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Sample records for algebraic modeling slam

  1. Magnetic resonance Spectroscopy with Linear Algebraic Modeling (SLAM) for higher speed and sensitivity

    NASA Astrophysics Data System (ADS)

    Zhang, Yi; Gabr, Refaat E.; Schär, Michael; Weiss, Robert G.; Bottomley, Paul A.

    2012-05-01

    Speed and signal-to-noise ratio (SNR) are critical for localized magnetic resonance spectroscopy (MRS) of low-concentration metabolites. Matching voxels to anatomical compartments a priori yields better SNR than the spectra created by summing signals from constituent chemical-shift-imaging (CSI) voxels post-acquisition. Here, a new method of localized Spectroscopy using Linear Algebraic Modeling (SLAM) is presented, that can realize this additional SNR gain. Unlike prior methods, SLAM generates spectra from C signal-generating anatomic compartments utilizing a CSI sequence wherein essentially only the C central k-space phase-encoding gradient steps with highest SNR are retained. After MRI-based compartment segmentation, the spectra are reconstructed by solving a sub-set of linear simultaneous equations from the standard CSI algorithm. SLAM is demonstrated with one-dimensional CSI surface coil phosphorus MRS in phantoms, the human leg and the heart on a 3T clinical scanner. Its SNR performance, accuracy, sensitivity to registration errors and inhomogeneity, are evaluated. Compared to one-dimensional CSI, SLAM yielded quantitatively the same results 4-times faster in 24 cardiac patients and healthy subjects. SLAM is further extended with fractional phase-encoding gradients that optimize SNR and/or minimize both inter- and intra-compartmental contamination. In proactive cardiac phosphorus MRS of six healthy subjects, both SLAM and fractional-SLAM (fSLAM) produced results indistinguishable from CSI while preserving SNR gains of 36-45% in the same scan-time. Both SLAM and fSLAM are simple to implement and reduce the minimum scan-time for CSI, which otherwise limits the translation of higher SNR achievable at higher field strengths to faster scanning.

  2. Highly-accelerated quantitative 2D and 3D localized spectroscopy with linear algebraic modeling (SLAM) and sensitivity encoding

    PubMed Central

    Zhang, Yi; Gabr, Refaat E.; Zhou, Jinyuan; Weiss, Robert G.; Bottomley, Paul A.

    2013-01-01

    Noninvasive magnetic resonance spectroscopy (MRS) with chemical shift imaging (CSI) provides valuable metabolic information for research and clinical studies, but is often limited by long scan times. Recently, spectroscopy with linear algebraic modeling (SLAM) was shown to provide compartment-averaged spectra resolved in one spatial dimension with many-fold reductions in scan-time. This was achieved using a small subset of the CSI phase-encoding steps from central image k-space that maximized the signal-to-noise ratio. Here, SLAM is extended to two- and three-dimensions (2D, 3D). In addition, SLAM is combined with sensitivity-encoded (SENSE) parallel imaging techniques, enabling the replacement of even more CSI phase-encoding steps to further accelerate scan-speed. A modified SLAM reconstruction algorithm is introduced that significantly reduces the effects of signal nonuniformity within compartments. Finally, main-field inhomogeneity corrections are provided, analogous to CSI. These methods are all tested on brain proton MRS data from a total of 24 patients with brain tumors, and in a human cardiac phosphorus 3D SLAM study at 3T. Acceleration factors of up to 120-fold versus CSI are demonstrated, including speed-up factors of 5-fold relative to already-accelerated SENSE CSI. Brain metabolites are quantified in SLAM and SENSE SLAM spectra and found to be indistinguishable from CSI measures from the same compartments. The modified reconstruction algorithm demonstrated immunity to maladjusted segmentation and errors from signal heterogeneity in brain data. In conclusion, SLAM demonstrates the potential to supplant CSI in studies requiring compartment-average spectra or large volume coverage, by dramatically reducing scan-time while providing essentially the same quantitative results. PMID:24188921

  3. Highly-accelerated quantitative 2D and 3D localized spectroscopy with linear algebraic modeling (SLAM) and sensitivity encoding

    NASA Astrophysics Data System (ADS)

    Zhang, Yi; Gabr, Refaat E.; Zhou, Jinyuan; Weiss, Robert G.; Bottomley, Paul A.

    2013-12-01

    Noninvasive magnetic resonance spectroscopy (MRS) with chemical shift imaging (CSI) provides valuable metabolic information for research and clinical studies, but is often limited by long scan times. Recently, spectroscopy with linear algebraic modeling (SLAM) was shown to provide compartment-averaged spectra resolved in one spatial dimension with many-fold reductions in scan-time. This was achieved using a small subset of the CSI phase-encoding steps from central image k-space that maximized the signal-to-noise ratio. Here, SLAM is extended to two- and three-dimensions (2D, 3D). In addition, SLAM is combined with sensitivity-encoded (SENSE) parallel imaging techniques, enabling the replacement of even more CSI phase-encoding steps to further accelerate scan-speed. A modified SLAM reconstruction algorithm is introduced that significantly reduces the effects of signal nonuniformity within compartments. Finally, main-field inhomogeneity corrections are provided, analogous to CSI. These methods are all tested on brain proton MRS data from a total of 24 patients with brain tumors, and in a human cardiac phosphorus 3D SLAM study at 3T. Acceleration factors of up to 120-fold versus CSI are demonstrated, including speed-up factors of 5-fold relative to already-accelerated SENSE CSI. Brain metabolites are quantified in SLAM and SENSE SLAM spectra and found to be indistinguishable from CSI measures from the same compartments. The modified reconstruction algorithm demonstrated immunity to maladjusted segmentation and errors from signal heterogeneity in brain data. In conclusion, SLAM demonstrates the potential to supplant CSI in studies requiring compartment-average spectra or large volume coverage, by dramatically reducing scan-time while providing essentially the same quantitative results.

  4. An evaluation of attention models for use in SLAM

    NASA Astrophysics Data System (ADS)

    Dodge, Samuel; Karam, Lina

    2013-12-01

    In this paper we study the application of visual saliency models for the simultaneous localization and mapping (SLAM) problem. We consider visual SLAM, where the location of the camera and a map of the environment can be generated using images from a single moving camera. In visual SLAM, the interest point detector is of key importance. This detector must be invariant to certain image transformations so that features can be matched across di erent frames. Recent work has used a model of human visual attention to detect interest points, however it is unclear as to what is the best attention model for this purpose. To this aim, we compare the performance of interest points from four saliency models (Itti, GBVS, RARE, and AWS) with the performance of four traditional interest point detectors (Harris, Shi-Tomasi, SIFT, and FAST). We evaluate these detectors under several di erent types of image transformation and nd that the Itti saliency model, in general, achieves the best performance in terms of keypoint repeatability.

  5. An Improved Sensor Model on Appearance Based SLAM

    NASA Astrophysics Data System (ADS)

    Keßler, Jens; König, Alexander; Gross, Horst-Michael

    In our previous work on visual, appearance-based localization and mapping, we presented in [14] a novel SLAM approach to build visually labeled topological maps. The essential contribution of this work was an adaptive sensor model, which is estimated online, and a graph matching scheme to evaluate the likelihood of a given topological map. Both methods enable the combination of an appearance-based, visual localization and mapping concept with a Rao-Blackwellized Particle Filter (RBPF) as state estimator to a real-world suitable, online SLAM approach. In this paper we improve our algorithm by using a novel probability driven approximation of the local similarity function (the sensor model) to deal with dynamic changes of the appearance in the operation area.1

  6. Evaluating quantitative and conceptual models of speech production: how does SLAM fare?

    PubMed

    Walker, Grant M; Hickok, Gregory

    2016-04-01

    In a previous publication, we presented a new computational model called SLAM (Walker & Hickok, Psychonomic Bulletin & Review doi: 10.3758/s13423-015-0903 ), based on the hierarchical state feedback control (HSFC) theory (Hickok Nature Reviews Neuroscience, 13(2), 135-145, 2012). In his commentary, Goldrick (Psychonomic Bulletin & Review doi: 10.3758/s13423-015-0946-9 ) claims that SLAM does not represent a theoretical advancement, because it cannot be distinguished from an alternative lexical + postlexical (LPL) theory proposed by Goldrick and Rapp (Cognition, 102(2), 219-260, 2007). First, we point out that SLAM implements a portion of a conceptual model (HSFC) that encompasses LPL. Second, we show that SLAM accounts for a lexical bias present in sound-related errors that LPL does not explain. Third, we show that SLAM's explanatory advantage is not a result of approximating the architectural or computational assumptions of LPL, since an implemented version of LPL fails to provide the same fit improvements as SLAM. Finally, we show that incorporating a mechanism that violates some core theoretical assumptions of LPL-making it more like SLAM in terms of interactivity-allows the model to capture some of the same effects as SLAM. SLAM therefore provides new modeling constraints regarding interactions among processing levels, while also elaborating on the structure of the phonological level. We view this as evidence that an integration of psycholinguistic, neuroscience, and motor control approaches to speech production is feasible and may lead to substantial new insights. PMID:26537953

  7. Full-observability analysis and implementation of the general SLAM model

    NASA Astrophysics Data System (ADS)

    Souici, Ae.; Courdesses, M.; Ouldali, A.; Chatila, R.

    2013-03-01

    Simultaneous localisation and mapping (SLAM) problem is a non-linear system with dynamic state and measurement dimensions. The full observability of such system was ignored, in spite of the fact that system observability is a fundamental aspect in any state estimation problem. In this article, we present a full observability analysis of the general SLAM model. We show that known landmarks (anchor) solution does not guarantee full observability. Furthermore, we prove that to make the general SLAM model fully observable, a combination of known landmarks and invariant metrics are needed. Moreover, we propose a solution to implement a fully observable SLAM model based on mature landmark and virtual observation concepts. Simulations and experimental results are presented demonstrating the validity of the solutions in real world.

  8. A SLAM II simulation model for analyzing space station mission processing requirements

    NASA Technical Reports Server (NTRS)

    Linton, D. G.

    1985-01-01

    Space station mission processing is modeled via the SLAM 2 simulation language on an IBM 4381 mainframe and an IBM PC microcomputer with 620K RAM, two double-sided disk drives and an 8087 coprocessor chip. Using a time phased mission (payload) schedule and parameters associated with the mission, orbiter (space shuttle) and ground facility databases, estimates for ground facility utilization are computed. Simulation output associated with the science and applications database is used to assess alternative mission schedules.

  9. MODEL IDENTIFICATION AND COMPUTER ALGEBRA

    PubMed Central

    Bollen, Kenneth A.; Bauldry, Shawn

    2011-01-01

    Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local and global identification make this practice less than perfect. In this paper we outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. We demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. We illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. We present an identification procedure for Structural Equation Models that makes use of CAS and that is a useful complement to current methods. PMID:21769158

  10. MODEL IDENTIFICATION AND COMPUTER ALGEBRA.

    PubMed

    Bollen, Kenneth A; Bauldry, Shawn

    2010-10-01

    Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local and global identification make this practice less than perfect. In this paper we outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. We demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. We illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. We present an identification procedure for Structural Equation Models that makes use of CAS and that is a useful complement to current methods.

  11. Bohr model as an algebraic collective model

    SciTech Connect

    Rowe, D. J.; Welsh, T. A.; Caprio, M. A.

    2009-05-15

    Developments and applications are presented of an algebraic version of Bohr's collective model. Illustrative examples show that fully converged calculations can be performed quickly and easily for a large range of Hamiltonians. As a result, the Bohr model becomes an effective tool in the analysis of experimental data. The examples are chosen both to confirm the reliability of the algebraic collective model and to show the diversity of results that can be obtained by its use. The focus of the paper is to facilitate identification of the limitations of the Bohr model with a view to developing more realistic, computationally tractable models.

  12. Network simulation using the simulation language for alternate modeling (SLAM 2)

    NASA Technical Reports Server (NTRS)

    Shen, S.; Morris, D. W.

    1983-01-01

    The simulation language for alternate modeling (SLAM 2) is a general purpose language that combines network, discrete event, and continuous modeling capabilities in a single language system. The efficacy of the system's network modeling is examined and discussed. Examples are given of the symbolism that is used, and an example problem and model are derived. The results are discussed in terms of the ease of programming, special features, and system limitations. The system offers many features which allow rapid model development and provides an informative standardized output. The system also has limitations which may cause undetected errors and misleading reports unless the user is aware of these programming characteristics.

  13. Pseudolinear Model Based Solution to the SLAM Problem of Nonholonomic Mobile Robots

    NASA Astrophysics Data System (ADS)

    Pathiranage, Chandima Dedduwa; Watanabe, Keigo; Izumi, Kiyotaka

    This paper describes an improved solution to the simultaneous localization and mapping (SLAM) problem based on pseudolinear models. Accurate estimation of vehicle and landmark states is one of the key issues for successful mobile robot navigation if the configuration of the environment and initial robot location are unknown. A state estimator which can be designed to use the nonlinearity as it is coming from the original model has always been invaluable in which high accuracy is expected. Thus to accomplish the above highlighted point, pseudolinear model based Kalman filter (PLKF) state estimator is introduced. A less error prone vehicle process model is proposed to improve the accuracy and the faster convergence of state estimation. Evolution of vehicle motion is modeled using vehicle frame translation derived from successive dead reckoned poses as a control input. A measurement model with two sensor frames is proposed to improve the data association. The PLKF-based SLAM algorithm is simulated using Matlab for vehicle-landmarks system and results show that the proposed approach performs much accurately compared to the well known extended Kalman filter (EKF).

  14. Using Students' Interests as Algebraic Models

    ERIC Educational Resources Information Center

    Whaley, Kenneth A.

    2012-01-01

    Fostering algebraic thinking is an important goal for middle-grades mathematics teachers. Developing mathematical reasoning requires that teachers cultivate students' habits of mind. Teachers develop students' understanding of algebra by engaging them in tasks that involve modeling and representation. This study was designed to investigate how…

  15. Teaching Modeling and Axiomatization with Boolean Algebra.

    ERIC Educational Resources Information Center

    De Villiers, Michael D.

    1987-01-01

    Presented is an alternative approach to the traditional teaching of Boolean algebra for secondary school mathematics. The main aim of the approach is to use Boolean algebra to teach pupils such mathematical processes as modeling and axiomatization. A course using the approach is described. (RH)

  16. LERC-SLAM - THE NASA LEWIS RESEARCH CENTER SATELLITE LINK ATTENUATION MODEL PROGRAM (IBM PC VERSION)

    NASA Technical Reports Server (NTRS)

    Manning, R. M.

    1994-01-01

    The frequency and intensity of rain attenuation affecting the communication between a satellite and an earth terminal is an important consideration in planning satellite links. The NASA Lewis Research Center Satellite Link Attenuation Model Program (LeRC-SLAM) provides a static and dynamic statistical assessment of the impact of rain attenuation on a communications link established between an earth terminal and a geosynchronous satellite. The program is designed for use in the specification, design and assessment of satellite links for any terminal location in the continental United States. The basis for LeRC-SLAM is the ACTS Rain Attenuation Prediction Model, which uses a log-normal cumulative probability distribution to describe the random process of rain attenuation on satellite links. The derivation of the statistics for the rainrate process at the specified terminal location relies on long term rainfall records compiled by the U.S. Weather Service during time periods of up to 55 years in length. The theory of extreme value statistics is also utilized. The user provides 1) the longitudinal position of the satellite in geosynchronous orbit, 2) the geographical position of the earth terminal in terms of latitude and longitude, 3) the height above sea level of the terminal site, 4) the yearly average rainfall at the terminal site, and 5) the operating frequency of the communications link (within 1 to 1000 GHz, inclusive). Based on the yearly average rainfall at the terminal location, LeRC-SLAM calculates the relevant rain statistics for the site using an internal data base. The program then generates rain attenuation data for the satellite link. This data includes a description of the static (i.e., yearly) attenuation process, an evaluation of the cumulative probability distribution for attenuation effects, and an evaluation of the probability of fades below selected fade depths. In addition, LeRC-SLAM calculates the elevation and azimuth angles of the terminal

  17. LERC-SLAM - THE NASA LEWIS RESEARCH CENTER SATELLITE LINK ATTENUATION MODEL PROGRAM (MACINTOSH VERSION)

    NASA Technical Reports Server (NTRS)

    Manning, R. M.

    1994-01-01

    The frequency and intensity of rain attenuation affecting the communication between a satellite and an earth terminal is an important consideration in planning satellite links. The NASA Lewis Research Center Satellite Link Attenuation Model Program (LeRC-SLAM) provides a static and dynamic statistical assessment of the impact of rain attenuation on a communications link established between an earth terminal and a geosynchronous satellite. The program is designed for use in the specification, design and assessment of satellite links for any terminal location in the continental United States. The basis for LeRC-SLAM is the ACTS Rain Attenuation Prediction Model, which uses a log-normal cumulative probability distribution to describe the random process of rain attenuation on satellite links. The derivation of the statistics for the rainrate process at the specified terminal location relies on long term rainfall records compiled by the U.S. Weather Service during time periods of up to 55 years in length. The theory of extreme value statistics is also utilized. The user provides 1) the longitudinal position of the satellite in geosynchronous orbit, 2) the geographical position of the earth terminal in terms of latitude and longitude, 3) the height above sea level of the terminal site, 4) the yearly average rainfall at the terminal site, and 5) the operating frequency of the communications link (within 1 to 1000 GHz, inclusive). Based on the yearly average rainfall at the terminal location, LeRC-SLAM calculates the relevant rain statistics for the site using an internal data base. The program then generates rain attenuation data for the satellite link. This data includes a description of the static (i.e., yearly) attenuation process, an evaluation of the cumulative probability distribution for attenuation effects, and an evaluation of the probability of fades below selected fade depths. In addition, LeRC-SLAM calculates the elevation and azimuth angles of the terminal

  18. AUTOMATIC CALIBRATION OF A STOCHASTIC-LAGRANGIAN TRANSPORT MODEL (SLAM)

    EPA Science Inventory

    Numerical models are a useful tool in evaluating and designing NAPL remediation systems. Traditional constitutive finite difference and finite element models are complex and expensive to apply. For this reason, this paper presents the application of a simplified stochastic-Lagran...

  19. Algebraic operator approach to gas kinetic models

    NASA Astrophysics Data System (ADS)

    Il'ichov, L. V.

    1997-02-01

    Some general properties of the linear Boltzmann kinetic equation are used to present it in the form ∂ tϕ = - †Âϕ with the operators Âand† possessing some nontrivial algebraic properties. When applied to the Keilson-Storer kinetic model, this method gives an example of quantum ( q-deformed) Lie algebra. This approach provides also a natural generalization of the “kangaroo model”.

  20. Computational algebraic geometry of epidemic models

    NASA Astrophysics Data System (ADS)

    Rodríguez Vega, Martín.

    2014-06-01

    Computational Algebraic Geometry is applied to the analysis of various epidemic models for Schistosomiasis and Dengue, both, for the case without control measures and for the case where control measures are applied. The models were analyzed using the mathematical software Maple. Explicitly the analysis is performed using Groebner basis, Hilbert dimension and Hilbert polynomials. These computational tools are included automatically in Maple. Each of these models is represented by a system of ordinary differential equations, and for each model the basic reproductive number (R0) is calculated. The effects of the control measures are observed by the changes in the algebraic structure of R0, the changes in Groebner basis, the changes in Hilbert dimension, and the changes in Hilbert polynomials. It is hoped that the results obtained in this paper become of importance for designing control measures against the epidemic diseases described. For future researches it is proposed the use of algebraic epidemiology to analyze models for airborne and waterborne diseases.

  1. Solving stochastic epidemiological models using computer algebra

    NASA Astrophysics Data System (ADS)

    Hincapie, Doracelly; Ospina, Juan

    2011-06-01

    Mathematical modeling in Epidemiology is an important tool to understand the ways under which the diseases are transmitted and controlled. The mathematical modeling can be implemented via deterministic or stochastic models. Deterministic models are based on short systems of non-linear ordinary differential equations and the stochastic models are based on very large systems of linear differential equations. Deterministic models admit complete, rigorous and automatic analysis of stability both local and global from which is possible to derive the algebraic expressions for the basic reproductive number and the corresponding epidemic thresholds using computer algebra software. Stochastic models are more difficult to treat and the analysis of their properties requires complicated considerations in statistical mathematics. In this work we propose to use computer algebra software with the aim to solve epidemic stochastic models such as the SIR model and the carrier-borne model. Specifically we use Maple to solve these stochastic models in the case of small groups and we obtain results that do not appear in standard textbooks or in the books updated on stochastic models in epidemiology. From our results we derive expressions which coincide with those obtained in the classical texts using advanced procedures in mathematical statistics. Our algorithms can be extended for other stochastic models in epidemiology and this shows the power of computer algebra software not only for analysis of deterministic models but also for the analysis of stochastic models. We also perform numerical simulations with our algebraic results and we made estimations for the basic parameters as the basic reproductive rate and the stochastic threshold theorem. We claim that our algorithms and results are important tools to control the diseases in a globalized world.

  2. Shapes and stability of algebraic nuclear models

    NASA Technical Reports Server (NTRS)

    Lopez-Moreno, Enrique; Castanos, Octavio

    1995-01-01

    A generalization of the procedure to study shapes and stability of algebraic nuclear models introduced by Gilmore is presented. One calculates the expectation value of the Hamiltonian with respect to the coherent states of the algebraic structure of the system. Then equilibrium configurations of the resulting energy surface, which depends in general on state variables and a set of parameters, are classified through the Catastrophe theory. For one- and two-body interactions in the Hamiltonian of the interacting Boson model-1, the critical points are organized through the Cusp catastrophe. As an example, we apply this Separatrix to describe the energy surfaces associated to the Rutenium and Samarium isotopes.

  3. GPS-Supported Visual SLAM with a Rigorous Sensor Model for a Panoramic Camera in Outdoor Environments

    PubMed Central

    Shi, Yun; Ji, Shunping; Shi, Zhongchao; Duan, Yulin; Shibasaki, Ryosuke

    2013-01-01

    Accurate localization of moving sensors is essential for many fields, such as robot navigation and urban mapping. In this paper, we present a framework for GPS-supported visual Simultaneous Localization and Mapping with Bundle Adjustment (BA-SLAM) using a rigorous sensor model in a panoramic camera. The rigorous model does not cause system errors, thus representing an improvement over the widely used ideal sensor model. The proposed SLAM does not require additional restrictions, such as loop closing, or additional sensors, such as expensive inertial measurement units. In this paper, the problems of the ideal sensor model for a panoramic camera are analysed, and a rigorous sensor model is established. GPS data are then introduced for global optimization and georeferencing. Using the rigorous sensor model with the geometric observation equations of BA, a GPS-supported BA-SLAM approach that combines ray observations and GPS observations is then established. Finally, our method is applied to a set of vehicle-borne panoramic images captured from a campus environment, and several ground control points (GCP) are used to check the localization accuracy. The results demonstrated that our method can reach an accuracy of several centimetres. PMID:23344377

  4. GPS-supported visual SLAM with a rigorous sensor model for a panoramic camera in outdoor environments.

    PubMed

    Shi, Yun; Ji, Shunping; Shi, Zhongchao; Duan, Yulin; Shibasaki, Ryosuke

    2012-12-21

    Accurate localization of moving sensors is essential for many fields, such as robot navigation and urban mapping. In this paper, we present a framework for GPS-supported visual Simultaneous Localization and Mapping with Bundle Adjustment (BA-SLAM) using a rigorous sensor model in a panoramic camera. The rigorous model does not cause system errors, thus representing an improvement over the widely used ideal sensor model. The proposed SLAM does not require additional restrictions, such as loop closing, or additional sensors, such as expensive inertial measurement units. In this paper, the problems of the ideal sensor model for a panoramic camera are analysed, and a rigorous sensor model is established. GPS data are then introduced for global optimization and georeferencing. Using the rigorous sensor model with the geometric observation equations of BA, a GPS-supported BA-SLAM approach that combines ray observations and GPS observations is then established. Finally, our method is applied to a set of vehicle-borne panoramic images captured from a campus environment, and several ground control points (GCP) are used to check the localization accuracy. The results demonstrated that our method can reach an accuracy of several centimetres.

  5. GPS-supported visual SLAM with a rigorous sensor model for a panoramic camera in outdoor environments.

    PubMed

    Shi, Yun; Ji, Shunping; Shi, Zhongchao; Duan, Yulin; Shibasaki, Ryosuke

    2012-01-01

    Accurate localization of moving sensors is essential for many fields, such as robot navigation and urban mapping. In this paper, we present a framework for GPS-supported visual Simultaneous Localization and Mapping with Bundle Adjustment (BA-SLAM) using a rigorous sensor model in a panoramic camera. The rigorous model does not cause system errors, thus representing an improvement over the widely used ideal sensor model. The proposed SLAM does not require additional restrictions, such as loop closing, or additional sensors, such as expensive inertial measurement units. In this paper, the problems of the ideal sensor model for a panoramic camera are analysed, and a rigorous sensor model is established. GPS data are then introduced for global optimization and georeferencing. Using the rigorous sensor model with the geometric observation equations of BA, a GPS-supported BA-SLAM approach that combines ray observations and GPS observations is then established. Finally, our method is applied to a set of vehicle-borne panoramic images captured from a campus environment, and several ground control points (GCP) are used to check the localization accuracy. The results demonstrated that our method can reach an accuracy of several centimetres. PMID:23344377

  6. Slamming Arkansas Schools!

    ERIC Educational Resources Information Center

    Scott, W. Clayton

    2010-01-01

    In this article, the author, a poet and teaching artist, shares how he successfully brought slam poetry to College Hill Middle School in Texarkana, Arkansas. In 2001 he discovered slam poetry--a poetry-reading format in which poets compete in dramatic readings of their works--and went to Slam Nationals in Seattle on the Arkansas slam team. He…

  7. A process algebra model of QED

    NASA Astrophysics Data System (ADS)

    Sulis, William

    2016-03-01

    The process algebra approach to quantum mechanics posits a finite, discrete, determinate ontology of primitive events which are generated by processes (in the sense of Whitehead). In this ontology, primitive events serve as elements of an emergent space-time and of emergent fundamental particles and fields. Each process generates a set of primitive elements, using only local information, causally propagated as a discrete wave, forming a causal space termed a causal tapestry. Each causal tapestry forms a discrete and finite sampling of an emergent causal manifold (space-time) M and emergent wave function. Interactions between processes are described by a process algebra which possesses 8 commutative operations (sums and products) together with a non-commutative concatenation operator (transitions). The process algebra possesses a representation via nondeterministic combinatorial games. The process algebra connects to quantum mechanics through the set valued process and configuration space covering maps, which associate each causal tapestry with sets of wave functions over M. Probabilities emerge from interactions between processes. The process algebra model has been shown to reproduce many features of the theory of non-relativistic scalar particles to a high degree of accuracy, without paradox or divergences. This paper extends the approach to a semi-classical form of quantum electrodynamics.

  8. A stochastic, Lagrangian model of sinking biogenic aggregates in the ocean (SLAMS 1.0): model formulation, validation and sensitivity

    NASA Astrophysics Data System (ADS)

    Jokulsdottir, Tinna; Archer, David

    2016-04-01

    We present a new mechanistic model, stochastic, Lagrangian aggregate model of sinking particles (SLAMS) for the biological pump in the ocean, which tracks the evolution of individual particles as they aggregate, disaggregate, sink, and are altered by chemical and biological processes. SLAMS considers the impacts of ballasting by mineral phases, binding of aggregates by transparent exopolymer particles (TEP), zooplankton grazing and the fractal geometry (porosity) of the aggregates. Parameterizations for age-dependent organic carbon (orgC) degradation kinetics, and disaggregation driven by zooplankton grazing and TEP degradation, are motivated by observed particle fluxes and size spectra throughout the water column. The model is able to explain observed variations in orgC export efficiency and rain ratio from the euphotic zone and to the sea floor as driven by sea surface temperature and the primary production rate and seasonality of primary production. The model provides a new mechanistic framework with which to predict future changes on the flux attenuation of orgC in response to climate change forcing.

  9. Distributed SLAM

    NASA Astrophysics Data System (ADS)

    Binns, Lewis A.; Valachis, Dimitris; Anderson, Sean; Gough, David W.; Nicholson, David; Greenway, Phil

    2002-07-01

    Previously, we have developed techniques for Simultaneous Localization and Map Building based on the augmented state Kalman filter. Here we report the results of experiments conducted over multiple vehicles each equipped with a laser range finder for sensing the external environment, and a laser tracking system to provide highly accurate ground truth. The goal is simultaneously to build a map of an unknown environment and to use that map to navigate a vehicle that otherwise would have no way of knowing its location, and to distribute this process over several vehicles. We have constructed an on-line, distributed implementation to demonstrate the principle. In this paper we describe the system architecture, the nature of the experimental set up, and the results obtained. These are compared with the estimated ground truth. We show that distributed SLAM has a clear advantage in the sense that it offers a potential super-linear speed-up over single vehicle SLAM. In particular, we explore the time taken to achieve a given quality of map, and consider the repeatability and accuracy of the method. Finally, we discuss some practical implementation issues.

  10. A novel combined SLAM based on RBPF-SLAM and EIF-SLAM for mobile system sensing in a large scale environment.

    PubMed

    He, Bo; Zhang, Shujing; Yan, Tianhong; Zhang, Tao; Liang, Yan; Zhang, Hongjin

    2011-01-01

    Mobile autonomous systems are very important for marine scientific investigation and military applications. Many algorithms have been studied to deal with the computational efficiency problem required for large scale simultaneous localization and mapping (SLAM) and its related accuracy and consistency. Among these methods, submap-based SLAM is a more effective one. By combining the strength of two popular mapping algorithms, the Rao-Blackwellised particle filter (RBPF) and extended information filter (EIF), this paper presents a combined SLAM-an efficient submap-based solution to the SLAM problem in a large scale environment. RBPF-SLAM is used to produce local maps, which are periodically fused into an EIF-SLAM algorithm. RBPF-SLAM can avoid linearization of the robot model during operating and provide a robust data association, while EIF-SLAM can improve the whole computational speed, and avoid the tendency of RBPF-SLAM to be over-confident. In order to further improve the computational speed in a real time environment, a binary-tree-based decision-making strategy is introduced. Simulation experiments show that the proposed combined SLAM algorithm significantly outperforms currently existing algorithms in terms of accuracy and consistency, as well as the computing efficiency. Finally, the combined SLAM algorithm is experimentally validated in a real environment by using the Victoria Park dataset.

  11. A novel combined SLAM based on RBPF-SLAM and EIF-SLAM for mobile system sensing in a large scale environment.

    PubMed

    He, Bo; Zhang, Shujing; Yan, Tianhong; Zhang, Tao; Liang, Yan; Zhang, Hongjin

    2011-01-01

    Mobile autonomous systems are very important for marine scientific investigation and military applications. Many algorithms have been studied to deal with the computational efficiency problem required for large scale simultaneous localization and mapping (SLAM) and its related accuracy and consistency. Among these methods, submap-based SLAM is a more effective one. By combining the strength of two popular mapping algorithms, the Rao-Blackwellised particle filter (RBPF) and extended information filter (EIF), this paper presents a combined SLAM-an efficient submap-based solution to the SLAM problem in a large scale environment. RBPF-SLAM is used to produce local maps, which are periodically fused into an EIF-SLAM algorithm. RBPF-SLAM can avoid linearization of the robot model during operating and provide a robust data association, while EIF-SLAM can improve the whole computational speed, and avoid the tendency of RBPF-SLAM to be over-confident. In order to further improve the computational speed in a real time environment, a binary-tree-based decision-making strategy is introduced. Simulation experiments show that the proposed combined SLAM algorithm significantly outperforms currently existing algorithms in terms of accuracy and consistency, as well as the computing efficiency. Finally, the combined SLAM algorithm is experimentally validated in a real environment by using the Victoria Park dataset. PMID:22346639

  12. A New Reynolds Stress Algebraic Equation Model

    NASA Technical Reports Server (NTRS)

    Shih, Tsan-Hsing; Zhu, Jiang; Lumley, John L.

    1994-01-01

    A general turbulent constitutive relation is directly applied to propose a new Reynolds stress algebraic equation model. In the development of this model, the constraints based on rapid distortion theory and realizability (i.e. the positivity of the normal Reynolds stresses and the Schwarz' inequality between turbulent velocity correlations) are imposed. Model coefficients are calibrated using well-studied basic flows such as homogeneous shear flow and the surface flow in the inertial sublayer. The performance of this model is then tested in complex turbulent flows including the separated flow over a backward-facing step and the flow in a confined jet. The calculation results are encouraging and point to the success of the present model in modeling turbulent flows with complex geometries.

  13. A Novel Combined SLAM Based on RBPF-SLAM and EIF-SLAM for Mobile System Sensing in a Large Scale Environment

    PubMed Central

    He, Bo; Zhang, Shujing; Yan, Tianhong; Zhang, Tao; Liang, Yan; Zhang, Hongjin

    2011-01-01

    Mobile autonomous systems are very important for marine scientific investigation and military applications. Many algorithms have been studied to deal with the computational efficiency problem required for large scale Simultaneous Localization and Mapping (SLAM) and its related accuracy and consistency. Among these methods, submap-based SLAM is a more effective one. By combining the strength of two popular mapping algorithms, the Rao-Blackwellised particle filter (RBPF) and extended information filter (EIF), this paper presents a Combined SLAM—an efficient submap-based solution to the SLAM problem in a large scale environment. RBPF-SLAM is used to produce local maps, which are periodically fused into an EIF-SLAM algorithm. RBPF-SLAM can avoid linearization of the robot model during operating and provide a robust data association, while EIF-SLAM can improve the whole computational speed, and avoid the tendency of RBPF-SLAM to be over-confident. In order to further improve the computational speed in a real time environment, a binary-tree-based decision-making strategy is introduced. Simulation experiments show that the proposed Combined SLAM algorithm significantly outperforms currently existing algorithms in terms of accuracy and consistency, as well as the computing efficiency. Finally, the Combined SLAM algorithm is experimentally validated in a real environment by using the Victoria Park dataset. PMID:22346639

  14. MonoSLAM: real-time single camera SLAM.

    PubMed

    Davison, Andrew J; Reid, Ian D; Molton, Nicholas D; Stasse, Olivier

    2007-06-01

    We present a real-time algorithm which can recover the 3D trajectory of a monocular camera, moving rapidly through a previously unknown scene. Our system, which we dub MonoSLAM, is the first successful application of the SLAM methodology from mobile robotics to the "pure vision" domain of a single uncontrolled camera, achieving real time but drift-free performance inaccessible to Structure from Motion approaches. The core of the approach is the online creation of a sparse but persistent map of natural landmarks within a probabilistic framework. Our key novel contributions include an active approach to mapping and measurement, the use of a general motion model for smooth camera movement, and solutions for monocular feature initialization and feature orientation estimation. Together, these add up to an extremely efficient and robust algorithm which runs at 30 Hz with standard PC and camera hardware. This work extends the range of robotic systems in which SLAM can be usefully applied, but also opens up new areas. We present applications of MonoSLAM to real-time 3D localization and mapping for a high-performance full-size humanoid robot and live augmented reality with a hand-held camera.

  15. A spatial operator algebra for manipulator modeling and control

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.; Jain, A.; Kreutz-Delgado, K.

    1991-01-01

    A recently developed spatial operator algebra for manipulator modeling, control, and trajectory design is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and for control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced conceptual and physical understanding of manipulator dynamics and kinematics.

  16. Preparing Secondary Mathematics Teachers: A Focus on Modeling in Algebra

    ERIC Educational Resources Information Center

    Jung, Hyunyi; Mintos, Alexia; Newton, Jill

    2015-01-01

    This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities.…

  17. On explicit algebraic stress models for complex turbulent flows

    NASA Technical Reports Server (NTRS)

    Gatski, T. B.; Speziale, C. G.

    1992-01-01

    Explicit algebraic stress models that are valid for three-dimensional turbulent flows in noninertial frames are systematically derived from a hierarchy of second-order closure models. This represents a generalization of the model derived by Pope who based his analysis on the Launder, Reece, and Rodi model restricted to two-dimensional turbulent flows in an inertial frame. The relationship between the new models and traditional algebraic stress models -- as well as anistropic eddy visosity models -- is theoretically established. The need for regularization is demonstrated in an effort to explain why traditional algebraic stress models have failed in complex flows. It is also shown that these explicit algebraic stress models can shed new light on what second-order closure models predict for the equilibrium states of homogeneous turbulent flows and can serve as a useful alternative in practical computations.

  18. L∞-algebra models and higher Chern-Simons theories

    NASA Astrophysics Data System (ADS)

    Ritter, Patricia; Sämann, Christian

    2016-10-01

    We continue our study of zero-dimensional field theories in which the fields take values in a strong homotopy Lie algebra. In the first part, we review in detail how higher Chern-Simons theories arise in the AKSZ-formalism. These theories form a universal starting point for the construction of L∞-algebra models. We then show how to describe superconformal field theories and how to perform dimensional reductions in this context. In the second part, we demonstrate that Nambu-Poisson and multisymplectic manifolds are closely related via their Heisenberg algebras. As a byproduct of our discussion, we find central Lie p-algebra extensions of 𝔰𝔬(p + 2). Finally, we study a number of L∞-algebra models which are physically interesting and which exhibit quantized multisymplectic manifolds as vacuum solutions.

  19. Action Algebras and Model Algebras in Denotational Semantics

    NASA Astrophysics Data System (ADS)

    Guedes, Luiz Carlos Castro; Haeusler, Edward Hermann

    This article describes some results concerning the conceptual separation of model dependent and language inherent aspects in a denotational semantics of a programming language. Before going into the technical explanation, the authors wish to relate a story that illustrates how correctly and precisely posed questions can influence the direction of research. By means of his questions, Professor Mosses aided the PhD research of one of the authors of this article and taught the other, who at the time was a novice supervisor, the real meaning of careful PhD supervision. The student’s research had been partially developed towards the implementation of programming languages through denotational semantics specification, and the student had developed a prototype [12] that compared relatively well to some industrial compilers of the PASCAL language. During a visit to the BRICS lab in Aarhus, the student’s supervisor gave Professor Mosses a draft of an article describing the prototype and its implementation experiments. The next day, Professor Mosses asked the supervisor, “Why is the generated code so efficient when compared to that generated by an industrial compiler?” and “You claim that the efficiency is simply a consequence of the Object- Orientation mechanisms used by the prototype programming language (C++); this should be better investigated. Pay more attention to the class of programs that might have this good comparison profile.” As a result of these aptly chosen questions and comments, the student and supervisor made great strides in the subsequent research; the advice provided by Professor Mosses made them perceive that the code generated for certain semantic domains was efficient because it mapped to the “right aspect” of the language semantics. (Certain functional types, used to represent mappings such as Stores and Environments, were pushed to the level of the object language (as in gcc). This had the side-effect of generating

  20. Applied Algebra: The Modeling Technique of Least Squares

    ERIC Educational Resources Information Center

    Zelkowski, Jeremy; Mayes, Robert

    2008-01-01

    The article focuses on engaging students in algebra through modeling real-world problems. The technique of least squares is explored, encouraging students to develop a deeper understanding of the method. (Contains 2 figures and a bibliography.)

  1. Algebraic Modeling of Information Retrieval in XML Documents

    NASA Astrophysics Data System (ADS)

    Georgiev, Bozhidar; Georgieva, Adriana

    2009-11-01

    This paper presents an information retrieval approach in XML documents using tools, based on the linear algebra. The well-known transformation languages as XSLT (XPath) are grounded on the features of higher-order logic for manipulating hierarchical trees. The presented conception is compared to existing higher-order logic formalisms, where the queries are realized by both languages XSLT and XPath. The possibilities of the proposed linear algebraic model combined with hierarchy data models permit more efficient solutions for searching, extracting and manipulating semi-structured data with hierarchical structures avoiding the global navigation over the XML tree components. The main purpose of this algebraic model representation, applied to the hierarchical relationships in the XML data structures, is to make the implementation of linear algebra tools possible for XML data manipulations and to eliminate existing problems, related to regular grammars theory and also to avoid the difficulties, connected with higher -order logic (first-order logic, monadic second- order logic etc.).

  2. A spatial operator algebra for manipulator modeling and control

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.; Kreutz, K.; Milman, M.

    1988-01-01

    A powerful new spatial operator algebra for modeling, control, and trajectory design of manipulators is discussed along with its implementation in the Ada programming language. Applications of this algebra to robotics include an operator representation of the manipulator Jacobian matrix; the robot dynamical equations formulated in terms of the spatial algebra, showing the complete equivalence between the recursive Newton-Euler formulations to robot dynamics; the operator factorization and inversion of the manipulator mass matrix which immediately results in O(N) recursive forward dynamics algorithms; the joint accelerations of a manipulator due to a tip contact force; the recursive computation of the equivalent mass matrix as seen at the tip of a manipulator; and recursive forward dynamics of a closed chain system. Finally, additional applications and current research involving the use of the spatial operator algebra are discussed in general terms.

  3. An algebraic cluster model based on the harmonic oscillator basis

    NASA Technical Reports Server (NTRS)

    Levai, Geza; Cseh, J.

    1995-01-01

    We discuss the semimicroscopic algebraic cluster model introduced recently, in which the internal structure of the nuclear clusters is described by the harmonic oscillator shell model, while their relative motion is accounted for by the Vibron model. The algebraic formulation of the model makes extensive use of techniques associated with harmonic oscillators and their symmetry group, SU(3). The model is applied to some cluster systems and is found to reproduce important characteristics of nuclei in the sd-shell region. An approximate SU(3) dynamical symmetry is also found to hold for the C-12 + C-12 system.

  4. A Cognitive Model of Experts' Algebraic Solving Methods

    ERIC Educational Resources Information Center

    Cortes, Anibal

    2003-01-01

    We studied experts' solving methods and analyzed the nature of mathematical knowledge as well as their efficiency in algebraic calculations. We constructed a model of the experts cognitive functioning (notably teachers) in which the observed automatisms were modeled in terms of schemes and instruments. Mathematical justification of transformation…

  5. Inverse Modelling Problems in Linear Algebra Undergraduate Courses

    ERIC Educational Resources Information Center

    Martinez-Luaces, Victor E.

    2013-01-01

    This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

  6. Optical linear algebra processors: noise and error-source modeling.

    PubMed

    Casasent, D; Ghosh, A

    1985-06-01

    The modeling of system and component noise and error sources in optical linear algebra processors (OLAP's) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.

  7. Optical linear algebra processors - Noise and error-source modeling

    NASA Technical Reports Server (NTRS)

    Casasent, D.; Ghosh, A.

    1985-01-01

    The modeling of system and component noise and error sources in optical linear algebra processors (OLAPs) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.

  8. A spatial operator algebra for manipulator modeling and control

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.; Kreutz, Kenneth; Jain, Abhinandan

    1989-01-01

    A recently developed spatial operator algebra, useful for modeling, control, and trajectory design of manipulators is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high level framework for describing the dynamic and kinematic behavior of a manipulator and control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced conceptual and physical understanding of manipulator dynamics and kinematics. Furthermore, implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection. Thus, the transition from an abstract problem formulation and solution to the detailed mechanizaton of specific algorithms is greatly simplified. The analytical formulation of the operator algebra, as well as its implementation in the Ada programming language are discussed.

  9. Algebraic approach to small-world network models

    NASA Astrophysics Data System (ADS)

    Rudolph-Lilith, Michelle; Muller, Lyle E.

    2014-01-01

    We introduce an analytic model for directed Watts-Strogatz small-world graphs and deduce an algebraic expression of its defining adjacency matrix. The latter is then used to calculate the small-world digraph's asymmetry index and clustering coefficient in an analytically exact fashion, valid nonasymptotically for all graph sizes. The proposed approach is general and can be applied to all algebraically well-defined graph-theoretical measures, thus allowing for an analytical investigation of finite-size small-world graphs.

  10. Seeking Simplicity: Algebraic and Topological Modelling in Educational Research.

    ERIC Educational Resources Information Center

    Preece, Peter F. W.

    2001-01-01

    Quantitative algebraic and qualitative topological models can be used in the quest for simple explanations in the field of teaching and learning. The examples described cover such diverse topics as teacher anxiety and classroom control, process-product studies, aptitude-treatment interactions, the pace of instruction, the size of classes, and…

  11. Phase transitions for rotational states within an algebraic cluster model

    NASA Astrophysics Data System (ADS)

    López Moreno, E.; Morales Hernández, G. E.; Hess, P. O.; Yépez Martínez, H.

    2016-07-01

    The ground state and excited, rotational phase transitions are investigated within the Semimicroscopic Algebraic Cluster Model (SACM). The catastrophe theory is used to describe these phase transitions. Short introductions to the SACM and the catastrophe theory are given. We apply the formalism to the case of 16O+α→20Ne.

  12. Generalization of Richardson-Gaudin models to rank-2 algebras

    SciTech Connect

    Errea, B; Lerma, S; Dukelsky, J; Dimitrova, S S; Pittel, S; Van Isacker, P; Gueorguiev, V G

    2006-07-20

    A generalization of Richardson-Gaudin models to the rank-2 SO(5) and SO(3,2) algebras is used to describe systems of two kinds of fermions or bosons interacting through a pairing force. They are applied to the proton-neutron neutron isovector pairing model and to the Interacting Boson Model 2, in the transition from vibration to gamma-soft nuclei, respectively. In both cases, the integrals of motion and their eigenvalues are obtained.

  13. Models of quadratic quantum algebras and their relation to classical superintegrable systems

    SciTech Connect

    Kalnins, E. G.; Miller, W.; Post, S.

    2009-05-15

    We show how to construct realizations (models) of quadratic algebras for 2D second order superintegrable systems in terms of differential or difference operators in one variable. We demonstrate how various models of the quantum algebras arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras related to superintegrable systems in n dimensions and are intimately related to multivariable orthogonal polynomials.

  14. Augmenting ViSP's 3D Model-Based Tracker with RGB-D SLAM for 3D Pose Estimation in Indoor Environments

    NASA Astrophysics Data System (ADS)

    Li-Chee-Ming, J.; Armenakis, C.

    2016-06-01

    This paper presents a novel application of the Visual Servoing Platform's (ViSP) for pose estimation in indoor and GPS-denied outdoor environments. Our proposed solution integrates the trajectory solution from RGBD-SLAM into ViSP's pose estimation process. Li-Chee-Ming and Armenakis (2015) explored the application of ViSP in mapping large outdoor environments, and tracking larger objects (i.e., building models). Their experiments revealed that tracking was often lost due to a lack of model features in the camera's field of view, and also because of rapid camera motion. Further, the pose estimate was often biased due to incorrect feature matches. This work proposes a solution to improve ViSP's pose estimation performance, aiming specifically to reduce the frequency of tracking losses and reduce the biases present in the pose estimate. This paper explores the integration of ViSP with RGB-D SLAM. We discuss the performance of the combined tracker in mapping indoor environments and tracking 3D wireframe indoor building models, and present preliminary results from our experiments.

  15. Inverse modelling problems in linear algebra undergraduate courses

    NASA Astrophysics Data System (ADS)

    Martinez-Luaces, Victor E.

    2013-10-01

    This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different presentations will be discussed. Finally, several results will be presented and some conclusions proposed.

  16. A comparison of SLAM and SCIPUFF using SEADEX tracer data

    SciTech Connect

    Atchison, M.K.

    1999-07-01

    The transport and diffusion models SCIPUFF (Second-order Closure Integrated Puff) and SLAM (Short-range Layered Atmospheric Model) were compared against each other using the land-sea breeze tracer data set SEADEX (The Shoreline Environment Atmospheric Dispersion Experiment). Predicted concentrations from both of these models were compared to observed concentrations at distances up to 15 km from a source for two of nine SEADEX releases. Emphasis was placed on a comparison of model output produced using various types of weather data (surface and upper-air). For the SEADEX release 1, SLAM was better at predicting the peak concentrations while SCIPUFF did a better job of predicting the overall plume widths. For SEADEX release 6, both SCIPUFF and SLAM performed similarly. However, SLAM moved the plume too fast compared to SCIPUFF and the actual observed plume location.

  17. Assessment of an Explicit Algebraic Reynolds Stress Model

    NASA Technical Reports Server (NTRS)

    Carlson, Jan-Renee

    2005-01-01

    This study assesses an explicit algebraic Reynolds stress turbulence model in the in the three-dimensional Reynolds averaged Navier-Stokes (RANS) solver, ISAAC (Integrated Solution Algorithm for Arbitrary Con gurations). Additionally, it compares solutions for two select configurations between ISAAC and the RANS solver PAB3D. This study compares with either direct numerical simulation data, experimental data, or empirical models for several different geometries with compressible, separated, and high Reynolds number flows. In general, the turbulence model matched data or followed experimental trends well, and for the selected configurations, the computational results of ISAAC closely matched those of PAB3D using the same turbulence model.

  18. A spatial operator algebra for manipulator modeling and control

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.; Kreutz, K.; Jain, A.

    1989-01-01

    A spatial operator algebra for modeling the control and trajectory design of manipulation is discussed, with emphasis on its analytical formulation and implementation in the Ada programming language. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of the manipulator. Inversion is obtained using techniques of recursive filtering and smoothing. The operator alegbra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and control and trajectory design algorithms. Implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection, thus greatly simplifying the transition from an abstract problem formulation and solution to the detailed mechanization of a specific algorithm.

  19. A Realizable Reynolds Stress Algebraic Equation Model

    NASA Technical Reports Server (NTRS)

    Shih, Tsan-Hsing; Zhu, Jiang; Lumley, John L.

    1993-01-01

    The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.

  20. Algebraic Turbulence-Chemistry Interaction Model

    NASA Technical Reports Server (NTRS)

    Norris, Andrew T.

    2012-01-01

    The results of a series of Perfectly Stirred Reactor (PSR) and Partially Stirred Reactor (PaSR) simulations are compared to each other over a wide range of operating conditions. It is found that the PaSR results can be simulated by a PSR solution with just an adjusted chemical reaction rate. A simple expression has been developed that gives the required change in reaction rate for a PSR solution to simulate the PaSR results. This expression is the basis of a simple turbulence-chemistry interaction model. The interaction model that has been developed is intended for use with simple one-step global reaction mechanisms and for steady-state flow simulations. Due to the simplicity of the model there is very little additional computational cost in adding it to existing CFD codes.

