G-sequentially connectedness for topological groups with operations

NASA Astrophysics Data System (ADS)

Mucuk, Osman; Cakalli, Huseyin

2016-08-01

It is a well-known fact that for a Hausdorff topological group X, the limits of convergent sequences in X define a function denoted by lim from the set of all convergent sequences in X to X. This notion has been modified by Connor and Grosse-Erdmann for real functions by replacing lim with an arbitrary linear functional G defined on a linear subspace of the vector space of all real sequences. Recently some authors have extended the concept to the topological group setting and introduced the concepts of G-sequential continuity, G-sequential compactness and G-sequential connectedness. In this work, we present some results about G-sequentially closures, G-sequentially connectedness and fundamental system of G-sequentially open neighbourhoods for topological group with operations which include topological groups, topological rings without identity, R-modules, Lie algebras, Jordan algebras, and many others.

Topological charge quantization via path integration: An application of the Kustaanheimo-Stiefel transformation

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

Inomata, A.; Junker, G.; Wilson, R.

1993-08-01

The unified treatment of the Dirac monopole, the Schwinger monopole, and the Aharonov-Bahn problem by Barut and Wilson is revisited via a path integral approach. The Kustaanheimo-Stiefel transformation of space and time is utilized to calculate the path integral for a charged particle in the singular vector potential. In the process of dimensional reduction, a topological charge quantization rule is derived, which contains Dirac's quantization condition as a special case. 32 refs.

Segmentation of radiologic images with self-organizing maps: the segmentation problem transformed into a classification task

NASA Astrophysics Data System (ADS)

Pelikan, Erich; Vogelsang, Frank; Tolxdorff, Thomas

1996-04-01

The texture-based segmentation of x-ray images of focal bone lesions using topological maps is introduced. Texture characteristics are described by image-point correlation of feature images to feature vectors. For the segmentation, the topological map is labeled using an improved labeling strategy. Results of the technique are demonstrated on original and synthetic x-ray images and quantified with the aid of quality measures. In addition, a classifier-specific contribution analysis is applied for assessing the feature space.

Crystallographic Topology 2: Overview and Work in Progress

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

Johnson, C.K.

1999-08-01

This overview describes an application of contemporary geometric topology and stochastic process concepts to structural crystallography. In this application, crystallographic groups become orbifolds, crystal structures become Morse functions on orbifolds, and vibrating atoms in a crystal become vector valued Gaussian measures with the Radon-Nikodym property. Intended crystallographic benefits include new methods for visualization of space groups and crystal structures, analysis of the thermal motion patterns seen in ORTEP drawings, and a classification scheme for crystal structures based on their Heegaard splitting properties.

The effects of dissipation on topological mechanical systems

NASA Astrophysics Data System (ADS)

Xiong, Ye; Wang, Tianxiang; Tong, Peiqing

2016-09-01

We theoretically study the effects of isotropic dissipation in a topological mechanical system which is an analogue of Chern insulator in mechanical vibrational lattice. The global gauge invariance is still conserved in this system albeit it is destroyed by the dissipation in the quantum counterpart. The chiral edge states in this system are therefore robust against strong dissipation. The dissipation also causes a dispersion of damping for the eigenstates. It will modify the equation of motion of a wave packet by an extra effective force. After taking into account the Berry curvature in the wave vector space, the trace of a free wave packet in the real space should be curved, feinting to break the Newton’s first law.

Modeling and control of fuel cell based distributed generation systems

NASA Astrophysics Data System (ADS)

Jung, Jin Woo

This dissertation presents circuit models and control algorithms of fuel cell based distributed generation systems (DGS) for two DGS topologies. In the first topology, each DGS unit utilizes a battery in parallel to the fuel cell in a standalone AC power plant and a grid-interconnection. In the second topology, a Z-source converter, which employs both the L and C passive components and shoot-through zero vectors instead of the conventional DC/DC boost power converter in order to step up the DC-link voltage, is adopted for a standalone AC power supply. In Topology 1, two applications are studied: a standalone power generation (Single DGS Unit and Two DGS Units) and a grid-interconnection. First, dynamic model of the fuel cell is given based on electrochemical process. Second, two full-bridge DC to DC converters are adopted and their controllers are designed: an unidirectional full-bridge DC to DC boost converter for the fuel cell and a bidirectional full-bridge DC to DC buck/boost converter for the battery. Third, for a three-phase DC to AC inverter without or with a Delta/Y transformer, a discrete-time state space circuit model is given and two discrete-time feedback controllers are designed: voltage controller in the outer loop and current controller in the inner loop. And last, for load sharing of two DGS units and power flow control of two DGS units or the DGS connected to the grid, real and reactive power controllers are proposed. Particularly, for the grid-connected DGS application, a synchronization issue between an islanding mode and a paralleling mode to the grid is investigated, and two case studies are performed. To demonstrate the proposed circuit models and control strategies, simulation test-beds using Matlab/Simulink are constructed for each configuration of the fuel cell based DGS with a three-phase AC 120 V (L-N)/60 Hz/50 kVA and various simulation results are presented. In Topology 2, this dissertation presents system modeling, modified space vector PWM implementation (MSVPWM) and design of a closed-loop controller of the Z-source converter which utilizes L and C components and shoot-through zero vectors for the standalone AC power generation. The fuel cell system is modeled by an electrical R-C circuit in order to include slow dynamics of the fuel cells and a voltage-current characteristic of a cell is also considered. A discrete-time state space model is derived to implement digital control and a space vector pulse-width modulation (SVPWM) technique is modified to realize the shoot-through zero vectors that boost the DC-link voltage. Also, three discrete-time feedback controllers are designed: a discrete-time optimal voltage controller, a discrete-time sliding mode current controller, and a discrete-time PI DC-link voltage controller. Furthermore, an asymptotic observer is used to reduce the number of sensors and enhance the reliability of the system. To demonstrate the analyzed circuit model and proposed control strategy, various simulation results using Matlab/Simulink are presented under both light/heavy loads and linear/nonlinear loads for a three-phase AC 208 V (L-L)/60 Hz/10 kVA.

Representation and display of vector field topology in fluid flow data sets

NASA Technical Reports Server (NTRS)

Helman, James; Hesselink, Lambertus

1989-01-01

The visualization of physical processes in general and of vector fields in particular is discussed. An approach to visualizing flow topology that is based on the physics and mathematics underlying the physical phenomenon is presented. It involves determining critical points in the flow where the velocity vector vanishes. The critical points, connected by principal lines or planes, determine the topology of the flow. The complexity of the data is reduced without sacrificing the quantitative nature of the data set. By reducing the original vector field to a set of critical points and their connections, a representation of the topology of a two-dimensional vector field that is much smaller than the original data set but retains with full precision the information pertinent to the flow topology is obtained. This representation can be displayed as a set of points and tangent curves or as a graph. Analysis (including algorithms), display, interaction, and implementation aspects are discussed.

The effects of dissipation on topological mechanical systems

PubMed Central

Xiong, Ye; Wang, Tianxiang; Tong, Peiqing

2016-01-01

We theoretically study the effects of isotropic dissipation in a topological mechanical system which is an analogue of Chern insulator in mechanical vibrational lattice. The global gauge invariance is still conserved in this system albeit it is destroyed by the dissipation in the quantum counterpart. The chiral edge states in this system are therefore robust against strong dissipation. The dissipation also causes a dispersion of damping for the eigenstates. It will modify the equation of motion of a wave packet by an extra effective force. After taking into account the Berry curvature in the wave vector space, the trace of a free wave packet in the real space should be curved, feinting to break the Newton’s first law. PMID:27605247

Hamiltonian indices and rational spectral densities

NASA Technical Reports Server (NTRS)

Byrnes, C. I.; Duncan, T. E.

1980-01-01

Several (global) topological properties of various spaces of linear systems, particularly symmetric, lossless, and Hamiltonian systems, and multivariable spectral densities of fixed McMillan degree are announced. The study is motivated by a result asserting that on a connected but not simply connected manifold, it is not possible to find a vector field having a sink as its only critical point. In the scalar case, this is illustrated by showing that only on the space of McMillan degree = /Cauchy index/ = n, scalar transfer functions can one define a globally convergent vector field. This result holds both in discrete-time and for the nonautonomous case. With these motivations in mind, theorems of Bochner and Fogarty are used in showing that spaces of transfer functions defined by symmetry conditions are, in fact, smooth algebraic manifolds.

Time, space and equilibrium means of continuous vector functions on the phase space of a dynamical system

NASA Astrophysics Data System (ADS)

Gurevich, Boris M.; Tempel'man, Arcady A.

2010-05-01

For a dynamical system \\tau with 'time' \\mathbb Z^d and compact phase space X, we introduce three subsets of the space \\mathbb R^m related to a continuous function f\\colon X\\to\\mathbb R^m: the set of time means of f and two sets of space means of f, namely those corresponding to all \\tau-invariant probability measures and those corresponding to some equilibrium measures on X. The main results concern topological properties of these sets of means and their mutual position. Bibliography: 18 titles.

Polarization pattern of vector vortex beams generated by q-plates with different topological charges.

PubMed

Cardano, Filippo; Karimi, Ebrahim; Slussarenko, Sergei; Marrucci, Lorenzo; de Lisio, Corrado; Santamato, Enrico

2012-04-01

We describe the polarization topology of the vector beams emerging from a patterned birefringent liquid crystal plate with a topological charge q at its center (q-plate). The polarization topological structures for different q-plates and different input polarization states have been studied experimentally by measuring the Stokes parameters point-by-point in the beam transverse plane. Furthermore, we used a tuned q=1/2-plate to generate cylindrical vector beams with radial or azimuthal polarizations, with the possibility of switching dynamically between these two cases by simply changing the linear polarization of the input beam.

Topological magnetoelectric effects in microwave far-field radiation

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

Berezin, M.; Kamenetskii, E. O.; Shavit, R.

2016-07-21

Similar to electromagnetism, described by the Maxwell equations, the physics of magnetoelectric (ME) phenomena deals with the fundamental problem of the relationship between electric and magnetic fields. Despite a formal resemblance between the two notions, they concern effects of different natures. In general, ME-coupling effects manifest in numerous macroscopic phenomena in solids with space and time symmetry breakings. Recently, it was shown that the near fields in the proximity of a small ferrite particle with magnetic-dipolar-mode (MDM) oscillations have the space and time symmetry breakings and the topological properties of these fields are different from the topological properties of themore » free-space electromagnetic fields. Such MDM-originated fields—called magnetoelectric (ME) fields—carry both spin and orbital angular momenta. They are characterized by power-flow vortices and non-zero helicity. In this paper, we report on observation of the topological ME effects in far-field microwave radiation based on a small microwave antenna with a MDM ferrite resonator. We show that the microwave far-field radiation can be manifested with a torsion structure where an angle between the electric and magnetic field vectors varies. We discuss the question on observation of the regions of localized ME energy in far-field microwave radiation.« less

Pre-vector variational inequality

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

Lin, Lai-Jiu

1994-12-31

Let X be a Hausdorff topological vector space, (Y, D) be an ordered Hausdorff topological vector space ordered by convex cone D. Let L(X, Y) be the space of all bounded linear operator, E {improper_subset} X be a nonempty set, T : E {yields} L(X, Y), {eta} : E {times} E {yields} E be functions. For x, y {element_of} Y, we denote x {not_lt} y if y - x intD, where intD is the interior of D. We consider the following two problems: Find x {element_of} E such that < T(x), {eta}(y, x) > {not_lt} 0 for all y {element_of}more » E and find x {element_of} E, < T(x), {eta}(y, x) > {not_gt} 0 for all y {element_of} E and < T(x), {eta}(y, x) >{element_of} C{sub p}{sup w+} = {l_brace} {element_of} L(X, Y) {vert_bar}< l, {eta}(x, 0) >{not_lt} 0 for all x {element_of} E{r_brace} where < T(x), y > denotes linear operator T(x) at y, that is T(x), (y). We called Pre-VVIP the Pre-vector variational inequality problem and Pre-VCP complementary problem. If X = R{sup n}, Y = R, D = R{sub +} {eta}(y, x) = y - x, then our problem is the well-known variational inequality first studies by Hartman and Stampacchia. If Y = R, D = R{sub +}, {eta}(y, x) = y - x, our problem is the variational problem in infinite dimensional space. In this research, we impose different condition on T(x), {eta}, X, and < T(x), {eta}(y, x) > and investigate the existences theorem of these problems. As an application of one of our results, we establish the existence theorem of weak minimum of the problem. (P) V - min f(x) subject to x {element_of} E where f : X {yields} Y si a Frechet differentiable invex function.« less

Clustering Tree-structured Data on Manifold

PubMed Central

Lu, Na; Miao, Hongyu

2016-01-01

Tree-structured data usually contain both topological and geometrical information, and are necessarily considered on manifold instead of Euclidean space for appropriate data parameterization and analysis. In this study, we propose a novel tree-structured data parameterization, called Topology-Attribute matrix (T-A matrix), so the data clustering task can be conducted on matrix manifold. We incorporate the structure constraints embedded in data into the non-negative matrix factorization method to determine meta-trees from the T-A matrix, and the signature vector of each single tree can then be extracted by meta-tree decomposition. The meta-tree space turns out to be a cone space, in which we explore the distance metric and implement the clustering algorithm based on the concepts like Fréchet mean. Finally, the T-A matrix based clustering (TAMBAC) framework is evaluated and compared using both simulated data and real retinal images to illus trate its efficiency and accuracy. PMID:26660696

Three Dimensional Photonic Dirac Points in Metamaterials

NASA Astrophysics Data System (ADS)

Guo, Qinghua; Yang, Biao; Xia, Lingbo; Gao, Wenlong; Liu, Hongchao; Chen, Jing; Xiang, Yuanjiang; Zhang, Shuang

2017-11-01

Topological semimetals, representing a new topological phase that lacks a full band gap in bulk states and exhibiting nontrivial topological orders, recently have been extended to photonic systems, predominantly in photonic crystals and to a lesser extent metamaterials. Photonic crystal realizations of Dirac degeneracies are protected by various space symmetries, where Bloch modes span the spin and orbital subspaces. Here, we theoretically show that Dirac points can also be realized in effective media through the intrinsic degrees of freedom in electromagnetism under electromagnetic duality. A pair of spin-polarized Fermi-arc-like surface states is observed at the interface between air and the Dirac metamaterials. Furthermore, eigenreflection fields show the decoupling process from a Dirac point to two Weyl points. We also find the topological correlation between a Dirac point and vortex or vector beams in classical photonics. The experimental feasibility of our scheme is demonstrated by designing a realistic metamaterial structure. The theoretical proposal of the photonic Dirac point lays the foundation for unveiling the connection between intrinsic physics and global topology in electromagnetism.

Topological Photonics for Continuous Media

NASA Astrophysics Data System (ADS)

Silveirinha, Mario

Photonic crystals have revolutionized light-based technologies during the last three decades. Notably, it was recently discovered that the light propagation in photonic crystals may depend on some topological characteristics determined by the manner how the light states are mutually entangled. The usual topological classification of photonic crystals explores the fact that these structures are periodic. The periodicity is essential to ensure that the underlying wave vector space is a closed surface with no boundary. In this talk, we prove that it is possible calculate Chern invariants for a wide class of continuous bianisotropic electromagnetic media with no intrinsic periodicity. The nontrivial topology of the relevant continuous materials is linked with the emergence of edge states. Moreover, we will demonstrate that continuous photonic media with the time-reversal symmetry can be topologically characterized by a Z2 integer. This novel classification extends for the first time the theory of electronic topological insulators to a wide range of photonic platforms, and is expected to have an impact in the design of novel photonic systems that enable a topologically protected transport of optical energy. This work is supported in part by Fundacao para a Ciencia e a Tecnologia Grant Number PTDC/EEI-TEL/4543/2014.

A new theory of phylogeny inference through construction of multidimensional vector space.

PubMed

Kitazoe, Y; Kurihara, Y; Narita, Y; Okuhara, Y; Tominaga, A; Suzuki, T

2001-05-01

Here, a new theory of molecular phylogeny is developed in a multidimensional vector space (MVS). The molecular evolution is represented as a successive splitting of branch vectors in the MVS. The end points of these vectors are the extant species and indicate the specific directions reflected by their individual histories of evolution in the past. This representation makes it possible to infer the phylogeny (evolutionary histories) from the spatial positions of the end points. Search vectors are introduced to draw out the groups of species distributed around them. These groups are classified according to the nearby order of branches with them. A law of physics is applied to determine the species positions in the MVS. The species are regarded as the particles moving in time according to the equation of motion, finally falling into the lowest-energy state in spite of their randomly distributed initial condition. This falling into the ground state results in the construction of an MVS in which the relative distances between two particles are equal to the substitution distances. The species positions are obtained prior to the phylogeny inference. Therefore, as the number of species increases, the species vectors can be more specific in an MVS of a larger size, such that the vector analysis gives a more stable and reliable topology. The efficacy of the present method was examined by using computer simulations of molecular evolution in which all the branch- and end-point sequences of the trees are known in advance. In the phylogeny inference from the end points with 100 multiple data sets, the present method consistently reconstructed the correct topologies, in contrast to standard methods. In applications to 185 vertebrates in the alpha-hemoglobin, the vector analysis drew out the two lineage groups of birds and mammals. A core member of the mammalian radiation appeared at the base of the mammalian lineage. Squamates were isolated from the bird lineage to compose the outgroup, while the other living reptilians were directly coupled with birds without forming any sister groups. This result is in contrast to the morphological phylogeny and is also different from those of recent molecular analyses.

PSOFuzzySVM-TMH: identification of transmembrane helix segments using ensemble feature space by incorporated fuzzy support vector machine.

PubMed

Hayat, Maqsood; Tahir, Muhammad

2015-08-01

Membrane protein is a central component of the cell that manages intra and extracellular processes. Membrane proteins execute a diversity of functions that are vital for the survival of organisms. The topology of transmembrane proteins describes the number of transmembrane (TM) helix segments and its orientation. However, owing to the lack of its recognized structures, the identification of TM helix and its topology through experimental methods is laborious with low throughput. In order to identify TM helix segments reliably, accurately, and effectively from topogenic sequences, we propose the PSOFuzzySVM-TMH model. In this model, evolutionary based information position specific scoring matrix and discrete based information 6-letter exchange group are used to formulate transmembrane protein sequences. The noisy and extraneous attributes are eradicated using an optimization selection technique, particle swarm optimization, from both feature spaces. Finally, the selected feature spaces are combined in order to form ensemble feature space. Fuzzy-support vector Machine is utilized as a classification algorithm. Two benchmark datasets, including low and high resolution datasets, are used. At various levels, the performance of the PSOFuzzySVM-TMH model is assessed through 10-fold cross validation test. The empirical results reveal that the proposed framework PSOFuzzySVM-TMH outperforms in terms of classification performance in the examined datasets. It is ascertained that the proposed model might be a useful and high throughput tool for academia and research community for further structure and functional studies on transmembrane proteins.

Dynamics in the Decompositions Approach to Quantum Mechanics

NASA Astrophysics Data System (ADS)

Harding, John

2017-12-01

In Harding (Trans. Amer. Math. Soc. 348(5), 1839-1862 1996) it was shown that the direct product decompositions of any non-empty set, group, vector space, and topological space X form an orthomodular poset Fact X. This is the basis for a line of study in foundational quantum mechanics replacing Hilbert spaces with other types of structures. Here we develop dynamics and an abstract version of a time independent Schrödinger's equation in the setting of decompositions by considering representations of the group of real numbers in the automorphism group of the orthomodular poset Fact X of decompositions.

The Ehrenfest force field: Topology and consequences for the definition of an atom in a molecule.

PubMed

Martín Pendás, A; Hernández-Trujillo, J

2012-10-07

The Ehrenfest force is the force acting on the electrons in a molecule due to the presence of the other electrons and the nuclei. There is an associated force field in three-dimensional space that is obtained by the integration of the corresponding Hermitian quantum force operator over the spin coordinates of all of the electrons and the space coordinates of all of the electrons but one. This paper analyzes the topology induced by this vector field and its consequences for the definition of molecular structure and of an atom in a molecule. Its phase portrait reveals: that the nuclei are attractors of the Ehrenfest force, the existence of separatrices yielding a dense partitioning of three-dimensional space into disjoint regions, and field lines connecting the attractors through these separatrices. From the numerical point of view, when the Ehrenfest force field is obtained as minus the divergence of the kinetic stress tensor, the induced topology was found to be highly sensitive to choice of gaussian basis sets at long range. Even the use of large split valence and highly uncontracted basis sets can yield spurious critical points that may alter the number of attraction basins. Nevertheless, at short distances from the nuclei, in general, the partitioning of three-dimensional space with the Ehrenfest force field coincides with that induced by the gradient field of the electron density. However, exceptions are found in molecules where the electron density yields results in conflict with chemical intuition. In these cases, the molecular graphs of the Ehrenfest force field reveal the expected atomic connectivities. This discrepancy between the definition of an atom in a molecule between the two vector fields casts some doubts on the physical meaning of the integration of Ehrenfest forces over the basins of the electron density.

Topological side-chain classification of beta-turns: ideal motifs for peptidomimetic development.

PubMed

Tran, Tran Trung; McKie, Jim; Meutermans, Wim D F; Bourne, Gregory T; Andrews, Peter R; Smythe, Mark L

2005-08-01

Beta-turns are important topological motifs for biological recognition of proteins and peptides. Organic molecules that sample the side chain positions of beta-turns have shown broad binding capacity to multiple different receptors, for example benzodiazepines. Beta-turns have traditionally been classified into various types based on the backbone dihedral angles (phi2, psi2, phi3 and psi3). Indeed, 57-68% of beta-turns are currently classified into 8 different backbone families (Type I, Type II, Type I', Type II', Type VIII, Type VIa1, Type VIa2 and Type VIb and Type IV which represents unclassified beta-turns). Although this classification of beta-turns has been useful, the resulting beta-turn types are not ideal for the design of beta-turn mimetics as they do not reflect topological features of the recognition elements, the side chains. To overcome this, we have extracted beta-turns from a data set of non-homologous and high-resolution protein crystal structures. The side chain positions, as defined by C(alpha)-C(beta) vectors, of these turns have been clustered using the kth nearest neighbor clustering and filtered nearest centroid sorting algorithms. Nine clusters were obtained that cluster 90% of the data, and the average intra-cluster RMSD of the four C(alpha)-C(beta) vectors is 0.36. The nine clusters therefore represent the topology of the side chain scaffold architecture of the vast majority of beta-turns. The mean structures of the nine clusters are useful for the development of beta-turn mimetics and as biological descriptors for focusing combinatorial chemistry towards biologically relevant topological space.

Machine Learning Prediction of the Energy Gap of Graphene Nanoflakes Using Topological Autocorrelation Vectors.

PubMed

Fernandez, Michael; Abreu, Jose I; Shi, Hongqing; Barnard, Amanda S

2016-11-14

The possibility of band gap engineering in graphene opens countless new opportunities for application in nanoelectronics. In this work, the energy gaps of 622 computationally optimized graphene nanoflakes were mapped to topological autocorrelation vectors using machine learning techniques. Machine learning modeling revealed that the most relevant correlations appear at topological distances in the range of 1 to 42 with prediction accuracy higher than 80%. The data-driven model can statistically discriminate between graphene nanoflakes with different energy gaps on the basis of their molecular topology.

Topological events on the lines of circular polarization in nonparaxial vector optical fields.

PubMed

Freund, Isaac

2017-02-01

In nonparaxial vector optical fields, the following topological events are shown to occur in apparent violation of charge conservation: as one translates the observation plane along a line of circular polarization (a C line), the points on the line (C points) are seen to change not only the signs of their topological charges, but also their handedness, and, at turning points on the line, paired C points with the same topological charge and opposite handedness are seen to nucleate. These counter-intuitive events cannot occur in paraxial fields.

Cross-entropy embedding of high-dimensional data using the neural gas model.

PubMed

Estévez, Pablo A; Figueroa, Cristián J; Saito, Kazumi

2005-01-01

A cross-entropy approach to mapping high-dimensional data into a low-dimensional space embedding is presented. The method allows to project simultaneously the input data and the codebook vectors, obtained with the Neural Gas (NG) quantizer algorithm, into a low-dimensional output space. The aim of this approach is to preserve the relationship defined by the NG neighborhood function for each pair of input and codebook vectors. A cost function based on the cross-entropy between input and output probabilities is minimized by using a Newton-Raphson method. The new approach is compared with Sammon's non-linear mapping (NLM) and the hierarchical approach of combining a vector quantizer such as the self-organizing feature map (SOM) or NG with the NLM recall algorithm. In comparison with these techniques, our method delivers a clear visualization of both data points and codebooks, and it achieves a better mapping quality in terms of the topology preservation measure q(m).

Metrics for comparing neuronal tree shapes based on persistent homology.

PubMed

Li, Yanjie; Wang, Dingkang; Ascoli, Giorgio A; Mitra, Partha; Wang, Yusu

2017-01-01

As more and more neuroanatomical data are made available through efforts such as NeuroMorpho.Org and FlyCircuit.org, the need to develop computational tools to facilitate automatic knowledge discovery from such large datasets becomes more urgent. One fundamental question is how best to compare neuron structures, for instance to organize and classify large collection of neurons. We aim to develop a flexible yet powerful framework to support comparison and classification of large collection of neuron structures efficiently. Specifically we propose to use a topological persistence-based feature vectorization framework. Existing methods to vectorize a neuron (i.e, convert a neuron to a feature vector so as to support efficient comparison and/or searching) typically rely on statistics or summaries of morphometric information, such as the average or maximum local torque angle or partition asymmetry. These simple summaries have limited power in encoding global tree structures. Based on the concept of topological persistence recently developed in the field of computational topology, we vectorize each neuron structure into a simple yet informative summary. In particular, each type of information of interest can be represented as a descriptor function defined on the neuron tree, which is then mapped to a simple persistence-signature. Our framework can encode both local and global tree structure, as well as other information of interest (electrophysiological or dynamical measures), by considering multiple descriptor functions on the neuron. The resulting persistence-based signature is potentially more informative than simple statistical summaries (such as average/mean/max) of morphometric quantities-Indeed, we show that using a certain descriptor function will give a persistence-based signature containing strictly more information than the classical Sholl analysis. At the same time, our framework retains the efficiency associated with treating neurons as points in a simple Euclidean feature space, which would be important for constructing efficient searching or indexing structures over them. We present preliminary experimental results to demonstrate the effectiveness of our persistence-based neuronal feature vectorization framework.

Metrics for comparing neuronal tree shapes based on persistent homology

PubMed Central

Li, Yanjie; Wang, Dingkang; Ascoli, Giorgio A.; Mitra, Partha

2017-01-01

As more and more neuroanatomical data are made available through efforts such as NeuroMorpho.Org and FlyCircuit.org, the need to develop computational tools to facilitate automatic knowledge discovery from such large datasets becomes more urgent. One fundamental question is how best to compare neuron structures, for instance to organize and classify large collection of neurons. We aim to develop a flexible yet powerful framework to support comparison and classification of large collection of neuron structures efficiently. Specifically we propose to use a topological persistence-based feature vectorization framework. Existing methods to vectorize a neuron (i.e, convert a neuron to a feature vector so as to support efficient comparison and/or searching) typically rely on statistics or summaries of morphometric information, such as the average or maximum local torque angle or partition asymmetry. These simple summaries have limited power in encoding global tree structures. Based on the concept of topological persistence recently developed in the field of computational topology, we vectorize each neuron structure into a simple yet informative summary. In particular, each type of information of interest can be represented as a descriptor function defined on the neuron tree, which is then mapped to a simple persistence-signature. Our framework can encode both local and global tree structure, as well as other information of interest (electrophysiological or dynamical measures), by considering multiple descriptor functions on the neuron. The resulting persistence-based signature is potentially more informative than simple statistical summaries (such as average/mean/max) of morphometric quantities—Indeed, we show that using a certain descriptor function will give a persistence-based signature containing strictly more information than the classical Sholl analysis. At the same time, our framework retains the efficiency associated with treating neurons as points in a simple Euclidean feature space, which would be important for constructing efficient searching or indexing structures over them. We present preliminary experimental results to demonstrate the effectiveness of our persistence-based neuronal feature vectorization framework. PMID:28809960

Correlation between topological structure and its properties in dynamic singular vector fields.

PubMed

Vasilev, Vasyl; Soskin, Marat

2016-04-20

A new technique for establishment of topology measurements for static and dynamic singular vector fields is elaborated. It is based on precise measurement of the 3D landscape of ellipticity distribution for a checked singular optical field with C points on the tops of ellipticity hills. Vector fields possess three-component topology: areas with right-hand (RH) and left-hand (LH) ellipses, and delimiting those L lines as the singularities of handedness. The azimuth map of polarization ellipses is common for both RH and LH ellipses of vector fields and do not feel L lines. The strict rules were confirmed experimentally, which define the connection between the sign of underlying optical vortices and morphological parameters of upper-lying C points. Percolation phenomena explain their realization in-between singular vector fields and long duration of their chains of 10³  s order.

Some remarks on the topology of hyperbolic actions of Rn on n-manifolds

NASA Astrophysics Data System (ADS)

Bouloc, Damien

2017-11-01

This paper contains some results on the topology of a nondegenerate action of Rn on a compact connected n-manifold M when the action is totally hyperbolic (i.e. its toric degree is zero). We study the R-action generated by a fixed vector of Rn, that provides some results on the number of hyperbolic domains and the number of fixed points of the action. We study with more details the case of the 2-sphere, in particular we investigate some combinatorial properties of the associated 4-valent graph embedded in S2. We also construct hyperbolic actions in dimension 3, on the sphere S3 and on the projective space RP3.

Visualization of Morse connection graphs for topologically rich 2D vector fields.

PubMed

Szymczak, Andrzej; Sipeki, Levente

2013-12-01

Recent advances in vector field topologymake it possible to compute its multi-scale graph representations for autonomous 2D vector fields in a robust and efficient manner. One of these representations is a Morse Connection Graph (MCG), a directed graph whose nodes correspond to Morse sets, generalizing stationary points and periodic trajectories, and arcs - to trajectories connecting them. While being useful for simple vector fields, the MCG can be hard to comprehend for topologically rich vector fields, containing a large number of features. This paper describes a visual representation of the MCG, inspired by previous work on graph visualization. Our approach aims to preserve the spatial relationships between the MCG arcs and nodes and highlight the coherent behavior of connecting trajectories. Using simulations of ocean flow, we show that it can provide useful information on the flow structure. This paper focuses specifically on MCGs computed for piecewise constant (PC) vector fields. In particular, we describe extensions of the PC framework that make it more flexible and better suited for analysis of data on complex shaped domains with a boundary. We also describe a topology simplification scheme that makes our MCG visualizations less ambiguous. Despite the focus on the PC framework, our approach could also be applied to graph representations or topological skeletons computed using different methods.

GRASS GIS: The first Open Source Temporal GIS

NASA Astrophysics Data System (ADS)

Gebbert, Sören; Leppelt, Thomas

2015-04-01

GRASS GIS is a full featured, general purpose Open Source geographic information system (GIS) with raster, 3D raster and vector processing support[1]. Recently, time was introduced as a new dimension that transformed GRASS GIS into the first Open Source temporal GIS with comprehensive spatio-temporal analysis, processing and visualization capabilities[2]. New spatio-temporal data types were introduced in GRASS GIS version 7, to manage raster, 3D raster and vector time series. These new data types are called space time datasets. They are designed to efficiently handle hundreds of thousands of time stamped raster, 3D raster and vector map layers of any size. Time stamps can be defined as time intervals or time instances in Gregorian calendar time or relative time. Space time datasets are simplifying the processing and analysis of large time series in GRASS GIS, since these new data types are used as input and output parameter in temporal modules. The handling of space time datasets is therefore equal to the handling of raster, 3D raster and vector map layers in GRASS GIS. A new dedicated Python library, the GRASS GIS Temporal Framework, was designed to implement the spatio-temporal data types and their management. The framework provides the functionality to efficiently handle hundreds of thousands of time stamped map layers and their spatio-temporal topological relations. The framework supports reasoning based on the temporal granularity of space time datasets as well as their temporal topology. It was designed in conjunction with the PyGRASS [3] library to support parallel processing of large datasets, that has a long tradition in GRASS GIS [4,5]. We will present a subset of more than 40 temporal modules that were implemented based on the GRASS GIS Temporal Framework, PyGRASS and the GRASS GIS Python scripting library. These modules provide a comprehensive temporal GIS tool set. The functionality range from space time dataset and time stamped map layer management over temporal aggregation, temporal accumulation, spatio-temporal statistics, spatio-temporal sampling, temporal algebra, temporal topology analysis, time series animation and temporal topology visualization to time series import and export capabilities with support for NetCDF and VTK data formats. We will present several temporal modules that support parallel processing of raster and 3D raster time series. [1] GRASS GIS Open Source Approaches in Spatial Data Handling In Open Source Approaches in Spatial Data Handling, Vol. 2 (2008), pp. 171-199, doi:10.1007/978-3-540-74831-19 by M. Neteler, D. Beaudette, P. Cavallini, L. Lami, J. Cepicky edited by G. Brent Hall, Michael G. Leahy [2] Gebbert, S., Pebesma, E., 2014. A temporal GIS for field based environmental modeling. Environ. Model. Softw. 53, 1-12. [3] Zambelli, P., Gebbert, S., Ciolli, M., 2013. Pygrass: An Object Oriented Python Application Programming Interface (API) for Geographic Resources Analysis Support System (GRASS) Geographic Information System (GIS). ISPRS Intl Journal of Geo-Information 2, 201-219. [4] Löwe, P., Klump, J., Thaler, J. (2012): The FOSS GIS Workbench on the GFZ Load Sharing Facility compute cluster, (Geophysical Research Abstracts Vol. 14, EGU2012-4491, 2012), General Assembly European Geosciences Union (Vienna, Austria 2012). [5] Akhter, S., Aida, K., Chemin, Y., 2010. "GRASS GIS on High Performance Computing with MPI, OpenMP and Ninf-G Programming Framework". ISPRS Conference, Kyoto, 9-12 August 2010

Magnetic reconnection in terms of catastrophe theory

NASA Astrophysics Data System (ADS)

Echkina, E. Y.; Inovenkov, I. N.; Nefedov, V. V.

2017-12-01

Magnetic field line reconnection (magnetic reconnection) is a phenomenon that occurs in space and laboratory plasma. Magnetic reconnection allows both the change the magnetic topology and the conversion of the magnetic energy into energy of fast particles. The critical point (critical line or plane in higher dimensional cases) of the magnetic field play an important role in process of magnetic reconnection, as in its neighborhood occurs a change of its topology of a magnetic field and redistribution of magnetic field energy. A lot of literature is devoted to the analytical and numerical investigation of the reconnection process. The main result of these investigations as the result of magnetic reconnection the current sheet is formed and the magnetic topology is changed. While the studies of magnetic reconnection in 2D and 3D configurations have a led to several important results, many questions remain open, including the behavior of a magnetic field in the neighborhood of a critical point of high order. The magnetic reconnection problem is closely related to the problem of the structural stability of vector fields. Since the magnetic field topology changes during both spontaneous and induced magnetic reconnection, it is natural to expect that the magnetic field should evolve from a structurally unstable into a structurally stable configuration. Note that, in this case, the phenomenon under analysis is more complicated since, during magnetic reconnection in a highly conducting plasma, we deal with the non-linear interaction between two vector fields: the magnetic field and the field of the plasma velocities. The aim of our article is to consider the process of magnetic reconnection and transformation of the magnetic topology from the viewpoint of catastrophe theory. Bifurcations in similar configurations (2D magnetic configuration with null high order point) with varying parameters were thoroughly discussed in a monograph by Poston and Stewart.

Towards a Phylogenetic Approach to the Composition of Species Complexes in the North and Central American Triatoma, Vectors of Chagas Disease

PubMed Central

de la Rúa, Nicholas M.; Bustamante, Dulce M.; Menes, Marianela; Stevens, Lori; Monroy, Carlota; Kilpatrick, William; Rizzo, Donna; Klotz, Stephen A.; Schmidt, Justin; Axen, Heather J.; Dorn, Patricia L.

2014-01-01

Phylogenetic relationships of insect vectors of parasitic diseases are important for understanding the evolution of epidemiologically relevant traits, and may be useful in vector control. The subfamily Triatominae (Hemiptera:Reduviidae) includes ~140 extant species arranged in five tribes comprised of 15 genera. The genus Triatoma is the most species-rich and contains important vectors of Trypanosoma cruzi, the causative agent of Chagas disease. Triatoma species were grouped into complexes originally by morphology and more recently with the addition of information from molecular phylogenetics (the four-complex hypothesis); however, without a strict adherence to monophyly. To date, the validity of proposed species complexes has not been tested by statistical tests of topology. The goal of this study was to clarify the systematics of 19 Triatoma species from North and Central America. We inferred their evolutionary relatedness using two independent data sets: the complete nuclear Internal Transcribed Spacer-2 ribosomal DNA (ITS-2 rDNA) and head morphometrics. In addition, we used the Shimodaira-Hasegawa statistical test of topology to assess the fit of the data to a set of competing systematic hypotheses (topologies). An unconstrained topology inferred from the ITS-2 data was compared to topologies constrained based on the four-complex hypothesis or one inferred from our morphometry results. The unconstrained topology represents a statistically significant better fit of the molecular data than either the four-complex or the morphometric topology. We propose an update to the composition of species complexes in the North and Central American Triatoma, based on a phylogeny inferred from ITS-2 as a first step towards updating the phylogeny of the complexes based on monophyly and statistical tests of topologies. PMID:24681261

Topological features of vector vortex beams perturbed with uniformly polarized light

PubMed Central

D’Errico, Alessio; Maffei, Maria; Piccirillo, Bruno; de Lisio, Corrado; Cardano, Filippo; Marrucci, Lorenzo

2017-01-01

Optical singularities manifesting at the center of vector vortex beams are unstable, since their topological charge is higher than the lowest value permitted by Maxwell’s equations. Inspired by conceptually similar phenomena occurring in the polarization pattern characterizing the skylight, we show how perturbations that break the symmetry of radially symmetric vector beams lead to the formation of a pair of fundamental and stable singularities, i.e. points of circular polarization. We prepare a superposition of a radial (or azimuthal) vector beam and a uniformly linearly polarized Gaussian beam; by varying the amplitudes of the two fields, we control the formation of pairs of these singular points and their spatial separation. We complete this study by applying the same analysis to vector vortex beams with higher topological charges, and by investigating the features that arise when increasing the intensity of the Gaussian term. Our results can find application in the context of singularimetry, where weak fields are measured by considering them as perturbations of unstable optical beams. PMID:28079134

Topological features of vector vortex beams perturbed with uniformly polarized light

NASA Astrophysics Data System (ADS)

D'Errico, Alessio; Maffei, Maria; Piccirillo, Bruno; de Lisio, Corrado; Cardano, Filippo; Marrucci, Lorenzo

2017-01-01

Optical singularities manifesting at the center of vector vortex beams are unstable, since their topological charge is higher than the lowest value permitted by Maxwell’s equations. Inspired by conceptually similar phenomena occurring in the polarization pattern characterizing the skylight, we show how perturbations that break the symmetry of radially symmetric vector beams lead to the formation of a pair of fundamental and stable singularities, i.e. points of circular polarization. We prepare a superposition of a radial (or azimuthal) vector beam and a uniformly linearly polarized Gaussian beam; by varying the amplitudes of the two fields, we control the formation of pairs of these singular points and their spatial separation. We complete this study by applying the same analysis to vector vortex beams with higher topological charges, and by investigating the features that arise when increasing the intensity of the Gaussian term. Our results can find application in the context of singularimetry, where weak fields are measured by considering them as perturbations of unstable optical beams.

Topological features of vector vortex beams perturbed with uniformly polarized light.

PubMed

D'Errico, Alessio; Maffei, Maria; Piccirillo, Bruno; de Lisio, Corrado; Cardano, Filippo; Marrucci, Lorenzo

2017-01-12

Optical singularities manifesting at the center of vector vortex beams are unstable, since their topological charge is higher than the lowest value permitted by Maxwell's equations. Inspired by conceptually similar phenomena occurring in the polarization pattern characterizing the skylight, we show how perturbations that break the symmetry of radially symmetric vector beams lead to the formation of a pair of fundamental and stable singularities, i.e. points of circular polarization. We prepare a superposition of a radial (or azimuthal) vector beam and a uniformly linearly polarized Gaussian beam; by varying the amplitudes of the two fields, we control the formation of pairs of these singular points and their spatial separation. We complete this study by applying the same analysis to vector vortex beams with higher topological charges, and by investigating the features that arise when increasing the intensity of the Gaussian term. Our results can find application in the context of singularimetry, where weak fields are measured by considering them as perturbations of unstable optical beams.

Some exact solutions for maximally symmetric topological defects in Anti de Sitter space

NASA Astrophysics Data System (ADS)

Alvarez, Orlando; Haddad, Matthew

2018-03-01

We obtain exact analytical solutions for a class of SO( l) Higgs field theories in a non-dynamic background n-dimensional anti de Sitter space. These finite transverse energy solutions are maximally symmetric p-dimensional topological defects where n = ( p + 1) + l. The radius of curvature of anti de Sitter space provides an extra length scale that allows us to study the equations of motion in a limit where the masses of the Higgs field and the massive vector bosons are both vanishing. We call this the double BPS limit. In anti de Sitter space, the equations of motion depend on both p and l. The exact analytical solutions are expressed in terms of standard special functions. The known exact analytical solutions are for kink-like defects ( p = 0 , 1 , 2 , . . . ; l = 1), vortex-like defects ( p = 1 , 2 , 3; l = 2), and the 't Hooft-Polyakov monopole ( p = 0; l = 3). A bonus is that the double BPS limit automatically gives a maximally symmetric classical glueball type solution. In certain cases where we did not find an analytic solution, we present numerical solutions to the equations of motion. The asymptotically exponentially increasing volume with distance of anti de Sitter space imposes different constraints than those found in the study of defects in Minkowski space.

Control of Grid Connected Photovoltaic System Using Three-Level T-Type Inverter

NASA Astrophysics Data System (ADS)

Zorig, Abdelmalik; Belkeiri, Mohammed; Barkat, Said; Rabhi, Abdelhamid

2016-08-01

Three-level T-Type inverter (3LT2I) topology has numerous advantageous compared to three-level neutral-point-clamped (NPC) inverter. The main benefits of 3LT2I inverter are the efficiency, inverter cost, switching losses, and the quality of output voltage waveforms. In this paper, a photovoltaic distributed generation system based on dual-stage topology of DC-DC boost converter and 3LT2I is introduced. To that end, a decoupling control strategy of 3LT2I is proposed to control the current injected into the grid, reactive power compensation, and DC-link voltage. The resulting system is able to extract the maximum power from photovoltaic generator, to achieve sinusoidal grid currents, and to ensure reactive power compensation. The voltage-balancing control of two split DC capacitors of the 3LT2I is achieved using three-level space vector modulation with balancing strategy based on the effective use of the redundant switching states of the inverter voltage vectors. The proposed system performance is investigated at different operating conditions.

Intelligent feature selection techniques for pattern classification of Lamb wave signals

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

Hinders, Mark K.; Miller, Corey A.

2014-02-18

Lamb wave interaction with flaws is a complex, three-dimensional phenomenon, which often frustrates signal interpretation schemes based on mode arrival time shifts predicted by dispersion curves. As the flaw severity increases, scattering and mode conversion effects will often dominate the time-domain signals, obscuring available information about flaws because multiple modes may arrive on top of each other. Even for idealized flaw geometries the scattering and mode conversion behavior of Lamb waves is very complex. Here, multi-mode Lamb waves in a metal plate are propagated across a rectangular flat-bottom hole in a sequence of pitch-catch measurements corresponding to the double crossholemore » tomography geometry. The flaw is sequentially deepened, with the Lamb wave measurements repeated at each flaw depth. Lamb wave tomography reconstructions are used to identify which waveforms have interacted with the flaw and thereby carry information about its depth. Multiple features are extracted from each of the Lamb wave signals using wavelets, which are then fed to statistical pattern classification algorithms that identify flaw severity. In order to achieve the highest classification accuracy, an optimal feature space is required but it’s never known a priori which features are going to be best. For structural health monitoring we make use of the fact that physical flaws, such as corrosion, will only increase over time. This allows us to identify feature vectors which are topologically well-behaved by requiring that sequential classes “line up” in feature vector space. An intelligent feature selection routine is illustrated that identifies favorable class distributions in multi-dimensional feature spaces using computational homology theory. Betti numbers and formal classification accuracies are calculated for each feature space subset to establish a correlation between the topology of the class distribution and the corresponding classification accuracy.« less

A split ubiquitin system to reveal topology and released peptides of membrane proteins.

PubMed

Li, Qiu-Ping; Wang, Shuai; Gou, Jin-Ying

2017-09-02

Membrane proteins define biological functions of membranes in cells. Extracellular peptides of transmembrane proteins receive signals from pathogens or environments, and are the major targets of drug developments. Despite of their essential roles, membrane proteins remain elusive in topological studies due to technique difficulties in their expressions and purifications. First, the target gene is cloned into a destination vector to fuse with C terminal ubiquitin at the N or C terminus. Then, Cub vector with target gene and Nub WT or Nub G vectors are transformed into AP4 or AP5 yeast cells, respectively. After mating, the diploid cells are dipped onto selection medium to check the growth. Topology of the target protein is determined according to Table 1. We present a split ubiquitin topology (SUT) analysis system to study the topology and truncation peptide of membrane proteins in a simple yeast experiment. In the SUT system, transcription activator (TA) fused with a nucleo-cytoplasmic protein shows strong auto-activation with both positive and negative control vectors. TA fused with the cytoplasmic end of membrane proteins activates reporter genes only with positive control vector with a wild type N terminal ubiquitin (Nub WT ). However, TA fused with the extracellular termini of membrane proteins can't activate reporter genes even with Nub WT . Interestingly,TA fused with the released peptide of a membrane protein shows autoactivation in the SUT system. The SUT system is a simple and fast experimental procedure complementary to computational predictions and large scale proteomic techniques. The preliminary data from SUT are valuable for pathogen recognitions and new drug developments.

Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion

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

Skraba, Primoz; Rosen, Paul; Wang, Bei

Vector field topology has been successfully applied to represent the structure of steady vector fields. Critical points, one of the essential components of vector field topology, play an important role in describing the complexity of the extracted structure. Simplifying vector fields via critical point cancellation has practical merit for interpreting the behaviors of complex vector fields such as turbulence. However, there is no effective technique that allows direct cancellation of critical points in 3D. This work fills this gap and introduces the first framework to directly cancel pairs or groups of 3D critical points in a hierarchical manner with amore » guaranteed minimum amount of perturbation based on their robustness, a quantitative measure of their stability. In addition, our framework does not require the extraction of the entire 3D topology, which contains non-trivial separation structures, and thus is computationally effective. Furthermore, our algorithm can remove critical points in any subregion of the domain whose degree is zero and handle complex boundary configurations, making it capable of addressing challenging scenarios that may not be resolved otherwise. Here, we apply our method to synthetic and simulation datasets to demonstrate its effectiveness.« less

Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion.

PubMed

Skraba, Primoz; Rosen, Paul; Wang, Bei; Chen, Guoning; Bhatia, Harsh; Pascucci, Valerio

2016-02-29

Vector field topology has been successfully applied to represent the structure of steady vector fields. Critical points, one of the essential components of vector field topology, play an important role in describing the complexity of the extracted structure. Simplifying vector fields via critical point cancellation has practical merit for interpreting the behaviors of complex vector fields such as turbulence. However, there is no effective technique that allows direct cancellation of critical points in 3D. This work fills this gap and introduces the first framework to directly cancel pairs or groups of 3D critical points in a hierarchical manner with a guaranteed minimum amount of perturbation based on their robustness, a quantitative measure of their stability. In addition, our framework does not require the extraction of the entire 3D topology, which contains non-trivial separation structures, and thus is computationally effective. Furthermore, our algorithm can remove critical points in any subregion of the domain whose degree is zero and handle complex boundary configurations, making it capable of addressing challenging scenarios that may not be resolved otherwise. We apply our method to synthetic and simulation datasets to demonstrate its effectiveness.

Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion

DOE PAGES

Skraba, Primoz; Rosen, Paul; Wang, Bei; ...

2016-02-29

Vector field topology has been successfully applied to represent the structure of steady vector fields. Critical points, one of the essential components of vector field topology, play an important role in describing the complexity of the extracted structure. Simplifying vector fields via critical point cancellation has practical merit for interpreting the behaviors of complex vector fields such as turbulence. However, there is no effective technique that allows direct cancellation of critical points in 3D. This work fills this gap and introduces the first framework to directly cancel pairs or groups of 3D critical points in a hierarchical manner with amore » guaranteed minimum amount of perturbation based on their robustness, a quantitative measure of their stability. In addition, our framework does not require the extraction of the entire 3D topology, which contains non-trivial separation structures, and thus is computationally effective. Furthermore, our algorithm can remove critical points in any subregion of the domain whose degree is zero and handle complex boundary configurations, making it capable of addressing challenging scenarios that may not be resolved otherwise. Here, we apply our method to synthetic and simulation datasets to demonstrate its effectiveness.« less

Autorotation

NASA Astrophysics Data System (ADS)

Bohr, Jakob; Markvorsen, Steen

2016-02-01

A continuous autorotation vector field along a framed space curve is defined, which describes the rotational progression of the frame. We obtain an exact integral for the length of the autorotation vector. This invokes the infinitesimal rotation vector of the frame progression and the unit vector field for the corresponding autorotation vector field. For closed curves we define an autorotation number whose integer value depends on the starting point of the curve. Upon curve deformations, the autorotation number is either constant, or can make a jump of (multiples of) plus-minus two, which corresponds to a change in rotation of multiples of 4π. The autorotation number is therefore not topologically conserved under all transformations. We discuss this within the context of generalised inflection points and of frame revisit points. The results may be applicable to physical systems such as polymers, proteins, and DNA. Finally, turbulence is discussed in the light of autorotation, as is the Philippine wine dance, the Dirac belt trick, and the 4π cycle of the flying snake. This paper is dedicated to Ian K Robinson on the occasion of Ian receiving the Gregori Aminoff Prize 2015.

Mathematics for Physics

NASA Astrophysics Data System (ADS)

Stone, Michael; Goldbart, Paul

2009-07-01

Preface; 1. Calculus of variations; 2. Function spaces; 3. Linear ordinary differential equations; 4. Linear differential operators; 5. Green functions; 6. Partial differential equations; 7. The mathematics of real waves; 8. Special functions; 9. Integral equations; 10. Vectors and tensors; 11. Differential calculus on manifolds; 12. Integration on manifolds; 13. An introduction to differential topology; 14. Group and group representations; 15. Lie groups; 16. The geometry of fibre bundles; 17. Complex analysis I; 18. Applications of complex variables; 19. Special functions and complex variables; Appendixes; Reference; Index.

LETTER TO THE EDITOR: A theorem on topologically massive gravity

NASA Astrophysics Data System (ADS)

Aliev, A. N.; Nutku, Y.

1996-03-01

We show that for three dimensional spacetimes admitting a hypersurface orthogonal Killing vector field, Deser, Jackiw and Templeton's vacuum field equations of topologically massive gravity allow only the trivial flat spacetime solution. Thus spin is necessary to support topological mass.

Topology driven modeling: the IS metaphor.

PubMed

Merelli, Emanuela; Pettini, Marco; Rasetti, Mario

In order to define a new method for analyzing the immune system within the realm of Big Data, we bear on the metaphor provided by an extension of Parisi's model, based on a mean field approach. The novelty is the multilinearity of the couplings in the configurational variables. This peculiarity allows us to compare the partition function [Formula: see text] with a particular functor of topological field theory-the generating function of the Betti numbers of the state manifold of the system-which contains the same global information of the system configurations and of the data set representing them. The comparison between the Betti numbers of the model and the real Betti numbers obtained from the topological analysis of phenomenological data, is expected to discover hidden n-ary relations among idiotypes and anti-idiotypes. The data topological analysis will select global features, reducible neither to a mere subgraph nor to a metric or vector space. How the immune system reacts, how it evolves, how it responds to stimuli is the result of an interaction that took place among many entities constrained in specific configurations which are relational. Within this metaphor, the proposed method turns out to be a global topological application of the S[B] paradigm for modeling complex systems.

An improved fault-tolerant control scheme for PWM inverter-fed induction motor-based EVs.

PubMed

Tabbache, Bekheïra; Benbouzid, Mohamed; Kheloui, Abdelaziz; Bourgeot, Jean-Matthieu; Mamoune, Abdeslam

2013-11-01

This paper proposes an improved fault-tolerant control scheme for PWM inverter-fed induction motor-based electric vehicles. The proposed strategy deals with power switch (IGBTs) failures mitigation within a reconfigurable induction motor control. To increase the vehicle powertrain reliability regarding IGBT open-circuit failures, 4-wire and 4-leg PWM inverter topologies are investigated and their performances discussed in a vehicle context. The proposed fault-tolerant topologies require only minimum hardware modifications to the conventional off-the-shelf six-switch three-phase drive, mitigating the IGBTs failures by specific inverter control. Indeed, the two topologies exploit the induction motor neutral accessibility for fault-tolerant purposes. The 4-wire topology uses then classical hysteresis controllers to account for the IGBT failures. The 4-leg topology, meanwhile, uses a specific 3D space vector PWM to handle vehicle requirements in terms of size (DC bus capacitors) and cost (IGBTs number). Experiments on an induction motor drive and simulations on an electric vehicle are carried-out using a European urban driving cycle to show that the proposed fault-tolerant control approach is effective and provides a simple configuration with high performance in terms of speed and torque responses. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Symplectic Quantization of a Vector-Tensor Gauge Theory with Topological Coupling

NASA Astrophysics Data System (ADS)

Barcelos-Neto, J.; Silva, M. B. D.

We use the symplectic formalism to quantize a gauge theory where vectors and tensors fields are coupled in a topological way. This is an example of reducible theory and a procedure like of ghosts-of-ghosts of the BFV method is applied but in terms of Lagrange multipliers. Our final results are in agreement with the ones found in the literature by using the Dirac method.

Phase contrast imaging X-ray computed tomography: quantitative characterization of human patellar cartilage matrix with topological and geometrical features

NASA Astrophysics Data System (ADS)

Nagarajan, Mahesh B.; Coan, Paola; Huber, Markus B.; Diemoz, Paul C.; Wismüller, Axel

2014-03-01

Current assessment of cartilage is primarily based on identification of indirect markers such as joint space narrowing and increased subchondral bone density on x-ray images. In this context, phase contrast CT imaging (PCI-CT) has recently emerged as a novel imaging technique that allows a direct examination of chondrocyte patterns and their correlation to osteoarthritis through visualization of cartilage soft tissue. This study investigates the use of topological and geometrical approaches for characterizing chondrocyte patterns in the radial zone of the knee cartilage matrix in the presence and absence of osteoarthritic damage. For this purpose, topological features derived from Minkowski Functionals and geometric features derived from the Scaling Index Method (SIM) were extracted from 842 regions of interest (ROI) annotated on PCI-CT images of healthy and osteoarthritic specimens of human patellar cartilage. The extracted features were then used in a machine learning task involving support vector regression to classify ROIs as healthy or osteoarthritic. Classification performance was evaluated using the area under the receiver operating characteristic (ROC) curve (AUC). The best classification performance was observed with high-dimensional geometrical feature vectors derived from SIM (0.95 ± 0.06) which outperformed all Minkowski Functionals (p < 0.001). These results suggest that such quantitative analysis of chondrocyte patterns in human patellar cartilage matrix involving SIM-derived geometrical features can distinguish between healthy and osteoarthritic tissue with high accuracy.

Visualizing the activity of Escherichia coli divergent promoters and probing their dependence on superhelical density using dual-colour fluorescent reporter vector

PubMed Central

Masulis, Irina S.; Babaeva, Zaira Sh.; Chernyshov, Sergey V.; Ozoline, Olga N.

2015-01-01

Mosaic pattern of transcription in alternating directions is a common feature of prokaryotic and eukaryotic genomes which rationality and origin remain enigmatic. In Escherichia coli approximately 25% of genes comprise pairs of topologically linked divergently transcribed units. Given that transcriptional complex formation at each promoter in the pair induces topological changes and is itself sensitive to DNA structural perturbations, study of the functional anatomy in such areas requires special approaches. Here we suggested the dual-colour promoter probe vector which may become an ideal tool for divergent transcription profiling. The vector was used to characterize the specific genomic region nearby appY with multiple bidirectional promoters predicted in silico. Only three promoters of this region were shown to be engaged in the transcription initiation resulting in the expression of reporter genes. RNA product transcribed in antisense direction is suggested as a novel RNA. Nalidixin-induced topological modulation differentially affected transcription in sense and antisense directions thus exemplifying anticooperative mode in the response to topological alterations. PMID:26081797

Topological Aspects of Information Retrieval.

ERIC Educational Resources Information Center

Egghe, Leo; Rousseau, Ronald

1998-01-01

Discusses topological aspects of theoretical information retrieval, including retrieval topology; similarity topology; pseudo-metric topology; document spaces as topological spaces; Boolean information retrieval as a subsystem of any topological system; and proofs of theorems. (LRW)

Knots in electromagnetism

NASA Astrophysics Data System (ADS)

Arrayás, M.; Bouwmeester, D.; Trueba, J. L.

2017-01-01

Maxwell equations in vacuum allow for solutions with a non-trivial topology in the electric and magnetic field line configurations at any given moment in time. One example is a space filling congruence of electric and magnetic field lines forming circles lying on the surfaces of nested tori. In this example the electric, magnetic and Poynting vector fields are orthogonal everywhere. As time evolves the electric and magnetic fields expand and deform without changing the topology and energy, while the Poynting vector structure remains unchanged while propagating with the speed of light. The topology is characterized by the concept of helicity of the field configuration. Helicity is an important fundamental concept and for massless fields it is a conserved quantity under conformal transformations. We will review several methods by which linked and knotted electromagnetic (spin-1) fields can be derived. A first method, introduced by A. Rañada, uses the formulation of the Maxwell equations in terms of differential forms combined with the Hopf map from the three-sphere S3 to the two-sphere S2. A second method is based on spinor and twistor theory developed by R. Penrose in which elementary twistor functions correspond to the family of electromagnetic torus knots. A third method uses the Bateman construction of generating null solutions from complex Euler potentials. And a fourth method uses special conformal transformations, in particular conformal inversion, to generate new linked and knotted field configurations from existing ones. This fourth method is often accompanied by shifting singularities in the field to complex space-time points. Of course the various methods must be closely related to one another although they have been developed largely independently and they suggest different directions in which to expand the study of topologically non-trivial field configurations. It will be shown how the twistor formulation allows for a direct extension to massless fields of other spin values, such as spin-2 fields satisfying the linearized Einstein vacuum equation, and how the formulation by A. Rañada can be extended to fields for which the electric and magnetic fields are not orthogonal everywhere. Underlying the various methods is the fact that electric and magnetic field lines can be described as the level curves of complex functions. Compactification of R3 naturally leads to finite energy solutions because the fields at infinity in all directions should all converge towards zero. An intriguing question that is raised by the finite energy is whether there is a connection to the quantization of the classical electromagnetic field. We will review some issues related to this question. Another interesting question is why the general formulation of topologically non-trivial solutions uses the electric and magnetic fields instead of the electromagnetic vector potentials. This leads to a discussion of the Clebsch representation of the electromagnetic field strength 2-form. Finally, a topic of great interest is the possibility of experimentally generating and investigating linked and knotted field configurations. Since the non-trivial topological field solutions exploit the special conformal symmetry of the underlying vacuum wave-equations it will only be possible to approximate the solutions in an experiment, which necessarily introduces material objects that will break the special conformal symmetry. We will review the research on plasma configurations in which the magnetic field-line configuration approximates plasma torus knots leading to the prediction of topological solitons in plasma.

Managing focal fields of vector beams with multiple polarization singularities.

PubMed

Han, Lei; Liu, Sheng; Li, Peng; Zhang, Yi; Cheng, Huachao; Gan, Xuetao; Zhao, Jianlin

2016-11-10

We explore the tight focusing behavior of vector beams with multiple polarization singularities, and analyze the influences of the number, position, and topological charge of the singularities on the focal fields. It is found that the ellipticity of the local polarization states at the focal plane could be determined by the spatial distribution of the polarization singularities of the vector beam. When the spatial location and topological charge of singularities have even-fold rotation symmetry, the transverse fields at the focal plane are locally linearly polarized. Otherwise, the polarization state becomes a locally hybrid one. By appropriately arranging the distribution of the polarization singularities in the vector beam, the polarization distributions of the focal fields could be altered while the intensity maintains unchanged.

Visualization of 3-D tensor fields

NASA Technical Reports Server (NTRS)

Hesselink, L.

1996-01-01

Second-order tensor fields have applications in many different areas of physics, such as general relativity and fluid mechanics. The wealth of multivariate information in tensor fields makes them more complex and abstract than scalar and vector fields. Visualization is a good technique for scientists to gain new insights from them. Visualizing a 3-D continuous tensor field is equivalent to simultaneously visualizing its three eigenvector fields. In the past, research has been conducted in the area of two-dimensional tensor fields. It was shown that degenerate points, defined as points where eigenvalues are equal to each other, are the basic singularities underlying the topology of tensor fields. Moreover, it was shown that eigenvectors never cross each other except at degenerate points. Since we live in a three-dimensional world, it is important for us to understand the underlying physics of this world. In this report, we describe a new method for locating degenerate points along with the conditions for classifying them in three-dimensional space. Finally, we discuss some topological features of three-dimensional tensor fields, and interpret topological patterns in terms of physical properties.

The Topology of Symmetric Tensor Fields

NASA Technical Reports Server (NTRS)

Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval

1997-01-01

Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.

Surface representations of two- and three-dimensional fluid flow topology

NASA Technical Reports Server (NTRS)

Helman, James L.; Hesselink, Lambertus

1990-01-01

We discuss our work using critical point analysis to generate representations of the vector field topology of numerical flow data sets. Critical points are located and characterized in a two-dimensional domain, which may be either a two-dimensional flow field or the tangential velocity field near a three-dimensional body. Tangent curves are then integrated out along the principal directions of certain classes of critical points. The points and curves are linked to form a skeleton representing the two-dimensional vector field topology. When generated from the tangential velocity field near a body in a three-dimensional flow, the skeleton includes the critical points and curves which provide a basis for analyzing the three-dimensional structure of the flow separation. The points along the separation curves in the skeleton are used to start tangent curve integrations to generate surfaces representing the topology of the associated flow separations.

U(1) mediation of flux supersymmetry breaking

NASA Astrophysics Data System (ADS)

Grimm, Thomas W.; Klemm, Albrecht

2008-10-01

We study the mediation of supersymmetry breaking triggered by background fluxes in Type II string compactifications with Script N = 1 supersymmetry. The mediation arises due to an U(1) vector multiplet coupling to both a hidden supersymmetry breaking flux sector and a visible D-brane sector. The required internal manifolds can be constructed by non-Kähler resolutions of singular Calabi-Yau manifolds. The effective action encoding the U(1) coupling is then determined in terms of the global topological properties of the internal space. We investigate suitable local geometries for the hidden and visible sector in detail. This includes a systematic study of orientifold symmetries of del Pezzo surfaces realized in compact geometries after geometric transition. We construct compact examples admitting the key properties to realize flux supersymmetry breaking and U(1) mediation. Their toric realization allows us to analyze the geometry of curve classes and confirm the topological connection between the hidden and visible sector.

Unwinding the amplituhedron in binary

NASA Astrophysics Data System (ADS)

Arkani-Hamed, Nima; Thomas, Hugh; Trnka, Jaroslav

2018-01-01

We present new, fundamentally combinatorial and topological characterizations of the amplituhedron. Upon projecting external data through the amplituhedron, the resulting configuration of points has a specified (and maximal) generalized "winding number". Equivalently, the amplituhedron can be fully described in binary: canonical projections of the geometry down to one dimension have a specified (and maximal) number of "sign flips" of the projected data. The locality and unitarity of scattering amplitudes are easily derived as elementary consequences of this binary code. Minimal winding defines a natural "dual" of the amplituhedron. This picture gives us an avatar of the amplituhedron purely in the configuration space of points in vector space (momentum-twistor space in the physics), a new interpretation of the canonical amplituhedron form, and a direct bosonic understanding of the scattering super-amplitude in planar N = 4 SYM as a differential form on the space of physical kinematical data.

Semilinear (topological) spaces and applications

NASA Technical Reports Server (NTRS)

Prakash, P.; Sertel, M. R.

1971-01-01

Semivector spaces are defined and some of their algebraic aspects are developed including some structure theory. These spaces are then topologized to obtain semilinear topological spaces for which a hierarchy of local convexity axioms is identified. A number of fixed point and minmax theorems for spaces with various local convexity properties are established. The spaces of concern arise naturally as various hyperspaces of linear and semilinear (topological) spaces. It is indicated briefly how all this can be applied in socio-economic analysis and optimization.

Soft connectedness of soft topological space

NASA Astrophysics Data System (ADS)

Mishra, Sanjay

2017-07-01

Recently, Shabir and Naz in [4] introduced the notion of Soft Topological Spaces (STS). They defined and studied about soft topology on the collection τ of soft sets over X. After the initiation of soft topological space many researcher developed its basic theory as like soft continuity, soft compactness and soft countability. Our main objective in this paper is to study the soft connectedness properties of soft topological space and also establish relations of soft connectedness with other properties of STS.

Robustness-Based Simplification of 2D Steady and Unsteady Vector Fields.

PubMed

Skraba, Primoz; Bei Wang; Guoning Chen; Rosen, Paul

2015-08-01

Vector field simplification aims to reduce the complexity of the flow by removing features in order of their relevance and importance, to reveal prominent behavior and obtain a compact representation for interpretation. Most existing simplification techniques based on the topological skeleton successively remove pairs of critical points connected by separatrices, using distance or area-based relevance measures. These methods rely on the stable extraction of the topological skeleton, which can be difficult due to instability in numerical integration, especially when processing highly rotational flows. In this paper, we propose a novel simplification scheme derived from the recently introduced topological notion of robustness which enables the pruning of sets of critical points according to a quantitative measure of their stability, that is, the minimum amount of vector field perturbation required to remove them. This leads to a hierarchical simplification scheme that encodes flow magnitude in its perturbation metric. Our novel simplification algorithm is based on degree theory and has minimal boundary restrictions. Finally, we provide an implementation under the piecewise-linear setting and apply it to both synthetic and real-world datasets. We show local and complete hierarchical simplifications for steady as well as unsteady vector fields.

t-topology on the n-dimensional Minkowski space

NASA Astrophysics Data System (ADS)

Agrawal, Gunjan; Shrivastava, Sampada

2009-05-01

In this paper, a topological study of the n-dimensional Minkowski space, n >1, with t-topology, denoted by Mt, has been carried out. This topology, unlike the usual Euclidean one, is more physically appealing being defined by means of the Lorentzian metric. It shares many topological properties with similar candidate topologies and it has the advantage of being first countable. Compact sets of Mt and continuous maps into Mt are studied using the notion of Zeno sequences besides characterizing those sets that have the same subspace topologies induced from the Euclidean and t-topologies on n-dimensional Minkowski space. A necessary and sufficient condition for a compact set in the Euclidean n-space to be compact in Mt is obtained, thereby proving that the n-cube, n >1, as a subspace of Mt, is not compact, while a segment on a timelike line is compact in Mt. This study leads to the nonsimply connectedness of Mt, for n =2. Further, Minkowski space with s-topology has also been dealt with.

