crystals is described here with band gaps that are independent or almost-independent of the imposed mechanical deformation, which enables the design of phononic crystals with robust performance. This remarkable behaviour originates from transformation elasticity theory, which leaves the wave equation and the eigenfrequencies invariant after deformation. The necessary condition to achieve such a property is that the Lagrangian elasticity tensor of the hyperelastic material should be constant, i.e. independent of deformation. It is demonstrated that incompressible neo-Hookean materials exhibit such a unique property. Semilinear materials also possess this property under special loading conditions. Phononic crystals composed of these two materials are studied theoretically and the predictions of invariance, or the manner in which the response deviates from invariance, are confirmed via numerical simulation. PMID:28484331

Connecting orbits and invariant manifolds in the spatial restricted three-body problem

NASA Astrophysics Data System (ADS)

Gómez, G.; Koon, W. S.; Lo, M. W.; Marsden, J. E.; Masdemont, J.; Ross, S. D.

2004-09-01

The invariant manifold structures of the collinear libration points for the restricted three-body problem provide the framework for understanding transport phenomena from a geometrical point of view. In particular, the stable and unstable invariant manifold tubes associated with libration point orbits are the phase space conduits transporting material between primary bodies for separate three-body systems. These tubes can be used to construct new spacecraft trajectories, such as a 'Petit Grand Tour' of the moons of Jupiter. Previous work focused on the planar circular restricted three-body problem. This work extends the results to the three-dimensional case. Besides providing a full description of different kinds of libration motions in a large vicinity of these points, this paper numerically demonstrates the existence of heteroclinic connections between pairs of libration orbits, one around the libration point L1 and the other around L2. Since these connections are asymptotic orbits, no manoeuvre is needed to perform the transfer from one libration point orbit to the other. A knowledge of these orbits can be very useful in the design of missions such as the Genesis Discovery Mission, and may provide the backbone for other interesting orbits in the future.

Symmetries and conservation laws of a nonlinear sigma model with gravitino

NASA Astrophysics Data System (ADS)

Jost, Jürgen; Keßler, Enno; Tolksdorf, Jürgen; Wu, Ruijun; Zhu, Miaomiao

2018-06-01

We study the symmetries and invariances of a version of the action functional of the nonlinear sigma model with gravitino, as considered in Jost et al. (2017). The action is invariant under rescaled conformal transformations, super Weyl transformations, and diffeomorphisms. In particular cases the functional possesses a degenerate supersymmetry. The corresponding conservation laws lead to a geometric interpretation of the energy-momentum tensor and supercurrent as holomorphic sections of appropriate bundles.

On the deep structure of the blowing-up of curve singularities

NASA Astrophysics Data System (ADS)

Elias, Juan

2001-09-01

Let C be a germ of curve singularity embedded in (kn, 0). It is well known that the blowing-up of C centred on its closed ring, Bl(C), is a finite union of curve singularities. If C is reduced we can iterate this process and, after a finite number of steps, we find only non-singular curves. This is the desingularization process. The main idea of this paper is to linearize the blowing-up of curve singularities Bl(C) [rightward arrow] C. We perform this by studying the structure of [script O]Bl(C)/[script O]C as W-module, where W is a discrete valuation ring contained in [script O]C. Since [script O]Bl(C)/[script O]C is a torsion W-module, its structure is determined by the invariant factors of [script O]C in [script O]Bl(C). The set of invariant factors is called in this paper as the set of micro-invariants of C (see Definition 1·2).In the first section we relate the micro-invariants of C to the Hilbert function of C (Proposition 1·3), and we show how to compute them from the Hilbert function of some quotient of [script O]C (see Proposition 1·4).The main result of this paper is Theorem 3·3 where we give upper bounds of the micro-invariants in terms of the regularity, multiplicity and embedding dimension. As a corollary we improve and we recover some results of [6]. These bounds can be established as a consequence of the study of the Hilbert function of a filtration of ideals g = {g[r,i+1]}i [gt-or-equal, slanted] 0 of the tangent cone of [script O]C (see Section 2). The main property of g is that the ideals g[r,i+1] have initial degree bigger than the Castelnuovo-Mumford regularity of the tangent cone of [script O]C.Section 4 is devoted to computation the micro-invariants of branches; we show how to compute them from the semigroup of values of C and Bl(C) (Proposition 4·3). The case of monomial curve singularities is especially studied; we end Section 4 with some explicit computations.In the last section we study some geometric properties of C that can be deduced from special values of the micro-invariants, and we specially study the relationship of the micro-invariants with the Hilbert function of [script O]Bl(C). We end the paper studying the natural equisingularity criteria that can be defined from the micro-invariants and its relationship with some of the known equisingularity criteria.

The singularity structure of scale-invariant rank-2 Coulomb branches

NASA Astrophysics Data System (ADS)

Argyres, Philip C.; Long, Cody; Martone, Mario

2018-05-01

We compute the spectrum of scaling dimensions of Coulomb branch operators in 4d rank-2 N=2 superconformal field theories. Only a finite rational set of scaling dimensions is allowed. It is determined by using information about the global topology of the locus of metric singularities on the Coulomb branch, the special Kähler geometry near those singularities, and electric-magnetic duality monodromies along orbits of the U(1) R symmetry. A set of novel topological and geometric results are developed which promise to be useful for the study and classification of Coulomb branch geometries at all ranks.

Geometry Of Discrete Sets With Applications To Pattern Recognition

NASA Astrophysics Data System (ADS)

Sinha, Divyendu

1990-03-01

In this paper we present a new framework for discrete black and white images that employs only integer arithmetic. This framework is shown to retain the essential characteristics of the framework for Euclidean images. We propose two norms and based on them, the permissible geometric operations on images are defined. The basic invariants of our geometry are line images, structure of image and the corresponding local property of strong attachment of pixels. The permissible operations also preserve the 3x3 neighborhoods, area, and perpendicularity. The structure, patterns, and the inter-pattern gaps in a discrete image are shown to be conserved by the magnification and contraction process. Our notions of approximate congruence, similarity and symmetry are similar, in character, to the corresponding notions, for Euclidean images [1]. We mention two discrete pattern recognition algorithms that work purely with integers, and which fit into our framework. Their performance has been shown to be at par with the performance of traditional geometric schemes. Also, all the undesired effects of finite length registers in fixed point arithmetic that plague traditional algorithms, are non-existent in this family of algorithms.

The First Fundamental Theorem of Invariant Theory for the Orthosymplectic Supergroup

NASA Astrophysics Data System (ADS)

Lehrer, G. I.; Zhang, R. B.

2017-01-01

We give an elementary and explicit proof of the first fundamental theorem of invariant theory for the orthosymplectic supergroup by generalising the geometric method of Atiyah, Bott and Patodi to the supergroup context. We use methods from super-algebraic geometry to convert invariants of the orthosymplectic supergroup into invariants of the corresponding general linear supergroup on a different space. In this way, super Schur-Weyl-Brauer duality is established between the orthosymplectic supergroup of superdimension ( m|2 n) and the Brauer algebra with parameter m - 2 n. The result may be interpreted either in terms of the group scheme OSp( V) over C, where V is a finite dimensional super space, or as a statement about the orthosymplectic Lie supergroup over the infinite dimensional Grassmann algebra {Λ}. We take the latter point of view here, and also state a corresponding theorem for the orthosymplectic Lie superalgebra, which involves an extra invariant generator, the super-Pfaffian.

Fisher metric, geometric entanglement, and spin networks

NASA Astrophysics Data System (ADS)

Chirco, Goffredo; Mele, Fabio M.; Oriti, Daniele; Vitale, Patrizia

2018-02-01

Starting from recent results on the geometric formulation of quantum mechanics, we propose a new information geometric characterization of entanglement for spin network states in the context of quantum gravity. For the simple case of a single-link fixed graph (Wilson line), we detail the construction of a Riemannian Fisher metric tensor and a symplectic structure on the graph Hilbert space, showing how these encode the whole information about separability and entanglement. In particular, the Fisher metric defines an entanglement monotone which provides a notion of distance among states in the Hilbert space. In the maximally entangled gauge-invariant case, the entanglement monotone is proportional to a power of the area of the surface dual to the link thus supporting a connection between entanglement and the (simplicial) geometric properties of spin network states. We further extend such analysis to the study of nonlocal correlations between two nonadjacent regions of a generic spin network graph characterized by the bipartite unfolding of an intertwiner state. Our analysis confirms the interpretation of spin network bonds as a result of entanglement and to regard the same spin network graph as an information graph, whose connectivity encodes, both at the local and nonlocal level, the quantum correlations among its parts. This gives a further connection between entanglement and geometry.

Some New Results in Astrophysical Problems of Nonlinear Theory of Radiative Transfer

NASA Astrophysics Data System (ADS)

Pikichyan, H. V.

2017-07-01

In the interpretation of the observed astrophysical spectra, a decisive role is related to nonlinear problems of radiative transfer, because the processes of multiple interactions of matter of cosmic medium with the exciting intense radiation ubiquitously occur in astrophysical objects, and in their vicinities. Whereas, the intensity of the exciting radiation changes the physical properties of the original medium, and itself was modified, simultaneously, in a self-consistent manner under its influence. In the present report, we show that the consistent application of the principle of invariance in the nonlinear problem of bilateral external illumination of a scattering/absorbing one-dimensional anisotropic medium of finite geometrical thickness allows for simplifications that were previously considered as a prerogative only of linear problems. The nonlinear problem is analyzed through the three methods of the principle of invariance: (i) an adding of layers, (ii) its limiting form, described by differential equations of invariant imbedding, and (iii) a transition to the, so-called, functional equations of the "Ambartsumyan's complete invariance". Thereby, as an alternative to the Boltzmann equation, a new type of equations, so-called "kinetic equations of equivalence", are obtained. By the introduction of new functions - the so-called "linear images" of solution of nonlinear problem of radiative transfer, the linear structure of the solution of the nonlinear problem under study is further revealed. Linear images allow to convert naturally the statistical characteristics of random walk of a "single quantum" or their "beam of unit intensity", as well as widely known "probabilistic interpretation of phenomena of transfer", to the field of nonlinear problems. The structure of the equations obtained for determination of linear images is typical of linear problems.

Anisotropic Invariance and the Distribution of Quantum Correlations.

PubMed

Cheng, Shuming; Hall, Michael J W

2017-01-06

We report the discovery of two new invariants for three-qubit states which, similarly to the three-tangle, are invariant under local unitary transformations and permutations of the parties. These quantities have a direct interpretation in terms of the anisotropy of pairwise spin correlations. Applications include a universal ordering of pairwise quantum correlation measures for pure three-qubit states; trade-off relations for anisotropy, three-tangle and Bell nonlocality; strong monogamy relations for Bell inequalities, Einstein-Podolsky-Rosen steering inequalities, geometric discord and fidelity of remote state preparation (including results for arbitrary three-party states); and a statistical and reference-frame-independent form of quantum secret sharing.

Anisotropic Invariance and the Distribution of Quantum Correlations

NASA Astrophysics Data System (ADS)

Cheng, Shuming; Hall, Michael J. W.

2017-01-01

We report the discovery of two new invariants for three-qubit states which, similarly to the three-tangle, are invariant under local unitary transformations and permutations of the parties. These quantities have a direct interpretation in terms of the anisotropy of pairwise spin correlations. Applications include a universal ordering of pairwise quantum correlation measures for pure three-qubit states; trade-off relations for anisotropy, three-tangle and Bell nonlocality; strong monogamy relations for Bell inequalities, Einstein-Podolsky-Rosen steering inequalities, geometric discord and fidelity of remote state preparation (including results for arbitrary three-party states); and a statistical and reference-frame-independent form of quantum secret sharing.

On the dynamical and geometrical symmetries of Keplerian motion

NASA Astrophysics Data System (ADS)

Wulfman, Carl E.

2009-05-01

The dynamical symmetries of classical, relativistic and quantum-mechanical Kepler systems are considered to arise from geometric symmetries in PQET phase space. To establish their interconnection, the symmetries are related with the aid of a Lie-algebraic extension of Dirac's correspondence principle, a canonical transformation containing a Cunningham-Bateman inversion, and a classical limit involving a preliminary canonical transformation in ET space. The Lie-algebraic extension establishes the conditions under which the uncertainty principle allows the local dynamical symmetry of a quantum-mechanical system to be the same as the geometrical phase-space symmetry of its classical counterpart. The canonical transformation converts Poincaré-invariant free-particle systems into ISO(3,1) invariant relativistic systems whose classical limit produces Keplerian systems. Locally Cartesian relativistic PQET coordinates are converted into a set of eight conjugate position and momentum coordinates whose classical limit contains Fock projective momentum coordinates and the components of Runge-Lenz vectors. The coordinate systems developed via the transformations are those in which the evolution and degeneracy groups of the classical system are generated by Poisson-bracket operators that produce ordinary rotation, translation and hyperbolic motions in phase space. The way in which these define classical Keplerian symmetries and symmetry coordinates is detailed. It is shown that for each value of the energy of a Keplerian system, the Poisson-bracket operators determine two invariant functions of positions and momenta, which together with its regularized Hamiltonian, define the manifold in six-dimensional phase space upon which motions evolve.

Graph cuts with invariant object-interaction priors: application to intervertebral disc segmentation.

PubMed

Ben Ayed, Ismail; Punithakumar, Kumaradevan; Garvin, Gregory; Romano, Walter; Li, Shuo

2011-01-01

This study investigates novel object-interaction priors for graph cut image segmentation with application to intervertebral disc delineation in magnetic resonance (MR) lumbar spine images. The algorithm optimizes an original cost function which constrains the solution with learned prior knowledge about the geometric interactions between different objects in the image. Based on a global measure of similarity between distributions, the proposed priors are intrinsically invariant with respect to translation and rotation. We further introduce a scale variable from which we derive an original fixed-point equation (FPE), thereby achieving scale-invariance with only few fast computations. The proposed priors relax the need of costly pose estimation (or registration) procedures and large training sets (we used a single subject for training), and can tolerate shape deformations, unlike template-based priors. Our formulation leads to an NP-hard problem which does not afford a form directly amenable to graph cut optimization. We proceeded to a relaxation of the problem via an auxiliary function, thereby obtaining a nearly real-time solution with few graph cuts. Quantitative evaluations over 60 intervertebral discs acquired from 10 subjects demonstrated that the proposed algorithm yields a high correlation with independent manual segmentations by an expert. We further demonstrate experimentally the invariance of the proposed geometric attributes. This supports the fact that a single subject is sufficient for training our algorithm, and confirms the relevance of the proposed priors to disc segmentation.

GEMPIC: geometric electromagnetic particle-in-cell methods

NASA Astrophysics Data System (ADS)

Kraus, Michael; Kormann, Katharina; Morrison, Philip J.; Sonnendrücker, Eric

2017-08-01

We present a novel framework for finite element particle-in-cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining properties of a bracket, anti-symmetry and the Jacobi identity, as well as conservation of its Casimir invariants, implying that the semi-discrete system is still a Hamiltonian system. In order to obtain a fully discrete Poisson integrator, the semi-discrete bracket is used in conjunction with Hamiltonian splitting methods for integration in time. Techniques from finite element exterior calculus ensure conservation of the divergence of the magnetic field and Gauss' law as well as stability of the field solver. The resulting methods are gauge invariant, feature exact charge conservation and show excellent long-time energy and momentum behaviour. Due to the generality of our framework, these conservation properties are guaranteed independently of a particular choice of the finite element basis, as long as the corresponding finite element spaces satisfy certain compatibility conditions.

Approaches to linear local gauge-invariant observables in inflationary cosmologies

NASA Astrophysics Data System (ADS)

Fröb, Markus B.; Hack, Thomas-Paul; Khavkine, Igor

2018-06-01

We review and relate two recent complementary constructions of linear local gauge-invariant observables for cosmological perturbations in generic spatially flat single-field inflationary cosmologies. After briefly discussing their physical significance, we give explicit, covariant and mutually invertible transformations between the two sets of observables, thus resolving any doubts about their equivalence. In this way, we get a geometric interpretation and show the completeness of both sets of observables, while previously each of these properties was available only for one of them.

Protein structure similarity from Principle Component Correlation analysis.

PubMed

Zhou, Xiaobo; Chou, James; Wong, Stephen T C

2006-01-25

Owing to rapid expansion of protein structure databases in recent years, methods of structure comparison are becoming increasingly effective and important in revealing novel information on functional properties of proteins and their roles in the grand scheme of evolutionary biology. Currently, the structural similarity between two proteins is measured by the root-mean-square-deviation (RMSD) in their best-superimposed atomic coordinates. RMSD is the golden rule of measuring structural similarity when the structures are nearly identical; it, however, fails to detect the higher order topological similarities in proteins evolved into different shapes. We propose new algorithms for extracting geometrical invariants of proteins that can be effectively used to identify homologous protein structures or topologies in order to quantify both close and remote structural similarities. We measure structural similarity between proteins by correlating the principle components of their secondary structure interaction matrix. In our approach, the Principle Component Correlation (PCC) analysis, a symmetric interaction matrix for a protein structure is constructed with relationship parameters between secondary elements that can take the form of distance, orientation, or other relevant structural invariants. When using a distance-based construction in the presence or absence of encoded N to C terminal sense, there are strong correlations between the principle components of interaction matrices of structurally or topologically similar proteins. The PCC method is extensively tested for protein structures that belong to the same topological class but are significantly different by RMSD measure. The PCC analysis can also differentiate proteins having similar shapes but different topological arrangements. Additionally, we demonstrate that when using two independently defined interaction matrices, comparison of their maximum eigenvalues can be highly effective in clustering structurally or topologically similar proteins. We believe that the PCC analysis of interaction matrix is highly flexible in adopting various structural parameters for protein structure comparison.

Populating a Library of Reusable H-Boms Assessment of a Feasible Image Based Modeling Workflow

NASA Astrophysics Data System (ADS)

Santagati, C.; Lo Turco, M.; D'Agostino, G.

2017-08-01

The paper shows the intermediate results of a research activity aimed at populating a library of reusable Historical Building Object Models (H-BOMs) by testing a full digital workflow that takes advantages from using Structure from Motion (SfM) models and is centered on the geometrical/stylistic/materic analysis of the architectural element (portal, window, altar). The aim is to find common (invariant) and uncommon (variant) features in terms of identification of architectural parts and their relationships, geometrical rules, dimensions and proportions, construction materials and measure units, in order to model archetypal shapes from which it is possible to derive all the style variations. At this regard, a set of 14th - 16th century gothic portals of the catalan-aragonese architecture in Etnean area of Eastern Sicily has been studied and used to assess the feasibility of the identified workflow. This approach tries to answer the increasingly demand for guidelines and standards in the field of Cultural Heritage Conservation to create and manage semantic-aware 3D models able to include all the information (both geometrical and alphanumerical ones) concerning historical buildings and able to be reused in several projects.

QWT: Retrospective and New Applications

NASA Astrophysics Data System (ADS)

Xu, Yi; Yang, Xiaokang; Song, Li; Traversoni, Leonardo; Lu, Wei

Quaternion wavelet transform (QWT) achieves much attention in recent years as a new image analysis tool. In most cases, it is an extension of the real wavelet transform and complex wavelet transform (CWT) by using the quaternion algebra and the 2D Hilbert transform of filter theory, where analytic signal representation is desirable to retrieve phase-magnitude description of intrinsically 2D geometric structures in a grayscale image. In the context of color image processing, however, it is adapted to analyze the image pattern and color information as a whole unit by mapping sequential color pixels to a quaternion-valued vector signal. This paper provides a retrospective of QWT and investigates its potential use in the domain of image registration, image fusion, and color image recognition. It is indicated that it is important for QWT to induce the mechanism of adaptive scale representation of geometric features, which is further clarified through two application instances of uncalibrated stereo matching and optical flow estimation. Moreover, quaternionic phase congruency model is defined based on analytic signal representation so as to operate as an invariant feature detector for image registration. To achieve better localization of edges and textures in image fusion task, we incorporate directional filter bank (DFB) into the quaternion wavelet decomposition scheme to greatly enhance the direction selectivity and anisotropy of QWT. Finally, the strong potential use of QWT in color image recognition is materialized in a chromatic face recognition system by establishing invariant color features. Extensive experimental results are presented to highlight the exciting properties of QWT.

All Chern-Simons invariants of 4D, N = 1 gauged superform hierarchies

NASA Astrophysics Data System (ADS)

Becker, Katrin; Becker, Melanie; Linch, William D.; Randall, Stephen; Robbins, Daniel

2017-04-01

We give a geometric description of supersymmetric gravity/(non-)abelian p-form hierarchies in superspaces with 4D, N = 1 super-Poincaré invariance. These hierarchies give rise to Chern-Simons-like invariants, such as those of the 5D, N = 1 graviphoton and the eleven-dimensional 3-form but also generalizations such as Green-Schwarz-like/ BF -type couplings. Previous constructions based on prepotential superfields are reinterpreted in terms of p-forms in superspace thereby elucidating the underlying geometry. This vastly simplifies the calculations of superspace field-strengths, Bianchi identities, and Chern-Simons invariants. Using this, we prove the validity of a recursive formula for the conditions defining these actions for any such tensor hierarchy. Solving it at quadratic and cubic orders, we recover the known results for the BF -type and cubic Chern-Simons actions. As an application, we compute the quartic invariant ˜ AdAdAdA + . . . relevant, for example, to seven-dimensional supergravity compactifications.

Immortal homogeneous Ricci flows

NASA Astrophysics Data System (ADS)

Böhm, Christoph; Lafuente, Ramiro A.

2018-05-01

We show that for an immortal homogeneous Ricci flow solution any sequence of parabolic blow-downs subconverges to a homogeneous expanding Ricci soliton. This is established by constructing a new Lyapunov function based on curvature estimates which come from real geometric invariant theory.

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.

Sparse approximation of currents for statistics on curves and surfaces.

PubMed

Durrleman, Stanley; Pennec, Xavier; Trouvé, Alain; Ayache, Nicholas

2008-01-01

Computing, processing, visualizing statistics on shapes like curves or surfaces is a real challenge with many applications ranging from medical image analysis to computational geometry. Modelling such geometrical primitives with currents avoids feature-based approach as well as point-correspondence method. This framework has been proved to be powerful to register brain surfaces or to measure geometrical invariants. However, if the state-of-the-art methods perform efficiently pairwise registrations, new numerical schemes are required to process groupwise statistics due to an increasing complexity when the size of the database is growing. Statistics such as mean and principal modes of a set of shapes often have a heavy and highly redundant representation. We propose therefore to find an adapted basis on which mean and principal modes have a sparse decomposition. Besides the computational improvement, this sparse representation offers a way to visualize and interpret statistics on currents. Experiments show the relevance of the approach on 34 sets of 70 sulcal lines and on 50 sets of 10 meshes of deep brain structures.

On the properties of stochastic intermittency in rainfall processes.

PubMed

Molini, A; La, Barbera P; Lanza, L G

2002-01-01

In this work we propose a mixed approach to deal with the modelling of rainfall events, based on the analysis of geometrical and statistical properties of rain intermittency in time, combined with the predictability power derived from the analysis of no-rain periods distribution and from the binary decomposition of the rain signal. Some recent hypotheses on the nature of rain intermittency are reviewed too. In particular, the internal intermittent structure of a high resolution pluviometric time series covering one decade and recorded at the tipping bucket station of the University of Genova is analysed, by separating the internal intermittency of rainfall events from the inter-arrival process through a simple geometrical filtering procedure. In this way it is possible to associate no-rain intervals with a probability distribution both in virtue of their position within the event and their percentage. From this analysis, an invariant probability distribution for the no-rain periods within the events is obtained at different aggregation levels and its satisfactory agreement with a typical extreme value distribution is shown.

Structure analysis and spectroscopic characterization of 2-Fluoro-3-Methylpyridine-5-Boronic Acid with experimental (FT-IR, Raman, NMR and XRD) techniques and quantum chemical calculations

NASA Astrophysics Data System (ADS)

Alver, Özgür; Dikmen, Gökhan

2016-03-01

Possible stable conformers, geometrical molecular structures, vibrational properties as well as band assignments, nuclear magnetic shielding tensors of 2-Fluoro-3-Methylpyridine-5-Boronic Acid (2F3MP5BA) were studied experimentally and theoretically using FT-IR, Raman, (CP/MAS) NMR and XRD spectroscopic methods. FT-IR and Raman spectra were evaluated in the region of 3500-400 cm-1, and 3200-400 cm-1, respectively. The optimized geometric structures, vibrational wavenumbers and nuclear magnetic shielding tensors were examined using Becke-3-Lee-Yang-Parr (B3LYP) hybrid density functional theory method with 6-311++G(d, p) basis set. 1H, 13C NMR chemical shifts were calculated using the gauge invariant atomic orbital (GIAO) method. 1H, 13C, APT and HETCOR NMR experiments of title molecule were carried out in DMSO solution. 13C CP/MAS NMR measurement was done with 4 mm zirconium rotor and glycine was used as an external standard. Single crystal of 2F3MP5BA was also prepared for XRD measurements. Assignments of vibrational wavenumbers were also strengthened by calculating the total energy distribution (TED) values using scaled quantum mechanical (SQM) method.

iGRaND: an invariant frame for RGBD sensor feature detection and descriptor extraction with applications

NASA Astrophysics Data System (ADS)

Willis, Andrew R.; Brink, Kevin M.

2016-06-01

This article describes a new 3D RGBD image feature, referred to as iGRaND, for use in real-time systems that use these sensors for tracking, motion capture, or robotic vision applications. iGRaND features use a novel local reference frame derived from the image gradient and depth normal (hence iGRaND) that is invariant to scale and viewpoint for Lambertian surfaces. Using this reference frame, Euclidean invariant feature components are computed at keypoints which fuse local geometric shape information with surface appearance information. The performance of the feature for real-time odometry is analyzed and its computational complexity and accuracy is compared with leading alternative 3D features.

Unified field theory from the classical wave equation: Preliminary application to atomic and nuclear structure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Múnera, Héctor A., E-mail: hmunera@hotmail.com; Retired professor, Department of Physics, Universidad Nacional de Colombia, Bogotá, Colombia, South America

2016-07-07

It is postulated that there exists a fundamental energy-like fluid, which occupies the flat three-dimensional Euclidean space that contains our universe, and obeys the two basic laws of classical physics: conservation of linear momentum, and conservation of total energy; the fluid is described by the classical wave equation (CWE), which was Schrödinger’s first candidate to develop his quantum theory. Novel solutions for the CWE discovered twenty years ago are nonharmonic, inherently quantized, and universal in the sense of scale invariance, thus leading to quantization at all scales of the universe, from galactic clusters to the sub-quark world, and yielding amore » unified Lorentz-invariant quantum theory ab initio. Quingal solutions are isomorphic under both neo-Galilean and Lorentz transformations, and exhibit nother remarkable property: intrinsic unstability for large values of ℓ (a quantum number), thus limiting the size of each system at a given scale. Unstability and scale-invariance together lead to nested structures observed in our solar system; unstability may explain the small number of rows in the chemical periodic table, and nuclear unstability of nuclides beyond lead and bismuth. Quingal functions lend mathematical basis for Boscovich’s unified force (which is compatible with many pieces of evidence collected over the past century), and also yield a simple geometrical solution for the classical three-body problem, which is a useful model for electronic orbits in simple diatomic molecules. A testable prediction for the helicoidal-type force is suggested.« less

On Topological Indices of Certain Families of Nanostar Dendrimers.

PubMed

Husin, Mohamad Nazri; Hasni, Roslan; Arif, Nabeel Ezzulddin; Imran, Muhammad

2016-06-24

A topological index of graph G is a numerical parameter related to G which characterizes its molecular topology and is usually graph invariant. In the field of quantitative structure-activity (QSAR)/quantitative structure-activity structure-property (QSPR) research, theoretical properties of the chemical compounds and their molecular topological indices such as the Randić connectivity index, atom-bond connectivity (ABC) index and geometric-arithmetic (GA) index are used to predict the bioactivity of different chemical compounds. A dendrimer is an artificially manufactured or synthesized molecule built up from the branched units called monomers. In this paper, the fourth version of ABC index and the fifth version of GA index of certain families of nanostar dendrimers are investigated. We derive the analytical closed formulas for these families of nanostar dendrimers. The obtained results can be of use in molecular data mining, particularly in researching the uniqueness of tested (hyper-branched) molecular graphs.

Accurate single-scattering simulation of ice cloud using the invariant-imbedding T-matrix method and the physical-geometric optics method

NASA Astrophysics Data System (ADS)

Sun, B.; Yang, P.; Kattawar, G. W.; Zhang, X.

2017-12-01

The ice cloud single-scattering properties can be accurately simulated using the invariant-imbedding T-matrix method (IITM) and the physical-geometric optics method (PGOM). The IITM has been parallelized using the Message Passing Interface (MPI) method to remove the memory limitation so that the IITM can be used to obtain the single-scattering properties of ice clouds for sizes in the geometric optics regime. Furthermore, the results associated with random orientations can be analytically achieved once the T-matrix is given. The PGOM is also parallelized in conjunction with random orientations. The single-scattering properties of a hexagonal prism with height 400 (in units of lambda/2*pi, where lambda is the incident wavelength) and an aspect ratio of 1 (defined as the height over two times of bottom side length) are given by using the parallelized IITM and compared to the counterparts using the parallelized PGOM. The two results are in close agreement. Furthermore, the integrated single-scattering properties, including the asymmetry factor, the extinction cross-section, and the scattering cross-section, are given in a completed size range. The present results show a smooth transition from the exact IITM solution to the approximate PGOM result. Because the calculation of the IITM method has reached the geometric regime, the IITM and the PGOM can be efficiently employed to accurately compute the single-scattering properties of ice cloud in a wide spectral range.

Gibbsian Stationary Non-equilibrium States

NASA Astrophysics Data System (ADS)

De Carlo, Leonardo; Gabrielli, Davide

2017-09-01

We study the structure of stationary non-equilibrium states for interacting particle systems from a microscopic viewpoint. In particular we discuss two different discrete geometric constructions. We apply both of them to determine non reversible transition rates corresponding to a fixed invariant measure. The first one uses the equivalence of this problem with the construction of divergence free flows on the transition graph. Since divergence free flows are characterized by cyclic decompositions we can generate families of models from elementary cycles on the configuration space. The second construction is a functional discrete Hodge decomposition for translational covariant discrete vector fields. According to this, for example, the instantaneous current of any interacting particle system on a finite torus can be canonically decomposed in a gradient part, a circulation term and an harmonic component. All the three components are associated with functions on the configuration space. This decomposition is unique and constructive. The stationary condition can be interpreted as an orthogonality condition with respect to an harmonic discrete vector field and we use this decomposition to construct models having a fixed invariant measure.

Symmetry-Adapted Machine Learning for Tensorial Properties of Atomistic Systems.

PubMed

Grisafi, Andrea; Wilkins, David M; Csányi, Gábor; Ceriotti, Michele

2018-01-19

Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and transferability of these models are increased significantly by encoding into the learning procedure the fundamental symmetries of rotational and permutational invariance of scalar properties. However, the prediction of tensorial properties requires that the model respects the appropriate geometric transformations, rather than invariance, when the reference frame is rotated. We introduce a formalism that extends existing schemes and makes it possible to perform machine learning of tensorial properties of arbitrary rank, and for general molecular geometries. To demonstrate it, we derive a tensor kernel adapted to rotational symmetry, which is the natural generalization of the smooth overlap of atomic positions kernel commonly used for the prediction of scalar properties at the atomic scale. The performance and generality of the approach is demonstrated by learning the instantaneous response to an external electric field of water oligomers of increasing complexity, from the isolated molecule to the condensed phase.

Transport and Capture of Comets

NASA Astrophysics Data System (ADS)

Ross, S. D.; Koon, W. S.; Lo, M. W.; Marsden, J. E.

2001-11-01

The dynamics of comets and other solar system objects which have a three-body energy close to that of the collinear libration points are known to exhibit a complicated array of behaviors such as rapid transition between the interior and exterior Hill's regions, temporary capture, and collision. The invariant manifold structures of the collinear libration points for the restricted three-body problem, which exist for a range of energies, provide the framework for understanding these transport phenomena from a geometric point of view. In particular, the stable and unstable invariant manifold "tubes" associated to libration point orbits are the phase space conduits transporting material to and from the smaller primary body (e.g., Jupiter), and between primary bodies for separate three-body systems (e.g., Saturn and Jupiter). This point of view has worked well in describing the planar circular restricted three-body problem. The current work seeks to extend the results to three degrees of freedom. This work was supported by the National Science Foundation Grant No. KDI/ATM-9873133 under a contract with the Jet Propulsion Laboratory, NASA.

Symmetry-Adapted Machine Learning for Tensorial Properties of Atomistic Systems

NASA Astrophysics Data System (ADS)

Grisafi, Andrea; Wilkins, David M.; Csányi, Gábor; Ceriotti, Michele

2018-01-01

Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and transferability of these models are increased significantly by encoding into the learning procedure the fundamental symmetries of rotational and permutational invariance of scalar properties. However, the prediction of tensorial properties requires that the model respects the appropriate geometric transformations, rather than invariance, when the reference frame is rotated. We introduce a formalism that extends existing schemes and makes it possible to perform machine learning of tensorial properties of arbitrary rank, and for general molecular geometries. To demonstrate it, we derive a tensor kernel adapted to rotational symmetry, which is the natural generalization of the smooth overlap of atomic positions kernel commonly used for the prediction of scalar properties at the atomic scale. The performance and generality of the approach is demonstrated by learning the instantaneous response to an external electric field of water oligomers of increasing complexity, from the isolated molecule to the condensed phase.

Rare-event statistics and modular invariance

NASA Astrophysics Data System (ADS)

Nechaev, S. K.; Polovnikov, K.

2018-01-01

Simple geometric arguments based on constructing the Euclid orchard are presented, which explain the equivalence of various types of distributions that result from rare-event statistics. In particular, the spectral density of the exponentially weighted ensemble of linear polymer chains is examined for its number-theoretic properties. It can be shown that the eigenvalue statistics of the corresponding adjacency matrices in the sparse regime show a peculiar hierarchical structure and are described by the popcorn (Thomae) function discontinuous in the dense set of rational numbers. Moreover, the spectral edge density distribution exhibits Lifshitz tails, reminiscent of 1D Anderson localization. Finally, a continuous approximation for the popcorn function is suggested based on the Dedekind η-function, and the hierarchical ultrametric structure of the popcorn-like distributions is demonstrated to be related to hidden SL(2,Z) modular symmetry.

Gravity dual for a model of perception

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakayama, Yu, E-mail: nakayama@berkeley.edu

2011-01-15

One of the salient features of human perception is its invariance under dilatation in addition to the Euclidean group, but its non-invariance under special conformal transformation. We investigate a holographic approach to the information processing in image discrimination with this feature. We claim that a strongly coupled analogue of the statistical model proposed by Bialek and Zee can be holographically realized in scale invariant but non-conformal Euclidean geometries. We identify the Bayesian probability distribution of our generalized Bialek-Zee model with the GKPW partition function of the dual gravitational system. We provide a concrete example of the geometric configuration based onmore » a vector condensation model coupled with the Euclidean Einstein-Hilbert action. From the proposed geometry, we study sample correlation functions to compute the Bayesian probability distribution.« less

Universal freezing of quantum correlations within the geometric approach

PubMed Central

Cianciaruso, Marco; Bromley, Thomas R.; Roga, Wojciech; Lo Franco, Rosario; Adesso, Gerardo

2015-01-01

Quantum correlations in a composite system can be measured by resorting to a geometric approach, according to which the distance from the state of the system to a suitable set of classically correlated states is considered. Here we show that all distance functions, which respect natural assumptions of invariance under transposition, convexity, and contractivity under quantum channels, give rise to geometric quantifiers of quantum correlations which exhibit the peculiar freezing phenomenon, i.e., remain constant during the evolution of a paradigmatic class of states of two qubits each independently interacting with a non-dissipative decohering environment. Our results demonstrate from first principles that freezing of geometric quantum correlations is independent of the adopted distance and therefore universal. This finding paves the way to a deeper physical interpretation and future practical exploitation of the phenomenon for noisy quantum technologies. PMID:26053239

A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric constructions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pesin, Y.; Weiss, H.

1997-01-01

In this paper we establish the complete multifractal formalism for equilibrium measures for Holder continuous conformal expanding maps and expanding Markov Moran-like geometric constructions. Examples include Markov maps of an interval, beta transformations of an interval, rational maps with hyperbolic Julia sets, and conformal total endomorphisms. We also construct a Holder continuous homeomorphism of a compact metric space with an ergodic invariant measure of positive entropy for which the dimension spectrum is not convex, and hence the multifractal formalism fails.

Theoretical crystal chemistry of M{sub x}(TO{sub 4}){sub y} sulfates and selenates: Topological analysis and classification of suprapolyhedral invariants

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ilyushin, G. D.; Blatov, V. A.

2006-05-15

A geometric topological analysis of orthotetrahedral phases M{sub x}(TO{sub 4}){sub y} (T = S or Se) is performed for 46 sulfates and 17 selenates with the TOPOS 3.2 software package. The values of coordination sequences {l_brace}N{sub k}{r_brace} of T atoms are used as classification parameters of topologically different MTO nets. The crystal structures are analyzed within 12 coordination spheres of T sites and assigned to 26 topological types. It is established that only 7 types are common for the structures of sulfates and selenates, 16 types include only sulfates, and 3 types include only selenates. The average values of themore » bond lengths are determined: = 1.48(2) A and = 1.63(2) A. The hierarchical ordering of the crystal structure is performed using the concept of a polyhedral microensemble of the structure.« less

How many invariant polynomials are needed to decide local unitary equivalence of qubit states?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maciążek, Tomasz; Faculty of Physics, University of Warsaw, ul. Hoża 69, 00-681 Warszawa; Oszmaniec, Michał

2013-09-15

Given L-qubit states with the fixed spectra of reduced one-qubit density matrices, we find a formula for the minimal number of invariant polynomials needed for solving local unitary (LU) equivalence problem, that is, problem of deciding if two states can be connected by local unitary operations. Interestingly, this number is not the same for every collection of the spectra. Some spectra require less polynomials to solve LU equivalence problem than others. The result is obtained using geometric methods, i.e., by calculating the dimensions of reduced spaces, stemming from the symplectic reduction procedure.

Higher-dimensional attractors with absolutely continuous invariant probability

NASA Astrophysics Data System (ADS)

Bocker, Carlos; Bortolotti, Ricardo

2018-05-01

Consider a dynamical system given by , where E is a linear expanding map of , C is a linear contracting map of and f is in . We provide sufficient conditions for E that imply the existence of an open set of pairs for which the corresponding dynamic T admits a unique absolutely continuous invariant probability. A geometrical characteristic of transversality between self-intersections of images of is present in the dynamic of the maps in . In addition, we give a condition between E and C under which it is possible to perturb f to obtain a pair in .

The Camassa-Holm equation as an incompressible Euler equation: A geometric point of view

NASA Astrophysics Data System (ADS)

Gallouët, Thomas; Vialard, François-Xavier

2018-04-01

The group of diffeomorphisms of a compact manifold endowed with the L2 metric acting on the space of probability densities gives a unifying framework for the incompressible Euler equation and the theory of optimal mass transport. Recently, several authors have extended optimal transport to the space of positive Radon measures where the Wasserstein-Fisher-Rao distance is a natural extension of the classical L2-Wasserstein distance. In this paper, we show a similar relation between this unbalanced optimal transport problem and the Hdiv right-invariant metric on the group of diffeomorphisms, which corresponds to the Camassa-Holm (CH) equation in one dimension. Geometrically, we present an isometric embedding of the group of diffeomorphisms endowed with this right-invariant metric in the automorphisms group of the fiber bundle of half densities endowed with an L2 type of cone metric. This leads to a new formulation of the (generalized) CH equation as a geodesic equation on an isotropy subgroup of this automorphisms group; On S1, solutions to the standard CH thus give radially 1-homogeneous solutions of the incompressible Euler equation on R2 which preserves a radial density that has a singularity at 0. An other application consists in proving that smooth solutions of the Euler-Arnold equation for the Hdiv right-invariant metric are length minimizing geodesics for sufficiently short times.

(3+1)-Dimensional topologically massive 2-form gauge theory: geometrical superfield approach

NASA Astrophysics Data System (ADS)

Kumar, R.; Mukhopadhyay, Debmalya

2018-06-01

We derive the complete set of off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations corresponding to the combined "scalar" and "vector" gauge symmetry transformations for the (3+1)-dimensional (4D) topologically massive non-Abelian (B \\wedge F) theory with the help of geometrical superfield formalism. For this purpose, we use three horizontality conditions (HCs). The first HC produces the (anti-)BRST transformations for the 1-form gauge field and corresponding (anti-)ghost fields whereas the second HC yields the (anti-)BRST transformations for 2-form field and associated (anti-)ghost fields. The integrability of second HC produces third HC. The latter HC produces the (anti-)BRST symmetry transformations for the compensating auxiliary vector field and corresponding ghosts. We obtain five (anti-)BRST invariant Curci-Ferrari (CF)-type conditions which emerge very naturally as the off-shoots of superfield formalism. Out of five CF-type conditions, two are fermionic in nature. These CF-type conditions play a decisive role in providing the absolute anticommutativity of the (anti-)BRST transformations and also responsible for the derivation of coupled but equivalent (anti-)BRST invariant Lagrangian densities. Furthermore, we capture the (anti-)BRST invariance of the coupled Lagrangian densities in terms of the superfields and translation generators along the Grassmannian directions θ and \\bar{θ }.

Enhanced definition and required examples of common datum imposed by ISO standard

NASA Astrophysics Data System (ADS)

Yan, Yiqing; Bohn, Martin

2017-12-01

According to the ISO Geometrical Product Specifications (GPS), the establishment and definition of common datum for geometrical components are not fully defined. There are two main limitations of this standard. Firstly: the explications of ISO examples of common datums are not matched with their corresponding definitions, and secondly: a full definition of common datum is missing. This paper suggests a new approach for an enhanced definition and concrete examples of common datum and proposes a holistic methodology for establishment of common datum for each geometrical component. This research is based on the analysis of physical behaviour of geometrical components, orientation constraints and invariance classes of datums. This approach fills the definition gaps of common datum based on ISO GPS, thereby eliminating those deficits. As a result, an improved methodology for a fully functional defined definition of common datum was formulated.

Geometric descriptions of entangled states by auxiliary varieties

NASA Astrophysics Data System (ADS)

Holweck, Frédéric; Luque, Jean-Gabriel; Thibon, Jean-Yves

2012-10-01

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 × 2 × (n + 1), for n ⩾ 1, quantum systems and a new description with the 2 × 3 × 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.

Motions, efforts and actuations in constrained dynamic systems: a multi-link open-chain example

NASA Astrophysics Data System (ADS)

Duke Perreira, N.

1999-08-01

The effort-motion method, which describes the dynamics of open- and closed-chain topologies of rigid bodies interconnected with revolute and prismatic pairs, is interpreted geometrically. Systems are identified for which the simultaneous control of forces and velocities is desirable, and a representative open-chain system is selected for use in the ensuing analysis. Gauge invariant transformations are used to recast the commonly used kinetic and kinematic equations into a dimensional gauge invariant form. Constraint elimination techniques based on singular value decompositions then recast the invariant equations into orthogonal and reciprocal sets of motion and effort equations written in state variable form. The ideal actuation is found that simultaneously achieves the obtainable portions of the desired constraining efforts and motions. The performance is then evaluated of using the actuation closest to the ideal actuation.

Drainage networks after wildfire

USGS Publications Warehouse

Kinner, D.A.; Moody, J.A.

2005-01-01

Predicting runoff and erosion from watersheds burned by wildfires requires an understanding of the three-dimensional structure of both hillslope and channel drainage networks. We investigate the small-and large-scale structures of drainage networks using field studies and computer analysis of 30-m digital elevation model. Topologic variables were derived from a composite 30-m DEM, which included 14 order 6 watersheds within the Pikes Peak batholith. Both topologic and hydraulic variables were measured in the field in two smaller burned watersheds (3.7 and 7.0 hectares) located within one of the order 6 watersheds burned by the 1996 Buffalo Creek Fire in Central Colorado. Horton ratios of topologic variables (stream number, drainage area, stream length, and stream slope) for small-scale and large-scale watersheds are shown to scale geometrically with stream order (i.e., to be scale invariant). However, the ratios derived for the large-scale drainage networks could not be used to predict the rill and gully drainage network structure. Hydraulic variables (width, depth, cross-sectional area, and bed roughness) for small-scale drainage networks were found to be scale invariant across 3 to 4 stream orders. The relation between hydraulic radius and cross-sectional area is similar for rills and gullies, suggesting that their geometry can be treated similarly in hydraulic modeling. Additionally, the rills and gullies have relatively small width-to-depth ratios, implying sidewall friction may be important to the erosion and evolutionary process relative to main stem channels.

Spatiotemporal canards in neural field equations

NASA Astrophysics Data System (ADS)

Avitabile, D.; Desroches, M.; Knobloch, E.

2017-04-01

Canards are special solutions to ordinary differential equations that follow invariant repelling slow manifolds for long time intervals. In realistic biophysical single-cell models, canards are responsible for several complex neural rhythms observed experimentally, but their existence and role in spatially extended systems is largely unexplored. We identify and describe a type of coherent structure in which a spatial pattern displays temporal canard behavior. Using interfacial dynamics and geometric singular perturbation theory, we classify spatiotemporal canards and give conditions for the existence of folded-saddle and folded-node canards. We find that spatiotemporal canards are robust to changes in the synaptic connectivity and firing rate. The theory correctly predicts the existence of spatiotemporal canards with octahedral symmetry in a neural field model posed on the unit sphere.

Quaternions, Torsion and the Physical Vacuum: Theories of M. Sachs and G. Shipov Compared

NASA Astrophysics Data System (ADS)

Cyganski, David; Page, William S.

Of several developments of unified field theories in the spirit of Einstein's original objective of a fully geometric description of all classical fields as well as quantum mechanics, two are particularly noteworthy. The works of Mendel Sachs and Gennady Shipov stand apart as major life works comprising tens of papers, several monographs and decades of effort. Direct comparison of these theories is hampered however by differences in notation and conceptual view-point. Despite these differences, there are many parallels between the fundamental mathematical structures appearing in each. In this paper we discuss the main tenets of the two approaches and demonstrate that they both give rise to a factorization of the invariant interval of general relativity.

Dielectric-based subwavelength metallic meanders for wide-angle band absorbers.

PubMed

Shen, Su; Qiao, Wen; Ye, Yan; Zhou, Yun; Chen, Linsen

2015-01-26

We propose nano-meanders that can achieve wide-angle band absorption in visible regime. The nano-meander consists of a subwavelength dielectric grating covered by continuous ultra-thin Aluminum film (less than one tenth of the incident wavelength). The excited photonic resonant modes, such as cavity mode, surface plasmonic mode and Rayleigh-Wood anomaly, are discussed in detail. Nearly total resonant absorption due to funneling mechanism in the air nano-groove is almost invariant with large incident angle in transverse magnetic polarization. From both the structural geometry and the nanofabrication point of view, the light absorber has a very simple geometrical structure and it is easy to be integrated into complex photonic devices. The highly efficient angle-robust light absorber can be potential candidate for a range of passive and active photonic applications, including solar-energy harvesting as well as producing artificial colors on a large scale substrate.

Structural, vibrational and nuclear magnetic resonance investigations of 4-bromoisoquinoline by experimental and theoretical DFT methods.

PubMed

Arjunan, V; Thillai Govindaraja, S; Jayapraksh, A; Mohan, S

2013-04-15

Quantum chemical calculations of energy, structural parameters and vibrational wavenumbers of 4-bromoisoquinoline (4BIQ) were carried out by using B3LYP method using 6-311++G(**), cc-pVTZ and LANL2DZ basis sets. The optimised geometrical parameters obtained by DFT calculations are in good agreement with electron diffraction data. Interpretations of the experimental FTIR and FT-Raman spectra have been reported with the aid of the theoretical wavenumbers. The differences between the observed and scaled wavenumber values of most of the fundamentals are very small. The thermodynamic parameters have also been computed. Electronic properties of the molecule were discussed through the molecular electrostatic potential surface, HOMO-LUMO energy gap and NBO analysis. To provide precise assignments of (1)H and (13)CNMR spectra, isotropic shielding and chemical shifts were calculated with the Gauge-Invariant Atomic Orbital (GIAO) method. Copyright © 2013 Elsevier B.V. All rights reserved.

Estimation of the Invariance of Factor Structures Across Sex and Race with Implications for Hypothesis Testing

ERIC Educational Resources Information Center

Katzenmeyer, W. G.; Stenner, A. Jackson

1977-01-01

The problem of demonstrating invariance of factor structures across criterion groups is addressed. Procedures are outlined which combine the replication of factor structures across sex-race groups with use of the coefficient of invariance to demonstrate the level of invariance associated with factors identified in a self concept measure.…

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.

Electromagnetic wave propagating along a space curve

NASA Astrophysics Data System (ADS)

Lai, Meng-Yun; Wang, Yong-Long; Liang, Guo-Hua; Wang, Fan; Zong, Hong-Shi

2018-03-01

By using the thin-layer approach, we derive the effective equation for the electromagnetic wave propagating along a space curve. We find intrinsic spin-orbit, extrinsic spin-orbit, and extrinsic orbital angular-momentum and intrinsic orbital angular-momentum couplings induced by torsion, which can lead to geometric phase, spin, and orbital Hall effects. And we show the helicity inversion induced by curvature that can convert a right-handed circularly polarized electromagnetic wave into a left-handed polarized one, vice versa. Finally, we demonstrate that the gauge invariance of the effective dynamics is protected by the geometrically induced gauge potential.

Formation of propagation invariant laser beams with anamorphic optical systems

NASA Astrophysics Data System (ADS)

Soskind, Y. G.

2015-03-01

Propagation invariant structured laser beams play an important role in several photonics applications. A majority of propagation invariant beams are usually produced in the form of laser modes emanating from stable laser cavities. This work shows that anamorphic optical systems can be effectively employed to transform input propagation invariant laser beams and produce a variety of alternative propagation invariant structured laser beam distributions with different shapes and phase structures. This work also presents several types of anamorphic lens systems suitable for transforming the input laser modes into a variety of structured propagation invariant beams. The transformations are applied to different laser mode types, including Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian field distributions. The influence of the relative azimuthal orientation between the input laser modes and the anamorphic optical systems on the resulting transformed propagation invariant beams is presented as well.

Discrete Thermodynamics

DOE PAGES

Margolin, L. G.; Hunter, A.

2017-10-18

Here, we consider the dependence of velocity probability distribution functions on the finite size of a thermodynamic system. We are motivated by applications to computational fluid dynamics, hence discrete thermodynamics. We then begin by describing a coarsening process that represents geometric renormalization. Then, based only on the requirements of conservation, we demonstrate that the pervasive assumption of local thermodynamic equilibrium is not form invariant. We develop a perturbative correction that restores form invariance to second-order in a small parameter associated with macroscopic gradients. Finally, we interpret the corrections in terms of unresolved kinetic energy and discuss the implications of ourmore » results both in theory and as applied to numerical simulation.« less

Discrete Thermodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Margolin, L. G.; Hunter, A.