  1. Modelling Simply, Without Algebra: Beyond the Spreadsheet

    ERIC Educational Resources Information Center

    Lawrence, Ian

    2004-01-01

    Using computers to provide dynamic modelling of physical situations is a valuable teaching tool. This is the first of two articles which look in detail at the use of two tools: this article considers the use of VnR whilst the second considers Modellus. This article provides useful approaches using VnR to teach physics. It also considers the…

  2. Structure of the measles virus hemagglutinin bound to its cellular receptor SLAM.

    PubMed

    Hashiguchi, Takao; Ose, Toyoyuki; Kubota, Marie; Maita, Nobuo; Kamishikiryo, Jun; Maenaka, Katsumi; Yanagi, Yusuke

    2011-02-01

    Measles virus, a major cause of childhood morbidity and mortality worldwide, predominantly infects immune cells using signaling lymphocyte activation molecule (SLAM) as a cellular receptor. Here we present crystal structures of measles virus hemagglutinin (MV-H), the receptor-binding glycoprotein, in complex with SLAM. The MV-H head domain binds to a β-sheet of the membrane-distal ectodomain of SLAM using the side of its β-propeller fold. This is distinct from attachment proteins of other paramyxoviruses that bind receptors using the top of their β-propeller. The structure provides templates for antiviral drug design, an explanation for the effectiveness of the measles virus vaccine, and a model of the homophilic SLAM-SLAM interaction involved in immune modulations. Notably, the crystal structures obtained show two forms of the MV-H-SLAM tetrameric assembly (dimer of dimers), which may have implications for the mechanism of fusion triggering.

  3. Local Frame Junction Trees in SLAM

    NASA Astrophysics Data System (ADS)

    Kuehnel, Frank O.

    2005-11-01

    Junction trees (JT) is a general purpose tool for exact inference on graphical models. Many of the existing algorithms for building junction trees require a fixed static graphical model. The construction process is not unique, finding the one with the best computational structure (smallest clique size) is also a hard problem. For large scale inference problems, such as Geo-referencing using triangular geodetic networks or equivalent, the simultaneous localization and mapping (SLAM) problem in robotics pose some challenges to junction tree applications. Incremental junction tree techniques for dynamic graphical models prescribe heuristic methods for growing the tree structure, and are applicable to large scale graphical models. Of concern are the proliferative widening of the tree, which makes message passing expensive. In the context of SLAM we present a new apporach that exploits the local frame dependence of novel observation variables.

  4. Numerical investigation of algebraic oceanic turbulent mixing-layer models

    NASA Astrophysics Data System (ADS)

    Chacón-Rebollo, T.; Gómez-Mármol, M.; Rubino, S.

    2013-11-01

    In this paper we investigate the finite-time and asymptotic behaviour of algebraic turbulent mixing-layer models by numerical simulation. We compare the performances given by three different settings of the eddy viscosity. We consider Richardson number-based vertical eddy viscosity models. Two of these are classical algebraic turbulence models usually used in numerical simulations of global oceanic circulation, i.e. the Pacanowski-Philander and the Gent models, while the other one is a more recent model (Bennis et al., 2010) proposed to prevent numerical instabilities generated by physically unstable configurations. The numerical schemes are based on the standard finite element method. We perform some numerical tests for relatively large deviations of realistic initial conditions provided by the Tropical Atmosphere Ocean (TAO) array. These initial conditions correspond to states close to mixing-layer profiles, measured on the Equatorial Pacific region called the West-Pacific Warm Pool. We conclude that mixing-layer profiles could be considered as kinds of "absorbing configurations" in finite time that asymptotically evolve to steady states under the application of negative surface energy fluxes.

  5. Measles Virus Infection of SLAM (CD150) Knockin Mice Reproduces Tropism and Immunosuppression in Human Infection▿

    PubMed Central

    Ohno, Shinji; Ono, Nobuyuki; Seki, Fumio; Takeda, Makoto; Kura, Shinobu; Tsuzuki, Teruhisa; Yanagi, Yusuke

    2007-01-01

    The human signaling lymphocyte activation molecule (SLAM, also called CD150), a regulator of antigen-driven T-cell responses and macrophage functions, acts as a cellular receptor for measles virus (MV), and its V domain is necessary and sufficient for receptor function. We report here the generation of SLAM knockin mice in which the V domain of mouse SLAM was replaced by that of human SLAM. The chimeric SLAM had an expected distribution and normal function in the knockin mice. Splenocytes from the SLAM knockin mice permitted the in vitro growth of a virulent MV strain but not that of the Edmonston vaccine strain. Unlike in vitro infection, MV could grow only in SLAM knockin mice that also lacked the type I interferon receptor (IFNAR). After intraperitoneal or intranasal inoculation, MV was detected in the spleen and lymph nodes throughout the body but not in the thymus. Notably, the virus appeared first in the mediastinal lymph node after intranasal inoculation. Splenocytes from MV-infected IFNAR−/− SLAM knockin mice showed suppression of proliferative responses to concanavalin A. Thus, MV infection of SLAM knockin mice reproduces lymphotropism and immunosuppression in human infection, serving as a useful small animal model for measles. PMID:17135325

  6. Topological basis realization for BMW algebra and Heisenberg XXZ spin chain model

    NASA Astrophysics Data System (ADS)

    Liu, Bo; Xue, Kang; Wang, Gangcheng; Liu, Ying; Sun, Chunfang

    2015-04-01

    In this paper, we study three-dimensional (3D) reduced Birman-Murakami-Wenzl (BMW) algebra based on topological basis theory. Several examples of BMW algebra representations are reviewed. We also discuss a special solution of BMW algebra, which can be used to construct Heisenberg XXZ model. The theory of topological basis provides a useful method to solve quantum spin chain models. It is also shown that the ground state of XXZ spin chain is superposition state of topological basis.

  7. A Frame Manipulation Algebra for ER Logical Stage Modelling

    NASA Astrophysics Data System (ADS)

    Furtado, Antonio L.; Casanova, Marco A.; Breitman, Karin K.; Barbosa, Simone D. J.

    The ER model is arguably today's most widely accepted basis for the conceptual specification of information systems. A further common practice is to use the Relational Model at an intermediate logical stage, in order to adequately prepare for physical implementation. Although the Relational Model still works well in contexts relying on standard databases, it imposes certain restrictions, not inherent in ER specifications, which make it less suitable in Web environments. This paper proposes frames as an alternative to move from ER specifications to logical stage modelling, and treats frames as an abstract data type equipped with a Frame Manipulation Algebra (FMA). It is argued that frames, with a long tradition in AI applications, are able to accommodate the irregularities of semi-structured data, and that frame-sets generalize relational tables, allowing to drop the strict homogeneity requirement. A prototype logic-programming tool has been developed to experiment with FMA. Examples are included to help describe the use of the operators.

  8. Applying FastSLAM to Articulated Rovers

    NASA Astrophysics Data System (ADS)

    Hewitt, Robert Alexander

    This thesis presents the navigation algorithms designed for use on Kapvik, a 30 kg planetary micro-rover built for the Canadian Space Agency; the simulations used to test the algorithm; and novel techniques for terrain classification using Kapvik's LIDAR (Light Detection And Ranging) sensor. Kapvik implements a six-wheeled, skid-steered, rocker-bogie mobility system. This warrants a more complicated kinematic model for navigation than a typical 4-wheel differential drive system. The design of a 3D navigation algorithm is presented that includes nonlinear Kalman filtering and Simultaneous Localization and Mapping (SLAM). A neural network for terrain classification is used to improve navigation performance. Simulation is used to train the neural network and validate the navigation algorithms. Real world tests of the terrain classification algorithm validate the use of simulation for training and the improvement to SLAM through the reduction of extraneous LIDAR measurements in each scan.

  9. A Process Algebraic Framework for Modeling Resource Demand and Supply

    NASA Astrophysics Data System (ADS)

    Philippou, Anna; Lee, Insup; Sokolsky, Oleg; Choi, Jin-Young

    As real-time embedded systems become more complex, resource partitioning is increasingly used to guarantee real-time performance. Recently, several compositional frameworks of resource partitioning have been proposed using real-time scheduling theory with various notions of real-time tasks running under restricted resource supply environments. However, these real-time scheduling-based approaches are limited in their expressiveness in that, although capable of describing resource-demand tasks, they are unable to model resource supply. This paper describes a process algebraic framework for reasoning about resource demand and supply inspired by the timed process algebra ACSR. In ACSR, real-time tasks are specified by enunciating their consumption needs for resources. To also accommodate resource-supply processes we define PADS where, given a resource CPU, the complimented resource overline{CPU} denotes for availability of CPU for the corresponding demand process. Using PADS, we define a supply-demand relation where a pair (S, T) belongs to the relation if the demand process T can be scheduled under supply S. We develop a theory of compositional schedulability analysis as well as a technique for synthesizing an optimal supply process for a set of tasks. We illustrate our technique via a number of examples.

  10. Visual SLAM for Handheld Monocular Endoscope.

    PubMed

    Grasa, Óscar G; Bernal, Ernesto; Casado, Santiago; Gil, Ismael; Montiel, J M M

    2014-01-01

    Simultaneous localization and mapping (SLAM) methods provide real-time estimation of 3-D models from the sole input of a handheld camera, routinely in mobile robotics scenarios. Medical endoscopic sequences mimic a robotic scenario in which a handheld camera (monocular endoscope) moves along an unknown trajectory while observing an unknown cavity. However, the feasibility and accuracy of SLAM methods have not been extensively validated with human in vivo image sequences. In this work, we propose a monocular visual SLAM algorithm tailored to deal with medical image sequences in order to provide an up-to-scale 3-D map of the observed cavity and the endoscope trajectory at frame rate. The algorithm is validated over synthetic data and human in vivo sequences corresponding to 15 laparoscopic hernioplasties where accurate ground-truth distances are available. It can be concluded that the proposed procedure is: 1) noninvasive, because only a standard monocular endoscope and a surgical tool are used; 2) convenient, because only a hand-controlled exploratory motion is needed; 3) fast, because the algorithm provides the 3-D map and the trajectory in real time; 4) accurate, because it has been validated with respect to ground-truth; and 5) robust to inter-patient variability, because it has performed successfully over the validation sequences.

  11. Visual SLAM for Handheld Monocular Endoscope.

    PubMed

    Grasa, Óscar G; Bernal, Ernesto; Casado, Santiago; Gil, Ismael; Montiel, J M M

    2014-01-01

    Simultaneous localization and mapping (SLAM) methods provide real-time estimation of 3-D models from the sole input of a handheld camera, routinely in mobile robotics scenarios. Medical endoscopic sequences mimic a robotic scenario in which a handheld camera (monocular endoscope) moves along an unknown trajectory while observing an unknown cavity. However, the feasibility and accuracy of SLAM methods have not been extensively validated with human in vivo image sequences. In this work, we propose a monocular visual SLAM algorithm tailored to deal with medical image sequences in order to provide an up-to-scale 3-D map of the observed cavity and the endoscope trajectory at frame rate. The algorithm is validated over synthetic data and human in vivo sequences corresponding to 15 laparoscopic hernioplasties where accurate ground-truth distances are available. It can be concluded that the proposed procedure is: 1) noninvasive, because only a standard monocular endoscope and a surgical tool are used; 2) convenient, because only a hand-controlled exploratory motion is needed; 3) fast, because the algorithm provides the 3-D map and the trajectory in real time; 4) accurate, because it has been validated with respect to ground-truth; and 5) robust to inter-patient variability, because it has performed successfully over the validation sequences. PMID:24107925

  12. Lie algebraic similarity transformed Hamiltonians for lattice model systems

    NASA Astrophysics Data System (ADS)

    Wahlen-Strothman, Jacob M.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Scuseria, Gustavo E.

    2015-01-01

    We present a class of Lie algebraic similarity transformations generated by exponentials of two-body on-site Hermitian operators whose Hausdorff series can be summed exactly without truncation. The correlators are defined over the entire lattice and include the Gutzwiller factor ni ↑ni ↓ , and two-site products of density (ni ↑+ni ↓) and spin (ni ↑-ni ↓) operators. The resulting non-Hermitian many-body Hamiltonian can be solved in a biorthogonal mean-field approach with polynomial computational cost. The proposed similarity transformation generates locally weighted orbital transformations of the reference determinant. Although the energy of the model is unbound, projective equations in the spirit of coupled cluster theory lead to well-defined solutions. The theory is tested on the one- and two-dimensional repulsive Hubbard model where it yields accurate results for small and medium sized interaction strengths.

  13. An algebraic turbulence model for three-dimensional viscous flows

    NASA Technical Reports Server (NTRS)

    Chima, R. V.; Giel, P. W.; Boyle, R. J.

    1993-01-01

    An algebraic turbulence model is proposed for use with three-dimensional Navier-Stokes analyses. It incorporates features of both the Baldwin-Lomax and Cebeci-Smith models. The Baldwin-Lomax model uses the maximum of a function f(y) to determine length and velocity scales. An analysis of the Baldwin-Lomax model shows that f(y) can have a spurious maximum close to the wall, causing numerical problems and non-physical results. The proposed model uses integral relations to determine delta(*) u(sub e) and delta used in the Cebeci-Smith mode. It eliminates a constant in the Baldwin-Lomax model and determines the two remaining constants by comparison to the Cebeci-Smith formulation. Pressure gradient effects, a new wake model, and the implementation of these features in a three-dimensional Navier-Stokes code are also described. Results are shown for a flat plate boundary layer, an annular turbine cascade, and endwall heat transfer in a linear turbine cascade. The heat transfer results agree well with experimental data which shows large variations in endwall Stanton number contours with Reynolds number.

  14. Re"modeling" College Algebra: An Active Learning Approach

    ERIC Educational Resources Information Center

    Pinzon, D.; Pinzon, K.; Stackpole, M.

    2016-01-01

    In this paper, we discuss active learning in College Algebra at Georgia Gwinnett College. This approach has been used in more than 20 sections of College Algebra taught by the authors in the past four semesters. Students work in small, structured groups on guided inquiry activities after watching 15-20 minutes of videos before class. We discuss a…

  15. A Modeling-Based College Algebra Course and Its Effect on Student Achievement

    ERIC Educational Resources Information Center

    Ellington, Aimee J.

    2005-01-01

    In Fall 2004, Virginia Commonwealth University (VCU) piloted a modeling-based approach to college algebra. This paper describes the course and an assessment that was conducted to determine the effect of this approach on student achievement in comparison to a traditional approach to college algebra. The results show that compared with their…

  16. Excited states of the Calogero-Sutherland model and singular vectors of the WN algebra

    NASA Astrophysics Data System (ADS)

    Awata, Hidetoshi; Matsuo, Yutaka; Odake, Satoru; Shiraishi, Jun'ichi

    1995-02-01

    Using the collective field method, we find a relation between the Jack symmetric polynomials, which describe the excited states of the Calogero-Sutherland model, and the singular vectors of the WN algebra. Based on this relation, we obtain their integral representations. We also give a direct algebraic method which leads to the same result, and integral representations of the skew-Jack polynomials.

  17. Slam Poetry and Cultural Experience for Children

    ERIC Educational Resources Information Center

    Boudreau, Kathryn E.

    2009-01-01

    Slam poetry, being not just recitation or memorization, affords children the opportunity to express their own personal cultural experiences and values. Slam is a spoken word performance; a competition among poets. Audience commentary is ongoing during the performance and vigorous audience participation is essential in a slam format. The founders…

  18. Grand slam on cancer.

    PubMed

    Gartrell, Nanette

    2014-01-01

    A winner of 59 Grand Slam championships including a record 9 Wimbledon singles titles, Martina Navratilova is the most successful woman tennis player of the modern era. Martina was inducted into the International Tennis Hall of Fame, named "Tour Player of the Year" seven times by the Women's Tennis Association, declared "Female Athlete of the Year" by the Associated Press, and ranked one of the "Top Forty Athletes of All-Time" by Sports Illustrated. Equally accomplished off the court, Martina is an author, philanthropist, TV commentator, and activist who has dedicated her life to educating people about prejudice and stereotypes. After coming out as a lesbian in 1981, Martina became a tireless advocate of equal rights for lesbian, gay, bisexual, and transgender (LGBT) people, and she has contributed generously to the LGBT community. Martina is the author of seven books, including most recently Shape Your Self: My 6-Step Diet and Fitness Plan to Achieve the Best Shape of your Life, an inspiring guide to healthy living and personal fitness. Martina was diagnosed with breast cancer in 2010. PMID:24400624

  19. Grand slam on cancer.

    PubMed

    Gartrell, Nanette

    2014-01-01

    A winner of 59 Grand Slam championships including a record 9 Wimbledon singles titles, Martina Navratilova is the most successful woman tennis player of the modern era. Martina was inducted into the International Tennis Hall of Fame, named "Tour Player of the Year" seven times by the Women's Tennis Association, declared "Female Athlete of the Year" by the Associated Press, and ranked one of the "Top Forty Athletes of All-Time" by Sports Illustrated. Equally accomplished off the court, Martina is an author, philanthropist, TV commentator, and activist who has dedicated her life to educating people about prejudice and stereotypes. After coming out as a lesbian in 1981, Martina became a tireless advocate of equal rights for lesbian, gay, bisexual, and transgender (LGBT) people, and she has contributed generously to the LGBT community. Martina is the author of seven books, including most recently Shape Your Self: My 6-Step Diet and Fitness Plan to Achieve the Best Shape of your Life, an inspiring guide to healthy living and personal fitness. Martina was diagnosed with breast cancer in 2010.

  20. SLAM in a van

    NASA Astrophysics Data System (ADS)

    Binns, Lewis A.; Valachis, Dimitris; Anderson, Sean; Gough, David W.; Nicholson, David; Greenway, Phil

    2002-07-01

    We have developed techniques for Simultaneous Localization and Map Building based on the augmented state Kalman filter, and demonstrated this in real time using laboratory robots. Here we report the results of experiments conducted out doors in an unstructured, unknown, representative environment, using a van equipped with a laser range finder for sensing the external environment, and GPS to provide an estimate of ground truth. The goal is simultaneously to build a map of an unknown environment and to use that map to navigate a vehicle that otherwise would have no way of knowing its location. In this paper we describe the system architecture, the nature of the experimental set up, and the results obtained. These are compared with the estimated ground truth. We show that SLAM is both feasible and useful in real environments. In particular, we explore its repeatability and accuracy, and discuss some practical implementation issues. Finally, we look at the way forward for a real implementation on ground and air vehicles operating in very demanding, harsh environments.

  1. Analysis of DIRAC's behavior using model checking with process algebra

    NASA Astrophysics Data System (ADS)

    Remenska, Daniela; Templon, Jeff; Willemse, Tim; Bal, Henri; Verstoep, Kees; Fokkink, Wan; Charpentier, Philippe; Graciani Diaz, Ricardo; Lanciotti, Elisa; Roiser, Stefan; Ciba, Krzysztof

    2012-12-01

    DIRAC is the grid solution developed to support LHCb production activities as well as user data analysis. It consists of distributed services and agents delivering the workload to the grid resources. Services maintain database back-ends to store dynamic state information of entities such as jobs, queues, staging requests, etc. Agents use polling to check and possibly react to changes in the system state. Each agent's logic is relatively simple; the main complexity lies in their cooperation. Agents run concurrently, and collaborate using the databases as shared memory. The databases can be accessed directly by the agents if running locally or through a DIRAC service interface if necessary. This shared-memory model causes entities to occasionally get into inconsistent states. Tracing and fixing such problems becomes formidable due to the inherent parallelism present. We propose more rigorous methods to cope with this. Model checking is one such technique for analysis of an abstract model of a system. Unlike conventional testing, it allows full control over the parallel processes execution, and supports exhaustive state-space exploration. We used the mCRL2 language and toolset to model the behavior of two related DIRAC subsystems: the workload and storage management system. Based on process algebra, mCRL2 allows defining custom data types as well as functions over these. This makes it suitable for modeling the data manipulations made by DIRAC's agents. By visualizing the state space and replaying scenarios with the toolkit's simulator, we have detected race-conditions and deadlocks in these systems, which, in several cases, were confirmed to occur in the reality. Several properties of interest were formulated and verified with the tool. Our future direction is automating the translation from DIRAC to a formal model.

  2. Developing ontological model of computational linear algebra - preliminary considerations

    NASA Astrophysics Data System (ADS)

    Wasielewska, K.; Ganzha, M.; Paprzycki, M.; Lirkov, I.

    2013-10-01

    The aim of this paper is to propose a method for application of ontologically represented domain knowledge to support Grid users. The work is presented in the context provided by the Agents in Grid system, which aims at development of an agent-semantic infrastructure for efficient resource management in the Grid. Decision support within the system should provide functionality beyond the existing Grid middleware, specifically, help the user to choose optimal algorithm and/or resource to solve a problem from a given domain. The system assists the user in at least two situations. First, for users without in-depth knowledge about the domain, it should help them to select the method and the resource that (together) would best fit the problem to be solved (and match the available resources). Second, if the user explicitly indicates the method and the resource configuration, it should "verify" if her choice is consistent with the expert recommendations (encapsulated in the knowledge base). Furthermore, one of the goals is to simplify the use of the selected resource to execute the job; i.e., provide a user-friendly method of submitting jobs, without required technical knowledge about the Grid middleware. To achieve the mentioned goals, an adaptable method of expert knowledge representation for the decision support system has to be implemented. The selected approach is to utilize ontologies and semantic data processing, supported by multicriterial decision making. As a starting point, an area of computational linear algebra was selected to be modeled, however, the paper presents a general approach that shall be easily extendable to other domains.

  3. Excel Spreadsheets for Algebra: Improving Mental Modeling for Problem Solving

    ERIC Educational Resources Information Center

    Engerman, Jason; Rusek, Matthew; Clariana, Roy

    2014-01-01

    This experiment investigates the effectiveness of Excel spreadsheets in a high school algebra class. Students in the experiment group convincingly outperformed the control group on a post lesson assessment. The student responses, teacher observations involving Excel spreadsheet revealed that it operated as a mindtool, which formed the users'…

  4. From matrix models' topological expansion to topological string theories: counting surfaces with algebraic geometry

    NASA Astrophysics Data System (ADS)

    Orantin, N.

    2007-09-01

    The 2-matrix model has been introduced to study Ising model on random surfaces. Since then, the link between matrix models and combinatorics of discrete surfaces has strongly tightened. This manuscript aims to investigate these deep links and extend them beyond the matrix models, following my work's evolution. First, I take care to define properly the hermitian 2 matrix model which gives rise to generating functions of discrete surfaces equipped with a spin structure. Then, I show how to compute all the terms in the topological expansion of any observable by using algebraic geometry tools. They are obtained as differential forms on an algebraic curve associated to the model: the spectral curve. In a second part, I show how to define such differentials on any algebraic curve even if it does not come from a matrix model. I then study their numerous symmetry properties under deformations of the algebraic curve. In particular, I show that these objects coincide with the topological expansion of the observable of a matrix model if the algebraic curve is the spectral curve of this model. Finally, I show that fine tuning the parameters ensure that these objects can be promoted to modular invariants and satisfy the holomorphic anomaly equation of the Kodaira-Spencer theory. This gives a new hint that the Dijkgraaf-Vafa conjecture is correct.

  5. Waves of 3D marine structures slamming at different initial poses in complex wind-wave-flow environments

    NASA Astrophysics Data System (ADS)

    Zhu, Liang-sheng; Yu, Long-fei

    2016-10-01

    Aimed at the hydrodynamic response for marine structures slamming into water, based on the mechanism analysis to the slamming process, and by combining 3D N-S equation and k- ɛ turbulent kinetic equation with structure fully 6DOF motion equation, a mathematical model for the wind-fluid-solid interaction is established in 3D marine structure slamming wave at free poses and wind-wave-flow complex environments. Compared with the results of physical model test, the numerical results from the slamming wave well correspond with the experimental results. Through the mathematical model, the wave-making issue of 3D marine structure at initial pose falls into water in different complex wind, wave and flow environments is investigated. The research results show that various kinds of natural factors and structure initial poses have different influence on the slamming wave, and there is an obvious rule in this process.

  6. Improving model-based diagnosis through algebraic analysis: The Petri net challenge

    SciTech Connect

    Portinale, L.

    1996-12-31

    The present paper describes the empirical evaluation of a linear algebra approach to model-based diagnosis, in case the behavioral model of the device under examination is described through a Petri net model. In particular, we show that algebraic analysis based on P-invariants of the net model, can significantly improve the performance of a model-based diagnostic system, while keeping the integrity of a general framework defined from a formal logical theory. A system called INVADS is described and experimental results, performed on a car fault domain and involving the comparison of different implementations of P-invariant based diagnosis, are then discussed.

  7. The case of bruce: A teacher's model of his students' algebraic thinking about equivalent expressions

    NASA Astrophysics Data System (ADS)

    Hallagan, Jean E.

    2006-05-01

    The purpose of this article is to describe a middle school mathematics teacher's model of his students' responses to algebraic tasks involving equivalent expressions and the distributive property. The teacher engaged in two model-eliciting activities designed for teachers by creating a library of his students' work and an accompanying "Ways of Thinking"[WOT] sheet (Doerr & Lesh, 2003). These activities were designed to help reveal the teachers' models of students' algebraic thinking and to promote the development of that model. Results of the analysis showed that the teacher developed a clearer understanding of the role of a variable in algebraic instruction. The teacher employed visual strategies for the first time and began to perceive their usefulness in helping students understand the equivalence of two expressions.

  8. Algebraic turbulence models for the computation of two-dimensional high speed flows using unstructured grids

    NASA Technical Reports Server (NTRS)

    Rostand, Philippe

    1988-01-01

    The incorporation of algebraic turbulence models in a solver for the 2-D compressible Navier-Stokes equations using triangular grids is described. A practical way to use the Cebeci Smith model, and to modify it in separated regions is proposed. The ability of the model to predict high speed, perfect gas boundary layers is investigated from a numerical point of view.

  9. Designing Tasks for Math Modeling in College Algebra: A Critical Review

    ERIC Educational Resources Information Center

    Staats, Susan; Robertson, Douglas

    2014-01-01

    Over the last decade, the pedagogical approach known as mathematical modeling has received increased interest in college algebra classes in the United States. Math modeling assignments ask students to develop their own problem-solving tools to address non-routine, realistic scenarios. The open-ended quality of modeling activities creates dilemmas…

  10. Supersymmetry and the discrete light-cone quantization limit of the Lie 3-algebra model of M theory

    NASA Astrophysics Data System (ADS)

    Sato, Matsuo

    2012-02-01

    In M. Sato, J. High Energy Phys.JHEPFG1029-8479 07 (2010) 02610.1007/JHEP07(2010)026, we proposed two models of M theory, the Hermitian 3-algebra model and Lie 3-algebra model. In this paper, we study the Lie 3-algebra model with a Lorentzian Lie 3-algebra. This model is ghost-free despite the Lorentzian 3-algebra. We show that our model satisfies two criteria as a model of M theory. First, we show that the model possesses N=1 supersymmetry in 11 dimensions. Second, we show the model reduces to Banks-Fischler-Shenker-Susskind matrix theory with finite size matrices in a discrete light-cone quantization limit.

  11. AN ADA LINEAR ALGEBRA PACKAGE MODELED AFTER HAL/S

    NASA Technical Reports Server (NTRS)

    Klumpp, A. R.

    1994-01-01

    This package extends the Ada programming language to include linear algebra capabilities similar to those of the HAL/S programming language. The package is designed for avionics applications such as Space Station flight software. In addition to the HAL/S built-in functions, the package incorporates the quaternion functions used in the Shuttle and Galileo projects, and routines from LINPAK that solve systems of equations involving general square matrices. Language conventions in this package follow those of HAL/S to the maximum extent practical and minimize the effort required for writing new avionics software and translating existent software into Ada. Valid numeric types in this package include scalar, vector, matrix, and quaternion declarations. (Quaternions are fourcomponent vectors used in representing motion between two coordinate frames). Single precision and double precision floating point arithmetic is available in addition to the standard double precision integer manipulation. Infix operators are used instead of function calls to define dot products, cross products, quaternion products, and mixed scalar-vector, scalar-matrix, and vector-matrix products. The package contains two generic programs: one for floating point, and one for integer. The actual component type is passed as a formal parameter to the generic linear algebra package. The procedures for solving systems of linear equations defined by general matrices include GEFA, GECO, GESL, and GIDI. The HAL/S functions include ABVAL, UNIT, TRACE, DET, INVERSE, TRANSPOSE, GET, PUT, FETCH, PLACE, and IDENTITY. This package is written in Ada (Version 1.2) for batch execution and is machine independent. The linear algebra software depends on nothing outside the Ada language except for a call to a square root function for floating point scalars (such as SQRT in the DEC VAX MATHLIB library). This program was developed in 1989, and is a copyrighted work with all copyright vested in NASA.

  12. Multiple robot system for decentralized SLAM investigations

    NASA Astrophysics Data System (ADS)

    Deaves, Rob H.; Nicholson, David; Gough, David W.; Binns, Lewis A.; Vangasse, Paul; Greenway, Phil

    2000-10-01

    Technical details of laboratory based robotic system for researching decentralized Simultaneous Localization and Map building (SLAM) are provided. The main components of the system are Pioneer (ActivMedia) robots, laboratory environment for mapping, laser tracking system for testing the SLAM accuracy and a suite of SLAM software algorithms. The system is used to provide a demonstration and initial practical results of decentralized multiple-platform SLAM. The paper concludes that useful system has been set-up for researching this technology area. Further, the demonstration highlights important benefits of multiple- platform decentralized SLAM over a single platform approach. These include an increase in map accuracy, an improvement in the completeness and timeliness of the map, and an increase in platform accuracy although that platform was not extrinsically sensed. Future research areas are discussed.

  13. Mathematical modelling in engineering: an alternative way to teach Linear Algebra

    NASA Astrophysics Data System (ADS)

    Domínguez-García, S.; García-Planas, M. I.; Taberna, J.

    2016-10-01

    Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic classroom approach in which students modelled real-world problems and turn gain a deeper knowledge of the Linear Algebra subject. Considering that most students are digital natives, we use the e-portfolio as a tool of communication between students and teachers, besides being a good place making the work visible. In this article, we present an overview of the design and implementation of a project-based learning for a Linear Algebra course taught during the 2014-2015 at the 'ETSEIB'of Universitat Politècnica de Catalunya (UPC).

  14. A note on probabilistic models over strings: the linear algebra approach.

    PubMed

    Bouchard-Côté, Alexandre

    2013-12-01

    Probabilistic models over strings have played a key role in developing methods that take into consideration indels as phylogenetically informative events. There is an extensive literature on using automata and transducers on phylogenies to do inference on these probabilistic models, in which an important theoretical question is the complexity of computing the normalization of a class of string-valued graphical models. This question has been investigated using tools from combinatorics, dynamic programming, and graph theory, and has practical applications in Bayesian phylogenetics. In this work, we revisit this theoretical question from a different point of view, based on linear algebra. The main contribution is a set of results based on this linear algebra view that facilitate the analysis and design of inference algorithms on string-valued graphical models. As an illustration, we use this method to give a new elementary proof of a known result on the complexity of inference on the "TKF91" model, a well-known probabilistic model over strings. Compared to previous work, our proving method is easier to extend to other models, since it relies on a novel weak condition, triangular transducers, which is easy to establish in practice. The linear algebra view provides a concise way of describing transducer algorithms and their compositions, opens the possibility of transferring fast linear algebra libraries (for example, based on GPUs), as well as low rank matrix approximation methods, to string-valued inference problems. PMID:24135792

  15. A note on probabilistic models over strings: the linear algebra approach.

    PubMed

    Bouchard-Côté, Alexandre

    2013-12-01

    Probabilistic models over strings have played a key role in developing methods that take into consideration indels as phylogenetically informative events. There is an extensive literature on using automata and transducers on phylogenies to do inference on these probabilistic models, in which an important theoretical question is the complexity of computing the normalization of a class of string-valued graphical models. This question has been investigated using tools from combinatorics, dynamic programming, and graph theory, and has practical applications in Bayesian phylogenetics. In this work, we revisit this theoretical question from a different point of view, based on linear algebra. The main contribution is a set of results based on this linear algebra view that facilitate the analysis and design of inference algorithms on string-valued graphical models. As an illustration, we use this method to give a new elementary proof of a known result on the complexity of inference on the "TKF91" model, a well-known probabilistic model over strings. Compared to previous work, our proving method is easier to extend to other models, since it relies on a novel weak condition, triangular transducers, which is easy to establish in practice. The linear algebra view provides a concise way of describing transducer algorithms and their compositions, opens the possibility of transferring fast linear algebra libraries (for example, based on GPUs), as well as low rank matrix approximation methods, to string-valued inference problems.

  16. Fully-Explicit and Self-Consistent Algebraic Reynolds Stress Models

    NASA Technical Reports Server (NTRS)

    Girimaji, Sharath S.

    1995-01-01

    A fully-explicit, self-consistent algebraic expression for the Reynolds stress, which is the exact solution to the Reynolds stress transport equation in the 'weak equilibrium' limit for two-dimensional mean flows for all linear and some quasi-linear pressure-strain models, is derived. Current explicit algebraic Reynolds stress models derived by employing the 'weak equilibrium' assumption treat the production-to-dissipation (P/epsilon) ratio implicitly, resulting in an effective viscosity that can be singular away from the equilibrium limit. In the present paper, the set of simultaneous algebraic Reynolds stress equations are solved in the full non-linear form and the eddy viscosity is found to be non-singular. Preliminary tests indicate that the model performs adequately, even for three dimensional mean flow cases. Due to the explicit and non-singular nature of the effective viscosity, this model should mitigate many of the difficulties encountered in computing complex turbulent flows with the algebraic Reynolds stress models.

  17. Graded Poisson-sigma models and dilaton-deformed 2D supergravity algebra

    NASA Astrophysics Data System (ADS)

    Bergamin, Luzi; Kummer, Wolfgang

    2003-05-01

    Supergravity extensions of generic 2d gravity theories obtained from the graded Poisson-Sigma model (gPSM) approach show a large degree of ambiguity. On the other hand, obstructions may reduce the allowed range of fields as given by the bosonic theory, or even prohibit any extension in certain cases. In our present work we relate the finite W-algebras inherent in the gPSM algebra of constraints to supergravity algebras (Neuveu-Schwarz or Ramond algebras resp.), deformed by the presence of the dilaton field. With very straightforward and natural assumptions on them - like the one linking the anti-commutator of certain fermionic charges to the Hamiltonian constraint without deformation - we are able not only to remove the ambiguities but, at the same time, the singularities referred to above. Thus all especially interesting bosonic models (spherically reduced gravity, the Jackiw-Teitelboim model etc.) under these conditions possess a unique fermionic extension and are free from new singularities. The superspace supergravity model of Howe is found as a special case of this supergravity action. For this class of models the relation between bosonic potential and prepotential does not introduce obstructions as well.

  18. A stochastic extension of the explicit algebraic subgrid-scale models

    SciTech Connect

    Rasam, A. Brethouwer, G.; Johansson, A. V.

    2014-05-15

    The explicit algebraic subgrid-scale (SGS) stress model (EASM) of Marstorp et al. [“Explicit algebraic subgrid stress models with application to rotating channel flow,” J. Fluid Mech. 639, 403–432 (2009)] and explicit algebraic SGS scalar flux model (EASFM) of Rasam et al. [“An explicit algebraic model for the subgrid-scale passive scalar flux,” J. Fluid Mech. 721, 541–577 (2013)] are extended with stochastic terms based on the Langevin equation formalism for the subgrid-scales by Marstorp et al. [“A stochastic subgrid model with application to turbulent flow and scalar mixing,” Phys. Fluids 19, 035107 (2007)]. The EASM and EASFM are nonlinear mixed and tensor eddy-diffusivity models, which improve large eddy simulation (LES) predictions of the mean flow, Reynolds stresses, and scalar fluxes of wall-bounded flows compared to isotropic eddy-viscosity and eddy-diffusivity SGS models, especially at coarse resolutions. The purpose of the stochastic extension of the explicit algebraic SGS models is to further improve the characteristics of the kinetic energy and scalar variance SGS dissipation, which are key quantities that govern the small-scale mixing and dispersion dynamics. LES of turbulent channel flow with passive scalar transport shows that the stochastic terms enhance SGS dissipation statistics such as length scale, variance, and probability density functions and introduce a significant amount of backscatter of energy from the subgrid to the resolved scales without causing numerical stability problems. The improvements in the SGS dissipation predictions in turn enhances the predicted resolved statistics such as the mean scalar, scalar fluxes, Reynolds stresses, and correlation lengths. Moreover, the nonalignment between the SGS stress and resolved strain-rate tensors predicted by the EASM with stochastic extension is in much closer agreement with direct numerical simulation data.

  19. Using computer algebra and SMT-solvers to analyze a mathematical model of cholera propagation

    NASA Astrophysics Data System (ADS)

    Trujillo Arredondo, Mariana

    2014-06-01

    We analyze a mathematical model for the transmission of cholera. The model is already defined and involves variables such as the pathogen agent, which in this case is the bacterium Vibrio cholera, and the human population. The human population is divided into three classes: susceptible, infectious and removed. Using Computer Algebra, specifically Maple we obtain two equilibrium states: the disease free state and the endemic state. Using Maple it is possible to prove that the disease free state is locally asymptotically stable if and only if R0 < 1. Using Maple it is possible to prove that the endemic equilibrium state is locally stable when it exists, it is to say when R0 > 1. Using the package Red-Log of the Computer algebra system Reduce and the SMT-Solver Z3Py it is possible to obtain numerical conditions for the model. The formula for the basic reproductive number makes a synthesis with all epidemic parameters in the model. Also it is possible to make numerical simulations which are very illustrative about the epidemic patters that are expected to be observed in real situations. We claim that these kinds of software are very useful in the analysis of epidemic models given that the symbolic computation provides algebraic formulas for the basic reproductive number and such algebraic formulas are very useful to derive control measures. For other side, computer algebra software is a powerful tool to make the stability analysis for epidemic models given that the all steps in the stability analysis can be made automatically: finding the equilibrium points, computing the jacobian, computing the characteristic polynomial for the jacobian, and applying the Routh-Hurwitz theorem to the characteristic polynomial. Finally, using SMT-Solvers is possible to make automatically checks of satisfiability, validity and quantifiers elimination being these computations very useful to analyse complicated epidemic models.

  20. Existence of standard models of conic fibrations over non-algebraically-closed fields

    SciTech Connect

    Avilov, A A

    2014-12-31

    We prove an analogue of Sarkisov's theorem on the existence of a standard model of a conic fibration over an algebraically closed field of characteristic different from two for three-dimensional conic fibrations over an arbitrary field of characteristic zero with an action of a finite group. Bibliography: 16 titles.

  1. Mathematical Modelling in Engineering: An Alternative Way to Teach Linear Algebra

    ERIC Educational Resources Information Center

    Domínguez-García, S.; García-Planas, M. I.; Taberna, J.

    2016-01-01

    Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic…

  2. Gup-Based and Snyder Noncommutative Algebras, Relativistic Particle Models, Deformed Symmetries and Interaction: a Unified Approach

    NASA Astrophysics Data System (ADS)

    Pramanik, Souvik; Ghosh, Subir

    2013-08-01

    We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space-time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.

  3. Gup-Based and Snyder Noncommutative Algebras, Relativistic Particle Models, Deformed Symmetries and Interaction: a Unified Approach

    NASA Astrophysics Data System (ADS)

    Pramanik, Souvik; Ghosh, Subir

    2013-10-01

    We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space-time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.

  4. CSOS models descending from chiral Potts models: degeneracy of the eigenspace and loop algebra

    NASA Astrophysics Data System (ADS)

    Au-Yang, Helen; Perk, Jacques H. H.

    2016-04-01

    Monodromy matrices of the {{\\boldsymbol{τ }}}2\\phantom{^{\\prime }} model are known to satisfy a Yang-Baxter equation with a six-vertex R-matrix as the intertwiner. The commutation relations of the elements of the monodromy matrices are completely determined by this R-matrix. We show the reason why in the superintegrable case the eigenspace is degenerate, but not in the general case. We then show that the eigenspaces of special CSOS models descending from the chiral Potts model are also degenerate. The existence of an L({{sl}}2) quantum loop algebra (or subalgebra) in these models is established by showing that the Serre relations hold for the generators. The highest weight polynomial (or the Drinfeld polynomial) of the representation is obtained by using the method of Baxter for the superintegrable case. As a byproduct, the eigenvalues of all such CSOS models are given explicitly.

  5. Teaching Algebra without Algebra

    ERIC Educational Resources Information Center

    Kalman, Richard S.

    2008-01-01

    Algebra is, among other things, a shorthand way to express quantitative reasoning. This article illustrates ways for the classroom teacher to convert algebraic solutions to verbal problems into conversational solutions that can be understood by students in the lower grades. Three reasonably typical verbal problems that either appeared as or…

  6. CoSLAM: collaborative visual SLAM in dynamic environments.

    PubMed

    Zou, Danping; Tan, Ping

    2013-02-01

    This paper studies the problem of vision-based simultaneous localization and mapping (SLAM) in dynamic environments with multiple cameras. These cameras move independently and can be mounted on different platforms. All cameras work together to build a global map, including 3D positions of static background points and trajectories of moving foreground points. We introduce intercamera pose estimation and intercamera mapping to deal with dynamic objects in the localization and mapping process. To further enhance the system robustness, we maintain the position uncertainty of each map point. To facilitate intercamera operations, we cluster cameras into groups according to their view overlap, and manage the split and merge of camera groups in real time. Experimental results demonstrate that our system can work robustly in highly dynamic environments and produce more accurate results in static environments. PMID:22547430

  7. Predicting NonInertial Effects with Algebraic Stress Models which Account for Dissipation Rate Anisotropies

    NASA Technical Reports Server (NTRS)

    Jongen, T.; Machiels, L.; Gatski, T. B.

    1997-01-01

    Three types of turbulence models which account for rotational effects in noninertial frames of reference are evaluated for the case of incompressible, fully developed rotating turbulent channel flow. The different types of models are a Coriolis-modified eddy-viscosity model, a realizable algebraic stress model, and an algebraic stress model which accounts for dissipation rate anisotropies. A direct numerical simulation of a rotating channel flow is used for the turbulent model validation. This simulation differs from previous studies in that significantly higher rotation numbers are investigated. Flows at these higher rotation numbers are characterized by a relaminarization on the cyclonic or suction side of the channel, and a linear velocity profile on the anticyclonic or pressure side of the channel. The predictive performance of the three types of models are examined in detail, and formulation deficiencies are identified which cause poor predictive performance for some of the models. Criteria are identified which allow for accurate prediction of such flows by algebraic stress models and their corresponding Reynolds stress formulations.

  8. Concurrent initialization for Bearing-Only SLAM.

    PubMed

    Munguía, Rodrigo; Grau, Antoni

    2010-01-01

    Simultaneous Localization and Mapping (SLAM) is perhaps the most fundamental problem to solve in robotics in order to build truly autonomous mobile robots. The sensors have a large impact on the algorithm used for SLAM. Early SLAM approaches focused on the use of range sensors as sonar rings or lasers. However, cameras have become more and more used, because they yield a lot of information and are well adapted for embedded systems: they are light, cheap and power saving. Unlike range sensors which provide range and angular information, a camera is a projective sensor which measures the bearing of images features. Therefore depth information (range) cannot be obtained in a single step. This fact has propitiated the emergence of a new family of SLAM algorithms: the Bearing-Only SLAM methods, which mainly rely in especial techniques for features system-initialization in order to enable the use of bearing sensors (as cameras) in SLAM systems. In this work a novel and robust method, called Concurrent Initialization, is presented which is inspired by having the complementary advantages of the Undelayed and Delayed methods that represent the most common approaches for addressing the problem. The key is to use concurrently two kinds of feature representations for both undelayed and delayed stages of the estimation. The simulations results show that the proposed method surpasses the performance of previous schemes.

  9. Concurrent initialization for Bearing-Only SLAM.

    PubMed

    Munguía, Rodrigo; Grau, Antoni

    2010-01-01

    Simultaneous Localization and Mapping (SLAM) is perhaps the most fundamental problem to solve in robotics in order to build truly autonomous mobile robots. The sensors have a large impact on the algorithm used for SLAM. Early SLAM approaches focused on the use of range sensors as sonar rings or lasers. However, cameras have become more and more used, because they yield a lot of information and are well adapted for embedded systems: they are light, cheap and power saving. Unlike range sensors which provide range and angular information, a camera is a projective sensor which measures the bearing of images features. Therefore depth information (range) cannot be obtained in a single step. This fact has propitiated the emergence of a new family of SLAM algorithms: the Bearing-Only SLAM methods, which mainly rely in especial techniques for features system-initialization in order to enable the use of bearing sensors (as cameras) in SLAM systems. In this work a novel and robust method, called Concurrent Initialization, is presented which is inspired by having the complementary advantages of the Undelayed and Delayed methods that represent the most common approaches for addressing the problem. The key is to use concurrently two kinds of feature representations for both undelayed and delayed stages of the estimation. The simulations results show that the proposed method surpasses the performance of previous schemes. PMID:22294884

  10. Concurrent Initialization for Bearing-Only SLAM

    PubMed Central

    Munguía, Rodrigo; Grau, Antoni

    2010-01-01

    Simultaneous Localization and Mapping (SLAM) is perhaps the most fundamental problem to solve in robotics in order to build truly autonomous mobile robots. The sensors have a large impact on the algorithm used for SLAM. Early SLAM approaches focused on the use of range sensors as sonar rings or lasers. However, cameras have become more and more used, because they yield a lot of information and are well adapted for embedded systems: they are light, cheap and power saving. Unlike range sensors which provide range and angular information, a camera is a projective sensor which measures the bearing of images features. Therefore depth information (range) cannot be obtained in a single step. This fact has propitiated the emergence of a new family of SLAM algorithms: the Bearing-Only SLAM methods, which mainly rely in especial techniques for features system-initialization in order to enable the use of bearing sensors (as cameras) in SLAM systems. In this work a novel and robust method, called Concurrent Initialization, is presented which is inspired by having the complementary advantages of the Undelayed and Delayed methods that represent the most common approaches for addressing the problem. The key is to use concurrently two kinds of feature representations for both undelayed and delayed stages of the estimation. The simulations results show that the proposed method surpasses the performance of previous schemes. PMID:22294884

  11. Petri nets modeling and analysis using extended bag-theoretic relational algebra.

    PubMed

    Kim, Y C; Kim, T G

    1996-01-01

    Petri nets are a powerful modeling tool for studying reactive, concurrent systems. Analysis of the nets can reveal important information concerning the behavior of a modeled system. While various means for the analysis of the nets has been developed, a major limitation in the analysis, is explosion of large states space in simulation. An efficient method to manage large states space would overcome such a limitation. This paper proposes a framework for the modeling and analysis of Petri nets using relational database technologies. Formalism of the framework is based on a bag-theoretic relational algebra extended from the conventional, Within the framework, Petri nets are formalized by bag relations, and analysis algorithms are developed based on such formal relations. Properties associated with the nets are formalized by queries described in terms of the bag-theoretic relational algebra. The framework has been realized in a commercial relational database system using a standard SQL.

  12. High Pathogenicity of Wild-Type Measles Virus Infection in CD150 (SLAM) Transgenic Mice

    PubMed Central

    Sellin, Caroline I.; Davoust, Nathalie; Guillaume, Vanessa; Baas, Dominique; Belin, Marie-Françoise; Buckland, Robin; Wild, T. Fabian; Horvat, Branka

    2006-01-01

    Measles virus (MV) infection causes an acute childhood disease, associated in certain cases with infection of the central nervous system and development of a severe neurological disease. We have generated transgenic mice ubiquitously expressing the human protein SLAM (signaling lymphocytic activation molecule), or CD150, recently identified as an MV receptor. In contrast to all other MV receptor transgenic models described so far, in these mice infection with wild-type MV strains is highly pathogenic. Intranasal infection of SLAM transgenic suckling mice leads to MV spread to different organs and the development of an acute neurological syndrome, characterized by lethargy, seizures, ataxia, weight loss, and death within 3 weeks. In addition, in this model, vaccine and wild-type MV strains can be distinguished by virulence. Furthermore, intracranial MV infection of adult transgenic mice generates a subclinical infection associated with a high titer of MV-specific antibodies in the serum. Finally, to analyze new antimeasles therapeutic approaches, we created a recombinant soluble form of SLAM and demonstrated its important antiviral activity both in vitro and in vivo. Taken together, our results show the high susceptibility of SLAM transgenic mice to MV-induced neurological disease and open new perspectives for the analysis of the implication of SLAM in the neuropathogenicity of other morbilliviruses, which also use this molecule as a receptor. Moreover, this transgenic model, in allowing a simple readout of the efficacy of an antiviral treatment, provides unique experimental means to test novel anti-MV preventive and therapeutic strategies. PMID:16775330

  13. Entanglement in a model for Hawking radiation: An application of quadratic algebras

    SciTech Connect

    Bambah, Bindu A.; Mukku, C.; Shreecharan, T.; Siva Prasad, K.

    2013-03-15

    Quadratic polynomially deformed su(1,1) and su(2) algebras are utilized in model Hamiltonians to show how the gravitational system consisting of a black hole, infalling radiation and outgoing (Hawking) radiation can be solved exactly. The models allow us to study the long-time behaviour of the black hole and its outgoing modes. In particular, we calculate the bipartite entanglement entropies of subsystems consisting of (a) infalling plus outgoing modes and (b) black hole modes plus the infalling modes, using the Janus-faced nature of the model. The long-time behaviour also gives us glimpses of modifications in the character of Hawking radiation. Finally, we study the phenomenon of superradiance in our model in analogy with atomic Dicke superradiance. - Highlights: Black-Right-Pointing-Pointer We examine a toy model for Hawking radiation with quantized black hole modes. Black-Right-Pointing-Pointer We use quadratic polynomially deformed su(1,1) algebras to study its entanglement properties. Black-Right-Pointing-Pointer We study the 'Dicke Superradiance' in black hole radiation using quadratically deformed su(2) algebras. Black-Right-Pointing-Pointer We study the modification of the thermal character of Hawking radiation due to quantized black hole modes.

