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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

    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.

  3. 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

  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. 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

  6. Super High Frequency (SHF) Link Analysis Model (SLAM) for nonsatellite applications

    NASA Astrophysics Data System (ADS)

    James, R. R.; Rockway, J. W.

    1990-06-01

    A point-to-point link analysis model has been developed for the Super High Frequency (SHF) band. It was developed to evaluate ship-to-ship and ship-to-air links. The SHF Link Analysis Model (SLAM) evaluates a communication link and determines system margin. The link margin is determined after a user defines the transmitter subsystem, the receiver subsystem, the specified level of system performance, and the propagation channel. The propagation channel incorporates the Engineer's Refractive Effects Prediction System (EREPS) and includes the effects of the evaporation duct. A rain model developed by NASA is also included in the channel. SLAM provides a detailed discussion of the link equation, the propagation effects, the rain model, and the antenna characteristics. In addition, a detailed explanation of the operation of the SLAM computer program is given. Two communication links are evaluated and these examples are used to demonstrate the computer program's capabilities.

  7. 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.

  8. 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.

  9. 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).

  10. 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

  11. 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

  12. 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. PMID:21769158

  13. 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...

  14. 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)

  15. One-Equation Algebraic Model Of Turbulence

    NASA Technical Reports Server (NTRS)

    Baldwin, B. S.; Barth, T. J.

    1993-01-01

    One-equation model of turbulence based on standard equations of k-epsilon model of turbulence, where k is turbulent energy and e is rate of dissipation of k. Derivation of one-equation model motivated partly by inaccuracies of flows computed by some Navier-Stokes-equations-solving algorithms incorporating algebraic models of turbulence. Satisfies need to avoid having to determine algebraic length scales.

  16. 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…

  17. 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

  18. 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

  19. 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.

  20. Host-virus specificity of morbilliviruses predicted by structural modeling of the marine mammal SLAM, a receptor.

    PubMed

    Ohishi, Kazue; Ando, Akiko; Suzuki, Rintaro; Takishita, Kiyotaka; Kawato, Masaru; Katsumata, Etsuko; Ohtsu, Dai; Okutsu, Kenji; Tokutake, Koji; Miyahara, Hirokazu; Nakamura, Hirotaka; Murayama, Tsukasa; Maruyama, Tadashi

    2010-05-01

    Signaling lymphocyte activation molecule (SLAM) is thought to be a major cellular receptor for high-host specificity morbilliviruses, which cause devastating and highly infectious diseases in mammals. We determined the sequences of SLAM cDNA from five species of marine mammal, including two cetaceans, two pinnipeds and one sirenian, and generated three-dimensional models to understand the receptor-virus interaction. Twenty-one amino acid residues in the immunoglobulin-like V domains of the SLAMs were shown to bind the viral protein. Notably, the sequences from pinnipeds and dogs were highly homologous, which is consistent with the fact that canine distemper virus was previously shown to cause a mass die-off of seals. Among these twenty-one residues, eight (63, 66, 68, 72, 84, 119, 121 and 130) were shared by animal groups susceptible to a particular morbillivirus species. This set of residues appears to determine host-virus specificity and may be useful for risk estimation for morbilliviruses. PMID:19027953

  1. 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”.

  2. 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.

  3. Algebraic models of flexible manufacturing systems

    NASA Astrophysics Data System (ADS)

    Leskin, Aleksei Alekseevich

    Various aspects of the use of mathematical methods in the development of flexible manufacturing systems are examined. Attention is given to dynamical and structural models of flexible manufacturing systems developed by using methods of algebraic and differential geometry, topology, polynomial algebra, and extreme value problem theory. The principles of model integration are discussed, and approaches are proposed for solving problems related to the selection of flexible manufacturing equipment, real-time modeling of the manufacturing process, and optimization of local automation systems. The discussion is illustrated by examples.

  4. 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

  5. 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.

  6. 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.

  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. An algebraic approach to the Hubbard model

    NASA Astrophysics Data System (ADS)

    de Leeuw, Marius; Regelskis, Vidas

    2016-02-01

    We study the algebraic structure of an integrable Hubbard-Shastry type lattice model associated with the centrally extended su (2 | 2) superalgebra. This superalgebra underlies Beisert's AdS/CFT worldsheet R-matrix and Shastry's R-matrix. The considered model specializes to the one-dimensional Hubbard model in a certain limit. We demonstrate that Yangian symmetries of the R-matrix specialize to the Yangian symmetry of the Hubbard model found by Korepin and Uglov. Moreover, we show that the Hubbard model Hamiltonian has an algebraic interpretation as the so-called secret symmetry. We also discuss Yangian symmetries of the A and B models introduced by Frolov and Quinn.

  9. 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

  10. 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. PMID:17431302

  11. Multi-Matrix Models and Noncommutative Frobenius Algebras Obtained from Symmetric Groups and Brauer Algebras

    NASA Astrophysics Data System (ADS)

    Kimura, Yusuke

    2015-07-01

    It has been understood that correlation functions of multi-trace operators in SYM can be neatly computed using the group algebra of symmetric groups or walled Brauer algebras. On the other hand, such algebras have been known to construct 2D topological field theories (TFTs). After reviewing the construction of 2D TFTs based on symmetric groups, we construct 2D TFTs based on walled Brauer algebras. In the construction, the introduction of a dual basis manifests a similarity between the two theories. We next construct a class of 2D field theories whose physical operators have the same symmetry as multi-trace operators constructed from some matrices. Such field theories correspond to non-commutative Frobenius algebras. A matrix structure arises as a consequence of the noncommutativity. Correlation functions of the Gaussian complex multi-matrix models can be translated into correlation functions of the two-dimensional field theories.

  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. Wave slamming on offshore structures

    NASA Astrophysics Data System (ADS)

    Miller, B. L.

    1980-03-01

    Experimental and theoretical work on the slamming of circular cylinders is surveyed. Data are included from controlled drop tests. The influence of inclined impact and beam dynamics on the resulting stresses is calculated for a wide range of wave conditions. The statistical distributions of the estimated stresses are analyzed to provide data for the calculation of slamming loads on fixed offshore structures using simple formulas in which the slamming coefficients incorporate both the member dynamics and the sea wave statistics. Slamming coefficients and associated stress calculation methods are presented for extreme values and fatigue damage. These may also be used for slamming during jacket launching. A film of wave slam was also produced.

  14. 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.

  15. 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.

  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. 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

  18. Prediction of Complex Aerodynamic Flows with Explicit Algebraic Stress Models

    NASA Technical Reports Server (NTRS)

    Abid, Ridha; Morrison, Joseph H.; Gatski, Thomas B.; Speziale, Charles G.

    1996-01-01

    An explicit algebraic stress equation, developed by Gatski and Speziale, is used in the framework of K-epsilon formulation to predict complex aerodynamic turbulent flows. The nonequilibrium effects are modeled through coefficients that depend nonlinearly on both rotational and irrotational strains. The proposed model was implemented in the ISAAC Navier-Stokes code. Comparisons with the experimental data are presented which clearly demonstrate that explicit algebraic stress models can predict the correct response to nonequilibrium flow.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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…

  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. The Effects of the Content Enhancement Model in College Algebra

    ERIC Educational Resources Information Center

    VanCleave, Janet Milleret

    2010-01-01

    The purpose of this study was to investigate The Content Enhancement Model in the field of college algebra in a mid-western community college. The Content Enhancement Model is a teaching technique that teachers use to help students acquire the content information by helping them identify, organize, comprehend, and memorize material. This study…

  6. 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.

  7. Cognitive Load and Modelling of an Algebra Problem

    ERIC Educational Resources Information Center

    Chinnappan, Mohan

    2010-01-01

    In the present study, I examine a modelling strategy as employed by a teacher in the context of an algebra lesson. The actions of this teacher suggest that a modelling approach will have a greater impact on enriching student learning if we do not lose sight of the need to manage associated cognitive loads that could either aid or hinder the…

  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. 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.

  10. 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.

  11. 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.

  12. Algebraic turbulence modeling for unstructured and adaptive meshes

    NASA Technical Reports Server (NTRS)

    Mavriplis, Dimitri J.

    1990-01-01

    An algebraic turbulence model based on the Baldwin-Lomax model, has been implemented for use on unstructured grids. The implementation is based on the use of local background structured turbulence meshes. At each time-step, flow variables are interpolated from the unstructured mesh onto the background structured meshes, the turbulence model is executed on these meshes, and the resulting eddy viscosity values are interpolated back to the unstructured mesh. Modifications to the algebraic model were required to enable the treatment of more complicated flows, such as confluent boundary layers and wakes. The model is used in conjuction with an efficient unstructured multigrid finite-element Navier-Stokes solver in order to compute compressible turbulent flows on fully unstructured meshes. Solutions about single and multiple element airfoils are obtained and compared with experimental data.

  13. 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

  14. Highest weight representation for Sklyanin algebra sl(3)(u) with application to the Gaudin model

    SciTech Connect

    Burdik, C.; Navratil, O.

    2011-06-15

    We study the infinite-dimensional Sklyanin algebra sl(3)(u). Specifically we construct the highest weight representation for this algebra in an explicit form. Its application to the Gaudin model is mentioned.

  15. Boundary algebras and Kac modules for logarithmic minimal models

    NASA Astrophysics Data System (ADS)

    Morin-Duchesne, Alexi; Rasmussen, Jørgen; Ridout, David

    2015-10-01

    Virasoro Kac modules were originally introduced indirectly as representations whose characters arise in the continuum scaling limits of certain transfer matrices in logarithmic minimal models, described using Temperley-Lieb algebras. The lattice transfer operators include seams on the boundary that use Wenzl-Jones projectors. If the projectors are singular, the original prescription is to select a subspace of the Temperley-Lieb modules on which the action of the transfer operators is non-singular. However, this prescription does not, in general, yield representations of the Temperley-Lieb algebras and the Virasoro Kac modules have remained largely unidentified. Here, we introduce the appropriate algebraic framework for the lattice analysis as a quotient of the one-boundary Temperley-Lieb algebra. The corresponding standard modules are introduced and examined using invariant bilinear forms and their Gram determinants. The structures of the Virasoro Kac modules are inferred from these results and are found to be given by finitely generated submodules of Feigin-Fuchs modules. Additional evidence for this identification is obtained by comparing the formalism of lattice fusion with the fusion rules of the Virasoro Kac modules. These are obtained, at the character level, in complete generality by applying a Verlinde-like formula and, at the module level, in many explicit examples by applying the Nahm-Gaberdiel-Kausch fusion algorithm.

  16. 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.

  17. Applications of algebraic image operators to model-based vision

    NASA Technical Reports Server (NTRS)

    Lerner, Bao-Ting; Morelli, Michael V.; Thomas, Hans J.

    1989-01-01

    A highly structured and compact algebraic representation of grey-level images is expanded. Addition and multiplication are defined for the set of all grey-level images, which can then be described as polynomials of two variables. Utilizing this new algebraic structure, an innovative, efficient edge-detection scheme is devised. A robust method for linear feature extraction is developed by combining the techniques of a Hough transform and a line follower with this new edge detection scheme. The major advantage of this feature extractor is its general, object-independent nature. Target attributes, such as line segment lengths, intersections, angles of intersection, and endpoints are derived by the feature extraction algorithm and employed during model matching. The feature extractor and model matcher are being incorporated into a distributed robot-control system.

  18. 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

  19. 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.

  20. Integrability in three dimensions: Algebraic Bethe ansatz for anyonic models

    NASA Astrophysics Data System (ADS)

    Khachatryan, Sh.; Ferraz, A.; Klümper, A.; Sedrakyan, A.

    2015-10-01

    We extend basic properties of two dimensional integrable models within the Algebraic Bethe Ansatz approach to 2 + 1 dimensions and formulate the sufficient conditions for the commutativity of transfer matrices of different spectral parameters, in analogy with Yang-Baxter or tetrahedron equations. The basic ingredient of our models is the R-matrix, which describes the scattering of a pair of particles over another pair of particles, the quark-anti-quark (meson) scattering on another quark-anti-quark state. We show that the Kitaev model belongs to this class of models and its R-matrix fulfills well-defined equations for integrability.

  1. 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.

  2. 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.

  3. 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.

  4. An algebraic turbulence model for turbomachinery

    NASA Astrophysics Data System (ADS)

    Chima, Rodrick V.

    This paper presents a description and verification of RVC3D (rotor viscous code 3-D) which provides a Euler or Navier-Stokes analysis for steady three dimensional flows in turbomachinery. A motivation for this analysis is the calculation of turbine endwall heat transfer. Features of the turbulence model code include thin-layer formulation, Baldwin-Lomax or Cebeci-Smith turbulence models, node-centered finite difference formulation, and explicit four-stage Runge-Kutta time marching scheme. Results for flat plate, annular turbine cascade, turbine endwall heat transfer, and supersonic compressor blade test cases are presented.

  5. 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…

  6. Automorphism groups of composition algebras and quark models

    SciTech Connect

    Bjerregard, P.A.; Gonzalez, C.M.

    1996-12-01

    In this the authors study the automorphisms and derivations of real composition algebras with a view to its physical interpretations. They obtain canonical forms with a special stress in the four and eight dimensional cases. Also, using this description, they work with two mathematical models which describe some particles with certain observables in a surprising way. A first model, split g{sub 2}, describes two observables for three quarks, their antiquarks, and eight mesons combining the quarks involved. A second one, so(4,4) {circle_plus} so(2,2), describes all the observables for all quarks (u, d, s, c, b and t).

  7. Applications Of Algebraic Image Operators To Model-Based Vision

    NASA Astrophysics Data System (ADS)

    Lerner, Bao-Ting; Morelli, Michael V.; Thomas, Hans J.

    1989-03-01

    This paper extends our previous research on a highly structured and compact algebraic representation of grey-level images. Addition and multiplication are defined for the set of all grey-level images, which can then be described as polynomials of two variables. Utilizing this new algebraic structure, we have devised an innovative, efficient edge detection scheme.We have developed a robust method for linear feature extraction by combining the techniques of a Hough transform and a line follower with this new edge detection scheme. The major advantage of this feature extractor is its general, object-independent nature. Target attributes, such as line segment lengths, intersections, angles of intersection, and endpoints are derived by the feature extraction algorithm and employed during model matching. The feature extractor and model matcher are being incorporated into a distributed robot control system. Model matching is accomplished using both top-down and bottom-up processing: a priori sensor and world model information are used to constrain the search of the image space for features, while extracted image information is used to update the model.

  8. 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.

  9. 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

  10. 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.

  11. 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.

  12. An Algebraic Spline Model of Molecular Surfaces for Energetic Computations

    PubMed Central

    Zhao, Wenqi; Bajaj, Chandrajit; Xu, Guoliang

    2009-01-01

    In this paper, we describe a new method to generate a smooth algebraic spline (AS) approximation of the molecular surface (MS) based on an initial coarse triangulation derived from the atomic coordinate information of the biomolecule, resident in the PDB (Protein data bank). Our method first constructs a triangular prism scaffold covering the PDB structure, and then generates a piecewise polynomial F on the Bernstein-Bezier (BB) basis within the scaffold. An ASMS model of the molecular surface is extracted as the zero contours of F which is nearly C1 and has dual implicit and parametric representations. The dual representations allow us easily do the point sampling on the ASMS model and apply it to the accurate estimation of the integrals involved in the electrostatic solvation energy computations. Meanwhile comparing with the trivial piecewise linear surface model, fewer number of sampling points are needed for the ASMS, which effectively reduces the complexity of the energy estimation. PMID:21519111

  13. A Structural Model of Algebra Achievement: Computational Fluency and Spatial Visualisation as Mediators of the Effect of Working Memory on Algebra Achievement

    ERIC Educational Resources Information Center

    Tolar, Tammy Daun; Lederberg, Amy R.; Fletcher, Jack M.

    2009-01-01

    The goal of this study was to develop and evaluate a structural model of the relations among cognitive abilities and arithmetic skills and college students' algebra achievement. The model of algebra achievement was compared to a model of performance on the Scholastic Assessment in Mathematics (SAT-M) to determine whether the pattern of relations…

  14. Measles virus replication in lymphatic cells and organs of CD150 (SLAM) transgenic mice

    PubMed Central

    Welstead, G. Grant; Iorio, Caterina; Draker, Ryan; Bayani, Jane; Squire, Jeremy; Vongpunsawad, Sompong; Cattaneo, Roberto; Richardson, Christopher D.

    2005-01-01

    A transgenic mouse containing the complete human SLAM (hSLAM/CD150) gene, including its endogenous promoter for transcription, was generated by using human genomic DNA cloned into a bacterial artificial chromosome. hSLAM, the primary receptor for measles viruses (MV), was expressed on activated B, T, and dendritic cells with an expression profile equivalent to that of humans. We demonstrated that hSLAM+ cells obtained from the transgenic mouse, including activated B, T, and dendritic cells, were susceptible to MV infection in a receptor-dependent manner. Evidence was provided for transient infection in the nasal lymph nodes of hSLAM+ mice after intranasal inoculation. Virus was rapidly cleared without signs of secondary replication. To improve the efficiency of MV production, the hSLAM+ mice were bred with mice having a Stat1-deficient background. These mice were more susceptible to MV infection and produced more virus particles. After intranasal and intraperitoneal inoculation of these mice with MV, infections of the thymus, spleen, nasal, mesenteric, and leg lymph nodes were detected. Upon necropsy, enlarged lymph nodes and spleen were apparent. Flow cytometric analysis showed that abnormally large numbers of mature neutrophils and natural killer cells caused the splenomegaly. The hSLAM transgenic mouse constitutes an improved rodent model for studying the interaction of MV with immune cells that more accurately reflects the infection pattern found in humans. PMID:16260741

  15. Phases and phase transitions in the algebraic microscopic shell model

    NASA Astrophysics Data System (ADS)

    Georgieva, A. I.; Drumev, K. P.

    2016-01-01

    We explore the dynamical symmetries of the shell model number conserving algebra, which define three types of pairing and quadrupole phases, with the aim to obtain the prevailing phase or phase transition for the real nuclear systems in a single shell. This is achieved by establishing a correspondence between each of the pairing bases with the Elliott's SU(3) basis that describes collective rotation of nuclear systems. This allows for a complete classification of the basis states of different number of particles in all the limiting cases. The probability distribution of the SU(3) basis states within theirs corresponding pairing states is also obtained. The relative strengths of dynamically symmetric quadrupole-quadrupole interaction in respect to the isoscalar, isovector and total pairing interactions define a control parameter, which estimates the importance of each term of the Hamiltonian in the correct reproduction of the experimental data for the considered nuclei.

  16. 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.

  17. 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…

  18. Instant outdoor localization and SLAM initialization from 2.5D maps.

    PubMed

    Arth, Clemens; Pirchheim, Christian; Ventura, Jonathan; Schmalstieg, Dieter; Lepetit, Vincent

    2015-11-01

    We present a method for large-scale geo-localization and global tracking of mobile devices in urban outdoor environments. In contrast to existing methods, we instantaneously initialize and globally register a SLAM map by localizing the first keyframe with respect to widely available untextured 2.5D maps. Given a single image frame and a coarse sensor pose prior, our localization method estimates the absolute camera orientation from straight line segments and the translation by aligning the city map model with a semantic segmentation of the image. We use the resulting 6DOF pose, together with information inferred from the city map model, to reliably initialize and extend a 3D SLAM map in a global coordinate system, applying a model-supported SLAM mapping approach. We show the robustness and accuracy of our localization approach on a challenging dataset, and demonstrate unconstrained global SLAM mapping and tracking of arbitrary camera motion on several sequences. PMID:26340773

  19. WOCSS as a preprocessor for SLAM

    SciTech Connect

    Kienzle, M.A.; Seely, S.L.