Here, we consider the dependence of velocity probability distribution functions on the finite size of a thermodynamic system. We are motivated by applications to computational fluid dynamics, hence discrete thermodynamics. We then begin by describing a coarsening process that represents geometric renormalization. Then, based only on the requirements of conservation, we demonstrate that the pervasive assumption of local thermodynamic equilibrium is not form invariant. We develop a perturbative correction that restores form invariance to second-order in a small parameter associated with macroscopic gradients. Finally, we interpret the corrections in terms of unresolved kinetic energy and discuss the implications of ourmore » results both in theory and as applied to numerical simulation.« less

Failure detection and identification

NASA Technical Reports Server (NTRS)

Massoumnia, Mohammad-Ali; Verghese, George C.; Willsky, Alan S.

1989-01-01

Using the geometric concept of an unobservability subspace, a solution is given to the problem of detecting and identifying control system component failures in linear, time-invariant systems. Conditions are developed for the existence of a causal, linear, time-invariant processor that can detect and uniquely identify a component failure, first for the case where components can fail simultaneously, and then for the case where they fail only one at a time. Explicit design algorithms are provided when these conditions are satisfied. In addition to time-domain solvability conditions, frequency-domain interpretations of the results are given, and connections are drawn with results already available in the literature.

Invariant Geometric Evolutions of Surfaces and Volumetric Smoothing

DTIC Science & Technology

1994-04-15

1991. [40] D. G. Lowe, "Organization of smooth image curves at multiple scales," International Journal of Computer Vision 3, pp. 119-130, 1989. [41] E ... Lutwak , "On some affine isoperimetric inequalities," J. Differential Geometry 23, pp. 1-13, 1986. [42] F. Mokhatarian and A. Mackworth, "A theory of

A QR Code Based Zero-Watermarking Scheme for Authentication of Medical Images in Teleradiology Cloud

PubMed Central

Seenivasagam, V.; Velumani, R.

2013-01-01

Healthcare institutions adapt cloud based archiving of medical images and patient records to share them efficiently. Controlled access to these records and authentication of images must be enforced to mitigate fraudulent activities and medical errors. This paper presents a zero-watermarking scheme implemented in the composite Contourlet Transform (CT)—Singular Value Decomposition (SVD) domain for unambiguous authentication of medical images. Further, a framework is proposed for accessing patient records based on the watermarking scheme. The patient identification details and a link to patient data encoded into a Quick Response (QR) code serves as the watermark. In the proposed scheme, the medical image is not subjected to degradations due to watermarking. Patient authentication and authorized access to patient data are realized on combining a Secret Share with the Master Share constructed from invariant features of the medical image. The Hu's invariant image moments are exploited in creating the Master Share. The proposed system is evaluated with Checkmark software and is found to be robust to both geometric and non geometric attacks. PMID:23970943

A QR code based zero-watermarking scheme for authentication of medical images in teleradiology cloud.

PubMed

Seenivasagam, V; Velumani, R

2013-01-01

Healthcare institutions adapt cloud based archiving of medical images and patient records to share them efficiently. Controlled access to these records and authentication of images must be enforced to mitigate fraudulent activities and medical errors. This paper presents a zero-watermarking scheme implemented in the composite Contourlet Transform (CT)-Singular Value Decomposition (SVD) domain for unambiguous authentication of medical images. Further, a framework is proposed for accessing patient records based on the watermarking scheme. The patient identification details and a link to patient data encoded into a Quick Response (QR) code serves as the watermark. In the proposed scheme, the medical image is not subjected to degradations due to watermarking. Patient authentication and authorized access to patient data are realized on combining a Secret Share with the Master Share constructed from invariant features of the medical image. The Hu's invariant image moments are exploited in creating the Master Share. The proposed system is evaluated with Checkmark software and is found to be robust to both geometric and non geometric attacks.

Constancy and trade-offs in the neuroanatomical and metabolic design of the cerebral cortex

PubMed Central

Karbowski, Jan

2014-01-01

Mammalian brains span about four orders of magnitude in cortical volume and have to operate in different environments that require diverse behavioral skills. Despite these geometric and behavioral diversities, the examination of cerebral cortex across species reveals that it contains a substantial number of conserved characteristics that are associated with neuroanatomy and metabolism, i.e., with neuronal connectivity and function. Some of these cortical constants or invariants have been known for a long time but not sufficiently appreciated, and others were only recently discovered. The focus of this review is to present the cortical invariants and discuss their role in the efficient information processing. Global conservation in neuroanatomy and metabolism, as well as their correlated regional and developmental variability suggest that these two parallel systems are mutually coupled. It is argued that energetic constraint on cortical organization can be strong if cerebral blood supplied is either below or above a certain level, and it is rather soft otherwise. Moreover, because maximization or minimization of parameters associated with cortical connectivity, function and cost often leads to conflicts in design, it is argued that the architecture of the cerebral cortex is a result of structural and functional compromises. PMID:24574975

Asymptotics with a positive cosmological constant: I. Basic framework

NASA Astrophysics Data System (ADS)

Ashtekar, Abhay; Bonga, Béatrice; Kesavan, Aruna

2015-01-01

The asymptotic structure of the gravitational field of isolated systems has been analyzed in great detail in the case when the cosmological constant Λ is zero. The resulting framework lies at the foundation of research in diverse areas in gravitational science. Examples include: (i) positive energy theorems in geometric analysis; (ii) the coordinate invariant characterization of gravitational waves in full, nonlinear general relativity; (iii) computations of the energy-momentum emission in gravitational collapse and binary mergers in numerical relativity and relativistic astrophysics; and (iv) constructions of asymptotic Hilbert spaces to calculate S-matrices and analyze the issue of information loss in the quantum evaporation of black holes. However, by now observations have led to a strong consensus that Λ is positive in our universe. In this paper we show that, unfortunately, the standard framework does not extend from the Λ =0 case to the Λ \\gt 0 case in a physically useful manner. In particular, we do not have positive energy theorems, nor an invariant notion of gravitational waves in the nonlinear regime, nor asymptotic Hilbert spaces in dynamical situations of semi-classical gravity. A suitable framework to address these conceptual issues of direct physical importance is developed in subsequent papers.

Groups of adjacent contour segments for object detection.

PubMed

Ferrari, V; Fevrier, L; Jurie, F; Schmid, C

2008-01-01

We present a family of scale-invariant local shape features formed by chains of k connected, roughly straight contour segments (kAS), and their use for object class detection. kAS are able to cleanly encode pure fragments of an object boundary, without including nearby clutter. Moreover, they offer an attractive compromise between information content and repeatability, and encompass a wide variety of local shape structures. We also define a translation and scale invariant descriptor encoding the geometric configuration of the segments within a kAS, making kAS easy to reuse in other frameworks, for example as a replacement or addition to interest points. Software for detecting and describing kAS is released on lear.inrialpes.fr/software. We demonstrate the high performance of kAS within a simple but powerful sliding-window object detection scheme. Through extensive evaluations, involving eight diverse object classes and more than 1400 images, we 1) study the evolution of performance as the degree of feature complexity k varies and determine the best degree; 2) show that kAS substantially outperform interest points for detecting shape-based classes; 3) compare our object detector to the recent, state-of-the-art system by Dalal and Triggs [4].

Modular amplitudes and flux-superpotentials on elliptic Calabi-Yau fourfolds

NASA Astrophysics Data System (ADS)

Cota, Cesar Fierro; Klemm, Albrecht; Schimannek, Thorsten

2018-01-01

We discuss the period geometry and the topological string amplitudes on elliptically fibered Calabi-Yau fourfolds in toric ambient spaces. In particular, we describe a general procedure to fix integral periods. Using some elementary facts from homological mirror symmetry we then obtain Bridgelands involution and its monodromy action on the integral basis for non-singular elliptically fibered fourfolds. The full monodromy group contains a subgroup that acts as PSL(2,Z) on the Kähler modulus of the fiber and we analyze the consequences of this modularity for the genus zero and genus one amplitudes as well as the associated geometric invariants. We find holomorphic anomaly equations for the amplitudes, reflecting precisely the failure of exact PSL(2,Z) invariance that relates them to quasi-modular forms. Finally we use the integral basis of periods to study the horizontal flux superpotential and the leading order Kähler potential for the moduli fields in F-theory compactifications globally on the complex structure moduli space. For a particular example we verify attractor behaviour at the generic conifold given an aligned choice of flux which we expect to be universal. Furthermore we analyze the superpotential at the orbifold points but find no stable vacua.

Fractal dimension and nonlinear dynamical processes

NASA Astrophysics Data System (ADS)

McCarty, Robert C.; Lindley, John P.

1993-11-01

Mandelbrot, Falconer and others have demonstrated the existence of dimensionally invariant geometrical properties of non-linear dynamical processes known as fractals. Barnsley defines fractal geometry as an extension of classical geometry. Such an extension, however, is not mathematically trivial Of specific interest to those engaged in signal processing is the potential use of fractal geometry to facilitate the analysis of non-linear signal processes often referred to as non-linear time series. Fractal geometry has been used in the modeling of non- linear time series represented by radar signals in the presence of ground clutter or interference generated by spatially distributed reflections around the target or a radar system. It was recognized by Mandelbrot that the fractal geometries represented by man-made objects had different dimensions than the geometries of the familiar objects that abound in nature such as leaves, clouds, ferns, trees, etc. The invariant dimensional property of non-linear processes suggests that in the case of acoustic signals (active or passive) generated within a dispersive medium such as the ocean environment, there exists much rich structure that will aid in the detection and classification of various objects, man-made or natural, within the medium.

Strings on complex multiplication tori and rational conformal field theory with matrix level

NASA Astrophysics Data System (ADS)

Nassar, Ali

Conformal invariance in two dimensions is a powerful symmetry. Two-dimensional quantum field theories which enjoy conformal invariance, i.e., conformal field theories (CFTs) are of great interest in both physics and mathematics. CFTs describe the dynamics of the world sheet in string theory where conformal symmetry arises as a remnant of reparametrization invariance of the world-sheet coordinates. In statistical mechanics, CFTs describe the critical points of second order phase transitions. On the mathematics side, conformal symmetry gives rise to infinite dimensional chiral algebras like the Virasoro algebra or extensions thereof. This gave rise to the study of vertex operator algebras (VOAs) which is an interesting branch of mathematics. Rational conformal theories are a simple class of CFTs characterized by a finite number of representations of an underlying chiral algebra. The chiral algebra leads to a set of Ward identities which gives a complete non-perturbative solution of the RCFT. Identifying the chiral algebra of an RCFT is a very important step in solving it. Particularly interesting RCFTs are the ones which arise from the compactification of string theory as sigma-models on a target manifold M. At generic values of the geometric moduli of M, the corresponding CFT is not rational. Rationality can arise at particular values of the moduli of M. At these special values of the moduli, the chiral algebra is extended. This interplay between the geometric picture and the algebraic description encoded in the chiral algebra makes CFTs/RCFTs a perfect link between physics and mathematics. It is always useful to find a geometric interpretation of a chiral algebra in terms of a sigma-model on some target manifold M. Then the next step is to figure out the conditions on the geometric moduli of M which gives a RCFT. In this thesis, we limit ourselves to the simplest class of string compactifications, i.e., strings on tori. As Gukov and Vafa proved, rationality selects the complex-multiplication tori. On the other hand, the study of the matrix-level affine algebra Um,K is motivated by conformal field theory and the fractional quantum Hall effect. Gannon completed the classification of U m,K modular-invariant partition functions. Here we connect the algebra U2,K to strings on 2-tori describable by rational conformal field theories. We point out that the rational conformal field theories describing strings on complex-multiplication tori have characters and partition functions identical to those of the matrix-level algebra Um,K. This connection makes obvious that the rational theories are dense in the moduli space of strings on Tm, and may prove useful in other ways.

LDFT-based watermarking resilient to local desynchronization attacks.

PubMed

Tian, Huawei; Zhao, Yao; Ni, Rongrong; Qin, Lunming; Li, Xuelong

2013-12-01

Up to now, a watermarking scheme that is robust against desynchronization attacks (DAs) is still a grand challenge. Most image watermarking resynchronization schemes in literature can survive individual global DAs (e.g., rotation, scaling, translation, and other affine transforms), but few are resilient to challenging cropping and local DAs. The main reason is that robust features for watermark synchronization are only globally invariable rather than locally invariable. In this paper, we present a blind image watermarking resynchronization scheme against local transform attacks. First, we propose a new feature transform named local daisy feature transform (LDFT), which is not only globally but also locally invariable. Then, the binary space partitioning (BSP) tree is used to partition the geometrically invariant LDFT space. In the BSP tree, the location of each pixel is fixed under global transform, local transform, and cropping. Lastly, the watermarking sequence is embedded bit by bit into each leaf node of the BSP tree by using the logarithmic quantization index modulation watermarking embedding method. Simulation results show that the proposed watermarking scheme can survive numerous kinds of distortions, including common image-processing attacks, local and global DAs, and noninvertible cropping.

Detection of ferromagnetic target based on mobile magnetic gradient tensor system

NASA Astrophysics Data System (ADS)

Gang, Y. I. N.; Yingtang, Zhang; Zhining, Li; Hongbo, Fan; Guoquan, Ren

2016-03-01

Attitude change of mobile magnetic gradient tensor system critically affects the precision of gradient measurements, thereby increasing ambiguity in target detection. This paper presents a rotational invariant-based method for locating and identifying ferromagnetic targets. Firstly, unit magnetic moment vector was derived based on the geometrical invariant, such that the intermediate eigenvector of the magnetic gradient tensor is perpendicular to the magnetic moment vector and the source-sensor displacement vector. Secondly, unit source-sensor displacement vector was derived based on the characteristic that the angle between magnetic moment vector and source-sensor displacement is a rotational invariant. By introducing a displacement vector between two measurement points, the magnetic moment vector and the source-sensor displacement vector were theoretically derived. To resolve the problem of measurement noises existing in the realistic detection applications, linear equations were formulated using invariants corresponding to several distinct measurement points and least square solution of magnetic moment vector and source-sensor displacement vector were obtained. Results of simulation and principal verification experiment showed the correctness of the analytical method, along with the practicability of the least square method.

Shaping through buckling in elastic gridshells: from camping tents to architectural roofs

NASA Astrophysics Data System (ADS)

Reis, Pedro

Elastic gridshells comprise an initially planar network of elastic rods that is actuated into a 3D shell-like structure by loading its extremities. This shaping results from elastic buckling and the subsequent geometrically nonlinear deformation of the grid structure. Architectural elastic gridshells first appeared in the 1970's. However, to date, only a limited number of examples have been constructed around the world, primarily due to the challenges involved in their structural design. Yet, elastic gridshells are highly appealing: they can cover wide spans with low self-weight, they allow for aesthetically pleasing shapes and their construction is typically simple and rapid. We study the mechanics of elastic gridshells by combining precision model experiments that explore their scale invariance, together with computer simulations that employ the Discrete Elastic Rods method. Excellent agreement is found between the two. Upon validation, the numerics are then used to systematically explore parameter space and identify general design principles for specific target final shapes. Our findings are rationalized using the theory of discrete Chebyshev nets, together with the group theory for crystals. Higher buckling modes occur for some configurations due to geometric incompatibility at the boundary and result in symmetry breaking. Along with the systematic classification of the various possible modes of deformation, we provide a reduced model that rationalizes form-finding in elastic gridshells. This work was done in collaboration with Changyeob Baek, Khalid Jawed and Andrew Sageman-Furnas. We are grateful to the NSF for funding (CAREER, CMMI-1351449).

Testing Structural Invariance of the Achievement Goal Questionnaire in American, Chinese, and Dutch College Students

ERIC Educational Resources Information Center

Sun, Huaping; Hernandez, Diley

2012-01-01

This study investigates the structural invariance of the Achievement Goal Questionnaire (AGQ) in American, Chinese, and Dutch college students. Using confirmatory factor analyses (CFA), the authors found evidence for the four-factor structure of achievement goals in all three samples. Subsequent multigroup CFAs supported structural invariance of…

Behavioral Consequences of Drinking: An Investigation of Factorial Invariance across Gender

ERIC Educational Resources Information Center

Derby, Dustin C.; Smith, Thomas J.

2014-01-01

The purpose of the current study was to assess the gender invariance of an a priori four-factor solution of behavioral consequences of drinking. Results evidenced strong partial measurement invariance, with marginal structural invariance, which signals that the underlying constructs possessed the same theoretical structure for both men and women.

The consequences of ignoring measurement invariance for path coefficients in structural equation models

PubMed Central

Guenole, Nigel; Brown, Anna

2014-01-01

We report a Monte Carlo study examining the effects of two strategies for handling measurement non-invariance – modeling and ignoring non-invariant items – on structural regression coefficients between latent variables measured with item response theory models for categorical indicators. These strategies were examined across four levels and three types of non-invariance – non-invariant loadings, non-invariant thresholds, and combined non-invariance on loadings and thresholds – in simple, partial, mediated and moderated regression models where the non-invariant latent variable occupied predictor, mediator, and criterion positions in the structural regression models. When non-invariance is ignored in the latent predictor, the focal group regression parameters are biased in the opposite direction to the difference in loadings and thresholds relative to the referent group (i.e., lower loadings and thresholds for the focal group lead to overestimated regression parameters). With criterion non-invariance, the focal group regression parameters are biased in the same direction as the difference in loadings and thresholds relative to the referent group. While unacceptable levels of parameter bias were confined to the focal group, bias occurred at considerably lower levels of ignored non-invariance than was previously recognized in referent and focal groups. PMID:25278911

Strain-induced topological quantum phase transition in phosphorene oxide

NASA Astrophysics Data System (ADS)

Kang, Seoung-Hun; Park, Jejune; Woo, Sungjong; Kwon, Young-Kyun

Using ab initio density functional theory, we investigate the structural stability and electronic properties of phosphorene oxides (POx) with different oxygen compositions x. A variety of configurations are modeled and optimized geometrically to search for the equilibrium structure for each x value. Our electronic structure calculations on the equilibrium configuration obtained for each x reveal that the band gap tends to increase with the oxygen composition of x < 0.5, and then to decrease with x > 0.5. We further explore the strain effect on the electronic structure of the fully oxidized phosphorene, PO, with x = 1. At a particular strain without spin-orbit coupling (SOC) is observed a band gap closure near the Γ point in the k space. We further find the strain in tandem with SOC induces an interesting band inversion with a reopened very small band gap (5 meV), and thus gives rise to a topological quantum phase transition from a normal insulator to a topological insulator. Such a topological phase transition is confirmed by the wave function analysis and the band topology identified by the Z2 invariant calculation.

Factor Structure and Measurement Invariance of the Need-Supportive Teaching Style Scale for Physical Education.

PubMed

Liu, Jing-Dong; Chung, Pak-Kwong

2017-08-01

The purpose of the current study was to examine the factor structure and measurement invariance of a scale measuring students' perceptions of need-supportive teaching (Need-Supportive Teaching Style Scale in Physical Education; NSTSSPE). We sampled 615 secondary school students in Hong Kong, 200 of whom also completed a follow-up assessment two months later. Factor structure of the scale was examined through exploratory structural equation modeling (ESEM). Further, nomological validity of the NSTSSPE was evaluated by examining the relationships between need-supportive teaching style and student satisfaction of psychological needs. Finally, four measurement models-configural, metric invariance, scalar invariance, and item uniqueness invariance-were assessed using multiple group ESEM to test the measurement invariance of the scale across gender, grade, and time. ESEM results suggested a three-factor structure of the NSTSSPE. Nomological validity was supported, and weak, strong, and strict measurement invariance of the NSTSSPE was evidenced across gender, grade, and time. The current study provides initial psychometric support for the NSTSSPE to assess student perceptions of teachers' need-supportive teaching style in physical education classes.

Einstein-Cartan calculus for exceptional geometry

NASA Astrophysics Data System (ADS)

Godazgar, Hadi; Godazgar, Mahdi; Nicolai, Hermann

2014-06-01

In this paper we establish and clarify the link between the recently found E7(7) generalised geometric structures, which are based on the SU(8) invariant reformulation of D = 11 supergravity proposed long ago, and newer results obtained in the framework of recent approaches to generalised geometry, where E7(7) duality is built in and manifest from the outset. In making this connection, the so-called generalised vielbein postulate plays a key role. We explicitly show how this postulate can be used to define an E7(7) valued affine connection and an associated covariant derivative, which yields a generalised curvature tensor for the E7(7) based exceptional geometry. The analysis of the generalised vielbein postulate also provides a natural explanation for the emergence of the embedding tensor from higher dimensions.

Redshift Space Distortion on the Small Scale Clustering of Structure

NASA Astrophysics Data System (ADS)

Park, Hyunbae; Sabiu, Cristiano; Li, Xiao-dong; Park, Changbom; Kim, Juhan

2018-01-01

The positions of galaxies in comoving Cartesian space varies under different cosmological parameter choices, inducing a redshift-dependent scaling in the galaxy distribution. The shape of the two-point correlation of galaxies exhibits a significant redshift evolution when the galaxy sample is analyzed under a cosmology differing from the true, simulated one. In our previous works, we can made use of this geometrical distortion to constrain the values of cosmological parameters governing the expansion history of the universe. This current work is a continuation of our previous works as a strategy to constrain cosmological parameters using redshift-invariant physical quantities. We now aim to understand the redshift evolution of the full shape of the small scale, anisotropic galaxy clustering and give a firmer theoretical footing to our previous works.

Conformal higher spin theory and twistor space actions

NASA Astrophysics Data System (ADS)

Hähnel, Philipp; McLoughlin, Tristan

2017-12-01

We consider the twistor description of conformal higher spin theories and give twistor space actions for the self-dual sector of theories with spin greater than two that produce the correct flat space-time spectrum. We identify a ghost-free subsector, analogous to the embedding of Einstein gravity with cosmological constant in Weyl gravity, which generates the unique spin-s three-point anti-MHV amplitude consistent with Poincaré invariance and helicity constraints. By including interactions between the infinite tower of higher-spin fields we give a geometric interpretation to the twistor equations of motion as the integrability condition for a holomorphic structure on an infinite jet bundle. Finally, we conjecture anti-self-dual interaction terms which give an implicit definition of a twistor action for the full conformal higher spin theory.

Differential characters and cohomology of the moduli of flat connections

NASA Astrophysics Data System (ADS)

Castrillón López, Marco; Ferreiro Pérez, Roberto

2018-05-01

Let π {:} P→ M be a principal bundle and p an invariant polynomial of degree r on the Lie algebra of the structure group. The theory of Chern-Simons differential characters is exploited to define a homology map χ k {:} H_{2r-k-1}(M)× Hk(F/G)→ R/Z , for k

Radial Photonic Crystal for detection of frequency and position of radiation sources.

PubMed

Carbonell, J; Díaz-Rubio, A; Torrent, D; Cervera, F; Kirleis, M A; Piqué, A; Sánchez-Dehesa, J

2012-01-01

Based on the concepts of artificially microstructured materials, i.e. metamaterials, we present here the first practical realization of a radial wave crystal. This type of device was introduced as a theoretical proposal in the field of acoustics, and can be briefly defined as a structured medium with radial symmetry, where the constitutive parameters are invariant under radial geometrical translations. Our practical demonstration is realized in the electromagnetic microwave spectrum, because of the equivalence between the wave problems in both fields. A device has been designed, fabricated and experimentally characterized. It is able to perform beam shaping of punctual wave sources, and also to sense position and frequency of external radiators. Owing to the flexibility offered by the design concept, other possible applications are discussed.

Prescribing the mixed scalar curvature of a foliated Riemann-Cartan manifold

NASA Astrophysics Data System (ADS)

Rovenski, Vladimir Y.; Zelenko, Leonid

2018-03-01

The mixed scalar curvature is the simplest curvature invariant of a foliated Riemannian manifold. We explore the problem of prescribing the leafwise constant mixed scalar curvature of a foliated Riemann-Cartan manifold by conformal change of the structure in tangent and normal to the leaves directions. Under certain geometrical assumptions and in two special cases: along a compact leaf and for a closed fibered manifold, we reduce the problem to solution of a nonlinear leafwise elliptic equation for the conformal factor. We are looking for its solutions that are stable stationary solutions of the associated parabolic equation. Our main tool is using of majorizing and minorizing nonlinear heat equations with constant coefficients and application of comparison theorems for solutions of Cauchy's problem for parabolic equations.

A geometric construction of the Riemann scalar curvature in Regge calculus

NASA Astrophysics Data System (ADS)

McDonald, Jonathan R.; Miller, Warner A.

2008-10-01

The Riemann scalar curvature plays a central role in Einstein's geometric theory of gravity. We describe a new geometric construction of this scalar curvature invariant at an event (vertex) in a discrete spacetime geometry. This allows one to constructively measure the scalar curvature using only clocks and photons. Given recent interest in discrete pre-geometric models of quantum gravity, we believe is it ever so important to reconstruct the curvature scalar with respect to a finite number of communicating observers. This derivation makes use of a new fundamental lattice cell built from elements inherited from both the original simplicial (Delaunay) spacetime and its circumcentric dual (Voronoi) lattice. The orthogonality properties between these two lattices yield an expression for the vertex-based scalar curvature which is strikingly similar to the corresponding hinge-based expression in Regge calculus (deficit angle per unit Voronoi dual area). In particular, we show that the scalar curvature is simply a vertex-based weighted average of deficits per weighted average of dual areas.

Geometric descriptions of entangled states by auxiliary varieties

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 themore » 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.« less

Lie symmetry analysis and reduction for exact solution of (2+1)-dimensional Bogoyavlensky-Konopelchenko equation by geometric approach

NASA Astrophysics Data System (ADS)

Ray, S. Saha

2018-04-01

In this paper, the symmetry analysis and similarity reduction of the (2+1)-dimensional Bogoyavlensky-Konopelchenko (B-K) equation are investigated by means of the geometric approach of an invariance group, which is equivalent to the classical Lie symmetry method. Using the extended Harrison and Estabrook’s differential forms approach, the infinitesimal generators for (2+1)-dimensional B-K equation are obtained. Firstly, the vector field associated with the Lie group of transformation is derived. Then the symmetry reduction and the corresponding explicit exact solution of (2+1)-dimensional B-K equation is obtained.

Reconstructed imaging of acoustic cloak using time-lapse reversal method

NASA Astrophysics Data System (ADS)

Zhou, Chen; Cheng, Ying; Xu, Jian-yi; Li, Bo; Liu, Xiao-jun

2014-08-01

We proposed and investigated a solution to the inverse acoustic cloak problem, an anti-stealth technology to make cloaks visible, using the time-lapse reversal (TLR) method. The TLR method reconstructs the image of an unknown acoustic cloak by utilizing scattered acoustic waves. Compared to previous anti-stealth methods, the TLR method can determine not only the existence of a cloak but also its exact geometric information like definite shape, size, and position. Here, we present the process for TLR reconstruction based on time reversal invariance. This technology may have potential applications in detecting various types of cloaks with different geometric parameters.

Scale invariance in natural and artificial collective systems: a review

PubMed Central

Huepe, Cristián

2017-01-01

Self-organized collective coordinated behaviour is an impressive phenomenon, observed in a variety of natural and artificial systems, in which coherent global structures or dynamics emerge from local interactions between individual parts. If the degree of collective integration of a system does not depend on size, its level of robustness and adaptivity is typically increased and we refer to it as scale-invariant. In this review, we first identify three main types of self-organized scale-invariant systems: scale-invariant spatial structures, scale-invariant topologies and scale-invariant dynamics. We then provide examples of scale invariance from different domains in science, describe their origins and main features and discuss potential challenges and approaches for designing and engineering artificial systems with scale-invariant properties. PMID:29093130

Geometric foundations of the theory of feedback equivalence

NASA Technical Reports Server (NTRS)

Hermann, R.

1987-01-01

A description of feedback control is presented within the context of differential equations, differential geometry, and Lie theory. Work related to the integration of differential geometry with the control techniques of feedback linearization is summarized. Particular attention is given to the application of the theory of vector field systems. Feedback invariants for control systems in state space form are also addressed.

Finite-dimensional integrable systems: A collection of research problems

NASA Astrophysics Data System (ADS)

Bolsinov, A. V.; Izosimov, A. M.; Tsonev, D. M.

2017-05-01

This article suggests a series of problems related to various algebraic and geometric aspects of integrability. They reflect some recent developments in the theory of finite-dimensional integrable systems such as bi-Poisson linear algebra, Jordan-Kronecker invariants of finite dimensional Lie algebras, the interplay between singularities of Lagrangian fibrations and compatible Poisson brackets, and new techniques in projective geometry.

The fractal geometry of life.

PubMed

Losa, Gabriele A

2009-01-01

The extension of the concepts of Fractal Geometry (Mandelbrot [1983]) toward the life sciences has led to significant progress in understanding complex functional properties and architectural / morphological / structural features characterising cells and tissues during ontogenesis and both normal and pathological development processes. It has even been argued that fractal geometry could provide a coherent description of the design principles underlying living organisms (Weibel [1991]). Fractals fulfil a certain number of theoretical and methodological criteria including a high level of organization, shape irregularity, functional and morphological self-similarity, scale invariance, iterative pathways and a peculiar non-integer fractal dimension [FD]. Whereas mathematical objects are deterministic invariant or self-similar over an unlimited range of scales, biological components are statistically self-similar only within a fractal domain defined by upper and lower limits, called scaling window, in which the relationship between the scale of observation and the measured size or length of the object can be established (Losa and Nonnenmacher [1996]). Selected examples will contribute to depict complex biological shapes and structures as fractal entities, and also to show why the application of the fractal principle is valuable for measuring dimensional, geometrical and functional parameters of cells, tissues and organs occurring within the vegetal and animal realms. If the criteria for a strict description of natural fractals are met, then it follows that a Fractal Geometry of Life may be envisaged and all natural objects and biological systems exhibiting self-similar patterns and scaling properties may be considered as belonging to the new subdiscipline of "fractalomics".

Shear, principal, and equivalent strains in equal-channel angular deformation

NASA Astrophysics Data System (ADS)

Xia, K.; Wang, J.

2001-10-01

The shear and principal strains involved in equal channel angular deformation (ECAD) were analyzed using a variety of methods. A general expression for the total shear strain calculated by integrating infinitesimal strain increments gave the same result as that from simple geometric considerations. The magnitude and direction of the accumulated principal strains were calculated based on a geometric and a matrix algebra method, respectively. For an intersecting angle of π/2, the maximum normal strain is 0.881 in the direction at π/8 (22.5 deg) from the longitudinal direction of the material in the exit channel. The direction of the maximum principal strain should be used as the direction of grain elongation. Since the principal direction of strain rotates during ECAD, the total shear strain and principal strains so calculated do not have the same meaning as those in a strain tensor. Consequently, the “equivalent” strain based on the second invariant of a strain tensor is no longer an invariant. Indeed, the equivalent strains calculated using the total shear strain and that using the total principal strains differed as the intensity of deformation increased. The method based on matrix algebra is potentially useful in mathematical analysis and computer calculation of ECAD.

Differential geometric invariants for time-reversal symmetric Bloch-bundles: The “Real” case

DOE Office of Scientific and Technical Information (OSTI.GOV)

De Nittis, Giuseppe, E-mail: gidenittis@mat.puc.cl; Gomi, Kiyonori, E-mail: kgomi@math.shinshu-u.ac.jp

2016-05-15

Topological quantum systems subjected to an even (resp. odd) time-reversal symmetry can be classified by looking at the related “Real” (resp. “Quaternionic”) Bloch-bundles. If from one side the topological classification of these time-reversal vector bundle theories has been completely described in De Nittis and Gomi [J. Geom. Phys. 86, 303–338 (2014)] for the “Real” case and in De Nittis and Gomi [Commun. Math. Phys. 339, 1–55 (2015)] for the “Quaternionic” case, from the other side it seems that a classification in terms of differential geometric invariants is still missing in the literature. With this article and its companion [G. Demore » Nittis and K. Gomi (unpublished)] we want to cover this gap. More precisely, we extend in an equivariant way the theory of connections on principal bundles and vector bundles endowed with a time-reversal symmetry. In the “Real” case we generalize the Chern-Weil theory and we show that the assignment of a “Real” connection, along with the related differential Chern class and its holonomy, suffices for the classification of “Real” vector bundles in low dimensions.« less

A novel scheme for automatic nonrigid image registration using deformation invariant feature and geometric constraint

NASA Astrophysics Data System (ADS)

Deng, Zhipeng; Lei, Lin; Zhou, Shilin

2015-10-01

Automatic image registration is a vital yet challenging task, particularly for non-rigid deformation images which are more complicated and common in remote sensing images, such as distorted UAV (unmanned aerial vehicle) images or scanning imaging images caused by flutter. Traditional non-rigid image registration methods are based on the correctly matched corresponding landmarks, which usually needs artificial markers. It is a rather challenging task to locate the accurate position of the points and get accurate homonymy point sets. In this paper, we proposed an automatic non-rigid image registration algorithm which mainly consists of three steps: To begin with, we introduce an automatic feature point extraction method based on non-linear scale space and uniform distribution strategy to extract the points which are uniform distributed along the edge of the image. Next, we propose a hybrid point matching algorithm using DaLI (Deformation and Light Invariant) descriptor and local affine invariant geometric constraint based on triangulation which is constructed by K-nearest neighbor algorithm. Based on the accurate homonymy point sets, the two images are registrated by the model of TPS (Thin Plate Spline). Our method is demonstrated by three deliberately designed experiments. The first two experiments are designed to evaluate the distribution of point set and the correctly matching rate on synthetic data and real data respectively. The last experiment is designed on the non-rigid deformation remote sensing images and the three experimental results demonstrate the accuracy, robustness, and efficiency of the proposed algorithm compared with other traditional methods.

Shaping propagation invariant laser beams

NASA Astrophysics Data System (ADS)

Soskind, Michael; Soskind, Rose; Soskind, Yakov

2015-11-01

Propagation-invariant structured laser beams possess several unique properties and play an important role in various photonics applications. The majority of propagation invariant beams are produced in the form of laser modes emanating from stable laser cavities. Therefore, their spatial structure is limited by the intracavity mode formation. We show that several types of anamorphic optical systems (AOSs) can be effectively employed to shape laser beams into a variety of propagation invariant structured fields with different shapes and phase distributions. We present a propagation matrix approach for designing AOSs and defining mode-matching conditions required for preserving propagation invariance of the output shaped fields. The propagation matrix approach was selected, as it provides a more straightforward approach in designing AOSs for shaping propagation-invariant laser beams than the alternative technique based on the Gouy phase evolution, especially in the case of multielement AOSs. Several practical configurations of optical systems that are suitable for shaping input laser beams into a diverse variety of structured propagation invariant laser beams are also presented. The laser beam shaping approach was applied by modeling propagation characteristics of several input laser beam types, including Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian structured field distributions. The influence of the Ince-Gaussian beam semifocal separation parameter and the azimuthal orientation between the input laser beams and the AOSs onto the resulting shape of the propagation invariant laser beams is presented as well.

Dynamics of vortex domain walls in ferromagnetic nanowires - A possible method for chirality manipulation

NASA Astrophysics Data System (ADS)

Li, Y.; Lu, Z.; Chen, C.; Cheng, M.; Yin, H.; Wang, W.; Li, C.; Liu, Y.; Xiong, R.; Shi, J.

2018-06-01

The dynamic behaviors of vortex domain walls (VDWs) in ferromagnetic nanowires driven by a magnetic field above Walker breakdown field (Hw) were investigated using micromagnetic simulation. It was found when nanowire has proper geometrical dimensions, the VDW may oscillate in a chirality invariant mode or a chirality switching mode depending on applied field and damping constant. At fixed damping constant, the oscillation mode can be controlled by applied field - with the increase of applied field, the oscillation of VDW change from a chirality invariant mode to a variant one. As the oscillation of VDW changes from chirality invariant regime to chirality switching regime, the oscillation frequency and amplification will undergo an abnormal change, which may offer a fingerprint for the switch of oscillation mode. Our finding proposes a simple way to control the chirality of a VDW by properly manipulating nanowire geometry and applied field, which may have important applications in VDW-based devices.

Gauge interaction as periodicity modulation

NASA Astrophysics Data System (ADS)

Dolce, Donatello

2012-06-01

The paper is devoted to a geometrical interpretation of gauge invariance in terms of the formalism of field theory in compact space-time dimensions (Dolce, 2011) [8]. In this formalism, the kinematic information of an interacting elementary particle is encoded on the relativistic geometrodynamics of the boundary of the theory through local transformations of the underlying space-time coordinates. Therefore gauge interactions are described as invariance of the theory under local deformations of the boundary. The resulting local variations of the field solution are interpreted as internal transformations. The internal symmetries of the gauge theory turn out to be related to corresponding space-time local symmetries. In the approximation of local infinitesimal isometric transformations, Maxwell's kinematics and gauge invariance are inferred directly from the variational principle. Furthermore we explicitly impose periodic conditions at the boundary of the theory as semi-classical quantization condition in order to investigate the quantum behavior of gauge interaction. In the abelian case the result is a remarkable formal correspondence with scalar QED.

Using Global Invariant Manifolds to Understand Metastability in the Burgers Equation With Small Viscosity

NASA Astrophysics Data System (ADS)

Beck, Margaret; Wayne, C. Eugene

2009-01-01

The large-time behavior of solutions to the Burgers equation with small viscosity is described using invariant manifolds. In particular, a geometric explanation is provided for a phenomenon known as metastability, which in the present context means that solutions spend a very long time near the family of solutions known as diffusive N-waves before finally converging to a stable self-similar diffusion wave. More precisely, it is shown that in terms of similarity, or scaling, variables in an algebraically weighted L^2 space, the self-similar diffusion waves correspond to a one-dimensional global center manifold of stationary solutions. Through each of these fixed points there exists a one-dimensional, global, attractive, invariant manifold corresponding to the diffusive N-waves. Thus, metastability corresponds to a fast transient in which solutions approach this metastable manifold of diffusive N-waves, followed by a slow decay along this manifold, and, finally, convergence to the self-similar diffusion wave.

Spacetime encodings. III. Second order Killing tensors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brink, Jeandrew

2010-01-15

This paper explores the Petrov type D, stationary axisymmetric vacuum (SAV) spacetimes that were found by Carter to have separable Hamilton-Jacobi equations, and thus admit a second-order Killing tensor. The derivation of the spacetimes presented in this paper borrows from ideas about dynamical systems, and illustrates concepts that can be generalized to higher-order Killing tensors. The relationship between the components of the Killing equations and metric functions are given explicitly. The origin of the four separable coordinate systems found by Carter is explained and classified in terms of the analytic structure associated with the Killing equations. A geometric picture ofmore » what the orbital invariants may represent is built. Requiring that a SAV spacetime admits a second-order Killing tensor is very restrictive, selecting very few candidates from the group of all possible SAV spacetimes. This restriction arises due to the fact that the consistency conditions associated with the Killing equations require that the field variables obey a second-order differential equation, as opposed to a fourth-order differential equation that imposes the weaker condition that the spacetime be SAV. This paper introduces ideas that could lead to the explicit computation of more general orbital invariants in the form of higher-order Killing tensors.« less

Information geometry and its application to theoretical statistics and diffusion tensor magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Wisniewski, Nicholas Andrew

This dissertation is divided into two parts. First we present an exact solution to a generalization of the Behrens-Fisher problem by embedding the problem in the Riemannian manifold of Normal distributions. From this we construct a geometric hypothesis testing scheme. Secondly we investigate the most commonly used geometric methods employed in tensor field interpolation for DT-MRI analysis and cardiac computer modeling. We computationally investigate a class of physiologically motivated orthogonal tensor invariants, both at the full tensor field scale and at the scale of a single interpolation by doing a decimation/interpolation experiment. We show that Riemannian-based methods give the best results in preserving desirable physiological features.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baguet, A.; Pope, Christopher N.; Samtleben, H.

We prove an old conjecture by Duff, Nilsson, Pope and Warner asserting that the NSNS sector of supergravity (and more general the bosonic string) allows for a consistent Pauli reduction on any d-dimensional group manifold G, keeping the full set of gauge bosons of the G×G isometry group of the bi-invariant metric on G. The main tool of the construction is a particular generalised Scherk–Schwarz reduction ansatz in double field theory which we explicitly construct in terms of the group's Killing vectors. Examples include the consistent reduction from ten dimensions on S3×S3 and on similar product spaces. The construction ismore » another example of globally geometric non-toroidal compactifications inducing non-geometric fluxes.« less

Asymptotic symmetries and geometry on the boundary in the first order formalism

NASA Astrophysics Data System (ADS)

Korovin, Yegor

2018-03-01

Proper understanding of the geometry on the boundary of a spacetime is a critical step on the way to extending holography to spaces with non-AdS asymptotics. In general the boundary cannot be described in terms of the Riemannian geometry and the first order formalism is more appropriate as we show. We analyze the asymptotic symmetries in the first order formalism for large classes of theories on AdS, Lifshitz or flat space. In all cases the asymptotic symmetry algebra is realized on the first order variables as a gauged symmetry algebra. First order formalism geometrizes and simplifies the analysis. We apply our framework to the issue of scale versus conformal invariance in AdS/CFT and obtain new perspective on the structure of asymptotic expansions for AdS and flat spaces.

Non-holonomic integrators

NASA Astrophysics Data System (ADS)

Cortés, J.; Martínez, S.

2001-09-01

We introduce a discretization of the Lagrange-d'Alembert principle for Lagrangian systems with non-holonomic constraints, which allows us to construct numerical integrators that approximate the continuous flow. We study the geometric invariance properties of the discrete flow which provide an explanation for the good performance of the proposed method. This is tested on two examples: a non-holonomic particle with a quadratic potential and a mobile robot with fixed orientation.

Birkhoff theorem and conformal Killing-Yano tensors

NASA Astrophysics Data System (ADS)

Ferrando, Joan Josep; Sáez, Juan Antonio

2015-06-01

We analyze the main geometric conditions imposed by the hypothesis of the Jebsen-Birkhoff theorem. We show that the result (existence of an additional Killing vector) does not necessarily require a three-dimensional isometry group on two-dimensional orbits but only the existence of a conformal Killing-Yano tensor. In this approach the (additional) isometry appears as the known invariant Killing vector that the -metrics admit.

Geometrical Effects in Two-Dimensional Arrays of Josephson Junctions

DTIC Science & Technology

1992-05-01

Iot (4.3.4.b) dyd a .. s -f sin =o0 (4.3.4.c) ~r Tdr n snadrs where a, 13, and rare the gauge-invariant phase differences denoted in Fig. 4.8. If we...Receive Slit Coils *_ * Slit Set-screw / -Tr Drive Coil IDrive Leads if Coil Fig. 8.7. Schematic drawing of the two-coil mututal-inductance apparatus we

Geometrization of the Dirac theory of the electron

NASA Technical Reports Server (NTRS)

Fock, V.

1977-01-01

Using the concept of parallel displacement of a half vector, the Dirac equations are generally written in invariant form. The energy tensor is formed and both the macroscopic and quantum mechanic equations of motion are set up. The former have the usual form: divergence of the energy tensor equals the Lorentz force and the latter are essentially identical with those of the geodesic line.

Dimensionality and measurement invariance in the Satisfaction with Life Scale in Norway.

PubMed

Clench-Aas, Jocelyne; Nes, Ragnhild Bang; Dalgard, Odd Steffen; Aarø, Leif Edvard

2011-10-01

Results from previous studies examining the dimensionality and factorial invariance of the Satisfaction with Life Scale (SWLS) are inconsistent and often based on small samples. This study examines the factorial structure and factorial invariance of the SWLS in a Norwegian sample. Confirmatory factor analysis (AMOS) was conducted to explore dimensionality and test for measurement invariance in factor structure, factor loadings, intercepts, and residual variance across gender and four age groups in a large (N = 4,984), nationally representative sample of Norwegian men and women (15-79 years). The data supported a modified unidimensional structure. Factor loadings could be constrained to equality between the sexes, indicating metric invariance between genders. Further testing indicated invariance also at the strong and strict levels, thus allowing analyses involving group means. The SWLS was shown to be sensitive to age, however, at the strong and strict levels of invariance testing. In conclusion, the results in this Norwegian study seem to confirm that a unidimensional structure is acceptable, but that a modified single-factor model with correlations between error terms of items 4 and 5 is preferred. Additionally, comparisons may be made between the genders. Caution must be exerted when comparing age groups.

Factor structure and invariance test of the alcohol use disorder identification test (AUDIT): Comparison and further validation in a U.S. and Philippines college student sample.

PubMed

Tuliao, Antover P; Landoy, Bernice Vania N; McChargue, Dennis E

2016-01-01

The Alcohol Use Disorder Identification Test's factor structure varies depending on population and culture. Because of this inconsistency, this article examined the factor structure of the test and conducted a factorial invariance test between a U.S. and a Philippines college sample. Confirmatory factor analyses indicated that a three-factor solution outperforms the one- and two-factor solution in both samples. Factorial invariance analyses further supports the confirmatory findings by showing that factor loadings were generally invariant across groups; however, item intercepts show non-invariance. Country differences between factors show that Filipino consumption factor mean scores were significantly lower than their U.S. counterparts.

Insight of endo-1,4-xylanase II from Trichoderma reesei: conserved water-mediated H-bond and ion pairs interactions.

PubMed

Vijayakumar, Balakrishnan; Velmurugan, Devadasan

2013-12-01

Endo-1,4-Xylanase II is an enzyme which degrades the linear polysaccharide beta-1,4-xylan into xylose. This enzyme shows highest enzyme activity around 55 °C, even without being stabilized by the disulphide bridges. A set of nine high resolution crystal structures of Xylanase II (1.11-1.80 Å) from Trichoderma reesei were selected and analyzed in order to identify the invariant water molecules, ion pairs and water-mediated ionic interactions. The crystal structure (PDB-id: 2DFB) solved at highest resolution (1.11 Å) was chosen as the reference and the remaining structures were treated as mobile molecules. These structures were then superimposed with the reference molecule to observe the invariant water molecules using 3-dimensional structural superposition server. A total of 37 water molecules were identified to be invariant molecules in all the crystal structures, of which 26 invariant molecules have hydrogen bond interactions with the back bone of residues and 21 invariant water molecules have interactions with side chain residues. The structural and functional roles of these water molecules and ion pairs have been discussed. The results show that the invariant water molecules and ion pairs may be involved in maintaining the structural architecture, dynamics and function of the Endo-1,4-Xylanase II.

Symmetry of semi-reduced lattices.

PubMed

Stróż, Kazimierz

2015-05-01

The main result of this work is extension of the famous characterization of Bravais lattices according to their metrical, algebraic and geometric properties onto a wide class of primitive lattices (including Buerger-reduced, nearly Buerger-reduced and a substantial part of Delaunay-reduced) related to low-restricted semi-reduced descriptions (s.r.d.'s). While the `geometric' operations in Bravais lattices map the basis vectors into themselves, the `arithmetic' operators in s.r.d. transform the basis vectors into cell vectors (basis vectors, face or space diagonals) and are represented by matrices from the set {\\bb V} of all 960 matrices with the determinant ±1 and elements {0, ±1} of the matrix powers. A lattice is in s.r.d. if the moduli of off-diagonal elements in both the metric tensors M and M(-1) are smaller than corresponding diagonal elements sharing the same column or row. Such lattices are split into 379 s.r.d. types relative to the arithmetic holohedries. Metrical criteria for each type do not need to be explicitly given but may be modelled as linear derivatives {\\bb M}(p,q,r), where {\\bb M} denotes the set of 39 highest-symmetry metric tensors, and p,q,r describe changes of appropriate interplanar distances. A sole filtering of {\\bb V} according to an experimental s.r.d. metric and subsequent geometric interpretation of the filtered matrices lead to mathematically stable and rich information on the Bravais-lattice symmetry and deviations from the exact symmetry. The emphasis on the crystallographic features of lattices was obtained by shifting the focus (i) from analysis of a lattice metric to analysis of symmetry matrices [Himes & Mighell (1987). Acta Cryst. A43, 375-384], (ii) from the isometric approach and invariant subspaces to the orthogonality concept {some ideas in Le Page [J. Appl. Cryst. (1982), 15, 255-259]} and splitting indices [Stróż (2011). Acta Cryst. A67, 421-429] and (iii) from fixed cell transformations to transformations derivable via geometric information (Himes & Mighell, 1987; Le Page, 1982). It is illustrated that corresponding arithmetic and geometric holohedries share space distribution of symmetry elements. Moreover, completeness of the s.r.d. types reveals their combinatorial structure and simplifies the crystallographic description of structural phase transitions, especially those observed with the use of powder diffraction. The research proves that there are excellent theoretical and practical reasons for looking at crystal lattice symmetry from an entirely new and surprising point of view - the combinatorial set {\\bb V} of matrices, their semi-reduced lattice context and their geometric properties.

Cosmological Constraints from the Redshift Dependence of the Volume Effect Using the Galaxy 2-point Correlation Function across the Line of Sight

NASA Astrophysics Data System (ADS)

Li, Xiao-Dong; Park, Changbom; Sabiu, Cristiano G.; Park, Hyunbae; Cheng, Cheng; Kim, Juhan; Hong, Sungwook E.

2017-08-01

We develop a methodology to use the redshift dependence of the galaxy 2-point correlation function (2pCF) across the line of sight, ξ ({r}\\perp ), as a probe of cosmological parameters. The positions of galaxies in comoving Cartesian space varies under different cosmological parameter choices, inducing a redshift-dependent scaling in the galaxy distribution. This geometrical distortion can be observed as a redshift-dependent rescaling in the measured ξ ({r}\\perp ). We test this methodology using a sample of 1.75 billion mock galaxies at redshifts 0, 0.5, 1, 1.5, and 2, drawn from the Horizon Run 4 N-body simulation. The shape of ξ ({r}\\perp ) can exhibit a significant redshift evolution when the galaxy sample is analyzed under a cosmology differing from the true, simulated one. Other contributions, including the gravitational growth of structure, galaxy bias, and the redshift space distortions, do not produce large redshift evolution in the shape. We show that one can make use of this geometrical distortion to constrain the values of cosmological parameters governing the expansion history of the universe. This method could be applicable to future large-scale structure surveys, especially photometric surveys such as DES and LSST, to derive tight cosmological constraints. This work is a continuation of our previous works as a strategy to constrain cosmological parameters using redshift-invariant physical quantities.

On Liapunov and Exponential Stability of Rossby-Haurwitz Waves in Invariant Sets of Perturbations

NASA Astrophysics Data System (ADS)

Skiba, Yuri N.