  14. Integrating programming features with an algebraic modeling language for optimization

    SciTech Connect

    Fourer, R.; Gay, D.

    1994-12-31

    In describing optimization models to a computer, programming is best avoided. In using models as part of a larger scheme, however, programs must be written to specify how information is passed between models. We describe a programming environment for this purpose that has been integrated with the AMPL modeling language.

  15. Accurate Mobile Urban Mapping via Digital Map-Based SLAM †.

    PubMed

    Roh, Hyunchul; Jeong, Jinyong; Cho, Younggun; Kim, Ayoung

    2016-01-01

    This paper presents accurate urban map generation using digital map-based Simultaneous Localization and Mapping (SLAM). Throughout this work, our main objective is generating a 3D and lane map aiming for sub-meter accuracy. In conventional mapping approaches, achieving extremely high accuracy was performed by either (i) exploiting costly airborne sensors or (ii) surveying with a static mapping system in a stationary platform. Mobile scanning systems recently have gathered popularity but are mostly limited by the availability of the Global Positioning System (GPS). We focus on the fact that the availability of GPS and urban structures are both sporadic but complementary. By modeling both GPS and digital map data as measurements and integrating them with other sensor measurements, we leverage SLAM for an accurate mobile mapping system. Our proposed algorithm generates an efficient graph SLAM and achieves a framework running in real-time and targeting sub-meter accuracy with a mobile platform. Integrated with the SLAM framework, we implement a motion-adaptive model for the Inverse Perspective Mapping (IPM). Using motion estimation derived from SLAM, the experimental results show that the proposed approaches provide stable bird's-eye view images, even with significant motion during the drive. Our real-time map generation framework is validated via a long-distance urban test and evaluated at randomly sampled points using Real-Time Kinematic (RTK)-GPS. PMID:27548175

  16. Accurate Mobile Urban Mapping via Digital Map-Based SLAM †.

    PubMed

    Roh, Hyunchul; Jeong, Jinyong; Cho, Younggun; Kim, Ayoung

    2016-08-18

    This paper presents accurate urban map generation using digital map-based Simultaneous Localization and Mapping (SLAM). Throughout this work, our main objective is generating a 3D and lane map aiming for sub-meter accuracy. In conventional mapping approaches, achieving extremely high accuracy was performed by either (i) exploiting costly airborne sensors or (ii) surveying with a static mapping system in a stationary platform. Mobile scanning systems recently have gathered popularity but are mostly limited by the availability of the Global Positioning System (GPS). We focus on the fact that the availability of GPS and urban structures are both sporadic but complementary. By modeling both GPS and digital map data as measurements and integrating them with other sensor measurements, we leverage SLAM for an accurate mobile mapping system. Our proposed algorithm generates an efficient graph SLAM and achieves a framework running in real-time and targeting sub-meter accuracy with a mobile platform. Integrated with the SLAM framework, we implement a motion-adaptive model for the Inverse Perspective Mapping (IPM). Using motion estimation derived from SLAM, the experimental results show that the proposed approaches provide stable bird's-eye view images, even with significant motion during the drive. Our real-time map generation framework is validated via a long-distance urban test and evaluated at randomly sampled points using Real-Time Kinematic (RTK)-GPS.

  17. Accurate Mobile Urban Mapping via Digital Map-Based SLAM

    PubMed Central

    Roh, Hyunchul; Jeong, Jinyong; Cho, Younggun; Kim, Ayoung

    2016-01-01

    This paper presents accurate urban map generation using digital map-based Simultaneous Localization and Mapping (SLAM). Throughout this work, our main objective is generating a 3D and lane map aiming for sub-meter accuracy. In conventional mapping approaches, achieving extremely high accuracy was performed by either (i) exploiting costly airborne sensors or (ii) surveying with a static mapping system in a stationary platform. Mobile scanning systems recently have gathered popularity but are mostly limited by the availability of the Global Positioning System (GPS). We focus on the fact that the availability of GPS and urban structures are both sporadic but complementary. By modeling both GPS and digital map data as measurements and integrating them with other sensor measurements, we leverage SLAM for an accurate mobile mapping system. Our proposed algorithm generates an efficient graph SLAM and achieves a framework running in real-time and targeting sub-meter accuracy with a mobile platform. Integrated with the SLAM framework, we implement a motion-adaptive model for the Inverse Perspective Mapping (IPM). Using motion estimation derived from SLAM, the experimental results show that the proposed approaches provide stable bird’s-eye view images, even with significant motion during the drive. Our real-time map generation framework is validated via a long-distance urban test and evaluated at randomly sampled points using Real-Time Kinematic (RTK)-GPS. PMID:27548175

  18. Intelligently deciphering unintelligible designs: algorithmic algebraic model checking in systems biology

    PubMed Central

    Mishra, Bud

    2009-01-01

    Systems biology, as a subject, has captured the imagination of both biologists and systems scientists alike. But what is it? This review provides one researcher's somewhat idiosyncratic view of the subject, but also aims to persuade young scientists to examine the possible evolution of this subject in a rich historical context. In particular, one may wish to read this review to envision a subject built out of a consilience of many interesting concepts from systems sciences, logic and model theory, and algebra, culminating in novel tools, techniques and theories that can reveal deep principles in biology—seen beyond mere observations. A particular focus in this review is on approaches embedded in an embryonic program, dubbed ‘algorithmic algebraic model checking’, and its powers and limitations. PMID:19364723

  19. Construction of linear models: A framework based on commutative Jordan algebras

    NASA Astrophysics Data System (ADS)

    Covas, R.; Carvalho, F.

    2016-06-01

    We show how to obtain the necessary structures for statistical analysis of the folllowing orthogonal models Y˜(1 μ +∑i Xiβi ,∑j σj2Mj+σ2I ) . These structures rely on the existence of Jordan algebras, in the sequence of [24], [8], [12], [9], [5] and [10].

  20. On the Gaudin model associated to Lie algebras of classical types

    NASA Astrophysics Data System (ADS)

    Lu, Kang; Mukhin, E.; Varchenko, A.

    2016-10-01

    We derive explicit formulas for solutions of the Bethe ansatz equations of the Gaudin model associated to the tensor product of one arbitrary finite-dimensional irreducible module and one vector representation for all simple Lie algebras of classical type. We use this result to show that the Bethe ansatz is complete in any tensor product where all but one factor are vector representations and the evaluation parameters are generic.

  1. Visual SLAM Using Variance Grid Maps

    NASA Technical Reports Server (NTRS)

    Howard, Andrew B.; Marks, Tim K.

    2011-01-01

    An algorithm denoted Gamma-SLAM performs further processing, in real time, of preprocessed digitized images acquired by a stereoscopic pair of electronic cameras aboard an off-road robotic ground vehicle to build accurate maps of the terrain and determine the location of the vehicle with respect to the maps. Part of the name of the algorithm reflects the fact that the process of building the maps and determining the location with respect to them is denoted simultaneous localization and mapping (SLAM). Most prior real-time SLAM algorithms have been limited in applicability to (1) systems equipped with scanning laser range finders as the primary sensors in (2) indoor environments (or relatively simply structured outdoor environments). The few prior vision-based SLAM algorithms have been feature-based and not suitable for real-time applications and, hence, not suitable for autonomous navigation on irregularly structured terrain. The Gamma-SLAM algorithm incorporates two key innovations: Visual odometry (in contradistinction to wheel odometry) is used to estimate the motion of the vehicle. An elevation variance map (in contradistinction to an occupancy or an elevation map) is used to represent the terrain. The Gamma-SLAM algorithm makes use of a Rao-Blackwellized particle filter (RBPF) from Bayesian estimation theory for maintaining a distribution over poses and maps. The core idea of the RBPF approach is that the SLAM problem can be factored into two parts: (1) finding the distribution over robot trajectories, and (2) finding the map conditioned on any given trajectory. The factorization involves the use of a particle filter in which each particle encodes both a possible trajectory and a map conditioned on that trajectory. The base estimate of the trajectory is derived from visual odometry, and the map conditioned on that trajectory is a Cartesian grid of elevation variances. In comparison with traditional occupancy or elevation grid maps, the grid elevation variance

  2. ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra

    PubMed Central

    2011-01-01

    Background Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. Results We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Conclusions Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on

  3. Closure of the algebra of constraints for a nonprojectable Horava model

    SciTech Connect

    Bellorin, Jorge; Restuccia, Alvaro

    2011-02-15

    We perform the Hamiltonian analysis for a nonprojectable Horava model whose potential is composed of R and R{sup 2} terms. We show that Dirac's algorithm for the preservation of the constraints can be done in a closed way, hence the algebra of constraints for this model is consistent. The model has an extra, odd, scalar mode whose decoupling limit can be seen in a linear-order perturbative analysis on weakly varying backgrounds. Although our results for this model point in favor of the consistency of the Horava theory, the validity of the full nonprojectable theory still remains unanswered.

  4. On the consistency analysis of A-SLAM for UAV navigation

    NASA Astrophysics Data System (ADS)

    Oguz, A. E.; Temeltas, Hakan

    2014-06-01

    Simultaneous Localization and Mapping (SLAM) is a good choice for UAV navigation when both UAV's position and region map are not known. Due to nonlinearity of kinematic equations of a UAV, Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are employed. In this study, EKF and UKF based A-SLAM concepts are discussed in details by presenting the formulations and simulation results. The UAV kinematic model and the state-observation models for EKF and UKF based A-SLAM methods are developed to analyze the filters' consistencies. Analysis during landmark observation exhibits an inconsistency in the form of a jagged UAV trajectory. It has been found that unobservable subspaces and the Jacobien matrices used for linearization are two major sources of the inconsistencies observed. UKF performs better in terms of filter consistency since it does not require the Jacobien matrix linearization.

  5. A deformation of quantum affine algebra in squashed Wess-Zumino-Novikov-Witten models

    SciTech Connect

    Kawaguchi, Io; Yoshida, Kentaroh

    2014-06-01

    We proceed to study infinite-dimensional symmetries in two-dimensional squashed Wess-Zumino-Novikov-Witten models at the classical level. The target space is given by squashed S³ and the isometry is SU(2){sub L}×U(1){sub R}. It is known that SU(2){sub L} is enhanced to a couple of Yangians. We reveal here that an infinite-dimensional extension of U(1){sub R} is a deformation of quantum affine algebra, where a new deformation parameter is provided with the coefficient of the Wess-Zumino term. Then we consider the relation between the deformed quantum affine algebra and the pair of Yangians from the viewpoint of the left-right duality of monodromy matrices. The integrable structure is also discussed by computing the r/s-matrices that satisfy the extended classical Yang-Baxter equation. Finally, two degenerate limits are discussed.

  6. A realizable explicit algebraic Reynolds stress model for compressible turbulent flow with significant mean dilatation

    NASA Astrophysics Data System (ADS)

    Grigoriev, I. A.; Wallin, S.; Brethouwer, G.; Johansson, A. V.

    2013-10-01

    The explicit algebraic Reynolds stress model of Wallin and Johansson [J. Fluid Mech. 403, 89 (2000)] is extended to compressible and variable-density turbulent flows. This is achieved by correctly taking into account the influence of the mean dilatation on the rapid pressure-strain correlation. The resulting model is formally identical to the original model in the limit of constant density. For two-dimensional mean flows the model is analyzed and the physical root of the resulting quartic equation is identified. Using a fixed-point analysis of homogeneously sheared and strained compressible flows, we show that the new model is realizable, unlike the previous model. Application of the model together with a K - ω model to quasi one-dimensional plane nozzle flow, transcending from subsonic to supersonic regime, also demonstrates realizability. Negative "dilatational" production of turbulence kinetic energy competes with positive "incompressible" production, eventually making the total production negative during the spatial evolution of the nozzle flow. Finally, an approach to include the baroclinic effect into the dissipation equation is proposed and an algebraic model for density-velocity correlations is outlined to estimate the corrections associated with density fluctuations. All in all, the new model can become a significant tool for CFD (computational fluid dynamics) of compressible flows.

  7. Teaching Algebra and Geometry Concepts by Modeling Telescope Optics

    ERIC Educational Resources Information Center

    Siegel, Lauren M.; Dickinson, Gail; Hooper, Eric J.; Daniels, Mark

    2008-01-01

    This article describes preparation and delivery of high school mathematics lessons that integrate mathematics and astronomy through The Geometer's Sketchpad models, traditional proof, and inquiry-based activities. The lessons were created by a University of Texas UTeach preservice teacher as part of a project-based field experience in which high…

  8. The addition of algebraic turbulence modeling to program LAURA

    NASA Astrophysics Data System (ADS)

    Cheatwood, F. Mcneil; Thompson, R. A.

    1993-04-01

    The Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) is modified to allow the calculation of turbulent flows. This is accomplished using the Cebeci-Smith and Baldwin-Lomax eddy-viscosity models in conjunction with the thin-layer Navier-Stokes options of the program. Turbulent calculations can be performed for both perfect-gas and equilibrium flows. However, a requirement of the models is that the flow be attached. It is seen that for slender bodies, adequate resolution of the boundary-layer gradients may require more cells in the normal direction than a laminar solution, even when grid stretching is employed. Results for axisymmetric and three-dimensional flows are presented. Comparison with experimental data and other numerical results reveal generally good agreement, except in the regions of detached flow.

  9. Efficient approach for binocular vision-SLAM

    NASA Astrophysics Data System (ADS)

    Zhu, Dai-Xian

    2010-08-01

    This paper presents an approach to binocular vision simultaneous localization and mapping (SLAM). SIFT (Scale Invariant Feature Transform) algorithm is used to extract the Natural landmarks. But SIFT algorithm is complicated and computation time is long. Firstly, the linear combination of cityblock distance and chessboard distance is comparability measurement; secondly, partial features are used to matching. SLAM is completed by fusing the information of SIFT features and robot information with EKF. Mahalanobisis distance is used in data association which solve the problem that the scale of data association increase with the map grows in process of SLAM .The simulation experiment indicate that the proposed method reduce computational complexity, and with high localization precision in indoor environments.

  10. Algebraic approach to the projected deformed oscillator model

    NASA Astrophysics Data System (ADS)

    Asherova, R. M.; Smirnov, Yu. F.; Tolstoy, V. N.; Shustov, A. P.

    1981-03-01

    A new method of calculation in terms of the projected deformed oscillator model is proposed. The method involves expansion of its wave functions in terms of the wave functions of an isotropic oscillator potential. Only overlap integrals between projected wave functions and reduced probabilities B(E2) of E2 transitions are examined. B(E2) values are expressed as a series containing the corresponding values of the Elliott SU(3) scheme. The convergence of these expansions is shown to be fairly good. The expectation values of operators ( QQ) and ( QQQ), which characterize the effective internal non-sphericity and non-axiality of the nucleus, are also calculated and discussed.

  11. Sensitivity analysis and model reduction of nonlinear differential-algebraic systems. Final progress report

    SciTech Connect

    Petzold, L.R.; Rosen, J.B.

    1997-12-30

    Differential-algebraic equations arise in a wide variety of engineering and scientific problems. Relatively little work has been done regarding sensitivity analysis and model reduction for this class of problems. Efficient methods for sensitivity analysis are required in model development and as an intermediate step in design optimization of engineering processes. Reduced order models are needed for modelling complex physical phenomena like turbulent reacting flows, where it is not feasible to use a fully-detailed model. The objective of this work has been to develop numerical methods and software for sensitivity analysis and model reduction of nonlinear differential-algebraic systems, including large-scale systems. In collaboration with Peter Brown and Alan Hindmarsh of LLNL, the authors developed an algorithm for finding consistent initial conditions for several widely occurring classes of differential-algebraic equations (DAEs). The new algorithm is much more robust than the previous algorithm. It is also very easy to use, having been designed to require almost no information about the differential equation, Jacobian matrix, etc. in addition to what is already needed to take the subsequent time steps. The new algorithm has been implemented in a version of the software for solution of large-scale DAEs, DASPK, which has been made available on the internet. The new methods and software have been used to solve a Tokamak edge plasma problem at LLNL which could not be solved with the previous methods and software because of difficulties in finding consistent initial conditions. The capability of finding consistent initial values is also needed for the sensitivity and optimization efforts described in this paper.

  12. Steady state analysis of Boolean molecular network models via model reduction and computational algebra

    PubMed Central

    2014-01-01

    Background A key problem in the analysis of mathematical models of molecular networks is the determination of their steady states. The present paper addresses this problem for Boolean network models, an increasingly popular modeling paradigm for networks lacking detailed kinetic information. For small models, the problem can be solved by exhaustive enumeration of all state transitions. But for larger models this is not feasible, since the size of the phase space grows exponentially with the dimension of the network. The dimension of published models is growing to over 100, so that efficient methods for steady state determination are essential. Several methods have been proposed for large networks, some of them heuristic. While these methods represent a substantial improvement in scalability over exhaustive enumeration, the problem for large networks is still unsolved in general. Results This paper presents an algorithm that consists of two main parts. The first is a graph theoretic reduction of the wiring diagram of the network, while preserving all information about steady states. The second part formulates the determination of all steady states of a Boolean network as a problem of finding all solutions to a system of polynomial equations over the finite number system with two elements. This problem can be solved with existing computer algebra software. This algorithm compares favorably with several existing algorithms for steady state determination. One advantage is that it is not heuristic or reliant on sampling, but rather determines algorithmically and exactly all steady states of a Boolean network. The code for the algorithm, as well as the test suite of benchmark networks, is available upon request from the corresponding author. Conclusions The algorithm presented in this paper reliably determines all steady states of sparse Boolean networks with up to 1000 nodes. The algorithm is effective at analyzing virtually all published models even those of moderate

  13. Generalized model of double random phase encoding based on linear algebra

    NASA Astrophysics Data System (ADS)

    Nakano, Kazuya; Takeda, Masafumi; Suzuki, Hiroyuki; Yamaguchi, Masahiro

    2013-01-01

    We propose a generalized model for double random phase encoding (DRPE) based on linear algebra. We defined the DRPE procedure in six steps. The first three steps form an encryption procedure, while the later three steps make up a decryption procedure. We noted that the first (mapping) and second (transform) steps can be generalized. As an example of this generalization, we used 3D mapping and a transform matrix, which is a combination of a discrete cosine transform and two permutation matrices. Finally, we investigated the sensitivity of the proposed model to errors in the decryption key.

  14. Comparison of real-time performance of Kalman filter-based slam methods for unmanned ground vehicle (UGV) navigation

    NASA Astrophysics Data System (ADS)

    Temeltaş, Hakan; Kavak, Deniz

    2009-05-01

    Simultaneous Localization and Mapping (SLAM) using for the mobile robot navigation has two main problems. First problem is the computational complexity due to the growing state vector with the added landmark in the environment. Second problem is data association which matches the observations and landmarks in the state vector. In this study, we compare Extended Kalman Filter (EKF) based SLAM which is well-developed and well-known algorithm, and Compressed Extended Kalman Filter (CEKF) based SLAM developed for decreasing of the computational complexity of the EKF based SLAM. We write two simulation program to investigate these techniques. Firts program is written for the comparison of EKF and CEKF based SLAM according to the computational complexity and covariance matrix error with the different numbers of landmarks. In the second program, EKF and CEKF based SLAM simulations are presented. For this simulation differential drive vehicle that moves in a 10m square trajectory and LMS 200 2-D laser range finder are modelled and landmarks are randomly scattered in that 10m square environment.

  15. Using process algebra to develop predator-prey models of within-host parasite dynamics.

    PubMed

    McCaig, Chris; Fenton, Andy; Graham, Andrea; Shankland, Carron; Norman, Rachel

    2013-07-21

    As a first approximation of immune-mediated within-host parasite dynamics we can consider the immune response as a predator, with the parasite as its prey. In the ecological literature of predator-prey interactions there are a number of different functional responses used to describe how a predator reproduces in response to consuming prey. Until recently most of the models of the immune system that have taken a predator-prey approach have used simple mass action dynamics to capture the interaction between the immune response and the parasite. More recently Fenton and Perkins (2010) employed three of the most commonly used prey-dependent functional response terms from the ecological literature. In this paper we make use of a technique from computing science, process algebra, to develop mathematical models. The novelty of the process algebra approach is to allow stochastic models of the population (parasite and immune cells) to be developed from rules of individual cell behaviour. By using this approach in which individual cellular behaviour is captured we have derived a ratio-dependent response similar to that seen in the previous models of immune-mediated parasite dynamics, confirming that, whilst this type of term is controversial in ecological predator-prey models, it is appropriate for models of the immune system.

  16. Semantic data association for planar features in outdoor 6D-SLAM using lidar

    NASA Astrophysics Data System (ADS)

    Ulas, C.; Temeltas, H.

    2013-05-01

    Simultaneous Localization and Mapping (SLAM) is a fundamental problem of the autonomous systems in GPS (Global Navigation System) denied environments. The traditional probabilistic SLAM methods uses point features as landmarks and hold all the feature positions in their state vector in addition to the robot pose. The bottleneck of the point-feature based SLAM methods is the data association problem, which are mostly based on a statistical measure. The data association performance is very critical for a robust SLAM method since all the filtering strategies are applied after a known correspondence. For point-features, two different but very close landmarks in the same scene might be confused while giving the correspondence decision when their positions and error covariance matrix are solely taking into account. Instead of using the point features, planar features can be considered as an alternative landmark model in the SLAM problem to be able to provide a more consistent data association. Planes contain rich information for the solution of the data association problem and can be distinguished easily with respect to point features. In addition, planar maps are very compact since an environment has only very limited number of planar structures. The planar features does not have to be large structures like building wall or roofs; the small plane segments can also be used as landmarks like billboards, traffic posts and some part of the bridges in urban areas. In this paper, a probabilistic plane-feature extraction method from 3DLiDAR data and the data association based on the extracted semantic information of the planar features is introduced. The experimental results show that the semantic data association provides very satisfactory result in outdoor 6D-SLAM.

  17. A computer code for calculations in the algebraic collective model of the atomic nucleus

    NASA Astrophysics Data System (ADS)

    Welsh, T. A.; Rowe, D. J.

    2016-03-01

    A Maple code is presented for algebraic collective model (ACM) calculations. The ACM is an algebraic version of the Bohr model of the atomic nucleus, in which all required matrix elements are derived by exploiting the model's SU(1 , 1) × SO(5) dynamical group. This paper reviews the mathematical formulation of the ACM, and serves as a manual for the code. The code enables a wide range of model Hamiltonians to be analysed. This range includes essentially all Hamiltonians that are rational functions of the model's quadrupole moments qˆM and are at most quadratic in the corresponding conjugate momenta πˆN (- 2 ≤ M , N ≤ 2). The code makes use of expressions for matrix elements derived elsewhere and newly derived matrix elements of the operators [ π ˆ ⊗ q ˆ ⊗ π ˆ ] 0 and [ π ˆ ⊗ π ˆ ] LM. The code is made efficient by use of an analytical expression for the needed SO(5)-reduced matrix elements, and use of SO(5) ⊃ SO(3)  Clebsch-Gordan coefficients obtained from precomputed data files provided with the code.

  18. Explicit algebraic reynolds stress models for anisotropic wall-bounded flows

    NASA Astrophysics Data System (ADS)

    Menter, F. R.; Garbaruk, A. V.; Egorov, Y.

    2012-01-01

    In the present paper, two variants of Explicit Algebraic Reynolds Stress Model (EARSM) are presented and applied to a number of test cases. Both formulations start from the Wallin Johansson (WJ) EARSM stress-strain relationship. The goal of the first step was to combine the EARSM with the ω-equation-based Baseline (BSL) model, to avoid freestream sensitivities and ambiguities in comparison with the Shear Stress Transport (SST) model. This could be achieved by a slight change in the A1 constant. In addition, the standard eddy-viscosity formulation is used in the diffusion terms of the k- and the ω-equations. Secondly, a simplified version of the stress-strain relationship was developed. It is based on a linear form of the implicit algebraic model. It is not clear at the time if this formulation possess significant advantages against the WJ stress-strain model. For the current cases, both variants produced essentially identical results. Several test cases have been computed. The main interest in the simulations was on corner flow separation.

  19. A computer code for calculations in the algebraic collective model of the atomic nucleus

    NASA Astrophysics Data System (ADS)

    Welsh, T. A.; Rowe, D. J.

    2016-03-01

    A Maple code is presented for algebraic collective model (ACM) calculations. The ACM is an algebraic version of the Bohr model of the atomic nucleus, in which all required matrix elements are derived by exploiting the model's SU(1 , 1) × SO(5) dynamical group. This paper reviews the mathematical formulation of the ACM, and serves as a manual for the code. The code enables a wide range of model Hamiltonians to be analysed. This range includes essentially all Hamiltonians that are rational functions of the model's quadrupole moments qˆM and are at most quadratic in the corresponding conjugate momenta πˆN (- 2 ≤ M , N ≤ 2). The code makes use of expressions for matrix elements derived elsewhere and newly derived matrix elements of the operators [ π ˆ ⊗ q ˆ ⊗ π ˆ ] 0 and [ π ˆ ⊗ π ˆ ] LM. The code is made efficient by use of an analytical expression for the needed SO(5)-reduced matrix elements, and use of SO(5) ⊃ SO(3) Clebsch-Gordan coefficients obtained from precomputed data files provided with the code.

  20. Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model

    NASA Astrophysics Data System (ADS)

    Cirilo António, N.; Manojlović, N.; Salom, I.

    2014-12-01

    We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the corresponding Bethe vectors through the so-called quasi-classical limit. Moreover, this action is as simple as it could possibly be, yielding the spectrum and the Bethe equations of the Gaudin model.

  1. Visual EKF-SLAM from Heterogeneous Landmarks.

    PubMed

    Esparza-Jiménez, Jorge Othón; Devy, Michel; Gordillo, José L

    2016-04-07

    Many applications require the localization of a moving object, e.g., a robot, using sensory data acquired from embedded devices. Simultaneous localization and mapping from vision performs both the spatial and temporal fusion of these data on a map when a camera moves in an unknown environment. Such a SLAM process executes two interleaved functions: the front-end detects and tracks features from images, while the back-end interprets features as landmark observations and estimates both the landmarks and the robot positions with respect to a selected reference frame. This paper describes a complete visual SLAM solution, combining both point and line landmarks on a single map. The proposed method has an impact on both the back-end and the front-end. The contributions comprehend the use of heterogeneous landmark-based EKF-SLAM (the management of a map composed of both point and line landmarks); from this perspective, the comparison between landmark parametrizations and the evaluation of how the heterogeneity improves the accuracy on the camera localization, the development of a front-end active-search process for linear landmarks integrated into SLAM and the experimentation methodology.

  2. Visual EKF-SLAM from Heterogeneous Landmarks.

    PubMed

    Esparza-Jiménez, Jorge Othón; Devy, Michel; Gordillo, José L

    2016-01-01

    Many applications require the localization of a moving object, e.g., a robot, using sensory data acquired from embedded devices. Simultaneous localization and mapping from vision performs both the spatial and temporal fusion of these data on a map when a camera moves in an unknown environment. Such a SLAM process executes two interleaved functions: the front-end detects and tracks features from images, while the back-end interprets features as landmark observations and estimates both the landmarks and the robot positions with respect to a selected reference frame. This paper describes a complete visual SLAM solution, combining both point and line landmarks on a single map. The proposed method has an impact on both the back-end and the front-end. The contributions comprehend the use of heterogeneous landmark-based EKF-SLAM (the management of a map composed of both point and line landmarks); from this perspective, the comparison between landmark parametrizations and the evaluation of how the heterogeneity improves the accuracy on the camera localization, the development of a front-end active-search process for linear landmarks integrated into SLAM and the experimentation methodology. PMID:27070602

  3. Topological SLAM Using Fast Vision Techniques

    NASA Astrophysics Data System (ADS)

    Werner, Felix; Maire, Frederic; Sitte, Joaquin

    In this paper we propose a method for vision only topological simultaneous localisation and mapping (SLAM). Our approach does not use motion or odometric information but a sequence of noisy visual measurements observed by traversing an environment. In particular, we address the perceptual aliasing problem which occurs using external observations only in topological navigation.

  4. But Slams Will Never Hurt Them.

    ERIC Educational Resources Information Center

    Villalobos, Marco

    2003-01-01

    Describes Youth Speaks NY Fifth Annual Teen Poetry Slam. Considers how Youth Speaks offers free after school writing workshops for teens. Notes that this nonprofit spoken word program Youth Speaks plays host to an auditorium of teen poets who "bust at the seams with verse." (SG)

  5. Current state of the art of vision based SLAM

    NASA Astrophysics Data System (ADS)

    Muhammad, Naveed; Fofi, David; Ainouz, Samia

    2009-02-01

    The ability of a robot to localise itself and simultaneously build a map of its environment (Simultaneous Localisation and Mapping or SLAM) is a fundamental characteristic required for autonomous operation of the robot. Vision Sensors are very attractive for application in SLAM because of their rich sensory output and cost effectiveness. Different issues are involved in the problem of vision based SLAM and many different approaches exist in order to solve these issues. This paper gives a classification of state-of-the-art vision based SLAM techniques in terms of (i) imaging systems used for performing SLAM which include single cameras, stereo pairs, multiple camera rigs and catadioptric sensors, (ii) features extracted from the environment in order to perform SLAM which include point features and line/edge features, (iii) initialisation of landmarks which can either be delayed or undelayed, (iv) SLAM techniques used which include Extended Kalman Filtering, Particle Filtering, biologically inspired techniques like RatSLAM, and other techniques like Local Bundle Adjustment, and (v) use of wheel odometry information. The paper also presents the implementation and analysis of stereo pair based EKF SLAM for synthetic data. Results prove the technique to work successfully in the presence of considerable amounts of sensor noise. We believe that state of the art presented in the paper can serve as a basis for future research in the area of vision based SLAM. It will permit further research in the area to be carried out in an efficient and application specific way.

  6. Fast and accurate computation of system matrix for area integral model-based algebraic reconstruction technique

    NASA Astrophysics Data System (ADS)

    Zhang, Shunli; Zhang, Dinghua; Gong, Hao; Ghasemalizadeh, Omid; Wang, Ge; Cao, Guohua

    2014-11-01

    Iterative algorithms, such as the algebraic reconstruction technique (ART), are popular for image reconstruction. For iterative reconstruction, the area integral model (AIM) is more accurate for better reconstruction quality than the line integral model (LIM). However, the computation of the system matrix for AIM is more complex and time-consuming than that for LIM. Here, we propose a fast and accurate method to compute the system matrix for AIM. First, we calculate the intersection of each boundary line of a narrow fan-beam with pixels in a recursive and efficient manner. Then, by grouping the beam-pixel intersection area into six types according to the slopes of the two boundary lines, we analytically compute the intersection area of the narrow fan-beam with the pixels in a simple algebraic fashion. Overall, experimental results show that our method is about three times faster than the Siddon algorithm and about two times faster than the distance-driven model (DDM) in computation of the system matrix. The reconstruction speed of our AIM-based ART is also faster than the LIM-based ART that uses the Siddon algorithm and DDM-based ART, for one iteration. The fast reconstruction speed of our method was accomplished without compromising the image quality.

  7. Algebraic turbulence models for the computation of two-dimensional high-speed flows using unstructured grids

    NASA Technical Reports Server (NTRS)

    Rostand, Philippe

    1989-01-01

    The incorporation of algebraic turbulence models in a solver for the 2-D compressible Navier-Stokes equations using triangular grids is described. A practial way to use the Cebeci Smith model, and to modify it in separated regions is proposed. The ability of the model to predict high speed, perfect gas boundary layers is investigated from a numerical point of view.

  8. Computer Algebra.

    ERIC Educational Resources Information Center

    Pavelle, Richard; And Others

    1981-01-01

    Describes the nature and use of computer algebra and its applications to various physical sciences. Includes diagrams illustrating, among others, a computer algebra system and flow chart of operation of the Euclidean algorithm. (SK)

  9. Development of an algebraic stress/two-layer model for calculating thrust chamber flow fields

    NASA Astrophysics Data System (ADS)

    Chen, C. P.; Shang, H. M.; Huang, J.

    1993-07-01

    Following the consensus of a workshop in Turbulence Modeling for Liquid Rocket Thrust Chambers, the current effort was undertaken to study the effects of second-order closure on the predictions of thermochemical flow fields. To reduce the instability and computational intensity of the full second-order Reynolds Stress Model, an Algebraic Stress Model (ASM) coupled with a two-layer near wall treatment was developed. Various test problems, including the compressible boundary layer with adiabatic and cooled walls, recirculating flows, swirling flows and the entire SSME nozzle flow were studied to assess the performance of the current model. Detailed calculations for the SSME exit wall flow around the nozzle manifold were executed. As to the overall flow predictions, the ASM removes another assumption for appropriate comparison with experimental data, to account for the non-isotropic turbulence effects.

  10. Development of an algebraic stress/two-layer model for calculating thrust chamber flow fields

    NASA Technical Reports Server (NTRS)

    Chen, C. P.; Shang, H. M.; Huang, J.

    1993-01-01

    Following the consensus of a workshop in Turbulence Modeling for Liquid Rocket Thrust Chambers, the current effort was undertaken to study the effects of second-order closure on the predictions of thermochemical flow fields. To reduce the instability and computational intensity of the full second-order Reynolds Stress Model, an Algebraic Stress Model (ASM) coupled with a two-layer near wall treatment was developed. Various test problems, including the compressible boundary layer with adiabatic and cooled walls, recirculating flows, swirling flows and the entire SSME nozzle flow were studied to assess the performance of the current model. Detailed calculations for the SSME exit wall flow around the nozzle manifold were executed. As to the overall flow predictions, the ASM removes another assumption for appropriate comparison with experimental data, to account for the non-isotropic turbulence effects.

  11. Differential algebraic methods for space charge modeling and applications to the University of Maryland Electron Ring

    NASA Astrophysics Data System (ADS)

    Nissen, Edward W.

    2011-12-01

    The future of particle accelerators is moving towards the intensity frontier; the need to place more particles into a smaller space is a common requirement of nearly all applications of particle accelerators. Putting large numbers of particles in a small space means that the mutual repulsion of these charged particles becomes a significant factor, this effect is called space charge. In this work we develop a series of differential algebra based methods to simulate the effects of space charge in particle accelerators. These methods were used to model the University of Maryland Electron Ring, a small 3.8 meter diameter 10 KeV electron storage ring designed to observe the effects of space charge in a safe, cost effective manner. The methods developed here are designed to not only simulate the effects of space charge on the motions of the test particles in the system but to add their effects to the transfer map of the system. Once they have been added useful information about the beam, such as tune shifts and chromaticities, can be extracted directly from the map. In order to make the simulation self consistent, the statistical moments of the distribution are used to create a self consistent Taylor series representing the distribution function, which is combined with pre-stored integrals solved using a Duffy transformation to find the potential. This method can not only find the map of the system, but also advance the particles under most conditions. For conditions where it cannot be used to accurately advance the particles a differential algebra based fast multipole method is implemented. By using differential algebras to create local expansions, noticeable time savings are found.

  12. ηc elastic and transition form factors: Contact interaction and algebraic model

    NASA Astrophysics Data System (ADS)

    Bedolla, Marco A.; Raya, Khépani; Cobos-Martínez, J. J.; Bashir, Adnan

    2016-05-01

    For the flavor-singlet heavy-quark system of charmonia in the pseudoscalar [ηc(1 S ) ] channel, we calculate the elastic (EFF) and transition form factors (TFFs) [ηc(1 S )→γ γ* ] for a wide range of photon momentum transfer squared (Q2). The framework for this analysis is provided by a symmetry-preserving Schwinger-Dyson equation and Bethe-Salpeter equation treatment of a vector×vector contact interaction. We also employ an algebraic model, developed earlier to describe the light-quark systems. It correctly correlates infrared and ultraviolet dynamics of quantum chromodynamics (QCD). The contact interaction results agree with the lattice data for low Q2. For Q2≥Q02 , the results start deviating from the lattice results by more than 20%. Q02≈2.5 GeV2 for the EFF, and ≈25 GeV2 for the TFF. We also present the results for the EFF, TFF, and ηc(1 S ) parton distribution amplitude for the algebraic model. Wherever the comparison is possible, these results are in excellent agreement with the lattice, perturbative QCD, results obtained through a Schwinger-Dyson equation-Bethe-Salpeter equation study, employing refined truncations, and the experimental findings of the BABAR experiment.

  13. Multiobjective algebraic synthesis of neural control systems by implicit model following.

    PubMed

    Ferrari, Silvia

    2009-03-01

    The advantages brought about by using classical linear control theory in conjunction with neural approximators have long been recognized in the literature. In particular, using linear controllers to obtain the starting neural control design has been shown to be a key step for the successful development and implementation of adaptive-critic neural controllers. Despite their adaptive capabilities, neural controllers are often criticized for not providing the same performance and stability guarantees as classical linear designs. Therefore, this paper develops an algebraic synthesis procedure for designing dynamic output-feedback neural controllers that are closed-loop stable and meet the same performance objectives as any classical linear design. The performance synthesis problem is addressed by deriving implicit model-following algebraic relationships between model matrices, obtained from the classical design, and the neural control parameters. Additional linear matrix inequalities (LMIs) conditions for closed-loop exponential stability of the neural controller are derived using existing integral quadratic constraints (IQCs) for operators with repeated slope-restricted nonlinearities. The approach is demonstrated by designing a recurrent neural network controller for a highly maneuverable tailfin-controlled missile that meets multiple design objectives, including pole placement for transient tuning, H(infinity) and H(2) performance in the presence of parameter uncertainty, and command-input tracking. PMID:19203887

  14. Algebraic solutions for two-level pairing model in IBM-2 and IVBM

    NASA Astrophysics Data System (ADS)

    Jalili-Majarshin, A.; Jafarizadeh, M. A.; Fouladi, N.

    2016-09-01

    In this paper the affine SU(1,1) approach is applied to numerically solve two pairing problems. A dynamical symmetry limit of the two-fluid interacting boson model-2 (IBM-2) and of the interacting vector boson model (IVBM) defined through the chains U_{π}(6) ⊗ U_{ν}(6) supset SO_{π}(5)⊗ SO_{ν}(5) supset SO_{π}(3) ⊗ SO_{ν}(3) supset SO(3) and U(6) supset U_{π}(3) ⊗ U_{ν}(3) supset SO_{π}(3) ⊗ SO_{ν}(3) supset SO(3) are introduced, respectively. The quantum phase transition between spherical and γ-soft shapes in medium-mass nuclei is analyzed using U(5) leftrightarrow SO(6) transitional nuclei in IBM-2 and one case U_{π}(3) ⊗ U_{ν}(3) leftrightarrow SO(6) transitional nuclei in IVBM found by using an infinite dimensional algebraic method based on affine SU(1,1) Lie algebra. The calculated energy spectra, energy ratio and energy staggering of Mo isotopes are compared with experimental results. The interplay between phase transitions and configuration mixing of intruder excitations between spherical vibrations and the γ-soft shapes in Mo isotopes is succinctly addressed and displays fingerprints of the transitional dynamical symmetry E(5).

  15. A rigorous approach to investigating common assumptions about disease transmission: Process algebra as an emerging modelling methodology for epidemiology.

    PubMed

    McCaig, Chris; Begon, Mike; Norman, Rachel; Shankland, Carron

    2011-03-01

    Changing scale, for example, the ability to move seamlessly from an individual-based model to a population-based model, is an important problem in many fields. In this paper, we introduce process algebra as a novel solution to this problem in the context of models of infectious disease spread. Process algebra allows us to describe a system in terms of the stochastic behaviour of individuals, and is a technique from computer science. We review the use of process algebra in biological systems, and the variety of quantitative and qualitative analysis techniques available. The analysis illustrated here solves the changing scale problem: from the individual behaviour we can rigorously derive equations to describe the mean behaviour of the system at the level of the population. The biological problem investigated is the transmission of infection, and how this relates to individual interactions.

  16. A possible framework of the Lipkin model obeying the SU(n) algebra in arbitrary fermion number. I: The SU(2) algebras extended from the conventional fermion pair and determination of the minimum weight states

    NASA Astrophysics Data System (ADS)

    Tsue, Yasuhiko; Providência, Constança; Providência, João da; Yamamura, Masatoshi

    2016-08-01

    The minimum weight states of the Lipkin model consisting of n single-particle levels and obeying the SU(n) algebra are investigated systematically. The basic idea is to use the SU(2) algebra, which is independent of the SU(n) algebra. This idea has already been presented by the present authors in the case of the conventional Lipkin model consisting of two single-particle levels and obeying the SU(2) algebra. If this idea is followed, the minimum weight states are determined for any fermion number appropriately occupying n single-particle levels. Naturally, the conventional minimum weight state is included: all fermions occupy energetically the lowest single-particle level in the absence of interaction. The cases n=2, 3, 4, and 5 are discussed in some detail.

  17. "We Want a Statement That Is Always True": Criteria for Good Algebraic Representations and the Development of Modeling Knowledge.

    ERIC Educational Resources Information Center

    Izsak, Andrew

    2003-01-01

    Presents a case study in which two 8th grade students developed knowledge for modeling a physical device called a winch. Demonstrates that students have and can use criteria for evaluating algebraic representations. Explains how students can develop modeling knowledge by coordinating criteria with knowledge for generating and using algebraic…

  18. Comparing Cognitive Models of Domain Mastery and Task Performance in Algebra: Validity Evidence for a State Assessment

    ERIC Educational Resources Information Center

    Warner, Zachary B.

    2013-01-01

    This study compared an expert-based cognitive model of domain mastery with student-based cognitive models of task performance for Integrated Algebra. Interpretations of student test results are limited by experts' hypotheses of how students interact with the items. In reality, the cognitive processes that students use to solve each item may be…

  19. RGB-D SLAM Combining Visual Odometry and Extended Information Filter

    PubMed Central

    Zhang, Heng; Liu, Yanli; Tan, Jindong; Xiong, Naixue

    2015-01-01

    In this paper, we present a novel RGB-D SLAM system based on visual odometry and an extended information filter, which does not require any other sensors or odometry. In contrast to the graph optimization approaches, this is more suitable for online applications. A visual dead reckoning algorithm based on visual residuals is devised, which is used to estimate motion control input. In addition, we use a novel descriptor called binary robust appearance and normals descriptor (BRAND) to extract features from the RGB-D frame and use them as landmarks. Furthermore, considering both the 3D positions and the BRAND descriptors of the landmarks, our observation model avoids explicit data association between the observations and the map by marginalizing the observation likelihood over all possible associations. Experimental validation is provided, which compares the proposed RGB-D SLAM algorithm with just RGB-D visual odometry and a graph-based RGB-D SLAM algorithm using the publicly-available RGB-D dataset. The results of the experiments demonstrate that our system is quicker than the graph-based RGB-D SLAM algorithm. PMID:26263990

  20. Constructing a coherent problem model to facilitate algebra problem solving in a chemistry context

    NASA Astrophysics Data System (ADS)

    Hiong Ngu, Bing; Seeshing Yeung, Alexander; Phan, Huy P.

    2015-04-01

    An experiment using a sample of 11th graders compared text editing and worked examples approaches in learning to solve dilution and molarity algebra word problems in a chemistry context. Text editing requires students to assess the structure of a word problem by specifying whether the problem text contains sufficient, missing, or irrelevant information for reaching a solution. Worked examples direct students to follow steps toward the solution, and its emphasis is on computation instead of the formation of a coherent problem model. Text editing yielded higher scores in a transfer test (which shared the same solution procedure as in the acquisition problems but differed in contexts), but not a similar test (which resembled acquisition problems in terms of both solution procedure and context). Results provide some theoretical support and practical implications for using text editing to develop a coherent problem model to facilitate problem-solving skills in chemistry.

  1. Conceptual explanation for the algebra in the noncommutative approach to the standard model.

    PubMed

    Chamseddine, Ali H; Connes, Alain

    2007-11-01

    The purpose of this Letter is to remove the arbitrariness of the ad hoc choice of the algebra and its representation in the noncommutative approach to the standard model, which was begging for a conceptual explanation. We assume as before that space-time is the product of a four-dimensional manifold by a finite noncommmutative space F. The spectral action is the pure gravitational action for the product space. To remove the above arbitrariness, we classify the irreducible geometries F consistent with imposing reality and chiral conditions on spinors, to avoid the fermion doubling problem, which amounts to have total dimension 10 (in the K-theoretic sense). It gives, almost uniquely, the standard model with all its details, predicting the number of fermions per generation to be 16, their representations and the Higgs breaking mechanism, with very little input.

  2. Structure of 23Al from a multi-channel algebraic scattering model based on mirror symmetry

    NASA Astrophysics Data System (ADS)

    Fraser, P. R.; Kadyrov, A. S.; Massen-Hane, K.; Amos, K.; Canton, L.; Karataglidis, S.; van der Knijff, D.; Bray, I.

    2016-09-01

    The proton-rich nucleus 23Al has a ground state just 123 keV below the one-proton emission threshold, and as a result comparatively little is known experimentally about its properties, as with many such nuclei. Theoretical investigations have tended to model exclusively the ground and first one to three excited states known. In this paper, we theoretically model most of the known spectrum, and predict what states may as yet be unobserved. We use the multichannel algebraic scattering method to describe states as resonances of a valence proton coupled to a 22Mg rotor core. Six states with low-excitation energies and defined {J}π are matched, and we make the first prediction of the properties of four others and propound the possible existence of several more.

  3. Unifying Algebraic and Large-Scale Shell-Model Approaches in Nuclear Structure Calculations

    NASA Astrophysics Data System (ADS)

    Draayer, Jerry P.

    1997-04-01

    The shell model is the most robust theory for addressing nuclear structure questions. Unfortunately, it is only as good as the input hamiltonian and the appropriateness of the selected model space, and both of these elements usually prove to be a significant challenge. There are three basic theories: 1) algebraic models, boson and fermion, which focus on symmetries, exact and approximate, of a hamiltonian and usually use model spaces that are severely truncated; 2) numerically oriented schemes that accommodate larger spaces but rely on special techniques and algorithms for producing convergent results; and 3) models that employ statistical concepts, like statistical spectroscopy of the 70s and 80s and Monte Carlo methods of the 90s, schemes that are not limited by the usual dimensionality considerations. These three approaches and their various realizations and extensions, with their pluses and minuses, will be considered. In addition, opportunities that exist for defining a scheme that employs the best of all three approaches to yield a symmetry adapted theory that is not limited to simplified spaces and hamiltonians and yet remains tractable even for large-scale calculations of the type that are required for testing a theory against experimental data and for predicting new physical phenomena will be explored. Special attention will be focused on unifying themes linking the shell-model with the simpler and yet highly successful mean-field and collective-model theories. As a example of the latter, some recent results using the symplectic shell model will be presented.

  4. Extension of the algebraic transition model for the wall roughness effect

    NASA Astrophysics Data System (ADS)

    Straka, Petr; Příhoda, Jaromír

    2016-03-01

    The contribution deals with the simulation of the laminar/turbulent transition taking into account the effect of wall roughness. The correlation for the transition onset proposed by Straka and Příhoda [1] was modified for the effect of the wall roughness using the correlation according to Boyle and Stripf [2]. This correlation derived for the wall roughness formed by regularly distributed truncated cones was modified for flows over the distributed wall roughness. The algebraic transition model proposed by Straka and Příhoda [1] with the modified relation for the transition onset was verified by means of the incompressible flat-plate boundary-layer and the compressible flow through the turbine blade cascade with rough blades.

  5. Algebraic geometry methods associated to the one-dimensional Hubbard model

    NASA Astrophysics Data System (ADS)

    Martins, M. J.

    2016-06-01

    In this paper we study the covering vertex model of the one-dimensional Hubbard Hamiltonian constructed by Shastry in the realm of algebraic geometry. We show that the Lax operator sits in a genus one curve which is not isomorphic but only isogenous to the curve suitable for the AdS/CFT context. We provide an uniformization of the Lax operator in terms of ratios of theta functions allowing us to establish relativistic like properties such as crossing and unitarity. We show that the respective R-matrix weights lie on an Abelian surface being birational to the product of two elliptic curves with distinct J-invariants. One of the curves is isomorphic to that of the Lax operator but the other is solely fourfold isogenous. These results clarify the reason the R-matrix can not be written using only difference of spectral parameters of the Lax operator.

  6. Modelling and temporal performances evaluation of networked control systems using (max, +) algebra

    NASA Astrophysics Data System (ADS)

    Ammour, R.; Amari, S.

    2015-01-01

    In this paper, we address the problem of temporal performances evaluation of producer/consumer networked control systems. The aim is to develop a formal method for evaluating the response time of this type of control systems. Our approach consists on modelling, using Petri nets classes, the behaviour of the whole architecture including the switches that support multicast communications used by this protocol. (max, +) algebra formalism is then exploited to obtain analytical formulas of the response time and the maximal and minimal bounds. The main novelty is that our approach takes into account all delays experienced at the different stages of networked automation systems. Finally, we show how to apply the obtained results through an example of networked control system.

  7. Validating Cognitive Models of Task Performance in Algebra on the SAT®. Research Report No. 2009-3

    ERIC Educational Resources Information Center

    Gierl, Mark J.; Leighton, Jacqueline P.; Wang, Changjiang; Zhou, Jiawen; Gokiert, Rebecca; Tan, Adele

    2009-01-01

    The purpose of the study is to present research focused on validating the four algebra cognitive models in Gierl, Wang, et al., using student response data collected with protocol analysis methods to evaluate the knowledge structures and processing skills used by a sample of SAT test takers.

  8. Study of Transitions in the Atmospheric Boundary Layer Using Explicit Algebraic Turbulence Models

    NASA Astrophysics Data System (ADS)

    Lazeroms, W. M. J.; Svensson, G.; Bazile, E.; Brethouwer, G.; Wallin, S.; Johansson, A. V.