    1996-12-31

    The modeling of pollutant transport using simple Gaussian diffusion gives reasonably reliable results in environments with uniform terrain and steady winds. A less ideal environment surrounds the Idaho National Engineering Laboratory (INE), the site of the short-range Airborne Chemical Effluent Experiment (ACE III) experiment (source-to-sampler distance of 150 km or less). The release point was situated near the center of a valley with small canyons and mountainous terrain to the north. More complex wind patterns such as up- or down-valley flow and flow through complex terrain may cause simpler Gaussian models to produce unreliable results. In an effort to obtain improved atmospheric transport, wind fields input to the SLAM model (Short-Range Layered Atmospheric Model) were pre-processed using WOCSS. WOCSS (Winds On Critical Streamline Surfaces) produces a three-dimensional mass-consistent wind field to more accurately depict the local flows.

  20. 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.

  1. Clifford algebra-based spatio-temporal modelling and analysis for complex geo-simulation data

    NASA Astrophysics Data System (ADS)

    Luo, Wen; Yu, Zhaoyuan; Hu, Yong; Yuan, Linwang

    2013-10-01

    The spatio-temporal data simulating Ice-Land-Ocean interaction of Antarctic are used to demonstrate the Clifford algebra-based data model construction, spatio-temporal query and data analysis. The results suggest that Clifford algebra provides a powerful mathematical tool for the whole modelling and analysis chains for complex geo-simulation data. It can also help implement spatio-temporal analysis algorithms more clearly and simply.

  2. Algebraic multigrid preconditioner for the cardiac bidomain model.

    PubMed

    Plank, Gernot; Liebmann, Manfred; Weber dos Santos, Rodrigo; Vigmond, Edward J; Haase, Gundolf

    2007-04-01

    The bidomain equations are considered to be one of the most complete descriptions of the electrical activity in cardiac tissue, but large scale simulations, as resulting from discretization of an entire heart, remain a computational challenge due to the elliptic portion of the problem, the part associated with solving the extracellular potential. In such cases, the use of iterative solvers and parallel computing environments are mandatory to make parameter studies feasible. The preconditioned conjugate gradient (PCG) method is a standard choice for this problem. Although robust, its efficiency greatly depends on the choice of preconditioner. On structured grids, it has been demonstrated that a geometric multigrid preconditioner performs significantly better than an incomplete LU (ILU) preconditioner. However, unstructured grids are often preferred to better represent organ boundaries and allow for coarser discretization in the bath far from cardiac surfaces. Under these circumstances, algebraic multigrid (AMG) methods are advantageous since they compute coarser levels directly from the system matrix itself, thus avoiding the complexity of explicitly generating coarser, geometric grids. In this paper, the performance of an AMG preconditioner (BoomerAMG) is compared with that of the standard ILU preconditioner and a direct solver. BoomerAMG is used in two different ways, as a preconditioner and as a standalone solver. Two 3-D simulation examples modeling the induction of arrhythmias in rabbit ventricles were used to measure performance in both sequential and parallel simulations. It is shown that the AMG preconditioner is very well suited for the solution of the bidomain equation, being clearly superior to ILU preconditioning in all regards, with speedups by factors in the range 5.9-7.7. PMID:17405366

  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. Symmetric structure of field algebra of G-spin models determined by a normal subgroup

    SciTech Connect

    Xin, Qiaoling Jiang, Lining

    2014-09-15

    Let G be a finite group and H a normal subgroup. D(H; G) is the crossed product of C(H) and CG which is only a subalgebra of D(G), the double algebra of G. One can construct a C*-subalgebra F{sub H} of the field algebra F of G-spin models, so that F{sub H} is a D(H; G)-module algebra, whereas F is not. Then the observable algebra A{sub (H,G)} is obtained as the D(H; G)-invariant subalgebra of F{sub H}, and there exists a unique C*-representation of D(H; G) such that D(H; G) and A{sub (H,G)} are commutants with each other.

  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. 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.

  8. Performance of Renormalization Group Algebraic Turbulence Model on Boundary Layer Transition Simulation

    NASA Technical Reports Server (NTRS)

    Ahn, Kyung H.

    1994-01-01

    The RNG-based algebraic turbulence model, with a new method of solving the cubic equation and applying new length scales, is introduced. An analysis is made of the RNG length scale which was previously reported and the resulting eddy viscosity is compared with those from other algebraic turbulence models. Subsequently, a new length scale is introduced which actually uses the two previous RNG length scales in a systematic way to improve the model performance. The performance of the present RNG model is demonstrated by simulating the boundary layer flow over a flat plate and the flow over an airfoil.

  9. 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

  10. 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

  11. 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.

  12. A Galilean Invariant Explicit Algebraic Reynolds Stress Model for Curved Flows

    NASA Technical Reports Server (NTRS)

    Girimaji, Sharath

    1996-01-01

    A Galilean invariant weak-equilbrium hypothesis that is sensitive to streamline curvature is proposed. The hypothesis leads to an algebraic Reynolds stress model for curved flows that is fully explicit and self-consistent. The model is tested in curved homogeneous shear flow: the agreement is excellent with Reynolds stress closure model and adequate with available experimental data.

  13. 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…

  14. 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

  15. 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.

  16. Slam!

    NASA Technical Reports Server (NTRS)

    2006-01-01

    2 August 2006 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows an impact crater on the martian northern plains. This crater is roughly the size of the famous Meteor Crater in Arizona on the North American continent.

    Location near: 43.0oN, 231.7oW Image width: 3 km (1.9 mi) Illumination from: lower left Season: Northern Spring

  17. EPQ Models under Permissible Payment Delay: An Algebraic Approach

    NASA Astrophysics Data System (ADS)

    Huang, Yung-Fu; Hsu, Kuang-Hua

    The purpose of this research is to relax this assumption and establish the retailer`s inventory system as a cost minimization problem to determine the retailer`s optimal inventory cycle time. Then, an algebraic approach is provided and an easy-to-use theorem is derived to efficiently determine the optimal cycle time. From the final numerical examples, result implies that the retailer will order less quantity to take the benefits of the permissible delay in payments more frequently when the larger the differences between the unit selling price per item and the unit purchasing price per item.

  18. q-Deformation of symplectic dynamical symmetries in algebraic models of nuclear structure

    SciTech Connect

    Georgieva, A. I.; Sviratcheva, K. D.; Ivanov, M. I.; Draayer, J. P.

    2011-06-15

    With a view toward further nuclear structure applications of approaches based on quantum-deformed (or q-deformed) algebras, introduced to the authors by Yu.F. Smirnov, we construct a q analog of a boson realization of the symplectic noncompact sp(4, R) algebra together with a q analog of a fermion realization of the symplectic compact sp(4) algebra. The first study, on the q-deformed Sp(4,R) symmetry, is applied to the development of a q analog of the two-dimensional Interacting Boson Model with q-deformed SU(3) the underpinning dynamical symmetry group. An explicit realization in terms of q-tensor operators with respect to the standard su{sub q}(2) algebra is given. The group-subgroup structure of this framework yields the physical interpretation of the generators of the groups under consideration. The second symplectic algebra, the q-deformed sp(4), is applied to studying isovector pairing correlations in atomic nuclei. A specific q deformation of the sp(4) algebra is realized in terms of q deformed fermion creation and annihilation operators of the shell model. The generators of the algebra close on four distinct realizations of the u{sub q}(2) subalgebra. These reductions, which correspond to different types of pairing interactions, yield a complete classification of the basis states. An analysis of the role of the q deformation is based on a comparison of the results for energies of the lowest isovector-paired 0{sup +} states in the deformed and nondeformed cases.

  19. 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

  20. 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

  1. The Model Method: Singapore Children's Tool for Representing and Solving Algebraic Word Problems

    ERIC Educational Resources Information Center

    Ng, Swee Fong; Lee, Kerry

    2009-01-01

    Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…

  2. Development of an algebraic turbulence model for analysis of propulsion flows

    NASA Technical Reports Server (NTRS)

    Georgiadis, N. J.; Drummond, J. E.; Leonard, B. P.

    1992-01-01

    A simple turbulence model that will be applicable to propulsion flows having both wall bounded and unbounded regions was developed and installed within the PARC Navier-Stokes code by linking two existing algebraic turbulence models. The first is the Modified Mixing Length (MML) model which is optimized for wall bounded flows. The second is the Thomas model, the standard algebraic turbulence model in PARC which has been used to calculate both bounded and unbounded turbulent flows but was optimized for the latter. This paper discusses both models and the method employed to link them into one model (referred to as the MMLT model). The PARC code with the MMLT model was applied to two dimensional turbulent flows over a flat plate and over a backward facing step to validate and optimize the model and to compare its predictions to those obtained with the three turbulence models already available in PARC.

  3. 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

  4. Constructing and Modeling Algebraic Statements in the Multiplicative Domain: Investigating Fourth-Grade Student and Teacher Learning

    ERIC Educational Resources Information Center

    Grandau, Laura

    2013-01-01

    This study of fourth-grade students and teachers explores mathematics teaching and learning that focuses on discovering and modeling algebraic relationships. The study has two parts: an investigation of how students learn to construct algebraic statements and models for comparisons and measurement situations in the multiplicative domain, and an…

  5. 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.

  6. Hyperbolic Kac-Moody algebras and chaos in Kaluza-Klein models

    NASA Astrophysics Data System (ADS)

    Damour, T.; Henneaux, M.; Julia, B.; Nicolai, H.

    2001-06-01

    Some time ago, it was found that the never-ending oscillatory chaotic behaviour discovered by Belinskii, Khalatnikov and Lifshitz (BKL) for the generic solution of the vacuum Einstein equations in the vicinity of a spacelike (``cosmological'') singularity disappears in spacetime dimensions /D≡d+1>10. Recently, a study of the generalization of the BKL chaotic behaviour to the superstring effective Lagrangians has revealed that this chaos is rooted in the structure of the fundamental Weyl chamber of some underlying hyperbolic Kac-Moody algebra. In this Letter we show that the same connection applies to pure gravity in any spacetime dimension />=4, where the relevant algebras are AEd. In this way the disappearance of chaos in pure gravity models in /D>=11 dimensions becomes linked to the fact that the Kac-Moody algebras AEd are no longer hyperbolic for /d>=10.

  7. 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.

  8. 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.

  9. The Application of Boolean Algebra in Modelling of Leakage Condition of a Car Hydraulic Braking System

    NASA Astrophysics Data System (ADS)

    Idzikowski, A.; Salamon, S.

    2013-06-01

    A general characteristics of a car hydraulic braking system (CHBS) is presented in this publication. A graphical model of properties-component objects is developed for the above-mentioned system. Moreover, four mathematical models in terms of logic, the set theory and the Boolean algebra of Boolean functions are developed. The examination is ended with a general model of the CHBS for n - Boolean variables and the construction and mathematical-technical interpretation of this model is presented.

  10. 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.

  11. The algebraic Bethe ansatz for scalar products in SU(3)-invariant integrable models

    NASA Astrophysics Data System (ADS)

    Belliard, S.; Pakuliak, S.; Ragoucy, E.; Slavnov, N. A.

    2012-10-01

    We study SU(3)-invariant integrable models solvable by a nested algebraic Bethe ansatz. We obtain a determinant representation for the particular case of scalar products of Bethe vectors. This representation can be used for the calculation of form factors and correlation functions of the XXX SU(3)-invariant Heisenberg chain.

  12. 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…

  13. 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.

  14. 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.

  15. 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…

  16. 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.

  17. 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.

  18. Interplay between the pairing and quadrupole interactions in the algebraic realization of the microscopic shell model

    NASA Astrophysics Data System (ADS)

    Drumev, Kalin; Georgieva, Ana

    2015-04-01

    We explore the algebraic realization of the Pairing-Plus-Quadrupole Model/PQM/ in the framework of the Elliott‘s SU(3) Model with the aim to obtain the complementary and competing features of the two interactions through the relation between the pairing and the SU(3) bases. First, we establish a correspondence between the SO(8) pairing basis and the Elliott's SU(3) basis. It is derived from their complementarity to the same LST coupling chain of the shell-model number-conserving algebra. The probability distribution of the SU(3) basis states within the SO(8) pairing states is also obtained and allows the investigation of the interplay between the pairing and quadrupole interactions in the Hamiltonian of the PQM, containing both of them as limiting cases. The description of some realistic N∼Z nuclear systems is investigated in a SU(3)-symmetry-adapted basis within a model space of one and two oscillator shells.

  19. 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)

  20. 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

  1. 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.

  2. 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.

  3. 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

  4. Constraint algebra of general relativity from a formal continuum limit of canonical tensor model

    NASA Astrophysics Data System (ADS)

    Sasakura, Naoki; Sato, Yuki

    2015-10-01

    Canonical tensor model (CTM for short below) is a rank-three tensor model formulated as a totally constrained system in the canonical formalism. In the classical case, the constraints form a first-class constraint Poisson algebra with structures similar to that of the ADM formalism of general relativity, qualifying CTM as a possible discrete formalism for quantum gravity. In this paper, we show that, in a formal continuum limit, the constraint Poisson algebra of CTM with no cosmological constant exactly reproduces that of the ADM formalism. To this end, we obtain the expression of the metric tensor field in general relativity in terms of one of the dynamical rank-three tensors in CTM, and determine the correspondence between the constraints of CTM and those of the ADM formalism. On the other hand, the cosmological constant term of CTM seems to induce non-local dynamics, and is inconsistent with an assumption about locality of the continuum limit.

  5. 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].

  6. 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.

  7. Modeling scalar dissipation and scalar variance in large eddy simulation: Algebraic and transport equation closures

    NASA Astrophysics Data System (ADS)

    Knudsen, E.; Richardson, E. S.; Doran, E. M.; Pitsch, H.; Chen, J. H.

    2012-05-01

    Scalar dissipation rates and subfilter scalar variances are important modeling parameters in large eddy simulations (LES) of reacting flows. Currently available models capture the general behavior of these parameters, but these models do not always perform with the degree of accuracy that is needed for predictive LES. Here, two direct numerical simulations (DNS) are used to analyze LES dissipation rate and variance models, and to propose a new model for the dissipation rate that is based on a transport equation. The first DNS that is considered is a non-premixed auto-igniting C2H4 jet flame simulation originally performed by Yoo et al. [Proc. Combust. Inst. 33, 1619-1627 (2011)], 10.1016/j.proci.2010.06.147. A LES of this case is run using algebraic models for the dissipation rate and subfilter variance. It is shown that the algebraic models fail to adequately reproduce the DNS results. This motivates the introduction of a transport equation model for the LES dissipation rate. Closure of the equation is addressed by formulating a new adapted dynamic approach. This approach borrows dynamically computed information from LES quantities that, unlike the dissipation rate, do not reside on the smallest flow length scales. The adapted dynamic approach is analyzed by considering a second DNS of scalar mixing in homogeneous isotropic turbulence. Data from this second DNS are used to confirm that the adapted dynamic approach successfully closes the dissipation rate equation over a wide range of LES filter widths. The first reacting jet case is then returned to and used to test the LES transport equation models. The transport equation model for the dissipation rate is shown to be more accurate than its algebraic counterpoint, and the dissipation rate is eliminated as a source of error in the transported variance model.

  8. 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.

  9. 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

  10. 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…

  11. The addition of algebraic turbulence modeling to program LAURA

    NASA Technical Reports Server (NTRS)

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

    1993-01-01

    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.

  12. 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.

  13. Real-time RGBD SLAM system

    NASA Astrophysics Data System (ADS)

    Czupryński, BłaŻej; Strupczewski, Adam

    2015-09-01

    A real-time tracking and mapping SLAM system is presented. The developed system uses input from an RGBD sensor and tracks the camera pose from frame to frame. The tracking is based on matched feature points and is performed with respect to selected keyframes. The system is robust and scalable, as an arbitrary number of keyframes can be chosen for visualization and tracking depending on the desired accuracy and speed. The presented system is also a good platform for further research.

  14. Extensions of algebraic image operators: An approach to model-based vision

    NASA Technical Reports Server (NTRS)

    Lerner, Bao-Ting; Morelli, Michael V.

    1990-01-01

    Researchers extend their previous research on a highly structured and compact algebraic representation of grey-level images which can be viewed as fuzzy sets. Addition and multiplication are defined for the set of all grey-level images, which can then be described as polynomials of two variables. Utilizing this new algebraic structure, researchers devised an innovative, efficient edge detection scheme. An accurate method for deriving gradient component information from this edge detector is presented. Based upon this new edge detection system researchers developed a robust method for linear feature extraction by combining the techniques of a Hough transform and a line follower. The major advantage of this feature extractor is its general, object-independent nature. Target attributes, such as line segment lengths, intersections, angles of intersection, and endpoints are derived by the feature extraction algorithm and employed during model matching. The algebraic operators are global operations which are easily reconfigured to operate on any size or shape region. This provides a natural platform from which to pursue dynamic scene analysis. A method for optimizing the linear feature extractor which capitalizes on the spatially reconfiguration nature of the edge detector/gradient component operator is discussed.

  15. Algebraic Construction of the Eigenstates for the Second Conserved Operator of the Quantum Calogero Model

    NASA Astrophysics Data System (ADS)

    Ujino, Hideaki; Wadati, Miki

    1996-03-01

    An algebraic construction of the eigenstates for the quantum Calogero modelis investigated. Extending the method of Lapointe and Vinet, weconstruct the eigenstates for the second conservedoperator of the quantum Calogero model.All the eigenstates can be factorizedinto symmetric polynomials which we call “Hi-Jack symmetric polynomials”and the ground state wave function.The conjectured formula for the eigenvalue of the second conserved operatoris confirmed.The Hi-Jack polynomials are strong candidates for the orthogonalbasis of the quantum Calogero model.

  16. 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.

  17. 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.

  18. Modeling boyciana-fish-human interaction with partial differential algebraic equations.

    PubMed

    Jiang, Yushan; Zhang, Qingling; Wang, Haiyan

    2016-07-01

    Under the influence of human population distribution, the boyciana-fish ecological system is considered. First, the system can be described as a nonlinear partial differential algebraic equations system (PDAEs) with Neumann boundary conditions and ratio-dependent functional response. Second, we examine the system's persistence properties: the loacl stabilities of positive steady states, the absorbtion region and the global stability. And the proposed approach is illustrated by numerical simulation. Finally, by using the realistic data collected in the past fourteen years, the PDAEs parameter optimization model is built to predict the boyciana population. PMID:27155570

  19. Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions

    NASA Astrophysics Data System (ADS)

    Lavau, Sylvain; Samtleben, Henning; Strobl, Thomas

    2014-12-01

    We disclose the mathematical structure underlying the gauge field sector of the recently constructed non-abelian superconformal models in six space-time dimensions. This is a coupled system of 1-form, 2-form, and 3-form gauge fields. We show that the algebraic consistency constraints governing this system permit to define a Lie 3-algebra, generalizing the structural Lie algebra of a standard Yang-Mills theory to the setting of a higher bundle. Reformulating the Lie 3-algebra in terms of a nilpotent degree 1 BRST-type operator Q, this higher bundle can be compactly described by means of a Q-bundle; its fiber is the shifted tangent of the Q-manifold corresponding to the Lie 3-algebra and its base the odd tangent bundle of space-time equipped with the de Rham differential. The generalized Bianchi identities can then be retrieved concisely from Q2 = 0, which encode all the essence of the structural identities. Gauge transformations are identified as vertical inner automorphisms of such a bundle, their algebra being determined from a Q-derived bracket.

  20. 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.

  1. 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.