2018-01-01

In this work, the stability of the Rossby-Haurwitz (RH) waves from the subspace H1\\oplus Hn is considered (n≥2 ) where Hk is the subspace of the homogeneous spherical polynomials of degree k. A conservation law for arbitrary perturbations of the RH wave is derived, and all perturbations are divided into three invariant sets M-n , M0n and M+n in which the mean spectral number χ (ψ ^' }) of any perturbation ψ ^' } is less than, equal to or greater than n(n+1) , respectively. In turn, the set M0n is divided into the invariant subsets Hn and M0n{\\setminus } Hn . Quotient spaces and norms of the perturbations are introduced, a hyperbolic law for the perturbations belonging to the sets M-n and M+n is derived, and a geometric interpretation of variations in the kinetic energy of perturbations is given. It is proved that any non-zonal RH wave from H1\\oplus Hn (n≥2 ) is Liapunov unstable in the invariant set M-n . Also, it is shown that a stationary RH wave from H1\\oplus Hn may be exponentially unstable only in the invariant set M0n{\\setminus } Hn , while any perturbation of the invariant set Hn conserves its form with time and hence is neutral. Since a Legendre polynomial flow aPn(μ ) and zonal RH wave - ω μ +aPn(μ ) are particular cases of the RH waves of H1\\oplus Hn , the major part of the stability results obtained here is also true for them.

Factor structure and longitudinal measurement invariance of the demand control support model: an evidence from the Swedish Longitudinal Occupational Survey of Health (SLOSH).

PubMed

Chungkham, Holendro Singh; Ingre, Michael; Karasek, Robert; Westerlund, Hugo; Theorell, Töres

2013-01-01

To examine the factor structure and to evaluate the longitudinal measurement invariance of the demand-control-support questionnaire (DCSQ), using the Swedish Longitudinal Occupational Survey of Health (SLOSH). A confirmatory factor analysis (CFA) and multi-group confirmatory factor analysis (MGCFA) models within the framework of structural equation modeling (SEM) have been used to examine the factor structure and invariance across time. Four factors: psychological demand, skill discretion, decision authority and social support, were confirmed by CFA at baseline, with the best fit obtained by removing the item repetitive work of skill discretion. A measurement error correlation (0.42) between work fast and work intensively for psychological demands was also detected. Acceptable composite reliability measures were obtained except for skill discretion (0.68). The invariance of the same factor structure was established, but caution in comparing mean levels of factors over time is warranted as lack of intercept invariance was evident. However, partial intercept invariance was established for work intensively. Our findings indicate that skill discretion and decision authority represent two distinct constructs in the retained model. However removing the item repetitive work along with either work fast or work intensively would improve model fit. Care should also be taken while making comparisons in the constructs across time. Further research should investigate invariance across occupations or socio-economic classes.

Factor Structure and Longitudinal Measurement Invariance of the Demand Control Support Model: An Evidence from the Swedish Longitudinal Occupational Survey of Health (SLOSH)

PubMed Central

Chungkham, Holendro Singh; Ingre, Michael; Karasek, Robert; Westerlund, Hugo; Theorell, Töres

2013-01-01

Objectives To examine the factor structure and to evaluate the longitudinal measurement invariance of the demand-control-support questionnaire (DCSQ), using the Swedish Longitudinal Occupational Survey of Health (SLOSH). Methods A confirmatory factor analysis (CFA) and multi-group confirmatory factor analysis (MGCFA) models within the framework of structural equation modeling (SEM) have been used to examine the factor structure and invariance across time. Results Four factors: psychological demand, skill discretion, decision authority and social support, were confirmed by CFA at baseline, with the best fit obtained by removing the item repetitive work of skill discretion. A measurement error correlation (0.42) between work fast and work intensively for psychological demands was also detected. Acceptable composite reliability measures were obtained except for skill discretion (0.68). The invariance of the same factor structure was established, but caution in comparing mean levels of factors over time is warranted as lack of intercept invariance was evident. However, partial intercept invariance was established for work intensively. Conclusion Our findings indicate that skill discretion and decision authority represent two distinct constructs in the retained model. However removing the item repetitive work along with either work fast or work intensively would improve model fit. Care should also be taken while making comparisons in the constructs across time. Further research should investigate invariance across occupations or socio-economic classes. PMID:23950957

Comparative study of palm print authentication system using geometric features

NASA Astrophysics Data System (ADS)

Shreyas, Kamath K. M.; Rajeev, Srijith; Panetta, Karen; Agaian, Sos S.

2017-05-01

Biometrics, particularly palm print authentication has been a stimulating research area due to its abundance of features. Stable features and effective matching are the most crucial steps for an authentication system. In conventional palm print authentication systems, matching is based on flexion creases, friction ridges, and minutiae points. Currently, contactless palm print imaging is an emerging technology. However, they tend to involve fluctuations in the image quality and texture loss due to factors such as varying illumination conditions, occlusions, noise, pose, and ghosting. These variations decrease the performance of the authentication systems. Furthermore, real-time palm print authentication in large databases continue to be a challenging task. In order to effectively solve these problems, features which are invariant to these anomalies are required. This paper proposes a robust palm print matching framework by making a comparative study of different local geometric features such as Difference-of-Gaussian, Hessian, Hessian-Laplace, Harris-Laplace, and Multiscale Harris for feature detection. These detectors are coupled with Scale Invariant Feature Transformation (SIFT) descriptor to describe the identified features. Additionally, a two-stage refinement process is carried out to obtain the best stable matches. Computer simulations demonstrate that the accuracy of the system has increased effectively with an EER of 0.86% when Harris-Laplace detector is used on IITD database.

3-D Deformation analysis via invariant geodetic obsevations.

NASA Astrophysics Data System (ADS)

Ardalan, A.; Esmaeili, R.

2003-04-01

In this paper a new method for 3-D deformation analysis based on invariant observations like distances and spatial angles is presented. Displacement field that is used in the classical deformation analysis is not reliable because the stability of the coordinate systems between successive epochs of observations cannot be guaranteed. On the contrary distances and spatial angles, i.e. measurements that are related to geometry between the constituent points of an object is independent of the definition of coordinate system. In this paper we have devised a new approach for the calculation of elements of the strain tensor directly from the geometrical observations such as angels and distances. This new method besides enjoys 3-D nature and as such guarantees the complete deformation study in 3-D space.

Spatial Analysis of Handwritten Texts as a Marker of Cognitive Control.

PubMed

Crespo, Y; Soriano, M F; Iglesias-Parro, S; Aznarte, J I; Ibáñez-Molina, A J

2017-12-01

We explore the idea that cognitive demands of the handwriting would influence the degree of automaticity of the handwriting process, which in turn would affect the geometric parameters of texts. We compared the heterogeneity of handwritten texts in tasks with different cognitive demands; the heterogeneity of texts was analyzed with lacunarity, a measure of geometrical invariance. In Experiment 1, we asked participants to perform two tasks that varied in cognitive demands: transcription and exposition about an autobiographical episode. Lacunarity was significantly lower in transcription. In Experiment 2, we compared a veridical and a fictitious version of a personal event. Lacunarity was lower in veridical texts. We contend that differences in lacunarity of handwritten texts reveal the degree of automaticity in handwriting.

Static holes in the geometrically frustrated bow-tie ladder

NASA Astrophysics Data System (ADS)

Martins, George B.; Brenig, Wolfram

2008-10-01

We investigate the doping of a geometrically frustrated spin ladder with static holes by a complementary approach using exact diagonalization and quantum dimers. Results for thermodynamic properties, the singlet density of states, the hole-binding energy and the spin correlations will be presented. For the undoped systems the ground state is non-degenerate, with translationally invariant nearest-neighbor spin correlations. For the doped case, we find that static holes polarize their vicinity through a localization of singlets, reducing the frustration. This polarization induces short range repulsive forces between two holes and an oscillatory behavior of the long range two-hole energy. For most quantities investigated, we find very good agreement between the quantum dimer approach and the results from exact diagonalization.

Geometric model of topological insulators from the Maxwell algebra

NASA Astrophysics Data System (ADS)

Palumbo, Giandomenico

2017-11-01

We propose a novel geometric model of time-reversal-invariant topological insulators in three dimensions in presence of an external electromagnetic field. Their gapped boundary supports relativistic quantum Hall states and is described by a Chern-Simons theory, where the gauge connection takes values in the Maxwell algebra. This represents a non-central extension of the Poincaré algebra and takes into account both the Lorentz and magnetic-translation symmetries of the surface states. In this way, we derive a relativistic version of the Wen-Zee term and we show that the non-minimal coupling between the background geometry and the electromagnetic field in the model is in agreement with the main properties of the relativistic quantum Hall states in the flat space.

Glomerular epithelial foot processes in normal man and rats. Distribution of true width and its intra- and inter-individual variation.

PubMed

Gundersen, H J; Seefeldt, T; Osterby, R

1980-01-01

The width of individual glomerular epithelial foot processes appears very different on electron micrographs. A method for obtainining distributions of the true width of foot processes from that of their apparent width on electron micrographs has been developed based on geometric probability theory pertaining to a specific geometric model. Analyses of foot process width in humans and rats show a remarkable interindividual invariance implying rigid control and therefore great biological significance of foot process width or a derivative thereof. The very low inter-individual variation of the true width, shown in the present paper, makes it possible to demonstrate slight changes in rather small groups of patients or experimental animals.

Consistent Pauli reduction on group manifolds

DOE PAGES

Baguet, A.; Pope, Christopher N.; Samtleben, H.

2016-01-01

We prove an old conjecture by Duff, Nilsson, Pope and Warner asserting that the NSNS sector of supergravity (and more general the bosonic string) allows for a consistent Pauli reduction on any d-dimensional group manifold G, keeping the full set of gauge bosons of the G×G isometry group of the bi-invariant metric on G. The main tool of the construction is a particular generalised Scherk–Schwarz reduction ansatz in double field theory which we explicitly construct in terms of the group's Killing vectors. Examples include the consistent reduction from ten dimensions on S3×S3 and on similar product spaces. The construction ismore » another example of globally geometric non-toroidal compactifications inducing non-geometric fluxes.« less

Invariance of parent ratings of the ADHD symptoms in Australian and Malaysian, and north European Australian and Malay Malaysia children: a mean and covariance structures analysis approach.

PubMed

Gomez, Rapson

2009-03-01

This study used the mean and covariance structures analysis approach to examine the equality or invariance of ratings of the 18 ADHD symptoms. 783 Australian and 928 Malaysian parents provided ratings for an ADHD rating scale. Invariance was tested across these groups (Comparison 1), and North European Australian (n = 623) and Malay Malaysian (n = 571, Comparison 2) groups. Results indicate support for form and item factor loading invariance; more than half the total number of symptoms showed item intercept invariance, and 14 symptoms showed invariance for error variances. There was invariance for both the factor variances and the covariance, and the latent mean scores for hyperactivity/impulsivity. For inattention latent scores, the Malaysian (Comparison 1) and Malay Malaysian (Comparison 2) groups had higher scores. These results indicate fairly good support for invariance for parent ratings of the ADHD symptoms across the groups compared.

Higher-Order Neural Networks Applied to 2D and 3D Object Recognition

NASA Technical Reports Server (NTRS)

Spirkovska, Lilly; Reid, Max B.

1994-01-01

A Higher-Order Neural Network (HONN) can be designed to be invariant to geometric transformations such as scale, translation, and in-plane rotation. Invariances are built directly into the architecture of a HONN and do not need to be learned. Thus, for 2D object recognition, the network needs to be trained on just one view of each object class, not numerous scaled, translated, and rotated views. Because the 2D object recognition task is a component of the 3D object recognition task, built-in 2D invariance also decreases the size of the training set required for 3D object recognition. We present results for 2D object recognition both in simulation and within a robotic vision experiment and for 3D object recognition in simulation. We also compare our method to other approaches and show that HONNs have distinct advantages for position, scale, and rotation-invariant object recognition. The major drawback of HONNs is that the size of the input field is limited due to the memory required for the large number of interconnections in a fully connected network. We present partial connectivity strategies and a coarse-coding technique for overcoming this limitation and increasing the input field to that required by practical object recognition problems.

Mobile visual object identification: from SIFT-BoF-RANSAC to Sketchprint

NASA Astrophysics Data System (ADS)

Voloshynovskiy, Sviatoslav; Diephuis, Maurits; Holotyak, Taras

2015-03-01

Mobile object identification based on its visual features find many applications in the interaction with physical objects and security. Discriminative and robust content representation plays a central role in object and content identification. Complex post-processing methods are used to compress descriptors and their geometrical information, aggregate them into more compact and discriminative representations and finally re-rank the results based on the similarity geometries of descriptors. Unfortunately, most of the existing descriptors are not very robust and discriminative once applied to the various contend such as real images, text or noise-like microstructures next to requiring at least 500-1'000 descriptors per image for reliable identification. At the same time, the geometric re-ranking procedures are still too complex to be applied to the numerous candidates obtained from the feature similarity based search only. This restricts that list of candidates to be less than 1'000 which obviously causes a higher probability of miss. In addition, the security and privacy of content representation has become a hot research topic in multimedia and security communities. In this paper, we introduce a new framework for non- local content representation based on SketchPrint descriptors. It extends the properties of local descriptors to a more informative and discriminative, yet geometrically invariant content representation. In particular it allows images to be compactly represented by 100 SketchPrint descriptors without being fully dependent on re-ranking methods. We consider several use cases, applying SketchPrint descriptors to natural images, text documents, packages and micro-structures and compare them with the traditional local descriptors.

Structural invariance of multiple intelligences, based on the level of execution.

PubMed

Almeida, Leandro S; Prieto, María Dolores; Ferreira, Arístides; Ferrando, Mercedes; Ferrandiz, Carmen; Bermejo, Rosario; Hernández, Daniel

2011-11-01

The independence of multiple intelligences (MI) of Gardner's theory has been debated since its conception. This article examines whether the one- factor structure of the MI theory tested in previous studies is invariant for low and high ability students. Two hundred ninety-four children (aged 5 to 7) participated in this study. A set of Gardner's Multiple Intelligence assessment tasks based on the Spectrum Project was used. To analyze the invariance of a general dimension of intelligence, the different models of behaviours were studied in samples of participants with different performance on the Spectrum Project tasks with Multi-Group Confirmatory Factor Analysis (MGCFA). Results suggest an absence of structural invariance in Gardner's tasks. Exploratory analyses suggest a three-factor structure for individuals with higher performance levels and a two-factor structure for individuals with lower performance levels.

Complex reflection groups, logarithmic connections and bi-flat F-manifolds

NASA Astrophysics Data System (ADS)

Arsie, Alessandro; Lorenzoni, Paolo

2017-10-01

We show that bi-flat F-manifolds can be interpreted as natural geometrical structures encoding the almost duality for Frobenius manifolds without metric. Using this framework, we extend Dubrovin's duality between orbit spaces of Coxeter groups and Veselov's ěe -systems, to the orbit spaces of exceptional well-generated complex reflection groups of rank 2 and 3. On the Veselov's ěe -systems side, we provide a generalization of the notion of ěe -systems that gives rise to a dual connection which coincides with a Dunkl-Kohno-type connection associated with such groups. In particular, this allows us to treat on the same ground several different examples including Coxeter and Shephard groups. Remarkably, as a by-product of our results, we prove that in some examples, basic flat invariants are not uniquely defined. As far as we know, such a phenomenon has never been pointed out before.

Diffraction patterns in Fresnel approximation of periodic objects for a colorimeter of two apertures

NASA Astrophysics Data System (ADS)

Cortes-Reynoso, Jose-German R.; Suarez-Romero, Jose G.; Hurtado-Ramos, Juan B.; Tepichin-Rodriguez, Eduardo; Solorio-Leyva, Juan Carlos

2004-10-01

In this work, we present a study of Fresnel diffraction of periodic structures in an optical system of two apertures. This system of two apertures was used successfully for measuring color in textile samples solving the problems of illumination and directionality that present current commercial equipments. However, the system is sensible to the spatial frequency of the periodic sample"s area enclosed in its optical field of view. The study of Fresnel diffraction allows us to establish criteria for geometrical parameters of measurements in order to assure invariance in angular rotations and spatial positions. In this work, we use the theory of partial coherence to calculate the diffraction through two continuous apertures. In the calculation process, we use the concept of point-spread function of the system for partial coherence, in this way we avoid complicated statistical processes commonly used in the partial coherence theory.

Supertranslations: redundancies of horizon data and global symmetries at null infinity

NASA Astrophysics Data System (ADS)

Sousa, K.; Miláns del Bosch, G.; Reina, B.

2018-03-01

We characterise the geometrical nature of smooth supertranslations defined on a generic non-expanding horizon (NEH) embedded in vacuum. To this end we consider the constraints imposed by the vacuum Einstein’s equations on the NEH structure, and discuss the transformation properties of their solutions under supertranslations. We present a freely specifiable data set which is both necessary and sufficient to reconstruct the full horizon geometry, and is composed of objects which are invariant under supertranslations. We conclude that smooth supertranslations do not transform the geometry of the NEH and that they should be regarded as pure gauge. Our results apply both to stationary and non-stationary states of a NEH, the latter ones being able to describe radiative processes taking place on the horizon. As a consistency check we repeat the analysis for Bondi–Metzner–Sachs (BMS) supertranslations defined on null infinity, \

Topological Mechanics of Origami and Kirigami

NASA Astrophysics Data System (ADS)

Chen, Bryan Gin-ge; Liu, Bin; Evans, Arthur A.; Paulose, Jayson; Cohen, Itai; Vitelli, Vincenzo; Santangelo, C. D.

2016-04-01

Origami and kirigami have emerged as potential tools for the design of mechanical metamaterials whose properties such as curvature, Poisson ratio, and existence of metastable states can be tuned using purely geometric criteria. A major obstacle to exploiting this property is the scarcity of tools to identify and program the flexibility of fold patterns. We exploit a recent connection between spring networks and quantum topological states to design origami with localized folding motions at boundaries and study them both experimentally and theoretically. These folding motions exist due to an underlying topological invariant rather than a local imbalance between constraints and degrees of freedom. We give a simple example of a quasi-1D folding pattern that realizes such topological states. We also demonstrate how to generalize these topological design principles to two dimensions. A striking consequence is that a domain wall between two topologically distinct, mechanically rigid structures is deformable even when constraints locally match the degrees of freedom.

General Second-Order Scalar-Tensor Theory and Self-Tuning

NASA Astrophysics Data System (ADS)

Charmousis, Christos; Copeland, Edmund J.; Padilla, Antonio; Saffin, Paul M.

2012-02-01

Starting from the most general scalar-tensor theory with second-order field equations in four dimensions, we establish the unique action that will allow for the existence of a consistent self-tuning mechanism on Friedmann-Lemaître-Robertson-Walker backgrounds, and show how it can be understood as a combination of just four base Lagrangians with an intriguing geometric structure dependent on the Ricci scalar, the Einstein tensor, the double dual of the Riemann tensor, and the Gauss-Bonnet combination. Spacetime curvature can be screened from the net cosmological constant at any given moment because we allow the scalar field to break Poincaré invariance on the self-tuning vacua, thereby evading the Weinberg no-go theorem. We show how the four arbitrary functions of the scalar field combine in an elegant way opening up the possibility of obtaining nontrivial cosmological solutions.

Measurement invariance of the alcohol use disorders identification test: Establishing its factor structure in different settings and across gender.

PubMed

Moehring, Anne; Krause, Kristian; Guertler, Diana; Bischof, Gallus; Hapke, Ulfert; Freyer-Adam, Jennis; Baumann, Sophie; Batra, Anil; Rumpf, Hans-Juergen; Ulbricht, Sabina; John, Ulrich; Meyer, Christian

2018-05-31

The Alcohol Use Disorders Identification Test (AUDIT) is an internationally well-established screening tool for the assessment of hazardous and harmful alcohol consumption. To be valid for group comparisons, the AUDIT should measure the same latent construct with the same structure across groups. This is determined by measurement invariance. So far, measurement invariance of the AUDIT has rarely been investigated. We analyzed measurement invariance across gender and samples from different settings (i.e., inpatients from general hospital, patients from general medical practices, general population). A sample of n = 28,345 participants from general hospitals, general medical practices and the general population was provided from six studies. First, we used Confirmatory Factor Analysis (CFA) to establish the factorial structure of the AUDIT by comparing a single-factor model to a two-factor model for each group. Next, Multiple Group CFA was used to investigate measurement invariance. The two-factor structure was shown to be preferable for all groups. Furthermore, strict measurement invariance was established across all groups for the AUDIT. A two-factor structure for the AUDIT is preferred. Nevertheless, the one-factor structure also showed a good fit to the data. The findings support the AUDIT as a psychometrically valid and reliable screening instrument. Copyright © 2018 Elsevier B.V. All rights reserved.

Gauge-theoretic invariants for topological insulators: a bridge between Berry, Wess-Zumino, and Fu-Kane-Mele

NASA Astrophysics Data System (ADS)

Monaco, Domenico; Tauber, Clément

2017-07-01

We establish a connection between two recently proposed approaches to the understanding of the geometric origin of the Fu-Kane-Mele invariant FKM\\in Z_2, arising in the context of two-dimensional time-reversal symmetric topological insulators. On the one hand, the Z_2 invariant can be formulated in terms of the Berry connection and the Berry curvature of the Bloch bundle of occupied states over the Brillouin torus. On the other, using techniques from the theory of bundle gerbes, it is possible to provide an expression for FKM containing the square root of the Wess-Zumino amplitude for a certain U( N)-valued field over the Brillouin torus. We link the two formulas by showing directly the equality between the above-mentioned Wess-Zumino amplitude and the Berry phase, as well as between their square roots. An essential tool of independent interest is an equivariant version of the adjoint Polyakov-Wiegmann formula for fields T^2 → U(N), of which we provide a proof employing only basic homotopy theory and circumventing the language of bundle gerbes.

Neural-network classifiers for automatic real-world aerial image recognition

NASA Astrophysics Data System (ADS)

Greenberg, Shlomo; Guterman, Hugo

1996-08-01

We describe the application of the multilayer perceptron (MLP) network and a version of the adaptive resonance theory version 2-A (ART 2-A) network to the problem of automatic aerial image recognition (AAIR). The classification of aerial images, independent of their positions and orientations, is required for automatic tracking and target recognition. Invariance is achieved by the use of different invariant feature spaces in combination with supervised and unsupervised neural networks. The performance of neural-network-based classifiers in conjunction with several types of invariant AAIR global features, such as the Fourier-transform space, Zernike moments, central moments, and polar transforms, are examined. The advantages of this approach are discussed. The performance of the MLP network is compared with that of a classical correlator. The MLP neural-network correlator outperformed the binary phase-only filter (BPOF) correlator. It was found that the ART 2-A distinguished itself with its speed and its low number of required training vectors. However, only the MLP classifier was able to deal with a combination of shift and rotation geometric distortions.

Neural-network classifiers for automatic real-world aerial image recognition.

PubMed

Greenberg, S; Guterman, H

1996-08-10

We describe the application of the multilayer perceptron (MLP) network and a version of the adaptive resonance theory version 2-A (ART 2-A) network to the problem of automatic aerial image recognition (AAIR). The classification of aerial images, independent of their positions and orientations, is required for automatic tracking and target recognition. Invariance is achieved by the use of different invariant feature spaces in combination with supervised and unsupervised neural networks. The performance of neural-network-based classifiers in conjunction with several types of invariant AAIR global features, such as the Fourier-transform space, Zernike moments, central moments, and polar transforms, are examined. The advantages of this approach are discussed. The performance of the MLP network is compared with that of a classical correlator. The MLP neural-network correlator outperformed the binary phase-only filter (BPOF) correlator. It was found that the ART 2-A distinguished itself with its speed and its low number of required training vectors. However, only the MLP classifier was able to deal with a combination of shift and rotation geometric distortions.

Defining the electronic and geometric structure of one-electron oxidized copper-bis-phenoxide complexes.

PubMed

Storr, Tim; Verma, Pratik; Pratt, Russell C; Wasinger, Erik C; Shimazaki, Yuichi; Stack, T Daniel P

2008-11-19

The geometric and electronic structure of an oxidized Cu complex ([CuSal](+); Sal = N,N'-bis(3,5-di-tert-butylsalicylidene)-1,2-cyclohexane-(1R,2R)-diamine) with a non-innocent salen ligand has been investigated both in the solid state and in solution. Integration of information from UV-vis-NIR spectroscopy, magnetic susceptibility, electrochemistry, resonance Raman spectroscopy, X-ray crystallography, X-ray absorption spectroscopy, and density functional theory calculations provides critical insights into the nature of the localization/delocalization of the oxidation locus. In contrast to the analogous Ni derivative [NiSal](+) (Storr, T.; et al. Angew. Chem., Int. Ed. 2007, 46, 5198), which exists solely in the Ni(II) ligand-radical form, the locus of oxidation is metal-based for [CuSal](+), affording exclusively a Cu(III) species in the solid state (4-300 K). Variable-temperature solution studies suggest that [CuSal](+) exists in a reversible spin-equilibrium between a ligand-radical species [Cu(II)Sal(*)](+) (S = 1) and the high-valent metal form [Cu(III)Sal](+) (S = 0), indicative of nearly isoenergetic species. It is surprising that a bis-imine-bis-phenolate ligation stabilizes the Cu(III) oxidation state, and even more surprising that in solution a spin equilibrium occurs without a change in coordination number. The oxidized tetrahydrosalen analogue [CuSal(red)](+) (Sal(red) = N,N'-bis(3,5-di- tert-butylhydroxybenzyl)-1,2-cyclohexane-(1R,2R)-diamine) exists as a temperature-invariant Cu(II)-ligand-radical complex in solution, demonstrating that ostensibly simple variations of the ligand structure affect the locus of oxidation in Cu-bis-phenoxide complexes.

Defining the Electronic and Geometric Structure of One-Electron Oxidized Copper–Bis-phenoxide Complexes

PubMed Central

Storr, Tim; Verma, Pratik; Pratt, Russell C.; Wasinger, Erik C.; Shimazaki, Yuichi; Stack, T. Daniel P.

2009-01-01

The geometric and electronic structure of an oxidized Cu complex ([CuSal]+; Sal = N, N′-bis(3,5-di-tert-butylsalicylidene)-1,2-cyclohexane-(1R,2R)-diamine) with a non-innocent salen ligand has been investigated both in the solid state and in solution. Integration of information from UV–vis–NIR spectroscopy, magnetic susceptibility, electrochemistry, resonance Raman spectroscopy, X-ray crystallography, X-ray absorption spectroscopy, and density functional theory calculations provides critical insights into the nature of the localization/delocalization of the oxidation locus. In contrast to the analogous Ni derivative [NiSal]+ (Storr, T.; et al. Angew. Chem., Int. Ed. 2007, 46, 5198), which exists solely in the Ni(II) ligand-radical form, the locus of oxidation is metal-based for [CuSal]+, affording exclusively a Cu(III) species in the solid state (4–300 K). Variable-temperature solution studies suggest that [CuSal]+ exists in a reversible spin-equilibrium between a ligand-radical species [Cu(II)Sal•]+ (S = 1) and the high-valent metal form [Cu(III)Sal]+ (S = 0), indicative of nearly isoenergetic species. It is surprising that a bis-imine–bis-phenolate ligation stabilizes the Cu(III) oxidation state, and even more surprising that in solution a spin equilibrium occurs without a change in coordination number. The oxidized tetrahydrosalen analogue [CuSalred]+ (Salred = N, N′-bis(3,5-di-tert-butylhydroxybenzyl)-1,2-cyclohexane-(1R,2R)-diamine) exists as a temperature-invariant Cu(II)–ligand-radical complex in solution, demonstrating that ostensibly simple variations of the ligand structure affect the locus of oxidation in Cu–bis-phenoxide complexes. PMID:18939830

Trajectory analysis via a geometric feature space approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rintoul, Mark D.; Wilson, Andrew T.

This study aimed to organize a body of trajectories in order to identify, search for and classify both common and uncommon behaviors among objects such as aircraft and ships. Existing comparison functions such as the Fréchet distance are computationally expensive and yield counterintuitive results in some cases. We propose an approach using feature vectors whose components represent succinctly the salient information in trajectories. These features incorporate basic information such as the total distance traveled and the distance between start/stop points as well as geometric features related to the properties of the convex hull, trajectory curvature and general distance geometry. Additionally,more » these features can generally be mapped easily to behaviors of interest to humans who are searching large databases. Most of these geometric features are invariant under rigid transformation. Furthermore, we demonstrate the use of different subsets of these features to identify trajectories similar to an exemplar, cluster a database of several hundred thousand trajectories and identify outliers.« less

Measuring the Scalar Curvature with Clocks and Photons: Voronoi-Delaunay Lattices in Regge Calculus

NASA Astrophysics Data System (ADS)

Miller, Warner; McDonald, Jonathan

2008-04-01

The Riemann scalar curvature plays a central role in Einstein's geometric theory of gravity. We describe a new geometric construction of this scalar curvature invariant at an event (vertex) in a discrete spacetime geometry. This allows one to constructively measure the scalar curvature using only clocks and photons. Given recent interest in discrete pre-geometric models of quantum gravity, we believe it is ever so important to reconstruct the curvature scalar with respect to a finite number of communicating observers. This derivation makes use of a fundamental lattice cell built from elements inherited from both the original simplicial (Delaunay) spacetime and its circumcentric dual (Voronoi) lattice. The orthogonality properties between these two lattices yield an expression for the vertex-based scalar curvature which is strikingly similar to the corresponding hinge-based expression in Regge Calculus (deficit angle per unit Voronoi dual area). In particular, we show that the scalar curvature is simply a vertex-based weighted average of deficits per weighted average of dual areas.

Trajectory analysis via a geometric feature space approach

DOE PAGES

Rintoul, Mark D.; Wilson, Andrew T.

2015-10-05

This study aimed to organize a body of trajectories in order to identify, search for and classify both common and uncommon behaviors among objects such as aircraft and ships. Existing comparison functions such as the Fréchet distance are computationally expensive and yield counterintuitive results in some cases. We propose an approach using feature vectors whose components represent succinctly the salient information in trajectories. These features incorporate basic information such as the total distance traveled and the distance between start/stop points as well as geometric features related to the properties of the convex hull, trajectory curvature and general distance geometry. Additionally,more » these features can generally be mapped easily to behaviors of interest to humans who are searching large databases. Most of these geometric features are invariant under rigid transformation. Furthermore, we demonstrate the use of different subsets of these features to identify trajectories similar to an exemplar, cluster a database of several hundred thousand trajectories and identify outliers.« less

Multipartite entanglement in fermionic systems via a geometric measure

NASA Astrophysics Data System (ADS)

Lari, Behzad; Durganandini, P.; Joag, Pramod S.

2010-12-01

We study multipartite entanglement in a system consisting of indistinguishable fermions. Specifically, we have proposed a geometric entanglement measure for N spin-(1)/(2) fermions distributed over 2L modes (single-particle states). The measure is defined on the 2L qubit space isomorphic to the Fock space for 2L single-particle states. This entanglement measure is defined for a given partition of 2L modes containing m⩾2 subsets. Thus this measure applies to m⩽2L partite fermionic systems where L is any finite number, giving the number of sites. The Hilbert spaces associated with these subsets may have different dimensions. Further, we have defined the local quantum operations with respect to a given partition of modes. This definition is generic and unifies different ways of dividing a fermionic system into subsystems. We have shown, using a representative case, that the geometric measure is invariant under local unitary operators corresponding to a given partition. We explicitly demonstrate the use of the measure to calculate multipartite entanglement in some correlated electron systems.

Theoretical foundations of spatially-variant mathematical morphology part ii: gray-level images.

PubMed

Bouaynaya, Nidhal; Schonfeld, Dan

2008-05-01

In this paper, we develop a spatially-variant (SV) mathematical morphology theory for gray-level signals and images in the Euclidean space. The proposed theory preserves the geometrical concept of the structuring function, which provides the foundation of classical morphology and is essential in signal and image processing applications. We define the basic SV gray-level morphological operators (i.e., SV gray-level erosion, dilation, opening, and closing) and investigate their properties. We demonstrate the ubiquity of SV gray-level morphological systems by deriving a kernel representation for a large class of systems, called V-systems, in terms of the basic SV graylevel morphological operators. A V-system is defined to be a gray-level operator, which is invariant under gray-level (vertical) translations. Particular attention is focused on the class of SV flat gray-level operators. The kernel representation for increasing V-systems is a generalization of Maragos' kernel representation for increasing and translation-invariant function-processing systems. A representation of V-systems in terms of their kernel elements is established for increasing and upper-semi-continuous V-systems. This representation unifies a large class of spatially-variant linear and non-linear systems under the same mathematical framework. Finally, simulation results show the potential power of the general theory of gray-level spatially-variant mathematical morphology in several image analysis and computer vision applications.

Factor structure of the CES-D and measurement invariance across gender in Mainland Chinese adolescents.

PubMed

Wang, Mengcheng; Armour, Cherie; Wu, Yan; Ren, Fen; Zhu, Xiongzhao; Yao, Shuqiao

2013-09-01

The primary aim was to examine the depressive symptom structure of Mainland China adolescents using the Center for Epidemiologic Studies Depression Scale (CES-D). Exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) were simultaneously conducted to determine the structure of the CES-D in a large scale, representative adolescent samples recruited from Mainland China. Multigroup CFA (N = 5059, 48% boys, mean = 16.55±1.06) was utilized to test the factorial invariance of the depressive symptom structure, which was generated by EFA and confirmed by CFA across gender. The CES-D can be interpreted in terms of 3 symptom dimensions. Additionally, factorial invariance of the new proposed model across gender was supported at all assuming different degrees of invariance. Mainland Chinese adolescents have specific depressive symptom structure, which is consistent across gender. © 2013 Wiley Periodicals, Inc.

Geometry of the theory space in the exact renormalization group formalism

NASA Astrophysics Data System (ADS)

Pagani, C.; Sonoda, H.

2018-01-01

We consider the theory space as a manifold whose coordinates are given by the couplings appearing in the Wilson action. We discuss how to introduce connections on this theory space. A particularly intriguing connection can be defined directly from the solution of the exact renormalization group (ERG) equation. We advocate a geometric viewpoint that lets us define straightforwardly physically relevant quantities invariant under the changes of a renormalization scheme.

Aspects of Shape Coexistence in the Geometric Collective Model of Nuclei

NASA Astrophysics Data System (ADS)

Georgoudis, P. E.; Leviatan, A.

2018-02-01

We examine the coexistence of spherical and γ-unstable deformed nuclear shapes, described by an SO(5)-invariant Bohr Hamiltonian, along the critical-line. Calculations are performed in the Algebraic Collective Model by introducing two separate bases, optimized to accommodate simultaneously different forms of dynamics. We demonstrate the need to modify the β-dependence of the moments of inertia, in order to obtain an adequate description of such shape-coexistence.

Quantitative characterization and comparison of precipitate and grain shape in Nickel -base superalloys using moment invariants

NASA Astrophysics Data System (ADS)

Callahan, Patrick Gregory

A fundamental objective of materials science and engineering is to understand the structure-property-processing-performance relationship. We need to know the true 3-D microstructure of a material to understand certain geometric properties of a material, and thus fulfill this objective. Focused ion beam (FIB) serial sectioning allows us to find the true 3-D microstructure of Ni-base superalloys. Once the true 3-D microstructure is obtained, an accurate quantitative description and characterization of precipitate and/or grain shapes is needed to understand the microstructure and describe it in an unbiased way. In this thesis, second order moment invariants, the shape quotient Q, a convexity measure relating the volume of an object to the volume of its convex hull, V/Vconv, and Gaussian curvature have been used to compare an experimentally observed polycrystalline IN100 microstructure to three synthetic microstructures. The three synthetic microstructures used different shape classes to produce starting grain shapes. The three shape classes are ellipsoids, superellipsoids, and the shapes generated when truncating a cube with an octahedron. The microstructures are compared using a distance measure, the Hellinger distance. The Hellinger distance is used to compare distributions of shape descriptors for the grains in each microstructure. The synthetic microstructure that has the smallest Hellinger distance, and so best matched the experimentally observed microstructure is the microstructure that used superellipsoids as a starting grain shape. While it has the smallest Hellinger distance, and is approaching realistic grain morphologies, the superellipsoidal microstructure is still not realistic. Second order moment invariants, Q, and V/V conv have also been used to characterize the γ' precipitate shapes from four experimental Ru-containing Ni-base superalloys with differences in alloying additions. The superalloys are designated UM-F9, UM-F18, UM-F19, and UM-F22. The different alloying additions in each sample cause differences in lattice misfit and γ' precipitate shape morphology, varying from spherical, to cuboidal, to intermediate morphologies. 3-D datasets from each alloy were collected via automated Focused Ion Beam (FIB) serial sectioning. Digital image processing methods are used to register, clean, and segment the images in each of the datasets in order to digitally reconstruct the microstructures in 3-D. The distributions of the shape descriptors of the γ' precipitates from each microstructure are compared using the Hellinger distance. The Hellinger distance determines if there are quantitative differences in the γ' precipitate morphologies, or if they are the same. It was found that comparing distributions of the second order affine moment invariant Ω 3 with the Hellinger distance is sufficient for recognizing that alloys have different compositions. The secondary γ' precipitate shapes in two Ni-based superalloys, one from a UM-F20 alloy with cuboidal precipitates, and one from a Rene-88 DT alloy with more complex dendritic precipitates, have been decomposed and reconstructed using 3-D Zernike functions, which are orthogonal over the unit ball; they can be used to decompose an arbitrary shape scaled to fit inside an embedding sphere into spherical harmonics. Relatively complex shapes can be decomposed into, and reconstructed from, 3-D Zernike functions. In this thesis we show the 3-D Zernike functions and a method to derive expressions for Zernike moments from the more familiar geometric moments. Then Zernike moment reconstructions up to order 20 of precipitates from the two Ni-base superalloys are presented. The Zernike moment reconstructions were characterized using second order moment invariants, and have yielded good reconstructions of cuboidal precipitates. More orders of Zernike moments may be needed to accurately reconstruct the dendritic precipitates. We also introduce the concept of moment invariant density maps to describe 3-D shapes using 2-D moment invariants. To do this we characterize 2-D sections of a 3-D microstructure using 2-D moment invariants. The statistical distribution of 2-D moment invariants from the sections are compared to a library of density maps produced from different shapes. The sectioning plane is random so each group of particles produces a statistical distribution of 2-D moments that can represent a microstructure. Then we show three example applications: determination of a 3-D shape by computing the Hellinger distance between moment invariant density maps derived from random 2-D section micrographs and the density map database; automated detection and quantification of rafting in cuboidal microstructures; and quantitative comparison of pairs of microstructures.

Star products on graded manifolds and α′-corrections to Courant algebroids from string theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deser, Andreas, E-mail: andreas.deser@itp.uni-hannover.de

2015-09-15

Courant algebroids, originally used to study integrability conditions for Dirac structures, have turned out to be of central importance to study the effective supergravity limit of string theory. The search for a geometric description of T-duality leads to Double Field Theory (DFT), whose gauge algebra is governed by the C-bracket, a generalization of the Courant bracket in the sense that it reduces to the latter by solving a specific constraint. Recently, in DFT deformations of the C-bracket and O(d, d)-invariant bilinear form to first order in the closed string sigma model coupling, α′ were derived by analyzing the transformation propertiesmore » of the Neveu-Schwarz B-field. By choosing a particular Poisson structure on the Drinfel’d double corresponding to the Courant algebroid structure of the generalized tangent bundle, we are able to interpret the C-bracket and bilinear form in terms of Poisson brackets. As a result, we reproduce the α′-deformations for a specific solution to the strong constraint of DFT as expansion of a graded version of the Moyal-Weyl star product.« less

Theoretical investigation on the molecular structure, Infrared, Raman and NMR spectra of para-halogen benzenesulfonamides, 4-X-C 6H 4SO 2NH 2 (X = Cl, Br or F)

NASA Astrophysics Data System (ADS)

Karabacak, Mehmet; Çınar, Mehmet; Çoruh, Ali; Kurt, Mustafa

2009-02-01

In the present study, the structural properties of para-halogen benzenesulfonamides, 4-XC 6H 4SO 2NH 2 (4-chlorobenzenesulfonamide (I), 4-bromobenzenesulfonamide (II) and 4-fluorobenzenesulfonamide (III)) have been studied extensively utilizing ab initio Hartree-Fock (HF) and density functional theory (DFT) employing B3LYP exchange correlation. The vibrational frequencies were calculated and scaled values were compared with experimental values. The complete assignments were performed on the basis of the total energy distribution (TED) of the vibrational modes, calculated with scaled quantum mechanics (SQM) method. The effects of the halogen substituent on the characteristic benzenesulfonamides bands in the spectra are discussed. The 1H and 13C nuclear magnetic resonance (NMR) chemical shifts of the molecules were calculated using the Gauge-Invariant Atomic Orbital (GIAO) method. Finally, geometric parameters, vibrational bands and chemical shifts were compared with available experimental data of the molecules. The fully optimized geometries of the molecules were found to be consistent with the X-ray crystal structures. The observed and calculated frequencies and chemical shifts were found to be in very good agreement.

Orthogonal Invariant Sets of the Diffusion Tensor and the Development of a Curvilinear Set Suitable for Low-Anisotropy Tissues

PubMed Central

Damion, Robin A.; Radjenovic, Aleksandra; Ingham, Eileen; Jin, Zhongmin; Ries, Michael E.

2013-01-01

We develop a curvilinear invariant set of the diffusion tensor which may be applied to Diffusion Tensor Imaging measurements on tissues and porous media. This new set is an alternative to the more common invariants such as fractional anisotropy and the diffusion mode. The alternative invariant set possesses a different structure to the other known invariant sets; the second and third members of the curvilinear set measure the degree of orthotropy and oblateness/prolateness, respectively. The proposed advantage of these invariants is that they may work well in situations of low diffusion anisotropy and isotropy, as is often observed in tissues such as cartilage. We also explore the other orthogonal invariant sets in terms of their geometry in relation to eigenvalue space; a cylindrical set, a spherical set (including fractional anisotropy and the mode), and a log-Euclidean set. These three sets have a common structure. The first invariant measures the magnitude of the diffusion, the second and third invariants capture aspects of the anisotropy; the magnitude of the anisotropy and the shape of the diffusion ellipsoid (the manner in which the anisotropy is realised). We also show a simple method to prove the orthogonality of the invariants within a set. PMID:24244366

Measurement invariance of the strength of motivation for medical school: a multi-group confirmatory factor analysis.

PubMed

An, M; Kusurkar, R A; Li, L; Xiao, Y; Zheng, C; Hu, J; Chen, M

2017-07-11

The Strength of Motivation for Medical School-Revised (SMMS-R) questionnaire measures students' motivation for studying medicine. It includes three subscales: 'willingness to sacrifice', 'readiness to start', and 'persistence'. Measurement invariance is a prerequisite for group comparisons. The objectives of this study were to verify the factorial structure of the SMMS-R questionnaire and to investigate it's measurement invariance. A total of 989 medical students were approached, 930 cases were kept for data analysis. Factorial structure of and measurement invariance of the SMMS-R were tested using single and multiple group confirmatory factor analyses with Mplus. Trational Cronbach's α along with McDonald's ω and glb were used to measure internal consistency for each subscale. Internal consistency for subscales and the full instrument were within the acceptable range. A 3-factor structure of the Chinese version of the SMMS-R was supported. Full configural, metric and partial scalar invariance were obtained. The SMMS-R showed measurement invariance across gender and two independent samples. So it can be used for group and cross-cultural comparisons.

The Green-Schwarz mechanism and geometric anomaly relations in 2d (0,2) F-theory vacua

NASA Astrophysics Data System (ADS)

Weigand, Timo; Xu, Fengjun

2018-04-01

We study the structure of gauge and gravitational anomalies in 2d N = (0 , 2) theories obtained by compactification of F-theory on elliptically fibered Calabi-Yau 5-folds. Abelian gauge anomalies, induced at 1-loop in perturbation theory, are cancelled by a generalized Green-Schwarz mechanism operating at the level of chiral scalar fields in the 2d supergravity theory. We derive closed expressions for the gravitational and the non-abelian and abelian gauge anomalies including the Green-Schwarz counterterms. These expressions involve topological invariants of the underlying elliptic fibration and the gauge background thereon. Cancellation of anomalies in the effective theory predicts intricate topological identities which must hold on every elliptically fibered Calabi-Yau 5-fold. We verify these relations in a non-trivial example, but their proof from a purely mathematical perspective remains as an interesting open problem. Some of the identities we find on elliptic 5-folds are related in an intriguing way to previously studied topological identities governing the structure of anomalies in 6d N = (1 , 0) and 4d N = 1 theories obtained from F-theory.

TopologyNet: Topology based deep convolutional and multi-task neural networks for biomolecular property predictions

PubMed Central

2017-01-01

Although deep learning approaches have had tremendous success in image, video and audio processing, computer vision, and speech recognition, their applications to three-dimensional (3D) biomolecular structural data sets have been hindered by the geometric and biological complexity. To address this problem we introduce the element-specific persistent homology (ESPH) method. ESPH represents 3D complex geometry by one-dimensional (1D) topological invariants and retains important biological information via a multichannel image-like representation. This representation reveals hidden structure-function relationships in biomolecules. We further integrate ESPH and deep convolutional neural networks to construct a multichannel topological neural network (TopologyNet) for the predictions of protein-ligand binding affinities and protein stability changes upon mutation. To overcome the deep learning limitations from small and noisy training sets, we propose a multi-task multichannel topological convolutional neural network (MM-TCNN). We demonstrate that TopologyNet outperforms the latest methods in the prediction of protein-ligand binding affinities, mutation induced globular protein folding free energy changes, and mutation induced membrane protein folding free energy changes. Availability: weilab.math.msu.edu/TDL/ PMID:28749969

Periodic minimal surfaces

NASA Astrophysics Data System (ADS)

Mackay, Alan L.

1985-04-01

A minimal surface is one for which, like a soap film with the same pressure on each side, the mean curvature is zero and, thus, is one where the two principal curvatures are equal and opposite at every point. For every closed circuit in the surface, the area is a minimum. Schwarz1 and Neovius2 showed that elements of such surfaces could be put together to give surfaces periodic in three dimensions. These periodic minimal surfaces are geometrical invariants, as are the regular polyhedra, but the former are curved. Minimal surfaces are appropriate for the description of various structures where internal surfaces are prominent and seek to adopt a minimum area or a zero mean curvature subject to their topology; thus they merit more complete numerical characterization. There seem to be at least 18 such surfaces3, with various symmetries and topologies, related to the crystallographic space groups. Recently, glyceryl mono-oleate (GMO) was shown by Longley and McIntosh4 to take the shape of the F-surface. The structure postulated is shown here to be in good agreement with an analysis of the fundamental geometry of periodic minimal surfaces.

Electric dipole moments with and beyond flavor invariants

NASA Astrophysics Data System (ADS)

Smith, Christopher; Touati, Selim

2017-11-01

In this paper, the flavor structure of quark and lepton electric dipole moments in the SM and beyond is investigated using tools inspired from Minimal Flavor Violation. While Jarlskog-like flavor invariants are adequate for estimating CP-violation from closed fermion loops, non-invariant structures arise from rainbow-like processes. Our goal is to systematically construct these latter flavor structures in the quark and lepton sectors, assuming different mechanisms for generating neutrino masses. Numerically, they are found typically much larger, and not necessarily correlated with, Jarlskog-like invariants. Finally, the formalism is adapted to deal with a third class of flavor structures, sensitive to the flavored U (1) phases, and used to study the impact of the strong CP-violating interaction and the interplay between the neutrino Majorana phases and possible baryon and/or lepton number violating interactions.

Locality and Unitarity of Scattering Amplitudes from Singularities and Gauge Invariance

NASA Astrophysics Data System (ADS)

Arkani-Hamed, Nima; Rodina, Laurentiu; Trnka, Jaroslav

2018-06-01

We conjecture that the leading two-derivative tree-level amplitudes for gluons and gravitons can be derived from gauge invariance together with mild assumptions on their singularity structure. Assuming locality (that the singularities are associated with the poles of cubic graphs), we prove that gauge invariance in just n -1 particles together with minimal power counting uniquely fixes the amplitude. Unitarity in the form of factorization then follows from locality and gauge invariance. We also give evidence for a stronger conjecture: assuming only that singularities occur when the sum of a subset of external momenta go on shell, we show in nontrivial examples that gauge invariance and power counting demand a graph structure for singularities. Thus, both locality and unitarity emerge from singularities and gauge invariance. Similar statements hold for theories of Goldstone bosons like the nonlinear sigma model and Dirac-Born-Infeld by replacing the condition of gauge invariance with an appropriate degree of vanishing in soft limits.

Fractal Signals & Space-Time Cartoons

NASA Astrophysics Data System (ADS)

Oetama, H. C. Jakob; Maksoed, W. H.

2016-03-01

In ``Theory of Scale Relativity'', 1991- L. Nottale states whereas ``scale relativity is a geometrical & fractal space-time theory''. It took in comparisons to ``a unified, wavelet based framework for efficiently synthetizing, analyzing ∖7 processing several broad classes of fractal signals''-Gregory W. Wornell:``Signal Processing with Fractals'', 1995. Furthers, in Fig 1.1. a simple waveform from statistically scale-invariant random process [ibid.,h 3 ]. Accompanying RLE Technical Report 566 ``Synthesis, Analysis & Processing of Fractal Signals'' as well as from Wornell, Oct 1991 herewith intended to deducts =a Δt + (1 - β Δ t) ...in Petersen, et.al: ``Scale invariant properties of public debt growth'',2010 h. 38006p2 to [1/{1- (2 α (λ) /3 π) ln (λ/r)}depicts in Laurent Nottale,1991, h 24. Acknowledgment devotes to theLates HE. Mr. BrigadierGeneral-TNI[rtd].Prof. Ir. HANDOJO.

Fully invariant wavelet enhanced minimum average correlation energy filter for object recognition in cluttered and occluded environments

NASA Astrophysics Data System (ADS)

Tehsin, Sara; Rehman, Saad; Riaz, Farhan; Saeed, Omer; Hassan, Ali; Khan, Muazzam; Alam, Muhammad S.

2017-05-01

A fully invariant system helps in resolving difficulties in object detection when camera or object orientation and position are unknown. In this paper, the proposed correlation filter based mechanism provides the capability to suppress noise, clutter and occlusion. Minimum Average Correlation Energy (MACE) filter yields sharp correlation peaks while considering the controlled correlation peak value. Difference of Gaussian (DOG) Wavelet has been added at the preprocessing stage in proposed filter design that facilitates target detection in orientation variant cluttered environment. Logarithmic transformation is combined with a DOG composite minimum average correlation energy filter (WMACE), capable of producing sharp correlation peaks despite any kind of geometric distortion of target object. The proposed filter has shown improved performance over some of the other variant correlation filters which are discussed in the result section.

Geometry of quantum Hall states: Gravitational anomaly and transport coefficients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Can, Tankut, E-mail: tcan@scgp.stonybrook.edu; Laskin, Michael; Wiegmann, Paul B.

2015-11-15

We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly. We develop a general method to compute correlation functions of FQH states in a curved space, where local transformation properties of these states are examined through local geometric variations. We introduce the notion of a generating functional and relate it to geometric invariant functionals recently studied in geometry. We develop two complementary methods to study the geometry of the FQHE. One method is based on iteratingmore » a Ward identity, while the other is based on a field theoretical formulation of the FQHE through a path integral formalism.« less

A Geometric Method for Model Reduction of Biochemical Networks with Polynomial Rate Functions.

