On the validation of a code and a turbulence model appropriate to circulation control airfoils

NASA Technical Reports Server (NTRS)

Viegas, J. R.; Rubesin, M. W.; Maccormack, R. W.

1988-01-01

A computer code for calculating flow about a circulation control airfoil within a wind tunnel test section has been developed. This code is being validated for eventual use as an aid to design such airfoils. The concept of code validation being used is explained. The initial stages of the process have been accomplished. The present code has been applied to a low-subsonic, 2-D flow about a circulation control airfoil for which extensive data exist. Two basic turbulence models and variants thereof have been successfully introduced into the algorithm, the Baldwin-Lomax algebraic and the Jones-Launder two-equation models of turbulence. The variants include adding a history of the jet development for the algebraic model and adding streamwise curvature effects for both models. Numerical difficulties and difficulties in the validation process are discussed. Turbulence model and code improvements to proceed with the validation process are also discussed.

Discrete Dynamical Modeling.

ERIC Educational Resources Information Center

Sandefur, James T.

1991-01-01

Discussed is the process of translating situations involving changing quantities into mathematical relationships. This process, called dynamical modeling, allows students to learn new mathematics while sharpening their algebraic skills. A description of dynamical systems, problem-solving methods, a graphical analysis, and available classroom…

Testing an algebraic model of self-reflexion.

PubMed

Grice, James W; McDaniel, Brenda L; Thompsen, Dana

2005-06-01

Self-reflexion is the conscious process of taking the position of an observer in relation to one's own thoughts, feelings, and experiences. Building on the work of Lefebvre, Lefebvre, and Adams-Webber, we used a formal algebraic model of self-reflexion to derive several predictions regarding the frequencies with which individuals would rate themselves and others positively on bipolar scales anchored by adjective terms. The current results from 108 participants (41 men, 67 women; M age= 20.2 yr.) confirmed two predictions derived from the model. Three other predictions, however, were not supported even though the observed frequencies were close to the predicted values. Although not as promising as results reported by Lefebvre, et al., these mixed findings were interpreted as encouraging support for the validity of Lefebvre's algebraic model of self-reflexion. Differences between the current methods and those from previous investigations were also examined, and methodological implications for further studies were discussed.

How the twain can meet: Prospect theory and models of heuristics in risky choice.

PubMed

Pachur, Thorsten; Suter, Renata S; Hertwig, Ralph

2017-03-01

Two influential approaches to modeling choice between risky options are algebraic models (which focus on predicting the overt decisions) and models of heuristics (which are also concerned with capturing the underlying cognitive process). Because they rest on fundamentally different assumptions and algorithms, the two approaches are usually treated as antithetical, or even incommensurable. Drawing on cumulative prospect theory (CPT; Tversky & Kahneman, 1992) as the currently most influential instance of a descriptive algebraic model, we demonstrate how the two modeling traditions can be linked. CPT's algebraic functions characterize choices in terms of psychophysical (diminishing sensitivity to probabilities and outcomes) as well as psychological (risk aversion and loss aversion) constructs. Models of heuristics characterize choices as rooted in simple information-processing principles such as lexicographic and limited search. In computer simulations, we estimated CPT's parameters for choices produced by various heuristics. The resulting CPT parameter profiles portray each of the choice-generating heuristics in psychologically meaningful ways-capturing, for instance, differences in how the heuristics process probability information. Furthermore, CPT parameters can reflect a key property of many heuristics, lexicographic search, and track the environment-dependent behavior of heuristics. Finally, we show, both in an empirical and a model recovery study, how CPT parameter profiles can be used to detect the operation of heuristics. We also address the limits of CPT's ability to capture choices produced by heuristics. Our results highlight an untapped potential of CPT as a measurement tool to characterize the information processing underlying risky choice. Copyright © 2017 Elsevier Inc. All rights reserved.

Directed Abelian algebras and their application to stochastic models.

PubMed

Alcaraz, F C; Rittenberg, V

2008-10-01

With each directed acyclic graph (this includes some D-dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D. One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent sigma_(tau)=32 ). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found sigma_(tau)=1.780+/-0.005 .

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.

Optical pattern recognition algorithms on neural-logic equivalent models and demonstration of their prospects and possible implementations

NASA Astrophysics Data System (ADS)

Krasilenko, Vladimir G.; Nikolsky, Alexander I.; Zaitsev, Alexandr V.; Voloshin, Victor M.

2001-03-01

Historic information regarding the appearance and creation of fundamentals of algebra-logical apparatus-`equivalental algebra' for description of neuro-nets paradigms and algorithms is considered which is unification of theory of neuron nets (NN), linear algebra and the most generalized neuro-biology extended for matrix case. A survey is given of `equivalental models' of neuron nets and associative memory is suggested new, modified matrix-tenzor neurological equivalental models (MTNLEMS) are offered with double adaptive-equivalental weighing (DAEW) for spatial-non- invariant recognition (SNIR) and space-invariant recognition (SIR) of 2D images (patterns). It is shown, that MTNLEMS DAEW are the most generalized, they can describe the processes in NN both within the frames of known paradigms and within new `equivalental' paradigm of non-interaction type, and the computing process in NN under using the offered MTNLEMs DAEW is reduced to two-step and multi-step algorithms and step-by-step matrix-tenzor procedures (for SNIR) and procedures of defining of space-dependent equivalental functions from two images (for SIR).

The Algebra of Sleepiness: Investigating the Interaction of Homeostatic (S) and Circadian (C) Processes in Sleepiness Using Linear Metrics"

ERIC Educational Resources Information Center

Mairesse, Olivier; Hofmans, Joeri; Neu, Daniel; Dinis Monica de Oliveira, Armando Luis; Cluydts, Raymond; Theuns, Peter

2010-01-01

The present studies were conducted to contribute to the debate on the interaction between circadian (C) and homeostatic (S) processes in models of sleep regulation. The Two-Process Model of Sleep Regulation assumes a linear relationship between processes S and C. However, recent elaborations of the model, based on data from forced desynchrony…

Mathematical Modeling for Inherited Diseases.

PubMed

Anis, Saima; Khan, Madad; Khan, Saqib

2017-01-01

We introduced a new nonassociative algebra, namely, left almost algebra, and discussed some of its genetic properties. We discussed the relation of this algebra with flexible algebra, Jordan algebra, and generalized Jordan algebra.

Exponential Models of Legislative Turnover. [and] The Dynamics of Political Mobilization, I: A Model of the Mobilization Process, II: Deductive Consequences and Empirical Application of the Model. Applications of Calculus to American Politics. [and] Public Support for Presidents. Applications of Algebra to American Politics. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 296-300.

ERIC Educational Resources Information Center

Casstevens, Thomas W.; And Others

This document consists of five units which all view applications of mathematics to American politics. The first three view calculus applications, the last two deal with applications of algebra. The first module is geared to teach a student how to: 1) compute estimates of the value of the parameters in negative exponential models; and draw…

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…

Mathematical Modeling for Inherited Diseases

PubMed Central

Khan, Saqib

2017-01-01

We introduced a new nonassociative algebra, namely, left almost algebra, and discussed some of its genetic properties. We discussed the relation of this algebra with flexible algebra, Jordan algebra, and generalized Jordan algebra. PMID:28781606

Capitalizing on Basic Brain Processes in Developmental Algebra--Part 2

ERIC Educational Resources Information Center

Laughbaum, Edward D.

2011-01-01

Basic brain function is not a mystery. Given that neuroscientists understand its basic functioning processes, one wonders what their research suggests to teachers of developmental algebra. What if we knew how to teach so as to improve understanding of the algebra taught to developmental algebra students? What if we knew how the brain processes…

Capitalizing on Basic Brain Processes in Developmental Algebra--Part One

ERIC Educational Resources Information Center

Laughbaum, Edward D.

2011-01-01

Basic brain function is not a mystery. Given that neuroscientists understand the brain's basic functioning processes, one wonders what their research suggests to teachers of developmental algebra. What if we knew how to teach so as to improve understanding of the algebra taught to developmental algebra students? What if we knew how the brain…

Algebra for Enterprise Ontology: towards analysis and synthesis of enterprise models

NASA Astrophysics Data System (ADS)

Suga, Tetsuya; Iijima, Junichi

2018-03-01

Enterprise modeling methodologies have made enterprises more likely to be the object of systems engineering rather than craftsmanship. However, the current state of research in enterprise modeling methodologies lacks investigations of the mathematical background embedded in these methodologies. Abstract algebra, a broad subfield of mathematics, and the study of algebraic structures may provide interesting implications in both theory and practice. Therefore, this research gives an empirical challenge to establish an algebraic structure for one aspect model proposed in Design & Engineering Methodology for Organizations (DEMO), which is a major enterprise modeling methodology in the spotlight as a modeling principle to capture the skeleton of enterprises for developing enterprise information systems. The results show that the aspect model behaves well in the sense of algebraic operations and indeed constructs a Boolean algebra. This article also discusses comparisons with other modeling languages and suggests future work.

Electrokinetics Models for Micro and Nano Fluidic Impedance Sensors

DTIC Science & Technology

2010-11-01

primitive Differential-Algebraic Equations (DAEs), used to process and interpret the experimentally measured electrical impedance data (Sun and Morgan...field, and species respectively. A second-order scheme was used to calculate the ionic species distribution. The linearized algebraic equations were...is governed by the Poisson equation 2 0 0 r i i i F z cε ε φ∇ + =∑ where ε0 and εr are, respectively, the electrical permittivity in the vacuum

Analytically Solvable Model of Spreading Dynamics with Non-Poissonian Processes

NASA Astrophysics Data System (ADS)

Jo, Hang-Hyun; Perotti, Juan I.; Kaski, Kimmo; Kertész, János

2014-01-01

Non-Poissonian bursty processes are ubiquitous in natural and social phenomena, yet little is known about their effects on the large-scale spreading dynamics. In order to characterize these effects, we devise an analytically solvable model of susceptible-infected spreading dynamics in infinite systems for arbitrary inter-event time distributions and for the whole time range. Our model is stationary from the beginning, and the role of the lower bound of inter-event times is explicitly considered. The exact solution shows that for early and intermediate times, the burstiness accelerates the spreading as compared to a Poisson-like process with the same mean and same lower bound of inter-event times. Such behavior is opposite for late-time dynamics in finite systems, where the power-law distribution of inter-event times results in a slower and algebraic convergence to a fully infected state in contrast to the exponential decay of the Poisson-like process. We also provide an intuitive argument for the exponent characterizing algebraic convergence.

Dynamical Correspondence in a Generalized Quantum Theory

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

2015-05-01

In order to figure out why quantum physics needs the complex Hilbert space, many attempts have been made to distinguish the C*-algebras and von Neumann algebras in more general classes of abstractly defined Jordan algebras (JB- and JBW-algebras). One particularly important distinguishing property was identified by Alfsen and Shultz and is the existence of a dynamical correspondence. It reproduces the dual role of the selfadjoint operators as observables and generators of dynamical groups in quantum mechanics. In the paper, this concept is extended to another class of nonassociative algebras, arising from recent studies of the quantum logics with a conditional probability calculus and particularly of those that rule out third-order interference. The conditional probability calculus is a mathematical model of the Lüders-von Neumann quantum measurement process, and third-order interference is a property of the conditional probabilities which was discovered by Sorkin (Mod Phys Lett A 9:3119-3127, 1994) and which is ruled out by quantum mechanics. It is shown then that the postulates that a dynamical correspondence exists and that the square of any algebra element is positive still characterize, in the class considered, those algebras that emerge from the selfadjoint parts of C*-algebras equipped with the Jordan product. Within this class, the two postulates thus result in ordinary quantum mechanics using the complex Hilbert space or, vice versa, a genuine generalization of quantum theory must omit at least one of them.

Identification of control targets in Boolean molecular network models via computational algebra.

PubMed

Murrugarra, David; Veliz-Cuba, Alan; Aguilar, Boris; Laubenbacher, Reinhard

2016-09-23

Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This paper focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type considered is that of Boolean networks. The potential control targets can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system. This paper presents a method for the identification of potential intervention targets in Boolean molecular network models using algebraic techniques. The approach exploits an algebraic representation of Boolean networks to encode the control candidates in the network wiring diagram as the solutions of a system of polynomials equations, and then uses computational algebra techniques to find such controllers. The control methods in this paper are validated through the identification of combinatorial interventions in the signaling pathways of previously reported control targets in two well studied systems, a p53-mdm2 network and a blood T cell lymphocyte granular leukemia survival signaling network. Supplementary data is available online and our code in Macaulay2 and Matlab are available via http://www.ms.uky.edu/~dmu228/ControlAlg . This paper presents a novel method for the identification of intervention targets in Boolean network models. The results in this paper show that the proposed methods are useful and efficient for moderately large networks.

NPTool: Towards Scalability and Reliability of Business Process Management

NASA Astrophysics Data System (ADS)

Braghetto, Kelly Rosa; Ferreira, João Eduardo; Pu, Calton

Currently one important challenge in business process management is provide at the same time scalability and reliability of business process executions. This difficulty becomes more accentuated when the execution control assumes complex countless business processes. This work presents NavigationPlanTool (NPTool), a tool to control the execution of business processes. NPTool is supported by Navigation Plan Definition Language (NPDL), a language for business processes specification that uses process algebra as formal foundation. NPTool implements the NPDL language as a SQL extension. The main contribution of this paper is a description of the NPTool showing how the process algebra features combined with a relational database model can be used to provide a scalable and reliable control in the execution of business processes. The next steps of NPTool include reuse of control-flow patterns and support to data flow management.

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…

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.

Some aspects of mathematical and chemical modeling of complex chemical processes

NASA Technical Reports Server (NTRS)

Nemes, I.; Botar, L.; Danoczy, E.; Vidoczy, T.; Gal, D.

1983-01-01

Some theoretical questions involved in the mathematical modeling of the kinetics of complex chemical process are discussed. The analysis is carried out for the homogeneous oxidation of ethylbenzene in the liquid phase. Particular attention is given to the determination of the general characteristics of chemical systems from an analysis of mathematical models developed on the basis of linear algebra.

Yang-Baxter algebras, integrable theories and Bethe Ansatz

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

De Vega, H.J.

1990-03-10

This paper presents the Yang-Baxter algebras (YBA) in a general framework stressing their power to exactly solve the lattice models associated to them. The algebraic Behe Ansatz is developed as an eigenvector construction based on the YBA. The six-vertex model solution is given explicitly. The generalization of YB algebras to face language is considered. The algebraic BA for the SOS model of Andrews, Baxter and Forrester is described using these face YB algebras. It is explained how these lattice models yield both solvable massive QFT and conformal models in appropriated scaling (continuous) limits within the lattice light-cone approach. This approachmore » permit to define and solve rigorously massive QFT as an appropriate continuum limit of gapless vertex models. The deep links between the YBA and Lie algebras are analyzed including the quantum groups that underlay the trigonometric/hyperbolic YBA. Braid and quantum groups are derived from trigonometric/hyperbolic YBA in the limit of infinite spectral parameter. To conclude, some recent developments in the domain of integrable theories are summarized.« less

Testing Transitivity of Preferences on Two-Alternative Forced Choice Data

PubMed Central

Regenwetter, Michel; Dana, Jason; Davis-Stober, Clintin P.

2010-01-01

As Duncan Luce and other prominent scholars have pointed out on several occasions, testing algebraic models against empirical data raises difficult conceptual, mathematical, and statistical challenges. Empirical data often result from statistical sampling processes, whereas algebraic theories are nonprobabilistic. Many probabilistic specifications lead to statistical boundary problems and are subject to nontrivial order constrained statistical inference. The present paper discusses Luce's challenge for a particularly prominent axiom: Transitivity. The axiom of transitivity is a central component in many algebraic theories of preference and choice. We offer the currently most complete solution to the challenge in the case of transitivity of binary preference on the theory side and two-alternative forced choice on the empirical side, explicitly for up to five, and implicitly for up to seven, choice alternatives. We also discuss the relationship between our proposed solution and weak stochastic transitivity. We recommend to abandon the latter as a model of transitive individual preferences. PMID:21833217

An Arithmetic-Algebraic Work Space for the Promotion of Arithmetic and Algebraic Thinking: Triangular Numbers

ERIC Educational Resources Information Center

Hitt, Fernando; Saboya, Mireille; Cortés Zavala, Carlos

2016-01-01

This paper presents an experiment that attempts to mobilise an arithmetic-algebraic way of thinking in order to articulate between arithmetic thinking and the early algebraic thinking, which is considered a prelude to algebraic thinking. In the process of building this latter way of thinking, researchers analysed pupils' spontaneous production…

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.

Students’ Algebraic Thinking Process in Context of Point and Line Properties

NASA Astrophysics Data System (ADS)

Nurrahmi, H.; Suryadi, D.; Fatimah, S.

2017-09-01

Learning of schools algebra is limited to symbols and operating procedures, so students are able to work on problems that only require the ability to operate symbols but unable to generalize a pattern as one of part of algebraic thinking. The purpose of this study is to create a didactic design that facilitates students to do algebraic thinking process through the generalization of patterns, especially in the context of the property of point and line. This study used qualitative method and includes Didactical Design Research (DDR). The result is students are able to make factual, contextual, and symbolic generalization. This happen because the generalization arises based on facts on local terms, then the generalization produced an algebraic formula that was described in the context and perspective of each student. After that, the formula uses the algebraic letter symbol from the symbol t hat uses the students’ language. It can be concluded that the design has facilitated students to do algebraic thinking process through the generalization of patterns, especially in the context of property of the point and line. The impact of this study is this design can use as one of material teaching alternative in learning of school algebra.

The VATES-Diamond as a Verifier's Best Friend

NASA Astrophysics Data System (ADS)

Glesner, Sabine; Bartels, Björn; Göthel, Thomas; Kleine, Moritz

Within a model-based software engineering process it needs to be ensured that properties of abstract specifications are preserved by transformations down to executable code. This is even more important in the area of safety-critical real-time systems where additionally non-functional properties are crucial. In the VATES project, we develop formal methods for the construction and verification of embedded systems. We follow a novel approach that allows us to formally relate abstract process algebraic specifications to their implementation in a compiler intermediate representation. The idea is to extract a low-level process algebraic description from the intermediate code and to formally relate it to previously developed abstract specifications. We apply this approach to a case study from the area of real-time operating systems and show that this approach has the potential to seamlessly integrate modeling, implementation, transformation and verification stages of embedded system development.

A Electro-Optical Image Algebra Processing System for Automatic Target Recognition

NASA Astrophysics Data System (ADS)

Coffield, Patrick Cyrus

The proposed electro-optical image algebra processing system is designed specifically for image processing and other related computations. The design is a hybridization of an optical correlator and a massively paralleled, single instruction multiple data processor. The architecture of the design consists of three tightly coupled components: a spatial configuration processor (the optical analog portion), a weighting processor (digital), and an accumulation processor (digital). The systolic flow of data and image processing operations are directed by a control buffer and pipelined to each of the three processing components. The image processing operations are defined in terms of basic operations of an image algebra developed by the University of Florida. The algebra is capable of describing all common image-to-image transformations. The merit of this architectural design is how it implements the natural decomposition of algebraic functions into spatially distributed, point use operations. The effect of this particular decomposition allows convolution type operations to be computed strictly as a function of the number of elements in the template (mask, filter, etc.) instead of the number of picture elements in the image. Thus, a substantial increase in throughput is realized. The implementation of the proposed design may be accomplished in many ways. While a hybrid electro-optical implementation is of primary interest, the benefits and design issues of an all digital implementation are also discussed. The potential utility of this architectural design lies in its ability to control a large variety of the arithmetic and logic operations of the image algebra's generalized matrix product. The generalized matrix product is the most powerful fundamental operation in the algebra, thus allowing a wide range of applications. No other known device or design has made this claim of processing speed and general implementation of a heterogeneous image algebra.

Modeling Stochastic Complexity in Complex Adaptive Systems: Non-Kolmogorov Probability and the Process Algebra Approach.

PubMed

Sulis, William H

2017-10-01

Walter Freeman III pioneered the application of nonlinear dynamical systems theories and methodologies in his work on mesoscopic brain dynamics.Sadly, mainstream psychology and psychiatry still cling to linear correlation based data analysis techniques, which threaten to subvert the process of experimentation and theory building. In order to progress, it is necessary to develop tools capable of managing the stochastic complexity of complex biopsychosocial systems, which includes multilevel feedback relationships, nonlinear interactions, chaotic dynamics and adaptability. In addition, however, these systems exhibit intrinsic randomness, non-Gaussian probability distributions, non-stationarity, contextuality, and non-Kolmogorov probabilities, as well as the absence of mean and/or variance and conditional probabilities. These properties and their implications for statistical analysis are discussed. An alternative approach, the Process Algebra approach, is described. It is a generative model, capable of generating non-Kolmogorov probabilities. It has proven useful in addressing fundamental problems in quantum mechanics and in the modeling of developing psychosocial systems.

Robust algebraic image enhancement for intelligent control systems

NASA Technical Reports Server (NTRS)

Lerner, Bao-Ting; Morrelli, Michael

1993-01-01

Robust vision capability for intelligent control systems has been an elusive goal in image processing. The computationally intensive techniques a necessary for conventional image processing make real-time applications, such as object tracking and collision avoidance difficult. In order to endow an intelligent control system with the needed vision robustness, an adequate image enhancement subsystem capable of compensating for the wide variety of real-world degradations, must exist between the image capturing and the object recognition subsystems. This enhancement stage must be adaptive and must operate with consistency in the presence of both statistical and shape-based noise. To deal with this problem, we have developed an innovative algebraic approach which provides a sound mathematical framework for image representation and manipulation. Our image model provides a natural platform from which to pursue dynamic scene analysis, and its incorporation into a vision system would serve as the front-end to an intelligent control system. We have developed a unique polynomial representation of gray level imagery and applied this representation to develop polynomial operators on complex gray level scenes. This approach is highly advantageous since polynomials can be manipulated very easily, and are readily understood, thus providing a very convenient environment for image processing. Our model presents a highly structured and compact algebraic representation of grey-level images which can be viewed as fuzzy sets.

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

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

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.

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.)

Visual Salience of Algebraic Transformations

ERIC Educational Resources Information Center

Kirshner, David; Awtry, Thomas

2004-01-01

Information processing researchers have assumed that algebra symbol skills depend on mastery of the abstract rules presented in the curriculum (Matz, 1980; Sleeman, 1986). Thus, students' ubiquitous algebra errors have been taken as indicating the need to embed algebra in rich contextual settings (Kaput, 1995; National Council of Teachers of…

A comparison of three algebraic stress closures for combustor flow calculations

NASA Technical Reports Server (NTRS)

Nikjooy, M.; So, R. M. C.; Hwang, B. C.

1985-01-01

A comparison is made of the performance of two locally nonequilibrium and one equilibrium algebraic stress closures in calculating combustor flows. Effects of four different pressure-strain models on these closure models are also analyzed. The results show that the pressure-strain models have a much greater influence on the calculated mean velocity and turbulence field than the algebraic stress closures, and that the best mean strain model for the pressure-strain terms is that proposed by Launder, Reece and Rodi (1975). However, the equilibrium algebraic stress closure with the Rotta return-to-isotropy model (1951) for the pressure-strain terms gives as good a correlation with measurements as when the Launder et al. mean strain model is included in the pressure-strain model. Finally, comparison of the calculations with the standard k-epsilon closure results show that the algebraic stress closures are better suited for simple turbulent flow calculations.

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

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

Burdik, C., E-mail: burdik@kmlinux.fjfi.cvut.cz; 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.

On Alternative Formulations for Linearised Miss Distance Analysis

DTIC Science & Technology

2013-05-01

is traditionally employed by analysts as part of the solution process . To gain further insight into the nature of the missile-target engagement...a constant. Thus, following this process , the revised block diagram model for the linearised equations is presented in Figure 13. This model is... process is known as reducing the block to its fundamental closed loop form and has been achieved here using standard block diagram algebra. This

Topics in elementary particle physics

NASA Astrophysics Data System (ADS)

Jin, Xiang

The author of this thesis discusses two topics in elementary particle physics: n-ary algebras and their applications to M-theory (Part I), and functional evolution and Renormalization Group flows (Part II). In part I, Lie algebra is extended to four different n-ary algebraic structure: generalized Lie algebra, Filippov algebra, Nambu algebra and Nambu-Poisson tensor; though there are still many other n-ary algebras. A natural property of Generalized Lie algebras — the Bremner identity, is studied, and proved with a totally different method from its original version. We extend Bremner identity to n-bracket cases, where n is an arbitrary odd integer. Filippov algebras do not focus on associativity, and are defined by the Fundamental identity. We add associativity to Filippov algebras, and give examples of how to construct Filippov algebras from su(2), bosonic oscillator, Virasoro algebra. We try to include fermionic charges into the ternary Virasoro-Witt algebra, but the attempt fails because fermionic charges keep generating new charges that make the algebra not closed. We also study the Bremner identity restriction on Nambu algebras and Nambu-Poisson tensors. So far, the only example 3-algebra being used in physics is the BLG model with 3-algebra A4, describing two M2-branes interactions. Its extension with Nambu algebra, BLG-NB model, is believed to describe infinite M2-branes condensation. Also, there is another propose for M2-brane interactions, the ABJM model, which is constructed by ordinary Lie algebra. We compare the symmetry properties between them, and discuss the possible approaches to include these three models into a grand unification theory. In Part II, we give an approximate solution for Schroeder's equations, based on series and conjugation methods. We use the logistic map as an example, and demonstrate that this approximate solution converges to known analytical solutions around the fixed point, around which the approximate solution is constructed. Although the closed-form solutions for Schroeder's equations can not always be approached analytically, by fitting the approximation solutions, one can still obtain closed-form solutions sometimes. Based on Schroeder's theory, approximate solutions for trajectories, velocities and potentials can also be constructed. The approximate solution is significantly useful to calculate the beta function in renormalization group trajectory. By "wrapping" the series solutions with the conjugations from different inverse functions, we generate different branches of the trajectory, and construct a counterexample for a folk theorem about limited cycles.

Principles of Stagewise Separation Process Calculations: A Simple Algebraic Approach Using Solvent Extraction.

ERIC Educational Resources Information Center

Crittenden, Barry D.

1991-01-01

A simple liquid-liquid equilibrium (LLE) system involving a constant partition coefficient based on solute ratios is used to develop an algebraic understanding of multistage contacting in a first-year separation processes course. This algebraic approach to the LLE system is shown to be operable for the introduction of graphical techniques…

An Algebraic Approach to the Eigenstates of the Calogero Model

NASA Astrophysics Data System (ADS)

Ujino, Hideaki

2002-11-01

An algebraic treatment of the eigenstates of the (AN-1-) Calogero model is presented, which provides an algebraic construction of the nonsymmetric orthogonal eigenvectors, symmetrization, antisymmetrization and calculation of square norms in a unified way.

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

Schertzer, Daniel, E-mail: Daniel.Schertzer@enpc.fr; Tchiguirinskaia, Ioulia, E-mail: Ioulia.Tchiguirinskaia@enpc.fr

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 upmore » 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.« less

A set for relational reasoning: Facilitation of algebraic modeling by a fraction task.

PubMed

DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J

2016-12-01

Recent work has identified correlations between early mastery of fractions and later math achievement, especially in algebra. However, causal connections between aspects of reasoning with fractions and improved algebra performance have yet to be established. The current study investigated whether relational reasoning with fractions facilitates subsequent algebraic reasoning using both pre-algebra students and adult college students. Participants were first given either a relational reasoning fractions task or a fraction algebra procedures control task. Then, all participants solved word problems and constructed algebraic equations in either multiplication or division format. The word problems and the equation construction tasks involved simple multiplicative comparison statements such as "There are 4 times as many students as teachers in a classroom." Performance on the algebraic equation construction task was enhanced for participants who had previously completed the relational fractions task compared with those who completed the fraction algebra procedures task. This finding suggests that relational reasoning with fractions can establish a relational set that promotes students' tendency to model relations using algebraic expressions. Copyright © 2016 Elsevier Inc. All rights reserved.

General Algebraic Modeling System Tutorial | High-Performance Computing |

Science.gov Websites

power generation from two different fuels. The goal is to minimize the cost for one of the fuels while Here's a basic tutorial for modeling optimization problems with the General Algebraic Modeling System (GAMS). Overview The GAMS (General Algebraic Modeling System) package is essentially a compiler for a

Meanings Given to Algebraic Symbolism in Problem-Posing

ERIC Educational Resources Information Center

Cañadas, María C.; Molina, Marta; del Río, Aurora

2018-01-01

Some errors in the learning of algebra suggest that students might have difficulties giving meaning to algebraic symbolism. In this paper, we use problem posing to analyze the students' capacity to assign meaning to algebraic symbolism and the difficulties that students encounter in this process, depending on the characteristics of the algebraic…

On the quantum symmetry of the chiral Ising model

NASA Astrophysics Data System (ADS)

Vecsernyés, Peter

1994-03-01

We introduce the notion of rational Hopf algebras that we think are able to describe the superselection symmetries of rational quantum field theories. As an example we show that a six-dimensional rational Hopf algebra H can reproduce the fusion rules, the conformal weights, the quantum dimensions and the representation of the modular group of the chiral Ising model. H plays the role of the global symmetry algebra of the chiral Ising model in the following sense: (1) a simple field algebra F and a representation π on Hπ of it is given, which contains the c = {1}/{2} unitary representations of the Virasoro algebra as subrepresentations; (2) the embedding U: H → B( Hπ) is such that the observable algebra π( A) - is the invariant subalgebra of B( Hπ) with respect to the left adjoint action of H and U(H) is the commutant of π( A); (3) there exist H-covariant primary fields in B( Hπ), which obey generalized Cuntz algebra properties and intertwine between the inequivalent sectors of the observables.

Students’ Algebraic Reasonsing In Solving Mathematical Problems With Adversity Quotient

NASA Astrophysics Data System (ADS)

Aryani, F.; Amin, S. M.; Sulaiman, R.

2018-01-01

Algebraic reasoning is a process in which students generalize mathematical ideas from a set of particular instances and express them in increasingly formal and age-appropriate ways. Using problem solving approach to develop algebraic reasoning of mathematics may enhace the long-term learning trajectory of the majority students. The purpose of this research was to describe the algebraic reasoning of quitter, camper, and climber junior high school students in solving mathematical problems. This research used qualitative descriptive method. Subjects were determined by purposive sampling. The technique of collecting data was done by task-based interviews.The results showed that the algebraic reasoning of three students in the process of pattern seeking by identifying the things that are known and asked in a similar way. But three students found the elements of pattern recognition in different ways or method. So, they are generalize the problem of pattern formation with different ways. The study of algebraic reasoning and problem solving can be a learning paradigm in the improve students’ knowledge and skills in algebra work. The goal is to help students’ improve academic competence, develop algebraic reasoning in problem solving.

Mastering algebra retrains the visual system to perceive hierarchical structure in equations.

PubMed

Marghetis, Tyler; Landy, David; Goldstone, Robert L

2016-01-01

Formal mathematics is a paragon of abstractness. It thus seems natural to assume that the mathematical expert should rely more on symbolic or conceptual processes, and less on perception and action. We argue instead that mathematical proficiency relies on perceptual systems that have been retrained to implement mathematical skills. Specifically, we investigated whether the visual system-in particular, object-based attention-is retrained so that parsing algebraic expressions and evaluating algebraic validity are accomplished by visual processing. Object-based attention occurs when the visual system organizes the world into discrete objects, which then guide the deployment of attention. One classic signature of object-based attention is better perceptual discrimination within, rather than between, visual objects. The current study reports that object-based attention occurs not only for simple shapes but also for symbolic mathematical elements within algebraic expressions-but only among individuals who have mastered the hierarchical syntax of algebra. Moreover, among these individuals, increased object-based attention within algebraic expressions is associated with a better ability to evaluate algebraic validity. These results suggest that, in mastering the rules of algebra, people retrain their visual system to represent and evaluate abstract mathematical structure. We thus argue that algebraic expertise involves the regimentation and reuse of evolutionarily ancient perceptual processes. Our findings implicate the visual system as central to learning and reasoning in mathematics, leading us to favor educational approaches to mathematics and related STEM fields that encourage students to adapt, not abandon, their use of perception.

Category-theoretic models of algebraic computer systems

NASA Astrophysics Data System (ADS)

Kovalyov, S. P.

2016-01-01

A computer system is said to be algebraic if it contains nodes that implement unconventional computation paradigms based on universal algebra. A category-based approach to modeling such systems that provides a theoretical basis for mapping tasks to these systems' architecture is proposed. The construction of algebraic models of general-purpose computations involving conditional statements and overflow control is formally described by a reflector in an appropriate category of algebras. It is proved that this reflector takes the modulo ring whose operations are implemented in the conventional arithmetic processors to the Łukasiewicz logic matrix. Enrichments of the set of ring operations that form bases in the Łukasiewicz logic matrix are found.

An Algebraic Formulation of Level One Wess-Zumino Models

NASA Astrophysics Data System (ADS)

Böckenhauer, Jens

The highest weight modules of the chiral algebra of orthogonal WZW models at level one possess a realization in fermionic representation spaces; the Kac-Moody and Virasoro generators are represented as unbounded limits of even CAR algebras. It is shown that the representation theory of the underlying even CAR algebras reproduces precisely the sectors of the chiral algebra. This fact allows to develop a theory of local von Neumann algebras on the punctured circle, fitting nicely in the Doplicher-Haag-Roberts framework. The relevant localized endomorphisms which generate the charged sectors are explicitly constructed by means of Bogoliubov transformations. Using CAR theory, the fusion rules in terms of sector equivalence classes are proven.