  2. Computation of turbulent rotating channel flow with an algebraic Reynolds stress model

    NASA Technical Reports Server (NTRS)

    Warfield, M. J.; Lakshminarayana, B.

    1986-01-01

    An Algebraic Reynolds Stress Model has been implemented to modify the Kolmogorov-Prandtl eddy viscosity relation to produce an anisotropic turbulence model. The eddy viscosity relation becomes a function of the local turbulent production to dissipation ratio and local turbulence/rotation parameters. The model is used to predict fully-developed rotating channel flow over a diverse range of rotation numbers. In addition, predictions are obtained for a developing channel flow with high rotation. The predictions are compared with the experimental data available. Good predictions are achieved for mean velocity and wall shear stress over most of the rotation speeds tested. There is some prediction breakdown at high rotation (rotation number greater than .10) where the effects of the rotation on turbulence become quite complex. At high rotation and low Reynolds number, the laminarization on the trailing side represents a complex effect of rotation which is difficult to predict with the described models.

  3. 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.

  4. 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.

  5. 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

  6. Early Childhood Teachers' Professional Learning in Early Algebraic Thinking: A Model that Supports New Knowledge and Pedagogy

    ERIC Educational Resources Information Center

    Warren, Elizabeth

    2009-01-01

    The implementation of a new mathematics syllabus in the elementary context is problematic, especially if it contains a new content area. A professional development model, Transformative Teaching in the Early Years Mathematics (TTEYM) was specifically developed to support the implementation of the new Patterns and Algebra strand. The model was…

  7. 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…

  8. 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

  9. Performance of a parallel algebraic multilevel preconditioner for stabilized finite element semiconductor device modeling

    SciTech Connect

    Lin, Paul T. Shadid, John N.; Sala, Marzio; Tuminaro, Raymond S.; Hennigan, Gary L.; Hoekstra, Robert J.

    2009-09-20

    In this study results are presented for the large-scale parallel performance of an algebraic multilevel preconditioner for solution of the drift-diffusion model for semiconductor devices. The preconditioner is the key numerical procedure determining the robustness, efficiency and scalability of the fully-coupled Newton-Krylov based, nonlinear solution method that is employed for this system of equations. The coupled system is comprised of a source term dominated Poisson equation for the electric potential, and two convection-diffusion-reaction type equations for the electron and hole concentration. The governing PDEs are discretized in space by a stabilized finite element method. Solution of the discrete system is obtained through a fully-implicit time integrator, a fully-coupled Newton-based nonlinear solver, and a restarted GMRES Krylov linear system solver. The algebraic multilevel preconditioner is based on an aggressive coarsening graph partitioning of the nonzero block structure of the Jacobian matrix. Representative performance results are presented for various choices of multigrid V-cycles and W-cycles and parameter variations for smoothers based on incomplete factorizations. Parallel scalability results are presented for solution of up to 10{sup 8} unknowns on 4096 processors of a Cray XT3/4 and an IBM POWER eServer system.

  10. Performance of a parallel algebraic multilevel preconditioner for stabilized finite element semiconductor device modeling

    NASA Astrophysics Data System (ADS)

    Lin, Paul T.; Shadid, John N.; Sala, Marzio; Tuminaro, Raymond S.; Hennigan, Gary L.; Hoekstra, Robert J.

    2009-09-01

    In this study results are presented for the large-scale parallel performance of an algebraic multilevel preconditioner for solution of the drift-diffusion model for semiconductor devices. The preconditioner is the key numerical procedure determining the robustness, efficiency and scalability of the fully-coupled Newton-Krylov based, nonlinear solution method that is employed for this system of equations. The coupled system is comprised of a source term dominated Poisson equation for the electric potential, and two convection-diffusion-reaction type equations for the electron and hole concentration. The governing PDEs are discretized in space by a stabilized finite element method. Solution of the discrete system is obtained through a fully-implicit time integrator, a fully-coupled Newton-based nonlinear solver, and a restarted GMRES Krylov linear system solver. The algebraic multilevel preconditioner is based on an aggressive coarsening graph partitioning of the nonzero block structure of the Jacobian matrix. Representative performance results are presented for various choices of multigrid V-cycles and W-cycles and parameter variations for smoothers based on incomplete factorizations. Parallel scalability results are presented for solution of up to 108 unknowns on 4096 processors of a Cray XT3/4 and an IBM POWER eServer system.

  11. 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.

  12. Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model

    NASA Astrophysics Data System (ADS)

    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.

  13. 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.

  14. Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model

    SciTech Connect

    Chamseddine, Ali H.; Connes, Alain

    2007-11-09

    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.

  15. SLAM family receptors and the SLAM-associated protein (SAP) modulate T cell functions

    PubMed Central

    Keszei, Marton; Romero, Xavier; Tsokos, George C.

    2010-01-01

    One or more of the signaling lymphocytic activation molecule (SLAM) family (SLAMF) of cell surface receptors, which consists of nine transmembrane proteins, i.e., SLAMF1-9, are expressed on most hematopoietic cells. While most SLAMF receptors serve as self-ligands, SLAMF2 and SLAMF4 use each other as counter structures. Six of the receptors carry one or more copies of a unique intracellular tyrosine-based switch motif, which has high affinity for the single SH2-domain signaling molecules SLAM-associated protein and EAT-2. Whereas SLAMF receptors are costimulatory molecules on the surface of CD4+, CD8+, and natural killer (NK) T cells, they also involved in early phases of lineage commitment during hematopoiesis. SLAMF receptors regulate T lymphocyte development and function and modulate lytic activity, cytokine production, and major histocompatibility complex-independent cell inhibition of NK cells. Furthermore, they modulate B cell activation and memory generation, neutrophil, dendritic cell, macrophage and eosinophil function, and platelet aggregation. In this review, we will discuss the role of SLAM receptors and their adapters in Tcell function, and we will examine the role of these receptors and their adapters in X-linked lymphoproliferative disease and their contribution to disease susceptibility in systemic lupus erythematosus. PMID:20146065

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. The Competent Use of the Analytic Method in the Solution of Algebraic Word Problems: A Didactical Model Based on a Numerical Approach with Junior High Students

    ERIC Educational Resources Information Center

    Rubio, Guillermo; del Valle, Rafael

    2004-01-01

    The study proves that a didactical model based in a method to solve word problems of increasing complexity which uses a numerical approach was essential to develop the analytical ability and the competent use of the algebraic language with students from three different performance levels in elementary algebra. It is shown that before using the…

  1. Elliptic-blending second-moment turbulence closure using an algebraic anisotropic dissipation rate tensor model

    NASA Astrophysics Data System (ADS)

    Shin, Jong-Keun; Seo, Jeong-Sik; Choi, Young-Don

    2009-06-01

    This study describes the amendment of an algebraic anisotropic dissipation rate model (ADRM) and its application to various turbulent flows to test the model's performance. Modeling anisotropies for the turbulence dissipation rate is considered by an analysis of the exact transport equation for the dissipation rate tensor. The second-moment closure, which is based on the explicit amended ADRM, is proposed and it is closely linked to the elliptic-blending model that is used for the prediction of Reynolds stresses. To develop and calibrate the present elliptic-blending second-moment closure that uses the amended ADRM, firstly, the distributions of both the mean velocity and Reynolds stress are solved for flows in a fully developed non-rotating channel and a straight square duct. And then, the fully developed turbulent flows in a rotating channel and a rotating straight square duct are predicted to test the ability of the explicit amended ADRM that is combined with the rotation effect. The prediction results are directly compared with the DNS and the large-eddy simulation (LES) to assess the performance of the new model predictions and to show their reasonable agreement with the DNS and LES data for all the flow fields that are analyzed for the present study. This paper is a modified version of the original article from the Proceedings of the 5th International Symposium on Turbulence and Shear Flow Phenomena held in Munich, Germany on 27-29 August 2007.

  2. Virasoro algebra in the KN algebra; Bosonic string with fermionic ghosts on Riemann surfaces

    SciTech Connect

    Koibuchi, H. )

    1991-10-10

    In this paper the bosonic string model with fermionic ghosts is considered in the framework of the KN algebra. The authors' attentions are paid to representations of KN algebra and a Clifford algebra of the ghosts. The authors show that a Virasoro-like algebra is obtained from KN algebra when KN algebra has certain antilinear anti-involution, and that it is isomorphic to the usual Virasoro algebra. The authors show that there is an expected relation between a central charge of this Virasoro-like algebra and an anomaly of the combined system.

  3. 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

  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. 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…

  6. 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.…

  7. 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.

  8. Coherent States and Schwinger Models for Pseudo Generalization of the Heisenberg Algebra

    NASA Astrophysics Data System (ADS)

    Fakhri, H.; Mojaveri, B.; Dehghani, A.

    We show that the non-Hermitian Hamiltonians of the simple harmonic oscillator with {PT} and {C} symmetries involve a pseudo generalization of the Heisenberg algebra via two pairs of creation and annihilation operators which are {T}-pseudo-Hermiticity and {P}-anti-pseudo-Hermiticity of each other. The non-unitary Heisenberg algebra is represented by each of the pair of the operators in two different ways. Consequently, the coherent and the squeezed coherent states are calculated in two different approaches. Moreover, it is shown that the approach of Schwinger to construct the su(2), su(1, 1) and sp(4, ℝ) unitary algebras is promoted so that unitary algebras with more linearly dependent number of generators are made.

  9. Slam: Hip-Hop Meets Poetry--A Strategy for Violence Intervention.

    ERIC Educational Resources Information Center

    Bruce, Heather E.; Davis, Bryan Dexter

    2000-01-01

    Describes one strategy used in high school English classrooms to teach for peace and dislodge violence: the poetry slam, a burgeoning pop culture phenomenon that combines poetry and performance art. Describes poetry slams that incorporate hip-hop culture. Discusses promoting slams in English classrooms to show students the power of words and…

  10. Image Sensor Model Using Geometric Algebra: From Calibration to Motion Estimation

    NASA Astrophysics Data System (ADS)

    Debaecker, Thibaud; Benosman, Ryad; Ieng, Sio H.

    In computer vision image sensors have universally been defined as the nonparametric association of projection rays in the 3D world to pixels in the images. If the pixels' physical topology can be often neglected in the case of perspective cameras, this approximation is no longer valid in the case of variant scale sensors, which are now widely used in robotics. Neglecting the nonnull pixel area and then the pixel volumic field of view implies that geometric reconstruction problems are solved by minimizing a cost function that combines the reprojection errors in the 2D images. This paper provides a complete and realistic cone-pixel camera model that equally fits constant or variant scale resolution together with a protocol to calibrate such a sensor. The proposed model involves a new characterization of pixel correspondences with 3D-cone intersections computed using convex hull and twists in Conformal Geometric Algebra. Simulated experiments show that standard methods and especially Bundle Adjustment are sometimes unable to reach the correct motion, because of their ray-pixel approach and the choice of reprojection error as a cost function which does not particularly fit the physical reality. This problem can be solved using a nonprojective cone intersection cost function as introduced below.

  11. 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.

  12. SLAM, the development of an EO Service to support the legal obligations of Swiss and Italian Geological Risk Services in landslide risk forecasting and prevention.

    NASA Astrophysics Data System (ADS)

    Paganini, M.; Palazzo, F.; Manunta, P.; Ferretti, A.; Gontier, E.; Wunderle, S.; Pasquali, P.; van Westen, C.; Strozzi, T.; Zilger, J.

    2003-04-01

    The numerous of hydro-geological disastrous events that have occurred recently in Switzerland and in Italy have increased the awareness of the risk factors for the population exposed and gave rise to a strong and responsible political action. In particular the necessity to produce landslide hazard maps has been considered of paramount importance by all stakeholders as well as the importance to monitor slope movement with regularly updated activity maps. The combination of state of the art Remote Sensing observations and Geographical Information System (GIS) modeling has proven to be a promising technique that can significantly contribute to the mitigation of Landslide Hazards. There is however a general consensus that additional demonstration projects are still needed before the development of an operational hazard and risk monitoring system with reliable, accurate and up-to-date EO observation data can be considered. The European Space Agency has started the SLAM (Service for Landslide Monitoring) initiative in 2001 under the framework of its Data User Programme (DUP) to develop an EO Service that could support the forecasting and prevention activities of Italian and Swiss Geological Risk Services involved in Landslide Risk mitigations. The SLAM Initiative has been conceived by the European Space Agency along 3 consecutive sets of activities: 1. a SLAM Service Feasibility study with the objective to critically review and assess the possibility to use Remote Sensing technologies within Landslide monitoring and risk assessment in a reliable and cost-effective manner. 2. Some SLAM Service Definition projects with the objective to carry out, with the close collaboration of user organizations, all preliminary tasks that would build the foundation for the implementation of a wide scale SLAM information service. This implied principally the identification and engagement of user organizations based on their statutory duties, and the definition and specification of SLAM

  13. 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.

  14. 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.

  15. 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. PMID:23701896

  16. 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.

  17. A Comparison of Explicit Algebraic Turbulence Models and the Energy-Flux Budget (EFB) Closure in Gabls

    NASA Astrophysics Data System (ADS)

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

    2014-12-01

    Turbulent flows with buoyancy effects occur in many situations, both in industry and in the atmosphere. It is challenging to correctly model such flows, especially in the case of stably stratified turbulence, where vertical motions are damped by buoyancy forces. For this purpose, we have derived a so-called explicit algebraic model for the Reynolds stresses and turbulent heat flux that gives accurate predictions in flows with buoyancy effects. Although inspired by turbulence models from engineering, the main aim of our work is to improve the parametrization of turbulence in the atmospheric boundary layer (ABL). Explicit algebraic turbulence models are a class of parametrizations that, on the one hand, are more advanced than standard eddy-diffusivity relations. On the other hand, they are signficantly easier to handle numerically than models that require the solution of the full flux-budget equations. To derive the algebraic model, we apply the assumption that transport terms of dimensionless fluxes can be neglected. Careful considerations of the algebra lead to a consistent formulation of the Reynolds stresses and turbulent heat flux, which is more general and robust than previous models of a similar kind. The model is shown to give good results compared to direct numerical simulations of engineering test cases, such as turbulent channel flow. Recent work has been aimed at testing the model in an atmospheric context. The first of these tests makes use of the GABLS1 case, in which a stable atmospheric boundary layer develops through a constant surface cooling rate. The model is able to give good predictions of this case compared to LES (see attached figure). Interestingly, the results are very close to the outcome of the recently developed Energy-Flux-Budget (EFB) closure by Zilitinkevich et al. (2013). A detailed discussion of the similarities and differences between these models will be given, which can give insight in the more general gap between engineering and

  18. 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

  19. 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…

  20. 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…

  1. Algebraic Bethe Ansatz for Open XXX Model with Triangular Boundary Matrices

    NASA Astrophysics Data System (ADS)

    Belliard, Samuel; Crampé, Nicolas; Ragoucy, Eric

    2013-05-01

    We consider an open XXX spin chain with two general boundary matrices whose entries obey a relation, which is equivalent to the possibility to put simultaneously the two matrices in a upper-triangular form. We construct Bethe vectors by means of a generalized algebraic Bethe ansatz. As usual, the method uses Bethe equations and provides transfer matrix eigenvalues.

  2. 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…

  3. 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…

  4. 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.

  5. 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.

  6. Higher level twisted Zhu algebras

    SciTech Connect

    Ekeren, Jethro van

    2011-05-15

    The study of twisted representations of graded vertex algebras is important for understanding orbifold models in conformal field theory. In this paper, we consider the general setup of a vertex algebra V, graded by {Gamma}/Z for some subgroup {Gamma} of R containing Z, and with a Hamiltonian operator H having real (but not necessarily integer) eigenvalues. We construct the directed system of twisted level p Zhu algebras Zhu{sub p,{Gamma}}(V), and we prove the following theorems: For each p, there is a bijection between the irreducible Zhu{sub p,{Gamma}}(V)-modules and the irreducible {Gamma}-twisted positive energy V-modules, and V is ({Gamma}, H)-rational if and only if all its Zhu algebras Zhu{sub p,{Gamma}}(V) are finite dimensional and semisimple. The main novelty is the removal of the assumption of integer eigenvalues for H. We provide an explicit description of the level p Zhu algebras of a universal enveloping vertex algebra, in particular of the Virasoro vertex algebra Vir{sup c} and the universal affine Kac-Moody vertex algebra V{sup k}(g) at non-critical level. We also compute the inverse limits of these directed systems of algebras.

  7. Algebraic Squares: Complete and Incomplete.

    ERIC Educational Resources Information Center

    Gardella, Francis J.

    2000-01-01

    Illustrates ways of using algebra tiles to give students a visual model of competing squares that appear in algebra as well as in higher mathematics. Such visual representations give substance to the symbolic manipulation and give students who do not learn symbolically a way of understanding the underlying concepts of completing the square. (KHR)

  8. Algebraic Thinking in Adult Education

    ERIC Educational Resources Information Center

    Manly, Myrna; Ginsburg, Lynda

    2010-01-01

    In adult education, algebraic thinking can be a sense-making tool that introduces coherence among mathematical concepts for those who previously have had trouble learning math. Further, a modeling approach to algebra connects mathematics and the real world, demonstrating the usefulness of math to those who have seen it as just an academic…

  9. 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

  10. 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

  11. 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

  12. 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.

  13. 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

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

    PubMed

    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

  15. 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.

  16. 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.

  17. 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,…

  18. 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…

  19. 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

  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. 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

  2. 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

  3. 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.

  4. Distance geometry and geometric algebra

    NASA Astrophysics Data System (ADS)

    Dress, Andreas W. M.; Havel, Timothy F.

    1993-10-01

    As part of his program to unify linear algebra and geometry using the language of Clifford algebra, David Hestenes has constructed a (well-known) isomorphism between the conformal group and the orthogonal group of a space two dimensions higher, thus obtaining homogeneous coordinates for conformal geometry.(1) In this paper we show that this construction is the Clifford algebra analogue of a hyperbolic model of Euclidean geometry that has actually been known since Bolyai, Lobachevsky, and Gauss, and we explore its wider invariant theoretic implications. In particular, we show that the Euclidean distance function has a very simple representation in this model, as demonstrated by J. J. Seidel.(18)

  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. 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.

  7. 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.

  8. 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.

  9. 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.

  10. Quantum solvable models with gl(2, c) Lie algebra symmetry embedded into the extension of unitary parasupersymmetry

    NASA Astrophysics Data System (ADS)

    Fakhri, H.; Chenaghlou, A.

    2007-05-01

    Introducing p - 1 new parameters into the multilinear relations, we extend the standard unitary parasupersymmetry algebra of order p so that by embedding the quantum solvable models possessing gl(2, c) Lie algebra symmetry into it, the partitions of integer numbers p - 1 and \\frac{1}{2}p(p-1) are established. These two partitions are performed by the new parameters and the product of new parameters with their labels, respectively. The former partition is just necessary for the real form h4; however, both of them are essential for the real forms u(2) and u(1, 1). By occupying these parameters with arbitrary values, the energy spectra are determined by the mean value of proposed parameters for the real form h4 with their label weight function as well as for the real forms u(2) and u(1, 1) with the weight function of their squared label. So for the given energies, the multilinear behaviour of parasupercharges is not specified uniquely by varying the new parameters continuously.

  11. 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

  12. 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. PMID:24650980

  13. Twisted Quantum Toroidal Algebras

    NASA Astrophysics Data System (ADS)

    Jing, Naihuan; Liu, Rongjia

    2014-09-01

    We construct a principally graded quantum loop algebra for the Kac-Moody algebra. As a special case a twisted analog of the quantum toroidal algebra is obtained together with the quantum Serre relations.