PubMed

Samal, Satya Swarup; Grigoriev, Dima; Fröhlich, Holger; Weber, Andreas; Radulescu, Ovidiu

2015-12-01

Model reduction of biochemical networks relies on the knowledge of slow and fast variables. We provide a geometric method, based on the Newton polytope, to identify slow variables of a biochemical network with polynomial rate functions. The gist of the method is the notion of tropical equilibration that provides approximate descriptions of slow invariant manifolds. Compared to extant numerical algorithms such as the intrinsic low-dimensional manifold method, our approach is symbolic and utilizes orders of magnitude instead of precise values of the model parameters. Application of this method to a large collection of biochemical network models supports the idea that the number of dynamical variables in minimal models of cell physiology can be small, in spite of the large number of molecular regulatory actors.

Testing Cross-Cultural Generalizability of the Task and Ego Orientation in Sport Questionnaire across American and Chinese Samples

PubMed Central

Monsma, Eva

2016-01-01

This paper examines the factor structure and measurement invariance of the Task and Ego Orientation in Sport Questionnaire (TEOSQ) across American and Chinese samples. Results based on the mean and covariance structure analyses supported configural invariance, metric invariance and scalar invariance across groups. Latent means analyses revealed that American sample had significantly higher mean scores on task and ego orientations than the Chinese sample. The findings suggest that the TEOSQ is a valid and reliable instrument in assessing achievement motivation across these two diverse populations. PMID:27399869

Kinematic assumptions and their consequences on the structure of field equations in continuum dislocation theory

NASA Astrophysics Data System (ADS)

Silbermann, C. B.; Ihlemann, J.

2016-03-01

Continuum Dislocation Theory (CDT) relates gradients of plastic deformation in crystals with the presence of geometrically necessary dislocations. Therefore, the dislocation tensor is introduced as an additional thermodynamic state variable which reflects tensorial properties of dislocation ensembles. Moreover, the CDT captures both the strain energy from the macroscopic deformation of the crystal and the elastic energy of the dislocation network, as well as the dissipation of energy due to dislocation motion. The present contribution deals with the geometrically linear CDT. More precise, the focus is on the role of dislocation kinematics for single and multi-slip and its consequences on the field equations. Thereby, the number of active slip systems plays a crucial role since it restricts the degrees of freedom of plastic deformation. Special attention is put on the definition of proper, well-defined invariants of the dislocation tensor in order to avoid any spurious dependence of the resulting field equations on the coordinate system. It is shown how a slip system based approach can be in accordance with the tensor nature of the involved quantities. At first, only dislocation glide in one active slip system of the crystal is allowed. Then, the special case of two orthogonal (interacting) slip systems is considered and the governing field equations are presented. In addition, the structure and symmetry of the backstress tensor is investigated from the viewpoint of thermodynamical consistency. The results will again be used in order to facilitate the set of field equations and to prepare for a robust numerical implementation.

Hidden scale invariance of metals

NASA Astrophysics Data System (ADS)

Hummel, Felix; Kresse, Georg; Dyre, Jeppe C.; Pedersen, Ulf R.

2015-11-01

Density functional theory (DFT) calculations of 58 liquid elements at their triple point show that most metals exhibit near proportionality between the thermal fluctuations of the virial and the potential energy in the isochoric ensemble. This demonstrates a general "hidden" scale invariance of metals making the condensed part of the thermodynamic phase diagram effectively one dimensional with respect to structure and dynamics. DFT computed density scaling exponents, related to the Grüneisen parameter, are in good agreement with experimental values for the 16 elements where reliable data were available. Hidden scale invariance is demonstrated in detail for magnesium by showing invariance of structure and dynamics. Computed melting curves of period three metals follow curves with invariance (isomorphs). The experimental structure factor of magnesium is predicted by assuming scale invariant inverse power-law (IPL) pair interactions. However, crystal packings of several transition metals (V, Cr, Mn, Fe, Nb, Mo, Ta, W, and Hg), most post-transition metals (Ga, In, Sn, and Tl), and the metalloids Si and Ge cannot be explained by the IPL assumption. The virial-energy correlation coefficients of iron and phosphorous are shown to increase at elevated pressures. Finally, we discuss how scale invariance explains the Grüneisen equation of state and a number of well-known empirical melting and freezing rules.

Holonomy Attractor Connecting Spaces of Different Curvature Responsible for ``Anomalies''

NASA Astrophysics Data System (ADS)

Binder, Bernd

2009-03-01

In this lecture paper we derive Magic Angle Precession (MAP) from first geometric principles. MAP can arise in situations, where precession is multiply related to spin, linearly by time or distance (dynamic phase, rolling, Gauss law) and transcendentally by the holonomy loop path (geometric phase). With linear spin-precession coupling, gyroscopes can be spun up and down to very high frequencies via low frequency holonomy control induced by external accelerations, which provides for extreme coupling strengths or "anomalies" that can be tested by the powerball or gyrotwister device. Geometrically, a gyroscopic manifold with spherical metric is tangentially aligned to a precession wave channel with conic or hyperbolic metric (like the relativistic Thomas precession). Transporting triangular spin/precession vector relations across the tangential boundary of contact with SO(3) Lorentz symmetry, we get extreme vector currents near the attractor fixed points in precession phase space, where spin currents remain intact while crossing the contact boundaries between regions of different curvature signature (-1, 0, +1). The problem can be geometrically solved by considering a curvature invariant triangular condition, which holds on surfaces with different curvature that are in contact and locally parallel. In this case two out of three angles are identical, whereas the third angle is different due to holonomy. If we require that the side length ratio corresponding to these angles are invariant we get a geodesic chaotic attractor, which is a cosine map cos(x)˜Mx in parameter space providing for fixed points, limit cycle bifurcations, and singularities. The situation could be quite natural and common in the context of vector currents in curved spacetime and gauge theories. MAP could even be part of the electromagnetic interaction, where the electric charge is the geometric U(1) precession spin current and gauge potential with magnetic effects given by extra rotations under the SO(3). MAP can be extended to a neural network, where the synaptic connection of the holonomy attractor is just the mathematical condition adjusting and bridging spaces with positive (spherical) and negative (hyperbolic) curvature allowing for lossless/supra spin currents. Another strategy is to look for existing spin/precession anomalies and corresponding nonlinear holonomy conditions at the most fundamental level from the quark level to the cosmic scale. In these sceneries the geodesic attractor could control holonomy and curvature near the fixed points. It was proposed in 2002 that this should happen with electrons in atomic orbits showing a Berry phase part of the Rydberg or Sommerfeld fine structure constant and in 2003 that this effect could be responsible for (in)stabilities in the nuclear range and in superconductors. In 2008 it was shown that the attractor is part of the chaotic mechanical dynamics successfully at work in the Gyro-twister fitness device, and in 2007-2009 that there could be some deep relevance to "anomalies" in many scenarios even on the cosmic scales. Thus, we will point to and discuss some possible future applications that could be utilized for metric engineering: generating artificial holonomy and curvature (DC effect) for propulsion, or forcing holonomy waves (AC effect) in hyperbolic space-time, which are just gravitational waves interesting for communication.

The geometrical structure of quantum theory as a natural generalization of information geometry

NASA Astrophysics Data System (ADS)

Reginatto, Marcel

2015-01-01

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.

On the geometry of inhomogeneous quantum groups

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aschieri, Paolo

1998-01-01

The author gives a pedagogical introduction to the differential calculus on quantum groups by stressing at all stages the connection with the classical case. He further analyzes the relation between differential calculus and quantum Lie algebra of left (right) invariant vectorfields. Equivalent definitions of bicovariant differential calculus are studied and their geometrical interpretation is explained. From these data he constructs and analyzes the space of vectorfields, and naturally introduces a contraction operator and a Lie derivative. Their properties are discussed.

Geometric phase of cosmological scalar and tensor perturbations in f(R) gravity

NASA Astrophysics Data System (ADS)

Balajany, Hamideh; Mehrafarin, Mohammad

2018-05-01

By using the conformal equivalence of f(R) gravity in vacuum and the usual Einstein theory with scalar-field matter, we derive the Hamiltonian of the linear cosmological scalar and tensor perturbations in f(R) gravity in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes as a Lewis-Riesenfeld phase.

On Nonlinear Functionals of Random Spherical Eigenfunctions

NASA Astrophysics Data System (ADS)

Marinucci, Domenico; Wigman, Igor

2014-05-01

We prove central limit theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combines asymptotic analysis of higher order moments for Legendre polynomials and, in addition, recent results on Malliavin calculus and total variation bounds for Gaussian subordinated fields. We discuss applications to geometric functionals like the defect and invariant statistics, e.g., polyspectra of isotropic spherical random fields. Both of these have relevance for applications, especially in an astrophysical environment.

CMB in the river frame and gauge invariance at second order

NASA Astrophysics Data System (ADS)

Roldan, Omar

2018-03-01

Gauge invariance: the Sachs-Wolfe formula describing the Cosmic Microwave Background (CMB) temperature anisotropies is one of the most important relations in cosmology. Despite its importance, the gauge invariance of this formula has only been discussed at first order. Here we discuss the subtle issue of second-order gauge transformations on the CMB. By introducing two rules (needed to handle the subtle issues), we prove the gauge invariance of the second-order Sachs-Wolfe formula and provide several compact expressions which can be useful for the study of gauge transformations on cosmology. Our results go beyond a simple technicality: we discuss from a physical point of view several aspects that improve our understanding of the CMB. We also elucidate how crucial it is to understand gauge transformations on the CMB in order to avoid errors and/or misconceptions as occurred in the past. The river frame: we introduce a cosmological frame which we call the river frame. In this frame, photons and any object can be thought as fishes swimming in the river and relations are easily expressed in either the metric or the covariant formalism then ensuring a transparent geometric meaning. Finally, our results show that the river frame is useful to make perturbative and non-perturbative analysis. In particular, it was already used to obtain the fully nonlinear generalization of the Sachs-Wolfe formula and is used here to describe second-order perturbations.

Blind readers break mirror invariance as sighted do.

PubMed

de Heering, Adélaïde; Collignon, Olivier; Kolinsky, Régine

2018-04-01

Mirror invariance refers to a predisposition of humans, including infants and animals, which urge them to consider mirrored images as corresponding to the same object. Yet in order to learn to read a written system that incorporates mirrored letters (e.g., vs. in the Latin alphabet), humans learn to break this perceptual bias. Here we examined the role visual experience and input modality play in the emergence of this bias. To this end, we tested congenital blind (CB) participants in two same-different tactile comparison tasks including pairs of mirrored and non-mirrored Braille letters as well as embossed unfamiliar geometric shapes and Latin letters, and compared their results to those of age-matched sighted participants involved in similar but visually-presented tasks. Sighted participants showed a classical pattern of results for their material of expertise, Latin letters. CB's results signed for their expertise with the Braille script compared to the other two materials that they processed according to an internal frame of reference. They also evidenced that they automatically break mirror invariance for different materials explored through the tactile modality, including Braille letters. Altogether, these results demonstrate that learning to read Braille through the tactile modality allows breaking mirror invariance in a comparable way to what is observed in sighted individuals for the mirrored letters of the Latin alphabet. Copyright © 2018 Elsevier Ltd. All rights reserved.

Measurement invariance of the Illness Intrusiveness Ratings Scale's three-factor structure in men and women with cancer.

PubMed

Mah, Kenneth; Bezjak, Andrea; Loblaw, D Andrew; Gotowiec, Andrew; Devins, Gerald M

2011-02-01

Illness- and treatment-related disruptions to valued activities and interests (illness intrusiveness) are central to quality of life in chronic disease and are captured by three subscales of the Illness Intrusiveness Ratings Scale (IIRS): the Instrumental, Intimacy, and Relationships and Personal Development subscales. Using individual (CFA) and multisample confirmatory factor analyses (MSCFA), we evaluated measurement invariance of the IIRS's 3-factor structure in men and women with cancer. Men (n = 210) and women (n = 206) with 1 of 4 cancer diagnoses (gastrointestinal, head and neck, lymphoma, lung) recruited from outpatient clinics completed the IIRS. In the MSCFA, we applied an analysis of means and covariance structures approach to test increasingly stringent equality constraints on factor structure parameters to evaluate weak, strong, and strict measurement invariance of the 3-factor structure between men and women. Individual CFAs demonstrated fit of the hypothesized 3-factor structure for men and women, although more consistently for men. The 3-factor structure was superior to an alternative 1-factor structure. MSCFA results indicated that parameters of the 3-factor structure could be considered equivalent between the sexes up to the level of strong invariance. Strict invariance was not supported. Overall, IIRS scores can be interpreted similarly for men and women with cancer. Illness intrusiveness can be considered as important in the psychosocial adaptation of people with cancer as it is for people affected by other chronic conditions. (c) 2011 APA, all rights reserved

Invariance of Parent Ratings of the ADHD Symptoms in Australian and Malaysian, and North European Australian and Malay Malaysia Children: A Mean and Covariance Structures Analysis Approach

ERIC Educational Resources Information Center

Gomez, Rapson

2009-01-01

Objective: This study used the mean and covariance structures analysis approach to examine the equality or invariance of ratings of the 18 ADHD symptoms. Method: 783 Australian and 928 Malaysian parents provided ratings for an ADHD rating scale. Invariance was tested across these groups (Comparison 1), and North European Australian (n = 623) and…

Groenewold-Moyal product, α*-cohomology, and classification of translation-invariant non-commutative structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Varshovi, Amir Abbass

2013-07-15

The theory of α*-cohomology is studied thoroughly and it is shown that in each cohomology class there exists a unique 2-cocycle, the harmonic form, which generates a particular Groenewold-Moyal star product. This leads to an algebraic classification of translation-invariant non-commutative structures and shows that any general translation-invariant non-commutative quantum field theory is physically equivalent to a Groenewold-Moyal non-commutative quantum field theory.

Long-range correlations, geometrical structure, and transport properties of macromolecular solutions. The equivalence of configurational statistics and geometrodynamics of large molecules.

PubMed

Mezzasalma, Stefano A

2007-12-04

A special theory of Brownian relativity was previously proposed to describe the universal picture arising in ideal polymer solutions. In brief, it redefines a Gaussian macromolecule in a 4-dimensional diffusive spacetime, establishing a (weak) Lorentz-Poincaré invariance between liquid and polymer Einstein's laws for Brownian movement. Here, aimed at inquiring into the effect of correlations, we deepen the extension of the special theory to a general formulation. The previous statistical equivalence, for dynamic trajectories of liquid molecules and static configurations of macromolecules, and rather obvious in uncorrelated systems, is enlarged by a more general principle of equivalence, for configurational statistics and geometrodynamics. Accordingly, the three geodesic motion, continuity, and field equations could be rewritten, and a number of scaling behaviors were recovered in a spacetime endowed with general static isotropic metric (i.e., for equilibrium polymer solutions). We also dealt with universality in the volume fraction and, unexpectedly, found that a hyperscaling relation of the form, (average size) x (diffusivity) x (viscosity)1/2 ~f(N0, phi0) is fulfilled in several regimes, both in the chain monomer number (N) and polymer volume fraction (phi). Entangled macromolecular dynamics was treated as a geodesic light deflection, entaglements acting in close analogy to the field generated by a spherically symmetric mass source, where length fluctuations of the chain primitive path behave as azimuth fluctuations of its shape. Finally, the general transformation rule for translational and diffusive frames gives a coordinate gauge invariance, suggesting a widened Lorentz-Poincaré symmetry for Brownian statistics. We expect this approach to find effective applications to solutions of arbitrarily large molecules displaying a variety of structures, where the effect of geometry is more explicit and significant in itself (e.g., surfactants, lipids, proteins).

Computation of pattern invariance in brain-like structures.

PubMed

Ullman, S; Soloviev, S

1999-10-01

A fundamental capacity of the perceptual systems and the brain in general is to deal with the novel and the unexpected. In vision, we can effortlessly recognize a familiar object under novel viewing conditions, or recognize a new object as a member of a familiar class, such as a house, a face, or a car. This ability to generalize and deal efficiently with novel stimuli has long been considered a challenging example of brain-like computation that proved extremely difficult to replicate in artificial systems. In this paper we present an approach to generalization and invariant recognition. We focus our discussion on the problem of invariance to position in the visual field, but also sketch how similar principles could apply to other domains.The approach is based on the use of a large repertoire of partial generalizations that are built upon past experience. In the case of shift invariance, visual patterns are described as the conjunction of multiple overlapping image fragments. The invariance to the more primitive fragments is built into the system by past experience. Shift invariance of complex shapes is obtained from the invariance of their constituent fragments. We study by simulations aspects of this shift invariance method and then consider its extensions to invariant perception and classification by brain-like structures.

The 9-item Bergen Burnout Inventory: factorial validity across organizations and measurements of longitudinal data.

PubMed

Feldt, Taru; Rantanen, Johanna; Hyvönen, Katriina; Mäkikangas, Anne; Huhtala, Mari; Pihlajasaari, Pia; Kinnunen, Ulla

2014-01-01

The present study tested the factorial validity of the 9-item Bergen Burnout Inventory (BBI-9). The BBI-9 is comprised of three core dimensions: (1) exhaustion at work; (2) cynicism toward the meaning of work; and (3) sense of inadequacy at work. The study further investigated whether the three-factor structure of the BBI-9 remains the same across different organizations (group invariance) and measurement time points (time invariance). The factorial group invariance was tested using a cross-sectional design with data pertaining to managers (n=742), and employees working in a bank (n=162), an engineering office (n=236), a public sector organization divided into three service areas: administration (n=102), education and culture (n=581), and social affairs and health (n=1,505). Factorial time invariance was tested using longitudinal data pertaining to managers, with three measurements over a four-year follow-up period. The confirmatory factor analysis revealed that the three-factor structure of the BBI-9 was invariant across cross-sectional samples. The factorial invariance was also supported across measurement times. To conclude, the factorial structure of the BBI-9 was found to remain the same regardless of the sample properties and measurement times.

The geometrical structure of quantum theory as a natural generalization of information geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 usingmore » geometrical quantities. This suggests that quantum theory has its roots in information geometry.« less

A Generic Theory of the Integer Quantum Hall Effect

NASA Astrophysics Data System (ADS)

Shen, Yu

The integer quantum Hall effect (IQHE) is usually modeled by a Galilean or rotationally invariant Hamiltonian. These are not generic symmetries for electrons moving in a crystal background and can potentially confuse non-topological quantities with topological ones and identify otherwise distinct geometrical properties. In this thesis we present a generic theory for the IQHE. First we show that a generic guiding-center coherent state, defined by a natural metric in each Landau level, has the form of an antiholomorphic function times a Gaussian factor. Then by numerically solving the eigenproblem for a quartic Hamiltonian and finding the roots of the antiholomorphic part we are able to define a topological spin sn = n + 1/2 where n is the number of central roots that are enclosed by the semiclassical orbit. We derive a generic formula for the Hall viscosity in the absence of rotational symmetry and show that the previous interpretation of the scalar Hall viscosity as the "intrinsic orbital angular momentum" breaks down since the concept of angular momentum requires the presence of rotational symmetry. We also calculate generic electromagnetic responses and differentiate between universal terms that are diagonal with respect to Landau level index and non-universal terms that depend on inter-Landau-level mixing. We conclude that the generic theory offers a fundamental definition for the topological spin and reveals finer structure in the geometrical properties of the IQHE.

Detection of Structural Abnormalities Using Neural Nets

NASA Technical Reports Server (NTRS)

Zak, M.; Maccalla, A.; Daggumati, V.; Gulati, S.; Toomarian, N.

1996-01-01

This paper describes a feed-forward neural net approach for detection of abnormal system behavior based upon sensor data analyses. A new dynamical invariant representing structural parameters of the system is introduced in such a way that any structural abnormalities in the system behavior are detected from the corresponding changes to the invariant.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Isić, Goran, E-mail: isicg@ipb.ac.rs; Gajić, Radoš

It is well known that due to the high conductivity of noble metals at terahertz frequencies and scalability of macroscopic Maxwell equations, a geometrical downscaling of a terahertz resonator results in the linear upscaling of its resonance frequency. However, the scaling laws of modal decay rates, important for the resonator excitation efficiency, are much less known. Here, we investigate the extent to which the scale-invariance of decay rates is violated due to the finite conductivity of the metal. We find that the resonance quality factor or the excitation efficiency may be substantially affected by scaling and show that this happensmore » as a result of the scale-dependence of the metal absorption rate, while the radiative decay and the dielectric cavity absorption rates are approximately scale-invariant. In particular, we find that by downscaling overcoupled resonators, their excitation efficiency increases, while the opposite happens with undercoupled resonators.« less

Arnold Diffusion of Charged Particles in ABC Magnetic Fields

NASA Astrophysics Data System (ADS)

Luque, Alejandro; Peralta-Salas, Daniel

2017-06-01

We prove the existence of diffusing solutions in the motion of a charged particle in the presence of ABC magnetic fields. The equations of motion are modeled by a 3DOF Hamiltonian system depending on two parameters. For small values of these parameters, we obtain a normally hyperbolic invariant manifold and we apply the so-called geometric methods for a priori unstable systems developed by A. Delshams, R. de la Llave and T.M. Seara. We characterize explicitly sufficient conditions for the existence of a transition chain of invariant tori having heteroclinic connections, thus obtaining global instability (Arnold diffusion). We also check the obtained conditions in a computer-assisted proof. ABC magnetic fields are the simplest force-free-type solutions of the magnetohydrodynamics equations with periodic boundary conditions, and can be considered as an elementary model for the motion of plasma-charged particles in a tokamak.

On the zigzagging causality EPR model: Answer to Vigier and coworkers and to Sutherland

NASA Astrophysics Data System (ADS)

Costa de Beauregard, O.

1987-08-01

The concept of “propagation in time” of Vigier and co-workers (V et al.) implies the idea of a supertime; it is thus alien to most Minkowskian pictures and certainly to mine. From this stems much of V et al.'s misunderstandings of my position. In steady motion of a classical fluid nobody thinks that “momentum conservation is violated,” or that “momentum is shot upstream without cause” because of the suction from the sinks! Similarly with momentum-energy in space-time and the acceptance of an advanced causality. As for the CT invariance of the Feynman propagator, the causality asymmetry it entails is factlike, not lawlike. The geometrical counterpart of the symmetry between prediction and retrodiction and between retarded and advanced waves, as expressed in the alternative expressions == for a transition amplitude between a preparation |A> and a measurement |B>, is CPT-invariant, not PT-invariant. These three expressions respectively illustrate the collapse, the retrocollapse, and the symmetric collapse-and-retrocollapse concepts. As for Sutherland's argument, what it “falsifies” is not my retrocausation concept but the hidden-variables assumption he has unwittingly made.

Narayanaswamy's 1971 aging theory and material time

NASA Astrophysics Data System (ADS)

Dyre, Jeppe C.

2015-09-01

The Bochkov-Kuzovlev nonlinear fluctuation-dissipation theorem is used to derive Narayanaswamy's phenomenological theory of physical aging, in which this highly nonlinear phenomenon is described by a linear material-time convolution integral. A characteristic property of the Narayanaswamy aging description is material-time translational invariance, which is here taken as the basic assumption of the derivation. It is shown that only one possible definition of the material time obeys this invariance, namely, the square of the distance travelled from a configuration of the system far back in time. The paper concludes with suggestions for computer simulations that test for consequences of material-time translational invariance. One of these is the "unique-triangles property" according to which any three points on the system's path form a triangle such that two side lengths determine the third; this is equivalent to the well-known triangular relation for time-autocorrelation functions of aging spin glasses [L. F. Cugliandolo and J. Kurchan, J. Phys. A: Math. Gen. 27, 5749 (1994)]. The unique-triangles property implies a simple geometric interpretation of out-of-equilibrium time-autocorrelation functions, which extends to aging a previously proposed framework for such functions in equilibrium [J. C. Dyre, e-print arXiv:cond-mat/9712222 (1997)].

Zigzagging causality EPR model: answer to Vigier and coworkers and to Sutherland

DOE Office of Scientific and Technical Information (OSTI.GOV)

de Beauregard, O.C.

1987-08-01

The concept of propagation in time of Vigier and co-workers (V et al.) implies the ideal of a supertime; it is thus alien to most Minkowskian pictures and certainly to the authors. From this stems much of V et al.'s misunderstandings of his position. In steady motion of a classical fluid nobody thinks that momentum conservation is violated, or that momentum is shot upstream without cause because of the suction from the sinks. Similarly with momentum-energy in spacetime and the acceptance of an advanced causality. As for the CT invariance of the Feynman propagator, the causality asymmetry it entails ismore » factlike, not lawlike. The geometrical counterpart of the symmetry between prediction and retrodiction and between retarded and advanced waves, as expressed in the alternative expressions = = for a transition amplitude between a preparation lt. slashA> and a measurement lt. slashB>, is CPT-invariant, not PT-invariant. These three expressions respectively illustrate the collapse, the retrocollapse, and the symmetric collapse-and-retrocollapse concepts. As for Sutherland's argument, what it falsifies is not the authors retrocausation concept but the hidden-variables assumption he has unwittingly made.« less

Knotty structures of the evolving heliospheric magnetic fields.

NASA Astrophysics Data System (ADS)

Roth, Ilan

2013-04-01

The analogy between MHD and knot theory is utilized in an analysis of structure, stability and evolution of complex magnetic heliospheric flux tubes. Planar projection of a three-dimensional magnetic configuration depicts the structure as a two-dimensional diagram with crossings, to which one may assign mathematical operations leading to robust topological invariants. These invariants enrich the topological information of magnetic configurations beyond helicity. It is conjectured that the field which emerges from the solar photosphere is structured as one of simplest knot invariants - unknot or prime knot, and these flux ropes are then stretched while carried by the solar wind into the interplanetary medium. Preservation of invariants for small diffusivity and large cross section of the emerging magnetic flux makes them impervious to large scale reconnection, allowing us to predict the observed structures at 1AU as elongated prime knots. Similar structures may be observed in magnetic clouds which got disconnected from their foot-points and in ion drop-out configurations from a compact flare source in solar impulsive solar events. Observation of small scale magnetic features consistent with prime knot may indicate spatial intermittency and non-Gaussian statistics in the turbulent cascade process. For flux tubes with higher resistivity, magnetic energy decay rate should decrease with increased knot complexity as the invariants are then harder to be violated. Future measurements are suggested for distinctly oriented magnetic fields with directionally varying suprathermal particle fluxes.

Invariant Poisson-Nijenhuis structures on Lie groups and classification

NASA Astrophysics Data System (ADS)

Ravanpak, Zohreh; Rezaei-Aghdam, Adel; Haghighatdoost, Ghorbanali

We study right-invariant (respectively, left-invariant) Poisson-Nijenhuis structures (P-N) on a Lie group G and introduce their infinitesimal counterpart, the so-called r-n structures on the corresponding Lie algebra 𝔤. We show that r-n structures can be used to find compatible solutions of the classical Yang-Baxter equation (CYBE). Conversely, two compatible r-matrices from which one is invertible determine an r-n structure. We classify, up to a natural equivalence, all r-matrices and all r-n structures with invertible r on four-dimensional symplectic real Lie algebras. The result is applied to show that a number of dynamical systems which can be constructed by r-matrices on a phase space whose symmetry group is Lie group a G, can be specifically determined.

Geometrization of quantum physics

NASA Astrophysics Data System (ADS)

Ol'Khov, O. A.

2009-12-01

It is shown that the Dirac equation for free particle can be considered as a description of specific distortion of the space euclidean geometry (space topological defect). This approach is based on possibility of interpretation of the wave function as vector realizing representation of the fundamental group of the closed topological space-time 4-manifold. Mass and spin appear to be topological invariants. Such concept explains all so called “strange” properties of quantum formalism: probabilities, wave-particle duality, nonlocal instantaneous correlation between noninteracting particles (EPR-paradox) and so on. Acceptance of suggested geometrical concept means rejection of atomistic concept where all matter is considered as consisting of more and more small elementary particles. There is no any particles a priori, before measurement: the notions of particles appear as a result of classical interpretation of the contact of the region of the curved space with a device.

Proportional-delayed controllers design for LTI-systems: a geometric approach

NASA Astrophysics Data System (ADS)

Hernández-Díez, J.-E.; Méndez-Barrios, C.-F.; Mondié, S.; Niculescu, S.-I.; González-Galván, E. J.

2018-04-01

This paper focuses on the design of P-δ controllers for single-input-single-output linear time-invariant systems. The basis of this work is a geometric approach allowing to partitioning the parameter space in regions with constant number of unstable roots. This methodology defines the hyper-planes separating the aforementioned regions and characterises the way in which the number of unstable roots changes when crossing such a hyper-plane. The main contribution of the paper is that it provides an explicit tool to find P-δ gains ensuring the stability of the closed-loop system. In addition, the proposed methodology allows to design a non-fragile controller with a desired exponential decay rate σ. Several numerical examples illustrate the results and a haptic experimental set-up shows the effectiveness of P-δ controllers.

Quantum Hurwitz numbers and Macdonald polynomials

NASA Astrophysics Data System (ADS)

Harnad, J.

2016-11-01

Parametric families in the center Z(C[Sn]) of the group algebra of the symmetric group are obtained by identifying the indeterminates in the generating function for Macdonald polynomials as commuting Jucys-Murphy elements. Their eigenvalues provide coefficients in the double Schur function expansion of 2D Toda τ-functions of hypergeometric type. Expressing these in the basis of products of power sum symmetric functions, the coefficients may be interpreted geometrically as parametric families of quantum Hurwitz numbers, enumerating weighted branched coverings of the Riemann sphere. Combinatorially, they give quantum weighted sums over paths in the Cayley graph of Sn generated by transpositions. Dual pairs of bases for the algebra of symmetric functions with respect to the scalar product in which the Macdonald polynomials are orthogonal provide both the geometrical and combinatorial significance of these quantum weighted enumerative invariants.

Transient Invariant and Quasi-Invariant Structures in an Example of an Aperiodically Time Dependent Fluid Flow

NASA Astrophysics Data System (ADS)

Fortunati, Alessandro; Wiggins, Stephen

Starting from the concept of invariant KAM tori for nearly-integrable Hamiltonian systems with periodic or quasi-periodic nonautonomous perturbation, the paper analyzes the “analogue” of this class of invariant objects when the dependence on time is aperiodic. The investigation is carried out in a model motivated by the problem of a traveling wave in a channel over a smooth, quasi- and asymptotically flat (from which the “transient” feature) bathymetry, representing a case in which the described structures play the role of barriers to fluid transport in phase space. The paper provides computational evidence for the existence of transient structures also for “large” values of the perturbation size, as a complement to the rigorous results already proven by the first author for real-analytic bathymetry functions.

Tissue Tracking: Applications for Brain MRI Classification

DTIC Science & Technology

2007-01-01

General Hospital, Center for Morphometric Analysis.10,11 The IBSR data-sets are T1-weighted, 3D coronal brain scans after having been positionally...learned priors,” Image Processing, IEEE Transactions on 9(2), pp. 299–301, 2000. 5. P. Olver, G. Sapiro, and A. Tannenbaum, “Invariant Geometric Evolutions...MRI,” NeuroImage 22(3), pp. 1060–1075, 2004. 16. A. Zijdenbos, B. Dawant, R. Margolin, and A. Palmer, “ Morphometric analysis of white matter lesions in

A scattering database of marine particles and its application in optical analysis

NASA Astrophysics Data System (ADS)

Xu, G.; Yang, P.; Kattawar, G.; Zhang, X.

2016-12-01

In modeling the scattering properties of marine particles (e.g. phytoplankton), the laboratory studies imply a need to properly account for the influence of particle morphology, in addition to size and composition. In this study, a marine particle scattering database is constructed using a collection of distorted hexahedral shapes. Specifically, the scattering properties of each size bin and refractive index are obtained by the ensemble average associated with distorted hexahedra with randomly tilted facets and selected aspect ratios (from elongated to flattened). The randomness degree in shape-generation process defines the geometric irregularity of the particles in the group. The geometric irregularity and particle aspect ratios constitute a set of "shape factors" to be accounted for (e.g. in best-fit analysis). To cover most of the marine particle size range, we combine the Invariant Imbedding T-matrix (II-TM) method and the Physical-Geometric Optics Hybrid (PGOH) method in the calculations. The simulated optical properties are shown and compared with those obtained from Lorenz-Mie Theory. Using the scattering database, we present a preliminary optical analysis of laboratory-measured optical properties of marine particles.

On Flexible Tubes Conveying Fluid: Geometric Nonlinear Theory, Stability and Dynamics

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Putkaradze, Vakhtang

2015-08-01

We derive a fully three-dimensional, geometrically exact theory for flexible tubes conveying fluid. The theory also incorporates the change of the cross section available to the fluid motion during the dynamics. Our approach is based on the symmetry-reduced, exact geometric description for elastic rods, coupled with the fluid transport and subject to the volume conservation constraint for the fluid. We first derive the equations of motion directly, by using an Euler-Poincaré variational principle. We then justify this derivation with a more general theory elucidating the interesting mathematical concepts appearing in this problem, such as partial left (elastic) and right (fluid) invariance of the system, with the added holonomic constraint (volume). We analyze the fully nonlinear behavior of the model when the axis of the tube remains straight. We then proceed to the linear stability analysis and show that our theory introduces important corrections to previously derived results, both in the consistency at all wavelength and in the effects arising from the dynamical change of the cross section. Finally, we derive and analyze several analytical, fully nonlinear solutions of traveling wave type in two dimensions.

Movement Timing and Invariance Arise from Several Geometries

PubMed Central

Bennequin, Daniel; Fuchs, Ronit; Berthoz, Alain; Flash, Tamar

2009-01-01

Human movements show several prominent features; movement duration is nearly independent of movement size (the isochrony principle), instantaneous speed depends on movement curvature (captured by the 2/3 power law), and complex movements are composed of simpler elements (movement compositionality). No existing theory can successfully account for all of these features, and the nature of the underlying motion primitives is still unknown. Also unknown is how the brain selects movement duration. Here we present a new theory of movement timing based on geometrical invariance. We propose that movement duration and compositionality arise from cooperation among Euclidian, equi-affine and full affine geometries. Each geometry posses a canonical measure of distance along curves, an invariant arc-length parameter. We suggest that for continuous movements, the actual movement duration reflects a particular tensorial mixture of these canonical parameters. Near geometrical singularities, specific combinations are selected to compensate for time expansion or compression in individual parameters. The theory was mathematically formulated using Cartan's moving frame method. Its predictions were tested on three data sets: drawings of elliptical curves, locomotion and drawing trajectories of complex figural forms (cloverleaves, lemniscates and limaçons, with varying ratios between the sizes of the large versus the small loops). Our theory accounted well for the kinematic and temporal features of these movements, in most cases better than the constrained Minimum Jerk model, even when taking into account the number of estimated free parameters. During both drawing and locomotion equi-affine geometry was the most dominant geometry, with affine geometry second most important during drawing; Euclidian geometry was second most important during locomotion. We further discuss the implications of this theory: the origin of the dominance of equi-affine geometry, the possibility that the brain uses different mixtures of these geometries to encode movement duration and speed, and the ontogeny of such representations. PMID:19593380

A geometric rationale for invariance, covariance and constitutive relations

NASA Astrophysics Data System (ADS)

Romano, Giovanni; Barretta, Raffaele; Diaco, Marina

2018-01-01

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 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.

Circumventing Imprecise Geometric Information and Development of a Unified Modeling Technique for Various Flow Regimes in Capillary Tubes

NASA Astrophysics Data System (ADS)

Abbasi, Bahman

2012-11-01

Owing to their manufacturability and reliability, capillary tubes are the most common expansion devices in household refrigerators. Therefore, investigating flow properties in the capillary tubes is of immense appeal in the said business. The models to predict pressure drop in two-phase internal flows invariably rely upon highly precise geometric information. The manner in which capillary tubes are manufactured makes them highly susceptible to geometric imprecisions, which renders geometry-based models unreliable to the point of obsoleteness. Aware of the issue, manufacturers categorize capillary tubes based on Nitrogen flow rate through them. This categorization method presents an opportunity to substitute geometric details with Nitrogen flow data as the basis for customized models. The simulation tools developed by implementation of this technique have the singular advantage of being applicable across flow regimes. Thus the error-prone process of identifying compatible correlations is eliminated. Equally importantly, compressibility and chocking effects can be incorporated in the same model. The outcome is a standalone correlation that provides accurate predictions, regardless of any particular fluid or flow regime. Thereby, exploratory investigations for capillary tube design and optimization are greatly simplified. Bahman Abbasi, Ph.D., is Lead Advanced Systems Engineer at General Electric Appliances in Louisville, KY. He conducts research projects across disciplines in the household refrigeration industry.

Magnetohydrodynamic motion of a two-fluid plasma

DOE PAGES

Burby, Joshua W.

2017-07-21

Here, the two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell’s equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally-exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, asmore » well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-orders closure may be obtained in closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-orders bracket gives explicit expressions for a number of the full closure’s conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.« less

Visual Odometry Based on Structural Matching of Local Invariant Features Using Stereo Camera Sensor

PubMed Central

Núñez, Pedro; Vázquez-Martín, Ricardo; Bandera, Antonio

2011-01-01

This paper describes a novel sensor system to estimate the motion of a stereo camera. Local invariant image features are matched between pairs of frames and linked into image trajectories at video rate, providing the so-called visual odometry, i.e., motion estimates from visual input alone. Our proposal conducts two matching sessions: the first one between sets of features associated to the images of the stereo pairs and the second one between sets of features associated to consecutive frames. With respect to previously proposed approaches, the main novelty of this proposal is that both matching algorithms are conducted by means of a fast matching algorithm which combines absolute and relative feature constraints. Finding the largest-valued set of mutually consistent matches is equivalent to finding the maximum-weighted clique on a graph. The stereo matching allows to represent the scene view as a graph which emerge from the features of the accepted clique. On the other hand, the frame-to-frame matching defines a graph whose vertices are features in 3D space. The efficiency of the approach is increased by minimizing the geometric and algebraic errors to estimate the final displacement of the stereo camera between consecutive acquired frames. The proposed approach has been tested for mobile robotics navigation purposes in real environments and using different features. Experimental results demonstrate the performance of the proposal, which could be applied in both industrial and service robot fields. PMID:22164016

Magnetohydrodynamic motion of a two-fluid plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burby, Joshua W.

Here, the two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell’s equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally-exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, asmore » well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-orders closure may be obtained in closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-orders bracket gives explicit expressions for a number of the full closure’s conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.« less

The 9-item Bergen Burnout Inventory: Factorial Validity Across Organizations and Measurements of Longitudinal Data

PubMed Central

Feldt, Taru; RANTANEN, Johanna; HYVÖNEN, Katriina; MÄKIKANGAS, Anne; HUHTALA, Mari; PIHLAJASAARI, Pia; KINNUNEN, Ulla

2013-01-01

The present study tested the factorial validity of the 9-item Bergen Burnout Inventory (BBI-9)1). The BBI-9 is comprised of three core dimensions: (1) exhaustion at work; (2) cynicism toward the meaning of work; and (3) sense of inadequacy at work. The study further investigated whether the three-factor structure of the BBI-9 remains the same across different organizations (group invariance) and measurement time points (time invariance). The factorial group invariance was tested using a cross-sectional design with data pertaining to managers (n=742), and employees working in a bank (n=162), an engineering office (n=236), a public sector organization divided into three service areas: administration (n=102), education and culture (n=581), and social affairs and health (n=1,505). Factorial time invariance was tested using longitudinal data pertaining to managers, with three measurements over a four-year follow-up period. The confirmatory factor analysis revealed that the three-factor structure of the BBI-9 was invariant across cross-sectional samples. The factorial invariance was also supported across measurement times. To conclude, the factorial structure of the BBI-9 was found to remain the same regardless of the sample properties and measurement times. PMID:24366535

Some Properties of Estimated Scale Invariant Covariance Structures.

ERIC Educational Resources Information Center

Dijkstra, T. K.

1990-01-01

An example of scale invariance is provided via the LISREL model that is subject only to classical normalizations and zero constraints on the parameters. Scale invariance implies that the estimated covariance matrix must satisfy certain equations, and the nature of these equations depends on the fitting function used. (TJH)

Testing for Factorial Invariance in the Context of Construct Validation

ERIC Educational Resources Information Center

Dimitrov, Dimiter M.

2010-01-01

This article describes the logic and procedures behind testing for factorial invariance across groups in the context of construct validation. The procedures include testing for configural, measurement, and structural invariance in the framework of multiple-group confirmatory factor analysis (CFA). The "forward" (sequential constraint imposition)…

The Factor Structure of Effortful Control and Measurement Invariance Across Ethnicity and Sex in a High-Risk Sample

PubMed Central

Huerta, Snjezana; Zerr, Argero A.; Eisenberg, Nancy; Spinrad, Tracy L.; Valiente, Carlos; Di Giunta, Laura; Pina, Armando A.; Eggum, Natalie D.; Sallquist, Julie; Edwards, Alison; Kupfer, Anne; Lonigan, Christopher J.; Phillips, Beth M.; Wilson, Shauna B.; Clancy-Menchetti, Jeanine; Landry, Susan H.; Swank, Paul R.; Assel, Michael A.; Taylor, Heather B.

2010-01-01

Measurement invariance of a one-factor model of effortful control (EC) was tested for 853 low-income preschoolers (M age = 4.48 years). Using a teacher-report questionnaire and seven behavioral measures, configural invariance (same factor structure across groups), metric invariance (same pattern of factor loadings across groups), and partial scalar invariance (mostly the same intercepts across groups) were established across ethnicity (European Americans, African Americans and Hispanics) and across sex. These results suggest that the latent construct of EC behaved in a similar way across ethnic groups and sex, and that comparisons of mean levels of EC are valid across sex and probably valid across ethnicity, especially when larger numbers of tasks are used. The findings also support the use of diverse behavioral measures as indicators of a single latent EC construct. PMID:20593008

Validating the Student-Teacher Relationship Scale: testing factor structure and measurement invariance across child gender and age in a Dutch sample.

PubMed

Koomen, Helma M Y; Verschueren, Karine; van Schooten, Erik; Jak, Suzanne; Pianta, Robert C

2012-04-01

The Student-Teacher Relationship Scale (STRS) is widely used to examine teachers' relationships with young students in terms of closeness, conflict, and dependency. This study aimed to verify the dimensional structure of the STRS with confirmatory factor analysis, test its measurement invariance across child gender and age, improve its measurement of the dependency construct, and extend its age range. Teachers completed a slightly adapted STRS for a Dutch sample of 2335 children aged 3 to 12. Overall, the 3-factor model showed an acceptable fit. Results indicated metric invariance across gender and age up to 8years. Scalar invariance generally did not hold. Lack of metric invariance at ages 8 to 12 primarily involved Conflict items, whereas scale differences across gender and age primarily involved Closeness items. The adapted Dependency scale showed strong invariance and higher internal consistencies than the original scale for this Dutch sample. Importantly, the revealed non-invariance for gender and age did not influence mean group comparisons. Copyright © 2011 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.

Invariance of visual operations at the level of receptive fields

PubMed Central

Lindeberg, Tony

2013-01-01

The brain is able to maintain a stable perception although the visual stimuli vary substantially on the retina due to geometric transformations and lighting variations in the environment. This paper presents a theory for achieving basic invariance properties already at the level of receptive fields. Specifically, the presented framework comprises (i) local scaling transformations caused by objects of different size and at different distances to the observer, (ii) locally linearized image deformations caused by variations in the viewing direction in relation to the object, (iii) locally linearized relative motions between the object and the observer and (iv) local multiplicative intensity transformations caused by illumination variations. The receptive field model can be derived by necessity from symmetry properties of the environment and leads to predictions about receptive field profiles in good agreement with receptive field profiles measured by cell recordings in mammalian vision. Indeed, the receptive field profiles in the retina, LGN and V1 are close to ideal to what is motivated by the idealized requirements. By complementing receptive field measurements with selection mechanisms over the parameters in the receptive field families, it is shown how true invariance of receptive field responses can be obtained under scaling transformations, affine transformations and Galilean transformations. Thereby, the framework provides a mathematically well-founded and biologically plausible model for how basic invariance properties can be achieved already at the level of receptive fields and support invariant recognition of objects and events under variations in viewpoint, retinal size, object motion and illumination. The theory can explain the different shapes of receptive field profiles found in biological vision, which are tuned to different sizes and orientations in the image domain as well as to different image velocities in space-time, from a requirement that the visual system should be invariant to the natural types of image transformations that occur in its environment. PMID:23894283

Global Existence Results for Viscoplasticity at Finite Strain

NASA Astrophysics Data System (ADS)

Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe

2018-01-01

We study a model for rate-dependent gradient plasticity at finite strain based on the multiplicative decomposition of the strain tensor, and investigate the existence of global-in-time solutions to the related PDE system. We reveal its underlying structure as a generalized gradient system, where the driving energy functional is highly nonconvex and features the geometric nonlinearities related to finite-strain elasticity as well as the multiplicative decomposition of finite-strain plasticity. Moreover, the dissipation potential depends on the left-invariant plastic rate, and thus depends on the plastic state variable. The existence theory is developed for a class of abstract, nonsmooth, and nonconvex gradient systems, for which we introduce suitable notions of solutions, namely energy-dissipation-balance and energy-dissipation-inequality solutions. Hence, we resort to the toolbox of the direct method of the calculus of variations to check that the specific energy and dissipation functionals for our viscoplastic models comply with the conditions of the general theory.

Dynamical gauge effects in an open quantum network

NASA Astrophysics Data System (ADS)

Zhao, Jianshi; Price, Craig; Liu, Qi; Gemelke, Nathan

2016-05-01

We describe new experimental techniques for simulation of high-energy field theories based on an analogy between open thermodynamic systems and effective dynamical gauge-fields following SU(2) × U(1) Yang-Mills models. By coupling near-resonant laser-modes to atoms moving in a disordered optical environment, we create an open system which exhibits a non-equilibrium phase transition between two steady-state behaviors, exhibiting scale-invariant behavior near the transition. By measuring transport of atoms through the disordered network, we observe two distinct scaling behaviors, corresponding to the classical and quantum limits for the dynamical gauge field. This behavior is loosely analogous to dynamical gauge effects in quantum chromodynamics, and can mapped onto generalized open problems in theoretical understanding of quantized non-Abelian gauge theories. Additional, the scaling behavior can be understood from the geometric structure of the gauge potential and linked to the measure of information in the local disordered potential, reflecting an underlying holographic principle. We acknowledge support from NSF Award No.1068570, and the Charles E. Kaufman Foundation.

Variational approach to probabilistic finite elements

NASA Technical Reports Server (NTRS)

Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.

1991-01-01

Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Variational approach to probabilistic finite elements

NASA Astrophysics Data System (ADS)

Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.

1991-08-01

Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Variational approach to probabilistic finite elements

NASA Technical Reports Server (NTRS)

Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.

1987-01-01

Probabilistic finite element method (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties, and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Pulse-coupled neural nets: translation, rotation, scale, distortion, and intensity signal invariance for images.

PubMed

Johnson, J L

1994-09-10

The linking-field neural network model of Eckhorn et al. [Neural Comput. 2, 293-307 (1990)] was introduced to explain the experimentally observed synchronous activity among neural assemblies in the cat cortex induced by feature-dependent visual activity. The model produces synchronous bursts of pulses from neurons with similar activity, effectively grouping them by phase and pulse frequency. It gives a basic new function: grouping by similarity. The synchronous bursts are obtained in the limit of strong linking strengths. The linking-field model in the limit of moderate-to-weak linking characterized by few if any multiple bursts is investigated. In this limit dynamic, locally periodic traveling waves exist whose time signal encodes the geometrical structure of a two-dimensional input image. The signal can be made insensitive to translation, scale, rotation, distortion, and intensity. The waves transmit information beyond the physical interconnect distance. The model is implemented in an optical hybrid demonstration system. Results of the simulations and the optical system are presented.

Computation at a coordinate singularity

NASA Astrophysics Data System (ADS)

Prusa, Joseph M.

2018-05-01

Coordinate singularities are sometimes encountered in computational problems. An important example involves global atmospheric models used for climate and weather prediction. Classical spherical coordinates can be used to parameterize the manifold - that is, generate a grid for the computational spherical shell domain. This particular parameterization offers significant benefits such as orthogonality and exact representation of curvature and connection (Christoffel) coefficients. But it also exhibits two polar singularities and at or near these points typical continuity/integral constraints on dependent fields and their derivatives are generally inadequate and lead to poor model performance and erroneous results. Other parameterizations have been developed that eliminate polar singularities, but problems of weaker singularities and enhanced grid noise compared to spherical coordinates (away from the poles) persist. In this study reparameterization invariance of geometric objects (scalars, vectors and the forms generated by their covariant derivatives) is utilized to generate asymptotic forms for dependent fields of interest valid in the neighborhood of a pole. The central concept is that such objects cannot be altered by the metric structure of a parameterization. The new boundary conditions enforce symmetries that are required for transformations of geometric objects. They are implemented in an implicit polar filter of a structured grid, nonhydrostatic global atmospheric model that is simulating idealized Held-Suarez flows. A series of test simulations using different configurations of the asymptotic boundary conditions are made, along with control simulations that use the default model numerics with no absorber, at three different grid sizes. Typically the test simulations are ∼ 20% faster in wall clock time than the control-resulting from a decrease in noise at the poles in all cases. In the control simulations adverse numerical effects from the polar singularity are observed to increase with grid resolution. In contrast, test simulations demonstrate robust polar behavior independent of grid resolution.

Relating Measurement Invariance, Cross-Level Invariance, and Multilevel Reliability.

PubMed

Jak, Suzanne; Jorgensen, Terrence D

2017-01-01

Data often have a nested, multilevel structure, for example when data are collected from children in classrooms. This kind of data complicate the evaluation of reliability and measurement invariance, because several properties can be evaluated at both the individual level and the cluster level, as well as across levels. For example, cross-level invariance implies equal factor loadings across levels, which is needed to give latent variables at the two levels a similar interpretation. Reliability at a specific level refers to the ratio of true score variance over total variance at that level. This paper aims to shine light on the relation between reliability, cross-level invariance, and strong factorial invariance across clusters in multilevel data. Specifically, we will illustrate how strong factorial invariance across clusters implies cross-level invariance and perfect reliability at the between level in multilevel factor models.

The Factor Structure and Age-Related Factorial Invariance of the Delis-Kaplan Executive Function System (D-KEFS)

ERIC Educational Resources Information Center

Latzman, Robert D.; Markon, Kristian E.

2010-01-01

There has been an increased interest in the structure of and relations among executive functions.The present study examined the factor structure as well as age-related factorial invariance of the Delis-Kaplan Executive Function System (D-KEFS), a widely used inventory aimed at assessing executive functions. Analyses were first conducted using data…

Invariance in the Factor Structure of Translated Instruments: Multiple Group Confirmatory Factor Analysis and MIMIC Models

ERIC Educational Resources Information Center

Ayyad, Fatma

2011-01-01

When factorial invariance is established across translated forms of an instrument, the meaning of the construct crosses language/cultures. If factorial invariance is not established, score discrepancies may represent true language group differences or faulty translation. This study seeks to disentangle this by determining whether…

The Role of Measurement Quality on Practical Guidelines for Assessing Measurement and Structural Invariance

ERIC Educational Resources Information Center

Kang, Yoonjeong; McNeish, Daniel M.; Hancock, Gregory R.