Monotonically improving approximate answers to relational algebra queries

NASA Technical Reports Server (NTRS)

Smith, Kenneth P.; Liu, J. W. S.

1989-01-01

We present here a query processing method that produces approximate answers to queries posed in standard relational algebra. This method is monotone in the sense that the accuracy of the approximate result improves with the amount of time spent producing the result. This strategy enables us to trade the time to produce the result for the accuracy of the result. An approximate relational model that characterizes appromimate relations and a partial order for comparing them is developed. Relational operators which operate on and return approximate relations are defined.

Contractions and deformations of quasiclassical Lie algebras preserving a nondegenerate quadratic Casimir operator

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

Campoamor-Stursberg, R., E-mail: rutwig@mat.ucm.e

2008-05-15

By means of contractions of Lie algebras, we obtain new classes of indecomposable quasiclassical Lie algebras that satisfy the Yang-Baxter equations in its reformulation in terms of triple products. These algebras are shown to arise naturally from noncompact real simple algebras with nonsimple complexification, where we impose that a nondegenerate quadratic Casimir operator is preserved by the limiting process. We further consider the converse problem and obtain sufficient conditions on integrable cocycles of quasiclassical Lie algebras in order to preserve nondegenerate quadratic Casimir operators by the associated linear deformations.

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…

Using Students' Interests as Algebraic Models

ERIC Educational Resources Information Center

Whaley, Kenneth A.

2012-01-01

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

Turbulence Model Predictions of Strongly Curved Flow in a U-Duct

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.; Gatski, Thomas B.; Morrison, Joseph H.

2000-01-01

The ability of three types of turbulence models to accurately predict the effects of curvature on the flow in a U-duct is studied. An explicit algebraic stress model performs slightly better than one- or two-equation linear eddy viscosity models, although it is necessary to fully account for the variation of the production-to-dissipation-rate ratio in the algebraic stress model formulation. In their original formulations, none of these turbulence models fully captures the suppressed turbulence near the convex wall, whereas a full Reynolds stress model does. Some of the underlying assumptions used in the development of algebraic stress models are investigated and compared with the computed flowfield from the full Reynolds stress model. Through this analysis, the assumption of Reynolds stress anisotropy equilibrium used in the algebraic stress model formulation is found to be incorrect in regions of strong curvature. By the accounting for the local variation of the principal axes of the strain rate tensor, the explicit algebraic stress model correctly predicts the suppressed turbulence in the outer part of the boundary layer near the convex wall.

Image Algebra Matlab language version 2.3 for image processing and compression research

NASA Astrophysics Data System (ADS)

Schmalz, Mark S.; Ritter, Gerhard X.; Hayden, Eric

2010-08-01

Image algebra is a rigorous, concise notation that unifies linear and nonlinear mathematics in the image domain. Image algebra was developed under DARPA and US Air Force sponsorship at University of Florida for over 15 years beginning in 1984. Image algebra has been implemented in a variety of programming languages designed specifically to support the development of image processing and computer vision algorithms and software. The University of Florida has been associated with development of the languages FORTRAN, Ada, Lisp, and C++. The latter implementation involved a class library, iac++, that supported image algebra programming in C++. Since image processing and computer vision are generally performed with operands that are array-based, the Matlab™ programming language is ideal for implementing the common subset of image algebra. Objects include sets and set operations, images and operations on images, as well as templates and image-template convolution operations. This implementation, called Image Algebra Matlab (IAM), has been found to be useful for research in data, image, and video compression, as described herein. Due to the widespread acceptance of the Matlab programming language in the computing community, IAM offers exciting possibilities for supporting a large group of users. The control over an object's computational resources provided to the algorithm designer by Matlab means that IAM programs can employ versatile representations for the operands and operations of the algebra, which are supported by the underlying libraries written in Matlab. In a previous publication, we showed how the functionality of IAC++ could be carried forth into a Matlab implementation, and provided practical details of a prototype implementation called IAM Version 1. In this paper, we further elaborate the purpose and structure of image algebra, then present a maturing implementation of Image Algebra Matlab called IAM Version 2.3, which extends the previous implementation of IAM to include polymorphic operations over different point sets, as well as recursive convolution operations and functional composition. We also show how image algebra and IAM can be employed in image processing and compression research, as well as algorithm development and analysis.

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

NASA Astrophysics Data System (ADS)

Zhang, Tianjie; Gao, Xing; Guo, Li

2016-10-01

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

Development of a Computerized Adaptive Testing for Diagnosing the Cognitive Process of Grade 7 Students in Learning Algebra, Using Multidimensional Item Response Theory

ERIC Educational Resources Information Center

Senarat, Somprasong; Tayraukham, Sombat; Piyapimonsit, Chatsiri; Tongkhambanjong, Sakesan

2013-01-01

The purpose of this research is to develop a multidimensional computerized adaptive test for diagnosing the cognitive process of grade 7 students in learning algebra by applying multidimensional item response theory. The research is divided into 4 steps: 1) the development of item bank of algebra, 2) the development of the multidimensional…

Image model: new perspective for image processing and computer vision

NASA Astrophysics Data System (ADS)

Ziou, Djemel; Allili, Madjid

2004-05-01

We propose a new image model in which the image support and image quantities are modeled using algebraic topology concepts. The image support is viewed as a collection of chains encoding combination of pixels grouped by dimension and linking different dimensions with the boundary operators. Image quantities are encoded using the notion of cochain which associates values for pixels of given dimension that can be scalar, vector, or tensor depending on the problem that is considered. This allows obtaining algebraic equations directly from the physical laws. The coboundary and codual operators, which are generic operations on cochains allow to formulate the classical differential operators as applied for field functions and differential forms in both global and local forms. This image model makes the association between the image support and the image quantities explicit which results in several advantages: it allows the derivation of efficient algorithms that operate in any dimension and the unification of mathematics and physics to solve classical problems in image processing and computer vision. We show the effectiveness of this model by considering the isotropic diffusion.

Derivation of rigorous conditions for high cell-type diversity by algebraic approach.

PubMed

Yoshida, Hiroshi; Anai, Hirokazu; Horimoto, Katsuhisa

2007-01-01

The development of a multicellular organism is a dynamic process. Starting with one or a few cells, the organism develops into different types of cells with distinct functions. We have constructed a simple model by considering the cell number increase and the cell-type order conservation, and have assessed conditions for cell-type diversity. This model is based on a stochastic Lindenmayer system with cell-to-cell interactions for three types of cells. In the present model, we have successfully derived complex but rigorous algebraic relations between the proliferation and transition rates for cell-type diversity by using a symbolic method: quantifier elimination (QE). Surprisingly, three modes for the proliferation and transition rates have emerged for large ratios of the initial cells to the developed cells. The three modes have revealed that the equality between the development rates for the highest cell-type diversity is reduced during the development process of multicellular organisms. Furthermore, we have found that the highest cell-type diversity originates from order conservation.

A new family of N dimensional superintegrable double singular oscillators and quadratic algebra Q(3) ⨁ so(n) ⨁ so(N-n)

NASA Astrophysics Data System (ADS)

Fazlul Hoque, Md; Marquette, Ian; Zhang, Yao-Zhong

2015-11-01

We introduce a new family of N dimensional quantum superintegrable models consisting of double singular oscillators of type (n, N-n). The special cases (2,2) and (4,4) have previously been identified as the duals of 3- and 5-dimensional deformed Kepler-Coulomb systems with u(1) and su(2) monopoles, respectively. The models are multiseparable and their wave functions are obtained in (n, N-n) double-hyperspherical coordinates. We obtain the integrals of motion and construct the finitely generated polynomial algebra that is the direct sum of a quadratic algebra Q(3) involving three generators, so(n), so(N-n) (i.e. Q(3) ⨁ so(n) ⨁ so(N-n)). The structure constants of the quadratic algebra itself involve the Casimir operators of the two Lie algebras so(n) and so(N-n). Moreover, we obtain the finite dimensional unitary representations (unirreps) of the quadratic algebra and present an algebraic derivation of the degenerate energy spectrum of the superintegrable model.

Dynamical systems defined on infinite dimensional lie algebras of the ''current algebra'' or ''Kac-Moody'' type

NASA Astrophysics Data System (ADS)

Hermann, Robert

1982-07-01

Recent work by Morrison, Marsden, and Weinstein has drawn attention to the possibility of utilizing the cosymplectic structure of the dual of the Lie algebra of certain infinite dimensional Lie groups to study hydrodynamical and plasma systems. This paper treats certain models arising in elementary particle physics, considered by Lee, Weinberg, and Zumino; Sugawara; Bardacki, Halpern, and Frishman; Hermann; and Dolan. The lie algebras involved are associated with the ''current algebras'' of Gell-Mann. This class of Lie algebras contains certain of the algebras that are called ''Kac-Moody algebras'' in the recent mathematics and mathematical physics literature.

Structural identifiability analyses of candidate models for in vitro Pitavastatin hepatic uptake.

PubMed

Grandjean, Thomas R B; Chappell, Michael J; Yates, James W T; Evans, Neil D

2014-05-01

In this paper a review of the application of four different techniques (a version of the similarity transformation approach for autonomous uncontrolled systems, a non-differential input/output observable normal form approach, the characteristic set differential algebra and a recent algebraic input/output relationship approach) to determine the structural identifiability of certain in vitro nonlinear pharmacokinetic models is provided. The Organic Anion Transporting Polypeptide (OATP) substrate, Pitavastatin, is used as a probe on freshly isolated animal and human hepatocytes. Candidate pharmacokinetic non-linear compartmental models have been derived to characterise the uptake process of Pitavastatin. As a prerequisite to parameter estimation, structural identifiability analyses are performed to establish that all unknown parameters can be identified from the experimental observations available. Copyright © 2013. Published by Elsevier Ireland Ltd.

Tensor models, Kronecker coefficients and permutation centralizer algebras

NASA Astrophysics Data System (ADS)

Geloun, Joseph Ben; Ramgoolam, Sanjaye

2017-11-01

We show that the counting of observables and correlators for a 3-index tensor model are organized by the structure of a family of permutation centralizer algebras. These algebras are shown to be semi-simple and their Wedderburn-Artin decompositions into matrix blocks are given in terms of Clebsch-Gordan coefficients of symmetric groups. The matrix basis for the algebras also gives an orthogonal basis for the tensor observables which diagonalizes the Gaussian two-point functions. The centres of the algebras are associated with correlators which are expressible in terms of Kronecker coefficients (Clebsch-Gordan multiplicities of symmetric groups). The color-exchange symmetry present in the Gaussian model, as well as a large class of interacting models, is used to refine the description of the permutation centralizer algebras. This discussion is extended to a general number of colors d: it is used to prove the integrality of an infinite family of number sequences related to color-symmetrizations of colored graphs, and expressible in terms of symmetric group representation theory data. Generalizing a connection between matrix models and Belyi maps, correlators in Gaussian tensor models are interpreted in terms of covers of singular 2-complexes. There is an intriguing difference, between matrix and higher rank tensor models, in the computational complexity of superficially comparable correlators of observables parametrized by Young diagrams.

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…

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.

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.

Contributions of Domain-General Cognitive Resources and Different Forms of Arithmetic Development to Pre-Algebraic Knowledge

PubMed Central

Fuchs, Lynn S.; Compton, Donald L.; Fuchs, Douglas; Powell, Sarah R.; Schumacher, Robin F.; Hamlett, Carol L.; Vernier, Emily; Namkung, Jessica M.; Vukovic, Rose K.

2012-01-01

The purpose of this study was to investigate the contributions of domain-general cognitive resources and different forms of arithmetic development to individual differences in pre-algebraic knowledge. Children (n=279; mean age=7.59 yrs) were assessed on 7 domain-general cognitive resources as well as arithmetic calculations and word problems at start of 2nd grade and on calculations, word problems, and pre-algebraic knowledge at end of 3rd grade. Multilevel path analysis, controlling for instructional effects associated with the sequence of classrooms in which students were nested across grades 2–3, indicated arithmetic calculations and word problems are foundational to pre-algebraic knowledge. Also, results revealed direct contributions of nonverbal reasoning and oral language to pre-algebraic knowledge, beyond indirect effects that are mediated via arithmetic calculations and word problems. By contrast, attentive behavior, phonological processing, and processing speed contributed to pre-algebraic knowledge only indirectly via arithmetic calculations and word problems. PMID:22409764

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

ERIC Educational Resources Information Center

Ellington, Aimee J.

2005-01-01

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

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.

Literal algebra for satellite dynamics. [perturbation analysis

NASA Technical Reports Server (NTRS)

Gaposchkin, E. M.

1975-01-01

A description of the rather general class of operations available is given and the operations are related to problems in satellite dynamics. The implementation of an algebra processor is discussed. The four main categories of symbol processors are related to list processing, string manipulation, symbol manipulation, and formula manipulation. Fundamental required operations for an algebra processor are considered. It is pointed out that algebra programs have been used for a number of problems in celestial mechanics with great success. The advantage of computer algebra is its accuracy and speed.

Mathematics and Information Retrieval.

ERIC Educational Resources Information Center

Salton, Gerald

1979-01-01

Examines the main mathematical approaches to information retrieval, including both algebraic and probabilistic models, and describes difficulties which impede formalization of information retrieval processes. A number of developments are covered where new theoretical understandings have directly led to improved retrieval techniques and operations.…

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…

Lattice Virasoro algebra and corner transfer matrices in the Baxter eight-vertex model

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

Itoyama, H.; Thacker, H.B.

1987-04-06

A lattice Virasoro algebra is constructed for the Baxter eight-vertex model. The operator L/sub 0/ is obtained from the logarithm of the corner transfer matrix and is given by the first moment of the XYZ spin-chain Hamiltonian. The algebra is valid even when the Hamiltonian includes a mass term, in which case it represents lattice coordinate transformations which distinguish between even and odd sublattices. We apply the quantum inverse scattering method to demonstrate that the Virasoro algebra follows from the Yang-Baxter relations.

Field validation of a free-agent cellular automata model of fire spread with fire–atmosphere coupling

Treesearch

Gary Achtemeier

2012-01-01

A cellular automata fire model represents ‘elements’ of fire by autonomous agents. A few simple algebraic expressions substituted for complex physical and meteorological processes and solved iteratively yield simulations for ‘super-diffusive’ fire spread and coupled surface-layer (2-m) fire–atmosphere processes. Pressure anomalies, which are integrals of the thermal...

Individual Differences in Algebraic Cognition: Relation to the Approximate Number and Sematic Memory Systems

PubMed Central

Geary, David C.; Hoard, Mary K.; Nugent, Lara; Rouder, Jeffrey N.

2015-01-01

The relation between performance on measures of algebraic cognition and acuity of the approximate number system (ANS) and memory for addition facts was assessed for 171 (92 girls) 9th graders, controlling parental education, sex, reading achievement, speed of numeral processing, fluency of symbolic number processing, intelligence, and the central executive component of working memory. The algebraic tasks assessed accuracy in placing x,y pairs in the coordinate plane, speed and accuracy of expression evaluation, and schema memory for algebra equations. ANS acuity was related to accuracy of placements in the coordinate plane and expression evaluation, but not schema memory. Frequency of fact-retrieval errors was related to schema memory but not coordinate plane or expression evaluation accuracy. The results suggest the ANS may contribute to or is influenced by spatial-numerical and numerical only quantity judgments in algebraic contexts, whereas difficulties in committing addition facts to long-term memory may presage slow formation of memories for the basic structure of algebra equations. More generally, the results suggest different brain and cognitive systems are engaged during the learning of different components of algebraic competence, controlling demographic and domain general abilities. PMID:26255604

Teaching Linear Algebra: Must the Fog Always Roll In?

ERIC Educational Resources Information Center

Carlson, David

1993-01-01

Proposes methods to teach the more difficult concepts of linear algebra. Examines features of the Linear Algebra Curriculum Study Group Core Syllabus, and presents problems from the core syllabus that utilize the mathematical process skills of making conjectures, proving the results, and communicating the results to colleagues. Presents five…

Affine q-deformed symmetry and the classical Yang-Baxter σ-model

NASA Astrophysics Data System (ADS)

Delduc, F.; Kameyama, T.; Magro, M.; Vicedo, B.

2017-03-01

The Yang-Baxter σ-model is an integrable deformation of the principal chiral model on a Lie group G. The deformation breaks the G × G symmetry to U(1)rank( G) × G. It is known that there exist non-local conserved charges which, together with the unbroken U(1)rank( G) local charges, form a Poisson algebra [InlineMediaObject not available: see fulltext.], which is the semiclassical limit of the quantum group {U}_q(g) , with g the Lie algebra of G. For a general Lie group G with rank( G) > 1, we extend the previous result by constructing local and non-local conserved charges satisfying all the defining relations of the infinite-dimensional Poisson algebra [InlineMediaObject not available: see fulltext.], the classical analogue of the quantum loop algebra {U}_q(Lg) , where Lg is the loop algebra of g. Quite unexpectedly, these defining relations are proved without encountering any ambiguity related to the non-ultralocality of this integrable σ-model.

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.

Open-Closed Homotopy Algebras and Strong Homotopy Leibniz Pairs Through Koszul Operad Theory

NASA Astrophysics Data System (ADS)

Hoefel, Eduardo; Livernet, Muriel

2012-08-01

Open-closed homotopy algebras (OCHA) and strong homotopy Leibniz pairs (SHLP) were introduced by Kajiura and Stasheff in 2004. In an appendix to their paper, Markl observed that an SHLP is equivalent to an algebra over the minimal model of a certain operad, without showing that the operad is Koszul. In the present paper, we show that both OCHA and SHLP are algebras over the minimal model of the zeroth homology of two versions of the Swiss-cheese operad and prove that these two operads are Koszul. As an application, we show that the OCHA operad is non-formal as a 2-colored operad but is formal as an algebra in the category of 2-collections.

A description of pseudo-bosons in terms of nilpotent Lie algebras

NASA Astrophysics Data System (ADS)

Bagarello, Fabio; Russo, Francesco G.

2018-02-01

We show how the one-mode pseudo-bosonic ladder operators provide concrete examples of nilpotent Lie algebras of dimension five. It is the first time that an algebraic-geometric structure of this kind is observed in the context of pseudo-bosonic operators. Indeed we do not find the well known Heisenberg algebras, which are involved in several quantum dynamical systems, but different Lie algebras which may be decomposed into the sum of two abelian Lie algebras in a prescribed way. We introduce the notion of semidirect sum (of Lie algebras) for this scope and find that it describes very well the behavior of pseudo-bosonic operators in many quantum models.

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.

Development process of in-service training intended for teachers to perform teaching of mathematics with computer algebra systems

NASA Astrophysics Data System (ADS)

Ardıç, Mehmet Alper; Işleyen, Tevfik

2018-01-01

In this study, we deal with the development process of in-service training activities designed in order for mathematics teachers of secondary education to realize teaching of mathematics, utilizing computer algebra systems. In addition, the results obtained from the researches carried out during and after the in-service training were summarized. Last section focuses on suggestions any teacher can use to carry out activities aimed at using computer algebra systems in teaching environments.

Bootstrapping non-commutative gauge theories from L∞ algebras

NASA Astrophysics Data System (ADS)

Blumenhagen, Ralph; Brunner, Ilka; Kupriyanov, Vladislav; Lüst, Dieter

2018-05-01

Non-commutative gauge theories with a non-constant NC-parameter are investigated. As a novel approach, we propose that such theories should admit an underlying L∞ algebra, that governs not only the action of the symmetries but also the dynamics of the theory. Our approach is well motivated from string theory. We recall that such field theories arise in the context of branes in WZW models and briefly comment on its appearance for integrable deformations of AdS5 sigma models. For the SU(2) WZW model, we show that the earlier proposed matrix valued gauge theory on the fuzzy 2-sphere can be bootstrapped via an L∞ algebra. We then apply this approach to the construction of non-commutative Chern-Simons and Yang-Mills theories on flat and curved backgrounds with non-constant NC-structure. More concretely, up to the second order, we demonstrate how derivative and curvature corrections to the equations of motion can be bootstrapped in an algebraic way from the L∞ algebra. The appearance of a non-trivial A∞ algebra is discussed, as well.

Integrability and superintegrability of the generalized n-level many-mode Jaynes-Cummings and Dicke models

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

Skrypnyk, T.

2009-10-15

We analyze symmetries of the integrable generalizations of Jaynes-Cummings and Dicke models associated with simple Lie algebras g and their reductive subalgebras g{sub K}[T. Skrypnyk, 'Generalized n-level Jaynes-Cummings and Dicke models, classical rational r-matrices and nested Bethe ansatz', J. Phys. A: Math. Theor. 41, 475202 (2008)]. We show that their symmetry algebras contain commutative subalgebras isomorphic to the Cartan subalgebras of g, which can be added to the commutative algebras of quantum integrals generated with the help of the quantum Lax operators. We diagonalize additional commuting integrals and constructed with their help the most general integrable quantum Hamiltonian of themore » generalized n-level many-mode Jaynes-Cummings and Dicke-type models using nested algebraic Bethe ansatz.« less

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.

Measurement theory in local quantum physics

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

Okamura, Kazuya, E-mail: okamura@math.cm.is.nagoya-u.ac.jp; Ozawa, Masanao, E-mail: ozawa@is.nagoya-u.ac.jp

In this paper, we aim to establish foundations of measurement theory in local quantum physics. For this purpose, we discuss a representation theory of completely positive (CP) instruments on arbitrary von Neumann algebras. We introduce a condition called the normal extension property (NEP) and establish a one-to-one correspondence between CP instruments with the NEP and statistical equivalence classes of measuring processes. We show that every CP instrument on an atomic von Neumann algebra has the NEP, extending the well-known result for type I factors. Moreover, we show that every CP instrument on an injective von Neumann algebra is approximated bymore » CP instruments with the NEP. The concept of posterior states is also discussed to show that the NEP is equivalent to the existence of a strongly measurable family of posterior states for every normal state. Two examples of CP instruments without the NEP are obtained from this result. It is thus concluded that in local quantum physics not every CP instrument represents a measuring process, but in most of physically relevant cases every CP instrument can be realized by a measuring process within arbitrary error limits, as every approximately finite dimensional von Neumann algebra on a separable Hilbert space is injective. To conclude the paper, the concept of local measurement in algebraic quantum field theory is examined in our framework. In the setting of the Doplicher-Haag-Roberts and Doplicher-Roberts theory describing local excitations, we show that an instrument on a local algebra can be extended to a local instrument on the global algebra if and only if it is a CP instrument with the NEP, provided that the split property holds for the net of local algebras.« less

Capitalizing on Basic Brain Processes in Developmental Algebra--Part 3

ERIC Educational Resources Information Center

Laughbaum, Edward D.

2011-01-01

In Part Three, the author reviews the basic ideas presented in Parts One and Two while arguing why the traditional equation-solving developmental algebra curricula is not a good choice for implementing neural response strategies presented in the first two parts. He continues by showing that the developmental algebra student audience is simply…

Calif. Laws Shift Gears on Algebra, Textbooks

ERIC Educational Resources Information Center

Robelen, Erik W.

2012-01-01

New laws in California have set the state on a course for some potentially significant changes to the curriculum, including a measure that revisits the matter of teaching Algebra 1 in 8th grade and another that revamps the state's textbook-adoption process and hands districts greater leeway in choosing instructional materials. The algebra-related…

An Algorithm for Interactive Modeling of Space-Transportation Engine Simulations: A Constraint Satisfaction Approach

NASA Technical Reports Server (NTRS)

Mitra, Debasis; Thomas, Ajai; Hemminger, Joseph; Sakowski, Barbara

2001-01-01

In this research we have developed an algorithm for the purpose of constraint processing by utilizing relational algebraic operators. Van Beek and others have investigated in the past this type of constraint processing from within a relational algebraic framework, producing some unique results. Apart from providing new theoretical angles, this approach also gives the opportunity to use the existing efficient implementations of relational database management systems as the underlying data structures for any relevant algorithm. Our algorithm here enhances that framework. The algorithm is quite general in its current form. Weak heuristics (like forward checking) developed within the Constraint-satisfaction problem (CSP) area could be also plugged easily within this algorithm for further enhancements of efficiency. The algorithm as developed here is targeted toward a component-oriented modeling problem that we are currently working on, namely, the problem of interactive modeling for batch-simulation of engineering systems (IMBSES). However, it could be adopted for many other CSP problems as well. The research addresses the algorithm and many aspects of the problem IMBSES that we are currently handling.

On the Performance of an Algebraic MultigridSolver on Multicore Clusters

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

Baker, A H; Schulz, M; Yang, U M

2010-04-29

Algebraic multigrid (AMG) solvers have proven to be extremely efficient on distributed-memory architectures. However, when executed on modern multicore cluster architectures, we face new challenges that can significantly harm AMG's performance. We discuss our experiences on such an architecture and present a set of techniques that help users to overcome the associated problems, including thread and process pinning and correct memory associations. We have implemented most of the techniques in a MultiCore SUPport library (MCSup), which helps to map OpenMP applications to multicore machines. We present results using both an MPI-only and a hybrid MPI/OpenMP model.

Chiral algebras in Landau-Ginzburg models

NASA Astrophysics Data System (ADS)

Dedushenko, Mykola

2018-03-01

Chiral algebras in the cohomology of the {\\overline{Q}}+ supercharge of two-dimensional N=(0,2) theories on flat spacetime are discussed. Using the supercurrent multiplet, we show that the answer is renormalization group invariant for theories with an R-symmetry. For N=(0,2) Landau-Ginzburg models, the chiral algebra is determined by the operator equations of motion, which preserve their classical form, and quantum renormalization of composite operators. We study these theories and then specialize to the N=(2,2) models and consider some examples.

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.

Deformed oscillator algebra approach of some quantum superintegrable Lissajous systems on the sphere and of their rational extensions

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

Marquette, Ian, E-mail: i.marquette@uq.edu.au; Quesne, Christiane, E-mail: cquesne@ulb.ac.be

2015-06-15

We extend the construction of 2D superintegrable Hamiltonians with separation of variables in spherical coordinates using combinations of shift, ladder, and supercharge operators to models involving rational extensions of the two-parameter Lissajous systems on the sphere. These new families of superintegrable systems with integrals of arbitrary order are connected with Jacobi exceptional orthogonal polynomials of type I (or II) and supersymmetric quantum mechanics. Moreover, we present an algebraic derivation of the degenerate energy spectrum for the one- and two-parameter Lissajous systems and the rationally extended models. These results are based on finitely generated polynomial algebras, Casimir operators, realizations as deformedmore » oscillator algebras, and finite-dimensional unitary representations. Such results have only been established so far for 2D superintegrable systems separable in Cartesian coordinates, which are related to a class of polynomial algebras that display a simpler structure. We also point out how the structure function of these deformed oscillator algebras is directly related with the generalized Heisenberg algebras spanned by the nonpolynomial integrals.« less

A mechanized process algebra for verification of device synchronization protocols

NASA Technical Reports Server (NTRS)

Schubert, E. Thomas

1992-01-01

We describe the formalization of a process algebra based on CCS within the Higher Order Logic (HOL) theorem-proving system. The representation of four types of device interactions and a correctness proof of the communication between a microprocessor and MMU is presented.

The Role of Cognitive Processes, Foundational Math Skill, and Calculation Accuracy and Fluency in Word-Problem Solving versus Pre-Algebraic Knowledge

PubMed Central

Fuchs, Lynn S.; Gilbert, Jennifer K.; Powell, Sarah R.; Cirino, Paul T.; Fuchs, Douglas; Hamlett, Carol L.; Seethaler, Pamela M.; Tolar, Tammy D.

2016-01-01

The purpose of this study was to examine child-level pathways in development of pre-algebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculation, word-problem, and number knowledge at start of grade 2; calculation accuracy and calculation fluency at end of grade 2; and pre-algebraic knowledge and word-problem solving at end of grade 4. Important similarities in pathways were identified, but path analysis also indicated that language comprehension is more critical for later word-problem solving than pre-algebraic knowledge. We conclude that pathways in development of these forms of 4th-grade mathematics performance are more alike than different, but demonstrate the need to fine-tune instruction for strands of the mathematics curriculum in ways that address individual students’ foundational mathematics skills or cognitive processes. PMID:27786534

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…

Thought beyond language: neural dissociation of algebra and natural language.

PubMed

Monti, Martin M; Parsons, Lawrence M; Osherson, Daniel N

2012-08-01

A central question in cognitive science is whether natural language provides combinatorial operations that are essential to diverse domains of thought. In the study reported here, we addressed this issue by examining the role of linguistic mechanisms in forging the hierarchical structures of algebra. In a 3-T functional MRI experiment, we showed that processing of the syntax-like operations of algebra does not rely on the neural mechanisms of natural language. Our findings indicate that processing the syntax of language elicits the known substrate of linguistic competence, whereas algebraic operations recruit bilateral parietal brain regions previously implicated in the representation of magnitude. This double dissociation argues against the view that language provides the structure of thought across all cognitive domains.

Selecting Students for Pre-Algebra: Examination of the Relative Utility of the Anchorage Pre-Algebra Screening Tests and the State of Alaska Standards Based Benchmark 2 Mathematics Study. An Examination of Consequential Validity and Recommendation.

ERIC Educational Resources Information Center

Fenton, Ray

This study examined the relative efficacy of the Anchorage (Alaska) Pre-Algebra Test and the State of Alaska Benchmark in 2 Math examination as tools used in the process of recommending grade 6 students for grade 7 Pre-Algebra placement. The consequential validity of the tests is explored in the context of class placements and grades earned. The…

Individual differences in algebraic cognition: Relation to the approximate number and semantic memory systems.

PubMed

Geary, David C; Hoard, Mary K; Nugent, Lara; Rouder, Jeffrey N

2015-12-01

The relation between performance on measures of algebraic cognition and acuity of the approximate number system (ANS) and memory for addition facts was assessed for 171 ninth graders (92 girls) while controlling for parental education, sex, reading achievement, speed of numeral processing, fluency of symbolic number processing, intelligence, and the central executive component of working memory. The algebraic tasks assessed accuracy in placing x,y pairs in the coordinate plane, speed and accuracy of expression evaluation, and schema memory for algebra equations. ANS acuity was related to accuracy of placements in the coordinate plane and expression evaluation but not to schema memory. Frequency of fact retrieval errors was related to schema memory but not to coordinate plane or expression evaluation accuracy. The results suggest that the ANS may contribute to or be influenced by spatial-numerical and numerical-only quantity judgments in algebraic contexts, whereas difficulties in committing addition facts to long-term memory may presage slow formation of memories for the basic structure of algebra equations. More generally, the results suggest that different brain and cognitive systems are engaged during the learning of different components of algebraic competence while controlling for demographic and domain general abilities. Copyright © 2015 Elsevier Inc. All rights reserved.

Implementing Computer Algebra Enabled Questions for the Assessment and Learning of Mathematics

ERIC Educational Resources Information Center

Sangwin, Christopher J.; Naismith, Laura

2008-01-01

We present principles for the design of an online system to support computer algebra enabled questions for use within the teaching and learning of mathematics in higher education. The introduction of a computer algebra system (CAS) into a computer aided assessment (CAA) system affords sophisticated response processing of student provided answers.…

Syntax and Meaning as Sensuous, Visual, Historical Forms of Algebraic Thinking

ERIC Educational Resources Information Center

Radford, Luis; Puig, Luis

2007-01-01

Before the advent of symbolism, i.e. before the end of the 16th Century, algebraic calculations were made using natural language. Through a kind of metaphorical process, a few terms from everyday life (e.g. thing, root) acquired a technical mathematical status and constituted the specialized language of algebra. The introduction of letters and…

Strategies for Solving Fraction Tasks and Their Link to Algebraic Thinking

ERIC Educational Resources Information Center

Pearn, Catherine; Stephens, Max

2015-01-01

Many researchers argue that a deep understanding of fractions is important for a successful transition to algebra. Teaching, especially in the middle years, needs to focus specifically on those areas of fraction knowledge and operations that support subsequent solution processes for algebraic equations. This paper focuses on the results of Year 6…

Eigenvectors determination of the ribosome dynamics model during mRNA translation using the Kleene Star algorithm

NASA Astrophysics Data System (ADS)

Ernawati; Carnia, E.; Supriatna, A. K.

2018-03-01

Eigenvalues and eigenvectors in max-plus algebra have the same important role as eigenvalues and eigenvectors in conventional algebra. In max-plus algebra, eigenvalues and eigenvectors are useful for knowing dynamics of the system such as in train system scheduling, scheduling production systems and scheduling learning activities in moving classes. In the translation of proteins in which the ribosome move uni-directionally along the mRNA strand to recruit the amino acids that make up the protein, eigenvalues and eigenvectors are used to calculate protein production rates and density of ribosomes on the mRNA. Based on this, it is important to examine the eigenvalues and eigenvectors in the process of protein translation. In this paper an eigenvector formula is given for a ribosome dynamics during mRNA translation by using the Kleene star algorithm in which the resulting eigenvector formula is simpler and easier to apply to the system than that introduced elsewhere. This paper also discusses the properties of the matrix {B}λ \\otimes n of model. Among the important properties, it always has the same elements in the first column for n = 1, 2,… if the eigenvalue is the time of initiation, λ = τin , and the column is the eigenvector of the model corresponding to λ.

A differential operator realisation approach for constructing Casimir operators of non-semisimple Lie algebras

NASA Astrophysics Data System (ADS)

Alshammari, Fahad; Isaac, Phillip S.; Marquette, Ian

2018-02-01

We introduce a search algorithm that utilises differential operator realisations to find polynomial Casimir operators of Lie algebras. To demonstrate the algorithm, we look at two classes of examples: (1) the model filiform Lie algebras and (2) the Schrödinger Lie algebras. We find that an abstract form of dimensional analysis assists us in our algorithm, and greatly reduces the complexity of the problem.