    2016-10-01

    We test a recently developed engineering turbulence model, a so-called explicit algebraic Reynolds-stress (EARS) model, in the context of the atmospheric boundary layer. First of all, we consider a stable boundary layer used as the well-known first test case from the Global Energy and Water Cycle Experiment Atmospheric Boundary Layer Study (GABLS1). The model is shown to agree well with data from large-eddy simulations (LES), and this agreement is significantly better than for a standard operational scheme with a prognostic equation for turbulent kinetic energy. Furthermore, we apply the model to a case with a (idealized) diurnal cycle and make a qualitative comparison with a simpler first-order model. Some interesting features of the model are highlighted, pertaining to its stronger foundation on physical principles. In particular, the use of more prognostic equations in the model is shown to give a more realistic dynamical behaviour. This qualitative study is the first step towards a more detailed comparison, for which additional LES data are needed.

  9. Study of Transitions in the Atmospheric Boundary Layer Using Explicit Algebraic Turbulence Models

    NASA Astrophysics Data System (ADS)

    Lazeroms, W. M. J.; Svensson, G.; Bazile, E.; Brethouwer, G.; Wallin, S.; Johansson, A. V.

    2016-08-01

    We test a recently developed engineering turbulence model, a so-called explicit algebraic Reynolds-stress (EARS) model, in the context of the atmospheric boundary layer. First of all, we consider a stable boundary layer used as the well-known first test case from the Global Energy and Water Cycle Experiment Atmospheric Boundary Layer Study (GABLS1). The model is shown to agree well with data from large-eddy simulations (LES), and this agreement is significantly better than for a standard operational scheme with a prognostic equation for turbulent kinetic energy. Furthermore, we apply the model to a case with a (idealized) diurnal cycle and make a qualitative comparison with a simpler first-order model. Some interesting features of the model are highlighted, pertaining to its stronger foundation on physical principles. In particular, the use of more prognostic equations in the model is shown to give a more realistic dynamical behaviour. This qualitative study is the first step towards a more detailed comparison, for which additional LES data are needed.

  10. The algebra of the general Markov model on phylogenetic trees and networks.

    PubMed

    Sumner, J G; Holland, B R; Jarvis, P D

    2012-04-01

    It is known that the Kimura 3ST model of sequence evolution on phylogenetic trees can be extended quite naturally to arbitrary split systems. However, this extension relies heavily on mathematical peculiarities of the associated Hadamard transformation, and providing an analogous augmentation of the general Markov model has thus far been elusive. In this paper, we rectify this shortcoming by showing how to extend the general Markov model on trees to include incompatible edges; and even further to more general network models. This is achieved by exploring the algebra of the generators of the continuous-time Markov chain together with the “splitting” operator that generates the branching process on phylogenetic trees. For simplicity, we proceed by discussing the two state case and then show that our results are easily extended to more states with little complication. Intriguingly, upon restriction of the two state general Markov model to the parameter space of the binary symmetric model, our extension is indistinguishable from the Hadamard approach only on trees; as soon as any incompatible splits are introduced the two approaches give rise to differing probability distributions with disparate structure. Through exploration of a simple example, we give an argument that our extension to more general networks has desirable properties that the previous approaches do not share. In particular, our construction allows for convergent evolution of previously divergent lineages; a property that is of significant interest for biological applications.

  11. 47 CFR 64.1140 - Carrier liability for slamming.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 47 Telecommunication 3 2010-10-01 2010-10-01 false Carrier liability for slamming. 64.1140 Section 64.1140 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES... Providers § 64.1140 Carrier liability for slamming. (a) Carrier Liability for Charges. Any...

  12. Modelling for Feedback Control of Skin Friction Drag in Algebraic Growth

    NASA Astrophysics Data System (ADS)

    Jones, Bryn; Kerrigan, Eric; Naguib, Ahmed; Morrison, Jonathan

    2008-11-01

    We address the following problem: given spanwise arrays of wall- mounted shear-stress sensors at upstream and downstream locations, obtain accurate estimates of the flow field above an array of actuators located between the sensors. The accuracy of these estimates is of crucial importance in the design of any closed-loop drag reduction controller. To achieve satisfactory estimates we employ feedback from the sensors in conjunction with a dynamic model, based on that of Luchini (2000), describing perturbation evolution within a laminar boundary layer. The novelty of this work lies in the derivation of a state-space model of sufficiently low order to enable Kalman filter synthesis. Rather than obtaining a reduced- order model via numerical methods such as balanced truncation (Zhou, Doyle, Glover; 1996), we employ a series of approximations based on the results of Andersson, Berggren et al. (1999), to derive a low-order model analytically. A Kalman filter is synthesised and tested on the algebraic growth region of the DNS of Zaki (2005). Despite the use of a low-order model and significant free-stream turbulence, the results demonstrate good performance of the filter.

  13. Earth Algebra.

    ERIC Educational Resources Information Center

    Schaufele, Christopher; Zumoff, Nancy

    Earth Algebra is an entry level college algebra course that incorporates the spirit of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics at the college level. The context of the course places mathematics at the center of one of the major current concerns of the world. Through…

  14. Kiddie Algebra

    ERIC Educational Resources Information Center

    Cavanagh, Sean

    2009-01-01

    As educators and policymakers search for ways to prepare students for the rigors of algebra, teachers in the Helena, Montana, school system are starting early by attempting to nurture students' algebraic-reasoning ability, as well as their basic number skills, in early elementary school, rather than waiting until middle or early high school.…

  15. Critical RSOS and minimal models: fermionic paths, Virasoro algebra and fields

    NASA Astrophysics Data System (ADS)

    Feverati, Giovanni; Pearce, Paul A.

    2003-07-01

    A framework is presented to extend the finitized characters and recursion methods of (off-critical) corner transfer matrices (CTMs), in a self-consistent fashion, to the calculation of CFT characters and conformal partition functions. More specifically, in this paper we consider sℓ(2) minimal conformal field theories on a cylinder from a lattice perspective. We argue that a general energy-preserving bijection exists between the one-dimensional configuration paths of the AL restricted solid-on-solid (RSOS) lattice models and the eigenstates of their double row transfer matrices and exhibit this bijection for the critical and tricritical Ising models in the vacuum sector. To each allowed one-dimensional configuration path we associate a physical state and a monomial in a finite fermionic algebra. The orthonormal states produced by the action of these monomials on the primary states | h> generate finite Virasoro modules with dimensions given by the finitized Virasoro characters χ( N) h( q). These finitized characters are the generating functions for the double row transfer matrix spectra of the critical RSOS models. We also propose a general level-by-level algorithm to build matrix representations of the Virasoro generators and chiral vertex operators (CVOs). The algorithm employs a distinguished basis which we call the L1-basis. Our results extend to ZL-1 parafermion models by duality.

  16. A computational neural model of orientation detection based on multiple guesses: comparison of geometrical and algebraic models.

    PubMed

    Wei, Hui; Ren, Yuan; Wang, Zi Yan

    2013-10-01

    The implementation of Hubel-Wiesel hypothesis that orientation selectivity of a simple cell is based on ordered arrangement of its afferent cells has some difficulties. It requires the receptive fields (RFs) of those ganglion cells (GCs) and LGN cells to be similar in size and sub-structure and highly arranged in a perfect order. It also requires an adequate number of regularly distributed simple cells to match ubiquitous edges. However, the anatomical and electrophysiological evidence is not strong enough to support this geometry-based model. These strict regularities also make the model very uneconomical in both evolution and neural computation. We propose a new neural model based on an algebraic method to estimate orientations. This approach synthesizes the guesses made by multiple GCs or LGN cells and calculates local orientation information subject to a group of constraints. This algebraic model need not obey the constraints of Hubel-Wiesel hypothesis, and is easily implemented with a neural network. By using the idea of a satisfiability problem with constraints, we also prove that the precision and efficiency of this model are mathematically practicable. The proposed model makes clear several major questions which Hubel-Wiesel model does not account for. Image-rebuilding experiments are conducted to check whether this model misses any important boundary in the visual field because of the estimation strategy. This study is significant in terms of explaining the neural mechanism of orientation detection, and finding the circuit structure and computational route in neural networks. For engineering applications, our model can be used in orientation detection and as a simulation platform for cell-to-cell communications to develop bio-inspired eye chips. PMID:24427212

  17. G/G gauged WZW-matter model, Bethe Ansatz for q-boson model and Commutative Frobenius algebra

    NASA Astrophysics Data System (ADS)

    Okuda, Satoshi; Yoshida, Yutaka

    2014-03-01

    We investigate the correspondence between two dimensional topological gauge theories and quantum integrable systems discovered by Moore, Nekrasov, Shatashvili. This correspondence means that the hidden quantum integrable structure exists in the topological gauge theories. We showed the correspondence between the G/G gauged WZW model and the phase model in JHEP 11 (2012) 146 (arXiv:1209.3800). In this paper, we study a one-parameter deformation for this correspondence and show that the G/G gauged WZW model coupled to additional matters corresponds to the q-boson model. Furthermore, we investigate this correspondence from the viewpoint of the commutative Frobenius algebra, the axiom of the two dimensional topological quantum field theory.

  18. Calculus domains modelled using an original bool algebra based on polygons

    NASA Astrophysics Data System (ADS)

    Oanta, E.; Panait, C.; Raicu, A.; Barhalescu, M.; Axinte, T.

    2016-08-01

    Analytical and numerical computer based models require analytical definitions of the calculus domains. The paper presents a method to model a calculus domain based on a bool algebra which uses solid and hollow polygons. The general calculus relations of the geometrical characteristics that are widely used in mechanical engineering are tested using several shapes of the calculus domain in order to draw conclusions regarding the most effective methods to discretize the domain. The paper also tests the results of several CAD commercial software applications which are able to compute the geometrical characteristics, being drawn interesting conclusions. The tests were also targeting the accuracy of the results vs. the number of nodes on the curved boundary of the cross section. The study required the development of an original software consisting of more than 1700 computer code lines. In comparison with other calculus methods, the discretization using convex polygons is a simpler approach. Moreover, this method doesn't lead to large numbers as the spline approximation did, in that case being required special software packages in order to offer multiple, arbitrary precision. The knowledge resulted from this study may be used to develop complex computer based models in engineering.

  19. Mathematical Model for Dengue Epidemics with Differential Susceptibility and Asymptomatic Patients Using Computer Algebra

    NASA Astrophysics Data System (ADS)

    Saldarriaga Vargas, Clarita

    When there are diseases affecting large populations where the social, economic and cultural diversity is significant within the same region, the biological parameters that determine the behavior of the dispersion disease analysis are affected by the selection of different individuals. Therefore and because of the variety and magnitude of the communities at risk of contracting dengue disease around all over the world, suggest defining differentiated populations with individual contributions in the results of the dispersion dengue disease analysis. In this paper those conditions were taken in account when several epidemiologic models were analyzed. Initially a stability analysis was done for a SEIR mathematical model of Dengue disease without differential susceptibility. Both free disease and endemic equilibrium states were found in terms of the basic reproduction number and were defined in the Theorem (3.1). Then a DSEIR model was solved when a new susceptible group was introduced to consider the effects of important biological parameters of non-homogeneous populations in the spreading analysis. The results were compiled in the Theorem (3.2). Finally Theorems (3.3) and (3.4) resumed the basic reproduction numbers for three and n different susceptible groups respectively, giving an idea of how differential susceptibility affects the equilibrium states. The computations were done using an algorithmic method implemented in Maple 11, a general-purpose computer algebra system.

  20. Computation of turbulent boundary layer flows with an algebraic stress turbulence model

    NASA Technical Reports Server (NTRS)

    Kim, Sang-Wook; Chen, Yen-Sen

    1986-01-01

    An algebraic stress turbulence model is presented, characterized by the following: (1) the eddy viscosity expression is derived from the Reynolds stress turbulence model; (2) the turbulent kinetic energy dissipation rate equation is improved by including a production range time scale; and (3) the diffusion coefficients for turbulence equations are adjusted so that the kinetic energy profile extends further into the free stream region found in most experimental data. The turbulent flow equations were solved using a finite element method. Examples include: fully developed channel flow, fully developed pipe flow, flat plate boundary layer flow, plane jet exhausting into a moving stream, circular jet exhausting into a moving stream, and wall jet flow. Computational results compare favorably with experimental data for most of the examples considered. Significantly improved results were obtained for the plane jet flow, the circular jet flow, and the wall jet flow; whereas the remainder are comparable to those obtained by finite difference methods using the standard kappa-epsilon turbulence model. The latter seems to be promising with further improvement of the expression for the eddy viscosity coefficient.

  1. Dynamical analysis of a differential algebraic bio-economic model with stage-structured and stochastic fluctuations

    NASA Astrophysics Data System (ADS)

    Zhang, Yue; Zheng, Yan; Liu, Xi; Zhang, Qingling; Li, Aihua

    2016-11-01

    This study considers a class of differential algebraic stage-structured bio-economic models with stochastic fluctuations. The stochastic bio-economic model is simplified to an Itô equation using the stochastic averaging method. The stochastic stability, Hopf bifurcation, and P-bifurcation are discussed based on the singular boundary theory of the diffusion process for the system and the invariant measure theory of dynamic systems. Numerical simulations are presented to illustrate our main results.

  2. Theory of equivalence systems for describing algebraic closures of a generalized estimation model. II

    NASA Astrophysics Data System (ADS)

    D'Yakonov, A. G.

    2011-03-01

    Characteristic matrices and metrics of equivalence systems are studied that help give an efficient description of conjunctions of equivalence systems. Using these results, families of correct polynomials in the algebraic approach to classification are described.

  3. Modifications of the law of the wall and algebraic turbulence modelling for separated boundary layers

    NASA Technical Reports Server (NTRS)

    Baldwin, B. S.; Maccormack, R. W.

    1976-01-01

    Various modifications of the conventional algebraic eddy viscosity turbulence model are investigated for application to separated flows. Friction velocity is defined in a way that avoids singular behavior at separation and reattachment but reverts to the conventional definition for flows with small pressure gradients. This leads to a modified law of the wall for separated flows. The effect on the calculated flow field of changes in the model that affect the eddy viscosity at various distances from the wall are determined by (1) switching from Prandtl's form to an inner layer formula due to Clauser at various distances from the wall, (2) varying the constant in the Van Driest damping factor, (3) using Clauser's inner layer formula all the way to the wall, and (4) applying a relaxation procedure in the evaluation of the constant in Clauser's inner layer formula. Numerical solutions of the compressible Navier-Stokes equations are used to determine the effects of the modifications. Experimental results from shock-induced separated flows at Mach numbers 2.93 and 8.45 are used for comparison. For these cases improved predictions of wall pressure distribution and positions of separation and reattachment are obtained from the relaxation version of the Clauser inner layer eddy viscosity formula.

  4. Super-Lie n-algebra extensions, higher WZW models and super-p-branes with tensor multiplet fields

    NASA Astrophysics Data System (ADS)

    Fiorenza, Domenico; Sati, Hisham; Schreiber, Urs

    2015-12-01

    We formalize higher-dimensional and higher gauge WZW-type sigma-model local prequantum field theory, and discuss its rationalized/perturbative description in (super-)Lie n-algebra homotopy theory (the true home of the "FDA"-language used in the supergravity literature). We show generally how the intersection laws for such higher WZW-type σ-model branes (open brane ending on background brane) are encoded precisely in (super-)L∞-extension theory and how the resulting "extended (super-)space-times" formalize spacetimes containing σ-model brane condensates. As an application we prove in Lie n-algebra homotopy theory that the complete super-p-brane spectrum of superstring/M-theory is realized this way, including the pure σ-model branes (the "old brane scan") but also the branes with tensor multiplet worldvolume fields, notably the D-branes and the M5-brane. For instance the degree-0 piece of the higher symmetry algebra of 11-dimensional (11D) spacetime with an M2-brane condensate turns out to be the "M-theory super-Lie algebra". We also observe that in this formulation there is a simple formal proof of the fact that type IIA spacetime with a D0-brane condensate is the 11D sugra/M-theory spacetime, and of (prequantum) S-duality for type IIB string theory. Finally we give the non-perturbative description of all this by higher WZW-type σ-models on higher super-orbispaces with higher WZW terms in stacky differential cohomology.

  5. Second-Order Algebraic Theories

    NASA Astrophysics Data System (ADS)

    Fiore, Marcelo; Mahmoud, Ola

    Fiore and Hur [10] recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a formal deductive system for languages with variable binding and parameterised metavariables. This work completes the foundations of the subject from the viewpoint of categorical algebra. Specifically, the paper introduces the notion of second-order algebraic theory and develops its basic theory. Two categorical equivalences are established: at the syntactic level, that of second-order equational presentations and second-order algebraic theories; at the semantic level, that of second-order algebras and second-order functorial models. Our development includes a mathematical definition of syntactic translation between second-order equational presentations. This gives the first formalisation of notions such as encodings and transforms in the context of languages with variable binding.

  6. SLAM algorithm applied to robotics assistance for navigation in unknown environments

    PubMed Central

    2010-01-01

    results have shown a consistent reconstruction of the environment. The obtained map was stored inside the Muscle-Computer Interface. Conclusions The integration of a highly demanding processing algorithm (SLAM) with a MCI and the communication between both in real time have shown to be consistent and successful. The metric map generated by the mobile robot would allow possible future autonomous navigation without direct control of the user, whose function could be relegated to choose robot destinations. Also, the mobile robot shares the same kinematic model of a motorized wheelchair. This advantage can be exploited for wheelchair autonomous navigation. PMID:20163735

  7. Efficient data association for robot 3D vision-SLAM

    NASA Astrophysics Data System (ADS)

    Wang, Xiao-hua; Zhu, Dai-xian

    2010-08-01

    A new approach to vision-based simultaneous localization and mapping (SLAM) is proposed. the scale invariant feature transform (SIFT) features is landmarks, The minimal connected dominating set(CDS) approach is used in data association which solve the problem that the scale of data association increase with the map grows in process of SLAM. SLAM is completed by fusing the information of binocular vision and robot pose with Extended Kalman Filter (EKF). The system has been implemented and tested on data gathered with a mobile robot in a typical office environment. Experiments presented demonstrate that proposed method improves the data association and in this way leads to more accurate maps.

  8. Short Large-Amplitude Magnetic Structures (SLAMS) at Venus

    NASA Technical Reports Server (NTRS)

    Collinson, G. A.; Wilson, L. B.; Sibeck, D. G.; Shane, N.; Zhang, T. L.; Moore, T. E.; Coates, A. J.; Barabash, S.

    2012-01-01

    We present the first observation of magnetic fluctuations consistent with Short Large-Amplitude Magnetic Structures (SLAMS) in the foreshock of the planet Venus. Three monolithic magnetic field spikes were observed by the Venus Express on the 11th of April 2009. The structures were approx.1.5->11s in duration, had magnetic compression ratios between approx.3->6, and exhibited elliptical polarization. These characteristics are consistent with the SLAMS observed at Earth, Jupiter, and Comet Giacobini-Zinner, and thus we hypothesize that it is possible SLAMS may be found at any celestial body with a foreshock.

  9. On some spurious mode issues in shallow-water models using a linear algebra approach

    NASA Astrophysics Data System (ADS)

    Le Roux, D. Y.; Sène, A.; Rostand, V.; Hanert, E.

    Numerical methods that are usually employed in ocean modelling are typically finite-difference, finite and spectral-element techniques. For most of these methods the coupling between the momentum and continuity equations is a delicate problem and it usually leads to spurious solutions in the representation of inertia-gravity waves. The spurious modes have a wide range of characteristics and may take the form of pressure (surface-elevation), velocity and/or Coriolis modes. The modes usually cause aliasing and an accumulation of energy in the smallest-resolvable scale, leading to noisy solutions. The Fourier analysis has proven practical and beneficial to describe the spurious solutions of several classical schemes. However it is restricted to uniform meshes on which the variables are regularly distributed. In this paper, a linear algebra approach is proposed to study the existence and the behaviour of stationary spurious modes associated with zero frequency, for some popular finite-difference and finite-element grids. The present approach is performed on uniform meshes but it applies equally well to regular as well as unstructured meshes with irregular geometry for the finite-element schemes.

  10. Topological phase entanglements of membrane solitons in division algebra sigma models with a Hopf term

    NASA Astrophysics Data System (ADS)

    Tze, Chia-Hsiung; Nam, Soonkeon

    1989-08-01

    Exploiting the unique connection between the division algebras of the complex numbers ( C), quaternions ( H), octonions ( Ω) and the essential Hopf maps S2 n - 1 → Sn with n = 2, 4, 8, we study Sn - 2 -membrane solitons in three D-dimensional KP(1) σ-models with a Hopf term, (D, K) = (3, C), (7, H), and (15, Ω). We present a comprehensive analysis of their topological phase entanglements. Extending Polyakov's approach to Fermi-Bose transmutations to higher dimensions, we detail a geometric regularization of Gauss' linking coefficient, its connections to the self-linking, twisting, writhing numbers of the Feynman paths of the solitons in their thin membrane limit. Alternative forms of the Hopf invariant show the latter as an Aharonov-Bohm-Berry phase of topologically massive, rank ( n - 1) antisymmetric tensor U(1) gauge fields coupled to the Sn - 2 -membranes. Via a K-bundle formulation of the dynamics of electrically and magnetically charged extended objects these phases are shown to induce a dyon-like structure on these membranes. We briefly discuss the connections to harmonic mappings, higher dimensional monopoles and instantons. We point out the relevance of the Gauss-Bonnet-Chern theorem on the connection between spin and statistics. By way of the topology of the infinite groups of sphere mappings Sn → Sn, n = 2, 4, 8, we also analyze the implications of the Hopf phases on the fractional spin and statistics of the membranes.

  11. Modelling and performance analysis of clinical pathways using the stochastic process algebra PEPA

    PubMed Central

    2012-01-01

    Background Hospitals nowadays have to serve numerous patients with limited medical staff and equipment while maintaining healthcare quality. Clinical pathway informatics is regarded as an efficient way to solve a series of hospital challenges. To date, conventional research lacks a mathematical model to describe clinical pathways. Existing vague descriptions cannot fully capture the complexities accurately in clinical pathways and hinders the effective management and further optimization of clinical pathways. Method Given this motivation, this paper presents a clinical pathway management platform, the Imperial Clinical Pathway Analyzer (ICPA). By extending the stochastic model performance evaluation process algebra (PEPA), ICPA introduces a clinical-pathway-specific model: clinical pathway PEPA (CPP). ICPA can simulate stochastic behaviours of a clinical pathway by extracting information from public clinical databases and other related documents using CPP. Thus, the performance of this clinical pathway, including its throughput, resource utilisation and passage time can be quantitatively analysed. Results A typical clinical pathway on stroke extracted from a UK hospital is used to illustrate the effectiveness of ICPA. Three application scenarios are tested using ICPA: 1) redundant resources are identified and removed, thus the number of patients being served is maintained with less cost; 2) the patient passage time is estimated, providing the likelihood that patients can leave hospital within a specific period; 3) the maximum number of input patients are found, helping hospitals to decide whether they can serve more patients with the existing resource allocation. Conclusions ICPA is an effective platform for clinical pathway management: 1) ICPA can describe a variety of components (state, activity, resource and constraints) in a clinical pathway, thus facilitating the proper understanding of complexities involved in it; 2) ICPA supports the performance analysis of

  12. Nonlinear Algebraic Reynolds Stress Model for Two-Phase Turbulent Flows Laden with Small Heavy Particles in Circular Tube

    NASA Astrophysics Data System (ADS)

    Mukin, R. V.; Alipchenkov, V. M.; Zaichik, L. I.; Mukina, L. S.; Strizhov, V. F.

    2011-12-01

    The purpose of the study is to present an explicit algebraic Reynolds stress (nonlinear turbulent viscosity) model combined with modified k - ɛ turbulence model taking into account particles effect on turbulence for calculating the main turbulent characteristics of two-phase flows. For calculating particles distribution in space we used diffusion-inertia model (DIM). The turbulence attenuating in the presence of particles is clearly observed, investigated and compared with the experimental data. The developed model adequately described turbulence anisotropy and the influence of particles inertia and concentration on the turbulence intensity.

  13. A new model for algebraic Rossby solitary waves in rotation fluid and its solution

    NASA Astrophysics Data System (ADS)

    Chen, Yao-Deng; Yang, Hong-Wei; Gao, Yu-Fang; Yin, Bao-Shu; Feng, Xing-Ru

    2015-09-01

    A generalized Boussinesq equation that includes the dissipation effect is derived to describe a kind of algebraic Rossby solitary waves in a rotating fluid by employing perturbation expansions and stretching transformations of time and space. Using this equation, the conservation laws of algebraic Rossby solitary waves are discussed. It is found that the mass, the momentum, the energy, and the velocity of center of gravity of the algebraic solitary waves are conserved in the propagation process. Finally, the analytical solution of the equation is generated. Based on the analytical solution, the properties of the algebraic solitary waves and the dissipation effect are discussed. The results point out that, similar to classic solitary waves, the dissipation can cause the amplitude and the speed of solitary waves to decrease; however, unlike classic solitary waves, the algebraic solitary waves can split during propagation and the decrease of the detuning parameter can accelerate the occurrence of the solitary waves fission phenomenon. Project supported by the Shandong Provincial Key Laboratory of Marine Ecology and Environment and Disaster Prevention and Mitigation Project, China (Grant No. 2012010), the National Natural Science Foundation of China (Grant Nos. 41205082 and 41476019), the Special Funds for Theoretical Physics of the National Natural Science Foundation of China (Grant No. 11447205), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), China.

  14. NPN fuzzy sets and NPN qualitative algebra: a computational framework for bipolar cognitive modeling and multiagent decision analysis.

    PubMed

    Zhang, W R

    1996-01-01

    An NPN (Negative-Positive-Neutral) fuzzy set theory and an NPN qualitative algebra (Q-algebra) are proposed which form a computational framework for bipolar cognitive modeling and multiagent decision analysis. First a 6-valued NPN logic is introduced which extends the usual 4-valued Q-algebra (S, approximately , plus sign in circle,multiply sign in circle) and S={+,-,0,?} by adding one more level of specification; and then a real-valued NPN fuzzy logic is introduced which extends the 6-valued model to the real space { for all(x,y)|(x,y)in[-1,0]x[0,1]} and adds infinite levels of specifications, As a generalization, a fuzzy set theory is presented that allows beta-level fuzzy number-based NPN variables (x,y) to be substituted into (S, approximately , plus sign in circle,multiply sign in circle) where multiply sign in circle stands for any NPN T-norm; plus sign in circle stands for disjunction (V) or union ( union or logical sum), and beta is the number of alpha-cuts.

  15. Solving multi-customer FPR model with quality assurance and discontinuous deliveries using a two-phase algebraic approach.

    PubMed

    Chiu, Yuan-Shyi Peter; Chou, Chung-Li; Chang, Huei-Hsin; Chiu, Singa Wang

    2016-01-01

    A multi-customer finite production rate (FPR) model with quality assurance and discontinuous delivery policy was investigated in a recent paper (Chiu et al. in J Appl Res Technol 12(1):5-13, 2014) using differential calculus approach. This study employs mathematical modeling along with a two-phase algebraic method to resolve such a specific multi-customer FPR model. As a result, the optimal replenishment lot size and number of shipments can be derived without using the differential calculus. Such a straightforward method may assist practitioners who with insufficient knowledge of calculus in learning and managing the real multi-customer FPR systems more effectively. PMID:27186457

  16. Structure of CD84 Provides Insight into SLAM Family Function

    SciTech Connect

    Yan,Q.; Malashkevich, V.; Fedorov, A.; Fedorov, E.; Cao, E.; Lary, J.; Cole, J.; Nathenson, S.; Almo, S.

    2007-01-01

    The signaling lymphocyte activation molecule (SLAM) family includes homophilic and heterophilic receptors that modulate both adaptive and innate immune responses. These receptors share a common ectodomain organization: a membrane-proximal immunoglobulin constant domain and a membrane-distal immunoglobulin variable domain that is responsible for ligand recognition. CD84 is a homophilic family member that enhances IFN-{gamma} secretion in activated T cells. Our solution studies revealed that CD84 strongly self-associates with a K{sub d} in the submicromolar range. These data, in combination with previous reports, demonstrate that the SLAM family homophilic affinities span at least three orders of magnitude and suggest that differences in the affinities may contribute to the distinct signaling behavior exhibited by the individual family members. The 2.0 {angstrom} crystal structure of the human CD84 immunoglobulin variable domain revealed an orthogonal homophilic dimer with high similarity to the recently reported homophilic dimer of the SLAM family member NTB-A. Structural and chemical differences in the homophilic interfaces provide a mechanism to prevent the formation of undesired heterodimers among the SLAM family homophilic receptors. These structural data also suggest that, like NTB-A, all SLAM family homophilic dimers adopt a highly kinked organization spanning an end-to-end distance of {approx}140 {angstrom}. This common molecular dimension provides an opportunity for all two-domain SLAM family receptors to colocalize within the immunological synapse and bridge the T cell and antigen-presenting cell.

  17. The connection-set algebra--a novel formalism for the representation of connectivity structure in neuronal network models.

    PubMed

    Djurfeldt, Mikael

    2012-07-01

    The connection-set algebra (CSA) is a novel and general formalism for the description of connectivity in neuronal network models, from small-scale to large-scale structure. The algebra provides operators to form more complex sets of connections from simpler ones and also provides parameterization of such sets. CSA is expressive enough to describe a wide range of connection patterns, including multiple types of random and/or geometrically dependent connectivity, and can serve as a concise notation for network structure in scientific writing. CSA implementations allow for scalable and efficient representation of connectivity in parallel neuronal network simulators and could even allow for avoiding explicit representation of connections in computer memory. The expressiveness of CSA makes prototyping of network structure easy. A C+ + version of the algebra has been implemented and used in a large-scale neuronal network simulation (Djurfeldt et al., IBM J Res Dev 52(1/2):31-42, 2008b) and an implementation in Python has been publicly released.

  18. Constructing a Coherent Problem Model to Facilitate Algebra Problem Solving in a Chemistry Context

    ERIC Educational Resources Information Center

    Ngu, Bing Hiong; Yeung, Alexander Seeshing; Phan, Huy P.

    2015-01-01

    An experiment using a sample of 11th graders compared text editing and worked examples approaches in learning to solve dilution and molarity algebra word problems in a chemistry context. Text editing requires students to assess the structure of a word problem by specifying whether the problem text contains sufficient, missing, or irrelevant…

  19. Flipping an Algebra Classroom: Analyzing, Modeling, and Solving Systems of Linear Equations

    ERIC Educational Resources Information Center

    Kirvan, Rebecca; Rakes, Christopher R.; Zamora, Regie

    2015-01-01

    The present study investigated whether flipping an algebra classroom led to a stronger focus on conceptual understanding and improved learning of systems of linear equations for 54 seventh- and eighth-grade students using teacher journal data and district-mandated unit exam items. Multivariate analysis of covariance was used to compare scores on…

  20. Proposing and Testing a Model to Explain Traits of Algebra Preparedness

    ERIC Educational Resources Information Center

    Venenciano, Linda; Heck, Ronald

    2016-01-01

    Early experiences with theoretical thinking and generalization in measurement are hypothesized to develop constructs we name here as logical reasoning and preparedness for algebra. Based on work of V. V. Davydov (1975), the Measure Up (MU) elementary grades experimental mathematics curriculum uses quantities of area, length, volume, and mass to…

  1. Prospective Mathematics Teachers' Sense Making of Polynomial Multiplication and Factorization Modeled with Algebra Tiles

    ERIC Educational Resources Information Center

    Caglayan, Günhan

    2013-01-01

    This study is about prospective secondary mathematics teachers' understanding and sense making of representational quantities generated by algebra tiles, the quantitative units (linear vs. areal) inherent in the nature of these quantities, and the quantitative addition and multiplication operations--referent preserving versus referent…

  2. Developing Pre-Algebraic Thinking in Generalizing Repeating Pattern Using SOLO Model

    ERIC Educational Resources Information Center

    Lian, Lim Hooi; Yew, Wun Thiam

    2011-01-01

    In this paper, researchers discussed the application of the generalization perspective in helping the primary school pupils to develop their pre-algebraic thinking in generalizing repeating pattern. There are two main stages of the generalization perspective had been adapted, namely investigating and generalizing the pattern. Since the Biggs and…

  3. Algebraic grid adaptation method using non-uniform rational B-spline surface modeling

    NASA Technical Reports Server (NTRS)

    Yang, Jiann-Cherng; Soni, B. K.

    1992-01-01

    An algebraic adaptive grid system based on equidistribution law and utilized by the Non-Uniform Rational B-Spline (NURBS) surface for redistribution is presented. A weight function, utilizing a properly weighted boolean sum of various flow field characteristics is developed. Computational examples are presented to demonstrate the success of this technique.

  4. BatSLAM: Simultaneous Localization and Mapping Using Biomimetic Sonar

    PubMed Central

    Steckel, Jan; Peremans, Herbert

    2013-01-01

    We propose to combine a biomimetic navigation model which solves a simultaneous localization and mapping task with a biomimetic sonar mounted on a mobile robot to address two related questions. First, can robotic sonar sensing lead to intelligent interactions with complex environments? Second, can we model sonar based spatial orientation and the construction of spatial maps by bats? To address these questions we adapt the mapping module of RatSLAM, a previously published navigation system based on computational models of the rodent hippocampus. We analyze the performance of the proposed robotic implementation operating in the real world. We conclude that the biomimetic navigation model operating on the information from the biomimetic sonar allows an autonomous agent to map unmodified (office) environments efficiently and consistently. Furthermore, these results also show that successful navigation does not require the readings of the biomimetic sonar to be interpreted in terms of individual objects/landmarks in the environment. We argue that the system has applications in robotics as well as in the field of biology as a simple, first order, model for sonar based spatial orientation and map building. PMID:23365647

  5. BatSLAM: Simultaneous localization and mapping using biomimetic sonar.

    PubMed

    Steckel, Jan; Peremans, Herbert

    2013-01-01

    We propose to combine a biomimetic navigation model which solves a simultaneous localization and mapping task with a biomimetic sonar mounted on a mobile robot to address two related questions. First, can robotic sonar sensing lead to intelligent interactions with complex environments? Second, can we model sonar based spatial orientation and the construction of spatial maps by bats? To address these questions we adapt the mapping module of RatSLAM, a previously published navigation system based on computational models of the rodent hippocampus. We analyze the performance of the proposed robotic implementation operating in the real world. We conclude that the biomimetic navigation model operating on the information from the biomimetic sonar allows an autonomous agent to map unmodified (office) environments efficiently and consistently. Furthermore, these results also show that successful navigation does not require the readings of the biomimetic sonar to be interpreted in terms of individual objects/landmarks in the environment. We argue that the system has applications in robotics as well as in the field of biology as a simple, first order, model for sonar based spatial orientation and map building. PMID:23365647

  6. BatSLAM: Simultaneous localization and mapping using biomimetic sonar.

    PubMed

    Steckel, Jan; Peremans, Herbert

    2013-01-01

    We propose to combine a biomimetic navigation model which solves a simultaneous localization and mapping task with a biomimetic sonar mounted on a mobile robot to address two related questions. First, can robotic sonar sensing lead to intelligent interactions with complex environments? Second, can we model sonar based spatial orientation and the construction of spatial maps by bats? To address these questions we adapt the mapping module of RatSLAM, a previously published navigation system based on computational models of the rodent hippocampus. We analyze the performance of the proposed robotic implementation operating in the real world. We conclude that the biomimetic navigation model operating on the information from the biomimetic sonar allows an autonomous agent to map unmodified (office) environments efficiently and consistently. Furthermore, these results also show that successful navigation does not require the readings of the biomimetic sonar to be interpreted in terms of individual objects/landmarks in the environment. We argue that the system has applications in robotics as well as in the field of biology as a simple, first order, model for sonar based spatial orientation and map building.

  7. Comparison of different algebraic stress models in predicting temperature fluctuations and mean velocity in liquid-metals

    SciTech Connect

    de Lemos, M.J.S.

    1985-01-01

    The present work consists of a numerical investigation comparing three algebraic stress closures for turbulence in predicting the variance of temperature fluctuations and mean velocity for flow of mercury. The models of Ljuboja and Rodi, Sha and Launder, and Lemos and Sesonske are used, as they handle differently the modeling of the dissipation rate of temperature fluctuations, and several terms in the algebraic equations for the turbulent fluxes. A sensitivity analysis on some constants of the latter model is also presented. Pipe flow with constant wall heat flux were the geometry and boundary condition. The range for Re was from 30000 to 60000, and the buoyancy parameter Ra/Re/sup 2/ was varied from 10/sup -5/ to 10/sup -4/, where Ra is the Rayleigh number. The model of Lemos and Sesonske shows a substantial improvement in predicting temperature fluctuations, whereas predictions for the mean velocity show a weak dependence on the model used. Nevertheless, the model of Lemos and Sesonske gives results closer to available experimental data.

  8. Spatial-Operator Algebra For Robotic Manipulators

    NASA Technical Reports Server (NTRS)

    Rodriguez, Guillermo; Kreutz, Kenneth K.; Milman, Mark H.

    1991-01-01

    Report discusses spatial-operator algebra developed in recent studies of mathematical modeling, control, and design of trajectories of robotic manipulators. Provides succinct representation of mathematically complicated interactions among multiple joints and links of manipulator, thereby relieving analyst of most of tedium of detailed algebraic manipulations. Presents analytical formulation of spatial-operator algebra, describes some specific applications, summarizes current research, and discusses implementation of spatial-operator algebra in the Ada programming language.

  9. Seismo-Lineament Analysis Method (SLAM) Applied to the South Napa Earthquake

    NASA Astrophysics Data System (ADS)

    Worrell, V. E.; Cronin, V. S.

    2014-12-01

    We used the seismo-lineament analysis method (SLAM; http://bearspace.baylor.edu/Vince_Cronin/www/SLAM/) to "predict" the location of the fault that produced the M 6.0 South Napa earthquake of 24 August 2014, using hypocenter and focal mechanism data from NCEDC (http://www.ncedc.org/ncedc/catalog-search.html) and a digital elevation model from the USGS National Elevation Dataset (http://viewer.nationalmap.gov/viewer/). The ground-surface trace of the causative fault (i.e., the Browns Valley strand of the West Napa fault zone; Bryant, 2000, 1982) and virtually all of the ground-rupture sites reported by the USGS and California Geological Survey (http://www.eqclearinghouse.org/2014-08-24-south-napa/) were located within the north-striking seismo-lineament. We also used moment tensors published online by the USGS and GCMT (http://comcat.cr.usgs.gov/earthquakes/eventpage/nc72282711#scientific_moment-tensor) as inputs to SLAM and found that their northwest-striking seismo-lineaments correlated spatially with the causative fault. We concluded that SLAM could have been used as soon as these mechanism solutions were available to help direct the search for the trace of the causative fault and possible rupture-related damage. We then considered whether the seismogenic fault could have been identified using SLAM prior to the 24 August event, based on the focal mechanisms of smaller prior earthquakes reported by the NCEDC or ISC (http://www.isc.ac.uk). Seismo-lineaments from three M~3.5 events from 1990 and 2012, located in the Vallejo-Crockett area, correlate spatially with the Napa County Airport strand of the West Napa fault and extend along strike toward the Browns Valley strand (Bryant, 2000, 1982). Hence, we might have used focal mechanisms from smaller earthquakes to establish that the West Napa fault is likely seismogenic prior to the South Napa earthquake. Early recognition that a fault with a mapped ground-surface trace is seismogenic, based on smaller earthquakes

  10. Large-scale experimental design for decentralized SLAM

    NASA Astrophysics Data System (ADS)

    Cunningham, Alex; Dellaert, Frank

    2012-06-01

    This paper presents an analysis of large scale decentralized SLAM under a variety of experimental conditions to illustrate design trade-offs relevant to multi-robot mapping in challenging environments. As a part of work through the MAST CTA, the focus of these robot teams is on the use of small-scale robots with limited sensing, communication and computational resources. To evaluate mapping algorithms with large numbers (50+) of robots, we developed a simulation incorporating sensing of unlabeled landmarks, line-of-sight blocking obstacles, and communication modeling. Scenarios are randomly generated with variable models for sensing, communication, and robot behavior. The underlying Decentralized Data Fusion (DDF) algorithm in these experiments enables robots to construct a map of their surroundings by fusing local sensor measurements with condensed map information from neighboring robots. Each robot maintains a cache of previously collected condensed maps from neighboring robots, and actively distributes these maps throughout the network to ensure resilience to communication and node failures. We bound the size of the robot neighborhoods to control the growth of the size of neighborhood maps. We present the results of experiments conducted in these simulated scenarios under varying measurement models and conditions while measuring mapping performance. We discuss the trade-offs between mapping performance and scenario design, including robot teams separating and joining, multi-robot data association, exploration bounding, and neighborhood sizes.

  11. A differential algebraic approach for the modeling of polycrystalline ferromagnetic hysteresis with minor loops and frequency dependence

    NASA Astrophysics Data System (ADS)

    Wang, Dan; Wang, Linxiang; Melnik, Roderick

    2016-07-01

    In the current paper, a nonlinear differential algebraic approach is proposed for the modeling of hysteretic dynamics of polycrystalline ferromagnetic materials. The model is constructed by employing a phenomenological theory to the magnetization orientation switching. For the modeling of hysteresis in polycrystalline ferromagnetic materials, the single crystal model is applied to each magnetic domain along its own principal axis. The overall dynamics of the polycrystalline materials is obtained by taking a weighted combination of the dynamics of all magnetic domains. The weight function for the combination is taken as the distribution function of the principal axes. Numerical simulations are performed and comparisons with its experimental counterparts are presented. The hysteretic dynamics caused by orientation switching processes is accurately captured by the proposed model. Minor hysteresis loops associated with partial-amplitude loadings are also captured. Rate dependence of the hysteresis loops are inherently incorporated into the model due to its differential nature.

  12. Thinking Visually about Algebra

    ERIC Educational Resources Information Center

    Baroudi, Ziad

    2015-01-01

    Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…

  13. The Effect of Scheduling Models for Introductory Algebra on 9th-Grade Students, Test Scores and Grades

    ERIC Educational Resources Information Center

    O'Hanlon, Angela L.

    2011-01-01

    The purpose of the study was to determine the effect of pacing and scheduling of algebra coursework on assigned 9th-grade students who traditionally would qualify for pre-algebra instruction and same course 9th-grade students who traditionally would qualify for standard algebra instruction. Students were selected based on completion of first-year…

  14. Genetic hotels for the standard genetic code: evolutionary analysis based upon novel three-dimensional algebraic models.

    PubMed

    José, Marco V; Morgado, Eberto R; Govezensky, Tzipe

    2011-07-01

    Herein, we rigorously develop novel 3-dimensional algebraic models called Genetic Hotels of the Standard Genetic Code (SGC). We start by considering the primeval RNA genetic code which consists of the 16 codons of type RNY (purine-any base-pyrimidine). Using simple algebraic operations, we show how the RNA code could have evolved toward the current SGC via two different intermediate evolutionary stages called Extended RNA code type I and II. By rotations or translations of the subset RNY, we arrive at the SGC via the former (type I) or via the latter (type II), respectively. Biologically, the Extended RNA code type I, consists of all codons of the type RNY plus codons obtained by considering the RNA code but in the second (NYR type) and third (YRN type) reading frames. The Extended RNA code type II, comprises all codons of the type RNY plus codons that arise from transversions of the RNA code in the first (YNY type) and third (RNR) nucleotide bases. Since the dimensions of remarkable subsets of the Genetic Hotels are not necessarily integer numbers, we also introduce the concept of algebraic fractal dimension. A general decoding function which maps each codon to its corresponding amino acid or the stop signals is also derived. The Phenotypic Hotel of amino acids is also illustrated. The proposed evolutionary paths are discussed in terms of the existing theories of the evolution of the SGC. The adoption of 3-dimensional models of the Genetic and Phenotypic Hotels will facilitate the understanding of the biological properties of the SGC.

  15. Algebraic multigrid

    NASA Technical Reports Server (NTRS)

    Ruge, J. W.; Stueben, K.

    1987-01-01

    The state of the art in algebraic multgrid (AMG) methods is discussed. The interaction between the relaxation process and the coarse grid correction necessary for proper behavior of the solution probes is discussed in detail. Sufficient conditions on relaxation and interpolation for the convergence of the V-cycle are given. The relaxation used in AMG, what smoothing means in an algebraic setting, and how it relates to the existing theory are considered. Some properties of the coarse grid operator are discussed, and results on the convergence of two-level and multilevel convergence are given. Details of an algorithm particularly studied for problems obtained by discretizing a single elliptic, second order partial differential equation are given. Results of experiments with such problems using both finite difference and finite element discretizations are presented.

  16. Three-Dimensional Algebraic Models of the tRNA Code and 12 Graphs for Representing the Amino Acids.

    PubMed

    José, Marco V; Morgado, Eberto R; Guimarães, Romeu Cardoso; Zamudio, Gabriel S; de Farías, Sávio Torres; Bobadilla, Juan R; Sosa, Daniela

    2014-01-01

    Three-dimensional algebraic models, also called Genetic Hotels, are developed to represent the Standard Genetic Code, the Standard tRNA Code (S-tRNA-C), and the Human tRNA code (H-tRNA-C). New algebraic concepts are introduced to be able to describe these models, to wit, the generalization of the 2n-Klein Group and the concept of a subgroup coset with a tail. We found that the H-tRNA-C displayed broken symmetries in regard to the S-tRNA-C, which is highly symmetric. We also show that there are only 12 ways to represent each of the corresponding phenotypic graphs of amino acids. The averages of statistical centrality measures of the 12 graphs for each of the three codes are carried out and they are statistically compared. The phenotypic graphs of the S-tRNA-C display a common triangular prism of amino acids in 10 out of the 12 graphs, whilst the corresponding graphs for the H-tRNA-C display only two triangular prisms. The graphs exhibit disjoint clusters of amino acids when their polar requirement values are used. We contend that the S-tRNA-C is in a frozen-like state, whereas the H-tRNA-C may be in an evolving state. PMID:25370377

  17. Three-Dimensional Algebraic Models of the tRNA Code and 12 Graphs for Representing the Amino Acids

    PubMed Central

    José, Marco V.; Morgado, Eberto R.; Guimarães, Romeu Cardoso; Zamudio, Gabriel S.; de Farías, Sávio Torres; Bobadilla, Juan R.; Sosa, Daniela

    2014-01-01

    Three-dimensional algebraic models, also called Genetic Hotels, are developed to represent the Standard Genetic Code, the Standard tRNA Code (S-tRNA-C), and the Human tRNA code (H-tRNA-C). New algebraic concepts are introduced to be able to describe these models, to wit, the generalization of the 2n-Klein Group and the concept of a subgroup coset with a tail. We found that the H-tRNA-C displayed broken symmetries in regard to the S-tRNA-C, which is highly symmetric. We also show that there are only 12 ways to represent each of the corresponding phenotypic graphs of amino acids. The averages of statistical centrality measures of the 12 graphs for each of the three codes are carried out and they are statistically compared. The phenotypic graphs of the S-tRNA-C display a common triangular prism of amino acids in 10 out of the 12 graphs, whilst the corresponding graphs for the H-tRNA-C display only two triangular prisms. The graphs exhibit disjoint clusters of amino acids when their polar requirement values are used. We contend that the S-tRNA-C is in a frozen-like state, whereas the H-tRNA-C may be in an evolving state. PMID:25370377

  18. Analyzing the nonlinear vibrational wave differential equation for the simplified model of Tower Cranes by Algebraic Method

    NASA Astrophysics Data System (ADS)

    Akbari, M. R.; Ganji, D. D.; Ahmadi, A. R.; Kachapi, Sayyid H. Hashemi

    2014-03-01

    In the current paper, a simplified model of Tower Cranes has been presented in order to investigate and analyze the nonlinear differential equation governing on the presented system in three different cases by Algebraic Method (AGM). Comparisons have been made between AGM and Numerical Solution, and these results have been indicated that this approach is very efficient and easy so it can be applied for other nonlinear equations. It is citable that there are some valuable advantages in this way of solving differential equations and also the answer of various sets of complicated differential equations can be achieved in this manner which in the other methods, so far, they have not had acceptable solutions. The simplification of the solution procedure in Algebraic Method and its application for solving a wide variety of differential equations not only in Vibrations but also in different fields of study such as fluid mechanics, chemical engineering, etc. make AGM be a powerful and useful role model for researchers in order to solve complicated nonlinear differential equations.

  19. Three-Dimensional Algebraic Models of the tRNA Code and 12 Graphs for Representing the Amino Acids.

    PubMed

    José, Marco V; Morgado, Eberto R; Guimarães, Romeu Cardoso; Zamudio, Gabriel S; de Farías, Sávio Torres; Bobadilla, Juan R; Sosa, Daniela

    2014-08-11

    Three-dimensional algebraic models, also called Genetic Hotels, are developed to represent the Standard Genetic Code, the Standard tRNA Code (S-tRNA-C), and the Human tRNA code (H-tRNA-C). New algebraic concepts are introduced to be able to describe these models, to wit, the generalization of the 2n-Klein Group and the concept of a subgroup coset with a tail. We found that the H-tRNA-C displayed broken symmetries in regard to the S-tRNA-C, which is highly symmetric. We also show that there are only 12 ways to represent each of the corresponding phenotypic graphs of amino acids. The averages of statistical centrality measures of the 12 graphs for each of the three codes are carried out and they are statistically compared. The phenotypic graphs of the S-tRNA-C display a common triangular prism of amino acids in 10 out of the 12 graphs, whilst the corresponding graphs for the H-tRNA-C display only two triangular prisms. The graphs exhibit disjoint clusters of amino acids when their polar requirement values are used. We contend that the S-tRNA-C is in a frozen-like state, whereas the H-tRNA-C may be in an evolving state.

  20. New validation algorithm for data association in SLAM.

    PubMed

    Guerra, Edmundo; Munguia, Rodrigo; Bolea, Yolanda; Grau, Antoni

    2013-09-01

    In this work, a novel data validation algorithm for a single-camera SLAM system is introduced. A 6-degree-of-freedom monocular SLAM method based on the delayed inverse-depth (DI-D) feature initialization is used as a benchmark. This SLAM methodology has been improved with the introduction of the proposed data association batch validation technique, the highest order hypothesis compatibility test, HOHCT. This new algorithm is based on the evaluation of statistically compatible hypotheses, and a search algorithm designed to exploit the characteristics of delayed inverse-depth technique. In order to show the capabilities of the proposed technique, experimental tests have been compared with classical methods. The results of the proposed technique outperformed the results of the classical approaches.