Fine topology and locally Minkowskian manifolds

NASA Astrophysics Data System (ADS)

Agrawal, Gunjan; Sinha, Soami Pyari

2018-05-01

Fine topology is one of the several well-known topologies of physical and mathematical relevance. In the present paper, it is obtained that the nonempty open sets of different dimensional Minkowski spaces with the fine topology are not homeomorphic. This leads to the introduction of a new class of manifolds. It turns out that the technique developed here is also applicable to some other topologies, namely, the s-topology, space topology, f-topology, and A-topology.

Nonlocal optical response in topological phase transitions in the graphene family

NASA Astrophysics Data System (ADS)

Rodriguez-Lopez, Pablo; Kort-Kamp, Wilton J. M.; Dalvit, Diego A. R.; Woods, Lilia M.

2018-01-01

We investigate the electromagnetic response of staggered two-dimensional materials of the graphene family, including silicene, germanene, and stanene, as they are driven through various topological phase transitions using external fields. Utilizing Kubo formalism, we compute their optical conductivity tensor taking into account the frequency and wave vector of the electromagnetic excitations, and study its behavior over the full electronic phase diagram of the materials. In particular, we find that the resonant behavior of the nonlocal Hall conductivity is strongly affected by the various topological phases present in these materials. We also consider the plasmon excitations in the graphene family and find that nonlocality in the optical response can affect the plasmon dispersion spectra of the various phases. We find a regime of wave vectors for which the plasmon relations for phases with trivial topology are essentially indistinguishable, while those for phases with nontrivial topology are distinct and are redshifted as the corresponding Chern number increases. The expressions for the conductivity components are valid for the entire graphene family and can be readily used by others.

Nonlocal optical response in topological phase transitions in the graphene family

DOE PAGES

Rodriguez-Lopez, Pablo; de Melo Kort-Kamp, Wilton Junior; Dalvit, Diego Alejandro Roberto; ...

2018-01-22

We investigate the electromagnetic response of staggered two-dimensional materials of the graphene family, including silicene, germanene, and stanene, as they are driven through various topological phase transitions using external fields. Utilizing Kubo formalism, we compute their optical conductivity tensor taking into account the frequency and wave vector of the electromagnetic excitations, and study its behavior over the full electronic phase diagram of the materials. In particular, we find that the resonant behavior of the nonlocal Hall conductivity is strongly affected by the various topological phases present in these materials. We also consider the plasmon excitations in the graphene family andmore » find that nonlocality in the optical response can affect the plasmon dispersion spectra of the various phases. Here, we find a regime of wave vectors for which the plasmon relations for phases with trivial topology are essentially indistinguishable, while those for phases with nontrivial topology are distinct and are redshifted as the corresponding Chern number increases. Finally, the expressions for the conductivity components are valid for the entire graphene family and can be readily used by others.« less

Nonlocal optical response in topological phase transitions in the graphene family

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

Rodriguez-Lopez, Pablo; de Melo Kort-Kamp, Wilton Junior; Dalvit, Diego Alejandro Roberto

We investigate the electromagnetic response of staggered two-dimensional materials of the graphene family, including silicene, germanene, and stanene, as they are driven through various topological phase transitions using external fields. Utilizing Kubo formalism, we compute their optical conductivity tensor taking into account the frequency and wave vector of the electromagnetic excitations, and study its behavior over the full electronic phase diagram of the materials. In particular, we find that the resonant behavior of the nonlocal Hall conductivity is strongly affected by the various topological phases present in these materials. We also consider the plasmon excitations in the graphene family andmore » find that nonlocality in the optical response can affect the plasmon dispersion spectra of the various phases. Here, we find a regime of wave vectors for which the plasmon relations for phases with trivial topology are essentially indistinguishable, while those for phases with nontrivial topology are distinct and are redshifted as the corresponding Chern number increases. Finally, the expressions for the conductivity components are valid for the entire graphene family and can be readily used by others.« less

Physical Characterization of Gemini Surfactant-Based Synthetic Vectors for the Delivery of Linear Covalently Closed (LCC) DNA Ministrings

PubMed Central

Sum, Chi Hong; Nafissi, Nafiseh; Slavcev, Roderick A.; Wettig, Shawn

2015-01-01

In combination with novel linear covalently closed (LCC) DNA minivectors, referred to as DNA ministrings, a gemini surfactant-based synthetic vector for gene delivery has been shown to exhibit enhanced delivery and bioavailability while offering a heightened safety profile. Due to topological differences from conventional circular covalently closed (CCC) plasmid DNA vectors, the linear topology of LCC DNA ministrings may present differences with regards to DNA interaction and the physicochemical properties influencing DNA-surfactant interactions in the formulation of lipoplexed particles. In this study, N,N-bis(dimethylhexadecyl)-α,ω-propanediammonium(16-3-16)gemini-based synthetic vectors, incorporating either CCC plasmid or LCC DNA ministrings, were characterized and compared with respect to particle size, zeta potential, DNA encapsulation, DNase sensitivity, and in vitro transgene delivery efficacy. Through comparative analysis, differences between CCC plasmid DNA and LCC DNA ministrings led to variations in the physical properties of the resulting lipoplexes after complexation with 16-3-16 gemini surfactants. Despite the size disparities between the plasmid DNA vectors (CCC) and DNA ministrings (LCC), differences in DNA topology resulted in the generation of lipoplexes of comparable particle sizes. The capacity for ministring (LCC) derived lipoplexes to undergo complete counterion release during lipoplex formation contributed to improved DNA encapsulation, protection from DNase degradation, and in vitro transgene delivery. PMID:26561857

The Topology of Three-Dimensional Symmetric Tensor Fields

NASA Technical Reports Server (NTRS)

Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus

1994-01-01

We study the topology of 3-D symmetric tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Finally, we demonstrate the use of tensor field topology for the interpretation of the two-force Boussinesq problem.

Engineering topological edge states in two dimensional magnetic photonic crystal

NASA Astrophysics Data System (ADS)

Yang, Bing; Wu, Tong; Zhang, Xiangdong

2017-01-01

Based on a perturbative approach, we propose a simple and efficient method to engineer the topological edge states in two dimensional magnetic photonic crystals. The topological edge states in the microstructures can be constructed and varied by altering the parameters of the microstructure according to the field-energy distributions of the Bloch states at the related Bloch wave vectors. The validity of the proposed method has been demonstrated by exact numerical calculations through three concrete examples. Our method makes the topological edge states "designable."

Acceleration of convergence of vector sequences

NASA Technical Reports Server (NTRS)

Sidi, A.; Ford, W. F.; Smith, D. A.

1983-01-01

A general approach to the construction of convergence acceleration methods for vector sequence is proposed. Using this approach, one can generate some known methods, such as the minimal polynomial extrapolation, the reduced rank extrapolation, and the topological epsilon algorithm, and also some new ones. Some of the new methods are easier to implement than the known methods and are observed to have similar numerical properties. The convergence analysis of these new methods is carried out, and it is shown that they are especially suitable for accelerating the convergence of vector sequences that are obtained when one solves linear systems of equations iteratively. A stability analysis is also given, and numerical examples are provided. The convergence and stability properties of the topological epsilon algorithm are likewise given.

On load paths and load bearing topology from finite element analysis

NASA Astrophysics Data System (ADS)

Kelly, D.; Reidsema, C.; Lee, M.

2010-06-01

Load paths can be mapped from vector plots of 'pointing stress vectors'. They define a path along which a component of load remains constant as it traverses the solution domain. In this paper the theory for the paths is first defined. Properties of the plots that enable a designer to interpret the structural behavior from the contours are then identified. Because stress is a second order tensor defined on an orthogonal set of axes, the vector plots define separate paths for load transfer in each direction of the set of axes. An algorithm is therefore presented that combines the vectors to define a topology to carry the loads. The algorithm is shown to straighten the paths reducing bending moments and removing stress concentration. Application to a bolted joint, a racing car body and a yacht hull demonstrate the usefulness of the plots.

Topology of quantum discord

NASA Astrophysics Data System (ADS)

Nguyen, Nga T. T.; Joynt, Robert

2017-04-01

Quantum discord is an important measure of quantum correlations that can serve as a resource for certain types of quantum information processing. Like entanglement, discord is subject to destruction by external noise. The routes by which this destruction can take place depends on the shape of the hypersurface of zero discord C in the space of generalized Bloch vectors. For 2 qubits, we show that with a few points subtracted, this hypersurface is a simply-connected 9-dimensional manifold embedded in a 15-dimensional background space. We do this by constructing an explicit homeomorphism from a known manifold to the subtracted version of C . We also construct a coordinate map on C that can be used for integration or other purposes. This topological characterization of C has important implications for the classification of the possible time evolutions of discord in physical models. The classification for discord contrasts sharply with the possible evolutions of entanglement. We classify the possible joint evolutions of entanglement and discord. There are 9 allowed categories: 6 categories for a Markovian process and 3 categories for a non-Markovian process, respectively. We illustrate these conclusions with an anisotropic XY spin model. All 9 categories can be obtained by adjusting parameters in this model.

A topological multilayer model of the human body.

PubMed

Barbeito, Antonio; Painho, Marco; Cabral, Pedro; O'Neill, João

2015-11-04

Geographical information systems deal with spatial databases in which topological models are described with alphanumeric information. Its graphical interfaces implement the multilayer concept and provide powerful interaction tools. In this study, we apply these concepts to the human body creating a representation that would allow an interactive, precise, and detailed anatomical study. A vector surface component of the human body is built using a three-dimensional (3-D) reconstruction methodology. This multilayer concept is implemented by associating raster components with the corresponding vector surfaces, which include neighbourhood topology enabling spatial analysis. A root mean square error of 0.18 mm validated the three-dimensional reconstruction technique of internal anatomical structures. The expansion of the identification and the development of a neighbourhood analysis function are the new tools provided in this model.

Realization of space-time inversion-invariant topological semimetal-bands in superconducting quantum circuits.

NASA Astrophysics Data System (ADS)

Yu, Y.; Tan, X.; Liu, Q.; Xue, G.; Yu, H.; Zhao, Y.; Wang, Z.

Topological band theory has attracted much attention since several types of topological metals and semimetals have been explored. These robustness of nodal band structures are symmetry-protected, whose topological features have deepened and widened the understandings of condensed matter physics. Meanwhile, as artificial quantum systems superconducting circuits possess high controllability, supplying a powerful approach to investigate topological properties of condensed matter systems. We realize a Hamiltonian with space-time (PT) symmetry by mapping momentum space of nodal band structure to parameter space in a superconducting quantum circuit. By measuring energy spectrum of the system, we observe the gapless band structure of topological semimetals, shown as Dirac points in momentum space. The phase transition from topological semimetal to topological insulator can be realized by continuously tuning the parameter in Hamiltonian. We add perturbation to broken time reversal symmetry. As long as the combined PT symmetry is preserved, the Dirac points of the topological semimetal are still observable, suggesting the robustness of the topological protection of the gapless energy band. Our work open a platform to simulate the relation between the symmetry and topological stability in condensed matter systems. Supported by the NKRDP of China (2016YFA0301802) and the GRF of Hong Kong (HKU173051/14P&HKU173055/15P).

Inhomogeneous Weyl and Dirac Semimetals: Transport in Axial Magnetic Fields and Fermi Arc Surface States from Pseudo-Landau Levels

NASA Astrophysics Data System (ADS)

Grushin, Adolfo G.; Venderbos, Jörn W. F.; Vishwanath, Ashvin; Ilan, Roni

2016-10-01

Topological Dirac and Weyl semimetals have an energy spectrum that hosts Weyl nodes appearing in pairs of opposite chirality. Topological stability is ensured when the nodes are separated in momentum space and unique spectral and transport properties follow. In this work, we study the effect of a space-dependent Weyl node separation, which we interpret as an emergent background axial-vector potential, on the electromagnetic response and the energy spectrum of Weyl and Dirac semimetals. This situation can arise in the solid state either from inhomogeneous strain or nonuniform magnetization and can also be engineered in cold atomic systems. Using a semiclassical approach, we show that the resulting axial magnetic field B5 is observable through an enhancement of the conductivity as σ ˜B52 due to an underlying chiral pseudomagnetic effect. We then use two lattice models to analyze the effect of B5 on the spectral properties of topological semimetals. We describe the emergent pseudo-Landau-level structure for different spatial profiles of B5, revealing that (i) the celebrated surface states of Weyl semimetals, the Fermi arcs, can be reinterpreted as n =0 pseudo-Landau levels resulting from a B5 confined to the surface, (ii) as a consequence of position-momentum locking, a bulk B5 creates pseudo-Landau levels interpolating in real space between Fermi arcs at opposite surfaces, and (iii) there are equilibrium bound currents proportional to B5 that average to zero over the sample, which are the analogs of bound currents in magnetic materials. We conclude by discussing how our findings can be probed experimentally.

Identifying Turbulent Structures through Topological Segmentation

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

Bremer, Peer-Timo; Gruber, Andrea; Bennett, Janine C.

2016-01-01

A new method of extracting vortical structures from a turbulent flow is proposed whereby topological segmentation of an indicator function scalar field is used to identify the regions of influence of the individual vortices. This addresses a long-standing challenge in vector field topological analysis: indicator functions commonly used produce a scalar field based on the local velocity vector field; reconstructing regions of influence for a particular structure requires selecting a threshold to define vortex extent. In practice, the same threshold is rarely meaningful throughout a given flow. By also considering the topology of the indicator field function, the characteristics ofmore » vortex strength and extent can be separated and the ambiguity in the choice of the threshold reduced. The proposed approach is able to identify several types of vortices observed in a jet in cross-flow configuration simultaneously where no single threshold value for a selection of common indicator functions appears able to identify all of these vortex types.« less

Topological framework for local structure analysis in condensed matter

PubMed Central

Lazar, Emanuel A.; Han, Jian; Srolovitz, David J.

2015-01-01

Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent particles, understanding that structure is a primary objective of condensed matter research. Although perfect crystals are fully described by a set of translation and basis vectors, real-world materials are never perfect, as thermal vibrations and defects introduce significant deviation from ideal order. Meanwhile, liquids and glasses present yet more complexity. A complete understanding of structure thus remains a central, open problem. Here we propose a unified mathematical framework, based on the topology of the Voronoi cell of a particle, for classifying local structure in ordered and disordered systems that is powerful and practical. We explain the underlying reason why this topological description of local structure is better suited for structural analysis than continuous descriptions. We demonstrate the connection of this approach to the behavior of physical systems and explore how crystalline structure is compromised at elevated temperatures. We also illustrate potential applications to identifying defects in plastically deformed polycrystals at high temperatures, automating analysis of complex structures, and characterizing general disordered systems. PMID:26460045

Topological nature of nonlinear optical effects in solids.

PubMed

Morimoto, Takahiro; Nagaosa, Naoto

2016-05-01

There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by strong light irradiation to materials that results in nonlinear polarizations in the electric field. These are of great importance in studying the physics of excited states of the system as well as for applications to optical devices and solar cells. Nonlinear properties of materials are usually described by nonlinear susceptibilities, which have complex expressions including many matrix elements and energy denominators. On the other hand, a nonequilibrium steady state under an electric field periodic in time has a concise description in terms of the Floquet bands of electrons dressed by photons. We show theoretically, using the Floquet formalism, that various nonlinear optical effects, such as the shift current in noncentrosymmetric materials, photovoltaic Hall response, and photo-induced change of order parameters under the continuous irradiation of monochromatic light, can be described in a unified fashion by topological quantities involving the Berry connection and Berry curvature. We found that vector fields defined with the Berry connections in the space of momentum and/or parameters govern the nonlinear responses. This topological view offers a route to designing nonlinear optical materials.

Topological nature of nonlinear optical effects in solids

PubMed Central

Morimoto, Takahiro; Nagaosa, Naoto

2016-01-01

There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by strong light irradiation to materials that results in nonlinear polarizations in the electric field. These are of great importance in studying the physics of excited states of the system as well as for applications to optical devices and solar cells. Nonlinear properties of materials are usually described by nonlinear susceptibilities, which have complex expressions including many matrix elements and energy denominators. On the other hand, a nonequilibrium steady state under an electric field periodic in time has a concise description in terms of the Floquet bands of electrons dressed by photons. We show theoretically, using the Floquet formalism, that various nonlinear optical effects, such as the shift current in noncentrosymmetric materials, photovoltaic Hall response, and photo-induced change of order parameters under the continuous irradiation of monochromatic light, can be described in a unified fashion by topological quantities involving the Berry connection and Berry curvature. We found that vector fields defined with the Berry connections in the space of momentum and/or parameters govern the nonlinear responses. This topological view offers a route to designing nonlinear optical materials. PMID:27386523

Theory of the Quantized Hall Conductance in Periodic Systems: a Topological Analysis.

NASA Astrophysics Data System (ADS)

Czerwinski, Michael Joseph

The integral quantization of the Hall conductance in two-dimensional periodic systems is investigated from a topological point of view. Attention is focused on the contributions from the electronic sub-bands which arise from perturbed Landau levels. After reviewing the theoretical work leading to the identification of the Hall conductance as a topological quantum number, both a determination and interpretation of these quantized values for the sub-band conductances is made. It is shown that the Hall conductance of each sub-band can be regarded as the sum of two terms which will be referred to as classical and nonclassical. Although each of these contributions individually leads to a fractional conductance, the sum of these two contributions does indeed yield an integer. These integral conductances are found to be given by the solution of a simple Diophantine equation which depends on the periodic perturbation. A connection between the quantized value of the Hall conductance and the covering of real space by the zeroes of the sub-band wavefunctions allows for a determination of these conductances under more general potentials. A method is described for obtaining the conductance values from only those states bordering the Brillouin zone, and not the states in its interior. This method is demonstrated to give Hall conductances in agreement with those obtained from the Diophantine equation for the sinusoidal potential case explored earlier. Generalizing a simple gauge invariance argument from real space to k-space, a k-space 'vector potential' is introduced. This allows for a explicit identification of the Hall conductance with the phase winding number of the sub-band wavefunction around the Brillouin zone. The previously described division of the Hall conductance into classical and nonclassical contributions is in this way made more rigorous; based on periodicity considerations alone, these terms are identified as the winding numbers associated with (i) the basis states and (ii) the coefficients of these basis states, respectively. In this way a general Diophantine equation, independent of the periodic potential, is obtained. Finally, the use of the 'parallel transport' of state vectors in the determination of an overall phase convention for these states is described. This is seen to lead to a simple and straightforward method for determining the Hall conductance. This method is based on the states directly, without reference to the particular component wavefunctions of these states. Mention is made of the generality of calculations of this type, within the context of the geometric (or Berry) phases acquired by systems under an adiabatic modification of their environment.

Localizing softness and stress along loops in 3D topological metamaterials

NASA Astrophysics Data System (ADS)

Baardink, Guido; Souslov, Anton; Paulose, Jayson; Vitelli, Vincenzo

2018-01-01

Topological states can be used to control the mechanical properties of a material along an edge or around a localized defect. The rigidity of elastic networks is characterized by a topological invariant called the polarization; materials with a well-defined uniform polarization display a dramatic range of edge softness depending on the orientation of the polarization relative to the terminating surface. However, in all 3D mechanical metamaterials proposed to date, the topological modes are mixed with bulk soft modes, which organize themselves in Weyl loops. Here, we report the design of a 3D topological metamaterial without Weyl lines and with a uniform polarization that leads to an asymmetry between the number of soft modes on opposing surfaces. We then use this construction to localize topological soft modes in interior regions of the material by including defect lines—dislocation loops—that are unique to three dimensions. We derive a general formula that relates the difference in the number of soft modes and states of self-stress localized along the dislocation loop to the handedness of the vector triad formed by the lattice polarization, Burgers vector, and dislocation-line direction. Our findings suggest a strategy for preprogramming failure and softness localized along lines in 3D, while avoiding extended soft Weyl modes.

Hyperfunction solutions of the zero rest mass equations and representations of LIE groups

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

Dunne, E.G.

1984-01-01

Recently, hyperfunctions have arisen in an essential way in separate results in mathematical physics and in representation theory. In the setting of the twistor program, Wells, with others, has extended the Penrose transform to hyperfunction solutions of the zero rest mass equations, showing that the fundamental isomorphisms hold for this larger space. Meanwhile, Schmid has shown the existence of a canonical globalization of a Harish-Chandra module, V, to a representation of the group. This maximal globalization may be realized as the completion of V in a locally convex vector space in the hyperfunction topology. This thesis shows that the formermore » is a particular case of the latter where the globalization can be done by hand. This explicit globalization is then carried out for a more general case of the Radon transform on homogeneous spaces.« less

Communications and control for electric power systems

NASA Technical Reports Server (NTRS)

Kirkham, H.; Goettsche, A.; Niebur, D.; Friend, H.; Johnston, A.

1991-01-01

The first section of the report describes the AbNET system, a hardware and software communications system designed for distribution automation (it can also find application in substation monitoring and control). The topology of the power system fixes the topology of the communications network, which can therefore be expected to include a larger number of branch points, tap points, and interconnections. These features make this communications network unlike any other. The network operating software has to solve the problem of communicating to all the nodes of a very complex network in as reliable a way as possible even if the network is damaged, and it has to do so with minimum transmission delays and at minimum cost. The design of the operating protocols is described within the framework of the seven-layer Open System Interconnection hierarchy of the International Standards Organization. Section 2 of the report describes the development and testing of a high voltage sensor based on an electro-optic polymer. The theory of operation is reviewed. Bulk fabrication of the polymer is discussed, as well as results of testing of the electro-optic coefficient of the material. Fabrication of a complete prototype sensor suitable for use in the range 1-20 kV is described. The electro-optic polymer is shown to be an important material for fiber optic sensing applications. Appendix A is theoretical support for this work. The third section of the report presents the application of an artificial neural network, Kohonen's self-organizing feature map, for the classification of power system states. This classifier maps vectors of an N-dimensional space to a 2-dimensional neural net in a nonlinear way preserving the topological order of the input vectors. These mappings are studied using a nonlinear power system model.

A Split-GFP Gateway Cloning System for Topology Analyses of Membrane Proteins in Plants.

PubMed

Xie, Wenjun; Nielsen, Mads Eggert; Pedersen, Carsten; Thordal-Christensen, Hans

2017-01-01

To understand the function of membrane proteins, it is imperative to know their topology. For such studies, a split green fluorescent protein (GFP) method is useful. GFP is barrel-shaped, consisting of 11 β-sheets. When the first ten β-sheets (GFP1-10) and the 11th β-sheet (GFP11) are expressed from separate genes they will self-assembly and reconstitute a fluorescent GFP protein. However, this will only occur when the two domains co-localize in the same cellular compartment. We have developed an easy-to-use Gateway vector set for determining on which side of the membrane the N- and C-termini are located. Two vectors were designed for making N- and C-terminal fusions between the membrane proteins-of-interest and GFP11, while another three plasmids were designed to express GFP1-10 in either the cytosol, the endoplasmic reticulum (ER) lumen or the apoplast. We tested functionality of the system by applying the vector set for the transmembrane domain, CNXTM, of the ER membrane protein, calnexin, after transient expression in Nicotiana benthamiana leaves. We observed GFP signal from the ER when we reciprocally co-expressed GFP11-CNXTM with GFP1-10-HDEL and CNXTM-GFP with cytosolic GFP1-10. The opposite combinations did not result in GFP signal emission. This test using the calnexin ER-membrane domain demonstrated its C-terminus to be in the cytosol and its N-terminus in the ER lumen. This result confirmed the known topology of calnexin, and we therefore consider this split-GFP system highly useful for ER membrane topology studies. Furthermore, the vector set provided is useful for detecting the topology of proteins on other membranes in the cell, which we confirmed for a plasma membrane syntaxin. The set of five Ti-plasmids are easily and efficiently used for Gateway cloning and transient transformation of N. benthamiana leaves.

The inner topological structure and defect control of magnetic skyrmions

NASA Astrophysics Data System (ADS)

Ren, Ji-Rong; Yu, Zhong-Xi

2017-10-01

We prove that the integrand of magnetic skyrmions can be expressed as curvature tensor of Wu-Yang potential. Taking the projection of the normalized magnetization vector on the 2-dim material surface, and according to Duan's decomposition theory of gauge potential, we reveal that every single skyrmion is just characterized by Hopf index and Brouwer degree at the zero point of this vector field. Our theory meet the results that experimental physicists have achieved by many technologies. The inner topological structure expression of skyrmion with Hopf index and Brouwer degree will be indispensable mathematical basis of skyrmion logic gates.

Novel methods for parameter-based analysis of myocardial tissue in MR images

NASA Astrophysics Data System (ADS)

Hennemuth, A.; Behrens, S.; Kuehnel, C.; Oeltze, S.; Konrad, O.; Peitgen, H.-O.

2007-03-01

The analysis of myocardial tissue with contrast-enhanced MR yields multiple parameters, which can be used to classify the examined tissue. Perfusion images are often distorted by motion, while late enhancement images are acquired with a different size and resolution. Therefore, it is common to reduce the analysis to a visual inspection, or to the examination of parameters related to the 17-segment-model proposed by the American Heart Association (AHA). As this simplification comes along with a considerable loss of information, our purpose is to provide methods for a more accurate analysis regarding topological and functional tissue features. In order to achieve this, we implemented registration methods for the motion correction of the perfusion sequence and the matching of the late enhancement information onto the perfusion image and vice versa. For the motion corrected perfusion sequence, vector images containing the voxel enhancement curves' semi-quantitative parameters are derived. The resulting vector images are combined with the late enhancement information and form the basis for the tissue examination. For the exploration of data we propose different modes: the inspection of the enhancement curves and parameter distribution in areas automatically segmented using the late enhancement information, the inspection of regions segmented in parameter space by user defined threshold intervals and the topological comparison of regions segmented with different settings. Results showed a more accurate detection of distorted regions in comparison to the AHA-model-based evaluation.

Topological responses from chiral anomaly in multi-Weyl semimetals

NASA Astrophysics Data System (ADS)

Huang, Ze-Min; Zhou, Jianhui; Shen, Shun-Qing

2017-08-01

Multi-Weyl semimetals are a kind of topological phase of matter with discrete Weyl nodes characterized by multiple monopole charges, in which the chiral anomaly, the anomalous nonconservation of an axial current, occurs in the presence of electric and magnetic fields. Electronic transport properties related to the chiral anomaly in the presence of both electromagnetic fields and axial electromagnetic fields in multi-Weyl semimetals are systematically studied. It has been found that the anomalous Hall conductivity has a modification linear in the axial vector potential from inhomogeneous strains. The axial electric field leads to an axial Hall current that is proportional to the distance of Weyl nodes in momentum space. This axial current may generate chirality accumulation of Weyl fermions through delicately engineering the axial electromagnetic fields even in the absence of external electromagnetic fields. Therefore this work provides a nonmagnetic mechanism of generation of chirality accumulation in Weyl semimetals and might shed new light on the application of Weyl semimetals in the emerging field of valleytronics.

Biot-Savart helicity versus physical helicity: A topological description of ideal flows

NASA Astrophysics Data System (ADS)

Sahihi, Taliya; Eshraghi, Homayoon

2014-08-01

For an isentropic (thus compressible) flow, fluid trajectories are considered as orbits of a family of one parameter, smooth, orientation-preserving, and nonsingular diffeomorphisms on a compact and smooth-boundary domain in the Euclidian 3-space which necessarily preserve a finite measure, later interpreted as the fluid mass. Under such diffeomorphisms the Biot-Savart helicity of the pushforward of a divergence-free and tangent to the boundary vector field is proved to be conserved and since these circumstances present an isentropic flow, the conservation of the "Biot-Savart helicity" is established for such flows. On the other hand, the well known helicity conservation in ideal flows which here we call it "physical helicity" is found to be an independent constant with respect to the Biot-Savart helicity. The difference between these two helicities reflects some topological features of the domain as well as the velocity and vorticity fields which is discussed and is shown for simply connected domains the two helicities coincide. The energy variation of the vorticity field is shown to be formally the same as for the incompressible flow obtained before. For fluid domains consisting of several disjoint solid tori, at each time, the harmonic knot subspace of smooth vector fields on the fluid domain is found to have two independent base sets with a special type of orthogonality between these two bases by which a topological description of the vortex and velocity fields depending on the helicity difference is achieved since this difference is shown to depend only on the harmonic knot parts of velocity, vorticity, and its Biot-Savart vector field. For an ideal magnetohydrodynamics (MHD) flow three independent constant helicities are reviewed while the helicity of magnetic potential is generalized for non-simply connected domains by inserting a special harmonic knot field in the dynamics of the magnetic potential. It is proved that the harmonic knot part of the vorticity in hydrodynamics and the magnetic field in MHD is presented by constant coefficients (fluxes) when expanded in terms of one of the time dependent base functions.

Singular trajectories: space-time domain topology of developing speckle fields

NASA Astrophysics Data System (ADS)

Vasil'ev, Vasiliy; Soskin, Marat S.

2010-02-01

It is shown the space-time dynamics of optical singularities is fully described by singularities trajectories in space-time domain, or evolution of transverse coordinates(x, y) in some fixed plane z0. The dynamics of generic developing speckle fields was realized experimentally by laser induced scattering in LiNbO3:Fe photorefractive crystal. The space-time trajectories of singularities can be divided topologically on two classes with essentially different scenario and duration. Some of them (direct topological reactions) consist from nucleation of singularities pair at some (x, y, z0, t) point, their movement and annihilation. They possess form of closed loops with relatively short time of existence. Another much more probable class of trajectories are chain topological reactions. Each of them consists from sequence of links, i.e. of singularities nucleation in various points (xi yi, ti) and following annihilation of both singularities in other space-time points with alien singularities of opposite topological indices. Their topology and properties are established. Chain topological reactions can stop on the borders of a developing speckle field or go to infinity. Examples of measured both types of topological reactions for optical vortices (polarization C points) in scalar (elliptically polarized) natural developing speckle fields are presented.

Vector Beam Polarization State Spectrum Analyzer.

PubMed

Moreno, Ignacio; Davis, Jeffrey A; Badham, Katherine; Sánchez-López, María M; Holland, Joseph E; Cottrell, Don M

2017-05-22

We present a proof of concept for a vector beam polarization state spectrum analyzer based on the combination of a polarization diffraction grating (PDG) and an encoded harmonic q-plate grating (QPG). As a result, a two-dimensional polarization diffraction grating is formed that generates six different q-plate channels with topological charges from -3 to +3 in the horizontal direction, and each is split in the vertical direction into the six polarization channels at the cardinal points of the corresponding higher-order Poincaré sphere. Consequently, 36 different channels are generated in parallel. This special polarization diffractive element is experimentally demonstrated using a single phase-only spatial light modulator in a reflective optical architecture. Finally, we show that this system can be used as a vector beam polarization state spectrum analyzer, where both the topological charge and the state of polarization of an input vector beam can be simultaneously determined in a single experiment. We expect that these results would be useful for applications in optical communications.

Finite Topological Spaces as a Pedagogical Tool

ERIC Educational Resources Information Center

Helmstutler, Randall D.; Higginbottom, Ryan S.

2012-01-01

We propose the use of finite topological spaces as examples in a point-set topology class especially suited to help students transition into abstract mathematics. We describe how carefully chosen examples involving finite spaces may be used to reinforce concepts, highlight pathologies, and develop students' non-Euclidean intuition. We end with a…

Topological BF Theories

NASA Astrophysics Data System (ADS)

Sǎraru, Silviu-Constantin

Topological field theories originate in the papers of Schwarz and Witten. Initially, Schwarz shown that one of the topological invariants, namely the Ray-Singer torsion, can be represented as the partition function of a certain quantum field theory. Subsequently, Witten constructed a framework for understanding Morse theory in terms of supersymmetric quantum mechanics. These two constructions represent the prototypes of all topological field theories. The model used by Witten has been applied to classical index theorems and, moreover, suggested some generalizations that led to new mathematical results on holomorphic Morse inequalities. Starting with these results, further developments in the domain of topological field theories have been achieved. The Becchi-Rouet-Stora-Tyutin (BRST) symmetry allowed for a new definition of topological ...eld theories as theories whose BRST-invariant Hamiltonian is also BRST-exact. An important class of topological theories of Schwarz type is the class of BF models. This type of models describes three-dimensional quantum gravity and is useful at the study of four-dimensional quantum gravity in Ashtekar-Rovelli-Smolin formulation. Two-dimensional BF models are correlated to Poisson sigma models from various two-dimensional gravities. The analysis of Poisson sigma models, including their relationship to two-dimensional gravity and the study of classical solutions, has been intensively studied in the literature. In this thesis we approach the problem of construction of some classes of interacting BF models in the context of the BRST formalism. In view of this, we use the method of the deformation of the BRST charge and BRST-invariant Hamiltonian. Both methods rely on specific techniques of local BRST cohomology. The main hypotheses in which we construct the above mentioned interactions are: space-time locality, Poincare invariance, smoothness of deformations in the coupling constant and the preservation of the number of derivatives on each field. The first two hypotheses implies that the resulting interacting theory must be local in space-time and Poincare invariant. The smoothness of deformations means that the deformed objects that contribute to the construction of interactions must be smooth in the coupling constant and reduce to the objects corresponding to the free theory in the zero limit of the coupling constant. The preservation of the number of derivatives on each field imp! lies two aspects that must be simultaneously fulfilled: (i) the differential order of each free field equation must coincide with that of the corresponding interacting field equation; (ii) the maximum number of space-time derivatives from the interacting vertices cannot exceed the maximum number of derivatives from the free Lagrangian. The main results obtained can be synthesized into: obtaining self-interactions for certain classes of BF models; generation of couplings between some classes of BF theories and matter theories; construction of interactions between a class of BF models and a system of massless vector fields.

C library for topological study of the electronic charge density.

PubMed

Vega, David; Aray, Yosslen; Rodríguez, Jesús

2012-12-05

The topological study of the electronic charge density is useful to obtain information about the kinds of bonds (ionic or covalent) and the atom charges on a molecule or crystal. For this study, it is necessary to calculate, at every space point, the electronic density and its electronic density derivatives values up to second order. In this work, a grid-based method for these calculations is described. The library, implemented for three dimensions, is based on a multidimensional Lagrange interpolation in a regular grid; by differentiating the resulting polynomial, the gradient vector, the Hessian matrix and the Laplacian formulas were obtained for every space point. More complex functions such as the Newton-Raphson method (to find the critical points, where the gradient is null) and the Cash-Karp Runge-Kutta method (used to make the gradient paths) were programmed. As in some crystals, the unit cell has angles different from 90°, the described library includes linear transformations to correct the gradient and Hessian when the grid is distorted (inclined). Functions were also developed to handle grid containing files (grd from DMol® program, CUBE from Gaussian® program and CHGCAR from VASP® program). Each one of these files contains the data for a molecular or crystal electronic property (such as charge density, spin density, electrostatic potential, and others) in a three-dimensional (3D) grid. The library can be adapted to make the topological study in any regular 3D grid by modifying the code of these functions. Copyright © 2012 Wiley Periodicals, Inc.

Phylogenetic mixtures and linear invariants for equal input models.

PubMed

Casanellas, Marta; Steel, Mike

2017-04-01

The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the 'equal input model'. This model generalizes the 'Felsenstein 1981' model (and thereby the Jukes-Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a 'random cluster' process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees-the so called 'model invariants'), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of [Formula: see text] leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167-191, 1987).

Search for Dark Matter and Supersymmetry with a Compressed Mass Spectrum in the Vector Boson Fusion Topology in Proton-Proton Collisions at s = 8 TeV

DOE PAGES

Khachatryan, V.; Sirunyan, A. M.; Tumasyan, A.; ...

2017-01-12

A first search for pair production of dark matter candidates through vector boson fusion in proton-proton collisions atmore » $$\\sqrt{s}$$=8 TeV is performed with the CMS detector. The vector boson fusion topology enhances missing transverse momentum, providing a way to probe supersymmetry, even in the case of a compressed mass spectrum. The data sample corresponds to an integrated luminosity of 18.5 fb $-$1, recorded by the CMS experiment. The observed dijet mass spectrum is consistent with the standard model expectation. In an effective field theory, dark matter masses are explored as a function of contact interaction strength. Lastly, the most stringent limit on bottom squark production with mass below 315 GeV is also reported, assuming a 5 GeV mass difference with respect to the lightest neutralino.« less

Search for Dark Matter and Supersymmetry with a Compressed Mass Spectrum in the Vector Boson Fusion Topology in Proton-Proton Collisions at s = 8 TeV

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

Khachatryan, V.; Sirunyan, A. M.; Tumasyan, A.

A first search for pair production of dark matter candidates through vector boson fusion in proton-proton collisions atmore » $$\\sqrt{s}$$=8 TeV is performed with the CMS detector. The vector boson fusion topology enhances missing transverse momentum, providing a way to probe supersymmetry, even in the case of a compressed mass spectrum. The data sample corresponds to an integrated luminosity of 18.5 fb $-$1, recorded by the CMS experiment. The observed dijet mass spectrum is consistent with the standard model expectation. In an effective field theory, dark matter masses are explored as a function of contact interaction strength. Lastly, the most stringent limit on bottom squark production with mass below 315 GeV is also reported, assuming a 5 GeV mass difference with respect to the lightest neutralino.« less

Search for Dark Matter and Supersymmetry with a Compressed Mass Spectrum in the Vector Boson Fusion Topology in Proton-Proton Collisions at sqrt[s]=8  TeV.

PubMed

Khachatryan, V; Sirunyan, A M; Tumasyan, A; Adam, W; Asilar, E; Bergauer, T; Brandstetter, J; Brondolin, E; Dragicevic, M; Erö, J; Flechl, M; Friedl, M; Frühwirth, R; Ghete, V M; Hartl, C; Hörmann, N; Hrubec, J; Jeitler, M; König, A; Krätschmer, I; Liko, D; Matsushita, T; Mikulec, I; Rabady, D; Rad, N; Rahbaran, B; Rohringer, H; Schieck, J; Strauss, J; Treberer-Treberspurg, W; Waltenberger, W; Wulz, C-E; Mossolov, V; Shumeiko, N; Suarez Gonzalez, J; Alderweireldt, S; Cornelis, T; De Wolf, E A; Janssen, X; Knutsson, A; Lauwers, J; Luyckx, S; Van De Klundert, M; Van Haevermaet, H; Van Mechelen, P; Van Remortel, N; Van Spilbeeck, A; Abu Zeid, S; Blekman, F; D'Hondt, J; Daci, N; De Bruyn, I; Deroover, K; Heracleous, N; Lowette, S; Moortgat, S; Moreels, L; Olbrechts, A; Python, Q; Tavernier, S; Van Doninck, W; Van Mulders, P; Van Parijs, I; Brun, H; Caillol, C; Clerbaux, B; De Lentdecker, G; Delannoy, H; Fasanella, G; Favart, L; Goldouzian, R; Grebenyuk, A; Karapostoli, G; Lenzi, T; Léonard, A; Maerschalk, T; Marinov, A; Randle-Conde, A; Seva, T; Vander Velde, C; Vanlaer, P; Yonamine, R; Zenoni, F; Zhang, F; Cimmino, A; Dobur, D; Fagot, A; Garcia, G; Gul, M; Mccartin, J; Poyraz, D; Salva, S; Schöfbeck, R; Tytgat, M; Van Driessche, W; Yazgan, E; Zaganidis, N; Beluffi, C; Bondu, O; Brochet, S; Bruno, G; Caudron, A; Ceard, L; De Visscher, S; Delaere, C; Delcourt, M; Forthomme, L; Francois, B; Giammanco, A; Jafari, A; Jez, P; Komm, M; Lemaitre, V; Magitteri, A; Mertens, A; Musich, M; Nuttens, C; Piotrzkowski, K; Quertenmont, L; Selvaggi, M; Vidal Marono, M; Wertz, S; Beliy, N; Aldá Júnior, W L; Alves, F L; Alves, G A; Brito, L; Correa Martins Junior, M; Hensel, C; Moraes, A; Pol, M E; Rebello Teles, P; Belchior Batista Das Chagas, E; Carvalho, W; Chinellato, J; Custódio, A; Da Costa, E M; Da Silveira, G G; De Jesus Damiao, D; De Oliveira Martins, C; Fonseca De Souza, S; Huertas Guativa, L M; Malbouisson, H; Matos Figueiredo, D; Mora Herrera, C; Mundim, L; Nogima, H; Prado Da Silva, W L; Santoro, A; Sznajder, A; Tonelli Manganote, E J; Vilela Pereira, A; Ahuja, S; Bernardes, C A; Dogra, S; Fernandez Perez Tomei, T R; Gregores, E M; Mercadante, P G; Moon, C S; Novaes, S F; Padula, Sandra S; Romero Abad, D; Ruiz Vargas, J C; Aleksandrov, A; Hadjiiska, R; Iaydjiev, P; Rodozov, M; Stoykova, S; Sultanov, G; Vutova, M; Dimitrov, A; Glushkov, I; Litov, L; Pavlov, B; Petkov, P; Fang, W; Ahmad, M; Bian, J G; Chen, G M; Chen, H S; Chen, M; Chen, Y; Cheng, T; Du, R; Jiang, C H; Leggat, D; Liu, Z; Romeo, F; Shaheen, S M; Spiezia, A; Tao, J; Wang, C; Wang, Z; Zhang, H; Zhao, J; Asawatangtrakuldee, C; Ban, Y; Li, Q; Liu, S; Mao, Y; Qian, S J; Wang, D; Xu, Z; Avila, C; Cabrera, A; Chaparro Sierra, L F; Florez, C; Gomez, J P; Ruiz Alvarez, J D; Sanabria, J C; Godinovic, N; Lelas, D; Puljak, I; Ribeiro Cipriano, P M; Antunovic, Z; Kovac, M; Brigljevic, V; Ferencek, D; Kadija, K; Luetic, J; Micanovic, S; Sudic, L; Attikis, A; Mavromanolakis, G; Mousa, J; Nicolaou, C; Ptochos, F; Razis, P A; Rykaczewski, H; Finger, M; Finger, M; Carrera Jarrin, E; Awad, A; Elgammal, S; Mohamed, A; Salama, E; Calpas, B; Kadastik, M; Murumaa, M; Perrini, L; Raidal, M; Tiko, A; Veelken, C; Eerola, P; Pekkanen, J; Voutilainen, M; Härkönen, J; Karimäki, V; Kinnunen, R; Lampén, T; Lassila-Perini, K; Lehti, S; Lindén, T; Luukka, P; Peltola, T; Tuominiemi, J; Tuovinen, E; Wendland, L; Talvitie, J; Tuuva, T; Besancon, M; Couderc, F; Dejardin, M; Denegri, D; Fabbro, B; Faure, J L; Favaro, C; Ferri, F; Ganjour, S; Ghosh, S; Givernaud, A; Gras, P; Hamel de Monchenault, G; Jarry, P; Locci, E; Machet, M; Malcles, J; Rander, J; Rosowsky, A; Titov, M; Zghiche, A; Abdulsalam, A; Antropov, I; Baffioni, S; Beaudette, F; Busson, P; Cadamuro, L; Chapon, E; Charlot, C; Davignon, O; Granier de Cassagnac, R; Jo, M; Lisniak, S; Miné, P; Naranjo, I N; Nguyen, M; Ochando, C; Ortona, G; Paganini, P; Pigard, P; Regnard, S; Salerno, R; Sirois, Y; Strebler, T; Yilmaz, Y; Zabi, A; Agram, J-L; Andrea, J; Aubin, A; Bloch, D; Brom, J-M; Buttignol, M; Chabert, E C; Chanon, N; Collard, C; Conte, E; Coubez, X; Fontaine, J-C; Gelé, D; Goerlach, U; Le Bihan, A-C; Merlin, J A; Skovpen, K; Van Hove, P; Gadrat, S; Beauceron, S; Bernet, C; Boudoul, G; Bouvier, E; Carrillo Montoya, C A; Chierici, R; Contardo, D; Courbon, B; Depasse, P; El Mamouni, H; Fan, J; Fay, J; Gascon, S; Gouzevitch, M; Grenier, G; Ille, B; Lagarde, F; Laktineh, I B; Lethuillier, M; Mirabito, L; Pequegnot, A L; Perries, S; Popov, A; Sabes, D; Sordini, V; Vander Donckt, M; Verdier, P; Viret, S; Toriashvili, T; Tsamalaidze, Z; Autermann, C; Beranek, S; Feld, L; Heister, A; Kiesel, M K; Klein, K; Lipinski, M; Ostapchuk, A; Preuten, M; Raupach, F; Schael, S; Schomakers, C; Schulte, J F; Schulz, J; Verlage, T; Weber, H; Zhukov, V; Ata, M; Brodski, M; Dietz-Laursonn, E; Duchardt, D; Endres, M; Erdmann, M; Erdweg, S; Esch, T; Fischer, R; Güth, A; Hebbeker, T; Heidemann, C; Hoepfner, K; Knutzen, S; Merschmeyer, M; Meyer, A; Millet, P; Mukherjee, S; Olschewski, M; Padeken, K; Papacz, P; Pook, T; Radziej, M; Reithler, H; Rieger, M; Scheuch, F; Sonnenschein, L; Teyssier, D; Thüer, S; Cherepanov, V; Erdogan, Y; Flügge, G; Geenen, H; Geisler, M; Hoehle, F; Kargoll, B; Kress, T; Künsken, A; Lingemann, J; Nehrkorn, A; Nowack, A; Nugent, I M; Pistone, C; Pooth, O; Stahl, A; Aldaya Martin, M; Asin, I; Beernaert, K; Behnke, O; Behrens, U; Bin Anuar, A A; Borras, K; Campbell, A; Connor, P; Contreras-Campana, C; Costanza, F; Diez Pardos, C; Dolinska, G; Eckerlin, G; Eckstein, D; Eichhorn, T; Gallo, E; Garay Garcia, J; Geiser, A; Gizhko, A; Grados Luyando, J M; Gunnellini, P; Harb, A; Hauk, J; Hempel, M; Jung, H; Kalogeropoulos, A; Karacheban, O; Kasemann, M; Kieseler, J; Kleinwort, C; Korol, I; Lange, W; Lelek, A; Leonard, J; Lipka, K; Lobanov, A; Lohmann, W; Mankel, R; Melzer-Pellmann, I-A; Meyer, A B; Mittag, G; Mnich, J; Mussgiller, A; Ntomari, E; Pitzl, D; Placakyte, R; Raspereza, A; Roland, B; Sahin, M Ö; Saxena, P; Schoerner-Sadenius, T; Seitz, C; Spannagel, S; 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Ruggles, T; Savin, A; Sharma, A; Smith, N; Smith, W H; Taylor, D; Verwilligen, P; Woods, N

2017-01-13

A first search for pair production of dark matter candidates through vector boson fusion in proton-proton collisions at sqrt[s]=8  TeV is performed with the CMS detector. The vector boson fusion topology enhances missing transverse momentum, providing a way to probe supersymmetry, even in the case of a compressed mass spectrum. The data sample corresponds to an integrated luminosity of 18.5  fb^{-1}, recorded by the CMS experiment. The observed dijet mass spectrum is consistent with the standard model expectation. In an effective field theory, dark matter masses are explored as a function of contact interaction strength. The most stringent limit on bottom squark production with mass below 315 GeV is also reported, assuming a 5 GeV mass difference with respect to the lightest neutralino.

Search for Dark Matter and Supersymmetry with a Compressed Mass Spectrum in the Vector Boson Fusion Topology in Proton-Proton Collisions at √{s }=8 TeV

NASA Astrophysics Data System (ADS)