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.

Window of Opportunity? Adolescence, Music, and Algebra

ERIC Educational Resources Information Center

Helmrich, Barbara H.

2010-01-01

Research has suggested that musicians process music in the same cortical regions that adolescents process algebra. An early adolescence synaptogenesis might present a window of opportunity during middle school for music to create and strengthen enduring neural connections in those regions. Six school districts across Maryland provided scores from…

Filiform Lie algebras of order 3

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

Navarro, R. M., E-mail: rnavarro@unex.es

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 lamore » 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.« less

Conformal field algebras with quantum symmetry from the theory of superselection sectors

NASA Astrophysics Data System (ADS)

Mack, Gerhard; Schomerus, Volker

1990-11-01

According to the theory of superselection sectors of Doplicher, Haag, and Roberts, field operators which make transitions between different superselection sectors—i.e. different irreducible representations of the observable algebra—are to be constructed by adjoining localized endomorphisms to the algebra of local observables. We find the relevant endomorphisms of the chiral algebra of observables in the minimal conformal model with central charge c=1/2 (Ising model). We show by explicit and elementary construction how they determine a representation of the braid group B ∞ which is associated with a Temperley-Lieb-Jones algebra. We recover fusion rules, and compute the quantum dimensions of the superselection sectors. We exhibit a field algebra which is quantum group covariant and acts in the Hilbert space of physical states. It obeys local braid relations in an appropriate weak sense.

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.

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.

On the correspondence between boundary and bulk lattice models and (logarithmic) conformal field theories

NASA Astrophysics Data System (ADS)

Belletête, J.; Gainutdinov, A. M.; Jacobsen, J. L.; Saleur, H.; Vasseur, R.

2017-12-01

The relationship between bulk and boundary properties is one of the founding features of (rational) conformal field theory (CFT). Our goal in this paper is to explore the possibility of having an equivalent relationship in the context of lattice models. We focus on models based on the Temperley-Lieb algebra, and use the concept of ‘braid translation’, which is a natural way, in physical terms, to ‘close’ an open spin chain by adding an interaction between the first and last spins using braiding to ‘bring’ them next to each other. The interaction thus obtained is in general non-local, but has the key feature that it is expressed solely in terms of the algebra for the open spin chain—the ‘ordinary’ Temperley-Lieb algebra and its blob algebra generalization. This is in contrast with the usual periodic spin chains which involve only local interactions, and are described by the periodic Temperley-Lieb algebra. We show that for the restricted solid-on-solid models, which are known to be described by minimal unitary CFTs (with central charge c<1 ) in the continuum limit, the braid translation in fact does provide the ordinary periodic model starting from the open model with fixed (identical) boundary conditions on the two sides of the strip. This statement has a precise mathematical formulation, which is a pull-back map between irreducible modules of, respectively, the blob algebra and the affine Temperley-Lieb algebra. We then turn to the same kind of analysis for two models whose continuum limits are logarithmic CFTs (LCFTs)—the alternating gl(1\\vert 1) and sl(2\\vert 1) spin chains. We find that the result for minimal models does not hold any longer: braid translation of the relevant (in that case, indecomposable but not irreducible) modules of the Temperley-Lieb algebra does not give rise to the modules known to be present in the periodic chains. In the gl(1\\vert 1) case, the content in terms of the irreducibles is the same, as well as the spectrum, but the detailed structure (like logarithmic coupling) is profoundly different. This carries over to the continuum limit. The situation is similar for the sl(2\\vert 1) case. The problem of relating bulk and boundary lattice models for LCFTs thus remains open.

Analysis of algebraic reasoning ability of cognitive style perspectives on field dependent field independent and gender

NASA Astrophysics Data System (ADS)

Rosita, N. T.

2018-03-01

The purpose of this study is to analyse algebraic reasoning ability using the SOLO model as a theoretical framework to assess students’ algebraic reasoning abilities of Field Dependent cognitive (FD), Field Independent (FI) and Gender perspectives. The method of this study is a qualitative research. The instrument of this study is the researcher himself assisted with algebraic reasoning tests, the problems have been designed based on NCTM indicators and algebraic reasoning according to SOLO model. While the cognitive style of students is determined using Group Embedded Figure Test (GEFT), as well as interviews on the subject as triangulation. The subjects are 15 female and 15 males of the sixth semester students of mathematics education, STKIP Sebelas April. The results of the qualitative data analysis is that most subjects are at the level of unistructural and multi-structural, subjects at the relational level have difficulty in forming a new linear pattern. While the subjects at the extended abstract level are able to meet all the indicators of algebraic reasoning ability even though some of the answers are not perfect yet. Subjects of FI tend to have higher algebraic reasoning abilities than of the subject of FD.

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.

Applied Algebra: The Modeling Technique of Least Squares

ERIC Educational Resources Information Center

Zelkowski, Jeremy; Mayes, Robert

2008-01-01

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

Tracking problem solving by multivariate pattern analysis and Hidden Markov Model algorithms.

PubMed

Anderson, John R

2012-03-01

Multivariate pattern analysis can be combined with Hidden Markov Model algorithms to track the second-by-second thinking as people solve complex problems. Two applications of this methodology are illustrated with a data set taken from children as they interacted with an intelligent tutoring system for algebra. The first "mind reading" application involves using fMRI activity to track what students are doing as they solve a sequence of algebra problems. The methodology achieves considerable accuracy at determining both what problem-solving step the students are taking and whether they are performing that step correctly. The second "model discovery" application involves using statistical model evaluation to determine how many substates are involved in performing a step of algebraic problem solving. This research indicates that different steps involve different numbers of substates and these substates are associated with different fluency in algebra problem solving. Copyright © 2011 Elsevier Ltd. All rights reserved.

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…

Mathematical Modelling in Engineering: A Proposal to Introduce Linear Algebra Concepts

ERIC Educational Resources Information Center

Cárcamo Bahamonde, Andrea; Gómez Urgelles, Joan; Fortuny Aymemí, Josep

2016-01-01

The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasise the development of mathematical abilities primarily associated with modelling and interpreting, which are not exclusively calculus abilities. Considering this, an instructional design was created based on mathematical modelling and…

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.

Modelling of nanoscale quantum tunnelling structures using algebraic topology method

NASA Astrophysics Data System (ADS)

Sankaran, Krishnaswamy; Sairam, B.

2018-05-01

We have modelled nanoscale quantum tunnelling structures using Algebraic Topology Method (ATM). The accuracy of ATM is compared to the analytical solution derived based on the wave nature of tunnelling electrons. ATM provides a versatile, fast, and simple model to simulate complex structures. We are currently expanding the method for modelling electrodynamic systems.

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…

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.

Modeling the Water Balloon Slingshot

NASA Astrophysics Data System (ADS)

Bousquet, Benjamin D.; Figura, Charles C.

2013-01-01

In the introductory physics courses at Wartburg College, we have been working to create a lab experience focused on the scientific process itself rather than verification of physical laws presented in the classroom or textbook. To this end, we have developed a number of open-ended modeling exercises suitable for a variety of learning environments, from non-science major classes to algebra-based and calculus-based introductory physics classes.

Braided Categories of Endomorphisms as Invariants for Local Quantum Field Theories

NASA Astrophysics Data System (ADS)

Giorgetti, Luca; Rehren, Karl-Henning

2018-01-01

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

Recurrence approach and higher order polynomial algebras for superintegrable monopole systems

NASA Astrophysics Data System (ADS)

Hoque, Md Fazlul; Marquette, Ian; Zhang, Yao-Zhong

2018-05-01

We revisit the MIC-harmonic oscillator in flat space with monopole interaction and derive the polynomial algebra satisfied by the integrals of motion and its energy spectrum using the ad hoc recurrence approach. We introduce a superintegrable monopole system in a generalized Taub-Newman-Unti-Tamburino (NUT) space. The Schrödinger equation of this model is solved in spherical coordinates in the framework of Stäckel transformation. It is shown that wave functions of the quantum system can be expressed in terms of the product of Laguerre and Jacobi polynomials. We construct ladder and shift operators based on the corresponding wave functions and obtain the recurrence formulas. By applying these recurrence relations, we construct higher order algebraically independent integrals of motion. We show that the integrals form a polynomial algebra. We construct the structure functions of the polynomial algebra and obtain the degenerate energy spectra of the model.

Three-dimensional fractional-spin gravity

NASA Astrophysics Data System (ADS)

Boulanger, Nicolas; Sundell, Per; Valenzuela, Mauricio

2014-02-01

Using Wigner-deformed Heisenberg oscillators, we construct 3D Chern-Simons models consisting of fractional-spin fields coupled to higher-spin gravity and internal nonabelian gauge fields. The gauge algebras consist of Lorentz-tensorial Blencowe-Vasiliev higher-spin algebras and compact internal algebras intertwined by infinite-dimensional generators in lowest-weight representations of the Lorentz algebra with fractional spin. In integer or half-integer non-unitary cases, there exist truncations to gl(ℓ , ℓ ± 1) or gl(ℓ|ℓ ± 1) models. In all non-unitary cases, the internal gauge fields can be set to zero. At the semi-classical level, the fractional-spin fields are either Grassmann even or odd. The action requires the enveloping-algebra representation of the deformed oscillators, while their Fock-space representation suffices on-shell. The project was funded in part by F.R.S.-FNRS " Ulysse" Incentive Grant for Mobility in Scientific Research.

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

PubMed

Casasent, D; Ghosh, A

1985-06-01

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

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…

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.

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. © 2016 The Author(s).

A Cohomological Perspective on Algebraic Quantum Field Theory

NASA Astrophysics Data System (ADS)

Hawkins, Eli

2018-05-01

Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of constructing interacting QFT models. Symmetry is the primary tool for understanding the structure and properties of a QFT model. This perspective leads to a generalization of the algebraic quantum field theory framework, as well as a more general definition of symmetry. This means that some models may have symmetries that were not previously recognized or exploited. To first order, a deformation of a QFT model is described by a Hochschild cohomology class. A deformation could, for example, correspond to adding an interaction term to a Lagrangian. The cohomology class for such an interaction is computed here. However, the result is more general and does not require the undeformed model to be constructed from a Lagrangian. This computation leads to a more concrete version of the construction of perturbative algebraic quantum field theory.

High-performance image processing architecture

NASA Astrophysics Data System (ADS)

Coffield, Patrick C.

1992-04-01

The proposed architecture is a logical design specifically for image processing and other related computations. The design is a hybrid electro-optical concept consisting of three tightly coupled components: a spatial configuration processor (the optical analog portion), a weighting processor (digital), and an accumulation processor (digital). The systolic flow of data and image processing operations are directed by a control buffer and pipelined to each of the three processing components. The image processing operations are defined by an image algebra developed by the University of Florida. The algebra is capable of describing all common image-to-image transformations. The merit of this architectural design is how elegantly it handles the natural decomposition of algebraic functions into spatially distributed, point-wise operations. The effect of this particular decomposition allows convolution type operations to be computed strictly as a function of the number of elements in the template (mask, filter, etc.) instead of the number of picture elements in the image. Thus, a substantial increase in throughput is realized. The logical architecture may take any number of physical forms. While a hybrid electro-optical implementation is of primary interest, the benefits and design issues of an all digital implementation are also discussed. The potential utility of this architectural design lies in its ability to control all the arithmetic and logic operations of the image algebra's generalized matrix product. This is the most powerful fundamental formulation in the algebra, thus allowing a wide range of applications.

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

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

A Process Algebraic Approach to Software Architecture Design

NASA Astrophysics Data System (ADS)

Aldini, Alessandro; Bernardo, Marco; Corradini, Flavio

Process algebra is a formal tool for the specification and the verification of concurrent and distributed systems. It supports compositional modeling through a set of operators able to express concepts like sequential composition, alternative composition, and parallel composition of action-based descriptions. It also supports mathematical reasoning via a two-level semantics, which formalizes the behavior of a description by means of an abstract machine obtained from the application of structural operational rules and then introduces behavioral equivalences able to relate descriptions that are syntactically different. In this chapter, we present the typical behavioral operators and operational semantic rules for a process calculus in which no notion of time, probability, or priority is associated with actions. Then, we discuss the three most studied approaches to the definition of behavioral equivalences - bisimulation, testing, and trace - and we illustrate their congruence properties, sound and complete axiomatizations, modal logic characterizations, and verification algorithms. Finally, we show how these behavioral equivalences and some of their variants are related to each other on the basis of their discriminating power.

The Effects of Representations, Constructivist Approaches, and Engagement on Middle School Students' Algebraic Procedure and Conceptual Understanding

ERIC Educational Resources Information Center

Ross, Amanda; Willson, Victor

2012-01-01

This study examined the effects of types of representations, constructivist teaching approaches, and student engagement on middle school algebra students' procedural knowledge and conceptual understanding. Data gathered from 16 video lessons and algebra pretest/posttests were used to run three multilevel structural equation models. Symbolic…

Mathematical Modelling and the Learning Trajectory: Tools to Support the Teaching of Linear Algebra

ERIC Educational Resources Information Center

Cárcamo Bahamonde, Andrea Dorila; Fortuny Aymemí, Josep Maria; Gómez i Urgellés, Joan Vicenç

2017-01-01

In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and…

Modeling formalisms in Systems Biology

PubMed Central

2011-01-01

Systems Biology has taken advantage of computational tools and high-throughput experimental data to model several biological processes. These include signaling, gene regulatory, and metabolic networks. However, most of these models are specific to each kind of network. Their interconnection demands a whole-cell modeling framework for a complete understanding of cellular systems. We describe the features required by an integrated framework for modeling, analyzing and simulating biological processes, and review several modeling formalisms that have been used in Systems Biology including Boolean networks, Bayesian networks, Petri nets, process algebras, constraint-based models, differential equations, rule-based models, interacting state machines, cellular automata, and agent-based models. We compare the features provided by different formalisms, and discuss recent approaches in the integration of these formalisms, as well as possible directions for the future. PMID:22141422

Temporal mapping and analysis

NASA Technical Reports Server (NTRS)

O'Hara, Charles G. (Inventor); Shrestha, Bijay (Inventor); Vijayaraj, Veeraraghavan (Inventor); Mali, Preeti (Inventor)

2011-01-01

A compositing process for selecting spatial data collected over a period of time, creating temporal data cubes from the spatial data, and processing and/or analyzing the data using temporal mapping algebra functions. In some embodiments, the temporal data cube is creating a masked cube using the data cubes, and computing a composite from the masked cube by using temporal mapping algebra.

Distributed Sensing and Processing: A Graphical Model Approach

DTIC Science & Technology

2005-11-30

that Ramanujan graph toplogies maximize the convergence rate of distributed detection consensus algorithms, improving over three orders of...small world type network designs. 14. SUBJECT TERMS Ramanujan graphs, sensor network topology, sensor network...that Ramanujan graphs, for which there are explicit algebraic constructions, have large eigenratios, converging much faster than structured graphs

pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations

DOE PAGES

Nicholson, Bethany; Siirola, John D.; Watson, Jean-Paul; ...

2017-12-20

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differentialmore » equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers.« less

pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations

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

Nicholson, Bethany; Siirola, John D.; Watson, Jean-Paul

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differentialmore » equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers.« less

The Standard Model in noncommutative geometry: fundamental fermions as internal forms

NASA Astrophysics Data System (ADS)

Dąbrowski, Ludwik; D'Andrea, Francesco; Sitarz, Andrzej

2018-05-01

Given the algebra, Hilbert space H, grading and real structure of the finite spectral triple of the Standard Model, we classify all possible Dirac operators such that H is a self-Morita equivalence bimodule for the associated Clifford algebra.

Rosen's (M,R) system in process algebra.

PubMed

Gatherer, Derek; Galpin, Vashti

2013-11-17

Robert Rosen's Metabolism-Replacement, or (M,R), system can be represented as a compact network structure with a single source and three products derived from that source in three consecutive reactions. (M,R) has been claimed to be non-reducible to its components and algorithmically non-computable, in the sense of not being evaluable as a function by a Turing machine. If (M,R)-like structures are present in real biological networks, this suggests that many biological networks will be non-computable, with implications for those branches of systems biology that rely on in silico modelling for predictive purposes. We instantiate (M,R) using the process algebra Bio-PEPA, and discuss the extent to which our model represents a true realization of (M,R). We observe that under some starting conditions and parameter values, stable states can be achieved. Although formal demonstration of algorithmic computability remains elusive for (M,R), we discuss the extent to which our Bio-PEPA representation of (M,R) allows us to sidestep Rosen's fundamental objections to computational systems biology. We argue that the behaviour of (M,R) in Bio-PEPA shows life-like properties.

Current algebra, statistical mechanics and quantum models

NASA Astrophysics Data System (ADS)

Vilela Mendes, R.

2017-11-01

Results obtained in the past for free boson systems at zero and nonzero temperatures are revisited to clarify the physical meaning of current algebra reducible functionals which are associated to systems with density fluctuations, leading to observable effects on phase transitions. To use current algebra as a tool for the formulation of quantum statistical mechanics amounts to the construction of unitary representations of diffeomorphism groups. Two mathematical equivalent procedures exist for this purpose. One searches for quasi-invariant measures on configuration spaces, the other for a cyclic vector in Hilbert space. Here, one argues that the second approach is closer to the physical intuition when modelling complex systems. An example of application of the current algebra methodology to the pairing phenomenon in two-dimensional fermion systems is discussed.

Survey of Turbulence Models for the Computation of Turbulent Jet Flow and Noise

NASA Technical Reports Server (NTRS)

Nallasamy, N.

1999-01-01

The report presents an overview of jet noise computation utilizing the computational fluid dynamic solution of the turbulent jet flow field. The jet flow solution obtained with an appropriate turbulence model provides the turbulence characteristics needed for the computation of jet mixing noise. A brief account of turbulence models that are relevant for the jet noise computation is presented. The jet flow solutions that have been directly used to calculate jet noise are first reviewed. Then, the turbulent jet flow studies that compute the turbulence characteristics that may be used for noise calculations are summarized. In particular, flow solutions obtained with the k-e model, algebraic Reynolds stress model, and Reynolds stress transport equation model are reviewed. Since, the small scale jet mixing noise predictions can be improved by utilizing anisotropic turbulence characteristics, turbulence models that can provide the Reynolds stress components must now be considered for jet flow computations. In this regard, algebraic stress models and Reynolds stress transport models are good candidates. Reynolds stress transport models involve more modeling and computational effort and time compared to algebraic stress models. Hence, it is recommended that an algebraic Reynolds stress model (ASM) be implemented in flow solvers to compute the Reynolds stress components.

A finite element computation of turbulent boundary layer flows with an algebraic stress turbulence model

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook; Chen, Yen-Sen

1988-01-01

An algebraic stress turbulence model and a computational procedure for turbulent boundary layer flows which is based on the semidiscrete Galerkin FEM are discussed. In the algebraic stress turbulence model, the eddy viscosity expression is obtained from the Reynolds stress turbulence model, and the turbulent kinetic energy dissipation rate equation is improved by including a production range time scale. Good agreement with experimental data is found for the examples of a fully developed channel flow, a fully developed pipe flow, a flat plate boundary layer flow, a plane jet exhausting into a moving stream, a circular jet exhausting into a moving stream, and a wall jet flow.

Identification of Biokinetic Models Using the Concept of Extents.

PubMed

Mašić, Alma; Srinivasan, Sriniketh; Billeter, Julien; Bonvin, Dominique; Villez, Kris

2017-07-05

The development of a wide array of process technologies to enable the shift from conventional biological wastewater treatment processes to resource recovery systems is matched by an increasing demand for predictive capabilities. Mathematical models are excellent tools to meet this demand. However, obtaining reliable and fit-for-purpose models remains a cumbersome task due to the inherent complexity of biological wastewater treatment processes. In this work, we present a first study in the context of environmental biotechnology that adopts and explores the use of extents as a way to simplify and streamline the dynamic process modeling task. In addition, the extent-based modeling strategy is enhanced by optimal accounting for nonlinear algebraic equilibria and nonlinear measurement equations. Finally, a thorough discussion of our results explains the benefits of extent-based modeling and its potential to turn environmental process modeling into a highly automated task.

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.

Continual Lie algebras and noncommutative counterparts of exactly solvable models

NASA Astrophysics Data System (ADS)

Zuevsky, A.

2004-01-01

Noncommutative counterparts of exactly solvable models are introduced on the basis of a generalization of Saveliev-Vershik continual Lie algebras. Examples of noncommutative Liouville and sin/h-Gordon equations are given. The simplest soliton solution to the noncommutative sine-Gordon equation is found.

The Bethe ansatz

NASA Astrophysics Data System (ADS)

Levkovich-Maslyuk, Fedor

2016-08-01

We give a pedagogical introduction to the Bethe ansatz techniques in integrable QFTs and spin chains. We first discuss and motivate the general framework of asymptotic Bethe ansatz for the spectrum of integrable QFTs in large volume, based on the exact S-matrix. Then we illustrate this method in several concrete theories. The first case we study is the SU(2) chiral Gross-Neveu model. We derive the Bethe equations via algebraic Bethe ansatz, solving in the process the Heisenberg XXX spin chain. We discuss this famous spin chain model in some detail, covering in particular the coordinate Bethe ansatz, some properties of Bethe states, and the classical scaling limit leading to finite-gap equations. Then we proceed to the more involved SU(3) chiral Gross-Neveu model and derive the Bethe equations using nested algebraic Bethe ansatz to solve the arising SU(3) spin chain. Finally we show how a method similar to the Bethe ansatz works in a completely different setting, namely for the 1D oscillator in quantum mechanics.

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.

Distributed Secure Coordinated Control for Multiagent Systems Under Strategic Attacks.

PubMed

Feng, Zhi; Wen, Guanghui; Hu, Guoqiang

2017-05-01

This paper studies a distributed secure consensus tracking control problem for multiagent systems subject to strategic cyber attacks modeled by a random Markov process. A hybrid stochastic secure control framework is established for designing a distributed secure control law such that mean-square exponential consensus tracking is achieved. A connectivity restoration mechanism is considered and the properties on attack frequency and attack length rate are investigated, respectively. Based on the solutions of an algebraic Riccati equation and an algebraic Riccati inequality, a procedure to select the control gains is provided and stability analysis is studied by using Lyapunov's method.. The effect of strategic attacks on discrete-time systems is also investigated. Finally, numerical examples are provided to illustrate the effectiveness of theoretical analysis.

A path model for Whittaker vectors

NASA Astrophysics Data System (ADS)

Di Francesco, Philippe; Kedem, Rinat; Turmunkh, Bolor

2017-06-01

In this paper we construct weighted path models to compute Whittaker vectors in the completion of Verma modules, as well as Whittaker functions of fundamental type, for all finite-dimensional simple Lie algebras, affine Lie algebras, and the quantum algebra U_q(slr+1) . This leads to series expressions for the Whittaker functions. We show how this construction leads directly to the quantum Toda equations satisfied by these functions, and to the q-difference equations in the quantum case. We investigate the critical limit of affine Whittaker functions computed in this way.

Tracking the Success of Pre-College Algebra Workshop Students in Subsequent College Mathematics Classes

ERIC Educational Resources Information Center

Fuller, Edgar; Deshler, Jessica M.; Kuhn, Betsy; Squire, Douglas

2014-01-01

In 2007 the Department of Mathematics at our institution began developing a placement process designed to identify at-risk students entering mathematics courses at the College Algebra and Calculus levels. Major changes in our placement testing process and the resulting interventions for at-risk students were put in place in Fall of 2008. At the…

Using Technology to Optimize and Generalize: The Least-Squares Line

ERIC Educational Resources Information Center

Burke, Maurice J.; Hodgson, Ted R.

2007-01-01

With the help of technology and a basic high school algebra method for finding the vertex of a quadratic polynomial, students can develop and prove the formula for least-squares lines. Students are exposed to the power of a computer algebra system to generalize processes they understand and to see deeper patterns in those processes. (Contains 4…

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…

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…

Tensor Algebra Library for NVidia Graphics Processing Units

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

Liakh, Dmitry

This is a general purpose math library implementing basic tensor algebra operations on NVidia GPU accelerators. This software is a tensor algebra library that can perform basic tensor algebra operations, including tensor contractions, tensor products, tensor additions, etc., on NVidia GPU accelerators, asynchronously with respect to the CPU host. It supports a simultaneous use of multiple NVidia GPUs. Each asynchronous API function returns a handle which can later be used for querying the completion of the corresponding tensor algebra operation on a specific GPU. The tensors participating in a particular tensor operation are assumed to be stored in local RAMmore » of a node or GPU RAM. The main research area where this library can be utilized is the quantum many-body theory (e.g., in electronic structure theory).« less

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

NASA Astrophysics Data System (ADS)

Trujillo Arredondo, Mariana

2014-06-01

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

Unification of the general non-linear sigma model and the Virasoro master equation

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

Boer, J. de; Halpern, M.B.

1997-06-01

The Virasoro master equation describes a large set of conformal field theories known as the affine-Virasoro constructions, in the operator algebra (affinie Lie algebra) of the WZW model, while the einstein equations of the general non-linear sigma model describe another large set of conformal field theories. This talk summarizes recent work which unifies these two sets of conformal field theories, together with a presumable large class of new conformal field theories. The basic idea is to consider spin-two operators of the form L{sub ij}{partial_derivative}x{sup i}{partial_derivative}x{sup j} in the background of a general sigma model. The requirement that these operators satisfymore » the Virasoro algebra leads to a set of equations called the unified Einstein-Virasoro master equation, in which the spin-two spacetime field L{sub ij} cuples to the usual spacetime fields of the sigma model. The one-loop form of this unified system is presented, and some of its algebraic and geometric properties are discussed.« less

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…

Wronski Brackets and the Ferris Wheel

NASA Astrophysics Data System (ADS)

Martin, Keye

2005-11-01

We connect the Bayesian order on classical states to a certain Lie algebra on C^infty[0,1]. This special Lie algebra structure, made precise by an idea we introduce called a Wronski bracket, suggests new phenomena the Bayesian order naturally models. We then study Wronski brackets on associative algebras, and in the commutative case, discover the beautiful result that they are equivalent to derivations.

Global identifiability of linear compartmental models--a computer algebra algorithm.

PubMed

Audoly, S; D'Angiò, L; Saccomani, M P; Cobelli, C

1998-01-01

A priori global identifiability deals with the uniqueness of the solution for the unknown parameters of a model and is, thus, a prerequisite for parameter estimation of biological dynamic models. Global identifiability is however difficult to test, since it requires solving a system of algebraic nonlinear equations which increases both in nonlinearity degree and number of terms and unknowns with increasing model order. In this paper, a computer algebra tool, GLOBI (GLOBal Identifiability) is presented, which combines the topological transfer function method with the Buchberger algorithm, to test global identifiability of linear compartmental models. GLOBI allows for the automatic testing of a priori global identifiability of general structure compartmental models from general multi input-multi output experiments. Examples of usage of GLOBI to analyze a priori global identifiability of some complex biological compartmental models are provided.

On superintegrable monopole systems

NASA Astrophysics Data System (ADS)

Fazlul Hoque, Md; Marquette, Ian; Zhang, Yao-Zhong

2018-02-01

Superintegrable systems with monopole interactions in flat and curved spaces have attracted much attention. For example, models in spaces with a Taub-NUT metric are well-known to admit the Kepler-type symmetries and provide non-trivial generalizations of the usual Kepler problems. In this paper, we overview new families of superintegrable Kepler, MIC-harmonic oscillator and deformed Kepler systems interacting with Yang-Coulomb monopoles in the flat and curved Taub-NUT spaces. We present their higher-order, algebraically independent integrals of motion via the direct and constructive approaches which prove the superintegrability of the models. The integrals form symmetry polynomial algebras of the systems with structure constants involving Casimir operators of certain Lie algebras. Such algebraic approaches provide a deeper understanding to the degeneracies of the energy spectra and connection between wave functions and differential equations and geometry.

Polynomial algebra of discrete models in systems biology.

PubMed

Veliz-Cuba, Alan; Jarrah, Abdul Salam; Laubenbacher, Reinhard

2010-07-01

An increasing number of discrete mathematical models are being published in Systems Biology, ranging from Boolean network models to logical models and Petri nets. They are used to model a variety of biochemical networks, such as metabolic networks, gene regulatory networks and signal transduction networks. There is increasing evidence that such models can capture key dynamic features of biological networks and can be used successfully for hypothesis generation. This article provides a unified framework that can aid the mathematical analysis of Boolean network models, logical models and Petri nets. They can be represented as polynomial dynamical systems, which allows the use of a variety of mathematical tools from computer algebra for their analysis. Algorithms are presented for the translation into polynomial dynamical systems. Examples are given of how polynomial algebra can be used for the model analysis. alanavc@vt.edu Supplementary data are available at Bioinformatics online.

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…

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.

Use of transport models for wildfire behavior simulations

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

Linn, R.R.; Harlow, F.H.

1998-01-01

Investigators have attempted to describe the behavior of wildfires for over fifty years. Current models for numerical description are mainly algebraic and based on statistical or empirical ideas. The authors have developed a transport model called FIRETEC. The use of transport formulations connects the propagation rates to the full conservation equations for energy, momentum, species concentrations, mass, and turbulence. In this paper, highlights of the model formulation and results are described. The goal of the FIRETEC model is to describe most probable average behavior of wildfires in a wide variety of conditions. FIRETEC represents the essence of the combination ofmore » many small-scale processes without resolving each process in complete detail.« less

Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes

DOE PAGES

Günaydin, Murat; Lüst, Dieter; Malek, Emanuel

2016-11-07

We propose a non-associative phase space algebra for M-theory backgrounds with locally non-geometric fluxes based on the non-associative algebra of octonions. Our proposal is based on the observation that the non-associative algebra of the non-geometric R-flux background in string theory can be obtained by a proper contraction of the simple Malcev algebra generated by imaginary octonions. Furthermore, by studying a toy model of a four-dimensional locally non-geometric M-theory background which is dual to a twisted torus, we show that the non-geometric background is “missing” a momentum mode. The resulting seven-dimensional phase space can thus be naturally identified with the imaginarymore » octonions. This allows us to interpret the full uncontracted algebra of imaginary octonions as the uplift of the string theory R-flux algebra to M-theory, with the contraction parameter playing the role of the string coupling constant g s.« less

Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes

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

Günaydin, Murat; Lüst, Dieter; Malek, Emanuel

We propose a non-associative phase space algebra for M-theory backgrounds with locally non-geometric fluxes based on the non-associative algebra of octonions. Our proposal is based on the observation that the non-associative algebra of the non-geometric R-flux background in string theory can be obtained by a proper contraction of the simple Malcev algebra generated by imaginary octonions. Furthermore, by studying a toy model of a four-dimensional locally non-geometric M-theory background which is dual to a twisted torus, we show that the non-geometric background is “missing” a momentum mode. The resulting seven-dimensional phase space can thus be naturally identified with the imaginarymore » octonions. This allows us to interpret the full uncontracted algebra of imaginary octonions as the uplift of the string theory R-flux algebra to M-theory, with the contraction parameter playing the role of the string coupling constant g s.« less

An algebraic interpretation of PSP composition.

PubMed

Vaucher, G

1998-01-01

The introduction of time in artificial neurons is a delicate problem on which many groups are working. Our approach combines some properties of biological models and the algebraic properties of McCulloch and Pitts artificial neuron (AN) (McCulloch and Pitts, 1943) to produce a new model which links both characteristics. In this extended artificial neuron, postsynaptic potentials (PSPs) are considered as numerical elements, having two degrees of freedom, on which the neuron computes operations. Modelled in this manner, a group of neurons can be seen as a computer with an asynchronous architecture. To formalize the functioning of this computer, we propose an algebra of impulses. This approach might also be interesting in the modelling of the passive electrical properties in some biological neurons.

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

PubMed

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

2013-05-01

Quantification of magnetization-transfer (MT) experiments are typically based on the assumption of the binary spin-bath model. This model allows for the extraction of up to six parameters (relative pool sizes, relaxation times, and exchange rate constants) for the characterization of macromolecules, which are coupled via exchange processes to the water in tissues. Here, an approach is presented for estimating MT parameters acquired with arbitrary saturation schemes and imaging pulse sequences. It uses matrix algebra to solve the Bloch-McConnell equations without unwarranted simplifications, such as assuming steady-state conditions for pulsed saturation schemes or neglecting imaging pulses. The algorithm achieves sufficient efficiency for voxel-by-voxel MT parameter estimations by using a polynomial interpolation technique. Simulations, as well as experiments in agar gels with continuous-wave and pulsed MT preparation, were performed for validation and for assessing approximations in previous modeling approaches. In vivo experiments in the normal human brain yielded results that were consistent with published data. Copyright © 2013 Elsevier Inc. All rights reserved.