  1. Geometric projection filter: an efficient solution to the SLAM problem

    NASA Astrophysics Data System (ADS)

    Newman, Paul M.; Durrant-Whyte, Hugh F.

    2001-10-01

    This paper is concerned with the simultaneous localization and map building (SLAM) problem. The SLAM problem asks if it is possible for an autonomous vehicle to start in an unknown location in an unknown environment and then to incrementally build a map of this environment while simultaneously using this map to compute absolute vehicle location. Conventional approaches to this problem are plagued with a prohibitively large increase in computation with the size of the environment. This paper offers a new solution to the SLAM problem that is both consistent and computationally feasible. The proposed algorithm builds a map expressing the relationships between landmarks which is then transformed into landmark locations. Experimental results are presented employing the new algorithm on a subsea vehicle using a scanning sonar sensor.

  2. A research on SLAM aided INS/GPS navigation system

    NASA Astrophysics Data System (ADS)

    Cao, Menglong; Cui, Pingyuan

    2007-11-01

    Simultaneous Localization and Mapping (SLAM) aided INS/GPS navigation system is a landmark based terrain aided autonomous integrated system that has the capability for online map building and simultaneously utilizing the generated map to bind the errors in the Inertial Navigation System (INS) when GPS is not available. If GPS information is available, the SLAM integrated system builds a landmark-based map using an INS/GPS solution. If GPS is not available, the previously newly generated map is used to constrain the INS errors. The SLAM augmented INS/GPS system shows two capabilities of landmark tracking and mapping using GPS information and more importantly, aiding the INS under GPS denied situation. The validity of the proposed method is demonstrated by computer simulation.

  3. An Ada Linear-Algebra Software Package Modeled After HAL/S

    NASA Technical Reports Server (NTRS)

    Klumpp, Allan R.; Lawson, Charles L.

    1990-01-01

    New avionics software written more easily. Software package extends Ada programming language to include linear-algebra capabilities similar to those of HAL/S programming language. Designed for such avionics applications as Space Station flight software. In addition to built-in functions of HAL/S, package incorporates quaternion functions used in Space Shuttle and Galileo projects and routines from LINPAK solving systems of equations involving general square matrices. Contains two generic programs: one for floating-point computations and one for integer computations. Written on IBM/AT personal computer running under PC DOS, v.3.1.

  4. Algebraic Bethe ansatz for the sℓ (2) Gaudin model with boundary

    NASA Astrophysics Data System (ADS)

    Cirilo António, N.; Manojlović, N.; Ragoucy, E.; Salom, I.

    2015-04-01

    Following Sklyanin's proposal in the periodic case, we derive the generating function of the Gaudin Hamiltonians with boundary terms. Our derivation is based on the quasi-classical expansion of the linear combination of the transfer matrix of the XXX Heisenberg spin chain and the central element, the so-called Sklyanin determinant. The corresponding Gaudin Hamiltonians with boundary terms are obtained as the residues of the generating function. By defining the appropriate Bethe vectors which yield strikingly simple off shell action of the generating function, we fully implement the algebraic Bethe ansatz, obtaining the spectrum of the generating function and the corresponding Bethe equations.

  5. Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz

    NASA Astrophysics Data System (ADS)

    Belliard, Samuel; Crampé, Nicolas

    2013-11-01

    We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations) formally similar to the ones obtained in the periodic case or with diagonal boundaries.

  6. A Deterministic Interfacial Cyclic Oxidation Spalling Model. Part 2; Algebraic Approximation, Descriptive Parameters, and Normalized Universal Curve

    NASA Technical Reports Server (NTRS)

    Smialek, James L.

    2002-01-01

    A cyclic oxidation interfacial spalling model has been developed in Part 1. The governing equations have been simplified here by substituting a new algebraic expression for the series (Good-Smialek approximation). This produced a direct relationship between cyclic oxidation weight change and model input parameters. It also allowed for the mathematical derivation of various descriptive parameters as a function of the inputs. It is shown that the maximum in weight change varies directly with the parabolic rate constant and cycle duration and inversely with the spall fraction, all to the 1/2 power. The number of cycles to reach maximum and zero weight change vary inversely with the spall fraction, and the ratio of these cycles is exactly 1:3 for most oxides. By suitably normalizing the weight change and cycle number, it is shown that all cyclic oxidation weight change model curves can be represented by one universal expression for a given oxide scale.

  7. Analysis of different feature selection criteria based on a covariance convergence perspective for a SLAM algorithm.

    PubMed

    Auat Cheein, Fernando A; Carelli, Ricardo

    2011-01-01

    This paper introduces several non-arbitrary feature selection techniques for a Simultaneous Localization and Mapping (SLAM) algorithm. The feature selection criteria are based on the determination of the most significant features from a SLAM convergence perspective. The SLAM algorithm implemented in this work is a sequential EKF (Extended Kalman filter) SLAM. The feature selection criteria are applied on the correction stage of the SLAM algorithm, restricting it to correct the SLAM algorithm with the most significant features. This restriction also causes a decrement in the processing time of the SLAM. Several experiments with a mobile robot are shown in this work. The experiments concern the map reconstruction and a comparison between the different proposed techniques performance. The experiments were carried out at an outdoor environment composed by trees, although the results shown herein are not restricted to a special type of features. PMID:22346568

  8. Analysis of Different Feature Selection Criteria Based on a Covariance Convergence Perspective for a SLAM Algorithm

    PubMed Central

    Auat Cheein, Fernando A.; Carelli, Ricardo

    2011-01-01

    This paper introduces several non-arbitrary feature selection techniques for a Simultaneous Localization and Mapping (SLAM) algorithm. The feature selection criteria are based on the determination of the most significant features from a SLAM convergence perspective. The SLAM algorithm implemented in this work is a sequential EKF (Extended Kalman filter) SLAM. The feature selection criteria are applied on the correction stage of the SLAM algorithm, restricting it to correct the SLAM algorithm with the most significant features. This restriction also causes a decrement in the processing time of the SLAM. Several experiments with a mobile robot are shown in this work. The experiments concern the map reconstruction and a comparison between the different proposed techniques performance. The experiments were carried out at an outdoor environment composed by trees, although the results shown herein are not restricted to a special type of features. PMID:22346568

  9. Twisted C⋆-algebra formulation of quantum cosmology with application to the Bianchi I model

    NASA Astrophysics Data System (ADS)

    Rosenbaum, Marcos; Vergara, J. David; Juárez, Román; Minzoni, A. A.

    2014-04-01

    A twisted C⋆-algebra of the extended (noncommutative) Heisenberg-Weyl group has been constructed which takes into account the uncertainty principle for coordinates in the Planck-length regime. This general construction is then used to generate an appropriate Hilbert space and observables for the noncommutative theory which, when applied to the Bianchi I cosmology, leads to a new set of equations that describe the quantum evolution of the Universe. We find that this formulation matches theories based on a reticular Heisenberg-Weyl algebra in the bouncing and expanding regions of a collapsing Bianchi universe. There is, however, an additional effect introduced by the dynamics generated by the noncommutativity. This is an oscillation in the spectrum of the volume operator of the Universe, within the bouncing region of the commutative theories. We show that this effect is generic and produced by the noncommutative momentum exchange between the degrees of freedom in the cosmology. We give asymptotic and numerical solutions which show the above mentioned effects of the noncommutativity.

  10. Algebraic Reynolds stress modeling of turbulence subject to rapid homogeneous and non-homogeneous compression or expansion

    NASA Astrophysics Data System (ADS)

    Grigoriev, I. A.; Wallin, S.; Brethouwer, G.; Grundestam, O.; Johansson, A. V.

    2016-02-01

    A recently developed explicit algebraic Reynolds stress model (EARSM) by Grigoriev et al. ["A realizable explicit algebraic Reynolds stress model for compressible turbulent flow with significant mean dilatation," Phys. Fluids 25(10), 105112 (2013)] and the related differential Reynolds stress model (DRSM) are used to investigate the influence of homogeneous shear and compression on the evolution of turbulence in the limit of rapid distortion theory (RDT). The DRSM predictions of the turbulence kinetic energy evolution are in reasonable agreement with RDT while the evolution of diagonal components of anisotropy correctly captures the essential features, which is not the case for standard compressible extensions of DRSMs. The EARSM is shown to give a realizable anisotropy tensor and a correct trend of the growth of turbulence kinetic energy K, which saturates at a power law growth versus compression ratio, as well as retaining a normalized strain in the RDT regime. In contrast, an eddy-viscosity model results in a rapid exponential growth of K and excludes both realizability and high magnitude of the strain rate. We illustrate the importance of using a proper algebraic treatment of EARSM in systems with high values of dilatation and vorticity but low shear. A homogeneously compressed and rotating gas cloud with cylindrical symmetry, related to astrophysical flows and swirling supercritical flows, was investigated too. We also outline the extension of DRSM and EARSM to include the effect of non-homogeneous density coupled with "local mean acceleration" which can be important for, e.g., stratified flows or flows with heat release. A fixed-point analysis of direct numerical simulation data of combustion in a wall-jet flow demonstrates that our model gives quantitatively correct predictions of both streamwise and cross-stream components of turbulent density flux as well as their influence on the anisotropies. In summary, we believe that our approach, based on a proper

  11. Machine Learning and Geometric Technique for SLAM

    NASA Astrophysics Data System (ADS)

    Bernal-Marin, Miguel; Bayro-Corrochano, Eduardo

    This paper describes a new approach for building 3D geometric maps using a laser rangefinder, a stereo camera system and a mathematical system the Conformal Geometric Algebra. The use of a known visual landmarks in the map helps to carry out a good localization of the robot. A machine learning technique is used for recognition of objects in the environment. These landmarks are found using the Viola and Jones algorithm and are represented with their position in the 3D virtual map.

  12. Coverings of topological semi-abelian algebras

    NASA Astrophysics Data System (ADS)

    Mucuk, Osman; Demir, Serap

    2016-08-01

    In this work, we study on a category of topological semi-abelian algebras which are topological models of given an algebraic theory T whose category of models is semi-abelian; and investigate some results on the coverings of topological models of such theories yielding semi-abelian categories. We also consider the internal groupoid structure in the semi-abelian category of T-algebras, and give a criteria for the lifting of internal groupoid structure to the covering groupoids.

  13. Algebraic trigonometry

    NASA Astrophysics Data System (ADS)

    Vaninsky, Alexander

    2011-04-01

    This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos - satisfying an axiom sin2 + cos2 = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two different interpretations of the TF are discussed with many others potentially possible. The main objective of this article is to introduce a broader view of trigonometry that can serve as motivation for mathematics students and teachers to study and teach abstract algebraic structures.

  14. Filiform Lie algebras of order 3

    SciTech Connect

    Navarro, R. M.

    2014-04-15

    The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases.

  15. Hopf algebras of rooted forests, cocyles, and free Rota-Baxter algebras

    NASA Astrophysics Data System (ADS)

    Zhang, Tianjie; Gao, Xing; Guo, Li

    2016-10-01

    The Hopf algebra and the Rota-Baxter algebra are the two algebraic structures underlying the algebraic approach of Connes and Kreimer to renormalization of perturbative quantum field theory. In particular, the Hopf algebra of rooted trees serves as the "baby model" of Feynman graphs in their approach and can be characterized by certain universal properties involving a Hochschild 1-cocycle. Decorated rooted trees have also been applied to study Feynman graphs. We will continue the study of universal properties of various spaces of decorated rooted trees with such a 1-cocycle, leading to the concept of a cocycle Hopf algebra. We further apply the universal properties to equip a free Rota-Baxter algebra with the structure of a cocycle Hopf algebra.

  16. Modular properties of doubly extended N = 4 superconformal algebras and their connection to rational torus models (I)

    NASA Astrophysics Data System (ADS)

    Petersen, Jens Lyng; Taormina, Anne

    1991-05-01

    The doubly extended N = 4 superconformal algebra, which contains all conventional extended superconformal algebras, is analyzed when one of the central extensions is set to 1. The modular transformations of the characters are derived, the relation between the characters and those of the N = 2 minimal is clarified, and in the process it is shown how rather simple extensions of the algebra based on rational torus theories, give rise to finite dimensional representations of the modular group.

  17. Hopf algebras and topological recursion

    NASA Astrophysics Data System (ADS)

    Esteves, João N.

    2015-11-01

    We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293-309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347-452).

  18. a Laser-Slam Algorithm for Indoor Mobile Mapping

    NASA Astrophysics Data System (ADS)

    Zhang, Wenjun; Zhang, Qiao; Sun, Kai; Guo, Sheng

    2016-06-01

    A novel Laser-SLAM algorithm is presented for real indoor environment mobile mapping. SLAM algorithm can be divided into two classes, Bayes filter-based and graph optimization-based. The former is often difficult to guarantee consistency and accuracy in largescale environment mapping because of the accumulative error during incremental mapping. Graph optimization-based SLAM method often assume predetermined landmarks, which is difficult to be got in unknown environment mapping. And there most likely has large difference between the optimize result and the real data, because the constraints are too few. This paper designed a kind of sub-map method, which could map more accurately without predetermined landmarks and avoid the already-drawn map impact on agent's location. The tree structure of sub-map can be indexed quickly and reduce the amount of memory consuming when mapping. The algorithm combined Bayes-based and graph optimization-based SLAM algorithm. It created virtual landmarks automatically by associating data of sub-maps for graph optimization. Then graph optimization guaranteed consistency and accuracy in large-scale environment mapping and improved the reasonability and reliability of the optimize results. Experimental results are presented with a laser sensor (UTM 30LX) in official buildings and shopping centres, which prove that the proposed algorithm can obtain 2D maps within 10cm precision in indoor environment range from several hundreds to 12000 square meter.

  19. Distributed SLAM using improved particle filter for mobile robot localization.

    PubMed

    Pei, Fujun; Wu, Mei; Zhang, Simin

    2014-01-01

    The distributed SLAM system has a similar estimation performance and requires only one-fifth of the computation time compared with centralized particle filter. However, particle impoverishment is inevitably because of the random particles prediction and resampling applied in generic particle filter, especially in SLAM problem that involves a large number of dimensions. In this paper, particle filter use in distributed SLAM was improved in two aspects. First, we improved the important function of the local filters in particle filter. The adaptive values were used to replace a set of constants in the computational process of importance function, which improved the robustness of the particle filter. Second, an information fusion method was proposed by mixing the innovation method and the number of effective particles method, which combined the advantages of these two methods. And this paper extends the previously known convergence results for particle filter to prove that improved particle filter converges to the optimal filter in mean square as the number of particles goes to infinity. The experiment results show that the proposed algorithm improved the virtue of the DPF-SLAM system in isolate faults and enabled the system to have a better tolerance and robustness. PMID:24883362

  20. Monocular SLAM for Autonomous Robots with Enhanced Features Initialization

    PubMed Central

    Guerra, Edmundo; Munguia, Rodrigo; Grau, Antoni

    2014-01-01

    This work presents a variant approach to the monocular SLAM problem focused in exploiting the advantages of a human-robot interaction (HRI) framework. Based upon the delayed inverse-depth feature initialization SLAM (DI-D SLAM), a known monocular technique, several but crucial modifications are introduced taking advantage of data from a secondary monocular sensor, assuming that this second camera is worn by a human. The human explores an unknown environment with the robot, and when their fields of view coincide, the cameras are considered a pseudo-calibrated stereo rig to produce estimations for depth through parallax. These depth estimations are used to solve a related problem with DI-D monocular SLAM, namely, the requirement of a metric scale initialization through known artificial landmarks. The same process is used to improve the performance of the technique when introducing new landmarks into the map. The convenience of the approach taken to the stereo estimation, based on SURF features matching, is discussed. Experimental validation is provided through results from real data with results showing the improvements in terms of more features correctly initialized, with reduced uncertainty, thus reducing scale and orientation drift. Additional discussion in terms of how a real-time implementation could take advantage of this approach is provided. PMID:24699284

  1. Distributed SLAM Using Improved Particle Filter for Mobile Robot Localization

    PubMed Central

    Pei, Fujun; Wu, Mei; Zhang, Simin

    2014-01-01

    The distributed SLAM system has a similar estimation performance and requires only one-fifth of the computation time compared with centralized particle filter. However, particle impoverishment is inevitably because of the random particles prediction and resampling applied in generic particle filter, especially in SLAM problem that involves a large number of dimensions. In this paper, particle filter use in distributed SLAM was improved in two aspects. First, we improved the important function of the local filters in particle filter. The adaptive values were used to replace a set of constants in the computational process of importance function, which improved the robustness of the particle filter. Second, an information fusion method was proposed by mixing the innovation method and the number of effective particles method, which combined the advantages of these two methods. And this paper extends the previously known convergence results for particle filter to prove that improved particle filter converges to the optimal filter in mean square as the number of particles goes to infinity. The experiment results show that the proposed algorithm improved the virtue of the DPF-SLAM system in isolate faults and enabled the system to have a better tolerance and robustness. PMID:24883362

  2. Visual EKF-SLAM from Heterogeneous Landmarks †

    PubMed Central

    Esparza-Jiménez, Jorge Othón; Devy, Michel; Gordillo, José L.

    2016-01-01

    Many applications require the localization of a moving object, e.g., a robot, using sensory data acquired from embedded devices. Simultaneous localization and mapping from vision performs both the spatial and temporal fusion of these data on a map when a camera moves in an unknown environment. Such a SLAM process executes two interleaved functions: the front-end detects and tracks features from images, while the back-end interprets features as landmark observations and estimates both the landmarks and the robot positions with respect to a selected reference frame. This paper describes a complete visual SLAM solution, combining both point and line landmarks on a single map. The proposed method has an impact on both the back-end and the front-end. The contributions comprehend the use of heterogeneous landmark-based EKF-SLAM (the management of a map composed of both point and line landmarks); from this perspective, the comparison between landmark parametrizations and the evaluation of how the heterogeneity improves the accuracy on the camera localization, the development of a front-end active-search process for linear landmarks integrated into SLAM and the experimentation methodology. PMID:27070602

  3. Distributed SLAM using improved particle filter for mobile robot localization.

    PubMed

    Pei, Fujun; Wu, Mei; Zhang, Simin

    2014-01-01

    The distributed SLAM system has a similar estimation performance and requires only one-fifth of the computation time compared with centralized particle filter. However, particle impoverishment is inevitably because of the random particles prediction and resampling applied in generic particle filter, especially in SLAM problem that involves a large number of dimensions. In this paper, particle filter use in distributed SLAM was improved in two aspects. First, we improved the important function of the local filters in particle filter. The adaptive values were used to replace a set of constants in the computational process of importance function, which improved the robustness of the particle filter. Second, an information fusion method was proposed by mixing the innovation method and the number of effective particles method, which combined the advantages of these two methods. And this paper extends the previously known convergence results for particle filter to prove that improved particle filter converges to the optimal filter in mean square as the number of particles goes to infinity. The experiment results show that the proposed algorithm improved the virtue of the DPF-SLAM system in isolate faults and enabled the system to have a better tolerance and robustness.

  4. Monocular SLAM for autonomous robots with enhanced features initialization.

    PubMed

    Guerra, Edmundo; Munguia, Rodrigo; Grau, Antoni

    2014-04-02

    This work presents a variant approach to the monocular SLAM problem focused in exploiting the advantages of a human-robot interaction (HRI) framework. Based upon the delayed inverse-depth feature initialization SLAM (DI-D SLAM), a known monocular technique, several but crucial modifications are introduced taking advantage of data from a secondary monocular sensor, assuming that this second camera is worn by a human. The human explores an unknown environment with the robot, and when their fields of view coincide, the cameras are considered a pseudo-calibrated stereo rig to produce estimations for depth through parallax. These depth estimations are used to solve a related problem with DI-D monocular SLAM, namely, the requirement of a metric scale initialization through known artificial landmarks. The same process is used to improve the performance of the technique when introducing new landmarks into the map. The convenience of the approach taken to the stereo estimation, based on SURF features matching, is discussed. Experimental validation is provided through results from real data with results showing the improvements in terms of more features correctly initialized, with reduced uncertainty, thus reducing scale and orientation drift. Additional discussion in terms of how a real-time implementation could take advantage of this approach is provided.

  5. Priority in Process Algebras

    NASA Technical Reports Server (NTRS)

    Cleaveland, Rance; Luettgen, Gerald; Natarajan, V.

    1999-01-01

    This paper surveys the semantic ramifications of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. These enriched formalisms allow one to model system features such as interrupts, prioritized choice, or real-time behavior. Approaches to priority in process algebras can be classified according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global pre-emption and static priorities and led to formalisms for modeling interrupts and aspects of real-time, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of pre-emption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the efficient encoding of real-time semantics. Technically, this paper studies the different models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local pre- emption. In each case the operational semantics of CCS is modified appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for different process-algebraic settings are discussed.

  6. 3-D seakeeping analysis with water on deck and slamming. Part 1: Numerical solver

    NASA Astrophysics Data System (ADS)

    Greco, M.; Lugni, C.

    2012-08-01

    A three-dimensional seakeeping numerical solver is developed to handle occurrence and effects of water-on-deck and bottom slamming. It couples (A) the rigid-ship motions with (B) the water flowing along the deck and (C) bottom slamming events. Problem A is studied with a 3-D weakly nonlinear potential flow solver based on the weak-scatterer hypothesis. Problem B, and so local and global induced green-water loads, are investigated by assuming shallow-water conditions onto the deck. Problem C is examined through a Wagner-type wedge-impact analysis. Within the coupling between A and B: the external seakeeping problem furnishes the initial and boundary conditions to the in-deck solver in terms of water level and velocity along the deck profile; in return the shallow-water problem makes available to the seakeeping solver the green-water loads to be introduced as additional loads into the rigid-motion equations. Within the coupling between A and C: the instantaneous ship configuration and its kinematic and dynamic conditions with respect to the incident waves will fix the parameters for the local impact problem; in return the slamming and water-entry pressures are integrated in the vessel region of interest and introduced as additional loads into the rigid-motion equations. The resulting numerical solver can study efficiently the ship interaction with regular and irregular sea states and the forward motion with limited speed of the vessel. This is crucial to perform reliable and feasible statistical investigations of vessel behavior. Main elements of the solver are described and validated against reference numerical solutions and model tests.

  7. A two-dimensional algebraic quantum liquid produced by an atomic simulator of the quantum Lifshitz model

    PubMed Central

    Po, Hoi Chun; Zhou, Qi

    2015-01-01

    Bosons have a natural instinct to condense at zero temperature. It is a long-standing challenge to create a high-dimensional quantum liquid that does not exhibit long-range order at the ground state, as either extreme experimental parameters or sophisticated designs of microscopic Hamiltonians are required for suppressing the condensation. Here we show that synthetic gauge fields for ultracold atoms, using either the Raman scheme or shaken lattices, provide physicists a simple and practical scheme to produce a two-dimensional algebraic quantum liquid at the ground state. This quantum liquid arises at a critical Lifshitz point, where a two-dimensional quartic dispersion emerges in the momentum space, and many fundamental properties of two-dimensional bosons are changed in its proximity. Such an ideal simulator of the quantum Lifshitz model allows experimentalists to directly visualize and explore the deconfinement transition of topological excitations, an intriguing phenomenon that is difficult to access in other systems. PMID:26268154

  8. A two-dimensional algebraic quantum liquid produced by an atomic simulator of the quantum Lifshitz model.

    PubMed

    Po, Hoi Chun; Zhou, Qi

    2015-08-13

    Bosons have a natural instinct to condense at zero temperature. It is a long-standing challenge to create a high-dimensional quantum liquid that does not exhibit long-range order at the ground state, as either extreme experimental parameters or sophisticated designs of microscopic Hamiltonians are required for suppressing the condensation. Here we show that synthetic gauge fields for ultracold atoms, using either the Raman scheme or shaken lattices, provide physicists a simple and practical scheme to produce a two-dimensional algebraic quantum liquid at the ground state. This quantum liquid arises at a critical Lifshitz point, where a two-dimensional quartic dispersion emerges in the momentum space, and many fundamental properties of two-dimensional bosons are changed in its proximity. Such an ideal simulator of the quantum Lifshitz model allows experimentalists to directly visualize and explore the deconfinement transition of topological excitations, an intriguing phenomenon that is difficult to access in other systems.

  9. A two-dimensional algebraic quantum liquid produced by an atomic simulator of the quantum Lifshitz model

    NASA Astrophysics Data System (ADS)

    Po, Hoi Chun; Zhou, Qi

    2015-08-01

    Bosons have a natural instinct to condense at zero temperature. It is a long-standing challenge to create a high-dimensional quantum liquid that does not exhibit long-range order at the ground state, as either extreme experimental parameters or sophisticated designs of microscopic Hamiltonians are required for suppressing the condensation. Here we show that synthetic gauge fields for ultracold atoms, using either the Raman scheme or shaken lattices, provide physicists a simple and practical scheme to produce a two-dimensional algebraic quantum liquid at the ground state. This quantum liquid arises at a critical Lifshitz point, where a two-dimensional quartic dispersion emerges in the momentum space, and many fundamental properties of two-dimensional bosons are changed in its proximity. Such an ideal simulator of the quantum Lifshitz model allows experimentalists to directly visualize and explore the deconfinement transition of topological excitations, an intriguing phenomenon that is difficult to access in other systems.

  10. A Non-Econometric Analysis with Algebraic Models to Forecast the Numbers of Newly Hired and Retirement of Public Primary School Teachers in Taiwan

    ERIC Educational Resources Information Center

    Lung-Hsing, Kuo; Hung-Jen, Yang; Ying-Wen, Lin; Shang-Ming, Su

    2011-01-01

    In recent years, the "street teachers" issue has caused social concern in Taiwan. This study estimates the retirement of and needs for newly hired and public primary school teachers in 2010 using an algebraic model from the paper by Husssar (1999). This recursive methodology predicts the number of newly hired public primary school teachers due to…

  11. The roles of prefrontal and posterior parietal cortex in algebra problem solving: a case of using cognitive modeling to inform neuroimaging data.

    PubMed

    Danker, Jared F; Anderson, John R

    2007-04-15

    In naturalistic algebra problem solving, the cognitive processes of representation and retrieval are typically confounded, in that transformations of the equations typically require retrieval of mathematical facts. Previous work using cognitive modeling has associated activity in the prefrontal cortex with the retrieval demands of algebra problems and activity in the posterior parietal cortex with the transformational demands of algebra problems, but these regions tend to behave similarly in response to task manipulations (Anderson, J.R., Qin, Y., Sohn, M.-H., Stenger, V.A., Carter, C.S., 2003. An information-processing model of the BOLD response in symbol manipulation tasks. Psychon. Bull. Rev. 10, 241-261; Qin, Y., Carter, C.S., Silk, E.M., Stenger, A., Fissell, K., Goode, A., Anderson, J.R., 2004. The change of brain activation patterns as children learn algebra equation solving. Proc. Natl. Acad. Sci. 101, 5686-5691). With this study we attempt to isolate activity in these two regions by using a multi-step algebra task in which transformation (parietal) is manipulated in the first step and retrieval (prefrontal) is manipulated in the second step. Counter to our initial predictions, both brain regions were differentially active during both steps. We designed two cognitive models, one encompassing our initial assumptions and one in which both processes were engaged during both steps. The first model provided a poor fit to the behavioral and neural data, while the second model fit both well. This simultaneously emphasizes the strong relationship between retrieval and representation in mathematical reasoning and demonstrates that cognitive modeling can serve as a useful tool for understanding task manipulations in neuroimaging experiments. PMID:17355908

  12. The roles of prefrontal and posterior parietal cortex in algebra problem solving: a case of using cognitive modeling to inform neuroimaging data.

    PubMed

    Danker, Jared F; Anderson, John R

    2007-04-15

    In naturalistic algebra problem solving, the cognitive processes of representation and retrieval are typically confounded, in that transformations of the equations typically require retrieval of mathematical facts. Previous work using cognitive modeling has associated activity in the prefrontal cortex with the retrieval demands of algebra problems and activity in the posterior parietal cortex with the transformational demands of algebra problems, but these regions tend to behave similarly in response to task manipulations (Anderson, J.R., Qin, Y., Sohn, M.-H., Stenger, V.A., Carter, C.S., 2003. An information-processing model of the BOLD response in symbol manipulation tasks. Psychon. Bull. Rev. 10, 241-261; Qin, Y., Carter, C.S., Silk, E.M., Stenger, A., Fissell, K., Goode, A., Anderson, J.R., 2004. The change of brain activation patterns as children learn algebra equation solving. Proc. Natl. Acad. Sci. 101, 5686-5691). With this study we attempt to isolate activity in these two regions by using a multi-step algebra task in which transformation (parietal) is manipulated in the first step and retrieval (prefrontal) is manipulated in the second step. Counter to our initial predictions, both brain regions were differentially active during both steps. We designed two cognitive models, one encompassing our initial assumptions and one in which both processes were engaged during both steps. The first model provided a poor fit to the behavioral and neural data, while the second model fit both well. This simultaneously emphasizes the strong relationship between retrieval and representation in mathematical reasoning and demonstrates that cognitive modeling can serve as a useful tool for understanding task manipulations in neuroimaging experiments.

  13. New directions in algebraic dynamical systems

    NASA Astrophysics Data System (ADS)

    Schmidt, Klaus; Verbitskiy, Evgeny

    2011-02-01

    The logarithmic Mahler measure of certain multivariate polynomials occurs frequently as the entropy or the free energy of solvable lattice models (especially dimer models). It is also known that the entropy of an algebraic dynamical system is the logarithmic Mahler measure of the defining polynomial. The connection between the lattice models and the algebraic dynamical systems is still rather mysterious.

  14. Comparing the Impact of Traditional and Modeling College Algebra Courses on Student Performance in Survey of Calculus

    ERIC Educational Resources Information Center

    West, Jerry G.

    2013-01-01

    Students in higher education deserve opportunities to succeed and learning environments which maximize success. Mathematics courses can create a barrier for success for some students. College algebra is a course that serves as a gateway to required courses in many bachelor's degree programs. The content in college algebra should serve to…

  15. Algebraic Mean Field Theory

    NASA Astrophysics Data System (ADS)

    Dankova, T. S.; Rosensteel, G.

    1998-10-01

    Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.

  16. RGB-D SLAM Based on Extended Bundle Adjustment with 2D and 3D Information

    PubMed Central

    Di, Kaichang; Zhao, Qiang; Wan, Wenhui; Wang, Yexin; Gao, Yunjun

    2016-01-01

    In the study of SLAM problem using an RGB-D camera, depth information and visual information as two types of primary measurement data are rarely tightly coupled during refinement of camera pose estimation. In this paper, a new method of RGB-D camera SLAM is proposed based on extended bundle adjustment with integrated 2D and 3D information on the basis of a new projection model. First, the geometric relationship between the image plane coordinates and the depth values is constructed through RGB-D camera calibration. Then, 2D and 3D feature points are automatically extracted and matched between consecutive frames to build a continuous image network. Finally, extended bundle adjustment based on the new projection model, which takes both image and depth measurements into consideration, is applied to the image network for high-precision pose estimation. Field experiments show that the proposed method has a notably better performance than the traditional method, and the experimental results demonstrate the effectiveness of the proposed method in improving localization accuracy. PMID:27529256

  17. RGB-D SLAM Based on Extended Bundle Adjustment with 2D and 3D Information.

    PubMed

    Di, Kaichang; Zhao, Qiang; Wan, Wenhui; Wang, Yexin; Gao, Yunjun

    2016-08-13

    In the study of SLAM problem using an RGB-D camera, depth information and visual information as two types of primary measurement data are rarely tightly coupled during refinement of camera pose estimation. In this paper, a new method of RGB-D camera SLAM is proposed based on extended bundle adjustment with integrated 2D and 3D information on the basis of a new projection model. First, the geometric relationship between the image plane coordinates and the depth values is constructed through RGB-D camera calibration. Then, 2D and 3D feature points are automatically extracted and matched between consecutive frames to build a continuous image network. Finally, extended bundle adjustment based on the new projection model, which takes both image and depth measurements into consideration, is applied to the image network for high-precision pose estimation. Field experiments show that the proposed method has a notably better performance than the traditional method, and the experimental results demonstrate the effectiveness of the proposed method in improving localization accuracy.

  18. RGB-D SLAM Based on Extended Bundle Adjustment with 2D and 3D Information.

    PubMed

    Di, Kaichang; Zhao, Qiang; Wan, Wenhui; Wang, Yexin; Gao, Yunjun

    2016-01-01

    In the study of SLAM problem using an RGB-D camera, depth information and visual information as two types of primary measurement data are rarely tightly coupled during refinement of camera pose estimation. In this paper, a new method of RGB-D camera SLAM is proposed based on extended bundle adjustment with integrated 2D and 3D information on the basis of a new projection model. First, the geometric relationship between the image plane coordinates and the depth values is constructed through RGB-D camera calibration. Then, 2D and 3D feature points are automatically extracted and matched between consecutive frames to build a continuous image network. Finally, extended bundle adjustment based on the new projection model, which takes both image and depth measurements into consideration, is applied to the image network for high-precision pose estimation. Field experiments show that the proposed method has a notably better performance than the traditional method, and the experimental results demonstrate the effectiveness of the proposed method in improving localization accuracy. PMID:27529256

  19. The algebras of large N matrix mechanics

    SciTech Connect

    Halpern, M.B.; Schwartz, C.

    1999-09-16

    Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden!) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.

  20. Application of real-time single camera SLAM technology for image-guided targeting in neurosurgery

    NASA Astrophysics Data System (ADS)

    Chang, Yau-Zen; Hou, Jung-Fu; Tsao, Yi Hsiang; Lee, Shih-Tseng

    2012-10-01

    In this paper, we propose an application of augmented reality technology for targeting tumors or anatomical structures inside the skull. The application is a combination of the technologies of MonoSLAM (Single Camera Simultaneous Localization and Mapping) and computer graphics. A stereo vision system is developed to construct geometric data of human face for registration with CT images. Reliability and accuracy of the application is enhanced by the use of fiduciary markers fixed to the skull. The MonoSLAM keeps track of the current location of the camera with respect to an augmented reality (AR) marker using the extended Kalman filter. The fiduciary markers provide reference when the AR marker is invisible to the camera. Relationship between the markers on the face and the augmented reality marker is obtained by a registration procedure by the stereo vision system and is updated on-line. A commercially available Android based tablet PC equipped with a 320×240 front-facing camera was used for implementation. The system is able to provide a live view of the patient overlaid by the solid models of tumors or anatomical structures, as well as the missing part of the tool inside the skull.

  1. Central charge and quasihole scaling dimensions from model wavefunctions: toward relating Jack wavefunctions to {\\cal W} -algebras

    NASA Astrophysics Data System (ADS)

    Bernevig, B. Andrei; Gurarie, Victor; Simon, Steven H.

    2009-06-01

    We present a general method for obtaining the central charge and the quasihole scaling dimension directly from ground-state and quasihole wavefunctions. Our method applies to wavefunctions satisfying specific clustering properties. We then use our method to examine the relation between Jack symmetric functions and certain {\\cal W} -algebras. We add substantially to the evidence that the (k, r) admissible Jack functions correspond to correlators of the conformal field theory {\\cal W}_k(k+1,k+r) by calculating the central charge and scaling dimensions of some of the fields in both cases and showing that they match. For the Jacks described by unitary {\\cal W} -models, the central charge and quasihole exponents match those previously obtained from analyzing the physics of the edge excitations. For the Jacks described by non-unitary {\\cal W} -models the central charge and quasihole scaling dimensions obtained from the wavefunctions differ from those obtained from the edge physics, which instead agree with the 'effective' central charge of the corresponding {\\cal W} -model.

  2. Matrix-algebra-based calculations of the time evolution of the binary spin-bath model for magnetization transfer.

    PubMed

    Müller, Dirk K; Pampel, André; Möller, Harald E

    2013-05-01

    Quantification of magnetization-transfer (MT) experiments are typically based on the assumption of the binary spin-bath model. This model allows for the extraction of up to six parameters (relative pool sizes, relaxation times, and exchange rate constants) for the characterization of macromolecules, which are coupled via exchange processes to the water in tissues. Here, an approach is presented for estimating MT parameters acquired with arbitrary saturation schemes and imaging pulse sequences. It uses matrix algebra to solve the Bloch-McConnell equations without unwarranted simplifications, such as assuming steady-state conditions for pulsed saturation schemes or neglecting imaging pulses. The algorithm achieves sufficient efficiency for voxel-by-voxel MT parameter estimations by using a polynomial interpolation technique. Simulations, as well as experiments in agar gels with continuous-wave and pulsed MT preparation, were performed for validation and for assessing approximations in previous modeling approaches. In vivo experiments in the normal human brain yielded results that were consistent with published data.

  3. Implementation of algebraic stress models in a general 3-D Navier-Stokes method (PAB3D)

    NASA Technical Reports Server (NTRS)

    Abdol-Hamid, Khaled S.

    1995-01-01

    A three-dimensional multiblock Navier-Stokes code, PAB3D, which was developed for propulsion integration and general aerodynamic analysis, has been used extensively by NASA Langley and other organizations to perform both internal (exhaust) and external flow analysis of complex aircraft configurations. This code was designed to solve the simplified Reynolds Averaged Navier-Stokes equations. A two-equation k-epsilon turbulence model has been used with considerable success, especially for attached flows. Accurate predicting of transonic shock wave location and pressure recovery in separated flow regions has been more difficult. Two algebraic Reynolds stress models (ASM) have been recently implemented in the code that greatly improved the code's ability to predict these difficult flow conditions. Good agreement with Direct Numerical Simulation (DNS) for a subsonic flat plate was achieved with ASM's developed by Shih, Zhu, and Lumley and Gatski and Speziale. Good predictions were also achieved at subsonic and transonic Mach numbers for shock location and trailing edge boattail pressure recovery on a single-engine afterbody/nozzle model.

  4. Numerical algebraic geometry and algebraic kinematics

    NASA Astrophysics Data System (ADS)

    Wampler, Charles W.; Sommese, Andrew J.

    In this article, the basic constructs of algebraic kinematics (links, joints, and mechanism spaces) are introduced. This provides a common schema for many kinds of problems that are of interest in kinematic studies. Once the problems are cast in this algebraic framework, they can be attacked by tools from algebraic geometry. In particular, we review the techniques of numerical algebraic geometry, which are primarily based on homotopy methods. We include a review of the main developments of recent years and outline some of the frontiers where further research is occurring. While numerical algebraic geometry applies broadly to any system of polynomial equations, algebraic kinematics provides a body of interesting examples for testing algorithms and for inspiring new avenues of work.

  5. Investigation of quantum phase transitions in the spdf interacting boson model based on dual algebraic structures for the four-level pairing model

    NASA Astrophysics Data System (ADS)

    Jafarizadeh, M. A.; Jalili Majarshin, A.; Fouladi, N.; Ghapanvari, M.

    2016-09-01

    The building blocks of the interacting boson model (IBM) are associated with both s and d bosons for positive parity states. An extension of sd-IBM along these models to spdf-IBM can provide the appropriate framework to describe negative parity states. In this paper, a solvable extended transitional Hamiltonian based on the affine \\widehat{{SU}(1,1)} Lie algebra is proposed to describe low lying positive and negative parity states between the spherical and deformed gamma-unstable shape. Quantum phase transitions (QPTs) are investigated based on dual algebraic structures for the four-level pairing model. Numerical extraction to low-lying energy levels and transition rates within the control parameters of this evaluated Hamiltonian are presented for various N values. By reproducing the experimental results, the method based on the signatures of the phase transition, such as the expectation value of the boson number operators in the lowest excited states, are used to provide a better description of Ru isotopes in this transitional region.

  6. vSLAM: vision-based SLAM for autonomous vehicle navigation

    NASA Astrophysics Data System (ADS)

    Goncalves, Luis; Karlsson, Niklas; Ostrowski, Jim; Di Bernardo, Enrico; Pirjanian, Paolo

    2004-09-01

    Among the numerous challenges of building autonomous/unmanned vehicles is that of reliable and autonomous localization in an unknown environment. In this paper we present a system that can efficiently and autonomously solve the robotics 'SLAM' problem, where a robot placed in an unknown environment, simultaneously must localize itself and make a map of the environment. The system is vision-based, and makes use of Evolution Robotic's powerful object recognition technology. As the robot explores the environment, it is continuously performing four tasks, using information from acquired images and the drive system odometry. The robot: (1) recognizes previously created 3-D visual landmarks; (2) builds new 3-D visual landmarks; (3) updates the current estimate of its location, using the map; (4) updates the landmark map. In indoor environments, the system can build a map of a 5m by 5m area in approximately 20 minutes, and can localize itself with an accuracy of approximately 15 cm in position and 3 degrees in orientation relative to the global reference frame of the landmark map. The same system can be adapted for outdoor, vehicular use.

  7. An algebraic model on the performance of a direct methanol fuel cell with consideration of methanol crossover

    NASA Astrophysics Data System (ADS)

    Yin, Ken-Ming

    An algebraic one-dimensional model on the membrane-electrode-assembly (MEA) of direct methanol fuel cell (DMFC) is proposed. Non-linear regression procedure was imposed on the model to retrieve important parameters: solid polymer electrolyte conductivity κ m, exchange current density of methanol electro-oxidation at anode catalyst surface i oM,ref, and mass diffusivity of methanol in aqueous phase within the porous electrode D a that correspond to the experimentally measured polarization curves. Although numerical iteration is required for a complete solution, the explicit relationships of methanol concentration, methanol crossover rate, oxygen concentration and cell discharge current density do provide a clear picture of the mass transport and electrochemical kinetics within the various porous media in the MEA. It is shown the cathode mixed potential induced by the parallel reactions of oxygen reduction and oxidation of crossover methanol elucidates the potential drop of the cathode and the decrease of the cell open circuit voltage (OCV). Methanol transport in the membrane is described by the diffusion, electro-osmosis, and pressure induced convection. Detailed accounts of the effects of anode methanol and cathode oxygen feed concentrations on the cell discharge performance are given with correlation to the physical structure and chemical compositions of the catalyst layers (CLs).

  8. Global localization from monocular SLAM on a mobile phone.

    PubMed

    Ventura, Jonathan; Arth, Clemens; Reitmayr, Gerhard; Schmalstieg, Dieter

    2014-04-01

    We propose the combination of a keyframe-based monocular SLAM system and a global localization method. The SLAM system runs locally on a camera-equipped mobile client and provides continuous, relative 6DoF pose estimation as well as keyframe images with computed camera locations. As the local map expands, a server process localizes the keyframes with a pre-made, globally-registered map and returns the global registration correction to the mobile client. The localization result is updated each time a keyframe is added, and observations of global anchor points are added to the client-side bundle adjustment process to further refine the SLAM map registration and limit drift. The end result is a 6DoF tracking and mapping system which provides globally registered tracking in real-time on a mobile device, overcomes the difficulties of localization with a narrow field-of-view mobile phone camera, and is not limited to tracking only in areas covered by the offline reconstruction.

  9. A priori direct numerical simulation assessment of algebraic flame surface density models for turbulent premixed flames in the context of large eddy simulation

    NASA Astrophysics Data System (ADS)

    Chakraborty, Nilanjan; Klein, Markus

    2008-08-01

    Flame surface density (FSD) based reaction rate closure is one of the most important approaches in turbulent premixed flame modeling. The algebraic models for FSD based on power laws often require information about the fractal dimension D and the inner cut-off scale ηi. In the present study, two three-dimensional direct numerical simulation (DNS) databases for freely propagating statistically planar turbulent premixed flames are analyzed among which the flame in one case belongs to the corrugated flamelet (CF) regime, whereas the other falls well within the thin reaction zone (TRZ) regime. It is found that D for the flame in the TRZ regime is greater than the value obtained for the flame in the CF regime. For the flame within the TRZ regime, the fractal dimension is found to be 7/3, which is the same as D for a material surface in a turbulent environment. For the flame in the CF regime, ηi is found to scale with the Gibson scale, whereas ηi is found to scale with the Kolmogorov length scale for the flame in the TRZ regime. Based on these observations a new algebraic model for FSD is proposed, where D and ηi are expressed as functions of Karlovitz number. The performances of the new and existing algebraic models for FSD are compared with the corresponding values obtained from DNS databases.

  10. Quantization of Algebraic Reduction

    SciTech Connect

    Sniatycki, Jeodrzej

    2007-11-14

    For a Poisson algebra obtained by algebraic reduction of symmetries of a quantizable system we develop an analogue of geometric quantization based on the quantization structure of the original system.

  11. Learning Algebra in a Computer Algebra Environment

    ERIC Educational Resources Information Center

    Drijvers, Paul

    2004-01-01

    This article summarises a doctoral thesis entitled "Learning algebra in a computer algebra environment, design research on the understanding of the concept of parameter" (Drijvers, 2003). It describes the research questions, the theoretical framework, the methodology and the results of the study. The focus of the study is on the understanding of…

  12. Algebraic theory of molecules

    NASA Technical Reports Server (NTRS)

    Iachello, Franco

    1995-01-01

    An algebraic formulation of quantum mechanics is presented. In this formulation, operators of interest are expanded onto elements of an algebra, G. For bound state problems in nu dimensions the algebra G is taken to be U(nu + 1). Applications to the structure of molecules are presented.

  13. Profiles of Algebraic Competence

    ERIC Educational Resources Information Center

    Humberstone, J.; Reeve, R.A.

    2008-01-01

    The algebraic competence of 72 12-year-old female students was examined to identify profiles of understanding reflecting different algebraic knowledge states. Beginning algebraic competence (mapping abilities: word-to-symbol and vice versa, classifying, and solving equations) was assessed. One week later, the nature of assistance required to map…

  14. Orientation in operator algebras

    PubMed Central

    Alfsen, Erik M.; Shultz, Frederic W.

    1998-01-01

    A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics. PMID:9618457

  15. Developing Thinking in Algebra

    ERIC Educational Resources Information Center

    Mason, John; Graham, Alan; Johnson-Wilder, Sue

    2005-01-01

    This book is for people with an interest in algebra whether as a learner, or as a teacher, or perhaps as both. It is concerned with the "big ideas" of algebra and what it is to understand the process of thinking algebraically. The book has been structured according to a number of pedagogic principles that are exposed and discussed along the way,…

  16. Connecting Arithmetic to Algebra

    ERIC Educational Resources Information Center

    Darley, Joy W.; Leapard, Barbara B.

    2010-01-01

    Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…

  17. Comparison of an algebraic multigrid algorithm to two iterative solvers used for modeling ground water flow and transport

    USGS Publications Warehouse

    Detwiler, R.L.; Mehl, S.; Rajaram, H.; Cheung, W.W.

    2002-01-01

    Numerical solution of large-scale ground water flow and transport problems is often constrained by the convergence behavior of the iterative solvers used to solve the resulting systems of equations. We demonstrate the ability of an algebraic multigrid algorithm (AMG) to efficiently solve the large, sparse systems of equations that result from computational models of ground water flow and transport in large and complex domains. Unlike geometric multigrid methods, this algorithm is applicable to problems in complex flow geometries, such as those encountered in pore-scale modeling of two-phase flow and transport. We integrated AMG into MODFLOW 2000 to compare two- and three-dimensional flow simulations using AMG to simulations using PCG2, a preconditioned conjugate gradient solver that uses the modified incomplete Cholesky preconditioner and is included with MODFLOW 2000. CPU times required for convergence with AMG were up to 140 times faster than those for PCG2. The cost of this increased speed was up to a nine-fold increase in required random access memory (RAM) for the three-dimensional problems and up to a four-fold increase in required RAM for the two-dimensional problems. We also compared two-dimensional numerical simulations of steady-state transport using AMG and the generalized minimum residual method with an incomplete LU-decomposition preconditioner. For these transport simulations, AMG yielded increased speeds of up to 17 times with only a 20% increase in required RAM. The ability of AMG to solve flow and transport problems in large, complex flow systems and its ready availability make it an ideal solver for use in both field-scale and pore-scale modeling.

  18. Generalized algebraic relation for predicting developing curved channel flow with a k-epsilon model of turbulence

    SciTech Connect

    Humphrey, J.A.C.; Pourahmadi, F.

    1981-06-01

    Using algebraic approximations for the Reynolds stress equations a general expression has been derived for C/sub ..mu../ in ..nu../sub t/ = C/sub ..mu../ k/sup 2//epsilon which accounts simultaneously for the effects of streamline curvature and pressure-strain in the flow, including wall-induced influences on the velocity fluctuations. The expression derived can be shown to encompass similar but more specific formulations proposed by Bradshaw, Rodi, and Leschziner and Rodi. The present formulation has been used in conjunction with k-epsilon model of turbulence to predict developing, two-dimensional, curved channel flows where both curvature and pressure-strain effects can be large. Minor modifications to include the influence of curvature on the length scale of the flow near the walls produces a significant improvement in the calculations. While, in general, predictions are in good agreement with experimental measurements of mildly and strongly curved flows, the model tends to overpredict the kinetic energy of turbulence in the inner-radius (convex) wall region. This is attributed to a breakdown of the assumption that u/sub i/u/sub j/k is a constant in the derivation of the general expression for C/sub ..mu../. Most of the experimental results suggest the presence of a weak cross-stream motion due to Taylor-Goertler vortices which cannot be resolved by the calculation scheme. Despite its limitations the present formulation provides a degree of generality not previously available in two-equation modeling of turbulent flows.

  19. Generalized algebraic relation for predicting developing curved channel flow with a k-epsilon model of turbulence

    SciTech Connect

    Humphrey, J.A.C.; Pourahmadi, F.