2016-01-01

Although differences in goodness-of-fit indices (?GOFs) have been advocated for assessing measurement invariance, studies that advanced recommended differential cutoffs for adjudicating invariance actually utilized a very limited range of values representing the quality of indicator variables (i.e., magnitude of loadings). Because quality of…

Measurement Invariance and the Five-Factor Model of Personality: Asian International and Euro American Cultural Groups.

PubMed

Rollock, David; Lui, P Priscilla

2016-10-01

This study examined measurement invariance of the NEO Five-Factor Inventory (NEO-FFI), assessing the five-factor model (FFM) of personality among Euro American (N = 290) and Asian international (N = 301) students (47.8% women, Mage = 19.69 years). The full 60-item NEO-FFI data fit the expected five-factor structure for both groups using exploratory structural equation modeling, and achieved configural invariance. Only 37 items significantly loaded onto the FFM-theorized factors for both groups and demonstrated metric invariance. Threshold invariance was not supported with this reduced item set. Groups differed the most in the item-factor relationships for Extraversion and Agreeableness, as well as in response styles. Asian internationals were more likely to use midpoint responses than Euro Americans. While the FFM can characterize broad nomothetic patterns of personality traits, metric invariance with only the subset of NEO-FFI items identified limits direct group comparisons of correlation coefficients among personality domains and with other constructs, and of mean differences on personality domains. © The Author(s) 2015.

An analytical method for predicting the geometrical and optical properties of the human lens under accommodation

PubMed Central

Sheil, Conor J.; Bahrami, Mehdi; Goncharov, Alexander V.

2014-01-01

We present an analytical method to describe the accommodative changes in the human crystalline lens. The method is based on the geometry-invariant lens model, in which the gradient-index (GRIN) iso-indicial contours are coupled to the external shape. This feature ensures that any given number of iso-indicial contours does not change with accommodation, which preserves the optical integrity of the GRIN structure. The coupling also enables us to define the GRIN structure if the radii and asphericities of the external lens surfaces are known. As an example, the accommodative changes in lenticular radii and central thickness were taken from the literature, while the asphericities of the external surfaces were derived analytically by adhering to the basic physical conditions of constant lens volume and its axial position. The resulting changes in lens geometry are consistent with experimental data, and the optical properties are in line with expected values for optical power and spherical aberration. The aim of the paper is to provide an anatomically and optically accurate lens model that is valid for 3 mm pupils and can be used as a new tool for better understanding of accommodation. PMID:24877022

An analytical method for predicting the geometrical and optical properties of the human lens under accommodation.

PubMed

Sheil, Conor J; Bahrami, Mehdi; Goncharov, Alexander V

2014-05-01

We present an analytical method to describe the accommodative changes in the human crystalline lens. The method is based on the geometry-invariant lens model, in which the gradient-index (GRIN) iso-indicial contours are coupled to the external shape. This feature ensures that any given number of iso-indicial contours does not change with accommodation, which preserves the optical integrity of the GRIN structure. The coupling also enables us to define the GRIN structure if the radii and asphericities of the external lens surfaces are known. As an example, the accommodative changes in lenticular radii and central thickness were taken from the literature, while the asphericities of the external surfaces were derived analytically by adhering to the basic physical conditions of constant lens volume and its axial position. The resulting changes in lens geometry are consistent with experimental data, and the optical properties are in line with expected values for optical power and spherical aberration. The aim of the paper is to provide an anatomically and optically accurate lens model that is valid for 3 mm pupils and can be used as a new tool for better understanding of accommodation.

Special Relativity at the Quantum Scale

PubMed Central

Lam, Pui K.

2014-01-01

It has been suggested that the space-time structure as described by the theory of special relativity is a macroscopic manifestation of a more fundamental quantum structure (pre-geometry). Efforts to quantify this idea have come mainly from the area of abstract quantum logic theory. Here we present a preliminary attempt to develop a quantum formulation of special relativity based on a model that retains some geometric attributes. Our model is Feynman's “checker-board” trajectory for a 1-D relativistic free particle. We use this model to guide us in identifying (1) the quantum version of the postulates of special relativity and (2) the appropriate quantum “coordinates”. This model possesses a useful feature that it admits an interpretation both in terms of paths in space-time and in terms of quantum states. Based on the quantum version of the postulates, we derive a transformation rule for velocity. This rule reduces to the Einstein's velocity-addition formula in the macroscopic limit and reveals an interesting aspect of time. The 3-D case, time-dilation effect, and invariant interval are also discussed in term of this new formulation. This is a preliminary investigation; some results are derived, while others are interesting observations at this point. PMID:25531675

Special relativity at the quantum scale.

PubMed

Lam, Pui K

2014-01-01

It has been suggested that the space-time structure as described by the theory of special relativity is a macroscopic manifestation of a more fundamental quantum structure (pre-geometry). Efforts to quantify this idea have come mainly from the area of abstract quantum logic theory. Here we present a preliminary attempt to develop a quantum formulation of special relativity based on a model that retains some geometric attributes. Our model is Feynman's "checker-board" trajectory for a 1-D relativistic free particle. We use this model to guide us in identifying (1) the quantum version of the postulates of special relativity and (2) the appropriate quantum "coordinates". This model possesses a useful feature that it admits an interpretation both in terms of paths in space-time and in terms of quantum states. Based on the quantum version of the postulates, we derive a transformation rule for velocity. This rule reduces to the Einstein's velocity-addition formula in the macroscopic limit and reveals an interesting aspect of time. The 3-D case, time-dilation effect, and invariant interval are also discussed in term of this new formulation. This is a preliminary investigation; some results are derived, while others are interesting observations at this point.

Geometric Model of Topological Insulators from the Maxwell Algebra

NASA Astrophysics Data System (ADS)

Palumbo, Giandomenico

I propose a novel geometric model of time-reversal-invariant topological insulators in three dimensions in presence of an external electromagnetic field. Their gapped boundary supports relativistic quantum Hall states and is described by a Chern-Simons theory, where the gauge connection takes values in the Maxwell algebra. This represents a non-central extension of the Poincare' algebra and takes into account both the Lorentz and magnetic-translation symmetries of the surface states. In this way, I derive a relativistic version of the Wen-Zee term and I show that the non-minimal coupling between the background geometry and the electromagnetic field in the model is in agreement with the main properties of the relativistic quantum Hall states in the flat space. This work is part of the DITP consortium, a program of the Netherlands Organisation for Scientific Research (NWO) that is funded by the Dutch Ministry of Education, Culture and Science (OCW).

Exact moduli space metrics for hyperbolic vortex polygons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krusch, S.; Speight, J. M.

2010-02-15

Exact metrics on some totally geodesic submanifolds of the moduli space of static hyperbolic N-vortices are derived. These submanifolds, denoted as {sigma}{sub n,m}, are spaces of C{sub n}-invariant vortex configurations with n single vortices at the vertices of a regular polygon and m=N-n coincident vortices at the polygon's center. The geometric properties of {sigma}{sub n,m} are investigated, and it is found that {sigma}{sub n,n-1} is isometric to the hyperbolic plane of curvature -(3{pi}n){sup -1}. The geodesic flow on {sigma}{sub n,m} and a geometrically natural variant of geodesic flow recently proposed by Collie and Tong ['The dynamics of Chern-Simons vortices', Phys.more » Rev. D Part. Fields Gravit. Cosmol. 78, 065013 (2008);e-print arXiv:hep-th/0805.0602] are analyzed in detail.« less

SIFT optimization and automation for matching images from multiple temporal sources

NASA Astrophysics Data System (ADS)

Castillo-Carrión, Sebastián; Guerrero-Ginel, José-Emilio

2017-05-01

Scale Invariant Feature Transformation (SIFT) was applied to extract tie-points from multiple source images. Although SIFT is reported to perform reliably under widely different radiometric and geometric conditions, using the default input parameters resulted in too few points being found. We found that the best solution was to focus on large features as these are more robust and not prone to scene changes over time, which constitutes a first approach to the automation of processes using mapping applications such as geometric correction, creation of orthophotos and 3D models generation. The optimization of five key SIFT parameters is proposed as a way of increasing the number of correct matches; the performance of SIFT is explored in different images and parameter values, finding optimization values which are corroborated using different validation imagery. The results show that the optimization model improves the performance of SIFT in correlating multitemporal images captured from different sources.

On the hierarchy of partially invariant submodels of differential equations

NASA Astrophysics Data System (ADS)

Golovin, Sergey V.

2008-07-01

It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.

Multiscale Path Metrics for the Analysis of Discrete Geometric Structures

DTIC Science & Technology

2017-11-30

Report: Multiscale Path Metrics for the Analysis of Discrete Geometric Structures The views, opinions and/or findings contained in this report are those...Analysis of Discrete Geometric Structures Report Term: 0-Other Email: tomasi@cs.duke.edu Distribution Statement: 1-Approved for public release

Finding Mutual Exclusion Invariants in Temporal Planning Domains

NASA Technical Reports Server (NTRS)

Bernardini, Sara; Smith, David E.

2011-01-01

We present a technique for automatically extracting temporal mutual exclusion invariants from PDDL2.2 planning instances. We first identify a set of invariant candidates by inspecting the domain and then check these candidates against properties that assure invariance. If these properties are violated, we show that it is sometimes possible to refine a candidate by adding additional propositions and turn it into a real invariant. Our technique builds on other approaches to invariant synthesis presented in the literature, but departs from their limited focus on instantaneous discrete actions by addressing temporal and numeric domains. To deal with time, we formulate invariance conditions that account for both the entire structure of the operators (including the conditions, rather than just the effects) and the possible interactions between operators. As a result, we construct a technique that is not only capable of identifying invariants for temporal domains, but is also able to find a broader set of invariants for non-temporal domains than the previous techniques.

Confirmatory Factor Analytic Structure and Measurement Invariance of Quantitative Autistic Traits Measured by the Social Responsiveness Scale-2

ERIC Educational Resources Information Center

Frazier, Thomas W.; Ratliff, Kristin R.; Gruber, Chris; Zhang, Yi; Law, Paul A.; Constantino, John N.

2014-01-01

Understanding the factor structure of autistic symptomatology is critical to the discovery and interpretation of causal mechanisms in autism spectrum disorder. We applied confirmatory factor analysis and assessment of measurement invariance to a large ("N" = 9635) accumulated collection of reports on quantitative autistic traits using…

User's manual for GAMNAS: Geometric and Material Nonlinear Analysis of Structures

NASA Technical Reports Server (NTRS)

Whitcomb, J. D.; Dattaguru, B.

1984-01-01

GAMNAS (Geometric and Material Nonlinear Analysis of Structures) is a two dimensional finite-element stress analysis program. Options include linear, geometric nonlinear, material nonlinear, and combined geometric and material nonlinear analysis. The theory, organization, and use of GAMNAS are described. Required input data and results for several sample problems are included.

Invariant Spatial Context Is Learned but Not Retrieved in Gaze-Contingent Tunnel-View Search

ERIC Educational Resources Information Center

Zang, Xuelian; Jia, Lina; Müller, Hermann J.; Shi, Zhuanghua

2015-01-01

Our visual brain is remarkable in extracting invariant properties from the noisy environment, guiding selection of where to look and what to identify. However, how the brain achieves this is still poorly understood. Here we explore interactions of local context and global structure in the long-term learning and retrieval of invariant display…

Narayanaswamy’s 1971 aging theory and material time

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dyre, Jeppe C., E-mail: dyre@ruc.dk

2015-09-21

The Bochkov-Kuzovlev nonlinear fluctuation-dissipation theorem is used to derive Narayanaswamy’s phenomenological theory of physical aging, in which this highly nonlinear phenomenon is described by a linear material-time convolution integral. A characteristic property of the Narayanaswamy aging description is material-time translational invariance, which is here taken as the basic assumption of the derivation. It is shown that only one possible definition of the material time obeys this invariance, namely, the square of the distance travelled from a configuration of the system far back in time. The paper concludes with suggestions for computer simulations that test for consequences of material-time translational invariance.more » One of these is the “unique-triangles property” according to which any three points on the system’s path form a triangle such that two side lengths determine the third; this is equivalent to the well-known triangular relation for time-autocorrelation functions of aging spin glasses [L. F. Cugliandolo and J. Kurchan, J. Phys. A: Math. Gen. 27, 5749 (1994)]. The unique-triangles property implies a simple geometric interpretation of out-of-equilibrium time-autocorrelation functions, which extends to aging a previously proposed framework for such functions in equilibrium [J. C. Dyre, e-print arXiv:cond-mat/9712222 (1997)].« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balakrishnan, S.; Sankaranarayanan, R.

Nonlocal two-qubit gates are geometrically represented by tetrahedron known as Weyl chamber within which perfect entanglers form a polyhedron. We identify that all edges of the Weyl chamber and polyhedron are formed by single parametric gates. Nonlocal attributes of these edges are characterized using entangling power and local invariants. In particular, SWAP{sup -{alpha}} family of gates with 0{<=}{alpha}{<=}1 constitutes one edge of the Weyl chamber with SWAP{sup -1/2} being the only perfect entangler. Finally, optimal constructions of controlled-NOT using SWAP{sup -1/2} gate and gates belong to three edges of the polyhedron are presented.

Geometric approach to nuclear pasta phases

NASA Astrophysics Data System (ADS)

Kubis, Sebastian; Wójcik, Włodzimierz

2016-12-01

By use of the variational methods and differential geometry in the framework of the liquid drop model we formulate appropriate equilibrium equations for pasta phases with imposed periodicity. The extension of the Young-Laplace equation in the case of charged fluid is obtained. The β equilibrium and virial theorem are also generalized. All equations are shown in gauge invariant form. For the first time, the pasta shape stability analysis is carried out. The proper stability condition in the form of the generalized Jacobi equation is derived. The presented formalism is tested on some particular cases.

A Rigorous Geometric Derivation of the Chiral Anomaly in Curved Backgrounds

NASA Astrophysics Data System (ADS)

Bär, Christian; Strohmaier, Alexander

2016-11-01

We discuss the chiral anomaly for a Weyl field in a curved background and show that a novel index theorem for the Lorentzian Dirac operator can be applied to describe the gravitational chiral anomaly. A formula for the total charge generated by the gravitational and gauge field background is derived directly in Lorentzian signature and in a mathematically rigorous manner. It contains a term identical to the integrand in the Atiyah-Singer index theorem and another term involving the {η}-invariant of the Cauchy hypersurfaces.

Perceptual geometry of space and form: visual perception of natural scenes and their virtual representation

NASA Astrophysics Data System (ADS)

Assadi, Amir H.

2001-11-01

Perceptual geometry is an emerging field of interdisciplinary research whose objectives focus on study of geometry from the perspective of visual perception, and in turn, apply such geometric findings to the ecological study of vision. Perceptual geometry attempts to answer fundamental questions in perception of form and representation of space through synthesis of cognitive and biological theories of visual perception with geometric theories of the physical world. Perception of form and space are among fundamental problems in vision science. In recent cognitive and computational models of human perception, natural scenes are used systematically as preferred visual stimuli. Among key problems in perception of form and space, we have examined perception of geometry of natural surfaces and curves, e.g. as in the observer's environment. Besides a systematic mathematical foundation for a remarkably general framework, the advantages of the Gestalt theory of natural surfaces include a concrete computational approach to simulate or recreate images whose geometric invariants and quantities might be perceived and estimated by an observer. The latter is at the very foundation of understanding the nature of perception of space and form, and the (computer graphics) problem of rendering scenes to visually invoke virtual presence.

Cross-National Invariance of Attention-Deficit/Hyperactivity Disorder Factors in Japanese and U.S. University Students

ERIC Educational Resources Information Center

Davis, J. Mark; Cheung, Shu Fai; Takahashi, Tomone; Shinoda, Haruo; Lindstrom, William A.

2011-01-01

Prior research with children generally supports the two-dimensional structure of Attention-Deficit/Hyperactivity Disorder (ADHD; inattentive and hyperactive/impulsive factors) of the DSM-IV-TR as well as invariance of the two-factor structure across nations and cultures. Research with adults supports either a two-factor or three-factor structure…

The Higher Order Factor Structure and Gender Invariance of the Pathological Narcissism Inventory

ERIC Educational Resources Information Center

Wright, Aidan G. C.; Lukowitsky, Mark R.; Pincus, Aaron L.; Conroy, David E.

2010-01-01

The Pathological Narcissism Inventory (PNI) is a recently developed multidimensional inventory for the assessment of pathological narcissism. The authors describe and report the results of two studies that investigate the higher order factor structure and gender invariance of the PNI. The results of the first study indicate that the PNI has a…

Turkish Version of the Survey of Attitudes toward Statistics: Factorial Structure Invariance by Gender

ERIC Educational Resources Information Center

Sarikaya, Esma Emmioglu; Ok, Ahmet; Aydin, Yesim Capa; Schau, Candace

2018-01-01

This study examines factorial structure and the gender invariance of the Turkish version of the Survey of Attitudes toward Statistics (SATS-36). The SATS-36 has 36 items measuring six components: affect, cognitive competence, value, difficulty, effort, and interest. Data were collected from 347 university students. Results showed that the Turkish…

Factor Structure Invariance of the Kaufman Adolescent and Adult Intelligence Test across Male and Female Samples

ERIC Educational Resources Information Center

Immekus, Jason C.; Maller, Susan J.

2010-01-01

Multisample confirmatory factor analysis (MCFA) and latent mean structures analysis (LMS) were used to test measurement invariance and latent mean differences on the Kaufman Adolescent and Adult Intelligence Scale[TM] (KAIT) across males and females in the standardization sample. MCFA found that the parameters of the KAIT two-factor model were…

Examining Factorial Validity and Measurement Invariance of the Student-Teacher Relationship Scale

ERIC Educational Resources Information Center

Webb, Mi-young L.; Neuharth-Pritchett, Stacey

2011-01-01

The purposes of this study were to (a) test the hypothesized factor structure of the Student-Teacher Relationship Scale (STRS; Pianta, 2001) for 308 African American (AA) and European American (EA) children using confirmatory factor analysis (CFA) and (b) examine the measurement invariance of the factor structure across AA and EA children. CFA of…

The Cross-Cultural Invariance of Creative Cognition: A Case Study of Creative Writing in U.S. and Russian College Students

ERIC Educational Resources Information Center

Kornilov, Sergey A.; Kornilova, Tatiana V.; Grigorenko, Elena L.

2016-01-01

Unlike intelligence, creativity has rarely been investigated from the standpoint of cross-cultural invariance of the structure of the instruments used to measure it. In the study reported in this article, we investigated the cross-cultural invariance of expert ratings of creative stories written by undergraduate students from the Russian…

Testing the Factorial Invariance of the English and Filipino Versions of the Inventory of School Motivation with Bilingual Students in the Philippines

ERIC Educational Resources Information Center

Ganotice, Fraide A., Jr.; Bernardo, Allan B. I.; King, Ronnel B.

2012-01-01

The study explored the invariance of Filipino and English versions of the Inventory of School Motivation (ISM) for Filipino-English bilingual students. There was invariance in the factor structure and factor loadings across the two language versions. Between-network construct validation showed consistent associations between ISM-mastery goals and…

An Evaluation of a Theoretical Model Predicting Dieting Behaviors: Tests of Measurement and Structural Invariance across Ethnicity and Gender

ERIC Educational Resources Information Center

Boie, Ioana; Lopez, Anna L.; Sass, Daniel A.

2013-01-01

This study evaluated a model linking internalization and dieting behaviors in a sample ("n" = 499) of Latina/o and White college students. Analyses revealed that the scales were invariant across ethnic and gender groups and generally supported the invariance of the proposed model across these groups. Analyses also revealed no ethnic mean…

Approximating Reflectance and Transmittance of Vegetation Using Multiple Spectral Invariants

NASA Astrophysics Data System (ADS)

Mottus, M.

2011-12-01

Canopy spectral invariants, eigenvalues of the radiative transfer equation and photon recollision probability are some of the new theoretical tools that have been applied in remote sensing of vegetation and atmosphere. The theoretical approach based on spectral invariants, informally also referred to as the p-theory, owns its attractivity to several factors. Firstly, it provides a rapid and physically-based way of describing canopy scattering. Secondly, the p-theory aims at parameterizing canopy structure in reflectance models using a simple and intuitive concept which can be applied at various structural levels, from shoot to tree crown. The theory has already been applied at scales from the molecular level to forest stands. The most important shortcoming of the p-theory lies in its inability to predict the directionality of scattering. The theory is currently based on only one physical parameter, the photon recollision probability p. It is evident that one parameter cannot contain enough information to reasonably predict the observed complex reflectance patterns produced by natural vegetation canopies. Without estimating scattering directionality, however, the theory cannot be compared with even the most simple (and well-tested) two-stream vegetation reflectance models. In this study, we evaluate the possibility to use additional parameters to fit the measured reflectance and transmittance of a vegetation stand. As a first step, the parameters are applied to separate canopy scattering into reflectance and transmittance. New parameters are introduced following the general approach of eigenvector expansion. Thus, the new parameters are coined higher-order spectral invariants. Calculation of higher-order invariants is based on separating first-order scattering from total scattering. Thus, the method explicitly accounts for different view geometries with different fractions of visible sunlit canopy (e.g., hot-spot). It additionally allows to produce different irradiation levels on leaf surfaces for direct and diffuse incidence, thus (in theory) allowing more accurate calculation of potential photosynthesis rates. Similarly to the p-theory, the use of multiple spectral invariants facilitates easy parametrization of canopy structure and scaling between different structural levels (leaf-shoot-stand). Spectral invariant-based remote sensing approaches are well suited for relatively large pixels even when no detailed ground truth information is available. In a case study, the theory of multiple spectral invariants was applied to measured canopy scattering. Spectral reflectance and transmittance measurements were carried out in gray alder (Alnus incana) plantation at Tartu Observatory, Estonia, in August 2006. The equations produced by the theory of spectral invariants were fitted to measured radiation fluxes. Preliminary results indicate that quantities with invariant-like behavior may indeed be used to approximate canopy scattering directionality.

Invariant domain watermarking using heaviside function of order alpha and fractional Gaussian field.

PubMed

Abbasi, Almas; Woo, Chaw Seng; Ibrahim, Rabha Waell; Islam, Saeed

2015-01-01

Digital image watermarking is an important technique for the authentication of multimedia content and copyright protection. Conventional digital image watermarking techniques are often vulnerable to geometric distortions such as Rotation, Scaling, and Translation (RST). These distortions desynchronize the watermark information embedded in an image and thus disable watermark detection. To solve this problem, we propose an RST invariant domain watermarking technique based on fractional calculus. We have constructed a domain using Heaviside function of order alpha (HFOA). The HFOA models the signal as a polynomial for watermark embedding. The watermark is embedded in all the coefficients of the image. We have also constructed a fractional variance formula using fractional Gaussian field. A cross correlation method based on the fractional Gaussian field is used for watermark detection. Furthermore the proposed method enables blind watermark detection where the original image is not required during the watermark detection thereby making it more practical than non-blind watermarking techniques. Experimental results confirmed that the proposed technique has a high level of robustness.

Invariant Domain Watermarking Using Heaviside Function of Order Alpha and Fractional Gaussian Field

PubMed Central

Abbasi, Almas; Woo, Chaw Seng; Ibrahim, Rabha Waell; Islam, Saeed

2015-01-01

Digital image watermarking is an important technique for the authentication of multimedia content and copyright protection. Conventional digital image watermarking techniques are often vulnerable to geometric distortions such as Rotation, Scaling, and Translation (RST). These distortions desynchronize the watermark information embedded in an image and thus disable watermark detection. To solve this problem, we propose an RST invariant domain watermarking technique based on fractional calculus. We have constructed a domain using Heaviside function of order alpha (HFOA). The HFOA models the signal as a polynomial for watermark embedding. The watermark is embedded in all the coefficients of the image. We have also constructed a fractional variance formula using fractional Gaussian field. A cross correlation method based on the fractional Gaussian field is used for watermark detection. Furthermore the proposed method enables blind watermark detection where the original image is not required during the watermark detection thereby making it more practical than non-blind watermarking techniques. Experimental results confirmed that the proposed technique has a high level of robustness. PMID:25884854

Dissipative N-point-vortex Models in the Plane

NASA Astrophysics Data System (ADS)

Shashikanth, Banavara N.

2010-02-01

A method is presented for constructing point vortex models in the plane that dissipate the Hamiltonian function at any prescribed rate and yet conserve the level sets of the invariants of the Hamiltonian model arising from the SE (2) symmetries. The method is purely geometric in that it uses the level sets of the Hamiltonian and the invariants to construct the dissipative field and is based on elementary classical geometry in ℝ3. Extension to higher-dimensional spaces, such as the point vortex phase space, is done using exterior algebra. The method is in fact general enough to apply to any smooth finite-dimensional system with conserved quantities, and, for certain special cases, the dissipative vector field constructed can be associated with an appropriately defined double Nambu-Poisson bracket. The most interesting feature of this method is that it allows for an infinite sequence of such dissipative vector fields to be constructed by repeated application of a symmetric linear operator (matrix) at each point of the intersection of the level sets.

Topological string, supersymmetric gauge theory and bps counting

NASA Astrophysics Data System (ADS)

Pan, Guang

In this thesis we study the Donaldson-Thomas theory on the local curve geometry, which arises in the context of geometric engineering of supersymmetric gauge theory from type IIA string compactification. The topological A-model amplitude gives the F-term interaction of the compactified theory. In particular, it is related to the instanton partition function via Nekrasov conjecture. We will introduce ADHM sheaves on curve, as an alternative description of local Donaldson-Thomas theory. We derive the wallcrossing of ADHM invariants and their refinements. We show that it is equivalent to the semi-primitive wallcrossing from supergravity, and the Kontsevich-Soibelman wallcrossing formula. As an application, we discuss the connection between ADHM moduli space with Hitchin system. In particular we give a recursive formula for the Poincare polynomial of Hitchin system in terms of instanton partition function, from refined wallcrossing. We also introduce higher rank generalization of Donaldson-Thomas invariant in the context of ADHM sheaves. We study their wallcrossing and discuss their physical interpretation via string duality.

Altered perceptual sensitivity to kinematic invariants in Parkinson's disease.

PubMed

Dayan, Eran; Inzelberg, Rivka; Flash, Tamar

2012-01-01

Ample evidence exists for coupling between action and perception in neurologically healthy individuals, yet the precise nature of the internal representations shared between these domains remains unclear. One experimentally derived view is that the invariant properties and constraints characterizing movement generation are also manifested during motion perception. One prominent motor invariant is the "two-third power law," describing the strong relation between the kinematics of motion and the geometrical features of the path followed by the hand during planar drawing movements. The two-thirds power law not only characterizes various movement generation tasks but also seems to constrain visual perception of motion. The present study aimed to assess whether motor invariants, such as the two thirds power law also constrain motion perception in patients with Parkinson's disease (PD). Patients with PD and age-matched controls were asked to observe the movement of a light spot rotating on an elliptical path and to modify its velocity until it appeared to move most uniformly. As in previous reports controls tended to choose those movements close to obeying the two-thirds power law as most uniform. Patients with PD displayed a more variable behavior, choosing on average, movements closer but not equal to a constant velocity. Our results thus demonstrate impairments in how the two-thirds power law constrains motion perception in patients with PD, where this relationship between velocity and curvature appears to be preserved but scaled down. Recent hypotheses on the role of the basal ganglia in motor timing may explain these irregularities. Alternatively, these impairments in perception of movement may reflect similar deficits in motor production.

A comparative experimental and quantum chemical study on monomeric and dimeric structures of 3,5-dibromoanthranilic acid.

PubMed

Karabacak, Mehmet; Cinar, Mehmet

2012-10-01

This study presents the structural and spectroscopic characterization of 3,5-dibromoanthranilic acid with help of experimental techniques (FT-IR, FT-Raman, UV, NMR) and quantum chemical calculations. The vibrational spectra of title compound were recorded in solid state with FT-IR and FT-Raman in the range of 4000-400 and 4000-50 cm(-1), respectively. The vibrational frequencies were also computed using B3LYP method of DFT with 6-311++G(d,p) basis set. The fundamental assignments were done on the basis of the total energy distribution (TED) of the vibrational modes, calculated with scaled quantum mechanical (SQM) method. The (1)H, (13)C and DEPT NMR spectra were recorded in DMSO solution and calculated by gauge-invariant atomic orbitals (GIAO) method. The UV absorption spectra of the compound were recorded in the range of 200-400 nm in ethanol, water and DMSO solutions. Solvent effects were calculated using time-dependent density functional theory and CIS method. The ground state geometrical structure of compound was predicted by B3LYP method and compared with the crystallographic structure of similar compounds. All calculations were made for monomeric and dimeric structure of compound. Moreover, molecular electrostatic potential (MEP) and thermodynamic properties were performed. Mulliken atomic charges of neutral and anionic form of the molecule were computed and compared with anthranilic acid. Copyright © 2012 Elsevier B.V. All rights reserved.

Simplified and refined finite element approaches for determining stresses and internal forces in geometrically nonlinear structural analysis

NASA Technical Reports Server (NTRS)

Robinson, J. C.

1979-01-01

Two methods for determining stresses and internal forces in geometrically nonlinear structural analysis are presented. The simplified approach uses the mid-deformed structural position to evaluate strains when rigid body rotation is present. The important feature of this approach is that it can easily be used with a general-purpose finite-element computer program. The refined approach uses element intrinsic or corotational coordinates and a geometric transformation to determine element strains from joint displacements. Results are presented which demonstrate the capabilities of these potentially useful approaches for geometrically nonlinear structural analysis.

Complex Ordered Patterns in Mechanical Instability Induced Geometrically Frustrated Triangular Cellular Structures

NASA Astrophysics Data System (ADS)

Kang, Sung Hoon; Shan, Sicong; Košmrlj, Andrej; Noorduin, Wim L.; Shian, Samuel; Weaver, James C.; Clarke, David R.; Bertoldi, Katia

2014-03-01

Geometrical frustration arises when a local order cannot propagate throughout the space because of geometrical constraints. This phenomenon plays a major role in many systems leading to disordered ground-state configurations. Here, we report a theoretical and experimental study on the behavior of buckling-induced geometrically frustrated triangular cellular structures. To our surprise, we find that buckling induces complex ordered patterns which can be tuned by controlling the porosity of the structures. Our analysis reveals that the connected geometry of the cellular structure plays a crucial role in the generation of ordered states in this frustrated system.

Measuring social desirability across language and sex: A comparison of Marlowe-Crowne Social Desirability Scale factor structures in English and Mandarin Chinese in Malaysia.

PubMed

Kurz, A Solomon; Drescher, Christopher F; Chin, Eu Gene; Johnson, Laura R

2016-06-01

Malaysia is a Southeast Asian country in which multiple languages are prominently spoken, including English and Mandarin Chinese. As psychological science continues to develop within Malaysia, there is a need for psychometrically sound instruments that measure psychological phenomena in multiple languages. For example, assessment tools for measuring social desirability could be a useful addition in psychological assessments and research studies in a Malaysian context. This study examined the psychometric performance of the English and Mandarin Chinese versions of the Marlowe-Crowne Social Desirability Scale when used in Malaysia. Two hundred and eighty-three students (64% female; 83% Chinese, 9% Indian) from two college campuses completed the Marlowe-Crowne Social Desirability Scale in their language of choice (i.e., English or Mandarin Chinese). Proposed factor structures were compared with confirmatory factor analysis, and multiple indicators-multiple causes models were used to examine measurement invariance across language and sex. Factor analyses supported a two-factor structure (i.e., Attribution and Denial) for the measure. Invariance tests revealed the scale was invariant by sex, indicating that social desirability can be interpreted similarly across sex. The scale was partially invariant by language version, with some non-invariance observed within the Denial factor. Non-invariance may be related to differences in the English and Mandarin Chinese languages, as well as cultural differences. Directions for further research include examining the measurement of social desirability in other contexts where both English and Mandarin Chinese are spoken (i.e., China) and further examining the causes of non-invariance on specific items. © 2016 The Institute of Psychology, Chinese Academy of Sciences and John Wiley & Sons Australia, Ltd.

The chaotic set and the cross section for chaotic scattering in three degrees of freedom

NASA Astrophysics Data System (ADS)

Jung, C.; Merlo, O.; Seligman, T. H.; Zapfe, W. P. K.

2010-10-01

This article treats chaotic scattering with three degrees of freedom, where one of them is open and the other two are closed, as a first step towards a more general understanding of chaotic scattering in higher dimensions. Despite the strong restrictions, it breaks the essential simplicity implicit in any two-dimensional time-independent scattering problem. Introducing the third degree of freedom by breaking a continuous symmetry, we first explore the topological structure of the homoclinic/heteroclinic tangle and the structures in the scattering functions. Then we work out the implications of these structures for the doubly differential cross section. The most prominent structures in the cross section are rainbow singularities. They form a fractal pattern that reflects the fractal structure of the chaotic invariant set. This allows us to determine structures in the cross section from the invariant set and, conversely, to obtain information about the topology of the invariant set from the cross section. The latter is a contribution to the inverse scattering problem for chaotic systems.

Psychometric assessment of the processes of change scale for sun protection.

PubMed

Sillice, Marie A; Babbin, Steven F; Redding, Colleen A; Rossi, Joseph S; Paiva, Andrea L; Velicer, Wayne F

2018-01-01

The fourteen-factor Processes of Change Scale for Sun Protection assesses behavioral and experiential strategies that underlie the process of sun protection acquisition and maintenance. Variations of this measure have been used effectively in several randomized sun protection trials, both for evaluation and as a basis for intervention. However, there are no published studies, to date, that evaluate the psychometric properties of the scale. The present study evaluated factorial invariance and scale reliability in a national sample (N = 1360) of adults involved in a Transtheoretical model tailored intervention for exercise and sun protection, at baseline. Invariance testing ranged from least to most restrictive: Configural Invariance (constraints only factor structure and zero loadings); Pattern Identity Invariance (equal factor loadings across target groups); and Strong Factorial Invariance (equal factor loadings and measurement errors). Multi-sample structural equation modeling tested the invariance of the measurement model across seven subgroups: age, education, ethnicity, gender, race, skin tone, and Stage of Change for Sun Protection. Strong factorial invariance was found across all subgroups. Internal consistency coefficient Alpha and factor rho reliability, respectively, were .83 and .80 for behavioral processes, .91 and .89 for experiential processes, and .93 and .91 for the global scale. These results provide strong empirical evidence that the scale is consistent, has internal validity and can be used in research interventions with population-based adult samples.

Reliability, Factor Structure, and Measurement Invariance of the Dominic Interactive Across European Countries: Cross-Country Utility of a Child Mental Health Self-Report

PubMed Central

Kuijpers, Rowella C. W. M.; Otten, Roy; Vermulst, Ad A.; Bitfoi, Adina; Goelitz, Dietmar; Koç, Ceren; Mihova, Zlatka; Pez, Ondine; Carta, Mauro; Keyes, Katherine; Lesinskiene, Sigita; Engels, Rutger C. M. E.; Kovess, Viviane

2015-01-01

Large-scale international surveys are important to globally evaluate, monitor, and promote children's mental health. However, use of young children's self-reports in these studies is still controversial. The Dominic Interactive, a computerized DSM-IV–based child mental health self-report questionnaire, has unique characteristics that may make it preeminently appropriate for usage in cross-country comparisons. This study aimed to determine scale score reliabilities (omega) of the Dominic Interactive in a sample of 8,135 primary school children, ages 6–11 years old, in 7 European countries, to confirm the proposed 7-scale factor structure, and to test for measurement invariance of scale and item scores across countries. Omega reliability values for scale scores were good to high in every country, and the factor structure was confirmed for all countries. A thorough examination of measurement invariance provided evidence for cross-country test score comparability of 5 of the 7 scales and partial scale score invariance of 2 anxiety scales. Possible explanations for this partial invariance include cross-country differences in conceptualizing items and defining what is socially and culturally acceptable anxiety. The convincing evidence for validity of score interpretation makes the Dominic Interactive an indispensable tool for cross-country screening purposes. PMID:26237209

Information processing of motion in facial expression and the geometry of dynamical systems

NASA Astrophysics Data System (ADS)

Assadi, Amir H.; Eghbalnia, Hamid; McMenamin, Brenton W.

2005-01-01

An interesting problem in analysis of video data concerns design of algorithms that detect perceptually significant features in an unsupervised manner, for instance methods of machine learning for automatic classification of human expression. A geometric formulation of this genre of problems could be modeled with help of perceptual psychology. In this article, we outline one approach for a special case where video segments are to be classified according to expression of emotion or other similar facial motions. The encoding of realistic facial motions that convey expression of emotions for a particular person P forms a parameter space XP whose study reveals the "objective geometry" for the problem of unsupervised feature detection from video. The geometric features and discrete representation of the space XP are independent of subjective evaluations by observers. While the "subjective geometry" of XP varies from observer to observer, levels of sensitivity and variation in perception of facial expressions appear to share a certain level of universality among members of similar cultures. Therefore, statistical geometry of invariants of XP for a sample of population could provide effective algorithms for extraction of such features. In cases where frequency of events is sufficiently large in the sample data, a suitable framework could be provided to facilitate the information-theoretic organization and study of statistical invariants of such features. This article provides a general approach to encode motion in terms of a particular genre of dynamical systems and the geometry of their flow. An example is provided to illustrate the general theory.

The mental health continuum-short form: The structure and application for cross-cultural studies-A 38 nation study.

PubMed

Żemojtel-Piotrowska, Magdalena; Piotrowski, Jarosław P; Osin, Evgeny N; Cieciuch, Jan; Adams, Byron G; Ardi, Rahkman; Bălţătescu, Sergiu; Bogomaz, Sergey; Bhomi, Arbinda Lal; Clinton, Amanda; de Clunie, Gisela T; Czarna, Anna Z; Esteves, Carla; Gouveia, Valdiney; Halik, Murnizam H J; Hosseini, Ashraf; Khachatryan, Narine; Kamble, Shanmukh Vasant; Kawula, Anna; Lun, Vivian Miu-Chi; Ilisko, Dzintra; Klicperova-Baker, Martina; Liik, Kadi; Letovancova, Eva; Cerrato, Sara Malo; Michalowski, Jaroslaw; Malysheva, Natalia; Marganski, Alison; Nikolic, Marija; Park, Joonha; Paspalanova, Elena; de Leon, Pablo Perez; Pék, Győző; Różycka-Tran, Joanna; Samekin, Adil; Shahbaz, Wahab; Khanh Ha, Truong Thi; Tiliouine, Habib; Van Hiel, Alain; Vauclair, Melanie; Wills-Herrera, Eduardo; Włodarczyk, Anna; Yahiiaev, Illia; Maltby, John

2018-06-01

The Mental Health Continuum-Short Form (MHC-SF) is a brief scale measuring positive human functioning. The study aimed to examine the factor structure and to explore the cross-cultural utility of the MHC-SF using bifactor models and exploratory structural equation modelling. Using multigroup confirmatory analysis (MGCFA) we examined the measurement invariance of the MHC-SF in 38 countries (university students, N = 8,066; 61.73% women, mean age 21.55 years). MGCFA supported the cross-cultural replicability of a bifactor structure and a metric level of invariance between student samples. The average proportion of variance explained by the general factor was high (ECV = .66), suggesting that the three aspects of mental health (emotional, social, and psychological well-being) can be treated as a single dimension of well-being. The metric level of invariance offers the possibility of comparing correlates and predictors of positive mental functioning across countries; however, the comparison of the levels of mental health across countries is not possible due to lack of scalar invariance. Our study has preliminary character and could serve as an initial assessment of the structure of the MHC-SF across different cultural settings. Further studies on general populations are required for extending our findings. © 2018 Wiley Periodicals, Inc.

Sample Invariance of the Structural Equation Model and the Item Response Model: A Case Study.

ERIC Educational Resources Information Center

Breithaupt, Krista; Zumbo, Bruno D.

2002-01-01

Evaluated the sample invariance of item discrimination statistics in a case study using real data, responses of 10 random samples of 500 people to a depression scale. Results lend some support to the hypothesized superiority of a two-parameter item response model over the common form of structural equation modeling, at least when responses are…

Multiple-Group Confirmatory Factor Analysis in R--A Tutorial in Measurement Invariance with Continuous and Ordinal Indicators

ERIC Educational Resources Information Center

Hirschfeld, Gerrit; von Brachel, Ruth

2014-01-01

Multiple-group confirmatory factor analysis (MG-CFA) is among the most productive extensions of structural equation modeling. Many researchers conducting cross-cultural or longitudinal studies are interested in testing for measurement and structural invariance. The aim of the present paper is to provide a tutorial in MG-CFA using the freely…

The Learning and Study Strategies Inventory-High School Version: Issues of Factorial Invariance Across Gender and Ethnicity

ERIC Educational Resources Information Center

Stevens, Tara; Tallent-Runnels, Mary K.

2004-01-01

The purpose of this study was to investigate the latent structure of the Learning and Study Strategies Inventory-High School (LASSI-HS) through confirmatory factor analysis and factorial invariance models. A simple modification of the three-factor structure was considered. Using a larger sample, cross-validation was completed and the equality of…

Measurement Invariance and Latent Mean Differences in the Reynolds Intellectual Assessment Scales (RIAS): Does the German Version of the RIAS Allow a Valid Assessment of Individuals with a Migration Background?

PubMed Central

Gygi, Jasmin T.; Fux, Elodie; Grob, Alexander; Hagmann-von Arx, Priska

2016-01-01

This study examined measurement invariance and latent mean differences in the German version of the Reynolds Intellectual Assessment Scales (RIAS) for 316 individuals with a migration background (defined as speaking German as a second language) and 316 sex- and age-matched natives. The RIAS measures general intelligence (single-factor structure) and its two components, verbal and nonverbal intelligence (two-factor structure). Results of a multi-group confirmatory factor analysis showed scalar invariance for the two-factor and partial scalar invariance for the single-factor structure. We conclude that the two-factor structure of the RIAS is comparable across groups. Hence, verbal and nonverbal intelligence but not general intelligence should be considered when comparing RIAS test results of individuals with and without a migration background. Further, latent mean differences especially on the verbal, but also on the nonverbal intelligence index indicate language barriers for individuals with a migration background, as subtests corresponding to verbal intelligence require higher skills in German language. Moreover, cultural, environmental, and social factors that have to be taken into account when assessing individuals with a migration background are discussed. PMID:27846270

Inertial Spontaneous Symmetry Breaking and Quantum Scale Invariance

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ferreira, Pedro G.; Hill, Christopher T.; Ross, Graham G.

Weyl invariant theories of scalars and gravity can generate all mass scales spontaneously, initiated by a dynamical process of "inertial spontaneous symmetry breaking" that does not involve a potential. This is dictated by the structure of the Weyl current,more » $$K_\\mu$$, and a cosmological phase during which the universe expands and the Einstein-Hilbert effective action is formed. Maintaining exact Weyl invariance in the renormalised quantum theory is straightforward when renormalisation conditions are referred back to the VEV's of fields in the action of the theory, which implies a conserved Weyl current. We do not require scale invariant regulators. We illustrate the computation of a Weyl invariant Coleman-Weinberg potential.« less

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.

Evolution of heliospheric magnetized configurations via topological invariants

NASA Astrophysics Data System (ADS)

Roth, Ilan

2013-07-01

The analogy between magnetohydrodynamics (MHD) and knot theory is utilized in presenting a new method for an analysis of stability and evolution of complex magnetic heliospheric flux tubes. Planar projection of a three-dimensional magnetic configuration depicts the structure as a two-dimensional diagram with crossings, to which one may assign mathematical operations leading to robust topological invariants. These invariants enrich the topological information of magnetic configurations beyond helicity. It is conjectured that the field which emerges from the solar photosphere is structured as one of the simplest knots-unknot or prime knot-and these flux ropes are then stretched while carried by the solar wind into the interplanetary medium. Preservation of invariants for small diffusivity and large cross section of the emerging magnetic flux makes them impervious to large scale reconnection, allowing us to predict the observed structures at 1 AU as elongated prime knots. Similar structures may be observed in magnetic clouds which got disconnected from their footpoints and in ion drop-out configurations from a compact flare source in solar impulsive solar events. Observation of small scale magnetic features consistent with prime knots may indicate spatial intermittency and non-Gaussian statistics in the turbulent cascade process. For flux tubes with higher resistivity, magnetic energy decay rate should decrease with increased knot complexity as the invariants are then harder to be violated. These observations could be confirmed if adjacent satellites happen to measure distinctly oriented magnetic fields with directionally varying suprathermal particle fluxes.

Factor structure and measurement invariance of the Health Education Impact Questionnaire: Does the subjectivity of the response perspective threaten the contextual validity of inferences?

PubMed

Elsworth, Gerald R; Nolte, Sandra; Osborne, Richard H

2015-01-01

On-going evidence is required to support the validity of inferences about change and group differences in the evaluation of health programs, particularly when self-report scales requiring substantial subjectivity in response generation are used as outcome measures. Following this reasoning, the aim of this study was to replicate the factor structure and investigate the measurement invariance of the latest version of the Health Education Impact Questionnaire, a widely used health program evaluation measure. An archived dataset of responses to the most recent version of the English-language Health Education Impact Questionnaire that uses four rather than six response options (N = 3221) was analysed using exploratory structural equation modelling and confirmatory factor analysis appropriate for ordered categorical data. Metric and scalar invariance were studied following recent recommendations in the literature to apply fully invariant unconditional models with minimum constraints necessary for model identification. The original eight-factor structure was replicated and all but one of the scales (Self Monitoring and Insight) was found to consist of unifactorial items with reliability of ⩾0.8 and satisfactory discriminant validity. Configural, metric and scalar invariance were established across pre-test to post-test and population sub-groups (sex, age, education, ethnic background). The results support the high level of interest in the Health Education Impact Questionnaire, particularly for use as a pre-test/post-test measure in experimental studies, other pre-post evaluation designs and system-level monitoring and evaluation.

Linear systems with structure group and their feedback invariants

NASA Technical Reports Server (NTRS)

Martin, C.; Hermann, R.

1977-01-01

A general method described by Hermann and Martin (1976) for the study of the feedback invariants of linear systems is considered. It is shown that this method, which makes use of ideas of topology and algebraic geometry, is very useful in the investigation of feedback problems for which the classical methods are not suitable. The transfer function as a curve in the Grassmanian is examined. The general concepts studied in the context of specific systems and applications are organized in terms of the theory of Lie groups and algebraic geometry. Attention is given to linear systems which have a structure group, linear mechanical systems, and feedback invariants. The investigation shows that Lie group techniques are powerful and useful tools for analysis of the feedback structure of linear systems.

Local phase space and edge modes for diffeomorphism-invariant theories

NASA Astrophysics Data System (ADS)

Speranza, Antony J.

2018-02-01

We discuss an approach to characterizing local degrees of freedom of a subregion in diffeomorphism-invariant theories using the extended phase space of Donnelly and Freidel [36]. Such a characterization is important for defining local observables and entanglement entropy in gravitational theories. Traditional phase space constructions for subregions are not invariant with respect to diffeomorphisms that act at the boundary. The extended phase space remedies this problem by introducing edge mode fields at the boundary whose transformations under diffeomorphisms render the extended symplectic structure fully gauge invariant. In this work, we present a general construction for the edge mode symplectic structure. We show that the new fields satisfy a surface symmetry algebra generated by the Noether charges associated with the edge mode fields. For surface-preserving symmetries, the algebra is universal for all diffeomorphism-invariant theories, comprised of diffeomorphisms of the boundary, SL(2, ℝ) transformations of the normal plane, and, in some cases, normal shearing transformations. We also show that if boundary conditions are chosen such that surface translations are symmetries, the algebra acquires a central extension.

Size invariance of the granular Rayleigh-Taylor instability.

PubMed

Vinningland, Jan Ludvig; Johnsen, Øistein; Flekkøy, Eirik G; Toussaint, Renaud; Måløy, Knut Jørgen

2010-04-01

The size scaling behavior of the granular Rayleigh-Taylor instability [J. L. Vinningland, Phys. Rev. Lett. 99, 048001 (2007)] is investigated experimentally, numerically, and theoretically. An upper layer of grains displaces a lower gap of air by organizing into dense fingers of falling grains separated by rising bubbles of air. The dependence of these structures on the system and grain sizes is investigated. A spatial measurement of the finger structures is obtained by the Fourier power spectrum of the wave number k. As the size of the grains increases the wave number decreases accordingly which leaves the dimensionless product of wave number and grain diameter, dk, invariant. A theoretical interpretation of the invariance, based on the scaling properties of the model equations, suggests a gradual breakdown of the invariance for grains smaller than approximately 70 microm or greater than approximately 570 microm in diameter.

Symmetry as Bias: Rediscovering Special Relativity

NASA Technical Reports Server (NTRS)

Lowry, Michael R.

1992-01-01

This paper describes a rational reconstruction of Einstein's discovery of special relativity, validated through an implementation: the Erlanger program. Einstein's discovery of special relativity revolutionized both the content of physics and the research strategy used by theoretical physicists. This research strategy entails a mutual bootstrapping process between a hypothesis space for biases, defined through different postulated symmetries of the universe, and a hypothesis space for physical theories. The invariance principle mutually constrains these two spaces. The invariance principle enables detecting when an evolving physical theory becomes inconsistent with its bias, and also when the biases for theories describing different phenomena are inconsistent. Structural properties of the invariance principle facilitate generating a new bias when an inconsistency is detected. After a new bias is generated. this principle facilitates reformulating the old, inconsistent theory by treating the latter as a limiting approximation. The structural properties of the invariance principle can be suitably generalized to other types of biases to enable primal-dual learning.

Permutation-invariant distance between atomic configurations

NASA Astrophysics Data System (ADS)

Ferré, Grégoire; Maillet, Jean-Bernard; Stoltz, Gabriel

2015-09-01

We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables us to directly compare different atomic environments with an arbitrary number of particles, without going through a space of reduced dimensionality (i.e., fingerprints) as an intermediate step. Moreover, this distance is naturally invariant through permutations of atoms, avoiding the time consuming associated minimization required by other common criteria (like the root mean square distance). Finally, the invariance through global rotations is accounted for by a minimization procedure in the space of rotations solved by Monte Carlo simulated annealing. A formal framework is also introduced, showing that the distance we propose verifies the property of a metric on the space of atomic configurations. Two examples of applications are proposed. The first one consists in evaluating faithfulness of some fingerprints (or descriptors), i.e., their capacity to represent the structural information of a configuration. The second application concerns structural analysis, where our distance proves to be efficient in discriminating different local structures and even classifying their degree of similarity.

Impulsivity and the sexes: measurement and structural invariance of the UPPS-P Impulsive Behavior Scale.