Signal Processing for Radar Target Tracking and Identification

DTIC Science & Technology

1996-12-01

Computes the likelihood for various potential jump moves. 12. matrix_mult.m: Parallel implementation of linear algebra ... Elementary Lineary Algebra with Applications, John Wiley k Sons, Inc., New York, 1987. [9] A. K. Bhattacharyya, and D. L. Sengupta, Radar Cross...Miller, ’Target Tracking and Recognition Using Jump-Diffusion Processes," ARO’s 11th Army Conf. on Applied Mathemat- ics and Computing, June 8-11

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

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

Bambah, Bindu A., E-mail: bbsp@uohyd.ernet.in; Mukku, C., E-mail: mukku@iiit.ac.in; Shreecharan, T., E-mail: shreecharan@gmail.com

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, wemore » 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.« less

Algebraic reasoning for the enhancement of data-driven building reconstructions

NASA Astrophysics Data System (ADS)

Meidow, Jochen; Hammer, Horst

2016-04-01

Data-driven approaches for the reconstruction of buildings feature the flexibility needed to capture objects of arbitrary shape. To recognize man-made structures, geometric relations such as orthogonality or parallelism have to be detected. These constraints are typically formulated as sets of multivariate polynomials. For the enforcement of the constraints within an adjustment process, a set of independent and consistent geometric constraints has to be determined. Gröbner bases are an ideal tool to identify such sets exactly. A complete workflow for geometric reasoning is presented to obtain boundary representations of solids based on given point clouds. The constraints are formulated in homogeneous coordinates, which results in simple polynomials suitable for the successful derivation of Gröbner bases for algebraic reasoning. Strategies for the reduction of the algebraical complexity are presented. To enforce the constraints, an adjustment model is introduced, which is able to cope with homogeneous coordinates along with their singular covariance matrices. The feasibility and the potential of the approach are demonstrated by the analysis of a real data set.

ADAM: analysis of discrete models of biological systems using computer algebra.

PubMed

Hinkelmann, Franziska; Brandon, Madison; Guang, Bonny; McNeill, Rustin; Blekherman, Grigoriy; Veliz-Cuba, Alan; Laubenbacher, Reinhard

2011-07-20

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

SATA II - Stochastic Algebraic Topology and Applications

DTIC Science & Technology

2017-01-30

AFRL-AFOSR-UK-TR-2017-0018 SATA II - Stochastic Algebraic Topology and Applications 150032 Robert Adler TECHNION ISRAEL INSTITUTE OF TECHNOLOGY Final...REPORT TYPE Final 3. DATES COVERED (From - To) 15 Dec 2014 to 14 Dec 2016 4. TITLE AND SUBTITLE SATA II - Stochastic Algebraic Topology and Applications ...has recently been submitted to AFOSR. 15. SUBJECT TERMS Network Theory, Sensor Technology, Mathematical Modeling, EOARD 16. SECURITY CLASSIFICATION OF

Stability Analysis of Finite Difference Schemes for Hyperbolic Systems, and Problems in Applied and Computational Linear Algebra.

DTIC Science & Technology

FINITE DIFFERENCE THEORY, * LINEAR ALGEBRA , APPLIED MATHEMATICS, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, COMPUTATIONS, HYPERBOLAS, MATHEMATICAL MODELS, NUMERICAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, STABILITY.

A Nonlinear, Multiinput, Multioutput Process Control Laboratory Experiment

ERIC Educational Resources Information Center

Young, Brent R.; van der Lee, James H.; Svrcek, William Y.

2006-01-01

Experience in using a user-friendly software, Mathcad, in the undergraduate chemical reaction engineering course is discussed. Example problems considered for illustration deal with simultaneous solution of linear algebraic equations (kinetic parameter estimation), nonlinear algebraic equations (equilibrium calculations for multiple reactions and…

RANS modeling of scalar dispersion from localized sources within a simplified urban-area model

NASA Astrophysics Data System (ADS)

Rossi, Riccardo; Capra, Stefano; Iaccarino, Gianluca

2011-11-01

The dispersion of a passive scalar downstream a localized source within a simplified urban-like geometry is examined by means of RANS scalar flux models. The computations are conducted under conditions of neutral stability and for three different incoming wind directions (0°, 45°, 90°) at a roughness Reynolds number of Ret = 391. A Reynolds stress transport model is used to close the flow governing equations whereas both the standard eddy-diffusivity closure and algebraic flux models are employed to close the transport equation for the passive scalar. The comparison with a DNS database shows improved reliability from algebraic scalar flux models towards predicting both the mean concentration and the plume structure. Since algebraic flux models do not increase substantially the computational effort, the results indicate that the use of tensorial-diffusivity can be promising tool for dispersion simulations for the urban environment.

Algebraic method for parameter identification of circuit models for batteries under non-zero initial condition

NASA Astrophysics Data System (ADS)

Devarakonda, Lalitha; Hu, Tingshu

2014-12-01

This paper presents an algebraic method for parameter identification of Thevenin's equivalent circuit models for batteries under non-zero initial condition. In traditional methods, it was assumed that all capacitor voltages have zero initial conditions at the beginning of each charging/discharging test. This would require a long rest time between two tests, leading to very lengthy tests for a charging/discharging cycle. In this paper, we propose an algebraic method which can extract the circuit parameters together with initial conditions. This would theoretically reduce the rest time to 0 and substantially accelerate the testing cycles.

Classical Yang-Baxter equations and quantum integrable systems

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

1989-06-01

Quantum integrable models associated with nondegenerate solutions of classical Yang-Baxter equations related to the simple Lie algebras are investigated. These models are diagonalized for rational and trigonometric solutions in the cases of sl(N)/gl(N)/, o(N) and sp(N) algebras. The analogy with the quantum inverse scattering method is demonstrated.

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

Effective Lagrangians and Current Algebra in Three Dimensions

NASA Astrophysics Data System (ADS)

Ferretti, Gabriele

In this thesis we study three dimensional field theories that arise as effective Lagrangians of quantum chromodynamics in Minkowski space with signature (2,1) (QCD3). In the first chapter, we explain the method of effective Langrangians and the relevance of current algebra techniques to field theory. We also provide the physical motivations for the study of QCD3 as a toy model for confinement and as a theory of quantum antiferromagnets (QAF). In chapter two, we derive the relevant effective Lagrangian by studying the low energy behavior of QCD3, paying particular attention to how the global symmetries are realized at the quantum level. In chapter three, we show how baryons arise as topological solitons of the effective Lagrangian and also show that their statistics depends on the number of colors as predicted by the quark model. We calculate mass splitting and magnetic moments of the soliton and find logarithmic corrections to the naive quark model predictions. In chapter four, we drive the current algebra of the theory. We find that the current algebra is a co -homologically non-trivial generalization of Kac-Moody algebras to three dimensions. This fact may provide a new, non -perturbative way to quantize the theory. In chapter five, we discuss the renormalizability of the model in the large-N expansion. We prove the validity of the non-renormalization theorem and compute the critical exponents in a specific limiting case, the CP^ {N-1} model with a Chern-Simons term. Finally, chapter six contains some brief concluding remarks.

Matrix product representation of the stationary state of the open zero range process

NASA Astrophysics Data System (ADS)

Bertin, Eric; Vanicat, Matthieu

2018-06-01

Many one-dimensional lattice particle models with open boundaries, like the paradigmatic asymmetric simple exclusion process (ASEP), have their stationary states represented in the form of a matrix product, with matrices that do not explicitly depend on the lattice site. In contrast, the stationary state of the open 1D zero-range process (ZRP) takes an inhomogeneous factorized form, with site-dependent probability weights. We show that in spite of the absence of correlations, the stationary state of the open ZRP can also be represented in a matrix product form, where the matrices are site-independent, non-commuting and determined from algebraic relations resulting from the master equation. We recover the known distribution of the open ZRP in two different ways: first, using an explicit representation of the matrices and boundary vectors; second, from the sole knowledge of the algebraic relations satisfied by these matrices and vectors. Finally, an interpretation of the relation between the matrix product form and the inhomogeneous factorized form is proposed within the framework of hidden Markov chains.

Journal Writing: Enlivening Elementary Linear Algebra.

ERIC Educational Resources Information Center

Meel, David E.

1999-01-01

Examines the various issues surrounding the implementation of journal writing in an undergraduate linear algebra course. Identifies the benefits of incorporating journal writing into an undergraduate mathematics course, which are supported with students' comments from their journals and their reflections on the process. Contains 14 references.…

Applications of rigged Hilbert spaces in quantum mechanics and signal processing

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

Celeghini, E., E-mail: celeghini@fi.infn.it; Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, Paseo Belén 7, 47011 Valladolid; Gadella, M., E-mail: manuelgadella1@gmail.com

Simultaneous use of discrete and continuous bases in quantum systems is not possible in the context of Hilbert spaces, but only in the more general structure of rigged Hilbert spaces (RHS). In addition, the relevant operators in RHS (but not in Hilbert space) are a realization of elements of a Lie enveloping algebra and support representations of semigroups. We explicitly construct here basis dependent RHS of the line and half-line and relate them to the universal enveloping algebras of the Weyl-Heisenberg algebra and su(1, 1), respectively. The complete sub-structure of both RHS and of the operators acting on them ismore » obtained from their algebraic structures or from the related fractional Fourier transforms. This allows us to describe both quantum and signal processing states and their dynamics. Two relevant improvements are introduced: (i) new kinds of filters related to restrictions to subspaces and/or the elimination of high frequency fluctuations and (ii) an operatorial structure that, starting from fix objects, describes their time evolution.« less

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.

Scaling in tournaments

NASA Astrophysics Data System (ADS)

Ben-Naim, E.; Redner, S.; Vazquez, F.

2007-02-01

We study a stochastic process that mimics single-game elimination tournaments. In our model, the outcome of each match is stochastic: the weaker player wins with upset probability q<=1/2, and the stronger player wins with probability 1-q. The loser is eliminated. Extremal statistics of the initial distribution of player strengths governs the tournament outcome. For a uniform initial distribution of strengths, the rank of the winner, x*, decays algebraically with the number of players, N, as x*~N-β. Different decay exponents are found analytically for sequential dynamics, βseq=1-2q, and parallel dynamics, \\beta_par=1+\\frac{\\ln (1-q)}{\\ln 2} . The distribution of player strengths becomes self-similar in the long time limit with an algebraic tail. Our theory successfully describes statistics of the US college basketball national championship tournament.

Symbolic-Numerical Modeling of the Influence of Damping Moments on Satellite Dynamics

NASA Astrophysics Data System (ADS)

Gutnik, Sergey A.; Sarychev, Vasily A.

2018-02-01

The dynamics of a satellite on a circular orbit under the influence of gravitational and active damping torques, which are proportional to the projections of the angular velocity of the satellite, is investigated. Computer algebra Gröbner basis methods for the determination of all equilibrium orientations of the satellite in the orbital coordinate system with given damping torque and given principal central moments of inertia were used. The conditions of the equilibria existence depending on three damping parameters were obtained from the analysis of the real roots of the algebraic equations spanned by the constructed Gröbner basis. Conditions of asymptotic stability of the satellite equilibria and the transition decay processes of the spatial oscillations of the satellite at different damping parameters have also been obtained.

Two dissimilar approaches to dynamical systems on hyper MV -algebras and their information entropy

NASA Astrophysics Data System (ADS)

Mehrpooya, Adel; Ebrahimi, Mohammad; Davvaz, Bijan

2017-09-01

Measuring the flow of information that is related to the evolution of a system which is modeled by applying a mathematical structure is of capital significance for science and usually for mathematics itself. Regarding this fact, a major issue in concern with hyperstructures is their dynamics and the complexity of the varied possible dynamics that exist over them. Notably, the dynamics and uncertainty of hyper MV -algebras which are hyperstructures and extensions of a central tool in infinite-valued Lukasiewicz propositional calculus that models many valued logics are of primary concern. Tackling this problem, in this paper we focus on the subject of dynamical systems on hyper MV -algebras and their entropy. In this respect, we adopt two varied approaches. One is the set-based approach in which hyper MV -algebra dynamical systems are developed by employing set functions and set partitions. By the other method that is based on points and point partitions, we establish the concept of hyper injective dynamical systems on hyper MV -algebras. Next, we study the notion of entropy for both kinds of systems. Furthermore, we consider essential ergodic characteristics of those systems and their entropy. In particular, we introduce the concept of isomorphic hyper injective and hyper MV -algebra dynamical systems, and we demonstrate that isomorphic systems have the same entropy. We present a couple of theorems in order to help calculate entropy. In particular, we prove a contemporary version of addition and Kolmogorov-Sinai Theorems. Furthermore, we provide a comparison between the indispensable properties of hyper injective and semi-independent dynamical systems. Specifically, we present and prove theorems that draw comparisons between the entropies of such systems. Lastly, we discuss some possible relationships between the theories of hyper MV -algebra and MV -algebra dynamical systems.

Developing learning environments which support early algebraic reasoning: a case from a New Zealand primary classroom

NASA Astrophysics Data System (ADS)

Hunter, Jodie

2014-12-01

Current reforms in mathematics education advocate the development of mathematical learning communities in which students have opportunities to engage in mathematical discourse and classroom practices which underlie algebraic reasoning. This article specifically addresses the pedagogical actions teachers take which structure student engagement in dialogical discourse and activity which facilitates early algebraic reasoning. Using videotaped recordings of classroom observations, the teacher and researcher collaboratively examined the classroom practices and modified the participatory practices to develop a learning environment which supported early algebraic reasoning. Facilitating change in the classroom environment was a lengthy process which required consistent and ongoing attention initially to the social norms and then to the socio-mathematical norms. Specific pedagogical actions such as the use of specifically designed tasks, materials and representations and a constant press for justification and generalisation were required to support students to link their numerical understandings to algebraic reasoning.

Computing algebraic transfer entropy and coupling directions via transcripts

NASA Astrophysics Data System (ADS)

Amigó, José M.; Monetti, Roberto; Graff, Beata; Graff, Grzegorz

2016-11-01

Most random processes studied in nonlinear time series analysis take values on sets endowed with a group structure, e.g., the real and rational numbers, and the integers. This fact allows to associate with each pair of group elements a third element, called their transcript, which is defined as the product of the second element in the pair times the first one. The transfer entropy of two such processes is called algebraic transfer entropy. It measures the information transferred between two coupled processes whose values belong to a group. In this paper, we show that, subject to one constraint, the algebraic transfer entropy matches the (in general, conditional) mutual information of certain transcripts with one variable less. This property has interesting practical applications, especially to the analysis of short time series. We also derive weak conditions for the 3-dimensional algebraic transfer entropy to yield the same coupling direction as the corresponding mutual information of transcripts. A related issue concerns the use of mutual information of transcripts to determine coupling directions in cases where the conditions just mentioned are not fulfilled. We checked the latter possibility in the lowest dimensional case with numerical simulations and cardiovascular data, and obtained positive results.

Asymptotic identity in min-plus algebra: a report on CPNS.

PubMed

Li, Ming; Zhao, Wei

2012-01-01

Network calculus is a theory initiated primarily in computer communication networks, especially in the aspect of real-time communications, where min-plus algebra plays a role. Cyber-physical networking systems (CPNSs) are recently developing fast and models in data flows as well as systems in CPNS are, accordingly, greatly desired. Though min-plus algebra may be a promising tool to linearize any node in CPNS as can be seen from its applications to the Internet computing, there are tough problems remaining unsolved in this regard. The identity in min-plus algebra is one problem we shall address. We shall point out the confusions about the conventional identity in the min-plus algebra and present an analytical expression of the asymptotic identity that may not cause confusions.

Asymptotic Identity in Min-Plus Algebra: A Report on CPNS

PubMed Central

Li, Ming; Zhao, Wei

2012-01-01

Network calculus is a theory initiated primarily in computer communication networks, especially in the aspect of real-time communications, where min-plus algebra plays a role. Cyber-physical networking systems (CPNSs) are recently developing fast and models in data flows as well as systems in CPNS are, accordingly, greatly desired. Though min-plus algebra may be a promising tool to linearize any node in CPNS as can be seen from its applications to the Internet computing, there are tough problems remaining unsolved in this regard. The identity in min-plus algebra is one problem we shall address. We shall point out the confusions about the conventional identity in the min-plus algebra and present an analytical expression of the asymptotic identity that may not cause confusions. PMID:21822446

Work Measurements: Interdisciplinary Overlap in Manufacturing and Algebra I

ERIC Educational Resources Information Center

Rose, Mary Annette

2007-01-01

Manufacturing engineering provides a relevant context from which to envision interdisciplinary learning experiences because engineers integrate their knowledge and skills of manufacturing and algebra processes in order to plan the efficient manufacture of products. In this article, the author describes an interdisciplinary learning activity that…

Applications of Maple To Algebraic Cryptography.

ERIC Educational Resources Information Center

Sigmon, Neil P.

1997-01-01

Demonstrates the use of technology to enhance the appreciation of applications involving abstract algebra. The symbolic manipulator Maple can perform computations required for a linear cryptosystem. One major benefit of this process is that students can encipher and decipher messages using a linear cryptosystem without becoming confused and…

Implementing Linear Algebra Related Algorithms on the TI-92+ Calculator.

ERIC Educational Resources Information Center

Alexopoulos, John; Abraham, Paul

2001-01-01

Demonstrates a less utilized feature of the TI-92+: its natural and powerful programming language. Shows how to implement several linear algebra related algorithms including the Gram-Schmidt process, Least Squares Approximations, Wronskians, Cholesky Decompositions, and Generalized Linear Least Square Approximations with QR Decompositions.…

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

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

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.

Solution of Algebraic Equations in the Analysis, Design, and Optimization of Continuous Ultrafiltration

ERIC Educational Resources Information Center

Foley, Greg

2011-01-01

Continuous feed and bleed ultrafiltration, modeled with the gel polarization model for the limiting flux, is shown to provide a rich source of non-linear algebraic equations that can be readily solved using numerical and graphical techniques familiar to undergraduate students. We present a variety of numerical problems in the design, analysis, and…

Geometric model of topological insulators from the Maxwell algebra

NASA Astrophysics Data System (ADS)

Palumbo, Giandomenico

2017-11-01

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

Sampled-Data Kalman Filtering and Multiple Model Adaptive Estimation for Infinite-Dimensional Continuous-Time Systems

DTIC Science & Technology

2007-03-01

mathematical frame- 1-6 work of linear algebra and functional analysis [122, 33], while Kalman-Bucy filtering [96, 32] is an especially important...Engineering, Air Force Institute of Technology (AU), Wright- Patterson AFB, Ohio, March 2002. 85. Hoffman, Kenneth and Ray Kunze. Linear Algebra (Second Edition...Engineering, Air Force Institute of Technology (AU), Wright- Patterson AFB, Ohio, December 1989. 189. Strang, Gilbert. Linear Algebra and Its Applications

Quantum walks, deformed relativity and Hopf algebra symmetries

PubMed Central

2016-01-01

We show how the Weyl quantum walk derived from principles in D'Ariano & Perinotti (D'Ariano & Perinotti 2014 Phys. Rev. A 90, 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 the κ-Poincaré algebras. PMID:27091171

Little strings, quasi-topological sigma model on loop group, and toroidal Lie algebras

NASA Astrophysics Data System (ADS)

Ashwinkumar, Meer; Cao, Jingnan; Luo, Yuan; Tan, Meng-Chwan; Zhao, Qin

2018-03-01

We study the ground states and left-excited states of the Ak-1 N = (2 , 0) little string theory. Via a theorem by Atiyah [1], these sectors can be captured by a supersymmetric nonlinear sigma model on CP1 with target space the based loop group of SU (k). The ground states, described by L2-cohomology classes, form modules over an affine Lie algebra, while the left-excited states, described by chiral differential operators, form modules over a toroidal Lie algebra. We also apply our results to analyze the 1/2 and 1/4 BPS sectors of the M5-brane worldvolume theory.

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

Xin, Qiaoling, E-mail: xinqiaoling0923@163.com; Jiang, Lining, E-mail: jianglining@bit.edu.cn

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.

Real-Time Algebraic Derivative Estimations Using a Novel Low-Cost Architecture Based on Reconfigurable Logic

PubMed Central

Morales, Rafael; Rincón, Fernando; Gazzano, Julio Dondo; López, Juan Carlos

2014-01-01

Time derivative estimation of signals plays a very important role in several fields, such as signal processing and control engineering, just to name a few of them. For that purpose, a non-asymptotic algebraic procedure for the approximate estimation of the system states is used in this work. The method is based on results from differential algebra and furnishes some general formulae for the time derivatives of a measurable signal in which two algebraic derivative estimators run simultaneously, but in an overlapping fashion. The algebraic derivative algorithm presented in this paper is computed online and in real-time, offering high robustness properties with regard to corrupting noises, versatility and ease of implementation. Besides, in this work, we introduce a novel architecture to accelerate this algebraic derivative estimator using reconfigurable logic. The core of the algorithm is implemented in an FPGA, improving the speed of the system and achieving real-time performance. Finally, this work proposes a low-cost platform for the integration of hardware in the loop in MATLAB. PMID:24859033

Processes and Reasoning in Representations of Linear Functions

ERIC Educational Resources Information Center

Adu-Gyamfi, Kwaku; Bossé, Michael J.

2014-01-01

This study examined student actions, interpretations, and language in respect to questions raised regarding tabular, graphical, and algebraic representations in the context of functions. The purpose was to investigate students' interpretations and specific ways of working within table, graph, and the algebraic on notions fundamental to a…

Algebra for All: California's Eighth-Grade Algebra Initiative as Constrained Curricula

ERIC Educational Resources Information Center

Domina, Thurston; Penner, Andrew M.; Penner, Emily K.; Conley, AnneMarie

2014-01-01

Background/Context: Across the United States, secondary school curricula are intensifying as a growing proportion of students enroll in high-level academic math courses. In many districts, this intensification process occurs as early as eighth grade, where schools are effectively constraining their mathematics curricula by restricting course…

Reading Bombelli's x-purgated Algebra.

ERIC Educational Resources Information Center

Arcavi, Abraham; Bruckheimer, Maxim

1991-01-01

Presents the algorithm to approximate square roots as reproduced from the 1579 edition of an algebra book by Rafael Bombelli. The sequence of activities illustrates that the process of understanding an original source of mathematics, first at the algorithmic level and then with respect to its mathematical validity in modern terms, can be an…

Teaching Linear Algebra: Proceeding More Efficiently by Staying Comfortably within Z

ERIC Educational Resources Information Center

Beaver, Scott

2015-01-01

For efficiency in a linear algebra course the instructor may wish to avoid the undue arithmetical distractions of rational arithmetic. In this paper we explore how to write fraction-free problems of various types including elimination, matrix inverses, orthogonality, and the (non-normalizing) Gram-Schmidt process.

Using Computer Symbolic Algebra to Solve Differential Equations.

ERIC Educational Resources Information Center

Mathews, John H.

1989-01-01

This article illustrates that mathematical theory can be incorporated into the process to solve differential equations by a computer algebra system, muMATH. After an introduction to functions of muMATH, several short programs for enhancing the capabilities of the system are discussed. Listed are six references. (YP)

A lattice approach to the conformal OSp(2S+2|2S) supercoset sigma model. Part I: Algebraic structures in the spin chain. The Brauer algebra

NASA Astrophysics Data System (ADS)

Candu, Constantin; Saleur, Hubert

2009-02-01

We define and study a lattice model which we argue is in the universality class of the OSp(2S+2|2S) supercoset sigma model for a large range of values of the coupling constant gσ2. In this first paper, we analyze in details the symmetries of this lattice model, in particular the decomposition of the space of the quantum spin chain V as a bimodule over OSp(2S+2|2S) and its commutant, the Brauer algebra B(2). It turns out that V is a nonsemisimple module for both OSp(2S+2|2S) and B(2). The results are used in the companion paper to elucidate the structure of the (boundary) conformal field theory.

Exceptional quantum geometry and particle physics

NASA Astrophysics Data System (ADS)

Dubois-Violette, Michel

2016-11-01

Based on an interpretation of the quark-lepton symmetry in terms of the unimodularity of the color group SU (3) and on the existence of 3 generations, we develop an argumentation suggesting that the "finite quantum space" corresponding to the exceptional real Jordan algebra of dimension 27 (the Euclidean Albert algebra) is relevant for the description of internal spaces in the theory of particles. In particular, the triality which corresponds to the 3 off-diagonal octonionic elements of the exceptional algebra is associated to the 3 generations of the Standard Model while the representation of the octonions as a complex 4-dimensional space C ⊕C3 is associated to the quark-lepton symmetry (one complex for the lepton and 3 for the corresponding quark). More generally it is suggested that the replacement of the algebra of real functions on spacetime by the algebra of functions on spacetime with values in a finite-dimensional Euclidean Jordan algebra which plays the role of "the algebra of real functions" on the corresponding almost classical quantum spacetime is relevant in particle physics. This leads us to study the theory of Jordan modules and to develop the differential calculus over Jordan algebras (i.e. to introduce the appropriate notion of differential forms). We formulate the corresponding definition of connections on Jordan modules.

Developing Algebra Structure Module and Model of Cooperative Learning Helping Concept Map Media for Improving Proofing Ability

ERIC Educational Resources Information Center

Syafari

2017-01-01

This research was purposed to develop module and learning model and instrument of proofing ability in algebra structure through cooperative learning with helping map concept media for students of mathematic major and mathematics education in State University and Private University in North Sumatra province. The subject of this research was the…

A site model for Pyrenean oak (Quercus pyrenaica) stands using a dynamic algebraic difference equation

Treesearch

Joao P. Carvalho; Bernard R. Parresol

2005-01-01

This paper presents a growth model for dominant-height and site-quality estimations for Pyrenean oak (Quercus pyrenaica Willd.) stands. The Bertalanffy–Richards function is used with the generalized algebraic difference approach to derive a dynamic site equation. This allows dominant-height and site-index estimations in a compatible way, using any...

Algebraic models of local period maps and Yukawa algebras

NASA Astrophysics Data System (ADS)

Bandiera, Ruggero; Manetti, Marco

2018-02-01

We describe some L_{∞} model for the local period map of a compact Kähler manifold. Applications include the study of deformations with associated variation of Hodge structure constrained by certain closed strata of the Grassmannian of the de Rham cohomology. As a by-product, we obtain an interpretation in the framework of deformation theory of the Yukawa coupling.

Microscopic approach based on a multiscale algebraic version of the resonating group model for radiative capture reactions

NASA Astrophysics Data System (ADS)

Solovyev, Alexander S.; Igashov, Sergey Yu.

2017-12-01

A microscopic approach to description of radiative capture reactions based on a multiscale algebraic version of the resonating group model is developed. The main idea of the approach is to expand wave functions of discrete spectrum and continuum for a nuclear system over different bases of the algebraic version of the resonating group model. These bases differ from each other by values of oscillator radius playing a role of scale parameter. This allows us in a unified way to calculate total and partial cross sections (astrophysical S factors) as well as branching ratio for the radiative capture reaction, to describe phase shifts for the colliding nuclei in the initial channel of the reaction, and at the same time to reproduce breakup thresholds of the final nucleus. The approach is applied to the theoretical study of the mirror 3H(α ,γ )7Li and 3He(α ,γ )7Be reactions, which are of great interest to nuclear astrophysics. The calculated results are compared with existing experimental data and with our previous calculations in the framework of the single-scale algebraic version of the resonating group model.

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

PubMed Central

2011-01-01

Background Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. Results We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Conclusions Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web-based tool for several different input formats, and it makes analysis of complex models accessible to a larger community, as it is platform independent as a web-service and does not require understanding of the underlying mathematics. PMID:21774817

Invariants of the Jacobi-Porstendorfer room model for radon progeny in indoor air.

PubMed

Thomas, Josef; Jilek, Karel

2012-06-01

The Jacobi-Porstendörfer room model, describing the dynamical behaviour of radon and radon progeny in indoor air, has been successfully used for decades. The inversion of the model-the determination of the five parameters from measured results which provide better information on the room environment than mere ratios of unattached and attached radon progeny-is treated as an algebraic task. The linear interdependence of the used equations strongly limits the algebraic invertibility of experimental results. For a unique solution, the fulfilment of two invariants of the room model for the measured results is required. Non-fulfilment of these model invariants by the measured results leads to a set of non-identical solutions and indicates the violation of the conditions required by the room model or the incorrectness or excessive uncertainties of the measured results. The limited and non-unique algebraic invertibility of the room model is analysed numerically using our own data for the radon progeny.

Energy spectra of vibron and cluster models in molecular and nuclear systems

NASA Astrophysics Data System (ADS)

Jalili Majarshin, A.; Sabri, H.; Jafarizadeh, M. A.

2018-03-01

The relation of the algebraic cluster model, i.e., of the vibron model and its extension, to the collective structure, is discussed. In the first section of the paper, we study the energy spectra of vibron model, for diatomic molecule then we derive the rotation-vibration spectrum of 2α, 3α and 4α configuration in the low-lying spectrum of 8Be, 12C and 16O nuclei. All vibrational and rotational states with ground and excited A, E and F states appear to have been observed, moreover the transitional descriptions of the vibron model and α-cluster model were considered by using an infinite-dimensional algebraic method based on the affine \\widehat{SU(1,1)} Lie algebra. The calculated energy spectra are compared with experimental data. Applications to the rotation-vibration spectrum for the diatomic molecule and many-body nuclear clusters indicate that there are solvable models and they can be approximated very well using the transitional theory.

Quantization, Frobenius and Bi algebras from the Categorical Framework of Quantum Mechanics to Natural Language Semantics

NASA Astrophysics Data System (ADS)

Sadrzadeh, Mehrnoosh

2017-07-01

Compact Closed categories and Frobenius and Bi algebras have been applied to model and reason about Quantum protocols. The same constructions have also been applied to reason about natural language semantics under the name: ``categorical distributional compositional'' semantics, or in short, the ``DisCoCat'' model. This model combines the statistical vector models of word meaning with the compositional models of grammatical structure. It has been applied to natural language tasks such as disambiguation, paraphrasing and entailment of phrases and sentences. The passage from the grammatical structure to vectors is provided by a functor, similar to the Quantization functor of Quantum Field Theory. The original DisCoCat model only used compact closed categories. Later, Frobenius algebras were added to it to model long distance dependancies such as relative pronouns. Recently, bialgebras have been added to the pack to reason about quantifiers. This paper reviews these constructions and their application to natural language semantics. We go over the theory and present some of the core experimental results.

Adler-Kostant-Symes scheme for face and Calogero-Moser-Sutherland-type models

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter

1998-07-01

We give the construction of quantum Lax equations for IRF models and the difference version of the Calogero-Moser-Sutherland model introduced by Ruijsenaars. We solve the equations using factorization properties of the underlying face Hopf algebras/elliptic quantum groups. This construction is in the spirit of the Adler-Kostant-Symes method and generalizes our previous work to the case of face Hopf algebras/elliptic quantum groups with dynamical R matrices.

Sample Size and Statistical Conclusions from Tests of Fit to the Rasch Model According to the Rasch Unidimensional Measurement Model (Rumm) Program in Health Outcome Measurement.

PubMed

Hagell, Peter; Westergren, Albert

Sample size is a major factor in statistical null hypothesis testing, which is the basis for many approaches to testing Rasch model fit. Few sample size recommendations for testing fit to the Rasch model concern the Rasch Unidimensional Measurement Models (RUMM) software, which features chi-square and ANOVA/F-ratio based fit statistics, including Bonferroni and algebraic sample size adjustments. This paper explores the occurrence of Type I errors with RUMM fit statistics, and the effects of algebraic sample size adjustments. Data with simulated Rasch model fitting 25-item dichotomous scales and sample sizes ranging from N = 50 to N = 2500 were analysed with and without algebraically adjusted sample sizes. Results suggest the occurrence of Type I errors with N less then or equal to 500, and that Bonferroni correction as well as downward algebraic sample size adjustment are useful to avoid such errors, whereas upward adjustment of smaller samples falsely signal misfit. Our observations suggest that sample sizes around N = 250 to N = 500 may provide a good balance for the statistical interpretation of the RUMM fit statistics studied here with respect to Type I errors and under the assumption of Rasch model fit within the examined frame of reference (i.e., about 25 item parameters well targeted to the sample).

Image understanding and the man-machine interface II; Proceedings of the Meeting, Los Angeles, CA, Jan. 17, 18, 1989

NASA Technical Reports Server (NTRS)

Barrett, Eamon B. (Editor); Pearson, James J. (Editor)

1989-01-01

Image understanding concepts and models, image understanding systems and applications, advanced digital processors and software tools, and advanced man-machine interfaces are among the topics discussed. Particular papers are presented on such topics as neural networks for computer vision, object-based segmentation and color recognition in multispectral images, the application of image algebra to image measurement and feature extraction, and the integration of modeling and graphics to create an infrared signal processing test bed.

Algebraic properties of automata associated to Petri nets and applications to computation in biological systems.

PubMed

Egri-Nagy, Attila; Nehaniv, Chrystopher L

2008-01-01

Biochemical and genetic regulatory networks are often modeled by Petri nets. We study the algebraic structure of the computations carried out by Petri nets from the viewpoint of algebraic automata theory. Petri nets comprise a formalized graphical modeling language, often used to describe computation occurring within biochemical and genetic regulatory networks, but the semantics may be interpreted in different ways in the realm of automata. Therefore, there are several different ways to turn a Petri net into a state-transition automaton. Here, we systematically investigate different conversion methods and describe cases where they may yield radically different algebraic structures. We focus on the existence of group components of the corresponding transformation semigroups, as these reflect symmetries of the computation occurring within the biological system under study. Results are illustrated by applications to the Petri net modelling of intermediary metabolism. Petri nets with inhibition are shown to be computationally rich, regardless of the particular interpretation method. Along these lines we provide a mathematical argument suggesting a reason for the apparent all-pervasiveness of inhibitory connections in living systems.