    1981-06-01

    Using algebraic approximations for the Reynolds stress equations a general expression has been derived for C/sub ..mu../ in ..nu../sub t/ = C/sub ..mu../ k/sup 2//epsilon which accounts simultaneously for the effects of streamline curvature and pressure-strain in the flow, including wall-induced influences on the velocity fluctuations. The expression derived can be shown to encompass smilar but more specific formulations proposed by Bradshaw, Rodi, and Leschziner and Rodi. The present formulation has been used in conjunction with a k-epsilon model of turbulence to predict developing, two-dimensional, curved channel flows where both curvature and pressure-strain effects can be large. Minor modifications to include the influence of curvature on the length scale of the flow near the walls produce a significant improvement in the calculations. While, in general, predictions are in good agreement with experimental measurements of mildly and strongly curved flows, the model tends to overpredict the kinetic energy of turbulence in the inner-radius (convex) wall region. This is attributed to a breakdown of the assumption that u/sub i/u/sub j//k is a constant in the derivation of the general expression for C/sub ..mu../. Most of the experimental results suggest the presence of a weak cross-stream motion due to Taylor-Goertler vortices which cannot be resolved by the calculation scheme. Despite its limitations the present formulation provides a degree of generality not previously available in two-equation modeling of turbulent flows.

  20. Algebraic multigrid preconditioning within parallel finite-element solvers for 3-D electromagnetic modelling problems in geophysics

    NASA Astrophysics Data System (ADS)

    Koldan, Jelena; Puzyrev, Vladimir; de la Puente, Josep; Houzeaux, Guillaume; Cela, José María

    2014-06-01

    We present an elaborate preconditioning scheme for Krylov subspace methods which has been developed to improve the performance and reduce the execution time of parallel node-based finite-element (FE) solvers for 3-D electromagnetic (EM) numerical modelling in exploration geophysics. This new preconditioner is based on algebraic multigrid (AMG) that uses different basic relaxation methods, such as Jacobi, symmetric successive over-relaxation (SSOR) and Gauss-Seidel, as smoothers and the wave front algorithm to create groups, which are used for a coarse-level generation. We have implemented and tested this new preconditioner within our parallel nodal FE solver for 3-D forward problems in EM induction geophysics. We have performed series of experiments for several models with different conductivity structures and characteristics to test the performance of our AMG preconditioning technique when combined with biconjugate gradient stabilized method. The results have shown that, the more challenging the problem is in terms of conductivity contrasts, ratio between the sizes of grid elements and/or frequency, the more benefit is obtained by using this preconditioner. Compared to other preconditioning schemes, such as diagonal, SSOR and truncated approximate inverse, the AMG preconditioner greatly improves the convergence of the iterative solver for all tested models. Also, when it comes to cases in which other preconditioners succeed to converge to a desired precision, AMG is able to considerably reduce the total execution time of the forward-problem code-up to an order of magnitude. Furthermore, the tests have confirmed that our AMG scheme ensures grid-independent rate of convergence, as well as improvement in convergence regardless of how big local mesh refinements are. In addition, AMG is designed to be a black-box preconditioner, which makes it easy to use and combine with different iterative methods. Finally, it has proved to be very practical and efficient in the

  1. A Theoretical Framework for Research in Algebra: Modification of Janvier's "Star" Model of Function Understanding.

    ERIC Educational Resources Information Center

    Bowman, Anita H.

    A pentagonal model, based on the star model of function understanding of C. Janvier (1987), is presented as a framework for the design and interpretation of research in the area of learning the concept of mathematical function. The five vertices of the pentagon correspond to five common representations of mathematical function: (1) graph; (2)…

  2. A non-linear algebraic model for the turbulent scalar fluxes

    SciTech Connect

    Younis, B.A.; Speziale, C.G.; Clark, T.T.

    1995-09-01

    The need for a new approach to modelling the scalar fluxes stems from the lack of realism in the performance of the simple gradient-transport models and the inadequacy of many of the assumptions underlying the more complicated scalar-flux transport closures. The problems with the simple gradient-transport closures are well known. In models of this type, the scalar fluxes are related to the mean scalar field via a scalar turbulent diffusivity. The purpose of this paper is to report on a novel approach to the modelling of the turbulent scalar fluxes (u{sub i}{theta}) which arise as a consequence of time averaging the transport equation for a mean scalar ({Theta}). The focus of this paper will be on the case where {Theta} is a `passive` scalar; the extension of this approach to cases involving buoyancy and compressibility will be briefly discussed. Models of this type fail badly in complex and strongly-buoyant flows.

  3. The BCS-Bogoliubov and the su(2)-Algebraic Approach to the Pairing Model in Many-Fermion System --- The Quasiparticle in the Conservation of the Fermion Number ---

    NASA Astrophysics Data System (ADS)

    Tsue, Y.; Providência, C.; Providência, J. d.; Yamamura, M.

    2012-10-01

    The relation between two approaches to the su(2)-algebraic many-fermion model is discussed: (1) the BCS-Bogoliubov approach in terms of the use of the quasiparticles representing all the degrees of freedom except those related to the Cooper-pairs and (2) the conventional algebraic approach in terms of the use of the minimum weight states, from which the Cooper-pairs are excluded. In order to arrive at the goal, the idea of the quasiparticles is brought up in the conservation of the fermion number. Under the c-number replacement for the three su(2)-generators, the quasiparticles suggested in this paper are reduced to those in the BCS-Bogoliubov approach. It is also shown that the two approaches are equivalent through the c-number replacement. Further, a certain modification of the BCS-Bogoliubov approach is discussed.

  4. Computer algebra and operators

    NASA Technical Reports Server (NTRS)

    Fateman, Richard; Grossman, Robert

    1989-01-01

    The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.

  5. A Metric Conceptual Space Algebra

    NASA Astrophysics Data System (ADS)

    Adams, Benjamin; Raubal, Martin

    The modeling of concepts from a cognitive perspective is important for designing spatial information systems that interoperate with human users. Concept representations that are built using geometric and topological conceptual space structures are well suited for semantic similarity and concept combination operations. In addition, concepts that are more closely grounded in the physical world, such as many spatial concepts, have a natural fit with the geometric structure of conceptual spaces. Despite these apparent advantages, conceptual spaces are underutilized because existing formalizations of conceptual space theory have focused on individual aspects of the theory rather than the creation of a comprehensive algebra. In this paper we present a metric conceptual space algebra that is designed to facilitate the creation of conceptual space knowledge bases and inferencing systems. Conceptual regions are represented as convex polytopes and context is built in as a fundamental element. We demonstrate the applicability of the algebra to spatial information systems with a proof-of-concept application.

  6. Algebraic Lattices in QFT Renormalization

    NASA Astrophysics Data System (ADS)

    Borinsky, Michael

    2016-07-01

    The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.

  7. Discrete Minimal Surface Algebras

    NASA Astrophysics Data System (ADS)

    Arnlind, Joakim; Hoppe, Jens

    2010-05-01

    We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sln (any semi-simple Lie algebra providing a trivial example by itself). A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically) the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.

  8. The Heisenberg-Weyl algebra on the circle and a related quantum mechanical model for hindered rotation.

    PubMed

    Kouri, Donald J; Markovich, Thomas; Maxwell, Nicholas; Bodmann, Bernhard G

    2009-07-01

    We discuss a periodic variant of the Heisenberg-Weyl algebra, associated with the group of translations and modulations on the circle. Our study of uncertainty minimizers leads to a periodic version of canonical coherent states. Unlike the canonical, Cartesian case, there are states for which the uncertainty product associated with the generators of the algebra vanishes. Next, we explore the supersymmetric (SUSY) quantum mechanical setting for the uncertainty-minimizing states and interpret them as leading to a family of "hindered rotors". Finally, we present a standard quantum mechanical treatment of one of these hindered rotor systems, including numerically generated eigenstates and energies.

  9. Computational algebraic geometry for statistical modeling FY09Q2 progress.

    SciTech Connect

    Thompson, David C.; Rojas, Joseph Maurice; Pebay, Philippe Pierre

    2009-03-01

    This is a progress report on polynomial system solving for statistical modeling. This is a progress report on polynomial system solving for statistical modeling. This quarter we have developed our first model of shock response data and an algorithm for identifying the chamber cone containing a polynomial system in n variables with n+k terms within polynomial time - a significant improvement over previous algorithms, all having exponential worst-case complexity. We have implemented and verified the chamber cone algorithm for n+3 and are working to extend the implementation to handle arbitrary k. Later sections of this report explain chamber cones in more detail; the next section provides an overview of the project and how the current progress fits into it.

  10. SDG fermion-pair algebraic SO(12) and Sp(10) models and their boson realizations

    SciTech Connect

    Navatil, P.; Geyer, H.B.; Dobes, J.

    1995-11-01

    It is shown how the boson mapping formalism may be applied as a useful many-body tool to solve a fermion problem. This is done in the context of generalized Ginocchio models for which the authors introduce S-, D-, and G-pairs of fermions and subsequently construct the sdg-boson realizations of the generalized Dyson type. The constructed SO(12) and Sp(10) fermion models are solved beyond the explicit symmetry limits. Phase transitions to rotational structures are obtained also in situations where there is no underlying SU(3) symmetry. 34 refs., 5 figs., 2 tabs.

  11. Deletion of Slam locus in mice reveals inhibitory role of SLAM family in NK cell responses regulated by cytokines and LFA-1.

    PubMed

    Guo, Huaijian; Cranert, Stacey A; Lu, Yan; Zhong, Ming-Chao; Zhang, Shaohua; Chen, Jun; Li, Rui; Mahl, Sarah E; Wu, Ning; Davidson, Dominique; Waggoner, Stephen N; Veillette, André

    2016-09-19

    Signaling lymphocytic activation molecule (SLAM) family receptors (SFRs) can mediate either activating or inhibitory effects during natural killer cell (NK cell) activation. In this study, we addressed the global role, regulation, and mechanism of action of the SLAM family in NK cells by analyzing a mouse lacking the entire ∼400-kilobase Slam locus, which encodes all six SFRs and CD48, the ligand of SFR 2B4. This mouse displayed enhanced NK cell activation responses toward hematopoietic target cells. Analyses of mice lacking individual SFRs showed that the inhibitory function of the Slam locus was due solely to 2B4 and was not influenced positively or negatively by other SFRs. Differences in NK cell responses between recognition of targets expressing or lacking ligands for SFRs were enhanced by IL-12 but suppressed by type I interferon. Cytokines also changed the levels of SLAM-associated protein adaptors, which prevent the inhibitory function of SFRs. The enhanced activation responses of SFR-deficient NK cells were dependent on integrin LFA-1 but not on DNAM-1 or NKG2D. SFR-mediated inhibition prevented the generation of activated forms of LFA-1. Hence, the Slam locus has an overall inhibitory role during NK cell activation that is solely dependent on 2B4. This effect is influenced by cytokines and leads to suppression of LFA-1 activity.

  12. Anatomically accurate high resolution modeling of human whole heart electromechanics: A strongly scalable algebraic multigrid solver method for nonlinear deformation

    PubMed Central

    Augustin, Christoph M.; Neic, Aurel; Liebmann, Manfred; Prassl, Anton J.; Niederer, Steven A.; Haase, Gundolf; Plank, Gernot

    2016-01-01

    Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which are not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate

  13. Anatomically accurate high resolution modeling of human whole heart electromechanics: A strongly scalable algebraic multigrid solver method for nonlinear deformation

    NASA Astrophysics Data System (ADS)

    Augustin, Christoph M.; Neic, Aurel; Liebmann, Manfred; Prassl, Anton J.; Niederer, Steven A.; Haase, Gundolf; Plank, Gernot

    2016-01-01

    Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which is not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate

  14. Tests of Predictions of the Algebraic Cluster Model: the Triangular D 3h Symmetry of 12C

    NASA Astrophysics Data System (ADS)

    Gai, Moshe

    2016-07-01

    A new theoretical approach to clustering in the frame of the Algebraic Cluster Model (ACM) has been developed. It predicts rotation-vibration structure with rotational band of an oblate equilateral triangular symmetric spinning top with a D 3h symmetry characterized by the sequence of states: 0+, 2+, 3-, 4±, 5- with a degenerate 4+ and 4- (parity doublet) states. Our measured new 2+ 2 in 12C allows the first study of rotation-vibration structure in 12C. The newly measured 5- state and 4- states fit very well the predicted ground state rotational band structure with the predicted sequence of states: 0+, 2+, 3-, 4±, 5- with almost degenerate 4+ and 4- (parity doublet) states. Such a D 3h symmetry is characteristic of triatomic molecules, but it is observed in the ground state rotational band of 12C for the first time in a nucleus. We discuss predictions of the ACM of other rotation-vibration bands in 12 C such as the (0+) Hoyle band and the (1-) bending mode with prediction of (“missing 3- and 4-”) states that may shed new light on clustering in 12C and light nuclei. In particular, the observation (or non observation) of the predicted (“missing”) states in the Hoyle band will allow us to conclude the geometrical arrangement of the three alpha particles composing the Hoyle state at 7.6542 MeV in 12C. We discuss proposed research programs at the Darmstadt S-DALINAC and at the newly constructed ELI-NP facility near Bucharest to test the predictions of the ACM in isotopes of carbon.

  15. The Effects of Female Mathematician Role Models on Eighth- and Ninth-Grade First-Year Algebra Students.

    ERIC Educational Resources Information Center

    O'Brien, Judith A.; Tracy, Dyanne M.

    In the United States female and male students supposedly have the same educational opportunities. Females continue to score below male students on the mathematics portions of standardized tests and less frequently choose mathematics-oriented careers. In this experimental study (n=95), 47 first-year algebra students participated in a month-long…

  16. Effectiveness of the Mind Research Institute's Algebra Readiness Curriculum on Student Achievement Implemented in a Tiered Response to Intervention Model

    ERIC Educational Resources Information Center

    Quick, Nancy

    2013-01-01

    Algebra is typically the gatekeeper for higher-level math coursework. Low math performance on standardized assessments impedes access to these higher-level math classes. Limited math progress in high school affects future career opportunities and quality of life. High school students who have historically struggled with math need interventions…

  17. Linear algebra of the permutation invariant Crow-Kimura model of prebiotic evolution.

    PubMed

    Bratus, Alexander S; Novozhilov, Artem S; Semenov, Yuri S

    2014-10-01

    A particular case of the famous quasispecies model - the Crow-Kimura model with a permutation invariant fitness landscape - is investigated. Using the fact that the mutation matrix in the case of a permutation invariant fitness landscape has a special tridiagonal form, a change of the basis is suggested such that in the new coordinates a number of analytical results can be obtained. In particular, using the eigenvectors of the mutation matrix as the new basis, we show that the quasispecies distribution approaches a binomial one and give simple estimates for the speed of convergence. Another consequence of the suggested approach is a parametric solution to the system of equations determining the quasispecies. Using this parametric solution we show that our approach leads to exact asymptotic results in some cases, which are not covered by the existing methods. In particular, we are able to present not only the limit behavior of the leading eigenvalue (mean population fitness), but also the exact formulas for the limit quasispecies eigenvector for special cases. For instance, this eigenvector has a geometric distribution in the case of the classical single peaked fitness landscape. On the biological side, we propose a mathematical definition, based on the closeness of the quasispecies to the binomial distribution, which can be used as an operational definition of the notorious error threshold. Using this definition, we suggest two approximate formulas to estimate the critical mutation rate after which the quasispecies delocalization occurs. PMID:25149562

  18. Linear algebra of the permutation invariant Crow-Kimura model of prebiotic evolution.

    PubMed

    Bratus, Alexander S; Novozhilov, Artem S; Semenov, Yuri S

    2014-10-01

    A particular case of the famous quasispecies model - the Crow-Kimura model with a permutation invariant fitness landscape - is investigated. Using the fact that the mutation matrix in the case of a permutation invariant fitness landscape has a special tridiagonal form, a change of the basis is suggested such that in the new coordinates a number of analytical results can be obtained. In particular, using the eigenvectors of the mutation matrix as the new basis, we show that the quasispecies distribution approaches a binomial one and give simple estimates for the speed of convergence. Another consequence of the suggested approach is a parametric solution to the system of equations determining the quasispecies. Using this parametric solution we show that our approach leads to exact asymptotic results in some cases, which are not covered by the existing methods. In particular, we are able to present not only the limit behavior of the leading eigenvalue (mean population fitness), but also the exact formulas for the limit quasispecies eigenvector for special cases. For instance, this eigenvector has a geometric distribution in the case of the classical single peaked fitness landscape. On the biological side, we propose a mathematical definition, based on the closeness of the quasispecies to the binomial distribution, which can be used as an operational definition of the notorious error threshold. Using this definition, we suggest two approximate formulas to estimate the critical mutation rate after which the quasispecies delocalization occurs.

  19. Martian Swarm Exploration and Mapping Using Laser Slam

    NASA Astrophysics Data System (ADS)

    Nowak, S.; Krüger, T.; Matthaei, J.; Bestmann, U.

    2013-08-01

    In order to explore planet Mars in detail and search for extra-terrestrial life the observation from orbit is not sufficient. To realize complex exploration tasks the use of automatic operating robots with a robust fault-tolerant method of navigation, independent of any infrastructure is a possibility. This work includes a concept of rotary-wing Unmanned Aerial Vehicles (UAVs) and Unmanned Ground Vehicles (UGVs) for Martian exploration in a swarm. Besides the scenario of Martian surrounding, with a small number of distinctive landmarks, the challenge consists of a Simultaneous Localization and Mapping (SLAM) concept using laser data of all swarm members.

  20. A modular approach to modeling an isolated power system on a finite voltage bus using a differential algebraic equation solving routine

    NASA Astrophysics Data System (ADS)

    Kipps, Mark R.

    1994-03-01

    The modeling of power systems has been primarily driven by the commercial power utility industry. These models usually involve the assumption that system bus voltage and frequency are constant. However, in applications such as shipboard power systems this infinite bus assumption is not valid. This thesis investigates the modeling of a synchronous generator and various loads in a modular fashion on a finite bus. The simulation presented allows the interconnection of multiple state-space models via a bus voltage model. The major difficulty encountered in building a model which computes bus voltage at each time step is that bus voltage is a function of current and current derivative terms. Bus voltage is also an input to the state equations which produce the current and current derivatives. This creates an algebraic loop which is a form of implicit differential equation. A routine has been developed by Linda Petzold of Lawrence Livermore Laboratory for solving these types of equations. The routine, called Differential Algebraic System Solver (DASSL), has been implemented in a pre-release version of the software Advanced Continuous Simulation Language (ACSL) and has been made available to the Naval Postgraduate School on a trial basis. An isolated power system is modeled using this software and the DASSL routine. The system response to several dynamic situations is studied and the results are presented.

  1. Performance analysis of the Microsoft Kinect sensor for 2D Simultaneous Localization and Mapping (SLAM) techniques.

    PubMed

    Kamarudin, Kamarulzaman; Mamduh, Syed Muhammad; Shakaff, Ali Yeon Md; Zakaria, Ammar

    2014-12-05

    This paper presents a performance analysis of two open-source, laser scanner-based Simultaneous Localization and Mapping (SLAM) techniques (i.e., Gmapping and Hector SLAM) using a Microsoft Kinect to replace the laser sensor. Furthermore, the paper proposes a new system integration approach whereby a Linux virtual machine is used to run the open source SLAM algorithms. The experiments were conducted in two different environments; a small room with no features and a typical office corridor with desks and chairs. Using the data logged from real-time experiments, each SLAM technique was simulated and tested with different parameter settings. The results show that the system is able to achieve real time SLAM operation. The system implementation offers a simple and reliable way to compare the performance of Windows-based SLAM algorithm with the algorithms typically implemented in a Robot Operating System (ROS). The results also indicate that certain modifications to the default laser scanner-based parameters are able to improve the map accuracy. However, the limited field of view and range of Kinect's depth sensor often causes the map to be inaccurate, especially in featureless areas, therefore the Kinect sensor is not a direct replacement for a laser scanner, but rather offers a feasible alternative for 2D SLAM tasks.

  2. Performance analysis of the Microsoft Kinect sensor for 2D Simultaneous Localization and Mapping (SLAM) techniques.

    PubMed

    Kamarudin, Kamarulzaman; Mamduh, Syed Muhammad; Shakaff, Ali Yeon Md; Zakaria, Ammar

    2014-01-01

    This paper presents a performance analysis of two open-source, laser scanner-based Simultaneous Localization and Mapping (SLAM) techniques (i.e., Gmapping and Hector SLAM) using a Microsoft Kinect to replace the laser sensor. Furthermore, the paper proposes a new system integration approach whereby a Linux virtual machine is used to run the open source SLAM algorithms. The experiments were conducted in two different environments; a small room with no features and a typical office corridor with desks and chairs. Using the data logged from real-time experiments, each SLAM technique was simulated and tested with different parameter settings. The results show that the system is able to achieve real time SLAM operation. The system implementation offers a simple and reliable way to compare the performance of Windows-based SLAM algorithm with the algorithms typically implemented in a Robot Operating System (ROS). The results also indicate that certain modifications to the default laser scanner-based parameters are able to improve the map accuracy. However, the limited field of view and range of Kinect's depth sensor often causes the map to be inaccurate, especially in featureless areas, therefore the Kinect sensor is not a direct replacement for a laser scanner, but rather offers a feasible alternative for 2D SLAM tasks. PMID:25490595

  3. Performance Analysis of the Microsoft Kinect Sensor for 2D Simultaneous Localization and Mapping (SLAM) Techniques

    PubMed Central

    Kamarudin, Kamarulzaman; Mamduh, Syed Muhammad; Shakaff, Ali Yeon Md; Zakaria, Ammar

    2014-01-01

    This paper presents a performance analysis of two open-source, laser scanner-based Simultaneous Localization and Mapping (SLAM) techniques (i.e., Gmapping and Hector SLAM) using a Microsoft Kinect to replace the laser sensor. Furthermore, the paper proposes a new system integration approach whereby a Linux virtual machine is used to run the open source SLAM algorithms. The experiments were conducted in two different environments; a small room with no features and a typical office corridor with desks and chairs. Using the data logged from real-time experiments, each SLAM technique was simulated and tested with different parameter settings. The results show that the system is able to achieve real time SLAM operation. The system implementation offers a simple and reliable way to compare the performance of Windows-based SLAM algorithm with the algorithms typically implemented in a Robot Operating System (ROS). The results also indicate that certain modifications to the default laser scanner-based parameters are able to improve the map accuracy. However, the limited field of view and range of Kinect's depth sensor often causes the map to be inaccurate, especially in featureless areas, therefore the Kinect sensor is not a direct replacement for a laser scanner, but rather offers a feasible alternative for 2D SLAM tasks. PMID:25490595

  4. A Richer Understanding of Algebra

    ERIC Educational Resources Information Center

    Foy, Michelle

    2008-01-01

    Algebra is one of those hard-to-teach topics where pupils seem to struggle to see it as more than a set of rules to learn, but this author recently used the software "Grid Algebra" from ATM, which engaged her Year 7 pupils in exploring algebraic concepts for themselves. "Grid Algebra" allows pupils to experience number, pre-algebra, and algebra…

  5. Connecting Algebra and Chemistry.

    ERIC Educational Resources Information Center

    O'Connor, Sean

    2003-01-01

    Correlates high school chemistry curriculum with high school algebra curriculum and makes the case for an integrated approach to mathematics and science instruction. Focuses on process integration. (DDR)

  6. Multibeam 3D Underwater SLAM with Probabilistic Registration.

    PubMed

    Palomer, Albert; Ridao, Pere; Ribas, David

    2016-04-20

    This paper describes a pose-based underwater 3D Simultaneous Localization and Mapping (SLAM) using a multibeam echosounder to produce high consistency underwater maps. The proposed algorithm compounds swath profiles of the seafloor with dead reckoning localization to build surface patches (i.e., point clouds). An Iterative Closest Point (ICP) with a probabilistic implementation is then used to register the point clouds, taking into account their uncertainties. The registration process is divided in two steps: (1) point-to-point association for coarse registration and (2) point-to-plane association for fine registration. The point clouds of the surfaces to be registered are sub-sampled in order to decrease both the computation time and also the potential of falling into local minima during the registration. In addition, a heuristic is used to decrease the complexity of the association step of the ICP from O(n2) to O(n) . The performance of the SLAM framework is tested using two real world datasets: First, a 2.5D bathymetric dataset obtained with the usual down-looking multibeam sonar configuration, and second, a full 3D underwater dataset acquired with a multibeam sonar mounted on a pan and tilt unit.

  7. Multibeam 3D Underwater SLAM with Probabilistic Registration.

    PubMed

    Palomer, Albert; Ridao, Pere; Ribas, David

    2016-01-01

    This paper describes a pose-based underwater 3D Simultaneous Localization and Mapping (SLAM) using a multibeam echosounder to produce high consistency underwater maps. The proposed algorithm compounds swath profiles of the seafloor with dead reckoning localization to build surface patches (i.e., point clouds). An Iterative Closest Point (ICP) with a probabilistic implementation is then used to register the point clouds, taking into account their uncertainties. The registration process is divided in two steps: (1) point-to-point association for coarse registration and (2) point-to-plane association for fine registration. The point clouds of the surfaces to be registered are sub-sampled in order to decrease both the computation time and also the potential of falling into local minima during the registration. In addition, a heuristic is used to decrease the complexity of the association step of the ICP from O(n2) to O(n) . The performance of the SLAM framework is tested using two real world datasets: First, a 2.5D bathymetric dataset obtained with the usual down-looking multibeam sonar configuration, and second, a full 3D underwater dataset acquired with a multibeam sonar mounted on a pan and tilt unit. PMID:27104538

  8. Validation of Underwater Sensor Package Using Feature Based SLAM.

    PubMed

    Cain, Christopher; Leonessa, Alexander

    2016-01-01

    Robotic vehicles working in new, unexplored environments must be able to locate themselves in the environment while constructing a picture of the objects in the environment that could act as obstacles that would prevent the vehicles from completing their desired tasks. In enclosed environments, underwater range sensors based off of acoustics suffer performance issues due to reflections. Additionally, their relatively high cost make them less than ideal for usage on low cost vehicles designed to be used underwater. In this paper we propose a sensor package composed of a downward facing camera, which is used to perform feature tracking based visual odometry, and a custom vision-based two dimensional rangefinder that can be used on low cost underwater unmanned vehicles. In order to examine the performance of this sensor package in a SLAM framework, experimental tests are performed using an unmanned ground vehicle and two feature based SLAM algorithms, the extended Kalman filter based approach and the Rao-Blackwellized, particle filter based approach, to validate the sensor package. PMID:26999142

  9. Multibeam 3D Underwater SLAM with Probabilistic Registration

    PubMed Central

    Palomer, Albert; Ridao, Pere; Ribas, David

    2016-01-01

    This paper describes a pose-based underwater 3D Simultaneous Localization and Mapping (SLAM) using a multibeam echosounder to produce high consistency underwater maps. The proposed algorithm compounds swath profiles of the seafloor with dead reckoning localization to build surface patches (i.e., point clouds). An Iterative Closest Point (ICP) with a probabilistic implementation is then used to register the point clouds, taking into account their uncertainties. The registration process is divided in two steps: (1) point-to-point association for coarse registration and (2) point-to-plane association for fine registration. The point clouds of the surfaces to be registered are sub-sampled in order to decrease both the computation time and also the potential of falling into local minima during the registration. In addition, a heuristic is used to decrease the complexity of the association step of the ICP from O(n2) to O(n). The performance of the SLAM framework is tested using two real world datasets: First, a 2.5D bathymetric dataset obtained with the usual down-looking multibeam sonar configuration, and second, a full 3D underwater dataset acquired with a multibeam sonar mounted on a pan and tilt unit. PMID:27104538

  10. Validation of Underwater Sensor Package Using Feature Based SLAM

    PubMed Central

    Cain, Christopher; Leonessa, Alexander

    2016-01-01

    Robotic vehicles working in new, unexplored environments must be able to locate themselves in the environment while constructing a picture of the objects in the environment that could act as obstacles that would prevent the vehicles from completing their desired tasks. In enclosed environments, underwater range sensors based off of acoustics suffer performance issues due to reflections. Additionally, their relatively high cost make them less than ideal for usage on low cost vehicles designed to be used underwater. In this paper we propose a sensor package composed of a downward facing camera, which is used to perform feature tracking based visual odometry, and a custom vision-based two dimensional rangefinder that can be used on low cost underwater unmanned vehicles. In order to examine the performance of this sensor package in a SLAM framework, experimental tests are performed using an unmanned ground vehicle and two feature based SLAM algorithms, the extended Kalman filter based approach and the Rao-Blackwellized, particle filter based approach, to validate the sensor package. PMID:26999142

  11. Validation of Underwater Sensor Package Using Feature Based SLAM.

    PubMed

    Cain, Christopher; Leonessa, Alexander

    2016-03-17

    Robotic vehicles working in new, unexplored environments must be able to locate themselves in the environment while constructing a picture of the objects in the environment that could act as obstacles that would prevent the vehicles from completing their desired tasks. In enclosed environments, underwater range sensors based off of acoustics suffer performance issues due to reflections. Additionally, their relatively high cost make them less than ideal for usage on low cost vehicles designed to be used underwater. In this paper we propose a sensor package composed of a downward facing camera, which is used to perform feature tracking based visual odometry, and a custom vision-based two dimensional rangefinder that can be used on low cost underwater unmanned vehicles. In order to examine the performance of this sensor package in a SLAM framework, experimental tests are performed using an unmanned ground vehicle and two feature based SLAM algorithms, the extended Kalman filter based approach and the Rao-Blackwellized, particle filter based approach, to validate the sensor package.

  12. Bearing-Only SLAM with an Omnicam Robust Selection of SIFT Features for Service Robots

    NASA Astrophysics Data System (ADS)

    Hochdorfer, Siegfried; Schlegel, Christian

    SLAM mechanisms are a key component towards advanced service robotics applications. Currently, a major hurdle are the still high costs of suitable range measuring devices. A solution are bearing-only SLAM approaches since these can be used with cheap sensors like omnicams. The general approach of using an Extended Kaiman Filter (EKF) for bearing-only SLAM based on artificial landmarks has been described and evaluated in [2][1]. Instead of artificial landmarks, we now use SIFT features [3] as natural landmarks.

  13. Z 2-graded classical r-matrices and algebraic Bethe ansatz: applications to integrable models of quantum optics and nuclear physics

    NASA Astrophysics Data System (ADS)

    Skrypnyk, T.

    2016-09-01

    We consider quantum integrable models based on the Lie algebra gl(n) and non-skew-symmetric classical r-matrices associated with Z 2-gradings of gl(n) of the following type: {gl}(n)={gl}{(n)}\\bar{0}+{gl}{(n)}\\bar{1}, where {gl}{(n)}\\bar{0}={gl}({n}1)\\oplus {gl}(n-{n}1). Among the considered models are Gaudin-type models with an external magnetic field, used in nuclear physics to produce proton–neutron Bardeen–Cooper–Schrieer-type models, n-level many-mode Jaynes–Cummings–Dicke-type models of quantum optics, matrix generalization of Bose–Hubbard dimers, etc. We diagonalize the constructed models by means of the ‘generalized’ nested Bethe ansatz.

  14. Z 2-graded classical r-matrices and algebraic Bethe ansatz: applications to integrable models of quantum optics and nuclear physics

    NASA Astrophysics Data System (ADS)

    Skrypnyk, T.

    2016-09-01

    We consider quantum integrable models based on the Lie algebra gl(n) and non-skew-symmetric classical r-matrices associated with Z 2-gradings of gl(n) of the following type: {gl}(n)={gl}{(n)}\\bar{0}+{gl}{(n)}\\bar{1}, where {gl}{(n)}\\bar{0}={gl}({n}1)\\oplus {gl}(n-{n}1). Among the considered models are Gaudin-type models with an external magnetic field, used in nuclear physics to produce proton-neutron Bardeen-Cooper-Schrieer-type models, n-level many-mode Jaynes-Cummings-Dicke-type models of quantum optics, matrix generalization of Bose-Hubbard dimers, etc. We diagonalize the constructed models by means of the ‘generalized’ nested Bethe ansatz.

  15. Algebraic distance on graphs.

    SciTech Connect

    Chen, J.; Safro, I.

    2011-01-01

    Measuring the connection strength between a pair of vertices in a graph is one of the most important concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the effects associated with short paths of lengths greater than one. In this paper, we consider an iterative process that smooths an associated value for nearby vertices, and we present a measure of the local connection strength (called the algebraic distance; see [D. Ron, I. Safro, and A. Brandt, Multiscale Model. Simul., 9 (2011), pp. 407-423]) based on this process. The proposed measure is attractive in that the process is simple, linear, and easily parallelized. An analysis of the convergence property of the process reveals that the local neighborhoods play an important role in determining the connectivity between vertices. We demonstrate the practical effectiveness of the proposed measure through several combinatorial optimization problems on graphs and hypergraphs.

  16. Linear-Algebra Programs

    NASA Technical Reports Server (NTRS)

    Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.

    1982-01-01

    The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.

  17. Ready, Set, Algebra?

    ERIC Educational Resources Information Center

    Levy, Alissa Beth

    2012-01-01

    The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this…

  18. Algebraic Reasoning through Patterns

    ERIC Educational Resources Information Center

    Rivera, F. D.; Becker, Joanne Rossi

    2009-01-01

    This article presents the results of a three-year study that explores students' performance on patterning tasks involving prealgebra and algebra. The findings, insights, and issues drawn from the study are intended to help teach prealgebra and algebra. In the remainder of the article, the authors take a more global view of the three-year study on…

  19. Teaching Structure in Algebra

    ERIC Educational Resources Information Center

    Merlin, Ethan M.

    2013-01-01

    This article describes how the author has developed tasks for students that address the missed "essence of the matter" of algebraic transformations. Specifically, he has found that having students practice "perceiving" algebraic structure--by naming the "glue" in the expressions, drawing expressions using…

  20. A Robust Approach for a Filter-Based Monocular Simultaneous Localization and Mapping (SLAM) System

    PubMed Central

    Munguía, Rodrigo; Castillo-Toledo, Bernardino; Grau, Antoni

    2013-01-01

    Simultaneous localization and mapping (SLAM) is an important problem to solve in robotics theory in order to build truly autonomous mobile robots. This work presents a novel method for implementing a SLAM system based on a single camera sensor. The SLAM with a single camera, or monocular SLAM, is probably one of the most complex SLAM variants. In this case, a single camera, which is freely moving through its environment, represents the sole sensor input to the system. The sensors have a large impact on the algorithm used for SLAM. Cameras are used more frequently, because they provide a lot of information and are well adapted for embedded systems: they are light, cheap and power-saving. Nevertheless, and unlike range sensors, which provide range and angular information, a camera is a projective sensor providing only angular measurements of image features. Therefore, depth information (range) cannot be obtained in a single step. In this case, special techniques for feature system-initialization are needed in order to enable the use of angular sensors (as cameras) in SLAM systems. The main contribution of this work is to present a novel and robust scheme for incorporating and measuring visual features in filtering-based monocular SLAM systems. The proposed method is based in a two-step technique, which is intended to exploit all the information available in angular measurements. Unlike previous schemes, the values of parameters used by the initialization technique are derived directly from the sensor characteristics, thus simplifying the tuning of the system. The experimental results show that the proposed method surpasses the performance of previous schemes. PMID:23823972

  1. A robust approach for a filter-based monocular simultaneous localization and mapping (SLAM) system.

    PubMed

    Munguía, Rodrigo; Castillo-Toledo, Bernardino; Grau, Antoni

    2013-07-03

    Simultaneous localization and mapping (SLAM) is an important problem to solve in robotics theory in order to build truly autonomous mobile robots. This work presents a novel method for implementing a SLAM system based on a single camera sensor. The SLAM with a single camera, or monocular SLAM, is probably one of the most complex SLAM variants. In this case, a single camera, which is freely moving through its environment, represents the sole sensor input to the system. The sensors have a large impact on the algorithm used for SLAM. Cameras are used more frequently, because they provide a lot of information and are well adapted for embedded systems: they are light, cheap and power-saving. Nevertheless, and unlike range sensors, which provide range and angular information, a camera is a projective sensor providing only angular measurements of image features. Therefore, depth information (range) cannot be obtained in a single step. In this case, special techniques for feature system-initialization are needed in order to enable the use of angular sensors (as cameras) in SLAM systems. The main contribution of this work is to present a novel and robust scheme for incorporating and measuring visual features in filtering-based monocular SLAM systems. The proposed method is based in a two-step technique, which is intended to exploit all the information available in angular measurements. Unlike previous schemes, the values of parameters used by the initialization technique are derived directly from the sensor characteristics, thus simplifying the tuning of the system. The experimental results show that the proposed method surpasses the performance of previous schemes.

  2. A robust approach for a filter-based monocular simultaneous localization and mapping (SLAM) system.

    PubMed

    Munguía, Rodrigo; Castillo-Toledo, Bernardino; Grau, Antoni

    2013-01-01

    Simultaneous localization and mapping (SLAM) is an important problem to solve in robotics theory in order to build truly autonomous mobile robots. This work presents a novel method for implementing a SLAM system based on a single camera sensor. The SLAM with a single camera, or monocular SLAM, is probably one of the most complex SLAM variants. In this case, a single camera, which is freely moving through its environment, represents the sole sensor input to the system. The sensors have a large impact on the algorithm used for SLAM. Cameras are used more frequently, because they provide a lot of information and are well adapted for embedded systems: they are light, cheap and power-saving. Nevertheless, and unlike range sensors, which provide range and angular information, a camera is a projective sensor providing only angular measurements of image features. Therefore, depth information (range) cannot be obtained in a single step. In this case, special techniques for feature system-initialization are needed in order to enable the use of angular sensors (as cameras) in SLAM systems. The main contribution of this work is to present a novel and robust scheme for incorporating and measuring visual features in filtering-based monocular SLAM systems. The proposed method is based in a two-step technique, which is intended to exploit all the information available in angular measurements. Unlike previous schemes, the values of parameters used by the initialization technique are derived directly from the sensor characteristics, thus simplifying the tuning of the system. The experimental results show that the proposed method surpasses the performance of previous schemes. PMID:23823972

  3. Measles virus interacts with human SLAM receptor on dendritic cells to cause immunosuppression

    PubMed Central

    Hahm, Bumsuk; Arbour, Nathalie; Oldstone, Michael B.A.

    2016-01-01

    Measles virus (MV) infects dendritic cells (DCs) resulting in immunosuppression. Human DCs express two MV receptors: CD46 and human signaling lymphocyte activation molecule (hSLAM); thus, the role played by either alone is unclear. Because wild-type (wt) MV uses hSLAM receptor preferentially, we dissected the molecular basis of MV–DC interaction and resultant immunosuppression through the hSLAM receptor by creating transgenic (tg) mice expressing hSLAM on DCs. After infection with wt MV, murine splenic DCs expressing hSLAM receptor had less B7-1, B7-2, CD40, MHC class I, and MHC class II molecules on their surfaces and displayed an increased rate of apoptosis when compared to uninfected DCs. Further, MV-infected DCs failed to stimulate allogeneic T cells and inhibited mitogen-dependent T-cell proliferation. Individual expression of human SLAM, interferon α/β receptor, tumor necrosis factor-α, and lymphotoxin-α or β from T cells was not required for MV-infected DCs to inhibit the proliferation of T cells. PMID:15193925

  4. Splash jet and slamming generated by a rotating flap

    NASA Astrophysics Data System (ADS)

    Sun, S. Y.; Sun, S. L.; Ren, H. L.; Wu, G. X.

    2015-09-01

    The hydrodynamic problem of slamming generated by a rotating flap, commonly known as Oyster in the wave energy sector, plunging into water, is analysed based on the incompressible velocity potential theory. The problem is solved through the boundary element method in the time domain. Two typical case studies are undertaken. One is the flap plunging into calm water and the other into an incoming wave. The splash jet formed during the flap plunging is included in the simulation. When the jet meets the main flow, it is treated through the domain decomposition method without taking account the secondary impact, which is similar to the mathematical method of Riemann's second sheet in the complex plane. The problem is solved in each non-overlapping subdomain, and the velocity and pressure continuity condition is imposed on the interface of the subdomains. Detailed results for the flap plunging into water with different velocities or accelerations are provided. The gravity and wave effects are also investigated.

  5. Lie algebra extensions of current algebras on S3

    NASA Astrophysics Data System (ADS)

    Kori, Tosiaki; Imai, Yuto

    2015-06-01

    An affine Kac-Moody algebra is a central extension of the Lie algebra of smooth mappings from S1 to the complexification of a Lie algebra. In this paper, we shall introduce a central extension of the Lie algebra of smooth mappings from S3 to the quaternization of a Lie algebra and investigate its root space decomposition. We think this extension of current algebra might give a mathematical tool for four-dimensional conformal field theory as Kac-Moody algebras give it for two-dimensional conformal field theory.

  6. Leibniz algebras associated with representations of filiform Lie algebras

    NASA Astrophysics Data System (ADS)

    Ayupov, Sh. A.; Camacho, L. M.; Khudoyberdiyev, A. Kh.; Omirov, B. A.

    2015-12-01

    In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra nn,1. We introduce a Fock module for the algebra nn,1 and provide classification of Leibniz algebras L whose corresponding Lie algebra L / I is the algebra nn,1 with condition that the ideal I is a Fock nn,1-module, where I is the ideal generated by squares of elements from L. We also consider Leibniz algebras with corresponding Lie algebra nn,1 and such that the action I ×nn,1 → I gives rise to a minimal faithful representation of nn,1. The classification up to isomorphism of such Leibniz algebras is given for the case of n = 4.

  7. Canine Distemper Virus Fusion Activation: Critical Role of Residue E123 of CD150/SLAM

    PubMed Central

    Khosravi, Mojtaba; Bringolf, Fanny; Röthlisberger, Silvan; Bieringer, Maria; Schneider-Schaulies, Jürgen; Zurbriggen, Andreas; Origgi, Francesco

    2015-01-01

    ABSTRACT Measles virus (MeV) and canine distemper virus (CDV) possess tetrameric attachment proteins (H) and trimeric fusion proteins, which cooperate with either SLAM or nectin 4 receptors to trigger membrane fusion for cell entry. While the MeV H-SLAM cocrystal structure revealed the binding interface, two distinct oligomeric H assemblies were also determined. In one of the conformations, two SLAM units were sandwiched between two discrete H head domains, thus spotlighting two binding interfaces (“front” and “back”). Here, we investigated the functional relevance of both interfaces in activating the CDV membrane fusion machinery. While alanine-scanning mutagenesis identified five critical regulatory residues in the front H-binding site of SLAM, the replacement of a conserved glutamate residue (E at position 123, replaced with A [E123A]) led to the most pronounced impact on fusion promotion. Intriguingly, while determination of the interaction of H with the receptor using soluble constructs revealed reduced binding for the identified SLAM mutants, no effect was recorded when physical interaction was investigated with the full-length counterparts of both molecules. Conversely, although mutagenesis of three strategically selected residues within the back H-binding site of SLAM did not substantially affect fusion triggering, nevertheless, the mutants weakened the H-SLAM interaction recorded with the membrane-anchored protein constructs. Collectively, our findings support a mode of binding between the attachment protein and the V domain of SLAM that is common to all morbilliviruses and suggest a major role of the SLAM residue E123, located at the front H-binding site, in triggering the fusion machinery. However, our data additionally support the hypothesis that other microdomain(s) of both glycoproteins (including the back H-binding site) might be required to achieve fully productive H-SLAM interactions. IMPORTANCE A complete understanding of the measles virus

  8. Degenerate Sklyanin algebras

    NASA Astrophysics Data System (ADS)

    Smirnov, Andrey

    2010-08-01

    New trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for sl(2;?). These solutions are shown to be related to the standard ones by the quasi-Hopf twist. We demonstrate that the quantum algebras arising from these new R-matrices can be obtained as special limits of the Sklyanin algebra. A representation for these algebras by the difference operators is found. The sl( N;?)-case is discussed.

  9. Degenerate Sklyanin algebras

    NASA Astrophysics Data System (ADS)

    Smirnov, Andrey

    2010-08-01

    New trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for sl(2;?). These solutions are shown to be related to the standard ones by the quasi-Hopf twist. We demonstrate that the quantum algebras arising from these new R-matrices can be obtained as special limits of the Sklyanin algebra. A representation for these algebras by the difference operators is found. The sl(N;?)-case is discussed.

  10. FAST TRACK COMMUNICATION: Kac Moody algebras and controlled chaos

    NASA Astrophysics Data System (ADS)

    Wesley, Daniel H.

    2007-02-01

    Compactification can control chaotic Mixmaster behaviour in gravitational systems with p-form matter: we consider this in light of the connection between supergravity models and Kac Moody algebras. We show that different compactifications define 'mutations' of the algebras associated with the noncompact theories. We list the algebras obtained in this way, and find novel examples of wall systems determined by Lorentzian (but not hyperbolic) algebras. Cosmological models with a smooth pre-big bang phase require that chaos is absent: we show that compactification alone cannot eliminate chaos in the simplest compactifications of the heterotic string on a Calabi Yau, or M theory on a manifold of G2 holonomy.

  11. Sensor Fusion of Monocular Cameras and Laser Rangefinders for Line-Based Simultaneous Localization and Mapping (SLAM) Tasks in Autonomous Mobile Robots

    PubMed Central

    Zhang, Xinzheng; Rad, Ahmad B.; Wong, Yiu-Kwong

    2012-01-01

    This paper presents a sensor fusion strategy applied for Simultaneous Localization and Mapping (SLAM) in dynamic environments. The designed approach consists of two features: (i) the first one is a fusion module which synthesizes line segments obtained from laser rangefinder and line features extracted from monocular camera. This policy eliminates any pseudo segments that appear from any momentary pause of dynamic objects in laser data. (ii) The second characteristic is a modified multi-sensor point estimation fusion SLAM (MPEF-SLAM) that incorporates two individual Extended Kalman Filter (EKF) based SLAM algorithms: monocular and laser SLAM. The error of the localization in fused SLAM is reduced compared with those of individual SLAM. Additionally, a new data association technique based on the homography transformation matrix is developed for monocular SLAM. This data association method relaxes the pleonastic computation. The experimental results validate the performance of the proposed sensor fusion and data association method. PMID:22368478

  12. Sensor fusion of monocular cameras and laser rangefinders for line-based Simultaneous Localization and Mapping (SLAM) tasks in autonomous mobile robots.

    PubMed

    Zhang, Xinzheng; Rad, Ahmad B; Wong, Yiu-Kwong

    2012-01-01

    This paper presents a sensor fusion strategy applied for Simultaneous Localization and Mapping (SLAM) in dynamic environments. The designed approach consists of two features: (i) the first one is a fusion module which synthesizes line segments obtained from laser rangefinder and line features extracted from monocular camera. This policy eliminates any pseudo segments that appear from any momentary pause of dynamic objects in laser data. (ii) The second characteristic is a modified multi-sensor point estimation fusion SLAM (MPEF-SLAM) that incorporates two individual Extended Kalman Filter (EKF) based SLAM algorithms: monocular and laser SLAM. The error of the localization in fused SLAM is reduced compared with those of individual SLAM. Additionally, a new data association technique based on the homography transformation matrix is developed for monocular SLAM. This data association method relaxes the pleonastic computation. The experimental results validate the performance of the proposed sensor fusion and data association method.

  13. Sensor fusion of monocular cameras and laser rangefinders for line-based Simultaneous Localization and Mapping (SLAM) tasks in autonomous mobile robots.

    PubMed

    Zhang, Xinzheng; Rad, Ahmad B; Wong, Yiu-Kwong

    2012-01-01

    This paper presents a sensor fusion strategy applied for Simultaneous Localization and Mapping (SLAM) in dynamic environments. The designed approach consists of two features: (i) the first one is a fusion module which synthesizes line segments obtained from laser rangefinder and line features extracted from monocular camera. This policy eliminates any pseudo segments that appear from any momentary pause of dynamic objects in laser data. (ii) The second characteristic is a modified multi-sensor point estimation fusion SLAM (MPEF-SLAM) that incorporates two individual Extended Kalman Filter (EKF) based SLAM algorithms: monocular and laser SLAM. The error of the localization in fused SLAM is reduced compared with those of individual SLAM. Additionally, a new data association technique based on the homography transformation matrix is developed for monocular SLAM. This data association method relaxes the pleonastic computation. The experimental results validate the performance of the proposed sensor fusion and data association method. PMID:22368478

  14. Algebraic integrability: a survey.

    PubMed

    Vanhaecke, Pol

    2008-03-28

    We give a concise introduction to the notion of algebraic integrability. Our exposition is based on examples and phenomena, rather than on detailed proofs of abstract theorems. We mainly focus on algebraic integrability in the sense of Adler-van Moerbeke, where the fibres of the momentum map are affine parts of Abelian varieties; as it turns out, most examples from classical mechanics are of this form. Two criteria are given for such systems (Kowalevski-Painlevé and Lyapunov) and each is illustrated in one example. We show in the case of a relatively simple example how one proves algebraic integrability, starting from the differential equations for the integrable vector field. For Hamiltonian systems that are algebraically integrable in the generalized sense, two examples are given, which illustrate the non-compact analogues of Abelian varieties which typically appear in such systems. PMID:17588863

  15. Algebraic Semantics for Narrative

    ERIC Educational Resources Information Center

    Kahn, E.

    1974-01-01

    This paper uses discussion of Edmund Spenser's "The Faerie Queene" to present a theoretical framework for explaining the semantics of narrative discourse. The algebraic theory of finite automata is used. (CK)

  16. Covariant deformed oscillator algebras

    NASA Technical Reports Server (NTRS)

    Quesne, Christiane

    1995-01-01

    The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.

  17. Aprepro - Algebraic Preprocessor

    2005-08-01

    Aprepro is an algebraic preprocessor that reads a file containing both general text and algebraic, string, or conditional expressions. It interprets the expressions and outputs them to the output file along witht the general text. Aprepro contains several mathematical functions, string functions, and flow control constructs. In addition, functions are included that, with some additional files, implement a units conversion system and a material database lookup system.

  18. Geometric Algebra for Physicists

    NASA Astrophysics Data System (ADS)

    Doran, Chris; Lasenby, Anthony

    2007-11-01

    Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.

  19. Quantum walks, deformed relativity and Hopf algebra symmetries.

    PubMed

    Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo

    2016-05-28

    We show how the Weyl quantum walk derived from principles in D'Ariano & Perinotti (D'Ariano & Perinotti 2014Phys. Rev. A90, 062106. (doi:10.1103/PhysRevA.90.062106)), enjoying a nonlinear Lorentz symmetry of dynamics, allows one to introduce Hopf algebras for position and momentum of the emerging particle. We focus on two special models of Hopf algebras-the usual Poincaré and theκ-Poincaré algebras.