Khachatryan, V.; Sirunyan, A. M.; Tumasyan, A.; Adam, W.; Asilar, E.; Bergauer, T.; Brandstetter, J.; Brondolin, E.; Dragicevic, M.; Erö, J.; Flechl, M.; Friedl, M.; Frühwirth, R.; Ghete, V. M.; Hartl, C.; Hörmann, N.; Hrubec, J.; Jeitler, M.; König, A.; Krätschmer, I.; Liko, D.; Matsushita, T.; Mikulec, I.; Rabady, D.; Rad, N.; Rahbaran, B.; Rohringer, H.; Schieck, J.; Strauss, J.; Treberer-Treberspurg, W.; Waltenberger, W.; Wulz, C.-E.; Mossolov, V.; Shumeiko, N.; Suarez Gonzalez, J.; Alderweireldt, S.; Cornelis, T.; De Wolf, E. A.; Janssen, X.; Knutsson, A.; Lauwers, J.; Luyckx, S.; Van De Klundert, M.; Van Haevermaet, H.; Van Mechelen, P.; Van Remortel, N.; Van Spilbeeck, A.; Abu Zeid, S.; Blekman, F.; D'Hondt, J.; Daci, N.; De Bruyn, I.; Deroover, K.; Heracleous, N.; Lowette, S.; Moortgat, S.; Moreels, L.; Olbrechts, A.; Python, Q.; Tavernier, S.; Van Doninck, W.; Van Mulders, P.; Van Parijs, I.; Brun, H.; Caillol, C.; Clerbaux, B.; De Lentdecker, G.; Delannoy, H.; Fasanella, G.; Favart, L.; Goldouzian, R.; Grebenyuk, A.; Karapostoli, G.; Lenzi, T.; Léonard, A.; Maerschalk, T.; Marinov, A.; Randle-conde, A.; Seva, T.; Vander Velde, C.; Vanlaer, P.; Yonamine, R.; Zenoni, F.; Zhang, F.; Cimmino, A.; Dobur, D.; Fagot, A.; Garcia, G.; Gul, M.; Mccartin, J.; Poyraz, D.; Salva, S.; Schöfbeck, R.; Tytgat, M.; Van Driessche, W.; Yazgan, E.; Zaganidis, N.; Beluffi, C.; Bondu, O.; Brochet, S.; Bruno, G.; Caudron, A.; Ceard, L.; De Visscher, S.; Delaere, C.; Delcourt, M.; Forthomme, L.; Francois, B.; Giammanco, A.; Jafari, A.; Jez, P.; Komm, M.; Lemaitre, V.; Magitteri, A.; Mertens, A.; Musich, M.; Nuttens, C.; Piotrzkowski, K.; Quertenmont, L.; Selvaggi, M.; Vidal Marono, M.; Wertz, S.; Beliy, N.; Aldá Júnior, W. L.; Alves, F. L.; Alves, G. A.; Brito, L.; Correa Martins Junior, M.; Hensel, C.; Moraes, A.; Pol, M. E.; Rebello Teles, P.; Belchior Batista Das Chagas, E.; Carvalho, W.; Chinellato, J.; Custódio, A.; Da Costa, E. M.; Da Silveira, G. G.; De Jesus Damiao, D.; De Oliveira Martins, C.; Fonseca De Souza, S.; Huertas Guativa, L. M.; Malbouisson, H.; Matos Figueiredo, D.; Mora Herrera, C.; Mundim, L.; Nogima, H.; Prado Da Silva, W. L.; Santoro, A.; Sznajder, A.; Tonelli Manganote, E. J.; Vilela Pereira, A.; Ahuja, S.; Bernardes, C. A.; Dogra, S.; Fernandez Perez Tomei, T. R.; Gregores, E. M.; Mercadante, P. G.; Moon, C. S.; Novaes, S. F.; Padula, Sandra S.; Romero Abad, D.; Ruiz Vargas, J. C.; Aleksandrov, A.; Hadjiiska, R.; Iaydjiev, P.; Rodozov, M.; Stoykova, S.; Sultanov, G.; Vutova, M.; Dimitrov, A.; Glushkov, I.; Litov, L.; Pavlov, B.; Petkov, P.; Fang, W.; Ahmad, M.; Bian, J. G.; Chen, G. M.; Chen, H. S.; Chen, M.; Chen, Y.; Cheng, T.; Du, R.; Jiang, C. H.; Leggat, D.; Liu, Z.; Romeo, F.; Shaheen, S. M.; Spiezia, A.; Tao, J.; Wang, C.; Wang, Z.; Zhang, H.; Zhao, J.; Asawatangtrakuldee, C.; Ban, Y.; Li, Q.; Liu, S.; Mao, Y.; Qian, S. J.; Wang, D.; Xu, Z.; Avila, C.; Cabrera, A.; Chaparro Sierra, L. F.; Florez, C.; Gomez, J. P.; Ruiz Alvarez, J. D.; Sanabria, J. C.; Godinovic, N.; Lelas, D.; Puljak, I.; Ribeiro Cipriano, P. M.; Antunovic, Z.; Kovac, M.; Brigljevic, V.; Ferencek, D.; Kadija, K.; Luetic, J.; Micanovic, S.; Sudic, L.; Attikis, A.; Mavromanolakis, G.; Mousa, J.; Nicolaou, C.; Ptochos, F.; Razis, P. A.; Rykaczewski, H.; Finger, M.; Finger, M.; Carrera Jarrin, E.; Awad, A.; Elgammal, S.; Mohamed, A.; Salama, E.; Calpas, B.; Kadastik, M.; Murumaa, M.; Perrini, L.; Raidal, M.; Tiko, A.; Veelken, C.; Eerola, P.; Pekkanen, J.; Voutilainen, M.; Härkönen, J.; Karimäki, V.; Kinnunen, R.; Lampén, T.; Lassila-Perini, K.; Lehti, S.; Lindén, T.; Luukka, P.; Peltola, T.; Tuominiemi, J.; Tuovinen, E.; Wendland, L.; Talvitie, J.; Tuuva, T.; Besancon, M.; Couderc, F.; Dejardin, M.; Denegri, D.; Fabbro, B.; Faure, J. L.; Favaro, C.; Ferri, F.; Ganjour, S.; Ghosh, S.; Givernaud, A.; Gras, P.; Hamel de Monchenault, G.; Jarry, P.; Locci, E.; Machet, M.; Malcles, J.; Rander, J.; Rosowsky, A.; Titov, M.; Zghiche, A.; Abdulsalam, A.; Antropov, I.; Baffioni, S.; Beaudette, F.; Busson, P.; Cadamuro, L.; Chapon, E.; Charlot, C.; Davignon, O.; Granier de Cassagnac, R.; Jo, M.; Lisniak, S.; Miné, P.; Naranjo, I. 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F.; Schulz, J.; Verlage, T.; Weber, H.; Zhukov, V.; Ata, M.; Brodski, M.; Dietz-Laursonn, E.; Duchardt, D.; Endres, M.; Erdmann, M.; Erdweg, S.; Esch, T.; Fischer, R.; Güth, A.; Hebbeker, T.; Heidemann, C.; Hoepfner, K.; Knutzen, S.; Merschmeyer, M.; Meyer, A.; Millet, P.; Mukherjee, S.; Olschewski, M.; Padeken, K.; Papacz, P.; Pook, T.; Radziej, M.; Reithler, H.; Rieger, M.; Scheuch, F.; Sonnenschein, L.; Teyssier, D.; Thüer, S.; Cherepanov, V.; Erdogan, Y.; Flügge, G.; Geenen, H.; Geisler, M.; Hoehle, F.; Kargoll, B.; Kress, T.; Künsken, A.; Lingemann, J.; Nehrkorn, A.; Nowack, A.; Nugent, I. M.; Pistone, C.; Pooth, O.; Stahl, A.; Aldaya Martin, M.; Asin, I.; Beernaert, K.; Behnke, O.; Behrens, U.; Bin Anuar, A. A.; Borras, K.; Campbell, A.; Connor, P.; Contreras-Campana, C.; Costanza, F.; Diez Pardos, C.; Dolinska, G.; Eckerlin, G.; Eckstein, D.; Eichhorn, T.; Gallo, E.; Garay Garcia, J.; Geiser, A.; Gizhko, A.; Grados Luyando, J. M.; Gunnellini, P.; Harb, A.; Hauk, J.; Hempel, M.; Jung, H.; Kalogeropoulos, A.; Karacheban, O.; Kasemann, M.; Kieseler, J.; Kleinwort, C.; Korol, I.; Lange, W.; Lelek, A.; Leonard, J.; Lipka, K.; Lobanov, A.; Lohmann, W.; Mankel, R.; Melzer-Pellmann, I.-A.; Meyer, A. B.; Mittag, G.; Mnich, J.; Mussgiller, A.; Ntomari, E.; Pitzl, D.; Placakyte, R.; Raspereza, A.; Roland, B.; Sahin, M. Ö.; Saxena, P.; Schoerner-Sadenius, T.; Seitz, C.; Spannagel, S.; Stefaniuk, N.; Trippkewitz, K. D.; Van Onsem, G. P.; Walsh, R.; Wissing, C.; Blobel, V.; Centis Vignali, M.; Draeger, A. R.; Dreyer, T.; Erfle, J.; Garutti, E.; Goebel, K.; Gonzalez, D.; Görner, M.; Haller, J.; Hoffmann, M.; Höing, R. 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J.; Ulrich, R.; Wagner-Kuhr, J.; Wayand, S.; Weber, M.; Weiler, T.; Williamson, S.; Wöhrmann, C.; Wolf, R.; Anagnostou, G.; Daskalakis, G.; Geralis, T.; Giakoumopoulou, V. A.; Kyriakis, A.; Loukas, D.; Topsis-Giotis, I.; Agapitos, A.; Kesisoglou, S.; Panagiotou, A.; Saoulidou, N.; Tziaferi, E.; Evangelou, I.; Flouris, G.; Foudas, C.; Kokkas, P.; Loukas, N.; Manthos, N.; Papadopoulos, I.; Paradas, E.; Filipovic, N.; Bencze, G.; Hajdu, C.; Hidas, P.; Horvath, D.; Sikler, F.; Veszpremi, V.; Vesztergombi, G.; Zsigmond, A. J.; Beni, N.; Czellar, S.; Karancsi, J.; Molnar, J.; Szillasi, Z.; Bartók, M.; Makovec, A.; Raics, P.; Trocsanyi, Z. L.; Ujvari, B.; Bahinipati, S.; Choudhury, S.; Mal, P.; Mandal, K.; Nayak, A.; Sahoo, D. K.; Sahoo, N.; Swain, S. K.; Bansal, S.; Beri, S. B.; Bhatnagar, V.; Chawla, R.; Gupta, R.; Bhawandeep, U.; Kalsi, A. K.; Kaur, A.; Kaur, M.; Kumar, R.; Mehta, A.; Mittal, M.; Singh, J. B.; Walia, G.; Kumar, Ashok; Bhardwaj, A.; Choudhary, B. C.; Garg, R. B.; Keshri, S.; Kumar, A.; Malhotra, S.; Naimuddin, M.; Nishu, N.; Ranjan, K.; Sharma, R.; Sharma, V.; Bhattacharya, R.; Bhattacharya, S.; Chatterjee, K.; Dey, S.; Dutt, S.; Dutta, S.; Ghosh, S.; Majumdar, N.; Modak, A.; Mondal, K.; Mukhopadhyay, S.; Nandan, S.; Purohit, A.; Roy, A.; Roy, D.; Roy Chowdhury, S.; Sarkar, S.; Sharan, M.; Thakur, S.; Behera, P. K.; Chudasama, R.; Dutta, D.; Jha, V.; Kumar, V.; Mohanty, A. K.; Netrakanti, P. K.; Pant, L. M.; Shukla, P.; Topkar, A.; Aziz, T.; Banerjee, S.; Bhowmik, S.; Chatterjee, R. M.; Dewanjee, R. K.; Dugad, S.; Ganguly, S.; Guchait, M.; Gurtu, A.; Jain, Sa.; Kole, G.; Kumar, S.; Mahakud, B.; Maity, M.; Majumder, G.; Mazumdar, K.; Mitra, S.; Mohanty, G. B.; Parida, B.; Sarkar, T.; Sur, N.; Sutar, B.; Wickramage, N.; Chauhan, S.; Dube, S.; Kapoor, A.; Kothekar, K.; Rane, A.; Sharma, S.; Bakhshiansohi, H.; Behnamian, H.; Chenarani, S.; Eskandari Tadavani, E.; Etesami, S. M.; Fahim, A.; Khakzad, M.; Mohammadi Najafabadi, M.; Naseri, M.; Paktinat Mehdiabadi, S.; Rezaei Hosseinabadi, F.; Safarzadeh, B.; Zeinali, M.; Felcini, M.; Grunewald, M.; Abbrescia, M.; Calabria, C.; Caputo, C.; Colaleo, A.; Creanza, D.; Cristella, L.; De Filippis, N.; De Palma, M.; Fiore, L.; Iaselli, G.; Maggi, G.; Maggi, M.; Miniello, G.; My, S.; Nuzzo, S.; Pompili, A.; Pugliese, G.; Radogna, R.; Ranieri, A.; Selvaggi, G.; Silvestris, L.; Venditti, R.; Abbiendi, G.; Battilana, C.; Bonacorsi, D.; Braibant-Giacomelli, S.; Brigliadori, L.; Campanini, R.; Capiluppi, P.; Castro, A.; Cavallo, F. R.; Chhibra, S. S.; Codispoti, G.; Cuffiani, M.; Dallavalle, G. M.; Fabbri, F.; Fanfani, A.; Fasanella, D.; Giacomelli, P.; Grandi, C.; Guiducci, L.; Marcellini, S.; Masetti, G.; Montanari, A.; Navarria, F. L.; Perrotta, A.; Rossi, A. M.; Rovelli, T.; Siroli, G. P.; Tosi, N.; Albergo, S.; Chiorboli, M.; Costa, S.; Di Mattia, A.; Giordano, F.; Potenza, R.; Tricomi, A.; Tuve, C.; Barbagli, G.; Ciulli, V.; Civinini, C.; D'Alessandro, R.; Focardi, E.; Gori, V.; Lenzi, P.; Meschini, M.; Paoletti, S.; Sguazzoni, G.; Viliani, L.; Benussi, L.; Bianco, S.; Fabbri, F.; Piccolo, D.; Primavera, F.; Calvelli, V.; Ferro, F.; Lo Vetere, M.; Monge, M. R.; Robutti, E.; Tosi, S.; Brianza, L.; Brivio, F.; Dinardo, M. E.; Fiorendi, S.; Gennai, S.; Ghezzi, A.; Govoni, P.; Malvezzi, S.; Manzoni, R. A.; Marzocchi, B.; Menasce, D.; Moroni, L.; Paganoni, M.; Pedrini, D.; Pigazzini, S.; Ragazzi, S.; Tabarelli de Fatis, T.; Buontempo, S.; Cavallo, N.; De Nardo, G.; Di Guida, S.; Esposito, M.; Fabozzi, F.; Iorio, A. O. M.; Lanza, G.; Lista, L.; Meola, S.; Merola, M.; Paolucci, P.; Sciacca, C.; Thyssen, F.; Azzi, P.; Bacchetta, N.; Benato, L.; Bisello, D.; Boletti, A.; Carlin, R.; Carvalho Antunes De Oliveira, A.; Checchia, P.; Dall'Osso, M.; De Castro Manzano, P.; Dorigo, T.; Dosselli, U.; Gasparini, F.; Gasparini, U.; Gozzelino, A.; Lacaprara, S.; Margoni, M.; Meneguzzo, A. T.; Pazzini, J.; Pozzobon, N.; Ronchese, P.; Simonetto, F.; Torassa, E.; Tosi, M.; Zanetti, M.; Zotto, P.; Zucchetta, A.; Zumerle, G.; Braghieri, A.; Magnani, A.; Montagna, P.; Ratti, S. P.; Re, V.; Riccardi, C.; Salvini, P.; Vai, I.; Vitulo, P.; Alunni Solestizi, L.; Bilei, G. M.; Ciangottini, D.; Fanò, L.; Lariccia, P.; Leonardi, R.; Mantovani, G.; Menichelli, M.; Saha, A.; Santocchia, A.; Androsov, K.; Azzurri, P.; Bagliesi, G.; Bernardini, J.; Boccali, T.; Castaldi, R.; Ciocci, M. A.; Dell'Orso, R.; Donato, S.; Fedi, G.; Giassi, A.; Grippo, M. T.; Ligabue, F.; Lomtadze, T.; Martini, L.; Messineo, A.; Palla, F.; Rizzi, A.; Savoy-Navarro, A.; Spagnolo, P.; Tenchini, R.; Tonelli, G.; Venturi, A.; Verdini, P. G.; Barone, L.; Cavallari, F.; Cipriani, M.; D'imperio, G.; Del Re, D.; Diemoz, M.; Gelli, S.; Jorda, C.; Longo, E.; Margaroli, F.; Meridiani, P.; Organtini, G.; Paramatti, R.; Preiato, F.; Rahatlou, S.; Rovelli, C.; Santanastasio, F.; Amapane, N.; Arcidiacono, R.; Argiro, S.; Arneodo, M.; Bartosik, N.; Bellan, R.; Biino, C.; Cartiglia, N.; Costa, M.; Covarelli, R.; Degano, A.; Demaria, N.; Finco, L.; Kiani, B.; Mariotti, C.; Maselli, S.; Migliore, E.; Monaco, V.; Monteil, E.; Obertino, M. M.; Pacher, L.; Pastrone, N.; Pelliccioni, M.; Pinna Angioni, G. L.; Ravera, F.; Romero, A.; Ruspa, M.; Sacchi, R.; Sola, V.; Solano, A.; Staiano, A.; Traczyk, P.; Belforte, S.; Candelise, V.; Casarsa, M.; Cossutti, F.; Della Ricca, G.; La Licata, C.; Schizzi, A.; Zanetti, A.; Kim, D. H.; Kim, G. N.; Kim, M. S.; Lee, S.; Lee, S. W.; Oh, Y. D.; Sekmen, S.; Son, D. C.; Yang, Y. C.; Kim, H.; Brochero Cifuentes, J. A.; Kim, T. J.; Cho, S.; Choi, S.; Go, Y.; Gyun, D.; Ha, S.; Hong, B.; Jo, Y.; Kim, Y.; Lee, B.; Lee, K.; Lee, K. S.; Lee, S.; Lim, J.; Park, S. K.; Roh, Y.; Almond, J.; Kim, J.; Seo, S. H.; Yang, U. K.; Yoo, H. D.; Yu, G. B.; Choi, M.; Kim, H.; Kim, H.; Kim, J. H.; Lee, J. S. H.; Park, I. C.; Ryu, G.; Ryu, M. S.; Choi, Y.; Goh, J.; Kim, D.; Kwon, E.; Lee, J.; Yu, I.; Dudenas, V.; Juodagalvis, A.; Vaitkus, J.; Ahmed, I.; Ibrahim, Z. A.; Komaragiri, J. R.; Md Ali, M. A. B.; Mohamad Idris, F.; Wan Abdullah, W. A. T.; Yusli, M. N.; Zolkapli, Z.; Casimiro Linares, E.; Castilla-Valdez, H.; De La Cruz-Burelo, E.; Heredia-De La Cruz, I.; Hernandez-Almada, A.; Lopez-Fernandez, R.; Mejia Guisao, J.; Sanchez-Hernandez, A.; Carrillo Moreno, S.; Vazquez Valencia, F.; Pedraza, I.; Salazar Ibarguen, H. A.; Uribe Estrada, C.; Morelos Pineda, A.; Krofcheck, D.; Butler, P. H.; Ahmad, A.; Ahmad, M.; Hassan, Q.; Hoorani, H. R.; Khan, W. A.; Khurshid, T.; Shoaib, M.; Waqas, M.; Bialkowska, H.; Bluj, M.; Boimska, B.; Frueboes, T.; Górski, M.; Kazana, M.; Nawrocki, K.; Romanowska-Rybinska, K.; Szleper, M.; Zalewski, P.; Bunkowski, K.; Byszuk, A.; Doroba, K.; Kalinowski, A.; Konecki, M.; Krolikowski, J.; Misiura, M.; Olszewski, M.; Walczak, M.; Bargassa, P.; Beirão Da Cruz E Silva, C.; Di Francesco, A.; Faccioli, P.; Ferreira Parracho, P. G.; Gallinaro, M.; Hollar, J.; Leonardo, N.; Lloret Iglesias, L.; Nemallapudi, M. V.; Nguyen, F.; Rodrigues Antunes, J.; Seixas, J.; Toldaiev, O.; Vadruccio, D.; Varela, J.; Vischia, P.; Bunin, P.; Golutvin, I.; Gorbounov, N.; Gorbunov, I.; Kamenev, A.; Karjavin, V.; Lanev, A.; Malakhov, A.; Matveev, V.; Moisenz, P.; Palichik, V.; Perelygin, V.; Savina, M.; Shmatov, S.; Shulha, S.; Skatchkov, N.; Smirnov, V.; Voytishin, N.; Zarubin, A.; Chtchipounov, L.; Golovtsov, V.; Ivanov, Y.; Kim, V.; Kuznetsova, E.; Murzin, V.; Oreshkin, V.; Sulimov, V.; Vorobyev, A.; Andreev, Yu.; Dermenev, A.; Gninenko, S.; Golubev, N.; Karneyeu, A.; Kirsanov, M.; Krasnikov, N.; Pashenkov, A.; Tlisov, D.; Toropin, A.; Epshteyn, V.; Gavrilov, V.; Lychkovskaya, N.; Popov, V.; Pozdnyakov, I.; Safronov, G.; Spiridonov, A.; Toms, M.; Vlasov, E.; Zhokin, A.; Chistov, R.; Danilov, M.; Rusinov, V.; Andreev, V.; Azarkin, M.; Dremin, I.; Kirakosyan, M.; Leonidov, A.; Rusakov, S. V.; Terkulov, A.; Baskakov, A.; Belyaev, A.; Boos, E.; Dubinin, M.; Dudko, L.; Ershov, A.; Gribushin, A.; Klyukhin, V.; Kodolova, O.; Lokhtin, I.; Miagkov, I.; Obraztsov, S.; Petrushanko, S.; Savrin, V.; Snigirev, A.; Azhgirey, I.; Bayshev, I.; Bitioukov, S.; Elumakhov, D.; Kachanov, V.; Kalinin, A.; Konstantinov, D.; Krychkine, V.; Petrov, V.; Ryutin, R.; Sobol, A.; Troshin, S.; Tyurin, N.; Uzunian, A.; Volkov, A.; Adzic, P.; Cirkovic, P.; Devetak, D.; Milosevic, J.; Rekovic, V.; Alcaraz Maestre, J.; Calvo, E.; Cerrada, M.; Chamizo Llatas, M.; Colino, N.; De La Cruz, B.; Delgado Peris, A.; Escalante Del Valle, A.; Fernandez Bedoya, C.; Fernández Ramos, J. P.; Flix, J.; Fouz, M. C.; Garcia-Abia, P.; Gonzalez Lopez, O.; Goy Lopez, S.; Hernandez, J. M.; Josa, M. I.; Navarro De Martino, E.; Pérez-Calero Yzquierdo, A.; Puerta Pelayo, J.; Quintario Olmeda, A.; Redondo, I.; Romero, L.; Soares, M. S.; de Trocóniz, J. F.; Missiroli, M.; Moran, D.; Cuevas, J.; Fernandez Menendez, J.; Gonzalez Caballero, I.; Palencia Cortezon, E.; Sanchez Cruz, S.; Vizan Garcia, J. M.; Cabrillo, I. J.; Calderon, A.; Castiñeiras De Saa, J. R.; Curras, E.; Fernandez, M.; Garcia-Ferrero, J.; Gomez, G.; Lopez Virto, A.; Marco, J.; Martinez Rivero, C.; Matorras, F.; Piedra Gomez, J.; Rodrigo, T.; Ruiz-Jimeno, A.; Scodellaro, L.; Trevisani, N.; Vila, I.; Vilar Cortabitarte, R.; Abbaneo, D.; Auffray, E.; Auzinger, G.; Bachtis, M.; Baillon, P.; Ball, A. H.; Barney, D.; Bloch, P.; Bocci, A.; Bonato, A.; Botta, C.; Camporesi, T.; Castello, R.; Cepeda, M.; Cerminara, G.; D'Alfonso, M.; d'Enterria, D.; Dabrowski, A.; Daponte, V.; David, A.; De Gruttola, M.; De Guio, F.; De Roeck, A.; Di Marco, E.; Dobson, M.; Dordevic, M.; Dorney, B.; du Pree, T.; Duggan, D.; Dünser, M.; Dupont, N.; Elliott-Peisert, A.; Fartoukh, S.; Franzoni, G.; Fulcher, J.; Funk, W.; Gigi, D.; Gill, K.; Girone, M.; Glege, F.; Gundacker, S.; Guthoff, M.; Hammer, J.; Harris, P.; Hegeman, J.; Innocente, V.; Janot, P.; Kirschenmann, H.; Knünz, V.; Kortelainen, M. J.; Kousouris, K.; Krammer, M.; Lecoq, P.; Lourenço, C.; Lucchini, M. T.; Magini, N.; Malgeri, L.; Mannelli, M.; Martelli, A.; Meijers, F.; Mersi, S.; Meschi, E.; Moortgat, F.; Morovic, S.; Mulders, M.; Neugebauer, H.; Orfanelli, S.; Orsini, L.; Pape, L.; Perez, E.; Peruzzi, M.; Petrilli, A.; Petrucciani, G.; Pfeiffer, A.; Pierini, M.; Racz, A.; Reis, T.; Rolandi, G.; Rovere, M.; Ruan, M.; Sakulin, H.; Sauvan, J. B.; Schäfer, C.; Schwick, C.; Seidel, M.; Sharma, A.; Silva, P.; Simon, M.; Sphicas, P.; Steggemann, J.; Stoye, M.; Takahashi, Y.; Treille, D.; Triossi, A.; Tsirou, A.; Veckalns, V.; Veres, G. I.; Wardle, N.; Zagozdzinska, A.; Zeuner, W. D.; Bertl, W.; Deiters, K.; Erdmann, W.; Horisberger, R.; Ingram, Q.; Kaestli, H. C.; Kotlinski, D.; Langenegger, U.; Rohe, T.; Bachmair, F.; Bäni, L.; Bianchini, L.; Casal, B.; Dissertori, G.; Dittmar, M.; Donegà, M.; Eller, P.; Grab, C.; Heidegger, C.; Hits, D.; Hoss, J.; Kasieczka, G.; Lecomte, P.; Lustermann, W.; Mangano, B.; Marionneau, M.; Martinez Ruiz del Arbol, P.; Masciovecchio, M.; Meinhard, M. T.; Meister, D.; Micheli, F.; Musella, P.; Nessi-Tedaldi, F.; Pandolfi, F.; Pata, J.; Pauss, F.; Perrin, G.; Perrozzi, L.; Quittnat, M.; Rossini, M.; Schönenberger, M.; Starodumov, A.; Takahashi, M.; Tavolaro, V. R.; Theofilatos, K.; Wallny, R.; Aarrestad, T. K.; Amsler, C.; Caminada, L.; Canelli, M. F.; Chiochia, V.; De Cosa, A.; Galloni, C.; Hinzmann, A.; Hreus, T.; Kilminster, B.; Lange, C.; Ngadiuba, J.; Pinna, D.; Rauco, G.; Robmann, P.; Salerno, D.; Yang, Y.; Chen, K. H.; Doan, T. H.; Jain, Sh.; Khurana, R.; Konyushikhin, M.; Kuo, C. M.; Lin, W.; Lu, Y. J.; Pozdnyakov, A.; Yu, S. S.; Kumar, Arun; Chang, P.; Chang, Y. H.; Chang, Y. W.; Chao, Y.; Chen, K. F.; Chen, P. H.; Dietz, C.; Fiori, F.; Hou, W.-S.; Hsiung, Y.; Liu, Y. F.; Lu, R.-S.; Miñano Moya, M.; Paganis, E.; Tsai, J. f.; Tzeng, Y. M.; Asavapibhop, B.; Singh, G.; Srimanobhas, N.; Suwonjandee, N.; Adiguzel, A.; Bakirci, M. N.; Damarseckin, S.; Demiroglu, Z. S.; Dozen, C.; Dumanoglu, I.; Girgis, S.; Gokbulut, G.; Guler, Y.; Gurpinar, E.; Hos, I.; Kangal, E. E.; Kayis Topaksu, A.; Onengut, G.; Ozdemir, K.; Sunar Cerci, D.; Tali, B.; Zorbilmez, C.; Bilin, B.; Bilmis, S.; Isildak, B.; Karapinar, G.; Yalvac, M.; Zeyrek, M.; Gülmez, E.; Kaya, M.; Kaya, O.; Yetkin, E. A.; Yetkin, T.; Cakir, A.; Cankocak, K.; Sen, S.; Vardarlı, F. I.; Grynyov, B.; Levchuk, L.; Sorokin, P.; Aggleton, R.; Ball, F.; Beck, L.; Brooke, J. J.; Burns, D.; Clement, E.; Cussans, D.; Flacher, H.; Goldstein, J.; Grimes, M.; Heath, G. P.; Heath, H. F.; Jacob, J.; Kreczko, L.; Lucas, C.; Meng, Z.; Newbold, D. M.; Paramesvaran, S.; Poll, A.; Sakuma, T.; Seif El Nasr-storey, S.; Senkin, S.; Smith, D.; Smith, V. J.; Bell, K. W.; Belyaev, A.; Brew, C.; Brown, R. M.; Calligaris, L.; Cieri, D.; Cockerill, D. J. A.; Coughlan, J. A.; Harder, K.; Harper, S.; Olaiya, E.; Petyt, D.; Shepherd-Themistocleous, C. H.; Thea, A.; Tomalin, I. R.; Williams, T.; Baber, M.; Bainbridge, R.; Buchmuller, O.; Bundock, A.; Burton, D.; Casasso, S.; Citron, M.; Colling, D.; Corpe, L.; Dauncey, P.; Davies, G.; De Wit, A.; Della Negra, M.; Dunne, P.; Elwood, A.; Futyan, D.; Haddad, Y.; Hall, G.; Iles, G.; Lane, R.; Laner, C.; Lucas, R.; Lyons, L.; Magnan, A.-M.; Malik, S.; Mastrolorenzo, L.; Nash, J.; Nikitenko, A.; Pela, J.; Penning, B.; Pesaresi, M.; Raymond, D. M.; Richards, A.; Rose, A.; Seez, C.; Tapper, A.; Uchida, K.; Vazquez Acosta, M.; Virdee, T.; Zenz, S. C.; Cole, J. E.; Hobson, P. R.; Khan, A.; Kyberd, P.; Leslie, D.; Reid, I. D.; Symonds, P.; Teodorescu, L.; Turner, M.; Borzou, A.; Call, K.; Dittmann, J.; Hatakeyama, K.; Liu, H.; Pastika, N.; Charaf, O.; Cooper, S. I.; Henderson, C.; Rumerio, P.; Arcaro, D.; Avetisyan, A.; Bose, T.; Gastler, D.; Rankin, D.; Richardson, C.; Rohlf, J.; Sulak, L.; Zou, D.; Benelli, G.; Berry, E.; Cutts, D.; Ferapontov, A.; Garabedian, A.; Hakala, J.; Heintz, U.; Jesus, O.; Laird, E.; Landsberg, G.; Mao, Z.; Narain, M.; Piperov, S.; Sagir, S.; Spencer, E.; Syarif, R.; Breedon, R.; Breto, G.; Burns, D.; Calderon De La Barca Sanchez, M.; Chauhan, S.; Chertok, M.; Conway, J.; Conway, R.; Cox, P. T.; Erbacher, R.; Flores, C.; Funk, G.; Gardner, M.; Ko, W.; Lander, R.; Mclean, C.; Mulhearn, M.; Pellett, D.; Pilot, J.; Ricci-Tam, F.; Shalhout, S.; Smith, J.; Squires, M.; Stolp, D.; Tripathi, M.; Wilbur, S.; Yohay, R.; Cousins, R.; Everaerts, P.; Florent, A.; Hauser, J.; Ignatenko, M.; Saltzberg, D.; Takasugi, E.; Valuev, V.; Weber, M.; Burt, K.; Clare, R.; Ellison, J.; Gary, J. W.; Hanson, G.; Heilman, J.; Jandir, P.; Kennedy, E.; Lacroix, F.; Long, O. R.; Malberti, M.; Olmedo Negrete, M.; Paneva, M. I.; Shrinivas, A.; Wei, H.; Wimpenny, S.; Yates, B. R.; Branson, J. G.; Cerati, G. B.; Cittolin, S.; D'Agnolo, R. T.; Derdzinski, M.; Gerosa, R.; Holzner, A.; Kelley, R.; Klein, D.; Letts, J.; Macneill, I.; Olivito, D.; Padhi, S.; Pieri, M.; Sani, M.; Sharma, V.; Simon, S.; Tadel, M.; Vartak, A.; Wasserbaech, S.; Welke, C.; Wood, J.; Würthwein, F.; Yagil, A.; Zevi Della Porta, G.; Bhandari, R.; Bradmiller-Feld, J.; Campagnari, C.; Dishaw, A.; Dutta, V.; Flowers, K.; Franco Sevilla, M.; Geffert, P.; George, C.; Golf, F.; Gouskos, L.; Gran, J.; Heller, R.; Incandela, J.; Mccoll, N.; Mullin, S. D.; Ovcharova, A.; Richman, J.; Stuart, D.; Suarez, I.; West, C.; Yoo, J.; Anderson, D.; Apresyan, A.; Bendavid, J.; Bornheim, A.; Bunn, J.; Chen, Y.; Duarte, J.; Mott, A.; Newman, H. B.; Pena, C.; Spiropulu, M.; Vlimant, J. R.; Xie, S.; Zhu, R. Y.; Andrews, M. B.; Azzolini, V.; Calamba, A.; Carlson, B.; Ferguson, T.; Paulini, M.; Russ, J.; Sun, M.; Vogel, H.; Vorobiev, I.; Cumalat, J. P.; Ford, W. T.; Jensen, F.; Johnson, A.; Krohn, M.; Mulholland, T.; Stenson, K.; Wagner, S. R.; Alexander, J.; Chatterjee, A.; Chaves, J.; Chu, J.; Dittmer, S.; Eggert, N.; Mirman, N.; Nicolas Kaufman, G.; Patterson, J. R.; Rinkevicius, A.; Ryd, A.; Skinnari, L.; Sun, W.; Tan, S. M.; Tao, Z.; Teo, W. D.; Thom, J.; Thompson, J.; Tucker, J.; Weng, Y.; Wittich, P.; Winn, D.; Abdullin, S.; Albrow, M.; Apollinari, G.; Banerjee, S.; Bauerdick, L. A. T.; Beretvas, A.; Berryhill, J.; Bhat, P. C.; Bolla, G.; Burkett, K.; Butler, J. N.; Cheung, H. W. K.; Chlebana, F.; Cihangir, S.; Cremonesi, M.; Elvira, V. D.; Fisk, I.; Freeman, J.; Gottschalk, E.; Gray, L.; Green, D.; Grünendahl, S.; Gutsche, O.; Hare, D.; Harris, R. M.; Hasegawa, S.; Hirschauer, J.; Hu, Z.; Jayatilaka, B.; Jindariani, S.; Johnson, M.; Joshi, U.; Klima, B.; Kreis, B.; Lammel, S.; Linacre, J.; Lincoln, D.; Lipton, R.; Liu, T.; Lopes De Sá, R.; Lykken, J.; Maeshima, K.; Marraffino, J. M.; Maruyama, S.; Mason, D.; McBride, P.; Merkel, P.; Mrenna, S.; Nahn, S.; Newman-Holmes, C.; O'Dell, V.; Pedro, K.; Prokofyev, O.; Rakness, G.; Ristori, L.; Sexton-Kennedy, E.; Soha, A.; Spalding, W. J.; Spiegel, L.; Stoynev, S.; Strobbe, N.; Taylor, L.; Tkaczyk, S.; Tran, N. V.; Uplegger, L.; Vaandering, E. W.; Vernieri, C.; Verzocchi, M.; Vidal, R.; Wang, M.; Weber, H. A.; Whitbeck, A.; Acosta, D.; Avery, P.; Bortignon, P.; Bourilkov, D.; Brinkerhoff, A.; Carnes, A.; Carver, M.; Curry, D.; Das, S.; Field, R. D.; Furic, I. K.; Konigsberg, J.; Korytov, A.; Ma, P.; Matchev, K.; Mei, H.; Milenovic, P.; Mitselmakher, G.; Rank, D.; Shchutska, L.; Sperka, D.; Thomas, L.; Wang, J.; Wang, S.; Yelton, J.; Linn, S.; Markowitz, P.; Martinez, G.; Rodriguez, J. L.; Ackert, A.; Adams, J. R.; Adams, T.; Askew, A.; Bein, S.; Diamond, B.; Hagopian, S.; Hagopian, V.; Johnson, K. F.; Khatiwada, A.; Prosper, H.; Santra, A.; Weinberg, M.; Baarmand, M. M.; Bhopatkar, V.; Colafranceschi, S.; Hohlmann, M.; Kalakhety, H.; Noonan, D.; Roy, T.; Yumiceva, F.; Adams, M. R.; Apanasevich, L.; Berry, D.; Betts, R. R.; Bucinskaite, I.; Cavanaugh, R.; Evdokimov, O.; Gauthier, L.; Gerber, C. E.; Hofman, D. J.; Kurt, P.; O'Brien, C.; Sandoval Gonzalez, I. D.; Turner, P.; Varelas, N.; Wu, Z.; Zakaria, M.; Zhang, J.; Bilki, B.; Clarida, W.; Dilsiz, K.; Durgut, S.; Gandrajula, R. P.; Haytmyradov, M.; Khristenko, V.; Merlo, J.-P.; Mermerkaya, H.; Mestvirishvili, A.; Moeller, A.; Nachtman, J.; Ogul, H.; Onel, Y.; Ozok, F.; Penzo, A.; Snyder, C.; Tiras, E.; Wetzel, J.; Yi, K.; Anderson, I.; Blumenfeld, B.; Cocoros, A.; Eminizer, N.; Fehling, D.; Feng, L.; Gritsan, A. V.; Maksimovic, P.; Osherson, M.; Roskes, J.; Sarica, U.; Swartz, M.; Xiao, M.; Xin, Y.; You, C.; Al-bataineh, A.; Baringer, P.; Bean, A.; Bruner, C.; Castle, J.; Kenny, R. P.; Kropivnitskaya, A.; Majumder, D.; Malek, M.; Mcbrayer, W.; Murray, M.; Sanders, S.; Stringer, R.; Wang, Q.; Ivanov, A.; Kaadze, K.; Khalil, S.; Makouski, M.; Maravin, Y.; Mohammadi, A.; Saini, L. K.; Skhirtladze, N.; Toda, S.; Lange, D.; Rebassoo, F.; Wright, D.; Anelli, C.; Baden, A.; Baron, O.; Belloni, A.; Calvert, B.; Eno, S. C.; Ferraioli, C.; Gomez, J. A.; Hadley, N. J.; Jabeen, S.; Kellogg, R. G.; Kolberg, T.; Kunkle, J.; Lu, Y.; Mignerey, A. C.; Shin, Y. H.; Skuja, A.; Tonjes, M. B.; Tonwar, S. C.; Apyan, A.; Barbieri, R.; Baty, A.; Bi, R.; Bierwagen, K.; Brandt, S.; Busza, W.; Cali, I. A.; Demiragli, Z.; Di Matteo, L.; Gomez Ceballos, G.; Goncharov, M.; Gulhan, D.; Hsu, D.; Iiyama, Y.; Innocenti, G. M.; Klute, M.; Kovalskyi, D.; Krajczar, K.; Lai, Y. S.; Lee, Y.-J.; Levin, A.; Luckey, P. D.; Marini, A. C.; Mcginn, C.; Mironov, C.; Narayanan, S.; Niu, X.; Paus, C.; Roland, C.; Roland, G.; Salfeld-Nebgen, J.; Stephans, G. S. F.; Sumorok, K.; Tatar, K.; Varma, M.; Velicanu, D.; Veverka, J.; Wang, J.; Wang, T. W.; Wyslouch, B.; Yang, M.; Zhukova, V.; Benvenuti, A. C.; Dahmes, B.; Evans, A.; Finkel, A.; Gude, A.; Hansen, P.; Kalafut, S.; Kao, S. C.; Klapoetke, K.; Kubota, Y.; Lesko, Z.; Mans, J.; Nourbakhsh, S.; Ruckstuhl, N.; Rusack, R.; Tambe, N.; Turkewitz, J.; Acosta, J. G.; Oliveros, S.; Avdeeva, E.; Bartek, R.; Bloom, K.; Bose, S.; Claes, D. R.; Dominguez, A.; Fangmeier, C.; Gonzalez Suarez, R.; Kamalieddin, R.; Knowlton, D.; Kravchenko, I.; Meier, F.; Monroy, J.; Siado, J. E.; Snow, G. R.; Stieger, B.; Alyari, M.; Dolen, J.; George, J.; Godshalk, A.; Harrington, C.; Iashvili, I.; Kaisen, J.; Kharchilava, A.; Kumar, A.; Parker, A.; Rappoccio, S.; Roozbahani, B.; Alverson, G.; Barberis, E.; Baumgartel, D.; Chasco, M.; Hortiangtham, A.; Massironi, A.; Morse, D. M.; Nash, D.; Orimoto, T.; Teixeira De Lima, R.; Trocino, D.; Wang, R.-J.; Wood, D.; Bhattacharya, S.; Hahn, K. A.; Kubik, A.; Low, J. F.; Mucia, N.; Odell, N.; Pollack, B.; Schmitt, M. H.; Sung, K.; Trovato, M.; Velasco, M.; Dev, N.; Hildreth, M.; Hurtado Anampa, K.; Jessop, C.; Karmgard, D. J.; Kellams, N.; Lannon, K.; Marinelli, N.; Meng, F.; Mueller, C.; Musienko, Y.; Planer, M.; Reinsvold, A.; Ruchti, R.; Rupprecht, N.; Smith, G.; Taroni, S.; Valls, N.; Wayne, M.; Wolf, M.; Woodard, A.; Alimena, J.; Antonelli, L.; Brinson, J.; Bylsma, B.; Durkin, L. S.; Flowers, S.; Francis, B.; Hart, A.; Hill, C.; Hughes, R.; Ji, W.; Liu, B.; Luo, W.; Puigh, D.; Rodenburg, M.; Winer, B. L.; Wulsin, H. W.; Driga, O.; Elmer, P.; Hardenbrook, J.; Hebda, P.; Marlow, D.; Medvedeva, T.; Mooney, M.; Olsen, J.; Palmer, C.; Piroué, P.; Stickland, D.; Tully, C.; Zuranski, A.; Malik, S.; Barker, A.; Barnes, V. E.; Benedetti, D.; Folgueras, S.; Gutay, L.; Jha, M. K.; Jones, M.; Jung, A. W.; Jung, K.; Miller, D. H.; Neumeister, N.; Radburn-Smith, B. C.; Shi, X.; Sun, J.; Svyatkovskiy, A.; Wang, F.; Xie, W.; Xu, L.; Parashar, N.; Stupak, J.; Adair, A.; Akgun, B.; Chen, Z.; Ecklund, K. M.; Geurts, F. J. M.; Guilbaud, M.; Li, W.; Michlin, B.; Northup, M.; Padley, B. P.; Redjimi, R.; Roberts, J.; Rorie, J.; Tu, Z.; Zabel, J.; Betchart, B.; Bodek, A.; de Barbaro, P.; Demina, R.; Duh, Y. t.; Eshaq, Y.; Ferbel, T.; Galanti, M.; Garcia-Bellido, A.; Han, J.; Hindrichs, O.; Khukhunaishvili, A.; Lo, K. H.; Tan, P.; Verzetti, M.; Chou, J. P.; Contreras-Campana, E.; Gershtein, Y.; Gómez Espinosa, T. A.; Halkiadakis, E.; Heindl, M.; Hidas, D.; Hughes, E.; Kaplan, S.; Kunnawalkam Elayavalli, R.; Kyriacou, S.; Lath, A.; Nash, K.; Saka, H.; Salur, S.; Schnetzer, S.; Sheffield, D.; Somalwar, S.; Stone, R.; Thomas, S.; Thomassen, P.; Walker, M.; Foerster, M.; Heideman, J.; Riley, G.; Rose, K.; Spanier, S.; Thapa, K.; Bouhali, O.; Castaneda Hernandez, A.; Celik, A.; Dalchenko, M.; De Mattia, M.; Delgado, A.; Dildick, S.; Eusebi, R.; Flanagan, W.; Gilmore, J.; Huang, T.; Juska, E.; Kamon, T.; Krutelyov, V.; Mueller, R.; Pakhotin, Y.; Patel, R.; Perloff, A.; Perniè, L.; Rathjens, D.; Rose, A.; Safonov, A.; Tatarinov, A.; Ulmer, K. A.; Akchurin, N.; Cowden, C.; Damgov, J.; Dragoiu, C.; Dudero, P. R.; Faulkner, J.; Kunori, S.; Lamichhane, K.; Lee, S. W.; Libeiro, T.; Undleeb, S.; Volobouev, I.; Wang, Z.; Delannoy, A. G.; Greene, S.; Gurrola, A.; Janjam, R.; Johns, W.; Maguire, C.; Melo, A.; Ni, H.; Sheldon, P.; Tuo, S.; Velkovska, J.; Xu, Q.; Arenton, M. W.; Barria, P.; Cox, B.; Goodell, J.; Hirosky, R.; Ledovskoy, A.; Li, H.; Neu, C.; Sinthuprasith, T.; Sun, X.; Wang, Y.; Wolfe, E.; Xia, F.; Clarke, C.; Harr, R.; Karchin, P. E.; Kottachchi Kankanamge Don, C.; Lamichhane, P.; Sturdy, J.; Belknap, D. A.; Dasu, S.; Dodd, L.; Duric, S.; Gomber, B.; Grothe, M.; Herndon, M.; Hervé, A.; Klabbers, P.; Lanaro, A.; Levine, A.; Long, K.; Loveless, R.; Ojalvo, I.; Perry, T.; Pierro, G. A.; Polese, G.; Ruggles, T.; Savin, A.; Sharma, A.; Smith, N.; Smith, W. H.; Taylor, D.; Verwilligen, P.; Woods, N.; CMS Collaboration

2017-01-01

A first search for pair production of dark matter candidates through vector boson fusion in proton-proton collisions at √{s }=8 TeV is performed with the CMS detector. The vector boson fusion topology enhances missing transverse momentum, providing a way to probe supersymmetry, even in the case of a compressed mass spectrum. The data sample corresponds to an integrated luminosity of 18.5 fb-1 , recorded by the CMS experiment. The observed dijet mass spectrum is consistent with the standard model expectation. In an effective field theory, dark matter masses are explored as a function of contact interaction strength. The most stringent limit on bottom squark production with mass below 315 GeV is also reported, assuming a 5 GeV mass difference with respect to the lightest neutralino.

Unveiling the nature of post-linear response Z-vector method for time-dependent density functional theory.

PubMed

Pastore, Mariachiara; Assfeld, Xavier; Mosconi, Edoardo; Monari, Antonio; Etienne, Thibaud

2017-07-14

We report a theoretical study on the analysis of the relaxed one-particle difference density matrix characterizing the passage from the ground to the excited state of a molecular system, as obtained from time-dependent density functional theory. In particular, this work aims at using the physics contained in the so-called Z-vector, which differentiates between unrelaxed and relaxed difference density matrices to analyze excited states' nature. For this purpose, we introduce novel quantum-mechanical quantities, based on the detachment/attachment methodology, for analysing the Z-vector transformation for different molecules and density functional theory functionals. A derivation pathway of these novel descriptors is reported, involving a numerical integration to be performed in the Euclidean space on the density functions. This topological analysis is then applied to two sets of chromophores, and the correlation between the level of theory and the behavior of our descriptors is properly rationalized. In particular, the effect of range-separation on the relaxation amplitude is discussed. The relaxation term is finally shown to be system-specific (for a given level of theory) and independent of the number of electrons (i.e., the relaxation amplitude is not simply the result of a collective phenomenon).

Extracting Topological Relations Between Indoor Spaces from Point Clouds

NASA Astrophysics Data System (ADS)

Tran, H.; Khoshelham, K.; Kealy, A.; Díaz-Vilariño, L.

2017-09-01

3D models of indoor environments are essential for many application domains such as navigation guidance, emergency management and a range of indoor location-based services. The principal components defined in different BIM standards contain not only building elements, such as floors, walls and doors, but also navigable spaces and their topological relations, which are essential for path planning and navigation. We present an approach to automatically reconstruct topological relations between navigable spaces from point clouds. Three types of topological relations, namely containment, adjacency and connectivity of the spaces are modelled. The results of initial experiments demonstrate the potential of the method in supporting indoor navigation.

Helicons in uniform fields. I. Wave diagnostics with hodograms

NASA Astrophysics Data System (ADS)

Urrutia, J. M.; Stenzel, R. L.

2018-03-01

The wave equation for whistler waves is well known and has been solved in Cartesian and cylindrical coordinates, yielding plane waves and cylindrical waves. In space plasmas, waves are usually assumed to be plane waves; in small laboratory plasmas, they are often assumed to be cylindrical "helicon" eigenmodes. Experimental observations fall in between both models. Real waves are usually bounded and may rotate like helicons. Such helicons are studied experimentally in a large laboratory plasma which is essentially a uniform, unbounded plasma. The waves are excited by loop antennas whose properties determine the field rotation and transverse dimensions. Both m = 0 and m = 1 helicon modes are produced and analyzed by measuring the wave magnetic field in three dimensional space and time. From Ampère's law and Ohm's law, the current density and electric field vectors are obtained. Hodograms for these vectors are produced. The sign ambiguity of the hodogram normal with respect to the direction of wave propagation is demonstrated. In general, electric and magnetic hodograms differ but both together yield the wave vector direction unambiguously. Vector fields of the hodogram normal yield the phase flow including phase rotation for helicons. Some helicons can have locally a linear polarization which is identified by the hodogram ellipticity. Alternatively the amplitude oscillation in time yields a measure for the wave polarization. It is shown that wave interference produces linear polarization. These observations emphasize that single point hodogram measurements are inadequate to determine the wave topology unless assuming plane waves. Observations of linear polarization indicate wave packets but not plane waves. A simple qualitative diagnostics for the wave polarization is the measurement of the magnetic field magnitude in time. Circular polarization has a constant amplitude; linear polarization results in amplitude modulations.

Fuzzy topological digital space and their properties of flat electroencephalography in epilepsy disease

NASA Astrophysics Data System (ADS)

Muzafar Shah, Mazlina; Fatah Wahab, Abdul

2017-09-01

There are an abnormal electric activities or irregular interference in brain of epilepsy patient. Then a sensor will be put in patient’s scalp to measure and records all electric activities in brain. The result of the records known as Electroencephalography (EEG). The EEG has been transfer to flat EEG because it’s easier to analyze. In this study, the uncertainty in flat EEG data will be considered as fuzzy digital space. The purpose of this research is to show that the flat EEG is fuzzy topological digital space. Therefore, the main focus for this research is to introduce fuzzy topological digital space concepts with their properties such as neighbourhood, interior and closure by using fuzzy set digital concept and Chang’s fuzzy topology approach. The product fuzzy topology digital also will be shown. By introduce this concept, the data in flat EEG can considering having fuzzy topology digital properties and can identify the area in fuzzy digital space that has been affected by epilepsy seizure in epileptic patient’s brain.

Disordered topological wires in a momentum-space lattice

NASA Astrophysics Data System (ADS)

Meier, Eric; An, Fangzhao; Gadway, Bryce

2017-04-01

One of the most interesting aspects of topological systems is the presence of boundary modes which remain robust in the presence of weak disorder. We explore this feature in the context of one-dimensional (1D) topological wires where staggered tunneling strengths lead to the creation of a mid-gap state in the lattice band structure. Using Bose-condensed 87Rb atoms in a 1D momentum-space lattice, we probe the robust topological character of this model when subjected to both site energy and tunneling disorder. We observe a transition to a topologically trivial phase when tailored disorder is applied, which we detect through both charge-pumping and Hamiltonian-quenching protocols. In addition, we report on efforts to probe the influence of interactions in topological momentum-space lattices.

Gauging Spatial Symmetries and the Classification of Topological Crystalline Phases

NASA Astrophysics Data System (ADS)

Thorngren, Ryan; Else, Dominic V.

2018-01-01

We put the theory of interacting topological crystalline phases on a systematic footing. These are topological phases protected by space-group symmetries. Our central tool is an elucidation of what it means to "gauge" such symmetries. We introduce the notion of a crystalline topological liquid and argue that most (and perhaps all) phases of interest are likely to satisfy this criterion. We prove a crystalline equivalence principle, which states that in Euclidean space, crystalline topological liquids with symmetry group G are in one-to-one correspondence with topological phases protected by the same symmetry G , but acting internally, where if an element of G is orientation reversing, it is realized as an antiunitary symmetry in the internal symmetry group. As an example, we explicitly compute, using group cohomology, a partial classification of bosonic symmetry-protected topological phases protected by crystalline symmetries in (3 +1 ) dimensions for 227 of the 230 space groups. For the 65 space groups not containing orientation-reversing elements (Sohncke groups), there are no cobordism invariants that may contribute phases beyond group cohomology, so we conjecture that our classification is complete.

A generalized graph-theoretical matrix of heterosystems and its application to the VMV procedure.

PubMed

Mozrzymas, Anna

2011-12-14

The extensions of generalized (molecular) graph-theoretical matrix and vector-matrix-vector procedure are considered. The elements of the generalized matrix are redefined in order to describe molecules containing heteroatoms and multiple bonds. The adjacency, distance, detour and reciprocal distance matrices of heterosystems, and corresponding vectors are derived from newly defined generalized graph matrix. The topological indices, which are most widely used in predicting physicochemical and biological properties/activities of various compounds, can be calculated from the new generalized vector-matrix-vector invariant. Copyright © 2011 Elsevier Ltd. All rights reserved.

Polarization Shaping for Control of Nonlinear Propagation.

PubMed

Bouchard, Frédéric; Larocque, Hugo; Yao, Alison M; Travis, Christopher; De Leon, Israel; Rubano, Andrea; Karimi, Ebrahim; Oppo, Gian-Luca; Boyd, Robert W

2016-12-02

We study the nonlinear optical propagation of two different classes of light beams with space-varying polarization-radially symmetric vector beams and Poincaré beams with lemon and star topologies-in a rubidium vapor cell. Unlike Laguerre-Gauss and other types of beams that quickly experience instabilities, we observe that their propagation is not marked by beam breakup while still exhibiting traits such as nonlinear confinement and self-focusing. Our results suggest that, by tailoring the spatial structure of the polarization, the effects of nonlinear propagation can be effectively controlled. These findings provide a novel approach to transport high-power light beams in nonlinear media with controllable distortions to their spatial structure and polarization properties.

Master equation for open two-band systems and its applications to Hall conductance

NASA Astrophysics Data System (ADS)

Shen, H. Z.; Zhang, S. S.; Dai, C. M.; Yi, X. X.

2018-02-01

Hall conductivity in the presence of a dephasing environment has recently been investigated with a dissipative term introduced phenomenologically. In this paper, we study the dissipative topological insulator (TI) and its topological transition in the presence of quantized electromagnetic environments. A Lindblad-type equation is derived to determine the dynamics of a two-band system. When the two-band model describes TIs, the environment may be the fluctuations of radiation that surround the TIs. We find the dependence of decay rates in the master equation on Bloch vectors in the two-band system, which leads to a mixing of the band occupations. Hence the environment-induced current is in general not perfectly topological in the presence of coupling to the environment, although deviations are small in the weak limit. As an illustration, we apply the Bloch-vector-dependent master equation to TIs and calculate the Hall conductance of tight-binding electrons in a two-dimensional lattice. The influence of environments on the Hall conductance is presented and discussed. The calculations show that the phase transition points of the TIs are robust against the quantized electromagnetic environment. The results might bridge the gap between quantum optics and topological photonic materials.

Deformations of the spin currents by topological screw dislocation and cosmic dispiration

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

Wang, Jianhua; Ma, Kai, E-mail: makainca@gmail.com; Li, Kang

2015-11-15

We study the spin currents induced by topological screw dislocation and cosmic dispiration. By using the extended Drude model, we find that the spin dependent forces are modified by the nontrivial geometry. For the topological screw dislocation, only the direction of spin current is bent by deforming the spin polarization vector. In contrast, the force induced by cosmic dispiration could affect both the direction and magnitude of the spin current. As a consequence, the spin-Hall conductivity does not receive corrections from screw dislocation.

Vector optical activity in the Weyl semimetal TaAs

DOE PAGES

Norman, M. R.

2015-12-15

Here, it is shown that the Weyl semimetal TaAs can have a significant polar vector contribution to its optical activity. This is quantified by ab initio calculations of the resonant x-ray diffraction at the Ta L1 edge. For the Bragg vector (400), this polar vector contribution to the circular intensity differential between left and right polarized x-rays is predicted to be comparable to that arising from linear dichroism. Implications this result has in regards to optical effects predicted for topological Weyl semimetals are discussed.

The Volatility of Data Space: Topology Oriented Sensitivity Analysis

PubMed Central

Du, Jing; Ligmann-Zielinska, Arika

2015-01-01

Despite the difference among specific methods, existing Sensitivity Analysis (SA) technologies are all value-based, that is, the uncertainties in the model input and output are quantified as changes of values. This paradigm provides only limited insight into the nature of models and the modeled systems. In addition to the value of data, a potentially richer information about the model lies in the topological difference between pre-model data space and post-model data space. This paper introduces an innovative SA method called Topology Oriented Sensitivity Analysis, which defines sensitivity as the volatility of data space. It extends SA into a deeper level that lies in the topology of data. PMID:26368929

Diffusion with finite-helicity field tensor: A mechanism of generating heterogeneity

NASA Astrophysics Data System (ADS)

Sato, N.; Yoshida, Z.

2018-02-01

Topological constraints on a dynamical system often manifest themselves as breaking of the Hamiltonian structure; well-known examples are nonholonomic constraints on Lagrangian mechanics. The statistical mechanics under such topological constraints is the subject of this study. Conventional arguments based on phase spaces, Jacobi identity, invariant measure, or the H theorem are no longer applicable since all these notions stem from the symplectic geometry underlying canonical Hamiltonian systems. Remembering that Hamiltonian systems are endowed with field tensors (canonical 2-forms) that have zero helicity, our mission is to extend the scope toward the class of systems governed by finite-helicity field tensors. Here, we introduce a class of field tensors that are characterized by Beltrami vectors. We prove an H theorem for this Beltrami class. The most general class of energy-conserving systems are non-Beltrami, for which we identify the "field charge" that prevents the entropy to maximize, resulting in creation of heterogeneous distributions. The essence of the theory can be delineated by classifying three-dimensional dynamics. We then generalize to arbitrary (finite) dimensions.

Interplay between topological phase and self-acceleration in a vortex symmetric Airy beam.

PubMed

Fang, Zhao-Xiang; Chen, Yue; Ren, Yu-Xuan; Gong, Lei; Lu, Rong-De; Zhang, An-Qi; Zhao, Hong-Ze; Wang, Pei

2018-03-19

Photons in an optical vortex usually carry orbital angular momentum, which boosts the application of the micro-rotation of absorbing particles and quantum information encoding. Such photons propagate along a straight line in free space or follow a curved trace once guided by an optical fiber. Teleportation of an optical vortex using a beam with non-diffraction and self-healing is quite challenging. We demonstrate the manipulation of the propagation trace of an optical vortex with a symmetric Airy beam (SAB) and found that the SAB experiences self-rotation with the implementation of a topological phase structure of coaxial vortex. Slight misalignment of the vortex and the SAB enables the guiding of the vortex into one of the self-accelerating channels. Multiple off-axis vortices embedded in SAB are also demonstrated to follow the trajectory of the major lobe for the SAB beam. The Poynting vector for the beams proves the direction of the energy flow corresponding to the intensity distribution. Hence, we anticipate that the proposed vortex symmetric Airy beam (VSAB) will provide new possibilities for optical manipulation and optical communication.

Evaluation of the topological characteristics of the turbulent flow in a `box of turbulence' through 2D time-resolved particle image velocimetry

NASA Astrophysics Data System (ADS)

Lian, Huan; Soulopoulos, Nikolaos; Hardalupas, Yannis

2017-09-01

The experimental evaluation of the topological characteristics of the turbulent flow in a `box' of homogeneous and isotropic turbulence (HIT) with zero mean velocity is presented. This requires an initial evaluation of the effect of signal noise on measurement of velocity invariants. The joint probability distribution functions (pdfs) of experimentally evaluated, noise contaminated, velocity invariants have a different shape than the corresponding noise-free joint pdfs obtained from the DNS data of the Johns Hopkins University (JHU) open resource HIT database. A noise model, based on Gaussian and impulsive Salt and Pepper noise, is established and added artificially to the DNS velocity vector field of the JHU database. Digital filtering methods, based on Median and Wiener Filters, are chosen to eliminate the modeled noise source and their capacity to restore the joint pdfs of velocity invariants to that of the noise-free DNS data is examined. The remaining errors after filtering are quantified by evaluating the global mean velocity, turbulent kinetic energy and global turbulent homogeneity, assessed through the behavior of the ratio of the standard deviation of the velocity fluctuations in two directions, the energy spectrum of the velocity fluctuations and the eigenvalues of the rate-of-strain tensor. A method of data filtering, based on median filtered velocity using different median filter window size, is used to quantify the clustering of zero velocity points of the turbulent field using the radial distribution function (RDF) and Voronoï analysis to analyze the 2D time-resolved particle image velocimetry (TR-PIV) velocity measurements. It was found that a median filter with window size 3 × 3 vector spacing is the effective and efficient approach to eliminate the experimental noise from PIV measured velocity images to a satisfactory level and extract the statistical two-dimensional topological turbulent flow patterns.

The topological structure of supergravity: an application to supersymmetric localization

NASA Astrophysics Data System (ADS)

Imbimbo, Camillo; Rosa, Dario

2018-05-01

The BRST algebra of supergravity is characterized by two different bilinears of the commuting supersymmetry ghosts: a vector γ μ and a scalar ϕ, the latter valued in the Yang-Mills Lie algebra. We observe that under BRST transformations γ and ϕ transform as the superghosts of, respectively, topological gravity and topological Yang-Mills coupled to topological gravity. This topological structure sitting inside any supergravity leads to universal equivariant cohomological equations for the curvatures 2-forms which hold on supersymmetric bosonic backgrounds. Additional equivariant cohomological equations can be derived for supersymmetric backgrounds of supergravities for which certain gauge invariant scalar bilinears of the commuting ghosts exist. Among those, N = (2 , 2) in d = 2, which we discuss in detail in this paper, and N = 2 in d = 4.

A structural topological optimization method for multi-displacement constraints and any initial topology configuration

NASA Astrophysics Data System (ADS)

Rong, J. H.; Yi, J. H.

2010-10-01

In density-based topological design, one expects that the final result consists of elements either black (solid material) or white (void), without any grey areas. Moreover, one also expects that the optimal topology can be obtained by starting from any initial topology configuration. An improved structural topological optimization method for multi- displacement constraints is proposed in this paper. In the proposed method, the whole optimization process is divided into two optimization adjustment phases and a phase transferring step. Firstly, an optimization model is built to deal with the varied displacement limits, design space adjustments, and reasonable relations between the element stiffness matrix and mass and its element topology variable. Secondly, a procedure is proposed to solve the optimization problem formulated in the first optimization adjustment phase, by starting with a small design space and advancing to a larger deign space. The design space adjustments are automatic when the design domain needs expansions, in which the convergence of the proposed method will not be affected. The final topology obtained by the proposed procedure in the first optimization phase, can approach to the vicinity of the optimum topology. Then, a heuristic algorithm is given to improve the efficiency and make the designed structural topology black/white in both the phase transferring step and the second optimization adjustment phase. And the optimum topology can finally be obtained by the second phase optimization adjustments. Two examples are presented to show that the topologies obtained by the proposed method are of very good 0/1 design distribution property, and the computational efficiency is enhanced by reducing the element number of the design structural finite model during two optimization adjustment phases. And the examples also show that this method is robust and practicable.

Topology Change and the Unity of Space

NASA Astrophysics Data System (ADS)

Callender, Craig; Weingard, Robert

Must space be a unity? This question, which exercised Aristotle, Descartes and Kant, is a specific instance of a more general one; namely, can the topology of physical space change with time? In this paper we show how the discussion of the unity of space has been altered but survives in contemporary research in theoretical physics. With a pedagogical review of the role played by the Euler characteristic in the mathematics of relativistic spacetimes, we explain how classical general relativity (modulo considerations about energy conditions) allows virtually unrestrained spatial topology change in four dimensions. We also survey the situation in many other dimensions of interest. However, topology change comes with a cost: a famous theorem by Robert Geroch shows that, for many interesting types of such change, transitions of spatial topology imply the existence of closed timelike curves or temporal non-orientability. Ways of living with this theorem and of evading it are discussed.

Topological superconductivity in monolayer transition metal dichalcogenides.

PubMed

Hsu, Yi-Ting; Vaezi, Abolhassan; Fischer, Mark H; Kim, Eun-Ah

2017-04-11

Theoretically, it has been known that breaking spin degeneracy and effectively realizing spinless fermions is a promising path to topological superconductors. Yet, topological superconductors are rare to date. Here we propose to realize spinless fermions by splitting the spin degeneracy in momentum space. Specifically, we identify monolayer hole-doped transition metal dichalcogenide (TMD)s as candidates for topological superconductors out of such momentum-space-split spinless fermions. Although electron-doped TMDs have recently been found superconducting, the observed superconductivity is unlikely topological because of the near spin degeneracy. Meanwhile, hole-doped TMDs with momentum-space-split spinless fermions remain unexplored. Employing a renormalization group analysis, we propose that the unusual spin-valley locking in hole-doped TMDs together with repulsive interactions selectively favours two topological superconducting states: interpocket paired state with Chern number 2 and intrapocket paired state with finite pair momentum. A confirmation of our predictions will open up possibilities for manipulating topological superconductors on the device-friendly platform of monolayer TMDs.

d-Neighborhood system and generalized F-contraction in dislocated metric space.

PubMed

Kumari, P Sumati; Zoto, Kastriot; Panthi, Dinesh

2015-01-01

This paper, gives an answer for the Question 1.1 posed by Hitzler (Generalized metrics and topology in logic programming semantics, 2001) by means of "Topological aspects of d-metric space with d-neighborhood system". We have investigated the topological aspects of a d-neighborhood system obtained from dislocated metric space (simply d-metric space) which has got useful applications in the semantic analysis of logic programming. Further more we have generalized the notion of F-contraction in the view of d-metric spaces and investigated the uniqueness of fixed point and coincidence point of such mappings.

Search for dark matter and supersymmetry in the vector boson fusion topology in proton-proton collisions at CMS

NASA Astrophysics Data System (ADS)

Celik, A.; Hernandez, A. M. C.; CMS Collaboration

2017-07-01

A search for pair production of dark matter candidates and supersymmetry (SUSY) production with two jets in vector-boson fusion (VBF) topology is presented using data collected by the Compact Muon Solenoid (CMS) detector in proton-proton collisions at the Large Hadron Collider (LHC). Final states with no leptons are expected in pair production of dark matter particles or scalar quarks in SUSY compressed mass-spectra scenarios. Final states with low-energy leptons are expected in the production of charginos and neutralinos in SUSY compressed mass-spectra scenarios. Results for both zero and two lepton final states at 8 TeV are presented with brief prospects at 13 TeV.

Search for dark matter and supersymmetry in the vector boson fusion topology in proton-proton collisions at CMS

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

Celik, A.; Hernandez, A. M.C.

A search for pair production of dark matter candidates and supersymmetry (SUSY) production with two jets in vector-boson fusion (VBF) topology is presented using data collected by the Compact Muon Solenoid (CMS) detector in proton-proton collisions at the Large Hadron Collider (LHC). Final states with no leptons are expected in pair production of dark matter particles or scalar quarks in SUSY compressed mass-spectra scenarios. Final states with low-energy leptons are expected in the production of charginos and neutralinos in SUSY compressed mass-spectra scenarios. Results for both zero and two lepton final states at 8 TeV are presented with brief prospectsmore » at 13 TeV.« less

Search for dark matter and supersymmetry in the vector boson fusion topology in proton-proton collisions at CMS

DOE PAGES

Celik, A.; Hernandez, A. M.C.

2017-07-01

A search for pair production of dark matter candidates and supersymmetry (SUSY) production with two jets in vector-boson fusion (VBF) topology is presented using data collected by the Compact Muon Solenoid (CMS) detector in proton-proton collisions at the Large Hadron Collider (LHC). Final states with no leptons are expected in pair production of dark matter particles or scalar quarks in SUSY compressed mass-spectra scenarios. Final states with low-energy leptons are expected in the production of charginos and neutralinos in SUSY compressed mass-spectra scenarios. Results for both zero and two lepton final states at 8 TeV are presented with brief prospectsmore » at 13 TeV.« less

Focusing properties of cylindrical vector vortex beams

NASA Astrophysics Data System (ADS)

Xiaoqiang, Zhang; Ruishan, Chen; Anting, Wang

2018-05-01

In this paper, following Richards and Wolf vectorial diffraction theory, the focusing properties of cylindrical vector vortex beams (CVVB) are investigated, and a diffractive optical element (DOE) is designed to spatially modulate the amplitude of the CVVB. Simulated results show that the CVVB focused by an objective also carry orbital angular momentum (OAM), and the optical fields near the focal region can be modulated by changing the topological charge of the CVVB. We numerically simulate the focus properties of radially and azimuthally polarized beams with topological charge equal to 0, 1, 2 and 10 respectively. As a result, a dark channel with a length about 20 λ can be obtained. These new properties have the potential applications such as particle acceleration, optical trapping and material processing.

Propagation of partially coherent vector anomalous vortex beam in turbulent atmosphere

NASA Astrophysics Data System (ADS)

Zhang, Xu; Wang, Haiyan; Tang, Lei

2018-01-01

A theoretical model is proposed to describe a partially coherent vector anomalous vortex(AV) beam. Based on the extended Huygens-Fresnel principle, analytical propagation formula for the proposed beams in turbulent atmosphere is derived. The spectral properties of the partially coherent vector AV beam are explored by using the unified theory of coherence and polarization in detail. It is interesting to find that the turbulence of atmosphere and the source parameter of the partially coherent vector AV beam( order, topological charge, coherence length, beam waist size etc) have significantly impacted the propagation properties of the partially coherent vector AV beam in turbulent atmosphere.

Supersymmetric black holes with lens-space topology.

PubMed

Kunduri, Hari K; Lucietti, James

2014-11-21

We present a new supersymmetric, asymptotically flat, black hole solution to five-dimensional supergravity. It is regular on and outside an event horizon of lens-space topology L(2,1). It is the first example of an asymptotically flat black hole with lens-space topology. The solution is characterized by a charge, two angular momenta, and a magnetic flux through a noncontractible disk region ending on the horizon, with one constraint relating these.

Voltage-induced switching of an antiferromagnetically ordered topological Dirac semimetal

NASA Astrophysics Data System (ADS)

Kim, Youngseok; Kang, Kisung; Schleife, André; Gilbert, Matthew J.

2018-04-01

An antiferromagnetic semimetal has been recently identified as a new member of topological semimetals that may host three-dimensional symmetry-protected Dirac fermions. A reorientation of the Néel vector may break the underlying symmetry and open a gap in the quasiparticle spectrum, inducing the (semi)metal-insulator transition. Here, we predict that such a transition may be controlled by manipulating the chemical potential location of the material. We perform both analytical and numerical analysis on the thermodynamic potential of the model Hamiltonian and find that the gapped spectrum is preferred when the chemical potential is located at the Dirac point. As the chemical potential deviates from the Dirac point, the system shows a possible transition from the gapped to the gapless phase and switches the corresponding Néel vector configuration. We perform density functional theory calculations to verify our analysis using a realistic material and discuss a two terminal transport measurement as a possible route to identify the voltage-induced switching of the Néel vector.

Magnetic structures of REPdBi half-Heusler bismuthides (RE = Gd, Tb, Dy, Ho, Er)

NASA Astrophysics Data System (ADS)

Pavlosiuk, Orest; Fabreges, Xavier; Gukasov, Arsen; Meven, Martin; Kaczorowski, Dariusz; Wiśniewski, Piotr

2018-05-01

We present results of neutron diffraction on single crystals of several equiatomic ternary compounds of rare-earth elements with palladium and bismuth, crystallizing with cubic MgAgAs-type structure (half-Heusler phases). Band structure calculations showed that many members of that family possess electronic band inversion, which may lead to occurrence of topological insulator or topological semimetal. But even for the compounds without intrinsic band inversion another way of topologically non-trivial state realization, through a specific antiferromagnetic order, has been theoretically proposed. Our results show that the antiferromagnetic structures of all studied bismuthides are characterized by the propagation vector, allowing for antiferromagnetic topological insulator state. Therefore, the antiferromagnetic representatives of half-Heusler family are excellent candidates for extended investigations of coexistence of superconductivity, magnetic order and non-trivial topology of electronic states.

Topological insulating phases from two-dimensional nodal loop semimetals

NASA Astrophysics Data System (ADS)

Li, Linhu; Araújo, Miguel A. N.

2016-10-01

Starting from a minimal model for a two-dimensional nodal loop semimetal, we study the effect of chiral mass gap terms. The resulting Dirac loop anomalous Hall insulator's Chern number is the phase-winding number of the mass gap terms on the loop. We provide simple lattice models, analyze the topological phases, and generalize a previous index characterizing topological transitions. The responses of the Dirac loop anomalous Hall and quantum spin Hall insulators to a magnetic field's vector potential are also studied both in weak- and strong-field regimes, as well as the edge states in a ribbon geometry.

(Dis)Orientation and Spatial Sense: Topological Thinking in the Middle Grades

ERIC Educational Resources Information Center

de Freitas, Elizabeth; McCarthy, MaryJean

2014-01-01

In this paper, we focus on topological approaches to space and we argue that experiences with topology allow middle school students to develop a more robust understanding of orientation and dimension. We frame our argument in terms of the phenomenological literature on perception and corporeal space. We discuss findings from a quasi-experimental…

Model Predictive Control of A Matrix-Converter Based Solid State Transformer for Utility Grid Interaction

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

Xue, Yaosuo

The matrix converter solid state transformer (MC-SST), formed from the back-to-back connection of two three-to-single-phase matrix converters, is studied for use in the interconnection of two ac grids. The matrix converter topology provides a light weight and low volume single-stage bidirectional ac-ac power conversion without the need for a dc link. Thus, the lifetime limitations of dc-bus storage capacitors are avoided. However, space vector modulation of this type of MC-SST requires to compute vectors for each of the two MCs, which must be carefully coordinated to avoid commutation failure. An additional controller is also required to control power exchange betweenmore » the two ac grids. In this paper, model predictive control (MPC) is proposed for an MC-SST connecting two different ac power grids. The proposed MPC predicts the circuit variables based on the discrete model of MC-SST system and the cost function is formulated so that the optimal switch vector for the next sample period is selected, thereby generating the required grid currents for the SST. Simulation and experimental studies are carried out to demonstrate the effectiveness and simplicity of the proposed MPC for such MC-SST-based grid interfacing systems.« less

Spatially-protected Topology and Group Cohomology in Band Insulators

NASA Astrophysics Data System (ADS)

Alexandradinata, A.

This thesis investigates band topologies which rely fundamentally on spatial symmetries. A basic geometric property that distinguishes spatial symmetry regards their transformation of the spatial origin. Point groups consist of spatial transformations that preserve the spatial origin, while un-split extensions of the point groups by spatial translations are referred to as nonsymmorphic space groups. The first part of the thesis addresses topological phases with discretely-robust surface properties: we introduce theories for the Cnv point groups, as well as certain nonsymmorphic groups that involve glide reflections. These band insulators admit a powerful characterization through the geometry of quasimomentum space; parallel transport in this space is represented by the Wilson loop. The non-symmorphic topology we study is naturally described by a further extension of the nonsymmorphic space group by quasimomentum translations (the Wilson loop), thus placing real and quasimomentum space on equal footing -- here, we introduce the language of group cohomology into the theory of band insulators. The second part of the thesis addresses topological phases without surface properties -- their only known physical consequences are discrete signatures in parallel transport. We provide two such case studies with spatial-inversion and discrete-rotational symmetries respectively. One lesson learned here regards the choice of parameter loops in which we carry out transport -- the loop must be chosen to exploit the symmetry that protects the topology. While straight loops are popular for their connection with the geometric theory of polarization, we show that bent loops also have utility in topological band theory.

Combinatorial-topological framework for the analysis of global dynamics.

PubMed

Bush, Justin; Gameiro, Marcio; Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstantin; Obayashi, Ippei; Pilarczyk, Paweł

2012-12-01

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications.

Combinatorial-topological framework for the analysis of global dynamics

NASA Astrophysics Data System (ADS)

Bush, Justin; Gameiro, Marcio; Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstantin; Obayashi, Ippei; Pilarczyk, Paweł

2012-12-01

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications.

Origin and structures of solar eruptions II: Magnetic modeling

NASA Astrophysics Data System (ADS)

Guo, Yang; Cheng, Xin; Ding, MingDe

2017-07-01

The topology and dynamics of the three-dimensional magnetic field in the solar atmosphere govern various solar eruptive phenomena and activities, such as flares, coronal mass ejections, and filaments/prominences. We have to observe and model the vector magnetic field to understand the structures and physical mechanisms of these solar activities. Vector magnetic fields on the photosphere are routinely observed via the polarized light, and inferred with the inversion of Stokes profiles. To analyze these vector magnetic fields, we need first to remove the 180° ambiguity of the transverse components and correct the projection effect. Then, the vector magnetic field can be served as the boundary conditions for a force-free field modeling after a proper preprocessing. The photospheric velocity field can also be derived from a time sequence of vector magnetic fields. Three-dimensional magnetic field could be derived and studied with theoretical force-free field models, numerical nonlinear force-free field models, magnetohydrostatic models, and magnetohydrodynamic models. Magnetic energy can be computed with three-dimensional magnetic field models or a time series of vector magnetic field. The magnetic topology is analyzed by pinpointing the positions of magnetic null points, bald patches, and quasi-separatrix layers. As a well conserved physical quantity, magnetic helicity can be computed with various methods, such as the finite volume method, discrete flux tube method, and helicity flux integration method. This quantity serves as a promising parameter characterizing the activity level of solar active regions.

Parallel and fault-tolerant algorithms for hypercube multiprocessors

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

Aykanat, C.

1988-01-01

Several techniques for increasing the performance of parallel algorithms on distributed-memory message-passing multi-processor systems are investigated. These techniques are effectively implemented for the parallelization of the Scaled Conjugate Gradient (SCG) algorithm on a hypercube connected message-passing multi-processor. Significant performance improvement is achieved by using these techniques. The SCG algorithm is used for the solution phase of an FE modeling system. Almost linear speed-up is achieved, and it is shown that hypercube topology is scalable for an FE class of problem. The SCG algorithm is also shown to be suitable for vectorization, and near supercomputer performance is achieved on a vectormore » hypercube multiprocessor by exploiting both parallelization and vectorization. Fault-tolerance issues for the parallel SCG algorithm and for the hypercube topology are also addressed.« less

Emergent Momentum-Space Skyrmion Texture on the Surface of Topological Insulators

NASA Astrophysics Data System (ADS)

Mohanta, Narayan; Kampf, Arno P.; Kopp, Thilo

The quantum anomalous Hall effect has been theoretically predicted and experimentally verified in magnetic topological insulators. In addition, the surface states of these materials exhibit a hedgehog-like ``spin'' texture in momentum space. Here, we apply the previously formulated low-energy model for Bi2Se3, a parent compound for magnetic topological insulators, to a slab geometry in which an exchange field acts only within one of the surface layers. In this sample set up, the hedgehog transforms into a skyrmion texture beyond a critical exchange field. This critical field marks a transition between two topologically distinct phases. The topological phase transition takes place without energy gap closing at the Fermi level and leaves the transverse Hall conductance unchanged and quantized to e2 / 2 h . The momentum-space skyrmion texture persists in a finite field range. It may find its realization in hybrid heterostructures with an interface between a three-dimensional topological insulator and a ferromagnetic insulator. The work was supported by the Deutsche Forschungsgemeinschaft through TRR 80.

Cosmic Topology

NASA Astrophysics Data System (ADS)

Luminet, Jean-Pierre

2015-08-01

Cosmic Topology is the name given to the study of the overall shape of the universe, which involves both global topological features and more local geometrical properties such as curvature. Whether space is finite or infinite, simply-connected or multi-connected like a torus, smaller or greater than the portion of the universe that we can directly observe, are questions that refer to topology rather than curvature. A striking feature of some relativistic, multi-connected "small" universe models is to create multiples images of faraway cosmic sources. While the most recent cosmological data fit the simplest model of a zero-curvature, infinite space model, they are also consistent with compact topologies of the three homogeneous and isotropic geometries of constant curvature, such as, for instance, the spherical Poincaré Dodecahedral Space, the flat hypertorus or the hyperbolic Picard horn. After a "dark age" period, the field of Cosmic Topology has recently become one of the major concerns in cosmology, not only for theorists but also for observational astronomers, leaving open a number of unsolved issues.

Summary of Work for Joint Research Interchanges with DARWIN Integrated Product Team 1998

NASA Technical Reports Server (NTRS)

Hesselink, Lambertus

1999-01-01

The intent of Stanford University's SciVis group is to develop technologies that enabled comparative analysis and visualization techniques for simulated and experimental flow fields. These techniques would then be made available under the Joint Research Interchange for potential injection into the DARWIN Workspace Environment (DWE). In the past, we have focused on techniques that exploited feature based comparisons such as shock and vortex extractions. Our current research effort focuses on finding a quantitative comparison of general vector fields based on topological features. Since the method relies on topological information, grid matching and vector alignment is not needed in the comparison. This is often a problem with many data comparison techniques. In addition, since only topology based information is stored and compared for each field, there is a significant compression of information that enables large databases to be quickly searched. This report will briefly (1) describe current technologies in the area of comparison techniques, (2) will describe the theory of our new method and finally (3) summarize a few of the results.

Summary of Work for Joint Research Interchanges with DARWIN Integrated Product Team

NASA Technical Reports Server (NTRS)

Hesselink, Lambertus

1999-01-01

The intent of Stanford University's SciVis group is to develop technologies that enabled comparative analysis and visualization techniques for simulated and experimental flow fields. These techniques would then be made available un- der the Joint Research Interchange for potential injection into the DARWIN Workspace Environment (DWE). In the past, we have focused on techniques that exploited feature based comparisons such as shock and vortex extractions. Our current research effort focuses on finding a quantitative comparison of general vector fields based on topological features. Since the method relies on topological information, grid matching an@ vector alignment is not needed in the comparison. This is often a problem with many data comparison techniques. In addition, since only topology based information is stored and compared for each field, there is a significant compression of information that enables large databases to be quickly searched. This report will briefly (1) describe current technologies in the area of comparison techniques, (2) will describe the theory of our new method and finally (3) summarize a few of the results.

Topological T-duality, automorphisms and classifying spaces

NASA Astrophysics Data System (ADS)

Pande, Ashwin S.

2014-08-01

We extend the formalism of Topological T-duality to spaces which are the total space of a principal S1-bundle p:E→W with an H-flux in H3(E,Z) together with an automorphism of the continuous-trace algebra on E determined by H. The automorphism is a ‘topological approximation’ to a gerby gauge transformation of spacetime. We motivate this physically from Buscher’s Rules for T-duality. Using the Equivariant Brauer Group, we connect this problem to the C∗-algebraic formalism of Topological T-duality of Mathai and Rosenberg (2005). We show that the study of this problem leads to the study of a purely topological problem, namely, Topological T-duality of triples (p,b,H) consisting of isomorphism classes of a principal circle bundle p:X→B and classes b∈H2(X,Z) and H∈H3(X,Z). We construct a classifying space R for triples in a manner similar to the work of Bunke and Schick (2005). We characterize R up to homotopy and study some of its properties. We show that it possesses a natural self-map which induces T-duality for triples. We study some properties of this map.

Global structure of five-dimensional fuzzballs

NASA Astrophysics Data System (ADS)

Gibbons, G. W.; Warner, N. P.

2014-01-01

We describe and study families of BPS microstate geometries, namely, smooth, horizonless asymptotically flat solutions to supergravity. We examine these solutions from the perspective of earlier attempts to find solitonic solutions in gravity and show how the microstate geometries circumvent the earlier ‘no-go’ theorems. In particular, we re-analyze the Smarr formula and show how it must be modified in the presence of non-trivial second homology. This, combined with the supergravity Chern-Simons terms, allows the existence of rich classes of BPS, globally hyperbolic, asymptotically flat, microstate geometries whose spatial topology is the connected sum of N copies of S2 × S2 with a ‘point at infinity’ removed. These solutions also exhibit ‘evanescent ergo-regions,’ that is, the non-space-like Killing vector guaranteed by supersymmetry is time-like everywhere except on time-like hypersurfaces (ergo-surfaces) where the Killing vector becomes null. As a by-product of our work, we are able to resolve the puzzle of why some regular soliton solutions violate the BPS bound: their spacetimes do not admit a spin structure.

Warped product space-times

NASA Astrophysics Data System (ADS)

An, Xinliang; Wong, Willie Wai Yeung

2018-01-01

Many classical results in relativity theory concerning spherically symmetric space-times have easy generalizations to warped product space-times, with a two-dimensional Lorentzian base and arbitrary dimensional Riemannian fibers. We first give a systematic presentation of the main geometric constructions, with emphasis on the Kodama vector field and the Hawking energy; the construction is signature independent. This leads to proofs of general Birkhoff-type theorems for warped product manifolds; our theorems in particular apply to situations where the warped product manifold is not necessarily Einstein, and thus can be applied to solutions with matter content in general relativity. Next we specialize to the Lorentzian case and study the propagation of null expansions under the assumption of the dominant energy condition. We prove several non-existence results relating to the Yamabe class of the fibers, in the spirit of the black-hole topology theorem of Hawking–Galloway–Schoen. Finally we discuss the effect of the warped product ansatz on matter models. In particular we construct several cosmological solutions to the Einstein–Euler equations whose spatial geometry is generally not isotropic.