Contextualizing symbol, symbolizing context

NASA Astrophysics Data System (ADS)

Maudy, Septiani Yugni; Suryadi, Didi; Mulyana, Endang

2017-08-01

When students learn algebra for the first time, inevitably they are experiencing transition from arithmetic to algebraic thinking. Once students could apprehend this essential mathematical knowledge, they are cultivating their ability in solving daily life problems by applying algebra. However, as we dig into this transitional stage, we identified possible students' learning obstacles to be dealt with seriously in order to forestall subsequent hindrance in studying more advance algebra. We come to realize this recurring problem as we undertook the processes of re-personalization and re-contextualization in which we scrutinize the very basic questions: 1) what is variable, linear equation with one variable and their relationship with the arithmetic-algebraic thinking? 2) Why student should learn such concepts? 3) How to teach those concepts to students? By positioning ourselves as a seventh grade student, we address the possibility of children to think arithmetically when confronted with the problems of linear equation with one variable. To help them thinking algebraically, Bruner's modes of representation developed contextually from concrete to abstract were delivered to enhance their interpretation toward the idea of variables. Hence, from the outset we designed the context for student to think symbolically initiated by exploring various symbols that could be contextualized in order to bridge student traversing the arithmetic-algebraic fruitfully.

A systematic investigation of the link between rational number processing and algebra ability.

PubMed

Hurst, Michelle; Cordes, Sara

2018-02-01

Recent research suggests that fraction understanding is predictive of algebra ability; however, the relative contributions of various aspects of rational number knowledge are unclear. Furthermore, whether this relationship is notation-dependent or rather relies upon a general understanding of rational numbers (independent of notation) is an open question. In this study, college students completed a rational number magnitude task, procedural arithmetic tasks in fraction and decimal notation, and an algebra assessment. Using these tasks, we measured three different aspects of rational number ability in both fraction and decimal notation: (1) acuity of underlying magnitude representations, (2) fluency with which symbols are mapped to the underlying magnitudes, and (3) fluency with arithmetic procedures. Analyses reveal that when looking at the measures of magnitude understanding, the relationship between adults' rational number magnitude performance and algebra ability is dependent upon notation. However, once performance on arithmetic measures is included in the relationship, individual measures of magnitude understanding are no longer unique predictors of algebra performance. Furthermore, when including all measures simultaneously, results revealed that arithmetic fluency in both fraction and decimal notation each uniquely predicted algebra ability. Findings are the first to demonstrate a relationship between rational number understanding and algebra ability in adults while providing a clearer picture of the nature of this relationship. © 2017 The British Psychological Society.

Generation of Custom DSP Transform IP Cores: Case Study Walsh-Hadamard Transform

DTIC Science & Technology

2002-09-01

mathematics and hardware design What I know: Finite state machine Pipelining Systolic array … What I know: Linear algebra Digital signal processing...state machine Pipelining Systolic array … What I know: Linear algebra Digital signal processing Adaptive filter theory … A math guy A hardware engineer...Synthesis Technology Libary Bit-width (8) HF factor (1,2,3,6) VF factor (1,2,4, ... 32) Xilinx FPGA Place&Route Xilinx FPGA Place&Route Performance

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"…

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

Mapping chemicals in air using an environmental CAT scanning system: evaluation of algorithms

NASA Astrophysics Data System (ADS)

Samanta, A.; Todd, L. A.

A new technique is being developed which creates near real-time maps of chemical concentrations in air for environmental and occupational environmental applications. This technique, we call Environmental CAT Scanning, combines the real-time measuring technique of open-path Fourier transform infrared spectroscopy with the mapping capabilitites of computed tomography to produce two-dimensional concentration maps. With this system, a network of open-path measurements is obtained over an area; measurements are then processed using a tomographic algorithm to reconstruct the concentrations. This research focussed on the process of evaluating and selecting appropriate reconstruction algorithms, for use in the field, by using test concentration data from both computer simultation and laboratory chamber studies. Four algorithms were tested using three types of data: (1) experimental open-path data from studies that used a prototype opne-path Fourier transform/computed tomography system in an exposure chamber; (2) synthetic open-path data generated from maps created by kriging point samples taken in the chamber studies (in 1), and; (3) synthetic open-path data generated using a chemical dispersion model to create time seires maps. The iterative algorithms used to reconstruct the concentration data were: Algebraic Reconstruction Technique without Weights (ART1), Algebraic Reconstruction Technique with Weights (ARTW), Maximum Likelihood with Expectation Maximization (MLEM) and Multiplicative Algebraic Reconstruction Technique (MART). Maps were evaluated quantitatively and qualitatively. In general, MART and MLEM performed best, followed by ARTW and ART1. However, algorithm performance varied under different contaminant scenarios. This study showed the importance of using a variety of maps, particulary those generated using dispersion models. The time series maps provided a more rigorous test of the algorithms and allowed distinctions to be made among the algorithms. A comprehensive evaluation of algorithms, for the environmental application of tomography, requires the use of a battery of test concentration data before field implementation, which models reality and tests the limits of the algorithms.

A Algebraic Approach to the Quantization of Constrained Systems: Finite Dimensional Examples.

NASA Astrophysics Data System (ADS)

Tate, Ranjeet Shekhar

1992-01-01

General relativity has two features in particular, which make it difficult to apply to it existing schemes for the quantization of constrained systems. First, there is no background structure in the theory, which could be used, e.g., to regularize constraint operators, to identify a "time" or to define an inner product on physical states. Second, in the Ashtekar formulation of general relativity, which is a promising avenue to quantum gravity, the natural variables for quantization are not canonical; and, classically, there are algebraic identities between them. Existing schemes are usually not concerned with such identities. Thus, from the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a general prescription to find the physical inner product, and is flexible enough to accommodate non -canonical variables. In this dissertation I present an algebraic formulation of the Dirac approach to the quantization of constrained systems. The Dirac quantization program is augmented by a general principle to find the inner product on physical states. Essentially, the Hermiticity conditions on physical operators determine this inner product. I also clarify the role in quantum theory of possible algebraic identities between the elementary variables. I use this approach to quantize various finite dimensional systems. Some of these models test the new aspects of the algebraic framework. Others bear qualitative similarities to general relativity, and may give some insight into the pitfalls lurking in quantum gravity. The previous quantizations of one such model had many surprising features. When this model is quantized using the algebraic program, there is no longer any unexpected behaviour. I also construct the complete quantum theory for a previously unsolved relativistic cosmology. All these models indicate that the algebraic formulation provides powerful new tools for quantization. In (spatially compact) general relativity, the Hamiltonian is constrained to vanish. I present various approaches one can take to obtain an interpretation of the quantum theory of such "dynamically constrained" systems. I apply some of these ideas to the Bianchi I cosmology, and analyze the issue of the initial singularity in quantum theory.

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

NASA Astrophysics Data System (ADS)

Nassar, Ali

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

Geometric and Algebraic Approaches in the Concept of Complex Numbers

ERIC Educational Resources Information Center

Panaoura, A.; Elia, I.; Gagatsis, A.; Giatilis, G.-P.

2006-01-01

This study explores pupils' performance and processes in tasks involving equations and inequalities of complex numbers requiring conversions from a geometric representation to an algebraic representation and conversions in the reverse direction, and also in complex numbers problem solving. Data were collected from 95 pupils of the final grade from…

Analysis of Secondary School Students’ Algebraic Thinking and Math-Talk Learning Community to Help Students Learn

NASA Astrophysics Data System (ADS)

Nurhayati, D. M.; Herman, T.; Suhendra, S.

2017-09-01

This study aims to determine the difficulties of algebraic thinking ability of students in one of secondary school on quadrilateral subject and to describe Math-Talk Learning Community as the alternative way that can be done to overcome the difficulties of the students’ algebraic thinking ability. Research conducted by using quantitative approach with descriptive method. The population in this research was all students of that school and twenty three students as the sample that was chosen by purposive sampling technique. Data of algebraic thinking were collected through essay test. The results showed the percentage of achievement of students’ algebraic thinking’s indicators on three aspects: a) algebra as generalized arithmetic with the indicators (conceptually based computational strategies and estimation); b) algebra as the language of mathematics (meaning of variables, variable expressions and meaning of solution); c) algebra as a tool for functions and mathematical modelling (representing mathematical ideas using equations, tables, or words and generalizing patterns and rules in real-world contexts) is still low. It is predicted that because the secondary school students was not familiar with the abstract problem and they are still at a semi-concrete stage where the stage of cognitive development is between concrete and abstract. Based on the percentage achievement of each indicators, it can be concluded that the level of achievement of student’s mathematical communication using conventional learning is still low, so students’ algebraic thinking ability need to be improved.

Simplifications for hydronic system models in modelica

DOE PAGES

Jorissen, F.; Wetter, M.; Helsen, L.

2018-01-12

Building systems and their heating, ventilation and air conditioning flow networks, are becoming increasingly complex. Some building energy simulation tools simulate these flow networks using pressure drop equations. These flow network models typically generate coupled algebraic nonlinear systems of equations, which become increasingly more difficult to solve as their sizes increase. This leads to longer computation times and can cause the solver to fail. These problems also arise when using the equation-based modelling language Modelica and Annex 60-based libraries. This may limit the applicability of the library to relatively small problems unless problems are restructured. This paper discusses two algebraicmore » loop types and presents an approach that decouples algebraic loops into smaller parts, or removes them completely. The approach is applied to a case study model where an algebraic loop of 86 iteration variables is decoupled into smaller parts with a maximum of five iteration variables.« less

A Tale of Two Students

ERIC Educational Resources Information Center

Gordon, Sheldon P.

2008-01-01

The article describes the performance of several individual students in a college algebra/precalculus course that focuses on the development of conceptual understanding and the use of mathematical modeling and discusses the likely differences in outcome if the students took a traditional algebra-skills focused course.

Comparison of CFD Predictions with Shuttle Global Flight Thermal Imagery and Discrete Surface Measurements

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.; Tang, chun Y.; Palmer, Grant E.; Hyatt, Andrew J.; Wise, Adam J.; McCloud, Peter L.

2010-01-01

Surface temperature measurements from the STS-119 boundary-layer transition experiment on the space shuttle orbiter Discovery provide a rare opportunity to assess turbulent CFD models at hypersonic flight conditions. This flight data was acquired by on-board thermocouples and by infrared images taken off-board by the Hypersonic Thermodynamic Infrared Measurements (HYTHIRM) team, and is suitable for hypersonic CFD turbulence assessment between Mach 6 and 14. The primary assessment is for the Baldwin-Lomax and Cebeci-Smith algebraic turbulence models in the DPLR and LAURA CFD codes, respectively. A secondary assessment is made of the Shear-Stress Transport (SST) two-equation turbulence model in the DPLR code. Based upon surface temperature comparisons at eleven thermocouple locations, the algebraic-model turbulent CFD results average 4% lower than the measurements for Mach numbers less than 11. For Mach numbers greater than 11, the algebraic-model turbulent CFD results average 5% higher than the three available thermocouple measurements. Surface temperature predictions from the two SST cases were consistently 3 4% higher than the algebraic-model results. The thermocouple temperatures exhibit a change in trend with Mach number at about Mach 11; this trend is not reflected in the CFD results. Because the temperature trends from the turbulent CFD simulations and the flight data diverge above Mach 11, extrapolation of the turbulent CFD accuracy to higher Mach numbers is not recommended.

An Information Theory Approach to Nonlinear, Nonequilibrium Thermodynamics

NASA Astrophysics Data System (ADS)

Rogers, David M.; Beck, Thomas L.; Rempe, Susan B.

2011-10-01

Using the problem of ion channel thermodynamics as an example, we illustrate the idea of building up complex thermodynamic models by successively adding physical information. We present a new formulation of information algebra that generalizes methods of both information theory and statistical mechanics. From this foundation we derive a theory for ion channel kinetics, identifying a nonequilibrium `process' free energy functional in addition to the well-known integrated work functionals. The Gibbs-Maxwell relation for the free energy functional is a Green-Kubo relation, applicable arbitrarily far from equilibrium, that captures the effect of non-local and time-dependent behavior from transient thermal and mechanical driving forces. Comparing the physical significance of the Lagrange multipliers to the canonical ensemble suggests definitions of nonequilibrium ensembles at constant capacitance or inductance in addition to constant resistance. Our result is that statistical mechanical descriptions derived from a few primitive algebraic operations on information can be used to create experimentally-relevant and computable models. By construction, these models may use information from more detailed atomistic simulations. Two surprising consequences to be explored in further work are that (in)distinguishability factors are automatically predicted from the problem formulation and that a direct analogue of the second law for thermodynamic entropy production is found by considering information loss in stochastic processes. The information loss identifies a novel contribution from the instantaneous information entropy that ensures non-negative loss.

A Clifford algebra approach to chiral symmetry breaking and fermion mass hierarchies

NASA Astrophysics Data System (ADS)

Lu, Wei

2017-09-01

We propose a Clifford algebra approach to chiral symmetry breaking and fermion mass hierarchies in the context of composite Higgs bosons. Standard model fermions are represented by algebraic spinors of six-dimensional binary Clifford algebra, while ternary Clifford algebra-related flavor projection operators control allowable flavor-mixing interactions. There are three composite electroweak Higgs bosons resulted from top quark, tau neutrino, and tau lepton condensations. Each of the three condensations gives rise to masses of four different fermions. The fermion mass hierarchies within these three groups are determined by four-fermion condensations, which break two global chiral symmetries. The four-fermion condensations induce axion-like pseudo-Nambu-Goldstone bosons and can be dark matter candidates. In addition to the 125 GeV Higgs boson observed at the Large Hadron Collider, we anticipate detection of tau neutrino composite Higgs boson via the charm quark decay channel.

On the modelling of non-reactive and reactive turbulent combustor flows

NASA Technical Reports Server (NTRS)

Nikjooy, Mohammad; So, Ronald M. C.

1987-01-01

A study of non-reactive and reactive axisymmetric combustor flows with and without swirl is presented. Closure of the Reynolds equations is achieved by three models: kappa-epsilon, algebraic stress and Reynolds stress closure. Performance of two locally nonequilibrium and one equilibrium algebraic stress models is analyzed assuming four pressure strain models. A comparison is also made of the performance of a high and a low Reynolds number model for combustor flow calculations using Reynolds stress closures. Effects of diffusion and pressure-strain models on these closures are also investigated. Two models for the scalar transport are presented. One employs the second-moment closure which solves the transport equations for the scalar fluxes, while the other solves the algebraic equations for the scalar fluxes. In addition, two cases of non-premixed and one case of premixed combustion are considered. Fast- and finite-rate chemistry models are applied to non-premixed combustion. Both show promise for application in gas turbine combustors. However, finite rate chemistry models need to be examined to establish a suitable coupling of the heat release effects on turbulence field and rate constants.

Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities

NASA Astrophysics Data System (ADS)

Spill, Fabian

In the following paper, which is based on the author's PhD thesis submitted to Imperial College London, we explore the applicability of Yangian symmetry to various integrable models, in particular, in relation with S-matrices. One of the main themes in this work is that, after a careful study of the mathematics of the symmetry algebras one finds that in an integrable model, one can directly reconstruct S-matrices just from the algebra. It has been known for a long time that S-matrices in integrable models are fixed by symmetry. However, Lie algebra symmetry, the Yang-Baxter equation, crossing and unitarity, which constrain the S-matrix in integrable models, are often taken to be separate, independent properties of the S-matrix. Here, we construct scattering matrices purely from the Yangian, showing that the Yangian is the right algebraic object to unify all required symmetries of many integrable models. In particular, we reconstruct the S-matrix of the principal chiral field, and, up to a CDD factor, of other integrable field theories with 𝔰𝔲(n) symmetry. Furthermore, we study the AdS/CFT correspondence, which is also believed to be integrable in the planar limit. We reconstruct the S-matrices at weak and at strong coupling from the Yangian or its classical limit. We give a pedagogical introduction into the subject, presenting a unified perspective of Yangians and their applications in physics. This paper should hence be accessible to mathematicians who would like to explore the application of algebraic objects to physics as well as to physicists interested in a deeper understanding of the mathematical origin of physical quantities.

Heterogeneous Software System Interoperability Through Computer-Aided Resolution of Modeling Differences

DTIC Science & Technology

2002-06-01

techniques for addressing the software component retrieval problem. Steigerwald [Ste91] introduced the use of algebraic specifications for defining the...provided in terms of a specification written using Luqi’s Prototype Specification Description Language (PSDL) [LBY88] augmented with an algebraic

Characterizing Preservice Teachers' Mathematical Understanding of Algebraic Relationships

ERIC Educational Resources Information Center

Nillas, Leah A.

2010-01-01

Qualitative research methods were employed to investigate characterization of preservice teachers' mathematical understanding. Responses on test items involving algebraic relationships were analyzed using with-in case analysis (Miles and Huberman, 1994) and Pirie and Kieren's (1994) model of growth of mathematical understanding. Five elementary…

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

PubMed

Djurfeldt, Mikael

2012-07-01

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

Exact solution of some linear matrix equations using algebraic methods

NASA Technical Reports Server (NTRS)

Djaferis, T. E.; Mitter, S. K.

1979-01-01

Algebraic methods are used to construct the exact solution P of the linear matrix equation PA + BP = - C, where A, B, and C are matrices with real entries. The emphasis of this equation is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The paper is divided into six sections which include the proof of the basic lemma, the Liapunov equation, and the computer implementation for the rational, integer and modular algorithms. Two numerical examples are given and the entire calculation process is depicted.

Complementary Reliability-Based Decodings of Binary Linear Block Codes

NASA Technical Reports Server (NTRS)

Fossorier, Marc P. C.; Lin, Shu

1997-01-01

This correspondence presents a hybrid reliability-based decoding algorithm which combines the reprocessing method based on the most reliable basis and a generalized Chase-type algebraic decoder based on the least reliable positions. It is shown that reprocessing with a simple additional algebraic decoding effort achieves significant coding gain. For long codes, the order of reprocessing required to achieve asymptotic optimum error performance is reduced by approximately 1/3. This significantly reduces the computational complexity, especially for long codes. Also, a more efficient criterion for stopping the decoding process is derived based on the knowledge of the algebraic decoding solution.

Teachers' Understanding of Algebraic Generalization

NASA Astrophysics Data System (ADS)

Hawthorne, Casey Wayne

Generalization has been identified as a cornerstone of algebraic thinking (e.g., Lee, 1996; Sfard, 1995) and is at the center of a rich conceptualization of K-8 algebra (Kaput, 2008; Smith, 2003). Moreover, mathematics teachers are being encouraged to use figural-pattern generalizing tasks as a basis of student-centered instruction, whereby teachers respond to and build upon the ideas that arise from students' explorations of these activities. Although more and more teachers are engaging their students in such generalizing tasks, little is known about teachers' understanding of generalization and their understanding of students' mathematical thinking in this domain. In this work, I addressed this gap, exploring the understanding of algebraic generalization of 4 exemplary 8th-grade teachers from multiple perspectives. A significant feature of this investigation is an examination of teachers' understanding of the generalization process, including the use of algebraic symbols. The research consisted of two phases. Phase I was an examination of the teachers' understandings of the underlying quantities and quantitative relationships represented by algebraic notation. In Phase II, I observed the instruction of 2 of these teachers. Using the lens of professional noticing of students' mathematical thinking, I explored the teachers' enacted knowledge of algebraic generalization, characterizing how it supported them to effectively respond to the needs and queries of their students. Results indicated that teachers predominantly see these figural patterns as enrichment activities, disconnected from course content. Furthermore, in my analysis, I identified conceptual difficulties teachers experienced when solving generalization tasks, in particular, connecting multiple symbolic representations with the quantities in the figures. Moreover, while the teachers strived to overcome the challenges of connecting different representations, they invoked both productive and unproductive conceptualizations of the symbols. Finally, by comparing two teachers' understandings of student thinking in the classroom, I developed an instructional trajectory to describe steps along students' generalization processes. This emergent framework serves as an instructional tool for teachers' use in identifying significant connections in supporting students to develop understanding of algebraic symbols as representations that communicate the quantities perceived in the figure.

Algebraic model checking for Boolean gene regulatory networks.

PubMed

Tran, Quoc-Nam

2011-01-01

We present a computational method in which modular and Groebner bases (GB) computation in Boolean rings are used for solving problems in Boolean gene regulatory networks (BN). In contrast to other known algebraic approaches, the degree of intermediate polynomials during the calculation of Groebner bases using our method will never grow resulting in a significant improvement in running time and memory space consumption. We also show how calculation in temporal logic for model checking can be done by means of our direct and efficient Groebner basis computation in Boolean rings. We present our experimental results in finding attractors and control strategies of Boolean networks to illustrate our theoretical arguments. The results are promising. Our algebraic approach is more efficient than the state-of-the-art model checker NuSMV on BNs. More importantly, our approach finds all solutions for the BN problems.

Linear maps preserving maximal deviation and the Jordan structure of quantum systems

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

Hamhalter, Jan

2012-12-15

In the algebraic approach to quantum theory, a quantum observable is given by an element of a Jordan algebra and a state of the system is modelled by a normalized positive functional on the underlying algebra. Maximal deviation of a quantum observable is the largest statistical deviation one can obtain in a particular state of the system. The main result of the paper shows that each linear bijective transformation between JBW algebras preserving maximal deviations is formed by a Jordan isomorphism or a minus Jordan isomorphism perturbed by a linear functional multiple of an identity. It shows that only onemore » numerical statistical characteristic has the power to determine the Jordan algebraic structure completely. As a consequence, we obtain that only very special maps can preserve the diameter of the spectra of elements. Nonlinear maps preserving the pseudometric given by maximal deviation are also described. The results generalize hitherto known theorems on preservers of maximal deviation in the case of self-adjoint parts of von Neumann algebras proved by Molnar.« less

Apprentissage dans un Environnement Informatique: Possibilite, Nature, Transfert des Acquis (Learning within an Information Environment: Possibilities, Native, and Transfer of Ideas).

ERIC Educational Resources Information Center

Dagher, Antoine

1996-01-01

Examines possibilities for learning offered by a piece of software, Fonctuse, likely to encourage the linking of algebraic and graphical representations of functions. Studied the influence of prior algebraic knowledge on the cognitive processes and constructions of knowledge at play in this environment. (Author/MKR)

Experiences in Evaluating Outcomes in Tool-Based, Competence Building Education in Dynamical Systems Using Symbolic Computer Algebra

ERIC Educational Resources Information Center

Perram, John W.; Andersen, Morten; Ellekilde, Lars-Peter; Hjorth, Poul G.

2004-01-01

This paper discusses experience with alternative assessment strategies for an introductory course in dynamical systems, where the use of computer algebra and calculus is fully integrated into the learning process, so that the standard written examination would not be appropriate. Instead, students' competence was assessed by grading three large…

A novel technique to solve nonlinear higher-index Hessenberg differential-algebraic equations by Adomian decomposition method.

PubMed

Benhammouda, Brahim

2016-01-01

Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by some transformations like index reductions before applying the ADM. The drawback of such transformations is that they can involve complex algorithms, can be computationally expensive and may lead to non-physical solutions. The purpose of this paper is to propose a novel technique that applies the ADM directly to solve a class of nonlinear higher-index Hessenberg DAEs systems efficiently. The main advantage of this technique is that; firstly it avoids complex transformations like index reductions and leads to a simple general algorithm. Secondly, it reduces the computational work by solving only linear algebraic systems with a constant coefficient matrix at each iteration, except for the first iteration where the algebraic system is nonlinear (if the DAE is nonlinear with respect to the algebraic variable). To demonstrate the effectiveness of the proposed technique, we apply it to a nonlinear index-three Hessenberg DAEs system with nonlinear algebraic constraints. This technique is straightforward and can be programmed in Maple or Mathematica to simulate real application problems.

Solution of the classical Yang-Baxter equation with an exotic symmetry, and integrability of a multi-species boson tunnelling model

NASA Astrophysics Data System (ADS)

Links, Jon

2017-03-01

Solutions of the classical Yang-Baxter equation provide a systematic method to construct integrable quantum systems in an algebraic manner. A Lie algebra can be associated with any solution of the classical Yang-Baxter equation, from which commuting transfer matrices may be constructed. This procedure is reviewed, specifically for solutions without skew-symmetry. A particular solution with an exotic symmetry is identified, which is not obtained as a limiting expansion of the usual Yang-Baxter equation. This solution facilitates the construction of commuting transfer matrices which will be used to establish the integrability of a multi-species boson tunnelling model. The model generalises the well-known two-site Bose-Hubbard model, to which it reduces in the one-species limit. Due to the lack of an apparent reference state, application of the algebraic Bethe Ansatz to solve the model is prohibitive. Instead, the Bethe Ansatz solution is obtained by the use of operator identities and tensor product decompositions.

Exactly solvable model of transitional nuclei based on dual algebraic structure for the three level pairing model in the framework of sdg interacting boson model

NASA Astrophysics Data System (ADS)

Jafarizadeh, M. A.; Ranjbar, Z.; Fouladi, N.; Ghapanvari, M.

2018-01-01

In this paper, a successful algebraic method based on the dual algebraic structure for three level pairing model in the framework of sdg IBM is proposed for transitional nuclei which show transitional behavior from spherical to gamma-unstable quantum shape phase transition. In this method complicated sdg Hamiltonian, which is a three level pairing Hamiltonian is determined easily via the exactly solvable method. This description provides a better interpretation of some observables such as BE (4) in nuclei which exhibits the necessity of inclusion of g boson in the sd IBM, while BE (4) cannot be explained in the sd boson model. Some observables such as Energy levels, BE (2), BE (4), the two neutron separation energies signature splitting of the γ-vibrational band and expectation values of the g-boson number operator are calculated and examined for 46 104 - 110Pd isotopes.

Process Algebra Approach for Action Recognition in the Maritime Domain

NASA Technical Reports Server (NTRS)

Huntsberger, Terry

2011-01-01

The maritime environment poses a number of challenges for autonomous operation of surface boats. Among these challenges are the highly dynamic nature of the environment, the onboard sensing and reasoning requirements for obeying the navigational rules of the road, and the need for robust day/night hazard detection and avoidance. Development of full mission level autonomy entails addressing these challenges, coupled with inference of the tactical and strategic intent of possibly adversarial vehicles in the surrounding environment. This paper introduces PACIFIC (Process Algebra Capture of Intent From Information Content), an onboard system based on formal process algebras that is capable of extracting actions/activities from sensory inputs and reasoning within a mission context to ensure proper responses. PACIFIC is part of the Behavior Engine in CARACaS (Cognitive Architecture for Robotic Agent Command and Sensing), a system that is currently running on a number of U.S. Navy unmanned surface and underwater vehicles. Results from a series of experimental studies that demonstrate the effectiveness of the system are also presented.

Tropical geometry of statistical models.

PubMed

Pachter, Lior; Sturmfels, Bernd

2004-11-16

This article presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are coordinates of a point in the variety, and the sum-product algorithm is an efficient tool for evaluating specific coordinates. Here, we address the question of how the solutions to various inference problems depend on the model parameters. The proposed answer is expressed in terms of tropical algebraic geometry. The Newton polytope of a statistical model plays a key role. Our results are applied to the hidden Markov model and the general Markov model on a binary tree.

Remarks towards the spectrum of the Heisenberg spin chain type models

NASA Astrophysics Data System (ADS)

Burdík, Č.; Fuksa, J.; Isaev, A. P.; Krivonos, S. O.; Navrátil, O.

2015-05-01

The integrable close and open chain models can be formulated in terms of generators of the Hecke algebras. In this review paper, we describe in detail the Bethe ansatz for the XXX and the XXZ integrable close chain models. We find the Bethe vectors for two-component and inhomogeneous models. We also find the Bethe vectors for the fermionic realization of the integrable XXX and XXZ close chain models by means of the algebraic and coordinate Bethe ansatz. Special modification of the XXZ closed spin chain model ("small polaron model") is considered. Finally, we discuss some questions relating to the general open Hecke chain models.

Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials

NASA Astrophysics Data System (ADS)

Hoque, Md. Fazlul; Marquette, Ian; Post, Sarah; Zhang, Yao-Zhong

2018-04-01

We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schrödinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms of Laguerre, Legendre and exceptional Jacobi polynomials (of hypergeometric type). We construct ladder and shift operators based on the corresponding wave functions and obtain their recurrence formulas. These recurrence relations are used to construct higher-order, algebraically independent integrals of motion to prove superintegrability of the Hamiltonian. The integrals form a higher rank polynomial algebra. By constructing the structure functions of the associated deformed oscillator algebras we derive the degeneracy of energy spectrum of the superintegrable system.

Robust image retrieval from noisy inputs using lattice associative memories

NASA Astrophysics Data System (ADS)

Urcid, Gonzalo; Nieves-V., José Angel; García-A., Anmi; Valdiviezo-N., Juan Carlos

2009-02-01

Lattice associative memories also known as morphological associative memories are fully connected feedforward neural networks with no hidden layers, whose computation at each node is carried out with lattice algebra operations. These networks are a relatively recent development in the field of associative memories that has proven to be an alternative way to work with sets of pattern pairs for which the storage and retrieval stages use minimax algebra. Different associative memory models have been proposed to cope with the problem of pattern recall under input degradations, such as occlusions or random noise, where input patterns can be composed of binary or real valued entries. In comparison to these and other artificial neural network memories, lattice algebra based memories display better performance for storage and recall capability; however, the computational techniques devised to achieve that purpose require additional processing or provide partial success when inputs are presented with undetermined noise levels. Robust retrieval capability of an associative memory model is usually expressed by a high percentage of perfect recalls from non-perfect input. The procedure described here uses noise masking defined by simple lattice operations together with appropriate metrics, such as the normalized mean squared error or signal to noise ratio, to boost the recall performance of either the min or max lattice auto-associative memories. Using a single lattice associative memory, illustrative examples are given that demonstrate the enhanced retrieval of correct gray-scale image associations from inputs corrupted with random noise.

Universal vertex-IRF transformation for quantum affine algebras

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

Buffenoir, E.; Roche, Ph.; Terras, V.

2012-10-15

We construct a universal solution of the generalized coboundary equation in the case of quantum affine algebras, which is an extension of our previous work to U{sub q}(A{sub r}{sup (1)}). This universal solution has a simple Gauss decomposition which is constructed using Sevostyanov's characters of twisted quantum Borel algebras. We show that in the evaluation representations it gives a vertex-face transformation between a vertex type solution and a face type solution of the quantum dynamical Yang-Baxter equation. In particular, in the evaluation representation of U{sub q}(A{sub 1}{sup (1)}), it gives Baxter's well-known transformation between the 8-vertex model and the interaction-round-facesmore » (IRF) height model.« less

Stable homotopical algebra and [Gamma]-spaces

NASA Astrophysics Data System (ADS)

Schwede, Stefan

1999-03-01

In this paper we advertise the category of [Gamma]-spaces as a convenient framework for doing ‘algebra’ over ‘rings’ in stable homotopy theory. [Gamma]-spaces were introduced by Segal [Se] who showed that they give rise to a homotopy category equivalent to the usual homotopy category of connective (i.e. ([minus sign]1)-connected) spectra. Bousfield and Friedlander [BF] later provided model category structures for [Gamma]-spaces. The study of ‘rings, modules and algebras’ based on [Gamma]-spaces became possible when Lydakis [Ly] introduced a symmetric monoidal smash product with good homotopical properties. Here we develop model category structures for modules and algebras, set up (derived) smash products and associated spectral sequences and compare simplicial modules and algebras to their Eilenberg-MacLane spectra counterparts.

Color Algebras

NASA Technical Reports Server (NTRS)

Mulligan, Jeffrey B.

2017-01-01

A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. The difficulty addressed here is the fact that, because of metamerism, we cannot know with certainty the spectrum that produced a particular color solely on the basis of sensory data. Knowledge of the spectrum is not required to compute additive mixture of colors, but is critical for subtractive (multiplicative) mixture. Therefore, we cannot predict with certainty the multiplicative interactions between colors based solely on sensory data. There are two potential applications of a color algebra: first, to aid modeling phenomena of human visual perception, such as color constancy and transparency; and, second, to provide better models of the interactions of lights and surfaces for computer graphics rendering.

Analytic derivation of an approximate SU(3) symmetry inside the symmetry triangle of the interacting boson approximation model

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

Bonatsos, Dennis; Karampagia, S.; Casten, R. F.

2011-05-15

Using a contraction of the SU(3) algebra to the algebra of the rigid rotator in the large-boson-number limit of the interacting boson approximation (IBA) model, a line is found inside the symmetry triangle of the IBA, along which the SU(3) symmetry is preserved. The line extends from the SU(3) vertex to near the critical line of the first-order shape/phase transition separating the spherical and prolate deformed phases, and it lies within the Alhassid-Whelan arc of regularity, the unique valley of regularity connecting the SU(3) and U(5) vertices in the midst of chaotic regions. In addition to providing an explanation formore » the existence of the arc of regularity, the present line represents an example of an analytically determined approximate symmetry in the interior of the symmetry triangle of the IBA. The method is applicable to algebraic models possessing subalgebras amenable to contraction. This condition is equivalent to algebras in which the equilibrium ground state and its rotational band become energetically isolated from intrinsic excitations, as typified by deformed solutions to the IBA for large numbers of valence nucleons.« less

Combinatorial Formulas for Characteristic Classes, and Localization of Secondary Topological Invariants.

NASA Astrophysics Data System (ADS)

Smirnov, Mikhail

1995-01-01

The problems solved in this thesis originated from combinatorial formulas for characteristic classes. This thesis deals with Chern-Simons classes, their generalizations and related algebraic and analytic problems. (1) In this thesis, I describe a new class of algebras whose elements contain Chern and generalized Chern -Simons classes. There is a Poisson bracket in these algebras, similar to the bracket in Kontsevich's noncommutative symplectic geometry (Kon). I prove that the Poisson bracket gives rise to a graded Lie algebra containing differential forms representing Chern and Chern-Simons classes. This is a new result. I describe algebraic analogs of the dilogarithm and higher polylogarithms in the algebra corresponding to Chern-Simons classes. (2) I study the properties of this bracket. It is possible to write the exterior differential and other operations in the algebra using this bracket. The bracket of any two Chern classes is zero and the bracket of a Chern class and a Chern-Simons class is d-closed. The construction developed here easily gives explicit formulas for known secondary classes and makes it possible to construct new ones. (3) I develop an algebraic model for the action of the gauge group and describe how elements of algebra corresponding to the secondary characteristic classes change under this action (see theorem 3 page xi). (4) It is possible give new explicit formulas for cocycles on a gauge group of a bundle and for the corresponding cocycles on the Lie algebra of the gauge group. I use formulas for secondary characteristic classes and an algebraic approach developed in chapter 1. I also use the work of Faddeev, Reiman and Semyonov-Tian-Shanskii (FRS) on cocycles as quantum anomalies. (5) I apply the methods of differential geometry of formal power series to construct universal characteristic and secondary characteristic classes. Given a pair of gauge equivalent connections using local formulas I obtain dilogarithmic and trilogarithmic analogs of Chern-Simons classes.