  20. Quantum walks, deformed relativity and Hopf algebra symmetries.

    PubMed

    Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo

    2016-05-28

    We show how the Weyl quantum walk derived from principles in D'Ariano & Perinotti (D'Ariano & Perinotti 2014Phys. Rev. A90, 062106. (doi:10.1103/PhysRevA.90.062106)), enjoying a nonlinear Lorentz symmetry of dynamics, allows one to introduce Hopf algebras for position and momentum of the emerging particle. We focus on two special models of Hopf algebras-the usual Poincaré and theκ-Poincaré algebras. PMID:27091171

  1. The Algebraic Way

    NASA Astrophysics Data System (ADS)

    Hiley, B. J.

    In this chapter, we examine in detail the non-commutative symplectic algebra underlying quantum dynamics. By using this algebra, we show that it contains both the Weyl-von Neumann and the Moyal quantum algebras. The latter contains the Wigner distribution as the kernel of the density matrix. The underlying non-commutative geometry can be projected into either of two Abelian spaces, so-called `shadow phase spaces'. One of these is the phase space of Bohmian mechanics, showing that it is a fragment of the basic underlying algebra. The algebraic approach is much richer, giving rise to two fundamental dynamical time development equations which reduce to the Liouville equation and the Hamilton-Jacobi equation in the classical limit. They also include the Schrödinger equation and its wave-function, showing that these features are a partial aspect of the more general non-commutative structure. We discuss briefly the properties of this more general mathematical background from which the non-commutative symplectic algebra emerges.

  2. Algebraic tools for dealing with the atomic shell model. I. Wavefunctions and integrals for hydrogen-like ions

    NASA Astrophysics Data System (ADS)

    Surzhykov, Andrey; Koval, Peter; Fritzsche, Stephan

    2005-01-01

    Today, the 'hydrogen atom model' is known to play its role not only in teaching the basic elements of quantum mechanics but also for building up effective theories in atomic and molecular physics, quantum optics, plasma physics, or even in the design of semiconductor devices. Therefore, the analytical as well as numerical solutions of the hydrogen-like ions are frequently required both, for analyzing experimental data and for carrying out quite advanced theoretical studies. In order to support a fast and consistent access to these (Coulomb-field) solutions, here we present the DIRAC program which has been developed originally for studying the properties and dynamical behavior of the (hydrogen-like) ions. In the present version, a set of MAPLE procedures is provided for the Coulomb wave and Green's functions by applying the (wave) equations from both, the nonrelativistic and relativistic theory. Apart from the interactive access to these functions, moreover, a number of radial integrals are also implemented in the DIRAC program which may help the user to construct transition amplitudes and cross sections as they occur frequently in the theory of ion-atom and ion-photon collisions. Program summaryTitle of program:DIRAC Catalogue number: ADUQ Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUQ Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: None Computer for which the program is designed and has been tested: All computers with a license of the computer algebra package MAPLE [1] Program language used: Maple 8 and 9 No. of lines in distributed program, including test data, etc.:2186 No. of bytes in distributed program, including test data, etc.: 162 591 Distribution format: tar gzip file CPC Program Library subprograms required: None Nature of the physical problem: Analytical solutions of the hydrogen atom are widely used in very different fields of physics [2,3]. Despite of the rather simple structure

  3. Spatial-Operator Algebra For Flexible-Link Manipulators

    NASA Technical Reports Server (NTRS)

    Jain, Abhinandan; Rodriguez, Guillermo

    1994-01-01

    Method of computing dynamics of multiple-flexible-link robotic manipulators based on spatial-operator algebra, which originally applied to rigid-link manipulators. Aspects of spatial-operator-algebra approach described in several previous articles in NASA Tech Briefs-most recently "Robot Control Based on Spatial-Operator Algebra" (NPO-17918). In extension of spatial-operator algebra to manipulators with flexible links, each link represented by finite-element model: mass of flexible link apportioned among smaller, lumped-mass rigid bodies, coupling of motions expressed in terms of vibrational modes. This leads to operator expression for modal-mass matrix of link.

  4. The Quiet Revolution of Poetry Slam: The Sustainability of Cultural Capital in the Light of Changing Artistic Conventions

    ERIC Educational Resources Information Center

    Gregory, Helen

    2008-01-01

    This paper considers the educational and theoretical implications of an analysis into the artistic movement of poetry slam. Slam is a successful and growing global phenomenon, which both directly and indirectly sets itself against the dominant literary world. As such, it could be viewed as presenting a challenge to dominant literary conventions…

  5. Shocklets, SLAMS, and Field-Aligned Ion Beams in the Terrestrial Foreshock

    NASA Technical Reports Server (NTRS)

    Wilson, L. B.; Koval, A.; Sibeck, D. G.; Szabo, A.; Cattell, C. A.; Kasper, J. C.; Maruca, B. A.; Pulupa, M.; Salem, C. S.; Wilber, M.

    2012-01-01

    We present Wind spacecraft observations of ion distributions showing field- aligned beams (FABs) and large-amplitude magnetic fluctuations composed of a series of shocklets and short large-amplitude magnetic structures (SLAMS). The FABs are found to have T(sub k) approx 80-850 eV, V(sub b)/V(sub sw) approx 1.3-2.4, T(sub perpendicular,b)/T(sub paralell,b) approx 1-8, and n(sub b)/n(sub o) approx 0.2-11%. Saturation amplitudes for ion/ion resonant and non-resonant instabilities are too small to explain the observed SLAMS amplitudes. We show two examples where groups of SLAMS can act like a local quasi-perpendicular shock reflecting ions to produce the FABs, a scenario distinct from the more-common production at the quasi-perpendicular bow shock. The SLAMS exhibit a foot-like magnetic enhancement with a leading magnetosonic whistler train, consistent with previous observations. Strong ion and electron heating are observed within the series of shocklets and SLAMS with temperatures increasing by factors approx > 5 and approx >3, respectively. Both the core and halo electron components show strong perpendicular heating inside the feature.

  6. A SLAM based on auxiliary marginalised particle filter and differential evolution

    NASA Astrophysics Data System (ADS)

    Havangi, R.; Nekoui, M. A.; Teshnehlab, M.; Taghirad, H. D.

    2014-09-01

    FastSLAM is a framework for simultaneous localisation and mapping (SLAM) using a Rao-Blackwellised particle filter. In FastSLAM, particle filter is used for the robot pose (position and orientation) estimation, and parametric filter (i.e. EKF and UKF) is used for the feature location's estimation. However, in the long term, FastSLAM is an inconsistent algorithm. In this paper, a new approach to SLAM based on hybrid auxiliary marginalised particle filter and differential evolution (DE) is proposed. In the proposed algorithm, the robot pose is estimated based on auxiliary marginal particle filter that operates directly on the marginal distribution, and hence avoids performing importance sampling on a space of growing dimension. In addition, static map is considered as a set of parameters that are learned using DE. Compared to other algorithms, the proposed algorithm can improve consistency for longer time periods and also, improve the estimation accuracy. Simulations and experimental results indicate that the proposed algorithm is effective.

  7. On-board SLAM for indoor UAV using a laser range finder

    NASA Astrophysics Data System (ADS)

    Alpen, M.; Willrodt, C.; Frick, K.; Horn, J.

    2010-04-01

    Here we present a real-time algorithm for on-board SLAM (simultaneous localization and mapping) of a quadrotor using a laser range finder. Based on successfully implemented techniques for ground robots, we developed an algorithm that merges a new scan into the global map without any iteration. This causes some inaccuracy of the global map which leads to an error propagation during the robot's mission. Therefore an optimization algorithm reducing this inaccuracy is essential. Within this optimization lines with the same orientation and an overlapping in one of the two possible coordinates of a 2D-plane are merged if their distance is below a certain threshold value. Due to reduction of the required computing power for SLAM calculation by using orthogonal SLAM a real time SLAM running on a microcontroller becomes possible. Because of the small weight and the low electric power consumption, this controller can be mounted on an industrial quadrotor. Therefore acting autonomously in an unknown indoor environment becomes possible. In this paper we also show the validation of the presented SLAM algorithm. The first step of validation is an offline implementation in Matlab and the second step is the online validation of our algorithm on the industrial quadrotor AR100B of the AirRobot Company.

  8. Simple but novel test method for quantitatively comparing robot mapping algorithms using SLAM and dead reckoning

    NASA Astrophysics Data System (ADS)

    Davey, Neil S.; Godil, Haris

    2013-05-01

    This article presents a comparative study between a well-known SLAM (Simultaneous Localization and Mapping) algorithm, called Gmapping, and a standard Dead-Reckoning algorithm; the study is based on experimental results of both approaches by using a commercial skid-based turning robot, P3DX. Five main base-case scenarios are conducted to evaluate and test the effectiveness of both algorithms. The results show that SLAM outperformed the Dead Reckoning in terms of map-making accuracy in all scenarios but one, since SLAM did not work well in a rapidly changing environment. Although the main conclusion about the excellence of SLAM is not surprising, the presented test method is valuable to professionals working in this area of mobile robots, as it is highly practical, and provides solid and valuable results. The novelty of this study lies in its simplicity. The simple but novel test method for quantitatively comparing robot mapping algorithms using SLAM and Dead Reckoning and some applications using autonomous robots are being patented by the authors in U.S. Patent Application Nos. 13/400,726 and 13/584,862.

  9. Evaluating the structural identifiability of the parameters of the EBPR sub-model in ASM2d by the differential algebra method.

    PubMed

    Zhang, Tian; Zhang, Daijun; Li, Zhenliang; Cai, Qing

    2010-05-01

    The calibration of ASMs is a prerequisite for their application to simulation of a wastewater treatment plant. This work should be made based on the evaluation of structural identifiability of model parameters. An EBPR sub-model including denitrification phosphorus removal has been incorporated in ASM2d. Yet no report is presented on the structural identifiability of the parameters in the EBPR sub-model. In this paper, the differential algebra approach was used to address this issue. The results showed that the structural identifiability of parameters in the EBPR sub-model could be improved by increasing the measured variables. The reduction factor eta(NO)(3) was identifiable when combined data of aerobic process and anoxic process were assumed. For K(PP), X(PAO) and q(PHA) of the anaerobic process to be uniquely identifiable, one of them is needed to be determined by other ways. Likewise, if prior information on one of the parameters, K(PHA), X(PAO) and q(PP) of the aerobic process, is known, all the parameters are identifiable. The above results could be of interest to the parameter estimation of the EBPR sub-model. The algorithm proposed in the paper is also suitable for other sub-models of ASMs.

  10. Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

    ERIC Educational Resources Information Center

    Wasserman, Nicholas H.

    2016-01-01

    This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…

  11. Adaptive Algebraic Multigrid Methods

    SciTech Connect

    Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S; Ruge, J

    2004-04-09

    Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.

  12. Ultra wide-band localization and SLAM: a comparative study for mobile robot navigation.

    PubMed

    Segura, Marcelo J; Auat Cheein, Fernando A; Toibero, Juan M; Mut, Vicente; Carelli, Ricardo

    2011-01-01

    In this work, a comparative study between an Ultra Wide-Band (UWB) localization system and a Simultaneous Localization and Mapping (SLAM) algorithm is presented. Due to its high bandwidth and short pulses length, UWB potentially allows great accuracy in range measurements based on Time of Arrival (TOA) estimation. SLAM algorithms recursively estimates the map of an environment and the pose (position and orientation) of a mobile robot within that environment. The comparative study presented here involves the performance analysis of implementing in parallel an UWB localization based system and a SLAM algorithm on a mobile robot navigating within an environment. Real time results as well as error analysis are also shown in this work.

  13. A fast map merging algorithm in the field of multirobot SLAM.

    PubMed

    Liu, Yanli; Fan, Xiaoping; Zhang, Heng

    2013-01-01

    In recent years, the research on single-robot simultaneous localization and mapping (SLAM) has made a great success. However, multirobot SLAM faces many challenging problems, including unknown robot poses, unshared map, and unstable communication. In this paper, a map merging algorithm based on virtual robot motion is proposed for multi-robot SLAM. The thinning algorithm is used to construct the skeleton of the grid map's empty area, and a mobile robot is simulated in one map. The simulated data is used as information sources in the other map to do partial map Monte Carlo localization; if localization succeeds, the relative pose hypotheses between the two maps can be computed easily. We verify these hypotheses using the rendezvous technique and use them as initial values to optimize the estimation by a heuristic random search algorithm.

  14. Ultra wide-band localization and SLAM: a comparative study for mobile robot navigation.

    PubMed

    Segura, Marcelo J; Auat Cheein, Fernando A; Toibero, Juan M; Mut, Vicente; Carelli, Ricardo

    2011-01-01

    In this work, a comparative study between an Ultra Wide-Band (UWB) localization system and a Simultaneous Localization and Mapping (SLAM) algorithm is presented. Due to its high bandwidth and short pulses length, UWB potentially allows great accuracy in range measurements based on Time of Arrival (TOA) estimation. SLAM algorithms recursively estimates the map of an environment and the pose (position and orientation) of a mobile robot within that environment. The comparative study presented here involves the performance analysis of implementing in parallel an UWB localization based system and a SLAM algorithm on a mobile robot navigating within an environment. Real time results as well as error analysis are also shown in this work. PMID:22319397

  15. A fast map merging algorithm in the field of multirobot SLAM.

    PubMed

    Liu, Yanli; Fan, Xiaoping; Zhang, Heng

    2013-01-01

    In recent years, the research on single-robot simultaneous localization and mapping (SLAM) has made a great success. However, multirobot SLAM faces many challenging problems, including unknown robot poses, unshared map, and unstable communication. In this paper, a map merging algorithm based on virtual robot motion is proposed for multi-robot SLAM. The thinning algorithm is used to construct the skeleton of the grid map's empty area, and a mobile robot is simulated in one map. The simulated data is used as information sources in the other map to do partial map Monte Carlo localization; if localization succeeds, the relative pose hypotheses between the two maps can be computed easily. We verify these hypotheses using the rendezvous technique and use them as initial values to optimize the estimation by a heuristic random search algorithm. PMID:24302855

  16. Ultra Wide-Band Localization and SLAM: A Comparative Study for Mobile Robot Navigation

    PubMed Central

    Segura, Marcelo J.; Auat Cheein, Fernando A.; Toibero, Juan M.; Mut, Vicente; Carelli, Ricardo

    2011-01-01

    In this work, a comparative study between an Ultra Wide-Band (UWB) localization system and a Simultaneous Localization and Mapping (SLAM) algorithm is presented. Due to its high bandwidth and short pulses length, UWB potentially allows great accuracy in range measurements based on Time of Arrival (TOA) estimation. SLAM algorithms recursively estimates the map of an environment and the pose (position and orientation) of a mobile robot within that environment. The comparative study presented here involves the performance analysis of implementing in parallel an UWB localization based system and a SLAM algorithm on a mobile robot navigating within an environment. Real time results as well as error analysis are also shown in this work. PMID:22319397

  17. Peer & Parent Encouragement of Early Algebra Enrollment & Mathematics Achievement

    ERIC Educational Resources Information Center

    Filer, Kimberly L.; Chang, Mido

    2008-01-01

    Using data from the National Education Longitudinal Study of 1988 (NELS:88), path analytic procedures were performed to test a model of the effects of parent and peer encouragement to take algebra on the mathematics achievement of eighth grade students. The effects of socio-economic status (SES) on middle school algebra course-taking and…

  18. Computer-Intensive Algebra and Students' Conceptual Knowledge of Functions.

    ERIC Educational Resources Information Center

    O'Callaghan, Brian R.

    1998-01-01

    Describes a research project that examined the effects of the Computer-Intensive Algebra (CIA) and traditional algebra curricula on students' (N=802) understanding of the function concept. Results indicate that CIA students achieved a better understanding of functions and were better at the components of modeling, interpreting, and translating.…

  19. Computer Program For Linear Algebra

    NASA Technical Reports Server (NTRS)

    Krogh, F. T.; Hanson, R. J.

    1987-01-01

    Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.

  20. Algebra for Gifted Third Graders.

    ERIC Educational Resources Information Center

    Borenson, Henry

    1987-01-01

    Elementary school children who are exposed to a concrete, hands-on experience in algebraic linear equations will more readily develop a positive mind-set and expectation for success in later formal, algebraic studies. (CB)

  1. Pseudo Algebraically Closed Extensions

    NASA Astrophysics Data System (ADS)

    Bary-Soroker, Lior

    2009-07-01

    This PhD deals with the notion of pseudo algebraically closed (PAC) extensions of fields. It develops a group-theoretic machinery, based on a generalization of embedding problems, to study these extensions. Perhaps the main result is that although there are many PAC extensions, the Galois closure of a proper PAC extension is separably closed. The dissertation also contains the following subjects. The group theoretical counterpart of pseudo algebraically closed extensions, the so-called projective pairs. Applications to seemingly unrelated subjects, e.g., an analog of Dirichlet's theorem about primes in arithmetic progression for polynomial rings in one variable over infinite fields.

  2. Integrating Map Algebra and Statistical Modeling for Spatio-Temporal Analysis of Monthly Mean Daily Incident Photosynthetically Active Radiation (PAR) over a Complex Terrain

    PubMed Central

    Evrendilek, Fatih

    2007-01-01

    This study aims at quantifying spatio-temporal dynamics of monthly mean daily incident photosynthetically active radiation (PAR) over a vast and complex terrain such as Turkey. The spatial interpolation method of universal kriging, and the combination of multiple linear regression (MLR) models and map algebra techniques were implemented to generate surface maps of PAR with a grid resolution of 500 × 500 m as a function of five geographical and 14 climatic variables. Performance of the geostatistical and MLR models was compared using mean prediction error (MPE), root-mean-square prediction error (RMSPE), average standard prediction error (ASE), mean standardized prediction error (MSPE), root-mean-square standardized prediction error (RMSSPE), and adjusted coefficient of determination (R2adj.). The best-fit MLR- and universal kriging-generated models of monthly mean daily PAR were validated against an independent 37-year observed dataset of 35 climate stations derived from 160 stations across Turkey by the Jackknifing method. The spatial variability patterns of monthly mean daily incident PAR were more accurately reflected in the surface maps created by the MLR-based models than in those created by the universal kriging method, in particular, for spring (May) and autumn (November). The MLR-based spatial interpolation algorithms of PAR described in this study indicated the significance of the multifactor approach to understanding and mapping spatio-temporal dynamics of PAR for a complex terrain over meso-scales.

  3. A new design for SLAM front-end based on recursive SOM

    NASA Astrophysics Data System (ADS)

    Yang, Xuesi; Xia, Shengping

    2015-12-01

    Aiming at the graph optimization-based monocular SLAM, a novel design for the front-end in single camera SLAM is proposed, based on the recursive SOM. Pixel intensities are directly used to achieve image registration and motion estimation, which can save time compared with the current appearance-based frameworks, usually including feature extraction and matching. Once a key-frame is identified, a recursive SOM is used to actualize loop-closure detecting, resulting a more precise location. The experiment on a public dataset validates our method on a computer with a quicker and effective result.

  4. Resting lymphocyte transduction with measles virus glycoprotein pseudotyped lentiviral vectors relies on CD46 and SLAM

    SciTech Connect

    Zhou Qi; Schneider, Irene C.; Gallet, Manuela; Kneissl, Sabrina; Buchholz, Christian J.

    2011-05-10

    The measles virus (MV) glycoproteins hemagglutinin (H) and fusion (F) were recently shown to mediate transduction of resting lymphocytes by lentiviral vectors. MV vaccine strains use CD46 or signaling lymphocyte activation molecule (SLAM) as receptor for cell entry. A panel of H protein mutants derived from vaccine strain or wild-type MVs that lost or gained CD46 or SLAM receptor usage were investigated for their ability to mediate gene transfer into unstimulated T lymphocytes. The results demonstrate that CD46 is sufficient for efficient vector particle association with unstimulated lymphocytes. For stable gene transfer into these cells, however, both MV receptors were found to be essential.

  5. What can be learnt from analysing insect orientation flights using probabilistic SLAM?

    PubMed

    Baddeley, Bartholomew; Philippides, Andrew; Graham, Paul; de Ibarra, Natalie Hempel; Collett, Thomas; Husbands, Phillip

    2009-09-01

    In this paper, we provide an analysis of orientation flights in bumblebees, employing a novel technique based on simultaneous localisation and mapping (SLAM) a probabilistic approach from autonomous robotics. We use SLAM to determine what bumblebees might learn about the locations of objects in the world through the arcing behaviours that are typical of these flights. Our results indicate that while the bees are clearly influenced by the presence of a conspicuous landmark, there is little evidence that they structure their flights to specifically learn about the position of the landmark. PMID:19639335

  6. Application of simultaneous localization and mapping (SLAM) in autonomous exploration of urban environments

    NASA Astrophysics Data System (ADS)

    Cooke, Andrew R.; Greenway, Phil; le Maistre, Mike; Manley, Richard; Mullin, David; Nicholson, David; Swinnerton, James; Valachis, Dimitris; Wright, Andy

    2003-08-01

    This paper describes an autonomous navigation system capable of exploring an unknown environment, as implemented by the Advanced Technology Centre of BAE SYSTEMS (ATC). An overview of the enabling technology of the autonomous system, simultaneous localization and mapping (SLAM), is given before describing in detail the utility functions used to perform the strategic decision making required for autonomous exploration. Relevant studies, performed in simulation, of the major issues involved in multi-platform SLAM are also described. Initial results and conclusions are given at the end of the paper. All experiments are conducted on the Pioneer all terrain mobile robots using common off the shelf sensing devices.

  7. What can be learnt from analysing insect orientation flights using probabilistic SLAM?

    PubMed

    Baddeley, Bartholomew; Philippides, Andrew; Graham, Paul; de Ibarra, Natalie Hempel; Collett, Thomas; Husbands, Phillip

    2009-09-01

    In this paper, we provide an analysis of orientation flights in bumblebees, employing a novel technique based on simultaneous localisation and mapping (SLAM) a probabilistic approach from autonomous robotics. We use SLAM to determine what bumblebees might learn about the locations of objects in the world through the arcing behaviours that are typical of these flights. Our results indicate that while the bees are clearly influenced by the presence of a conspicuous landmark, there is little evidence that they structure their flights to specifically learn about the position of the landmark.

  8. Assessing Elementary Algebra with STACK

    ERIC Educational Resources Information Center

    Sangwin, Christopher J.

    2007-01-01

    This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…

  9. Formal Formality of the Hypercommutative Algebras of Low Dimensional Calabi-Yau Varieties

    NASA Astrophysics Data System (ADS)

    Drummond-Cole, Gabriel C.

    2014-04-01

    There is a homotopy hypercommutative algebra structure on the cohomology of a Calabi-Yau variety. The truncation of this homotopy hypercommutative algebra to a strict hypercommutative algebra is well-known as a mathematical realization of the genus zero B-model. It is shown that this truncation loses no information for some cases, including all Calabi-Yau 3-folds.

  10. College Algebra II.

    ERIC Educational Resources Information Center

    Benjamin, Carl; And Others

    Presented are student performance objectives, a student progress chart, and assignment sheets with objective and diagnostic measures for the stated performance objectives in College Algebra II. Topics covered include: differencing and complements; real numbers; factoring; fractions; linear equations; exponents and radicals; complex numbers,…

  11. Computer Algebra versus Manipulation

    ERIC Educational Resources Information Center

    Zand, Hossein; Crowe, David

    2004-01-01

    In the UK there is increasing concern about the lack of skill in algebraic manipulation that is evident in students entering mathematics courses at university level. In this note we discuss how the computer can be used to ameliorate some of the problems. We take as an example the calculations needed in three dimensional vector analysis in polar…

  12. Algebraic Artful Aids.

    ERIC Educational Resources Information Center

    Glick, David

    1995-01-01

    Presents a technique that helps students concentrate more on the science and less on the mechanics of algebra while dealing with introductory physics formulas. Allows the teacher to do complex problems at a lower level and not be too concerned about the mathematical abilities of the students. (JRH)

  13. Computers in Abstract Algebra

    ERIC Educational Resources Information Center

    Nwabueze, Kenneth K.

    2004-01-01

    The current emphasis on flexible modes of mathematics delivery involving new information and communication technology (ICT) at the university level is perhaps a reaction to the recent change in the objectives of education. Abstract algebra seems to be one area of mathematics virtually crying out for computer instructional support because of the…

  14. On vertex algebra representations of the Schrödinger-Virasoro Lie algebra

    NASA Astrophysics Data System (ADS)

    Unterberger, Jérémie

    2009-12-01

    The Schrödinger-Virasoro Lie algebra sv is an extension of the Virasoro Lie algebra by a nilpotent Lie algebra formed with a bosonic current of weight 3/2 and a bosonic current of weight 1. It is also a natural infinite-dimensional extension of the Schrödinger Lie algebra, which — leaving aside the invariance under time-translation — has been proved to be a symmetry algebra for many statistical physics models undergoing a dynamics with dynamical exponent z=2. We define in this article general Schrödinger-Virasoro primary fields by analogy with conformal field theory, characterized by a 'spin' index and a (non-relativistic) mass, and construct vertex algebra representations of sv out of a charged symplectic boson and a free boson and its associated vertex operators. We also compute two- and three-point functions of still conjectural massive fields that are defined by an analytic continuation with respect to a formal parameter.

  15. Optical systolic solutions of linear algebraic equations

    NASA Technical Reports Server (NTRS)

    Neuman, C. P.; Casasent, D.

    1984-01-01

    The philosophy and data encoding possible in systolic array optical processor (SAOP) were reviewed. The multitude of linear algebraic operations achievable on this architecture is examined. These operations include such linear algebraic algorithms as: matrix-decomposition, direct and indirect solutions, implicit and explicit methods for partial differential equations, eigenvalue and eigenvector calculations, and singular value decomposition. This architecture can be utilized to realize general techniques for solving matrix linear and nonlinear algebraic equations, least mean square error solutions, FIR filters, and nested-loop algorithms for control engineering applications. The data flow and pipelining of operations, design of parallel algorithms and flexible architectures, application of these architectures to computationally intensive physical problems, error source modeling of optical processors, and matching of the computational needs of practical engineering problems to the capabilities of optical processors are emphasized.

  16. An algebra of discrete event processes

    NASA Technical Reports Server (NTRS)

    Heymann, Michael; Meyer, George

    1991-01-01

    This report deals with an algebraic framework for modeling and control of discrete event processes. The report consists of two parts. The first part is introductory, and consists of a tutorial survey of the theory of concurrency in the spirit of Hoare's CSP, and an examination of the suitability of such an algebraic framework for dealing with various aspects of discrete event control. To this end a new concurrency operator is introduced and it is shown how the resulting framework can be applied. It is further shown that a suitable theory that deals with the new concurrency operator must be developed. In the second part of the report the formal algebra of discrete event control is developed. At the present time the second part of the report is still an incomplete and occasionally tentative working paper.

  17. Algebraic surface design and finite element meshes

    NASA Technical Reports Server (NTRS)

    Bajaj, Chandrajit L.

    1992-01-01

    Some of the techniques are summarized which are used in constructing C sup 0 and C sup 1 continuous meshes of low degree, implicitly defined, algebraic surface patches in three dimensional space. These meshes of low degree algebraic surface patches are used to construct accurate computer models of physical objects. These meshes are also used in the finite element simulation of physical phenomena (e.g., heat dissipation, stress/strain distributions, fluid flow characteristics) required in the computer prototyping of both the manufacturability and functionality of the geometric design.

  18. Algebraic connectivity and graph robustness.

    SciTech Connect

    Feddema, John Todd; Byrne, Raymond Harry; Abdallah, Chaouki T.

    2009-07-01

    Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.

  19. Using Technology to Balance Algebraic Explorations

    ERIC Educational Resources Information Center

    Kurz, Terri L.

    2013-01-01

    In 2000, the "National Council of Teachers of Mathematics" recommended that Algebra Standards, "instructional programs from prekindergarten through grade 12 should enable all students to use mathematical models to represent and understand quantitative relationships." In this article, the authors suggest the "Balance"…

  20. Noise limitations in optical linear algebra processors.

    PubMed

    Batsell, S G; Jong, T L; Walkup, J F; Krile, T F

    1990-05-10

    A general statistical noise model is presented for optical linear algebra processors. A statistical analysis which includes device noise, the multiplication process, and the addition operation is undertaken. We focus on those processes which are architecturally independent. Finally, experimental results which verify the analytical predictions are also presented.

  1. A Microcomputer Lab for Algebra & Calculus.

    ERIC Educational Resources Information Center

    Avery, Chris; And Others

    An overview is provided of De Anza College's use of computerized instruction in its mathematics courses. After reviewing the ways in which computer technology is changing math instruction, the paper looks at the use of computers in several course sequences. The instructional model for the algebra sequence is based on a large group format of…

  2. A Linear Algebra Measure of Cluster Quality.

    ERIC Educational Resources Information Center

    Mather, Laura A.

    2000-01-01

    Discussion of models for information retrieval focuses on an application of linear algebra to text clustering, namely, a metric for measuring cluster quality based on the theory that cluster quality is proportional to the number of terms that are disjoint across the clusters. Explains term-document matrices and clustering algorithms. (Author/LRW)

  3. The geometric semantics of algebraic quantum mechanics.

    PubMed

    Cruz Morales, John Alexander; Zilber, Boris

    2015-08-01

    In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.

  4. Digital Maps, Matrices and Computer Algebra

    ERIC Educational Resources Information Center

    Knight, D. G.

    2005-01-01

    The way in which computer algebra systems, such as Maple, have made the study of complex problems accessible to undergraduate mathematicians with modest computational skills is illustrated by some large matrix calculations, which arise from representing the Earth's surface by digital elevation models. Such problems are often considered to lie in…

  5. A Visual Approach to Algebra Concepts.

    ERIC Educational Resources Information Center

    Morelli, Lynn

    1992-01-01

    Presents activities to visually explore the algebraic concepts of variable, constant, the distributive property, and combining like terms. Presents four transparencies that use visual models to understand exercises in students perform the same mental calculations on a number of their choice and obtain the same result. (MDH)

  6. AUV SLAM and Experiments Using a Mechanical Scanning Forward-Looking Sonar

    PubMed Central

    He, Bo; Liang, Yan; Feng, Xiao; Nian, Rui; Yan, Tianhong; Li, Minghui; Zhang, Shujing

    2012-01-01

    Navigation technology is one of the most important challenges in the applications of autonomous underwater vehicles (AUVs) which navigate in the complex undersea environment. The ability of localizing a robot and accurately mapping its surroundings simultaneously, namely the simultaneous localization and mapping (SLAM) problem, is a key prerequisite of truly autonomous robots. In this paper, a modified-FastSLAM algorithm is proposed and used in the navigation for our C-Ranger research platform, an open-frame AUV. A mechanical scanning imaging sonar is chosen as the active sensor for the AUV. The modified-FastSLAM implements the update relying on the on-board sensors of C-Ranger. On the other hand, the algorithm employs the data association which combines the single particle maximum likelihood method with modified negative evidence method, and uses the rank-based resampling to overcome the particle depletion problem. In order to verify the feasibility of the proposed methods, both simulation experiments and sea trials for C-Ranger are conducted. The experimental results show the modified-FastSLAM employed for the navigation of the C-Ranger AUV is much more effective and accurate compared with the traditional methods. PMID:23012549

  7. AUV SLAM and experiments using a mechanical scanning forward-looking sonar.

    PubMed

    He, Bo; Liang, Yan; Feng, Xiao; Nian, Rui; Yan, Tianhong; Li, Minghui; Zhang, Shujing

    2012-01-01

    Navigation technology is one of the most important challenges in the applications of autonomous underwater vehicles (AUVs) which navigate in the complex undersea environment. The ability of localizing a robot and accurately mapping its surroundings simultaneously, namely the simultaneous localization and mapping (SLAM) problem, is a key prerequisite of truly autonomous robots. In this paper, a modified-FastSLAM algorithm is proposed and used in the navigation for our C-Ranger research platform, an open-frame AUV. A mechanical scanning imaging sonar is chosen as the active sensor for the AUV. The modified-FastSLAM implements the update relying on the on-board sensors of C-Ranger. On the other hand, the algorithm employs the data association which combines the single particle maximum likelihood method with modified negative evidence method, and uses the rank-based resampling to overcome the particle depletion problem. In order to verify the feasibility of the proposed methods, both simulation experiments and sea trials for C-Ranger are conducted. The experimental results show the modified-FastSLAM employed for the navigation of the C-Ranger AUV is much more effective and accurate compared with the traditional methods. PMID:23012549

  8. AUV SLAM and experiments using a mechanical scanning forward-looking sonar.

    PubMed

    He, Bo; Liang, Yan; Feng, Xiao; Nian, Rui; Yan, Tianhong; Li, Minghui; Zhang, Shujing

    2012-01-01

    Navigation technology is one of the most important challenges in the applications of autonomous underwater vehicles (AUVs) which navigate in the complex undersea environment. The ability of localizing a robot and accurately mapping its surroundings simultaneously, namely the simultaneous localization and mapping (SLAM) problem, is a key prerequisite of truly autonomous robots. In this paper, a modified-FastSLAM algorithm is proposed and used in the navigation for our C-Ranger research platform, an open-frame AUV. A mechanical scanning imaging sonar is chosen as the active sensor for the AUV. The modified-FastSLAM implements the update relying on the on-board sensors of C-Ranger. On the other hand, the algorithm employs the data association which combines the single particle maximum likelihood method with modified negative evidence method, and uses the rank-based resampling to overcome the particle depletion problem. In order to verify the feasibility of the proposed methods, both simulation experiments and sea trials for C-Ranger are conducted. The experimental results show the modified-FastSLAM employed for the navigation of the C-Ranger AUV is much more effective and accurate compared with the traditional methods.

  9. Bridging Philosophy of Technology and Neurobiological Research: Interpreting Images from the "Slam Freezer"

    ERIC Educational Resources Information Center

    Rosenberger, Robert

    2005-01-01

    The swiftly growing field of neurobiological research utilizes highly advanced technologies (e.g., magnetic resonance imaging, electron microscopy) to mediate between investigators and the brains they investigate. Here, the author analyzes a device called the "slam freezer" that quick-freezes neurons to be studied under the microscope. Employing…

  10. Integrable generalized spin ladder models based on the SU(1|3) and SU(3|1) algebras

    NASA Astrophysics Data System (ADS)

    Tonel, Arlei Prestes; Foerster, Angela; Hibberd, Katrina; Links, Jon

    2003-12-01

    We present two integrable spin ladder models which possess a general free parameter besides the rung coupling J. The models are exactly solvable by means of the Bethe ansatz method and we present the Bethe ansatz equations. We analyze the elementary excitations of the models which reveal the existence of a gap for both models that depends on the free parameter.

  11. Exact duality of the dissipative Hofstadter model on a triangular lattice: T-duality and noncommutative algebra

    NASA Astrophysics Data System (ADS)

    Lee, Taejin

    2016-09-01

    We study the dissipative Hofstadter model on a triangular lattice, making use of the O(2, 2; R) T-dual transformation of string theory. The O(2, 2; R) dual transformation transcribes the model in a commutative basis into the model in a noncommutative basis. In the zero-temperature limit, the model exhibits an exact duality, which identifies equivalent points on the two-dimensional parameter space of the model. The exact duality also defines magic circles on the parameter space, where the model can be mapped onto the boundary sine-Gordon on a triangular lattice. The model describes the junction of three quantum wires in a uniform magnetic field background. An explicit expression of the equivalence relation, which identifies the points on the two-dimensional parameter space of the model by the exact duality, is obtained. It may help us to understand the structure of the phase diagram of the model.

  12. The Algebra Artist

    ERIC Educational Resources Information Center

    Beigie, Darin

    2014-01-01

    Most people who are attracted to STEM-related fields are drawn not by a desire to take mathematics tests but to create things. The opportunity to create an algebra drawing gives students a sense of ownership and adventure that taps into the same sort of energy that leads a young person to get lost in reading a good book, building with Legos®,…

  13. Algebra of Majorana doubling.

    PubMed

    Lee, Jaehoon; Wilczek, Frank

    2013-11-27

    Motivated by the problem of identifying Majorana mode operators at junctions, we analyze a basic algebraic structure leading to a doubled spectrum. For general (nonlinear) interactions the emergent mode creation operator is highly nonlinear in the original effective mode operators, and therefore also in the underlying electron creation and destruction operators. This phenomenon could open up new possibilities for controlled dynamical manipulation of the modes. We briefly compare and contrast related issues in the Pfaffian quantum Hall state.

  14. Algebraic Multigrid Benchmark

    SciTech Connect

    2013-05-06

    AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumps and an anisotropy in one part.

  15. Symmetric linear systems - An application of algebraic systems theory

    NASA Technical Reports Server (NTRS)

    Hazewinkel, M.; Martin, C.

    1983-01-01

    Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.

  16. A quantum affine algebra for the deformed Hubbard chain

    NASA Astrophysics Data System (ADS)

    Beisert, Niklas; Galleas, Wellington; Matsumoto, Takuya

    2012-09-01

    The integrable structure of the one-dimensional Hubbard model is based on Shastry's R-matrix and the Yangian of a centrally extended \\mathfrak {sl}(2|2) superalgebra. Alcaraz and Bariev have shown that the model admits an integrable deformation whose R-matrix has recently been found. This R-matrix is of trigonometric type and here we derive its underlying exceptional quantum affine algebra. We also show how the algebra reduces to the above-mentioned Yangian and to the conventional quantum affine \\mathfrak {sl}(2|2) algebra in two special limits.

  17. On the cohomology of Leibniz conformal algebras

    NASA Astrophysics Data System (ADS)

    Zhang, Jiao

    2015-04-01

    We construct a new cohomology complex of Leibniz conformal algebras with coefficients in a representation instead of a module. The low-dimensional cohomology groups of this complex are computed. Meanwhile, we construct a Leibniz algebra from a Leibniz conformal algebra and prove that the category of Leibniz conformal algebras is equivalent to the category of equivalence classes of formal distribution Leibniz algebras.

  18. Assessing Algebraic Solving Ability: A Theoretical Framework

    ERIC Educational Resources Information Center

    Lian, Lim Hooi; Yew, Wun Thiam

    2012-01-01

    Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…

  19. Duncan F. Gregory, William Walton and the development of British algebra: 'algebraical geometry', 'geometrical algebra', abstraction.

    PubMed

    Verburgt, Lukas M

    2016-01-01

    This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s. PMID:26806075

  20. Duncan F. Gregory, William Walton and the development of British algebra: 'algebraical geometry', 'geometrical algebra', abstraction.

    PubMed

    Verburgt, Lukas M

    2016-01-01

    This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s.

  1. How Structure Sense for Algebraic Expressions or Equations Is Related to Structure Sense for Abstract Algebra

    ERIC Educational Resources Information Center

    Novotna, Jarmila; Hoch, Maureen

    2008-01-01

    Many students have difficulties with basic algebraic concepts at high school and at university. In this paper two levels of algebraic structure sense are defined: for high school algebra and for university algebra. We suggest that high school algebra structure sense components are sub-components of some university algebra structure sense…

  2. Heisenberg Groups and their Automorphisms over Algebras with Central Involution

    NASA Astrophysics Data System (ADS)

    Johnson, Robert W.

    2015-08-01

    Heisenberg groups over algebras with central involution and their automorphism groups are constructed. The complex quaternion group algebra over a prime field is used as an example. Its subspaces provide finite models for each of the real and complex quadratic spaces with dimension 4 or less. A model for the representations of these Heisenberg groups and automorphism groups is constructed. A pseudo-differential operator enables a parallel treatment of spaces defined over finite and real fields.

  3. 2-Local derivations on matrix algebras over semi-prime Banach algebras and on AW*-algebras

    NASA Astrophysics Data System (ADS)

    Ayupov, Shavkat; Kudaybergenov, Karimbergen

    2016-03-01

    The paper is devoted to 2-local derivations on matrix algebras over unital semi-prime Banach algebras. For a unital semi-prime Banach algebra A with the inner derivation property we prove that any 2-local derivation on the algebra M 2n (A), n ≥ 2, is a derivation. We apply this result to AW*-algebras and show that any 2-local derivation on an arbitrary AW*-algebra is a derivation.

  4. Slam is an outer membrane protein that is required for the surface display of lipidated virulence factors in Neisseria.

    PubMed

    Hooda, Yogesh; Lai, Christine Chieh-Lin; Judd, Andrew; Buckwalter, Carolyn M; Shin, Hyejin Esther; Gray-Owen, Scott D; Moraes, Trevor F

    2016-01-01

    Lipoproteins decorate the surface of many Gram-negative bacterial pathogens, playing essential roles in immune evasion and nutrient acquisition. In Neisseria spp., the causative agents of gonorrhoea and meningococcal meningitis, surface lipoproteins (SLPs) are required for virulence and have been extensively studied as prime candidates for vaccine development. However, the machinery and mechanism that allow for the surface display of SLPs are not known. Here, we describe a transposon (Tn5)-based search for the proteins required to deliver SLPs to the surface of Neisseria meningitidis, revealing a family of proteins that we have named the surface lipoprotein assembly modulator (Slam). N. meningitidis contains two Slam proteins, each exhibiting distinct substrate preferences. The Slam proteins are sufficient to reconstitute SLP transport in laboratory strains of Escherichia coli, which are otherwise unable to efficiently display these lipoproteins on their cell surface. Immunoprecipitation and domain probing experiments suggest that the SLP, TbpB, interacts with Slam during the transit process; furthermore, the membrane domain of Slam is sufficient for selectivity and proper surface display of SLPs. Rather than being a Neisseria-specific factor, our bioinformatic analysis shows that Slam can be found throughout proteobacterial genomes, indicating a conserved but until now unrecognized virulence mechanism. PMID:27572441

  5. Plethystic algebras and vector symmetric functions.

    PubMed Central

    Rota, G C; Stein, J A

    1994-01-01

    An isomorphism is established between the plethystic Hopf algebra Pleth(Super[L]) and the algebra of vector symmetric functions. The Hall inner product of symmetric function theory is extended to the Hopf algebra Pleth(Super[L]). PMID:11607504

  6. Algebra and Algebraic Thinking in School Math: 70th YB

    ERIC Educational Resources Information Center

    National Council of Teachers of Mathematics, 2008

    2008-01-01

    Algebra is no longer just for college-bound students. After a widespread push by the National Council of Teachers of Mathematics (NCTM) and teachers across the country, algebra is now a required part of most curricula. However, students' standardized test scores are not at the level they should be. NCTM's seventieth yearbook takes a look at the…

  7. Abstract Algebra to Secondary School Algebra: Building Bridges

    ERIC Educational Resources Information Center

    Christy, Donna; Sparks, Rebecca

    2015-01-01

    The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…

  8. Handheld Computer Algebra Systems in the Pre-Algebra Classroom

    ERIC Educational Resources Information Center

    Gantz, Linda Ann Galofaro

    2010-01-01

    This mixed method analysis sought to investigate several aspects of student learning in pre-algebra through the use of computer algebra systems (CAS) as opposed to non-CAS learning. This research was broken into two main parts, one which compared results from both the experimental group (instruction using CAS, N = 18) and the control group…

  9. Deformable target tracking method based on Lie algebra

    NASA Astrophysics Data System (ADS)

    Liu, Yunpeng; Shi, Zelin; Li, Guangwei

    2007-11-01

    Conventional approaches to object tracking use area correlation, but they are difficult to solve the problem of deformation of object region during tracking. A novel target tracking method based on Lie algebra is presented. We use Gabor feature as target token, model deformation using affine Lie group, and optimize parameters directly on manifold, which can be solved by exponential mapping between Lie Group and its Lie algebra. We analyze the essence of our method and test the algorithm using real image sequences. The experimental results demonstrate that Lie algebra method outperforms other traditional algorithms in efficiency, stabilization and accuracy.

  10. Statecharts Via Process Algebra

    NASA Technical Reports Server (NTRS)

    Luttgen, Gerald; vonderBeeck, Michael; Cleaveland, Rance

    1999-01-01

    Statecharts is a visual language for specifying the behavior of reactive systems. The Language extends finite-state machines with concepts of hierarchy, concurrency, and priority. Despite its popularity as a design notation for embedded system, precisely defining its semantics has proved extremely challenging. In this paper, a simple process algebra, called Statecharts Process Language (SPL), is presented, which is expressive enough for encoding Statecharts in a structure-preserving and semantic preserving manner. It is establish that the behavioral relation bisimulation, when applied to SPL, preserves Statecharts semantics

  11. Algebraic Multigrid Benchmark

    2013-05-06

    AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumpsmore » and an anisotropy in one part.« less

  12. Linear Algebra and Image Processing

    ERIC Educational Resources Information Center

    Allali, Mohamed

    2010-01-01

    We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty. (Contains 2 tables and 11 figures.)

  13. Linear algebra and image processing

    NASA Astrophysics Data System (ADS)

    Allali, Mohamed

    2010-09-01

    We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty.

  14. A Programmed Course in Algebra.

    ERIC Educational Resources Information Center

    Mewborn, Ancel C.; Hively, Wells II

    This programed textbook consists of short sections of text interspersed with questions designed to aid the student in understanding the material. The course is designed to increase the student's understanding of some of the basic ideas of algebra. Some general experience and manipulative skill with respect to high school algebra is assumed.…

  15. Astro Algebra [CD-ROM].

    ERIC Educational Resources Information Center

    1997

    Astro Algebra is one of six titles in the Mighty Math Series from Edmark, a comprehensive line of math software for students from kindergarten through ninth grade. Many of the activities in Astro Algebra contain a unique technology that uses the computer to help students make the connection between concrete and abstract mathematics. This software…

  16. Gamow functionals on operator algebras

    NASA Astrophysics Data System (ADS)

    Castagnino, M.; Gadella, M.; Betán, R. Id; Laura, R.

    2001-11-01

    We obtain the precise form of two Gamow functionals representing the exponentially decaying part of a quantum resonance and its mirror image that grows exponentially, as a linear, positive and continuous functional on an algebra containing observables. These functionals do not admit normalization and, with an appropriate choice of the algebra, are time reversal of each other.

  17. Online Algebraic Tools for Teaching

    ERIC Educational Resources Information Center

    Kurz, Terri L.

    2011-01-01

    Many free online tools exist to complement algebraic instruction at the middle school level. This article presents findings that analyzed the features of algebraic tools to support learning. The findings can help teachers select appropriate tools to facilitate specific topics. (Contains 1 table and 4 figures.)

  18. Patterns to Develop Algebraic Reasoning

    ERIC Educational Resources Information Center

    Stump, Sheryl L.

    2011-01-01

    What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…

  19. Algebra: Grades 8-12.

    ERIC Educational Resources Information Center

    Instructional Objectives Exchange, Los Angeles, CA.

    A complete set of behavioral objectives for first-year algebra taught in any of grades 8 through 12 is presented. Three to six sample test items and answers are provided for each objective. Objectives were determined by surveying the most used secondary school algebra textbooks. Fourteen major categories are included: (1) whole numbers--operations…

  20. Elementary maps on nest algebras

    NASA Astrophysics Data System (ADS)

    Li, Pengtong

    2006-08-01

    Let , be algebras and let , be maps. An elementary map of is an ordered pair (M,M*) such that for all , . In this paper, the general form of surjective elementary maps on standard subalgebras of nest algebras is described. In particular, such maps are automatically additive.

  1. Condensing Algebra for Technical Mathematics.

    ERIC Educational Resources Information Center

    Greenfield, Donald R.

    Twenty Algebra-Packets (A-PAKS) were developed by the investigator for technical education students at the community college level. Each packet contained a statement of rationale, learning objectives, performance activities, performance test, and performance test answer key. The A-PAKS condensed the usual sixteen weeks of algebra into a six-week…

  2. The Algebra of the Arches

    ERIC Educational Resources Information Center

    Buerman, Margaret

    2007-01-01

    Finding real-world examples for middle school algebra classes can be difficult but not impossible. As we strive to accomplish teaching our students how to solve and graph equations, we neglect to teach the big ideas of algebra. One of those big ideas is functions. This article gives three examples of functions that are found in Arches National…

  3. An Algebraic Model for the mathfrak{su}(2|2) Light-Cone String Field Theory

    NASA Astrophysics Data System (ADS)

    Moriyama, S.

    We first revisit the light-cone string field theory on the flat andpp-wave background. By our systematic analysis, we find that some unsatisfactions in the previous construction can be overcome. After that, we head for the construction of the LCSFT on the bubbling geometry with an isometry [mathfrak{psu}(2|2)]^2 ltimes {mathbb R}. We clarify the structure of expansion and propose toy models for it. This proceeding is based on the collaboration with Kishimoto [I. Kishimoto and S. Moriyama, J. High Energy Phys. textbf{08} (2010), 013, arXiv:1005.4719 (Ref. 1)].

  4. Thermodynamics. [algebraic structure

    NASA Technical Reports Server (NTRS)

    Zeleznik, F. J.

    1976-01-01

    The fundamental structure of thermodynamics is purely algebraic, in the sense of atopological, and it is also independent of partitions, composite systems, the zeroth law, and entropy. The algebraic structure requires the notion of heat, but not the first law. It contains a precise definition of entropy and identifies it as a purely mathematical concept. It also permits the construction of an entropy function from heat measurements alone when appropriate conditions are satisfied. Topology is required only for a discussion of the continuity of thermodynamic properties, and then the weak topology is the relevant topology. The integrability of the differential form of the first law can be examined independently of Caratheodory's theorem and his inaccessibility axiom. Criteria are established by which one can determine when an integrating factor can be made intensive and the pseudopotential extensive and also an entropy. Finally, a realization of the first law is constructed which is suitable for all systems whether they are solids or fluids, whether they do or do not exhibit chemical reactions, and whether electromagnetic fields are or are not present.