Complete theory of symmetry-based indicators of band topology.

PubMed

Po, Hoi Chun; Vishwanath, Ashvin; Watanabe, Haruki

2017-06-30

The interplay between symmetry and topology leads to a rich variety of electronic topological phases, protecting states such as the topological insulators and Dirac semimetals. Previous results, like the Fu-Kane parity criterion for inversion-symmetric topological insulators, demonstrate that symmetry labels can sometimes unambiguously indicate underlying band topology. Here we develop a systematic approach to expose all such symmetry-based indicators of band topology in all the 230 space groups. This is achieved by first developing an efficient way to represent band structures in terms of elementary basis states, and then isolating the topological ones by removing the subset of atomic insulators, defined by the existence of localized symmetric Wannier functions. Aside from encompassing all earlier results on such indicators, including in particular the notion of filling-enforced quantum band insulators, our theory identifies symmetry settings with previously hidden forms of band topology, and can be applied to the search for topological materials.Understanding the role of topology in determining electronic structure can lead to the discovery, or appreciation, of materials with exotic properties such as protected surface states. Here, the authors present a framework for identifying topologically distinct band-structures for all 3D space groups.

Scale-space measures for graph topology link protein network architecture to function.

PubMed

Hulsman, Marc; Dimitrakopoulos, Christos; de Ridder, Jeroen

2014-06-15

The network architecture of physical protein interactions is an important determinant for the molecular functions that are carried out within each cell. To study this relation, the network architecture can be characterized by graph topological characteristics such as shortest paths and network hubs. These characteristics have an important shortcoming: they do not take into account that interactions occur across different scales. This is important because some cellular functions may involve a single direct protein interaction (small scale), whereas others require more and/or indirect interactions, such as protein complexes (medium scale) and interactions between large modules of proteins (large scale). In this work, we derive generalized scale-aware versions of known graph topological measures based on diffusion kernels. We apply these to characterize the topology of networks across all scales simultaneously, generating a so-called graph topological scale-space. The comprehensive physical interaction network in yeast is used to show that scale-space based measures consistently give superior performance when distinguishing protein functional categories and three major types of functional interactions-genetic interaction, co-expression and perturbation interactions. Moreover, we demonstrate that graph topological scale spaces capture biologically meaningful features that provide new insights into the link between function and protein network architecture. Matlab(TM) code to calculate the scale-aware topological measures (STMs) is available at http://bioinformatics.tudelft.nl/TSSA © The Author 2014. Published by Oxford University Press.

Binary black hole spacetimes with a helical Killing vector

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

Klein, Christian

Binary black hole spacetimes with a helical Killing vector, which are discussed as an approximation for the early stage of a binary system, are studied in a projection formalism. In this setting the four-dimensional Einstein equations are equivalent to a three-dimensional gravitational theory with a SL(2,R)/SO(1,1) sigma model as the material source. The sigma model is determined by a complex Ernst equation. 2+1 decompositions of the three-metric are used to establish the field equations on the orbit space of the Killing vector. The two Killing horizons of spherical topology which characterize the black holes, the cylinder of light where themore » Killing vector changes from timelike to spacelike, and infinity are singular points of the equations. The horizon and the light cylinder are shown to be regular singularities, i.e., the metric functions can be expanded in a formal power series in the vicinity. The behavior of the metric at spatial infinity is studied in terms of formal series solutions to the linearized Einstein equations. It is shown that the spacetime is not asymptotically flat in the strong sense to have a smooth null infinity under the assumption that the metric tends asymptotically to the Minkowski metric. In this case the metric functions have an oscillatory behavior in the radial coordinate in a nonaxisymmetric setting, the asymptotic multipoles are not defined. The asymptotic behavior of the Weyl tensor near infinity shows that there is no smooth null infinity.« less

Invariance of Topological Indices Under Hilbert Space Truncation

DOE PAGES

Huang, Zhoushen; Zhu, Wei; Arovas, Daniel P.; ...

2018-01-05

Here, we show that the topological index of a wave function, computed in the space of twisted boundary phases, is preserved under Hilbert space truncation, provided the truncated state remains normalizable. If truncation affects the boundary condition of the resulting state, the invariant index may acquire a different physical interpretation. If the index is symmetry protected, the truncation should preserve the protecting symmetry. We discuss implications of this invariance using paradigmatic integer and fractional Chern insulators, Z 2 topological insulators, and spin-1 Affleck-Kennedy-Lieb-Tasaki and Heisenberg chains, as well as its relation with the notion of bulk entanglement. As a possiblemore » application, we propose a partial quantum tomography scheme from which the topological index of a generic multicomponent wave function can be extracted by measuring only a small subset of wave function components, equivalent to the measurement of a bulk entanglement topological index.« less

Invariance of Topological Indices Under Hilbert Space Truncation

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

Huang, Zhoushen; Zhu, Wei; Arovas, Daniel P.

Here, we show that the topological index of a wave function, computed in the space of twisted boundary phases, is preserved under Hilbert space truncation, provided the truncated state remains normalizable. If truncation affects the boundary condition of the resulting state, the invariant index may acquire a different physical interpretation. If the index is symmetry protected, the truncation should preserve the protecting symmetry. We discuss implications of this invariance using paradigmatic integer and fractional Chern insulators, Z 2 topological insulators, and spin-1 Affleck-Kennedy-Lieb-Tasaki and Heisenberg chains, as well as its relation with the notion of bulk entanglement. As a possiblemore » application, we propose a partial quantum tomography scheme from which the topological index of a generic multicomponent wave function can be extracted by measuring only a small subset of wave function components, equivalent to the measurement of a bulk entanglement topological index.« less

Factorising the 3D topologically twisted index

NASA Astrophysics Data System (ADS)

Cabo-Bizet, Alejandro

2017-04-01

We explore the path integration — upon the contour of hermitian (non-auxliary) field configurations — of topologically twisted N=2 Chern-Simons-matter theory (TTCSM) on {S}_2 times a segment. In this way, we obtain the formula for the 3D topologically twisted index, first as a convolution of TTCSM on {S}_2 times halves of {S}_1 , second as TTCSM on {S}_2 times {S}_1 — with a puncture, — and third as TTCSM on {S}_2× {S}_1 . In contradistinction to the first two cases, in the third case, the vector multiplet auxiliary field D is constrained to be anti-hermitian.

T-scale as a novel vector of topological descriptors for amino acids and its application in QSARs of peptides

NASA Astrophysics Data System (ADS)

Tian, Feifei; Zhou, Peng; Li, Zhiliang

2007-03-01

In this paper, a new topological descriptor T-scale is derived from principal component analysis (PCA) on the collected 67 kinds of structural and topological variables of 135 amino acids. Applying T-scale to three peptide panels as 58 angiotensin-converting enzyme (ACE) inhibitors, 20 thromboplastin inhibitors (TI) and 28 bovine lactoferricin-(17-31)-pentadecapeptides (LFB), the resulting QSAR models, constructed by partial least squares (PLS), are all superior to reference reports, with correlative coefficient r2 and cross-validated q2 of 0.845, 0.786; 0.996, 0.782 (0.988, 0.961); 0.760, 0.627, respectively.

Topological Maxwell Metal Bands in a Superconducting Qutrit

NASA Astrophysics Data System (ADS)

Tan, Xinsheng; Zhang, Dan-Wei; Liu, Qiang; Xue, Guangming; Yu, Hai-Feng; Zhu, Yan-Qing; Yan, Hui; Zhu, Shi-Liang; Yu, Yang

2018-03-01

We experimentally explore the topological Maxwell metal bands by mapping the momentum space of condensed-matter models to the tunable parameter space of superconducting quantum circuits. An exotic band structure that is effectively described by the spin-1 Maxwell equations is imaged. Threefold degenerate points dubbed Maxwell points are observed in the Maxwell metal bands. Moreover, we engineer and observe the topological phase transition from the topological Maxwell metal to a trivial insulator, and report the first experiment to measure the Chern numbers that are higher than one.

Transmembrane protein topology prediction using support vector machines.

PubMed

Nugent, Timothy; Jones, David T

2009-05-26

Alpha-helical transmembrane (TM) proteins are involved in a wide range of important biological processes such as cell signaling, transport of membrane-impermeable molecules, cell-cell communication, cell recognition and cell adhesion. Many are also prime drug targets, and it has been estimated that more than half of all drugs currently on the market target membrane proteins. However, due to the experimental difficulties involved in obtaining high quality crystals, this class of protein is severely under-represented in structural databases. In the absence of structural data, sequence-based prediction methods allow TM protein topology to be investigated. We present a support vector machine-based (SVM) TM protein topology predictor that integrates both signal peptide and re-entrant helix prediction, benchmarked with full cross-validation on a novel data set of 131 sequences with known crystal structures. The method achieves topology prediction accuracy of 89%, while signal peptides and re-entrant helices are predicted with 93% and 44% accuracy respectively. An additional SVM trained to discriminate between globular and TM proteins detected zero false positives, with a low false negative rate of 0.4%. We present the results of applying these tools to a number of complete genomes. Source code, data sets and a web server are freely available from http://bioinf.cs.ucl.ac.uk/psipred/. The high accuracy of TM topology prediction which includes detection of both signal peptides and re-entrant helices, combined with the ability to effectively discriminate between TM and globular proteins, make this method ideally suited to whole genome annotation of alpha-helical transmembrane proteins.

Devaney chaos, Li-Yorke chaos, and multi-dimensional Li-Yorke chaos for topological dynamics

NASA Astrophysics Data System (ADS)

Dai, Xiongping; Tang, Xinjia

2017-11-01

Let π : T × X → X, written T↷π X, be a topological semiflow/flow on a uniform space X with T a multiplicative topological semigroup/group not necessarily discrete. We then prove: If T↷π X is non-minimal topologically transitive with dense almost periodic points, then it is sensitive to initial conditions. As a result of this, Devaney chaos ⇒ Sensitivity to initial conditions, for this very general setting. Let R+↷π X be a C0-semiflow on a Polish space; then we show: If R+↷π X is topologically transitive with at least one periodic point p and there is a dense orbit with no nonempty interior, then it is multi-dimensional Li-Yorke chaotic; that is, there is a uncountable set Θ ⊆ X such that for any k ≥ 2 and any distinct points x1 , … ,xk ∈ Θ, one can find two time sequences sn → ∞ ,tn → ∞ with Moreover, let X be a non-singleton Polish space; then we prove: Any weakly-mixing C0-semiflow R+↷π X is densely multi-dimensional Li-Yorke chaotic. Any minimal weakly-mixing topological flow T↷π X with T abelian is densely multi-dimensional Li-Yorke chaotic. Any weakly-mixing topological flow T↷π X is densely Li-Yorke chaotic. We in addition construct a completely Li-Yorke chaotic minimal SL (2 , R)-acting flow on the compact metric space R ∪ { ∞ }. Our various chaotic dynamics are sensitive to the choices of the topology of the phase semigroup/group T.

Relation of the runaway avalanche threshold to momentum space topology

NASA Astrophysics Data System (ADS)

McDevitt, Christopher J.; Guo, Zehua; Tang, Xian-Zhu

2018-02-01

The underlying physics responsible for the formation of an avalanche instability due to the generation of secondary electrons is studied. A careful examination of the momentum space topology of the runaway electron population is carried out with an eye toward identifying how qualitative changes in the momentum space of the runaway electrons is correlated with the avalanche threshold. It is found that the avalanche threshold is tied to the merger of an O and X point in the momentum space of the primary runaway electron population. Such a change of the momentum space topology is shown to be accurately described by a simple analytic model, thus providing a powerful means of determining the avalanche threshold for a range of model assumptions.

High-order optical vortex position detection using a Shack-Hartmann wavefront sensor.

PubMed

Luo, Jia; Huang, Hongxin; Matsui, Yoshinori; Toyoda, Haruyoshi; Inoue, Takashi; Bai, Jian

2015-04-06

Optical vortex (OV) beams have null-intensity singular points, and the intensities in the region surrounding the singular point are quite low. This low intensity region influences the position detection accuracy of phase singular point, especially for high-order OV beam. In this paper, we propose a new method for solving this problem, called the phase-slope-combining correlation matching method. A Shack-Hartmann wavefront sensor (SH-WFS) is used to measure phase slope vectors at lenslet positions of the SH-WFS. Several phase slope vectors are combined into one to reduce the influence of low-intensity regions around the singular point, and the combined phase slope vectors are used to determine the OV position with the aid of correlation matching with a pre-calculated database. Experimental results showed that the proposed method works with high accuracy, even when detecting an OV beam with a topological charge larger than six. The estimated precision was about 0.15 in units of lenslet size when detecting an OV beam with a topological charge of up to 20.

Skeletonization and Partitioning of Digital Images Using Discrete Morse Theory.

PubMed

Delgado-Friedrichs, Olaf; Robins, Vanessa; Sheppard, Adrian

2015-03-01

We show how discrete Morse theory provides a rigorous and unifying foundation for defining skeletons and partitions of grayscale digital images. We model a grayscale image as a cubical complex with a real-valued function defined on its vertices (the voxel values). This function is extended to a discrete gradient vector field using the algorithm presented in Robins, Wood, Sheppard TPAMI 33:1646 (2011). In the current paper we define basins (the building blocks of a partition) and segments of the skeleton using the stable and unstable sets associated with critical cells. The natural connection between Morse theory and homology allows us to prove the topological validity of these constructions; for example, that the skeleton is homotopic to the initial object. We simplify the basins and skeletons via Morse-theoretic cancellation of critical cells in the discrete gradient vector field using a strategy informed by persistent homology. Simple working Python code for our algorithms for efficient vector field traversal is included. Example data are taken from micro-CT images of porous materials, an application area where accurate topological models of pore connectivity are vital for fluid-flow modelling.

Two-component vector solitons in defocusing Kerr-type media with spatially modulated nonlinearity

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

Zhong, Wei-Ping, E-mail: zhongwp6@126.com; Texas A and M University at Qatar, P.O. Box 23874 Doha; Belić, Milivoj

2014-12-15

We present a class of exact solutions to the coupled (2+1)-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity and a special external potential, which describe the evolution of two-component vector solitons in defocusing Kerr-type media. We find a robust soliton solution, constructed with the help of Whittaker functions. For specific choices of the topological charge, the radial mode number and the modulation depth, the solitons may exist in various forms, such as the half-moon, necklace-ring, and sawtooth vortex-ring patterns. Our results show that the profile of such solitons can be effectively controlled by the topological charge, the radial mode number,more » and the modulation depth. - Highlights: • Two-component vector soliton clusters in defocusing Kerr-type media are reported. • These soliton clusters are constructed with the help of Whittaker functions. • The half-moon, necklace-ring and vortex-ring patterns are found. • The profile of these solitons can be effectively controlled by three soliton parameters.« less

STM Studies of Spin-­Orbit Coupled Phases in Real-­ and Momentum-­Space

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

Madhavan, Vidya

The recently discovered class of spin-orbit coupled materials with interesting topological character are fascinating both from fundamental as well as application point of view. Two striking examples are 3D topological insulators (TIs) and topological crystalline insulators (TCIs). These materials host linearly dispersing (Dirac like) surface states with an odd number of Dirac nodes and are predicted to carry a quantized half-integer value of the axion field. The non-trivial topological properties of TIs and TCIs arise from strong spin-orbit coupling leading to an inverted band structure; which also leads to the chiral spin texture in momentum space. In this project wemore » used low temperature scanning tunneling microscopy (STM) and spectroscopy (STS) to study materials with topological phases in real- and momentum-space. We studied both single crystals and thin films of topological materials which are susceptible to being tuned by doping, strain or gating, allowing us to explore their physical properties in the most interesting regimes and set the stage for future technological applications. .« less

Classification of topological insulators and superconductors in three spatial dimensions

NASA Astrophysics Data System (ADS)

Ryu, Shinsei; Schnyder, Andreas; Furusaki, Akira; Ludwig, Andreas

2009-03-01

We systematically study topological phases of insulators and superconductors (or superfluids) in 3D. We find that there exist 3D topologically non-trivial insulators or superconductors in five out of ten symmetry classes introduced in seminal work by Altland and Zirnbauer within the context of random matrix theory, more than a decade ago. One of these is the recently introduced Z2 topological insulator in the symplectic (or spin-orbit) symmetry class. We show there exist precisely four more topological insulators. For these systems, all of which are time-reversal invariant in 3D, the space of insulating ground states satisfying certain discrete symmetry properties is partitioned into topological sectors that are separated by quantum phase transitions. Three of the above five topologically non-trivial phases can be realized as time-reversal invariant superconductors, and in these the different topological sectors are characterized by an integer winding number defined in momentum space. When such 3D topological insulators are terminated by a 2D surface, they support stable surface Dirac (Majorana) fermion modes.

Control topologies for deep space formation flying spacecraft

NASA Technical Reports Server (NTRS)

Hadaegh, F. Y.; Smith, R. S.

2002-01-01

This paper gives a characterization of the equivalent topologies and uses this approach to show that there exists a control topology which achieves a global tracking objective using only local controllers.

Poisson traces, D-modules, and symplectic resolutions

NASA Astrophysics Data System (ADS)

Etingof, Pavel; Schedler, Travis

2018-03-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

Poisson traces, D-modules, and symplectic resolutions.

PubMed

Etingof, Pavel; Schedler, Travis

2018-01-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

Momentum space view of the ultrafast dynamics of surface photocurrents on topological insulators

NASA Astrophysics Data System (ADS)

Kuroda, K.; Reimann, J.; Güdde, J.; Höfer, U.

2017-02-01

The Dirac-cone surface states of topological insulators are characterized by a chiral spin texture in k-space with the electron spin locked to its parallel momentum. Mid-infrared pump pulses can induce spin-polarized photocurrents in such a topological surface state by optical transitions between the occupied and unoccupied part of the Dirac cone. We monitor the ultrafast dynamics of the corresponding asymmetric electron population in momentum space directly by time- and angle-resolved two-photon photoemission (2PPE). The elastic scattering times of 2.5 ps deduced for Sb2Te3 corresponds to a mean-fee path of 0.75 μm in real space.

A multi-element cosmological model with a complex space-time topology

NASA Astrophysics Data System (ADS)

Kardashev, N. S.; Lipatova, L. N.; Novikov, I. D.; Shatskiy, A. A.

2015-02-01

Wormhole models with a complex topology having one entrance and two exits into the same space-time of another universe are considered, as well as models with two entrances from the same space-time and one exit to another universe. These models are used to build a model of a multi-sheeted universe (a multi-element model of the "Multiverse") with a complex topology. Spherical symmetry is assumed in all the models. A Reissner-Norström black-hole model having no singularity beyond the horizon is constructed. The strength of the central singularity of the black hole is analyzed.

Momentum space topology of QCD

NASA Astrophysics Data System (ADS)

Zubkov, M. A.

2018-06-01

We discuss the possibility to consider quark matter as the topological material. We consider hadronic phase (HP), the quark-gluon plasma phase (QGP), and the hypothetical color-flavor locking (CFL) phase. In those phases we identify the relevant topological invariants in momentum space. The formalism is developed, which relates those invariants and massless fermions that reside on vortices and at the interphases. This formalism is illustrated by the example of vortices in the CFL phase.

Topological properties of a curved spacetime

NASA Astrophysics Data System (ADS)

Agrawal, Gunjan; Shrivastava, Sampada; Godani, Nisha; Sinha, Soami Pyari

2017-12-01

The present paper aims at the study of a topology on Lorentzian manifolds, defined by Göbel [4] using the ideas of Zeeman [16]. Observing that on the Minkowski space it is the same as Zeeman's time topology, it has been found that a Lorentzian manifold with this topology is path connected, nonfirst countable and nonsimply connected while the Minkowski space with time topology is, in addition nonregular and separable. Furthermore, using the notion of Zeno sequences it is obtained that a compact set does not contain a nonempty open set and that a set is compact if and only if each of its infinite subsets has a limit point if and only if each of its sequences has a convergent subsequence.

(3 + 1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

NASA Astrophysics Data System (ADS)

Dittrich, Bianca

2017-05-01

We apply the recently suggested strategy to lift state spaces and operators for (2 + 1)-dimensional topological quantum field theories to state spaces and operators for a (3 + 1)-dimensional TQFT with defects. We start from the (2 + 1)-dimensional TuraevViro theory and obtain a state space, consistent with the state space expected from the Crane-Yetter model with line defects.

Spacetime symmetries and topology in bimetric relativity

NASA Astrophysics Data System (ADS)

Torsello, Francesco; Kocic, Mikica; Högâs, Marcus; Mörtsell, Edvard

2018-04-01

We explore spacetime symmetries and topologies of the two metric sectors in Hassan-Rosen bimetric theory. We show that, in vacuum, the two sectors can either share or have separate spacetime symmetries. If stress-energy tensors are present, a third case can arise, with different spacetime symmetries within the same sector. This raises the question of the best definition of spacetime symmetry in Hassan-Rosen bimetric theory. We emphasize the possibility of imposing ansatzes and looking for solutions having different Killing vector fields or different isometries in the two sectors, which has gained little attention so far. We also point out that the topology of spacetime imposes a constraint on possible metric combinations.

Relation of the runaway avalanche threshold to momentum space topology

DOE PAGES

McDevitt, Christopher J.; Guo, Zehua; Tang, Xian -Zhu

2018-01-05

Here, the underlying physics responsible for the formation of an avalanche instability due to the generation of secondary electrons is studied. A careful examination of the momentum space topology of the runaway electron population is carried out with an eye toward identifying how qualitative changes in the momentum space of the runaway electrons is correlated with the avalanche threshold. It is found that the avalanche threshold is tied to the merger of an O and X point in the momentum space of the primary runaway electron population. Such a change of the momentum space topology is shown to be accuratelymore » described by a simple analytic model, thus providing a powerful means of determining the avalanche threshold for a range of model assumptions.« less

Relation of the runaway avalanche threshold to momentum space topology

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

McDevitt, Christopher J.; Guo, Zehua; Tang, Xian -Zhu

Here, the underlying physics responsible for the formation of an avalanche instability due to the generation of secondary electrons is studied. A careful examination of the momentum space topology of the runaway electron population is carried out with an eye toward identifying how qualitative changes in the momentum space of the runaway electrons is correlated with the avalanche threshold. It is found that the avalanche threshold is tied to the merger of an O and X point in the momentum space of the primary runaway electron population. Such a change of the momentum space topology is shown to be accuratelymore » described by a simple analytic model, thus providing a powerful means of determining the avalanche threshold for a range of model assumptions.« less

Formation of magnetic discontinuities through viscous relaxation

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

Kumar, Sanjay; Bhattacharyya, R.; Smolarkiewicz, P. K.

2014-05-15

According to Parker's magnetostatic theorem, tangential discontinuities in magnetic field, or current sheets (CSs), are generally unavoidable in an equilibrium magnetofluid with infinite electrical conductivity and complex magnetic topology. These CSs are due to a failure of a magnetic field in achieving force-balance everywhere and preserving its topology while remaining in a spatially continuous state. A recent work [Kumar, Bhattacharyya, and Smolarkiewicz, Phys. Plasmas 20, 112903 (2013)] demonstrated this CS formation utilizing numerical simulations in terms of the vector magnetic field. The magnetohydrodynamic simulations presented here complement the above work by demonstrating CS formation by employing a novel approach ofmore » describing the magnetofluid evolution in terms of magnetic flux surfaces instead of the vector magnetic field. The magnetic flux surfaces being the possible sites on which CSs develop, this approach provides a direct visualization of the CS formation, helpful in understanding the governing dynamics. The simulations confirm development of tangential discontinuities through a favorable contortion of magnetic flux surfaces, as the magnetofluid undergoes a topology-preserving viscous relaxation from an initial non-equilibrium state with twisted magnetic field. A crucial finding of this work is in its demonstration of CS formation at spatial locations away from the magnetic nulls.« less

A 125 year history of topographic mapping and GIS in the U.S. Geological Survey 1884-2009, part 2: 1980-2009

USGS Publications Warehouse

Usery, E. Lynn; Varanka, Dalia; Finn, Michael P.

2009-01-01

The United States Geological Survey (USGS) entered the mainstream of developments in computer-assisted technology for mapping during the 1970s. The introduction by USGS of digital line graphs (DLGs), digital elevation models (DEMs), and land use data analysis (LUDA) nationwide land-cover data provided a base for the rapid expansion of the use of GIS in the 1980s. Whereas USGS had developed the topologically structured DLG data and the Geographic Information Retrieval and Analysis System (GIRAS) for land-cover data, the Map Overlay Statistical System (MOSS), a nontopologically structured GIS software package developed by Autometric, Inc., under contract to the U.S. Fish and Wildlife Service, dominated the use of GIS by federal agencies in the 1970s. Thus, USGS data was used in MOSS, but the topological structure, which later became a requirement for GIS vector datasets, was not used in early GIS applications. The introduction of Esri's ARC/INFO in 1982 changed that, and by the end of the 1980s, topological structure for vector data was essential, and ARC/INFO was the dominant GIS software package used by federal agencies.

Modeling and distributed gain scheduling strategy for load frequency control in smart grids with communication topology changes.

PubMed

Liu, Shichao; Liu, Xiaoping P; El Saddik, Abdulmotaleb

2014-03-01

In this paper, we investigate the modeling and distributed control problems for the load frequency control (LFC) in a smart grid. In contrast with existing works, we consider more practical and real scenarios, where the communication topology of the smart grid changes because of either link failures or packet losses. These topology changes are modeled as a time-varying communication topology matrix. By using this matrix, a new closed-loop power system model is proposed to integrate the communication topology changes into the dynamics of a physical power system. The globally asymptotical stability of this closed-loop power system is analyzed. A distributed gain scheduling LFC strategy is proposed to compensate for the potential degradation of dynamic performance (mean square errors of state vectors) of the power system under communication topology changes. In comparison to conventional centralized control approaches, the proposed method can improve the robustness of the smart grid to the variation of the communication network as well as to reduce computation load. Simulation results show that the proposed distributed gain scheduling approach is capable to improve the robustness of the smart grid to communication topology changes. © 2013 ISA. Published by ISA. All rights reserved.

Topologically massive magnetic monopoles

NASA Astrophysics Data System (ADS)

Aliev, A. N.; Nutku, Y.; Saygili, K.

2000-10-01

We show that in the Maxwell-Chern-Simons theory of topologically massive electrodynamics the Dirac string of a monopole becomes a cone in anti-de Sitter space with the opening angle of the cone determined by the topological mass, which in turn is related to the square root of the cosmological constant. This proves to be an example of a physical system, a priori completely unrelated to gravity, which nevertheless requires curved spacetime for its very existence. We extend this result to topologically massive gravity coupled to topologically massive electrodynamics within the framework of the theory of Deser, Jackiw and Templeton. The two-component spinor formalism, which is a Newman-Penrose type approach for three dimensions, is extended to include both the electrodynamical and gravitational topologically massive field equations. Using this formalism exact solutions of the coupled Deser-Jackiw-Templeton and Maxwell-Chern-Simons field equations for a topologically massive monopole are presented. These are homogeneous spaces with conical deficit. Pure Einstein gravity coupled to the Maxwell-Chern-Simons field does not admit such a monopole solution.

Anomalous Rashba spin-orbit interaction in electrically controlled topological insulator based on InN/GaN quantum wells

NASA Astrophysics Data System (ADS)

Łepkowski, Sławomir P.; Bardyszewski, Witold

2017-05-01

We study theoretically the topological phase transition and the Rashba spin-orbit interaction in electrically biased InN/GaN quantum wells. We show that that for properly chosen widths of quantum wells and barriers, one can effectively tune the system through the topological phase transition applying an external electric field perpendicular to the QW plane. We find that in InN/GaN quantum wells with the inverted band structure, when the conduction band s-type level is below the heavy hole and light hole p-type levels, the spin splitting of the subbands decreases with increasing the amplitude of the electric field in the quantum wells, which reveals the anomalous Rashba effect. Derived effective Rashba Hamiltonians can describe the subband spin splitting only for very small wave vectors due to strong coupling between the subbands. Furthermore, we demonstrate that for InN/GaN quantum wells in a Hall bar geometry, the critical voltage for the topological phase transition depends distinctly on the width of the structure and a significant spin splitting of the edge states lying in the 2D band gap can be almost switched off by increasing the electric field in quantum wells only by a few percent. We show that the dependence of the spin splitting of the upper branch of the edge state dispersion curve on the wave vector has a threshold-like behavior with the on/off spin splitting ratio reaching two orders of magnitude for narrow Hall bars. The threshold wave vector depends weakly on the Hall bar width, whereas it increases significantly with the bias voltage due to an increase of the energetic distance between the s-type and p-type quantum well energy levels and a reduction of the coupling between the subbands.

Anomalous Rashba spin-orbit interaction in electrically controlled topological insulator based on InN/GaN quantum wells.

PubMed

Łepkowski, Sławomir P; Bardyszewski, Witold

2017-05-17

We study theoretically the topological phase transition and the Rashba spin-orbit interaction in electrically biased InN/GaN quantum wells. We show that that for properly chosen widths of quantum wells and barriers, one can effectively tune the system through the topological phase transition applying an external electric field perpendicular to the QW plane. We find that in InN/GaN quantum wells with the inverted band structure, when the conduction band s-type level is below the heavy hole and light hole p-type levels, the spin splitting of the subbands decreases with increasing the amplitude of the electric field in the quantum wells, which reveals the anomalous Rashba effect. Derived effective Rashba Hamiltonians can describe the subband spin splitting only for very small wave vectors due to strong coupling between the subbands. Furthermore, we demonstrate that for InN/GaN quantum wells in a Hall bar geometry, the critical voltage for the topological phase transition depends distinctly on the width of the structure and a significant spin splitting of the edge states lying in the 2D band gap can be almost switched off by increasing the electric field in quantum wells only by a few percent. We show that the dependence of the spin splitting of the upper branch of the edge state dispersion curve on the wave vector has a threshold-like behavior with the on/off spin splitting ratio reaching two orders of magnitude for narrow Hall bars. The threshold wave vector depends weakly on the Hall bar width, whereas it increases significantly with the bias voltage due to an increase of the energetic distance between the s-type and p-type quantum well energy levels and a reduction of the coupling between the subbands.

Continuity and Separation in Symmetric Topologies

ERIC Educational Resources Information Center

Harris, J.; Lynch, M.

2007-01-01

In this note, it is shown that in a symmetric topological space, the pairs of sets separated by the topology determine the topology itself. It is then shown that when the codomain is symmetric, functions which separate only those pairs of sets that are already separated are continuous, generalizing a result found by M. Lynch.

Manipulation of radial-variant polarization for creating tunable bifocusing spots.

PubMed

Gu, Bing; Pan, Yang; Wu, Jia-Lu; Cui, Yiping

2014-02-01

We propose and generate a new radial-variant vector field (RV-VF) with a distribution of states of polarization described by the square of the radius and exploit its focusing property. Theoretically, we present the analytical expressions for the three-dimensional electric field of the vector field focused by a thin lens under the nonparaxial and paraxial approximations based on the vectorial Rayleigh-Sommerfeld formulas. Numerical simulations indicate that this focused field exhibits bifocusing spots along the optical axis. The underlying mechanism for generating the bifocusing property is analyzed in detail. We give the analytical formula for the interval between two foci. Experimentally, we generate the RV-VFs with alterable topological charge and demonstrate that the interval between two foci is controllable by tuning the radial topological charge. This particular focal field has specific applications for biparticle trapping, manipulating, alignment, transportation, and accelerating along the optical axis.

Topological Triply Degenerate Points Induced by Spin-Tensor-Momentum Couplings

NASA Astrophysics Data System (ADS)

Hu, Haiping; Hou, Junpeng; Zhang, Fan; Zhang, Chuanwei

2018-06-01

The recent discovery of triply degenerate points (TDPs) in topological materials has opened a new perspective toward the realization of novel quasiparticles without counterparts in quantum field theory. The emergence of such protected nodes is often attributed to spin-vector-momentum couplings. We show that the interplay between spin-tensor- and spin-vector-momentum couplings can induce three types of TDPs, classified by different monopole charges (C =±2 , ±1 , 0). A Zeeman field can lift them into Weyl points with distinct numbers and charges. Different TDPs of the same type are connected by intriguing Fermi arcs at surfaces, and transitions between different types are accompanied by level crossings along high-symmetry lines. We further propose an experimental scheme to realize such TDPs in cold-atom optical lattices. Our results provide a framework for studying spin-tensor-momentum coupling-induced TDPs and other exotic quasiparticles.

The topology of evolutionary novelty and innovation in macroevolution

PubMed Central

2017-01-01

Sewall Wright's fitness landscape introduced the concept of evolutionary spaces in 1932. George Gaylord Simpson modified this to an adaptive, phenotypic landscape in 1944 and since then evolutionary spaces have played an important role in evolutionary theory through fitness and adaptive landscapes, phenotypic and functional trait spaces, morphospaces and related concepts. Although the topology of such spaces is highly variable, from locally Euclidean to pre-topological, evolutionary change has often been interpreted as a search through a pre-existing space of possibilities, with novelty arising by accessing previously inaccessible or difficult to reach regions of a space. Here I discuss the nature of evolutionary novelty and innovation within the context of evolutionary spaces, and argue that the primacy of search as a conceptual metaphor ignores the generation of new spaces as well as other changes that have played important evolutionary roles. This article is part of the themed issue ‘Process and pattern in innovations from cells to societies’. PMID:29061895

Self-consistent adjoint analysis for topology optimization of electromagnetic waves

NASA Astrophysics Data System (ADS)

Deng, Yongbo; Korvink, Jan G.

2018-05-01

In topology optimization of electromagnetic waves, the Gâteaux differentiability of the conjugate operator to the complex field variable results in the complexity of the adjoint sensitivity, which evolves the original real-valued design variable to be complex during the iterative solution procedure. Therefore, the self-inconsistency of the adjoint sensitivity is presented. To enforce the self-consistency, the real part operator has been used to extract the real part of the sensitivity to keep the real-value property of the design variable. However, this enforced self-consistency can cause the problem that the derived structural topology has unreasonable dependence on the phase of the incident wave. To solve this problem, this article focuses on the self-consistent adjoint analysis of the topology optimization problems for electromagnetic waves. This self-consistent adjoint analysis is implemented by splitting the complex variables of the wave equations into the corresponding real parts and imaginary parts, sequentially substituting the split complex variables into the wave equations with deriving the coupled equations equivalent to the original wave equations, where the infinite free space is truncated by the perfectly matched layers. Then, the topology optimization problems of electromagnetic waves are transformed into the forms defined on real functional spaces instead of complex functional spaces; the adjoint analysis of the topology optimization problems is implemented on real functional spaces with removing the variational of the conjugate operator; the self-consistent adjoint sensitivity is derived, and the phase-dependence problem is avoided for the derived structural topology. Several numerical examples are implemented to demonstrate the robustness of the derived self-consistent adjoint analysis.

Finite spaces and schemes

NASA Astrophysics Data System (ADS)

Sancho de Salas, Fernando

2017-12-01

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed space, endowed with a finite open covering, produces a ringed finite space. We introduce the notions of schematic finite space and schematic morphism, showing that they behave, with respect to quasi-coherence, like schemes and morphisms of schemes do. Finally, we construct a fully faithful and essentially surjective functor from a localization of a full subcategory of the category of schematic finite spaces and schematic morphisms to the category of quasi-compact and quasi-separated schemes.

Macroscopic Floquet topological crystalline steel and superconductor pump

NASA Astrophysics Data System (ADS)

Rossi, Anna M. E. B.; Bugase, Jonas; Fischer, Thomas M.

2017-08-01

The transport of a macroscopic steel sphere and a superconducting sphere on top of two-dimensional periodic magnetic patterns is studied experimentally and compared with the theory and with experiments on topological transport of magnetic colloids. Transport of the steel and superconducting sphere is achieved by moving an external permanent magnet on a closed loop around the two-dimensional crystal. The transport is topological, i.e., the spheres are transported by a primitive unit vector of the lattice when the external magnet loop winds around specific directions. We experimentally determine the set of directions the loops must enclose for nontrivial transport of the spheres into various directions. We show that the loops can be used to sort steel and superconducting spheres. We show that the topological transport is robust with respect to the scale of the system and therefore speculate on its down scalability to the molecular scale.

Topological RPdBi half-Heusler semimetals: A new family of noncentrosymmetric magnetic superconductors.

PubMed

Nakajima, Yasuyuki; Hu, Rongwei; Kirshenbaum, Kevin; Hughes, Alex; Syers, Paul; Wang, Xiangfeng; Wang, Kefeng; Wang, Renxiong; Saha, Shanta R; Pratt, Daniel; Lynn, Jeffrey W; Paglione, Johnpierre

2015-06-01

We report superconductivity and magnetism in a new family of topological semimetals, the ternary half-Heusler compound RPdBi (R: rare earth). In this series, tuning of the rare earth f-electron component allows for simultaneous control of both lattice density via lanthanide contraction and the strength of magnetic interaction via de Gennes scaling, allowing for a unique tuning of the normal-state band inversion strength, superconducting pairing, and magnetically ordered ground states. Antiferromagnetism with ordering vector (½,½,½) occurs below a Néel temperature that scales with de Gennes factor dG, whereas a superconducting transition is simultaneously supressed with increasing dG. With superconductivity appearing in a system with noncentrosymmetric crystallographic symmetry, the possibility of spin-triplet Cooper pairing with nontrivial topology analogous to that predicted for the normal-state electronic structure provides a unique and rich opportunity to realize both predicted and new exotic excitations in topological materials.

Joining of Components of Complex Structures for Improved Dynamic Response

DTIC Science & Technology

2011-10-28

system- level mass and stiffness matrices and force vector (at each frequency in the range of interest). To address this issue a series of complex...displacements of all candidate joint locations by using the system- level mass and stiffness matrices and force vector (at each frequency in the range of...joints. In contrast, Li et al. [10] proposed a fastener layout/topology that achieves an almost uniform stress level in each joint, and adopted

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

Hidden sector monopole, vector dark matter and dark radiation with Higgs portal

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

Baek, Seungwon; Ko, P.; Park, Wan-Il, E-mail: sbaek1560@gmail.com, E-mail: pko@kias.re.kr, E-mail: wipark@kias.re.kr

2014-10-01

We show that the 't Hooft-Polyakov monopole model in the hidden sector with Higgs portal interaction makes a viable dark matter model, where monopole and massive vector dark matter (VDM) are stable due to topological conservation and the unbroken subgroup U(1 {sub X}. We show that, even though observed CMB data requires the dark gauge coupling to be quite small, a right amount of VDM thermal relic can be obtained via s-channel resonant annihilation for the mass of VDM close to or smaller than the half of SM higgs mass, thanks to Higgs portal interaction. Monopole relic density turns outmore » to be several orders of magnitude smaller than the observed dark matter relic density. Direct detection experiments, particularly, the projected XENON1T experiment, may probe the parameter space where the dark Higgs is lighter than ∼< 50 GeV. In addition, the dark photon associated with the unbroken U(1 {sub X} contributes to the radiation energy density at present, giving Δ N{sub eff}{sup ν} ∼ 0.1 as the extra relativistic neutrino species.« less

Tracking the Topological: The Effects of Standardised Data upon Teachers' Practice

ERIC Educational Resources Information Center

Lewis, Steven; Hardy, Ian

2017-01-01

This article draws upon recent theorising of the "becoming topological" of space--specifically, how new social spaces are constituted through relations rather than physical locations--to explore how standardised data, and specifically test data, have influenced teachers' work and learning. We outline the varied ways in which teacher…

On the dual equivalence of the self-dual and topologically massive /B∧F models coupled to dynamical fermionic matter

NASA Astrophysics Data System (ADS)

Menezes, R.; Nascimento, J. R. S.; Ribeiro, R. F.; Wotzasek, C.

2002-06-01

We study the equivalence between the /B∧F self-dual (SDB∧F) and the /B∧F topologically massive (TMB∧F) models including the coupling to dynamical, U(1) charged fermionic matter. This is done through an iterative procedure of gauge embedding that produces the dual mapping. In the interactive cases, the minimal coupling adopted for both vector and tensor fields in the self-dual representation is transformed into a non-minimal magnetic like coupling in the topologically massive representation but with the currents swapped. It is known that to establish this equivalence a current-current interaction term is needed to render the matter sector unchanged. We show that both terms arise naturally from the embedding procedure.

Noncommuting Momenta of Topological Solitons

NASA Astrophysics Data System (ADS)

Watanabe, Haruki; Murayama, Hitoshi

2014-05-01

We show that momentum operators of a topological soliton may not commute among themselves when the soliton is associated with the second cohomology H2 of the target space. The commutation relation is proportional to the winding number, taking a constant value within each topological sector. The noncommutativity makes it impossible to specify the momentum of a topological soliton, and induces a Magnus force.

Gravity in twisted space

NASA Technical Reports Server (NTRS)

Farrar, Kelly A.; Melott, Adrian L.

1990-01-01

Numerical simulations with periodic boundary conditions are widely used in cosmology. These have a multiply connected topology known as a three-torus. Such nontrivial topologies for the actual universe may have arisen in the Big Bang. A two-dimensional numerical model with a twisted topology, sometimes a Klein bottle, is shown as well as the fact that local properties of the model are not dependent on topology.

Thermal Simulations, Open Boundary Conditions and Switches

NASA Astrophysics Data System (ADS)

Burnier, Yannis; Florio, Adrien; Kaczmarek, Olaf; Mazur, Lukas

2018-03-01

SU(N) gauge theories on compact spaces have a non-trivial vacuum structure characterized by a countable set of topological sectors and their topological charge. In lattice simulations, every topological sector needs to be explored a number of times which reflects its weight in the path integral. Current lattice simulations are impeded by the so-called freezing of the topological charge problem. As the continuum is approached, energy barriers between topological sectors become well defined and the simulations get trapped in a given sector. A possible way out was introduced by Lüscher and Schaefer using open boundary condition in the time extent. However, this solution cannot be used for thermal simulations, where the time direction is required to be periodic. In this proceedings, we present results obtained using open boundary conditions in space, at non-zero temperature. With these conditions, the topological charge is not quantized and the topological barriers are lifted. A downside of this method are the strong finite-size effects introduced by the boundary conditions. We also present some exploratory results which show how these conditions could be used on an algorithmic level to reshuffle the system and generate periodic configurations with non-zero topological charge.

Real-space mapping of topological invariants using artificial neural networks

NASA Astrophysics Data System (ADS)

Carvalho, D.; García-Martínez, N. A.; Lado, J. L.; Fernández-Rossier, J.

2018-03-01

Topological invariants allow one to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wave functions under twisted boundary conditions. However, those procedures do not allow one to calculate a topological invariant by evaluating the system locally, and thus require information about the wave functions in the whole system. Here we show that artificial neural networks can be trained to identify the topological order by evaluating a local projection of the density matrix. We demonstrate this for two different models, a one-dimensional topological superconductor and a two-dimensional quantum anomalous Hall state, both with spatially modulated parameters. Our neural network correctly identifies the different topological domains in real space, predicting the location of in-gap states. By combining a neural network with a calculation of the electronic states that uses the kernel polynomial method, we show that the local evaluation of the invariant can be carried out by evaluating a local quantity, in particular for systems without translational symmetry consisting of tens of thousands of atoms. Our results show that supervised learning is an efficient methodology to characterize the local topology of a system.

Persistent topological features of dynamical systems

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

Maletić, Slobodan, E-mail: slobodan@hitsz.edu.cn; Institute of Nuclear Sciences Vinča, University of Belgrade, Belgrade; Zhao, Yi, E-mail: zhao.yi@hitsz.edu.cn

Inspired by an early work of Muldoon et al., Physica D 65, 1–16 (1993), we present a general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure. The obtained simplicial complex preserves all pertinent topological features of the reconstructed phase space, and it may be analyzed from topological, combinatorial, and algebraic aspects. In focus of this study is the computation of homology of the invariant set of some well known dynamical systems that display chaotic behavior. Persistent homology of simplicial complex and its relationship with the embedding dimensions are examinedmore » by studying the lifetime of topological features and topological noise. The consistency of topological properties for different dynamic regimes and embedding dimensions is examined. The obtained results shed new light on the topological properties of the reconstructed phase space and open up new possibilities for application of advanced topological methods. The method presented here may be used as a generic method for constructing simplicial complex from a scalar time series that has a number of advantages compared to the mapping of the same time series to a complex network.« less

Efficient morse decompositions of vector fields.

PubMed

Chen, Guoning; Mischaikow, Konstantin; Laramee, Robert S; Zhang, Eugene

2008-01-01

Existing topology-based vector field analysis techniques rely on the ability to extract the individual trajectories such as fixed points, periodic orbits, and separatrices that are sensitive to noise and errors introduced by simulation and interpolation. This can make such vector field analysis unsuitable for rigorous interpretations. We advocate the use of Morse decompositions, which are robust with respect to perturbations, to encode the topological structures of a vector field in the form of a directed graph, called a Morse connection graph (MCG). While an MCG exists for every vector field, it need not be unique. Previous techniques for computing MCG's, while fast, are overly conservative and usually results in MCG's that are too coarse to be useful for the applications. To address this issue, we present a new technique for performing Morse decomposition based on the concept of tau-maps, which typically provides finer MCG's than existing techniques. Furthermore, the choice of tau provides a natural tradeoff between the fineness of the MCG's and the computational costs. We provide efficient implementations of Morse decomposition based on tau-maps, which include the use of forward and backward mapping techniques and an adaptive approach in constructing better approximations of the images of the triangles in the meshes used for simulation.. Furthermore, we propose the use of spatial tau-maps in addition to the original temporal tau-maps. These techniques provide additional trade-offs between the quality of the MCGs and the speed of computation. We demonstrate the utility of our technique with various examples in the plane and on surfaces including engine simulation data sets.

Energy loss analysis of an integrated space power distribution system

NASA Technical Reports Server (NTRS)

Kankam, M. D.; Ribeiro, P. F.

1992-01-01

The results of studies related to conceptual topologies of an integrated utility-like space power system are described. The system topologies are comparatively analyzed by considering their transmission energy losses as functions of mainly distribution voltage level and load composition. The analysis is expedited by use of a Distribution System Analysis and Simulation (DSAS) software. This recently developed computer program by the Electric Power Research Institute (EPRI) uses improved load models to solve the power flow within the system. However, present shortcomings of the software with regard to space applications, and incompletely defined characteristics of a space power system make the results applicable to only the fundamental trends of energy losses of the topologies studied. Accountability, such as included, for the effects of the various parameters on the system performance can constitute part of a planning tool for a space power distribution system.

Linear Magnetochiral effect in Weyl Semimetals

NASA Astrophysics Data System (ADS)

Cortijo, Alberto

We describe the presence of a linear magnetochiral effect in time reversal breaking Weyl semimetals. The magnetochiral effect consists in a simultaneous linear dependence of the magnetotransport coefficients with the magnetic field and a momentum vector. This simultaneous dependence is allowed by the Onsager reciprocity relations, being the separation vector between the Weyl nodes the vector that plays such role. This linear magnetochiral effect constitutes a new transport effect associated to the topological structures linked to time reversal breaking Weyl semimetals. European Union structural funds and the Comunidad de Madrid MAD2D-CM Program (S2013/MIT-3007) and MINECO (Spain) Grant No. FIS2015-73454-JIN.

Chern-Simons theory and Wilson loops in the Brillouin zone

NASA Astrophysics Data System (ADS)

Lian, Biao; Vafa, Cumrun; Vafa, Farzan; Zhang, Shou-Cheng

2017-03-01

Berry connection is conventionally defined as a static gauge field in the Brillouin zone. Here we show that for three-dimensional (3D) time-reversal invariant superconductors, a generalized Berry gauge field behaves as a fluctuating field of a Chern-Simons gauge theory. The gapless nodal lines in the momentum space play the role of Wilson loop observables, while their linking and knot invariants modify the gravitational theta angle. This angle induces a topological gravitomagnetoelectric effect where a temperature gradient induces a rotational energy flow. We also show how topological strings may be realized in the six-dimensional phase space, where the physical space defects play the role of topological D-branes.

Dynamical Chern-Simons Theory in the Brillouin Zone

NASA Astrophysics Data System (ADS)

Lian, Biao; Vafa, Cumrun; Vafa, Farzan; Zhang, Shou-Cheng

Berry connection is conventionally defined as a static gauge field in the Brillouin zone. Here we show that for three-dimensional (3d) time-reversal invariant superconductors, a generalized Berry gauge field behaves as a dynamical fluctuating field of a Chern-Simons gauge theory. The gapless nodal lines in the momentum space play the role of Wilson loop observables, while their linking and knot invariants modify the gravitational theta angle. This angle induces a topological gravitomagnetoelectric effect where a temperature gradient induces a rotational energy flow. We also show how topological strings may be realized in the 6 dimensional phase space, where the physical space defects play the role of topological D-branes.

The Existence of Topological Edge States in Honeycomb Plasmonic Lattices

NASA Astrophysics Data System (ADS)

Wang, Li

In this paper, we investigate the band properties of 2D honeycomb plasmonic lattices consisting of metallic nanoparticles. By means of the coupled dipole method and quasi-static approximation, we theoretically analyze the band structures stemming from near-field interaction of localized surface plasmon polaritons for both the infinite lattice and ribbons. Naturally, the interaction of point dipoles decouples into independent out-of-plane and in-plane polarizations. For the out-of-plane modes, both the bulk spectrum and the range of the momentum k∥ where edge states exist in ribbons are similar to the electronic bands in graphene. Nevertheless, the in-plane polarized modes show significant differences, which do not only possess additional non-flat edge states in ribbons, but also have different distributions of the flat edge states in reciprocal space. For in-plane polarized modes, we derived the bulk-edge correspondence, namely, the relation between the number of flat edge states at a fixed k∥, Zak phases of the bulk bands and the winding number associated with the bulk hamiltonian, and verified it through four typical ribbon boundaries, i.e. zigzag, bearded zigzag, armchair, and bearded armchair. Our approach gives a new topological understanding of edge states in such plasmonic systems, and may also apply to other 2D vector wave systems.

The existence of topological edge states in honeycomb plasmonic lattices

NASA Astrophysics Data System (ADS)

Wang, Li; Zhang, Ruo-Yang; Xiao, Meng; Han, Dezhuan; Chan, C. T.; Wen, Weijia

2016-10-01

In this paper, we investigate the band properties of 2D honeycomb plasmonic lattices consisting of metallic nanoparticles. By means of the coupled dipole method and quasi-static approximation, we theoretically analyze the band structures stemming from near-field interaction of localized surface plasmon polaritons for both the infinite lattice and ribbons. Naturally, the interaction of point dipoles decouples into independent out-of-plane and in-plane polarizations. For the out-of-plane modes, both the bulk spectrum and the range of the momentum k ∥ where edge states exist in ribbons are similar to the electronic bands in graphene. Nevertheless, the in-plane polarized modes show significant differences, which do not only possess additional non-flat edge states in ribbons, but also have different distributions of the flat edge states in reciprocal space. For in-plane polarized modes, we derived the bulk-edge correspondence, namely, the relation between the number of flat edge states at a fixed {k}\\parallel , Zak phases of the bulk bands and the winding number associated with the bulk Hamiltonian, and verified it through four typical ribbon boundaries, i.e. zigzag, bearded zigzag, armchair, and bearded armchair. Our approach gives a new topological understanding of edge states in such plasmonic systems, and may also apply to other 2D ‘vector wave’ systems.

Topological antiferromagnetic spintronics

NASA Astrophysics Data System (ADS)

Šmejkal, Libor; Mokrousov, Yuriy; Yan, Binghai; MacDonald, Allan H.

2018-03-01

The recent demonstrations of electrical manipulation and detection of antiferromagnetic spins have opened up a new chapter in the story of spintronics. Here, we review the emerging research field that is exploring the links between antiferromagnetic spintronics and topological structures in real and momentum space. Active topics include proposals to realize Majorana fermions in antiferromagnetic topological superconductors, to control topological protection and Dirac points by manipulating antiferromagnetic order parameters, and to exploit the anomalous and topological Hall effects of zero-net-moment antiferromagnets. We explain the basic concepts behind these proposals, and discuss potential applications of topological antiferromagnetic spintronics.

Topological modes bound to dislocations in mechanical metamaterials

NASA Astrophysics Data System (ADS)

Paulose, Jayson; Chen, Bryan Gin-Ge; Vitelli, Vincenzo

2015-02-01

Mechanical metamaterials are artificial structures with unusual properties, such as negative Poisson ratio, bistability or tunable vibrational properties, that originate in the geometry of their unit cell. Often at the heart of such unusual behaviour is a soft mode: a motion that does not significantly stretch or compress the links between constituent elements. When activated by motors or external fields, soft modes become the building blocks of robots and smart materials. Here, we demonstrate the existence of topological soft modes that can be positioned at desired locations in a metamaterial while being robust against a wide range of structural deformations or changes in material parameters. These protected modes, localized at dislocations in deformed kagome and square lattices, are the mechanical analogue of topological states bound to defects in electronic systems. We create physical realizations of the topological modes in prototypes of kagome lattices built out of rigid triangular plates. We show mathematically that they originate from the interplay between two Berry phases: the Burgers vector of the dislocation and the topological polarization of the lattice. Our work paves the way towards engineering topologically protected nanomechanical structures for molecular robotics or information storage and read-out.

Non-Abelian Geometric Phases Carried by the Quantum Noise Matrix

NASA Astrophysics Data System (ADS)

Bharath, H. M.; Boguslawski, Matthew; Barrios, Maryrose; Chapman, Michael

2017-04-01

Topological phases of matter are characterized by topological order parameters that are built using Berry's geometric phase. Berry's phase is the geometric information stored in the overall phase of a quantum state. We show that geometric information is also stored in the second and higher order spin moments of a quantum spin system, captured by a non-abelian geometric phase. The quantum state of a spin-S system is uniquely characterized by its spin moments up to order 2S. The first-order spin moment is the spin vector, and the second-order spin moment represents the spin fluctuation tensor, i.e., the quantum noise matrix. When the spin vector is transported along a loop in the Bloch ball, we show that the quantum noise matrix picks up a geometric phase. Considering spin-1 systems, we formulate this geometric phase as an SO(3) operator. Geometric phases are usually interpreted in terms of the solid angle subtended by the loop at the center. However, solid angles are not well defined for loops that pass through the center. Here, we introduce a generalized solid angle which is well defined for all loops inside the Bloch ball, in terms of which, we interpret the SO(3) geometric phase. This geometric phase can be used to characterize topological spin textures in cold atomic clouds.

Fuzzy topological digital space and digital fuzzy spline of electroencephalography during epileptic seizures

NASA Astrophysics Data System (ADS)

Shah, Mazlina Muzafar; Wahab, Abdul Fatah

2017-08-01

Epilepsy disease occurs because of there is a temporary electrical disturbance in a group of brain cells (nurons). The recording of electrical signals come from the human brain which can be collected from the scalp of the head is called Electroencephalography (EEG). EEG then considered in digital format and in fuzzy form makes it a fuzzy digital space data form. The purpose of research is to identify the area (curve and surface) in fuzzy digital space affected by inside epilepsy seizure in epileptic patient's brain. The main focus for this research is to generalize fuzzy topological digital space, definition and basic operation also the properties by using digital fuzzy set and the operations. By using fuzzy digital space, the theory of digital fuzzy spline can be introduced to replace grid data that has been use previously to get better result. As a result, the flat of EEG can be fuzzy topological digital space and this type of data can be use to interpolate the digital fuzzy spline.

Magnetic gating of a 2D topological insulator

NASA Astrophysics Data System (ADS)

Dang, Xiaoqian; Burton, J. D.; Tsymbal, Evgeny Y.

2016-09-01

Deterministic control of transport properties through manipulation of spin states is one of the paradigms of spintronics. Topological insulators offer a new playground for exploring interesting spin-dependent phenomena. Here, we consider a ferromagnetic ‘gate’ representing a magnetic adatom coupled to the topologically protected edge state of a two-dimensional (2D) topological insulator to modulate the electron transmission of the edge state. Due to the locked spin and wave vector of the transport electrons the transmission across the magnetic gate depends on the mutual orientation of the adatom magnetic moment and the current. If the Fermi energy matches an exchange-split bound state of the adatom, the electron transmission can be blocked due to the full back scattering of the incident wave. This antiresonance behavior is controlled by the adatom magnetic moment orientation so that the transmission of the edge state can be changed from 1 to 0. Expanding this consideration to a ferromagnetic gate representing a 1D chain of atoms shows a possibility to control the spin-dependent current of a strip of a 2D topological insulator by magnetization orientation of the ferromagnetic gate.

Electric and magnetic polarization singularities of first-order Laguerre-Gaussian beams diffracted at a half-plane screen.

PubMed

Luo, Yamei; Gao, Zenghui; Tang, Bihua; Lü, Baida

2013-08-01

Based on the vector Fresnel diffraction integrals, analytical expressions for the electric and magnetic components of first-order Laguerre-Gaussian beams diffracted at a half-plane screen are derived and used to study the electric and magnetic polarization singularities in the diffraction field for both two- and three-dimensional (2D and 3D) cases. It is shown that there exist 2D and 3D electric and magnetic polarization singularities in the diffraction field, which do not coincide each other in general. By suitably varying the waist width ratio, off-axis displacement parameter, amplitude ratio, or propagation distance, the motion, pair-creation, and annihilation of circular polarization singularities, and the motion of linear polarization singularities take place in 2D and 3D electric and magnetic fields. The V point, at which two circular polarization singularities with the same topological charge but opposite handedness collide, appears in the 2D electric field under certain conditions in the diffraction field and free-space propagation. A comparison with the free-space propagation is also made.

The Hantzsche-Wendt manifold in cosmic topology

NASA Astrophysics Data System (ADS)

Aurich, R.; Lustig, S.

2014-08-01

The Hantzsche-Wendt space is one of the 17 multiply connected spaces of the three-dimensional Euclidean space {{{E}}^{3}}. It is a compact and orientable manifold which can serve as a model for a spatial finite universe. Since it possesses much fewer matched back-to-back circle pairs on the cosmic microwave background (CMB) sky than the other compact flat spaces, it can escape the detection by a search for matched circle pairs. The suppression of temperature correlations C(\\vartheta ) on large angular scales on the CMB sky is studied. It is shown that the large-scale correlations are of the same order as for the three-torus topology but express a much larger variability. The Hantzsche-Wendt manifold provides a topological possibility with reduced large-angle correlations that can hide from searches for matched back-to-back circle pairs.

Emergent gauge fields and their nonperturbative effects in correlated electrons

NASA Astrophysics Data System (ADS)

Kim, Ki-Seok; Tanaka, Akihiro

2015-06-01

The history of modern condensed matter physics may be regarded as the competition and reconciliation between Stoner’s and Anderson’s physical pictures, where the former is based on momentum-space descriptions focusing on long wave-length fluctuations while the latter is based on real-space physics emphasizing emergent localized excitations. In particular, these two view points compete with each other in various nonperturbative phenomena, which range from the problem of high Tc superconductivity, quantum spin liquids in organic materials and frustrated spin systems, heavy-fermion quantum criticality, metal-insulator transitions in correlated electron systems such as doped silicons and two-dimensional electron systems, the fractional quantum Hall effect, to the recently discussed Fe-based superconductors. An approach to reconcile these competing frameworks is to introduce topologically nontrivial excitations into the Stoner’s description, which appear to be localized in either space or time and sometimes both, where scattering between itinerant electrons and topological excitations such as skyrmions, vortices, various forms of instantons, emergent magnetic monopoles, and etc. may catch nonperturbative local physics beyond the Stoner’s paradigm. In this review paper, we discuss nonperturbative effects of topological excitations on dynamics of correlated electrons. First, we focus on the problem of scattering between itinerant fermions and topological excitations in antiferromagnetic doped Mott insulators, expected to be relevant for the pseudogap phase of high Tc cuprates. We propose that nonperturbative effects of topological excitations can be incorporated within the perturbative framework, where an enhanced global symmetry with a topological term plays an essential role. In the second part, we go on to discuss the subject of symmetry protected topological states in a largely similar light. While we do not introduce itinerant fermions here, the nonperturbative dynamics of topological excitations is again seen to be crucial in classifying topologically nontrivial gapped systems. We point to some hidden links between several effective field theories with topological terms, starting with one-dimensional physics, and subsequently finding natural generalizations to higher dimensions.

Emergent Gauge Fields and Their Nonperturbative Effects in Correlated Electrons

NASA Astrophysics Data System (ADS)

Kim, Ki-Seok; Tanaka, Akihiro

The history of modern condensed matter physics may be regarded as the competition and reconciliation between Stoner's and Anderson's physical pictures, where the former is based on momentum-space descriptions focusing on long wave-length fluctuations while the latter is based on real-space physics emphasizing emergent localized excitations. In particular, these two view points compete with each other in various nonperturbative phenomena, which range from the problem of high Tc superconductivity, quantum spin liquids in organic materials and frustrated spin systems, heavy-fermion quantum criticality, metal-insulator transitions in correlated electron systems such as doped silicons and two-dimensional electron systems, the fractional quantum Hall effect, to the recently discussed Fe-based superconductors. An approach to reconcile these competing frameworks is to introduce topologically nontrivial excitations into the Stoner's description, which appear to be localized in either space or time and sometimes both, where scattering between itinerant electrons and topological excitations such as skyrmions, vortices, various forms of instantons, emergent magnetic monopoles, and etc. may catch nonperturbative local physics beyond the Stoner's paradigm. In this review article we discuss nonperturbative effects of topological excitations on dynamics of correlated electrons. First, we focus on the problem of scattering between itinerant fermions and topological excitations in antiferromagnetic doped Mott insulators, expected to be relevant for the pseudogap phase of high Tc cuprates. We propose that nonperturbative effects of topological excitations can be incorporated within the perturbative framework, where an enhanced global symmetry with a topological term plays an essential role. In the second part, we go on to discuss the subject of symmetry protected topological states in a largely similar light. While we do not introduce itinerant fermions here, the nonperturbative dynamics of topological excitations is again seen to be crucial in classifying topologically nontrivial gapped systems. We point to some hidden links between several effective field theories with topological terms, starting with one dimensional physics, and subsequently finding natural generalizations to higher dimensions.

Initial data sets and the topology of closed three-manifolds in general relativity

NASA Astrophysics Data System (ADS)

Carfora, M.

1983-10-01

The interaction between the matter content of a closed physical space associated with a generic gravitational configuration and the topology of the underlying closed three-manifold is discussed. Within the context of the conformal approach to the initial value problem, it is shown that the presence of enough matter and radiation favors the three-sphere topology or the worm-hole topology. It is argued that such topologies leave more room for possible gravitational initial data sets for the field equations.

Extrapolation methods for vector sequences

NASA Technical Reports Server (NTRS)

Smith, David A.; Ford, William F.; Sidi, Avram

1987-01-01

This paper derives, describes, and compares five extrapolation methods for accelerating convergence of vector sequences or transforming divergent vector sequences to convergent ones. These methods are the scalar epsilon algorithm (SEA), vector epsilon algorithm (VEA), topological epsilon algorithm (TEA), minimal polynomial extrapolation (MPE), and reduced rank extrapolation (RRE). MPE and RRE are first derived and proven to give the exact solution for the right 'essential degree' k. Then, Brezinski's (1975) generalization of the Shanks-Schmidt transform is presented; the generalized form leads from systems of equations to TEA. The necessary connections are then made with SEA and VEA. The algorithms are extended to the nonlinear case by cycling, the error analysis for MPE and VEA is sketched, and the theoretical support for quadratic convergence is discussed. Strategies for practical implementation of the methods are considered.

A topological extension of GR: Black holes induce dark energy

NASA Astrophysics Data System (ADS)

Spaans, M.

2013-02-01

A topological extension of general relativity is presented. The superposition principle of quantum mechanics, as formulated by the Feynman path integral, is taken as a starting point. It is argued that the trajectories that enter this path integral are distinct and thus that space-time topology is multiply connected. Specifically, space-time at the Planck scale consists of a lattice of three-tori that facilitates many distinct paths for particles to travel along. To add gravity, mini black holes are attached to this lattice. These mini black holes represent Wheeler's quantum foam and result from the fact that GR is not conformally invariant. The number of such mini black holes in any time-slice through four-space is found to be equal to the number of macroscopic (so long-lived) black holes in the entire universe. This connection, by which macroscopic black holes induce mini black holes, is a topological expression of Mach's principle. The proposed topological extension of GR can be tested because, if correct, the dark energy density of the universe should be proportional the total number of macroscopic black holes in the universe at any time. This prediction, although strange, agrees with current astrophysical observations.

Classical aspects of higher spin topologically massive gravity

NASA Astrophysics Data System (ADS)

Chen, Bin; Long, Jiang; Zhang, Jian-Dong

2012-10-01

We study the classical solutions of three-dimensional topologically massive gravity (TMG) and its higher spin generalization, in the first-order formulation. The action of higher spin TMG has been proposed by Chen and Long (2011 J. High Energy Phys. JHEP12(2011)114) to be of a Chern-Simons-like form. The equations of motion are more complicated than the ones in pure higher spin AdS3 gravity, but are still tractable. As all the solutions in higher spin gravity are automatically the solutions of higher spin TMG, we focus on other solutions. We manage to find the AdS pp-wave solutions with higher spin hair and find that the non-vanishing higher spin fields may or may not modify the pp-wave geometry. In order to discuss the warped spacetime, we introduce the notion of a special Killing vector, which is defined to be the symmetry on the frame-like fields. We reproduce various warped spacetimes of TMG in our framework, with the help of special Killing vectors.

Killing vector fields in three dimensions: a method to solve massive gravity field equations

NASA Astrophysics Data System (ADS)

Gürses, Metin

2010-10-01

Killing vector fields in three dimensions play an important role in the construction of the related spacetime geometry. In this work we show that when a three-dimensional geometry admits a Killing vector field then the Ricci tensor of the geometry is determined in terms of the Killing vector field and its scalars. In this way we can generate all products and covariant derivatives at any order of the Ricci tensor. Using this property we give ways to solve the field equations of topologically massive gravity (TMG) and new massive gravity (NMG) introduced recently. In particular when the scalars of the Killing vector field (timelike, spacelike and null cases) are constants then all three-dimensional symmetric tensors of the geometry, the Ricci and Einstein tensors, their covariant derivatives at all orders, and their products of all orders are completely determined by the Killing vector field and the metric. Hence, the corresponding three-dimensional metrics are strong candidates for solving all higher derivative gravitational field equations in three dimensions.

Microscale vortex laser with controlled topological charge

NASA Astrophysics Data System (ADS)

Wang, Xing-Yuan; Chen, Hua-Zhou; Li, Ying; Li, Bo; Ma, Ren-Min

2016-12-01

A microscale vortex laser is a new type of coherent light source with small footprint that can directly generate vector vortex beams. However, a microscale laser with controlled topological charge, which is crucial for virtually any of its application, is still unrevealed. Here we present a microscale vortex laser with controlled topological charge. The vortex laser eigenmode was synthesized in a metamaterial engineered non-Hermitian micro-ring cavity system at exceptional point. We also show that the vortex laser cavity can operate at exceptional point stably to lase under optical pumping. The microscale vortex laser with controlled topological charge can serve as a unique and general building block for next-generation photonic integrated circuits and coherent vortex beam sources. The method we used here can be employed to generate lasing eigenmode with other complex functionalities. Project supported by the “Youth 1000 Talent Plan” Fund, Ministry of Education of China (Grant No. 201421) and the National Natural Science Foundation of China (Grant Nos. 11574012 and 61521004).