  14. A Wave Equation including Leptons and Quarks for the Standard Model of Quantum Physics in Clifford Algebra

    NASA Astrophysics Data System (ADS)

    Daviau, Claude; Bertrand, Jacques

    A wave equation with mass term is studied for all particles and antiparticles of the first generation: electron and its neutrino, positron and antineutrino, quarks $u$ and $d$ with three states of color and antiquarks $\\overline{u}$ and $\\overline{d}$. This wave equation is form invariant under the $Cl_3^*$ group generalizing the relativistic invariance. It is gauge invariant under the $U(1)\\times SU(2) \\times SU(3)$ group of the standard model of quantum physics. The wave is a function of space and time with value in the Clifford algebra $Cl_{1,5}$. All features of the standard model, charge conjugation, color, left waves, Lagrangian formalism, are linked to the geometry of this extended space-time.

  15. Study of the “non-Abelian” current algebra of a non-linear σ-model

    NASA Astrophysics Data System (ADS)

    Ghosh, Subir

    2006-08-01

    A particular form of non-linear σ-model, having a global gauge invariance, is studied. The detailed discussion on current algebra structures reveals the non-Abelian nature of the invariance, with field dependent structure functions. Reduction of the field theory to a point particle framework yields a non-linear harmonic oscillator, which is a special case of similar models studied before in [J.F. Carinena et al., Nonlinearity 17 (2004) 1941, math-ph/0406002; J.F. Carinena et al., in: Proceedings of 10th International Conference in Modern Group Analysis, Larnaca, Cyprus, 2004, p. 39, arxiv:math-ph/0505028; J.F. Carinena et al., Rep. Math. Phys. 54 (2004) 285, arxiv:hep-th/0501106]. The connection with non-commutative geometry is also established.

  16. 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.

  17. 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.

  18. Algebraic vs physical N = 6 3-algebras

    SciTech Connect

    Cantarini, Nicoletta; Kac, Victor G.

    2014-01-15

    In our previous paper, we classified linearly compact algebraic simple N = 6 3-algebras. In the present paper, we classify their “physical” counterparts, which actually appear in the N = 6 supersymmetric 3-dimensional Chern-Simons theories.

  19. 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.

  20. 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.

  1. Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows

    NASA Astrophysics Data System (ADS)

    Aratyn, Henrik; van de Leur, Johan

    2007-02-01

    We use a Grassmannian framework to define multi-component tau functions as expectation values of certain multi-component Fermi operators satisfying simple bilinear commutation relations on Clifford algebra. The tau functions contain both positive and negative flows and are shown to satisfy the 2n-component KP hierarchy. The hierarchy equations can be formulated in terms of pseudo-differential equations for n × n matrix wave functions derived in terms of tau functions. These equations are cast in form of Sato-Wilson relations. A reduction process leads to the AKNS, two-component Camassa-Holm and Cecotti-Vafa models and the formalism provides simple formulas for their solutions.

  2. 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

  3. 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).

  4. 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…

  5. 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…

  6. 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.

  7. Historical Topics in Algebra.

    ERIC Educational Resources Information Center

    National Council of Teachers of Mathematics, Inc., Reston, VA.

    This is a reprint of the historical capsules dealing with algebra from the 31st Yearbook of NCTM,"Historical Topics for the Mathematics Classroom." Included are such themes as the change from a geometric to an algebraic solution of problems, the development of algebraic symbolism, the algebraic contributions of different countries, the origin and…

  8. 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.

  9. Deformations of 3-algebras

    SciTech Connect

    Figueroa-O'Farrill, Jose Miguel

    2009-11-15

    We phrase deformations of n-Leibniz algebras in terms of the cohomology theory of the associated Leibniz algebra. We do the same for n-Lie algebras and for the metric versions of n-Leibniz and n-Lie algebras. We place particular emphasis on the case of n=3 and explore the deformations of 3-algebras of relevance to three-dimensional superconformal Chern-Simons theories with matter.

  10. 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.

  11. Quantum cluster algebras and quantum nilpotent algebras

    PubMed Central

    Goodearl, Kenneth R.; Yakimov, Milen T.

    2014-01-01

    A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197

  12. 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.

  13. 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

  14. 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

  15. 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.

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

    NASA Astrophysics Data System (ADS)

    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.

  17. The SLAM family member CD48 (Slamf2) protects lupus-prone mice from autoimmune nephritis

    PubMed Central

    Koh, Anna E.; Njoroge, Sarah W.; Feliu, Marianela; Cook, Alexis; Selig, Martin K.; Latchman, Yvette E.; Sharpe, Arlene H.; Colvin, Robert B.; Paul, Elahna

    2011-01-01

    Polymorphisms in the SLAM family of leukocyte cell surface regulatory molecules have been associated with lupus-like phenotypes in both humans and mice. The murine Slamf gene cluster lies within the lupus-associated Sle1b region of mouse chromosome 1. Non-autoreactive C57BL/6 (B6) mice that have had this region replaced by syntenic segments from other mouse strains (i.e. 129, NZB and NZW) are B6 congenic strains that spontaneously produce non-nephritogenic lupus-like autoantibodies. We have recently reported that genetic ablation of the SLAM family member CD48 (Slamf2) drives full-blown autoimmune disease with severe proliferative glomerulonephritis (CD48GN) in B6 mice carrying 129 sequences of the Sle1b region (B6.129CD48-/-). We also discovered that BALB/c mice with the same 129-derived CD48-null allele (BALB.129CD48-/-) have neither nephritis nor anti-DNA autoantibodies, indicating that strain specific background genes modulate the effects of CD48 deficiency. Here we further examine this novel model of lupus nephritis in which CD48 deficiency transforms benign autoreactivity into fatal nephritis. CD48GN is characterized by glomerular hypertrophy with mesangial expansion, proliferation and leukocytic infiltration. Immune complexes deposit in mesangium and in sub-endothelial, sub-epithelial and intramembranous sites along the glomerular basement membrane. Afflicted mice have low grade proteinuria, intermittent hematuria and their progressive renal injury manifests with elevated urine NGAL levels and with uremia. In contrast to the lupus-like B6.129CD48-/- animals, neither BALB.129CD48-/- mice nor B6 × BALB/c F1.129CD48-/- progeny have autoimmune traits, indicating that B6-specific background genes modulate the effect of CD48 on lupus nephritis in a recessive manner. PMID:21561736

  18. 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

  19. 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

  20. 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

  1. 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

  2. Critical points of Potts and O(N) models from eigenvalue identities in periodic Temperley-Lieb algebras

    NASA Astrophysics Data System (ADS)

    Lykke Jacobsen, Jesper

    2015-11-01

    In previous work with Scullard, we have defined a graph polynomial P B (q, T) that gives access to the critical temperature T c of the q-state Potts model defined on a general two-dimensional lattice {L}. It depends on a basis B, containing n × m unit cells of {L}, and the relevant root T c(n, m) of P B (q, T) was observed to converge quickly to T c in the limit n,m\\to ∞ . Moreover, in exactly solvable cases there is no finite-size dependence at all. In this paper we show how to reformulate this method as an eigenvalue problem within the periodic Temperley-Lieb (TL) algebra. This corresponds to taking m\\to ∞ first, so that the bases B are semi-infinite cylinders of circumference n. The limit implies faster convergence in n, while maintaining the n-independence in exactly solvable cases. In this setup, T c(n) is determined by equating the largest eigenvalues of two topologically distinct sectors of the transfer matrix. Crucially, these two sectors determine the same critical exponent in the continuum limit, and the observed fast convergence is thus corroborated by results of conformal field theory. We obtain similar results for the dense and dilute phases of the O(N) loop model, using now a transfer matrix within the dilute periodic TL algebra. Compared with our previous study, the eigenvalue formulation allows us to double the size n for which T c(n) can be obtained, using the same computational effort. We study in details three significant cases: (i) bond percolation on the kagome lattice, up to n max = 14; (ii) site percolation on the square lattice, to n max = 21; and (iii) self-avoiding polygons on the square lattice, to n max = 19. Convergence properties of T c(n) and extrapolation schemes are studied in details for the first two cases. This leads to rather accurate values for the percolation thresholds: p c = 0.524 404 999 167 439(4) for bond percolation on the kagome lattice, and p c = 0.592 746 050 792 10(2) for site percolation on the square lattice.

  3. 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).

  4. Boundary Lax pairs from non-ultra-local Poisson algebras

    SciTech Connect

    Avan, Jean; Doikou, Anastasia

    2009-11-15

    We consider non-ultra-local linear Poisson algebras on a continuous line. Suitable combinations of representations of these algebras yield representations of novel generalized linear Poisson algebras or 'boundary' extensions. They are parametrized by a boundary scalar matrix and depend, in addition, on the choice of an antiautomorphism. The new algebras are the classical-linear counterparts of the known quadratic quantum boundary algebras. For any choice of parameters, the non-ultra-local contribution of the original Poisson algebra disappears. We also systematically construct the associated classical Lax pair. The classical boundary principal chiral model is examined as a physical example.

  5. 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…

  6. Algebra in the Early Years? Yes!

    ERIC Educational Resources Information Center

    Taylor-Cox, Jennifer

    2003-01-01

    Suggests ways early years educators can begin teaching young children to think algebraically and prepare them for success in algebra. Focuses on ways to promote mathematical patterns, mathematical situations and structures, models of quantitative relationship, and change. Describes how first-graders used real object representations to better…

  7. Young Mathematicians at Work: Constructing Algebra

    ERIC Educational Resources Information Center

    Fosnot, Catherine Twomey; Jacob, Bill

    2010-01-01

    This book provides a landscape of learning that helps teachers recognize, support, and celebrate their students' capacity to structure their worlds algebraically. It identifies the models, contexts, and landmarks that facilitate algebraic thinking in young students and provides insightful and practical methods for teachers, math supervisors, and…

  8. Realizations of Galilei algebras

    NASA Astrophysics Data System (ADS)

    Nesterenko, Maryna; Pošta, Severin; Vaneeva, Olena

    2016-03-01

    All inequivalent realizations of the Galilei algebras of dimensions not greater than five are constructed using the algebraic approach proposed by Shirokov. The varieties of the deformed Galilei algebras are discussed and families of one-parametric deformations are presented in explicit form. It is also shown that a number of well-known and physically interesting equations and systems are invariant with respect to the considered Galilei algebras or their deformations.

  9. Algebraic K-theory, K-regularity, and -duality of -stable C ∗-algebras

    NASA Astrophysics Data System (ADS)

    Mahanta, Snigdhayan

    2015-12-01

    We develop an algebraic formalism for topological -duality. More precisely, we show that topological -duality actually induces an isomorphism between noncommutative motives that in turn implements the well-known isomorphism between twisted K-theories (up to a shift). In order to establish this result we model topological K-theory by algebraic K-theory. We also construct an E ∞ -operad starting from any strongly self-absorbing C ∗-algebra . Then we show that there is a functorial topological K-theory symmetric spectrum construction on the category of separable C ∗-algebras, such that is an algebra over this operad; moreover, is a module over this algebra. Along the way we obtain a new symmetric spectra valued functorial model for the (connective) topological K-theory of C ∗-algebras. We also show that -stable C ∗-algebras are K-regular providing evidence for a conjecture of Rosenberg. We conclude with an explicit description of the algebraic K-theory of a x+ b-semigroup C ∗-algebras coming from number theory and that of -stabilized noncommutative tori.

  10. 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)…

  11. Fine Specificity and Molecular Competition in SLAM Family Receptor Signalling

    PubMed Central

    Wilson, Timothy J.; Garner, Lee I.; Metcalfe, Clive; King, Elliott; Margraf, Stefanie; Brown, Marion H.

    2014-01-01

    SLAM family receptors regulate activation and inhibition in immunity through recruitment of activating and inhibitory SH2 domain containing proteins to immunoreceptor tyrosine based switch motifs (ITSMs). Binding of the adaptors, SAP and EAT-2 to ITSMs in the cytoplasmic regions of SLAM family receptors is important for activation. We analysed the fine specificity of SLAM family receptor phosphorylated ITSMs and the conserved tyrosine motif in EAT-2 for SH2 domain containing signalling proteins. Consistent with the literature describing dependence of CRACC (SLAMF7) on EAT-2, CRACC bound EAT-2 (KD = 0.003 μM) with approximately 2 orders of magnitude greater affinity than SAP (KD = 0.44 μM). RNA interference in cytotoxicity assays in NK92 cells showed dependence of CRACC on SAP in addition to EAT-2, indicating selectivity of SAP and EAT-2 may depend on the relative concentrations of the two adaptors. The concentration of SAP was four fold higher than EAT-2 in NK92 cells. Compared with SAP, the significance of EAT-2 recruitment and its downstream effectors are not well characterised. We identified PLCγ1 and PLCγ2 as principal binding partners for the EAT-2 tail. Both PLCγ1 and PLCγ2 are functionally important for cytotoxicity in NK92 cells through CD244 (SLAMF4), NTB-A (SLAMF6) and CRACC. Comparison of the specificity of SH2 domains from activating and inhibitory signalling mediators revealed a hierarchy of affinities for CD244 (SLAMF4) ITSMs. While binding of phosphatase SH2 domains to individual ITSMs of CD244 was weak compared with SAP or EAT-2, binding of tandem SH2 domains of SHP-2 to longer peptides containing tandem phosphorylated ITSMs in human CD244 increased the affinity ten fold. The concentration of the tyrosine phosphatase, SHP-2 was in the order of a magnitude higher than the adaptors, SAP and EAT-2. These data demonstrate a mechanism for direct recruitment of phosphatases in inhibitory signalling by ITSMs, while explaining competitive

  12. 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

  13. 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.

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

    PubMed

    Detwiler, Russell L; Mehl, Steffen; Rajaram, Harihar; Cheung, Wendy 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. PMID:12019641

  15. 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.

  16. 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.

  17. 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

  18. 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,…

  19. 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…

  20. Applied Algebra Curriculum Modules.

    ERIC Educational Resources Information Center

    Texas State Technical Coll., Marshall.

    This collection of 11 applied algebra curriculum modules can be used independently as supplemental modules for an existing algebra curriculum. They represent diverse curriculum styles that should stimulate the teacher's creativity to adapt them to other algebra concepts. The selected topics have been determined to be those most needed by students…

  1. 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…

  2. Ternary Virasoro - Witt algebra.

    SciTech Connect

    Zachos, C.; Curtright, T.; Fairlie, D.; High Energy Physics; Univ. of Miami; Univ. of Durham

    2008-01-01

    A 3-bracket variant of the Virasoro-Witt algebra is constructed through the use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets acting on other 3-brackets in the algebra are discussed and verified in various situations.

  3. 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

  4. 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

  5. Beyond Dirac - a Unified Algebra

    NASA Astrophysics Data System (ADS)

    Lundberg, Wayne R.

    2001-10-01

    A introductory insight will be shared regarding a 'separation of variables' approach to understanding the relationship between QCD and the origins of cosmological and particle mass. The discussion will then build upon work presented at DFP 2000, focussing on the formal basis for using 3x3x3 matrix algebra as it underlies and extends Dirac notation. A set of restrictions are established which break the multiple symmetries of the 3x3x3 matrix algebra, yielding Standard Model QCD objects and interactions. It will be shown that the 3x3x3 matrix representation unifies the algebra of strong and weak (and by extension, electromagnetic) interactions. A direct correspondence to string theoretic objects is established by considering the string to be partitioned in thirds. Rubik's cube is used as a graphical means of handling algebraic manipulation of 3x3x3 algebra. Further, its potential utility for advancing pedagogical methods through active engagement is discussed. A simulated classroom exercize will be conducted.

  6. Efficient Multi-Valued Bounded Model Checking for LTL over Quasi-Boolean Algebras

    NASA Astrophysics Data System (ADS)

    Andrade, Jefferson O.; Kameyama, Yukiyoshi

    Multi-valued Model Checking extends classical, two-valued model checking to multi-valued logic such as Quasi-Boolean logic. The added expressivity is useful in dealing with such concepts as incompleteness and uncertainty in target systems, while it comes with the cost of time and space. Chechik and others proposed an efficient reduction from multi-valued model checking problems to two-valued ones, but to the authors' knowledge, no study was done for multi-valued bounded model checking. In this paper, we propose a novel, efficient algorithm for multi-valued bounded model checking. A notable feature of our algorithm is that it is not based on reduction of multi-values into two-values; instead, it generates a single formula which represents multi-valuedness by a suitable encoding, and asks a standard SAT solver to check its satisfiability. Our experimental results show a significant improvement in the number of variables and clauses and also in execution time compared with the reduction-based one.

  7. 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.

  8. 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.

  9. SDG Fermion-Pair Algebraic SO(12) and Sp(10) Models and Their Boson Realizations

    NASA Astrophysics Data System (ADS)

    Navratil, P.; Geyer, H. B.; Dobes, J.; Dobaczewski, 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 we 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.

  10. Algebraic expression for the diffuse irradiance reflectivity of water from the two-flow model.

    PubMed

    Jain, S C; Miller, J R

    1977-01-01

    A simple expression is obtained for the irradiance reflectance of the ocean based on a two-flow radiative transfer model. This expression is found to reproduce the Monte Carlo calculations to within 7% for scattering albedo values less than 0.8. On the basis of this expression, it is shown that the remotely sensed water color data can be interpreted with the help of iterative optimization techniques, provided that the variations of backscattering coefficient and absorption coefficient with wavelength can be modeled. PMID:20168452

  11. 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.

  12. 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

  13. Algebraic Lattices in QFT Renormalization

    NASA Astrophysics Data System (ADS)

    Borinsky, Michael

    2016-04-01

    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.

  14. 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.

  15. Computational triadic algebras of signs

    SciTech Connect

    Zadrozny, W.

    1996-12-31

    We present a finite model of Peirce`s ten classes of signs. We briefly describe Peirce`s taxonomy of signs; we prove that any finite collection of signs can be extended to a finite algebra of signs in which all interpretants are themselves being interpreted; and we argue that Peirce`s ten classes of signs can be defined using constraints on algebras of signs. The paper opens the possibility of defining multimodal cognitive agents using Peirce`s classes of signs, and is a first step towards building a computational logic of signs based on Peirce`s taxonomies.

  16. Modeling Genome-Scale mRNA Expression Datasets: From Matrix Algebra to Genetic Networks

    NASA Astrophysics Data System (ADS)

    Alter, Orly

    2003-03-01

    DNA microarray genome-wide expression data promise to enhance fundamental understanding of life on the molecular level, and may prove useful in medical diagnosis, treatment and drug design. Analysis of these new data requires mathematical tools that use large quantities of data and reduce the complexity of the data to make them comprehensible. These tools should provide predictive models, i.e., mathematical frameworks for the description of the data, in which the mathematical variables and operations may be assigned biological meaning. Such models will facilitate the unraveling of the cellular machineries that generate, sense and react to the expression signal. I will start with a description of the use of singular value decomposition (SVD) to construct the first model for genome-wide expression data. SVD is a unique data-driven linear transformation of the expression data from the genes × arrays space to the reduced ``eigengenes'' × ``eigenarrays'' space, where the eigengenes (eigenarrays) are unique orthonormal superpositions of the genes (arrays). Normalizing the data, by detecting and filtering out additive and multiplicative experimental artifacts and irrelevant biological processes, enables meaningful comparison of the expression of different genes across different arrays in different experiments. Sorting the data, according to a chosen subset of eigengenes (and eigenarrays), rather than by overall expression, gives a global picture of gene expression in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype, respectively. In some experiments, the significant eigengenes and eigenarrays can be associated with genome-wide effects of regulators, or with measured samples in which these regulators are overactive or underactive, respectively. I will then describe the use of generalized singular value decomposition (GSVD) to construct the first comparative model

  17. 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

  18. 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

  19. 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.