PubMed

Cyders, Melissa A

2013-02-01

Before it is possible to test whether men and women differ in impulsivity, it is necessary to evaluate whether impulsivity measures are invariant across sex. The UPPS-P Impulsive Behavior Scale (negative urgency, lack of premeditation, lack of perseverance, and sensation seeking, with added subscale of positive urgency) is one measure of five dispositions toward rash action that has shown to have robust and clinically useful relationships among risk-taking outcomes. In the current research, the author examined (a) the psychometric measurement invariance of the UPPS-P across sex, (b) the scale's structural invariance across sex, and (c) whether the five impulsivity traits differentially relate to risk outcomes as a function of sex. In a sample of 1,372 undergraduates, the author found evidence for measurement and invariance across sex: Thus, comparisons of men and women on the UPPS-P can be considered valid. Additionally, although males tend to report higher levels of sensation seeking and positive urgency (and possibly lack of perseverance), the relationships between the UPPS-P traits and risk outcomes were generally invariant across sex. The UPPS-P appears to function comparably across males and females, and mean differences on this scale between the sexes can be thought to reflect trait-level differences.

Non a Priori Automatic Discovery of 3D Chemical Patterns: Application to Mutagenicity.

PubMed

Rabatel, Julien; Fannes, Thomas; Lepailleur, Alban; Le Goff, Jérémie; Crémilleux, Bruno; Ramon, Jan; Bureau, Ronan; Cuissart, Bertrand

2017-10-01

This article introduces a new type of structural fragment called a geometrical pattern. Such geometrical patterns are defined as molecular graphs that include a labelling of atoms together with constraints on interatomic distances. The discovery of geometrical patterns in a chemical dataset relies on the induction of multiple decision trees combined in random forests. Each computational step corresponds to a refinement of a preceding set of constraints, extending a previous geometrical pattern. This paper focuses on the mutagenicity of chemicals via the definition of structural alerts in relation with these geometrical patterns. It follows an experimental assessment of the main geometrical patterns to show how they can efficiently originate the definition of a chemical feature related to a chemical function or a chemical property. Geometrical patterns have provided a valuable and innovative approach to bring new pieces of information for discovering and assessing structural characteristics in relation to a particular biological phenotype. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Unifying role of dissipative action in the dynamic failure of solids

NASA Astrophysics Data System (ADS)

Grady, Dennis E.

2015-04-01

A fourth-power law underlying the steady shock-wave structure and solid viscosity of condensed material has been observed for a wide range of metals and non-metals. The fourth-power law relates the steady-wave Hugoniot pressure to the fourth power of the strain rate during passage of the material through the structured shock wave. Preceding the fourth-power law was the observation in a shock transition that the product of the shock dissipation energy and the shock transition time is a constant independent of the shock pressure amplitude. Invariance of this energy-time product implies the fourth-power law. This property of the shock transition in solids was initially identified as a shock invariant. More recently, it has been referred to as the dissipative action, although no relationship to the accepted definitions of action in mechanics has been demonstrated. This same invariant property has application to a wider range of transient failure phenomena in solids. Invariance of this dissipation action has application to spall fracture, failure through adiabatic shear, shock compaction of granular media, and perhaps others. Through models of the failure processes, a clearer picture of the physics underlying the observed invariance is emerging. These insights in turn are leading to a better understanding of the shock deformation processes underlying the fourth-power law. Experimental result and material models encompassing the dynamic failure of solids are explored for the purpose of demonstrating commonalities leading to invariance of the dissipation action. Calculations are extended to aluminum and uranium metals with the intent of predicting micro-scale dynamics and spatial structure in the steady shock wave.

Validating the cross-cultural factor structure and invariance property of the Insomnia Severity Index: evidence based on ordinal EFA and CFA.

PubMed

Chen, Po-Yi; Yang, Chien-Ming; Morin, Charles M

2015-05-01

The purpose of this study is to examine the factor structure of the Insomnia Severity Index (ISI) across samples recruited from different countries. We tried to identify the most appropriate factor model for the ISI and further examined the measurement invariance property of the ISI across samples from different countries. Our analyses included one data set collected from a Taiwanese sample and two data sets obtained from samples in Hong Kong and Canada. The data set collected in Taiwan was analyzed with ordinal exploratory factor analysis (EFA) to obtain the appropriate factor model for the ISI. After that, we conducted a series of confirmatory factor analyses (CFAs), which is a special case of the structural equation model (SEM) that concerns the parameters in the measurement model, to the statistics collected in Canada and Hong Kong. The purposes of these CFA were to cross-validate the result obtained from EFA and further examine the cross-cultural measurement invariance of the ISI. The three-factor model outperforms other models in terms of global fit indices in Taiwan's population. Its external validity is also supported by confirmatory factor analyses. Furthermore, the measurement invariance analyses show that the strong invariance property between the samples from different cultures holds, providing evidence that the ISI results obtained in different cultures are comparable. The factorial validity of the ISI is stable in different populations. More importantly, its invariance property across cultures suggests that the ISI is a valid measure of the insomnia severity construct across countries. Copyright © 2014 Elsevier B.V. All rights reserved.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grady, Dennis E.

A fourth-power law underlying the steady shock-wave structure and solid viscosity of condensed material has been observed for a wide range of metals and non-metals. The fourth-power law relates the steady-wave Hugoniot pressure to the fourth power of the strain rate during passage of the material through the structured shock wave. Preceding the fourth-power law was the observation in a shock transition that the product of the shock dissipation energy and the shock transition time is a constant independent of the shock pressure amplitude. Invariance of this energy-time product implies the fourth-power law. This property of the shock transition inmore » solids was initially identified as a shock invariant. More recently, it has been referred to as the dissipative action, although no relationship to the accepted definitions of action in mechanics has been demonstrated. This same invariant property has application to a wider range of transient failure phenomena in solids. Invariance of this dissipation action has application to spall fracture, failure through adiabatic shear, shock compaction of granular media, and perhaps others. Through models of the failure processes, a clearer picture of the physics underlying the observed invariance is emerging. These insights in turn are leading to a better understanding of the shock deformation processes underlying the fourth-power law. Experimental result and material models encompassing the dynamic failure of solids are explored for the purpose of demonstrating commonalities leading to invariance of the dissipation action. Calculations are extended to aluminum and uranium metals with the intent of predicting micro-scale dynamics and spatial structure in the steady shock wave.« less

Measurement Invariance Conventions and Reporting: The State of the Art and Future Directions for Psychological Research

PubMed Central

Putnick, Diane L.; Bornstein, Marc H.

2016-01-01

Measurement invariance assesses the psychometric equivalence of a construct across groups or across time. Measurement noninvariance suggests that a construct has a different structure or meaning to different groups or on different measurement occasions in the same group, and so the construct cannot be meaningfully tested or construed across groups or across time. Hence, prior to testing mean differences across groups or measurement occasions (e.g., boys and girls, pretest and posttest), or differential relations of the construct across groups, it is essential to assess the invariance of the construct. Conventions and reporting on measurement invariance are still in flux, and researchers are often left with limited understanding and inconsistent advice. Measurement invariance is tested and established in different steps. This report surveys the state of measurement invariance testing and reporting, and details the results of a literature review of studies that tested invariance. Most tests of measurement invariance include configural, metric, and scalar steps; a residual invariance step is reported for fewer tests. Alternative fit indices (AFIs) are reported as model fit criteria for the vast majority of tests; χ2 is reported as the single index in a minority of invariance tests. Reporting AFIs is associated with higher levels of achieved invariance. Partial invariance is reported for about one-third of tests. In general, sample size, number of groups compared, and model size are unrelated to the level of invariance achieved. Implications for the future of measurement invariance testing, reporting, and best practices are discussed. PMID:27942093

Cross-Cultural Invariance of the Mental Toughness Inventory Among Australian, Chinese, and Malaysian Athletes: A Bayesian Estimation Approach.

PubMed

Gucciardi, Daniel F; Zhang, Chun-Qing; Ponnusamy, Vellapandian; Si, Gangyan; Stenling, Andreas

2016-04-01

The aims of this study were to assess the cross-cultural invariance of athletes' self-reports of mental toughness and to introduce and illustrate the application of approximate measurement invariance using Bayesian estimation for sport and exercise psychology scholars. Athletes from Australia (n = 353, Mage = 19.13, SD = 3.27, men = 161), China (n = 254, Mage = 17.82, SD = 2.28, men = 138), and Malaysia (n = 341, Mage = 19.13, SD = 3.27, men = 200) provided a cross-sectional snapshot of their mental toughness. The cross-cultural invariance of the mental toughness inventory in terms of (a) the factor structure (configural invariance), (b) factor loadings (metric invariance), and (c) item intercepts (scalar invariance) was tested using an approximate measurement framework with Bayesian estimation. Results indicated that approximate metric and scalar invariance was established. From a methodological standpoint, this study demonstrated the usefulness and flexibility of Bayesian estimation for single-sample and multigroup analyses of measurement instruments. Substantively, the current findings suggest that the measurement of mental toughness requires cultural adjustments to better capture the contextually salient (emic) aspects of this concept.

Milne boost from Galilean gauge theory

NASA Astrophysics Data System (ADS)

Banerjee, Rabin; Mukherjee, Pradip

2018-03-01

Physical origin of Milne boost invariance of the Newton Cartan spacetime is traced to the effect of local Galilean boosts in its metric structure, using Galilean gauge theory. Specifically, we do not require any gauge field to understand Milne boost invariance.

Webs on surfaces, rings of invariants, and clusters.

PubMed

Fomin, Sergey; Pylyavskyy, Pavlo

2014-07-08

We construct and study cluster algebra structures in rings of invariants of the special linear group action on collections of 3D vectors, covectors, and matrices. The construction uses Kuperberg's calculus of webs on marked surfaces with boundary.

Final Report for Geometric Analysis for Data Reduction and Structure Discovery DE-FG02-10ER25983, STRIPES award # DE-SC0004096

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vixie, Kevin R.

This is the final report for the project "Geometric Analysis for Data Reduction and Structure Discovery" in which insights and tools from geometric analysis were developed and exploited for their potential to large scale data challenges.

On the theory of 3-phase squirrel-cage induction motors including space harmonics and mutual slotting

DOE Office of Scientific and Technical Information (OSTI.GOV)

Papp, G.C.

1991-03-01

In this paper general equations for the asynchronous squirrel-cage motor which contain the influence of space harmonics and the mutual slotting are derived by using among others the power-invariant symmetrical component transformation and a time-dependent transformation with which, under certain circumstances, the rotor-position angle can be removed from the coefficient matrix. The developed models implemented in a machine-independent computer program form powerful tools, with which the influence of space harmonics in relation to the geometric data of specific motors can be analyzed for steady-state and transient performances.

Comparing an analytical spacetime metric for a merging binary to a fully nonlinear numerical evolution using curvature scalars

NASA Astrophysics Data System (ADS)

Sadiq, Jam; Zlochower, Yosef; Nakano, Hiroyuki

2018-04-01

We introduce a new geometrically invariant prescription for comparing two different spacetimes based on geodesic deviation. We use this method to compare a family of recently introduced analytical spacetime representing inspiraling black-hole binaries to fully nonlinear numerical solutions to the Einstein equations. Our method can be used to improve analytical spacetime models by providing a local measure of the effects that violations of the Einstein equations will have on timelike geodesics, and indirectly, gas dynamics. We also discuss the advantages and limitations of this method.

Application of Fourier analysis to multispectral/spatial recognition

NASA Technical Reports Server (NTRS)

Hornung, R. J.; Smith, J. A.

1973-01-01

One approach for investigating spectral response from materials is to consider spatial features of the response. This might be accomplished by considering the Fourier spectrum of the spatial response. The Fourier Transform may be used in a one-dimensional to multidimensional analysis of more than one channel of data. The two-dimensional transform represents the Fraunhofer diffraction pattern of the image in optics and has certain invariant features. Physically the diffraction pattern contains spatial features which are possibly unique to a given configuration or classification type. Different sampling strategies may be used to either enhance geometrical differences or extract additional features.

Calculus of nonrigid surfaces for geometry and texture manipulation.

PubMed

Bronstein, Alexander; Bronstein, Michael; Kimmel, Ron

2007-01-01

We present a geometric framework for automatically finding intrinsic correspondence between three-dimensional nonrigid objects. We model object deformation as near isometries and find the correspondence as the minimum-distortion mapping. A generalization of multidimensional scaling is used as the numerical core of our approach. As a result, we obtain the possibility to manipulate the extrinsic geometry and the texture of the objects as vectors in a linear space. We demonstrate our method on the problems of expression-invariant texture mapping onto an animated three-dimensional face, expression exaggeration, morphing between faces, and virtual body painting.

Arnold diffusion for smooth convex systems of two and a half degrees of freedom

NASA Astrophysics Data System (ADS)

Kaloshin, V.; Zhang, K.

2015-08-01

In the present note we announce a proof of a strong form of Arnold diffusion for smooth convex Hamiltonian systems. Let { T}2 be a 2-dimensional torus and B2 be the unit ball around the origin in { R}2 . Fix ρ > 0. Our main result says that for a ‘generic’ time-periodic perturbation of an integrable system of two degrees of freedom H_0(p)+\\varepsilon H_1(θ,p,t),\\quad θ\\in { T}^2, p\\in B^2, t\\in { T}={ R}/{ Z} , with a strictly convex H0, there exists a ρ-dense orbit (θε, pε, t)(t) in { T}2 × B2 × { T} , namely, a ρ-neighborhood of the orbit contains { T}2 × B2 × { T} . Our proof is a combination of geometric and variational methods. The fundamental elements of the construction are the usage of crumpled normally hyperbolic invariant cylinders from [9], flower and simple normally hyperbolic invariant manifolds from [36] as well as their kissing property at a strong double resonance. This allows us to build a ‘connected’ net of three-dimensional normally hyperbolic invariant manifolds. To construct diffusing orbits along this net we employ a version of the Mather variational method [41] equipped with weak KAM theory [28], proposed by Bernard in [7].

Dimer geometry, amoebae and a vortex dimer model

NASA Astrophysics Data System (ADS)

Nash, Charles; O'Connor, Denjoe

2017-09-01

We present a geometrical approach and introduce a connection for dimer problems on bipartite and non-bipartite graphs. In the bipartite case the connection is flat but has non-trivial {Z}2 holonomy round certain curves. This holonomy has the universality property that it does not change as the number of vertices in the fundamental domain of the graph is increased. It is argued that the K-theory of the torus, with or without punctures, is the appropriate underlying invariant. In the non-bipartite case the connection has non-zero curvature as well as non-zero Chern number. The curvature does not require the introduction of a magnetic field. The phase diagram of these models is captured by what is known as an amoeba. We introduce a dimer model with negative edge weights which correspond to vortices. The amoebae for various models are studied with particular emphasis on the case of negative edge weights. Vortices give rise to new kinds of amoebae with certain singular structures which we investigate. On the amoeba of the vortex full hexagonal lattice we find the partition function corresponds to that of a massless Dirac doublet.

Dirac’s magnetic monopole and the Kontsevich star product

NASA Astrophysics Data System (ADS)

Soloviev, M. A.

2018-03-01

We examine relationships between various quantization schemes for an electrically charged particle in the field of a magnetic monopole. Quantization maps are defined in invariant geometrical terms, appropriate to the case of nontrivial topology, and are constructed for two operator representations. In the first setting, the quantum operators act on the Hilbert space of sections of a nontrivial complex line bundle associated with the Hopf bundle, whereas the second approach uses instead a quaternionic Hilbert module of sections of a trivial quaternionic line bundle. We show that these two quantizations are naturally related by a bundle morphism and, as a consequence, induce the same phase-space star product. We obtain explicit expressions for the integral kernels of star-products corresponding to various operator orderings and calculate their asymptotic expansions up to the third order in the Planck constant \\hbar . We also show that the differential form of the magnetic Weyl product corresponding to the symmetric ordering agrees completely with the Kontsevich formula for deformation quantization of Poisson structures and can be represented by Kontsevich’s graphs.

Controllable band structure and topological phase transition in two-dimensional hydrogenated arsenene

PubMed Central

Wang, Ya-ping; Ji, Wei-xiao; Zhang, Chang-wen; Li, Ping; Li, Feng; Ren, Miao-juan; Chen, Xin-Lian; Yuan, Min; Wang, Pei-ji

2016-01-01

Discovery of two-dimensional (2D) topological insulator such as group-V films initiates challenges in exploring exotic quantum states in low dimensions. Here, we perform first-principles calculations to study the geometric and electronic properties in 2D arsenene monolayer with hydrogenation (HAsH). We predict a new σ-type Dirac cone related to the px,y orbitals of As atoms in HAsH, dependent on in-plane tensile strain. Noticeably, the spin-orbit coupling (SOC) opens a quantum spin Hall (QSH) gap of 193 meV at the Dirac cone. A single pair of topologically protected helical edge states is established for the edges, and its QSH phase is confirmed with topological invariant Z2 = 1. We also propose a 2D quantum well (QW) encapsulating HAsH with the h-BN sheet on each side, which harbors a nontrivial QSH state with the Dirac cone lying within the band gap of cladding BN substrate. These findings provide a promising innovative platform for QSH device design and fabrication operating at room temperature. PMID:26839209

Controllable band structure and topological phase transition in two-dimensional hydrogenated arsenene

NASA Astrophysics Data System (ADS)

Wang, Ya-Ping; Ji, Wei-Xiao; Zhang, Chang-Wen; Li, Ping; Li, Feng; Ren, Miao-Juan; Chen, Xin-Lian; Yuan, Min; Wang, Pei-Ji

2016-02-01

Discovery of two-dimensional (2D) topological insulator such as group-V films initiates challenges in exploring exotic quantum states in low dimensions. Here, we perform first-principles calculations to study the geometric and electronic properties in 2D arsenene monolayer with hydrogenation (HAsH). We predict a new σ-type Dirac cone related to the px,y orbitals of As atoms in HAsH, dependent on in-plane tensile strain. Noticeably, the spin-orbit coupling (SOC) opens a quantum spin Hall (QSH) gap of 193 meV at the Dirac cone. A single pair of topologically protected helical edge states is established for the edges, and its QSH phase is confirmed with topological invariant Z2 = 1. We also propose a 2D quantum well (QW) encapsulating HAsH with the h-BN sheet on each side, which harbors a nontrivial QSH state with the Dirac cone lying within the band gap of cladding BN substrate. These findings provide a promising innovative platform for QSH device design and fabrication operating at room temperature.

Robust photometric invariant features from the color tensor.

PubMed

van de Weijer, Joost; Gevers, Theo; Smeulders, Arnold W M

2006-01-01

Luminance-based features are widely used as low-level input for computer vision applications, even when color data is available. The extension of feature detection to the color domain prevents information loss due to isoluminance and allows us to exploit the photometric information. To fully exploit the extra information in the color data, the vector nature of color data has to be taken into account and a sound framework is needed to combine feature and photometric invariance theory. In this paper, we focus on the structure tensor, or color tensor, which adequately handles the vector nature of color images. Further, we combine the features based on the color tensor with photometric invariant derivatives to arrive at photometric invariant features. We circumvent the drawback of unstable photometric invariants by deriving an uncertainty measure to accompany the photometric invariant derivatives. The uncertainty is incorporated in the color tensor, hereby allowing the computation of robust photometric invariant features. The combination of the photometric invariance theory and tensor-based features allows for detection of a variety of features such as photometric invariant edges, corners, optical flow, and curvature. The proposed features are tested for noise characteristics and robustness to photometric changes. Experiments show that the proposed features are robust to scene incidental events and that the proposed uncertainty measure improves the applicability of full invariants.

Versatility and Invariance in the Evolution of Homologous Heteromeric Interfaces

PubMed Central

Andreani, Jessica; Faure, Guilhem; Guerois, Raphaël

2012-01-01

Evolutionary pressures act on protein complex interfaces so that they preserve their complementarity. Nonetheless, the elementary interactions which compose the interface are highly versatile throughout evolution. Understanding and characterizing interface plasticity across evolution is a fundamental issue which could provide new insights into protein-protein interaction prediction. Using a database of 1,024 couples of close and remote heteromeric structural interologs, we studied protein-protein interactions from a structural and evolutionary point of view. We systematically and quantitatively analyzed the conservation of different types of interface contacts. Our study highlights astonishing plasticity regarding polar contacts at complex interfaces. It also reveals that up to a quarter of the residues switch out of the interface when comparing two homologous complexes. Despite such versatility, we identify two important interface descriptors which correlate with an increased conservation in the evolution of interfaces: apolar patches and contacts surrounding anchor residues. These observations hold true even when restricting the dataset to transiently formed complexes. We show that a combination of six features related either to sequence or to geometric properties of interfaces can be used to rank positions likely to share similar contacts between two interologs. Altogether, our analysis provides important tracks for extracting meaningful information from multiple sequence alignments of conserved binding partners and for discriminating near-native interfaces using evolutionary information. PMID:22952442

Network approach to patterns in stratocumulus clouds

NASA Astrophysics Data System (ADS)

Glassmeier, Franziska; Feingold, Graham

2017-10-01

Stratocumulus clouds (Sc) have a significant impact on the amount of sunlight reflected back to space, with important implications for Earth’s climate. Representing Sc and their radiative impact is one of the largest challenges for global climate models. Sc fields self-organize into cellular patterns and thus lend themselves to analysis and quantification in terms of natural cellular networks. Based on large-eddy simulations of Sc fields, we present a first analysis of the geometric structure and self-organization of Sc patterns from this network perspective. Our network analysis shows that the Sc pattern is scale-invariant as a consequence of entropy maximization that is known as Lewis’s Law (scaling parameter: 0.16) and is largely independent of the Sc regime (cloud-free vs. cloudy cell centers). Cells are, on average, hexagonal with a neighbor number variance of about 2, and larger cells tend to be surrounded by smaller cells, as described by an Aboav-Weaire parameter of 0.9. The network structure is neither completely random nor characteristic of natural convection. Instead, it emerges from Sc-specific versions of cell division and cell merging that are shaped by cell expansion. This is shown with a heuristic model of network dynamics that incorporates our physical understanding of cloud processes.

Network approach to patterns in stratocumulus clouds.

PubMed

Glassmeier, Franziska; Feingold, Graham

2017-10-03

Stratocumulus clouds (Sc) have a significant impact on the amount of sunlight reflected back to space, with important implications for Earth's climate. Representing Sc and their radiative impact is one of the largest challenges for global climate models. Sc fields self-organize into cellular patterns and thus lend themselves to analysis and quantification in terms of natural cellular networks. Based on large-eddy simulations of Sc fields, we present a first analysis of the geometric structure and self-organization of Sc patterns from this network perspective. Our network analysis shows that the Sc pattern is scale-invariant as a consequence of entropy maximization that is known as Lewis's Law (scaling parameter: 0.16) and is largely independent of the Sc regime (cloud-free vs. cloudy cell centers). Cells are, on average, hexagonal with a neighbor number variance of about 2, and larger cells tend to be surrounded by smaller cells, as described by an Aboav-Weaire parameter of 0.9. The network structure is neither completely random nor characteristic of natural convection. Instead, it emerges from Sc-specific versions of cell division and cell merging that are shaped by cell expansion. This is shown with a heuristic model of network dynamics that incorporates our physical understanding of cloud processes.

Network approach to patterns in stratocumulus clouds

PubMed Central

Feingold, Graham

2017-01-01

Stratocumulus clouds (Sc) have a significant impact on the amount of sunlight reflected back to space, with important implications for Earth’s climate. Representing Sc and their radiative impact is one of the largest challenges for global climate models. Sc fields self-organize into cellular patterns and thus lend themselves to analysis and quantification in terms of natural cellular networks. Based on large-eddy simulations of Sc fields, we present a first analysis of the geometric structure and self-organization of Sc patterns from this network perspective. Our network analysis shows that the Sc pattern is scale-invariant as a consequence of entropy maximization that is known as Lewis’s Law (scaling parameter: 0.16) and is largely independent of the Sc regime (cloud-free vs. cloudy cell centers). Cells are, on average, hexagonal with a neighbor number variance of about 2, and larger cells tend to be surrounded by smaller cells, as described by an Aboav–Weaire parameter of 0.9. The network structure is neither completely random nor characteristic of natural convection. Instead, it emerges from Sc-specific versions of cell division and cell merging that are shaped by cell expansion. This is shown with a heuristic model of network dynamics that incorporates our physical understanding of cloud processes. PMID:28904097

Static Holes in Geometrically Frustrated Bow Tie Ladder

NASA Astrophysics Data System (ADS)

Martins, George; Brenig, Wolfram

2007-03-01

Doping of the geometrically frustrated bow-tie spin ladder with static holes is investigated by a complementary approach using exact diagonalization and hard-core quantum dimers. Results for the thermodynamics in the undoped case, the singlet density of states, the hole-binding energy, and the spin correlations will be presented. We find that the static holes polarize their vicinity by a localization of singlets in order to reduce the frustration. As a consequence the singlet polarization cloud induces short range repulsive forces between the holes with oscillatory longer range behavior. For those systems we have studied, most results for the quantum dimer approach are found to be qualitatively if not quantitatively in agreement with exact diagonalization. The ground state of the undoped system is non-degenerate with translationally invariant nearest-neighbor spin correlations up to a few unit cells, which is consistent with a spin liquid state or a valence bond crystal with very large unit cell. C. Waldtmann, A. Kreutzmann, U. Schollwock, K. Maisinger, and H.-U. Everts, Phys. Rev. B 62, 9472 (2000).

Probing the Topology of Density Matrices

NASA Astrophysics Data System (ADS)

Bardyn, Charles-Edouard; Wawer, Lukas; Altland, Alexander; Fleischhauer, Michael; Diehl, Sebastian

2018-01-01

The mixedness of a quantum state is usually seen as an adversary to topological quantization of observables. For example, exact quantization of the charge transported in a so-called Thouless adiabatic pump is lifted at any finite temperature in symmetry-protected topological insulators. Here, we show that certain directly observable many-body correlators preserve the integrity of topological invariants for mixed Gaussian quantum states in one dimension. Our approach relies on the expectation value of the many-body momentum-translation operator and leads to a physical observable—the "ensemble geometric phase" (EGP)—which represents a bona fide geometric phase for mixed quantum states, in the thermodynamic limit. In cyclic protocols, the EGP provides a topologically quantized observable that detects encircled spectral singularities ("purity-gap" closing points) of density matrices. While we identify the many-body nature of the EGP as a key ingredient, we propose a conceptually simple, interferometric setup to directly measure the latter in experiments with mesoscopic ensembles of ultracold atoms.

Two-stage Keypoint Detection Scheme for Region Duplication Forgery Detection in Digital Images.

PubMed

Emam, Mahmoud; Han, Qi; Zhang, Hongli

2018-01-01

In digital image forensics, copy-move or region duplication forgery detection became a vital research topic recently. Most of the existing keypoint-based forgery detection methods fail to detect the forgery in the smooth regions, rather than its sensitivity to geometric changes. To solve these problems and detect points which cover all the regions, we proposed two steps for keypoint detection. First, we employed the scale-invariant feature operator to detect the spatially distributed keypoints from the textured regions. Second, the keypoints from the missing regions are detected using Harris corner detector with nonmaximal suppression to evenly distribute the detected keypoints. To improve the matching performance, local feature points are described using Multi-support Region Order-based Gradient Histogram descriptor. Based on precision-recall rates and commonly tested dataset, comprehensive performance evaluation is performed. The results demonstrated that the proposed scheme has better detection and robustness against some geometric transformation attacks compared with state-of-the-art methods. © 2017 American Academy of Forensic Sciences.

PANTHER. Trajectory Analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rintoul, Mark Daniel; Wilson, Andrew T.; Valicka, Christopher G.

We want to organize a body of trajectories in order to identify, search for, classify and predict behavior among objects such as aircraft and ships. Existing compari- son functions such as the Fr'echet distance are computationally expensive and yield counterintuitive results in some cases. We propose an approach using feature vectors whose components represent succinctly the salient information in trajectories. These features incorporate basic information such as total distance traveled and distance be- tween start/stop points as well as geometric features related to the properties of the convex hull, trajectory curvature and general distance geometry. Additionally, these features can generallymore » be mapped easily to behaviors of interest to humans that are searching large databases. Most of these geometric features are invariant under rigid transformation. We demonstrate the use of different subsets of these features to iden- tify trajectories similar to an exemplar, cluster a database of several hundred thousand trajectories, predict destination and apply unsupervised machine learning algorithms.« less

Path following control of planar snake robots using virtual holonomic constraints: theory and experiments.

PubMed

Rezapour, Ehsan; Pettersen, Kristin Y; Liljebäck, Pål; Gravdahl, Jan T; Kelasidi, Eleni

This paper considers path following control of planar snake robots using virtual holonomic constraints. In order to present a model-based path following control design for the snake robot, we first derive the Euler-Lagrange equations of motion of the system. Subsequently, we define geometric relations among the generalized coordinates of the system, using the method of virtual holonomic constraints. These appropriately defined constraints shape the geometry of a constraint manifold for the system, which is a submanifold of the configuration space of the robot. Furthermore, we show that the constraint manifold can be made invariant by a suitable choice of feedback. In particular, we analytically design a smooth feedback control law to exponentially stabilize the constraint manifold. We show that enforcing the appropriately defined virtual holonomic constraints for the configuration variables implies that the robot converges to and follows a desired geometric path. Numerical simulations and experimental results are presented to validate the theoretical approach.

Factor structure and longitudinal measurement invariance of PHQ-9 for specialist mental health care patients with persistent major depressive disorder: Exploratory Structural Equation Modelling.

PubMed

Guo, Boliang; Kaylor-Hughes, Catherine; Garland, Anne; Nixon, Neil; Sweeney, Tim; Simpson, Sandra; Dalgleish, Tim; Ramana, Rajini; Yang, Min; Morriss, Richard

2017-09-01

The Patient Health Questionnaire-9 (PHQ-9) is a widely used instrument for measuring levels of depression in patients in clinical practice and academic research; its factor structure has been investigated in various samples, with limited evidence of measurement equivalence/invariance (ME/I) but not in patients with more severe depression of long duration. This study aims to explore the factor structure of the PHQ-9 and the ME/I between treatment groups over time for these patients. 187 secondary care patients with persistent major depressive disorder (PMDD) were recruited to a randomised controlled trial (RCT) with allocation to either a specialist depression team arm or a general mental health arm; their PHQ-9 score was measured at baseline, 3, 6, 9 and 12 months. Exploratory Structural Equational Modelling (ESEM) was performed to examine the factor structure for this specific patient group. ME/I between treatment arm at and across follow-up time were further explored by means of multiple-group ESEM approach using the best-fitted factor structure. A two-factor structure was evidenced (somatic and affective factor). This two-factor structure had strong factorial invariance between the treatment groups at and across follow up times. Participants were largely white British in a RCT with 40% attrition potentially limiting the study's generalisability. Not all two-factor modelling criteria were met at every time-point. PHQ-9 has a two-factor structure for PMDD patients, with strong measurement invariance between treatment groups at and across follow-up time, demonstrating its validity for RCTs and prospective longitudinal studies in chronic moderate to severe depression. Copyright © 2017. Published by Elsevier B.V.

Teen Dating Violence, Sexual Harassment, and Bullying Among Middle School Youth: Examining Measurement Invariance by Gender.

PubMed

Cutbush, Stacey; Williams, Jason

2016-12-01

This study investigated measurement invariance by gender among commonly used teen dating violence (TDV), sexual harassment, and bullying measures. Data were collected from one cohort of seventh-grade middle school students (N = 754) from four schools. Using structural equation modeling, exploratory and confirmatory factor analyses assessed measurement models and tested measurement invariance by gender for aggression measures. Analyses invoked baseline data only. Physical and psychological TDV perpetration measures achieved strict measurement invariance, while bullying perpetration demonstrated partial strict invariance. Electronic TDV and sexual harassment perpetration achieved metric/scalar invariance. Study findings lend validation to prior and future studies using these measures with similar populations. Future research should increase attention to measurement development, refinement, and testing among study measures. © 2016 The Authors. Journal of Research on Adolescence © 2016 Society for Research on Adolescence.

Crista egregia: a geometrical model of the crista ampullaris, a sensory surface that detects head rotations.

PubMed

Marianelli, Prisca; Berthoz, Alain; Bennequin, Daniel

2015-02-01

The crista ampullaris is the epithelium at the end of the semicircular canals in the inner ear of vertebrates, which contains the sensory cells involved in the transduction of the rotational head movements into neuronal activity. The crista surface has the form of a saddle, or a pair of saddles separated by a crux, depending on the species and the canal considered. In birds, it was described as a catenoid by Landolt et al. (J Comp Neurol 159(2):257-287, doi: 10.1002/cne.901590207 , 1972). In the present work, we establish that this particular form results from principles of invariance maximization and energy minimization. The formulation of the invariance principle was inspired by Takumida (Biol Sci Space 15(4):356-358, 2001). More precisely, we suppose that in functional conditions, the equations of linear elasticity are valid, and we assume that in a certain domain of the cupula, in proximity of the crista surface, (1) the stress tensor of the deformed cupula is invariant under the gradient of the pressure, (2) the dissipation of energy is minimum. Then, we deduce that in this domain the crista surface is a minimal surface and that it must be either a planar, or helicoidal Scherk surface, or a piece of catenoid, which is the unique minimal surface of revolution. If we add the hypothesis that the direction of invariance of the stress tensor is unique and that a bilateral symmetry of the crista exists, only the catenoid subsists. This finding has important consequences for further functional modeling of the role of the vestibular system in head motion detection and spatial orientation.

Numeric invariants from multidimensional persistence

DOE PAGES

Skryzalin, Jacek; Carlsson, Gunnar

2017-05-19

Topological data analysis is the study of data using techniques from algebraic topology. Often, one begins with a finite set of points representing data and a “filter” function which assigns a real number to each datum. Using both the data and the filter function, one can construct a filtered complex for further analysis. For example, applying the homology functor to the filtered complex produces an algebraic object known as a “one-dimensional persistence module”, which can often be interpreted as a finite set of intervals representing various geometric features in the data. If one runs the above process incorporating multiple filtermore » functions simultaneously, one instead obtains a multidimensional persistence module. Unfortunately, these are much more difficult to interpret. In this article, we analyze the space of multidimensional persistence modules from the perspective of algebraic geometry. First we build a moduli space of a certain subclass of easily analyzed multidimensional persistence modules, which we construct specifically to capture much of the information which can be gained by using multidimensional persistence instead of one-dimensional persistence. Fruthermore, we argue that the global sections of this space provide interesting numeric invariants when evaluated against our subclass of multidimensional persistence modules. Finally, we extend these global sections to the space of all multidimensional persistence modules and discuss how the resulting numeric invariants might be used to study data. This paper extends the results of Adcock et al. (Homol Homotopy Appl 18(1), 381–402, 2016) by constructing numeric invariants from the computation of a multidimensional persistence module as given by Carlsson et al. (J Comput Geom 1(1), 72–100, 2010).« less

Reconstruction of the spatial dependence of dielectric and geometrical properties of adhesively bonded structures

NASA Astrophysics Data System (ADS)

Mackay, C.; Hayward, D.; Mulholland, A. J.; McKee, S.; Pethrick, R. A.

2005-06-01

An inverse problem motivated by the nondestructive testing of adhesively bonded structures used in the aircraft industry is studied. Using transmission line theory, a model is developed which, when supplied with electrical and geometrical parameters, accurately predicts the reflection coefficient associated with such structures. Particular attention is paid to modelling the connection between the structures and the equipment used to measure the reflection coefficient. The inverse problem is then studied and an optimization approach employed to recover these electrical and geometrical parameters from experimentally obtained data. In particular the approach focuses on the recovery of spatially varying geometrical parameters as this is paramount to the successful reconstruction of electrical parameters. Reconstructions of structure geometry using this method are found to be in close agreement with experimental observations.

Finite-g Strings

NASA Astrophysics Data System (ADS)

Vicedo, Benoit

2008-10-01

In view of one day proving the AdS/CFT correspondence, a deeper understanding of string theory on certain curved backgrounds such as AdS_5xS^5 is required. In this dissertation we make a step in this direction by focusing on RxS^3. It was discovered in recent years that string theory on AdS_5xS^5 admits a Lax formulation. However, the complete statement of integrability requires not only the existence of a Lax formulation, but also that the resulting integrals of motion are in pairwise involution. This idea is central to the first part of this thesis. Exploiting this integrability we apply algebro-geometric methods to string theory on RxS^3 and obtain the general finite-gap solution. The construction is based on an invariant algebraic curve previously found in the AdS_5xS^5 case. However, encoding the dynamics of the solution requires specification of additional marked points. By restricting the symplectic structure of the string to this algebro-geometric data we derive the action-angle variables of the system. We then perform a first-principle semiclassical quantisation of string theory on RxS^3 as a toy model for strings on AdS_5xS^5. The result is exactly what one expects from the dual gauge theory perspective, namely the underlying algebraic curve discretises in a natural way. We also derive a general formula for the fluctuation energies around the generic finite-gap solution. The ideas used can be generalised to AdS_5xS^5.

Factor structure and measurement invariance of the Health Education Impact Questionnaire: Does the subjectivity of the response perspective threaten the contextual validity of inferences?

PubMed Central

Elsworth, Gerald R; Nolte, Sandra

2015-01-01

Objective: On-going evidence is required to support the validity of inferences about change and group differences in the evaluation of health programs, particularly when self-report scales requiring substantial subjectivity in response generation are used as outcome measures. Following this reasoning, the aim of this study was to replicate the factor structure and investigate the measurement invariance of the latest version of the Health Education Impact Questionnaire, a widely used health program evaluation measure. Methods: An archived dataset of responses to the most recent version of the English-language Health Education Impact Questionnaire that uses four rather than six response options (N = 3221) was analysed using exploratory structural equation modelling and confirmatory factor analysis appropriate for ordered categorical data. Metric and scalar invariance were studied following recent recommendations in the literature to apply fully invariant unconditional models with minimum constraints necessary for model identification. Results: The original eight-factor structure was replicated and all but one of the scales (Self Monitoring and Insight) was found to consist of unifactorial items with reliability of ⩾0.8 and satisfactory discriminant validity. Configural, metric and scalar invariance were established across pre-test to post-test and population sub-groups (sex, age, education, ethnic background). Conclusion: The results support the high level of interest in the Health Education Impact Questionnaire, particularly for use as a pre-test/post-test measure in experimental studies, other pre–post evaluation designs and system-level monitoring and evaluation. PMID:26770785

Motion prediction in MRI-guided radiotherapy based on interleaved orthogonal cine-MRI

NASA Astrophysics Data System (ADS)

Seregni, M.; Paganelli, C.; Lee, D.; Greer, P. B.; Baroni, G.; Keall, P. J.; Riboldi, M.

2016-01-01

In-room cine-MRI guidance can provide non-invasive target localization during radiotherapy treatment. However, in order to cope with finite imaging frequency and system latencies between target localization and dose delivery, tumour motion prediction is required. This work proposes a framework for motion prediction dedicated to cine-MRI guidance, aiming at quantifying the geometric uncertainties introduced by this process for both tumour tracking and beam gating. The tumour position, identified through scale invariant features detected in cine-MRI slices, is estimated at high-frequency (25 Hz) using three independent predictors, one for each anatomical coordinate. Linear extrapolation, auto-regressive and support vector machine algorithms are compared against systems that use no prediction or surrogate-based motion estimation. Geometric uncertainties are reported as a function of image acquisition period and system latency. Average results show that the tracking error RMS can be decreased down to a [0.2; 1.2] mm range, for acquisition periods between 250 and 750 ms and system latencies between 50 and 300 ms. Except for the linear extrapolator, tracking and gating prediction errors were, on average, lower than those measured for surrogate-based motion estimation. This finding suggests that cine-MRI guidance, combined with appropriate prediction algorithms, could relevantly decrease geometric uncertainties in motion compensated treatments.

Factorial invariance of pediatric patient self-reported fatigue across age and gender: a multigroup confirmatory factor analysis approach utilizing the PedsQL™ Multidimensional Fatigue Scale.

PubMed

Varni, James W; Beaujean, A Alexander; Limbers, Christine A

2013-11-01

In order to compare multidimensional fatigue research findings across age and gender subpopulations, it is important to demonstrate measurement invariance, that is, that the items from an instrument have equivalent meaning across the groups studied. This study examined the factorial invariance of the 18-item PedsQL™ Multidimensional Fatigue Scale items across age and gender and tested a bifactor model. Multigroup confirmatory factor analysis (MG-CFA) was performed specifying a three-factor model across three age groups (5-7, 8-12, and 13-18 years) and gender. MG-CFA models were proposed in order to compare the factor structure, metric, scalar, and error variance across age groups and gender. The analyses were based on 837 children and adolescents recruited from general pediatric clinics, subspecialty clinics, and hospitals in which children were being seen for well-child checks, mild acute illness, or chronic illness care. A bifactor model of the items with one general factor influencing all the items and three domain-specific factors representing the General, Sleep/Rest, and Cognitive Fatigue domains fit the data better than oblique factor models. Based on the multiple measures of model fit, configural, metric, and scalar invariance were found for almost all items across the age and gender groups, as was invariance in the factor covariances. The PedsQL™ Multidimensional Fatigue Scale demonstrated strict factorial invariance for child and adolescent self-report across gender and strong factorial invariance across age subpopulations. The findings support an equivalent three-factor structure across the age and gender groups studied. Based on these data, it can be concluded that pediatric patients across the groups interpreted the items in a similar manner regardless of their age or gender, supporting the multidimensional factor structure interpretation of the PedsQL™ Multidimensional Fatigue Scale.

Nuclear spin dependence of time reversal invariance violating effects in neutron scattering

NASA Astrophysics Data System (ADS)

Gudkov, Vladimir; Shimizu, Hirohiko M.

2018-06-01

The spin structure of parity violating and time reversal invariance violating effects in neutron scattering is discussed. The explicit relations between these effects are presented in terms of functions nuclear spins and neutron partial widths of p -wave resonances.

Finite Group Invariance and Solution of Jaynes-Cummings Hamiltonian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haydargil, Derya; Koc, Ramazan

2004-10-04

The finite group invariance of the E x {beta} and Jaynes-Cummings models are studied. A method is presented to obtain finite group invariance of the E x {beta} system.A suitable transformation of a Jaynes-Cummings Hamiltonian leads to equivalence of E x {beta} system. Then a general method is applied to obtain the solution of Jaynes-Cummings Hamiltonian with Kerr nonlinearity. Number operator for this structure and the generators of su(2) algebra are used to find the eigenvalues of the Jaynes-Cummings Hamiltonian for different states. By using the invariance of number operator the solution of modified Jaynes-Cummings Hamiltonian is also discussed.

Complex quantum network geometries: Evolution and phase transitions

NASA Astrophysics Data System (ADS)

Bianconi, Ginestra; Rahmede, Christoph; Wu, Zhihao

2015-08-01

Networks are topological and geometric structures used to describe systems as different as the Internet, the brain, or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e., simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a nonequilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network states. The quantum network states are characterized by quantum occupation numbers that can be mapped, respectively, to the nodes, links, and triangles incident to each link of the network. We call the geometric networks describing the evolution of quantum network states the quantum geometric networks. The quantum geometric networks have many properties common to complex networks, including small-world property, high clustering coefficient, high modularity, and scale-free degree distribution. Moreover, they can be distinguished between the Fermi-Dirac network and the Bose-Einstein network obeying, respectively, the Fermi-Dirac and Bose-Einstein statistics. We show that these networks can undergo structural phase transitions where the geometrical properties of the networks change drastically. Finally, we comment on the relation between quantum complex network geometries, spin networks, and triangulations.

Complex quantum network geometries: Evolution and phase transitions.

PubMed

Bianconi, Ginestra; Rahmede, Christoph; Wu, Zhihao

2015-08-01

Networks are topological and geometric structures used to describe systems as different as the Internet, the brain, or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e., simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a nonequilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network states. The quantum network states are characterized by quantum occupation numbers that can be mapped, respectively, to the nodes, links, and triangles incident to each link of the network. We call the geometric networks describing the evolution of quantum network states the quantum geometric networks. The quantum geometric networks have many properties common to complex networks, including small-world property, high clustering coefficient, high modularity, and scale-free degree distribution. Moreover, they can be distinguished between the Fermi-Dirac network and the Bose-Einstein network obeying, respectively, the Fermi-Dirac and Bose-Einstein statistics. We show that these networks can undergo structural phase transitions where the geometrical properties of the networks change drastically. Finally, we comment on the relation between quantum complex network geometries, spin networks, and triangulations.

Hierarchical Structure and Cross-Cultural Measurement Invariance of the Norwegian Version of the Personality Inventory for DSM-5.

PubMed

Thimm, Jens C; Jordan, Stian; Bach, Bo

2017-01-01

The Personality Inventory for DSM-5 (PID-5) was created to aid a trait-based diagnostic system for personality disorders (PDs) in the Diagnostic and Statistical Manual of Mental Disorders (5th ed. [DSM-5]; American Psychiatric Association, 2013a ). In this study, we aimed to evaluate the Norwegian version of the PID-5 by examining its score reliability, hierarchical structure, congruency with international findings, and cross-cultural measurement invariance with a matched U.S. For this purpose, 503 university students (76% females) were administered the PID-5. The Norwegian PID-5 showed good score reliability and structural validity from 1 to 5 factors. The 5-factor structure was generally congruent with international findings, and support for measurement invariance across the Norwegian and a matched U.S. sample was found. Conclusively, the results indicate that scores on the Norwegian PID-5 have sound psychometric properties, which are substantially comparable with the original U.S. version, supporting its use in a Norwegian population.

Hidden symmetries and Lie algebra structures from geometric and supergravity Killing spinors

NASA Astrophysics Data System (ADS)

Açık, Özgür; Ertem, Ümit

2016-08-01

We consider geometric and supergravity Killing spinors and the spinor bilinears constructed out of them. The spinor bilinears of geometric Killing spinors correspond to the antisymmetric generalizations of Killing vector fields which are called Killing-Yano forms. They constitute a Lie superalgebra structure in constant curvature spacetimes. We show that the Dirac currents of geometric Killing spinors satisfy a Lie algebra structure up to a condition on 2-form spinor bilinears. We propose that the spinor bilinears of supergravity Killing spinors give way to different generalizations of Killing vector fields to higher degree forms. It is also shown that those supergravity Killing forms constitute a Lie algebra structure in six- and ten-dimensional cases. For five- and eleven-dimensional cases, the Lie algebra structure depends on an extra condition on supergravity Killing forms.

Black hole shadows and invariant phase space structures

NASA Astrophysics Data System (ADS)

Grover, J.; Wittig, A.

2017-07-01

Utilizing concepts from dynamical systems theory, we demonstrate how the existence of light rings, or fixed points, in a spacetime will give rise to families of periodic orbits and invariant manifolds in phase space. It is shown that these structures can define the shape of the black hole shadow as well as a number of salient features of the spacetime lensing. We illustrate this through the analysis of lensing by a hairy black hole.

Scale-invariant entropy-based theory for dynamic ordering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mahulikar, Shripad P., E-mail: spm@iitmandi.ac.in, E-mail: spm@aero.iitb.ac.in; Department of Aerospace Engineering, Indian Institute of Technology Bombay, Mumbai 400076; Kumari, Priti

2014-09-01

Dynamically Ordered self-organized dissipative structure exists in various forms and at different scales. This investigation first introduces the concept of an isolated embedding system, which embeds an open system, e.g., dissipative structure and its mass and/or energy exchange with its surroundings. Thereafter, scale-invariant theoretical analysis is presented using thermodynamic principles for Order creation, existence, and destruction. The sustainability criterion for Order existence based on its structured mass and/or energy interactions with the surroundings is mathematically defined. This criterion forms the basis for the interrelationship of physical parameters during sustained existence of dynamic Order. It is shown that the sufficient conditionmore » for dynamic Order existence is approached if its sustainability criterion is met, i.e., its destruction path is blocked. This scale-invariant approach has the potential to unify the physical understanding of universal dynamic ordering based on entropy considerations.« less

Texture zeros and hierarchical masses from flavour (mis)alignment

NASA Astrophysics Data System (ADS)

Hollik, W. G.; Saldana-Salazar, U. J.

2018-03-01

We introduce an unconventional interpretation of the fermion mass matrix elements. As the full rotational freedom of the gauge-kinetic terms renders a set of infinite bases called weak bases, basis-dependent structures as mass matrices are unphysical. Matrix invariants, on the other hand, provide a set of basis-independent objects which are of more relevance. We employ one of these invariants to give a new parametrisation of the mass matrices. By virtue of it, one gains control over its implicit implications on several mass matrix structures. The key element is the trace invariant which resembles the equation of a hypersphere with a radius equal to the Frobenius norm of the mass matrix. With the concepts of alignment or misalignment we can identify texture zeros with certain alignments whereas Froggatt-Nielsen structures in the matrix elements are governed by misalignment. This method allows further insights of traditional approaches to the underlying flavour geometry.

Conserved water-mediated H-bonding dynamics of catalytic Asn 175 in plant thiol protease.

PubMed

Nandi, Tapas K; Bairagya, Hridoy R; Mukhopadhyay, Bishnu P; Sekar, K; Sukul, Dipankar; Bera, Asim K

2009-03-01

The role of invariant water molecules in the activity of plant cysteine protease is ubiquitous in nature. On analysing the 11 different Protein DataBank (PDB) structures of plant thiol proteases, the two invariant water molecules W1 and W2 (W220 and W222 in the template 1PPN structure) were observed to form H-bonds with the O b atom of Asn 175. Extensive energy minimization and molecular dynamics simulation studies up to 2 ns on all the PDB and solvated structures clearly revealed the involvement of the H-bonding association of the two water molecules in fixing the orientation of the asparagine residue of the catalytic triad. From this study,it is suggested that H-bonding of the water molecule at the W1 invariant site better stabilizes the Asn residue at the active site of the catalytic triad.

Factorial invariance of posttraumatic stress disorder symptoms across three veteran samples.

PubMed

McDonald, Scott D; Beckham, Jean C; Morey, Rajendra; Marx, Christine; Tupler, Larry A; Calhoun, Patrick S

2008-06-01

Research generally supports a 4-factor structure of posttraumatic stress disorder (PTSD) symptoms. However, few studies have established factor invariance by comparing multiple groups. This study examined PTSD symptom structure using the Davidson Trauma Scale (DTS) across three veteran samples: treatment-seeking Vietnam-era veterans, treatment-seeking post-Vietnam-era veterans, and Operation Enduring Freedom/Operation Iraqi Freedom (OEF/OIF) veteran research participants. Confirmatory factor analyses of DTS items demonstrated that a 4-factor structural model of the DTS (reexperiencing, avoidance, numbing, and hyperarousal) was superior to five alternate models, including the conventional 3-factor model proposed by the Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition (DSM-IV; American Psychiatric Association, 1994). Results supported factor invariance across the three veteran cohorts, suggesting that cross-group comparisons are interpretable. Implications and applications for DSM-IV nosology and the validity of symptom measures are discussed.