Skyrme insulators: insulators at the brink of superconductivity

DOE PAGES

Ertem, Onur; Chang, Po -Yao; Coleman, Piers; ...

2017-08-04

Current theories of superfluidity are based on the idea of a coherent quantum state with topologically protected, quantized circulation. When this topological protection is absent, as in the case of 3He-A, the coherent quantum state no longer supports persistent superflow. In this paper, we argue that the loss of topological protection in a superconductor gives rise to an insulating ground state. Specifically, we introduce the concept of a Skyrme insulator to describe the coherent dielectric state that results from the topological failure of superflow carried by a complex vector order parameter. Here, we apply this idea to the case ofmore » SmB6, arguing that the observation of a diamagnetic Fermi surface within an insulating bulk can be understood as a realization of this state. Our theory enables us to understand the linear specific heat of SmB6 in terms of a neutral Majorana Fermi sea and leads us to predict that in low fields of order a Gauss, SmB6 will develop a Meissner effect.« less

Magnetic manipulation of topological states in p-wave superconductors

NASA Astrophysics Data System (ADS)

Mercaldo, Maria Teresa; Cuoco, Mario; Kotetes, Panagiotis

2018-05-01

Substantial experimental investigation has provided evidence for spin-triplet pairing in diverse classes of materials and in a variety of artificial heterostructures. One of the fundamental challenges in this framework is how to manipulate the topological behavior of p-wave superconductors (PSC). In this work we investigate the magnetic field response of one-dimensional (1d) PSCs and we focus on the relation between the structure of the Cooper pair spin-configuration and the occurrence of topological phases with an enhanced number N of Majorana fermions per edge. The topological phase diagram, consisting of phases harboring Majorana modes, becomes significantly modified when one tunes the strength of the applied field, the direction of the d-vector and allows for long range hopping amplitudes in the 1d PSC. We find transitions between phases with different number N of Majorana fermions per edge and we show how they can be both induced by a variation of the hopping strength and a spin rotation of d.

Skyrme Insulators: Insulators at the Brink of Superconductivity

NASA Astrophysics Data System (ADS)

Erten, Onur; Chang, Po-Yao; Coleman, Piers; Tsvelik, Alexei M.

2017-08-01

Current theories of superfluidity are based on the idea of a coherent quantum state with topologically protected quantized circulation. When this topological protection is absent, as in the case of 3He -A , the coherent quantum state no longer supports persistent superflow. Here, we argue that the loss of topological protection in a superconductor gives rise to an insulating ground state. We specifically introduce the concept of a Skyrme insulator to describe the coherent dielectric state that results from the topological failure of superflow carried by a complex-vector order parameter. We apply this idea to the case of SmB6 , arguing that the observation of a diamagnetic Fermi surface within an insulating bulk can be understood as a realization of this state. Our theory enables us to understand the linear specific heat of SmB6 in terms of a neutral Majorana Fermi sea and leads us to predict that in low fields of order a Gauss, SmB6 will develop a Meissner effect.

Topological spin-hedgehog crystals of a chiral magnet as engineered with magnetic anisotropy

NASA Astrophysics Data System (ADS)

Kanazawa, N.; White, J. S.; Rønnow, H. M.; Dewhurst, C. D.; Morikawa, D.; Shibata, K.; Arima, T.; Kagawa, F.; Tsukazaki, A.; Kozuka, Y.; Ichikawa, M.; Kawasaki, M.; Tokura, Y.

2017-12-01

We report the engineering of spin-hedgehog crystals in thin films of the chiral magnet MnGe by tailoring the magnetic anisotropy. As evidenced by neutron scattering on films with different thicknesses and by varying a magnetic field, we can realize continuously deformable spin-hedgehog crystals, each of which is described as a superposition state of a different set of three spin spirals (a triple-q state). The directions of the three propagation vectors q vary systematically, gathering from the three orthogonal 〈100 〉 directions towards the film normal as the strength of the uniaxial magnetic anisotropy and/or the magnetic field applied along the film normal increase. The formation of triple-q states coincides with the onset of topological Hall signals, that are ascribed to skew scattering by an emergent magnetic field originating in the nontrivial topology of spin hedgehogs. These findings highlight how nanoengineering of chiral magnets makes possible the rational design of unique topological spin textures.

Magnetic hyperbolic optical metamaterials

DOE PAGES

Kruk, Sergey S.; Wong, Zi Jing; Pshenay-Severin, Ekaterina; ...

2016-04-13

Strongly anisotropic media where the principal components of electric permittivity or magnetic permeability tensors have opposite signs are termed as hyperbolic media. Such media support propagating electromagnetic waves with extremely large wave vectors exhibiting unique optical properties. However, in all artificial and natural optical materials studied to date, the hyperbolic dispersion originates solely from the electric response. This then restricts material functionality to one polarization of light and inhibits free-space impedance matching. Such restrictions can be overcome in media having components of opposite signs for both electric and magnetic tensors. Here we present the experimental demonstration of the magnetic hyperbolicmore » dispersion in three-dimensional metamaterials. We also measure metamaterial isofrequency contours and reveal the topological phase transition between the elliptic and hyperbolic dispersion. In the hyperbolic regime, we demonstrate the strong enhancement of thermal emission, which becomes directional, coherent and polarized. These findings show the possibilities for realizing efficient impedance-matched hyperbolic media for unpolarized light.« less

A spectral mimetic least-squares method

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

Bochev, Pavel; Gerritsma, Marc

We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are alsomore » satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.« less

A spectral mimetic least-squares method

DOE PAGES

Bochev, Pavel; Gerritsma, Marc

2014-09-01

We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are alsomore » satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.« less

Machine learning Z2 quantum spin liquids with quasiparticle statistics

NASA Astrophysics Data System (ADS)

Zhang, Yi; Melko, Roger G.; Kim, Eun-Ah

2017-12-01

After decades of progress and effort, obtaining a phase diagram for a strongly correlated topological system still remains a challenge. Although in principle one could turn to Wilson loops and long-range entanglement, evaluating these nonlocal observables at many points in phase space can be prohibitively costly. With growing excitement over topological quantum computation comes the need for an efficient approach for obtaining topological phase diagrams. Here we turn to machine learning using quantum loop topography (QLT), a notion we have recently introduced. Specifically, we propose a construction of QLT that is sensitive to quasiparticle statistics. We then use mutual statistics between the spinons and visons to detect a Z2 quantum spin liquid in a multiparameter phase space. We successfully obtain the quantum phase boundary between the topological and trivial phases using a simple feed-forward neural network. Furthermore, we demonstrate advantages of our approach for the evaluation of phase diagrams relating to speed and storage. Such statistics-based machine learning of topological phases opens new efficient routes to studying topological phase diagrams in strongly correlated systems.

Topology of actions and homogeneous spaces

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

Kozlov, Konstantin L

2013-04-30

Topologization of a group of homeomorphisms and its action provide additional possibilities for studying the topological space, the group of homeomorphisms, and their interconnections. The subject of the paper is the use of the property of d-openness of an action (introduced by Ancel under the name of weak micro-transitivity) in the study of spaces with various forms of homogeneity. It is proved that a d-open action of a Cech-complete group is open. A characterization of Polish SLH spaces using d-openness is given, and it is established that any separable metrizable SLH space has an SLH completion that is a Polishmore » space. Furthermore, the completion is realized in coordination with the completion of the acting group with respect to the two-sided uniformity. A sufficient condition is given for extension of a d-open action to the completion of the space with respect to the maximal equiuniformity with preservation of d-openness. A result of van Mill is generalized, namely, it is proved that any homogeneous CDH metrizable compactum is the only G-compactification of the space of rational numbers for the action of some Polish group. Bibliography: 39 titles.« less

Generalizations of γ-open set in topological spaces

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

Bhattacharya, Baby, E-mail: babybhatt75@gmail.com; Paul, Arnab, E-mail: mrarnabpaul87@gmail.com

The main aim of this work is to study three generalized forms of γ-open set due to D. Andrijevic (D. Andrijevic, On the Topology Generated by pre-open sets, Presented at the Sixth Prague Topological Symposium, 39 (1987), 367-376)in a topological space. Out of which the dual appearance of one is the stronger form of b-locally closed set in the sense of Arafa A. Nasef (A. A Nasef,On b-locally closed sets and related topics, CHAOS SOLITONS & FRACTALS 12(2001) 1909-1915). Also, we introduce the concept of different types of continuity and study their basic properties by using these newly defined sets.more » Finally, we establish the interrelationships among themselves together with some already existing generalized forms of continuity.« less

Optimal network alignment with graphlet degree vectors.

PubMed

Milenković, Tijana; Ng, Weng Leong; Hayes, Wayne; Przulj, Natasa

2010-06-30

Important biological information is encoded in the topology of biological networks. Comparative analyses of biological networks are proving to be valuable, as they can lead to transfer of knowledge between species and give deeper insights into biological function, disease, and evolution. We introduce a new method that uses the Hungarian algorithm to produce optimal global alignment between two networks using any cost function. We design a cost function based solely on network topology and use it in our network alignment. Our method can be applied to any two networks, not just biological ones, since it is based only on network topology. We use our new method to align protein-protein interaction networks of two eukaryotic species and demonstrate that our alignment exposes large and topologically complex regions of network similarity. At the same time, our alignment is biologically valid, since many of the aligned protein pairs perform the same biological function. From the alignment, we predict function of yet unannotated proteins, many of which we validate in the literature. Also, we apply our method to find topological similarities between metabolic networks of different species and build phylogenetic trees based on our network alignment score. The phylogenetic trees obtained in this way bear a striking resemblance to the ones obtained by sequence alignments. Our method detects topologically similar regions in large networks that are statistically significant. It does this independent of protein sequence or any other information external to network topology.

Multiscale vector fields for image pattern recognition

NASA Technical Reports Server (NTRS)

Low, Kah-Chan; Coggins, James M.

1990-01-01

A uniform processing framework for low-level vision computing in which a bank of spatial filters maps the image intensity structure at each pixel into an abstract feature space is proposed. Some properties of the filters and the feature space are described. Local orientation is measured by a vector sum in the feature space as follows: each filter's preferred orientation along with the strength of the filter's output determine the orientation and the length of a vector in the feature space; the vectors for all filters are summed to yield a resultant vector for a particular pixel and scale. The orientation of the resultant vector indicates the local orientation, and the magnitude of the vector indicates the strength of the local orientation preference. Limitations of the vector sum method are discussed. Investigations show that the processing framework provides a useful, redundant representation of image structure across orientation and scale.

Topological materials discovery using electron filling constraints

NASA Astrophysics Data System (ADS)

Chen, Ru; Po, Hoi Chun; Neaton, Jeffrey B.; Vishwanath, Ashvin

2018-01-01

Nodal semimetals are classes of topological materials that have nodal-point or nodal-line Fermi surfaces, which give them novel transport and topological properties. Despite being highly sought after, there are currently very few experimental realizations, and identifying new materials candidates has mainly relied on exhaustive database searches. Here we show how recent studies on the interplay between electron filling and nonsymmorphic space-group symmetries can guide the search for filling-enforced nodal semimetals. We recast the previously derived constraints on the allowed band-insulator fillings in any space group into a new form, which enables effective screening of materials candidates based solely on their space group, electron count in the formula unit, and multiplicity of the formula unit. This criterion greatly reduces the computation load for discovering topological materials in a database of previously synthesized compounds. As a demonstration, we focus on a few selected nonsymmorphic space groups which are predicted to host filling-enforced Dirac semimetals. Of the more than 30,000 entires listed, our filling criterion alone eliminates 96% of the entries before they are passed on for further analysis. We discover a handful of candidates from this guided search; among them, the monoclinic crystal Ca2Pt2Ga is particularly promising.

Topological nearly entropy

NASA Astrophysics Data System (ADS)

Gulamsarwar, Syazwani; Salleh, Zabidin

2017-08-01

The purpose of this paper is to generalize the notions of Adler's topological entropy along with their several fundamental properties. A function f : X → Y is said to be R-map if f-1 (V) is regular open in X for every regular open set V in Y. Thus, we initiated a notion of topological nearly entropy for topological R-dynamical systems which is based on nearly compact relative to the space by using R-map.

Mechanical topological insulator in zero dimensions

NASA Astrophysics Data System (ADS)

Lera, Natalia; Alvarez, J. V.

2018-04-01

We study linear vibrational modes in finite isostatic Maxwell lattices, mechanical systems where the number of degrees of freedom matches the number of constraints. Recent progress in topological mechanics exploits the nontrivial topology of BDI class Hamiltonians in one dimenson and arising topological floppy modes at the edges. A finite frame, or zero-dimensional system, also exhibits a nonzero topological index according to the classification table. We construct mechanical insulating models in zero dimensions that complete the BDI classification in the available real space dimensions. We compute and interpret its nontrivial invariant Z2.

Geometry, topology, and response in condensed matter systems

NASA Astrophysics Data System (ADS)

Varjas, Daniel

Topological order provides a new paradigm to view phases of matter. Unlike conventional symmetry breaking order, these states are not distinguished by different patterns of symmetry breaking, instead by their intricate mathematical structure, topology. By the bulk-boundary correspondence, the nontrivial topology of the bulk results in robust gapless excitations on symmetry preserving surfaces. We utilize both of these views to study topological phases together with the analysis of their quantized physical responses to perturbations. First we study the edge excitations of strongly interacting abelian fractional quantum Hall liquids on an infinite strip geometry. We use the infinite density matrix renormalization group method to numerically measure edge exponents in model systems, including subleading orders. Using analytic methods we derive a generalized Luttinger's theorem that relates momenta of edge excitations. Next we consider topological crystalline insulators protected by space group symmetry. After reviewing the general formalism, we present results about the quantization of the magnetoelectric response protected by orientation-reversing space group symmetries. We construct and analyze insulating and superconducting tight-binding models with glide symmetry in three dimensions to illustrate the general result. Following this, we derive constraints on weak indices of three dimensional topological insulators imposed by space group symmetries. We focus on spin-orbit coupled insulators with and without time reversal invariance and consider both symmorphic and nonsymmorphic symmetries. Finally, we calculate the response of metals and generalize the notion of the magnetoelectric effect to noninteracting gapless systems. We use semiclassical dynamics to study the magnetopiezoelectric effect, the current response to elastic strain in static external magnetic fields.

Vector calculus in non-integer dimensional space and its applications to fractal media

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-02-01

We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are defined. For simplification we consider scalar and vector fields that are independent of angles. We formulate a generalization of vector calculus for rotationally covariant scalar and vector functions. This generalization allows us to describe fractal media and materials in the framework of continuum models with non-integer dimensional space. As examples of application of the suggested calculus, we consider elasticity of fractal materials (fractal hollow ball and fractal cylindrical pipe with pressure inside and outside), steady distribution of heat in fractal media, electric field of fractal charged cylinder. We solve the correspondent equations for non-integer dimensional space models.

Towards Automatic Semantic Labelling of 3D City Models

NASA Astrophysics Data System (ADS)

Rook, M.; Biljecki, F.; Diakité, A. A.

2016-10-01

The lack of semantic information in many 3D city models is a considerable limiting factor in their use, as a lot of applications rely on semantics. Such information is not always available, since it is not collected at all times, it might be lost due to data transformation, or its lack may be caused by non-interoperability in data integration from other sources. This research is a first step in creating an automatic workflow that semantically labels plain 3D city model represented by a soup of polygons, with semantic and thematic information, as defined in the CityGML standard. The first step involves the reconstruction of the topology, which is used in a region growing algorithm that clusters upward facing adjacent triangles. Heuristic rules, embedded in a decision tree, are used to compute a likeliness score for these regions that either represent the ground (terrain) or a RoofSurface. Regions with a high likeliness score, to one of the two classes, are used to create a decision space, which is used in a support vector machine (SVM). Next, topological relations are utilised to select seeds that function as a start in a region growing algorithm, to create regions of triangles of other semantic classes. The topological relationships of the regions are used in the aggregation of the thematic building features. Finally, the level of detail is detected to generate the correct output in CityGML. The results show an accuracy between 85 % and 99 % in the automatic semantic labelling on four different test datasets. The paper is concluded by indicating problems and difficulties implying the next steps in the research.

Vectorization of optically sectioned brain microvasculature: learning aids completion of vascular graphs by connecting gaps and deleting open-ended segments.

PubMed

Kaufhold, John P; Tsai, Philbert S; Blinder, Pablo; Kleinfeld, David

2012-08-01

A graph of tissue vasculature is an essential requirement to model the exchange of gasses and nutriments between the blood and cells in the brain. Such a graph is derived from a vectorized representation of anatomical data, provides a map of all vessels as vertices and segments, and may include the location of nonvascular components, such as neuronal and glial somata. Yet vectorized data sets typically contain erroneous gaps, spurious endpoints, and spuriously merged strands. Current methods to correct such defects only address the issue of connecting gaps and further require manual tuning of parameters in a high dimensional algorithm. To address these shortcomings, we introduce a supervised machine learning method that (1) connects vessel gaps by "learned threshold relaxation"; (2) removes spurious segments by "learning to eliminate deletion candidate strands"; and (3) enforces consistency in the joint space of learned vascular graph corrections through "consistency learning." Human operators are only required to label individual objects they recognize in a training set and are not burdened with tuning parameters. The supervised learning procedure examines the geometry and topology of features in the neighborhood of each vessel segment under consideration. We demonstrate the effectiveness of these methods on four sets of microvascular data, each with >800(3) voxels, obtained with all optical histology of mouse tissue and vectorization by state-of-the-art techniques in image segmentation. Through statistically validated sampling and analysis in terms of precision recall curves, we find that learning with bagged boosted decision trees reduces equal-error error rates for threshold relaxation by 5-21% and strand elimination performance by 18-57%. We benchmark generalization performance across datasets; while improvements vary between data sets, learning always leads to a useful reduction in error rates. Overall, learning is shown to more than halve the total error rate, and therefore, human time spent manually correcting such vectorizations. Copyright © 2012 Elsevier B.V. All rights reserved.

Vectorization of optically sectioned brain microvasculature: Learning aids completion of vascular graphs by connecting gaps and deleting open-ended segments

PubMed Central

Kaufhold, John P.; Tsai, Philbert S.; Blinder, Pablo; Kleinfeld, David

2012-01-01

A graph of tissue vasculature is an essential requirement to model the exchange of gasses and nutriments between the blood and cells in the brain. Such a graph is derived from a vectorized representation of anatomical data, provides a map of all vessels as vertices and segments, and may include the location of nonvascular components, such as neuronal and glial somata. Yet vectorized data sets typically contain erroneous gaps, spurious endpoints, and spuriously merged strands. Current methods to correct such defects only address the issue of connecting gaps and further require manual tuning of parameters in a high dimensional algorithm. To address these shortcomings, we introduce a supervised machine learning method that (1) connects vessel gaps by “learned threshold relaxation”; (2) removes spurious segments by “learning to eliminate deletion candidate strands”; and (3) enforces consistency in the joint space of learned vascular graph corrections through “consistency learning.” Human operators are only required to label individual objects they recognize in a training set and are not burdened with tuning parameters. The supervised learning procedure examines the geometry and topology of features in the neighborhood of each vessel segment under consideration. We demonstrate the effectiveness of these methods on four sets of microvascular data, each with > 8003 voxels, obtained with all optical histology of mouse tissue and vectorization by state-of-the-art techniques in image segmentation. Through statistically validated sampling and analysis in terms of precision recall curves, we find that learning with bagged boosted decision trees reduces equal-error error rates for threshold relaxation by 5 to 21 % and strand elimination performance by 18 to 57 %. We benchmark generalization performance across datasets; while improvements vary between data sets, learning always leads to a useful reduction in error rates. Overall, learning is shown to more than halve the total error rate, and therefore, human time spent manually correcting such vectorizations. PMID:22854035

A vector-dyadic development of the equations of motion for N-coupled rigid bodies and point masses

NASA Technical Reports Server (NTRS)

Frisch, H. P.

1974-01-01

The equations of motion are derived, in vector-dyadic format, for a topological tree of coupled rigid bodies, point masses, and symmetrical momentum wheels. These equations were programmed, and form the basis for the general-purpose digital computer program N-BOD. A complete derivation of the equations of motion is included along with a description of the methods used for kinematics, constraint elimination, and for the inclusion of nongyroscope forces and torques acting external or internal to the system.

Nonparaxial and paraxial focusing of azimuthal-variant vector beams.

PubMed

Gu, Bing; Cui, Yiping

2012-07-30

Based on the vectorial Rayleigh-Sommerfeld formulas under the weak nonparaxial approximation, we investigate the propagation behavior of a lowest-order Laguerre-Gaussian beam with azimuthal-variant states of polarization. We present the analytical expressions for the radial, azimuthal, and longitudinal components of the electric field with an arbitrary integer topological charge m focused by a nonaperturing thin lens. We illustrate the three-dimensional optical intensities, energy flux distributions, beam waists, and focal shifts of the focused azimuthal-variant vector beams under the nonparaxial and paraxial approximations.

Classification of topological insulators and superconductors in three spatial dimensions

NASA Astrophysics Data System (ADS)

Schnyder, Andreas P.; Ryu, Shinsei; Furusaki, Akira; Ludwig, Andreas W. W.

2008-11-01

We systematically study topological phases of insulators and superconductors (or superfluids) in three spatial dimensions. We find that there exist three-dimensional (3D) topologically nontrivial insulators or superconductors in five out of ten symmetry classes introduced in seminal work by Altland and Zirnbauer within the context of random matrix theory, more than a decade ago. One of these is the recently introduced Z2 topological insulator in the symplectic (or spin-orbit) symmetry class. We show that there exist precisely four more topological insulators. For these systems, all of which are time-reversal invariant in three dimensions, the space of insulating ground states satisfying certain discrete symmetry properties is partitioned into topological sectors that are separated by quantum phase transitions. Three of the above five topologically nontrivial phases can be realized as time-reversal invariant superconductors. In these the different topological sectors are characterized by an integer winding number defined in momentum space. When such 3D topological insulators are terminated by a two-dimensional surface, they support a number (which may be an arbitrary nonvanishing even number for singlet pairing) of Dirac fermion (Majorana fermion when spin-rotation symmetry is completely broken) surface modes which remain gapless under arbitrary perturbations of the Hamiltonian that preserve the characteristic discrete symmetries, including disorder. In particular, these surface modes completely evade Anderson localization from random impurities. These topological phases can be thought of as three-dimensional analogs of well-known paired topological phases in two spatial dimensions such as the spinless chiral (px±ipy) -wave superconductor (or Moore-Read Pfaffian state). In the corresponding topologically nontrivial (analogous to “weak pairing”) and topologically trivial (analogous to “strong pairing”) 3D phases, the wave functions exhibit markedly distinct behavior. When an electromagnetic U(1) gauge field and fluctuations of the gap functions are included in the dynamics, the superconducting phases with nonvanishing winding number possess nontrivial topological ground-state degeneracies.

Communications and control for electric power systems: Power flow classification for static security assessment

NASA Technical Reports Server (NTRS)

Niebur, D.; Germond, A.

1993-01-01

This report investigates the classification of power system states using an artificial neural network model, Kohonen's self-organizing feature map. The ultimate goal of this classification is to assess power system static security in real-time. Kohonen's self-organizing feature map is an unsupervised neural network which maps N-dimensional input vectors to an array of M neurons. After learning, the synaptic weight vectors exhibit a topological organization which represents the relationship between the vectors of the training set. This learning is unsupervised, which means that the number and size of the classes are not specified beforehand. In the application developed in this report, the input vectors used as the training set are generated by off-line load-flow simulations. The learning algorithm and the results of the organization are discussed.

Supercurrent as a probe for topological superconductivity in magnetic adatom chains

NASA Astrophysics Data System (ADS)

Mohanta, Narayan; Kampf, Arno P.; Kopp, Thilo

2018-06-01

A magnetic adatom chain, proximity coupled to a conventional superconductor with spin-orbit coupling, exhibits locally an odd-parity, spin-triplet pairing amplitude. We show that the singlet-triplet junction, thus formed, leads to a net spin accumulation in the near vicinity of the chain. The accumulated spins are polarized along the direction of the local d vector for triplet pairing and generate an enhanced persistent current flowing around the chain. The spin polarization and the "supercurrent" reverse their directions beyond a critical exchange coupling strength at which the singlet superconducting order changes its sign on the chain. The current is strongly enhanced in the topological superconducting regime where Majorana bound states appear at the chain ends. The current and the spin profile offer alternative routes to characterize the topological superconducting state in adatom chains and islands.

Real-time imaging of perivascular transport of nanoparticles during convection-enhanced delivery in the rat cortex.

PubMed

Foley, Conor P; Nishimura, Nozomi; Neeves, Keith B; Schaffer, Chris B; Olbricht, William L

2012-02-01

Convection-enhanced delivery (CED) is a promising technique for administering large therapeutics that do not readily cross the blood brain barrier to neural tissue. It is of vital importance to understand how large drug constructs move through neural tissue during CED to optimize construct and delivery parameters so that drugs are concentrated in the targeted tissue, with minimal leakage outside the targeted zone. Experiments have shown that liposomes, viral vectors, high molecular weight tracers, and nanoparticles infused into neural tissue localize in the perivascular spaces of blood vessels within the brain parenchyma. In this work, we used two-photon excited fluorescence microscopy to monitor the real-time distribution of nanoparticles infused in the cortex of live, anesthetized rats via CED. Fluorescent nanoparticles of 24 and 100 nm nominal diameters were infused into rat cortex through microfluidic probes. We found that perivascular spaces provide a high permeability path for rapid convective transport of large nanoparticles through tissue, and that the effects of perivascular spaces on transport are more significant for larger particles that undergo hindered transport through the extracellular matrix. This suggests that the vascular topology of the target tissue volume must be considered when delivering large therapeutic constructs via CED.

Topologies on quantum topoi induced by quantization

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

Nakayama, Kunji

2013-07-15

In the present paper, we consider effects of quantization in a topos approach of quantum theory. A quantum system is assumed to be coded in a quantum topos, by which we mean the topos of presheaves on the context category of commutative subalgebras of a von Neumann algebra of bounded operators on a Hilbert space. A classical system is modeled by a Lie algebra of classical observables. It is shown that a quantization map from the classical observables to self-adjoint operators on the Hilbert space naturally induces geometric morphisms from presheaf topoi related to the classical system to the quantummore » topos. By means of the geometric morphisms, we give Lawvere-Tierney topologies on the quantum topos (and their equivalent Grothendieck topologies on the context category). We show that, among them, there exists a canonical one which we call a quantization topology. We furthermore give an explicit expression of a sheafification functor associated with the quantization topology.« less

Towards topological quantum computer

NASA Astrophysics Data System (ADS)

Melnikov, D.; Mironov, A.; Mironov, S.; Morozov, A.; Morozov, An.

2018-01-01

Quantum R-matrices, the entangling deformations of non-entangling (classical) permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates) for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern-Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.

Distributed control topologies for deep space formation flying spacecraft

NASA Technical Reports Server (NTRS)

Hadaegh, F. Y.; Smith, R. S.

2002-01-01

A formation of satellites flying in deep space can be specified in terms of the relative satellite positions and absolute satellite orientations. The redundancy in the relative position specification generates a family of control topologies with equivalent stability and reference tracking performance, one of which can be implemented without requiring communication between the spacecraft. A relative position design formulation is inherently unobservable, and a methodology for circumventing this problem is presented. Additional redundancy in the control actuation space can be exploited for feed-forward control of the formation centroid's location in space, or for minimization of total fuel consumption.

Uncertainty relations and topological-band insulator transitions in 2D gapped Dirac materials

NASA Astrophysics Data System (ADS)

Romera, E.; Calixto, M.

2015-05-01

Uncertainty relations are studied for a characterization of topological-band insulator transitions in 2D gapped Dirac materials isostructural with graphene. We show that the relative or Kullback-Leibler entropy in position and momentum spaces, and the standard variance-based uncertainty relation give sharp signatures of topological phase transitions in these systems.

Integral transformation solution of free-space cylindrical vector beams and prediction of modified Bessel-Gaussian vector beams.

PubMed

Li, Chun-Fang

2007-12-15

A unified description of free-space cylindrical vector beams is presented that is an integral transformation solution to the vector Helmholtz equation and the transversality condition. In the paraxial condition, this solution not only includes the known J(1) Bessel-Gaussian vector beam and the axisymmetric Laguerre-Gaussian vector beam that were obtained by solving the paraxial wave equations but also predicts two kinds of vector beam, called a modified Bessel-Gaussian vector beam.

Promising Aedes aegypti repellent chemotypes identified through integrated QSAE, virtual screening, synthesis, and bioassay

USDA-ARS?s Scientific Manuscript database

Molecular field topology analysis, scaffold hopping, and molecular docking were used as complementary computational tools for the design of repellents for Aedes aegypti, the insect vector for yellow fever, West Nile fever, and dengue fever. A large number of analogues were evaluated by virtual scree...

Certain topological properties and duals of the domain of a triangle matrix in a sequence space

NASA Astrophysics Data System (ADS)

Altay, Bilâl; Basar, Feyzi

2007-12-01

The matrix domain of the particular limitation methods Cesàro, Riesz, difference, summation and Euler were studied by several authors. In the present paper, certain topological properties and [beta]- and [gamma]-duals of the domain of a triangle matrix in a sequence space have been examined as an application of the characterization of the related matrix classes.

Emergence, evolution, and control of multistability in a hybrid topological quantum/classical system.

PubMed

Wang, Guanglei; Xu, Hongya; Lai, Ying-Cheng

2018-03-01

We present a novel class of nonlinear dynamical systems-a hybrid of relativistic quantum and classical systems and demonstrate that multistability is ubiquitous. A representative setting is coupled systems of a topological insulator and an insulating ferromagnet, where the former possesses an insulating bulk with topologically protected, dissipationless, and conducting surface electronic states governed by the relativistic quantum Dirac Hamiltonian and the latter is described by the nonlinear classical evolution of its magnetization vector. The interactions between the two are essentially the spin transfer torque from the topological insulator to the ferromagnet and the local proximity induced exchange coupling in the opposite direction. The hybrid system exhibits a rich variety of nonlinear dynamical phenomena besides multistability such as bifurcations, chaos, and phase synchronization. The degree of multistability can be controlled by an external voltage. In the case of two coexisting states, the system is effectively binary, opening a door to exploitation for developing spintronic memory devices. Because of the dissipationless and spin-momentum locking nature of the surface currents of the topological insulator, little power is needed for generating a significant current, making the system appealing for potential applications in next generation of low power memory devices.

Emergence, evolution, and control of multistability in a hybrid topological quantum/classical system

NASA Astrophysics Data System (ADS)

Wang, Guanglei; Xu, Hongya; Lai, Ying-Cheng

2018-03-01

We present a novel class of nonlinear dynamical systems—a hybrid of relativistic quantum and classical systems and demonstrate that multistability is ubiquitous. A representative setting is coupled systems of a topological insulator and an insulating ferromagnet, where the former possesses an insulating bulk with topologically protected, dissipationless, and conducting surface electronic states governed by the relativistic quantum Dirac Hamiltonian and the latter is described by the nonlinear classical evolution of its magnetization vector. The interactions between the two are essentially the spin transfer torque from the topological insulator to the ferromagnet and the local proximity induced exchange coupling in the opposite direction. The hybrid system exhibits a rich variety of nonlinear dynamical phenomena besides multistability such as bifurcations, chaos, and phase synchronization. The degree of multistability can be controlled by an external voltage. In the case of two coexisting states, the system is effectively binary, opening a door to exploitation for developing spintronic memory devices. Because of the dissipationless and spin-momentum locking nature of the surface currents of the topological insulator, little power is needed for generating a significant current, making the system appealing for potential applications in next generation of low power memory devices.

Vector Data Model: A New Model of HDF-EOS to Support GIS Applications in EOS

NASA Astrophysics Data System (ADS)

Chi, E.; Edmonds, R d

2001-05-01

NASA's Earth Science Data Information System (ESDIS) project has an active program of research and development of systems for the storage and management of Earth science data for Earth Observation System (EOS) mission, a key program of NASA Earth Science Enterprise. EOS has adopted an extension of the Hierarchical Data Format (HDF) as the format of choice for standard product distribution. Three new EOS specific datatypes - point, swath and grid - have been defined within the HDF framework. The enhanced data format is named HDF-EOS. Geographic Information Systems (GIS) are used by Earth scientists in EOS data product generation, visualization, and analysis. There are two major data types in GIS applications, raster and vector. The current HDF-EOS handles only raster type in the swath data model. The vector data model is identified and developed as a new HDFEOS format to meet the requirements of scientists working with EOS data products in vector format. The vector model is designed using a topological data structure, which defines the spatial relationships among points, lines, and polygons. The three major topological concepts that the vector model adopts are: a) lines connect to each other at nodes (connectivity), b) lines that connect to surround an area define a polygon (area definition), and c) lines have direction and left and right sides (contiguity). The vector model is implemented in HDF by mapping the conceptual model to HDF internal data models and structures, viz. Vdata, Vgroup, and their associated attribute structures. The point, line, and polygon geometry and attribute data are stored in similar tables. Further, the vector model utilizes the structure and product metadata, which characterize the HDF-EOS. Both types of metadata are stored as attributes in HDF-EOS files, and are encoded in text format by using Object Description Language (ODL) and stored as global attributes in HDF-EOS files. EOS has developed a series of routines for storing, retrieving, and manipulating vector data in category of access, definition, basic I/O, inquiry, and subsetting. The routines are tested and form a package, HDF-EOS/Vector. The alpha version of HDFEOS/Vector has been distributed through the HDF-EOS project web site at http://hdfeos.gsfc.nasa.gov. We are also developing translators between HDF-EOS vector format and variety of GIS formats, such as Shapefile. The HDF-EOS vector model enables EOS scientists to deliver EOS data in a way ready for Earth scientists to analyze using GIS software, and also provides EOS project a mechanism to store GIS data product in meaningful vector format with significant economy in storage.

Electronic properties of novel topological quantum materials studied by angle-resolved photoemission spectroscopy (ARPES)

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

Wu, Yun

The discovery of quantum Hall e ect has motivated the use of topology instead of broken symmetry to classify the states of matter. Quantum spin Hall e ect has been proposed to have a separation of spin currents as an analogue of the charge currents separation in quantum Hall e ect, leading us to the era of topological insulators. Three-dimensional analogue of the Dirac state in graphene has brought us the three-dimensional Dirac states. Materials with three-dimensional Dirac states could potentially be the parent compounds for Weyl semimetals and topological insulators when time-reversal or space inversion symmetry is broken. Inmore » addition to the single Dirac point linking the two dispersion cones in the Dirac/Weyl semimetals, Dirac points can form a line in the momentum space, resulting in a topological node line semimetal. These fascinating novel topological quantum materials could provide us platforms for studying the relativistic physics in condensed matter systems and potentially lead to design of new electronic devices that run faster and consume less power than traditional, silicon based transistors. In this thesis, we present the electronic properties of novel topological quantum materials studied by angle-resolved photoemission spectroscopy (ARPES).« less

The topology of Double Field Theory

NASA Astrophysics Data System (ADS)

Hassler, Falk

2018-04-01

We describe the doubled space of Double Field Theory as a group manifold G with an arbitrary generalized metric. Local information from the latter is not relevant to our discussion and so G only captures the topology of the doubled space. Strong Constraint solutions are maximal isotropic submanifold M in G. We construct them and their Generalized Geometry in Double Field Theory on Group Manifolds. In general, G admits different physical subspace M which are Poisson-Lie T-dual to each other. By studying two examples, we reproduce the topology changes induced by T-duality with non-trivial H-flux which were discussed by Bouwknegt, Evslin and Mathai [1].

Topological Semimetals Studied by Ab Initio Calculations

NASA Astrophysics Data System (ADS)

Hirayama, Motoaki; Okugawa, Ryo; Murakami, Shuichi

2018-04-01

In topological semimetals such as Weyl, Dirac, and nodal-line semimetals, the band gap closes at points or along lines in k space which are not necessarily located at high-symmetry positions in the Brillouin zone. Therefore, it is not straightforward to find these topological semimetals by ab initio calculations because the band structure is usually calculated only along high-symmetry lines. In this paper, we review recent studies on topological semimetals by ab initio calculations. We explain theoretical frameworks which can be used for the search for topological semimetal materials, and some numerical methods used in the ab initio calculations.

Discrete Data Transfer Technique for Fluid-Structure Interaction

NASA Technical Reports Server (NTRS)

Samareh, Jamshid A.

2007-01-01

This paper presents a general three-dimensional algorithm for data transfer between dissimilar meshes. The algorithm is suitable for applications of fluid-structure interaction and other high-fidelity multidisciplinary analysis and optimization. Because the algorithm is independent of the mesh topology, we can treat structured and unstructured meshes in the same manner. The algorithm is fast and accurate for transfer of scalar or vector fields between dissimilar surface meshes. The algorithm is also applicable for the integration of a scalar field (e.g., coefficients of pressure) on one mesh and injection of the resulting vectors (e.g., force vectors) onto another mesh. The author has implemented the algorithm in a C++ computer code. This paper contains a complete formulation of the algorithm with a few selected results.

Novel scanning procedure enabling the vectorization of entire rhizotron-grown root systems

PubMed Central

2013-01-01

This paper presents an original spit-and-combine imaging procedure that enables the complete vectorization of complex root systems grown in rhizotrons. The general principle of the method is to (1) separate the root system into a small number of large pieces to reduce root overlap, (2) scan these pieces one by one, (3) analyze separate images with a root tracing software and (4) combine all tracings into a single vectorized root system. This method generates a rich dataset containing morphological, topological and geometrical information of entire root systems grown in rhizotrons. The utility of the method is illustrated with a detailed architectural analysis of a 20-day old maize root system, coupled with a spatial analysis of water uptake patterns. PMID:23286457

Novel scanning procedure enabling the vectorization of entire rhizotron-grown root systems.

PubMed

Lobet, Guillaume; Draye, Xavier

2013-01-04

: This paper presents an original spit-and-combine imaging procedure that enables the complete vectorization of complex root systems grown in rhizotrons. The general principle of the method is to (1) separate the root system into a small number of large pieces to reduce root overlap, (2) scan these pieces one by one, (3) analyze separate images with a root tracing software and (4) combine all tracings into a single vectorized root system. This method generates a rich dataset containing morphological, topological and geometrical information of entire root systems grown in rhizotrons. The utility of the method is illustrated with a detailed architectural analysis of a 20-day old maize root system, coupled with a spatial analysis of water uptake patterns.

Unconventional Topological Phase Transition in Two-Dimensional Systems with Space-Time Inversion Symmetry

NASA Astrophysics Data System (ADS)

Ahn, Junyeong; Yang, Bohm-Jung

2017-04-01

We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and twofold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems, where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional twofold rotation symmetry is mediated by an emergent stable 2D Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry, the combination of time-reversal and twofold rotation symmetries, which guarantees the quantization of the Berry phase around a 2D Weyl point even in the presence of strong spin-orbit coupling. Pair creation and pair annihilation of Weyl points accompanying partner exchange between different pairs induces a jump of a 2D Z2 topological invariant leading to a topological phase transition. According to our theory, the topological phase transition in HgTe /CdTe quantum well structure is mediated by a stable 2D Weyl semimetal phase because the quantum well, lacking inversion symmetry intrinsically, has twofold rotation about the growth direction. Namely, the HgTe /CdTe quantum well can show 2D Weyl semimetallic behavior within a small but finite interval in the thickness of HgTe layers between a normal insulator and a quantum spin Hall insulator. We also propose that few-layer black phosphorus under perpendicular electric field is another candidate system to observe the unconventional topological phase transition mechanism accompanied by the emerging 2D Weyl semimetal phase protected by space-time inversion symmetry.

Concept Model on Topological Learning

NASA Astrophysics Data System (ADS)

Ae, Tadashi; Kioi, Kazumasa

2010-11-01

We discuss a new model for concept based on topological learning, where the learning process on the neural network is represented by mathematical topology. The topological learning of neural networks is summarized by a quotient of input space and the hierarchical step induces a tree where each node corresponds to a quotient. In general, the concept acquisition is a difficult problem, but the emotion for a subject is represented by providing the questions to a person. Therefore, a kind of concept is captured by such data and the answer sheet can be mapped into a topology consisting of trees. In this paper, we will discuss a way of mapping the emotional concept to a topological learning model.

Robust superconductivity with nodes in the superconducting topological insulator CuxBi2Se3 : Zeeman orbital field and nonmagnetic impurities

NASA Astrophysics Data System (ADS)

Nagai, Yuki

2015-02-01

We study the robustness against nonmagnetic impurities in the topological superconductor with point nodes, focusing on an effective model of CuxBi2Se3 . We find that the topological superconductivity with point nodes is not fragile against nonmagnetic impurities, although the superconductivity with nodes in past studies is usually fragile. Exchanging the role of spin with the one of orbital, and vice versa, we find that in the "dual" space the topological superconductor with point nodes is regarded as the intraorbital spin-singlet s -wave one. From the viewpoint of the dual space, we deduce that the point-node state is not fragile against nonmagnetic impurity, when the orbital imbalance in the normal states is small. Since the spin imbalance is induced by the Zeeman magnetic field, we shall name this key quantity for the impurity effects the Zeeman "orbital" field. The numerical calculations support that the deduction is correct. If the Zeeman orbital field is small, the topological superconductivity is not fragile in dirty materials, even with nodes. Thus, the topological superconductors cannot be simply regarded as one of the conventional unconventional superconductors.

Two Topologically Distinct Dirac-Line Semimetal Phases and Topological Phase Transitions in Rhombohedrally Stacked Honeycomb Lattices

NASA Astrophysics Data System (ADS)

Hyart, T.; Ojajärvi, R.; Heikkilä, T. T.

2018-04-01

Three-dimensional topological semimetals can support band crossings along one-dimensional curves in the momentum space (nodal lines or Dirac lines) protected by structural symmetries and topology. We consider rhombohedrally (ABC) stacked honeycomb lattices supporting Dirac lines protected by time-reversal, inversion and spin rotation symmetries. For typical band structure parameters there exists a pair of nodal lines in the momentum space extending through the whole Brillouin zone in the stacking direction. We show that these Dirac lines are topologically distinct from the usual Dirac lines which form closed loops inside the Brillouin zone. In particular, an energy gap can be opened only by first merging the Dirac lines going through the Brillouin zone in a pairwise manner so that they turn into closed loops inside the Brillouin zone, and then by shrinking these loops into points. We show that this kind of topological phase transition can occur in rhombohedrally stacked honeycomb lattices by tuning the ratio of the tunneling amplitudes in the directions perpendicular and parallel to the layers. We also discuss the properties of the surface states in the different phases of the model.

Topological Phenotypes Constitute a New Dimension in the Phenotypic Space of Leaf Venation Networks

PubMed Central

Ronellenfitsch, Henrik; Lasser, Jana; Daly, Douglas C.; Katifori, Eleni

2015-01-01

The leaves of angiosperms contain highly complex venation networks consisting of recursively nested, hierarchically organized loops. We describe a new phenotypic trait of reticulate vascular networks based on the topology of the nested loops. This phenotypic trait encodes information orthogonal to widely used geometric phenotypic traits, and thus constitutes a new dimension in the leaf venation phenotypic space. We apply our metric to a database of 186 leaves and leaflets representing 137 species, predominantly from the Burseraceae family, revealing diverse topological network traits even within this single family. We show that topological information significantly improves identification of leaves from fragments by calculating a “leaf venation fingerprint” from topology and geometry. Further, we present a phenomenological model suggesting that the topological traits can be explained by noise effects unique to specimen during development of each leaf which leave their imprint on the final network. This work opens the path to new quantitative identification techniques for leaves which go beyond simple geometric traits such as vein density and is directly applicable to other planar or sub-planar networks such as blood vessels in the brain. PMID:26700471

The Knaster-Kuratowski-Mazurkiewicz theorem and abstract convexities

NASA Astrophysics Data System (ADS)

Cain, George L., Jr.; González, Luis

2008-02-01

The Knaster-Kuratowski-Mazurkiewicz covering theorem (KKM), is the basic ingredient in the proofs of many so-called "intersection" theorems and related fixed point theorems (including the famous Brouwer fixed point theorem). The KKM theorem was extended from Rn to Hausdorff linear spaces by Ky Fan. There has subsequently been a plethora of attempts at extending the KKM type results to arbitrary topological spaces. Virtually all these involve the introduction of some sort of abstract convexity structure for a topological space, among others we could mention H-spaces and G-spaces. We have introduced a new abstract convexity structure that generalizes the concept of a metric space with a convex structure, introduced by E. Michael in [E. Michael, Convex structures and continuous selections, Canad. J. MathE 11 (1959) 556-575] and called a topological space endowed with this structure an M-space. In an article by Shie Park and Hoonjoo Kim [S. Park, H. Kim, Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl. 197 (1996) 173-187], the concepts of G-spaces and metric spaces with Michael's convex structure, were mentioned together but no kind of relationship was shown. In this article, we prove that G-spaces and M-spaces are close related. We also introduce here the concept of an L-space, which is inspired in the MC-spaces of J.V. Llinares [J.V. Llinares, Unified treatment of the problem of existence of maximal elements in binary relations: A characterization, J. Math. Econom. 29 (1998) 285-302], and establish relationships between the convexities of these spaces with the spaces previously mentioned.

Reversible Vector Ratchet Effect in Skyrmion Systems

NASA Astrophysics Data System (ADS)

Ma, Xiaoyu; Reichhardt, Charles; Reichhardt, Cynthia

Magnetic skyrmions are topological non-trivial spin textures found in several magnetic materials. Since their motion can be controlled using ultralow current densities, skyrmions are appealing for potential applications in spintronics as information carriers and processing devices. In this work, we studied the collective transport properties of driven skyrmions based on a particle-like model with molecular dynamics (MD) simulation. Our results show that ac driven skyrmions interacting with an asymmetric substrate provide a realization of a new class of ratchet system, which we call a vector ratchet, that arises due to the effect of the Magnus term on the skyrmion dynamics. In a vector ratchet, the dc motion induced by the ac drive can be described as a vector that can be rotated up to 360 degrees relative to the substrate asymmetry direction. This could represent a new method for controlling skyrmion motion for spintronic applications.

Semi-automatic feedback using concurrence between mixture vectors for general databases

NASA Astrophysics Data System (ADS)

Larabi, Mohamed-Chaker; Richard, Noel; Colot, Olivier; Fernandez-Maloigne, Christine

2001-12-01

This paper describes how a query system can exploit the basic knowledge by employing semi-automatic relevance feedback to refine queries and runtimes. For general databases, it is often useless to call complex attributes, because we have not sufficient information about images in the database. Moreover, these images can be topologically very different from one to each other and an attribute that is powerful for a database category may be very powerless for the other categories. The idea is to use very simple features, such as color histogram, correlograms, Color Coherence Vectors (CCV), to fill out the signature vector. Then, a number of mixture vectors is prepared depending on the number of very distinctive categories in the database. Knowing that a mixture vector is a vector containing the weight of each attribute that will be used to compute a similarity distance. We post a query in the database using successively all the mixture vectors defined previously. We retain then the N first images for each vector in order to make a mapping using the following information: Is image I present in several mixture vectors results? What is its rank in the results? These informations allow us to switch the system on an unsupervised relevance feedback or user's feedback (supervised feedback).

The geometric nature of weights in real complex networks

NASA Astrophysics Data System (ADS)

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

2017-01-01

The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of their complex topologies, this hypothesis yields the recipe for sustainable Internet's routing protocols, sheds light on the hierarchical organization of biochemical pathways in cells, and allows for a rich characterization of the evolution of international trade. Here we present empirical evidence that this geometric interpretation also applies to the weighted organization of real complex networks. We introduce a very general and versatile model and use it to quantify the level of coupling between their topology, their weights and an underlying metric space. Our model accurately reproduces both their topology and their weights, and our results suggest that the formation of connections and the assignment of their magnitude are ruled by different processes.

The Topological Field Theory of Data: a program towards a novel strategy for data mining through data language

NASA Astrophysics Data System (ADS)

Rasetti, M.; Merelli, E.

2015-07-01

This paper aims to challenge the current thinking in IT for the 'Big Data' question, proposing - almost verbatim, with no formulas - a program aiming to construct an innovative methodology to perform data analytics in a way that returns an automaton as a recognizer of the data language: a Field Theory of Data. We suggest to build, directly out of probing data space, a theoretical framework enabling us to extract the manifold hidden relations (patterns) that exist among data, as correlations depending on the semantics generated by the mining context. The program, that is grounded in the recent innovative ways of integrating data into a topological setting, proposes the realization of a Topological Field Theory of Data, transferring and generalizing to the space of data notions inspired by physical (topological) field theories and harnesses the theory of formal languages to define the potential semantics necessary to understand the emerging patterns.

Topology of three-dimensional separated flows

NASA Technical Reports Server (NTRS)

Tobak, M.; Peake, D. J.

1981-01-01

Based on the hypothesis that patterns of skin-friction lines and external streamlines reflect the properties of continuous vector fields, topology rules define a small number of singular points (nodes, saddle points, and foci) that characterize the patterns on the surface and on particular projections of the flow (e.g., the crossflow plane). The restricted number of singular points and the rules that they obey are considered as an organizing principle whose finite number of elements can be combined in various ways to connect together the properties common to all steady three dimensional viscous flows. Introduction of a distinction between local and global properties of the flow resolves an ambiguity in the proper definition of a three dimensional separated flow. Adoption of the notions of topological structure, structural stability, and bifurcation provides a framework to describe how three dimensional separated flows originate and succeed each other as the relevant parameters of the problem are varied.

Analysis of recurrent patterns in toroidal magnetic fields.

PubMed

Sanderson, Allen R; Chen, Guoning; Tricoche, Xavier; Pugmire, David; Kruger, Scott; Breslau, Joshua

2010-01-01

In the development of magnetic confinement fusion which will potentially be a future source for low cost power, physicists must be able to analyze the magnetic field that confines the burning plasma. While the magnetic field can be described as a vector field, traditional techniques for analyzing the field's topology cannot be used because of its Hamiltonian nature. In this paper we describe a technique developed as a collaboration between physicists and computer scientists that determines the topology of a toroidal magnetic field using fieldlines with near minimal lengths. More specifically, we analyze the Poincaré map of the sampled fieldlines in a Poincaré section including identifying critical points and other topological features of interest to physicists. The technique has been deployed into an interactive parallel visualization tool which physicists are using to gain new insight into simulations of magnetically confined burning plasmas.

Algebraic Structure of tt * Equations for Calabi-Yau Sigma Models

NASA Astrophysics Data System (ADS)

Alim, Murad

2017-08-01

The tt * equations define a flat connection on the moduli spaces of {2d, \\mathcal{N}=2} quantum field theories. For conformal theories with c = 3 d, which can be realized as nonlinear sigma models into Calabi-Yau d-folds, this flat connection is equivalent to special geometry for threefolds and to its analogs in other dimensions. We show that the non-holomorphic content of the tt * equations, restricted to the conformal directions, in the cases d = 1, 2, 3 is captured in terms of finitely many generators of special functions, which close under derivatives. The generators are understood as coordinates on a larger moduli space. This space parameterizes a freedom in choosing representatives of the chiral ring while preserving a constant topological metric. Geometrically, the freedom corresponds to a choice of forms on the target space respecting the Hodge filtration and having a constant pairing. Linear combinations of vector fields on that space are identified with the generators of a Lie algebra. This Lie algebra replaces the non-holomorphic derivatives of tt * and provides these with a finer and algebraic meaning. For sigma models into lattice polarized K3 manifolds, the differential ring of special functions on the moduli space is constructed, extending known structures for d = 1 and 3. The generators of the differential rings of special functions are given by quasi-modular forms for d = 1 and their generalizations in d = 2, 3. Some explicit examples are worked out including the case of the mirror of the quartic in {\\mathbbm{P}^3}, where due to further algebraic constraints, the differential ring coincides with quasi modular forms.

Stealthy false data injection attacks using matrix recovery and independent component analysis in smart grid

NASA Astrophysics Data System (ADS)

JiWei, Tian; BuHong, Wang; FuTe, Shang; Shuaiqi, Liu

2017-05-01

Exact state estimation is vital important to maintain common operations of smart grids. Existing researches demonstrate that state estimation output could be compromised by malicious attacks. However, to construct the attack vectors, a usual presumption in most works is that the attacker has perfect information regarding the topology and so on even such information is difficult to acquire in practice. Recent research shows that Independent Component Analysis (ICA) can be used for inferring topology information which can be used to originate undetectable attacks and even to alter the price of electricity for the profits of attackers. However, we found that the above ICA-based blind attack tactics is merely feasible in the environment with Gaussian noises. If there are outliers (device malfunction and communication errors), the Bad Data Detector will easily detect the attack. Hence, we propose a robust ICA based blind attack strategy that one can use matrix recovery to circumvent the outlier problem and construct stealthy attack vectors. The proposed attack strategies are tested with IEEE representative 14-bus system. Simulations verify the feasibility of the proposed method.

Vectorial structures of linear-polarized Butterfly-Gauss vortex beams in the far zone

NASA Astrophysics Data System (ADS)

Cheng, Ke; Zhou, Yan; Lu, Gang; Yao, Na; Zhong, Xianqiong

2018-05-01

By introducing the Butterfly catastrophe to optics, the far-zone vectorial structures of Butterfly-Gauss beam with vortex and non-vortex are studied using the angular spectrum representation and stationary phase method. The influence of topological charge, linear-polarized angle, off-axis distance and scaling length on the far-zone vectorial structures, especially in the Poynting vector and angular momentum density of the corresponding beam is emphasized. The results show that the embedded optical vortex at source plane lead to special dark zones in the far zone, where the number of dark zone equals the absolute value of topological charge of optical vortex. Furthermore, the symmetry and direction of the special dark zones can be controlled by off-axis distance and scaling length, respectively. The linear-polarized angle adjusts only the Poynting vectors of TE and TM terms, but it does not affect those of whole beam. Finally, the vectorial expressions also indicate that the total angular momentum density is certainly zero owing to the far-zone stable structures rather than rotation behaviors.

Spin Josephson effect in topological superconductor-ferromagnet junction

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

Ren, C. D.; Wang, J., E-mail: jwang@seu.edu.cn

2014-03-21

The composite topological superconductor (TS), made of one-dimensional spin-orbit coupled nanowire with proximity-induced s-wave superconductivity, is not a pure p-wave superconductor but still has a suppressed s-wave pairing. We propose to probe the spin texture of the p-wave pairing in this composite TS by examining possible spin supercurrents in an unbiased TS/ferromagnet junction. It is found that both the exchange-coupling induced and spin-flip reflection induced spin currents exist in the setup and survive even in the topological phase. We showed that besides the nontrivial p-wave pairing state accounting for Majorana Fermions, there shall be a trivial p-wave pairing state thatmore » contributes to spin supercurrent. The trivial p-wave pairing state is diagnosed from the mixing effect between the suppressed s-wave pairing and the topologically nontrivial p-wave pairing. The d vector of the TS is proved not to be rigorously perpendicular to the spin projection of p-wave pairings. Our findings are also confirmed by the Kitaev's p-wave model with a nonzero s-wave pairing.« less

Properties of field functionals and characterization of local functionals

NASA Astrophysics Data System (ADS)

Brouder, Christian; Dang, Nguyen Viet; Laurent-Gengoux, Camille; Rejzner, Kasia

2018-02-01

Functionals (i.e., functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the proper space of test functions (smooth functions) and of the relevant concept of differential (Bastiani differential) are discussed. The relation between the multiple derivatives of a functional and the corresponding distributions is described in detail. It is proved that, in a neighborhood of every test function, the support of a smooth functional is uniformly compactly supported and the order of the corresponding distribution is uniformly bounded. Relying on a recent work by Dabrowski, several spaces of functionals are furnished with a complete and nuclear topology. In view of physical applications, it is shown that most formal manipulations can be given a rigorous meaning. A new concept of local functionals is proposed and two characterizations of them are given: the first one uses the additivity (or Hammerstein) property, the second one is a variant of Peetre's theorem. Finally, the first step of a cohomological approach to quantum field theory is carried out by proving a global Poincaré lemma and defining multi-vector fields and graded functionals within our framework.

Raster profile development for the spatial data transfer standard

USGS Publications Warehouse

Szemraj, John A.

1993-01-01

The Spatial Data Transfer Standard (SDTS), recently approved as Federal Information Processing Standard (FIPS) Publication 173, is designed to transfer various types of spatial data. Implementing all of the standard's options at one time is impractical. Profiles, or limited subsets of the SDTS, are the mechanisms by which the standards will be implemented. The development of a raster profile is being coordinated by the U.S. Geological Survey's (USGS) SDTS Task Force. This raster profile is intended to accommodate digital georeferenced image data and regularly spaces, georeferenced gridded data. The USGS's digital elevation models (DEMs) and digital orthophoto quadrangles (DOQs), National Oceanic and Atmospheric Administration's (NOAA) advanced very huh resolution radiometer (AVHRR) and Landsat data, and National Aeronautics and Space Administration's (NASA) Earth observing system (EOS) data are among the candidate data sets for this profile. Other raster profiles, designed to support nongeoreferenced and other types of "raw" sensor data will be consider in the future. As with the Topological Vector Profile (TVP) for the SDTS, development of the raster profile includes designing a prototype profile, testing the prototype profile using sample data sets, and finally, requesting and receiving FIPS approval.

Stability and chaos in Kustaanheimo-Stiefel space induced by the Hopf fibration

NASA Astrophysics Data System (ADS)

Roa, Javier; Urrutxua, Hodei; Peláez, Jesús

2016-07-01

The need for the extra dimension in Kustaanheimo-Stiefel (KS) regularization is explained by the topology of the Hopf fibration, which defines the geometry and structure of KS space. A trajectory in Cartesian space is represented by a four-dimensional manifold called the fundamental manifold. Based on geometric and topological aspects classical concepts of stability are translated to KS language. The separation between manifolds of solutions generalizes the concept of Lyapunov stability. The dimension-raising nature of the fibration transforms fixed points, limit cycles, attractive sets, and Poincaré sections to higher dimensional subspaces. From these concepts chaotic systems are studied. In strongly perturbed problems, the numerical error can break the topological structure of KS space: points in a fibre are no longer transformed to the same point in Cartesian space. An observer in three dimensions will see orbits departing from the same initial conditions but diverging in time. This apparent randomness of the integration can only be understood in four dimensions. The concept of topological stability results in a simple method for estimating the time-scale in which numerical simulations can be trusted. Ideally, all trajectories departing from the same fibre should be KS transformed to a unique trajectory in three-dimensional space, because the fundamental manifold that they constitute is unique. By monitoring how trajectories departing from one fibre separate from the fundamental manifold a critical time, equivalent to the Lyapunov time, is estimated. These concepts are tested on N-body examples: the Pythagorean problem, and an example of field stars interacting with a binary.

Spaces of ideal convergent sequences.

PubMed

Mursaleen, M; Sharma, Sunil K

2014-01-01

In the present paper, we introduce some sequence spaces using ideal convergence and Musielak-Orlicz function ℳ = (M(k)). We also examine some topological properties of the resulting sequence spaces.

Neural Representation of Spatial Topology in the Rodent Hippocampus

PubMed Central

Chen, Zhe; Gomperts, Stephen N.; Yamamoto, Jun; Wilson, Matthew A.

2014-01-01

Pyramidal cells in the rodent hippocampus often exhibit clear spatial tuning in navigation. Although it has been long suggested that pyramidal cell activity may underlie a topological code rather than a topographic code, it remains unclear whether an abstract spatial topology can be encoded in the ensemble spiking activity of hippocampal place cells. Using a statistical approach developed previously, we investigate this question and related issues in greater details. We recorded ensembles of hippocampal neurons as rodents freely foraged in one and two-dimensional spatial environments, and we used a “decode-to-uncover” strategy to examine the temporally structured patterns embedded in the ensemble spiking activity in the absence of observed spatial correlates during periods of rodent navigation or awake immobility. Specifically, the spatial environment was represented by a finite discrete state space. Trajectories across spatial locations (“states”) were associated with consistent hippocampal ensemble spiking patterns, which were characterized by a state transition matrix. From this state transition matrix, we inferred a topology graph that defined the connectivity in the state space. In both one and two-dimensional environments, the extracted behavior patterns from the rodent hippocampal population codes were compared against randomly shuffled spike data. In contrast to a topographic code, our results support the efficiency of topological coding in the presence of sparse sample size and fuzzy space mapping. This computational approach allows us to quantify the variability of ensemble spiking activity, to examine hippocampal population codes during off-line states, and to quantify the topological complexity of the environment. PMID:24102128

Propagation of optical vortices with fractional topological charge in free space

NASA Astrophysics Data System (ADS)

Ali, Tamelia; Kreminska, Liubov; Golovin, Andrii B.; Crouse, David T.

2014-10-01

The behavior of the optical vortices with fractional topological charges in the far-field is assessed through numerical modeling and confirmed by experimental results. The generation of fractional topological charge variations of the phase within a Gaussian beam was achieved by using a liquid crystal spatial light modulator (LCoS SLM). It is shown that a laser beam carrying an optical vortex with a fractional topological charge evolves into a beam with a topological charge of integer value, specifically an integer value closer to the fractional number in the far field. A potential application of this work is for data transmission within optical telecommunication systems.

Homogeneous anisotropic solutions of topologically massive gravity with a cosmological constant and their homogeneous deformations

NASA Astrophysics Data System (ADS)

Moutsopoulos, George

2013-06-01

We solve the equations of topologically massive gravity (TMG) with a potentially non-vanishing cosmological constant for homogeneous metrics without isotropy. We only reproduce known solutions. We also discuss their homogeneous deformations, possibly with isotropy. We show that de Sitter space and hyperbolic space cannot be infinitesimally homogeneously deformed in TMG. We clarify some of their Segre-Petrov types and discuss the warped de Sitter spacetime.

Highly designable phenotypes and mutational buffers emerge from a systematic mapping between network topology and dynamic output.

PubMed

Nochomovitz, Yigal D; Li, Hao

2006-03-14

Deciphering the design principles for regulatory networks is fundamental to an understanding of biological systems. We have explored the mapping from the space of network topologies to the space of dynamical phenotypes for small networks. Using exhaustive enumeration of a simple model of three- and four-node networks, we demonstrate that certain dynamical phenotypes can be generated by an atypically broad spectrum of network topologies. Such dynamical outputs are highly designable, much like certain protein structures can be designed by an unusually broad spectrum of sequences. The network topologies that encode a highly designable dynamical phenotype possess two classes of connections: a fully conserved core of dedicated connections that encodes the stable dynamical phenotype and a partially conserved set of variable connections that controls the transient dynamical flow. By comparing the topologies and dynamics of the three- and four-node network ensembles, we observe a large number of instances of the phenomenon of "mutational buffering," whereby addition of a fourth node suppresses phenotypic variation amongst a set of three-node networks.

Persistent homology and non-Gaussianity

NASA Astrophysics Data System (ADS)

Cole, Alex; Shiu, Gary

2018-03-01

In this paper, we introduce the topological persistence diagram as a statistic for Cosmic Microwave Background (CMB) temperature anisotropy maps. A central concept in 'Topological Data Analysis' (TDA), the idea of persistence is to represent a data set by a family of topological spaces. One then examines how long topological features 'persist' as the family of spaces is traversed. We compute persistence diagrams for simulated CMB temperature anisotropy maps featuring various levels of primordial non-Gaussianity of local type. Postponing the analysis of observational effects, we show that persistence diagrams are more sensitive to local non-Gaussianity than previous topological statistics including the genus and Betti number curves, and can constrain Δ fNLloc= 35.8 at the 68% confidence level on the simulation set, compared to Δ fNLloc= 60.6 for the Betti number curves. Given the resolution of our simulations, we expect applying persistence diagrams to observational data will give constraints competitive with those of the Minkowski Functionals. This is the first in a series of papers where we plan to apply TDA to different shapes of non-Gaussianity in the CMB and Large Scale Structure.

Harmonic field in knotted space

NASA Astrophysics Data System (ADS)

Duan, Xiuqing; Yao, Zhenwei

2018-04-01

Knotted fields enrich a variety of physical phenomena, ranging from fluid flows, electromagnetic fields, to textures of ordered media. Maxwell's electrostatic equations, whose vacuum solution is mathematically known as a harmonic field, provide an ideal setting to explore the role of domain topology in determining physical fields in confined space. In this work, we show the uniqueness of a harmonic field in knotted tubes, and reduce the construction of a harmonic field to a Neumann boundary value problem. By analyzing the harmonic field in typical knotted tubes, we identify the torsion driven transition from bipolar to vortex patterns. We also analogously extend our discussion to the organization of liquid crystal textures in knotted tubes. These results further our understanding about the general role of topology in shaping a physical field in confined space, and may find applications in the control of physical fields by manipulation of surface topology.

The Vector Space as a Unifying Concept in School Mathematics.

ERIC Educational Resources Information Center

Riggle, Timothy Andrew

The purpose of this study was to show how the concept of vector space can serve as a unifying thread for mathematics programs--elementary school to pre-calculus college level mathematics. Indicated are a number of opportunities to demonstrate how emphasis upon the vector space structure can enhance the organization of the mathematics curriculum.…

Robust manipulation of light using topologically protected plasmonic modes.

PubMed

Liu, Chenxu; Gurudev Dutt, M V; Pekker, David

2018-02-05

We propose using a topological plasmonic crystal structure composed of an array of nearly parallel nanowires with unequal spacing for manipulating light. In the paraxial approximation, the Helmholtz equation that describes the propagation of light along the nanowires maps onto the Schrödinger equation of the Su-Schrieffer-Heeger (SSH) model. Using a full three-dimensional finite difference time domain solution of the Maxwell equations, we verify the existence of topological defect modes, with sub-wavelength localization, bound to domain walls of the plasmonic crystal. We show that by manipulating domain walls we can construct spatial mode filters that couple bulk modes to topological defect modes, and topological beam-splitters that couple two topological defect modes. Finally, we show that the structures are tolerant to fabrication errors with an inverse length-scale smaller than the topological band gap.

Topological Electride Y2C.

PubMed

Huang, Huaqing; Jin, Kyung-Hwan; Zhang, Shunhong; Liu, Feng

2018-03-14

Two-dimensional (2D) electrides are layered ionic crystals in which anionic electrons are confined in the interlayer space. Here, we report a discovery of nontrivial [Formula: see text] topology in the electronic structures of 2D electride Y 2 C. Based on first-principles calculations, we found a topological [Formula: see text] invariant of (1; 111) for the bulk band and topologically protected surface states in the surfaces of Y 2 C, signifying its nontrivial electronic topology. We suggest a spin-resolved angle-resolved photoemission spectroscopy (ARPES) measurement to detect the unique helical spin texture of the spin-polarized topological surface state, which will provide characteristic evidence for the nontrivial electronic topology of Y 2 C. Furthermore, the coexistence of 2D surface electride states and topological surface state enables us to explain the outstanding discrepancy between the recent ARPES experiments and theoretical calculations. Our findings establish a preliminary link between the electride in chemistry and the band topology in condensed-matter physics, which are expected to inspire further interdisciplinary research between these fields.