  20. 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

  1. 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…

  2. 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

  3. 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

  4. Application of reduced order modeling techniques to problems in heat conduction, isoelectric focusing and differential algebraic equations

    NASA Astrophysics Data System (ADS)

    Mathai, Pramod P.

    the uncertainty in the parameters of the differential equations. There is a clear need to design better experiments for IEF without the current overhead of expensive chemicals and labor. We show how with a simpler modeling of the underlying chemistry, we can still achieve the accuracy that has been achieved in existing literature for modeling small ranges of pH (hydrogen ion concentration) in IEF, but with far less computational time. We investigate a further reduction of time by modeling the IEF problem using the Proper Orthogonal Decomposition (POD) technique and show why POD may not be sufficient due to the underlying constraints. The final problem that we address in this thesis addresses a certain class of dynamics with high stiffness - in particular, differential algebraic equations. With the help of simple examples, we show how the traditional POD procedure will fail to model certain high stiffness problems due to a particular behavior of the vector field which we will denote as twist. We further show how a novel augmentation to the traditional POD algorithm can model-reduce problems with twist in a computationally cheap manner without any additional data requirements.

  5. 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.

  6. 3-D seakeeping analysis with water on deck and slamming. Part 2: Experiments and physical investigation

    NASA Astrophysics Data System (ADS)

    Greco, M.; Bouscasse, B.; Lugni, C.

    2012-08-01

    A synergic 3-D experimental and numerical investigation is conducted for wave-ship interactions involving the water-on-deck and slamming phenomena. The adopted solver has been developed in Greco and Lugni (in press) and combines (A) a weakly nonlinear external solution for the wave-vessel interactions with (B) a 2-D in-deck shallow-water approximation, which describes water shipping events, and (C) a local analytical analysis of the bottom-slamming phenomenon. This solver can handle regular and irregular sea states and vessels at rest or with limited speed. The experiments examine a patrol ship at rest or with forward speed that is free to oscillate in heave and pitch in regular and irregular waves. In this study, the head-sea regular-wave conditions are examined in terms of (1) response amplitude operators (RAOs) and relative motions, (2) occurrence, features and loads of water-on-deck, bottom-slamming and flare-slamming events and (3) added resistance in waves. A systematic and comprehensive analysis of the phenomena is made available in terms of the Froude number, incoming wavelength-to-ship length ratio and wave steepness for the examined ship geometry. The main parameters that affect the global and local quantities are identified and possible danger in terms of water-on-deck severity and structural consequences are determined. Different slamming behaviors were identified, depending on the spatial location of the impact on the vessel: single-peak, church-roof and double-peak behaviors. A bottom-slamming criterion, using the Ochi's (1964) velocity condition and the Greco and Lugni's (2012) pressure condition, is assessed. A statistical analysis of more than 100 events is needed for the bottom-slamming pressure peaks. The numerical solver is promising. The major discrepancies with the experiments are discussed, and the importance of viscous hull damping and flare impact for the most violent conditions is emphasized. Inclusion of these effects improved the

  7. 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…

  8. 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)

  9. 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…

  10. 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.

  11. 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.

  12. 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.

  13. Fuzzy-algebra uncertainty assessment

    SciTech Connect

    Cooper, J.A.; Cooper, D.K.

    1994-12-01

    A significant number of analytical problems (for example, abnormal-environment safety analysis) depend on data that are partly or mostly subjective. Since fuzzy algebra depends on subjective operands, we have been investigating its applicability to these forms of assessment, particularly for portraying uncertainty in the results of PRA (probabilistic risk analysis) and in risk-analysis-aided decision-making. Since analysis results can be a major contributor to a safety-measure decision process, risk management depends on relating uncertainty to only known (not assumed) information. The uncertainties due to abnormal environments are even more challenging than those in normal-environment safety assessments; and therefore require an even more judicious approach. Fuzzy algebra matches these requirements well. One of the most useful aspects of this work is that we have shown the potential for significant differences (especially in perceived margin relative to a decision threshold) between fuzzy assessment and probabilistic assessment based on subtle factors inherent in the choice of probability distribution models. We have also shown the relation of fuzzy algebra assessment to ``bounds`` analysis, as well as a description of how analyses can migrate from bounds analysis to fuzzy-algebra analysis, and to probabilistic analysis as information about the process to be analyzed is obtained. Instructive examples are used to illustrate the points.

  14. 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.

  15. Phase Boundaries in Algebraic Conformal QFT

    NASA Astrophysics Data System (ADS)

    Bischoff, Marcel; Kawahigashi, Yasuyuki; Longo, Roberto; Rehren, Karl-Henning

    2016-02-01

    We study the structure of local algebras in relativistic conformal quantum field theory with phase boundaries. Phase boundaries are instances of a more general notion of boundaries that give rise to a variety of algebraic structures. These can be formulated in a common framework originating in Algebraic QFT, with the principle of Einstein Causality playing a prominent role. We classify the phase boundary conditions by the centre of a certain universal construction, which produces a reducible representation in which all possible boundary conditions are realized. For a large class of models, the classification reproduces results obtained in a different approach by Fuchs et al. before.

  16. 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…

  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. 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.

  19. Catching Up on Algebra

    ERIC Educational Resources Information Center

    Cavanagh, Sean

    2008-01-01

    A popular humorist and avowed mathphobe once declared that in real life, there's no such thing as algebra. Kathie Wilson knows better. Most of the students in her 8th grade class will be thrust into algebra, the definitive course that heralds the beginning of high school mathematics, next school year. The problem: Many of them are about three…

  20. 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

  1. 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

  2. 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.

  3. SLAM examination of solar cells and solar cell welds. [Scanning Laser Acoustic Microscope

    NASA Technical Reports Server (NTRS)

    Stella, P. M.; Vorres, C. L.; Yuhas, D. E.

    1981-01-01

    The scanning laser acoustic microscope (SLAM) has been evaluated for non-destructive examination of solar cells and interconnector bonds. Using this technique, it is possible to view through materials in order to reveal regions of discontinuity such as microcracks and voids. Of particular interest is the ability to evaluate, in a unique manner, the bonds produced by parallel gap welding. It is possible to not only determine the area and geometry of the bond between the tab and cell, but also to reveal any microcracks incurred during the welding. By correlating the SLAM results with conventional techniques of weld evaluation a more confident weld parameter optimization can be obtained.

  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. Three-algebra for supermembrane and two-algebra for superstring

    NASA Astrophysics Data System (ADS)

    Lee, Kanghoon; Park, Jeong-Hyuck

    2009-04-01

    While string or Yang-Mills theories are based on Lie algebra or two-algebra structure, recent studies indicate that Script M-theory may require a one higher, three-algebra structure. Here we construct a covariant action for a supermembrane in eleven dimensions, which is invariant under global supersymmetry, local fermionic symmetry and worldvolume diffeomorphism. Our action is classically on-shell equivalent to the celebrated Bergshoeff-Sezgin-Townsend action. However, the novelty is that we spell the action genuinely in terms of Nambu three-brackets: All the derivatives appear through Nambu brackets and hence it manifests the three-algebra structure. Further the double dimensional reduction of our action gives straightforwardly to a type IIA string action featuring two-algebra. Applying the same method, we also construct a covariant action for type IIB superstring, leading directly to the IKKT matrix model.

  6. Semigroups and computer algebra in algebraic structures

    NASA Astrophysics Data System (ADS)

    Bijev, G.

    2012-11-01

    Some concepts in semigroup theory can be interpreted in several algebraic structures. A generalization fA,B,fA,B(X) = A(X')B of the complement operator (') on Boolean matrices is made, where A and B denote any rectangular Boolean matrices. While (') is an isomorphism between Boolean semilattices, the generalized complement operator is homomorphism in the general case. The map fA,B and its general inverse (fA,B)+ have quite similar properties to those in the linear algebra and are useful for solving linear equations in Boolean matrix algebras. For binary relations on a finite set, necessary and sufficient conditions for the equation αξβ = γ to have a solution ξ are proved. A generalization of Green's equivalence relations in semigroups for rectangular matrices is proposed. Relationships between them and the Moore-Penrose inverses are investigated. It is shown how any generalized Green's H-class could be constructed by given its corresponding linear subspaces and converted into a group isomorphic to a linear group. Some information about using computer algebra methods concerning this paper is given.

  7. 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.

  8. 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.

  9. SLAM, a Mathematica interface for SUSY spectrum generators

    NASA Astrophysics Data System (ADS)

    Marquard, Peter; Zerf, Nikolai

    2014-03-01

    We present and publish a Mathematica package, which can be used to automatically obtain any numerical MSSM input parameter from SUSY spectrum generators, which follow the SLHA standard, like SPheno, SOFTSUSY, SuSeFLAV or Suspect. The package enables a very comfortable way of numerical evaluations within the MSSM using Mathematica. It implements easy to use predefined high scale and low scale scenarios like mSUGRA or mhmax and if needed enables the user to directly specify the input required by the spectrum generators. In addition it supports an automatic saving and loading of SUSY spectra to and from a SQL data base, avoiding the rerun of a spectrum generator for a known spectrum. Catalogue identifier: AERX_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERX_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4387 No. of bytes in distributed program, including test data, etc.: 37748 Distribution format: tar.gz Programming language: Mathematica. Computer: Any computer where Mathematica version 6 or higher is running providing bash and sed. Operating system: Linux. Classification: 11.1. External routines: A SUSY spectrum generator such as SPheno, SOFTSUSY, SuSeFLAV or SUSPECT Nature of problem: Interfacing published spectrum generators for automated creation, saving and loading of SUSY particle spectra. Solution method: SLAM automatically writes/reads SLHA spectrum generator input/output and is able to save/load generated data in/from a data base. Restrictions: No general restrictions, specific restrictions are given in the manuscript. Running time: A single spectrum calculation takes much less than one second on a modern PC.

  10. Coreflections in Algebraic Quantum Logic

    NASA Astrophysics Data System (ADS)

    Jacobs, Bart; Mandemaker, Jorik

    2012-07-01

    Various generalizations of Boolean algebras are being studied in algebraic quantum logic, including orthomodular lattices, orthomodular po-sets, orthoalgebras and effect algebras. This paper contains a systematic study of the structure in and between categories of such algebras. It does so via a combination of totalization (of partially defined operations) and transfer of structure via coreflections.

  11. Developing Algebraic Thinking.

    ERIC Educational Resources Information Center

    Alejandre, Suzanne

    2002-01-01

    Presents a teaching experience that resulted in students getting to a point of full understanding of the kinesthetic activity and the algebra behind it. Includes a lesson plan for a traffic jam activity. (KHR)

  12. 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

  13. 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)

  14. 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

  15. 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

  16. 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…

  17. Slam, a Service for Landslide Monitoring Based on EO-Data

    NASA Astrophysics Data System (ADS)

    Manunta, P.; Brugioni, M.; Casagli, N.; Colombo, D.; Deflorio, A. M.; Farina, P.; Ferretti, A.; Gontier, E.; Graf, K.; Haeberle, J.; Lateltin, O.; Meloni, E.; Mayoraz, R.; Montini, G.; Moretti, S.; Paganini, M.; Palazzo, F.; Spina, D.; Sulli, L.; Strozzi, T.

    2004-06-01

    Every year slope instabilities cause large socio-economic losses on life and property worldwide. Indeed, the casualties caused by mass movements are among the highest in the industrialized world. In this contest the SLAM project is aimed to the implementation of landslides mapping and monitoring service that can be integrated into the current landslide management procedures. The innovative aspect of the SLAM project is the integration of the SAR techniques and EO data with the in situ documentation currently in use for the landslide monitoring. In particular, SLAM is designed to realise three types of products: Landslide Motion Survey, Landslide Displacement Monitoring and Landslide Susceptibility Mapping. The realization of SLAM project, entirely funded by ESA, is carried out by an international Consortium led by Planetek Italia (I) and formed by other five partners: Tele-Rilevamento Europa (I), Gamma Remote Sensing (CH), Spacebel (B), Geotest (CH) and Earth Science Department of the University of Firenze (I). For the Italian service cases the interferometric analysis is based on the PS technique, developed and patented by the Politecnico di Milano (Italy) and improved by Tele-Rilevamento Europa. For the Swiss service cases, multi-pass SAR interferometry, including the Interferometric Point Target Analysis (IPTA), is applied by Gamma Remote Sensing.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. Assessing the effect of Measurement-Based Care depression treatment on HIV medication adherence and health outcomes: rationale and design of the SLAM DUNC Study.

    PubMed

    Pence, Brian W; Gaynes, Bradley N; Williams, Quinn; Modi, Riddhi; Adams, Julie; Quinlivan, E Byrd; Heine, Amy; Thielman, Nathan; Mugavero, Michael J

    2012-07-01

    Depression affects 20-30% of people living with HIV/AIDS (PLWHA) in the U.S. and predicts greater sexual risk behaviors, lower antiretroviral (ARV) medication adherence, and worse clinical outcomes. Yet little experimental evidence addresses the critical clinical question of whether depression treatment improves ARV adherence and clinical outcomes in PLWHA with depression. The Strategies to Link Antidepressant and Antiretroviral Management at Duke, UAB, and UNC (SLAM DUNC) Study is a randomized clinical effectiveness trial funded by the National Institute for Mental Health. The objective of SLAM DUNC is to test whether a depression treatment program integrated into routine HIV clinical care affects ARV adherence. PLWHA with depression (n=390) are randomized to enhanced usual care or a depression treatment model called Measurement-Based Care (MBC). MBC deploys a clinically supervised Depression Care Manager (DCM) to provide evidence-based antidepressant treatment recommendations to a non-psychiatric prescribing provider, guided by systematic and ongoing measures of depressive symptoms and side effects. MBC has limited time requirements and the DCM role can be effectively filled by a range of personnel given appropriate training and supervision, enhancing replicability. In SLAM DUNC, MBC is integrated into HIV care to support HIV providers in antidepressant prescription and management. The primary endpoint is ARV adherence measured by unannounced telephone-based pill counts at 6 months with follow-up to 12 months and secondary endpoints including viral load, health care utilization, and depressive severity. Important outcomes of this study will be evidence of the effectiveness of MBC in treating depression in PLWHA and improving HIV-related outcomes. PMID:22542960

  3. 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

  4. 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.

  5. DG Poisson algebra and its universal enveloping algebra

    NASA Astrophysics Data System (ADS)

    Lü, JiaFeng; Wang, XingTing; Zhuang, GuangBin

    2016-05-01

    In this paper, we introduce the notions of differential graded (DG) Poisson algebra and DG Poisson module. Let $A$ be any DG Poisson algebra. We construct the universal enveloping algebra of $A$ explicitly, which is denoted by $A^{ue}$. We show that $A^{ue}$ has a natural DG algebra structure and it satisfies certain universal property. As a consequence of the universal property, it is proved that the category of DG Poisson modules over $A$ is isomorphic to the category of DG modules over $A^{ue}$. Furthermore, we prove that the notion of universal enveloping algebra $A^{ue}$ is well-behaved under opposite algebra and tensor product of DG Poisson algebras. Practical examples of DG Poisson algebras are given throughout the paper including those arising from differential geometry and homological algebra.

  6. 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

  7. Comparison of algebraic and analytical approaches to the formulation of the statistical model-based reconstruction problem for X-ray computed tomography.

    PubMed

    Cierniak, Robert; Lorent, Anna

    2016-09-01

    The main aim of this paper is to investigate properties of our originally formulated statistical model-based iterative approach applied to the image reconstruction from projections problem which are related to its conditioning, and, in this manner, to prove a superiority of this approach over ones recently used by other authors. The reconstruction algorithm based on this conception uses a maximum likelihood estimation with an objective adjusted to the probability distribution of measured signals obtained from an X-ray computed tomography system with parallel beam geometry. The analysis and experimental results presented here show that our analytical approach outperforms the referential algebraic methodology which is explored widely in the literature and exploited in various commercial implementations. PMID:27289536

  8. C-Graded vertex algebras and conformal flow

    SciTech Connect

    Laber, Rob; Mason, Geoffrey

    2014-01-15

    We consider C-graded vertex algebras, which are vertex algebras V with a C-grading such that V is an admissible V-module generated by “lowest weight vectors.” We show that such vertex algebras have a “good” representation theory in the sense that there is a Zhu algebra A(V) and a bijection between simple admissible V-modules and simple A(V)-modules. We also consider pseudo vertex operator algebras (PVOAs), which are C-graded vertex algebras with a conformal vector such that the homogeneous subspaces of V are generalized eigenspaces for L(0); essentially, these are VOAs that lack any semisimplicity or integrality assumptions on L(0). As a motivating example, we show that deformation of the conformal structure (conformal flow) of a strongly regular VOA (e.g., a lattice theory, or Wess-Zumino-Witten model) is a path in a space whose points are PVOAs.

  9. 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.

  10. 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

  11. On Griess Algebras

    NASA Astrophysics Data System (ADS)

    Roitman, Michael

    2008-08-01

    In this paper we prove that for any commutative (but in general non-associative) algebra A with an invariant symmetric non-degenerate bilinear form there is a graded vertex algebra V = V0 Å V2 Å V3 Å ¼, such that dim V0 = 1 and V2 contains A. We can choose V so that if A has a unit e, then 2e is the Virasoro element of V, and if G is a finite group of automorphisms of A, then G acts on V as well. In addition, the algebra V can be chosen with a non-degenerate invariant bilinear form, in which case it is simple.

  12. 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.

  13. 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…

  14. 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.

  15. Algebraic geometric codes

    NASA Technical Reports Server (NTRS)

    Shahshahani, M.

    1991-01-01

    The performance characteristics are discussed of certain algebraic geometric codes. Algebraic geometric codes have good minimum distance properties. On many channels they outperform other comparable block codes; therefore, one would expect them eventually to replace some of the block codes used in communications systems. It is suggested that it is unlikely that they will become useful substitutes for the Reed-Solomon codes used by the Deep Space Network in the near future. However, they may be applicable to systems where the signal to noise ratio is sufficiently high so that block codes would be more suitable than convolutional or concatenated codes.

  16. Extended conformal algebras

    NASA Astrophysics Data System (ADS)

    Bouwknegt, Peter

    1988-06-01

    We investigate extensions of the Virasoro algebra by a single primary field of integer or halfinteger conformal dimension Δ. We argue that for vanishing structure constant CΔΔΔ, the extended conformal algebra can only be associative for a generic c-value if Δ=1/2, 1, 3/2, 2 or 3. For the other Δ<=5 we compute the finite set of allowed c-values and identify the rational solutions. The case CΔΔΔ≠0 is also briefly discussed. I would like to thank Kareljan Schoutens for discussions and Sander Bais for a careful reading of the manuscript.

  17. 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.…

  18. Teaching Arithmetic and Algebraic Expressions

    ERIC Educational Resources Information Center

    Subramaniam, K.; Banerjee, Rakhi

    2004-01-01

    A teaching intervention study was conducted with sixth grade students to explore the interconnections between students' growing understanding of arithmetic expressions and beginning algebra. Three groups of students were chosen, with two groups receiving instruction in arithmetic and algebra, and one group in algebra without arithmetic. Students…

  19. 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…

  20. Spinors in the hyperbolic algebra

    NASA Astrophysics Data System (ADS)

    Ulrych, S.

    2006-01-01

    The three-dimensional universal complex Clifford algebra Cbar3,0 is used to represent relativistic vectors in terms of paravectors. In analogy to the Hestenes spacetime approach spinors are introduced in an algebraic form. This removes the dependance on an explicit matrix representation of the algebra.