  5. Open-closed homotopy algebra in mathematical physics

    SciTech Connect

    Kajiura, Hiroshige; Stasheff, Jim

    2006-02-15

    In this paper we discuss various aspects of open-closed homotopy algebras (OCHAs) presented in our previous paper, inspired by Zwiebach's open-closed string field theory, but that first paper concentrated on the mathematical aspects. Here we show how an OCHA is obtained by extracting the tree part of Zwiebach's quantum open-closed string field theory. We clarify the explicit relation of an OCHA with Kontsevich's deformation quantization and with the B-models of homological mirror symmetry. An explicit form of the minimal model for an OCHA is given as well as its relation to the perturbative expansion of open-closed string field theory. We show that our open-closed homotopy algebra gives us a general scheme for deformation of open string structures (A{sub {infinity}} algebras) by closed strings (L{sub {infinity}} algebras)

  6. Characterization of defects in Mn-Zn ferrites by scanning laser acoustic microscopy (SLAM)

    SciTech Connect

    Boehning, C.W.; Tuohig, W.D.

    1987-06-01

    A scanning laser acoustic microscope (SLAM) has been used to evaluate the integrity of Mn-Zn ferrite ceramic components which comprise part of the magnetic circuit in an electromechanical code interrogation device. Cracking of the ferrites during processing and assembly emerged as a significant manufacturing problem. Operations such as grinding, metallization, joining, and welding were suspected of causing damage, and acoustic microscopy was used to monitor these processes. Parts which produced suspicious acoustic images were dismantled and destructively sectioned to identify specific physical defects. Correlations between the defects and their acoustic signatures were established. This procedure has provided the basis for several process modifications and improvements which have resulted in acceptable production yields. The SLAM is used as an engineering tool for the detection and characterization of defects and is presently being used routinely to inspect production ferrite components.

  7. Loop Closing Detection in RGB-D SLAM Combining Appearance and Geometric Constraints

    PubMed Central

    Zhang, Heng; Liu, Yanli; Tan, Jindong

    2015-01-01

    A kind of multi feature points matching algorithm fusing local geometric constraints is proposed for the purpose of quickly loop closing detection in RGB-D Simultaneous Localization and Mapping (SLAM). The visual feature is encoded with BRAND (binary robust appearance and normals descriptor), which efficiently combines appearance and geometric shape information from RGB-D images. Furthermore, the feature descriptors are stored using the Locality-Sensitive-Hashing (LSH) technique and hierarchical clustering trees are used to search for these binary features. Finally, the algorithm for matching of multi feature points using local geometric constraints is provided, which can effectively reject the possible false closure hypotheses. We demonstrate the efficiency of our algorithms by real-time RGB-D SLAM with loop closing detection in indoor image sequences taken with a handheld Kinect camera and comparative experiments using other algorithms in RTAB-Map dealing with a benchmark dataset. PMID:26102492

  8. Loop Closing Detection in RGB-D SLAM Combining Appearance and Geometric Constraints.

    PubMed

    Zhang, Heng; Liu, Yanli; Tan, Jindong

    2015-01-01

    A kind of multi feature points matching algorithm fusing local geometric constraints is proposed for the purpose of quickly loop closing detection in RGB-D Simultaneous Localization and Mapping (SLAM). The visual feature is encoded with BRAND (binary robust appearance and normals descriptor), which efficiently combines appearance and geometric shape information from RGB-D images. Furthermore, the feature descriptors are stored using the Locality-Sensitive-Hashing (LSH) technique and hierarchical clustering trees are used to search for these binary features. Finally, the algorithm for matching of multi feature points using local geometric constraints is provided, which can effectively reject the possible false closure hypotheses. We demonstrate the efficiency of our algorithms by real-time RGB-D SLAM with loop closing detection in indoor image sequences taken with a handheld Kinect camera and comparative experiments using other algorithms in RTAB-Map dealing with a benchmark dataset. PMID:26102492

  9. Comparison of the Effectiveness of a Traditional Intermediate Algebra Course With That of a Less Rigorous Intermediate Algebra Course in Preparing Students for Success in a Subsequent Mathematics Course

    ERIC Educational Resources Information Center

    Sworder, Steven C.

    2007-01-01

    An experimental two-track intermediate algebra course was offered at Saddleback College, Mission Viejo, CA, between the Fall, 2002 and Fall, 2005 semesters. One track was modeled after the existing traditional California community college intermediate algebra course and the other track was a less rigorous intermediate algebra course in which the…

  10. An Algebra-Integrated Physics and Chemistry Workshop for Teachers as a Model for Increasing the Number of Minority Students in Science and Engineering

    NASA Astrophysics Data System (ADS)

    Obot, V.; Brown, B.; Wu, T.; Wunsch, G.; Miles, A.; Morris, P.; Lindstrom, M.; Allen, J.

    The need to increase minority representation in science and engineering disciplines is well documented. Many strategies for achieving this goal have evolved over the years; yet, minority representation is still minimal. It appears that while students are naturally curious about the universe, once mention is made of mathematics as a pre-requisite to the study of science and engineering, interest seems to wane. Perhaps a possible way to get around this phobia is to incorporate the mathematics into the science courses and the science into the mathematics courses at the secondary level. This will require mathematics and science teachers to work together, re-enforcing each other so that lessons can be truly interdisciplinary. For the past two summers, we have conducted workshops for secondary school mathematics and science teachers in a large urban school district. The workshops are called "Algebra-Integrated Physics and Chemistry". These workshops are designed to introduce the teachers to mathematical modeling of physical and chemical phenomenon. T chnology (graphic calculators) is used to dis covere functions that model a particular process. We have modeled linear functions by looking at the Celsius and Fahrenheit scales. A simple experiment is heating water, measuring the temperature in both Celsius and Fahrenheit scales, plotting Celsius versus Fahrenheit temperatures, and determining their mathematical relationship. At this point, the science teacher can also go into a discussion of the meaning of temperature. In some cases readily available data can be analyzed. The ellipse and Kepler's third law is ideal when studying conic sections. In this case, available data can be used, and by plotting appropriately, cubic functions can be studied and motions of planets in their orbits near and far from the sun can be discussed. This new approach to mathematics and science will take the student to a certain comfort level so that statements such as either " I like science

  11. A possible framework of the Lipkin model obeying the SU(n) algebra in arbitrary fermion number. II: Two subalgebras in the SU(n) Lipkin model and an approach to the construction of a linearly independent basis

    NASA Astrophysics Data System (ADS)

    Tsue, Yasuhiko; Providência, Constança; Providência, João da; Yamamura, Masatoshi

    2016-08-01

    Based on the results for the minimum weight states obtained in the previous paper (I), an idea of how to construct the linearly independent basis is proposed for the SU(n) Lipkin model. This idea starts in setting up m independent SU(2) subalgebras in the cases with n=2m and n=2m+1 (m=2,3,4,…). The original representation is re-formed in terms of the spherical tensors for the SU(n) generators built under the SU(2) subalgebras. Through this re-formation, the SU(m) subalgebra can be found. For constructing the linearly independent basis, not only the SU(2) algebras but also the SU(m) subalgebra play a central role. Some concrete results in the cases with n=2, 3, 4, and 5 are presented.

  12. Severe Psychosis, Drug Dependence, and Hepatitis C Related to Slamming Mephedrone.

    PubMed

    Dolengevich-Segal, Helen; Rodríguez-Salgado, Beatriz; Gómez-Arnau, Jorge; Sánchez-Mateos, Daniel

    2016-01-01

    Background. Synthetic cathinones (SCs), also known as "bath salts," are β-ketone amphetamine compounds derived from cathinone, a psychoactive substance found in Catha edulis. Mephedrone is the most representative SC. Slamming is the term used for the intravenous injection of these substances in the context of chemsex parties, in order to enhance sex experiences. Using IV mephedrone may lead to diverse medical and psychiatric complications like psychosis, aggressive behavior, and suicide ideation. Case. We report the case of a 25-year-old man admitted into a psychiatric unit, presenting with psychotic symptoms after slamming mephedrone almost every weekend for the last 4 months. He presents paranoid delusions, intense anxiety, and visual and kinesthetic hallucinations. He also shows intense craving, compulsive drug use, general malaise, and weakness. After four weeks of admission and antipsychotic treatment, delusions completely disappear. The patient is reinfected with hepatitis C. Discussion. Psychiatric and medical conditions related to chemsex and slamming have been reported in several European cities, but not in Spain. Psychotic symptoms have been associated with mephedrone and other SCs' consumption, with the IV route being prone to produce more severe symptomatology and addictive conducts. In the case we report, paranoid psychosis, addiction, and medical complications are described.

  13. Severe Psychosis, Drug Dependence, and Hepatitis C Related to Slamming Mephedrone

    PubMed Central

    Rodríguez-Salgado, Beatriz; Sánchez-Mateos, Daniel

    2016-01-01

    Background. Synthetic cathinones (SCs), also known as “bath salts,” are β-ketone amphetamine compounds derived from cathinone, a psychoactive substance found in Catha edulis. Mephedrone is the most representative SC. Slamming is the term used for the intravenous injection of these substances in the context of chemsex parties, in order to enhance sex experiences. Using IV mephedrone may lead to diverse medical and psychiatric complications like psychosis, aggressive behavior, and suicide ideation. Case. We report the case of a 25-year-old man admitted into a psychiatric unit, presenting with psychotic symptoms after slamming mephedrone almost every weekend for the last 4 months. He presents paranoid delusions, intense anxiety, and visual and kinesthetic hallucinations. He also shows intense craving, compulsive drug use, general malaise, and weakness. After four weeks of admission and antipsychotic treatment, delusions completely disappear. The patient is reinfected with hepatitis C. Discussion. Psychiatric and medical conditions related to chemsex and slamming have been reported in several European cities, but not in Spain. Psychotic symptoms have been associated with mephedrone and other SCs' consumption, with the IV route being prone to produce more severe symptomatology and addictive conducts. In the case we report, paranoid psychosis, addiction, and medical complications are described. PMID:27247820

  14. Severe Psychosis, Drug Dependence, and Hepatitis C Related to Slamming Mephedrone.

    PubMed

    Dolengevich-Segal, Helen; Rodríguez-Salgado, Beatriz; Gómez-Arnau, Jorge; Sánchez-Mateos, Daniel

    2016-01-01

    Background. Synthetic cathinones (SCs), also known as "bath salts," are β-ketone amphetamine compounds derived from cathinone, a psychoactive substance found in Catha edulis. Mephedrone is the most representative SC. Slamming is the term used for the intravenous injection of these substances in the context of chemsex parties, in order to enhance sex experiences. Using IV mephedrone may lead to diverse medical and psychiatric complications like psychosis, aggressive behavior, and suicide ideation. Case. We report the case of a 25-year-old man admitted into a psychiatric unit, presenting with psychotic symptoms after slamming mephedrone almost every weekend for the last 4 months. He presents paranoid delusions, intense anxiety, and visual and kinesthetic hallucinations. He also shows intense craving, compulsive drug use, general malaise, and weakness. After four weeks of admission and antipsychotic treatment, delusions completely disappear. The patient is reinfected with hepatitis C. Discussion. Psychiatric and medical conditions related to chemsex and slamming have been reported in several European cities, but not in Spain. Psychotic symptoms have been associated with mephedrone and other SCs' consumption, with the IV route being prone to produce more severe symptomatology and addictive conducts. In the case we report, paranoid psychosis, addiction, and medical complications are described. PMID:27247820

  15. An approach to robot SLAM based on incremental appearance learning with omnidirectional vision

    NASA Astrophysics Data System (ADS)

    Wu, Hua; Qin, Shi-Yin

    2011-03-01

    Localisation and mapping with an omnidirectional camera becomes more difficult as the landmark appearances change dramatically in the omnidirectional image. With conventional techniques, it is difficult to match the features of the landmark with the template. We present a novel robot simultaneous localisation and mapping (SLAM) algorithm with an omnidirectional camera, which uses incremental landmark appearance learning to provide posterior probability distribution for estimating the robot pose under a particle filtering framework. The major contribution of our work is to represent the posterior estimation of the robot pose by incremental probabilistic principal component analysis, which can be naturally incorporated into the particle filtering algorithm for robot SLAM. Moreover, the innovative method of this article allows the adoption of the severe distorted landmark appearances viewed with omnidirectional camera for robot SLAM. The experimental results demonstrate that the localisation error is less than 1 cm in an indoor environment using five landmarks, and the location of the landmark appearances can be estimated within 5 pixels deviation from the ground truth in the omnidirectional image at a fairly fast speed.

  16. Using Linear Algebra to Introduce Computer Algebra, Numerical Analysis, Data Structures and Algorithms (and To Teach Linear Algebra, Too).

    ERIC Educational Resources Information Center

    Gonzalez-Vega, Laureano

    1999-01-01

    Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)

  17. Transformation of time dependence to linear algebra

    NASA Astrophysics Data System (ADS)

    Menšík, Miroslav

    2005-10-01

    Reduced density matrix and memory function in the Nakajima-Zwanzig equation are expanded in properly chosen basis of special functions. This trick completely transforms time dependence to linear algebra. Then, the master equation for memory function is constructed and expanded in the same basis functions. For the model of a simple harmonic oscillator it is shown that this trick introduces infinite partial summation of the memory function in the system-bath interaction.

  18. Quantum algebra of N superspace

    SciTech Connect

    Hatcher, Nicolas; Restuccia, A.; Stephany, J.

    2007-08-15

    We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace, both in the case where there are no central charges in the algebra, and when they are present. This algebra is noncommutative for the position operators. We use the properties of superprojectors acting on the superfields to construct explicit position and momentum operators satisfying the algebra. They act on the projected wave functions associated to the various supermultiplets with defined superspin present in the representation. We show that the quantum algebra associated to the massive superparticle appears in our construction and is described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently. For the case N=2 with central charges, we present the equivalent results when the central charge and the mass are different. For the {kappa}-symmetric case when these quantities are equal, we discuss the reduction to the physical degrees of freedom of the corresponding superparticle and the construction of the associated quantum algebra.

  19. Constraint algebra in bigravity

    SciTech Connect

    Soloviev, V. O.

    2015-07-15

    The number of degrees of freedom in bigravity theory is found for a potential of general form and also for the potential proposed by de Rham, Gabadadze, and Tolley (dRGT). This aim is pursued via constructing a Hamiltonian formalismand studying the Poisson algebra of constraints. A general potential leads to a theory featuring four first-class constraints generated by general covariance. The vanishing of the respective Hessian is a crucial property of the dRGT potential, and this leads to the appearance of two additional second-class constraints and, hence, to the exclusion of a superfluous degree of freedom—that is, the Boulware—Deser ghost. The use of a method that permits avoiding an explicit expression for the dRGT potential is a distinctive feature of the present study.

  20. Constraint algebra in bigravity

    NASA Astrophysics Data System (ADS)

    Soloviev, V. O.

    2015-07-01

    The number of degrees of freedom in bigravity theory is found for a potential of general form and also for the potential proposed by de Rham, Gabadadze, and Tolley (dRGT). This aim is pursued via constructing a Hamiltonian formalismand studying the Poisson algebra of constraints. A general potential leads to a theory featuring four first-class constraints generated by general covariance. The vanishing of the respective Hessian is a crucial property of the dRGT potential, and this leads to the appearance of two additional second-class constraints and, hence, to the exclusion of a superfluous degree of freedom—that is, the Boulware—Deser ghost. The use of a method that permits avoiding an explicit expression for the dRGT potential is a distinctive feature of the present study.

  1. An Example of Competence-Based Learning: Use of Maxima in Linear Algebra for Engineers

    ERIC Educational Resources Information Center

    Diaz, Ana; Garcia, Alfonsa; de la Villa, Agustin

    2011-01-01

    This paper analyses the role of Computer Algebra Systems (CAS) in a model of learning based on competences. The proposal is an e-learning model Linear Algebra course for Engineering, which includes the use of a CAS (Maxima) and focuses on problem solving. A reference model has been taken from the Spanish Open University. The proper use of CAS is…

  2. Renormalization group flows and continual Lie algebras

    NASA Astrophysics Data System (ADS)

    Bakas, Ioannis

    2003-08-01

    We study the renormalization group flows of two-dimensional metrics in sigma models using the one-loop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the world-sheet length scale, t, is interpreted as Dynkin parameter on the root system of a novel continual Lie algebra, denoted by Script G(d/dt;1), with anti-symmetric Cartan kernel K(t,t') = delta'(t-t'); as such, it coincides with the Cartan matrix of the superalgebra sl(N|N+1) in the large-N limit. The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time, t. We provide the general solution of the renormalization group flows in terms of free fields, via Bäcklund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Zn to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra Script G(d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown.

  3. Readiness and Preparation for Beginning Algebra.

    ERIC Educational Resources Information Center

    Rotman, Jack W.

    Drawing from experience at Lansing Community College (LCC), this paper discusses how to best prepare students for success in a beginning algebra course. First, an overview is presented of LCC's developmental math sequence, which includes Basic Arithmetic (MTH 008), Pre-Algebra (MTH 009), Beginning Algebra (MTH 012), and Intermediate Algebra (MTH…

  4. Hopf algebras and Dyson-Schwinger equations

    NASA Astrophysics Data System (ADS)

    Weinzierl, Stefan

    2016-06-01

    In this paper I discuss Hopf algebras and Dyson-Schwinger equations. This paper starts with an introduction to Hopf algebras, followed by a review of the contribution and application of Hopf algebras to particle physics. The final part of the paper is devoted to the relation between Hopf algebras and Dyson-Schwinger equations.

  5. Two-parameter twisted quantum affine algebras

    NASA Astrophysics Data System (ADS)

    Jing, Naihuan; Zhang, Honglian

    2016-09-01

    We establish Drinfeld realization for the two-parameter twisted quantum affine algebras using a new method. The Hopf algebra structure for Drinfeld generators is given for both untwisted and twisted two-parameter quantum affine algebras, which include the quantum affine algebras as special cases.

  6. CULA: hybrid GPU accelerated linear algebra routines

    NASA Astrophysics Data System (ADS)

    Humphrey, John R.; Price, Daniel K.; Spagnoli, Kyle E.; Paolini, Aaron L.; Kelmelis, Eric J.

    2010-04-01

    The modern graphics processing unit (GPU) found in many standard personal computers is a highly parallel math processor capable of nearly 1 TFLOPS peak throughput at a cost similar to a high-end CPU and an excellent FLOPS/watt ratio. High-level linear algebra operations are computationally intense, often requiring O(N3) operations and would seem a natural fit for the processing power of the GPU. Our work is on CULA, a GPU accelerated implementation of linear algebra routines. We present results from factorizations such as LU decomposition, singular value decomposition and QR decomposition along with applications like system solution and least squares. The GPU execution model featured by NVIDIA GPUs based on CUDA demands very strong parallelism, requiring between hundreds and thousands of simultaneous operations to achieve high performance. Some constructs from linear algebra map extremely well to the GPU and others map poorly. CPUs, on the other hand, do well at smaller order parallelism and perform acceptably during low-parallelism code segments. Our work addresses this via hybrid a processing model, in which the CPU and GPU work simultaneously to produce results. In many cases, this is accomplished by allowing each platform to do the work it performs most naturally.

  7. Translating cosmological special relativity into geometric algebra

    NASA Astrophysics Data System (ADS)

    Horn, Martin Erik

    2012-11-01

    Geometric algebra and Clifford algebra are important tools to describe and analyze the physics of the world we live in. Although there is enormous empirical evidence that we are living in four dimensional spacetime, mathematical worlds of higher dimensions can be used to present the physical laws of our world in an aesthetical and didactical more appealing way. In physics and mathematics education we are therefore confronted with the question how these high dimensional spaces should be taught. But as an immediate confrontation of students with high dimensional compactified spacetimes would expect too much from them at the beginning of their university studies, it seems reasonable to approach the mathematics and physics of higher dimensions step by step. The first step naturally is the step from four dimensional spacetime of special relativity to a five dimensional spacetime world. As a toy model for this artificial world cosmological special relativity, invented by Moshe Carmeli, can be used. This five dimensional non-compactified approach describes a spacetime which consists not only of one time dimension and three space dimensions. In addition velocity is regarded as a fifth dimension. This model very probably will not represent physics correctly. But it can be used to discuss and analyze the consequences of an additional dimension in a clear and simple way. Unfortunately Carmeli has formulated cosmological special relativity in standard vector notation. Therefore a translation of cosmological special relativity into the mathematical language of Grassmann and Clifford (Geometric algebra) is given and the physics of cosmological special relativity is discussed.

  8. Cartooning in Algebra and Calculus

    ERIC Educational Resources Information Center

    Moseley, L. Jeneva

    2014-01-01

    This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.

  9. Ada Linear-Algebra Program

    NASA Technical Reports Server (NTRS)

    Klumpp, A. R.; Lawson, C. L.

    1988-01-01

    Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.

  10. GCD, LCM, and Boolean Algebra?

    ERIC Educational Resources Information Center

    Cohen, Martin P.; Juraschek, William A.

    1976-01-01

    This article investigates the algebraic structure formed when the process of finding the greatest common divisor and the least common multiple are considered as binary operations on selected subsets of positive integers. (DT)

  11. ALGEBRA v.1.27

    SciTech Connect

    Sjaardema, G.; Gilkey, A.; Smith, M.; Forsythe, C.

    2005-04-11

    The ALGEBRA program allows the user to manipulate data from a finite element analysis before it is plotted. The finite element output data is in the form of variable values (e.g., stress, strain, and velocity components) in an EXODUS II database. The ALGEBRA program evaluates user-supplied functions of the data and writes the results to an output EXODUS II database that can be read by plot programs.

  12. Algebraic isomorphism in two-dimensional anomalous gauge theories

    SciTech Connect

    Carvalhaes, C.G.; Natividade, C.P.

    1997-08-01

    The operator solution of the anomalous chiral Schwinger model is discussed on the basis of the general principles of Wightman field theory. Some basic structural properties of the model are analyzed taking a careful control on the Hilbert space associated with the Wightman functions. The isomorphism between gauge noninvariant and gauge invariant descriptions of the anomalous theory is established in terms of the corresponding field algebras. We show that (i) the {Theta}-vacuum representation and (ii) the suggested equivalence of vector Schwinger model and chiral Schwinger model cannot be established in terms of the intrinsic field algebra. {copyright} 1997 Academic Press, Inc.

  13. Algebraic Systems and Pushdown Automata

    NASA Astrophysics Data System (ADS)

    Petre, Ion; Salomaa, Arto

    We concentrate in this chapter on the core aspects of algebraic series, pushdown automata, and their relation to formal languages. We choose to follow here a presentation of their theory based on the concept of properness. We introduce in Sect. 2 some auxiliary notions and results needed throughout the chapter, in particular the notions of discrete convergence in semirings and C-cycle free infinite matrices. In Sect. 3 we introduce the algebraic power series in terms of algebraic systems of equations. We focus on interconnections with context-free grammars and on normal forms. We then conclude the section with a presentation of the theorems of Shamir and Chomsky-Schützenberger. We discuss in Sect. 4 the algebraic and the regulated rational transductions, as well as some representation results related to them. Section 5 is dedicated to pushdown automata and focuses on the interconnections with classical (non-weighted) pushdown automata and on the interconnections with algebraic systems. We then conclude the chapter with a brief discussion of some of the other topics related to algebraic systems and pushdown automata.

  14. A fast slam approach to freehand 3-d ultrasound reconstruction for catheter ablation guidance in the left atrium.

    PubMed

    Koolwal, Aditya B; Barbagli, Federico; Carlson, Christopher R; Liang, David H

    2011-12-01

    We present a method for real-time, freehand 3D ultrasound (3D-US) reconstruction of moving anatomy, with specific application towards guiding the catheter ablation procedure in the left atrium. Using an intracardiac echo (ICE) catheter with a pose (position/orientation) sensor mounted to its tip, we continually mosaic 2D-ICE images of a left atrium phantom model to form a 3D-US volume. Our mosaicing strategy employs a probabilistic framework based on simultaneous localization and mapping (SLAM), a technique commonly used in mobile robotics for creating maps of unexplored environments. The measured ICE catheter tip pose provides an initial estimate for compounding 2D-ICE image data into the 3D-US volume. However, we simultaneously consider the overlap-consistency shared between 2D-ICE images and the 3D-US volume, computing a "corrected" tip pose if need be to ensure spatially-consistent reconstruction. This allows us to compensate for anatomic movement and sensor drift that would otherwise cause motion artifacts in the 3D-US volume. Our approach incorporates 2D-ICE data immediately after acquisition, allowing us to continuously update the registration parameters linking sensor coordinates to 3D-US coordinates. This, in turn, enables real-time localization and display of sensorized therapeutic catheters within the 3D-US volume for facilitating procedural guidance.

  15. A fast slam approach to freehand 3-d ultrasound reconstruction for catheter ablation guidance in the left atrium.

    PubMed

    Koolwal, Aditya B; Barbagli, Federico; Carlson, Christopher R; Liang, David H

    2011-12-01

    We present a method for real-time, freehand 3D ultrasound (3D-US) reconstruction of moving anatomy, with specific application towards guiding the catheter ablation procedure in the left atrium. Using an intracardiac echo (ICE) catheter with a pose (position/orientation) sensor mounted to its tip, we continually mosaic 2D-ICE images of a left atrium phantom model to form a 3D-US volume. Our mosaicing strategy employs a probabilistic framework based on simultaneous localization and mapping (SLAM), a technique commonly used in mobile robotics for creating maps of unexplored environments. The measured ICE catheter tip pose provides an initial estimate for compounding 2D-ICE image data into the 3D-US volume. However, we simultaneously consider the overlap-consistency shared between 2D-ICE images and the 3D-US volume, computing a "corrected" tip pose if need be to ensure spatially-consistent reconstruction. This allows us to compensate for anatomic movement and sensor drift that would otherwise cause motion artifacts in the 3D-US volume. Our approach incorporates 2D-ICE data immediately after acquisition, allowing us to continuously update the registration parameters linking sensor coordinates to 3D-US coordinates. This, in turn, enables real-time localization and display of sensorized therapeutic catheters within the 3D-US volume for facilitating procedural guidance. PMID:22014856

  16. Multifractal vector fields and stochastic Clifford algebra

    NASA Astrophysics Data System (ADS)

    Schertzer, Daniel; Tchiguirinskaia, Ioulia

    2015-12-01

    In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.

  17. Multifractal vector fields and stochastic Clifford algebra

    SciTech Connect

    Schertzer, Daniel Tchiguirinskaia, Ioulia

    2015-12-15

    In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.

  18. Multifractal vector fields and stochastic Clifford algebra.

    PubMed

    Schertzer, Daniel; Tchiguirinskaia, Ioulia

    2015-12-01

    In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality. PMID:26723166

  19. Multifractal vector fields and stochastic Clifford algebra.

    PubMed

    Schertzer, Daniel; Tchiguirinskaia, Ioulia

    2015-12-01

    In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.

  20. Invertible linear transformations and the Lie algebras

    NASA Astrophysics Data System (ADS)

    Zhang, Yufeng; Tam, Honwah; Guo, Fukui

    2008-07-01

    With the help of invertible linear transformations and the known Lie algebras, a way to generate new Lie algebras is given. These Lie algebras obtained have a common feature, i.e. integrable couplings of solitary hierarchies could be obtained by using them, specially, the Hamiltonian structures of them could be worked out. Some ways to construct the loop algebras of the Lie algebras are presented. It follows that some various loop algebras are given. In addition, a few new Lie algebras are explicitly constructed in terms of the classification of Lie algebras proposed by Ma Wen-Xiu, which are bases for obtaining new Lie algebras by using invertible linear transformations. Finally, some solutions of a (2 + 1)-dimensional partial-differential equation hierarchy are obtained, whose Hamiltonian form-expressions are manifested by using the quadratic-form identity.

  1. The 2007 National Federation of the Blind Youth Slam: Making Astronomy Accessible to Students Who are Blind

    NASA Astrophysics Data System (ADS)

    Grice, Noreen A.

    2008-05-01

    In the summer of 2007, nearly two hundred blind and visually impaired high school students participated in a weeklong enrichment program at Johns Hopkins University called the National Federation of the Blind Youth Slam. They spent four days participating in hands-on science and engineering classes and exploring careers previously thought inaccessible to those without sight. The students were separated into "tracks” with each group focusing on a different field. Want to know what happened in the astronomy track? Come by this paper and see examples of accessible astronomy activities, including accessible star parties, from the Youth Slam!

  2. Ipsilateral carpal, metacarpal, and ankle fractures resulting from an attempted basketball slam-dunk. A case report.

    PubMed

    McClelland, S J; Fithian, D C

    1988-01-01

    A 23-year-old male recreational basketball player sustained an open ankle fracture and ipsilateral carpal and metacarpal fractures as a result of a fall while attempting a slam-dunk. The wrist and hand fractures were treated nonoperatively. The open ankle fracture required irrigation, debridement, and open reduction/internal fixation. In addition to the prerequisite leaping ability, long-term success in "playing above the rim" requires experience, exceptional physical agility, and the mental discipline to anticipate and avoid slam-dunk opportunities with high risk for personal injury.

  3. BRST charges for finite nonlinear algebras

    NASA Astrophysics Data System (ADS)

    Isaev, A. P.; Krivonos, S. O.; Ogievetsky, O. V.

    2010-07-01

    Some ingredients of the BRST construction for quantum Lie algebras are applied to a wider class of quadratic algebras of constraints. We build the BRST charge for a quantum Lie algebra with three generators and ghost-anti-ghosts commuting with constraints. We consider a one-parametric family of quadratic algebras with three generators and show that the BRST charge acquires the conventional form after a redefinition of ghosts. The modified ghosts form a quadratic algebra. The family possesses a nonlinear involution, which implies the existence of two independent BRST charges for each algebra in the family. These BRST charges anticommute and form a double BRST complex.

  4. Some Remarks on Kite Pseudo Effect Algebras

    NASA Astrophysics Data System (ADS)

    Dvurečenskij, Anatolij; Holland, W. Charles

    2014-05-01

    Recently a new family of pseudo effect algebras, called kite pseudo effect algebras, was introduced. Such an algebra starts with a po-group G, a set I and with two bijections λ, ρ: I→ I. Using a clever construction on the ordinal sum of ( G +) I and ( G -) I , we can define a pseudo effect algebra which can be non-commutative even if G is an Abelian po-group. In the paper we give a characterization of subdirect product of subdirectly irreducible kite pseudo effect algebras, and we show that every kite pseudo effect algebra is an interval in a unital po-loop.

  5. Operator product expansion algebra

    SciTech Connect

    Holland, Jan; Hollands, Stefan

    2013-07-15

    We establish conceptually important properties of the operator product expansion (OPE) in the context of perturbative, Euclidean φ{sup 4}-quantum field theory. First, we demonstrate, generalizing earlier results and techniques of hep-th/1105.3375, that the 3-point OPE, =Σ{sub C}C{sub A{sub 1A{sub 2A{sub 3}{sup C}}}}, usually interpreted only as an asymptotic short distance expansion, actually converges at finite, and even large, distances. We further show that the factorization identity C{sub A{sub 1A{sub 2A{sub 3}{sup B}}}}=Σ{sub C}C{sub A{sub 1A{sub 2}{sup C}}}C{sub CA{sub 3}{sup B}} is satisfied for suitable configurations of the spacetime arguments. Again, the infinite sum is shown to be convergent. Our proofs rely on explicit bounds on the remainders of these expansions, obtained using refined versions, mostly due to Kopper et al., of the renormalization group flow equation method. These bounds also establish that each OPE coefficient is a real analytic function in the spacetime arguments for non-coinciding points. Our results hold for arbitrary but finite loop orders. They lend support to proposals for a general axiomatic framework of quantum field theory, based on such “consistency conditions” and akin to vertex operator algebras, wherein the OPE is promoted to the defining structure of the theory.

  6. Constructing a parasupersymmetric Virasoro algebra

    NASA Astrophysics Data System (ADS)

    Kuwata, S.

    2011-03-01

    We construct a para SUSY Virasoro algebra by generalizing the ordinary fermion in SUSY Virasoro algebra (Ramond or Neveu-Schwarz algebra) to the parafermion. First, we obtain a polynomial relation (PR) between different-mode parafermion fi's by generalizing the corresponding single-mode PR to such that is invariant under the unitary transformation of fi (Green's condition). Differently from a usual context, where the Green's condition is imposed only on the defining relation of fi (degree three with respect to fi and fi†), we impose it on any degree of PR. For the case of order-two parafermion (the simplest case of para SUSY), we calculate a PR between the parasupercharge G0, the bosonic hamiltonian LB0 and parafermionic one LF0, although it is difficult to obtain a PR between G0 and the total hamiltonian L0 (= LB0 + LF0). Finally, we construct a para SUSY Virasoro algebra by generalizing L0 to the Ln's such that form a Virasoro algebra.

  7. Moving frames and prolongation algebras

    NASA Technical Reports Server (NTRS)

    Estabrook, F. B.

    1982-01-01

    Differential ideals generated by sets of 2-forms which can be written with constant coefficients in a canonical basis of 1-forms are considered. By setting up a Cartan-Ehresmann connection, in a fiber bundle over a base space in which the 2-forms live, one finds an incomplete Lie algebra of vector fields in the fields in the fibers. Conversely, given this algebra (a prolongation algebra), one can derive the differential ideal. The two constructs are thus dual, and analysis of either derives properties of both. Such systems arise in the classical differential geometry of moving frames. Examples of this are discussed, together with examples arising more recently: the Korteweg-de Vries and Harrison-Ernst systems.

  8. Algebraic Systems Biology: A Case Study for the Wnt Pathway.

    PubMed

    Gross, Elizabeth; Harrington, Heather A; Rosen, Zvi; Sturmfels, Bernd

    2016-01-01

    Steady-state analysis of dynamical systems for biological networks gives rise to algebraic varieties in high-dimensional spaces whose study is of interest in their own right. We demonstrate this for the shuttle model of the Wnt signaling pathway. Here, the variety is described by a polynomial system in 19 unknowns and 36 parameters. It has degree 9 over the parameter space. This case study explores multistationarity, model comparison, dynamics within regions of the state space, identifiability, and parameter estimation, from a geometric point of view. We employ current methods from computational algebraic geometry, polyhedral geometry, and combinatorics.

  9. Algebraic Systems Biology: A Case Study for the Wnt Pathway.

    PubMed

    Gross, Elizabeth; Harrington, Heather A; Rosen, Zvi; Sturmfels, Bernd

    2016-01-01

    Steady-state analysis of dynamical systems for biological networks gives rise to algebraic varieties in high-dimensional spaces whose study is of interest in their own right. We demonstrate this for the shuttle model of the Wnt signaling pathway. Here, the variety is described by a polynomial system in 19 unknowns and 36 parameters. It has degree 9 over the parameter space. This case study explores multistationarity, model comparison, dynamics within regions of the state space, identifiability, and parameter estimation, from a geometric point of view. We employ current methods from computational algebraic geometry, polyhedral geometry, and combinatorics. PMID:26645985

  10. On an approach for computing the generating functions of the characters of simple Lie algebras

    NASA Astrophysics Data System (ADS)

    Fernández Núñez, José; García Fuertes, Wifredo; Perelomov, Askold M.

    2014-04-01

    We describe a general approach to obtain the generating functions of the characters of simple Lie algebras which is based on the theory of the quantum trigonometric Calogero-Sutherland model. We show how the method works in practice by means of a few examples involving some low rank classical algebras.

  11. Colored Quantum Algebra and Its Bethe State

    NASA Astrophysics Data System (ADS)

    Wang, Jin-Zheng; Jia, Xiao-Yu; Wang, Shi-Kun

    2014-12-01

    We investigate the colored Yang—Baxter equation. Based on a trigonometric solution of colored Yang—Baxter equation, we construct a colored quantum algebra. Moreover we discuss its algebraic Bethe ansatz state and highest wight representation.

  12. Generalized Galilean algebras and Newtonian gravity

    NASA Astrophysics Data System (ADS)

    González, N.; Rubio, G.; Salgado, P.; Salgado, S.

    2016-04-01

    The non-relativistic versions of the generalized Poincaré algebras and generalized AdS-Lorentz algebras are obtained. These non-relativistic algebras are called, generalized Galilean algebras of type I and type II and denoted by GBn and GLn respectively. Using a generalized Inönü-Wigner contraction procedure we find that the generalized Galilean algebras of type I can be obtained from the generalized Galilean algebras type II. The S-expansion procedure allows us to find the GB5 algebra from the Newton Hooke algebra with central extension. The procedure developed in Ref. [1] allows us to show that the nonrelativistic limit of the five dimensional Einstein-Chern-Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.

  13. Motivating Activities that Lead to Algebra

    ERIC Educational Resources Information Center

    Menon, Ramakrishnan

    2004-01-01

    Four activities consisting of puzzles are introduced, which help students to recognize the strength of algebraic generalizations. They also assist them to comprehend algebraic concepts, and enable them to develop their individual puzzles and games.

  14. Scalable Parallel Algebraic Multigrid Solvers

    SciTech Connect

    Bank, R; Lu, S; Tong, C; Vassilevski, P

    2005-03-23

    The authors propose a parallel algebraic multilevel algorithm (AMG), which has the novel feature that the subproblem residing in each processor is defined over the entire partition domain, although the vast majority of unknowns for each subproblem are associated with the partition owned by the corresponding processor. This feature ensures that a global coarse description of the problem is contained within each of the subproblems. The advantages of this approach are that interprocessor communication is minimized in the solution process while an optimal order of convergence rate is preserved; and the speed of local subproblem solvers can be maximized using the best existing sequential algebraic solvers.

  15. Automatic Relocalization and Loop Closing for Real-Time Monocular SLAM.

    PubMed

    Williams, Brian; Klein, Georg; Reid, Ian

    2011-09-01

    Monocular SLAM has the potential to turn inexpensive cameras into powerful pose sensors for applications such as robotics and augmented reality. We present a relocalization module for such systems which solves some of the problems encountered by previous monocular SLAM systems--tracking failure, map merging, and loop closure detection. This module extends recent advances in keypoint recognition to determine the camera pose relative to the landmarks within a single frame time of 33 ms. We first show how this module can be used to improve the robustness of these systems. Blur, sudden motion, and occlusion can all cause tracking to fail, leading to a corrupted map. Using the relocalization module, the system can automatically detect and recover from tracking failure while preserving map integrity. Extensive tests show that the system can then reliably generate maps for long sequences even in the presence of frequent tracking failure. We then show that the relocalization module can be used to recognize overlap in maps, i.e., when the camera has returned to a previously mapped area. Having established an overlap, we determine the relative pose of the maps using trajectory alignment so that independent maps can be merged and loop closure events can be recognized. The system combining all of these abilities is able to map larger environments and for significantly longer periods than previous systems.

  16. Laser-Based Slam with Efficient Occupancy Likelihood Map Learning for Dynamic Indoor Scenes

    NASA Astrophysics Data System (ADS)

    Li, Li; Yao, Jian; Xie, Renping; Tu, Jinge; Feng, Chen

    2016-06-01

    Location-Based Services (LBS) have attracted growing attention in recent years, especially in indoor environments. The fundamental technique of LBS is the map building for unknown environments, this technique also named as simultaneous localization and mapping (SLAM) in robotic society. In this paper, we propose a novel approach for SLAMin dynamic indoor scenes based on a 2D laser scanner mounted on a mobile Unmanned Ground Vehicle (UGV) with the help of the grid-based occupancy likelihood map. Instead of applying scan matching in two adjacent scans, we propose to match current scan with the occupancy likelihood map learned from all previous scans in multiple scales to avoid the accumulation of matching errors. Due to that the acquisition of the points in a scan is sequential but not simultaneous, there unavoidably exists the scan distortion at different extents. To compensate the scan distortion caused by the motion of the UGV, we propose to integrate a velocity of a laser range finder (LRF) into the scan matching optimization framework. Besides, to reduce the effect of dynamic objects such as walking pedestrians often existed in indoor scenes as much as possible, we propose a new occupancy likelihood map learning strategy by increasing or decreasing the probability of each occupancy grid after each scan matching. Experimental results in several challenged indoor scenes demonstrate that our proposed approach is capable of providing high-precision SLAM results.

  17. Discrimination in a General Algebraic Setting.

    PubMed

    Fine, Benjamin; Gaglione, Anthony; Lipschutz, Seymour; Spellman, Dennis

    2015-01-01

    Discriminating groups were introduced by G. Baumslag, A. Myasnikov, and V. Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. Algebraic geometry over groups became the main method of attack on the solution of the celebrated Tarski conjectures. In this paper we explore the notion of discrimination in a general universal algebra context. As an application we provide a different proof of a theorem of Malcev on axiomatic classes of Ω-algebras.

  18. Discrimination in a General Algebraic Setting

    PubMed Central

    Fine, Benjamin; Gaglione, Anthony; Lipschutz, Seymour; Spellman, Dennis

    2015-01-01

    Discriminating groups were introduced by G. Baumslag, A. Myasnikov, and V. Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. Algebraic geometry over groups became the main method of attack on the solution of the celebrated Tarski conjectures. In this paper we explore the notion of discrimination in a general universal algebra context. As an application we provide a different proof of a theorem of Malcev on axiomatic classes of Ω-algebras. PMID:26171421

  19. Characteristic Numbers of Matrix Lie Algebras

    NASA Astrophysics Data System (ADS)

    Zhang, Yu-Feng; Fan, En-Gui

    2008-04-01

    A notion of characteristic number of matrix Lie algebras is defined, which is devoted to distinguishing various Lie algebras that are used to generate integrable couplings of soliton equations. That is, the exact classification of the matrix Lie algebras by using computational formulas is given. Here the characteristic numbers also describe the relations between soliton solutions of the stationary zero curvature equations expressed by various Lie algebras.

  20. Twining characters and orbit Lie algebras

    SciTech Connect

    Fuchs, Jurgen; Ray, Urmie; Schellekens, Bert; Schweigert, Christoph

    1996-12-05

    We associate to outer automorphisms of generalized Kac-Moody algebras generalized character-valued indices, the twining characters. A character formula for twining characters is derived which shows that they coincide with the ordinary characters of some other generalized Kac-Moody algebra, the so-called orbit Lie algebra. Some applications to problems in conformal field theory, algebraic geometry and the theory of sporadic simple groups are sketched.

  1. Compatible Relaxation and Coarsening in Algebraic Multigrid

    SciTech Connect

    Brannick, J J; Falgout, R D

    2009-09-22

    We introduce a coarsening algorithm for algebraic multigrid (AMG) based on the concept of compatible relaxation (CR). The algorithm is significantly different from standard methods, most notably because it does not rely on any notion of strength of connection. We study its behavior on a number of model problems, and evaluate the performance of an AMG algorithm that incorporates the coarsening approach. Lastly, we introduce a variant of CR that provides a sharper metric of coarse-grid quality and demonstrate its potential with two simple examples.

  2. Reasoning algebraically with IT: A cognitive perspective

    NASA Astrophysics Data System (ADS)

    Mok, Ida; Johnson, David

    2000-12-01

    The focus of this paper is on the implications of key findings and theoretical positions from social psychology and cognitive developmental psychology (Piagetian/neo-Piagetian) for the use of IT tools to support learning in algebra. Particular reference is made to the research of the UK Cognitive Acceleration through Mathematics Education (CAME) project. The feasibility of the CAME model in the exploration of mathematical relationships supported by graphics calculators was addressed in a small-scale study in Hong Kong. The research provides evidence that, with appropriate mediation, cognitive conflict can be utilised to provide valuable appropriate for students to engage in increasingly higher levels of mathematical thinking.

  3. New family of Maxwell like algebras

    NASA Astrophysics Data System (ADS)

    Concha, P. K.; Durka, R.; Merino, N.; Rodríguez, E. K.

    2016-08-01

    We introduce an alternative way of closing Maxwell like algebras. We show, through a suitable change of basis, that resulting algebras are given by the direct sums of the AdS and the Maxwell algebras already known in the literature. Casting the result into the S-expansion method framework ensures the straightaway construction of the gravity theories based on a found enlargement.

  4. Unifying the Algebra for All Movement

    ERIC Educational Resources Information Center

    Eddy, Colleen M.; Quebec Fuentes, Sarah; Ward, Elizabeth K.; Parker, Yolanda A.; Cooper, Sandi; Jasper, William A.; Mallam, Winifred A.; Sorto, M. Alejandra; Wilkerson, Trena L.

    2015-01-01

    There exists an increased focus on school mathematics, especially first-year algebra, due to recent efforts for all students to be college and career ready. In addition, there are calls, policies, and legislation advocating for all students to study algebra epitomized by four rationales of the "Algebra for All" movement. In light of this…

  5. Build an Early Foundation for Algebra Success

    ERIC Educational Resources Information Center

    Knuth, Eric; Stephens, Ana; Blanton, Maria; Gardiner, Angela

    2016-01-01

    Research tells us that success in algebra is a factor in many other important student outcomes. Emerging research also suggests that students who are started on an algebra curriculum in the earlier grades may have greater success in the subject in secondary school. What's needed is a consistent, algebra-infused mathematics curriculum all…

  6. Difficulties in Initial Algebra Learning in Indonesia

    ERIC Educational Resources Information Center

    Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja

    2014-01-01

    Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was…

  7. A Balancing Act: Making Sense of Algebra

    ERIC Educational Resources Information Center

    Gavin, M. Katherine; Sheffield, Linda Jensen

    2015-01-01

    For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…

  8. Algebra? A Gate! A Barrier! A Mystery!

    ERIC Educational Resources Information Center

    Mathematics Educatio Dialogues, 2000

    2000-01-01

    This issue of Mathematics Education Dialogues focuses on the nature and the role of algebra in the K-14 curriculum. Articles on this theme include: (1) "Algebra For All? Why?" (Nel Noddings); (2) "Algebra For All: It's a Matter of Equity, Expectations, and Effectiveness" (Dorothy S. Strong and Nell B. Cobb); (3) "Don't Delay: Build and Talk about…

  9. Computer Algebra Systems, Pedagogy, and Epistemology

    ERIC Educational Resources Information Center

    Bosse, Michael J.; Nandakumar, N. R.

    2004-01-01

    The advent of powerful Computer Algebra Systems (CAS) continues to dramatically affect curricula, pedagogy, and epistemology in secondary and college algebra classrooms. However, epistemological and pedagogical research regarding the role and effectiveness of CAS in the learning of algebra lags behind. This paper investigates concerns regarding…

  10. Teaching Strategies to Improve Algebra Learning

    ERIC Educational Resources Information Center

    Zbiek, Rose Mary; Larson, Matthew R.

    2015-01-01

    Improving student learning is the primary goal of every teacher of algebra. Teachers seek strategies to help all students learn important algebra content and develop mathematical practices. The new Institute of Education Sciences[IES] practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students"…

  11. Entropy algebras and Birkhoff factorization

    NASA Astrophysics Data System (ADS)

    Marcolli, Matilde; Tedeschi, Nicolas

    2015-11-01

    We develop notions of Rota-Baxter structures and associated Birkhoff factorizations, in the context of min-plus semirings and their thermodynamic deformations, including deformations arising from quantum information measures such as the von Neumann entropy. We consider examples related to Manin's renormalization and computation program, to Markov random fields and to counting functions and zeta functions of algebraic varieties.

  12. Algebraic Activities Aid Discovery Lessons

    ERIC Educational Resources Information Center

    Wallace-Gomez, Patricia

    2013-01-01

    After a unit on the rules for positive and negative numbers and the order of operations for evaluating algebraic expressions, many students believe that they understand these principles well enough, but they really do not. They clearly need more practice, but not more of the same kind of drill. Wallace-Gomez provides three graphing activities that…

  13. Putting the Modern in Algebra

    ERIC Educational Resources Information Center

    Bosse, Michael J.; Ries, Heather; Chandler, Kayla

    2012-01-01

    Secondary school mathematics teachers often need to answer the "Why do we do that?" question in such a way that avoids confusion and evokes student interest. Understanding the properties of number systems can provide an avenue to better grasp algebraic structures, which in turn builds students' conceptual knowledge of secondary mathematics. This…

  14. Dimension independence in exterior algebra.

    PubMed Central

    Hawrylycz, M

    1995-01-01

    The identities between homogeneous expressions in rank 1 vectors and rank n - 1 covectors in a Grassmann-Cayley algebra of rank n, in which one set occurs multilinearly, are shown to represent a set of dimension-independent identities. The theorem yields an infinite set of nontrivial geometric identities from a given identity. PMID:11607520

  15. Exploring Algebraic Misconceptions with Technology

    ERIC Educational Resources Information Center

    Sakow, Matthew; Karaman, Ruveyda

    2015-01-01

    Many students struggle with algebra, from simplifying expressions to solving systems of equations. Students also have misconceptions about the meaning of variables. In response to the question "Can x + y + z ever equal x + p + z?" during a student interview, the student claimed, "Never . . . because p has to have a different value…

  16. A New Age for Algebra

    ERIC Educational Resources Information Center

    Oishi, Lindsay

    2011-01-01

    "Solve for x." While many people first encountered this enigmatic instruction in high school, the last 20 years have seen a strong push to get students to take algebra in eighth grade or even before. Today, concerns about the economy highlight a familiar worry: American eighth-graders trailed their peers in five Asian countries on the 2007 TIMSS…

  17. Weaving Geometry and Algebra Together

    ERIC Educational Resources Information Center

    Cetner, Michelle

    2015-01-01

    When thinking about student reasoning and sense making, teachers must consider the nature of tasks given to students along with how to plan to use the tasks in the classroom. Students should be presented with tasks in a way that encourages them to draw connections between algebraic and geometric concepts. This article focuses on the idea that it…

  18. Algebraic methods in system theory

    NASA Technical Reports Server (NTRS)

    Brockett, R. W.; Willems, J. C.; Willsky, A. S.

    1975-01-01

    Investigations on problems of the type which arise in the control of switched electrical networks are reported. The main results concern the algebraic structure and stochastic aspects of these systems. Future reports will contain more detailed applications of these results to engineering studies.

  19. Algebra from Chips and Chopsticks

    ERIC Educational Resources Information Center

    Yun, Jeong Oak; Flores, Alfinio

    2012-01-01

    Students can use geometric representations of numbers as a way to explore algebraic ideas. With the help of these representations, students can think about the relations among the numbers, express them using their own words, and represent them with letters. The activities discussed here can stimulate students to try to find various ways of solving…

  20. Celestial mechanics with geometric algebra

    NASA Technical Reports Server (NTRS)

    Hestenes, D.

    1983-01-01

    Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.