Affine group formulation of the Standard Model coupled to gravity

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

Chou, Ching-Yi, E-mail: l2897107@mail.ncku.edu.tw; Ita, Eyo, E-mail: ita@usna.edu; Soo, Chopin, E-mail: cpsoo@mail.ncku.edu.tw

In this work we apply the affine group formalism for four dimensional gravity of Lorentzian signature, which is based on Klauder’s affine algebraic program, to the formulation of the Hamiltonian constraint of the interaction of matter and all forces, including gravity with non-vanishing cosmological constant Λ, as an affine Lie algebra. We use the hermitian action of fermions coupled to gravitation and Yang–Mills theory to find the density weight one fermionic super-Hamiltonian constraint. This term, combined with the Yang–Mills and Higgs energy densities, are composed with York’s integrated time functional. The result, when combined with the imaginary part of themore » Chern–Simons functional Q, forms the affine commutation relation with the volume element V(x). Affine algebraic quantization of gravitation and matter on equal footing implies a fundamental uncertainty relation which is predicated upon a non-vanishing cosmological constant. -- Highlights: •Wheeler–DeWitt equation (WDW) quantized as affine algebra, realizing Klauder’s program. •WDW formulated for interaction of matter and all forces, including gravity, as affine algebra. •WDW features Hermitian generators in spite of fermionic content: Standard Model addressed. •Constructed a family of physical states for the full, coupled theory via affine coherent states. •Fundamental uncertainty relation, predicated on non-vanishing cosmological constant.« less

The 6th International Conference on Computer Science and Computational Mathematics (ICCSCM 2017)

NASA Astrophysics Data System (ADS)

2017-09-01

The ICCSCM 2017 (The 6th International Conference on Computer Science and Computational Mathematics) has aimed to provide a platform to discuss computer science and mathematics related issues including Algebraic Geometry, Algebraic Topology, Approximation Theory, Calculus of Variations, Category Theory; Homological Algebra, Coding Theory, Combinatorics, Control Theory, Cryptology, Geometry, Difference and Functional Equations, Discrete Mathematics, Dynamical Systems and Ergodic Theory, Field Theory and Polynomials, Fluid Mechanics and Solid Mechanics, Fourier Analysis, Functional Analysis, Functions of a Complex Variable, Fuzzy Mathematics, Game Theory, General Algebraic Systems, Graph Theory, Group Theory and Generalizations, Image Processing, Signal Processing and Tomography, Information Fusion, Integral Equations, Lattices, Algebraic Structures, Linear and Multilinear Algebra; Matrix Theory, Mathematical Biology and Other Natural Sciences, Mathematical Economics and Financial Mathematics, Mathematical Physics, Measure Theory and Integration, Neutrosophic Mathematics, Number Theory, Numerical Analysis, Operations Research, Optimization, Operator Theory, Ordinary and Partial Differential Equations, Potential Theory, Real Functions, Rings and Algebras, Statistical Mechanics, Structure Of Matter, Topological Groups, Wavelets and Wavelet Transforms, 3G/4G Network Evolutions, Ad-Hoc, Mobile, Wireless Networks and Mobile Computing, Agent Computing & Multi-Agents Systems, All topics related Image/Signal Processing, Any topics related Computer Networks, Any topics related ISO SC-27 and SC- 17 standards, Any topics related PKI(Public Key Intrastructures), Artifial Intelligences(A.I.) & Pattern/Image Recognitions, Authentication/Authorization Issues, Biometric authentication and algorithms, CDMA/GSM Communication Protocols, Combinatorics, Graph Theory, and Analysis of Algorithms, Cryptography and Foundation of Computer Security, Data Base(D.B.) Management & Information Retrievals, Data Mining, Web Image Mining, & Applications, Defining Spectrum Rights and Open Spectrum Solutions, E-Comerce, Ubiquitous, RFID, Applications, Fingerprint/Hand/Biometrics Recognitions and Technologies, Foundations of High-performance Computing, IC-card Security, OTP, and Key Management Issues, IDS/Firewall, Anti-Spam mail, Anti-virus issues, Mobile Computing for E-Commerce, Network Security Applications, Neural Networks and Biomedical Simulations, Quality of Services and Communication Protocols, Quantum Computing, Coding, and Error Controls, Satellite and Optical Communication Systems, Theory of Parallel Processing and Distributed Computing, Virtual Visions, 3-D Object Retrievals, & Virtual Simulations, Wireless Access Security, etc. The success of ICCSCM 2017 is reflected in the received papers from authors around the world from several countries which allows a highly multinational and multicultural idea and experience exchange. The accepted papers of ICCSCM 2017 are published in this Book. Please check http://www.iccscm.com for further news. A conference such as ICCSCM 2017 can only become successful using a team effort, so herewith we want to thank the International Technical Committee and the Reviewers for their efforts in the review process as well as their valuable advices. We are thankful to all those who contributed to the success of ICCSCM 2017. The Secretary

Geometric Bioinspired Networks for Recognition of 2-D and 3-D Low-Level Structures and Transformations.

PubMed

Bayro-Corrochano, Eduardo; Vazquez-Santacruz, Eduardo; Moya-Sanchez, Eduardo; Castillo-Munis, Efrain

2016-10-01

This paper presents the design of radial basis function geometric bioinspired networks and their applications. Until now, the design of neural networks has been inspired by the biological models of neural networks but mostly using vector calculus and linear algebra. However, these designs have never shown the role of geometric computing. The question is how biological neural networks handle complex geometric representations involving Lie group operations like rotations. Even though the actual artificial neural networks are biologically inspired, they are just models which cannot reproduce a plausible biological process. Until now researchers have not shown how, using these models, one can incorporate them into the processing of geometric computing. Here, for the first time in the artificial neural networks domain, we address this issue by designing a kind of geometric RBF using the geometric algebra framework. As a result, using our artificial networks, we show how geometric computing can be carried out by the artificial neural networks. Such geometric neural networks have a great potential in robot vision. This is the most important aspect of this contribution to propose artificial geometric neural networks for challenging tasks in perception and action. In our experimental analysis, we show the applicability of our geometric designs, and present interesting experiments using 2-D data of real images and 3-D screw axis data. In general, our models should be used to process different types of inputs, such as visual cues, touch (texture, elasticity, temperature), taste, and sound. One important task of a perception-action system is to fuse a variety of cues coming from the environment and relate them via a sensor-motor manifold with motor modules to carry out diverse reasoned actions.

A feedback control model for network flow with multiple pure time delays

NASA Technical Reports Server (NTRS)

Press, J.

1972-01-01

A control model describing a network flow hindered by multiple pure time (or transport) delays is formulated. Feedbacks connect each desired output with a single control sector situated at the origin. The dynamic formulation invokes the use of differential difference equations. This causes the characteristic equation of the model to consist of transcendental functions instead of a common algebraic polynomial. A general graphical criterion is developed to evaluate the stability of such a problem. A digital computer simulation confirms the validity of such criterion. An optimal decision making process with multiple delays is presented.

Erosion of composite materials

NASA Technical Reports Server (NTRS)

Springer, G. S.

1980-01-01

A model for describing the response of uncoated and coated fiber reinforced composites subjected to repeated impingements of liquid (rain) droplets is presented. The model is based on the concept that fatigue is the dominant factor in the erosion process. Algebraic expressions are provided which give the incubation period, the rate of mass loss past the incubation period, and the total mass loss of the material during rain impact. The influence of material properties on erosion damage and the protection offered by different coatings are discussed and the use of the model in the design in the design of structures and components is illustrated.

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…

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'…

A Linear Algebra Measure of Cluster Quality.

ERIC Educational Resources Information Center

Mather, Laura A.

2000-01-01

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

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,…

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…

Meta-modelling, visualization and emulation of multi-dimensional data for virtual production intelligence

NASA Astrophysics Data System (ADS)

Schulz, Wolfgang; Hermanns, Torsten; Al Khawli, Toufik

2017-07-01

Decision making for competitive production in high-wage countries is a daily challenge where rational and irrational methods are used. The design of decision making processes is an intriguing, discipline spanning science. However, there are gaps in understanding the impact of the known mathematical and procedural methods on the usage of rational choice theory. Following Benjamin Franklin's rule for decision making formulated in London 1772, he called "Prudential Algebra" with the meaning of prudential reasons, one of the major ingredients of Meta-Modelling can be identified finally leading to one algebraic value labelling the results (criteria settings) of alternative decisions (parameter settings). This work describes the advances in Meta-Modelling techniques applied to multi-dimensional and multi-criterial optimization by identifying the persistence level of the corresponding Morse-Smale Complex. Implementations for laser cutting and laser drilling are presented, including the generation of fast and frugal Meta-Models with controlled error based on mathematical model reduction Reduced Models are derived to avoid any unnecessary complexity. Both, model reduction and analysis of multi-dimensional parameter space are used to enable interactive communication between Discovery Finders and Invention Makers. Emulators and visualizations of a metamodel are introduced as components of Virtual Production Intelligence making applicable the methods of Scientific Design Thinking and getting the developer as well as the operator more skilled.

A multiple-time-scale turbulence model based on variable partitioning of turbulent kinetic energy spectrum

NASA Technical Reports Server (NTRS)

Kim, S.-W.; Chen, C.-P.

1987-01-01

A multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method is presented. In the model, the effect of the ratio of the production rate to the dissipation rate on eddy viscosity is modeled by use of the multiple-time-scales and a variable partitioning of the turbulent kinetic energy spectrum. The concept of a variable partitioning of the turbulent kinetic energy spectrum and the rest of the model details are based on the previously reported algebraic stress turbulence model. Example problems considered include: a fully developed channel flow, a plane jet exhausting into a moving stream, a wall jet flow, and a weakly coupled wake-boundary layer interaction flow. The computational results compared favorably with those obtained by using the algebraic stress turbulence model as well as experimental data. The present turbulence model, as well as the algebraic stress turbulence model, yielded significantly improved computational results for the complex turbulent boundary layer flows, such as the wall jet flow and the wake boundary layer interaction flow, compared with available computational results obtained by using the standard kappa-epsilon turbulence model.

A multiple-time-scale turbulence model based on variable partitioning of the turbulent kinetic energy spectrum

NASA Technical Reports Server (NTRS)

Kim, S.-W.; Chen, C.-P.

1989-01-01

A multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method is presented. In the model, the effect of the ratio of the production rate to the dissipation rate on eddy viscosity is modeled by use of the multiple-time-scales and a variable partitioning of the turbulent kinetic energy spectrum. The concept of a variable partitioning of the turbulent kinetic energy spectrum and the rest of the model details are based on the previously reported algebraic stress turbulence model. Example problems considered include: a fully developed channel flow, a plane jet exhausting into a moving stream, a wall jet flow, and a weakly coupled wake-boundary layer interaction flow. The computational results compared favorably with those obtained by using the algebraic stress turbulence model as well as experimental data. The present turbulence model, as well as the algebraic stress turbulence model, yielded significantly improved computational results for the complex turbulent boundary layer flows, such as the wall jet flow and the wake boundary layer interaction flow, compared with available computational results obtained by using the standard kappa-epsilon turbulence model.

Horizon fluffs: In the context of generalized minimal massive gravity

NASA Astrophysics Data System (ADS)

Setare, Mohammad Reza; Adami, Hamed

2018-02-01

We consider a metric which describes Bañados geometries and show that the considered metric is a solution of the generalized minimal massive gravity (GMMG) model. We consider the Killing vector field which preserves the form of the considered metric. Using the off-shell quasi-local approach we obtain the asymptotic conserved charges of the given solution. Similar to the Einstein gravity in the presence of negative cosmological constant, for the GMMG model, we also show that the algebra among the asymptotic conserved charges is isomorphic to two copies of the Virasoro algebra. Eventually, we find a relation between the algebra of the near-horizon and the asymptotic conserved charges. This relation shows that the main part of the horizon fluffs proposed by Afshar et al., Sheikh-Jabbari and Yavartanoo appear for generic black holes in the class of Bañados geometries in the context of the GMMG model.

Geometric Model of Topological Insulators from the Maxwell Algebra

NASA Astrophysics Data System (ADS)

Palumbo, Giandomenico

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

Effects of Argumentation on Group Micro-Creativity: Statistical Discourse Analyses of Algebra Students' Collaborative Problem Solving

ERIC Educational Resources Information Center

Chiu, Ming Ming

2008-01-01

The micro-time context of group processes (such as argumentation) can affect a group's micro-creativity (new ideas). Eighty high school students worked in groups of four on an algebra problem. Groups with higher mathematics grades showed greater micro-creativity, and both were linked to better problem solving outcomes. Dynamic multilevel analyses…

Image Processing Language. Phase 1

DTIC Science & Technology

1988-05-01

their entirety. Nonetheless, they can serve as guidelines to which the construction of a useful and comprehensive imaging algebra might aspire. 3. TIH... guidelines to which the construction of a useful and comprehensive imaging algebra might aspire. * It was recognized that any structure which encompasses...Bernstein Polynomial Approximation Best Plane Fit ( BPF , Sobel, Roberts, Prewitt, Gradient) Boundary Finder Boundary Segmenter Chain Code Angle

Early Algebra with Graphics Software as a Type II Application of Technology

ERIC Educational Resources Information Center

Abramovich, Sergei

2006-01-01

This paper describes the use of Kid Pix-graphics software for creative activities of young children--in the context of early algebra as determined by the mathematics core curriculum of New York state. It shows how grade-two appropriate pedagogy makes it possible to bring about a qualitative change in the learning process of those commonly…

Application of the algebraic difference approach for developing self-referencing specific gravity and biomass equations

Treesearch

Lewis Jordan; Ray Souter; Bernard Parresol; Richard F. Daniels

2006-01-01

Biomass estimation is critical for looking at ecosystem processes and as a measure of stand yield. The density-integral approach allows for coincident estimation of stem profile and biomass. The algebraic difference approach (ADA) permits the derivation of dynamic or nonstatic functions. In this study we applied the ADA to develop a self-referencing specific gravity...

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

Kitanidis, Peter

As large-scale, commercial storage projects become operational, the problem of utilizing information from diverse sources becomes more critically important. In this project, we developed, tested, and applied an advanced joint data inversion system for CO 2 storage modeling with large data sets for use in site characterization and real-time monitoring. Emphasis was on the development of advanced and efficient computational algorithms for joint inversion of hydro-geophysical data, coupled with state-of-the-art forward process simulations. The developed system consists of (1) inversion tools using characterization data, such as 3D seismic survey (amplitude images), borehole log and core data, as well as hydraulic,more » tracer and thermal tests before CO 2 injection, (2) joint inversion tools for updating the geologic model with the distribution of rock properties, thus reducing uncertainty, using hydro-geophysical monitoring data, and (3) highly efficient algorithms for directly solving the dense or sparse linear algebra systems derived from the joint inversion. The system combines methods from stochastic analysis, fast linear algebra, and high performance computing. The developed joint inversion tools have been tested through synthetic CO 2 storage examples.« less

A study of the second and third order closure models of turbulence for prediction of separated shear flows

NASA Technical Reports Server (NTRS)

Amano, R. S.

1985-01-01

The hybrid model of the Reynolds-stress turbulence closure is tested for the computation of the flows over a step and disk. Here it is attempted to improve the redistributive action of the turbulence energy among the Reynolds stresses. By evaluating the existing models for the pressure-strain correlation, better coefficients are obtained for the prediction of separating shear flows. Furthermore, the diffusion rate of the Reynolds stresses is reevaluated adopting several algebraic correlations for the triple-velocity products. The models of Cormack et al., Daly-Harlow, Hanjalic-Launder, and Shir were tested for the reattaching shear flows. It was generally observed that all these algebraic models give considerably low values of the triple-velocity products. This is attributed to the fact that none of the algebraic models can take the convective effect of the triple-velocity products into account in the separating shear flows, thus resulting in much lower diffusion rate than Reynolds stresses. In order to improve the evaluation of these quantities correction factors are introduced based on the comparison with some experimental data.

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.

SPECIAL ISSUE ON OPTICAL PROCESSING OF INFORMATION: Method of implementation of optoelectronic multiparametric signal processing systems based on multivalued-logic principles

NASA Astrophysics Data System (ADS)

Arestova, M. L.; Bykovskii, A. Yu

1995-10-01

An architecture is proposed for a specialised optoelectronic multivalued logic processor based on the Allen—Givone algebra. The processor is intended for multiparametric processing of data arriving from a large number of sensors or for tackling spectral analysis tasks. The processor architecture makes it possible to obtain an approximate general estimate of the state of an object being diagnosed on a p-level scale. Optoelectronic systems are proposed for MAXIMUM, MINIMUM, and LITERAL logic gates, based on optical-frequency encoding of logic levels. Corresponding logic gates form a complete set of logic functions in the Allen—Givone algebra.

Does Calculation or Word-Problem Instruction Provide A Stronger Route to Pre-Algebraic Knowledge?

PubMed Central

Fuchs, Lynn S.; Powell, Sarah R.; Cirino, Paul T.; Schumacher, Robin F.; Marrin, Sarah; Hamlett, Carol L.; Fuchs, Douglas; Compton, Donald L.; Changas, Paul C.

2014-01-01

The focus of this study was connections among 3 aspects of mathematical cognition at 2nd grade: calculations, word problems, and pre-algebraic knowledge. We extended the literature, which is dominated by correlational work, by examining whether intervention conducted on calculations or word problems contributes to improved performance in the other domain and whether intervention in either or both domains contributes to pre-algebraic knowledge. Participants were 1102 children in 127 2nd-grade classrooms in 25 schools. Teachers were randomly assigned to 3 conditions: calculation intervention, word-problem intervention, and business-as-usual control. Intervention, which lasted 17 weeks, was designed to provide research-based linkages between arithmetic calculations or arithmetic word problems (depending on condition) to pre-algebraic knowledge. Multilevel modeling suggested calculation intervention improved calculation but not word-problem outcomes; word-problem intervention enhanced word-problem but not calculation outcomes; and word-problem intervention provided a stronger route than calculation intervention to pre-algebraic knowledge. PMID:25541565

Children's understanding of fraction and decimal symbols and the notation-specific relation to pre-algebra ability.

PubMed

Hurst, Michelle A; Cordes, Sara

2018-04-01

Fraction and decimal concepts are notoriously difficult for children to learn yet are a major component of elementary and middle school math curriculum and an important prerequisite for higher order mathematics (i.e., algebra). Thus, recently there has been a push to understand how children think about rational number magnitudes in order to understand how to promote rational number understanding. However, prior work investigating these questions has focused almost exclusively on fraction notation, overlooking the open questions of how children integrate rational number magnitudes presented in distinct notations (i.e., fractions, decimals, and whole numbers) and whether understanding of these distinct notations may independently contribute to pre-algebra ability. In the current study, we investigated rational number magnitude and arithmetic performance in both fraction and decimal notation in fourth- to seventh-grade children. We then explored how these measures of rational number ability predicted pre-algebra ability. Results reveal that children do represent the magnitudes of fractions and decimals as falling within a single numerical continuum and that, despite greater experience with fraction notation, children are more accurate when processing decimal notation than when processing fraction notation. Regression analyses revealed that both magnitude and arithmetic performance predicted pre-algebra ability, but magnitude understanding may be particularly unique and depend on notation. The educational implications of differences between children in the current study and previous work with adults are discussed. Copyright © 2017 Elsevier Inc. All rights reserved.

Automatic code generation in SPARK: Applications of computer algebra and compiler-compilers

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

Nataf, J.M.; Winkelmann, F.

We show how computer algebra and compiler-compilers are used for automatic code generation in the Simulation Problem Analysis and Research Kernel (SPARK), an object oriented environment for modeling complex physical systems that can be described by differential-algebraic equations. After a brief overview of SPARK, we describe the use of computer algebra in SPARK's symbolic interface, which generates solution code for equations that are entered in symbolic form. We also describe how the Lex/Yacc compiler-compiler is used to achieve important extensions to the SPARK simulation language, including parametrized macro objects and steady-state resetting of a dynamic simulation. The application of thesemore » methods to solving the partial differential equations for two-dimensional heat flow is illustrated.« less

Automatic code generation in SPARK: Applications of computer algebra and compiler-compilers

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

Nataf, J.M.; Winkelmann, F.

We show how computer algebra and compiler-compilers are used for automatic code generation in the Simulation Problem Analysis and Research Kernel (SPARK), an object oriented environment for modeling complex physical systems that can be described by differential-algebraic equations. After a brief overview of SPARK, we describe the use of computer algebra in SPARK`s symbolic interface, which generates solution code for equations that are entered in symbolic form. We also describe how the Lex/Yacc compiler-compiler is used to achieve important extensions to the SPARK simulation language, including parametrized macro objects and steady-state resetting of a dynamic simulation. The application of thesemore » methods to solving the partial differential equations for two-dimensional heat flow is illustrated.« less

Combinatorial operad actions on cochains

NASA Astrophysics Data System (ADS)

Berger, Clemens; Fresse, Benoit

2004-07-01

A classical E-infinity operad is formed by the bar construction of the symmetric groups. Such an operad has been introduced by M. Barratt and P. Eccles in the context of simplicial sets in order to have an analogue of the Milnor FK-construction for infinite loop spaces. The purpose of this paper is to prove that the associative algebra structure on the normalized cochain complex of a simplicial set extends to the structure of an algebra over the Barratt-Eccles operad. We also prove that differential graded algebras over the Barratt-Eccles operad form a closed model category. Similar results hold for the normalized Hochschild cochain complex of an associative algebra. More precisely, the Hochschild cochain complex is acted on by a suboperad of the Barratt-Eccles operad which is equivalent to the classical little squares operad.

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.

SD-CAS: Spin Dynamics by Computer Algebra System.

PubMed

Filip, Xenia; Filip, Claudiu

2010-11-01

A computer algebra tool for describing the Liouville-space quantum evolution of nuclear 1/2-spins is introduced and implemented within a computational framework named Spin Dynamics by Computer Algebra System (SD-CAS). A distinctive feature compared with numerical and previous computer algebra approaches to solving spin dynamics problems results from the fact that no matrix representation for spin operators is used in SD-CAS, which determines a full symbolic character to the performed computations. Spin correlations are stored in SD-CAS as four-entry nested lists of which size increases linearly with the number of spins into the system and are easily mapped into analytical expressions in terms of spin operator products. For the so defined SD-CAS spin correlations a set of specialized functions and procedures is introduced that are essential for implementing basic spin algebra operations, such as the spin operator products, commutators, and scalar products. They provide results in an abstract algebraic form: specific procedures to quantitatively evaluate such symbolic expressions with respect to the involved spin interaction parameters and experimental conditions are also discussed. Although the main focus in the present work is on laying the foundation for spin dynamics symbolic computation in NMR based on a non-matrix formalism, practical aspects are also considered throughout the theoretical development process. In particular, specific SD-CAS routines have been implemented using the YACAS computer algebra package (http://yacas.sourceforge.net), and their functionality was demonstrated on a few illustrative examples. Copyright © 2010 Elsevier Inc. All rights reserved.

Image-algebraic design of multispectral target recognition algorithms

NASA Astrophysics Data System (ADS)

Schmalz, Mark S.; Ritter, Gerhard X.

1994-06-01

In this paper, we discuss methods for multispectral ATR (Automated Target Recognition) of small targets that are sensed under suboptimal conditions, such as haze, smoke, and low light levels. In particular, we discuss our ongoing development of algorithms and software that effect intelligent object recognition by selecting ATR filter parameters according to ambient conditions. Our algorithms are expressed in terms of IA (image algebra), a concise, rigorous notation that unifies linear and nonlinear mathematics in the image processing domain. IA has been implemented on a variety of parallel computers, with preprocessors available for the Ada and FORTRAN languages. An image algebra C++ class library has recently been made available. Thus, our algorithms are both feasible implementationally and portable to numerous machines. Analyses emphasize the aspects of image algebra that aid the design of multispectral vision algorithms, such as parameterized templates that facilitate the flexible specification of ATR filters.

Pole-placement Predictive Functional Control for under-damped systems with real numbers algebra.

PubMed

Zabet, K; Rossiter, J A; Haber, R; Abdullah, M

2017-11-01

This paper presents the new algorithm of PP-PFC (Pole-placement Predictive Functional Control) for stable, linear under-damped higher-order processes. It is shown that while conventional PFC aims to get first-order exponential behavior, this is not always straightforward with significant under-damped modes and hence a pole-placement PFC algorithm is proposed which can be tuned more precisely to achieve the desired dynamics, but exploits complex number algebra and linear combinations in order to deliver guarantees of stability and performance. Nevertheless, practical implementation is easier by avoiding complex number algebra and hence a modified formulation of the PP-PFC algorithm is also presented which utilises just real numbers while retaining the key attributes of simple algebra, coding and tuning. The potential advantages are demonstrated with numerical examples and real-time control of a laboratory plant. Copyright © 2017 ISA. All rights reserved.

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.

Novel symmetries in Christ-Lee model

NASA Astrophysics Data System (ADS)

Kumar, R.; Shukla, A.

2016-07-01

We demonstrate that the gauge-fixed Lagrangian of the Christ-Lee model respects four fermionic symmetries, namely; (anti-)BRST symmetries, (anti-)co-BRST symmetries within the framework of BRST formalism. The appropriate anticommutators amongst the fermionic symmetries lead to a unique bosonic symmetry. It turns out that the algebra obeyed by the symmetry transformations (and their corresponding conserved charges) is reminiscent of the algebra satisfied by the de Rham cohomological operators of differential geometry. We also provide the physical realizations of the cohomological operators in terms of the symmetry properties. Thus, the present model provides a simple model for the Hodge theory.

Thin-layer approximation and algebraic model for separated turbulent flows

NASA Technical Reports Server (NTRS)

Baldwin, B.; Lomax, H.

1978-01-01

An algebraic turbulence model for two- and three-dimensional separated flows is specified that avoids the necessity for finding the edge of the boundary layer. Properties of the model are determined and comparisons made with experiment for an incident shock on a flat plate, separated flow over a compression corner, and transonic flow over an airfoil. Separation and reattachment points from numerical Navier-Stokes solutions agree with experiment within one boundary-layer thickness. Use of law-of-the-wall boundary conditions does not alter the predictions significantly. Applications of the model to other cases are contained in companion papers.

An Algebraic Implicitization and Specialization of Minimum KL-Divergence Models

NASA Astrophysics Data System (ADS)

Dukkipati, Ambedkar; Manathara, Joel George

In this paper we study representation of KL-divergence minimization, in the cases where integer sufficient statistics exists, using tools from polynomial algebra. We show that the estimation of parametric statistical models in this case can be transformed to solving a system of polynomial equations. In particular, we also study the case of Kullback-Csisźar iteration scheme. We present implicit descriptions of these models and show that implicitization preserves specialization of prior distribution. This result leads us to a Gröbner bases method to compute an implicit representation of minimum KL-divergence models.

A convenient basis for the Izergin-Korepin model

NASA Astrophysics Data System (ADS)

Qiao, Yi; Zhang, Xin; Hao, Kun; Cao, Junpeng; Li, Guang-Liang; Yang, Wen-Li; Shi, Kangjie

2018-05-01

We propose a convenient orthogonal basis of the Hilbert space for the quantum spin chain associated with the A2(2) algebra (or the Izergin-Korepin model). It is shown that compared with the original basis the monodromy-matrix elements acting on this basis take relatively simple forms, which is quite similar as that for the quantum spin chain associated with An algebra in the so-called F-basis. As an application of our general results, we present the explicit recursive expressions of the Bethe states in this basis for the Izergin-Korepin model.

Methods of mathematical modeling using polynomials of algebra of sets

NASA Astrophysics Data System (ADS)

Kazanskiy, Alexandr; Kochetkov, Ivan

2018-03-01

The article deals with the construction of discrete mathematical models for solving applied problems arising from the operation of building structures. Security issues in modern high-rise buildings are extremely serious and relevant, and there is no doubt that interest in them will only increase. The territory of the building is divided into zones for which it is necessary to observe. Zones can overlap and have different priorities. Such situations can be described using formulas algebra of sets. Formulas can be programmed, which makes it possible to work with them using computer models.

Algebraic, geometric, and stochastic aspects of genetic operators

NASA Technical Reports Server (NTRS)

Foo, N. Y.; Bosworth, J. L.

1972-01-01

Genetic algorithms for function optimization employ genetic operators patterned after those observed in search strategies employed in natural adaptation. Two of these operators, crossover and inversion, are interpreted in terms of their algebraic and geometric properties. Stochastic models of the operators are developed which are employed in Monte Carlo simulations of their behavior.

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.

Student Connections of Linear Algebra Concepts: An Analysis of Concept Maps

ERIC Educational Resources Information Center

Lapp, Douglas A.; Nyman, Melvin A.; Berry, John S.

2010-01-01

This article examines the connections of linear algebra concepts in a first course at the undergraduate level. The theoretical underpinnings of this study are grounded in the constructivist perspective (including social constructivism), Vernaud's theory of conceptual fields and Pirie and Kieren's model for the growth of mathematical understanding.…

Bicycles, Birds, Bats and Balloons: New Applications for Algebra Classes.

ERIC Educational Resources Information Center

Yoshiwara, Bruce; Yoshiwara, Kathy

This collection of activities is intended to enhance the teaching of college algebra through the use of modeling. The problems use real data and involve the representation and interpretation of the data. The concepts addressed include rates of change, linear and quadratic regression, and functions. The collection consists of eight problems, four…

A Method for the Microanalysis of Pre-Algebra Transfer

ERIC Educational Resources Information Center

Pavlik, Philip I., Jr.; Yudelson, Michael; Koedinger, Kenneth R.

2011-01-01

The objective of this research was to better understand the transfer of learning between different variations of pre-algebra problems. While the authors could have addressed a specific variation that might address transfer, they were interested in developing a general model of transfer, so we gathered data from multiple problem types and their…

Bethe vectors for XXX-spin chain

NASA Astrophysics Data System (ADS)

Burdík, Čestmír; Fuksa, Jan; Isaev, Alexei

2014-11-01

The paper deals with algebraic Bethe ansatz for XXX-spin chain. Generators of Yang-Baxter algebra are expressed in basis of free fermions and used to calculate explicit form of Bethe vectors. Their relation to N-component models is used to prove conjecture about their form in general. Some remarks on inhomogeneous XXX-spin chain are included.

An Authentic Task That Models Quadratics

ERIC Educational Resources Information Center

Baron, Lorraine M.

2015-01-01

As students develop algebraic reasoning in grades 5 to 9, they learn to recognize patterns and understand expressions, equations, and variables. Linear functions are a focus in eighth-grade mathematics, and by algebra 1, students must make sense of functions that are not linear. This article describes how students worked through a classroom task…

Superitem Test: An Alternative Assessment Tool to Assess Students' Algebraic Solving Ability

ERIC Educational Resources Information Center

Lian, Lim Hooi; Yew, Wun Thiam; Idris, Noraini

2010-01-01

Superitem test based on the SOLO model (Structure of the Observing Learning Outcome) has become a powerful alternative assessment tool for monitoring the growth of students' cognitive ability in solving mathematics problems. This article focused on developing a superitem test to assess students' algebraic solving ability through interview method.…

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…

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

ERIC Educational Resources Information Center

Lian, Lim Hooi; Yew, Wun Thiam

2011-01-01

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

Developing CORE model-based worksheet with recitation task to facilitate students’ mathematical communication skills in linear algebra course

NASA Astrophysics Data System (ADS)

Risnawati; Khairinnisa, S.; Darwis, A. H.

2018-01-01

The purpose of this study was to develop a CORE model-based worksheet with recitation task that were valid and practical and could facilitate students’ communication skills in Linear Algebra course. This study was conducted in mathematics education department of one public university in Riau, Indonesia. Participants of the study were media and subject matter experts as validators as well as students from mathematics education department. The objects of this study are students’ worksheet and students’ mathematical communication skills. The results of study showed that: (1) based on validation of the experts, the developed students’ worksheet was valid and could be applied for students in Linear Algebra courses; (2) based on the group trial, the practicality percentage was 92.14% in small group and 90.19% in large group, so the worksheet was very practical and could attract students to learn; and (3) based on the post test, the average percentage of ideals was 87.83%. In addition, the results showed that the students’ worksheet was able to facilitate students’ mathematical communication skills in linear algebra course.

A critical evaluation of various turbulence models as applied to internal fluid flows

NASA Technical Reports Server (NTRS)

Nallasamy, M.