Orientational Order on Surfaces: The Coupling of Topology, Geometry, and Dynamics

NASA Astrophysics Data System (ADS)

Nestler, M.; Nitschke, I.; Praetorius, S.; Voigt, A.

2018-02-01

We consider the numerical investigation of surface bound orientational order using unit tangential vector fields by means of a gradient flow equation of a weak surface Frank-Oseen energy. The energy is composed of intrinsic and extrinsic contributions, as well as a penalization term to enforce the unity of the vector field. Four different numerical discretizations, namely a discrete exterior calculus approach, a method based on vector spherical harmonics, a surface finite element method, and an approach utilizing an implicit surface description, the diffuse interface method, are described and compared with each other for surfaces with Euler characteristic 2. We demonstrate the influence of geometric properties on realizations of the Poincaré-Hopf theorem and show examples where the energy is decreased by introducing additional orientational defects.

Rhotrix Vector Spaces

ERIC Educational Resources Information Center

Aminu, Abdulhadi

2010-01-01

By rhotrix we understand an object that lies in some way between (n x n)-dimensional matrices and (2n - 1) x (2n - 1)-dimensional matrices. Representation of vectors in rhotrices is different from the representation of vectors in matrices. A number of vector spaces in matrices and their properties are known. On the other hand, little seems to be…

Majorana quasiparticles in semiconducting carbon nanotubes

NASA Astrophysics Data System (ADS)

Marganska, Magdalena; Milz, Lars; Izumida, Wataru; Strunk, Christoph; Grifoni, Milena

2018-02-01

Engineering effective p -wave superconductors hosting Majorana quasiparticles (MQPs) is nowadays of particular interest, also in view of the possible utilization of MQPs in fault-tolerant topological quantum computation. In quasi-one-dimensional systems, the parameter space for topological superconductivity is significantly reduced by the coupling between transverse modes. Together with the requirement of achieving the topological phase under experimentally feasible conditions, this strongly restricts in practice the choice of systems which can host MQPs. Here, we demonstrate that semiconducting carbon nanotubes (CNTs) in proximity with ultrathin s -wave superconductors, e.g., exfoliated NbSe2, satisfy these needs. By precise numerical tight-binding calculations in the real space, we show the emergence of localized zero-energy states at the CNT ends above a critical value of the applied magnetic field, of which we show the spatial evolution. Knowing the microscopic wave functions, we unequivocally demonstrate the Majorana nature of the localized states. An effective four-band model in the k -space, with parameters determined from the numerical spectrum, is used to calculate the topological phase diagram and its phase boundaries in analytic form. Finally, the impact of symmetry breaking contributions, like disorder and an axial component of the magnetic field, is investigated.

Electric field driven evolution of topological domain structure in hexagonal manganites

NASA Astrophysics Data System (ADS)

Yang, K. L.; Zhang, Y.; Zheng, S. H.; Lin, L.; Yan, Z. B.; Liu, J.-M.; Cheong, S.-W.

2017-10-01

Controlling and manipulating the topological state represents an important topic in condensed matters for both fundamental researches and applications. In this work, we focus on the evolution of a real-space topological domain structure in hexagonal manganites driven by electric field, using the analytical and numerical calculations based on the Ginzburg-Landau theory. It is revealed that the electric field drives a transition of the topological domain structure from the type-I pattern to the type-II one. In particular, it is identified that a high electric field can enforce the two antiphase-plus-ferroelectric (AP +FE ) domain walls with Δ Φ =π /3 to approach each other and to merge into one domain wall with Δ Φ = 2 π /3 eventually if the electric field is sufficiently high, where Δ Φ is the difference in the trimerization phase between two neighboring domains. Our simulations also reveal that the vortex cores of the topological structure can be disabled at a sufficiently high critical electric field by suppressing the structural trimerization therein, beyond which the vortex core region is replaced by a single ferroelectric domain without structural trimerization (Q = 0 ). Our results provide a stimulating reference for understanding the manipulation of real-space topological domain structure in hexagonal manganites.

Membrane Topology Mapping of the Na+-Pumping NADH: Quinone Oxidoreductase from Vibrio cholerae by PhoA- Green Fluorescent Protein Fusion Analysis▿

PubMed Central

Duffy, Ellen B.; Barquera, Blanca

2006-01-01

The membrane topologies of the six subunits of Na+-translocating NADH:quinone oxidoreductase (Na+-NQR) from Vibrio cholerae were determined by a combination of topology prediction algorithms and the construction of C-terminal fusions. Fusion expression vectors contained either bacterial alkaline phosphatase (phoA) or green fluorescent protein (gfp) genes as reporters of periplasmic and cytoplasmic localization, respectively. A majority of the topology prediction algorithms did not predict any transmembrane helices for NqrA. A lack of PhoA activity when fused to the C terminus of NqrA and the observed fluorescence of the green fluorescent protein C-terminal fusion confirm that this subunit is localized to the cytoplasmic side of the membrane. Analysis of four PhoA fusions for NqrB indicates that this subunit has nine transmembrane helices and that residue T236, the binding site for flavin mononucleotide (FMN), resides in the cytoplasm. Three fusions confirm that the topology of NqrC consists of two transmembrane helices with the FMN binding site at residue T225 on the cytoplasmic side. Fusion analysis of NqrD and NqrE showed almost mirror image topologies, each consisting of six transmembrane helices; the results for NqrD and NqrE are consistent with the topologies of Escherichia coli homologs YdgQ and YdgL, respectively. The NADH, flavin adenine dinucleotide, and Fe-S center binding sites of NqrF were localized to the cytoplasm. The determination of the topologies of the subunits of Na+-NQR provides valuable insights into the location of cofactors and identifies targets for mutagenesis to characterize this enzyme in more detail. The finding that all the redox cofactors are localized to the cytoplasmic side of the membrane is discussed. PMID:17041063

Synthetic space with arbitrary dimensions in a few rings undergoing dynamic modulation

NASA Astrophysics Data System (ADS)

Yuan, Luqi; Xiao, Meng; Lin, Qian; Fan, Shanhui

2018-03-01

We show that a single ring resonator undergoing dynamic modulation can be used to create a synthetic space with an arbitrary dimension. In such a system, the phases of the modulation can be used to create a photonic gauge potential in high dimensions. As an illustration of the implication of this concept, we show that the Haldane model, which exhibits nontrivial topology in two dimensions, can be implemented in the synthetic space using three rings. Our results point to a route toward exploring higher-dimensional topological physics in low-dimensional physical structures. The dynamics of photons in such synthetic spaces also provides a mechanism to control the spectrum of light.

Thyra Abstract Interface Package

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

Bartlett, Roscoe A.

2005-09-01

Thrya primarily defines a set of abstract C++ class interfaces needed for the development of abstract numerical atgorithms (ANAs) such as iterative linear solvers, transient solvers all the way up to optimization. At the foundation of these interfaces are abstract C++ classes for vectors, vector spaces, linear operators and multi-vectors. Also included in the Thyra package is C++ code for creating concrete vector, vector space, linear operator, and multi-vector subclasses as well as other utilities to aid in the development of ANAs. Currently, very general and efficient concrete subclass implementations exist for serial and SPMD in-core vectors and multi-vectors. Codemore » also currently exists for testing objects and providing composite objects such as product vectors.« less

Quantization and superselection sectors III: Multiply connected spaces and indistinguishable particles

NASA Astrophysics Data System (ADS)

Landsman, N. P. Klaas

2016-09-01

We reconsider the (non-relativistic) quantum theory of indistinguishable particles on the basis of Rieffel’s notion of C∗-algebraic (“strict”) deformation quantization. Using this formalism, we relate the operator approach of Messiah and Greenberg (1964) to the configuration space approach pioneered by Souriau (1967), Laidlaw and DeWitt-Morette (1971), Leinaas and Myrheim (1977), and others. In dimension d > 2, the former yields bosons, fermions, and paraparticles, whereas the latter seems to leave room for bosons and fermions only, apparently contradicting the operator approach as far as the admissibility of parastatistics is concerned. To resolve this, we first prove that in d > 2 the topologically non-trivial configuration spaces of the second approach are quantized by the algebras of observables of the first. Secondly, we show that the irreducible representations of the latter may be realized by vector bundle constructions, among which the line bundles recover the results of the second approach. Mathematically speaking, representations on higher-dimensional bundles (which define parastatistics) cannot be excluded, which render the configuration space approach incomplete. Physically, however, we show that the corresponding particle states may always be realized in terms of bosons and/or fermions with an unobserved internal degree of freedom (although based on non-relativistic quantum mechanics, this conclusion is analogous to the rigorous results of the Doplicher-Haag-Roberts analysis in algebraic quantum field theory, as well as to the heuristic arguments which led Gell-Mann and others to QCD (i.e. Quantum Chromodynamics)).

Optical Interface States Protected by Synthetic Weyl Points

NASA Astrophysics Data System (ADS)

Wang, Qiang; Xiao, Meng; Liu, Hui; Zhu, Shining; Chan, C. T.

2017-07-01

Weyl fermions have not been found in nature as elementary particles, but they emerge as nodal points in the band structure of electronic and classical wave crystals. Novel phenomena such as Fermi arcs and chiral anomaly have fueled the interest in these topological points which are frequently perceived as monopoles in momentum space. Here, we report the experimental observation of generalized optical Weyl points inside the parameter space of a photonic crystal with a specially designed four-layer unit cell. The reflection at the surface of a truncated photonic crystal exhibits phase vortexes due to the synthetic Weyl points, which in turn guarantees the existence of interface states between photonic crystals and any reflecting substrates. The reflection phase vortexes have been confirmed for the first time in our experiments, which serve as an experimental signature of the generalized Weyl points. The existence of these interface states is protected by the topological properties of the Weyl points, and the trajectories of these states in the parameter space resembles those of Weyl semimetal "Fermi arc surface states" in momentum space. Tracing the origin of interface states to the topological character of the parameter space paves the way for a rational design of strongly localized states with enhanced local field.

Topologically Nontrivial Magnon Bands in Artificial Square Spin Ices with Dzyaloshinskii-Moriya Interaction

NASA Astrophysics Data System (ADS)

Iacocca, Ezio; Heinonen, Olle

2017-09-01

Systems that exhibit topologically protected edge states are interesting both from a fundamental point of view as well as for potential applications, the latter because of the absence of backscattering and robustness to perturbations. It is desirable to be able to control and manipulate such edge states. Here, we show that artificial square ices can incorporate both features: an interfacial Dzyaloshinskii-Moriya interaction gives rise to topologically nontrivial magnon bands, and the equilibrium state of the spin ice is reconfigurable with different configurations having different magnon dispersions and topology. The topology is found to develop as odd-symmetry bulk and edge magnon bands approach each other so that constructive band inversion occurs in reciprocal space. Our results show that topologically protected bands are supported in square spin ices.

Topological Structure of the Space of Phenotypes: The Case of RNA Neutral Networks

PubMed Central

Aguirre, Jacobo; Buldú, Javier M.; Stich, Michael; Manrubia, Susanna C.

2011-01-01

The evolution and adaptation of molecular populations is constrained by the diversity accessible through mutational processes. RNA is a paradigmatic example of biopolymer where genotype (sequence) and phenotype (approximated by the secondary structure fold) are identified in a single molecule. The extreme redundancy of the genotype-phenotype map leads to large ensembles of RNA sequences that fold into the same secondary structure and can be connected through single-point mutations. These ensembles define neutral networks of phenotypes in sequence space. Here we analyze the topological properties of neutral networks formed by 12-nucleotides RNA sequences, obtained through the exhaustive folding of sequence space. A total of 412 sequences fragments into 645 subnetworks that correspond to 57 different secondary structures. The topological analysis reveals that each subnetwork is far from being random: it has a degree distribution with a well-defined average and a small dispersion, a high clustering coefficient, and an average shortest path between nodes close to its minimum possible value, i.e. the Hamming distance between sequences. RNA neutral networks are assortative due to the correlation in the composition of neighboring sequences, a feature that together with the symmetries inherent to the folding process explains the existence of communities. Several topological relationships can be analytically derived attending to structural restrictions and generic properties of the folding process. The average degree of these phenotypic networks grows logarithmically with their size, such that abundant phenotypes have the additional advantage of being more robust to mutations. This property prevents fragmentation of neutral networks and thus enhances the navigability of sequence space. In summary, RNA neutral networks show unique topological properties, unknown to other networks previously described. PMID:22028856

Compile-Time Schedulability Analysis of Communicating Concurrent Programs

DTIC Science & Technology

2006-06-28

synchronize via the read and write operations on the FIFO channels. These operations have been implemented with the help of semaphores , which...3 1.1.2 Synchronous Dataflow . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.3 Boolean Dataflow...described by concurrent programs . . . . . . . . . 4 1.3 A synchronous dataflow model, its topology matrix, and repetition vector . 10 1.4 Select and

Insights in luteovirid structural biology guided by chemical cross-linking and high resolution mass spectrometry

USDA-ARS?s Scientific Manuscript database

Interactions among plant pathogenic viruses in the family /react-text Luteoviridae react-text: 233 and their plant hosts and insect vectors are governed by the topology of the viral capsid, which is the sole vehicle for long distance movement of the viral genome. Previous application of a mass spect...

Nonpolynomial vector fields under the Lotka-Volterra normal form

NASA Astrophysics Data System (ADS)

Hernández-Bermejo, Benito; Fairén, Víctor

1995-02-01

We carry out the generalization of the Lotka-Volterra embedding to flows not explicitly recognizable under the generalized Lotka-Volterra format. The procedure introduces appropriate auxiliary variables, and it is shown how, to a great extent, the final Lotka-Volterra system is independent of their specific definition. Conservation of the topological equivalence during the process is also demonstrated.

Topological view of quantum tunneling coherent destruction

NASA Astrophysics Data System (ADS)

Bernardini, Alex E.; Chinaglia, Mariana

2017-08-01

Quantum tunneling of the ground and first excited states in a quantum superposition driven by a novel analytical configuration of a double-well (DW) potential is investigated. Symmetric and asymmetric potentials are considered as to support quantum mechanical zero mode and first excited state analytical solutions. Reporting about a symmetry breaking that supports the quantum conversion of a zero-mode stable vacuum into an unstable tachyonic quantum state, two inequivalent topological scenarios are supposed to drive stable tunneling and coherent tunneling destruction respectively. A complete prospect of the Wigner function dynamics, vector field fluxes and the time dependence of stagnation points is obtained for the analytical potentials that support stable and tachyonic modes.

New Term Weighting Formulas for the Vector Space Method in Information Retrieval

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

Chisholm, E.; Kolda, T.G.

The goal in information retrieval is to enable users to automatically and accurately find data relevant to their queries. One possible approach to this problem i use the vector space model, which models documents and queries as vectors in the term space. The components of the vectors are determined by the term weighting scheme, a function of the frequencies of the terms in the document or query as well as throughout the collection. We discuss popular term weighting schemes and present several new schemes that offer improved performance.

Momentum-space cigar geometry in topological phases

NASA Astrophysics Data System (ADS)

Palumbo, Giandomenico

2018-01-01

In this paper, we stress the importance of momentum-space geometry in the understanding of two-dimensional topological phases of matter. We focus, for simplicity, on the gapped boundary of three-dimensional topological insulators in class AII, which are described by a massive Dirac Hamiltonian and characterized by an half-integer Chern number. The gap is induced by introducing a magnetic perturbation, such as an external Zeeman field or a ferromagnet on the surface. The quantum Bures metric acquires a central role in our discussion and identifies a cigar geometry. We first derive the Chern number from the cigar geometry and we then show that the quantum metric can be seen as a solution of two-dimensional non-Abelian BF theory in momentum space. The gauge connection for this model is associated to the Maxwell algebra, which takes into account the Lorentz symmetries related to the Dirac theory and the momentum-space magnetic translations connected to the magnetic perturbation. The Witten black-hole metric is a solution of this gauge theory and coincides with the Bures metric. This allows us to calculate the corresponding momentum-space entanglement entropy that surprisingly carries information about the real-space conformal field theory describing the defect lines that can be created on the gapped boundary.

Stereotype locally convex spaces

NASA Astrophysics Data System (ADS)

Akbarov, S. S.

2000-08-01

We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis.

Extended vector-tensor theories

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

Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke, E-mail: rampei@th.phys.titech.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: yoshida@th.phys.titech.ac.jp

Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Procamore » theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.« less

Observation of Dirac-like energy band and ring-torus Fermi surface associated with the nodal line in topological insulator CaAgAs

NASA Astrophysics Data System (ADS)

Takane, Daichi; Nakayama, Kosuke; Souma, Seigo; Wada, Taichi; Okamoto, Yoshihiko; Takenaka, Koshi; Yamakawa, Youichi; Yamakage, Ai; Mitsuhashi, Taichi; Horiba, Koji; Kumigashira, Hiroshi; Takahashi, Takashi; Sato, Takafumi

2018-01-01

One of key challenges in current material research is to search for new topological materials with inverted bulk-band structure. In topological insulators, the band inversion caused by strong spin-orbit coupling leads to opening of a band gap in the entire Brillouin zone, whereas an additional crystal symmetry such as point-group and nonsymmorphic symmetries sometimes prohibits the gap opening at/on specific points or line in momentum space, giving rise to topological semimetals. Despite many theoretical predictions of topological insulators/semimetals associated with such crystal symmetries, the experimental realization is still relatively scarce. Here, using angle-resolved photoemission spectroscopy with bulk-sensitive soft-x-ray photons, we experimentally demonstrate that hexagonal pnictide CaAgAs belongs to a new family of topological insulators characterized by the inverted band structure and the mirror reflection symmetry of crystal. We have established the bulk valence-band structure in three-dimensional Brillouin zone, and observed the Dirac-like energy band and ring-torus Fermi surface associated with the line node, where bulk valence and conducting bands cross on a line in the momentum space under negligible spin-orbit coupling. Intriguingly, we found that no other bands cross the Fermi level and therefore the low-energy excitations are solely characterized by the Dirac-like band. CaAgAs provides an excellent platform to study the interplay among low-energy electron dynamics, crystal symmetry, and exotic topological properties.

Controlled Visual Sensing and Exploration

DTIC Science & Technology

2015-09-16

point cloud. This is clearly insufficient for most other tasks that require at least the topology of the scene to determine what surfaces or “objects...or whether it is empty space, as in the latter case it is traversable, in the former it is not. To this end, we have developed methods for topology ...Specific achievements include: • We have shown that surface topology and geometry can be computed without minimal surface bias, yielding water-tight

Multiple site receptor modeling with a minimal spanning tree combined with a Kohonen neural network

NASA Astrophysics Data System (ADS)

Hopke, Philip K.

1999-12-01

A combination of two pattern recognition methods has been developed that allows the generation of geographical emission maps form multivariate environmental data. In such a projection into a visually interpretable subspace by a Kohonen Self-Organizing Feature Map, the topology of the higher dimensional variables space can be preserved, but parts of the information about the correct neighborhood among the sample vectors will be lost. This can partly be compensated for by an additional projection of Prim's Minimal Spanning Tree into the trained neural network. This new environmental receptor modeling technique has been adapted for multiple sampling sites. The behavior of the method has been studied using simulated data. Subsequently, the method has been applied to mapping data sets from the Southern California Air Quality Study. The projection of a 17 chemical variables measured at up to 8 sampling sites provided a 2D, visually interpretable, geometrically reasonable arrangement of air pollution source sin the South Coast Air Basin.

Quasiparticle interference mapping of ZrSiS

NASA Astrophysics Data System (ADS)

Lodge, Michael; Hosen, Md Mofazzle; Neupane, Madhab; Ishigami, Masa; Chang, Guoqing; Singh, Bahadur; Lin, Hsin; Weber, Bent; Hellerstedt, Jack; Edmonds, Mark; Fuhrer, Michael; Kaczorowski, Dariusz

The emergent class of 3D Dirac semimetals presents intriguing new systems in which to study the rich physics of the robust, topologically-protected quasiparticles hosted within their bulk. For example, in nodal-line Dirac semimetals, the conductance and valence bands meet along a closed loop in momentum space and disperse linearly in the vicinity of the resultant line node. This results in novel scattering phenomena, owing to the unique Fermi surfaces and scattering selection rules of these systems. Here, we have performed scanning tunneling microscopy and spectroscopy of ZrSiS, one such nodal-line Dirac semimetal,at 4.5 K. We have visualized quasiparticle scattering using differential conductance mapping. In conjunction with numerical modeling, we identify at least six allowed scattering vectors in the material, which gives insight into the scattering selection rules of these novel materials. This work is based upon research supported by the National Science Foundation under Grant No. 0955625 (MSL and MI) and Fellowship No. 1614303 (MSL), and by the Australian Research Council under DECRA Fellowship No. DE160101334 (BW).

The problems in quantum foundations in the light of gauge theories

NASA Astrophysics Data System (ADS)

Ne'Eman, Yuval

1986-04-01

We review the issues of nonseparability and seemingly acausal propagation of information in EPR, as displayed by experiments and the failure of Bell's inequalities. We show that global effects are in the very nature of the geometric structure of modern physical theories, occurring even at the classical level. The Aharonov-Bohm effect, magnetic monopoles, instantons, etc. result from the topology and homotopy features of the fiber bundle manifolds of gauge theories. The conservation of probabilities, a supposedly highly quantum effect, is also achieved through global geometry equations. The EPR observables all fit in such geometries, and space-time is a truncated representation and is not the correct arena for their understanding. Relativistic quantum field theory represents the global action of the measurement operators as the zero-momentum (and therefore spatially infinitely spread) limit of their wave functions (form factors). We also analyze the collapse of the state vector as a case of spontaneous symmetry breakdown in the apparatus-observed state interaction.

Characteristic Functional of a Probability Measure Absolutely Continuous with Respect to a Gaussian Radon Measure

DTIC Science & Technology

1984-08-01

12. PERSONAL AUTHORISI Hiroshi Sato 13* TYPE OF REPORT TECHNICAL 13b. TIME COVERED PROM TO 14. OATE OF REPORT (Yr. Mo., Day) Aug. 1984...nectuary and identify by bloc* number) Let p and p.. be probability measures on a locally convex Hausdorff real topological linear space E. C.R. Baker [1...THIS PAGE ABSTRACT Let y and y1 be probability measures on a locally convex Hausdorff real topological linear space E. C.R. Baker [1] posed the

Renormalization group approach to symmetry protected topological phases

NASA Astrophysics Data System (ADS)

van Nieuwenburg, Evert P. L.; Schnyder, Andreas P.; Chen, Wei

2018-04-01

A defining feature of a symmetry protected topological phase (SPT) in one dimension is the degeneracy of the Schmidt values for any given bipartition. For the system to go through a topological phase transition separating two SPTs, the Schmidt values must either split or cross at the critical point in order to change their degeneracies. A renormalization group (RG) approach based on this splitting or crossing is proposed, through which we obtain an RG flow that identifies the topological phase transitions in the parameter space. Our approach can be implemented numerically in an efficient manner, for example, using the matrix product state formalism, since only the largest first few Schmidt values need to be calculated with sufficient accuracy. Using several concrete models, we demonstrate that the critical points and fixed points of the RG flow coincide with the maxima and minima of the entanglement entropy, respectively, and the method can serve as a numerically efficient tool to analyze interacting SPTs in the parameter space.

Structured caustic vector vortex optical field: manipulating optical angular momentum flux and polarization rotation.

PubMed

Chen, Rui-Pin; Chen, Zhaozhong; Chew, Khian-Hooi; Li, Pei-Gang; Yu, Zhongliang; Ding, Jianping; He, Sailing

2015-05-29

A caustic vector vortex optical field is experimentally generated and demonstrated by a caustic-based approach. The desired caustic with arbitrary acceleration trajectories, as well as the structured states of polarization (SoP) and vortex orders located in different positions in the field cross-section, is generated by imposing the corresponding spatial phase function in a vector vortex optical field. Our study reveals that different spin and orbital angular momentum flux distributions (including opposite directions) in different positions in the cross-section of a caustic vector vortex optical field can be dynamically managed during propagation by intentionally choosing the initial polarization and vortex topological charges, as a result of the modulation of the caustic phase. We find that the SoP in the field cross-section rotates during propagation due to the existence of the vortex. The unique structured feature of the caustic vector vortex optical field opens the possibility of multi-manipulation of optical angular momentum fluxes and SoP, leading to more complex manipulation of the optical field scenarios. Thus this approach further expands the functionality of an optical system.

Polarization Control with Plasmonic Antenna Tips: A Universal Approach to Optical Nanocrystallography and Vector-Field Imaging

NASA Astrophysics Data System (ADS)

Park, Kyoung-Duck; Raschke, Markus B.

2018-05-01

Controlling the propagation and polarization vectors in linear and nonlinear optical spectroscopy enables to probe the anisotropy of optical responses providing structural symmetry selective contrast in optical imaging. Here we present a novel tilted antenna-tip approach to control the optical vector-field by breaking the axial symmetry of the nano-probe in tip-enhanced near-field microscopy. This gives rise to a localized plasmonic antenna effect with significantly enhanced optical field vectors with control of both \\textit{in-plane} and \\textit{out-of-plane} components. We use the resulting vector-field specificity in the symmetry selective nonlinear optical response of second-harmonic generation (SHG) for a generalized approach to optical nano-crystallography and -imaging. In tip-enhanced SHG imaging of monolayer MoS$_2$ films and single-crystalline ferroelectric YMnO$_3$, we reveal nano-crystallographic details of domain boundaries and domain topology with enhanced sensitivity and nanoscale spatial resolution. The approach is applicable to any anisotropic linear and nonlinear optical response, and provides for optical nano-crystallographic imaging of molecular or quantum materials.

Topological String Theory and Enumerative Geometry

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

Song, Y. S

In this thesis we investigate several problems which have their roots in both topological string theory and enumerative geometry. In the former case, underlying theories are topological field theories, whereas the latter case is concerned with intersection theories on moduli spaces. A permeating theme in this thesis is to examine the close interplay between these two complementary fields of study. The main problems addressed are as follows: In considering the Hurwitz enumeration problem of branched covers of compact connected Riemann surfaces, we completely solve the problem in the case of simple Hurwitz numbers. In addition, utilizing the connection between Hurwitzmore » numbers and Hodge integrals, we derive a generating function for the latter on the moduli space {bar M}{sub g,2} of 2-pointed, genus-g Deligne-Mumford stable curves. We also investigate Givental's recent conjecture regarding semisimple Frobenius structures and Gromov-Witten invariants, both of which are closely related to topological field theories; we consider the case of a complex projective line P{sup 1} as a specific example and verify his conjecture at low genera. In the last chapter, we demonstrate that certain topological open string amplitudes can be computed via relative stable morphisms in the algebraic category.« less

An Integrated Vision-Based System for Spacecraft Attitude and Topology Determination for Formation Flight Missions

NASA Technical Reports Server (NTRS)

Rogers, Aaron; Anderson, Kalle; Mracek, Anna; Zenick, Ray

2004-01-01

With the space industry's increasing focus upon multi-spacecraft formation flight missions, the ability to precisely determine system topology and the orientation of member spacecraft relative to both inertial space and each other is becoming a critical design requirement. Topology determination in satellite systems has traditionally made use of GPS or ground uplink position data for low Earth orbits, or, alternatively, inter-satellite ranging between all formation pairs. While these techniques work, they are not ideal for extension to interplanetary missions or to large fleets of decentralized, mixed-function spacecraft. The Vision-Based Attitude and Formation Determination System (VBAFDS) represents a novel solution to both the navigation and topology determination problems with an integrated approach that combines a miniature star tracker with a suite of robust processing algorithms. By combining a single range measurement with vision data to resolve complete system topology, the VBAFDS design represents a simple, resource-efficient solution that is not constrained to certain Earth orbits or formation geometries. In this paper, analysis and design of the VBAFDS integrated guidance, navigation and control (GN&C) technology will be discussed, including hardware requirements, algorithm development, and simulation results in the context of potential mission applications.

Spacetime representation of topological phononics

NASA Astrophysics Data System (ADS)

Deymier, Pierre A.; Runge, Keith; Lucas, Pierre; Vasseur, Jérôme O.

2018-05-01

Non-conventional topology of elastic waves arises from breaking symmetry of phononic structures either intrinsically through internal resonances or extrinsically via application of external stimuli. We develop a spacetime representation based on twistor theory of an intrinsic topological elastic structure composed of a harmonic chain attached to a rigid substrate. Elastic waves in this structure obey the Klein–Gordon and Dirac equations and possesses spinorial character. We demonstrate the mapping between straight line trajectories of these elastic waves in spacetime and the twistor complex space. The twistor representation of these Dirac phonons is related to their topological and fermion-like properties. The second topological phononic structure is an extrinsic structure composed of a one-dimensional elastic medium subjected to a moving superlattice. We report an analogy between the elastic behavior of this time-dependent superlattice, the scalar quantum field theory and general relativity of two types of exotic particle excitations, namely temporal Dirac phonons and temporal ghost (tachyonic) phonons. These phonons live on separate sides of a two-dimensional frequency space and are delimited by ghost lines reminiscent of the conventional light cone. Both phonon types exhibit spinorial amplitudes that can be measured by mapping the particle behavior to the band structure of elastic waves.

Experimental observation of the topological structure of exceptional points in an ultrathin hybridized metamaterial

NASA Astrophysics Data System (ADS)

Kang, Ming; Zhu, Weiren; Rukhlenko, Ivan D.

2017-12-01

The exceptional point (EP), which is one of the most important branch-type singularities exclusive to non-Hermitian systems, has been observed recently in various synthetic materials, giving rise to counterintuitive phenomena due to the nontrivial topology of the EP. Here, we present a direct experimental observation of the topological structure of the EPs via the angle-resolved transmission measurement of a hybridized metamaterial. Both eigenvalues and eigenvectors show branch-point singularities in the investigated biparametric space of frequency and incident angle. Importantly, the angle-resolved transmission coefficients provide all the information about the eigenvalues as well as the corresponding eigenvectors in the biparametric space, revealing the nontrivial topological structure of the EP, such as mode switching and the topological phase for a parameter loop encircling the EP. It is shown that the appearance of the EP in the scattering matrix is related directly to the perfect unidirectional transmission and the chirality of the EP corresponds to the maximum or minimum value of the asymmetric factor. Our investigation uncovers the capabilities of metamaterials for exploring the physics of EPs and their potential for having extreme optical properties, which provide potential applications in the spectral band ranging from microwaves to visible frequencies.

Alternative probability theories for cognitive psychology.

PubMed

Narens, Louis

2014-01-01

Various proposals for generalizing event spaces for probability functions have been put forth in the mathematical, scientific, and philosophic literatures. In cognitive psychology such generalizations are used for explaining puzzling results in decision theory and for modeling the influence of context effects. This commentary discusses proposals for generalizing probability theory to event spaces that are not necessarily boolean algebras. Two prominent examples are quantum probability theory, which is based on the set of closed subspaces of a Hilbert space, and topological probability theory, which is based on the set of open sets of a topology. Both have been applied to a variety of cognitive situations. This commentary focuses on how event space properties can influence probability concepts and impact cognitive modeling. Copyright © 2013 Cognitive Science Society, Inc.

Yang Monopoles and Emergent Three-Dimensional Topological Defects in Interacting Bosons

NASA Astrophysics Data System (ADS)

Yan, Yangqian; Zhou, Qi

2018-06-01

The Yang monopole as a zero-dimensional topological defect has been well established in multiple fields in physics. However, it remains an intriguing question to understand the interaction effects on Yang monopoles. Here, we show that the collective motion of many interacting bosons gives rise to exotic topological defects that are distinct from Yang monopoles seen by a single particle. Whereas interactions may distribute Yang monopoles in the parameter space or glue them to a single giant one of multiple charges, three-dimensional topological defects also arise from continuous manifolds of degenerate many-body eigenstates. Their projections in lower dimensions lead to knotted nodal lines and nodal rings. Our results suggest that ultracold bosonic atoms can be used to create emergent topological defects and directly measure topological invariants that are not easy to access in solids.

Plurigon: three dimensional visualization and classification of high-dimensionality data

PubMed Central

Martin, Bronwen; Chen, Hongyu; Daimon, Caitlin M.; Chadwick, Wayne; Siddiqui, Sana; Maudsley, Stuart

2013-01-01

High-dimensionality data is rapidly becoming the norm for biomedical sciences and many other analytical disciplines. Not only is the collection and processing time for such data becoming problematic, but it has become increasingly difficult to form a comprehensive appreciation of high-dimensionality data. Though data analysis methods for coping with multivariate data are well-documented in technical fields such as computer science, little effort is currently being expended to condense data vectors that exist beyond the realm of physical space into an easily interpretable and aesthetic form. To address this important need, we have developed Plurigon, a data visualization and classification tool for the integration of high-dimensionality visualization algorithms with a user-friendly, interactive graphical interface. Unlike existing data visualization methods, which are focused on an ensemble of data points, Plurigon places a strong emphasis upon the visualization of a single data point and its determining characteristics. Multivariate data vectors are represented in the form of a deformed sphere with a distinct topology of hills, valleys, plateaus, peaks, and crevices. The gestalt structure of the resultant Plurigon object generates an easily-appreciable model. User interaction with the Plurigon is extensive; zoom, rotation, axial and vector display, feature extraction, and anaglyph stereoscopy are currently supported. With Plurigon and its ability to analyze high-complexity data, we hope to see a unification of biomedical and computational sciences as well as practical applications in a wide array of scientific disciplines. Increased accessibility to the analysis of high-dimensionality data may increase the number of new discoveries and breakthroughs, ranging from drug screening to disease diagnosis to medical literature mining. PMID:23885241

Compactly supported Wannier functions and algebraic K -theory

NASA Astrophysics Data System (ADS)

Read, N.

2017-03-01

In a tight-binding lattice model with n orbitals (single-particle states) per site, Wannier functions are n -component vector functions of position that fall off rapidly away from some location, and such that a set of them in some sense span all states in a given energy band or set of bands; compactly supported Wannier functions are such functions that vanish outside a bounded region. They arise not only in band theory, but also in connection with tensor-network states for noninteracting fermion systems, and for flat-band Hamiltonians with strictly short-range hopping matrix elements. In earlier work, it was proved that for general complex band structures (vector bundles) or general complex Hamiltonians—that is, class A in the tenfold classification of Hamiltonians and band structures—a set of compactly supported Wannier functions can span the vector bundle only if the bundle is topologically trivial, in any dimension d of space, even when use of an overcomplete set of such functions is permitted. This implied that, for a free-fermion tensor network state with a nontrivial bundle in class A, any strictly short-range parent Hamiltonian must be gapless. Here, this result is extended to all ten symmetry classes of band structures without additional crystallographic symmetries, with the result that in general the nontrivial bundles that can arise from compactly supported Wannier-type functions are those that may possess, in each of d directions, the nontrivial winding that can occur in the same symmetry class in one dimension, but nothing else. The results are obtained from a very natural usage of algebraic K -theory, based on a ring of polynomials in e±i kx,e±i ky,..., which occur as entries in the Fourier-transformed Wannier functions.

Dirac node arcs in PtSn 4

DOE PAGES

Wu, Yun; Wang, Lin -Lin; Mun, Eundeok; ...

2016-04-04

In topological quantum materials 1,2,3 the conduction and valence bands are connected at points or along lines in the momentum space. A number of studies have demonstrated that several materials are indeed Dirac/Weyl semimetals 4,5,6,7,8. However, there is still no experimental confirmation of materials with line nodes, in which the Dirac nodes form closed loops in the momentum space 2,3. Here we report the discovery of a novel topological structure—Dirac node arcs—in the ultrahigh magnetoresistive material PtSn 4 using laser-based angle-resolved photoemission spectroscopy data and density functional theory calculations. Unlike the closed loops of line nodes, the Dirac node arcmore » structure arises owing to the surface states and resembles the Dirac dispersion in graphene that is extended along a short line in the momentum space. Here, we propose that this reported Dirac node arc structure is a novel topological state that provides an exciting platform for studying the exotic properties of Dirac fermions.« less

Same-sign dilepton excesses and vector-like quarks

DOE PAGES

Chen, Chuan-Ren; Cheng, Hsin-Chia; Low, Ian

2016-03-15

Multiple analyses from ATLAS and CMS collaborations, including searches for ttH production, supersymmetric particles and vector-like quarks, observed excesses in the same-sign dilepton channel containing b-jets and missing transverse energy in the LHC Run 1 data. In the context of little Higgs theories with T parity, we explain these excesses using vector-like T-odd quarks decaying into a top quark, a W boson and the lightest T-odd particle (LTP). For heavy vector-like quarks, decay topologies containing the LTP have not been searched for at the LHC. The bounds on the masses of the T-odd quarks can be estimated in a simplifiedmore » model approach by adapting the search limits for top/bottom squarks in supersymmetry. Assuming a realistic decay branching fraction, a benchmark with a 750 GeV T-odd b' quark is proposed. In conclusion, we also comment on the possibility to fit excesses in different analyses in a common framework.« less

Datum Feature Extraction and Deformation Analysis Method Based on Normal Vector of Point Cloud

NASA Astrophysics Data System (ADS)

Sun, W.; Wang, J.; Jin, F.; Liang, Z.; Yang, Y.

2018-04-01

In order to solve the problem lacking applicable analysis method in the application of three-dimensional laser scanning technology to the field of deformation monitoring, an efficient method extracting datum feature and analysing deformation based on normal vector of point cloud was proposed. Firstly, the kd-tree is used to establish the topological relation. Datum points are detected by tracking the normal vector of point cloud determined by the normal vector of local planar. Then, the cubic B-spline curve fitting is performed on the datum points. Finally, datum elevation and the inclination angle of the radial point are calculated according to the fitted curve and then the deformation information was analyzed. The proposed approach was verified on real large-scale tank data set captured with terrestrial laser scanner in a chemical plant. The results show that the method could obtain the entire information of the monitor object quickly and comprehensively, and reflect accurately the datum feature deformation.

Manifolds for pose tracking from monocular video

NASA Astrophysics Data System (ADS)

Basu, Saurav; Poulin, Joshua; Acton, Scott T.

2015-03-01

We formulate a simple human-pose tracking theory from monocular video based on the fundamental relationship between changes in pose and image motion vectors. We investigate the natural embedding of the low-dimensional body pose space into a high-dimensional space of body configurations that behaves locally in a linear manner. The embedded manifold facilitates the decomposition of the image motion vectors into basis motion vector fields of the tangent space to the manifold. This approach benefits from the style invariance of image motion flow vectors, and experiments to validate the fundamental theory show reasonable accuracy (within 4.9 deg of the ground truth).

Charmless B_{(s)}→ VV decays in factorization-assisted topological-amplitude approach

NASA Astrophysics Data System (ADS)

Wang, Chao; Zhang, Qi-An; Li, Ying; Lü, Cai-Dian

2017-05-01

Within the factorization-assisted topological-amplitude approach, we studied the 33 charmless B_{(s)} → VV decays, where V stands for a light vector meson. According to the flavor flows, the amplitude of each process can be decomposed into eight different topologies. In contrast to the conventional flavor diagrammatic approach, we further factorize each topological amplitude into decay constant, form factors and unknown universal parameters. By χ ^2 fitting 46 experimental observables, we extracted 10 theoretical parameters with χ ^2 per degree of freedom around 2. Using the fitted parameters, we calculated the branching fractions, polarization fractions, CP asymmetries and relative phases between polarization amplitudes of each decay mode. The decay channels dominated by tree diagram have large branching fractions and large longitudinal polarization fraction. The branching fractions and longitudinal polarization fractions of color-suppressed decays become smaller. Current experimental data of large transverse polarization fractions in the penguin dominant decay channels can be explained by only one transverse amplitude of penguin annihilation diagram. Our predictions of the not yet measured channels can be tested in the ongoing LHCb experiment and the Belle-II experiment in the future.

A topological approach unveils system invariances and broken symmetries in the brain.

PubMed

Tozzi, Arturo; Peters, James F

2016-05-01

Symmetries are widespread invariances underscoring countless systems, including the brain. A symmetry break occurs when the symmetry is present at one level of observation but is hidden at another level. In such a general framework, a concept from algebraic topology, namely, the Borsuk-Ulam theorem (BUT), comes into play and sheds new light on the general mechanisms of nervous symmetries. The BUT tells us that we can find, on an n-dimensional sphere, a pair of opposite points that have the same encoding on an n - 1 sphere. This mapping makes it possible to describe both antipodal points with a single real-valued vector on a lower dimensional sphere. Here we argue that this topological approach is useful for the evaluation of hidden nervous symmetries. This means that symmetries can be found when evaluating the brain in a proper dimension, although they disappear (are hidden or broken) when we evaluate the same brain only one dimension lower. In conclusion, we provide a topological methodology for the evaluation of the most general features of brain activity, i.e., the symmetries, cast in a physical/biological fashion that has the potential to be operationalized. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Topological Band Theory for Non-Hermitian Hamiltonians

NASA Astrophysics Data System (ADS)

Shen, Huitao; Zhen, Bo; Fu, Liang

2018-04-01

We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped" bands in one and two dimensions by explicitly finding their topological invariants. We find nontrivial generalizations of the Chern number in two dimensions, and a new classification in one dimension, whose topology is determined by the energy dispersion rather than the energy eigenstates. We then study the bulk-edge correspondence and the topological phase transition in two dimensions. Different from the Hermitian case, the transition generically involves an extended intermediate phase with complex-energy band degeneracies at isolated "exceptional points" in momentum space. We also systematically classify all types of band degeneracies.

Persistent Homology to describe Solid and Fluid Structures during Multiphase Flow

NASA Astrophysics Data System (ADS)

Herring, A. L.; Robins, V.; Liu, Z.; Armstrong, R. T.; Sheppard, A.

2017-12-01

The question of how to accurately and effectively characterize essential fluid and solid distributions and structures is a long-standing topic within the field of porous media and fluid transport. For multiphase flow applications, considerable research effort has been made to describe fluid distributions under a range of conditions; including quantification of saturation levels, fluid-fluid pressure differences and interfacial areas, and fluid connectivity. Recent research has effectively used topological metrics to describe pore space and fluid connectivity, with researchers demonstrating links between pore-scale nonwetting phase topology to fluid mobilization and displacement mechanisms, relative permeability, fluid flow regimes, and thermodynamic models of multiphase flow. While topology is clearly a powerful tool to describe fluid distribution, topological metrics by definition provide information only on the connectivity of a phase, not its geometry (shape or size). Physical flow characteristics, e.g. the permeability of a fluid phase within a porous medium, are dependent on the connectivity of the pore space or fluid phase as well as the size of connections. Persistent homology is a technique which provides a direct link between topology and geometry via measurement of topological features and their persistence from the signed Euclidean distance transform of a segmented digital image (Figure 1). We apply persistent homology analysis to measure the occurrence and size of pore-scale topological features in a variety of sandstones, for both the dry state and the nonwetting phase fluid during two-phase fluid flow (drainage and imbibition) experiments, visualized with 3D X-ray microtomography. The results provide key insights into the dominant topological features and length scales of a media which control relevant field-scale engineering properties such as fluid trapping, absolute permeability, and relative permeability.

Planck 2013 results. XXVI. Background geometry and topology of the Universe

NASA Astrophysics Data System (ADS)

Planck Collaboration; Ade, P. A. R.; Aghanim, N.; Armitage-Caplan, C.; Arnaud, M.; Ashdown, M.; Atrio-Barandela, F.; Aumont, J.; Baccigalupi, C.; Banday, A. J.; Barreiro, R. B.; Bartlett, J. G.; Battaner, E.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.-P.; Bersanelli, M.; Bielewicz, P.; Bobin, J.; Bock, J. J.; Bonaldi, A.; Bonavera, L.; Bond, J. R.; Borrill, J.; Bouchet, F. R.; Bridges, M.; Bucher, M.; Burigana, C.; Butler, R. C.; Cardoso, J.-F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chiang, H. C.; Chiang, L.-Y.; Christensen, P. R.; Church, S.; Clements, D. L.; Colombi, S.; Colombo, L. P. L.; Couchot, F.; Coulais, A.; Crill, B. P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R. D.; Davis, R. J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Delouis, J.-M.; Désert, F.-X.; Diego, J. M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Dupac, X.; Efstathiou, G.; Enßlin, T. A.; Eriksen, H. K.; Fabre, O.; Finelli, F.; Forni, O.; Frailis, M.; Franceschi, E.; Galeotta, S.; Ganga, K.; Giard, M.; Giardino, G.; Giraud-Héraud, Y.; González-Nuevo, J.; Górski, K. M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Hansen, F. K.; Hanson, D.; Harrison, D. L.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S. R.; Hivon, E.; Hobson, M.; Holmes, W. A.; Hornstrup, A.; Hovest, W.; Huffenberger, K. M.; Jaffe, A. H.; Jaffe, T. R.; Jones, W. C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kisner, T. S.; Knoche, J.; Knox, L.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lähteenmäki, A.; Lamarre, J.-M.; Lasenby, A.; Laureijs, R. J.; Lawrence, C. R.; Leahy, J. P.; Leonardi, R.; Leroy, C.; Lesgourgues, J.; Liguori, M.; Lilje, P. B.; Linden-Vørnle, M.; López-Caniego, M.; Lubin, P. M.; Macías-Pérez, J. F.; Maffei, B.; Maino, D.; Mandolesi, N.; Maris, M.; Marshall, D. J.; Martin, P. G.; Martínez-González, E.; Masi, S.; Massardi, M.; Matarrese, S.; Matthai, F.; Mazzotta, P.; McEwen, J. D.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschênes, M.-A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Murphy, J. A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C. B.; Nørgaard-Nielsen, H. U.; Noviello, F.; Novikov, D.; Novikov, I.; Osborne, S.; Oxborrow, C. A.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Pasian, F.; Patanchon, G.; Peiris, H. V.; Perdereau, O.; Perotto, L.; Perrotta, F.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pogosyan, D.; Pointecouteau, E.; Polenta, G.; Ponthieu, N.; Popa, L.; Poutanen, T.; Pratt, G. W.; Prézeau, G.; Prunet, S.; Puget, J.-L.; Rachen, J. P.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Riazuelo, A.; Ricciardi, S.; Riller, T.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Roudier, G.; Rowan-Robinson, M.; Rusholme, B.; Sandri, M.; Santos, D.; Savini, G.; Scott, D.; Seiffert, M. D.; Shellard, E. P. S.; Spencer, L. D.; Starck, J.-L.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sureau, F.; Sutton, D.; Suur-Uski, A.-S.; Sygnet, J.-F.; Tauber, J. A.; Tavagnacco, D.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Varis, J.; Vielva, P.; Villa, F.; Vittorio, N.; Wade, L. A.; Wandelt, B. D.; Yvon, D.; Zacchei, A.; Zonca, A.

2014-11-01

The new cosmic microwave background (CMB) temperature maps from Planck provide the highest-quality full-sky view of the surface of last scattering available to date. This allows us to detect possible departures from the standard model of a globally homogeneous and isotropic cosmology on the largest scales. We search for correlations induced by a possible non-trivial topology with a fundamental domain intersecting, or nearly intersecting, the last scattering surface (at comoving distance χrec), both via a direct search for matched circular patterns at the intersections and by an optimal likelihood search for specific topologies. For the latter we consider flat spaces with cubic toroidal (T3), equal-sided chimney (T2) and slab (T1) topologies, three multi-connected spaces of constant positive curvature (dodecahedral, truncated cube and octahedral) and two compact negative-curvature spaces. These searches yield no detection of the compact topology with the scale below the diameter of the last scattering surface. For most compact topologies studied the likelihood maximized over the orientation of the space relative to the observed map shows some preference for multi-connected models just larger than the diameter of the last scattering surface. Since this effect is also present in simulated realizations of isotropic maps, we interpret it as the inevitable alignment of mild anisotropic correlations with chance features in a single sky realization; such a feature can also be present, in milder form, when the likelihood is marginalized over orientations. Thus marginalized, the limits on the radius ℛi of the largest sphere inscribed in topological domain (at log-likelihood-ratio Δln ℒ > -5 relative to a simply-connected flat Planck best-fit model) are: in a flat Universe, ℛi> 0.92χrec for the T3 cubic torus; ℛi> 0.71χrec for the T2 chimney; ℛi> 0.50χrec for the T1 slab; and in a positively curved Universe, ℛi> 1.03χrec for the dodecahedral space; ℛi> 1.0χrec for the truncated cube; and ℛi> 0.89χrec for the octahedral space. The limit for a wider class of topologies, i.e., those predicting matching pairs of back-to-back circles, among them tori and the three spherical cases listed above, coming from the matched-circles search, is ℛi> 0.94χrec at 99% confidence level. Similar limits apply to a wide, although not exhaustive, range of topologies. We also perform a Bayesian search for an anisotropic global Bianchi VIIh geometry. In the non-physical setting where the Bianchi cosmology is decoupled from the standard cosmology, Planck data favour the inclusion of a Bianchi component with a Bayes factor of at least 1.5 units of log-evidence. Indeed, the Bianchi pattern is quite efficient at accounting for some of the large-scale anomalies found in Planck data. However, the cosmological parameters that generate this pattern are in strong disagreement with those found from CMB anisotropy data alone. In the physically motivated setting where the Bianchi parameters are coupled and fitted simultaneously with the standard cosmological parameters, we find no evidence for a Bianchi VIIh cosmology and constrain the vorticity of such models to (ω/H)0< 8.1 × 10-10 (95% confidence level).

On orthogonal expansions of the space of vector functions which are square-summable over a given domain and the vector analysis operators

NASA Technical Reports Server (NTRS)

Bykhovskiy, E. B.; Smirnov, N. V.

1983-01-01

The Hilbert space L2(omega) of vector functions is studied. A breakdown of L2(omega) into orthogonal subspaces is discussed and the properties of the operators for projection onto these subspaces are investigated from the standpoint of preserving the differential properties of the vectors being projected. Finally, the properties of the operators are examined.

Finding topological center of a geographic space via road network

NASA Astrophysics Data System (ADS)

Gao, Liang; Miao, Yanan; Qin, Yuhao; Zhao, Xiaomei; Gao, Zi-You

2015-02-01

Previous studies show that the center of a geographic space is of great importance in urban and regional studies, including study of population distribution, urban growth modeling, and scaling properties of urban systems, etc. But how to well define and how to efficiently extract the center of a geographic space are still largely unknown. Recently, Jiang et al. have presented a definition of topological center by their block detection (BD) algorithm. Despite the fact that they first introduced the definition and discovered the 'true center', in human minds, their algorithm left several redundancies in its traversal process. Here, we propose an alternative road-cycle detection (RCD) algorithm to find the topological center, which extracts the outmost road-cycle recursively. To foster the application of the topological center in related research fields, we first reproduce the BD algorithm in Python (pyBD), then implement the RCD algorithm in two ways: the ArcPy implementation (arcRCD) and the Python implementation (pyRCD). After the experiments on twenty-four typical road networks, we find that the results of our RCD algorithm are consistent with those of Jiang's BD algorithm. We also find that the RCD algorithm is at least seven times more efficient than the BD algorithm on all the ten typical road networks.

Counting RG flows

DOE PAGES

Gukov, Sergei

2016-01-05

Here, interpreting renormalization group flows as solitons interpolating between different fixed points, we ask various questions that are normally asked in soliton physics but not in renormalization theory. Can one count RG flows? Are there different "topological sectors" for RG flows? What is the moduli space of an RG flow, and how does it compare to familiar moduli spaces of (supersymmetric) dowain walls? Analyzing these questions in a wide variety of contexts -- from counting RG walls to AdS/CFT correspondence -- will not only provide favorable answers, but will also lead us to a unified general framework that is powerfulmore » enough to account for peculiar RG flows and predict new physical phenomena. Namely, using Bott's version of Morse theory we relate the topology of conformal manifolds to certain properties of RG flows that can be used as precise diagnostics and "topological obstructions" for the strong form of the C-theorem in any dimension. Moreover, this framework suggests a precise mechanism for how the violation of the strong C-theorem happens and predicts "phase transitions" along the RG flow when the topological obstruction is non-trivial. Along the way, we also find new conformal manifolds in well-known 4d CFT's and point out connections with the superconformal index and classifying spaces of global symmetry groups.« less

Investigating the topological structure of quenched lattice QCD with overlap fermions using a multi-probing approximation

NASA Astrophysics Data System (ADS)

Zou, You-Hao; Zhang, Jian-Bo; Xiong, Guang-Yi; Chen, Ying; Liu, Chuan; Liu, Yu-Bin; Ma, Jian-Ping

2017-10-01

The topological charge density and topological susceptibility are determined by a multi-probing approximation using overlap fermions in quenched SU(3) gauge theory. Then we investigate the topological structure of the quenched QCD vacuum, and compare it with results from the all-scale topological density. The results are consistent. Random permuted topological charge density is used to check whether these structures represent underlying ordered properties. The pseudoscalar glueball mass is extracted from the two-point correlation function of the topological charge density. We study 3 ensembles of different lattice spacing a with the same lattice volume 163×32. The results are compatible with the results of all-scale topological charge density, and the topological structures revealed by multi-probing are much closer to all-scale topological charge density than those from eigenmode expansion. Supported by National Natural Science Foundation of China (NSFC) (11335001, 11275169, 11075167), It is also supported in part by the DFG and the NSFC (11261130311) through funds provided to the Sino-German CRC 110 "Symmetries and the Emergence of Structure in QCD". This work was also funded in part by National Basic Research Program of China (973 Program) (2015CB856700)

Bundles over nearly-Kahler homogeneous spaces in heterotic string theory

NASA Astrophysics Data System (ADS)

Klaput, Michael; Lukas, Andre; Matti, Cyril

2011-09-01

We construct heterotic vacua based on six-dimensional nearly-Kahler homogeneous manifolds and non-trivial vector bundles thereon. Our examples are based on three specific group coset spaces. It is shown how to construct line bundles over these spaces, compute their properties and build up vector bundles consistent with supersymmetry and anomaly cancelation. It turns out that the most interesting coset is SU(3)/U(1)2. This space supports a large number of vector bundles which lead to consistent heterotic vacua, some of them with three chiral families.

Search for supersymmetry in the vector-boson fusion topology in proton-proton collisions at √(s) = 8 TeV

DOE PAGES

Khachatryan, Vardan

2015-09-27

Our first search for supersymmetry in the vector-boson fusion topology is presented.The search targets final states with at least two leptons, large missing transverse momentum, and two jets with a large separation in rapidity. The data sample corresponds to an integrated luminosity of 19.7 fb -1 of proton-proton collisions at √s = 8 TeV collected with the CMS detector at the CERN LHC. The observed dijet invariant mass spectrum is found to be consistent with the expected standard model prediction. Upper limits are set on the cross sections for chargino and neutralino production with two associated jets, assuming the supersymmetricmore » partner of the τ lepton to be the lightest slepton and the lightest slepton to be lighter than the charginos. For a compressed-mass-spectrum scenario in which the mass difference between the lightest supersymmetric particle X ~0 1 and the next lightest, mass-degenerate, gaugino particles X ~0 2 and X ~± 1 is 50 GeV, a mass lower limit of 170 GeV is set for these latter two particles.« less

A multiblock multigrid three-dimensional Euler equation solver

NASA Technical Reports Server (NTRS)

Cannizzaro, Frank E.; Elmiligui, Alaa; Melson, N. Duane; Vonlavante, E.

1990-01-01

Current aerodynamic designs are often quite complex (geometrically). Flexible computational tools are needed for the analysis of a wide range of configurations with both internal and external flows. In the past, geometrically dissimilar configurations required different analysis codes with different grid topologies in each. The duplicity of codes can be avoided with the use of a general multiblock formulation which can handle any grid topology. Rather than hard wiring the grid topology into the program, it is instead dictated by input to the program. In this work, the compressible Euler equations, written in a body-fitted finite-volume formulation, are solved using a pseudo-time-marching approach. Two upwind methods (van Leer's flux-vector-splitting and Roe's flux-differencing) were investigated. Two types of explicit solvers (a two-step predictor-corrector and a modified multistage Runge-Kutta) were used with multigrid acceleration to enhance convergence. A multiblock strategy is used to allow greater geometric flexibility. A report on simple explicit upwind schemes for solving compressible flows is included.

Dual Vector Spaces and Physical Singularities

NASA Astrophysics Data System (ADS)

Rowlands, Peter

Though we often refer to 3-D vector space as constructed from points, there is no mechanism from within its definition for doing this. In particular, space, on its own, cannot accommodate the singularities that we call fundamental particles. This requires a commutative combination of space as we know it with another 3-D vector space, which is dual to the first (in a physical sense). The combination of the two spaces generates a nilpotent quantum mechanics/quantum field theory, which incorporates exact supersymmetry and ultimately removes the anomalies due to self-interaction. Among the many natural consequences of the dual space formalism are half-integral spin for fermions, zitterbewegung, Berry phase and a zero norm Berwald-Moor metric for fermionic states.

A Hybrid 3D Indoor Space Model

NASA Astrophysics Data System (ADS)

Jamali, Ali; Rahman, Alias Abdul; Boguslawski, Pawel

2016-10-01

GIS integrates spatial information and spatial analysis. An important example of such integration is for emergency response which requires route planning inside and outside of a building. Route planning requires detailed information related to indoor and outdoor environment. Indoor navigation network models including Geometric Network Model (GNM), Navigable Space Model, sub-division model and regular-grid model lack indoor data sources and abstraction methods. In this paper, a hybrid indoor space model is proposed. In the proposed method, 3D modeling of indoor navigation network is based on surveying control points and it is less dependent on the 3D geometrical building model. This research proposes a method of indoor space modeling for the buildings which do not have proper 2D/3D geometrical models or they lack semantic or topological information. The proposed hybrid model consists of topological, geometrical and semantical space.

Finding a Hadamard matrix by simulated annealing of spin vectors

NASA Astrophysics Data System (ADS)

Bayu Suksmono, Andriyan

2017-05-01

Reformulation of a combinatorial problem into optimization of a statistical-mechanics system enables finding a better solution using heuristics derived from a physical process, such as by the simulated annealing (SA). In this paper, we present a Hadamard matrix (H-matrix) searching method based on the SA on an Ising model. By equivalence, an H-matrix can be converted into a seminormalized Hadamard (SH) matrix, whose first column is unit vector and the rest ones are vectors with equal number of -1 and +1 called SH-vectors. We define SH spin vectors as representation of the SH vectors, which play a similar role as the spins on Ising model. The topology of the lattice is generalized into a graph, whose edges represent orthogonality relationship among the SH spin vectors. Starting from a randomly generated quasi H-matrix Q, which is a matrix similar to the SH-matrix without imposing orthogonality, we perform the SA. The transitions of Q are conducted by random exchange of {+, -} spin-pair within the SH-spin vectors that follow the Metropolis update rule. Upon transition toward zeroth energy, the Q-matrix is evolved following a Markov chain toward an orthogonal matrix, at which the H-matrix is said to be found. We demonstrate the capability of the proposed method to find some low-order H-matrices, including the ones that cannot trivially be constructed by the Sylvester method.

Stochastic quantization of topological field theory: Generalized Langevin equation with memory kernel

NASA Astrophysics Data System (ADS)

Menezes, G.; Svaiter, N. F.

2006-07-01

We use the method of stochastic quantization in a topological field theory defined in an Euclidean space, assuming a Langevin equation with a memory kernel. We show that our procedure for the Abelian Chern-Simons theory converges regardless of the nature of the Chern-Simons coefficient.

Redundant Manipulator Self-Motion Topology Under Joint Limits with an 8-DOF Case Study

NASA Technical Reports Server (NTRS)

Luck, C. L.; Lee, S.

1993-01-01

This paper investigates the topology of self-motion manifolds for serial redundant manipulators with revolute joints in the presence of joint limits. It is known that the preimages of singular taskpoints divide the configuration space into regions where self-motion manifolds are homotopic.

Disrupted topological organization of structural networks revealed by probabilistic diffusion tractography in Tourette syndrome children.

PubMed

Wen, Hongwei; Liu, Yue; Rekik, Islem; Wang, Shengpei; Zhang, Jishui; Zhang, Yue; Peng, Yun; He, Huiguang

2017-08-01

Tourette syndrome (TS) is a childhood-onset neurobehavioral disorder. Although previous TS studies revealed structural abnormalities in distinct corticobasal ganglia circuits, the topological alterations of the whole-brain white matter (WM) structural networks remain poorly understood. Here, we used diffusion MRI probabilistic tractography and graph theoretical analysis to investigate the topological organization of WM networks in 44 drug-naive TS children and 41 age- and gender-matched healthy children. The WM networks were constructed by estimating inter-regional connectivity probability and the topological properties were characterized using graph theory. We found that both TS and control groups showed an efficient small-world organization in WM networks. However, compared to controls, TS children exhibited decreased global and local efficiency, increased shortest path length and small worldness, indicating a disrupted balance between local specialization and global integration in structural networks. Although both TS and control groups showed highly similar hub distributions, TS children exhibited significant decreased nodal efficiency, mainly distributed in the default mode, language, visual, and sensorimotor systems. Furthermore, two separate networks showing significantly decreased connectivity in TS group were identified using network-based statistical (NBS) analysis, primarily composed of the parieto-occipital cortex, precuneus, and paracentral lobule. Importantly, we combined support vector machine and multiple kernel learning frameworks to fuse multiple levels of network topological features for classification of individuals, achieving high accuracy of 86.47%. Together, our study revealed the disrupted topological organization of structural networks related to pathophysiology of TS, and the discriminative topological features for classification are potential quantitative neuroimaging biomarkers for clinical TS diagnosis. Hum Brain Mapp 38:3988-4008, 2017. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

On F-Algebras M p  (1 < p < ∞) of Holomorphic Functions

PubMed Central

Meštrović, Romeo

2014-01-01

We consider the classes M p (1 < p < ∞) of holomorphic functions on the open unit disk 𝔻 in the complex plane. These classes are in fact generalizations of the class M introduced by Kim (1986). The space M p equipped with the topology given by the metric ρ p defined by ρ p(f, g) = ||f − g||p = (∫ 0 2πlogp(1 + M(f − g)(θ))(dθ/2π))1/p, with f, g∈M p and Mf(θ) = sup0⩽r<1 ⁡|f(re iθ)|, becomes an F-space. By a result of Stoll (1977), the Privalov space N p (1 < p < ∞) with the topology given by the Stoll metric d p is an F-algebra. By using these two facts, we prove that the spaces M p and N p coincide and have the same topological structure. Consequently, we describe a general form of continuous linear functionals on M p (with respect to the metric ρ p). Furthermore, we give a characterization of bounded subsets of the spaces M p. Moreover, we give the examples of bounded subsets of M p that are not relatively compact. PMID:24672388

Experimental phase diagram of zero-bias conductance peaks in superconductor/semiconductor nanowire devices

PubMed Central

Chen, Jun; Yu, Peng; Stenger, John; Hocevar, Moïra; Car, Diana; Plissard, Sébastien R.; Bakkers, Erik P. A. M.; Stanescu, Tudor D.; Frolov, Sergey M.

2017-01-01

Topological superconductivity is an exotic state of matter characterized by spinless p-wave Cooper pairing of electrons and by Majorana zero modes at the edges. The first signature of topological superconductivity is a robust zero-bias peak in tunneling conductance. We perform tunneling experiments on semiconductor nanowires (InSb) coupled to superconductors (NbTiN) and establish the zero-bias peak phase in the space of gate voltage and external magnetic field. Our findings are consistent with calculations for a finite-length topological nanowire and provide means for Majorana manipulation as required for braiding and topological quantum bits. PMID:28913432

Complex networks analysis of obstructive nephropathy data

NASA Astrophysics Data System (ADS)

Zanin, M.; Boccaletti, S.

2011-09-01

Congenital obstructive nephropathy (ON) is one of the most frequent and complex diseases affecting children, characterized by an abnormal flux of the urine, due to a partial or complete obstruction of the urinary tract; as a consequence, urine may accumulate in the kidney and disturb the normal operation of the organ. Despite important advances, pathological mechanisms are not yet fully understood. In this contribution, the topology of complex networks, based on vectors of features of control and ON subjects, is related with the severity of the pathology. Nodes in these networks represent genetic and metabolic profiles, while connections between them indicate an abnormal relation between their expressions. Resulting topologies allow discriminating ON subjects and detecting which genetic or metabolic elements are responsible for the malfunction.

Nonlinear analogue of the May−Wigner instability transition

PubMed Central

Fyodorov, Yan V.; Khoruzhenko, Boris A.

2016-01-01

We study a system of N≫1 degrees of freedom coupled via a smooth homogeneous Gaussian vector field with both gradient and divergence-free components. In the absence of coupling, the system is exponentially relaxing to an equilibrium with rate μ. We show that, while increasing the ratio of the coupling strength to the relaxation rate, the system experiences an abrupt transition from a topologically trivial phase portrait with a single equilibrium into a topologically nontrivial regime characterized by an exponential number of equilibria, the vast majority of which are expected to be unstable. It is suggested that this picture provides a global view on the nature of the May−Wigner instability transition originally discovered by local linear stability analysis. PMID:27274077

Effects of OCR Errors on Ranking and Feedback Using the Vector Space Model.

ERIC Educational Resources Information Center

Taghva, Kazem; And Others

1996-01-01

Reports on the performance of the vector space model in the presence of OCR (optical character recognition) errors in information retrieval. Highlights include precision and recall, a full-text test collection, smart vector representation, impact of weighting parameters, ranking variability, and the effect of relevance feedback. (Author/LRW)

Rényi-Fisher entropy product as a marker of topological phase transitions

NASA Astrophysics Data System (ADS)

Bolívar, J. C.; Nagy, Ágnes; Romera, Elvira

2018-05-01

The combined Rényi-Fisher entropy product of electrons plus holes displays a minimum at the charge neutrality points. The Stam-Rényi difference and the Stam-Rényi uncertainty product of the electrons plus holes, show maxima at the charge neutrality points. Topological quantum numbers capable of detecting the topological insulator and the band insulator phases, are defined. Upper and lower bounds for the position and momentum space Rényi-Fisher entropy products are derived.

Fuzzy spaces topology change as a possible solution to the black hole information loss paradox

NASA Astrophysics Data System (ADS)

Silva, C. A. S.

2009-06-01

The black hole information loss paradox is one of the most intricate problems in modern theoretical physics. A proposal to solve this is one related with topology change. However it has found some obstacles related to unitarity and cluster decomposition (locality). In this Letter we argue that modelling the black hole's event horizon as a noncommutative manifold - the fuzzy sphere - we can solve the problems with topology change, getting a possible solution to the black hole information loss paradox.

Spontaneously broken topological SL(5,R) gauge theory with standard gravity emerging

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

Mielke, Eckehard W.

2011-02-15

A completely metric-free sl(5,R) gauge framework is developed in four dimensions. After spontaneous symmetry breaking of the corresponding topological BF scheme, Einstein spaces with a tiny cosmological constant emerge, similarly as in (anti-)de Sitter gauge theories of gravity. The induced {Lambda} is related to the scale of the symmetry breaking. A ''background'' metric surfaces from a Higgs-like mechanism. The finiteness of such a topological scheme converts into asymptotic safeness after quantization of the spontaneously broken model.