Hierarchical pictorial structures for simultaneously localizing multiple organs in volumetric pre-scan CT

NASA Astrophysics Data System (ADS)

Montillo, Albert; Song, Qi; Das, Bipul; Yin, Zhye

2015-03-01

Parsing volumetric computed tomography (CT) into 10 or more salient organs simultaneously is a challenging task with many applications such as personalized scan planning and dose reporting. In the clinic, pre-scan data can come in the form of very low dose volumes acquired just prior to the primary scan or from an existing primary scan. To localize organs in such diverse data, we propose a new learning based framework that we call hierarchical pictorial structures (HPS) which builds multiple levels of models in a tree-like hierarchy that mirrors the natural decomposition of human anatomy from gross structures to finer structures. Each node of our hierarchical model learns (1) the local appearance and shape of structures, and (2) a generative global model that learns probabilistic, structural arrangement. Our main contribution is twofold. First we embed the pictorial structures approach in a hierarchical framework which reduces test time image interpretation and allows for the incorporation of additional geometric constraints that robustly guide model fitting in the presence of noise. Second we guide our HPS framework with the probabilistic cost maps extracted using random decision forests using volumetric 3D HOG features which makes our model fast to train and fast to apply to novel test data and posses a high degree of invariance to shape distortion and imaging artifacts. All steps require approximate 3 mins to compute and all organs are located with suitably high accuracy for our clinical applications such as personalized scan planning for radiation dose reduction. We assess our method using a database of volumetric CT scans from 81 subjects with widely varying age and pathology and with simulated ultra-low dose cadaver pre-scan data.

Protein-protein docking using region-based 3D Zernike descriptors

PubMed Central

2009-01-01

Background Protein-protein interactions are a pivotal component of many biological processes and mediate a variety of functions. Knowing the tertiary structure of a protein complex is therefore essential for understanding the interaction mechanism. However, experimental techniques to solve the structure of the complex are often found to be difficult. To this end, computational protein-protein docking approaches can provide a useful alternative to address this issue. Prediction of docking conformations relies on methods that effectively capture shape features of the participating proteins while giving due consideration to conformational changes that may occur. Results We present a novel protein docking algorithm based on the use of 3D Zernike descriptors as regional features of molecular shape. The key motivation of using these descriptors is their invariance to transformation, in addition to a compact representation of local surface shape characteristics. Docking decoys are generated using geometric hashing, which are then ranked by a scoring function that incorporates a buried surface area and a novel geometric complementarity term based on normals associated with the 3D Zernike shape description. Our docking algorithm was tested on both bound and unbound cases in the ZDOCK benchmark 2.0 dataset. In 74% of the bound docking predictions, our method was able to find a near-native solution (interface C-αRMSD ≤ 2.5 Å) within the top 1000 ranks. For unbound docking, among the 60 complexes for which our algorithm returned at least one hit, 60% of the cases were ranked within the top 2000. Comparison with existing shape-based docking algorithms shows that our method has a better performance than the others in unbound docking while remaining competitive for bound docking cases. Conclusion We show for the first time that the 3D Zernike descriptors are adept in capturing shape complementarity at the protein-protein interface and useful for protein docking prediction. Rigorous benchmark studies show that our docking approach has a superior performance compared to existing methods. PMID:20003235

Protein-protein docking using region-based 3D Zernike descriptors.

PubMed

Venkatraman, Vishwesh; Yang, Yifeng D; Sael, Lee; Kihara, Daisuke

2009-12-09

Protein-protein interactions are a pivotal component of many biological processes and mediate a variety of functions. Knowing the tertiary structure of a protein complex is therefore essential for understanding the interaction mechanism. However, experimental techniques to solve the structure of the complex are often found to be difficult. To this end, computational protein-protein docking approaches can provide a useful alternative to address this issue. Prediction of docking conformations relies on methods that effectively capture shape features of the participating proteins while giving due consideration to conformational changes that may occur. We present a novel protein docking algorithm based on the use of 3D Zernike descriptors as regional features of molecular shape. The key motivation of using these descriptors is their invariance to transformation, in addition to a compact representation of local surface shape characteristics. Docking decoys are generated using geometric hashing, which are then ranked by a scoring function that incorporates a buried surface area and a novel geometric complementarity term based on normals associated with the 3D Zernike shape description. Our docking algorithm was tested on both bound and unbound cases in the ZDOCK benchmark 2.0 dataset. In 74% of the bound docking predictions, our method was able to find a near-native solution (interface C-alphaRMSD < or = 2.5 A) within the top 1000 ranks. For unbound docking, among the 60 complexes for which our algorithm returned at least one hit, 60% of the cases were ranked within the top 2000. Comparison with existing shape-based docking algorithms shows that our method has a better performance than the others in unbound docking while remaining competitive for bound docking cases. We show for the first time that the 3D Zernike descriptors are adept in capturing shape complementarity at the protein-protein interface and useful for protein docking prediction. Rigorous benchmark studies show that our docking approach has a superior performance compared to existing methods.

Function Invariant and Parameter Scale-Free Transformation Methods

ERIC Educational Resources Information Center

Bentler, P. M.; Wingard, Joseph A.

1977-01-01

A scale-invariant simple structure function of previously studied function components for principal component analysis and factor analysis is defined. First and second partial derivatives are obtained, and Newton-Raphson iterations are utilized. The resulting solutions are locally optimal and subjectively pleasing. (Author/JKS)

Interacting Non-Abelian Anti-Symmetric Tensor Field Theories

NASA Astrophysics Data System (ADS)

Ekambaram, K.; Vytheeswaran, A. S.

2018-04-01

Non-Abelian Anti-symmetric Tensor fields interacting with vector fields have a complicated constraint structure. We enlarge the gauge invariance in this system. Relevant gauge invariant quantities including the Hamiltonian are obtained. We also make introductory remarks on a different but more complicated gauge theory.

Scale-invariant puddles in graphene: Geometric properties of electron-hole distribution at the Dirac point.

PubMed

Najafi, M N; Nezhadhaghighi, M Ghasemi

2017-03-01

We characterize the carrier density profile of the ground state of graphene in the presence of particle-particle interaction and random charged impurity in zero gate voltage. We provide detailed analysis on the resulting spatially inhomogeneous electron gas, taking into account the particle-particle interaction and the remote Coulomb disorder on an equal footing within the Thomas-Fermi-Dirac theory. We present some general features of the carrier density probability measure of the graphene sheet. We also show that, when viewed as a random surface, the electron-hole puddles at zero chemical potential show peculiar self-similar statistical properties. Although the disorder potential is chosen to be Gaussian, we show that the charge field is non-Gaussian with unusual Kondev relations, which can be regarded as a new class of two-dimensional random-field surfaces. Using Schramm-Loewner (SLE) evolution, we numerically demonstrate that the ungated graphene has conformal invariance and the random zero-charge density contours are SLE_{κ} with κ=1.8±0.2, consistent with c=-3 conformal field theory.

Shape equivalence under perspective and projective transformations.

PubMed

Wagemans, J; Lamote, C; Van Gool, L

1997-06-01

When a planar shape is viewed obliquely, it is deformed by a perspective deformation. If the visual system were to pick up geometrical invariants from such projections, these would necessarily be invariant under the wider class of projective transformations. To what extent can the visual system tell the difference between perspective and nonperspective but still projective deformations of shapes? To investigate this, observers were asked to indicate which of two test patterns most resembled a standard pattern. The test patterns were related to the standard pattern by a perspective or projective transformation, or they were completely unrelated. Performance was slightly better in a matching task with perspective and unrelated test patterns (92.6%) than in a projective-random matching task (88.8%). In a direct comparison, participants had a small preference (58.5%) for the perspectively related patterns over the projectively related ones. Preferences were based on the values of the transformation parameters (slant and shear). Hence, perspective and projective transformations yielded perceptual differences, but they were not treated in a categorically different manner by the human visual system.

Percolation in random-Sierpiński carpets: A real space renormalization group approach

NASA Astrophysics Data System (ADS)

Perreau, Michel; Peiro, Joaquina; Berthier, Serge

1996-11-01

The site percolation transition in random Sierpiński carpets is investigated by real space renormalization. The fixed point is not unique like in regular translationally invariant lattices, but depends on the number k of segmentation steps of the generation process of the fractal. It is shown that, for each scale invariance ratio n, the sequence of fixed points pn,k is increasing with k, and converges when k-->∞ toward a limit pn strictly less than 1. Moreover, in such scale invariant structures, the percolation threshold does not depend only on the scale invariance ratio n, but also on the scale. The sequence pn,k and pn are calculated for n=4, 8, 16, 32, and 64, and for k=1 to k=11, and k=∞. The corresponding thermal exponent sequence νn,k is calculated for n=8 and 16, and for k=1 to k=5, and k=∞. Suggestions are made for an experimental test in physical self-similar structures.

Model invariance across genders of the Broad Autism Phenotype Questionnaire.

PubMed

Broderick, Neill; Wade, Jordan L; Meyer, J Patrick; Hull, Michael; Reeve, Ronald E

2015-10-01

ASD is one of the most heritable neuropsychiatric disorders, though comprehensive genetic liability remains elusive. To facilitate genetic research, researchers employ the concept of the broad autism phenotype (BAP), a milder presentation of traits in undiagnosed relatives. Research suggests that the BAP Questionnaire (BAPQ) demonstrates psychometric properties superior to other self-report measures. To examine evidence regarding validity of the BAPQ, the current study used confirmatory factor analysis to test the assumption of model invariance across genders. Results of the current study upheld model invariance at each level of parameter constraint; however, model fit indices suggested limited goodness-of-fit between the proposed model and the sample. Exploratory analyses investigated alternate factor structure models but ultimately supported the proposed three-factor structure model.

Geometric modeling of subcellular structures, organelles, and multiprotein complexes

PubMed Central

Feng, Xin; Xia, Kelin; Tong, Yiying; Wei, Guo-Wei

2013-01-01

SUMMARY Recently, the structure, function, stability, and dynamics of subcellular structures, organelles, and multi-protein complexes have emerged as a leading interest in structural biology. Geometric modeling not only provides visualizations of shapes for large biomolecular complexes but also fills the gap between structural information and theoretical modeling, and enables the understanding of function, stability, and dynamics. This paper introduces a suite of computational tools for volumetric data processing, information extraction, surface mesh rendering, geometric measurement, and curvature estimation of biomolecular complexes. Particular emphasis is given to the modeling of cryo-electron microscopy data. Lagrangian-triangle meshes are employed for the surface presentation. On the basis of this representation, algorithms are developed for surface area and surface-enclosed volume calculation, and curvature estimation. Methods for volumetric meshing have also been presented. Because the technological development in computer science and mathematics has led to multiple choices at each stage of the geometric modeling, we discuss the rationales in the design and selection of various algorithms. Analytical models are designed to test the computational accuracy and convergence of proposed algorithms. Finally, we select a set of six cryo-electron microscopy data representing typical subcellular complexes to demonstrate the efficacy of the proposed algorithms in handling biomolecular surfaces and explore their capability of geometric characterization of binding targets. This paper offers a comprehensive protocol for the geometric modeling of subcellular structures, organelles, and multiprotein complexes. PMID:23212797

Geometrically Nonlinear Static Analysis of 3D Trusses Using the Arc-Length Method

NASA Technical Reports Server (NTRS)

Hrinda, Glenn A.

2006-01-01

Rigorous analysis of geometrically nonlinear structures demands creating mathematical models that accurately include loading and support conditions and, more importantly, model the stiffness and response of the structure. Nonlinear geometric structures often contain critical points with snap-through behavior during the response to large loads. Studying the post buckling behavior during a portion of a structure's unstable load history may be necessary. Primary structures made from ductile materials will stretch enough prior to failure for loads to redistribute producing sudden and often catastrophic collapses that are difficult to predict. The responses and redistribution of the internal loads during collapses and possible sharp snap-back of structures have frequently caused numerical difficulties in analysis procedures. The presence of critical stability points and unstable equilibrium paths are major difficulties that numerical solutions must pass to fully capture the nonlinear response. Some hurdles still exist in finding nonlinear responses of structures under large geometric changes. Predicting snap-through and snap-back of certain structures has been difficult and time consuming. Also difficult is finding how much load a structure may still carry safely. Highly geometrically nonlinear responses of structures exhibiting complex snap-back behavior are presented and analyzed with a finite element approach. The arc-length method will be reviewed and shown to predict the proper response and follow the nonlinear equilibrium path through limit points.

An examination of the factor structure and sex invariance of a French translation of the Body Appreciation Scale-2 in university students.

PubMed

Kertechian, Sevag; Swami, Viren

2017-06-01

The Body Appreciation Scale-2 (BAS-2) is a measure of positive body image that has been found that have a one-dimensional factor structure in a number of different cultural groups. Here, we examined the factor structure and sex-based measurement invariance of a French translation of the BAS-2. A total of 652 university students (age M=21.33, SD=3.18) completed a newly-translated French version of the BAS-2. Exploratory factor analyses with a randomly selected split-half subsample revealed that the BAS-2 had a one-dimensional factor structure in both sexes. Confirmatory factor analyses with a second split-half subsample indicated that the one-dimensional factor structure had adequate fit following modifications and was invariant across sex. French BAS-2 scores had adequate internal consistency and men had significantly higher body appreciation than women (ds=.16-.23). These results provide preliminary support for the factorial validity of the French BAS-2. Copyright © 2017 Elsevier Ltd. All rights reserved.

Bayesian SEM for Specification Search Problems in Testing Factorial Invariance.

PubMed

Shi, Dexin; Song, Hairong; Liao, Xiaolan; Terry, Robert; Snyder, Lori A

2017-01-01

Specification search problems refer to two important but under-addressed issues in testing for factorial invariance: how to select proper reference indicators and how to locate specific non-invariant parameters. In this study, we propose a two-step procedure to solve these issues. Step 1 is to identify a proper reference indicator using the Bayesian structural equation modeling approach. An item is selected if it is associated with the highest likelihood to be invariant across groups. Step 2 is to locate specific non-invariant parameters, given that a proper reference indicator has already been selected in Step 1. A series of simulation analyses show that the proposed method performs well under a variety of data conditions, and optimal performance is observed under conditions of large magnitude of non-invariance, low proportion of non-invariance, and large sample sizes. We also provide an empirical example to demonstrate the specific procedures to implement the proposed method in applied research. The importance and influences are discussed regarding the choices of informative priors with zero mean and small variances. Extensions and limitations are also pointed out.

Investigation of the structure of /sup 4/He in a translationally invariant oscillator basis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bartaya, O.L.; Macharadze, T.S.

1977-12-01

The binding energy, mean square radius, and charge form factor of the /sup 4/He nucleus are calculated using a translationally invariant basis. The realistic local nucleon-nucleon potential of Gogni, Pires, and De Tourreil (Phys. Lett. B 32B, 591 (1970)) is used in the calculations. Taken into account in the basis are all translationally invariant oscillator states with spatial symmetry (f)=4) and number of excitation quanta N< or =8 and with symmetry (f)=22) and N< or =6.

Assessing cross-cultural differences through use of multiple-group invariance analyses.

PubMed

Stein, Judith A; Lee, Jerry W; Jones, Patricia S

2006-12-01

The use of structural equation modeling in cross-cultural personality research has become a popular method for testing measurement invariance. In this report, we present an example of testing measurement invariance using the Sense of Coherence Scale of Antonovsky (1993) in 3 ethnic groups: Chinese, Japanese, and Whites. In a series of increasingly restrictive constraints on the measurement models of the 3 groups, we demonstrate how to assess differences among the groups. We also provide an example of construct validation.

Knot soliton in DNA and geometric structure of its free-energy density.

PubMed

Wang, Ying; Shi, Xuguang

2018-03-01

In general, the geometric structure of DNA is characterized using an elastic rod model. The Landau model provides us a new theory to study the geometric structure of DNA. By using the decomposition of the arc unit in the helical axis of DNA, we find that the free-energy density of DNA is similar to the free-energy density of a two-condensate superconductor. By using the φ-mapping topological current theory, the torus knot soliton hidden in DNA is demonstrated. We show the relation between the geometric structure and free-energy density of DNA and the Frenet equations in differential geometry theory are considered. Therefore, the free-energy density of DNA can be expressed by the curvature and torsion of the helical axis.

Apparatus for checking dimensions of workpieces

DOEpatents

Possati, Mario; Golinelli, Guido

1992-01-01

An apparatus for checking features of workpieces with rotational symmetry defining a geometrical axis, which includes a base, rest devices fixed to the base for supporting the workpiece with the geometrical axis horizontally arranged, and a support structure coupled to the base for rotation about a horizontal axis. A counterweight and sensor are coupled to the support structure and movable with the support structure from a rest position, allowing loading of the workpiece to be checked onto the rest devices to a working position where the sensor is brought into cooperation with the workpiece. The axis of rotation of the support structure is arranged below the axis of the workpiece, in correspondence to a vertical geometrical plane passing through the workpiece geometric axis when the workpiece is positioned on the rest devices.

Scale-invariance of sediment patterns - the fingerprint of fundamental drivers (Jean Baptiste Lamarck Medal Lecture)

NASA Astrophysics Data System (ADS)

Schlager, Wolfgang

2015-04-01

In contrast to the realms of magmatism and metamorphism, most depositional processes can be observed directly at the earth's surface. Observation of sediment patterns advanced significantly with the advent of remote sensing and 3D reflection seismics. Remote sensing is particularly relevant for the present topic because it documents mainly Holocene sediments - the best objects to link depositional processes to products. Classic examples of scale-invariant geometry are channel-fan systems, i.e. river-delta and canyon-fan complexes. The underlying control in both instances is the energy-dispersion of a channeled stream of water that discharges in a body of still water. The resulting fan-shaped sediment accumulations are scale-invariant over 7 orders of magnitude in linear size. The Mesozoic-Cenozoic record shows comparable trends and patterns. Further examples of depositional scale-invariance include foresets of non-cohesive sediments and braided-channel deposits. Reefs and carbonate platforms offer an example of scale-invariance related to biotic growth. Shallow-water carbonate platforms rimmed by reefs or reef-rimmed atolls with deep lagoons are characteristic morphologies of tropical carbonate deposits. The structure has been compared to a bucket where stiff reef rims hold a pile of loose sediment. Remote sensing data from the Maldive, Chagos and Laccadive archipelagos of the Indian Ocean show that bucket structures are the dominant depositional pattern from meter-size reefs to archipelagos of hundreds of kilometers in diameter, i.e. over more than 4 orders of magnitude in linear size. Over 2.5 orders of magnitude, the bucket structures qualify as statistical fractals. Ecologic and hydrodynamic studies on modern reefs suggest that the bucket structure is a form of biotic self-organization: The edge position in a reef is favored over the center position because bottom shear is higher and the diffusive boundary layer between reef and water thinner. Thus, the reef edge has easier access to nutrients. Moreover, the edge is less likely to be buried by sediment. The bucket structure is an ecologic response to these conditions. Buckets have been documented from all periods of the Phanerozoic and analogous structures from the late Proterozoic show that the microbial carbonate factory also built buckets. We conclude that a voyage through scales in the sediment realm reveals islands of scale-invariance wherever a single principle dominates the sedimentation process.

Classification of digital affine noncommutative geometries

NASA Astrophysics Data System (ADS)

Majid, Shahn; Pachoł, Anna

2018-03-01

It is known that connected translation invariant n-dimensional noncommutative differentials dxi on the algebra k[x1, …, xn] of polynomials in n-variables over a field k are classified by commutative algebras V on the vector space spanned by the coordinates. These data also apply to construct differentials on the Heisenberg algebra "spacetime" with relations [xμ, xν] = λΘμν, where Θ is an antisymmetric matrix, as well as to Lie algebras with pre-Lie algebra structures. We specialise the general theory to the field k =F2 of two elements, in which case translation invariant metrics (i.e., with constant coefficients) are equivalent to making V a Frobenius algebra. We classify all of these and their quantum Levi-Civita bimodule connections for n = 2, 3, with partial results for n = 4. For n = 2, we find 3 inequivalent differential structures admitting 1, 2, and 3 invariant metrics, respectively. For n = 3, we find 6 differential structures admitting 0, 1, 2, 3, 4, 7 invariant metrics, respectively. We give some examples for n = 4 and general n. Surprisingly, not all our geometries for n ≥ 2 have zero quantum Riemann curvature. Quantum gravity is normally seen as a weighted "sum" over all possible metrics but our results are a step towards a deeper approach in which we must also "sum" over differential structures. Over F2 we construct some of our algebras and associated structures by digital gates, opening up the possibility of "digital geometry."

Nuclear spin dependence of time reversal invariance violating effects in neutron scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gudkov, Vladimir; Shimizu, Hirohiko M.

In this study, the spin structure of parity violating and time reversal invariance violating effects in neutron scattering is discussed. The explicit relations between these effects are presented in terms of functions nuclear spins and neutron partial widths of p-wave resonances.

Nuclear spin dependence of time reversal invariance violating effects in neutron scattering

DOE PAGES

Gudkov, Vladimir; Shimizu, Hirohiko M.

2018-06-11

In this study, the spin structure of parity violating and time reversal invariance violating effects in neutron scattering is discussed. The explicit relations between these effects are presented in terms of functions nuclear spins and neutron partial widths of p-wave resonances.

Computer modeling of electromagnetic problems using the geometrical theory of diffraction

NASA Technical Reports Server (NTRS)

Burnside, W. D.

1976-01-01

Some applications of the geometrical theory of diffraction (GTD), a high frequency ray optical solution to electromagnetic problems, are presented. GTD extends geometric optics, which does not take into account the diffractions occurring at edges, vertices, and various other discontinuities. Diffraction solutions, analysis of basic structures, construction of more complex structures, and coupling using GTD are discussed.

BPS counting for knots and combinatorics on words

NASA Astrophysics Data System (ADS)

Kucharski, Piotr; Sułkowski, Piotr

2016-11-01

We discuss relations between quantum BPS invariants defined in terms of a product decomposition of certain series, and difference equations (quantum A-polynomials) that annihilate such series. We construct combinatorial models whose structure is encoded in the form of such difference equations, and whose generating functions (Hilbert-Poincaré series) are solutions to those equations and reproduce generating series that encode BPS invariants. Furthermore, BPS invariants in question are expressed in terms of Lyndon words in an appropriate language, thereby relating counting of BPS states to the branch of mathematics referred to as combinatorics on words. We illustrate these results in the framework of colored extremal knot polynomials: among others we determine dual quantum extremal A-polynomials for various knots, present associated combinatorial models, find corresponding BPS invariants (extremal Labastida-Mariño-Ooguri-Vafa invariants) and discuss their integrality.

Recognition of rotated images using the multi-valued neuron and rotation-invariant 2D Fourier descriptors

NASA Astrophysics Data System (ADS)

Aizenberg, Evgeni; Bigio, Irving J.; Rodriguez-Diaz, Eladio

2012-03-01

The Fourier descriptors paradigm is a well-established approach for affine-invariant characterization of shape contours. In the work presented here, we extend this method to images, and obtain a 2D Fourier representation that is invariant to image rotation. The proposed technique retains phase uniqueness, and therefore structural image information is not lost. Rotation-invariant phase coefficients were used to train a single multi-valued neuron (MVN) to recognize satellite and human face images rotated by a wide range of angles. Experiments yielded 100% and 96.43% classification rate for each data set, respectively. Recognition performance was additionally evaluated under effects of lossy JPEG compression and additive Gaussian noise. Preliminary results show that the derived rotation-invariant features combined with the MVN provide a promising scheme for efficient recognition of rotated images.

Factorial and Item-Level Invariance of a Principal Perspectives Survey: German and U.S. Principals.

PubMed

Wang, Chuang; Hancock, Dawson R; Muller, Ulrich

This study examined the factorial and item-level invariance of a survey of principals' job satisfaction and perspectives about reasons and barriers to becoming a principal with a sample of US principals and another sample of German principals. Confirmatory factor analysis (CFA) and differential item functioning (DIF) analysis were employed at the test and item level, respectively. A single group CFA was conducted first, and the model was found to fit the data collected. The factorial invariance between the German and the US principals was tested through three steps: (a) configural invariance; (b) measurement invariance; and (c) structural invariance. The results suggest that the survey is a viable measure of principals' job satisfaction and perspectives about reasons and barriers to becoming a principal because principals from two different cultures shared a similar pattern on all three constructs. The DIF analysis further revealed that 22 out of the 28 items functioned similarly between German and US principals.

How hairpin vortices emerge from exact invariant solutions

NASA Astrophysics Data System (ADS)

Schneider, Tobias M.; Farano, Mirko; de Palma, Pietro; Robinet, Jean-Christoph; Cherubini, Stefania

2017-11-01

Hairpin vortices are among the most commonly observed flow structures in wall-bounded shear flows. However, within the dynamical system approach to turbulence, those structures have not yet been described. They are not captured by known exact invariant solutions of the Navier-Stokes equations nor have other state-space structures supporting hairpins been identified. We show that hairpin structures are observed along an optimally growing trajectory leaving a well known exact traveling wave solution of plane Poiseuille flow. The perturbation triggering hairpins does not correspond to an unstable mode of the exact traveling wave but lies in the stable manifold where non-normality causes strong transient amplification.

Performance improvements of symmetry-breaking reflector structures in nonimaging devices

DOEpatents

Winston, Roland

2004-01-13

A structure and method for providing a broken symmetry reflector structure for a solar concentrator device. The component of the optical direction vector along the symmetry axis is conserved for all rays propagated through a translationally symmetric optical device. This quantity, referred to as the translational skew invariant, is conserved in rotationally symmetric optical systems. Performance limits for translationally symmetric nonimaging optical devices are derived from the distributions of the translational skew invariant for the optical source and for the target to which flux is to be transferred. A numerically optimized non-tracking solar concentrator utilizing symmetry-breaking reflector structures can overcome the performance limits associated with translational symmetry.

Lorentz invariance with an invariant energy scale.

PubMed

Magueijo, João; Smolin, Lee

2002-05-13

We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a nonlinear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.

Verification of Java Programs using Symbolic Execution and Invariant Generation

NASA Technical Reports Server (NTRS)

Pasareanu, Corina; Visser, Willem

2004-01-01

Software verification is recognized as an important and difficult problem. We present a norel framework, based on symbolic execution, for the automated verification of software. The framework uses annotations in the form of method specifications an3 loop invariants. We present a novel iterative technique that uses invariant strengthening and approximation for discovering these loop invariants automatically. The technique handles different types of data (e.g. boolean and numeric constraints, dynamically allocated structures and arrays) and it allows for checking universally quantified formulas. Our framework is built on top of the Java PathFinder model checking toolset and it was used for the verification of several non-trivial Java programs.

Digital and optical shape representation and pattern recognition; Proceedings of the Meeting, Orlando, FL, Apr. 4-6, 1988

NASA Technical Reports Server (NTRS)

Juday, Richard D. (Editor)

1988-01-01

The present conference discusses topics in pattern-recognition correlator architectures, digital stereo systems, geometric image transformations and their applications, topics in pattern recognition, filter algorithms, object detection and classification, shape representation techniques, and model-based object recognition methods. Attention is given to edge-enhancement preprocessing using liquid crystal TVs, massively-parallel optical data base management, three-dimensional sensing with polar exponential sensor arrays, the optical processing of imaging spectrometer data, hybrid associative memories and metric data models, the representation of shape primitives in neural networks, and the Monte Carlo estimation of moment invariants for pattern recognition.

Mapping repulsive to attractive interaction in driven-dissipative quantum systems

NASA Astrophysics Data System (ADS)

Li, Andy C. Y.; Koch, Jens

2017-11-01

Repulsive and attractive interactions usually lead to very different physics. Striking exceptions exist in the dynamics of driven-dissipative quantum systems. For the example of a photonic Bose-Hubbard dimer, we establish a one-to-one mapping relating cases of onsite repulsion and attraction. We prove that the mapping is valid for an entire class of Markovian open quantum systems with a time-reversal-invariant Hamiltonian and physically meaningful inverse-sign Hamiltonian. To underline the broad applicability of the mapping, we illustrate the one-to-one correspondence between the nonequilibrium dynamics in a geometrically frustrated spin lattice and those in a non-frustrated partner lattice.

Behavioral Scale Reliability and Measurement Invariance Evaluation Using Latent Variable Modeling

ERIC Educational Resources Information Center

Raykov, Tenko

2004-01-01

A latent variable modeling approach to reliability and measurement invariance evaluation for multiple-component measuring instruments is outlined. An initial discussion deals with the limitations of coefficient alpha, a frequently used index of composite reliability. A widely and readily applicable structural modeling framework is next described…

A Hamiltonian electromagnetic gyrofluid model

NASA Astrophysics Data System (ADS)

Waelbroeck, F. L.; Hazeltine, R. D.; Morrison, P. J.

2009-03-01

An isothermal truncation of the electromagnetic gyrofluid model of Snyder and Hammett [Phys. Plasmas 8, 3199 (2001)] is shown to be Hamiltonian. The corresponding noncanonical Lie-Poisson bracket and its Casimir invariants are presented. The invariants are used to obtain a set of coupled Grad-Shafranov equations describing equilibria and propagating coherent structures.

Male Role Norms Inventory-Short Form (MRNI-SF): development, confirmatory factor analytic investigation of structure, and measurement invariance across gender.

PubMed

Levant, Ronald F; Hall, Rosalie J; Rankin, Thomas J

2013-04-01

The current study reports the development from the Male Role Norms Inventory-Revised (MRNI-R; Levant, Rankin, Williams, Hasan, & Smalley, 2010) of the 21-item MRNI-Short Form (MRNI-SF). Confirmatory factor analysis of MRNI-SF responses from a sample of 1,017 undergraduate participants (549 men, 468 women) indicated that the best fitting "bifactor" model incorporated the hypothesized 7-factor structure while explicitly modeling an additional, general traditional masculinity ideology factor. Specifically, each item-level indicator loaded on 2 factors: a general traditional masculinity ideology factor and a specific factor corresponding to 1 of the 7 hypothesized traditional masculinity ideology norms. The bifactor model was assessed for measurement invariance across gender groups, with findings of full configural invariance and partial metric invariance, such that factor loadings were equivalent across the gender groups for the 7 specific factors but not for the general traditional masculinity ideology factor. Theoretical explanations for this latter result include the potential that men's sense of self or identity may be engaged when responding to questions asking to what extent they agree or disagree with normative statements about their behavior, a possibility that could be investigated in future research by examining the associations of the general and specific factors with measures of masculine identity. Additional exploratory invariance analyses demonstrated latent mean differences between men and women on 4 of the 8 factors, and equivocal results for invariance of item intercepts, item uniquenesses, and factor variances-covariances.

Linear algebra of the permutation invariant Crow-Kimura model of prebiotic evolution.

PubMed

Bratus, Alexander S; Novozhilov, Artem S; Semenov, Yuri S

2014-10-01

A particular case of the famous quasispecies model - the Crow-Kimura model with a permutation invariant fitness landscape - is investigated. Using the fact that the mutation matrix in the case of a permutation invariant fitness landscape has a special tridiagonal form, a change of the basis is suggested such that in the new coordinates a number of analytical results can be obtained. In particular, using the eigenvectors of the mutation matrix as the new basis, we show that the quasispecies distribution approaches a binomial one and give simple estimates for the speed of convergence. Another consequence of the suggested approach is a parametric solution to the system of equations determining the quasispecies. Using this parametric solution we show that our approach leads to exact asymptotic results in some cases, which are not covered by the existing methods. In particular, we are able to present not only the limit behavior of the leading eigenvalue (mean population fitness), but also the exact formulas for the limit quasispecies eigenvector for special cases. For instance, this eigenvector has a geometric distribution in the case of the classical single peaked fitness landscape. On the biological side, we propose a mathematical definition, based on the closeness of the quasispecies to the binomial distribution, which can be used as an operational definition of the notorious error threshold. Using this definition, we suggest two approximate formulas to estimate the critical mutation rate after which the quasispecies delocalization occurs. Copyright © 2014 Elsevier Inc. All rights reserved.

On differential photometric reconstruction for unknown, isotropic BRDFs.

PubMed

Chandraker, Manmohan; Bai, Jiamin; Ramamoorthi, Ravi

2013-12-01

This paper presents a comprehensive theory of photometric surface reconstruction from image derivatives in the presence of a general, unknown isotropic BRDF. We derive precise topological classes up to which the surface may be determined and specify exact priors for a full geometric reconstruction. These results are the culmination of a series of fundamental observations. First, we exploit the linearity of chain rule differentiation to discover photometric invariants that relate image derivatives to the surface geometry, regardless of the form of isotropic BRDF. For the problem of shape-from-shading, we show that a reconstruction may be performed up to isocontours of constant magnitude of the gradient. For the problem of photometric stereo, we show that just two measurements of spatial and temporal image derivatives, from unknown light directions on a circle, suffice to recover surface information from the photometric invariant. Surprisingly, the form of the invariant bears a striking resemblance to optical flow; however, it does not suffer from the aperture problem. This photometric flow is shown to determine the surface up to isocontours of constant magnitude of the surface gradient, as well as isocontours of constant depth. Further, we prove that specification of the surface normal at a single point completely determines the surface depth from these isocontours. In addition, we propose practical algorithms that require additional initial or boundary information, but recover depth from lower order derivatives. Our theoretical results are illustrated with several examples on synthetic and real data.

An Innovative Sensing Approach Using Carbon Nanotube-Based Composites for Structural Health Monitoring of Concrete Structures

NASA Astrophysics Data System (ADS)

Dwivedi, Vatsal

This thesis presents some work on two quite disparate kinds of dynamical systems described by Hamiltonian dynamics. The first part describes a computation of gauge anomalies and their macroscopic effects in a semiclassical picture. The geometric (symplectic) formulation of classical mechanics is used to describe the dynamics of Weyl fermions in even spacetime dimensions, the only quantum input to the symplectic form being the Berry curvature that encodes the spin-momentum locking. The (semi-)classical equations of motion are used in a kinetic theory setup to compute the gauge and singlet currents, whose conservation laws reproduce the nonabelian gauge and singlet anomalies. Anomalous contributions to the hydrodynamic currents for a gas of Weyl fermions at a finite temperature and chemical potential are also calculated, and are in agreement with similar results in literature which were obtained using thermodynamic and/or quantum field theoretical arguments. The second part describes a generalized transfer matrix formalism for noninteracting tight-binding models. The formalism is used to study the bulk and edge spectra, both of which are encoded in the spectrum of the transfer matrices, for some of the common tight-binding models for noninteracting electronic topological phases of matter. The topological invariants associated with the boundary states are interpreted as winding numbers for windings around noncontractible loops on a Riemann sheet constructed using the algebraic structure of the transfer matrices, as well as with a Maslov index on a symplectic group manifold, which is the space of transfer matrices.

Perceptual similarity and the neural correlates of geometrical illusions in human brain structure.

PubMed

Axelrod, Vadim; Schwarzkopf, D Samuel; Gilaie-Dotan, Sharon; Rees, Geraint

2017-01-09

Geometrical visual illusions are an intriguing phenomenon, in which subjective perception consistently misjudges the objective, physical properties of the visual stimulus. Prominent theoretical proposals have been advanced attempting to find common mechanisms across illusions. But empirically testing the similarity between illusions has been notoriously difficult because illusions have very different visual appearances. Here we overcome this difficulty by capitalizing on the variability of the illusory magnitude across participants. Fifty-nine healthy volunteers participated in the study that included measurement of individual illusion magnitude and structural MRI scanning. We tested the Muller-Lyer, Ebbinghaus, Ponzo, and vertical-horizontal geometrical illusions as well as a non-geometrical, contrast illusion. We found some degree of similarity in behavioral judgments of all tested geometrical illusions, but not between geometrical illusions and non-geometrical, contrast illusion. The highest similarity was found between Ebbinghaus and Muller-Lyer geometrical illusions. Furthermore, the magnitude of all geometrical illusions, and particularly the Ebbinghaus and Muller-Lyer illusions, correlated with local gray matter density in the parahippocampal cortex, but not in other brain areas. Our findings suggest that visuospatial integration and scene construction processes might partly mediate individual differences in geometric illusory perception. Overall, these findings contribute to a better understanding of the mechanisms behind geometrical illusions.

Influence of stochastic geometric imperfections on the load-carrying behaviour of thin-walled structures using constrained random fields

NASA Astrophysics Data System (ADS)

Lauterbach, S.; Fina, M.; Wagner, W.

2018-04-01

Since structural engineering requires highly developed and optimized structures, the thickness dependency is one of the most controversially debated topics. This paper deals with stability analysis of lightweight thin structures combined with arbitrary geometrical imperfections. Generally known design guidelines only consider imperfections for simple shapes and loading, whereas for complex structures the lower-bound design philosophy still holds. Herein, uncertainties are considered with an empirical knockdown factor representing a lower bound of existing measurements. To fully understand and predict expected bearable loads, numerical investigations are essential, including geometrical imperfections. These are implemented into a stand-alone program code with a stochastic approach to compute random fields as geometric imperfections that are applied to nodes of the finite element mesh of selected structural examples. The stochastic approach uses the Karhunen-Loève expansion for the random field discretization. For this approach, the so-called correlation length l_c controls the random field in a powerful way. This parameter has a major influence on the buckling shape, and also on the stability load. First, the impact of the correlation length is studied for simple structures. Second, since most structures for engineering devices are more complex and combined structures, these are intensively discussed with the focus on constrained random fields for e.g. flange-web-intersections. Specific constraints for those random fields are pointed out with regard to the finite element model. Further, geometrical imperfections vanish where the structure is supported.

Scope and Conceptual Issues in Testing the Race-Crime Invariance Thesis: Black, White, and Hispanic Comparisons*

PubMed Central

Ulmer, Jeffrey T.; Feldmeyer, Ben; Harris, Casey T.

2014-01-01

Our goal in this article is to contribute conceptually and empirically to assessments of the racial invariance hypothesis, which posits that structural disadvantage predicts violent crime in the same way for all racial and ethnic groups. Conceptually, we elucidate the scope of the racial invariance hypothesis and clarify the criteria used for evaluating it. Empirically, we use 1999–2001 averaged arrest data from California and New York to extend analyses of the invariance hypothesis within the context of the scope and definitional issues raised in our conceptual framing – most notably, by including Hispanic comparisons with blacks and whites, by examining the invariance assumption for homicide as well as the violent crime index, by using discrete as well as composite disadvantage measures, and by using census place localities as the study unit. The mixed findings we report from our comparisons (across whites, blacks, and Hispanics; offense types; type of disadvantage) suggest caution and uncertainty about the notion that structural sources of violence affect racial/ethnic groups in uniform ways. We conclude that the hypothesis should be regarded as provisional and its scope remains to be established as to whether it applies only under narrow conditions or is a principle of general applicability. PMID:25408558

Biomorphic networks: approach to invariant feature extraction and segmentation for ATR

NASA Astrophysics Data System (ADS)

Baek, Andrew; Farhat, Nabil H.

1998-10-01

Invariant features in two dimensional binary images are extracted in a single layer network of locally coupled spiking (pulsating) model neurons with prescribed synapto-dendritic response. The feature vector for an image is represented as invariant structure in the aggregate histogram of interspike intervals obtained by computing time intervals between successive spikes produced from each neuron over a given period of time and combining such intervals from all neurons in the network into a histogram. Simulation results show that the feature vectors are more pattern-specific and invariant under translation, rotation, and change in scale or intensity than achieved in earlier work. We also describe an application of such networks to segmentation of line (edge-enhanced or silhouette) images. The biomorphic spiking network's capabilities in segmentation and invariant feature extraction may prove to be, when they are combined, valuable in Automated Target Recognition (ATR) and other automated object recognition systems.

Constraints of recreational sport participation: measurement invariance and latent mean differences across sex and physical activity status.

PubMed

Liu, Jing Dong; Chung, Pak Kwong; Chen, Wing Ping

2014-10-01

The purpose of the current study was to (a) examine the measurement invariance of the Constraint Scale of Sport Participation across sex and physical activity status among the undergraduate students (N = 630) in Hong Kong and (b) compare the latent mean differences across groups. Measurement invariance of the Constraint Scale of Sport Participation across sex of and physical activity status of the participants was examined first. With receiving support on the measurement invariance across groups, latent mean differences of the scores across groups were examined. Multi-group confirmatory factor analysis revealed that the configural, metric, scalar, and structural invariance of the scale was supported across groups. The results of latent mean differences suggested that the women reported significantly higher constraints on time, partner, psychology, knowledge, and interest than the men. The physically inactive participants reported significantly higher scores on all constraints except for accessibility than the physically active participants.

Functionally essential, invariant glutamate near the C-terminus of strand beta 5 in various (alpha/beta)8-barrel enzymes as a possible indicator of their evolutionary relatedness.

PubMed

Janecek, S; Baláz, S

1995-08-01

Twelve different (alpha/beta)8-barrel enzymes belonging to three structurally distinct families were found to contain, near the C-terminus of their strand beta 5, a conserved invariant glutamic acid residue that plays an important functional role in each of these enzymes. The search was based on the idea that a conserved sequence region of an (alpha/beta)8-barrel enzyme should be more or less conserved also in the equivalent part of the structure of the other enzymes with this folding motif owing to their mutual evolutionary relatedness. For this purpose, the sequence region around the well conserved fifth beta-strand of alpha-amylase containing catalytic glutamate (Glu230, Aspergillus oryzae alpha-amylase numbering), was used as the sequence-structural template. The isolated sequence stretches of the 12 (alpha/beta)8-barrels are discussed from both the sequence-structural and the evolutionary point of view, the invariant glutamate residue being proposed to be a joining feature of the studied group of enzymes remaining from their ancestral (alpha/beta)8-barrel.

Secondary structure in solution of two anti-HIV-1 hammerhead ribozymes as investigated by two-dimensional 1H 500 MHz NMR spectroscopy in water

NASA Technical Reports Server (NTRS)

Sarma, R. H.; Sarma, M. H.; Rein, R.; Shibata, M.; Setlik, R. S.; Ornstein, R. L.; Kazim, A. L.; Cairo, A.; Tomasi, T. B.

1995-01-01

Two hammerhead chimeric RNA/DNA ribozymes (HRz) were synthesized in pure form. Both were 30 nucleotides long, and the sequences were such that they could be targeted to cleave the HIV-1 gag RNA. Named HRz-W and HRz-M, the former had its invariable core region conserved, the latter had a uridine in the invariable region replaced by a guanine. Their secodary structures were determined by 2D NOESY 1H 500 MHz NMR spectroscopy in 90% water and 10% D2(0), following the imino protons. The data show that both HRz-M and HRz-W form identical secondary structures with stem regions consisting of continuous stacks of AT and GT pairs. An energy minimized computer model of this stem region is provided. The results suggest that the loss of catalytic activity that is known to result when an invariant core residue is replaced is not related to the secondary structure of the ribozymes in the absence of substrate.

Evaluating Individual Students' Perceptions of Instructional Quality: An Investigation of their Factor Structure, Measurement Invariance, and Relations to Educational Outcomes.

PubMed

Scherer, Ronny; Nilsen, Trude; Jansen, Malte

2016-01-01

Students' perceptions of instructional quality are among the most important criteria for evaluating teaching effectiveness. The present study evaluates different latent variable modeling approaches (confirmatory factor analysis, exploratory structural equation modeling, and bifactor modeling), which are used to describe these individual perceptions with respect to their factor structure, measurement invariance, and the relations to selected educational outcomes (achievement, self-concept, and motivation in mathematics). On the basis of the Programme for International Student Assessment (PISA) 2012 large-scale data sets of Australia, Canada, and the USA (N = 26,746 students), we find support for the distinction between three factors of individual students' perceptions and full measurement invariance across countries for all modeling approaches. In this regard, bifactor exploratory structural equation modeling outperformed alternative approaches with respect to model fit. Our findings reveal significant relations to the educational outcomes. This study synthesizes different modeling approaches of individual students' perceptions of instructional quality and provides insights into the nature of these perceptions from an individual differences perspective. Implications for the measurement and modeling of individually perceived instructional quality are discussed.

Synchronization invariance under network structural transformations

NASA Astrophysics Data System (ADS)

Arola-Fernández, Lluís; Díaz-Guilera, Albert; Arenas, Alex

2018-06-01

Synchronization processes are ubiquitous despite the many connectivity patterns that complex systems can show. Usually, the emergence of synchrony is a macroscopic observable; however, the microscopic details of the system, as, e.g., the underlying network of interactions, is many times partially or totally unknown. We already know that different interaction structures can give rise to a common functionality, understood as a common macroscopic observable. Building upon this fact, here we propose network transformations that keep the collective behavior of a large system of Kuramoto oscillators invariant. We derive a method based on information theory principles, that allows us to adjust the weights of the structural interactions to map random homogeneous in-degree networks into random heterogeneous networks and vice versa, keeping synchronization values invariant. The results of the proposed transformations reveal an interesting principle; heterogeneous networks can be mapped to homogeneous ones with local information, but the reverse process needs to exploit higher-order information. The formalism provides analytical insight to tackle real complex scenarios when dealing with uncertainty in the measurements of the underlying connectivity structure.

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes with a nonlinear conjugate gradient method.

PubMed

Kim, Hwi; Min, Sung-Wook; Lee, Byoungho

2008-12-01

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes is described. In the analysis, a geometrical optics model of six-beam reflection patterns generated by an imperfect retroreflection corner cube is developed, and its structural error extraction is formulated as a nonlinear optimization problem. The nonlinear conjugate gradient method is employed for solving the nonlinear optimization problem, and its detailed implementation is described. The proposed method of analysis is a mathematical basis for the nondestructive optical inspection of imperfectly fabricated retroreflection corner cubes.

Crash-Energy Absorbing Composite Structure and Method of Fabrication

NASA Technical Reports Server (NTRS)

Kellas, Sotiris (Inventor); Carden, Huey D. (Inventor)

1998-01-01

A stand-alone, crash-energy absorbing structure and fabrication method are provided. A plurality of adjoining rigid cells are each constructed of resin-cured fiber reinforcement and are arranged in a geometric configuration. The geometric configuration of cells is integrated by means of continuous fibers wrapped thereabout in order to maintain the cells in the geometric configuration. The cured part results in a net shape, stable structure that can function on its own with no additional reinforcement and can withstand combined loading while crushing in a desired direction.

Faddeev-Jackiw quantization of topological invariants: Euler and Pontryagin classes

NASA Astrophysics Data System (ADS)

Escalante, Alberto; Medel-Portugal, C.

2018-04-01

The symplectic analysis for the four dimensional Pontryagin and Euler invariants is performed within the Faddeev-Jackiw context. The Faddeev-Jackiw constraints and the generalized Faddeev-Jackiw brackets are reported; we show that in spite of the Pontryagin and Euler classes give rise the same equations of motion, its respective symplectic structures are different to each other. In addition, a quantum state that solves the Faddeev-Jackiw constraints is found, and we show that the quantum states for these invariants are different to each other. Finally, we present some remarks and conclusions.

Translation invariant time-dependent massive gravity: Hamiltonian analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mourad, Jihad; Steer, Danièle A.; Noui, Karim, E-mail: mourad@apc.univ-paris7.fr, E-mail: karim.noui@lmpt.univ-tours.fr, E-mail: steer@apc.univ-paris7.fr

2014-09-01

The canonical structure of the massive gravity in the first order moving frame formalism is studied. We work in the simplified context of translation invariant fields, with mass terms given by general non-derivative interactions, invariant under the diagonal Lorentz group, depending on the moving frame as well as a fixed reference frame. We prove that the only mass terms which give 5 propagating degrees of freedom are the dRGT mass terms, namely those which are linear in the lapse. We also complete the Hamiltonian analysis with the dynamical evolution of the system.

Integration of element specific persistent homology and machine learning for protein-ligand binding affinity prediction.

PubMed

Cang, Zixuan; Wei, Guo-Wei

2018-02-01

Protein-ligand binding is a fundamental biological process that is paramount to many other biological processes, such as signal transduction, metabolic pathways, enzyme construction, cell secretion, and gene expression. Accurate prediction of protein-ligand binding affinities is vital to rational drug design and the understanding of protein-ligand binding and binding induced function. Existing binding affinity prediction methods are inundated with geometric detail and involve excessively high dimensions, which undermines their predictive power for massive binding data. Topology provides the ultimate level of abstraction and thus incurs too much reduction in geometric information. Persistent homology embeds geometric information into topological invariants and bridges the gap between complex geometry and abstract topology. However, it oversimplifies biological information. This work introduces element specific persistent homology (ESPH) or multicomponent persistent homology to retain crucial biological information during topological simplification. The combination of ESPH and machine learning gives rise to a powerful paradigm for macromolecular analysis. Tests on 2 large data sets indicate that the proposed topology-based machine-learning paradigm outperforms other existing methods in protein-ligand binding affinity predictions. ESPH reveals protein-ligand binding mechanism that can not be attained from other conventional techniques. The present approach reveals that protein-ligand hydrophobic interactions are extended to 40Å  away from the binding site, which has a significant ramification to drug and protein design. Copyright © 2017 John Wiley & Sons, Ltd.

Gender Invariance of Family, School, and Peer Influence on Volunteerism Scale

ERIC Educational Resources Information Center

Law, Ben; Shek, Daniel; Ma, Cecilia

2015-01-01

Objective: This article examines the measurement invariance of "Family, School, and Peer Influence on Volunteerism Scale" (FSPV) across genders using the mean and covariance structure analysis approach. Method: A total of 2,845 Chinese high school adolescents aged 11 to 15 years completed the FSPV scale. Results: Results of the…

The Potential for Differential Findings among Invariance Testing Strategies for Multisample Measured Variable Path Models

ERIC Educational Resources Information Center

Mann, Heather M.; Rutstein, Daisy W.; Hancock, Gregory R.

2009-01-01

Multisample measured variable path analysis is used to test whether causal/structural relations among measured variables differ across populations. Several invariance testing approaches are available for assessing cross-group equality of such relations, but the associated test statistics may vary considerably across methods. This study is a…

Testing Measurement Invariance of the Students' Affective Characteristics Model across Gender Sub-Groups

ERIC Educational Resources Information Center

Demir, Ergül

2017-01-01

In this study, the aim was to construct a significant structural measurement model comparing students' affective characteristics with their mathematic achievement. According to this model, the aim was to test the measurement invariances between gender sub-groups hierarchically. This study was conducted as basic and descriptive research. Secondary…

Invariance of an Extended Technology Acceptance Model Across Gender and Age Group

ERIC Educational Resources Information Center

Ahmad, Tunku Badariah Tunku; Madarsha, Kamal Basha; Zainuddin, Ahmad Marzuki; Ismail, Nik Ahmad Hisham; Khairani, Ahmad Zamri; Nordin, Mohamad Sahari

2011-01-01

In this study, we examined the likelihood of a TAME (extended technology acceptance model), in which the interrelationships among computer self-efficacy, perceived usefulness, intention to use and self-reported use of computer-mediated technology were tested. In addition, the gender- and age-invariant of its causal structure were evaluated. The…

Survey of Attitudes Toward Statistics: Factor Structure Invariance by Gender and by Administration Time

ERIC Educational Resources Information Center

Hilton, Sterling C.; Schau, Candace; Olsen, Joseph A.

2004-01-01

In addition to student learning, positive student attitudes have become an important course outcome for many introductory statistics instructors. To adequately assess changes in mean attitudes across introductory statistics courses, the attitude instruments used should be invariant by administration time. Attitudes toward statistics from 4,910…

Time-varying and time-invariant dimensions of depression in children and adolescents: Implications for cross-informant agreement.