1985-01-01

Models employed in the computation of turbulent flows are described and their application to internal flows is evaluated by examining the predictions of various turbulence models in selected flow configurations. The main conclusions are: (1) the k-epsilon model is used in a majority of all the two-dimensional flow calculations reported in the literature; (2) modified forms of the k-epsilon model improve the performance for flows with streamline curvature and heat transfer; (3) for flows with swirl, the k-epsilon model performs rather poorly; the algebraic stress model performs better in this case; and (4) for flows with regions of secondary flow (noncircular duct flows), the algebraic stress model performs fairly well for fully developed flow, for developing flow, the algebraic stress model performance is not good; a Reynolds stress model should be used. False diffusion and inlet boundary conditions are discussed. Countergradient transport and its implications in turbulence modeling is mentioned. Two examples of recirculating flow predictions obtained using PHOENICS code are discussed. The vortex method, large eddy simulation (modeling of subgrid scale Reynolds stresses), and direct simulation, are considered. Some recommendations for improving the model performance are made. The need for detailed experimental data in flows with strong curvature is emphasized.

Algebraic multigrid domain and range decomposition (AMG-DD / AMG-RD)*

DOE PAGES

Bank, R.; Falgout, R. D.; Jones, T.; ...

2015-10-29

In modern large-scale supercomputing applications, algebraic multigrid (AMG) is a leading choice for solving matrix equations. However, the high cost of communication relative to that of computation is a concern for the scalability of traditional implementations of AMG on emerging architectures. This paper introduces two new algebraic multilevel algorithms, algebraic multigrid domain decomposition (AMG-DD) and algebraic multigrid range decomposition (AMG-RD), that replace traditional AMG V-cycles with a fully overlapping domain decomposition approach. While the methods introduced here are similar in spirit to the geometric methods developed by Brandt and Diskin [Multigrid solvers on decomposed domains, in Domain Decomposition Methods inmore » Science and Engineering, Contemp. Math. 157, AMS, Providence, RI, 1994, pp. 135--155], Mitchell [Electron. Trans. Numer. Anal., 6 (1997), pp. 224--233], and Bank and Holst [SIAM J. Sci. Comput., 22 (2000), pp. 1411--1443], they differ primarily in that they are purely algebraic: AMG-RD and AMG-DD trade communication for computation by forming global composite “grids” based only on the matrix, not the geometry. (As is the usual AMG convention, “grids” here should be taken only in the algebraic sense, regardless of whether or not it corresponds to any geometry.) Another important distinguishing feature of AMG-RD and AMG-DD is their novel residual communication process that enables effective parallel computation on composite grids, avoiding the all-to-all communication costs of the geometric methods. The main purpose of this paper is to study the potential of these two algebraic methods as possible alternatives to existing AMG approaches for future parallel machines. As a result, this paper develops some theoretical properties of these methods and reports on serial numerical tests of their convergence properties over a spectrum of problem parameters.« less

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

NASA Astrophysics Data System (ADS)

Alim, Murad

2017-08-01

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

Numerical Methods for Forward and Inverse Problems in Discontinuous Media

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

Chartier, Timothy P.

The research emphasis under this grant's funding is in the area of algebraic multigrid methods. The research has two main branches: 1) exploring interdisciplinary applications in which algebraic multigrid can make an impact and 2) extending the scope of algebraic multigrid methods with algorithmic improvements that are based in strong analysis.The work in interdisciplinary applications falls primarily in the field of biomedical imaging. Work under this grant demonstrated the effectiveness and robustness of multigrid for solving linear systems that result from highly heterogeneous finite element method models of the human head. The results in this work also give promise tomore » medical advances possible with software that may be developed. Research to extend the scope of algebraic multigrid has been focused in several areas. In collaboration with researchers at the University of Colorado, Lawrence Livermore National Laboratory, and Los Alamos National Laboratory, the PI developed an adaptive multigrid with subcycling via complementary grids. This method has very cheap computing costs per iterate and is showing promise as a preconditioner for conjugate gradient. Recent work with Los Alamos National Laboratory concentrates on developing algorithms that take advantage of the recent advances in adaptive multigrid research. The results of the various efforts in this research could ultimately have direct use and impact to researchers for a wide variety of applications, including, astrophysics, neuroscience, contaminant transport in porous media, bi-domain heart modeling, modeling of tumor growth, and flow in heterogeneous porous media. This work has already led to basic advances in computational mathematics and numerical linear algebra and will continue to do so into the future.« less

How Visual Imagery Contributed to College: A Case of How Visual Imagery Contributes to a College Algebra Student's Understanding of the Concept of Function in the United States

ERIC Educational Resources Information Center

Lane, Rebekah M.

2011-01-01

This investigation utilized the qualitative case study method. Seventy-one College Algebra students were given a mathematical processing instrument. This testing device measured a student's preference for visual thinking. Two students were purposefully selected using the instrument. The visual mathematical learner (VL) was discussed in this…

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.

Algebraic Bethe ansatz for U(1) invariant integrable models: Compact and non-compact applications

NASA Astrophysics Data System (ADS)

Martins, M. J.; Melo, C. S.

2009-10-01

We apply the algebraic Bethe ansatz developed in our previous paper [C.S. Melo, M.J. Martins, Nucl. Phys. B 806 (2009) 567] to three different families of U(1) integrable vertex models with arbitrary N bond states. These statistical mechanics systems are based on the higher spin representations of the quantum group U[SU(2)] for both generic and non-generic values of q as well as on the non-compact discrete representation of the SL(2,R) algebra. We present for all these models the explicit expressions for both the on-shell and the off-shell properties associated to the respective transfer matrices eigenvalue problems. The amplitudes governing the vectors not parallel to the Bethe states are shown to factorize in terms of elementary building blocks functions. The results for the non-compact SL(2,R) model are argued to be derived from those obtained for the compact systems by taking suitable N→∞ limits. This permits us to study the properties of the non-compact SL(2,R) model starting from systems with finite degrees of freedom.

On the symmetries of integrability

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

Bellon, M.; Maillard, J.M.; Viallet, C.

1992-06-01

In this paper the authors show that the Yang-Baxter equations for two-dimensional models admit as a group of symmetry the infinite discrete group A{sub 2}{sup (1)}. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. The authors show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. The authors indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiatemore » the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non-trivial algebraic varieties, and lead to proper parametrizations of the models, be they integrable or not. The authors mention the relation existing between spin models and the Bose-Messner algebras of algebraic combinatorics. The authors' results also yield the generalization of the condition q{sup n} = 1 so often mentioned in the theory of quantum groups, when no q parameter is available.« less

The Standard Model Algebra - a summary

NASA Astrophysics Data System (ADS)

Cristinel Stoica, Ovidiu

2017-08-01

A generation of leptons and quarks and the gauge symmetries of the Standard Model can be obtained from the Clifford algebra ℂℓ 6. An instance of ℂℓ 6 is implicitly generated by the Dirac algebra combined with the electroweak symmetry, while the color symmetry gives another instance of ℂℓ 6 with a Witt decomposition. The minimal mathematical model proposed here results by identifying the two instances of ℂℓ 6. The left ideal decomposition generated by the Witt decomposition represents the leptons and quarks, and their antiparticles. The SU(3)c and U(1)em symmetries of the SM are the symmetries of this ideal decomposition. The patterns of electric charges, colors, chirality, weak isospins, and hypercharges, follow from this, without predicting additional particles or forces, or proton decay. The electroweak symmetry is present in its broken form, due to the geometry. The predicted Weinberg angle is given by sin2 W = 0.25. The model shares common features with previously known models, particularly with Chisholm and Farwell, 1996, Trayling and Baylis, 2004, and Furey, 2016.

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.

The smooth entropy formalism for von Neumann algebras

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

Berta, Mario, E-mail: berta@caltech.edu; Furrer, Fabian, E-mail: furrer@eve.phys.s.u-tokyo.ac.jp; Scholz, Volkher B., E-mail: scholz@phys.ethz.ch

2016-01-15

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.

A matrix dependent/algebraic multigrid approach for extruded meshes with applications to ice sheet modeling

DOE PAGES

Tuminaro, Raymond S.; Perego, Mauro; Tezaur, Irina Kalashnikova; ...

2016-10-06

A multigrid method is proposed that combines ideas from matrix dependent multigrid for structured grids and algebraic multigrid for unstructured grids. It targets problems where a three-dimensional mesh can be viewed as an extrusion of a two-dimensional, unstructured mesh in a third dimension. Our motivation comes from the modeling of thin structures via finite elements and, more specifically, the modeling of ice sheets. Extruded meshes are relatively common for thin structures and often give rise to anisotropic problems when the thin direction mesh spacing is much smaller than the broad direction mesh spacing. Within our approach, the first few multigridmore » hierarchy levels are obtained by applying matrix dependent multigrid to semicoarsen in a structured thin direction fashion. After sufficient structured coarsening, the resulting mesh contains only a single layer corresponding to a two-dimensional, unstructured mesh. Algebraic multigrid can then be employed in a standard manner to create further coarse levels, as the anisotropic phenomena is no longer present in the single layer problem. The overall approach remains fully algebraic, with the minor exception that some additional information is needed to determine the extruded direction. Furthermore, this facilitates integration of the solver with a variety of different extruded mesh applications.« less

Enlarged symmetry algebras of spin chains, loop models, and S-matrices

NASA Astrophysics Data System (ADS)

Read, N.; Saleur, H.

2007-08-01

The symmetry algebras of certain families of quantum spin chains are considered in detail. The simplest examples possess m states per site ( m⩾2), with nearest-neighbor interactions with U(m) symmetry, under which the sites transform alternately along the chain in the fundamental m and its conjugate representation m¯. We find that these spin chains, even with arbitrary coefficients of these interactions, have a symmetry algebra A much larger than U(m), which implies that the energy eigenstates fall into sectors that for open chains (i.e., free boundary conditions) can be labeled by j=0,1,…,L, for the 2 L-site chain such that the degeneracies of all eigenvalues in the jth sector are generically the same and increase rapidly with j. For large j, these degeneracies are much larger than those that would be expected from the U(m) symmetry alone. The enlarged symmetry algebra A(2L) consists of operators that commute in this space of states with the Temperley-Lieb algebra that is generated by the set of nearest-neighbor interaction terms; A(2L) is not a Yangian. There are similar results for supersymmetric chains with gl(m+n|n) symmetry of nearest-neighbor interactions, and a richer representation structure for closed chains (i.e., periodic boundary conditions). The symmetries also apply to the loop models that can be obtained from the spin chains in a spacetime or transfer matrix picture. In the loop language, the symmetries arise because the loops cannot cross. We further define tensor products of representations (for the open chains) by joining chains end to end. The fusion rules for decomposing the tensor product of representations labeled j and j take the same form as the Clebsch-Gordan series for SU(2). This and other structures turn the symmetry algebra A into a ribbon Hopf algebra, and we show that this is "Morita equivalent" to the quantum group U(sl) for m=q+q. The open-chain results are extended to the cases |m|<2 for which the algebras are no longer semisimple; these possess continuum limits that are critical (conformal) field theories, or massive perturbations thereof. Such models, for open and closed boundary conditions, arise in connection with disordered fermions, percolation, and polymers (self-avoiding walks), and certain non-linear sigma models, all in two dimensions. A product operation is defined in a related way for the Temperley-Lieb representations also, and the fusion rules for this are related to those for A or U(sl) representations; this is useful for the continuum limits also, as we discuss in a companion paper.

Explicating mathematical thinking in differential equations using a computer algebra system

NASA Astrophysics Data System (ADS)

Zeynivandnezhad, Fereshteh; Bates, Rachel

2018-07-01

The importance of developing students' mathematical thinking is frequently highlighted in literature regarding the teaching and learning of mathematics. Despite this importance, most curricula and instructional activities for undergraduate mathematics fail to bring the learner beyond the mathematics. The purpose of this study was to enhance students' mathematical thinking by implementing a computer algebra system and active learning pedagogical approaches. students' mathematical thinking processes were analyzed while completing specific differential equations tasks based on posed prompts and questions and Instrumental Genesis. Data were collected from 37 engineering students in a public Malaysian university. This study used the descriptive and interpretive qualitative research design to investigate the students' perspectives of emerging mathematical understanding and approaches to learning mathematics in an undergraduate differential equations course. Results of this study concluded that students used a variety of mathematical thinking processes in a non-sequential manner. Additionally, the outcomes provide justification for continued use of technologies such as computer algebra systems in undergraduate mathematics courses and the need for further studies to uncover the various processes students utilize to complete specific mathematical tasks.

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

NASA Astrophysics Data System (ADS)

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

2013-10-01

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

Plant growth and respiration re-visited: maintenance respiration defined – it is an emergent property of, not a separate process within, the system – and why the respiration : photosynthesis ratio is conservative

PubMed Central

Thornley, John H. M.

2011-01-01

Background and Aims Plant growth and respiration still has unresolved issues, examined here using a model. The aims of this work are to compare the model's predictions with McCree's observation-based respiration equation which led to the ‘growth respiration/maintenance respiration paradigm’ (GMRP) – this is required to give the model credibility; to clarify the nature of maintenance respiration (MR) using a model which does not represent MR explicitly; and to examine algebraic and numerical predictions for the respiration:photosynthesis ratio. Methods A two-state variable growth model is constructed, with structure and substrate, applicable on plant to ecosystem scales. Four processes are represented: photosynthesis, growth with growth respiration (GR), senescence giving a flux towards litter, and a recycling of some of this flux. There are four significant parameters: growth efficiency, rate constants for substrate utilization and structure senescence, and fraction of structure returned to the substrate pool. Key Results The model can simulate McCree's data on respiration, providing an alternative interpretation to the GMRP. The model's parameters are related to parameters used in this paradigm. MR is defined and calculated in terms of the model's parameters in two ways: first during exponential growth at zero growth rate; and secondly at equilibrium. The approaches concur. The equilibrium respiration:photosynthesis ratio has the value of 0·4, depending only on growth efficiency and recycling fraction. Conclusions McCree's equation is an approximation that the model can describe; it is mistaken to interpret his second coefficient as a maintenance requirement. An MR rate is defined and extracted algebraically from the model. MR as a specific process is not required and may be replaced with an approach from which an MR rate emerges. The model suggests that the respiration:photosynthesis ratio is conservative because it depends on two parameters only whose values are likely to be similar across ecosystems. PMID:21948663

Cyclotomic Gaudin Models: Construction and Bethe Ansatz

NASA Astrophysics Data System (ADS)

Vicedo, Benoît; Young, Charles

2016-05-01

To any finite-dimensional simple Lie algebra g and automorphism {σ: gto g we associate a cyclotomic Gaudin algebra. This is a large commutative subalgebra of {U(g)^{⊗ N}} generated by a hierarchy of cyclotomic Gaudin Hamiltonians. It reduces to the Gaudin algebra in the special case {σ =id}. We go on to construct joint eigenvectors and their eigenvalues for this hierarchy of cyclotomic Gaudin Hamiltonians, in the case of a spin chain consisting of a tensor product of Verma modules. To do so we generalize an approach to the Bethe ansatz due to Feigin, Frenkel and Reshetikhin involving vertex algebras and the Wakimoto construction. As part of this construction, we make use of a theorem concerning cyclotomic coinvariants, which we prove in a companion paper. As a byproduct, we obtain a cyclotomic generalization of the Schechtman-Varchenko formula for the weight function.

Automation of Presentation Record Production Based on Rich-Media Technology Using SNT Petri Nets Theory.

PubMed

Martiník, Ivo

2015-01-01

Rich-media describes a broad range of digital interactive media that is increasingly used in the Internet and also in the support of education. Last year, a special pilot audiovisual lecture room was built as a part of the MERLINGO (MEdia-rich Repository of LearnING Objects) project solution. It contains all the elements of the modern lecture room determined for the implementation of presentation recordings based on the rich-media technologies and their publication online or on-demand featuring the access of all its elements in the automated mode including automatic editing. Property-preserving Petri net process algebras (PPPA) were designed for the specification and verification of the Petri net processes. PPPA does not need to verify the composition of the Petri net processes because all their algebraic operators preserve the specified set of the properties. These original PPPA are significantly generalized for the newly introduced class of the SNT Petri process and agent nets in this paper. The PLACE-SUBST and ASYNC-PROC algebraic operators are defined for this class of Petri nets and their chosen properties are proved. The SNT Petri process and agent nets theory were significantly applied at the design, verification, and implementation of the programming system ensuring the pilot audiovisual lecture room functionality.

Automation of Presentation Record Production Based on Rich-Media Technology Using SNT Petri Nets Theory

PubMed Central

Martiník, Ivo

2015-01-01

Rich-media describes a broad range of digital interactive media that is increasingly used in the Internet and also in the support of education. Last year, a special pilot audiovisual lecture room was built as a part of the MERLINGO (MEdia-rich Repository of LearnING Objects) project solution. It contains all the elements of the modern lecture room determined for the implementation of presentation recordings based on the rich-media technologies and their publication online or on-demand featuring the access of all its elements in the automated mode including automatic editing. Property-preserving Petri net process algebras (PPPA) were designed for the specification and verification of the Petri net processes. PPPA does not need to verify the composition of the Petri net processes because all their algebraic operators preserve the specified set of the properties. These original PPPA are significantly generalized for the newly introduced class of the SNT Petri process and agent nets in this paper. The PLACE-SUBST and ASYNC-PROC algebraic operators are defined for this class of Petri nets and their chosen properties are proved. The SNT Petri process and agent nets theory were significantly applied at the design, verification, and implementation of the programming system ensuring the pilot audiovisual lecture room functionality. PMID:26258164

Quantum field theory and coalgebraic logic in theoretical computer science.

PubMed

Basti, Gianfranco; Capolupo, Antonio; Vitiello, Giuseppe

2017-11-01

We suggest that in the framework of the Category Theory it is possible to demonstrate the mathematical and logical dual equivalence between the category of the q-deformed Hopf Coalgebras and the category of the q-deformed Hopf Algebras in quantum field theory (QFT), interpreted as a thermal field theory. Each pair algebra-coalgebra characterizes a QFT system and its mirroring thermal bath, respectively, so to model dissipative quantum systems in far-from-equilibrium conditions, with an evident significance also for biological sciences. Our study is in fact inspired by applications to neuroscience where the brain memory capacity, for instance, has been modeled by using the QFT unitarily inequivalent representations. The q-deformed Hopf Coalgebras and the q-deformed Hopf Algebras constitute two dual categories because characterized by the same functor T, related with the Bogoliubov transform, and by its contravariant application T op , respectively. The q-deformation parameter is related to the Bogoliubov angle, and it is effectively a thermal parameter. Therefore, the different values of q identify univocally, and label the vacua appearing in the foliation process of the quantum vacuum. This means that, in the framework of Universal Coalgebra, as general theory of dynamic and computing systems ("labelled state-transition systems"), the so labelled infinitely many quantum vacua can be interpreted as the Final Coalgebra of an "Infinite State Black-Box Machine". All this opens the way to the possibility of designing a new class of universal quantum computing architectures based on this coalgebraic QFT formulation, as its ability of naturally generating a Fibonacci progression demonstrates. Copyright © 2017 Elsevier Ltd. All rights reserved.

The exact fundamental solution for the Benes tracking problem

NASA Astrophysics Data System (ADS)

Balaji, Bhashyam

2009-05-01

The universal continuous-discrete tracking problem requires the solution of a Fokker-Planck-Kolmogorov forward equation (FPKfe) for an arbitrary initial condition. Using results from quantum mechanics, the exact fundamental solution for the FPKfe is derived for the state model of arbitrary dimension with Benes drift that requires only the computation of elementary transcendental functions and standard linear algebra techniques- no ordinary or partial differential equations need to be solved. The measurement process may be an arbitrary, discrete-time nonlinear stochastic process, and the time step size can be arbitrary. Numerical examples are included, demonstrating its utility in practical implementation.

Bethe states of the trigonometric SU(3) spin chain with generic open boundaries

NASA Astrophysics Data System (ADS)

Sun, Pei; Xin, Zhirong; Qiao, Yi; Wen, Fakai; Hao, Kun; Cao, Junpeng; Li, Guang-Liang; Yang, Tao; Yang, Wen-Li; Shi, Kangjie

2018-06-01

By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the trigonometric SU (3) model with generic open boundaries. The eigenvalues of the transfer matrix are given in terms of an inhomogeneous T - Q relation, and the corresponding eigenstates are expressed in terms of nested Bethe-type eigenstates which have well-defined homogeneous limit. This exact solution provides a basis for further analyzing the thermodynamic properties and correlation functions of the anisotropic models associated with higher rank algebras.

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…

Counter Conjectures: Using Manipulatives to Scaffold the Development of Number Sense and Algebra

ERIC Educational Resources Information Center

West, John

2016-01-01

This article takes the position that teachers can use simple manipulative materials to model relatively complex situations and in doing so scaffold the development of students' number sense and early algebra skills. While students' early experiences are usually dominated by the cardinal aspect of number (i.e., counting the number of items in a…

Characterizing the Development of Specialized Mathematical Content Knowledge for Teaching in Algebraic Reasoning and Number Theory

ERIC Educational Resources Information Center

Bair, Sherry L.; Rich, Beverly S.

2011-01-01

This article characterizes the development of a deep and connected body of mathematical knowledge categorized by Ball and Bass' (2003b) model of Mathematical Knowledge for Teaching (MKT), as Specialized Content Knowledge for Teaching (SCK) in algebraic reasoning and number sense. The research employed multiple cases across three years from two…

Is the Role of Equations in the Doing of Word Problems in School Algebra Changing? Initial Indications from Teacher Study Groups

ERIC Educational Resources Information Center

Chazan, Daniel; Sela, Hagit; Herbst, Patricio

2012-01-01

We illustrate a method, which is modeled on "breaching experiments," for studying tacit norms that govern classroom interaction around particular mathematical content. Specifically, this study explores norms that govern teachers' expectations for the doing of word problems in school algebra. Teacher study groups discussed representations of…

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…

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…

Improving Machining Accuracy of CNC Machines with Innovative Design Methods

NASA Astrophysics Data System (ADS)

Yemelyanov, N. V.; Yemelyanova, I. V.; Zubenko, V. L.

2018-03-01

The article considers achieving the machining accuracy of CNC machines by applying innovative methods in modelling and design of machining systems, drives and machine processes. The topological method of analysis involves visualizing the system as matrices of block graphs with a varying degree of detail between the upper and lower hierarchy levels. This approach combines the advantages of graph theory and the efficiency of decomposition methods, it also has visual clarity, which is inherent in both topological models and structural matrices, as well as the resiliency of linear algebra as part of the matrix-based research. The focus of the study is on the design of automated machine workstations, systems, machines and units, which can be broken into interrelated parts and presented as algebraic, topological and set-theoretical models. Every model can be transformed into a model of another type, and, as a result, can be interpreted as a system of linear and non-linear equations which solutions determine the system parameters. This paper analyses the dynamic parameters of the 1716PF4 machine at the stages of design and exploitation. Having researched the impact of the system dynamics on the component quality, the authors have developed a range of practical recommendations which have enabled one to reduce considerably the amplitude of relative motion, exclude some resonance zones within the spindle speed range of 0...6000 min-1 and improve machining accuracy.

Exact joint density-current probability function for the asymmetric exclusion process.

PubMed

Depken, Martin; Stinchcombe, Robin

2004-07-23

We study the asymmetric simple exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system. We further consider the thermodynamic limit, showing that the resulting distribution is non-Gaussian and that the density fluctuations have a discontinuity at the continuous phase transition, while the current fluctuations are continuous. The derivations are performed by using the standard operator algebraic approach and by the introduction of new operators satisfying a modified version of the original algebra. Copyright 2004 The American Physical Society

Quantum theory of the generalised uncertainty principle

NASA Astrophysics Data System (ADS)

Bruneton, Jean-Philippe; Larena, Julien

2017-04-01

We extend significantly previous works on the Hilbert space representations of the generalized uncertainty principle (GUP) in 3 + 1 dimensions of the form [X_i,P_j] = i F_{ij} where F_{ij} = f({{P}}^2) δ _{ij} + g({{P}}^2) P_i P_j for any functions f. However, we restrict our study to the case of commuting X's. We focus in particular on the symmetries of the theory, and the minimal length that emerge in some cases. We first show that, at the algebraic level, there exists an unambiguous mapping between the GUP with a deformed quantum algebra and a quadratic Hamiltonian into a standard, Heisenberg algebra of operators and an aquadratic Hamiltonian, provided the boost sector of the symmetries is modified accordingly. The theory can also be mapped to a completely standard Quantum Mechanics with standard symmetries, but with momentum dependent position operators. Next, we investigate the Hilbert space representations of these algebraically equivalent models, and focus specifically on whether they exhibit a minimal length. We carry the functional analysis of the various operators involved, and show that the appearance of a minimal length critically depends on the relationship between the generators of translations and the physical momenta. In particular, because this relationship is preserved by the algebraic mapping presented in this paper, when a minimal length is present in the standard GUP, it is also present in the corresponding Aquadratic Hamiltonian formulation, despite the perfectly standard algebra of this model. In general, a minimal length requires bounded generators of translations, i.e. a specific kind of quantization of space, and this depends on the precise shape of the function f defined previously. This result provides an elegant and unambiguous classification of which universal quantum gravity corrections lead to the emergence of a minimal length.

Reflective thinking in solving an algebra problem: a case study of field independent-prospective teacher

NASA Astrophysics Data System (ADS)

Agustan, S.; Juniati, Dwi; Yuli Eko Siswono, Tatag

2017-10-01

Nowadays, reflective thinking is one of the important things which become a concern in learning mathematics, especially in solving a mathematical problem. The purpose of this paper is to describe how the student used reflective thinking when solved an algebra problem. The subject of this research is one female student who has field independent cognitive style. This research is a descriptive exploratory study with data analysis using qualitative approach to describe in depth reflective thinking of prospective teacher in solving an algebra problem. Four main categories are used to analyse the reflective thinking in solving an algebra problem: (1) formulation and synthesis of experience, (2) orderliness of experience, (3) evaluating the experience and (4) testing the selected solution based on the experience. The results showed that the subject described the problem by using another word and the subject also found the difficulties in making mathematical modelling. The subject analysed two concepts used in solving problem. For instance, geometry related to point and line while algebra is related to algebra arithmetic operation. The subject stated that solution must have four aspect to get effective solution, specifically the ability to (a) understand the meaning of every words; (b) make mathematical modelling; (c) calculate mathematically; (d) interpret solution obtained logically. To test the internal consistency or error in solution, the subject checked and looked back related procedures and operations used. Moreover, the subject tried to resolve the problem in a different way to compare the answers which had been obtained before. The findings supported the assertion that reflective thinking provides an opportunity for the students in improving their weakness in mathematical problem solving. It can make a grow accuracy and concentration in solving a mathematical problem. Consequently, the students will get the right and logic answer by reflective thinking.

Generalized EMV-Effect Algebras

NASA Astrophysics Data System (ADS)

Borzooei, R. A.; Dvurečenskij, A.; Sharafi, A. H.

2018-04-01

Recently in Dvurečenskij and Zahiri (2017), new algebraic structures, called EMV-algebras which generalize both MV-algebras and generalized Boolean algebras, were introduced. We present equivalent conditions for EMV-algebras. In addition, we define a partial algebraic structure, called a generalized EMV-effect algebra, which is close to generalized MV-effect algebras. Finally, we show that every generalized EMV-effect algebra is either an MV-effect algebra or can be embedded into an MV-effect algebra as a maximal ideal.

The Matrix Pencil and its Applications to Speech Processing

DTIC Science & Technology

2007-03-01

Elementary Linear Algebra ” 8th edition, pp. 278, 2000 John Wiley & Sons, Inc., New York [37] Wai C. Chu, “Speech Coding Algorithms”, New Jeresy: John...Ben; Daniel, James W.; “Applied Linear Algebra ”, pp. 342-345, 1988 Prentice Hall, Englewood Cliffs, NJ [35] Haykin, Simon “Applied Linear Adaptive...ABSTRACT Matrix Pencils facilitate the study of differential equations resulting from oscillating systems. Certain problems in linear ordinary

Balance point characterization of interstitial fluid volume regulation.

PubMed

Dongaonkar, R M; Laine, G A; Stewart, R H; Quick, C M

2009-07-01

The individual processes involved in interstitial fluid volume and protein regulation (microvascular filtration, lymphatic return, and interstitial storage) are relatively simple, yet their interaction is exceedingly complex. There is a notable lack of a first-order, algebraic formula that relates interstitial fluid pressure and protein to critical parameters commonly used to characterize the movement of interstitial fluid and protein. Therefore, the purpose of the present study is to develop a simple, transparent, and general algebraic approach that predicts interstitial fluid pressure (P(i)) and protein concentrations (C(i)) that takes into consideration all three processes. Eight standard equations characterizing fluid and protein flux were solved simultaneously to yield algebraic equations for P(i) and C(i) as functions of parameters characterizing microvascular, interstitial, and lymphatic function. Equilibrium values of P(i) and C(i) arise as balance points from the graphical intersection of transmicrovascular and lymph flows (analogous to Guyton's classical cardiac output-venous return curves). This approach goes beyond describing interstitial fluid balance in terms of conservation of mass by introducing the concept of inflow and outflow resistances. Algebraic solutions demonstrate that P(i) and C(i) result from a ratio of the microvascular filtration coefficient (1/inflow resistance) and effective lymphatic resistance (outflow resistance), and P(i) is unaffected by interstitial compliance. These simple algebraic solutions predict P(i) and C(i) that are consistent with reported measurements. The present work therefore presents a simple, transparent, and general balance point characterization of interstitial fluid balance resulting from the interaction of microvascular, interstitial, and lymphatic function.

Analysis and synthesis of distributed-lumped-active networks by digital computer

NASA Technical Reports Server (NTRS)

1973-01-01

The use of digital computational techniques in the analysis and synthesis of DLA (distributed lumped active) networks is considered. This class of networks consists of three distinct types of elements, namely, distributed elements (modeled by partial differential equations), lumped elements (modeled by algebraic relations and ordinary differential equations), and active elements (modeled by algebraic relations). Such a characterization is applicable to a broad class of circuits, especially including those usually referred to as linear integrated circuits, since the fabrication techniques for such circuits readily produce elements which may be modeled as distributed, as well as the more conventional lumped and active ones.

Color Algebras

NASA Technical Reports Server (NTRS)

Mulligan, Jeffrey B.

2017-01-01

A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. We would like it to match the well-defined algebra of spectral functions describing lights and surface reflectances, but an exact correspondence is impossible after the spectra have been projected to a three-dimensional color space, because of metamerism physically different spectra can produce the same color sensation. Metameric spectra are interchangeable for the purposes of addition, but not multiplication, so any color algebra is necessarily an approximation to physical reality. Nevertheless, because the majority of naturally-occurring spectra are well-behaved (e.g., continuous and slowly-varying), color algebras can be formulated that are largely accurate and agree well with human intuition. Here we explore the family of algebras that result from associating each color with a member of a three-dimensional manifold of spectra. This association can be used to construct a color product, defined as the color of the spectrum of the wavelength-wise product of the spectra associated with the two input colors. The choice of the spectral manifold determines the behavior of the resulting system, and certain special subspaces allow computational efficiencies. The resulting systems can be used to improve computer graphic rendering techniques, and to model various perceptual phenomena such as color constancy.

The optimal inventory policy for EPQ model under trade credit

NASA Astrophysics Data System (ADS)

Chung, Kun-Jen

2010-09-01

Huang and Huang [(2008), 'Optimal Inventory Replenishment Policy for the EPQ Model Under Trade Credit without Derivatives International Journal of Systems Science, 39, 539-546] use the algebraic method to determine the optimal inventory replenishment policy for the retailer in the extended model under trade credit. However, the algebraic method has its limit of application such that validities of proofs of Theorems 1-4 in Huang and Huang (2008) are questionable. The main purpose of this article is not only to indicate shortcomings but also to present the accurate proofs for Huang and Huang (2008).

Spectral properties of the Preisach hysteresis model with random input. II. Universality classes for symmetric elementary loops

NASA Astrophysics Data System (ADS)

Radons, Günter

2008-06-01

The Preisach model with symmetric elementary hysteresis loops and uncorrelated input is treated analytically in detail. It is shown that the appearance of long-time tails in the output correlations is a quite general feature of this model. The exponent η of the algebraic decay t-η , which may take any positive value, is determined by the tails of the input and the Preisach density. We identify the system classes leading to identical algebraic tails. These results imply the occurrence of 1/f noise for a large class of hysteretic systems.

Combinatorial quantization of the Hamiltonian Chern-Simons theory II

NASA Astrophysics Data System (ADS)

Alekseev, Anton Yu.; Grosse, Harald; Schomerus, Volker

1996-01-01

This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory advertised in [1]. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of quantum group gauge theory. This allows to discuss flatness of quantum connections so that we can give a mathematically rigorous definition of the algebra of observables A CS of the Chern Simons model. It is a *-algebra of “functions on the quantum moduli space of flat connections” and comes equipped with a positive functional ω (“integration”). We prove that this data does not depend on the particular choices which have been made in the construction. Following ideas of Fock and Rosly [2], the algebra A CS provides a deformation quantization of the algebra of functions on the moduli space along the natural Poisson bracket induced by the Chern Simons action. We evaluate a volume of the quantized moduli space and prove that it coincides with the Verlinde number. This answer is also interpreted as a partition partition function of the lattice Yang-Mills theory corresponding to a quantum gauge group.

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

Guedes, Carlos; Oriti, Daniele; Raasakka, Matti

The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a generalized notion of (non-commutative) Fourier transform, different from standard harmonic analysis, has been recently developed, and found several applications, especially in the quantum gravity literature. We show that this algebra representation can be defined on the sole basis of a quantization map of the classical Poisson algebra, and identify the conditions for its existence. In particular, the corresponding non-commutative star-productmore » carried by this representation is obtained directly from the quantization map via deformation quantization. We then clarify under which conditions a unitary intertwiner between such algebra representation and the usual group representation can be constructed giving rise to the non-commutative plane waves and consequently, the non-commutative Fourier transform. The compact groups U(1) and SU(2) are considered for different choices of quantization maps, such as the symmetric and the Duflo map, and we exhibit the corresponding star-products, algebra representations, and non-commutative plane waves.« less

Learning coefficient of generalization error in Bayesian estimation and vandermonde matrix-type singularity.