A vector space model approach to identify genetically related diseases.

PubMed

Sarkar, Indra Neil

2012-01-01

The relationship between diseases and their causative genes can be complex, especially in the case of polygenic diseases. Further exacerbating the challenges in their study is that many genes may be causally related to multiple diseases. This study explored the relationship between diseases through the adaptation of an approach pioneered in the context of information retrieval: vector space models. A vector space model approach was developed that bridges gene disease knowledge inferred across three knowledge bases: Online Mendelian Inheritance in Man, GenBank, and Medline. The approach was then used to identify potentially related diseases for two target diseases: Alzheimer disease and Prader-Willi Syndrome. In the case of both Alzheimer Disease and Prader-Willi Syndrome, a set of plausible diseases were identified that may warrant further exploration. This study furthers seminal work by Swanson, et al. that demonstrated the potential for mining literature for putative correlations. Using a vector space modeling approach, information from both biomedical literature and genomic resources (like GenBank) can be combined towards identification of putative correlations of interest. To this end, the relevance of the predicted diseases of interest in this study using the vector space modeling approach were validated based on supporting literature. The results of this study suggest that a vector space model approach may be a useful means to identify potential relationships between complex diseases, and thereby enable the coordination of gene-based findings across multiple complex diseases.

Observation of dynamical vortices after quenches in a system with topology

NASA Astrophysics Data System (ADS)

Fläschner, N.; Vogel, D.; Tarnowski, M.; Rem, B. S.; Lühmann, D.-S.; Heyl, M.; Budich, J. C.; Mathey, L.; Sengstock, K.; Weitenberg, C.

2018-03-01

Topological phases constitute an exotic form of matter characterized by non-local properties rather than local order parameters1. The paradigmatic Haldane model on a hexagonal lattice features such topological phases distinguished by an integer topological invariant known as the first Chern number2. Recently, the identification of non-equilibrium signatures of topology in the dynamics of such systems has attracted particular attention3-6. Here, we experimentally study the dynamical evolution of the wavefunction using time- and momentum-resolved full state tomography for spin-polarized fermionic atoms in driven optical lattices7. We observe the appearance, movement and annihilation of dynamical vortices in momentum space after sudden quenches close to the topological phase transition. These dynamical vortices can be interpreted as dynamical Fisher zeros of the Loschmidt amplitude8, which signal a so-called dynamical phase transition9,10. Our results pave the way to a deeper understanding of the connection between topological phases and non-equilibrium dynamics.

Recipe for Topological Polaritons

NASA Astrophysics Data System (ADS)

Karzig, Torsten; Bardyn, Charles-Edouard; Lindner, Netanel; Refael, Gil

2015-03-01

The interaction between light and matter can give rise to novel topological states. This principle was recently exemplified in Floquet topological insulators, where classical light was used to induce a topological electronic band structure. Here, in contrast, we show that mixing single photons with excitons can result in new topological polaritonic states -- or ``topolaritons''. Taken separately, the underlying photons and excitons are topologically trivial. Combined appropriately, however, they give rise to non-trivial polaritonic bands with chiral edge modes allowing for unidirectional polariton propagation. The main ingredient in our construction is an exciton-photon coupling with a phase that winds in momentum space. We demonstrate how this winding emerges from spin-orbit coupling in the electronic system and an applied Zeeman field. We discuss the requirements for obtaining a sizable topological gap in the polariton spectrum. Funded by the Institute for Quantum Information and Matter, the Bi-National Science Foundation and I-Core: the Israeli Excellence Center ``Circle of Light'', and Darpa under funding for FENA, and the Swiss National Science Foundation.

Topological nodal-line fermions in spin-orbit metal PbTaSe2

PubMed Central

Bian, Guang; Chang, Tay-Rong; Sankar, Raman; Xu, Su-Yang; Zheng, Hao; Neupert, Titus; Chiu, Ching-Kai; Huang, Shin-Ming; Chang, Guoqing; Belopolski, Ilya; Sanchez, Daniel S.; Neupane, Madhab; Alidoust, Nasser; Liu, Chang; Wang, BaoKai; Lee, Chi-Cheng; Jeng, Horng-Tay; Zhang, Chenglong; Yuan, Zhujun; Jia, Shuang; Bansil, Arun; Chou, Fangcheng; Lin, Hsin; Hasan, M. Zahid

2016-01-01

Topological semimetals can support one-dimensional Fermi lines or zero-dimensional Weyl points in momentum space, where the valence and conduction bands touch. While the degeneracy points in Weyl semimetals are robust against any perturbation that preserves translational symmetry, nodal lines require protection by additional crystalline symmetries such as mirror reflection. Here we report, based on a systematic theoretical study and a detailed experimental characterization, the existence of topological nodal-line states in the non-centrosymmetric compound PbTaSe2 with strong spin-orbit coupling. Remarkably, the spin-orbit nodal lines in PbTaSe2 are not only protected by the reflection symmetry but also characterized by an integer topological invariant. Our detailed angle-resolved photoemission measurements, first-principles simulations and theoretical topological analysis illustrate the physical mechanism underlying the formation of the topological nodal-line states and associated surface states for the first time, thus paving the way towards exploring the exotic properties of the topological nodal-line fermions in condensed matter systems. PMID:26829889

Topology-optimized metasurfaces: impact of initial geometric layout.

PubMed

Yang, Jianji; Fan, Jonathan A

2017-08-15

Topology optimization is a powerful iterative inverse design technique in metasurface engineering and can transform an initial layout into a high-performance device. With this method, devices are optimized within a local design phase space, making the identification of suitable initial geometries essential. In this Letter, we examine the impact of initial geometric layout on the performance of large-angle (75 deg) topology-optimized metagrating deflectors. We find that when conventional metasurface designs based on dielectric nanoposts are used as initial layouts for topology optimization, the final devices have efficiencies around 65%. In contrast, when random initial layouts are used, the final devices have ultra-high efficiencies that can reach 94%. Our numerical experiments suggest that device topologies based on conventional metasurface designs may not be suitable to produce ultra-high-efficiency, large-angle metasurfaces. Rather, initial geometric layouts with non-trivial topologies and shapes are required.

Topological Hall and Spin Hall Effects in Disordered Skyrmionic Textures

NASA Astrophysics Data System (ADS)

Ndiaye, Papa Birame; Akosa, Collins; Manchon, Aurelien; Spintronics Theory Group Team

We carry out a throughout study of the topological Hall and topological spin Hall effects in disordered skyrmionic systems: the dimensionless (spin) Hall angles are evaluated across the energy band structure in the multiprobe Landauer-Büttiker formalism and their link to the effective magnetic field emerging from the real space topology of the spin texture is highlighted. We discuss these results for an optimal skyrmion size and for various sizes of the sample and found that the adiabatic approximation still holds for large skyrmions as well as for few atomic size-nanoskyrmions. Finally, we test the robustness of the topological signals against disorder strength and show that topological Hall effect is highly sensitive to momentum scattering. This work was supported by the King Abdullah University of Science and Technology (KAUST) through the Award No OSR-CRG URF/1/1693-01 from the Office of Sponsored Research (OSR).

Research into topology optimization and the FDM method for a space cracked membrane

NASA Astrophysics Data System (ADS)

Hu, Qingxi; Li, Wanyuan; Zhang, Haiguang; Liu, Dali; Peng, Fujun; Duan, Yongchao

2017-07-01

The problem that the space membranes are easily torn open is the main focus in this paper, and a bionic strengthening-ribs structure is proposed for a space membrane based on interdisciplinary strengths, such as topology optimization, composite materials, and rapid prototyping. The optimization method and modeling method of membranes with bionic strengthening-ribs was studied. The PEEK and SCF/PEEK composite material which are applied to the space environment are chosen, and FDM technology is used. Through topology optimization, bionic strengthening-ribs with good tensile and tear capacities were obtained. Cracked membranes, cracked membranes with PEEK strengthening-ribs and SCF/PEEK strengthening-ribs were tested and test data were obtained. An extension situation and tension fracture were compared for three cases. The experimental results showed that membranes with the bionic strengthening-ribs structure have better mechanical properties, and the strength of the membranes with PEEK and SCF/PEEK strengthening-ribs were raised, respectively, up to 266.9% and 185.9%. The strengthening-ribs structure greatly improves the capacity to halt membrane crack-growth, which has an important significance to avoid membrane tear, and to ensure the spacecraft orbital lifetime.

High-dimensional structured light coding/decoding for free-space optical communications free of obstructions.

PubMed

Du, Jing; Wang, Jian

2015-11-01

Bessel beams carrying orbital angular momentum (OAM) with helical phase fronts exp(ilφ)(l=0;±1;±2;…), where φ is the azimuthal angle and l corresponds to the topological number, are orthogonal with each other. This feature of Bessel beams provides a new dimension to code/decode data information on the OAM state of light, and the theoretical infinity of topological number enables possible high-dimensional structured light coding/decoding for free-space optical communications. Moreover, Bessel beams are nondiffracting beams having the ability to recover by themselves in the face of obstructions, which is important for free-space optical communications relying on line-of-sight operation. By utilizing the OAM and nondiffracting characteristics of Bessel beams, we experimentally demonstrate 12 m distance obstruction-free optical m-ary coding/decoding using visible Bessel beams in a free-space optical communication system. We also study the bit error rate (BER) performance of hexadecimal and 32-ary coding/decoding based on Bessel beams with different topological numbers. After receiving 500 symbols at the receiver side, a zero BER of hexadecimal coding/decoding is observed when the obstruction is placed along the propagation path of light.

Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

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

None, None

Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. Our paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper also studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases we studied indicate that themore » Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.« less

Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

DOE PAGES

None, None

2016-11-21

Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. Our paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper also studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases we studied indicate that themore » Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.« less

Characterization of heterocyclic rings through quantum chemical topology.

PubMed

Griffiths, Mark Z; Popelier, Paul L A

2013-07-22

Five-membered rings are found in a myriad of molecules important in a wide range of areas such as catalysis, nutrition, and drug and agrochemical design. Systematic insight into their largely unexplored chemical space benefits from first principle calculations presented here. This study comprehensively investigates a grand total of 764 different rings, all geometry optimized at the B3LYP/6-311+G(2d,p) level, from the perspective of Quantum Chemical Topology (QCT). For the first time, a 3D space of local topological properties was introduced, in order to characterize rings compactly. This space is called RCP space, after the so-called ring critical point. This space is analogous to BCP space, named after the bond critical point, which compactly and successfully characterizes a chemical bond. The relative positions of the rings in RCP space are determined by the nature of the ring scaffold, such as the heteroatoms within the ring or the number of π-bonds. The summed atomic QCT charges of the five ring atoms revealed five features (number and type of heteroatom, number of π-bonds, substituent and substitution site) that dictate a ring's net charge. Each feature independently contributes toward a ring's net charge. Each substituent has its own distinct and systematic effect on the ring's net charge, irrespective of the ring scaffold. Therefore, this work proves the possibility of designing a ring with specific properties by fine-tuning it through manipulation of these five features.

All conjugate-maximal-helicity-violating amplitudes from topological open string theory in twistor space.

PubMed

Roiban, Radu; Volovich, Anastasia

2004-09-24

It has recently been proposed that the D-instanton expansion of the open topological B model on P(3|4) is equivalent to the perturbative expansion of the maximally supersymmetric Yang-Mills theory in four dimensions. In this letter we show how to construct the gauge theory results for all n-point conjugate-maximal-helicity-violating amplitudes by computing the integral over the moduli space of curves of degree n-3 in P(3|4), providing strong support to the string theory construction.

Use of nonlinear design optimization techniques in the comparison of battery discharger topologies for the space platform

NASA Technical Reports Server (NTRS)

Sable, Dan M.; Cho, Bo H.; Lee, Fred C.

1990-01-01

A detailed comparison of a boost converter, a voltage-fed, autotransformer converter, and a multimodule boost converter, designed specifically for the space platform battery discharger, is performed. Computer-based nonlinear optimization techniques are used to facilitate an objective comparison. The multimodule boost converter is shown to be the optimum topology at all efficiencies. The margin is greatest at 97 percent efficiency. The multimodule, multiphase boost converter combines the advantages of high efficiency, light weight, and ample margin on the component stresses, thus ensuring high reliability.

Geometry, topology, and string theory

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

Varadarajan, Uday

A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.

Entanglement entropy and entanglement spectrum of triplet topological superconductors.

PubMed

Oliveira, T P; Ribeiro, P; Sacramento, P D

2014-10-22

We analyze the entanglement entropy properties of a 2D p-wave superconductor with Rashba spin-orbit coupling, which displays a rich phase-space that supports non-trivial topological phases, as the chemical potential and the Zeeman term are varied. We show that the entanglement entropy and its derivatives clearly signal the topological transitions and we find numerical evidence that for this model the derivative with respect to the magnetization provides a sensible signature of each topological phase. Following the area law for the entanglement entropy, we systematically analyze the contributions that are proportional to or independent of the perimeter of the system, as a function of the Hamiltonian coupling constants and the geometry of the finite subsystem. For this model, we show that even though the topological entanglement entropy vanishes, it signals the topological phase transitions in a finite system. We also observe a relationship between a topological contribution to the entanglement entropy in a half-cylinder geometry and the number of edge states, and that the entanglement spectrum has robust modes associated with each edge state, as in other topological systems.

On the topological sensitivity of cellular automata

NASA Astrophysics Data System (ADS)

Baetens, Jan M.; De Baets, Bernard

2011-06-01

Ever since the conceptualization of cellular automata (CA), much attention has been paid to the dynamical properties of these discrete dynamical systems, and, more in particular, to their sensitivity to the initial condition from which they are evolved. Yet, the sensitivity of CA to the topology upon which they are based has received only minor attention, such that a clear insight in this dependence is still lacking and, furthermore, a quantification of this so-called topological sensitivity has not yet been proposed. The lack of attention for this issue is rather surprising since CA are spatially explicit, which means that their dynamics is directly affected by their topology. To overcome these shortcomings, we propose topological Lyapunov exponents that measure the divergence of two close trajectories in phase space originating from a topological perturbation, and we relate them to a measure grasping the sensitivity of CA to their topology that relies on the concept of topological derivatives, which is introduced in this paper. The validity of the proposed methodology is illustrated for the 256 elementary CA and for a family of two-state irregular totalistic CA.

Top-k similar graph matching using TraM in biological networks.

PubMed

Amin, Mohammad Shafkat; Finley, Russell L; Jamil, Hasan M

2012-01-01

Many emerging database applications entail sophisticated graph-based query manipulation, predominantly evident in large-scale scientific applications. To access the information embedded in graphs, efficient graph matching tools and algorithms have become of prime importance. Although the prohibitively expensive time complexity associated with exact subgraph isomorphism techniques has limited its efficacy in the application domain, approximate yet efficient graph matching techniques have received much attention due to their pragmatic applicability. Since public domain databases are noisy and incomplete in nature, inexact graph matching techniques have proven to be more promising in terms of inferring knowledge from numerous structural data repositories. In this paper, we propose a novel technique called TraM for approximate graph matching that off-loads a significant amount of its processing on to the database making the approach viable for large graphs. Moreover, the vector space embedding of the graphs and efficient filtration of the search space enables computation of approximate graph similarity at a throw-away cost. We annotate nodes of the query graphs by means of their global topological properties and compare them with neighborhood biased segments of the datagraph for proper matches. We have conducted experiments on several real data sets, and have demonstrated the effectiveness and efficiency of the proposed method

Mach Number effects on turbulent superstructures in wall bounded flows

NASA Astrophysics Data System (ADS)

Kaehler, Christian J.; Bross, Matthew; Scharnowski, Sven

2017-11-01

Planer and three-dimensional flow field measurements along a flat plat boundary layer in the Trisonic Wind Tunnel Munich (TWM) are examined with the aim to characterize the scaling, spatial organization, and topology of large scale turbulent superstructures in compressible flow. This facility is ideal for this investigation as the ratio of boundary layer thickness to test section spanwise extent ratio is around 1/25, ensuring minimal sidewall and corner effects on turbulent structures in the center of the test section. A major difficulty in the experimental investigation of large scale features is the mutual size of the superstructures which can extend over many boundary layer thicknesses. Using multiple PIV systems, it was possible to capture the full spatial extent of large-scale structures over a range of Mach numbers from Ma = 0.3 - 3. To calculate the average large-scale structure length and spacing, the acquired vector fields were analyzed by statistical multi-point methods that show large scale structures with a correlation length of around 10 boundary layer thicknesses over the range of Mach numbers investigated. Furthermore, the average spacing between high and low momentum structures is on the order of a boundary layer thicknesses. This work is supported by the Priority Programme SPP 1881 Turbulent Superstructures of the Deutsche Forschungsgemeinschaft.

On supersymmetric AdS6 solutions in 10 and 11 dimensions

NASA Astrophysics Data System (ADS)

Gutowski, J.; Papadopoulos, G.

2017-12-01

We prove a non-existence theorem for smooth, supersymmetric, warped AdS 6 solutions with connected, compact without boundary internal space in D = 11 and (massive) IIA supergravities. In IIB supergravity we show that if such AdS 6 solutions exist, then the NSNS and RR 3-form fluxes must be linearly independent and certain spinor bilinears must be appropriately restricted. Moreover we demonstrate that the internal space admits an so(3) action which leaves all the fields invariant and for smooth solutions the principal orbits must have co-dimension two. We also describe the topology and geometry of internal spaces that admit such a so(3) action and show that there are no solutions for which the internal space has topology F × S 2, where F is an oriented surface.

On the coplanar eccentric non-restricted co-orbital dynamics

NASA Astrophysics Data System (ADS)

Leleu, A.; Robutel, P.; Correia, A. C. M.

2018-03-01

We study the phase space of eccentric coplanar co-orbitals in the non-restricted case. Departing from the quasi-circular case, we describe the evolution of the phase space as the eccentricities increase. We find that over a given value of the eccentricity, around 0.5 for equal mass co-orbitals, important topological changes occur in the phase space. These changes lead to the emergence of new co-orbital configurations and open a continuous path between the previously distinct trojan domains near the L_4 and L_5 eccentric Lagrangian equilibria. These topological changes are shown to be linked with the reconnection of families of quasi-periodic orbits of non-maximal dimension.

The entropic boundary law in BF theory

NASA Astrophysics Data System (ADS)

Livine, Etera R.; Terno, Daniel R.

2009-01-01

We compute the entropy of a closed bounded region of space for pure 3d Riemannian gravity formulated as a topological BF theory for the gauge group SU(2) and show its holographic behavior. More precisely, we consider a fixed graph embedded in space and study the flat connection spin network state without and with particle-like topological defects. We regularize and compute exactly the entanglement for a bipartite splitting of the graph and show it scales at leading order with the number of vertices on the boundary (or equivalently with the number of loops crossing the boundary). More generally these results apply to BF theory with any compact gauge group in any space-time dimension.

Exotic Lifshitz transitions in topological materials

NASA Astrophysics Data System (ADS)

Volovik, G. E.

2018-01-01

Topological Lifshitz transitions involve many types of topological structures in momentum and frequency-momentum spaces, such as Fermi surfaces, Dirac lines, Dirac and Weyl points, etc., each of which has its own stability-supporting topological invariant ( N_1, N_2, N_3, {\\tilde N}_3, etc.). The topology of the shape of Fermi surfaces and Dirac lines and the interconnection of objects of different dimensionalities produce a variety of Lifshitz transition classes. Lifshitz transitions have important implications for many areas of physics. To give examples, transition-related singularities can increase the superconducting transition temperature; Lifshitz transitions are the possible origin of the small masses of elementary particles in our Universe, and a black hole horizon serves as the surface of the Lifshitz transition between vacua with type-I and type-II Weyl points.

Spintronics device made of topological materials

NASA Astrophysics Data System (ADS)

Wu, Jiansheng; Shi, Zhangsheng; Wang, Maoji

Topological Materials is a new state of matter of which the bulk states are gapped insulator or superconductor while the surface states are gapless metallic states. Such surface states are robust against local disorder and impurities due to its nontrivial topology. It induces unusual transport properties and shows nontrivial topological spin texture in real space. We have made use of these two exotic properties to make application in spintronics. For example, we propose to make spin-filter transistor using of 1D or 2D quantum anomalous Hall insulator or 2D topological Weyl semimetal, we also propose a device to measure the spin-polarization of current, a device to generate entangled entangled electron pairs. Startup funds of SUSTC, Shenzhen Peacock Plan, Shenzhen Free Exploration Plan with Grant Number JCYJ20150630145302225.

All ASD complex and real 4-dimensional Einstein spaces with Λ≠0 admitting a nonnull Killing vector

NASA Astrophysics Data System (ADS)

Chudecki, Adam

2016-12-01

Anti-self-dual (ASD) 4-dimensional complex Einstein spaces with nonzero cosmological constant Λ equipped with a nonnull Killing vector are considered. It is shown that any conformally nonflat metric of such spaces can be always brought to a special form and the Einstein field equations can be reduced to the Boyer-Finley-Plebański equation (Toda field equation). Some alternative forms of the metric are discussed. All possible real slices (neutral, Euclidean and Lorentzian) of ASD complex Einstein spaces with Λ≠0 admitting a nonnull Killing vector are found.

Topological magnetoelectric pump in three dimensions

NASA Astrophysics Data System (ADS)

Fukui, Takahiro; Fujiwara, Takanori

2017-11-01

We study the topological pump for a lattice fermion model mainly in three spatial dimensions. We first calculate the U(1) current density for the Dirac model defined in continuous space-time to review the known results as well as to introduce some technical details convenient for the calculations of the lattice model. We next investigate the U(1) current density for a lattice fermion model, a variant of the Wilson-Dirac model. The model we introduce is defined on a lattice in space but in continuous time, which is suited for the study of the topological pump. For such a model, we derive the conserved U(1) current density and calculate it directly for the (1 +1 )-dimensional system as well as (3 +1 )-dimensional system in the limit of the small lattice constant. We find that the current includes a nontrivial lattice effect characterized by the Chern number, and therefore the pumped particle number is quantized by the topological reason. Finally, we study the topological temporal pump in 3 +1 dimensions by numerical calculations. We discuss the relationship between the second Chern number and the first Chern number, the bulk-edge correspondence, and the generalized Streda formula which enables us to compute the second Chern number using the spectral asymmetry.

Single-cone finite-difference schemes for the (2+1)-dimensional Dirac equation in general electromagnetic textures

NASA Astrophysics Data System (ADS)

Pötz, Walter

2017-11-01

A single-cone finite-difference lattice scheme is developed for the (2+1)-dimensional Dirac equation in presence of general electromagnetic textures. The latter is represented on a (2+1)-dimensional staggered grid using a second-order-accurate finite difference scheme. A Peierls-Schwinger substitution to the wave function is used to introduce the electromagnetic (vector) potential into the Dirac equation. Thereby, the single-cone energy dispersion and gauge invariance are carried over from the continuum to the lattice formulation. Conservation laws and stability properties of the formal scheme are identified by comparison with the scheme for zero vector potential. The placement of magnetization terms is inferred from consistency with the one for the vector potential. Based on this formal scheme, several numerical schemes are proposed and tested. Elementary examples for single-fermion transport in the presence of in-plane magnetization are given, using material parameters typical for topological insulator surfaces.

A versatile zero ripple topology

NASA Astrophysics Data System (ADS)

Capel, A.; Spruyt, H.; Weinberg, A.; O'Sullivan, D.; Crausaz, A.

A lightweight and efficient converter topology is described that presents zero ripple current on both input and output terminals simultaneously. The static and dynamic analyses are performed by using state representation with the current-injected method. A hardware application suitable for a Space Station battery conditioner is presented as a validation of the theoretical model.

Order, topology and preference

NASA Technical Reports Server (NTRS)

Sertel, M. R.

1971-01-01

Some standard order-related and topological notions, facts, and methods are brought to bear on central topics in the theory of preference and the theory of optimization. Consequences of connectivity are considered, especially from the viewpoint of normally preordered spaces. Examples are given showing how the theory of preference, or utility theory, can be applied to social analysis.

Spectral Analysis of Rich Network Topology in Social Networks

ERIC Educational Resources Information Center

Wu, Leting

2013-01-01

Social networks have received much attention these days. Researchers have developed different methods to study the structure and characteristics of the network topology. Our focus is on spectral analysis of the adjacency matrix of the underlying network. Recent work showed good properties in the adjacency spectral space but there are few…

Transverse angular momentum in topological photonic crystals

NASA Astrophysics Data System (ADS)

Deng, Wei-Min; Chen, Xiao-Dong; Zhao, Fu-Li; Dong, Jian-Wen

2018-01-01

Engineering local angular momentum of structured light fields in real space enables applications in many fields, in particular, the realization of unidirectional robust transport in topological photonic crystals with a non-trivial Berry vortex in momentum space. Here, we show transverse angular momentum modes in silicon topological photonic crystals when considering transverse electric polarization. Excited by a chiral external source with either transverse spin angular momentum or transverse phase vortex, robust light flow propagating along opposite directions is observed in several kinds of sharp-turn interfaces between two topologically-distinct silicon photonic crystals. A transverse orbital angular momentum mode with alternating phase vortex exists at the boundary of two such photonic crystals. In addition, unidirectional transport is robust to the working frequency even when the ring size or location of the pseudo-spin source varies in a certain range, leading to the superiority of the broadband photonic device. These findings enable one to make use of transverse angular momentum, a kind of degree of freedom, to achieve unidirectional robust transport in the telecom region and other potential applications in integrated photonic circuits, such as on-chip robust delay lines.

A Search for Nontoroidal Topological Lensing in the Sloan Digital Sky Survey Quasar Catalog

NASA Astrophysics Data System (ADS)

Fujii, Hirokazu; Yoshii, Yuzuru

2013-08-01

Flat space models with multiply connected topology, which have compact dimensions, are tested against the distribution of high-redshift (z >= 4) quasars of the Sloan Digital Sky Survey (SDSS). When the compact dimensions are smaller in size than the observed universe, topological lensing occurs, in which multiple images of single objects (ghost images) are observed. We improve on the recently introduced method to identify ghost images by means of four-point statistics. Our method is valid for any of the 17 multiply connected flat models, including nontoroidal ones that are compacted by screw motions or glide reflection. Applying the method to the data revealed one possible case of topological lensing caused by sixth-turn screw motion, however, it is consistent with the simply connected model by this test alone. Moreover, simulations suggest that we cannot exclude the other space models despite the absence of their signatures. This uncertainty mainly originates from the patchy coverage of SDSS in the south Galactic cap, and this situation will be improved by future wide-field spectroscopic surveys.

Real-space imaging of a topologically protected edge state with ultracold atoms in an amplitude-chirped optical lattice

PubMed Central

Leder, Martin; Grossert, Christopher; Sitta, Lukas; Genske, Maximilian; Rosch, Achim; Weitz, Martin

2016-01-01

To describe a mobile defect in polyacetylene chains, Su, Schrieffer and Heeger formulated a model assuming two degenerate energy configurations that are characterized by two different topological phases. An immediate consequence was the emergence of a soliton-type edge state located at the boundary between two regions of different configurations. Besides giving first insights in the electrical properties of polyacetylene materials, interest in this effect also stems from its close connection to states with fractional charge from relativistic field theory. Here, using a one-dimensional optical lattice for cold rubidium atoms with a spatially chirped amplitude, we experimentally realize an interface between two spatial regions of different topological order in an atomic physics system. We directly observe atoms confined in the edge state at the intersection by optical real-space imaging and characterize the state as well as the size of the associated energy gap. Our findings hold prospects for the spectroscopy of surface states in topological matter and for the quantum simulation of interacting Dirac systems. PMID:27767054

Quantitative image processing in fluid mechanics

NASA Technical Reports Server (NTRS)

Hesselink, Lambertus; Helman, James; Ning, Paul

1992-01-01

The current status of digital image processing in fluid flow research is reviewed. In particular, attention is given to a comprehensive approach to the extraction of quantitative data from multivariate databases and examples of recent developments. The discussion covers numerical simulations and experiments, data processing, generation and dissemination of knowledge, traditional image processing, hybrid processing, fluid flow vector field topology, and isosurface analysis using Marching Cubes.

Learning with LOGO: Logo and Vectors.

ERIC Educational Resources Information Center

Lough, Tom; Tipps, Steve

1986-01-01

This is the first of a two-part series on the general concept of vector space. Provides tool procedures to allow investigation of vector properties, vector addition and subtraction, and X and Y components. Lists several sources of additional vector ideas. (JM)

Principal fiber bundle description of number scaling for scalars and vectors: application to gauge theory

NASA Astrophysics Data System (ADS)

Benioff, Paul

2015-05-01

The purpose of this paper is to put the description of number scaling and its effects on physics and geometry on a firmer foundation, and to make it more understandable. A main point is that two different concepts, number and number value are combined in the usual representations of number structures. This is valid as long as just one structure of each number type is being considered. It is not valid when different structures of each number type are being considered. Elements of base sets of number structures, considered by themselves, have no meaning. They acquire meaning or value as elements of a number structure. Fiber bundles over a space or space time manifold, M, are described. The fiber consists of a collection of many real or complex number structures and vector space structures. The structures are parameterized by a real or complex scaling factor, s. A vector space at a fiber level, s, has, as scalars, real or complex number structures at the same level. Connections are described that relate scalar and vector space structures at both neighbor M locations and at neighbor scaling levels. Scalar and vector structure valued fields are described and covariant derivatives of these fields are obtained. Two complex vector fields, each with one real and one imaginary field, appear, with one complex field associated with positions in M and the other with position dependent scaling factors. A derivation of the covariant derivative for scalar and vector valued fields gives the same vector fields. The derivation shows that the complex vector field associated with scaling fiber levels is the gradient of a complex scalar field. Use of these results in gauge theory shows that the imaginary part of the vector field associated with M positions acts like the electromagnetic field. The physical relevance of the other three fields, if any, is not known.

Managing the resilience space of the German energy system - A vector analysis.

PubMed

Schlör, Holger; Venghaus, Sandra; Märker, Carolin; Hake, Jürgen-Friedrich

2018-07-15

The UN Sustainable Development Goals formulated in 2016 confirmed the sustainability concept of the Earth Summit of 1992 and supported UNEP's green economy transition concept. The transformation of the energy system (Energiewende) is the keystone of Germany's sustainability strategy and of the German green economy concept. We use ten updated energy-related indicators of the German sustainability strategy to analyse the German energy system. The development of the sustainable indicators is examined in the monitoring process by a vector analysis performed in two-dimensional Euclidean space (Euclidean plane). The aim of the novel vector analysis is to measure the current status of the Energiewende in Germany and thereby provide decision makers with information about the strains for the specific remaining pathway of the single indicators and of the total system in order to meet the sustainability targets of the Energiewende. Within this vector model, three vectors (the normative sustainable development vector, the real development vector, and the green economy vector) define the resilience space of our analysis. The resilience space encloses a number of vectors representing different pathways with different technological and socio-economic strains to achieve a sustainable development of the green economy. In this space, the decision will be made as to whether the government measures will lead to a resilient energy system or whether a readjustment of indicator targets or political measures is necessary. The vector analysis enables us to analyse both the government's ambitiousness, which is expressed in the sustainability target for the indicators at the start of the sustainability strategy representing the starting preference order of the German government (SPO) and, secondly, the current preference order of German society in order to bridge the remaining distance to reach the specific sustainability goals of the strategy summarized in the current preference order (CPO). Copyright © 2018 Elsevier Ltd. All rights reserved.

Stable Defects in Semiconductor Nanowires.

PubMed

Sanchez, A M; Gott, J A; Fonseka, H A; Zhang, Y; Liu, H; Beanland, R

2018-05-09

Semiconductor nanowires are commonly described as being defect-free due to their ability to expel mobile defects with long-range strain fields. Here, we describe previously undiscovered topologically protected line defects with null Burgers vector that, unlike dislocations, are stable in nanoscale crystals. We analyze the defects present in semiconductor nanowires in regions of imperfect crystal growth, i.e., at the nanowire tip formed during consumption of the droplet in self-catalyzed vapor-liquid-solid growth and subsequent vapor-solid shell growth. We use a form of the Burgers circuit method that can be applied to multiply twinned material without difficulty. Our observations show that the nanowire microstructure is very different from bulk material, with line defects either (a) trapped by locks or other defects, (b) arranged as dipoles or groups with a zero total Burgers vector, or (c) have a zero Burgers vector. We find two new line defects with a null Burgers vector, formed from the combination of partial dislocations in twinned material. The most common defect is the three-monolayer high twin facet with a zero Burgers vector. Studies of individual nanowires using cathodoluminescence show that optical emission is quenched in defective regions, showing that they act as strong nonradiative recombination centers.

Vortex topology of rolling and pitching wings

NASA Astrophysics Data System (ADS)

Johnson, Kyle; Thurow, Brian; Wabick, Kevin; Buchholz, James; Berdon, Randall

2017-11-01

A flat, rectangular plate with an aspect ratio of 2 was articulated in roll and pitch, individually and simultaneously, to isolate the effects of each motion. The plate was immersed into a Re = 10,000 flow (based on chord length) to simulate forward, flapping flight. Measurements were made using a 3D-3C plenoptic PIV system to allow for the study of vortex topology in the instantaneous flow, in addition to phase-averaged results. The prominent focus is leading-edge vortex (LEV) stability and the lifespan of shed LEVs. The parameter space involves multiple values of advance coefficient J and reduced frequency k for roll and pitch, respectively. This space aims to determine the influence of each parameter on LEVs, which has been identified as an important factor for the lift enhancement seen in flapping wing flight. A variety of results are to be presented characterizing the variations in vortex topology across this parameter space. This work is supported by the Air Force Office of Scientific Research (Grant Number FA9550-16-1-0107, Dr. Douglas Smith, program manager).

Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries

NASA Astrophysics Data System (ADS)

Meljanac, Daniel; Meljanac, Stjepan; Pikutić, Danijel

2017-12-01

Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. A method for a general construction of the star product is presented. The corresponding twist, expressed in terms of phase space coordinates, in the Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincaré-Weyl generators or gl(n) generators are constructed and R-matrix is discussed. A classification of linear realizations leading to vector-like deformed phase spaces is given. There are three types of spaces: (i) commutative spaces, (ii) κ -Minkowski spaces and (iii) κ -Snyder spaces. The corresponding star products are (i) associative and commutative (but non-local), (ii) associative and non-commutative and (iii) non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed.

On the background independence of two-dimensional topological gravity

NASA Astrophysics Data System (ADS)

Imbimbo, Camillo

1995-04-01

We formulate two-dimensional topological gravity in a background covariant Lagrangian framework. We derive the Ward identities which characterize the dependence of physical correlators on the background world-sheet metric defining the gauge-slice. We point out the existence of an "anomaly" in Ward identitites involving correlators of observables with higher ghost number. This "anomaly" represents an obstruction for physical correlators to be globally defined forms on moduli space which could be integrated in a background independent way. Starting from the anomalous Ward identities, we derive "descent" equations whose solutions are cocycles of the Lie algebra of the diffeomorphism group with values in the space of local forms on the moduli space. We solve the descent equations and provide explicit formulas for the cocycles, which allow for the definition of background independent integrals of physical correlators on the moduli space.

Signal dimensionality and the emergence of combinatorial structure.

PubMed

Little, Hannah; Eryılmaz, Kerem; de Boer, Bart

2017-11-01

In language, a small number of meaningless building blocks can be combined into an unlimited set of meaningful utterances. This is known as combinatorial structure. One hypothesis for the initial emergence of combinatorial structure in language is that recombining elements of signals solves the problem of overcrowding in a signal space. Another hypothesis is that iconicity may impede the emergence of combinatorial structure. However, how these two hypotheses relate to each other is not often discussed. In this paper, we explore how signal space dimensionality relates to both overcrowding in the signal space and iconicity. We use an artificial signalling experiment to test whether a signal space and a meaning space having similar topologies will generate an iconic system and whether, when the topologies differ, the emergence of combinatorially structured signals is facilitated. In our experiments, signals are created from participants' hand movements, which are measured using an infrared sensor. We found that participants take advantage of iconic signal-meaning mappings where possible. Further, we use trajectory predictability, measures of variance, and Hidden Markov Models to measure the use of structure within the signals produced and found that when topologies do not match, then there is more evidence of combinatorial structure. The results from these experiments are interpreted in the context of the differences between the emergence of combinatorial structure in different linguistic modalities (speech and sign). Copyright © 2017 Elsevier B.V. All rights reserved.

Interactive Design and Visualization of Branched Covering Spaces.

PubMed

Roy, Lawrence; Kumar, Prashant; Golbabaei, Sanaz; Zhang, Yue; Zhang, Eugene

2018-01-01

Branched covering spaces are a mathematical concept which originates from complex analysis and topology and has applications in tensor field topology and geometry remeshing. Given a manifold surface and an -way rotational symmetry field, a branched covering space is a manifold surface that has an -to-1 map to the original surface except at the ramification points, which correspond to the singularities in the rotational symmetry field. Understanding the notion and mathematical properties of branched covering spaces is important to researchers in tensor field visualization and geometry processing, and their application areas. In this paper, we provide a framework to interactively design and visualize the branched covering space (BCS) of an input mesh surface and a rotational symmetry field defined on it. In our framework, the user can visualize not only the BCSs but also their construction process. In addition, our system allows the user to design the geometric realization of the BCS using mesh deformation techniques as well as connecting tubes. This enables the user to verify important facts about BCSs such as that they are manifold surfaces around singularities, as well as the Riemann-Hurwitz formula which relates the Euler characteristic of the BCS to that of the original mesh. Our system is evaluated by student researchers in scientific visualization and geometry processing as well as faculty members in mathematics at our university who teach topology. We include their evaluations and feedback in the paper.

Exotic dark spinor fields

NASA Astrophysics Data System (ADS)

Da Rocha, Roldão; Bernardini, Alex E.; da Silva, J. M. Hoff

2011-04-01

Exotic dark spinor fields are introduced and investigated in the context of inequivalent spin structures on arbitrary curved spacetimes, which induces an additional term on the associated Dirac operator, related to a Čech cohomology class. For the most kinds of spinor fields, any exotic term in the Dirac operator can be absorbed and encoded as a shift of the electromagnetic vector potential representing an element of the cohomology group {H^1}( {M,{{Z}_2}} ) . The possibility of concealing such an exotic term does not exist in case of dark (ELKO) spinor fields, as they cannot carry electromagnetic charge, so that the full topological analysis must be evaluated. Since exotic dark spinor fields also satisfy Klein-Gordon propagators, the dynamical constraints related to the exotic term in the Dirac equation can be explicitly calculated. It forthwith implies that the non-trivial topology associated to the spacetime can drastically engender — from the dynamics of dark spinor fields — constraints in the spacetime metric structure. Meanwhile, such constraints may be alleviated, at the cost of constraining the exotic spacetime topology. Besides being prime candidates to the dark matter problem, dark spinor fields are shown to be potential candidates to probe non-trivial topologies in spacetime, as well as probe the spacetime metric structure.

Magnetism in curved geometries

NASA Astrophysics Data System (ADS)

Streubel, Robert

Deterministically bending and twisting two-dimensional structures in the three-dimensional (3D) space provide means to modify conventional or to launch novel functionalities by tailoring curvature and 3D shape. The recent developments of 3D curved magnetic geometries, ranging from theoretical predictions over fabrication to characterization using integral means as well as advanced magnetic tomography, will be reviewed. Theoretical works predict a curvature-induced effective anisotropy and effective Dzyaloshinskii-Moriya interaction resulting in a vast of novel effects including magnetochiral effects (chirality symmetry breaking) and topologically induced magnetization patterning. The remarkable development of nanotechnology, e.g. preparation of high-quality extended thin films, nanowires and frameworks via chemical and physical deposition as well as 3D nano printing, has granted first insights into the fundamental properties of 3D shaped magnetic objects. Optimizing magnetic and structural properties of these novel 3D architectures demands new investigation methods, particularly those based on vector tomographic imaging. Magnetic neutron tomography and electron-based 3D imaging, such as electron holography and vector field electron tomography, are well-established techniques to investigate macroscopic and nanoscopic samples, respectively. At the mesoscale, the curved objects can be investigated using the novel method of magnetic X-ray tomography. In spite of experimental challenges to address the appealing theoretical predictions of curvature-induced effects, those 3D magnetic architectures have already proven their application potential for life sciences, targeted delivery, realization of 3D spin-wave filters, and magneto-encephalography devices, to name just a few. DOE BES MSED (DE-AC02-05-CH11231).

The Topological Panorama Camera: A New Tool for Teaching Concepts Related to Space and Time.

ERIC Educational Resources Information Center

Gelphman, Janet L.; And Others

1992-01-01

Included are the description, operating characteristics, uses, and future plans for the Topological Panorama Camera, which is an experimental, robotic photographic device capable of producing visual renderings of the mathematical characteristics of an equation in terms of position changes of an object or in terms of the shape of the space…

Probing the Topological Properties of Complex Networks Modeling Short Written Texts

PubMed Central

Amancio, Diego R.

2015-01-01

In recent years, graph theory has been widely employed to probe several language properties. More specifically, the so-called word adjacency model has been proven useful for tackling several practical problems, especially those relying on textual stylistic analysis. The most common approach to treat texts as networks has simply considered either large pieces of texts or entire books. This approach has certainly worked well—many informative discoveries have been made this way—but it raises an uncomfortable question: could there be important topological patterns in small pieces of texts? To address this problem, the topological properties of subtexts sampled from entire books was probed. Statistical analyses performed on a dataset comprising 50 novels revealed that most of the traditional topological measurements are stable for short subtexts. When the performance of the authorship recognition task was analyzed, it was found that a proper sampling yields a discriminability similar to the one found with full texts. Surprisingly, the support vector machine classification based on the characterization of short texts outperformed the one performed with entire books. These findings suggest that a local topological analysis of large documents might improve its global characterization. Most importantly, it was verified, as a proof of principle, that short texts can be analyzed with the methods and concepts of complex networks. As a consequence, the techniques described here can be extended in a straightforward fashion to analyze texts as time-varying complex networks. PMID:25719799

Topological susceptibility from twisted mass fermions using spectral projectors and the gradient flow

NASA Astrophysics Data System (ADS)

Alexandrou, Constantia; Athenodorou, Andreas; Cichy, Krzysztof; Constantinou, Martha; Horkel, Derek P.; Jansen, Karl; Koutsou, Giannis; Larkin, Conor

2018-04-01

We compare lattice QCD determinations of topological susceptibility using a gluonic definition from the gradient flow and a fermionic definition from the spectral-projector method. We use ensembles with dynamical light, strange and charm flavors of maximally twisted mass fermions. For both definitions of the susceptibility we employ ensembles at three values of the lattice spacing and several quark masses at each spacing. The data are fitted to chiral perturbation theory predictions with a discretization term to determine the continuum chiral condensate in the massless limit and estimate the overall discretization errors. We find that both approaches lead to compatible results in the continuum limit, but the gluonic ones are much more affected by cutoff effects. This finally yields a much smaller total error in the spectral-projector results. We show that there exists, in principle, a value of the spectral cutoff which would completely eliminate discretization effects in the topological susceptibility.

Topology assisted self-organization of colloidal nanoparticles: application to 2D large-scale nanomastering.

PubMed

Kadiri, Hind; Kostcheev, Serguei; Turover, Daniel; Salas-Montiel, Rafael; Nomenyo, Komla; Gokarna, Anisha; Lerondel, Gilles

2014-01-01

Our aim was to elaborate a novel method for fully controllable large-scale nanopatterning. We investigated the influence of the surface topology, i.e., a pre-pattern of hydrogen silsesquioxane (HSQ) posts, on the self-organization of polystyrene beads (PS) dispersed over a large surface. Depending on the post size and spacing, long-range ordering of self-organized polystyrene beads is observed wherein guide posts were used leading to single crystal structure. Topology assisted self-organization has proved to be one of the solutions to obtain large-scale ordering. Besides post size and spacing, the colloidal concentration and the nature of solvent were found to have a significant effect on the self-organization of the PS beads. Scanning electron microscope and associated Fourier transform analysis were used to characterize the morphology of the ordered surfaces. Finally, the production of silicon molds is demonstrated by using the beads as a template for dry etching.

Asymptotically locally Euclidean/Kaluza-Klein stationary vacuum black holes in five dimensions

NASA Astrophysics Data System (ADS)

Khuri, Marcus; Weinstein, Gilbert; Yamada, Sumio

2018-05-01

We produce new examples, both explicit and analytical, of bi-axisymmetric stationary vacuum black holes in five dimensions. A novel feature of these solutions is that they are asymptotically locally Euclidean, in which spatial cross-sections at infinity have lens space L(p,q) topology, or asymptotically Kaluza-Klein so that spatial cross-sections at infinity are topologically S^1× S^2. These are nondegenerate black holes of cohomogeneity 2, with any number of horizon components, where the horizon cross-section topology is any one of the three admissible types: S^3, S^1× S^2, or L(p,q). Uniqueness of these solutions is also established. Our method is to solve the relevant harmonic map problem with prescribed singularities, having target symmetric space SL(3,{R})/SO(3). In addition, we analyze the possibility of conical singularities and find a large family for which geometric regularity is guaranteed.

Space station common module power system network topology and hardware development

NASA Technical Reports Server (NTRS)

Landis, D. M.

1985-01-01

Candidate power system newtork topologies for the space station common module are defined and developed and the necessary hardware for test and evaluation is provided. Martin Marietta's approach to performing the proposed program is presented. Performance of the tasks described will assure systematic development and evaluation of program results, and will provide the necessary management tools, visibility, and control techniques for performance assessment. The plan is submitted in accordance with the data requirements given and includes a comprehensive task logic flow diagram, time phased manpower requirements, a program milestone schedule, and detailed descriptions of each program task.

Projective mappings and dimensions of vector spaces of three types of Killing-Yano tensors on pseudo Riemannian manifolds of constant curvature

NASA Astrophysics Data System (ADS)

Mikeš, Josef; Stepanov, Sergey; Hinterleitner, Irena

2012-07-01

In our paper we have determined the dimension of the space of conformal Killing-Yano tensors and the dimensions of its two subspaces of closed conformal Killing-Yano and Killing-Yano tensors on pseudo Riemannian manifolds of constant curvature. This result is a generalization of well known results on sharp upper bounds of the dimensions of the vector spaces of conformal Killing-Yano, Killing-Yano and concircular vector fields on pseudo Riemannian manifolds of constant curvature.

Energy Dissipation of Rayleigh Waves due to Absorption Along the Path by the Use of Finite Element Method

DTIC Science & Technology

1979-07-31

3 x 3 t Strain vector a ij,j Space derivative of the stress tensor Fi Force vector per unit volume o Density x CHAPTER III F Total force K Stiffness...matrix 6Vector displacements M Mass matrix B Space operating matrix DO Matrix moduli 2 x 3 DZ Operating matrix in Z direction N Matrix of shape...dissipating medium the deformation of a solid is a function of time, temperature and space . Creep phenomenon is a deformation process in which there is

The Sequential Implementation of Array Processors when there is Directional Uncertainty

DTIC Science & Technology

1975-08-01

University of Washington kindly supplied office space and ccputing facilities. -The author hat, benefited greatly from discussions with several other...if i Q- inverse of Q I L general observation space R general vector of observation _KR general observation vector of dimension K Exiv] "Tf -- ’ -"-T’T...7" i ’i ’:"’ - ’ ; ’ ’ ’ ’ ’ ’" ’"- Glossary of Symbols (continued) R. ith observation 1 Rm real vector space of dimension m R(T) autocorrelation

Topological nodal-line fermions in spin-orbit metal PbTaSe2

DOE PAGES

Bian, Guang; Chang, Tay-Rong; Sankar, Raman; ...

2016-02-02

Here we discuss how topological semimetals can support one-dimensional Fermi lines or zero-dimensional Weyl points in momentum space, where the valence and conduction bands touch. While the degeneracy points in Weyl semimetals are robust against any perturbation that preserves translational symmetry, nodal lines require protection by additional crystalline symmetries such as mirror reflection. Here we report, based on a systematic theoretical study and a detailed experimental characterization, the existence of topological nodal-line states in the non-centrosymmetric compound PbTaSe 2 with strong spin-orbit coupling. Remarkably, the spin-orbit nodal lines in PbTaSe 2 are not only protected by the reflection symmetry butmore » also characterized by an integer topological invariant. Our detailed angle-resolved photoemission measurements, first-principles simulations and theoretical topological analysis illustrate the physical mechanism underlying the formation of the topological nodal-line states and associated surface states for the first time, thus paving the way towards exploring the exotic properties of the topological nodal-line fermions in condensed matter systems.« less

Phase coherent transport in hybrid superconductor-topological insulator devices

NASA Astrophysics Data System (ADS)

Finck, Aaron

2015-03-01

Heterostructures of superconductors and topological insulators are predicted to host unusual zero energy bound states known as Majorana fermions, which can robustly store and process quantum information. Here, I will discuss our studies of such heterostructures through phase-coherent transport, which can act as a unique probe of Majorana fermions. We have extensively explored topological insulator Josephson junctions through SQUID and single-junction diffraction patterns, whose unusual behavior give evidence for low-energy Andreev bound states. In topological insulator devices with closely spaced normal and superconducting leads, we observe prominent Fabry-Perot oscillations, signifying gate-tunable, quasi-ballistic transport that can elegantly interact with Andreev reflection. Superconducting disks deposited on the surface of a topological insulator generate Aharonov-Bohm-like oscillations, giving evidence for unusual states lying near the interface between the superconductor and topological insulator surface. Our results point the way towards sophisticated interferometers that can detect and read out the state of Majorana fermions in topological systems. This work was done in collaboration with Cihan Kurter, Yew San Hor, and Dale Van Harlingen. We acknowledge funding from Microsoft Project Q.

Amorphous topological insulators constructed from random point sets

NASA Astrophysics Data System (ADS)

Mitchell, Noah P.; Nash, Lisa M.; Hexner, Daniel; Turner, Ari M.; Irvine, William T. M.

2018-04-01

The discovery that the band structure of electronic insulators may be topologically non-trivial has revealed distinct phases of electronic matter with novel properties1,2. Recently, mechanical lattices have been found to have similarly rich structure in their phononic excitations3,4, giving rise to protected unidirectional edge modes5-7. In all of these cases, however, as well as in other topological metamaterials3,8, the underlying structure was finely tuned, be it through periodicity, quasi-periodicity or isostaticity. Here we show that amorphous Chern insulators can be readily constructed from arbitrary underlying structures, including hyperuniform, jammed, quasi-crystalline and uniformly random point sets. While our findings apply to mechanical and electronic systems alike, we focus on networks of interacting gyroscopes as a model system. Local decorations control the topology of the vibrational spectrum, endowing amorphous structures with protected edge modes—with a chirality of choice. Using a real-space generalization of the Chern number, we investigate the topology of our structures numerically, analytically and experimentally. The robustness of our approach enables the topological design and self-assembly of non-crystalline topological metamaterials on the micro and macro scale.

Two-dimensional topological photonic systems

NASA Astrophysics Data System (ADS)

Sun, Xiao-Chen; He, Cheng; Liu, Xiao-Ping; Lu, Ming-Hui; Zhu, Shi-Ning; Chen, Yan-Feng

2017-09-01

The topological phase of matter, originally proposed and first demonstrated in fermionic electronic systems, has drawn considerable research attention in the past decades due to its robust transport of edge states and its potential with respect to future quantum information, communication, and computation. Recently, searching for such a unique material phase in bosonic systems has become a hot research topic worldwide. So far, many bosonic topological models and methods for realizing them have been discovered in photonic systems, acoustic systems, mechanical systems, etc. These discoveries have certainly yielded vast opportunities in designing material phases and related properties in the topological domain. In this review, we first focus on some of the representative photonic topological models and employ the underlying Dirac model to analyze the edge states and geometric phase. On the basis of these models, three common types of two-dimensional topological photonic systems are discussed: 1) photonic quantum Hall effect with broken time-reversal symmetry; 2) photonic topological insulator and the associated pseudo-time-reversal symmetry-protected mechanism; 3) time/space periodically modulated photonic Floquet topological insulator. Finally, we provide a summary and extension of this emerging field, including a brief introduction to the Weyl point in three-dimensional systems.

Finite energy quantization on a topology changing spacetime

NASA Astrophysics Data System (ADS)

Krasnikov, S.

2016-08-01

The "trousers" spacetime is a pair of flat two-dimensional cylinders ("legs") merging into a single one ("trunk"). In spite of its simplicity this spacetime has a few features (including, in particular, a naked singularity in the "crotch") each of which is presumably unphysical, but for none of which a mechanism is known able to prevent its occurrence. Therefore, it is interesting and important to study the behavior of the quantum fields in such a space. Anderson and DeWitt were the first to consider the free scalar field in the trousers spacetime. They argued that the crotch singularity produces an infinitely bright flash, which was interpreted as evidence that the topology of space is dynamically preserved. Similar divergencies were later discovered by Manogue, Copeland, and Dray who used a more exotic quantization scheme. Later yet the same result obtained within a somewhat different approach led Sorkin to the conclusion that the topological transition in question is suppressed in quantum gravity. In this paper I show that the Anderson-DeWitt divergence is an artifact of their choice of the Fock space. By choosing a different one-particle Hilbert space one gets a quantum state in which the components of the stress-energy tensor (SET) are bounded in the frame of a free-falling observer.

Quantum Entanglement and the Topological Order of Fractional Hall States

NASA Astrophysics Data System (ADS)

Rezayi, Edward

2015-03-01

Fractional quantum Hall states or, more generally, topological phases of matter defy Landau classification based on order parameter and broken symmetry. Instead they have been characterized by their topological order. Quantum information concepts, such as quantum entanglement, appear to provide the most efficient method of detecting topological order solely from the knowledge of the ground state wave function. This talk will focus on real-space bi-partitioning of quantum Hall states and will present both exact diagonalization and quantum Monte Carlo studies of topological entanglement entropy in various geometries. Results on the torus for non-contractible cuts are quite rich and, through the use of minimum entropy states, yield the modular S-matrix and hence uniquely determine the topological order, as shown in recent literature. Concrete examples of minimum entropy states from known quantum Hall wave functions and their corresponding quantum numbers, used in exact diagonalizations, will be given. In collaboration with Clare Abreu and Raul Herrera. Supported by DOE Grant DE-SC0002140.

Capabilities of software "Vector-M" for a diagnostics of the ionosphere state from auroral emissions images and plasma characteristics from the different orbits as a part of the system of control of space weather

NASA Astrophysics Data System (ADS)

Avdyushev, V.; Banshchikova, M.; Chuvashov, I.; Kuzmin, A.

2017-09-01

In the paper are presented capabilities of software "Vector-M" for a diagnostics of the ionosphere state from auroral emissions images and plasma characteristics from the different orbits as a part of the system of control of space weather. The software "Vector-M" is developed by the celestial mechanics and astrometry department of Tomsk State University in collaboration with Space Research Institute (Moscow) and Central Aerological Observatory of Russian Federal Service for Hydrometeorology and Environmental Monitoring. The software "Vector-M" is intended for calculation of attendant geophysical and astronomical information for the centre of mass of the spacecraft and the space of observations in the experiment with auroral imager Aurovisor-VIS/MP in the orbit of the perspective Meteor-MP spacecraft.

State-Space Formulation for Circuit Analysis

ERIC Educational Resources Information Center

Martinez-Marin, T.

2010-01-01

This paper presents a new state-space approach for temporal analysis of electrical circuits. The method systematically obtains the state-space formulation of nondegenerate linear networks without using concepts of topology. It employs nodal/mesh systematic analysis to reduce the number of undesired variables. This approach helps students to…

Black holes in quasi-topological gravity and conformal couplings

NASA Astrophysics Data System (ADS)

Chernicoff, Mariano; Fierro, Octavio; Giribet, Gaston; Oliva, Julio

2017-02-01

Lovelock theory of gravity provides a tractable model to investigate the effects of higher-curvature terms in the context of AdS/CFT. Yielding second order, ghost-free field equations, this theory represents a minimal setup in which higher-order gravitational couplings in asymptotically Anti-de Sitter (AdS) spaces, including black holes, can be solved analytically. This however has an obvious limitation as in dimensions lower than seven, the contribution from cubic or higher curvature terms is merely topological. Therefore, in order to go beyond quadratic order and study higher terms in AdS5 analytically, one is compelled to look for other toy models. One such model is the so-called quasi-topological gravity, which, despite being a higher-derivative theory, provides a tractable setup with R 3 and R 4 terms. In this paper, we investigate AdS5 black holes in quasi-topological gravity. We consider the theory conformally coupled to matter and in presence of Abelian gauge fields. We show that charged black holes in AdS5 which, in addition, exhibit a backreaction of the matter fields on the geometry can be found explicitly in this theory. These solutions generalize the black hole solution of quasi-topological gravity and exist in a region of the parameter spaces consistent with the constraints coming from causality and other consistency conditions. They have finite conserved charges and exhibit non-trivial thermodynamical properties.

NUDTSNA at TREC 2015 Microblog Track: A Live Retrieval System Framework for Social Network based on Semantic Expansion and Quality Model

DTIC Science & Technology

2015-11-20

between tweets and profiles as follow, • TFIDF Score, which calculates the cosine similarity between a tweet and a profile in vector space model with...TFIDF weight of terms. Vector space model is a model which represents a document as a vector. Tweets and profiles can be expressed as vectors, ~ T = (t...gain(Tr i ) (13) where Tr is the returned tweet sets, gain() is the score func- tion for a tweet. Not interesting, spam/ junk tweets receive a gain of 0

Extending topological surgery to natural processes and dynamical systems.

PubMed

Antoniou, Stathis; Lambropoulou, Sofia

2017-01-01

Topological surgery is a mathematical technique used for creating new manifolds out of known ones. We observe that it occurs in natural phenomena where a sphere of dimension 0 or 1 is selected, forces are applied and the manifold in which they occur changes type. For example, 1-dimensional surgery happens during chromosomal crossover, DNA recombination and when cosmic magnetic lines reconnect, while 2-dimensional surgery happens in the formation of tornadoes, in the phenomenon of Falaco solitons, in drop coalescence and in the cell mitosis. Inspired by such phenomena, we introduce new theoretical concepts which enhance topological surgery with the observed forces and dynamics. To do this, we first extend the formal definition to a continuous process caused by local forces. Next, for modeling phenomena which do not happen on arcs or surfaces but are 2-dimensional or 3-dimensional, we fill in the interior space by defining the notion of solid topological surgery. We further introduce the notion of embedded surgery in S3 for modeling phenomena which involve more intrinsically the ambient space, such as the appearance of knotting in DNA and phenomena where the causes and effect of the process lies beyond the initial manifold, such as the formation of black holes. Finally, we connect these new theoretical concepts with a dynamical system and we present it as a model for both 2-dimensional 0-surgery and natural phenomena exhibiting a 'hole drilling' behavior. We hope that through this study, topology and dynamics of many natural phenomena, as well as topological surgery itself, will be better understood.

Extending topological surgery to natural processes and dynamical systems

PubMed Central

Antoniou, Stathis; Lambropoulou, Sofia

2017-01-01

Topological surgery is a mathematical technique used for creating new manifolds out of known ones. We observe that it occurs in natural phenomena where a sphere of dimension 0 or 1 is selected, forces are applied and the manifold in which they occur changes type. For example, 1-dimensional surgery happens during chromosomal crossover, DNA recombination and when cosmic magnetic lines reconnect, while 2-dimensional surgery happens in the formation of tornadoes, in the phenomenon of Falaco solitons, in drop coalescence and in the cell mitosis. Inspired by such phenomena, we introduce new theoretical concepts which enhance topological surgery with the observed forces and dynamics. To do this, we first extend the formal definition to a continuous process caused by local forces. Next, for modeling phenomena which do not happen on arcs or surfaces but are 2-dimensional or 3-dimensional, we fill in the interior space by defining the notion of solid topological surgery. We further introduce the notion of embedded surgery in S3 for modeling phenomena which involve more intrinsically the ambient space, such as the appearance of knotting in DNA and phenomena where the causes and effect of the process lies beyond the initial manifold, such as the formation of black holes. Finally, we connect these new theoretical concepts with a dynamical system and we present it as a model for both 2-dimensional 0-surgery and natural phenomena exhibiting a ‘hole drilling’ behavior. We hope that through this study, topology and dynamics of many natural phenomena, as well as topological surgery itself, will be better understood. PMID:28915271

Trends in space activities in 2014: The significance of the space activities of governments

NASA Astrophysics Data System (ADS)

Paikowsky, Deganit; Baram, Gil; Ben-Israel, Isaac

2016-01-01

This article addresses the principal events of 2014 in the field of space activities, and extrapolates from them the primary trends that can be identified in governmental space activities. In 2014, global space activities centered on two vectors. The first was geopolitical, and the second relates to the matrix between increasing commercial space activities and traditional governmental space activities. In light of these two vectors, the article outlines and analyzes trends of space exploration, human spaceflights, industry and technology, cooperation versus self-reliance, and space security and sustainability. It also reviews the space activities of the leading space-faring nations.

Strain-induced topological magnon phase transitions: applications to kagome-lattice ferromagnets

NASA Astrophysics Data System (ADS)

Owerre, S. A.

2018-06-01

A common feature of topological insulators is that they are characterized by topologically invariant quantity such as the Chern number and the index. This quantity distinguishes a nontrivial topological system from a trivial one. A topological phase transition may occur when there are two topologically distinct phases, and it is usually defined by a gap closing point where the topologically invariant quantity is ill-defined. In this paper, we show that the magnon bands in the strained (distorted) kagome-lattice ferromagnets realize an example of a topological magnon phase transition in the realistic parameter regime of the system. When spin–orbit coupling (SOC) is neglected (i.e. no Dzyaloshinskii–Moriya interaction), we show that all three magnon branches are dispersive with no flat band, and there exists a critical point where tilted Dirac and semi-Dirac point coexist in the magnon spectra. The critical point separates two gapless magnon phases as opposed to the usual phase transition. Upon the inclusion of SOC, we realize a topological magnon phase transition point at the critical strain , where D and J denote the perturbative SOC and the Heisenberg spin exchange interaction respectively. It separates two distinct topological magnon phases with different Chern numbers for and for . The associated anomalous thermal Hall conductivity develops an abrupt change at , due to the divergence of the Berry curvature in momentum space. The proposed topological magnon phase transition is experimentally feasible by applying external perturbations such as uniaxial strain or pressure.

Topographic Independent Component Analysis reveals random scrambling of orientation in visual space

PubMed Central

Martinez-Garcia, Marina; Martinez, Luis M.

2017-01-01

Neurons at primary visual cortex (V1) in humans and other species are edge filters organized in orientation maps. In these maps, neurons with similar orientation preference are clustered together in iso-orientation domains. These maps have two fundamental properties: (1) retinotopy, i.e. correspondence between displacements at the image space and displacements at the cortical surface, and (2) a trade-off between good coverage of the visual field with all orientations and continuity of iso-orientation domains in the cortical space. There is an active debate on the origin of these locally continuous maps. While most of the existing descriptions take purely geometric/mechanistic approaches which disregard the network function, a clear exception to this trend in the literature is the original approach of Hyvärinen and Hoyer based on infomax and Topographic Independent Component Analysis (TICA). Although TICA successfully addresses a number of other properties of V1 simple and complex cells, in this work we question the validity of the orientation maps obtained from TICA. We argue that the maps predicted by TICA can be analyzed in the retinal space, and when doing so, it is apparent that they lack the required continuity and retinotopy. Here we show that in the orientation maps reported in the TICA literature it is easy to find examples of violation of the continuity between similarly tuned mechanisms in the retinal space, which suggest a random scrambling incompatible with the maps in primates. The new experiments in the retinal space presented here confirm this guess: TICA basis vectors actually follow a random salt-and-pepper organization back in the image space. Therefore, the interesting clusters found in the TICA topology cannot be interpreted as the actual cortical orientation maps found in cats, primates or humans. In conclusion, Topographic ICA does not reproduce cortical orientation maps. PMID:28640816

Topographic Independent Component Analysis reveals random scrambling of orientation in visual space.

PubMed

Martinez-Garcia, Marina; Martinez, Luis M; Malo, Jesús

2017-01-01

Neurons at primary visual cortex (V1) in humans and other species are edge filters organized in orientation maps. In these maps, neurons with similar orientation preference are clustered together in iso-orientation domains. These maps have two fundamental properties: (1) retinotopy, i.e. correspondence between displacements at the image space and displacements at the cortical surface, and (2) a trade-off between good coverage of the visual field with all orientations and continuity of iso-orientation domains in the cortical space. There is an active debate on the origin of these locally continuous maps. While most of the existing descriptions take purely geometric/mechanistic approaches which disregard the network function, a clear exception to this trend in the literature is the original approach of Hyvärinen and Hoyer based on infomax and Topographic Independent Component Analysis (TICA). Although TICA successfully addresses a number of other properties of V1 simple and complex cells, in this work we question the validity of the orientation maps obtained from TICA. We argue that the maps predicted by TICA can be analyzed in the retinal space, and when doing so, it is apparent that they lack the required continuity and retinotopy. Here we show that in the orientation maps reported in the TICA literature it is easy to find examples of violation of the continuity between similarly tuned mechanisms in the retinal space, which suggest a random scrambling incompatible with the maps in primates. The new experiments in the retinal space presented here confirm this guess: TICA basis vectors actually follow a random salt-and-pepper organization back in the image space. Therefore, the interesting clusters found in the TICA topology cannot be interpreted as the actual cortical orientation maps found in cats, primates or humans. In conclusion, Topographic ICA does not reproduce cortical orientation maps.

A nonrecursive order N preconditioned conjugate gradient: Range space formulation of MDOF dynamics

NASA Technical Reports Server (NTRS)

Kurdila, Andrew J.

1990-01-01

While excellent progress has been made in deriving algorithms that are efficient for certain combinations of system topologies and concurrent multiprocessing hardware, several issues must be resolved to incorporate transient simulation in the control design process for large space structures. Specifically, strategies must be developed that are applicable to systems with numerous degrees of freedom. In addition, the algorithms must have a growth potential in that they must also be amenable to implementation on forthcoming parallel system architectures. For mechanical system simulation, this fact implies that algorithms are required that induce parallelism on a fine scale, suitable for the emerging class of highly parallel processors; and transient simulation methods must be automatically load balancing for a wider collection of system topologies and hardware configurations. These problems are addressed by employing a combination range space/preconditioned conjugate gradient formulation of multi-degree-of-freedom dynamics. The method described has several advantages. In a sequential computing environment, the method has the features that: by employing regular ordering of the system connectivity graph, an extremely efficient preconditioner can be derived from the 'range space metric', as opposed to the system coefficient matrix; because of the effectiveness of the preconditioner, preliminary studies indicate that the method can achieve performance rates that depend linearly upon the number of substructures, hence the title 'Order N'; and the method is non-assembling. Furthermore, the approach is promising as a potential parallel processing algorithm in that the method exhibits a fine parallel granularity suitable for a wide collection of combinations of physical system topologies/computer architectures; and the method is easily load balanced among processors, and does not rely upon system topology to induce parallelism.