PubMed

Cole, David A; Martin, Joan M; Jacquez, Farrah M; Tram, Jane M; Zelkowitz, Rachel; Nick, Elizabeth A; Rights, Jason D

2017-07-01

The longitudinal structure of depression in children and adolescents was examined by applying a Trait-State-Occasion structural equation model to 4 waves of self, teacher, peer, and parent reports in 2 age groups (9 to 13 and 13 to 16 years old). Analyses revealed that the depression latent variable consisted of 2 longitudinal factors: a time-invariant dimension that was completely stable over time and a time-varying dimension that was not perfectly stable over time. Different sources of information were differentially sensitive to these 2 dimensions. Among adolescents, self- and parent reports better reflected the time-invariant aspects. For children and adolescents, peer and teacher reports better reflected the time-varying aspects. Relatively high cross-informant agreement emerged for the time-invariant dimension in both children and adolescents. Cross-informant agreement for the time-varying dimension was high for adolescents but very low for children. Implications emerge for theoretical models of depression and for its measurement, especially when attempting to predict changes in depression in the context of longitudinal studies. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Substance Use and Depression Symptomatology: Measurement Invariance of the Beck Depression Inventory (BDI-II) among Non-Users and Frequent-Users of Alcohol, Nicotine and Cannabis.

PubMed

Moore, Ashlee A; Neale, Michael C; Silberg, Judy L; Verhulst, Brad

2016-01-01

Depression is a highly heterogeneous condition, and identifying how symptoms present in various groups may greatly increase our understanding of its etiology. Importantly, Major Depressive Disorder is strongly linked with Substance Use Disorders, which may ameliorate or exacerbate specific depression symptoms. It is therefore quite plausible that depression may present with different symptom profiles depending on an individual's substance use status. Given these observations, it is important to examine the underlying construct of depression in groups of substance users compared to non-users. In this study we use a non-clinical sample to examine the measurement structure of the Beck Depression Inventory (BDI-II) in non-users and frequent-users of various substances. Specifically, measurement invariance was examined across those who do vs. do not use alcohol, nicotine, and cannabis. Results indicate strict factorial invariance across non-users and frequent-users of alcohol and cannabis, and metric invariance across non-users and frequent-users of nicotine. This implies that the factor structure of the BDI-II is similar across all substance use groups.

New evidence of factor structure and measurement invariance of the SDQ across five European nations.

PubMed

Ortuño-Sierra, Javier; Fonseca-Pedrero, Eduardo; Aritio-Solana, Rebeca; Velasco, Alvaro Moreno; de Luis, Edurne Chocarro; Schumann, Gunter; Cattrell, Anna; Flor, Herta; Nees, Frauke; Banaschewski, Tobias; Bokde, Arun; Whelan, Rob; Buechel, Christian; Bromberg, Uli; Conrod, Patricia; Frouin, Vincent; Papadopoulos, Dimitri; Gallinat, Juergen; Garavan, Hugh; Heinz, Andreas; Walter, Henrik; Struve, Maren; Gowland, Penny; Paus, Tomáš; Poustka, Luise; Martinot, Jean-Luc; Paillère-Martinot, Marie-Laure; Vetter, Nora C; Smolka, Michael N; Lawrence, Claire

2015-12-01

The main purpose of the present study was to analyse the internal structure and to test the measurement invariance of the Strengths and Difficulties Questionnaire (SDQ), self-reported version, in five European countries. The sample consisted of 3012 adolescents aged between 12 and 17 years (M = 14.20; SD = 0.83). The five-factor model (with correlated errors added), and the five-factor model (with correlated errors added) with the reverse-worded items allowed to cross-load on the Prosocial subscale, displayed adequate goodness of-fit indices. Multi-group confirmatory factor analysis showed that the five-factor model (with correlated errors added) had partial strong measurement invariance by countries. A total of 11 of the 25 items were non-invariant across samples. The level of internal consistency of the Total difficulties score was 0.84, ranging between 0.69 and 0.78 for the SDQ subscales. The findings indicate that the SDQ's subscales need to be modified in various ways for screening emotional and behavioural problems in the five European countries that were analysed.

Chaotic coordinates for the Large Helical Device

NASA Astrophysics Data System (ADS)

Hudson, Stuart; Suzuki, Yasuhiro

2014-10-01

The study of dynamical systems is facilitated by a coordinate framework with coordinate surfaces that coincide with invariant structures of the dynamical flow. For axisymmetric systems, a continuous family of invariant surfaces is guaranteed and straight-fieldline coordinates may be constructed. For non-integrable systems, e.g. stellarators, perturbed tokamaks, this continuous family is broken. Nevertheless, coordinates can still be constructed that simplify the description of the dynamics. The Poincare-Birkhoff theorem, the Aubry-Mather theorem, and the KAM theorem show that there are important structures that are invariant under the perturbed dynamics; namely the periodic orbits, the cantori, and the irrational flux surfaces. Coordinates adapted to these invariant sets, which we call chaotic coordinates, provide substantial advantages. The regular motion becomes straight, and the irregular motion is bounded by, and dissected by, coordinate surfaces that coincide with surfaces of locally-minimal magnetic-fieldline flux. The chaotic edge of the magnetic field, as calculated by HINT2 code, in the Large Helical Device (LHD) is examined, and a coordinate system is constructed so that the flux surfaces are ``straight'' and the islands become ``square.''

3D shape representation with spatial probabilistic distribution of intrinsic shape keypoints

NASA Astrophysics Data System (ADS)

Ghorpade, Vijaya K.; Checchin, Paul; Malaterre, Laurent; Trassoudaine, Laurent

2017-12-01

The accelerated advancement in modeling, digitizing, and visualizing techniques for 3D shapes has led to an increasing amount of 3D models creation and usage, thanks to the 3D sensors which are readily available and easy to utilize. As a result, determining the similarity between 3D shapes has become consequential and is a fundamental task in shape-based recognition, retrieval, clustering, and classification. Several decades of research in Content-Based Information Retrieval (CBIR) has resulted in diverse techniques for 2D and 3D shape or object classification/retrieval and many benchmark data sets. In this article, a novel technique for 3D shape representation and object classification has been proposed based on analyses of spatial, geometric distributions of 3D keypoints. These distributions capture the intrinsic geometric structure of 3D objects. The result of the approach is a probability distribution function (PDF) produced from spatial disposition of 3D keypoints, keypoints which are stable on object surface and invariant to pose changes. Each class/instance of an object can be uniquely represented by a PDF. This shape representation is robust yet with a simple idea, easy to implement but fast enough to compute. Both Euclidean and topological space on object's surface are considered to build the PDFs. Topology-based geodesic distances between keypoints exploit the non-planar surface properties of the object. The performance of the novel shape signature is tested with object classification accuracy. The classification efficacy of the new shape analysis method is evaluated on a new dataset acquired with a Time-of-Flight camera, and also, a comparative evaluation on a standard benchmark dataset with state-of-the-art methods is performed. Experimental results demonstrate superior classification performance of the new approach on RGB-D dataset and depth data.

Combining Statistical and Geometric Features for Colonic Polyp Detection in CTC Based on Multiple Kernel Learning

PubMed Central

Wang, Shijun; Yao, Jianhua; Petrick, Nicholas; Summers, Ronald M.

2010-01-01

Colon cancer is the second leading cause of cancer-related deaths in the United States. Computed tomographic colonography (CTC) combined with a computer aided detection system provides a feasible approach for improving colonic polyps detection and increasing the use of CTC for colon cancer screening. To distinguish true polyps from false positives, various features extracted from polyp candidates have been proposed. Most of these traditional features try to capture the shape information of polyp candidates or neighborhood knowledge about the surrounding structures (fold, colon wall, etc.). In this paper, we propose a new set of shape descriptors for polyp candidates based on statistical curvature information. These features called histograms of curvature features are rotation, translation and scale invariant and can be treated as complementing existing feature set. Then in order to make full use of the traditional geometric features (defined as group A) and the new statistical features (group B) which are highly heterogeneous, we employed a multiple kernel learning method based on semi-definite programming to learn an optimized classification kernel from the two groups of features. We conducted leave-one-patient-out test on a CTC dataset which contained scans from 66 patients. Experimental results show that a support vector machine (SVM) based on the combined feature set and the semi-definite optimization kernel achieved higher FROC performance compared to SVMs using the two groups of features separately. At a false positive per scan rate of 5, the sensitivity of the SVM using the combined features improved from 0.77 (Group A) and 0.73 (Group B) to 0.83 (p ≤ 0.01). PMID:20953299

The Feeding Practices and Structure Questionnaire (FPSQ-28): A parsimonious version validated for longitudinal use from 2 to 5 years.

PubMed

Jansen, Elena; Williams, Kate E; Mallan, Kimberley M; Nicholson, Jan M; Daniels, Lynne A

2016-05-01

Prospective studies and intervention evaluations that examine change over time assume that measurement tools measure the same construct at each occasion. In the area of parent-child feeding practices, longitudinal measurement properties of the questionnaires used are rarely verified. To ascertain that measured change in feeding practices reflects true change rather than change in the assessment, structure, or conceptualisation of the constructs over time, this study examined longitudinal measurement invariance of the Feeding Practices and Structure Questionnaire (FPSQ) subscales (9 constructs; 40 items) across 3 time points. Mothers participating in the NOURISH trial reported their feeding practices when children were aged 2, 3.7, and 5 years (N = 404). Confirmatory Factor Analysis (CFA) within a structural equation modelling framework was used. Comparisons of initial cross-sectional models followed by longitudinal modelling of subscales, resulted in the removal of 12 items, including two redundant or poorly performing subscales. The resulting 28-item FPSQ-28 comprised 7 multi-item subscales: Reward for Behaviour, Reward for Eating, Persuasive Feeding, Overt Restriction, Covert Restriction, Structured Meal Setting and Structured Meal Timing. All subscales showed good fit over 3 time points and each displayed at least partial scalar (thresholds equal) longitudinal measurement invariance. We recommend the use of a separate single item indicator to assess the family meal setting. This is the first study to examine longitudinal measurement invariance in a feeding practices questionnaire. Invariance was established, indicating that the subscales of the shortened FPSQ-28 can be used with mothers to validly assess change in 7 feeding constructs in samples of children aged 2-5 years of age. Copyright © 2016 Elsevier Ltd. All rights reserved.

The Forensic Symptoms Inventory-Revised (FSI-R Adults): Measurement and Structural Invariance Across Gender and Age Groups.

PubMed

van Horn, Joan E

2018-06-01

This article investigates the measurement and structural invariance of a newly developed self-report questionnaire, the Forensic Symptoms Inventory-Revised, aimed at measuring eight cognitive, emotional, and behavioral deficits (aggression, lack of social support, problematic substance use, lack of concentration, anger, poor self-regulation, impulsivity, and sexual problems) among adult forensic outpatients. The sample consisted of 716 outpatients (603 males, 113 females) with a mean age of 38.19 (SD = 12.47). Multi-Group Confirmatory Factor Analyses supported the measurement and structural invariance with respect to gender and age groups (18-23 years and ≥24 years). Between-group comparisons revealed that, compared to females, male outpatients reported more substance related problems, as well as incapacities to control verbal and/or physical aggression. Compared to adults, young adults displayed more inadequate self-regulation skills and reported more social support. These findings may promote the formulation of gender- and age-specific treatment goals.

Galilean field theories and conformal structure

NASA Astrophysics Data System (ADS)

Bagchi, Arjun; Chakrabortty, Joydeep; Mehra, Aditya

2018-04-01

We perform a detailed analysis of Galilean field theories, starting with free theories and then interacting theories. We consider non-relativistic versions of massless scalar and Dirac field theories before we go on to review our previous construction of Galilean Electrodynamics and Galilean Yang-Mills theory. We show that in all these cases, the field theories exhibit non-relativistic conformal structure (in appropriate dimensions). The surprising aspect of the analysis is that the non-relativistic conformal structure exhibited by these theories, unlike relativistic conformal invariance, becomes infinite dimensional even in spacetime dimensions greater than two. We then couple matter with Galilean gauge theories and show that there is a myriad of different sectors that arise in the non-relativistic limit from the parent relativistic theories. In every case, if the parent relativistic theory exhibited conformal invariance, we find an infinitely enhanced Galilean conformal invariance in the non-relativistic case. This leads us to suggest that infinite enhancement of symmetries in the non-relativistic limit is a generic feature of conformal field theories in any dimension.

Academic Performance Antecedent Scale: validation with native and recent immigrant children.

PubMed

Wang, Ru-Jer; Kuo, Kung-Bin; Cheng, Chien-Ming; Hsieh, Pei-Jung; Wang, Han-Yu; Chang, Ya-Wen; Shen, Chia-Yi

2013-06-01

This study aims to assess the measurement invariance of the three subscales of the newly developed Academic Performance Antecedent Scale (APAS)--School Factors, Mother's Parenting Style, and Individual Factors--across native and new immigrant children in Taiwan. The study sample comprised 527 Grade 4 students (M age = 10.4 yr., SD = 0.6), 263 boys and 264 girls. The three groups were urban and rural children of Taiwanese natives (n = 343, 65.1%), and 184 children with non-Taiwanese mothers (34.9%). The four-factor structure of the School Factors Subscale, the three-factor structure of the Mother's Parenting Style Subscale, and the five-factor structure of the Individual Factors Subscale all showed at least acceptable fit for the groups. In addition, metric invariance was confirmed for the School Factors and Individual Factors Subscales. Metric invariance was partially obtained for the Mother's Parenting Style Subscale. The findings provide validity evidences for cross-cultural generalizability of the APAS.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ferré, Grégoire; Maillet, Jean-Bernard; Stoltz, Gabriel

We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables us to directly compare different atomic environments with an arbitrary number of particles, without going through a space of reduced dimensionality (i.e., fingerprints) as an intermediate step. Moreover, this distance is naturally invariant through permutations of atoms, avoiding the time consuming associated minimization required by other common criteria (like the root mean square distance). Finally, the invariance through global rotations is accounted for by a minimization procedure in the space of rotations solved by Monte Carlo simulated annealing. A formal frameworkmore » is also introduced, showing that the distance we propose verifies the property of a metric on the space of atomic configurations. Two examples of applications are proposed. The first one consists in evaluating faithfulness of some fingerprints (or descriptors), i.e., their capacity to represent the structural information of a configuration. The second application concerns structural analysis, where our distance proves to be efficient in discriminating different local structures and even classifying their degree of similarity.« less

Geometrical Vortex Lattice Pinning and Melting in YBaCuO Submicron Bridges.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Papari, G. P.; Glatz, A.; Carillo, F.

Since the discovery of high-temperature superconductors (HTSs), most efforts of researchers have been focused on the fabrication of superconducting devices capable of immobilizing vortices, hence of operating at enhanced temperatures and magnetic fields. Recent findings that geometric restrictions may induce self-arresting hypervortices recovering the dissipation-free state at high fields and temperatures made superconducting strips a mainstream of superconductivity studies. Here in this paper we report on the geometrical melting of the vortex lattice in a wide YBCO submicron bridge preceded by magnetoresistance (MR) oscillations fingerprinting the underlying regular vortex structure. Combined magnetoresistance measurements and numerical simulations unambiguously relate the resistancemore » oscillations to the penetration of vortex rows with intermediate geometrical pinning and uncover the details of geometrical melting. Our findings offer a reliable and reproducible pathway for controlling vortices in geometrically restricted nanodevices and introduce a novel technique of geometrical spectroscopy, inferring detailed information of the structure of the vortex system through a combined use of MR curves and large-scale simulations.« less

Geometrical Vortex Lattice Pinning and Melting in YBaCuO Submicron Bridges.

DOE PAGES

Papari, G. P.; Glatz, A.; Carillo, F.; ...

2016-12-23

Since the discovery of high-temperature superconductors (HTSs), most efforts of researchers have been focused on the fabrication of superconducting devices capable of immobilizing vortices, hence of operating at enhanced temperatures and magnetic fields. Recent findings that geometric restrictions may induce self-arresting hypervortices recovering the dissipation-free state at high fields and temperatures made superconducting strips a mainstream of superconductivity studies. Here in this paper we report on the geometrical melting of the vortex lattice in a wide YBCO submicron bridge preceded by magnetoresistance (MR) oscillations fingerprinting the underlying regular vortex structure. Combined magnetoresistance measurements and numerical simulations unambiguously relate the resistancemore » oscillations to the penetration of vortex rows with intermediate geometrical pinning and uncover the details of geometrical melting. Our findings offer a reliable and reproducible pathway for controlling vortices in geometrically restricted nanodevices and introduce a novel technique of geometrical spectroscopy, inferring detailed information of the structure of the vortex system through a combined use of MR curves and large-scale simulations.« less

Reading off the nongeometric scalar potentials via the topological data of the compactifying Calabi-Yau manifolds

NASA Astrophysics Data System (ADS)

Shukla, Pramod

2016-10-01

In the context of studying the 4D-effective potentials of type IIB nongeometric flux compactifications, this article has a twofold goal. First, we present a modular invariant symplectic rearrangement of the tree level nongeometric scalar potential arising from a flux superpotential which includes the S-dual pairs of nongeometric fluxes (Q , P ), the standard NS-NS and RR three-form fluxes (F3 , H3 ), and the geometric flux (ω ). This "symplectic formulation" is valid for arbitrary numbers of Kähler moduli, and the complex structure moduli which are implicitly encoded in a set of symplectic matrices. In the second part, we further explicitly rewrite all the symplectic ingredients in terms of saxionic and axionic components of the complex structure moduli. The same leads to a compact form of the generic scalar potential being explicitly written out in terms of all the real moduli/axions. Moreover, the final form of the scalar potential needs only the knowledge of some topological data (such as Hodge numbers and the triple-intersection numbers) of the compactifying threefolds and their respective mirrors. Finally, we demonstrate how the same is equivalent to say that, for a given concrete example, various pieces of the scalar potential can be directly read off from our generic proposal, without the need of starting from the Kähler and superpotentials.

Transformation of light double cones in the human retina: the origin of trichromatism, of 4D-spatiotemporal vision, and of patchwise 4D Fourier transformation in Talbot imaging

NASA Astrophysics Data System (ADS)

Lauinger, Norbert

1997-09-01

The interpretation of the 'inverted' retina of primates as an 'optoretina' (a light cones transforming diffractive cellular 3D-phase grating) integrates the functional, structural, and oscillatory aspects of a cortical layer. It is therefore relevant to consider prenatal developments as a basis of the macro- and micro-geometry of the inner eye. This geometry becomes relevant for the postnatal trichromatic synchrony organization (TSO) as well as the adaptive levels of human vision. It is shown that the functional performances, the trichromatism in photopic vision, the monocular spatiotemporal 3D- and 4D-motion detection, as well as the Fourier optical image transformation with extraction of invariances all become possible. To transform light cones into reciprocal gratings especially the spectral phase conditions in the eikonal of the geometrical optical imaging before the retinal 3D-grating become relevant first, then in the von Laue resp. reciprocal von Laue equation for 3D-grating optics inside the grating and finally in the periodicity of Talbot-2/Fresnel-planes in the near-field behind the grating. It is becoming possible to technically realize -- at least in some specific aspects -- such a cortical optoretina sensor element with its typical hexagonal-concentric structure which leads to these visual functions.

Zonal-flow dynamics from a phase-space perspective

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ruiz, D. E.; Parker, J. B.; Shi, E. L.

The wave kinetic equation (WKE) describing drift-wave (DW) turbulence is widely used in the studies of zonal flows (ZFs) emerging from DW turbulence. But, this formulation neglects the exchange of enstrophy between DWs and ZFs and also ignores effects beyond the geometrical-optics limit. Furthermore, we derive a modified theory that takes both of these effects into account, while still treating DW quanta (“driftons”) as particles in phase space. The drifton dynamics is described by an equation of the Wigner–Moyal type, which is commonly known in the phase-space formulation of quantum mechanics. In the geometrical-optics limit, this formulation features additional termsmore » missing in the traditional WKE that ensure exact conservation of the total enstrophy of the system, in addition to the total energy, which is the only conserved invariant in previous theories based on the WKE. We present numerical simulations to illustrate the importance of these additional terms. The proposed formulation can be considered as a phase-space representation of the second-order cumulant expansion, or CE2.« less

Zonal-flow dynamics from a phase-space perspective

DOE PAGES

Ruiz, D. E.; Parker, J. B.; Shi, E. L.; ...

2016-12-16

The wave kinetic equation (WKE) describing drift-wave (DW) turbulence is widely used in the studies of zonal flows (ZFs) emerging from DW turbulence. But, this formulation neglects the exchange of enstrophy between DWs and ZFs and also ignores effects beyond the geometrical-optics limit. Furthermore, we derive a modified theory that takes both of these effects into account, while still treating DW quanta (“driftons”) as particles in phase space. The drifton dynamics is described by an equation of the Wigner–Moyal type, which is commonly known in the phase-space formulation of quantum mechanics. In the geometrical-optics limit, this formulation features additional termsmore » missing in the traditional WKE that ensure exact conservation of the total enstrophy of the system, in addition to the total energy, which is the only conserved invariant in previous theories based on the WKE. We present numerical simulations to illustrate the importance of these additional terms. The proposed formulation can be considered as a phase-space representation of the second-order cumulant expansion, or CE2.« less

Exact zeros of entanglement for arbitrary rank-two mixtures derived from a geometric view of the zero polytope

NASA Astrophysics Data System (ADS)

Osterloh, Andreas

2016-12-01

Here I present a method for how intersections of a certain density matrix of rank 2 with the zero polytope can be calculated exactly. This is a purely geometrical procedure which thereby is applicable to obtaining the zeros of SL- and SU-invariant entanglement measures of arbitrary polynomial degree. I explain this method in detail for a recently unsolved problem. In particular, I show how a three-dimensional view, namely, in terms of the Bloch-sphere analogy, solves this problem immediately. To this end, I determine the zero polytope of the three-tangle, which is an exact result up to computer accuracy, and calculate upper bounds to its convex roof which are below the linearized upper bound. The zeros of the three-tangle (in this case) induced by the zero polytope (zero simplex) are exact values. I apply this procedure to a superposition of the four-qubit Greenberger-Horne-Zeilinger and W state. It can, however, be applied to every case one has under consideration, including an arbitrary polynomial convex-roof measure of entanglement and for arbitrary local dimension.

Self-accommodation of B19' martensite in Ti-Ni shape memory alloys. Part III. Analysis of habit plane variant clusters by the geometrically nonlinear theory

NASA Astrophysics Data System (ADS)

Inamura, T.; Nishiura, T.; Kawano, H.; Hosoda, H.; Nishida, M.

2012-06-01

Competition between the invariant plane (IP) condition at the habit plane, the twin orientation relation (OR) and the kinematic compatibility (KC) at the junction plane (JP) of self-accommodated B19‧ martensite in Ti-Ni was investigated via the geometrically nonlinear theory to understand the habit plane variant (HPV) clusters presented in Parts I and II of this work. As the IP condition cannot be satisfied simultaneously with KC, an additional rotation Q is necessary to form compatible JPs for all HPV pairs. The rotation J necessary to form the exact twin OR between the major correspondence variants (CVs) in each HPV was also examined. The observed HPV cluster was not the cluster with the smallest Q but the one satisfying Q = J with a { ? 1}B19‧ type I twin at JP. Both Q and J are crucial to understanding the various HPV clusters in realistic transformations. Finally, a scheme for the ideal HPV cluster composed of six HPVs is also proposed.

The Quest for Comparability: Studying the Invariance of the Teachers’ Sense of Self-Efficacy (TSES) Measure across Countries

PubMed Central

Scherer, Ronny; Jansen, Malte; Nilsen, Trude; Areepattamannil, Shaljan; Marsh, Herbert W.

2016-01-01

Teachers’ self-efficacy is an important motivational construct that is positively related to a variety of outcomes for both the teachers and their students. This study addresses challenges associated with the commonly used ‘Teachers’ Sense of Self-Efficacy (TSES)’ measure across countries and provides a synergism between substantive research on teachers’ self-efficacy and the novel methodological approach of exploratory structural equation modeling (ESEM). These challenges include adequately representing the conceptual overlap between the facets of self-efficacy in a measurement model (cross-loadings) and comparing means and factor structures across countries (measurement invariance). On the basis of the OECD Teaching and Learning International Survey (TALIS) 2013 data set comprising 32 countries (N = 164,687), we investigate the effects of cross-loadings in the TSES measurement model on the results of measurement invariance testing and the estimation of relations to external constructs (i.e., working experience, job satisfaction). To further test the robustness of our results, we replicate the 32-countries analyses for three selected sub-groups of countries (i.e., Nordic, East and South-East Asian, and Anglo-Saxon country clusters). For each of the TALIS 2013 participating countries, we found that the factor structure of the self-efficacy measure is better represented by ESEM than by confirmatory factor analysis (CFA) models that do not allow for cross-loadings. For both ESEM and CFA, only metric invariance could be achieved. Nevertheless, invariance levels beyond metric invariance are better achieved with ESEM within selected country clusters. Moreover, the existence of cross-loadings did not affect the relations between the dimensions of teachers’ self-efficacy and external constructs. Overall, this study shows that a conceptual overlap between the facets of self-efficacy exists and can be well-represented by ESEM. We further argue for the cross-cultural generalizability of the corresponding measurement model. PMID:26959236

The Quest for Comparability: Studying the Invariance of the Teachers' Sense of Self-Efficacy (TSES) Measure across Countries.

PubMed

Scherer, Ronny; Jansen, Malte; Nilsen, Trude; Areepattamannil, Shaljan; Marsh, Herbert W

2016-01-01

Teachers' self-efficacy is an important motivational construct that is positively related to a variety of outcomes for both the teachers and their students. This study addresses challenges associated with the commonly used 'Teachers' Sense of Self-Efficacy (TSES)' measure across countries and provides a synergism between substantive research on teachers' self-efficacy and the novel methodological approach of exploratory structural equation modeling (ESEM). These challenges include adequately representing the conceptual overlap between the facets of self-efficacy in a measurement model (cross-loadings) and comparing means and factor structures across countries (measurement invariance). On the basis of the OECD Teaching and Learning International Survey (TALIS) 2013 data set comprising 32 countries (N = 164,687), we investigate the effects of cross-loadings in the TSES measurement model on the results of measurement invariance testing and the estimation of relations to external constructs (i.e., working experience, job satisfaction). To further test the robustness of our results, we replicate the 32-countries analyses for three selected sub-groups of countries (i.e., Nordic, East and South-East Asian, and Anglo-Saxon country clusters). For each of the TALIS 2013 participating countries, we found that the factor structure of the self-efficacy measure is better represented by ESEM than by confirmatory factor analysis (CFA) models that do not allow for cross-loadings. For both ESEM and CFA, only metric invariance could be achieved. Nevertheless, invariance levels beyond metric invariance are better achieved with ESEM within selected country clusters. Moreover, the existence of cross-loadings did not affect the relations between the dimensions of teachers' self-efficacy and external constructs. Overall, this study shows that a conceptual overlap between the facets of self-efficacy exists and can be well-represented by ESEM. We further argue for the cross-cultural generalizability of the corresponding measurement model.

Does Assessment Type Matter? A Measurement Invariance Analysis of Online and Paper and Pencil Assessment of the Community Assessment of Psychic Experiences (CAPE)

PubMed Central

Vleeschouwer, Marloes; Schubart, Chris D.; Henquet, Cecile; Myin-Germeys, Inez; van Gastel, Willemijn A.; Hillegers, Manon H. J.; van Os, Jim J.; Boks, Marco P. M.; Derks, Eske M.

2014-01-01

Background The psychometric properties of an online test are not necessarily identical to its paper and pencil original. The aim of this study is to test whether the factor structure of the Community Assessment of Psychic Experiences (CAPE) is measurement invariant with respect to online vs. paper and pencil assessment. Method The factor structure of CAPE items assessed by paper and pencil (N = 796) was compared with the factor structure of CAPE items assessed by the Internet (N = 21,590) using formal tests for Measurement Invariance (MI). The effect size was calculated by estimating the Signed Item Difference in the Sample (SIDS) index and the Signed Test Difference in the Sample (STDS) for a hypothetical subject who scores 2 standard deviations above average on the latent dimensions. Results The more restricted Metric Invariance model showed a significantly worse fit compared to the less restricted Configural Invariance model (χ2(23) = 152.75, p<0.001). However, the SIDS indices appear to be small, with an average of −0.11. A STDS of −4.80 indicates that Internet sample members who score 2 standard deviations above average would be expected to score 4.80 points lower on the CAPE total scale (ranging from 42 to 114 points) than would members of the Paper sample with the same latent trait score. Conclusions Our findings did not support measurement invariance with respect to assessment method. Because of the small effect sizes, the measurement differences between the online assessed CAPE and its paper and pencil original can be neglected without major consequences for research purposes. However, a person with a high vulnerability for psychotic symptoms would score 4.80 points lower on the total scale if the CAPE is assessed online compared to paper and pencil assessment. Therefore, for clinical purposes, one should be cautious with online assessment of the CAPE. PMID:24465389

Second-order statistics of colour codes modulate transformations that effectuate varying degrees of scene invariance and illumination invariance.

PubMed

Mausfeld, Rainer; Andres, Johannes

2002-01-01

We argue, from an ethology-inspired perspective, that the internal concepts 'surface colours' and 'illumination colours' are part of the data format of two different representational primitives. Thus, the internal concept of 'colour' is not a unitary one but rather refers to two different types of 'data structure', each with its own proprietary types of parameters and relations. The relation of these representational structures is modulated by a class of parameterised transformations whose effects are mirrored in the idealised computational achievements of illumination invariance of colour codes, on the one hand, and scene invariance, on the other hand. Because the same characteristics of a light array reaching the eye can be physically produced in many different ways, the visual system, then, has to make an 'inference' whether a chromatic deviation of the space-averaged colour codes from the neutral point is due to a 'non-normal', ie chromatic, illumination or due to an imbalanced spectral reflectance composition. We provide evidence that the visual system uses second-order statistics of chromatic codes of a single view of a scene in order to modulate corresponding transformations. In our experiments we used centre surround configurations with inhomogeneous surrounds given by a random structure of overlapping circles, referred to as Seurat configurations. Each family of surrounds has a fixed space-average of colour codes, but differs with respect to the covariance matrix of colour codes of pixels that defines the chromatic variance along some chromatic axis and the covariance between luminance and chromatic channels. We found that dominant wavelengths of red-green equilibrium settings of the infield exhibited a stable and strong dependence on the chromatic variance of the surround. High variances resulted in a tendency towards 'scene invariance', low variances in a tendency towards 'illumination invariance' of the infield.

Longitudinal multigroup invariance analysis of the satisfaction with food-related life scale in university students.

PubMed

Schnettler, Berta; Miranda, Horacio; Miranda-Zapata, Edgardo; Salinas-Oñate, Natalia; Grunert, Klaus G; Lobos, Germán; Sepúlveda, José; Orellana, Ligia; Hueche, Clementina; Bonilla, Héctor

2017-06-01

This study examined longitudinal measurement invariance in the Satisfaction with Food-related Life (SWFL) scale using follow-up data from university students. We examined this measure of the SWFL in different groups of students, separated by various characteristics. Through non-probabilistic longitudinal sampling, 114 university students (65.8% female, mean age: 22.5) completed the SWFL questionnaire three times, over intervals of approximately one year. Confirmatory factor analysis was used to examine longitudinal measurement invariance. Two types of analysis were conducted: first, a longitudinal invariance by time, and second, a multigroup longitudinal invariance by sex, age, socio-economic status and place of residence during the study period. Results showed that the 3-item version of the SWFL exhibited strong longitudinal invariance (equal factor loadings and equal indicator intercepts). Longitudinal multigroup invariance analysis also showed that the 3-item version of the SWFL displays strong invariance by socio-economic status and place of residence during the study period over time. Nevertheless, it was only possible to demonstrate equivalence of the longitudinal factor structure among students of both sexes, and among those older and younger than 22 years. Generally, these findings suggest that the SWFL scale has satisfactory psychometric properties for longitudinal measurement invariance in university students with similar characteristics as the students that participated in this research. It is also possible to suggest that satisfaction with food-related life is associated with sex and age. Copyright © 2017 Elsevier Ltd. All rights reserved.

Conformational, electronic, and spectroscopic characterization of isophthalic acid (monomer and dimer structures) experimentally and by DFT

NASA Astrophysics Data System (ADS)

Bardak, F.; Karaca, C.; Bilgili, S.; Atac, A.; Mavis, T.; Asiri, A. M.; Karabacak, M.; Kose, E.

2016-08-01

Isophthalic acid (C6H4(CO2H)2) is a noteworthy organic compound widely used in coating and synthesis of resins and the production of commercially important polymers such as drink plastic bottles. The effects of isophthalic acid (IPA) on human health, toxicology, and biodegradability are the main focus of many researchers. Because structural and spectroscopic investigation of molecules provides a deep understanding of interactional behaviors of compounds, this study stands for exploring those features. Therefore, the spectroscopic, structural, electronic, and thermodynamical properties of IPA were thoroughly studied in this work experimentally using UV-Vis, 1H and 13C NMR, FT-IR, FT-Raman and theoretically via DFT and TD-DFT calculations. The UV-Vis absorption spectrum in water was taken in the region 200-400 nm. The NMR chemical shifts (1H and 13C) were recorded in DMSO solution. The infrared and Raman spectra of the solid IPA were recorded in the range of 4000-400 cm- 1 and 3500-50 cm- 1, respectively. DFT and TD-DFT calculations were performed at the level of B3LYP/6-311++G(d,p) in determination of geometrical structure, electronic structure analysis and normal mode. The 13C and 1H nuclear magnetic resonance (NMR) spectra were estimated by using the gauge-invariant atomic orbital (GIAO) method. The scaled quantum mechanics (SQM) method was used to determine the total energy distribution (TED) to assign the vibrational modes accurately. Weak interactions such as hydrogen bonding and Van der Walls were analyzed via reduced density gradient (RDG) analysis in monomeric and dimeric forms. Furthermore, the excitation energies, density of state (DOS) diagram, thermodynamical properties, molecular electro-static potential (MEP), and nonlinear optical (NLO) properties were obtained.

Impact of measurement invariance on construct correlations, mean differences, and relations with external correlates: an illustrative example using Big Five and RIASEC measures.

PubMed

Schmitt, Neal; Golubovich, Juliya; Leong, Frederick T L

2011-12-01

The impact of measurement invariance and the provision for partial invariance in confirmatory factor analytic models on factor intercorrelations, latent mean differences, and estimates of relations with external variables is investigated for measures of two sets of widely assessed constructs: Big Five personality and the six Holland interests (RIASEC). In comparing models that include provisions for partial invariance with models that do not, the results indicate quite small differences in parameter estimates involving the relations between factors, one relatively large standardized mean difference in factors between the subgroups compared and relatively small differences in the regression coefficients when the factors are used to predict external variables. The results provide support for the use of partially invariant models, but there does not seem to be a great deal of difference between structural coefficients when the measurement model does or does not include separate estimates of subgroup parameters that differ across subgroups. Future research should include simulations in which the impact of various factors related to invariance is estimated.

Liquid structure and temperature invariance of sound velocity in supercooled Bi melt

DOE Office of Scientific and Technical Information (OSTI.GOV)

Emuna, M.; Mayo, M.; Makov, G.

2014-03-07

Structural rearrangement of liquid Bi in the vicinity of the melting point has been proposed due to the unique temperature invariant sound velocity observed above the melting temperature, the low symmetry of Bi in the solid phase and the necessity of overheating to achieve supercooling. The existence of this structural rearrangement is examined by measurements on supercooled Bi. The sound velocity of liquid Bi was measured into the supercooled region to high accuracy and it was found to be invariant over a temperature range of ∼60°, from 35° above the melting point to ∼25° into the supercooled region. The structuralmore » origin of this phenomenon was explored by neutron diffraction structural measurements in the supercooled temperature range. These measurements indicate a continuous modification of the short range order in the melt. The structure of the liquid is analyzed within a quasi-crystalline model and is found to evolve continuously, similar to other known liquid pnictide systems. The results are discussed in the context of two competing hypotheses proposed to explain properties of liquid Bi near the melting: (i) liquid bismuth undergoes a structural rearrangement slightly above melting and (ii) liquid Bi exhibits a broad maximum in the sound velocity located incidentally at the melting temperature.« less

Aeroelasticity of Axially Loaded Aerodynamic Structures for Truss-Braced Wing Aircraft

NASA Technical Reports Server (NTRS)

Nguyen, Nhan; Ting, Eric; Lebofsky, Sonia

2015-01-01

This paper presents an aeroelastic finite-element formulation for axially loaded aerodynamic structures. The presence of axial loading causes the bending and torsional sitffnesses to change. For aircraft with axially loaded structures such as the truss-braced wing aircraft, the aeroelastic behaviors of such structures are nonlinear and depend on the aerodynamic loading exerted on these structures. Under axial strain, a tensile force is created which can influence the stiffness of the overall aircraft structure. This tension stiffening is a geometric nonlinear effect that needs to be captured in aeroelastic analyses to better understand the behaviors of these types of aircraft structures. A frequency analysis of a rotating blade structure is performed to demonstrate the analytical method. A flutter analysis of a truss-braced wing aircraft is performed to analyze the effect of geometric nonlinear effect of tension stiffening on the flutter speed. The results show that the geometric nonlinear tension stiffening effect can have a significant impact on the flutter speed prediction. In general, increased wing loading results in an increase in the flutter speed. The study illustrates the importance of accounting for the geometric nonlinear tension stiffening effect in analyzing the truss-braced wing aircraft.

Pictorial depth probed through relative sizes

PubMed Central

Wagemans, Johan; van Doorn, Andrea J; Koenderink, Jan J

2011-01-01

In the physical environment familiar size is an effective depth cue because the distance from the eye to an object equals the ratio of its physical size to its angular extent in the visual field. Such simple geometrical relations do not apply to pictorial space, since the eye itself is not in pictorial space, and consequently the notion “distance from the eye” is meaningless. Nevertheless, relative size in the picture plane is often used by visual artists to suggest depth differences. The depth domain has no natural origin, nor a natural unit; thus only ratios of depth differences could have an invariant significance. We investigate whether the pictorial relative size cue yields coherent depth structures in pictorial spaces. Specifically, we measure the depth differences for all pairs of points in a 20-point configuration in pictorial space, and we account for these observations through 19 independent parameters (the depths of the points modulo an arbitrary offset), with no meaningful residuals. We discuss a simple formal framework that allows one to handle individual differences. We also compare the depth scale obtained by way of this method with depth scales obtained in totally different ways, finding generally good agreement. PMID:23145258

On an inductive approach to the standard conjecture for a fibred complex variety with strong semistable degeneracies

NASA Astrophysics Data System (ADS)

Tankeev, S. G.

2017-12-01

We prove that Grothendieck's standard conjecture B(X) of Lefschetz type on the algebraicity of the operators \\ast and Λ of Hodge theory holds for a 4-dimensional smooth projective complex variety fibred over a smooth projective curve C provided that every degenerate fibre is a union of smooth irreducible components of multiplicity 1 with normal crossings, the standard conjecture B(X\\overlineη) holds for a generic geometric fibre X\\overlineη, there is at least one degenerate fibre X_δ and the rational cohomology rings H^\\ast(V_i,{Q}) and H^\\ast(V_i\\cap V_j,{Q}) of the irreducible components V_i of every degenerate fibre X_δ=V_1+ \\dots+ V_m are generated by classes of algebraic cycles. We obtain similar results for 3-dimensional fibred varieties with algebraic invariant cycles (defined by the smooth part π'\\colon X'\\to C' of the structure morphism π\\colon X\\to C) or with a degenerate fibre all of whose irreducible components E_i possess the property H^2(E_i,{Q})= \\operatorname{NS}(E_i)\\otimes{Z}{Q}.

Communication of Geometrical Structure and Its Relationship to Student Mathematical Achievement.

ERIC Educational Resources Information Center

Norrie, Alexander L.

The purpose of this study was to examine whether the mathematical structures inherent in grade 7 geometry curriculum objectives can be used to improve the communication of the objectives to students. Teacher inservice based upon geometrical properties and structures was combined with student teaching materials to try to improve student achievement…

Framework for Evaluating Loop Invariant Detection Games in Relation to Automated Dynamic Invariant Detectors

DTIC Science & Technology

2015-09-01

Detectability ...............................................................................................37 Figure 20. Excel VBA Codes for Checker...National Vulnerability Database OS Operating System SQL Structured Query Language VC Verification Condition VBA Visual Basic for Applications...checks each of these assertions for detectability by Daikon. The checker is an Excel Visual Basic for Applications ( VBA ) script that checks the

Cyberbullying and Cybervictimization within a Cross-Cultural Context: A Study of Canadian and Tanzanian Adolescents

ERIC Educational Resources Information Center

Shapka, Jennifer D.; Onditi, Hezron Z.; Collie, Rebecca J.; Lapidot-Lefler, Noam

2018-01-01

This study explored cyberbullying and cybervictimization (CBCV), for adolescents aged 11-15 from Tanzania (N = 426) and Canada (N = 592). Measurement invariance and model invariance was found for CBCV. In addition, multigroup structural equation modeling was used to explore several variables: age, gender, average hours online each day, accessing…

Testing the Cultural Differences of School Characteristics with Measurement Invariance

ERIC Educational Resources Information Center

Demir, Ergül

2016-01-01

In this study, it was aimed to model the school characteristics in multivariate structure, and according to this model, aimed to test the invariance of this model across five randomly selected countries and economies from PISA 2012 sample. It is thought that significant differences across group in the context of school characteristics have the…

Dyadic Coping in an Eastern European Context: Validity and Measurement Invariance of the Romanian Version of Dyadic Coping Inventory

ERIC Educational Resources Information Center

Rusu, Petruta P.; Hilpert, Peter; Turliuc, Maria N.; Bodenmann, Guy

2016-01-01

This study investigates the psychometric properties of the Romanian version of the Dyadic Coping Inventory with data from 510 married couples. The results confirm the theoretical factorial structure of the Dyadic Coping Inventory for both partners, indicating convergent validity, discriminate validity, and measurement invariance (across genders…

Testing Measurement Invariance and Latent Mean Differences across Gender Groups in College Students' Internet-Specific Epistemic Beliefs

ERIC Educational Resources Information Center

Chiu, Yen-Lin; Tsai, Chin-Chung; Liang, Jyh-Chong

2015-01-01

The purposes of this study were to investigate the measurement invariance and gender differences in the Internet-specific epistemic beliefs between male and female undergraduates. A total of 735 university students in Taiwan were surveyed using the Internet-specific epistemic beliefs questionnaire (ISEQ). By conducting structural equation modeling…

Using Multigroup Confirmatory Factor Analysis to Test Measurement Invariance in Raters: A Clinical Skills Examination Application

ERIC Educational Resources Information Center

Kahraman, Nilufer; Brown, Crystal B.

2015-01-01

Psychometric models based on structural equation modeling framework are commonly used in many multiple-choice test settings to assess measurement invariance of test items across examinee subpopulations. The premise of the current article is that they may also be useful in the context of performance assessment tests to test measurement invariance…

Initial singularity and pure geometric field theories

NASA Astrophysics Data System (ADS)

Wanas, M. I.; Kamal, Mona M.; Dabash, Tahia F.

2018-01-01

In the present article we use a modified version of the geodesic equation, together with a modified version of the Raychaudhuri equation, to study initial singularities. These modified equations are used to account for the effect of the spin-torsion interaction on the existence of initial singularities in cosmological models. Such models are the results of solutions of the field equations of a class of field theories termed pure geometric. The geometric structure used in this study is an absolute parallelism structure satisfying the cosmological principle. It is shown that the existence of initial singularities is subject to some mathematical (geometric) conditions. The scheme suggested for this study can be easily generalized.

Dirac structures in nonequilibrium thermodynamics

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Yoshimura, Hiroaki

2018-01-01

Dirac structures are geometric objects that generalize both Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems. In this paper, we show that the evolution equations for nonequilibrium thermodynamics admit an intrinsic formulation in terms of Dirac structures, both on the Lagrangian and the Hamiltonian settings. In the absence of irreversible processes, these Dirac structures reduce to canonical Dirac structures associated with canonical symplectic forms on phase spaces. Our geometric formulation of nonequilibrium thermodynamic thus consistently extends the geometric formulation of mechanics, to which it reduces in the absence of irreversible processes. The Dirac structures are associated with the variational formulation of nonequilibrium thermodynamics developed in the work of Gay-Balmaz and Yoshimura, J. Geom. Phys. 111, 169-193 (2017a) and are induced from a nonlinear nonholonomic constraint given by the expression of the entropy production of the system.

Target recognition for ladar range image using slice image

NASA Astrophysics Data System (ADS)

Xia, Wenze; Han, Shaokun; Wang, Liang

2015-12-01

A shape descriptor and a complete shape-based recognition system using slice images as geometric feature descriptor for ladar range images are introduced. A slice image is a two-dimensional image generated by three-dimensional Hough transform and the corresponding mathematical transformation. The system consists of two processes, the model library construction and recognition. In the model library construction process, a series of range images are obtained after the model object is sampled at preset attitude angles. Then, all the range images are converted into slice images. The number of slice images is reduced by clustering analysis and finding a representation to reduce the size of the model library. In the recognition process, the slice image of the scene is compared with the slice image in the model library. The recognition results depend on the comparison. Simulated ladar range images are used to analyze the recognition and misjudgment rates, and comparison between the slice image representation method and moment invariants representation method is performed. The experimental results show that whether in conditions without noise or with ladar noise, the system has a high recognition rate and low misjudgment rate. The comparison experiment demonstrates that the slice image has better representation ability than moment invariants.

Vertical-axis wind turbine experiments at full dynamic similarity

NASA Astrophysics Data System (ADS)

Duvvuri, Subrahmanyam; Miller, Mark; Brownstein, Ian; Dabiri, John; Hultmark, Marcus

2017-11-01

This study presents results from pressurized (upto 200 atm) wind tunnel tests of a self-spinning 5-blade model Vertical-Axis Wind Turbine (VAWT). The model is geometrically similar (scale ratio 1:22) to a commercially available VAWT, which has a rotor diameter of 2.17 meters and blade span of 3.66 meters, and is used at the Stanford university field lab. The use of pressurized air as working fluid allows for the unique ability to obtain full dynamic similarity with field conditions in terms of matched Reynolds numbers (Re), tip-speed ratios (λ), and Mach number (M). Tests were performed across a wide range of Re and λ, with the highest Re exceeding the maximum operational field Reynolds number (Remax) by a factor of 3. With an extended range of accessible Re conditions, the peak turbine power efficiency was seen to occur roughly at Re = 2 Remax and λ = 1 . Beyond Re > 2 Remax the turbine performance is invariant in Re for all λ. A clear demonstration of Reynolds number invariance for an actual full-scale wind turbine lends novelty to this study, and overall the results show the viability of the present experimental technique in testing turbines at field conditions.

Connectivity strategies for higher-order neural networks applied to pattern recognition

NASA Technical Reports Server (NTRS)

Spirkovska, Lilly; Reid, Max B.

1990-01-01

Different strategies for non-fully connected HONNs (higher-order neural networks) are discussed, showing that by using such strategies an input field of 128 x 128 pixels can be attained while still achieving in-plane rotation and translation-invariant recognition. These techniques allow HONNs to be used with the larger input scenes required for practical pattern-recognition applications. The number of interconnections that must be stored has been reduced by a factor of approximately 200,000 in a T/C case and about 2000 in a Space Shuttle/F-18 case by using regional connectivity. Third-order networks have been simulated using several connection strategies. The method found to work best is regional connectivity. The main advantages of this strategy are the following: (1) it considers features of various scales within the image and thus gets a better sample of what the image looks like; (2) it is invariant to shape-preserving geometric transformations, such as translation and rotation; (3) the connections are predetermined so that no extra computations are necessary during run time; and (4) it does not require any extra storage for recording which connections were formed.

Why coronal flux tubes have axially invariant cross-section

NASA Astrophysics Data System (ADS)

Bellan, Paul

2001-10-01

We present here a model that not only explains the long-standing mystery^1 of why solar coronal flux tubes tend towards having axially invariant cross-sections but also explains several other enigmatic features, namely: rotating jets emanating from the ends (surges), counter-streaming beams, ingestion of photospheric material, and elevated pressure/temperature compared to adjacent plasma. The model shows that when a steady current flows along a flux tube with a bulging middle (i.e., a flux tube that is initially produced by a potential magnetic field), non-conservative forces develop which accelerate fluid axially from both ends towards the middle. Remarkably, this axial pumping of fluid into the flux tube causes the flux tube cross-section and volume to decrease in a manner such that the flux tube develops an axial uniform cross-section as observed in coronal loops. The pumping process produces counter-rotating, counter-streaming Alfvenic bulk motion consistent with observations. Collision of the counter-streaming beams causes non-localized bulk heating. This picture also has relevance to astrophysical jets and coaxial spheromak guns and explains why these systems tend to form an axial jet along the geometric axis. Supported by USDOE. l ^1 J. A. Klimchuk, Solar Phys. 193, 53 (2000)

Why coronal flux tubes have axially invariant cross-section

NASA Astrophysics Data System (ADS)

Bellan, P. M.

2001-12-01

We present here a model that not only explains the long-standing mystery of why solar coronal flux tubes tend towards having axially in-variant cross-sections but also explains several other enigmatic features, namely: rotating jets emanating from the ends (surges), counter-streaming beams, ingestion of photospheric material, and elevated pressure/temperature compared to adjacent plasma. The model shows that when a steady current flows along a flux tube with a bulging middle (i.e., a flux tube that is initially produced by a potential magnetic field), non-conservative forces develop which accelerate fluid axially from both ends towards the middle. Remarkably, this axial pumping of fluid into the flux tube causes the flux tube cross-section and volume to decrease in a manner such that the flux tube develops an axial uniform cross-section as observed in coronal loops. The pumping process produces counter-rotating, counter-streaming Alfvenic bulk motion consistent with observations. Collision of the counter-streaming beams causes non-localized bulk heating. This picture also has relevance to astrophysical jets and coaxial spheromak guns and explains why these systems tend to form an axial jet along the geometric axis. Supported by USDOE. [1]J. A. Klimchuk, Solar Phys. 193, 53 (2000)

Revealing the Topology of Fermi-Surface Wave Functions from Magnetic Quantum Oscillations

NASA Astrophysics Data System (ADS)

Alexandradinata, A.; Wang, Chong; Duan, Wenhui; Glazman, Leonid

2018-01-01

The modern semiclassical theory of a Bloch electron in a magnetic field now encompasses the orbital magnetic moment and the geometric phase. These two notions are encoded in the Bohr-Sommerfeld quantization condition as a phase (λ ) that is subleading in powers of the field; λ is measurable in the phase offset of the de Haas-van Alphen oscillation, as well as of fixed-bias oscillations of the differential conductance in tunneling spectroscopy. In some solids and for certain field orientations, λ /π are robustly integer valued, owing to the symmetry of the extremal orbit; i.e., they are the topological invariants of magnetotransport. Our comprehensive symmetry analysis identifies solids in any (magnetic) space group for which λ is a topological invariant, as well as the symmetry-enforced degeneracy of Landau levels. The analysis is simplified by our formulation of ten (and only ten) symmetry classes for closed, Fermi-surface orbits. Case studies are discussed for graphene, transition metal dichalcogenides, 3D Weyl and Dirac metals, and crystalline and Z2 topological insulators. In particular, we point out that a π phase offset in the fundamental oscillation should not be viewed as a smoking gun for a 3D Dirac metal.