  1. 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

  2. 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

  3. 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)

  4. From Arithmetic to Algebra

    ERIC Educational Resources Information Center

    Ketterlin-Geller, Leanne R.; Jungjohann, Kathleen; Chard, David J.; Baker, Scott

    2007-01-01

    Much of the difficulty that students encounter in the transition from arithmetic to algebra stems from their early learning and understanding of arithmetic. Too often, students learn about the whole number system and the operations that govern that system as a set of procedures to solve addition, subtraction, multiplication, and division problems.…

  5. 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…

  6. The Power of Algebra.

    ERIC Educational Resources Information Center

    Boiteau, Denise; Stansfield, David

    This document describes mathematical programs on the basic concepts of algebra produced by Louisiana Public Broadcasting. Programs included are: (1) "Inverse Operations"; (2) "The Order of Operations"; (3) "Basic Properties" (addition and multiplication of numbers and variables); (4) "The Positive and Negative Numbers"; and (5) "Using Positive…

  7. Pre-Algebra.

    ERIC Educational Resources Information Center

    Kennedy, John

    This text provides information and exercises on arithmetic topics which should be mastered before a student enrolls in an Elementary Algebra course. Section I describes the fundamental properties and relationships of whole numbers, focusing on basic operations, divisibility tests, exponents, order of operations, prime numbers, greatest common…

  8. 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…

  9. Permutation centralizer algebras and multimatrix invariants

    NASA Astrophysics Data System (ADS)

    Mattioli, Paolo; Ramgoolam, Sanjaye

    2016-03-01

    We introduce a class of permutation centralizer algebras which underly the combinatorics of multimatrix gauge-invariant observables. One family of such noncommutative algebras is parametrized by two integers. Its Wedderburn-Artin decomposition explains the counting of restricted Schur operators, which were introduced in the physics literature to describe open strings attached to giant gravitons and were subsequently used to diagonalize the Gaussian inner product for gauge invariants of two-matrix models. The structure of the algebra, notably its dimension, its center and its maximally commuting subalgebra, is related to Littlewood-Richardson numbers for composing Young diagrams. It gives a precise characterization of the minimal set of charges needed to distinguish arbitrary matrix gauge invariants, which are related to enhanced symmetries in gauge theory. The algebra also gives a star product for matrix invariants. The center of the algebra allows efficient computation of a sector of multimatrix correlators. These generate the counting of a certain class of bicoloured ribbon graphs with arbitrary genus.

  10. 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.

  11. XML algebras for data mining

    NASA Astrophysics Data System (ADS)

    Zhang, Ming; Yao, JingTao

    2004-04-01

    The XML is a new standard for data representation and exchange on the Internet. There are studies on XML query languages as well as XML algebras in literature. However, attention has not been paid to research on XML algebras for data mining due to partially the fact that there is no widely accepted definition of XML mining tasks. This paper tries to examine the XML mining tasks and provide guidelines to design XML algebras for data mining. Some summarization and comparison have been done to existing XML algebras. We argue that by adding additional operators for mining tasks, XML algebras may work well for data mining with XML documents.

  12. Activation by SLAM Family Receptors Contributes to NK Cell Mediated “Missing-Self” Recognition

    PubMed Central

    Alari-Pahissa, Elisenda; Grandclément, Camille; Jeevan-Raj, Beena; Leclercq, Georges; Veillette, André; Held, Werner

    2016-01-01

    Natural Killer (NK) cells attack normal hematopoietic cells that do not express inhibitory MHC class I (MHC-I) molecules, but the ligands that activate NK cells remain incompletely defined. Here we show that the expression of the Signaling Lymphocyte Activation Molecule (SLAM) family members CD48 and Ly9 (CD229) by MHC-I-deficient tumor cells significantly contributes to NK cell activation. When NK cells develop in the presence of T cells or B cells that lack inhibitory MHC-I but express activating CD48 and Ly9 ligands, the NK cells’ ability to respond to MHC-I-deficient tumor cells is severely compromised. In this situation, NK cells express normal levels of the corresponding activation receptors 2B4 (CD244) and Ly9 but these receptors are non-functional. This provides a partial explanation for the tolerance of NK cells to MHC-I-deficient cells in vivo. Activating signaling via 2B4 is restored when MHC-I-deficient T cells are removed, indicating that interactions with MHC-I-deficient T cells dominantly, but not permanently, impair the function of the 2B4 NK cell activation receptor. These data identify an important role of SLAM family receptors for NK cell mediated “missing-self” reactivity and suggest that NK cell tolerance in MHC-I mosaic mice is in part explained by an acquired dysfunction of SLAM family receptors. PMID:27054584

  13. 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

  14. 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

  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. 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. 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.

  18. 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.

  19. Fock representations of exchange algebras with involution

    SciTech Connect

    Liguori, A.; Mintchev, M.; Rossi, M.

    1997-06-01

    An associative algebra scr(A){sub R} with exchange properties generalizing the canonical (anti)commutation relations is considered. We introduce a family of involutions in scr(A){sub R} and construct the relative Fock representations, examining the positivity of the metric. As an application of the general results, we rigorously prove unitarity of the scattering operator of integrable models in 1+1 space-time dimensions. In this context the possibility of adopting various involutions in the Zamolodchikov{endash}Faddeev algebra is also explored. {copyright} {ital 1997 American Institute of Physics.}

  20. On Dunkl angular momenta algebra

    NASA Astrophysics Data System (ADS)

    Feigin, Misha; Hakobyan, Tigran

    2015-11-01

    We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl( N ) version of the subalge-bra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.

  1. 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.

  2. An Evaluation of Saxon's Algebra Test.

    ERIC Educational Resources Information Center

    Johnson, Dale M.; Smith, Blaine

    1987-01-01

    John Saxon's incremental development model has been proclaimed as a superior teaching strategy for mathematics. This study evaluated the Saxon approach and textbook using 276 Algebra I students in experimental and control groups. The groups were compared in cognitive and affective areas. Results are presented. (Author/MT)

  3. 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…

  4. 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"…

  5. 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. PMID:26124252

  6. An Application of Boolean Algebra to Biology

    ERIC Educational Resources Information Center

    McConnell, John W.

    1971-01-01

    Examines the model of interacting nerve systems based on a switching theory, which uses a mathematical structure familiar to many high school students and requires little knowledge of biology. Reviews the basic operation of nerves, and demonstrates how Boolean algebraic statements are applied to synaptic interactions. (PR)

  7. Quartic Poisson algebras and quartic associative algebras and realizations as deformed oscillator algebras

    SciTech Connect

    Marquette, Ian

    2013-07-15

    We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog, extend Daskaloyannis construction obtained in context of quadratic algebras, and also obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite-dimensional unitary irreducible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptional orthogonal polynomials introduced recently.

  8. Clifford Algebra Cℓ 3(ℂ) for Applications to Field Theories

    NASA Astrophysics Data System (ADS)

    Panicaud, B.

    2011-10-01

    The multivectorial algebras present yet both an academic and a technological interest. Difficulties can occur for their use. Indeed, in all applications care is taken to distinguish between polar and axial vectors and between scalars and pseudo scalars. Then a total of eight elements are often considered even if they are not given the correct name of multivectors. Eventually because of their simplicity, only the vectorial algebra or the quaternions algebra are explicitly used for physical applications. Nevertheless, it should be more convenient to use directly more complex algebras in order to have a wider range of application. The aim of this paper is to inquire into one particular Clifford algebra which could solve this problem. The present study is both didactic concerning its construction and pragmatic because of the introduced applications. The construction method is not an original one. But this latter allows to build up the associated real algebra as well as a peculiar formalism that enables a formal analogy with the classical vectorial algebra. Finally several fields of the theoretical physics will be described thanks to this algebra, as well as a more applied case in general relativity emphasizing simultaneously its relative validity in this particular domain and the easiness of modeling some physical problems.

  9. 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®,…

  10. 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.

  11. Vertex Algebras, Kac-Moody Algebras, and the Monster

    NASA Astrophysics Data System (ADS)

    Borcherds, Richard E.

    1986-05-01

    It is known that the adjoint representation of any Kac-Moody algebra A can be identified with a subquotient of a certain Fock space representation constructed from the root lattice of A. I define a product on the whole of the Fock space that restricts to the Lie algebra product on this subquotient. This product (together with a infinite number of other products) is constructed using a generalization of vertex operators. I also construct an integral form for the universal enveloping algebra of any Kac-Moody algebra that can be used to define Kac-Moody groups over finite fields, some new irreducible integrable representations, and a sort of affinization of any Kac-Moody algebra. The ``Moonshine'' representation of the Monster constructed by Frenkel and others also has products like the ones constructed for Kac-Moody algebras, one of which extends the Griess product on the 196884-dimensional piece to the whole representation.

  12. The tensor hierarchy algebra

    NASA Astrophysics Data System (ADS)

    Palmkvist, Jakob

    2014-01-01

    We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D - 2 - p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.

  13. The tensor hierarchy algebra

    SciTech Connect

    Palmkvist, Jakob

    2014-01-15

    We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D − 2 − p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.

  14. (I,q)-graded Lie algebraic extensions of the Poincaré algebra, constraints on I and q

    NASA Astrophysics Data System (ADS)

    Wills Toro, Luis Alberto

    1995-04-01

    The constraints on the index set I and on the function q of the (I,q)-graded Lie algebras over K containing the Poincaré Lie algebra are studied. By using the single-grading model, particular choices for I and q consistent with the found constraints are determined for K=C. Gradings are then found for which I⊆I=Z2×(Z4N×Z4N)×Gre, with N∈N and Gre an Abelian group. These gradings provide a way for algebraic extensions of the Poincaré Lie algebra beyond the Z2-gradings of supersymmetry and supergravity. In these algebraic extensions, each other commuting space-time parameter can either commute or anticommute with the further parameters of the (I,q)-graded (super) manifold. Different field representations can have—with each other—generalized commutative behavior beyond commutativity and anticommutativity.

  15. Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras

    NASA Astrophysics Data System (ADS)

    Paseka, Jan; Riečanová, Zdenka

    2010-12-01

    We prove that a de Morgan lattice is compactly generated if and only if its order topology is compatible with a uniformity on L generated by some separating function family on L. Moreover, if L is complete then L is (o)-topological. Further, if a basic algebra L (hence lattice with sectional antitone involutions) is compactly generated then L is atomic. Thus all non-atomic Boolean algebras as well as non-atomic lattice effect algebras (including non-atomic MV-algebras and orthomodular lattices) are not compactly generated.

  16. 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.

  17. Deformed Maxwell Algebras and their Realizations

    SciTech Connect

    Gomis, Joaquim; Kamimura, Kiyoshi; Lukierski, Jerzy

    2009-12-15

    We study all possible deformations of the Maxwell algebra. In D = d+1not =3 dimensions there is only one-parameter deformation. The deformed algebra is isomorphic to so(d+1, 1)+so(d, 1) or to so(d, 2)+so(d, 1) depending on the signs of the deformation parameter. We construct in the dS(AdS) space a model of massive particle interacting with Abelian vector field via nonlocal Lorentz force. In D = 2+1 the deformations depend on two parameters b and k. We construct a phase diagram, with two parts of the (b, k) plane with so(3, 1)+so(2, 1) and so( 2, 2)+so(2, 1) algebras separated by a critical curve along which the algebra is isomorphic to Iso(2, 1)+so(2, 1). We introduce in D = 2+1 the Volkov-Akulov type model for a Abelian Goldstone-Nambu vector field described by a non-linear action containing as its bilinear term the free Chern-Simons Lagrangean.

  18. Locally finite dimensional Lie algebras

    NASA Astrophysics Data System (ADS)

    Hennig, Johanna

    We prove that in a locally finite dimensional Lie algebra L, any maximal, locally solvable subalgebra is the stabilizer of a maximal, generalized flag in an integrable, faithful module over L. Then we prove two structure theorems for simple, locally finite dimensional Lie algebras over an algebraically closed field of characteristic p which give sufficient conditions for the algebras to be of the form [K(R, *), K( R, *)] / (Z(R) ∩ [ K(R, *), K(R, *)]) for a simple, locally finite dimensional associative algebra R with involution *. Lastly, we explore the noncommutative geometry of locally simple representations of the diagonal locally finite Lie algebras sl(ninfinity), o( ninfinity), and sp(n infinity).

  19. Quantum computation using geometric algebra

    NASA Astrophysics Data System (ADS)

    Matzke, Douglas James

    This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.

  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. PMID:26806075

  1. 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.

  2. 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…

  3. 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…

  4. 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.

  5. Changing Practice, Changing Minds, from Arithmetical to Algebraic Thinking: An Application of the Concerns-Based Adoption Model (CBAM)

    ERIC Educational Resources Information Center

    Tunks, Jeanne; Weller, Kirk

    2009-01-01

    This study examines the process of change among grade 4 teachers (students aged 9-10 years) who participated in a yearlong Teacher Quality Grant innovation program. The concerns-based adoption model (CBAM), which informed the design and implementation of the program, was used to examine the process of change. Two questions guided the…

  6. 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!

  7. 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…

  8. 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…

  9. 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…

  10. Adaptive Algebraic Smoothers

    SciTech Connect

    Philip, Bobby; Chartier, Dr Timothy

    2012-01-01

    methods based on Local Sensitivity Analysis (LSA). The method can be used in the context of geometric and algebraic multigrid methods for constructing smoothers, and in the context of Krylov methods for constructing block preconditioners. It is suitable for both constant and variable coecient problems. Furthermore, the method can be applied to systems arising from both scalar and coupled system partial differential equations (PDEs), as well as linear systems that do not arise from PDEs. The simplicity of the method will allow it to be easily incorporated into existing multigrid and Krylov solvers while providing a powerful tool for adaptively constructing methods tuned to a problem.

  11. 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

  12. 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

  13. The Algebra of Complex Numbers.

    ERIC Educational Resources Information Center

    LePage, Wilbur R.

    This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…

  14. 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…

  15. 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.)

  16. 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…

  17. 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.)

  18. 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…

  19. Exploring Algebraic Patterns through Literature.

    ERIC Educational Resources Information Center

    Austin, Richard A.; Thompson, Denisse R.

    1997-01-01

    Presents methods for using literature to develop algebraic thinking in an environment that connects algebra to various situations. Activities are based on the book "Anno's Magic Seeds" with additional resources listed. Students express a constant function, exponential function, and a recursive function in their own words as well as writing about…

  20. Learning Algebra from Worked Examples

    ERIC Educational Resources Information Center

    Lange, Karin E.; Booth, Julie L.; Newton, Kristie J.

    2014-01-01

    For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is…

  1. 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.

  2. Invariants of triangular Lie algebras

    NASA Astrophysics Data System (ADS)

    Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman

    2007-07-01

    Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated.

  3. 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

  4. 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)

  5. Infinite Dimensional Algebras and 2+1 Dimensional Field Theory:. yet another View of gl(∞) Some New Algebras

    NASA Astrophysics Data System (ADS)

    Hoppe, Jens

    Over the past years, associative algebras have come to play a major role in several areas of theoretical physics. Firstly, it has been realized that Yang Baxter algebras [1] constitute the relevant structure underlying 1+1 dimensional integrable models; in addition, their relation to braid groups, the theory of knots and links, and the exchange algebras of 1+1 dimensional conformal field theories [2] has been quite well understood by now. Secondly, deformations of Poisson structures that appeared in 2+1 dimensional field theories as infinite dimensional symmetry algebras possess underlying associative structures, which have also been studied in some detail (concerning higher spin theories see, e.g., [3, 4] and references therein, concerning the enveloping algebra of sl(2, C) see, e.g., [5], concerning deformations of diffAT2 — the Lie algebra of infinitesimal area preserving diffeomorphisms of the Torus — see [6, 7, 8, 9]). Ideas on how both investigations could eventually converge (i.e., a relation between 2+1 and 1+1 dimensions) have, e.g., been expressed in [10]. As indicated by the two subtitles there will be two parts to my paper: the first one presents a view on something I met long ago [11], and recently got interested in again [5, 7, 9, 12], while the second part introduces some algebraic structures that seem to be interesting, and possibly new.

  6. Dynamics of gelling liquids: algebraic relaxation.

    PubMed

    Srivastava, Sunita; Kumar, C N; Tankeshwar, K

    2009-08-19

    The sol-gel system which is known, experimentally, to exhibit a power law decay of stress autocorrelation function has been studied theoretically. A second-order nonlinear differential equation obtained from Mori's integro-differential equation is derived which provides the algebraic decay of a time correlation function. Involved parameters in the expression obtained are related to exact properties of the corresponding correlation function. The algebraic model has been applied to Lennard-Jones and sol-gel systems. The model shows the behaviour of viscosity as has been observed in computer simulation and theoretical studies. The expression obtained for the viscosity predicts a logarithmic divergence at a critical value of the parameter in agreement with the prediction of other theories. PMID:21828600

  7. 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…

  8. Structural Affects on the Slamming Pressures of High-Speed Planing Craft

    NASA Astrophysics Data System (ADS)

    Ikeda, Christine; Taravella, Brandon; Judge, Carolyn

    2015-11-01

    High-speed planing craft are subjected to repeated slamming events in waves that can be very extreme depending on the wave topography, impact angle of the ship, forward speed of the ship, encounter angle, and height out of the water. The current work examines this fluid-structure interaction problem through the use of wedge drop experiments and a CFD code. In the first set of experiments, a rigid 20-degree deadrise angle wedge was dropped from a range of heights (0 <= H <= 0 . 6 m) and while pressures and accelerations of the slam even were measured. The second set of experiments involved a flexible-bottom 15-degree deadrise angle wedge that was dropped from from the same range of heights. In these second experiments, the pressures, accelerations, and strain field were measured. Both experiments are compared with a non-linear boundary value flat cylinder theory code in order to compare the pressure loading. The code assumes a rigid structure, therefore, the results between the code and the first experiment are in good agreement. The second experiment shows pressure magnitudes that are lower than the predictions due to the energy required to deform the structure. Funding from University of New Orleans Office of Research and Sponsored Programs and the Office of Naval Research.

  9. 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. PMID:21358004

  10. 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.

  11. 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)

  12. 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.

  13. 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.

  14. Using Homemade Algebra Tiles To Develop Algebra and Prealgebra Concepts.

    ERIC Educational Resources Information Center

    Leitze, Annette Ricks; Kitt, Nancy A.

    2000-01-01

    Describes how to use homemade tiles, sketches, and the box method to reach a broader group of students for successful algebra learning. Provides a list of concepts appropriate for such an approach. (KHR)

  15. Loop Virasoro Lie conformal algebra

    SciTech Connect

    Wu, Henan Chen, Qiufan; Yue, Xiaoqing

    2014-01-15

    The Lie conformal algebra of loop Virasoro algebra, denoted by CW, is introduced in this paper. Explicitly, CW is a Lie conformal algebra with C[∂]-basis (L{sub i} | i∈Z) and λ-brackets [L{sub i} {sub λ} L{sub j}] = (−∂−2λ)L{sub i+j}. Then conformal derivations of CW are determined. Finally, rank one conformal modules and Z-graded free intermediate series modules over CW are classified.

  16. 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…

  17. 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.

  18. 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.

  19. 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.