Scaling theory of topological phase transitions

NASA Astrophysics Data System (ADS)

Chen, Wei

2016-02-01

Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may be Berry curvature, Berry connection, or other quantities depending on the system. Akin to stretching a messy string to reveal the number of knots it contains, a scaling procedure is proposed for the curvature function in inversion symmetric systems, from which the topological phase transition can be identified from the flow of the driving energy parameters that control the topology (hopping, chemical potential, etc) under scaling. At an infinitesimal operation, one obtains the renormalization group (RG) equations for the driving energy parameters. A length scale defined from the curvature function near the gap-closing momentum is suggested to characterize the scale invariance at critical points and fixed points, and displays a universal critical behavior in a variety of systems examined.

Formation stability analysis of unmanned multi-vehicles under interconnection topologies

NASA Astrophysics Data System (ADS)

Yang, Aolei; Naeem, Wasif; Fei, Minrui

2015-04-01

In this paper, the overall formation stability of an unmanned multi-vehicle is mathematically presented under interconnection topologies. A novel definition of formation error is first given and followed by the proposed formation stability hypothesis. Based on this hypothesis, a unique extension-decomposition-aggregation scheme is then employed to support the stability analysis for the overall multi-vehicle formation under a mesh topology. It is proved that the overall formation control system consisting of N number of nonlinear vehicles is not only asymptotically stable, but also exponentially stable in the sense of Lyapunov within a neighbourhood of the desired formation. This technique is shown to be applicable for a mesh topology but is equally applicable for other topologies. A simulation study of the formation manoeuvre of multiple Aerosonde UAVs (unmanned aerial vehicles), in 3-D space, is finally carried out verifying the achieved formation stability result.

Spin-orbit coupling in ultracold Fermi gases of 173Yb atoms

NASA Astrophysics Data System (ADS)

Song, Bo; He, Chengdong; Hajiyev, Elnur; Ren, Zejian; Seo, Bojeong; Cai, Geyue; Amanov, Dovran; Zhang, Shanchao; Jo, Gyu-Boong

2017-04-01

Synthetic spin-orbit coupling (SOC) in cold atoms opens an intriguing new way to probe nontrivial topological orders beyond natural conditions. Here, we report the realization of the SOC physics both in a bulk system and in an optical lattice. First, we demonstrate two hallmarks induced from SOC in a bulk system, spin dephasing in the Rabi oscillation and asymmetric atomic distribution in the momentum space respectively. Then we describe the observation of non-trivial spin textures and the determination of the topological phase transition in a spin-dependent optical lattice dressed by the periodic Raman field. Furthermore, we discuss the quench dynamics between topological and trivial states by suddenly changing the band topology. Our work paves a new way to study non-equilibrium topological states in a controlled manner. Funded by Croucher Foundation and Research Grants Council (RGC) of Hong Kong (Project ECS26300014, GRF16300215, GRF16311516, and Croucher Innovation Grants).

Observation of topological valley transport of sound in sonic crystals

NASA Astrophysics Data System (ADS)

Lu, Jiuyang; Qiu, Chunyin; Ye, Liping; Fan, Xiying; Ke, Manzhu; Zhang, Fan; Liu, Zhengyou

2017-04-01

The concept of valley pseudospin, labelling quantum states of energy extrema in momentum space, is attracting attention because of its potential as a new type of information carrier. Compared with the non-topological bulk valley transport, realized soon after predictions, topological valley transport in domain walls is extremely challenging owing to the inter-valley scattering inevitably induced by atomic-scale imperfections--but an electronic signature was recently observed in bilayer graphene. Here, we report the experimental observation of topological valley transport of sound in sonic crystals. The macroscopic nature of sonic crystals permits a flexible and accurate design of domain walls. In addition to a direct visualization of the valley-selective edge modes through spatial scanning of the sound field, reflection immunity is observed in sharply curved interfaces. The topologically protected interface transport of sound, strikingly different from that in traditional sound waveguides, may serve as the basis for designing devices with unconventional functions.

Three-component fermions with surface Fermi arcs in tungsten carbide

NASA Astrophysics Data System (ADS)

Ma, J.-Z.; He, J.-B.; Xu, Y.-F.; Lv, B. Q.; Chen, D.; Zhu, W.-L.; Zhang, S.; Kong, L.-Y.; Gao, X.; Rong, L.-Y.; Huang, Y.-B.; Richard, P.; Xi, C.-Y.; Choi, E. S.; Shao, Y.; Wang, Y.-L.; Gao, H.-J.; Dai, X.; Fang, C.; Weng, H.-M.; Chen, G.-F.; Qian, T.; Ding, H.

2018-04-01

Topological Dirac and Weyl semimetals not only host quasiparticles analogous to the elementary fermionic particles in high-energy physics, but also have a non-trivial band topology manifested by gapless surface states, which induce exotic surface Fermi arcs1,2. Recent advances suggest new types of topological semimetal, in which spatial symmetries protect gapless electronic excitations without high-energy analogues3-11. Here, using angle-resolved photoemission spectroscopy, we observe triply degenerate nodal points near the Fermi level of tungsten carbide with space group P 6 ¯m 2 (no. 187), in which the low-energy quasiparticles are described as three-component fermions distinct from Dirac and Weyl fermions. We further observe topological surface states, whose constant-energy contours constitute pairs of `Fermi arcs' connecting to the surface projections of the triply degenerate nodal points, proving the non-trivial topology of the newly identified semimetal state.

Gauging hidden symmetries in two dimensions

NASA Astrophysics Data System (ADS)

Samtleben, Henning; Weidner, Martin

2007-08-01

We initiate the systematic construction of gauged matter-coupled supergravity theories in two dimensions. Subgroups of the affine global symmetry group of toroidally compactified supergravity can be gauged by coupling vector fields with minimal couplings and a particular topological term. The gauge groups typically include hidden symmetries that are not among the target-space isometries of the ungauged theory. The gaugings constructed in this paper are described group-theoretically in terms of a constant embedding tensor subject to a number of constraints which parametrizes the different theories and entirely encodes the gauged Lagrangian. The prime example is the bosonic sector of the maximally supersymmetric theory whose ungauged version admits an affine fraktur e9 global symmetry algebra. The various parameters (related to higher-dimensional p-form fluxes, geometric and non-geometric fluxes, etc.) which characterize the possible gaugings, combine into an embedding tensor transforming in the basic representation of fraktur e9. This yields an infinite-dimensional class of maximally supersymmetric theories in two dimensions. We work out and discuss several examples of higher-dimensional origin which can be systematically analyzed using the different gradings of fraktur e9.

Robot Acquisition of Active Maps Through Teleoperation and Vector Space Analysis

NASA Technical Reports Server (NTRS)

Peters, Richard Alan, II

2003-01-01

The work performed under this contract was in the area of intelligent robotics. The problem being studied was the acquisition of intelligent behaviors by a robot. The method was to acquire action maps that describe tasks as sequences of reflexive behaviors. Action maps (a.k.a. topological maps) are graphs whose nodes represent sensorimotor states and whose edges represent the motor actions that cause the robot to proceed from one state to the next. The maps were acquired by the robot after being teleoperated or otherwise guided by a person through a task several times. During a guided task, the robot records all its sensorimotor signals. The signals from several task trials are partitioned into episodes of static behavior. The corresponding episodes from each trial are averaged to produce a task description as a sequence of characteristic episodes. The sensorimotor states that indicate episode boundaries become the nodes, and the static behaviors, the edges. It was demonstrated that if compound maps are constructed from a set of tasks then the robot can perform new tasks in which it was never explicitly trained.

Phase separation in living micellar networks

NASA Astrophysics Data System (ADS)

Cristobal, G.; Rouch, J.; Curély, J.; Panizza, P.

We present a lattice model based on two n→0 spin vectors, capable of treating the thermodynamics of living networks in micellar solutions at any surfactant concentration. We establish an isomorphism between the coupling constants in the two spin vector Hamiltonian and the surfactant energies involved in the micellar situation. Solving this Hamiltonian in the mean-field approximation allows one to calculate osmotic pressure, aggregation number, free end and cross-link densities at any surfactant concentration. We derive a phase diagram, including changes in topology such as the transition between spheres and rods and between saturated and unsaturated networks. A phase separation can be found between a saturated network and a dilute solution composed of long flexible micelles or a saturated network and a solution of spherical micelles.

Unveiling the photonic spin Hall effect of freely propagating fan-shaped cylindrical vector vortex beams.

PubMed

Zhang, Yi; Li, Peng; Liu, Sheng; Zhao, Jianlin

2015-10-01

An intriguing photonic spin Hall effect (SHE) for a freely propagating fan-shaped cylindrical vector (CV) vortex beam in a paraxial situation is theoretically and experimentally studied. A developed model to describe this kind of photonic SHE is proposed based on angular spectrum diffraction theory. With this model, the close dependences of spin-dependent splitting on the azimuthal order of polarization, the topological charge of the spiral phase, and the propagation distance are accurately revealed. Furthermore, it is demonstrated that the asymmetric spin-dependent splitting of a fan-shaped CV beam can be consciously managed, even with a constant azimuthal order of polarization. Such a controllable photonic SHE is experimentally verified by measuring the Stokes parameters.

The SAMEX Vector Magnetograph: A Design Study for a Space-Based Solar Vector Magnetograph

NASA Technical Reports Server (NTRS)

Hagyard, M. J.; Gary, G. A.; West, E. A.

1988-01-01

This report presents the results of a pre-phase A study performed by the Marshall Space Flight Center (MSFC) for the Air Force Geophysics Laboratory (AFGL) to develop a design concept for a space-based solar vector magnetograph and hydrogen-alpha telescope. These are two of the core instruments for a proposed Air Force mission, the Solar Activities Measurement Experiments (SAMEX). This mission is designed to study the processes which give rise to activity in the solar atmosphere and to develop techniques for predicting solar activity and its effects on the terrestrial environment.

Gauss-Manin Connection in Disguise: Calabi-Yau Threefolds

NASA Astrophysics Data System (ADS)

Alim, Murad; Movasati, Hossein; Scheidegger, Emanuel; Yau, Shing-Tung

2016-06-01

We describe a Lie Algebra on the moduli space of non-rigid compact Calabi-Yau threefolds enhanced with differential forms and its relation to the Bershadsky-Cecotti-Ooguri-Vafa holomorphic anomaly equation. In particular, we describe algebraic topological string partition functions {{F}g^alg, g ≥ 1}, which encode the polynomial structure of holomorphic and non-holomorphic topological string partition functions. Our approach is based on Grothendieck's algebraic de Rham cohomology and on the algebraic Gauss-Manin connection. In this way, we recover a result of Yamaguchi-Yau and Alim-Länge in an algebraic context. Our proofs use the fact that the special polynomial generators defined using the special geometry of deformation spaces of Calabi-Yau threefolds correspond to coordinates on such a moduli space. We discuss the mirror quintic as an example.

Conformational and functional analysis of molecular dynamics trajectories by Self-Organising Maps

PubMed Central

2011-01-01

Background Molecular dynamics (MD) simulations are powerful tools to investigate the conformational dynamics of proteins that is often a critical element of their function. Identification of functionally relevant conformations is generally done clustering the large ensemble of structures that are generated. Recently, Self-Organising Maps (SOMs) were reported performing more accurately and providing more consistent results than traditional clustering algorithms in various data mining problems. We present a novel strategy to analyse and compare conformational ensembles of protein domains using a two-level approach that combines SOMs and hierarchical clustering. Results The conformational dynamics of the α-spectrin SH3 protein domain and six single mutants were analysed by MD simulations. The Cα's Cartesian coordinates of conformations sampled in the essential space were used as input data vectors for SOM training, then complete linkage clustering was performed on the SOM prototype vectors. A specific protocol to optimize a SOM for structural ensembles was proposed: the optimal SOM was selected by means of a Taguchi experimental design plan applied to different data sets, and the optimal sampling rate of the MD trajectory was selected. The proposed two-level approach was applied to single trajectories of the SH3 domain independently as well as to groups of them at the same time. The results demonstrated the potential of this approach in the analysis of large ensembles of molecular structures: the possibility of producing a topological mapping of the conformational space in a simple 2D visualisation, as well as of effectively highlighting differences in the conformational dynamics directly related to biological functions. Conclusions The use of a two-level approach combining SOMs and hierarchical clustering for conformational analysis of structural ensembles of proteins was proposed. It can easily be extended to other study cases and to conformational ensembles from other sources. PMID:21569575

Dirac oscillator interacting with a topological defect

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

Carvalho, J.; Furtado, C.; Moraes, F.

In this work we study the interaction problem of a Dirac oscillator with gravitational fields produced by topological defects. The energy levels of the relativistic oscillator in the cosmic string and in the cosmic dislocation space-times are sensible to curvature and torsion associated to these defects and are important evidence of the influence of the topology on this system. In the presence of a localized magnetic field the energy levels acquire a term associated with the Aharonov-Bohm effect. We obtain the eigenfunctions and eigenvalues and see that in the nonrelativistic limit some results known in standard quantum mechanics are reached.

Edge-entanglement spectrum correspondence in a nonchiral topological phase and Kramers-Wannier duality

NASA Astrophysics Data System (ADS)

Ho, Wen Wei; Cincio, Lukasz; Moradi, Heidar; Gaiotto, Davide; Vidal, Guifre

2015-03-01

In a system with chiral topological order, there is a remarkable correspondence between the edge and entanglement spectra: the low-energy spectrum of the system in the presence of a physical edge coincides with the lowest part of the entanglement spectrum (ES) across a virtual cut of the system into two parts, up to rescaling and shifting. This correspondence is believed to be due to the existence of protected gapless edge modes. In this paper, we explore whether the edge-entanglement spectrum correspondence extends to nonchiral topological phases, where there are no protected gapless edge modes. Specifically, we consider the Wen-plaquette model, which is equivalent to the Kitaev toric code model and has Z2 topological order (quantum double of Z2) . The unperturbed Wen-plaquette model displays an exact correspondence: both the edge and entanglement spectra within each topological sector a (a =1 ,⋯,4 ) are flat and equally degenerate. Here, we show, through a detailed microscopic calculation, that in the presence of generic local perturbations: (i) the effective degrees of freedom for both the physical edge and the entanglement cut consist of a (spin-1 /2 ) spin chain, with effective Hamiltonians Hedgea and Henta, respectively, both of which have a Z2 symmetry enforced by the bulk topological order; (ii) there is in general no match between the low-energy spectra of Hedgea and Henta, that is, there is no edge-ES correspondence. However, if supplement the Z2 topological order with a global symmetry (translational invariance along the edge/entanglement cut), i.e., by considering the Wen-plaquette model as a symmetry-enriched topological phase (SET), then there is a finite domain in Hamiltonian space in which both Hedgea and Henta realize the critical Ising model, whose low-energy effective theory is the c =1 /2 Ising CFT. This is achieved because the presence of the global symmetry implies that the effective degrees of freedom of both the edge and entanglement cut are governed by Kramers-Wannier self-dual Hamiltonians, in addition to them being Z2 symmetric, which is imposed by the topological order. Thus, by considering the Wen-plaquette model as a SET, the topological order in the bulk together with the translation invariance of the perturbations along the edge/cut imply an edge-ES correspondence at least in some finite domain in Hamiltonian space.

Detection of a sudden change of the field time series based on the Lorenz system.

PubMed

Da, ChaoJiu; Li, Fang; Shen, BingLu; Yan, PengCheng; Song, Jian; Ma, DeShan

2017-01-01

We conducted an exploratory study of the detection of a sudden change of the field time series based on the numerical solution of the Lorenz system. First, the time when the Lorenz path jumped between the regions on the left and right of the equilibrium point of the Lorenz system was quantitatively marked and the sudden change time of the Lorenz system was obtained. Second, the numerical solution of the Lorenz system was regarded as a vector; thus, this solution could be considered as a vector time series. We transformed the vector time series into a time series using the vector inner product, considering the geometric and topological features of the Lorenz system path. Third, the sudden change of the resulting time series was detected using the sliding t-test method. Comparing the test results with the quantitatively marked time indicated that the method could detect every sudden change of the Lorenz path, thus the method is effective. Finally, we used the method to detect the sudden change of the pressure field time series and temperature field time series, and obtained good results for both series, which indicates that the method can apply to high-dimension vector time series. Mathematically, there is no essential difference between the field time series and vector time series; thus, we provide a new method for the detection of the sudden change of the field time series.

Anisotropic fractal media by vector calculus in non-integer dimensional space

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2014-08-01

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

Classification of small lesions in dynamic breast MRI: Eliminating the need for precise lesion segmentation through spatio-temporal analysis of contrast enhancement over time.

PubMed

Nagarajan, Mahesh B; Huber, Markus B; Schlossbauer, Thomas; Leinsinger, Gerda; Krol, Andrzej; Wismüller, Axel

2013-10-01

Characterizing the dignity of breast lesions as benign or malignant is specifically difficult for small lesions; they don't exhibit typical characteristics of malignancy and are harder to segment since margins are harder to visualize. Previous attempts at using dynamic or morphologic criteria to classify small lesions (mean lesion diameter of about 1 cm) have not yielded satisfactory results. The goal of this work was to improve the classification performance in such small diagnostically challenging lesions while concurrently eliminating the need for precise lesion segmentation. To this end, we introduce a method for topological characterization of lesion enhancement patterns over time. Three Minkowski Functionals were extracted from all five post-contrast images of sixty annotated lesions on dynamic breast MRI exams. For each Minkowski Functional, topological features extracted from each post-contrast image of the lesions were combined into a high-dimensional texture feature vector. These feature vectors were classified in a machine learning task with support vector regression. For comparison, conventional Haralick texture features derived from gray-level co-occurrence matrices (GLCM) were also used. A new method for extracting thresholded GLCM features was also introduced and investigated here. The best classification performance was observed with Minkowski Functionals area and perimeter , thresholded GLCM features f8 and f9, and conventional GLCM features f4 and f6. However, both Minkowski Functionals and thresholded GLCM achieved such results without lesion segmentation while the performance of GLCM features significantly deteriorated when lesions were not segmented ( p < 0.05). This suggests that such advanced spatio-temporal characterization can improve the classification performance achieved in such small lesions, while simultaneously eliminating the need for precise segmentation.

Conformal Nets II: Conformal Blocks

NASA Astrophysics Data System (ADS)

Bartels, Arthur; Douglas, Christopher L.; Henriques, André

2017-08-01

Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction of the `bundle of conformal blocks', a representation of the mapping class groupoid of closed topological surfaces into the category of finite-dimensional projective Hilbert spaces. We also construct infinite-dimensional spaces of conformal blocks for topological surfaces with smooth boundary. We prove that the conformal blocks satisfy a factorization formula for gluing surfaces along circles, and an analogous formula for gluing surfaces along intervals. We use this interval factorization property to give a new proof of the modularity of the category of representations of a conformal net.

Bosonization of fermions coupled to topologically massive gravity

NASA Astrophysics Data System (ADS)

Fradkin, Eduardo; Moreno, Enrique F.; Schaposnik, Fidel A.

2014-03-01

We establish a duality between massive fermions coupled to topologically massive gravity (TMG) in d=3 space-time dimensions and a purely gravity theory which also will turn out to be a TMG theory but with different parameters: the original graviton mass in the TMG theory coupled to fermions picks up a contribution from fermion bosonization. We obtain explicit bosonization rules for the fermionic currents and for the energy-momentum tensor showing that the identifications do not depend explicitly on the parameters of the theory. These results are the gravitational analog of the results for 2+1 Abelian and non-Abelian bosonization in flat space-time.

Wigner flow reveals topological order in quantum phase space dynamics.

PubMed

Steuernagel, Ole; Kakofengitis, Dimitris; Ritter, Georg

2013-01-18

The behavior of classical mechanical systems is characterized by their phase portraits, the collections of their trajectories. Heisenberg's uncertainty principle precludes the existence of sharply defined trajectories, which is why traditionally only the time evolution of wave functions is studied in quantum dynamics. These studies are quite insensitive to the underlying structure of quantum phase space dynamics. We identify the flow that is the quantum analog of classical particle flow along phase portrait lines. It reveals hidden features of quantum dynamics and extra complexity. Being constrained by conserved flow winding numbers, it also reveals fundamental topological order in quantum dynamics that has so far gone unnoticed.

Combined-probability space and certainty or uncertainty relations for a finite-level quantum system

NASA Astrophysics Data System (ADS)

Sehrawat, Arun

2017-08-01

The Born rule provides a probability vector (distribution) with a quantum state for a measurement setting. For two settings, we have a pair of vectors from the same quantum state. Each pair forms a combined-probability vector that obeys certain quantum constraints, which are triangle inequalities in our case. Such a restricted set of combined vectors, called the combined-probability space, is presented here for a d -level quantum system (qudit). The combined space is a compact convex subset of a Euclidean space, and all its extreme points come from a family of parametric curves. Considering a suitable concave function on the combined space to estimate the uncertainty, we deliver an uncertainty relation by finding its global minimum on the curves for a qudit. If one chooses an appropriate concave (or convex) function, then there is no need to search for the absolute minimum (maximum) over the whole space; it will be on the parametric curves. So these curves are quite useful for establishing an uncertainty (or a certainty) relation for a general pair of settings. We also demonstrate that many known tight certainty or uncertainty relations for a qubit can be obtained with the triangle inequalities.

NBOD2- PROGRAM TO DERIVE AND SOLVE EQUATIONS OF MOTION FOR COUPLED N-BODY SYSTEMS

NASA Technical Reports Server (NTRS)

Frisch, H. P.

1994-01-01

The analysis of the dynamic characteristics of a complex system, such as a spacecraft or a robot, is usually best accomplished through the study of a simulation model. The simulation model must have the same dynamic characteristics as the complex system, while lending itself to mathematical quantification. The NBOD2 computer program was developed to aid in the analysis of spacecraft attitude dynamics. NBOD2 is a very general program that may be applied to a large class of problems involving coupled N-body systems. NBOD2 provides the dynamics analyst with the capability to automatically derive and numerically solve the equations of motion for any system that can be modeled as a topological tree of coupled rigid bodies, flexible bodies, point masses, and symmetrical momentum wheels. NBOD2 uses a topological tree model of the dynamic system to derive the vector-dyadic equations of motion for the system. The user builds this topological tree model by using rigid and flexible bodies, point masses, and symmetrical momentum wheels with appropriate connections. To insure that the relative motion between contiguous bodies is kinematically constrained, NBOD2 assumes that contiguous rigid and flexible bodies are connected by physically reliable 0, 1, 2, and 3-degrees-of-freedom gimbals. These gimbals prohibit relative translational motion, while permitting up to 3 degrees of relative rotational freedom at hinge points. Point masses may have 0, 1, 2, or 3-degrees of relative translational freedom, and symmetric momentum wheels may have a single degree of rotational freedom relative to the body in which they are imbedded. Flexible bodies may possess several degrees of vibrational freedom in addition to the degrees of freedom associated with the connection gimbals. Data concerning the natural modes and vibrations of the flexible bodies must be supplied by the user. NBOD2 combines the best features of the discrete-body approach and the nested body approach to reduce the topological tree to a complete set of nonlinear equations of motion in vector-dyadic form for the system being analyzed. NBOD2 can then numerically solve the equations of motion. Input to NBOD2 consists of a user-supplied description of the system to be modeled. The NBOD2 system includes an interactive, tutorial, input support program to aid the NBOD2 user in preparing input data. Output from NBOD2 consists of a listing of the complete set of nonlinear equations of motion in vector-dyadic form and any userspecified set of system state variables. The NBOD2 program is written in FORTRAN 77 for batch execution and has been implemented on a DEC VAX-11/780 computer. The NBOD2 program was developed in 1978 and last updated in 1982.

Topological superconductivity in an ultrathin, magnetically-doped topological insulator proximity coupled to a conventional superconductor

NASA Astrophysics Data System (ADS)

Kim, Youngseok; Philip, Timothy M.; Park, Moon Jip; Gilbert, Matthew J.; University of Illinois at Urbana; Champaign Team

As a promising candidate system to realize topological superconductivity (SC), 3D time-reversal invariant topological insulators (TI) proximity-coupled to s-wave superconductors have been intensively studied. Recent experiments on proximity-coupled TI have shown that superconductivity may be induced in ultrathin TI. One proposal to observe the topological SC in proximity-coupled ultrathin TI system is to add magnetic dopants to the TI. However, detailed study on the impact of the experimental parameters on possible topological phase is sparse. In this work, we investigate ultrathin, magnetically-doped, proximity-coupled TI in order to determine the experimentally relevant parameters needed to observe topological SC. We find that, due to the spin-momentum locked nature of the surface states in TI, the induced s-wave order parameter within the surface states persists even at large magnitudes of the Zeeman energy, allowing us to explore the system in parameter space. We elucidate the phase diagram as a function of: the hybridization gap, Zeeman energy, and chemical potential of the TI system. Our findings provide a useful guide in choosing relevant parameters to facilitate the observation of topological SC in thin film TI-superconductor hybrid systems. National Science Foundation (NSF) under Grant CAREER ECCS-1351871.

Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1 dimensions

NASA Astrophysics Data System (ADS)

Wen, Xiao-Gang

2017-05-01

We propose a generic construction of exactly soluble local bosonic models that realize various topological orders with gappable boundaries. In particular, we construct an exactly soluble bosonic model that realizes a (3+1)-dimensional [(3+1)D] Z2-gauge theory with emergent fermionic Kramers doublet. We show that the emergence of such a fermion will cause the nucleation of certain topological excitations in space-time without pin+ structure. The exactly soluble model also leads to a statistical transmutation in (3+1)D. In addition, we construct exactly soluble bosonic models that realize 2 types of time-reversal symmetry-enriched Z2 topological orders in 2+1 dimensions, and 20 types of simplest time-reversal symmetry-enriched topological (SET) orders which have only one nontrivial pointlike and stringlike topological excitation. Many physical properties of those topological states are calculated using the exactly soluble models. We find that some time-reversal SET orders have pointlike excitations that carry Kramers doublet, a fractionalized time-reversal symmetry. We also find that some Z2 SET orders have stringlike excitations that carry anomalous (nononsite) Z2 symmetry, which can be viewed as a fractionalization of Z2 symmetry on strings. Our construction is based on cochains and cocycles in algebraic topology, which is very versatile. In principle, it can also realize emergent topological field theory beyond the twisted gauge theory.

Floquet topological phases in a spin-1 /2 double kicked rotor

NASA Astrophysics Data System (ADS)

Zhou, Longwen; Gong, Jiangbin

2018-06-01

The double kicked rotor model is a physically realizable extension of the paradigmatic kicked rotor model in the study of quantum chaos. Even before the concept of Floquet topological phases became widely known, the discovery of the Hofstadter butterfly spectrum in the double kicked rotor model [J. Wang and J. Gong, Phys. Rev. A 77, 031405 (2008), 10.1103/PhysRevA.77.031405] already suggested the importance of periodic driving to the generation of Floquet topological matter. In this work, we explore Floquet topological phases of a double kicked rotor with an extra spin-1 /2 degree of freedom. The latter has been experimentally engineered in a quantum kicked rotor recently by loading 87Rb condensates into a periodically pulsed optical lattice. Theoretically, we found that under the on-resonance condition, the spin-1 /2 double kicked rotor admits rich topological phases due to the interplay between its external and internal degrees of freedom. Each of these topological phases is characterized by a pair of winding numbers, whose combination predicts the number of topologically protected zero and π -quasienergy edge states in the system. Topological phases with arbitrarily large winding numbers can be easily found by tuning the kicking strength. We discuss an experimental proposal to realize this model in kicked 87Rb condensates, and suggest detecting its topological invariants by measuring the mean chiral displacement in momentum space.

Computations of Unsteady Viscous Compressible Flows Using Adaptive Mesh Refinement in Curvilinear Body-fitted Grid Systems

NASA Technical Reports Server (NTRS)

Steinthorsson, E.; Modiano, David; Colella, Phillip

1994-01-01

A methodology for accurate and efficient simulation of unsteady, compressible flows is presented. The cornerstones of the methodology are a special discretization of the Navier-Stokes equations on structured body-fitted grid systems and an efficient solution-adaptive mesh refinement technique for structured grids. The discretization employs an explicit multidimensional upwind scheme for the inviscid fluxes and an implicit treatment of the viscous terms. The mesh refinement technique is based on the AMR algorithm of Berger and Colella. In this approach, cells on each level of refinement are organized into a small number of topologically rectangular blocks, each containing several thousand cells. The small number of blocks leads to small overhead in managing data, while their size and regular topology means that a high degree of optimization can be achieved on computers with vector processors.

Combinational Reasoning of Quantitative Fuzzy Topological Relations for Simple Fuzzy Regions

PubMed Central

Liu, Bo; Li, Dajun; Xia, Yuanping; Ruan, Jian; Xu, Lili; Wu, Huanyi

2015-01-01

In recent years, formalization and reasoning of topological relations have become a hot topic as a means to generate knowledge about the relations between spatial objects at the conceptual and geometrical levels. These mechanisms have been widely used in spatial data query, spatial data mining, evaluation of equivalence and similarity in a spatial scene, as well as for consistency assessment of the topological relations of multi-resolution spatial databases. The concept of computational fuzzy topological space is applied to simple fuzzy regions to efficiently and more accurately solve fuzzy topological relations. Thus, extending the existing research and improving upon the previous work, this paper presents a new method to describe fuzzy topological relations between simple spatial regions in Geographic Information Sciences (GIS) and Artificial Intelligence (AI). Firstly, we propose a new definition for simple fuzzy line segments and simple fuzzy regions based on the computational fuzzy topology. And then, based on the new definitions, we also propose a new combinational reasoning method to compute the topological relations between simple fuzzy regions, moreover, this study has discovered that there are (1) 23 different topological relations between a simple crisp region and a simple fuzzy region; (2) 152 different topological relations between two simple fuzzy regions. In the end, we have discussed some examples to demonstrate the validity of the new method, through comparisons with existing fuzzy models, we showed that the proposed method can compute more than the existing models, as it is more expressive than the existing fuzzy models. PMID:25775452

Schmidt boundaries of foliated space-times

NASA Astrophysics Data System (ADS)

Barletta, Elisabetta; Dragomir, Sorin; Magliaro, Marco

2014-10-01

For every (p+q)-dimensional foliated Lorentzian manifold (M, g, F), where F is a codimension q space-like foliation, we build its Q-completion \\bar{M} and Q-boundary {{\\partial }Q}M. These are analogs, within transverse Lorentzian geometry of foliated manifolds, to the b-completion and b-boundary \\dot{M} (due to (Schmidt 1971 Gen. Relativ. Gravit. 1 269-80)). The bundle morphism {{h}\\bot }:O(M,F,g)\\to O(F,{{g}Q}) (mapping the o(p)+o(1,q-1)-component of the Levi-Civita connection 1-form of (M,g) into the unique torsion-free adapted connection on the bundle of Lorentzian transverse orthonormal frames) is shown to induce a surjective continuous map \\partial {{h}\\bot }:{{\\partial }adt}M\\to {{\\partial }Q}M of the adapted boundary ({{\\partial }adt}M\\subset \\dot{M}) of M onto its Q-boundary. Map \\partial {{h}\\bot } is used to characterize {{\\partial }Q}M as the set of end points {{lim }t\\to {{1-}}}γ (t), in the topology of \\bar{M}, of all Q-incomplete curves γ :[0,1)\\to M. As an application we determine a class {{(\\partial {{h}\\bot })}-1}(P)\\subset \\dot{M} of b-boundary points, where M={R}× (0,m)× {{S}2}, g is Schwartzschild's metric, and F is the codimension two foliation tangent to the Killing vector fields \\partial /\\partial t and \\partial /\\partial \\varphi .

Hydrologic Derivatives for Modeling and Analysis—A new global high-resolution database

USGS Publications Warehouse

Verdin, Kristine L.

2017-07-17

The U.S. Geological Survey has developed a new global high-resolution hydrologic derivative database. Loosely modeled on the HYDRO1k database, this new database, entitled Hydrologic Derivatives for Modeling and Analysis, provides comprehensive and consistent global coverage of topographically derived raster layers (digital elevation model data, flow direction, flow accumulation, slope, and compound topographic index) and vector layers (streams and catchment boundaries). The coverage of the data is global, and the underlying digital elevation model is a hybrid of three datasets: HydroSHEDS (Hydrological data and maps based on SHuttle Elevation Derivatives at multiple Scales), GMTED2010 (Global Multi-resolution Terrain Elevation Data 2010), and the SRTM (Shuttle Radar Topography Mission). For most of the globe south of 60°N., the raster resolution of the data is 3 arc-seconds, corresponding to the resolution of the SRTM. For the areas north of 60°N., the resolution is 7.5 arc-seconds (the highest resolution of the GMTED2010 dataset) except for Greenland, where the resolution is 30 arc-seconds. The streams and catchments are attributed with Pfafstetter codes, based on a hierarchical numbering system, that carry important topological information. This database is appropriate for use in continental-scale modeling efforts. The work described in this report was conducted by the U.S. Geological Survey in cooperation with the National Aeronautics and Space Administration Goddard Space Flight Center.

Blackfolds, plane waves and minimal surfaces

NASA Astrophysics Data System (ADS)

Armas, Jay; Blau, Matthias

2015-07-01

Minimal surfaces in Euclidean space provide examples of possible non-compact horizon geometries and topologies in asymptotically flat space-time. On the other hand, the existence of limiting surfaces in the space-time provides a simple mechanism for making these configurations compact. Limiting surfaces appear naturally in a given space-time by making minimal surfaces rotate but they are also inherent to plane wave or de Sitter space-times in which case minimal surfaces can be static and compact. We use the blackfold approach in order to scan for possible black hole horizon geometries and topologies in asymptotically flat, plane wave and de Sitter space-times. In the process we uncover several new configurations, such as black helicoids and catenoids, some of which have an asymptotically flat counterpart. In particular, we find that the ultraspinning regime of singly-spinning Myers-Perry black holes, described in terms of the simplest minimal surface (the plane), can be obtained as a limit of a black helicoid, suggesting that these two families of black holes are connected. We also show that minimal surfaces embedded in spheres rather than Euclidean space can be used to construct static compact horizons in asymptotically de Sitter space-times.

O Electromagnetic Power Waves and Power Density Components.

NASA Astrophysics Data System (ADS)

Petzold, Donald Wayne

1980-12-01

On January 10, 1884 Lord Rayleigh presented a paper entitled "On the Transfer of Energy in the Electromagnetic Field" to the Royal Society of London. This paper had been authored by the late Fellow of Trinity College, Cambridge, Professor J. H. Poynting and in it he claimed that there was a general law for the transfer of electromagnetic energy. He argued that associated with each point in space is a quantity, that has since been called the Poynting vector, that is a measure of the rate of energy flow per unit area. His analysis was concerned with the integration of this power density vector at all points over an enclosing surface of a specific volume. The interpretation of this Poynting vector as a true measure of the local power density was viewed with great skepticism unless the vector was integrated over a closed surface, as the development of the concept required. However, within the last decade or so Shadowitz indicates that a number of prominent authors have argued that the criticism of the interpretation of Poynting's vector as a local power density vector is unjustified. The present paper is not concerned with these arguments but instead is concerned with a decomposition of Poynting's power density vector into two and only two components: one vector which has the same direction as Poynting's vector and which is called the forward power density vector, and another vector, directed opposite to the Poynting vector and called the reverse power density vector. These new local forward and reverse power density vectors will be shown to be dependent upon forward and reverse power wave vectors and these vectors in turn will be related to newly defined forward and reverse components of the electric and magnetic fields. The sum of these forward and reverse power density vectors, which is simply the original Poynting vector, is associated with the total electromagnetic energy traveling past the local point. Another vector which is the difference between the forward and reverse power density vectors and which will be shown to be associated with the total electric and magnetic field energy densities existing at a local point will also be introduced. These local forward and reverse power density vectors may be integrated over a surface to determine the forward and reverse powers and from these results problems related to maximum power transfer or efficiency of electromagnetic energy transmission in space may be studied in a manner similar to that presently being done with transmission lines, wave guides, and more recently with two port multiport lumped parameter systems. These new forward and reverse power density vectors at a point in space are analogous to the forward and revoltages or currents and power waves as used with the transmission line, waveguide, or port. These power wave vectors in space are a generalization of the power waves as developed by Penfield, Youla, and Kurokawa and used with the scattering parameters associated with transmission lines, waveguides and ports.

Human action classification using procrustes shape theory

NASA Astrophysics Data System (ADS)

Cho, Wanhyun; Kim, Sangkyoon; Park, Soonyoung; Lee, Myungeun

2015-02-01

In this paper, we propose new method that can classify a human action using Procrustes shape theory. First, we extract a pre-shape configuration vector of landmarks from each frame of an image sequence representing an arbitrary human action, and then we have derived the Procrustes fit vector for pre-shape configuration vector. Second, we extract a set of pre-shape vectors from tanning sample stored at database, and we compute a Procrustes mean shape vector for these preshape vectors. Third, we extract a sequence of the pre-shape vectors from input video, and we project this sequence of pre-shape vectors on the tangent space with respect to the pole taking as a sequence of mean shape vectors corresponding with a target video. And we calculate the Procrustes distance between two sequences of the projection pre-shape vectors on the tangent space and the mean shape vectors. Finally, we classify the input video into the human action class with minimum Procrustes distance. We assess a performance of the proposed method using one public dataset, namely Weizmann human action dataset. Experimental results reveal that the proposed method performs very good on this dataset.

Computer calculation of Witten's 3-manifold invariant

NASA Astrophysics Data System (ADS)

Freed, Daniel S.; Gompf, Robert E.

1991-10-01

Witten's 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant.

Topological Defects and Structures in the Early Universe

NASA Astrophysics Data System (ADS)

Zhu, Yong

1997-08-01

This thesis discusses the topological defects generated in the early universe and their contributions to cosmic structure formation. First, we investigate non-Gaussian isocurvature perturbations generated by the evolution of Goldstone modes during inflation. If a global symmetry is broken before inflation, the resulting Goldstone modes are disordered during inflation in a precise and predictable way. After inflation these Goldstone modes order themselves in a self-similar way, much as Goldstone modes in field ordering scenarios based on the Kibble mechanism. For (Hi2/Mpl2)~10- 6, through their gravitational interaction these Goldstone modes generate density perturbations of approximately the right magnitude to explain the cosmic microwave background (CMB) anisotropy and seed the structure seen in the universe today. In such a model non-Gaussian perturbations result because to lowest order density perturbations are sourced by products of Gaussian fields. We explore the issue of phase dispersion and conclude that this non-Gaussian model predicts Doppler peaks in the CMB anisotropy. Topological defects generated from quantum fluctuations during inflation are studied in chapter four. We present a calculation of the power spectrum generated in a classically symmetry-breaking O(N) scalar field through inflationary quantum fluctuations, using the large-N limit. The effective potential of the theory in de Sitter space is obtained from a gap equation which is exact at large N. Quantum fluctuations restore the O(N) symmetry in de Sitter space, but for the finite values of N of interest, there is symmetry breaking and phase ordering after inflation, described by the classical nonlinear sigma model. The scalar field power spectrum is obtained as a function of the scalar field self-coupling. In the second part of the thesis, we investigate non-Abelian topological worm-holes, obtained when winding number one texture field is coupled to Einstein gravity with a conserved global charge. This topological wormhole has the same Euclidean action as axion wormholes and charged scalar wormholes. We find that free topological wormholes are spontaneously generated in the Euclidean space-time with finite density. It is then shown that wormholes with finite density might destroy any long range order in the global fields.

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

Swinteck, N., E-mail: swinteck@email.arizona.edu; Matsuo, S.; Runge, K.

Recent progress in electronic and electromagnetic topological insulators has led to the demonstration of one way propagation of electron and photon edge states and the possibility of immunity to backscattering by edge defects. Unfortunately, such topologically protected propagation of waves in the bulk of a material has not been observed. We show, in the case of sound/elastic waves, that bulk waves with unidirectional backscattering-immune topological states can be observed in a time-dependent elastic superlattice. The superlattice is realized via spatial and temporal modulation of the stiffness of an elastic material. Bulk elastic waves in this superlattice are supported by amore » manifold in momentum space with the topology of a single twist Möbius strip. Our results demonstrate the possibility of attaining one way transport and immunity to scattering of bulk elastic waves.« less

Coherent helix vacancy phonon and its ultrafast dynamics waning in topological Dirac semimetal C d3A s2

NASA Astrophysics Data System (ADS)

Sun, Fei; Wu, Q.; Wu, Y. L.; Zhao, H.; Yi, C. J.; Tian, Y. C.; Liu, H. W.; Shi, Y. G.; Ding, H.; Dai, X.; Richard, P.; Zhao, Jimin

2017-06-01

We report an ultrafast lattice dynamics investigation of the topological Dirac semimetal C d3A s2 . A coherent phonon beating among three evenly spaced A1 g optical phonon modes (of frequencies 1.80, 1.96, and 2.11 THz, respectively) is unambiguously observed. The two side modes originate from the counter helixes composing Cd vacancies. Significantly, such helix vacancy-induced phonon (HVP) modes experience prominent extra waning in their ultrafast dynamics as temperature increases, which is immune to the central mode. Above 200 K, the HVP becomes inactive, which may potentially affect the topological properties. Our results in the lattice degree of freedom suggest the indispensable role of temperature in considering topological properties of such quantum materials.

Exponential Thurston maps and limits of quadratic differentials

NASA Astrophysics Data System (ADS)

Hubbard, John; Schleicher, Dierk; Shishikura, Mitsuhiro

2009-01-01

We give a topological characterization of postsingularly finite topological exponential maps, i.e., universal covers g\\colon{C}to{C}setminus\\{0\\} such that 0 has a finite orbit. Such a map either is Thurston equivalent to a unique holomorphic exponential map λ e^z or it has a topological obstruction called a degenerate Levy cycle. This is the first analog of Thurston's topological characterization theorem of rational maps, as published by Douady and Hubbard, for the case of infinite degree. One main tool is a theorem about the distribution of mass of an integrable quadratic differential with a given number of poles, providing an almost compact space of models for the entire mass of quadratic differentials. This theorem is given for arbitrary Riemann surfaces of finite type in a uniform way.

The topological susceptibility in finite temperature QCD and axion cosmology

DOE PAGES

Petreczky, Peter; Schadler, Hans-Peter; Sharma, Sayantan

2016-10-06

We study the topological susceptibility in 2+1 flavor QCD above the chiral crossover transition temperature using Highly Improved Staggered Quark action and several lattice spacings corresponding to temporal extent of the lattice, N τ=6,8,10 and 12. We observe very distinct temperature dependences of the topological susceptibility in the ranges above and below 250MeV. While for temperatures above 250MeV, the dependence is found to be consistent with dilute instanton gas approximation, at lower temperatures the fall-off of topological susceptibility is milder. We discuss the consequence of our results for cosmology wherein we estimate the bounds on the axion decay constant andmore » the oscillation temperature if indeed the QCD axion is a possible dark matter candidate.« less

The topological susceptibility in finite temperature QCD and axion cosmology

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

Petreczky, Peter; Schadler, Hans-Peter; Sharma, Sayantan

We study the topological susceptibility in 2+1 flavor QCD above the chiral crossover transition temperature using Highly Improved Staggered Quark action and several lattice spacings corresponding to temporal extent of the lattice, N τ=6,8,10 and 12. We observe very distinct temperature dependences of the topological susceptibility in the ranges above and below 250MeV. While for temperatures above 250MeV, the dependence is found to be consistent with dilute instanton gas approximation, at lower temperatures the fall-off of topological susceptibility is milder. We discuss the consequence of our results for cosmology wherein we estimate the bounds on the axion decay constant andmore » the oscillation temperature if indeed the QCD axion is a possible dark matter candidate.« less

Realization of two-dimensional spin-orbit coupling for Bose-Einstein condensates.

PubMed

Wu, Zhan; Zhang, Long; Sun, Wei; Xu, Xiao-Tian; Wang, Bao-Zong; Ji, Si-Cong; Deng, Youjin; Chen, Shuai; Liu, Xiong-Jun; Pan, Jian-Wei

2016-10-07

Cold atoms with laser-induced spin-orbit (SO) interactions provide a platform to explore quantum physics beyond natural conditions of solids. Here we propose and experimentally realize two-dimensional (2D) SO coupling and topological bands for a rubidium-87 degenerate gas through an optical Raman lattice, without phase-locking or fine-tuning of optical potentials. A controllable crossover between 2D and 1D SO couplings is studied, and the SO effects and nontrivial band topology are observed by measuring the atomic cloud distribution and spin texture in momentum space. Our realization of 2D SO coupling with advantages of small heating and topological stability opens a broad avenue in cold atoms to study exotic quantum phases, including topological superfluids. Copyright © 2016, American Association for the Advancement of Science.

Effects of spatial constraints on channel network topology: Implications for geomorphological inference

NASA Astrophysics Data System (ADS)

Cabral, Mariza Castanheira De Moura Da Costa

In the fifty-two years since Robert Horton's 1945 pioneering quantitative description of channel network planform (or plan view morphology), no conclusive findings have been presented that permit inference of geomorphological processes from any measures of network planform. All measures of network planform studied exhibit limited geographic variability across different environments. Horton (1945), Langbein et al. (1947), Schumm (1956), Hack (1957), Melton (1958), and Gray (1961) established various "laws" of network planform, that is, statistical relationships between different variables which have limited variability. A wide variety of models which have been proposed to simulate the growth of channel networks in time over a landsurface are generally also in agreement with the above planform laws. An explanation is proposed for the generality of the channel network planform laws. Channel networks must be space filling, that is, they must extend over the landscape to drain every hillslope, leaving no large undrained areas, and with no crossing of channels, often achieving a roughly uniform drainage density in a given environment. It is shown that the space-filling constraint can reduce the sensitivity of planform variables to different network growth models, and it is proposed that this constraint may determine the planform laws. The "Q model" of network growth of Van Pelt and Verwer (1985) is used to generate samples of networks. Sensitivity to the model parameter Q is markedly reduced when the networks generated are required to be space filling. For a wide variety of Q values, the space-filling networks are in approximate agreement with the various channel network planform laws. Additional constraints, including of energy efficiency, were not studied but may further reduce the variability of planform laws. Inference of model parameter Q from network topology is successful only in networks not subject to spatial constraints. In space-filling networks, for a wide range of Q values, the maximal-likelihood Q parameter value is generally in the vicinity of 1/2, which yields topological randomness. It is proposed that space filling originates the appearance of randomness in channel network topology, and may cause difficulties to geomorphological inference from network planform.

Strain-induced topological magnon phase transitions: applications to kagome-lattice ferromagnets.

PubMed

Owerre, S A

2018-06-20

A common feature of topological insulators is that they are characterized by topologically invariant quantity such as the Chern number and the [Formula: see text] index. This quantity distinguishes a nontrivial topological system from a trivial one. A topological phase transition may occur when there are two topologically distinct phases, and it is usually defined by a gap closing point where the topologically invariant quantity is ill-defined. In this paper, we show that the magnon bands in the strained (distorted) kagome-lattice ferromagnets realize an example of a topological magnon phase transition in the realistic parameter regime of the system. When spin-orbit coupling (SOC) is neglected (i.e. no Dzyaloshinskii-Moriya interaction), we show that all three magnon branches are dispersive with no flat band, and there exists a critical point where tilted Dirac and semi-Dirac point coexist in the magnon spectra. The critical point separates two gapless magnon phases as opposed to the usual phase transition. Upon the inclusion of SOC, we realize a topological magnon phase transition point at the critical strain [Formula: see text], where D and J denote the perturbative SOC and the Heisenberg spin exchange interaction respectively. It separates two distinct topological magnon phases with different Chern numbers for [Formula: see text] and for [Formula: see text]. The associated anomalous thermal Hall conductivity develops an abrupt change at [Formula: see text], due to the divergence of the Berry curvature in momentum space. The proposed topological magnon phase transition is experimentally feasible by applying external perturbations such as uniaxial strain or pressure.

Application of hierarchical clustering method to classify of space-time rainfall patterns

NASA Astrophysics Data System (ADS)

Yu, Hwa-Lung; Chang, Tu-Je

2010-05-01

Understanding the local precipitation patterns is essential to the water resources management and flooding mitigation. The precipitation patterns can vary in space and time depending upon the factors from different spatial scales such as local topological changes and macroscopic atmospheric circulation. The spatiotemporal variation of precipitation in Taiwan is significant due to its complex terrain and its location at west pacific and subtropical area, where is the boundary between the pacific ocean and Asia continent with the complex interactions among the climatic processes. This study characterizes local-scale precipitation patterns by classifying the historical space-time precipitation records. We applied the hierarchical ascending clustering method to analyze the precipitation records from 1960 to 2008 at the six rainfall stations located in Lan-yang catchment at the northeast of the island. Our results identify the four primary space-time precipitation types which may result from distinct driving forces from the changes of atmospheric variables and topology at different space-time scales. This study also presents an important application of the statistical downscaling to combine large-scale upper-air circulation with local space-time precipitation patterns.

Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background.

PubMed

Luminet, Jean-Pierre; Weeks, Jeffrey R; Riazuelo, Alain; Lehoucq, Roland; Uzan, Jean-Philippe

2003-10-09

The current 'standard model' of cosmology posits an infinite flat universe forever expanding under the pressure of dark energy. First-year data from the Wilkinson Microwave Anisotropy Probe (WMAP) confirm this model to spectacular precision on all but the largest scales. Temperature correlations across the microwave sky match expectations on angular scales narrower than 60 degrees but, contrary to predictions, vanish on scales wider than 60 degrees. Several explanations have been proposed. One natural approach questions the underlying geometry of space--namely, its curvature and topology. In an infinite flat space, waves from the Big Bang would fill the universe on all length scales. The observed lack of temperature correlations on scales beyond 60 degrees means that the broadest waves are missing, perhaps because space itself is not big enough to support them. Here we present a simple geometrical model of a finite space--the Poincaré dodecahedral space--which accounts for WMAP's observations with no fine-tuning required. The predicted density is Omega(0) approximately 1.013 > 1, and the model also predicts temperature correlations in matching circles on the sky.

Interoperability Policy Roadmap

DTIC Science & Technology

2010-01-01

Retrieval – SMART The technique developed by Dr. Gerard Salton for automated information retrieval and text analysis is called the vector-space... Salton , G., Wong, A., Yang, C.S., “A Vector Space Model for Automatic Indexing”, Commu- nications of the ACM, 18, 613-620. [10] Salton , G., McGill

Unconventional spin distributions in thick Ni{sub 80}Fe{sub 20} nanodisks

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

Kumar, D.; Lupo, P.; Haldar, A.

2016-05-09

We study the spin distributions in permalloy (Py: Ni{sub 80}Fe{sub 20}) nanodisks as a function of diameter D (300 nm ≤ D ≤ 1 μm) and thickness L (30 nm ≤ L ≤ 100 nm). We observed that beyond a certain thickness, for a fixed disk diameter, an unconventional spin topology precipitates which is marked by the presence of a divergence field within the magnetic vortex curl. The strength of this divergence changes anti-symmetrically from negative to positive—depending on the core polarity—along the axis of the cylindrical nanodisk. This is also accompanied by a skyrmion-like out-of-plane bending of the spin vectors farther away from the disk center. Additionally, the vortex core dilatesmore » significantly when compared to its typical size. This has been directly observed using magnetic force microscopy. We determined from the ferromagnetic resonance spectroscopy measurements that the unconventional topology in the thicker nanodisks gyrated at a frequency, which is significantly lower than what is predicted by a magnetic vortex based analytical model. Micromagnetic simulations involving dipolar and exchange interactions appear to satisfactorily reproduce the experimentally observed static and dynamic behaviors. Besides providing a physical example of an unconventional topology, these results can also aid the design of topologically protected memory elements.« less

Signatures of bulk topology in the non-linear optical spectra of Dirac-Weyl materials

NASA Astrophysics Data System (ADS)

Kumar, Upendra; Kumar, Vipin; Enamullah; Setlur, Girish S.

2018-05-01

Graphene, topological insulators (TI) and the Weyl semimetal are shown to be well-characterized using the phenomenon of anomalous Rabi oscillation (ARO). These oscillations occur far from conventional resonance and Floquet theory shows them to be unique to these systems. Of particular interest is the bulk topological insulator (TI) where the wave-vector dependent frequency of the ARO is seen to be gapped in topologically trivial situations and gapless when there is a non-vanishing Chern number. It is shown that the Chern number may be directly inferred by performing a pump-probe experiment in the bulk without referring to surface states. A simpler alternative to the Lindblad method is invoked in order to incorporate dephasing effects that despite leading to a non-unitary time evolution of the wave-function, is nevertheless, probability conserving. The differential transmission coefficient versus the pump pulse duration (when all else is held fixed) has the form of a sinusoidal function with an amplitude that decays as a power law in the pump duration (alternatively, the "area" of the pump pulse). The exponent of this power law decay is indicative of the Chern number of the bulk in case of TI and more generally indicative of the particular member of the family of materials that may be collectively referred to as - Dirac-Weyl materials.

Semantic and topological classification of images in magnetically guided capsule endoscopy

NASA Astrophysics Data System (ADS)

Mewes, P. W.; Rennert, P.; Juloski, A. L.; Lalande, A.; Angelopoulou, E.; Kuth, R.; Hornegger, J.

2012-03-01

Magnetically-guided capsule endoscopy (MGCE) is a nascent technology with the goal to allow the steering of a capsule endoscope inside a water filled stomach through an external magnetic field. We developed a classification cascade for MGCE images with groups images in semantic and topological categories. Results can be used in a post-procedure review or as a starting point for algorithms classifying pathologies. The first semantic classification step discards over-/under-exposed images as well as images with a large amount of debris. The second topological classification step groups images with respect to their position in the upper gastrointestinal tract (mouth, esophagus, stomach, duodenum). In the third stage two parallel classifications steps distinguish topologically different regions inside the stomach (cardia, fundus, pylorus, antrum, peristaltic view). For image classification, global image features and local texture features were applied and their performance was evaluated. We show that the third classification step can be improved by a bubble and debris segmentation because it limits feature extraction to discriminative areas only. We also investigated the impact of segmenting intestinal folds on the identification of different semantic camera positions. The results of classifications with a support-vector-machine show the significance of color histogram features for the classification of corrupted images (97%). Features extracted from intestinal fold segmentation lead only to a minor improvement (3%) in discriminating different camera positions.

Coupling effect of topological states and Chern insulators in two-dimensional triangular lattices

NASA Astrophysics Data System (ADS)

Zhang, Jiayong; Zhao, Bao; Xue, Yang; Zhou, Tong; Yang, Zhongqin

2018-03-01

We investigate topological states of two-dimensional (2D) triangular lattices with multiorbitals. Tight-binding model calculations of a 2D triangular lattice based on px and py orbitals exhibit very interesting doubly degenerate energy points at different positions (Γ and K /K' ) in momentum space, with quadratic non-Dirac and linear Dirac band dispersions, respectively. Counterintuitively, the system shows a global topologically trivial rather than nontrivial state with consideration of spin-orbit coupling due to the "destructive interference effect" between the topological states at the Γ and K /K' points. The topologically nontrivial state can emerge by introducing another set of triangular lattices to the system (bitriangular lattices) due to the breakdown of the interference effect. With first-principles calculations, we predict an intrinsic Chern insulating behavior (quantum anomalous Hall effect) in a family of the 2D triangular lattice metal-organic framework of Co(C21N3H15) (TPyB-Co) from this scheme. Our results provide a different path and theoretical guidance for the search for and design of new 2D topological quantum materials.

Application of Hyperspectal Techniques to Monitoring & Management of Invasive Plant Species Infestation

DTIC Science & Technology

2008-01-09

The image data as acquired from the sensor is a data cloud in multi- dimensional space with each band generating an axis of dimension. When the data... The color of a material is defined by the direction of its unit vector in n- dimensional spectral space . The length of the vector relates only to how...to n- dimensional space . SAM determines the similarity

Development of a NEW Vector Magnetograph at Marshall Space Flight Center

NASA Technical Reports Server (NTRS)

West, Edward; Hagyard, Mona; Gary, Allen; Smith, James; Adams, Mitzi; Rose, M. Franklin (Technical Monitor)

2001-01-01

This paper will describe the Experimental Vector Magnetograph that has been developed at the Marshall Space Flight Center (MSFC). This instrument was designed to improve linear polarization measurements by replacing electro-optic and rotating waveplate modulators with a rotating linear analyzer. Our paper will describe the motivation for developing this magnetograph, compare this instrument with traditional magnetograph designs, and present a comparison of the data acquired by this instrument and original MSFC vector magnetograph.

Topological Frequency Conversion in Strongly Driven Quantum Systems

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

Martin, Ivar; Refael, Gil; Halperin, Bertrand

When a physical system is subjected to a strong external multi-frequency drive, its dynamics can be conveniently represented in the multi-dimensional Floquet lattice. The number of the Floquet lattice dimensions equals the number of irrationally-related drive frequencies, and the evolution occurs in response to a built-in effective \\electric" field, whose components are proportional to the corresponding drive frequencies. The mapping allows to engineer and study temporal analogs of many real-space phenomena. Here we focus on the specifc example of a two-level system under two-frequency drive that induces topologically nontrivial band structure in the 2D Floquet space. The observable consequence ofmore » such construction is quantized pumping of energy between the sources with frequencies w 1 and w 2. Finally, when the system is initialized into a Floquet band with the Chern number C, the pumping occurs at the rate P 12 = – P 21 = ( C/2π)hw 1w 2, an exact counterpart of the transverse current in a conventional topological insulator.« less

Topological Frequency Conversion in Strongly Driven Quantum Systems

DOE PAGES

Martin, Ivar; Refael, Gil; Halperin, Bertrand

2017-10-16

When a physical system is subjected to a strong external multi-frequency drive, its dynamics can be conveniently represented in the multi-dimensional Floquet lattice. The number of the Floquet lattice dimensions equals the number of irrationally-related drive frequencies, and the evolution occurs in response to a built-in effective \\electric" field, whose components are proportional to the corresponding drive frequencies. The mapping allows to engineer and study temporal analogs of many real-space phenomena. Here we focus on the specifc example of a two-level system under two-frequency drive that induces topologically nontrivial band structure in the 2D Floquet space. The observable consequence ofmore » such construction is quantized pumping of energy between the sources with frequencies w 1 and w 2. Finally, when the system is initialized into a Floquet band with the Chern number C, the pumping occurs at the rate P 12 = – P 21 = ( C/2π)hw 1w 2, an exact counterpart of the transverse current in a conventional topological insulator.« less

Topology assisted self-organization of colloidal nanoparticles: application to 2D large-scale nanomastering

PubMed Central

Kostcheev, Serguei; Turover, Daniel; Salas-Montiel, Rafael; Nomenyo, Komla; Gokarna, Anisha; Lerondel, Gilles

2014-01-01

Summary Our aim was to elaborate a novel method for fully controllable large-scale nanopatterning. We investigated the influence of the surface topology, i.e., a pre-pattern of hydrogen silsesquioxane (HSQ) posts, on the self-organization of polystyrene beads (PS) dispersed over a large surface. Depending on the post size and spacing, long-range ordering of self-organized polystyrene beads is observed wherein guide posts were used leading to single crystal structure. Topology assisted self-organization has proved to be one of the solutions to obtain large-scale ordering. Besides post size and spacing, the colloidal concentration and the nature of solvent were found to have a significant effect on the self-organization of the PS beads. Scanning electron microscope and associated Fourier transform analysis were used to characterize the morphology of the ordered surfaces. Finally, the production of silicon molds is demonstrated by using the beads as a template for dry etching. PMID:25161854

Phonon-induced topological transition to a type-II Weyl semimetal

DOE PAGES

Wang, Lin-Lin; Jo, Na Hyun; Wu, Yun; ...

2017-04-11

Given the importance of crystal symmetry for the emergence of topological quantum states, we have studied here, as exemplified in NbNiTe 2, the interplay of crystal symmetry, atomic displacements (lattice vibration), band degeneracy, and band topology. For the NbNiTe 2 structure in space-group 53 (Pmna)$-$ having an inversion center arising from two glide planes and one mirror plane with a two-fold rotation and screw axis$-$a full gap opening exists between two band manifolds near the Fermi energy. Upon atomic displacements by optical phonons, the symmetry lowers to space-group 28 (Pma2), eliminating one glide plane along c, the associated rotation andmore » screw axis, and the inversion center. As a result, 20 Weyl points emerge, including four type-IIWeyl points in the Γ-X direction at the boundary between a pair of adjacent electron and hole bands. Thus, optical phonons may offer control of the transition to a Weyl fermion state.« less

Lagrange multiplier and Wess-Zumino variable as extra dimensions in the torus universe

NASA Astrophysics Data System (ADS)

Nejad, Salman Abarghouei; Dehghani, Mehdi; Monemzadeh, Majid

2018-01-01

We study the effect of the simplest geometry which is imposed via the topology of the universe by gauging non-relativistic particle model on torus and 3-torus with the help of symplectic formalism of constrained systems. Also, we obtain generators of gauge transformations for gauged models. Extracting corresponding Poisson structure of existed constraints, we show the effect of the shape of the universe on canonical structure of phase-spaces of models and suggest some phenomenology to prove the topology of the universe and probable non-commutative structure of the space. In addition, we show that the number of extra dimensions in the phase-spaces of gauged embedded models are exactly two. Moreover, in classical form, we talk over modification of Newton's second law in order to study the origin of the terms appeared in the gauged theory.

Topology of polymer chains under nanoscale confinement.

PubMed

Satarifard, Vahid; Heidari, Maziar; Mashaghi, Samaneh; Tans, Sander J; Ejtehadi, Mohammad Reza; Mashaghi, Alireza

2017-08-24

Spatial confinement limits the conformational space accessible to biomolecules but the implications for bimolecular topology are not yet known. Folded linear biopolymers can be seen as molecular circuits formed by intramolecular contacts. The pairwise arrangement of intra-chain contacts can be categorized as parallel, series or cross, and has been identified as a topological property. Using molecular dynamics simulations, we determine the contact order distributions and topological circuits of short semi-flexible linear and ring polymer chains with a persistence length of l p under a spherical confinement of radius R c . At low values of l p /R c , the entropy of the linear chain leads to the formation of independent contacts along the chain and accordingly, increases the fraction of series topology with respect to other topologies. However, at high l p /R c , the fraction of cross and parallel topologies are enhanced in the chain topological circuits with cross becoming predominant. At an intermediate confining regime, we identify a critical value of l p /R c , at which all topological states have equal probability. Confinement thus equalizes the probability of more complex cross and parallel topologies to the level of the more simple, non-cooperative series topology. Moreover, our topology analysis reveals distinct behaviours for ring- and linear polymers under weak confinement; however, we find no difference between ring- and linear polymers under strong confinement. Under weak confinement, ring polymers adopt parallel and series topologies with equal likelihood, while linear polymers show a higher tendency for series arrangement. The radial distribution analysis of the topology reveals a non-uniform effect of confinement on the topology of polymer chains, thereby imposing more pronounced effects on the core region than on the confinement surface. Additionally, our results reveal that over a wide range of confining radii, loops arranged in parallel and cross topologies have nearly the same contact orders. Such degeneracy implies that the kinetics and transition rates between the topological states cannot be solely explained by contact order. We expect these findings to be of general importance in understanding chaperone assisted protein folding, chromosome architecture, and the evolution of molecular folds.

The Voronoi spatio-temporal data structure

NASA Astrophysics Data System (ADS)

Mioc, Darka

2002-04-01

Current GIS models cannot integrate the temporal dimension of spatial data easily. Indeed, current GISs do not support incremental (local) addition and deletion of spatial objects, and they can not support the temporal evolution of spatial data. Spatio-temporal facilities would be very useful in many GIS applications: harvesting and forest planning, cadastre, urban and regional planning, and emergency planning. The spatio-temporal model that can overcome these problems is based on a topological model---the Voronoi data structure. Voronoi diagrams are irregular tessellations of space, that adapt to spatial objects and therefore they are a synthesis of raster and vector spatial data models. The main advantage of the Voronoi data structure is its local and sequential map updates, which allows us to automatically record each event and performed map updates within the system. These map updates are executed through map construction commands that are composed of atomic actions (geometric algorithms for addition, deletion, and motion of spatial objects) on the dynamic Voronoi data structure. The formalization of map commands led to the development of a spatial language comprising a set of atomic operations or constructs on spatial primitives (points and lines), powerful enough to define the complex operations. This resulted in a new formal model for spatio-temporal change representation, where each update is uniquely characterized by the numbers of newly created and inactivated Voronoi regions. This is used for the extension of the model towards the hierarchical Voronoi data structure. In this model, spatio-temporal changes induced by map updates are preserved in a hierarchical data structure that combines events and corresponding changes in topology. This hierarchical Voronoi data structure has an implicit time ordering of events visible through changes in topology, and it is equivalent to an event structure that can support temporal data without precise temporal information. This formal model of spatio-temporal change representation is currently applied to retroactive map updates and visualization of map evolution. It offers new possibilities in the domains of temporal GIS, transaction processing, spatio-temporal queries, spatio-temporal analysis, map animation and map visualization.

Tightly-wound miniknot vectors for gene therapy: a potential improvement over supercoiled minicircle DNA.

PubMed

Tolmachov, Oleg E

2010-04-01

Minimized derivatives of bacterial plasmids with removed bacterial backbones are promising vectors for the efficient delivery and for the long-term expression of therapeutic genes. The absence of the bacterial plasmid backbone, a known inducer of innate immune response and a known silencer of transgene expression, provides a partial explanation for the high efficiency of gene transfer using minimized DNA vectors. Supercoiled minicircle DNA is a type of minimized DNA vector obtained via intra-plasmid recombination in bacteria. Minicircle vectors seem to get an additional advantage from their physical compactness, which reduces DNA damage due to the mechanical stress during gene delivery. An independent topological means for DNA compression is knotting, with some knotted DNA isoforms offering superior compactness. I propose that, firstly, knotted DNA can be a suitable compact DNA form for the efficient transfection of a range of human cells with therapeutic genes, and, secondly, that knotted minimized DNA vectors without bacterial backbones ("miniknot" vectors) can surpass supercoiled minicircle DNA vectors in the efficiency of therapeutic gene delivery. Crucially, while the introduction of a single nick to a supercoiled DNA molecule leads to the loss of the compact supercoiled status, the introduction of nicks to knotted DNA does not change knotting. Tight miniknot vectors can be readily produced by the direct action of highly concentrated type II DNA topoisomerase on minicircle DNA or, alternatively, by annealing of the 19-base cohesive ends of the minimized vectors confined within the capsids of Escherichia coli bacteriophage P2 or its satellite bacteriophage P4. After reaching the nucleoplasm of the target cell, the knotted DNA is expected to be unknotted through type II topoisomerase activity and thus to become available for transcription, chromosomal integration or episomal maintenance. The hypothesis can be tested by comparing the gene transfer efficiency achieved with the proposed miniknot vectors, the minicircle vectors described previously, knotted plasmid vectors and standard plasmid vectors. Tightly-wound miniknots can be particularly useful in the gene administration procedures involving considerable forces acting on vector DNA: aerosol inhalation, jet-injection, electroporation, particle bombardment and ultrasound DNA transfer. (c) 2009 Elsevier Ltd. All rights reserved.