  20. Sequential products on effect algebras

    NASA Astrophysics Data System (ADS)

    Gudder, Stan; Greechie, Richard

    2002-02-01

    A sequential effect algebra (SEA) is an effect algebra on which a sequential product with natural properties is defined. The properties of sequential products on Hilbert space effect algebras are discussed. For a general SEA, relationships between sequential independence, coexistence and compatibility are given. It is shown that the sharp elements of a SEA form an orthomodular poset. The sequential center of a SEA is discussed and a characterization of when the sequential center is isomorphic to a fuzzy set system is presented. It is shown that the existence, of a sequential product is a strong restriction that eliminates many effect algebras from being SEA's. For example, there are no finite nonboolean SEA's, A measure of sharpness called the sharpness index is studied. The existence of horizontal sums of SEA's is characterized and examples of horizontal sums and tensor products are presented.

  1. Curvature calculations with spacetime algebra

    SciTech Connect

    Hestenes, D.

    1986-06-01

    A new method for calculating the curvature tensor is developed and applied to the Scharzschild case. The method employs Clifford algebra and has definite advantages over conventional methods using differential forms or tensor analysis.

  2. 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)

  3. 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.

  4. 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.

  5. Semiclassical states on Lie algebras

    SciTech Connect

    Tsobanjan, Artur

    2015-03-15

    The effective technique for analyzing representation-independent features of quantum systems based on the semiclassical approximation (developed elsewhere) has been successfully used in the context of the canonical (Weyl) algebra of the basic quantum observables. Here, we perform the important step of extending this effective technique to the quantization of a more general class of finite-dimensional Lie algebras. The case of a Lie algebra with a single central element (the Casimir element) is treated in detail by considering semiclassical states on the corresponding universal enveloping algebra. Restriction to an irreducible representation is performed by “effectively” fixing the Casimir condition, following the methods previously used for constrained quantum systems. We explicitly determine the conditions under which this restriction can be consistently performed alongside the semiclassical truncation.

  6. GNSS algebraic structures

    NASA Astrophysics Data System (ADS)

    Lannes, A.; Teunissen, P. J. G.

    2011-05-01

    The first objective of this paper is to show that some basic concepts used in global navigation satellite systems (GNSS) are similar to those introduced in Fourier synthesis for handling some phase calibration problems. In experimental astronomy, the latter are at the heart of what is called `phase closure imaging.' In both cases, the analysis of the related structures appeals to the algebraic graph theory and the algebraic number theory. For example, the estimable functions of carrier-phase ambiguities, which were introduced in GNSS to correct some rank defects of the undifferenced equations, prove to be `closure-phase ambiguities:' the so-called `closure-delay' (CD) ambiguities. The notion of closure delay thus generalizes that of double difference (DD). The other estimable functional variables involved in the phase and code undifferenced equations are the receiver and satellite pseudo-clock biases. A related application, which corresponds to the second objective of this paper, concerns the definition of the clock information to be broadcasted to the network users for their precise point positioning (PPP). It is shown that this positioning can be achieved by simply having access to the satellite pseudo-clock biases. For simplicity, the study is restricted to relatively small networks. Concerning the phase for example, these biases then include five components: a frequency-dependent satellite-clock error, a tropospheric satellite delay, an ionospheric satellite delay, an initial satellite phase, and an integer satellite ambiguity. The form of the PPP equations to be solved by the network user is then similar to that of the traditional PPP equations. As soon as the CD ambiguities are fixed and validated, an operation which can be performed in real time via appropriate decorrelation techniques, estimates of these float biases can be immediately obtained. No other ambiguity is to be fixed. The satellite pseudo-clock biases can thus be obtained in real time. This is

  7. Slamming of a breaking wave on a wall.

    PubMed

    Shu, Jian-Jun

    2004-12-01

    This paper is intended to study impact forces of breaking waves on a rigid wall based on a nonlinear potential-flow theory. This is a model problem for some technologically important design issues such as the impact of breaking waves on ships, coastal and offshore structures. We are interested in the short-time successive triggering of nonlinear effects using a small-time expansion. The analytical solutions for the impact force on a rigid wall and the free-surface profile are derived. PMID:15697501

  8. ALGEBRA v.1.27

    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.

  9. Development of Kinematic 3D Laser Scanning System for Indoor Mapping and As-Built BIM Using Constrained SLAM

    PubMed Central

    Jung, Jaehoon; Yoon, Sanghyun; Ju, Sungha; Heo, Joon

    2015-01-01

    The growing interest and use of indoor mapping is driving a demand for improved data-acquisition facility, efficiency and productivity in the era of the Building Information Model (BIM). The conventional static laser scanning method suffers from some limitations on its operability in complex indoor environments, due to the presence of occlusions. Full scanning of indoor spaces without loss of information requires that surveyors change the scanner position many times, which incurs extra work for registration of each scanned point cloud. Alternatively, a kinematic 3D laser scanning system, proposed herein, uses line-feature-based Simultaneous Localization and Mapping (SLAM) technique for continuous mapping. Moreover, to reduce the uncertainty of line-feature extraction, we incorporated constrained adjustment based on an assumption made with respect to typical indoor environments: that the main structures are formed of parallel or orthogonal line features. The superiority of the proposed constrained adjustment is its reduction for uncertainties of the adjusted lines, leading to successful data association process. In the present study, kinematic scanning with and without constrained adjustment were comparatively evaluated in two test sites, and the results confirmed the effectiveness of the proposed system. The accuracy of the 3D mapping result was additionally evaluated by comparison with the reference points acquired by a total station: the Euclidean average distance error was 0.034 m for the seminar room and 0.043 m for the corridor, which satisfied the error tolerance for point cloud acquisition (0.051 m) according to the guidelines of the General Services Administration for BIM accuracy. PMID:26501292

  10. Development of kinematic 3D laser scanning system for indoor mapping and as-built BIM using constrained SLAM.

    PubMed

    Jung, Jaehoon; Yoon, Sanghyun; Ju, Sungha; Heo, Joon

    2015-01-01

    The growing interest and use of indoor mapping is driving a demand for improved data-acquisition facility, efficiency and productivity in the era of the Building Information Model (BIM). The conventional static laser scanning method suffers from some limitations on its operability in complex indoor environments, due to the presence of occlusions. Full scanning of indoor spaces without loss of information requires that surveyors change the scanner position many times, which incurs extra work for registration of each scanned point cloud. Alternatively, a kinematic 3D laser scanning system, proposed herein, uses line-feature-based Simultaneous Localization and Mapping (SLAM) technique for continuous mapping. Moreover, to reduce the uncertainty of line-feature extraction, we incorporated constrained adjustment based on an assumption made with respect to typical indoor environments: that the main structures are formed of parallel or orthogonal line features. The superiority of the proposed constrained adjustment is its reduction for uncertainties of the adjusted lines, leading to successful data association process. In the present study, kinematic scanning with and without constrained adjustment were comparatively evaluated in two test sites, and the results confirmed the effectiveness of the proposed system. The accuracy of the 3D mapping result was additionally evaluated by comparison with the reference points acquired by a total station: the Euclidean average distance error was 0.034 m for the seminar room and 0.043 m for the corridor, which satisfied the error tolerance for point cloud acquisition (0.051 m) according to the guidelines of the General Services Administration for BIM accuracy. PMID:26501292

  11. Using SLAM to Look For the Dog Valley Fault, Truckee Area, California

    NASA Astrophysics Data System (ADS)

    Cronin, V. S.; Ashburn, J. A.; Sverdrup, K. A.

    2014-12-01

    The Truckee earthquake (9/12/1966, ML6.0) was a left-lateral event on a previously unrecognized NW-trending fault. The Prosser Creek and Boca Dams sustained damage, and the trace of the suspected causative fault passes near or through the site of the then-incomplete Stampede Dam. Another M6 earthquake occurred along the same general trend in 1948 with an epicenter in Dog Valley ~14 km to the NW of the 1966 epicenter. This trend is called the Dog Valley Fault (DVF), and its location on the ground surface is suggested by a prominent but broad zone of geomorphic lineaments near the cloud of aftershock epicenters determined for the 1966 event. Various ground effects of the 1966 event described by Kachadoorian et al. (1967) were located within this broad zone. The upper shoreface of reservoirs in the Truckee-Prosser-Martis basin are now exposed due to persistent drought. We have examined fault strands in a roadcut and exposed upper shoreface adjacent to the NE abutment of Stampede Dam. These are interpreted to be small-displacement splays associated with the DVF -- perhaps elements of the DVF damage zone. We have used the Seismo-Lineament Analysis Method (SLAM) to help us constrain the location of the DVF, based on earthquake focal mechanisms. Seismo-lineaments were computed, using recent revisions in the SLAM code (bearspace.baylor.edu/Vince_Cronin/www/SLAM/), for the 1966 main earthquake and for the better-recorded earthquakes of 7/3/1983 (M4) and 8/30/1992 (M3.2) that are inferred to have occurred along the DVF. Associated geomorphic analysis and some field reconnaissance identified a trend that might be associated with a fault, extending from the NW end of Prosser Creek Reservoir ~32° toward the Stampede Dam area. Triangle-strain analysis using horizontal velocities of local Plate Boundary Observatory GPS sites P146, P149, P150 and SLID indicates that the area rotates clockwise ~1-2°/Myr relative to the stable craton, as might be expected because the study area is

  12. SLAM- and Nectin-4-Independent Noncytolytic Spread of Canine Distemper Virus in Astrocytes

    PubMed Central

    Alves, Lisa; Khosravi, Mojtaba; Avila, Mislay; Ader-Ebert, Nadine; Bringolf, Fanny; Zurbriggen, Andreas; Vandevelde, Marc

    2015-01-01

    ABSTRACT Measles and canine distemper viruses (MeV and CDV, respectively) first replicate in lymphatic and epithelial tissues by using SLAM and nectin-4 as entry receptors, respectively. The viruses may also invade the brain to establish persistent infections, triggering fatal complications, such as subacute sclerosis pan-encephalitis (SSPE) in MeV infection or chronic, multiple sclerosis-like, multifocal demyelinating lesions in the case of CDV infection. In both diseases, persistence is mediated by viral nucleocapsids that do not require packaging into particles for infectivity but are directly transmitted from cell to cell (neurons in SSPE or astrocytes in distemper encephalitis), presumably by relying on restricted microfusion events. Indeed, although morphological evidence of fusion remained undetectable, viral fusion machineries and, thus, a putative cellular receptor, were shown to contribute to persistent infections. Here, we first showed that nectin-4-dependent cell-cell fusion in Vero cells, triggered by a demyelinating CDV strain, remained extremely limited, thereby supporting a potential role of nectin-4 in mediating persistent infections in astrocytes. However, nectin-4 could not be detected in either primary cultured astrocytes or the white matter of tissue sections. In addition, a bioengineered “nectin-4-blind” recombinant CDV retained full cell-to-cell transmission efficacy in primary astrocytes. Combined with our previous report demonstrating the absence of SLAM expression in astrocytes, these findings are suggestive for the existence of a hitherto unrecognized third CDV receptor expressed by glial cells that contributes to the induction of noncytolytic cell-to-cell viral transmission in astrocytes. IMPORTANCE While persistent measles virus (MeV) infection induces SSPE in humans, persistent canine distemper virus (CDV) infection causes chronic progressive or relapsing demyelination in carnivores. Common to both central nervous system (CNS

  13. 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.

  14. Algebraic Flux Correction II

    NASA Astrophysics Data System (ADS)

    Kuzmin, Dmitri; Möller, Matthias; Gurris, Marcel

    Flux limiting for hyperbolic systems requires a careful generalization of the design principles and algorithms introduced in the context of scalar conservation laws. In this chapter, we develop FCT-like algebraic flux correction schemes for the Euler equations of gas dynamics. In particular, we discuss the construction of artificial viscosity operators, the choice of variables to be limited, and the transformation of antidiffusive fluxes. An a posteriori control mechanism is implemented to make the limiter failsafe. The numerical treatment of initial and boundary conditions is discussed in some detail. The initialization is performed using an FCT-constrained L 2 projection. The characteristic boundary conditions are imposed in a weak sense, and an approximate Riemann solver is used to evaluate the fluxes on the boundary. We also present an unconditionally stable semi-implicit time-stepping scheme and an iterative solver for the fully discrete problem. The results of a numerical study indicate that the nonlinearity and non-differentiability of the flux limiter do not inhibit steady state convergence even in the case of strongly varying Mach numbers. Moreover, the convergence rates improve as the pseudo-time step is increased.

  15. 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.

  16. 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.

  17. Heisenberg uncertainty in reduced power algebras

    NASA Astrophysics Data System (ADS)

    Rosinger, Elemér E.

    2012-12-01

    The Heisenberg uncertainty relation is known to be obtainable by a purely mathematical argument. Based on that fact, here it is shown that the Heisenberg uncertainty relation remains valid when Quantum Mechanics is re-formulated within far wider frameworks of scalars, namely, within one or the other of the infinitely many reduced power algebras which can replace the usual real numbers R, or complex numbers C. Three possible major advantages in Physics of such a reformulation are: 1) the disappearance of the well known and hard to deal with problem of the so called "infinities in Physics", 2) the possibilitiy to have infinitely many "levels of precision" instead of the only one existing at present, 3) the possibility to model "hierarchies of Planck constants", [2]. Last and not least, the scalars given by reduced power algebras contain as a particular case those obtained by Nonstandard Analysis, yet they are far more simple and easy to deal with, being in fact on the level of a first course in Algebra. A detailed version of this paper can be found in arxiv:0901.4825.

  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. Nonnumeric Computer Applications to Algebra, Trigonometry and Calculus.

    ERIC Educational Resources Information Center

    Stoutemyer, David R.

    1983-01-01

    Described are computer program packages requiring little or no knowledge of computer programing for college algebra, calculus, and abstract algebra. Widely available computer algebra systems are listed. (MNS)

  20. a Fast and Flexible Method for Meta-Map Building for Icp Based Slam

    NASA Astrophysics Data System (ADS)

    Kurian, A.; Morin, K. W.

    2016-06-01

    Recent developments in LiDAR sensors make mobile mapping fast and cost effective. These sensors generate a large amount of data which in turn improves the coverage and details of the map. Due to the limited range of the sensor, one has to collect a series of scans to build the entire map of the environment. If we have good GNSS coverage, building a map is a well addressed problem. But in an indoor environment, we have limited GNSS reception and an inertial solution, if available, can quickly diverge. In such situations, simultaneous localization and mapping (SLAM) is used to generate a navigation solution and map concurrently. SLAM using point clouds possesses a number of computational challenges even with modern hardware due to the shear amount of data. In this paper, we propose two strategies for minimizing the cost of computation and storage when a 3D point cloud is used for navigation and real-time map building. We have used the 3D point cloud generated by Leica Geosystems's Pegasus Backpack which is equipped with Velodyne VLP-16 LiDARs scanners. To improve the speed of the conventional iterative closest point (ICP) algorithm, we propose a point cloud sub-sampling strategy which does not throw away any key features and yet significantly reduces the number of points that needs to be processed and stored. In order to speed up the correspondence finding step, a dual kd-tree and circular buffer architecture is proposed. We have shown that the proposed method can run in real time and has excellent navigation accuracy characteristics.

  1. 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.

  2. Ternary generalization of Heisenberg's algebra

    NASA Astrophysics Data System (ADS)

    Kerner, Richard

    2015-06-01

    A concise study of ternary and cubic algebras with Z3 grading is presented. We discuss some underlying ideas leading to the conclusion that the discrete symmetry group of permutations of three objects, S3, and its abelian subgroup Z3 may play an important role in quantum physics. We show then how most of important algebras with Z2 grading can be generalized with ternary composition laws combined with a Z3 grading. We investigate in particular a ternary, Z3-graded generalization of the Heisenberg algebra. It turns out that introducing a non-trivial cubic root of unity, , one can define two types of creation operators instead of one, accompanying the usual annihilation operator. The two creation operators are non-hermitian, but they are mutually conjugate. Together, the three operators form a ternary algebra, and some of their cubic combinations generate the usual Heisenberg algebra. An analogue of Hamiltonian operator is constructed by analogy with the usual harmonic oscillator, and some properties of its eigenfunctions are briefly discussed.

  3. Slam Dunk

    ERIC Educational Resources Information Center

    Herek, Matthew

    2011-01-01

    There's nothing like a worldwide financial meltdown to kick-start an alumni association's career networking offerings. In 2009, the Northwestern University alumni board provided clear direction to its regional affiliates and to the full-time staff working at the Evanston, Illinois, campus: Develop ways to purposefully connect alumni with each…

  4. 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.

  5. Solution to the SLAM Problem in Low Dynamic Environments Using a Pose Graph and an RGB-D Sensor

    PubMed Central

    Lee, Donghwa; Myung, Hyun

    2014-01-01

    In this study, we propose a solution to the simultaneous localization and mapping (SLAM) problem in low dynamic environments by using a pose graph and an RGB-D (red-green-blue depth) sensor. The low dynamic environments refer to situations in which the positions of objects change over long intervals. Therefore, in the low dynamic environments, robots have difficulty recognizing the repositioning of objects unlike in highly dynamic environments in which relatively fast-moving objects can be detected using a variety of moving object detection algorithms. The changes in the environments then cause groups of false loop closing when the same moved objects are observed for a while, which means that conventional SLAM algorithms produce incorrect results. To address this problem, we propose a novel SLAM method that handles low dynamic environments. The proposed method uses a pose graph structure and an RGB-D sensor. First, to prune the falsely grouped constraints efficiently, nodes of the graph, that represent robot poses, are grouped according to the grouping rules with noise covariances. Next, false constraints of the pose graph are pruned according to an error metric based on the grouped nodes. The pose graph structure is reoptimized after eliminating the false information, and the corrected localization and mapping results are obtained. The performance of the method was validated in real experiments using a mobile robot system. PMID:25019633

  6. Solution to the SLAM problem in low dynamic environments using a pose graph and an RGB-D sensor.

    PubMed

    Lee, Donghwa; Myung, Hyun

    2014-01-01

    In this study, we propose a solution to the simultaneous localization and mapping (SLAM) problem in low dynamic environments by using a pose graph and an RGB-D (red-green-blue depth) sensor. The low dynamic environments refer to situations in which the positions of objects change over long intervals. Therefore, in the low dynamic environments, robots have difficulty recognizing the repositioning of objects unlike in highly dynamic environments in which relatively fast-moving objects can be detected using a variety of moving object detection algorithms. The changes in the environments then cause groups of false loop closing when the same moved objects are observed for a while, which means that conventional SLAM algorithms produce incorrect results. To address this problem, we propose a novel SLAM method that handles low dynamic environments. The proposed method uses a pose graph structure and an RGB-D sensor. First, to prune the falsely grouped constraints efficiently, nodes of the graph, that represent robot poses, are grouped according to the grouping rules with noise covariances. Next, false constraints of the pose graph are pruned according to an error metric based on the grouped nodes. The pose graph structure is reoptimized after eliminating the false information, and the corrected localization and mapping results are obtained. The performance of the method was validated in real experiments using a mobile robot system. PMID:25019633

  7. On the Generalized Unitary Parasupersymmetry Algebra of Beckers-Debergh

    NASA Astrophysics Data System (ADS)

    Chenaghlou, A.; Fakhri, H.

    An appropriate generalization of the unitary parasupersymmetry algebra of Beckers-Debergh to arbitrary order is presented in this paper. A special representation for realizing the even arbitrary order unitary parasupersymmetry algebra of Beckers-Debergh is analyzed by one-dimensional shape invariance solvable models, 2D and 3D quantum solvable models obtained from the shape invariance theory as well. In particular, in the special representation, it is shown that the isospectrum Hamiltonians consist of the two partner Hamiltonians of the shape invariance theory.

  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. PMID:26645985

  9. 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.

  10. Computer Algebra Systems in Undergraduate Instruction.

    ERIC Educational Resources Information Center

    Small, Don; And Others

    1986-01-01

    Computer algebra systems (such as MACSYMA and muMath) can carry out many of the operations of calculus, linear algebra, and differential equations. Use of them with sketching graphs of rational functions and with other topics is discussed. (MNS)

  11. 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.

  12. 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.

  13. Reverse engineering: algebraic boundary representations to constructive solid geometry.

    SciTech Connect

    Buchele, S. F.; Ellingson, W. A.

    1997-12-17

    Recent advances in reverse engineering have focused on recovering a boundary representation (b-rep) of an object, often for integration with rapid prototyping. This boundary representation may be a 3-D point cloud, a triangulation of points, or piecewise algebraic or parametric surfaces. This paper presents work in progress to develop an algorithm to extend the current state of the art in reverse engineering of mechanical parts. This algorithm will take algebraic surface representations as input and will produce a constructive solid geometry (CSG) description that uses solid primitives such as rectangular block, pyramid, sphere, cylinder, and cone. The proposed algorithm will automatically generate a CSG solid model of a part given its algebraic b-rep, thus allowing direct input into a CAD system and subsequent CSG model generation.

  14. Making Algebra Work: Instructional Strategies that Deepen Student Understanding, within and between Algebraic Representations

    ERIC Educational Resources Information Center

    Star, Jon R.; Rittle-Johnson, Bethany

    2009-01-01

    Competence in algebra is increasingly recognized as a critical milestone in students' middle and high school years. The transition from arithmetic to algebra is a notoriously difficult one, and improvements in algebra instruction are greatly needed (National Research Council, 2001). Algebra historically has represented students' first sustained…

  15. Cognitive Tutor[R] Algebra I. What Works Clearinghouse Intervention Report

    ERIC Educational Resources Information Center

    What Works Clearinghouse, 2009

    2009-01-01

    The "Cognitive Tutor[R] Algebra I" curriculum, published by Carnegie Learning, is an approach that combines algebra textbooks with interactive software. The software is developed around an artificial intelligence model that identifies strengths and weaknesses in each individual student's mastery of mathematical concepts. It then customizes prompts…

  16. Dual spaces of differential Lie algebras

    SciTech Connect

    Kupershmidt, B.A.

    1982-01-01

    We present a mathematical scheme which serves as an infinite-dimensional generalization of Poisson structures on dual spaces of finite-dimensional Lie algebras, which are well known and widely used in classical mechanics. These structures have recently appeared in the theory of Lax equations, long waves in hydrodynamics, and various other physical models: compressible hydrodynamics, magnetohydrodynamics, multifluid plasmas, elasticity, superfluid /sup 4/He and /sup 3/He-A, Ginzburg-Landau theory of superconductors, and classical chromohydrodynamics (the generalization of plasma physics to Yang-Mills interactions).

  17. 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.

  18. The weak Hopf algebras related to generalized Kac-Moody algebra

    SciTech Connect

    Wu Zhixiang

    2006-06-15

    We define a kind of quantized enveloping algebra of a generalized Kac-Moody algebra G by adding a generator J satisfying J{sup m}=J{sup m-1} for some integer m. We denote this algebra by wU{sub q}{sup {tau}}(G). This algebra is a weak Hopf algebra if and only if m=2. In general, it is a bialgebra, and contains a Hopf subalgebra. This Hopf subalgebra is isomorphic to the usually quantum envelope algebra U{sub q}(G) of a generalized Kac-Moody algebra G.

  19. 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…

  20. UCSMP Algebra. What Works Clearinghouse Intervention Report

    ERIC Educational Resources Information Center

    What Works Clearinghouse, 2007

    2007-01-01

    "University of Chicago School Mathematics Project (UCSMP) Algebra," designed to increase students' skills in algebra, is appropriate for students in grades 7-10, depending on the students' incoming knowledge. This one-year course highlights applications, uses statistics and geometry to develop the algebra of linear equations and inequalities, and…

  1. Graphing Calculator Use in Algebra Teaching

    ERIC Educational Resources Information Center

    Dewey, Brenda L.; Singletary, Ted J.; Kinzel, Margaret T.

    2009-01-01

    This study examines graphing calculator technology availability, characteristics of teachers who use it, teacher attitudes, and how use reflects changes to algebra curriculum and instructional practices. Algebra I and Algebra II teachers in 75 high school and junior high/middle schools in a diverse region of a northwestern state were surveyed.…

  2. 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.

  3. 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…

  4. 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…

  5. 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…

  6. 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"…

  7. Lessons for Algebraic Thinking. Grades K-2.

    ERIC Educational Resources Information Center

    von Rotz, Leyani; Burns, Marilyn

    Algebra is one of the top priorities of mathematics instruction for the elementary and middle grades. This book is designed to help K-2 teachers meet the challenge of making algebra an integral part of their mathematics instruction and realize both what to teach and how to teach central algebraic concepts. Classroom-tested lessons help teachers…

  8. 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…

  9. 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…

  10. Inequalities, Assessment and Computer Algebra

    ERIC Educational Resources Information Center

    Sangwin, Christopher J.

    2015-01-01

    The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in…

  11. 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…

  12. Implementing Change in College Algebra

    ERIC Educational Resources Information Center

    Haver, William E.

    2007-01-01

    In this paper, departments are urged to consider implementing the type of changes proposed in Beyond Crossroads in College Algebra. The author of this paper is chair of the Curriculum Renewal Across the First Two Years (CRAFTY) Committee of the Mathematical Association of America. The committee has members from two-year colleges, four-year…

  13. 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…

  14. 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.

  15. Algebra for All. Research Brief

    ERIC Educational Resources Information Center

    Bleyaert, Barbara

    2009-01-01

    The call for "algebra for all" is not a recent phenomenon. Concerns about the inadequacy of math (and science) preparation in America's high schools have been a steady drumbeat since the 1957 launch of Sputnik; a call for raising standards and the number of math (and science) courses required for graduation has been a part of countless national…

  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. 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…

  18. An Introduction to Algebraic Multigrid

    SciTech Connect

    Falgout, R D

    2006-04-25

    Algebraic multigrid (AMG) solves linear systems based on multigrid principles, but in a way that only depends on the coefficients in the underlying matrix. The author begins with a basic introduction to AMG methods, and then describes some more recent advances and theoretical developments

  19. Elementary Algebra Connections to Precalculus

    ERIC Educational Resources Information Center

    Lopez-Boada, Roberto; Daire, Sandra Arguelles

    2013-01-01

    This article examines the attitudes of some precalculus students to solve trigonometric and logarithmic equations and systems using the concepts of elementary algebra. With the goal of enticing the students to search for and use connections among mathematical topics, they are asked to solve equations or systems specifically designed to allow…

  20. Adventures in Flipping College Algebra

    ERIC Educational Resources Information Center

    Van Sickle, Jenna

    2015-01-01

    This paper outlines the experience of a university professor who implemented flipped learning in two sections of college algebra courses for two semesters. It details how the courses were flipped, what technology was used, advantages, challenges, and results. It explains what students do outside of class, what they do inside class, and discusses…

  1. Kinds of Knowledge in Algebra.

    ERIC Educational Resources Information Center

    Lewis, Clayton

    Solving equations in elementary algebra requires knowledge of the permitted operations, and knowledge of what operation to use at a given point in the solution process. While just these kinds of knowledge would be adequate for an ideal solver, human solvers appear to need and use other kinds of knowledge. First, many errors seem to indicate that…

  2. Algebra, Home Mortgages, and Recessions

    ERIC Educational Resources Information Center

    Mariner, Jean A. Miller; Miller, Richard A.

    2009-01-01

    The current financial crisis and recession in the United States present an opportunity to discuss relevant applications of some topics in typical first-and second-year algebra and precalculus courses. Real-world applications of percent change, exponential functions, and sums of finite geometric sequences can help students understand the problems…

  3. 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…

  4. 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.

  5. 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.

  6. Principals + Algebra (- Fear) = Instructional Leadership

    ERIC Educational Resources Information Center

    Carver, Cynthia L.

    2010-01-01

    Recent state legislation in Michigan mandates that all graduating seniors successfully pass algebra I and II. Numerous initiatives have been enacted to help mathematics teachers meet this challenge, yet school principals have had little preparation for the necessary curricular and instructional changes. To address this unmet need, university-based…

  7. Experts Question California's Algebra Edict

    ERIC Educational Resources Information Center

    Cavanagh, Sean

    2008-01-01

    Business leaders from important sectors of the American economy have been urging schools to set higher standards in math and science--and California officials, in mandating that 8th graders be tested in introductory algebra, have responded with one of the highest such standards in the land. Still, many California educators and school…

  8. Preliminary Use of the Seismo-Lineament Analysis Method (SLAM) to Investigate Seismogenic Faulting in the Grand Canyon Area, Northern Arizona

    NASA Astrophysics Data System (ADS)

    Cronin, V. S.; Cleveland, D. M.; Prochnow, S. J.

    2007-12-01

    This is a progress report on our application of the Seismo-Lineament Analysis Method (SLAM) to the eastern Grand Canyon area of northern Arizona. SLAM is a new integrated method for identifying potentially seismogenic faults using earthquake focal-mechanism solutions, geomorphic analysis and field work. There are two nodal planes associated with any double-couple focal-mechanism solution, one of which is thought to coincide with the fault that produced the earthquake; the slip vector is normal to the other (auxiliary) plane. When no uncertainty in the orientation of the fault-plane solution is reported, we use the reported vertical and horizontal uncertainties in the focal location to define a tabular uncertainty volume whose orientation coincides with that of the fault-plane solution. The intersection of the uncertainty volume and the ground surface (represented by the DEM) is termed a seismo-lineament. An image of the DEM surface is illuminated perpendicular to the strike of the seismo- lineament to accentuate geomorphic features within the seismo-lineament that may be related to seismogenic faulting. This evaluation of structural geomorphology is repeated for several different azimuths and elevations of illumination. A map is compiled that includes possible geomorphic indicators of faulting as well as previously mapped faults within each seismo-lineament, constituting a set of hypotheses for the possible location of seismogenic fault segments that must be evaluated through fieldwork. A fault observed in the field that is located within a seismo-lineament, and that has an orientation and slip characteristics that are statistically compatible with the fault-plane solution, is considered potentially seismogenic. We compiled a digital elevation model (DEM) of the Grand Canyon area from published data sets. We used earthquake focal-mechanism solutions produced by David Brumbaugh (2005, BSSA, v. 95, p. 1561-1566) for five M > 3.5 events reported between 1989 and 1995

  9. Lighter-Than-Air UAV with slam capabilities for mapping applications and atmpsphere analysys.

    NASA Astrophysics Data System (ADS)

    Colombatti, G.; Aboudan, A.; La Gloria, N.; Debei, S.; Flamini, E.

    Exploration of the planets and the moons of the Solar System has, up to now, been performed by remote sensing from Earth, fly-by probes, orbiters, landers and rovers. It must be outlined that remote sensing probes and orbiters can only provide non-contact, limited resolution imagery over a small number of spectral bands; on the other hand, landers provide high-resolution imagery and in-situ data collection and analysis capabilities, but only for a single site; while rovers allow imagery collection and in-situ science across their path. These characteristics of the described means highlight how mobility is a key requirement for planetary exploration missions. Autonomous Lighter-Than-Air systems can be used to explore unknown environments without obstacle avoidance problems, mapping large areas to different resolutions and perform a wide variety of measurements and experiments while traveling in the atmosphere. Sensor fusion between Inertial Measurement Unit (IMU) and vision systems can be used to support vehicle navigation and variable resolution surface mapping. In this work a minimal sensor suite composed by a navigation-grade IMU and stereo camera pair has been studied. At altitudes below 100 m stereo vision techniques can provide range, bearing and elevation measurements of a set of scattered points on the planetary surface. Simultaneous Localization and Mapping (SLAM) extended Kalman filter algorithm has been adapted to deal with stereo camera observations. Sensor fusion with IMU measurements is used to track rapid vehicle movements and to maintain the vehicle position and attitude estimation also if, for a limited period of time, no vision measurements are available. Moreover the SLAM algorithm produces a scattered points map of the complete traveled area. In this work we analyse the dynamics of the airship in response of the encountered environment of Titan moon. Possible trajectories for an extended survey are investigated; this allows to have a precise

  10. ICOS, SLAM and PD-1 expression and regulation on T lymphocytes reflect the immune dysregulation in patients with HIV-related illness with pulmonary tuberculosis

    PubMed Central

    Jurado, Javier Oscar; Pasquinelli, Virginia; Alvarez, Ivana Belén; Martínez, Gustavo Javier; Laufer, Natalia; Sued, Omar; Cahn, Pedro; Musella, Rosa María; Abbate, Eduardo; Salomón, Horacio; Quiroga, María Florencia

    2012-01-01

    Background Tuberculosis (TB) continues to be the most frequent cause of illness and death from an infectious agent globally, and its interaction with HIV is having devastating effects. To investigate how HIV alters the immune response to Mycobacterium tuberculosis (Mtb), we assessed basal and Mtb-induced proliferation, cytokine production, and expression of signalling lymphocytic activation molecule (SLAM), inducible costimulator (ICOS) and programmed death-1 (PD-1) on T lymphocytes from HIV-positive individuals coinfected with TB, HIV-positive subjects, TB patients and healthy donors (HD). Findings HIV-TB patients showed increased ICOS, SLAM and PD-1 basal levels on T lymphocytes, whereas HIV-positive individuals displayed elevated levels of SLAM and PD-1, TB patients high levels of SLAM, and HD low levels of the three proteins. Mtb-stimulation enhanced ICOS expression in the four groups, but only TB and HD increased SLAM and PD-1 levels. Conclusions These data show the immune deregulation that takes place during the immune response against TB in different study populations. PMID:22713261

  11. The Exocenter of a Generalized Effect Algebra

    NASA Astrophysics Data System (ADS)

    Foulis, David J.; Pulmannová, Sylvia

    2011-12-01

    Elements of the exocenter of a generalized effect algebra (GEA) correspond to decompositions of the GEA as a direct sum and thus the exocenter is a generalization to GEAs of the center of an effect algebra. The exocenter of a GEA is shown to be a boolean algebra, and the notion of a hull mapping for an effect algebra is generalized to a hull system for a GEA. We study Dedekind orthocompleteness of GEAs and extend to GEAs the notion of a centrally orthocomplete effect algebra.

  12. Array algebra estimation in signal processing

    NASA Astrophysics Data System (ADS)

    Rauhala, U. A.

    A general theory of linear estimators called array algebra estimation is interpreted in some terms of multidimensional digital signal processing, mathematical statistics, and numerical analysis. The theory has emerged during the past decade from the new field of a unified vector, matrix and tensor algebra called array algebra. The broad concepts of array algebra and its estimation theory cover several modern computerized sciences and technologies converting their established notations and terminology into one common language. Some concepts of digital signal processing are adopted into this language after a review of the principles of array algebra estimation and its predecessors in mathematical surveying sciences.

  13. A Renormalisation Group Method. I. Gaussian Integration and Normed Algebras

    NASA Astrophysics Data System (ADS)

    Brydges, David C.; Slade, Gordon

    2015-05-01

    This paper is the first in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. Our immediate motivation is a specific model, involving both boson and fermion fields, which arises as a representation of the continuous-time weakly self-avoiding walk. In this paper, we define normed algebras suitable for a renormalisation group analysis, and develop methods for performing analysis on these algebras. We also develop the theory of Gaussian integration on these normed algebras, and prove estimates for Gaussian integrals. The concepts and results developed here provide a foundation for the continuation of the method presented in subsequent papers in the series.

  14. Effective regularized algebraic reconstruction technique for computed tomography

    SciTech Connect

    Prun, V. E.; Nikolaev, D. P.; Buzmakov, A. V.; Chukalina, M. V.; Asadchikov, V. E.

    2013-12-15

    A new fast version of the reconstruction algorithm for computed tomography based on the simultaneous algebraic reconstruction technique (SART) is proposed. The algorithm iteration is asymptotically accelerated using the fast Hough transform from O(n{sup 3}) to O(n{sup 2}logn). Similarly to the algebraic reconstruction technique (RegART), which was proposed by us previously, the regularization operator is applied after each iteration. A bilateral filter plays the role of this operator. The algorithm behavior is investigated using the model experiment.

  15. The smooth entropy formalism for von Neumann algebras

    NASA Astrophysics Data System (ADS)

    Berta, Mario; Furrer, Fabian; Scholz, Volkher B.

    2016-01-01

    We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional min- and max-entropy, we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and discuss applications to quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra.

  16. LDRD final report : autotuning for scalable linear algebra.

    SciTech Connect

    Heroux, Michael Allen; Marker, Bryan

    2011-09-01

    This report summarizes the progress made as part of a one year lab-directed research and development (LDRD) project to fund the research efforts of Bryan Marker at the University of Texas at Austin. The goal of the project was to develop new techniques for automatically tuning the performance of dense linear algebra kernels. These kernels often represent the majority of computational time in an application. The primary outcome from this work is a demonstration of the value of model driven engineering as an approach to accurately predict and study performance trade-offs for dense linear algebra computations.

  17. Atomic effect algebras with compression bases

    SciTech Connect

    Caragheorgheopol, Dan; Tkadlec, Josef

    2011-01-15

    Compression base effect algebras were recently introduced by Gudder [Demonstr. Math. 39, 43 (2006)]. They generalize sequential effect algebras [Rep. Math. Phys. 49, 87 (2002)] and compressible effect algebras [Rep. Math. Phys. 54, 93 (2004)]. The present paper focuses on atomic compression base effect algebras and the consequences of atoms being foci (so-called projections) of the compressions in the compression base. Part of our work generalizes results obtained in atomic sequential effect algebras by Tkadlec [Int. J. Theor. Phys. 47, 185 (2008)]. The notion of projection-atomicity is introduced and studied, and several conditions that force a compression base effect algebra or the set of its projections to be Boolean are found. Finally, we apply some of these results to sequential effect algebras and strengthen a previously established result concerning a sufficient condition for them to be Boolean.

  18. Atomic effect algebras with compression bases

    NASA Astrophysics Data System (ADS)

    Caragheorgheopol, Dan; Tkadlec, Josef

    2011-01-01

    Compression base effect algebras were recently introduced by Gudder [Demonstr. Math. 39, 43 (2006)]. They generalize sequential effect algebras [Rep. Math. Phys. 49, 87 (2002)] and compressible effect algebras [Rep. Math. Phys. 54, 93 (2004)]. The present paper focuses on atomic compression base effect algebras and the consequences of atoms being foci (so-called projections) of the compressions in the compression base. Part of our work generalizes results obtained in atomic sequential effect algebras by Tkadlec [Int. J. Theor. Phys. 47, 185 (2008)]. The notion of projection-atomicity is introduced and studied, and several conditions that force a compression base effect algebra or the set of its projections to be Boolean are found. Finally, we apply some of these results to sequential effect algebras and strengthen a previously established result concerning a sufficient condition for them to be Boolean.

  19. An Attempt to Understand Students' Understanding of Basic Algebra.

    ERIC Educational Resources Information Center

    Sleeman, D.

    This paper reports the results obtained with a group of 24 14-year-old students when presented with a set of algebra tasks by the Leeds Modelling System (LMS). These same students were given a comparable paper-and-pencil test and detailed interviews some 4 months later. The latter studies uncovered several kinds of student misunderstanding that…

  20. Proof and Reasoning in Secondary School Algebra Textbooks

    ERIC Educational Resources Information Center

    Dituri, Philip

    2013-01-01

    The purpose of this study was to determine the extent to which the modeling of deductive reasoning and proof-type thinking occurs in a mathematics course in which students are not explicitly preparing to write formal mathematical proofs. Algebra was chosen because it is the course that typically directly precedes a student's first formal…