PubMed

Aoyagi, Miki; Nagata, Kenji

2012-06-01

The term algebraic statistics arises from the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry (Sturmfels, 2009 ). The purpose of our study is to consider the generalization error and stochastic complexity in learning theory by using the log-canonical threshold in algebraic geometry. Such thresholds correspond to the main term of the generalization error in Bayesian estimation, which is called a learning coefficient (Watanabe, 2001a , 2001b ). The learning coefficient serves to measure the learning efficiencies in hierarchical learning models. In this letter, we consider learning coefficients for Vandermonde matrix-type singularities, by using a new approach: focusing on the generators of the ideal, which defines singularities. We give tight new bound values of learning coefficients for the Vandermonde matrix-type singularities and the explicit values with certain conditions. By applying our results, we can show the learning coefficients of three-layered neural networks and normal mixture models.

Equations of motion for a spectrum-generating algebra: Lipkin Meshkov Glick model

NASA Astrophysics Data System (ADS)

Rosensteel, G.; Rowe, D. J.; Ho, S. Y.

2008-01-01

For a spectrum-generating Lie algebra, a generalized equations-of-motion scheme determines numerical values of excitation energies and algebra matrix elements. In the approach to the infinite particle number limit or, more generally, whenever the dimension of the quantum state space is very large, the equations-of-motion method may achieve results that are impractical to obtain by diagonalization of the Hamiltonian matrix. To test the method's effectiveness, we apply it to the well-known Lipkin-Meshkov-Glick (LMG) model to find its low-energy spectrum and associated generator matrix elements in the eigenenergy basis. When the dimension of the LMG representation space is 106, computation time on a notebook computer is a few minutes. For a large particle number in the LMG model, the low-energy spectrum makes a quantum phase transition from a nondegenerate harmonic vibrator to a twofold degenerate harmonic oscillator. The equations-of-motion method computes critical exponents at the transition point.

Special issue on cluster algebras in mathematical physics

NASA Astrophysics Data System (ADS)

Di Francesco, Philippe; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

2014-02-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics. Editorial policy The Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki. The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutations cluster structure on Poisson varieties cluster algebras and soliton interactions cluster positivity conjecture Y-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjecture T-system of transfer matrices of integrable lattice models dilogarithm identities in conformal field theory wall crossing in 4d N = 2 supersymmetric gauge theories 4d N = 1 quiver gauge theories described by networks scattering amplitudes of 4d N = 4 theories 3d N = 2 gauge theories described by flat connections on 3-manifolds integrability of dimer/Ising models on graphs. All contributions will be refereed and processed according to the usual procedure of the journal. Guidelines for preparation of contributions The deadline for contributed papers is 31 March 2014. This deadline will allow the special issue to appear at the end of 2014. There is no strict regulation on article size, but as a guide the preferable size is 15-30 pages for contributed papers and 40-60 pages for reviews. Further advice on publishing your work in Journal of Physics A may be found at iopscience.iop.org/jphysa. Contributions to the special issue should be submitted by web upload via ScholarOne Manuscripts, quoting 'JPhysA special issue on cluster algebras in mathematical physics'. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. The special issue will be published in the print and online versions of the journal.

Special issue on cluster algebras in mathematical physics

NASA Astrophysics Data System (ADS)

Di Francesco, Philippe; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

2013-12-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics. Editorial policy The Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki. The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutations cluster structure on Poisson varieties cluster algebras and soliton interactions cluster positivity conjecture Y-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjecture T-system of transfer matrices of integrable lattice models dilogarithm identities in conformal field theory wall crossing in 4d N = 2 supersymmetric gauge theories 4d N = 1 quiver gauge theories described by networks scattering amplitudes of 4d N = 4 theories 3d N = 2 gauge theories described by flat connections on 3-manifolds integrability of dimer/Ising models on graphs. All contributions will be refereed and processed according to the usual procedure of the journal. Guidelines for preparation of contributions The deadline for contributed papers is 31 March 2014. This deadline will allow the special issue to appear at the end of 2014. There is no strict regulation on article size, but as a guide the preferable size is 15-30 pages for contributed papers and 40-60 pages for reviews. Further advice on publishing your work in Journal of Physics A may be found at iopscience.iop.org/jphysa. Contributions to the special issue should be submitted by web upload via ScholarOne Manuscripts, quoting 'JPhysA special issue on cluster algebras in mathematical physics'. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. The special issue will be published in the print and online versions of the journal.

Special issue on cluster algebras in mathematical physics

NASA Astrophysics Data System (ADS)

Di Francesco, Philippe; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

2013-11-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics. Editorial policy The Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki. The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutations cluster structure on Poisson varieties cluster algebras and soliton interactions cluster positivity conjecture Y-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjecture T-system of transfer matrices of integrable lattice models dilogarithm identities in conformal field theory wall crossing in 4d N = 2 supersymmetric gauge theories 4d N = 1 quiver gauge theories described by networks scattering amplitudes of 4d N = 4 theories 3d N = 2 gauge theories described by flat connections on 3-manifolds integrability of dimer/Ising models on graphs. All contributions will be refereed and processed according to the usual procedure of the journal. Guidelines for preparation of contributions The deadline for contributed papers is 31 March 2014. This deadline will allow the special issue to appear at the end of 2014. There is no strict regulation on article size, but as a guide the preferable size is 15-30 pages for contributed papers and 40-60 pages for reviews. Further advice on publishing your work in Journal of Physics A may be found at iopscience.iop.org/jphysa. Contributions to the special issue should be submitted by web upload via ScholarOne Manuscripts, quoting 'JPhysA special issue on cluster algebras in mathematical physics'. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. The special issue will be published in the print and online versions of the journal.

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

PubMed

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

2012-04-01

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

Continuum analogues of contragredient Lie algebras (Lie algebras with a Cartan operator and nonlinear dynamical systems)

NASA Astrophysics Data System (ADS)

Saveliev, M. V.; Vershik, A. M.

1989-12-01

We present an axiomatic formulation of a new class of infinitedimensional Lie algebras-the generalizations of Z-graded Lie algebras with, generally speaking, an infinite-dimensional Cartan subalgebra and a contiguous set of roots. We call such algebras “continuum Lie algebras.” The simple Lie algebras of constant growth are encapsulated in our formulation. We pay particular attention to the case when the local algebra is parametrized by a commutative algebra while the Cartan operator (the generalization of the Cartan matrix) is a linear operator. Special examples of these algebras are the Kac-Moody algebras, algebras of Poisson brackets, algebras of vector fields on a manifold, current algebras, and algebras with differential or integro-differential cartan operator. The nonlinear dynamical systems associated with the continuum contragredient Lie algebras are also considered.

An advanced environment for hybrid modeling of biological systems based on modelica.

PubMed

Pross, Sabrina; Bachmann, Bernhard

2011-01-20

Biological systems are often very complex so that an appropriate formalism is needed for modeling their behavior. Hybrid Petri Nets, consisting of time-discrete Petri Net elements as well as continuous ones, have proven to be ideal for this task. Therefore, a new Petri Net library was implemented based on the object-oriented modeling language Modelica which allows the modeling of discrete, stochastic and continuous Petri Net elements by differential, algebraic and discrete equations. An appropriate Modelica-tool performs the hybrid simulation with discrete events and the solution of continuous differential equations. A special sub-library contains so-called wrappers for specific reactions to simplify the modeling process. The Modelica-models can be connected to Simulink-models for parameter optimization, sensitivity analysis and stochastic simulation in Matlab. The present paper illustrates the implementation of the Petri Net component models, their usage within the modeling process and the coupling between the Modelica-tool Dymola and Matlab/Simulink. The application is demonstrated by modeling the metabolism of Chinese Hamster Ovary Cells.

Metrics for Labeled Markov Systems

NASA Technical Reports Server (NTRS)

Desharnais, Josee; Jagadeesan, Radha; Gupta, Vineet; Panangaden, Prakash

1999-01-01

Partial Labeled Markov Chains are simultaneously generalizations of process algebra and of traditional Markov chains. They provide a foundation for interacting discrete probabilistic systems, the interaction being synchronization on labels as in process algebra. Existing notions of process equivalence are too sensitive to the exact probabilities of various transitions. This paper addresses contextual reasoning principles for reasoning about more robust notions of "approximate" equivalence between concurrent interacting probabilistic systems. The present results indicate that:We develop a family of metrics between partial labeled Markov chains to formalize the notion of distance between processes. We show that processes at distance zero are bisimilar. We describe a decision procedure to compute the distance between two processes. We show that reasoning about approximate equivalence can be done compositionally by showing that process combinators do not increase distance. We introduce an asymptotic metric to capture asymptotic properties of Markov chains; and show that parallel composition does not increase asymptotic distance.

Artificial Neural Networks: an overview and their use in the analysis of the AMPHORA-3 dataset.

PubMed

Buscema, Paolo Massimo; Massini, Giulia; Maurelli, Guido

2014-10-01

The Artificial Adaptive Systems (AAS) are theories with which generative algebras are able to create artificial models simulating natural phenomenon. Artificial Neural Networks (ANNs) are the more diffused and best-known learning system models in the AAS. This article describes an overview of ANNs, noting its advantages and limitations for analyzing dynamic, complex, non-linear, multidimensional processes. An example of a specific ANN application to alcohol consumption in Spain, as part of the EU AMPHORA-3 project, during 1961-2006 is presented. Study's limitations are noted and future needed research using ANN methodologies are suggested.

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.

Exact analysis of the spectral properties of the anisotropic two-bosons Rabi model

NASA Astrophysics Data System (ADS)

Cui, Shuai; Cao, Jun-Peng; Fan, Heng; Amico, Luigi

2017-05-01

We introduce the anisotropic two-photon Rabi model in which the rotating and counter rotating terms enters the Hamiltonian with two different coupling constants. Eigenvalues and eigenvectors are studied with exact means. We employ a variation of the Braak method based on Bogolubov rotation of the underlying su(1, 1) Lie algebra. Accordingly, the spectrum is provided by the analytical properties of a suitable meromorphic function. Our formalism applies to the two-modes Rabi model as well, sharing the same algebraic structure of the two-photon model. Through the analysis of the spectrum, we discover that the model displays close analogies to many-body systems undergoing quantum phase transitions.

The oscillator model for the Lie superalgebra sh(2|2) and Charlier polynomials

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

Jafarov, E. I.; Van der Jeugt, J.

2013-10-15

We investigate an algebraic model for the quantum oscillator based upon the Lie superalgebra sh(2|2), known as the Heisenberg–Weyl superalgebra or “the algebra of supersymmetric quantum mechanics,” and its Fock representation. The model offers some freedom in the choice of a position and a momentum operator, leading to a free model parameter γ. Using the technique of Jacobi matrices, we determine the spectrum of the position operator, and show that its wavefunctions are related to Charlier polynomials C{sub n} with parameter γ{sup 2}. Some properties of these wavefunctions are discussed, as well as some other properties of the current oscillatormore » model.« less

A Systematic Approach to Determining the Identifiability of Multistage Carcinogenesis Models.

PubMed

Brouwer, Andrew F; Meza, Rafael; Eisenberg, Marisa C

2017-07-01

Multistage clonal expansion (MSCE) models of carcinogenesis are continuous-time Markov process models often used to relate cancer incidence to biological mechanism. Identifiability analysis determines what model parameter combinations can, theoretically, be estimated from given data. We use a systematic approach, based on differential algebra methods traditionally used for deterministic ordinary differential equation (ODE) models, to determine identifiable combinations for a generalized subclass of MSCE models with any number of preinitation stages and one clonal expansion. Additionally, we determine the identifiable combinations of the generalized MSCE model with up to four clonal expansion stages, and conjecture the results for any number of clonal expansion stages. The results improve upon previous work in a number of ways and provide a framework to find the identifiable combinations for further variations on the MSCE models. Finally, our approach, which takes advantage of the Kolmogorov backward equations for the probability generating functions of the Markov process, demonstrates that identifiability methods used in engineering and mathematics for systems of ODEs can be applied to continuous-time Markov processes. © 2016 Society for Risk Analysis.

Phylogenetic mixtures and linear invariants for equal input models.

PubMed

Casanellas, Marta; Steel, Mike

2017-04-01

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

A plant-wide aqueous phase chemistry module describing pH variations and ion speciation/pairing in wastewater treatment process models.

PubMed

Flores-Alsina, Xavier; Kazadi Mbamba, Christian; Solon, Kimberly; Vrecko, Darko; Tait, Stephan; Batstone, Damien J; Jeppsson, Ulf; Gernaey, Krist V

2015-11-15

There is a growing interest within the Wastewater Treatment Plant (WWTP) modelling community to correctly describe physico-chemical processes after many years of mainly focusing on biokinetics. Indeed, future modelling needs, such as a plant-wide phosphorus (P) description, require a major, but unavoidable, additional degree of complexity when representing cationic/anionic behaviour in Activated Sludge (AS)/Anaerobic Digestion (AD) systems. In this paper, a plant-wide aqueous phase chemistry module describing pH variations plus ion speciation/pairing is presented and interfaced with industry standard models. The module accounts for extensive consideration of non-ideality, including ion activities instead of molar concentrations and complex ion pairing. The general equilibria are formulated as a set of Differential Algebraic Equations (DAEs) instead of Ordinary Differential Equations (ODEs) in order to reduce the overall stiffness of the system, thereby enhancing simulation speed. Additionally, a multi-dimensional version of the Newton-Raphson algorithm is applied to handle the existing multiple algebraic inter-dependencies. The latter is reinforced with the Simulated Annealing method to increase the robustness of the solver making the system not so dependent of the initial conditions. Simulation results show pH predictions when describing Biological Nutrient Removal (BNR) by the activated sludge models (ASM) 1, 2d and 3 comparing the performance of a nitrogen removal (WWTP1) and a combined nitrogen and phosphorus removal (WWTP2) treatment plant configuration under different anaerobic/anoxic/aerobic conditions. The same framework is implemented in the Benchmark Simulation Model No. 2 (BSM2) version of the Anaerobic Digestion Model No. 1 (ADM1) (WWTP3) as well, predicting pH values at different cationic/anionic loads. In this way, the general applicability/flexibility of the proposed approach is demonstrated, by implementing the aqueous phase chemistry module in some of the most frequently used WWTP process simulation models. Finally, it is shown how traditional wastewater modelling studies can be complemented with a rigorous description of aqueous phase and ion chemistry (pH, speciation, complexation). Copyright © 2015 Elsevier Ltd. All rights reserved.

Anomaly cancellation for super- W -gravity

NASA Astrophysics Data System (ADS)

Mansfield, P.; Spence, B.

1991-08-01

We generalise the description of minimal superconformal models coupled to supergravity, due to Distler, Hlousek and Kawaii, to super- W -gravity. When the chiral algebra is the generalisation of the W-algebra associated to any contragredient Lie superalgebra the total central charge vanishes as a result of Lie superalgebra identities. When the algebra has only fermionic simple roots there is N = 1 superconformal invariance and for this case we describe the Lax operators and construct gravitationally dressed primary superfields of weight zero. We also prove the anomaly cancellation associated with the generalised non-abelian Toda theories. Address from 1 October 1991: Physics Department, Imperial College, London SW7 2BZ, UK.

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

PubMed

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

2009-07-02

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

Comparison of Turbulent Thermal Diffusivity and Scalar Variance Models

NASA Technical Reports Server (NTRS)

Yoder, Dennis A.

2016-01-01

In this study, several variable turbulent Prandtl number formulations are examined for boundary layers, pipe flow, and axisymmetric jets. The model formulations include simple algebraic relations between the thermal diffusivity and turbulent viscosity as well as more complex models that solve transport equations for the thermal variance and its dissipation rate. Results are compared with available data for wall heat transfer and profile measurements of mean temperature, the root-mean-square (RMS) fluctuating temperature, turbulent heat flux and turbulent Prandtl number. For wall-bounded problems, the algebraic models are found to best predict the rise in turbulent Prandtl number near the wall as well as the log-layer temperature profile, while the thermal variance models provide a good representation of the RMS temperature fluctuations. In jet flows, the algebraic models provide no benefit over a constant turbulent Prandtl number approach. Application of the thermal variance models finds that some significantly overpredict the temperature variance in the plume and most underpredict the thermal growth rate of the jet. The models yield very similar fluctuating temperature intensities in jets from straight pipes and smooth contraction nozzles, in contrast to data that indicate the latter should have noticeably higher values. For the particular low subsonic heated jet cases examined, changes in the turbulent Prandtl number had no effect on the centerline velocity decay.

A New Biogeochemical Computational Framework Integrated within the Community Land Model

NASA Astrophysics Data System (ADS)

Fang, Y.; Li, H.; Liu, C.; Huang, M.; Leung, L.

2012-12-01

Terrestrial biogeochemical processes, particularly carbon cycle dynamics, have been shown to significantly influence regional and global climate changes. Modeling terrestrial biogeochemical processes within the land component of Earth System Models such as the Community Land model (CLM), however, faces three major challenges: 1) extensive efforts in modifying modeling structures and rewriting computer programs to incorporate biogeochemical processes with increasing complexity, 2) expensive computational cost to solve the governing equations due to numerical stiffness inherited from large variations in the rates of biogeochemical processes, and 3) lack of an efficient framework to systematically evaluate various mathematical representations of biogeochemical processes. To address these challenges, we introduce a new computational framework to incorporate biogeochemical processes into CLM, which consists of a new biogeochemical module with a generic algorithm and reaction database. New and updated biogeochemical processes can be incorporated into CLM without significant code modification. To address the stiffness issue, algorithms and criteria will be developed to identify fast processes, which will be replaced with algebraic equations and decoupled from slow processes. This framework can serve as a generic and user-friendly platform to test out different mechanistic process representations and datasets and gain new insight on the behavior of the terrestrial ecosystems in response to climate change in a systematic way.

The Effects of Computer Algebra System on Undergraduate Students' Spatial Visualization Skills in a Calculus Course

ERIC Educational Resources Information Center

Karakus, Fatih; Aydin, Bünyamin

2017-01-01

This study aimed at determining the effects of using a computer algebra system (CAS) on undergraduate students' spatial visualization skills in a calculus course. This study used an experimental design. The "one group pretest-posttest design" was the research model. The participants were 41 sophomore students (26 female and 15 male)…

A Symbolic Dance: The Interplay between Movement, Notation, and Mathematics on a Journey toward Solving Equations

ERIC Educational Resources Information Center

Hewitt, Dave

2014-01-01

This article analyzes the use of the software Grid Algebra with a mixed ability class of 21 nine-to-ten-year-old students who worked with complex formal notation involving all four arithmetic operations. Unlike many other models to support learning, Grid Algebra has formal notation ever present and allows students to "look through" that…

The Contributions of Working Memory and Executive Functioning to Problem Representation and Solution Generation in Algebraic Word Problems

ERIC Educational Resources Information Center

Lee, Kerry; Ng, Ee Lynn; Ng, Swee Fong

2009-01-01

Solving algebraic word problems involves multiple cognitive phases. The authors used a multitask approach to examine the extent to which working memory and executive functioning are associated with generating problem models and producing solutions. They tested 255 11-year-olds on working memory (Counting Recall, Letter Memory, and Keep Track),…

Solving a System of Nonlinear Algebraic Equations You Only Get Error Messages--What to Do Next?

ERIC Educational Resources Information Center

Shacham, Mordechai; Brauner, Neima

2017-01-01

Chemical engineering problems often involve the solution of systems of nonlinear algebraic equations (NLE). There are several software packages that can be used for solving NLE systems, but they may occasionally fail, especially in cases where the mathematical model contains discontinuities and/or regions where some of the functions are undefined.…

The Automation of Stochastization Algorithm with Use of SymPy Computer Algebra Library

NASA Astrophysics Data System (ADS)

Demidova, Anastasya; Gevorkyan, Migran; Kulyabov, Dmitry; Korolkova, Anna; Sevastianov, Leonid

2018-02-01

SymPy computer algebra library is used for automatic generation of ordinary and stochastic systems of differential equations from the schemes of kinetic interaction. Schemes of this type are used not only in chemical kinetics but also in biological, ecological and technical models. This paper describes the automatic generation algorithm with an emphasis on application details.

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.

ALGEBRA: ALgorithm for the heterogeneous dosimetry based on GEANT4 for BRAchytherapy.

PubMed

Afsharpour, H; Landry, G; D'Amours, M; Enger, S; Reniers, B; Poon, E; Carrier, J-F; Verhaegen, F; Beaulieu, L

2012-06-07

Task group 43 (TG43)-based dosimetry algorithms are efficient for brachytherapy dose calculation in water. However, human tissues have chemical compositions and densities different than water. Moreover, the mutual shielding effect of seeds on each other (interseed attenuation) is neglected in the TG43-based dosimetry platforms. The scientific community has expressed the need for an accurate dosimetry platform in brachytherapy. The purpose of this paper is to present ALGEBRA, a Monte Carlo platform for dosimetry in brachytherapy which is sufficiently fast and accurate for clinical and research purposes. ALGEBRA is based on the GEANT4 Monte Carlo code and is capable of handling the DICOM RT standard to recreate a virtual model of the treated site. Here, the performance of ALGEBRA is presented for the special case of LDR brachytherapy in permanent prostate and breast seed implants. However, the algorithm is also capable of handling other treatments such as HDR brachytherapy.

Strategies Toward Automation of Overset Structured Surface Grid Generation

NASA Technical Reports Server (NTRS)

Chan, William M.

2017-01-01

An outline of a strategy for automation of overset structured surface grid generation on complex geometries is described. The starting point of the process consists of an unstructured surface triangulation representation of the geometry derived from a native CAD, STEP, or IGES definition, and a set of discretized surface curves that captures all geometric features of interest. The procedure for surface grid generation is decomposed into an algebraic meshing step, a hyperbolic meshing step, and a gap-filling step. This paper will focus primarily on the high-level plan with details on the algebraic step. The algorithmic procedure for the algebraic step involves analyzing the topology of the network of surface curves, distributing grid points appropriately on these curves, identifying domains bounded by four curves that can be meshed algebraically, concatenating the resulting grids into fewer patches, and extending appropriate boundaries of the concatenated grids to provide proper overlap. Results are presented for grids created on various aerospace vehicle components.

Iterants, Fermions and Majorana Operators

NASA Astrophysics Data System (ADS)

Kauffman, Louis H.

Beginning with an elementary, oscillatory discrete dynamical system associated with the square root of minus one, we study both the foundations of mathematics and physics. Position and momentum do not commute in our discrete physics. Their commutator is related to the diffusion constant for a Brownian process and to the Heisenberg commutator in quantum mechanics. We take John Wheeler's idea of It from Bit as an essential clue and we rework the structure of that bit to a logical particle that is its own anti-particle, a logical Marjorana particle. This is our key example of the amphibian nature of mathematics and the external world. We show how the dynamical system for the square root of minus one is essentially the dynamics of a distinction whose self-reference leads to both the fusion algebra and the operator algebra for the Majorana Fermion. In the course of this, we develop an iterant algebra that supports all of matrix algebra and we end the essay with a discussion of the Dirac equation based on these principles.

Many-core graph analytics using accelerated sparse linear algebra routines

NASA Astrophysics Data System (ADS)

Kozacik, Stephen; Paolini, Aaron L.; Fox, Paul; Kelmelis, Eric

2016-05-01

Graph analytics is a key component in identifying emerging trends and threats in many real-world applications. Largescale graph analytics frameworks provide a convenient and highly-scalable platform for developing algorithms to analyze large datasets. Although conceptually scalable, these techniques exhibit poor performance on modern computational hardware. Another model of graph computation has emerged that promises improved performance and scalability by using abstract linear algebra operations as the basis for graph analysis as laid out by the GraphBLAS standard. By using sparse linear algebra as the basis, existing highly efficient algorithms can be adapted to perform computations on the graph. This approach, however, is often less intuitive to graph analytics experts, who are accustomed to vertex-centric APIs such as Giraph, GraphX, and Tinkerpop. We are developing an implementation of the high-level operations supported by these APIs in terms of linear algebra operations. This implementation is be backed by many-core implementations of the fundamental GraphBLAS operations required, and offers the advantages of both the intuitive programming model of a vertex-centric API and the performance of a sparse linear algebra implementation. This technology can reduce the number of nodes required, as well as the run-time for a graph analysis problem, enabling customers to perform more complex analysis with less hardware at lower cost. All of this can be accomplished without the requirement for the customer to make any changes to their analytics code, thanks to the compatibility with existing graph APIs.

Data-Driven Process Discovery: A Discrete Time Algebra for Relational Signal Analysis

DTIC Science & Technology

1996-12-01

would also like to thank Dr. Mark Oxley for his assistance in developing this abstract algebra and the mathematical notation found herein. Lastly, I... Mathematical Result.. 4-13 4.4. Demostration of Coefficient Signature Additon ........................ 4-14 4.5. Multivariate Relational Discovery...spaces with the recognition of cues in a specific space" [21]. Up to now, most of the Artificial Intelligence (Al) ’discovery’ work has emphasized one

A Comparison of Solver Performance for Complex Gastric Electrophysiology Models

PubMed Central

Sathar, Shameer; Cheng, Leo K.; Trew, Mark L.

2016-01-01

Computational techniques for solving systems of equations arising in gastric electrophysiology have not been studied for efficient solution process. We present a computationally challenging problem of simulating gastric electrophysiology in anatomically realistic stomach geometries with multiple intracellular and extracellular domains. The multiscale nature of the problem and mesh resolution required to capture geometric and functional features necessitates efficient solution methods if the problem is to be tractable. In this study, we investigated and compared several parallel preconditioners for the linear systems arising from tetrahedral discretisation of electrically isotropic and anisotropic problems, with and without stimuli. The results showed that the isotropic problem was computationally less challenging than the anisotropic problem and that the application of extracellular stimuli increased workload considerably. Preconditioning based on block Jacobi and algebraic multigrid solvers were found to have the best overall solution times and least iteration counts, respectively. The algebraic multigrid preconditioner would be expected to perform better on large problems. PMID:26736543

High-Fidelity Microstructural Characterization and Performance Modeling of Aluminized Composite Propellant

DOE PAGES

Kosiba, Graham D.; Wixom, Ryan R.; Oehlschlaeger, Matthew A.

2017-10-27

Image processing and stereological techniques were used to characterize the heterogeneity of composite propellant and inform a predictive burn rate model. Composite propellant samples made up of ammonium perchlorate (AP), hydroxyl-terminated polybutadiene (HTPB), and aluminum (Al) were faced with an ion mill and imaged with a scanning electron microscope (SEM) and x-ray tomography (micro-CT). Properties of both the bulk and individual components of the composite propellant were determined from a variety of image processing tools. An algebraic model, based on the improved Beckstead-Derr-Price model developed by Cohen and Strand, was used to predict the steady-state burning of the aluminized compositemore » propellant. In the presented model the presence of aluminum particles within the propellant was introduced. The thermal effects of aluminum particles are accounted for at the solid-gas propellant surface interface and aluminum combustion is considered in the gas phase using a single global reaction. In conclusion, properties derived from image processing were used directly as model inputs, leading to a sample-specific predictive combustion model.« less

High-Fidelity Microstructural Characterization and Performance Modeling of Aluminized Composite Propellant

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

Kosiba, Graham D.; Wixom, Ryan R.; Oehlschlaeger, Matthew A.

Image processing and stereological techniques were used to characterize the heterogeneity of composite propellant and inform a predictive burn rate model. Composite propellant samples made up of ammonium perchlorate (AP), hydroxyl-terminated polybutadiene (HTPB), and aluminum (Al) were faced with an ion mill and imaged with a scanning electron microscope (SEM) and x-ray tomography (micro-CT). Properties of both the bulk and individual components of the composite propellant were determined from a variety of image processing tools. An algebraic model, based on the improved Beckstead-Derr-Price model developed by Cohen and Strand, was used to predict the steady-state burning of the aluminized compositemore » propellant. In the presented model the presence of aluminum particles within the propellant was introduced. The thermal effects of aluminum particles are accounted for at the solid-gas propellant surface interface and aluminum combustion is considered in the gas phase using a single global reaction. In conclusion, properties derived from image processing were used directly as model inputs, leading to a sample-specific predictive combustion model.« less

On Finding and Using Identifiable Parameter Combinations in Nonlinear Dynamic Systems Biology Models and COMBOS: A Novel Web Implementation

PubMed Central

DiStefano, Joseph

2014-01-01

Parameter identifiability problems can plague biomodelers when they reach the quantification stage of development, even for relatively simple models. Structural identifiability (SI) is the primary question, usually understood as knowing which of P unknown biomodel parameters p 1,…, pi,…, pP are-and which are not-quantifiable in principle from particular input-output (I-O) biodata. It is not widely appreciated that the same database also can provide quantitative information about the structurally unidentifiable (not quantifiable) subset, in the form of explicit algebraic relationships among unidentifiable pi. Importantly, this is a first step toward finding what else is needed to quantify particular unidentifiable parameters of interest from new I–O experiments. We further develop, implement and exemplify novel algorithms that address and solve the SI problem for a practical class of ordinary differential equation (ODE) systems biology models, as a user-friendly and universally-accessible web application (app)–COMBOS. Users provide the structural ODE and output measurement models in one of two standard forms to a remote server via their web browser. COMBOS provides a list of uniquely and non-uniquely SI model parameters, and–importantly-the combinations of parameters not individually SI. If non-uniquely SI, it also provides the maximum number of different solutions, with important practical implications. The behind-the-scenes symbolic differential algebra algorithms are based on computing Gröbner bases of model attributes established after some algebraic transformations, using the computer-algebra system Maxima. COMBOS was developed for facile instructional and research use as well as modeling. We use it in the classroom to illustrate SI analysis; and have simplified complex models of tumor suppressor p53 and hormone regulation, based on explicit computation of parameter combinations. It’s illustrated and validated here for models of moderate complexity, with and without initial conditions. Built-in examples include unidentifiable 2 to 4-compartment and HIV dynamics models. PMID:25350289

Computational Science in Armenia (Invited Talk)

NASA Astrophysics Data System (ADS)

Marandjian, H.; Shoukourian, Yu.

This survey is devoted to the development of informatics and computer science in Armenia. The results in theoretical computer science (algebraic models, solutions to systems of general form recursive equations, the methods of coding theory, pattern recognition and image processing), constitute the theoretical basis for developing problem-solving-oriented environments. As examples can be mentioned: a synthesizer of optimized distributed recursive programs, software tools for cluster-oriented implementations of two-dimensional cellular automata, a grid-aware web interface with advanced service trading for linear algebra calculations. In the direction of solving scientific problems that require high-performance computing resources, examples of completed projects include the field of physics (parallel computing of complex quantum systems), astrophysics (Armenian virtual laboratory), biology (molecular dynamics study of human red blood cell membrane), meteorology (implementing and evaluating the Weather Research and Forecast Model for the territory of Armenia). The overview also notes that the Institute for Informatics and Automation Problems of the National Academy of Sciences of Armenia has established a scientific and educational infrastructure, uniting computing clusters of scientific and educational institutions of the country and provides the scientific community with access to local and international computational resources, that is a strong support for computational science in Armenia.

GENERAL A Hierarchy of Compatibility and Comeasurability Levels in Quantum Logics with Unique Conditional Probabilities

NASA Astrophysics Data System (ADS)

Gerd, Niestegge

2010-12-01

In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lüders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are: the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic (events) belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.

Nonparametric estimates of drift and diffusion profiles via Fokker-Planck algebra.

PubMed

Lund, Steven P; Hubbard, Joseph B; Halter, Michael

2014-11-06

Diffusion processes superimposed upon deterministic motion play a key role in understanding and controlling the transport of matter, energy, momentum, and even information in physics, chemistry, material science, biology, and communications technology. Given functions defining these random and deterministic components, the Fokker-Planck (FP) equation is often used to model these diffusive systems. Many methods exist for estimating the drift and diffusion profiles from one or more identifiable diffusive trajectories; however, when many identical entities diffuse simultaneously, it may not be possible to identify individual trajectories. Here we present a method capable of simultaneously providing nonparametric estimates for both drift and diffusion profiles from evolving density profiles, requiring only the validity of Langevin/FP dynamics. This algebraic FP manipulation provides a flexible and robust framework for estimating stationary drift and diffusion coefficient profiles, is not based on fluctuation theory or solved diffusion equations, and may facilitate predictions for many experimental systems. We illustrate this approach on experimental data obtained from a model lipid bilayer system exhibiting free diffusion and electric field induced drift. The wide range over which this approach provides accurate estimates for drift and diffusion profiles is demonstrated through simulation.

An algebra-based method for inferring gene regulatory networks.

PubMed

Vera-Licona, Paola; Jarrah, Abdul; Garcia-Puente, Luis David; McGee, John; Laubenbacher, Reinhard

2014-03-26

The inference of gene regulatory networks (GRNs) from experimental observations is at the heart of systems biology. This includes the inference of both the network topology and its dynamics. While there are many algorithms available to infer the network topology from experimental data, less emphasis has been placed on methods that infer network dynamics. Furthermore, since the network inference problem is typically underdetermined, it is essential to have the option of incorporating into the inference process, prior knowledge about the network, along with an effective description of the search space of dynamic models. Finally, it is also important to have an understanding of how a given inference method is affected by experimental and other noise in the data used. This paper contains a novel inference algorithm using the algebraic framework of Boolean polynomial dynamical systems (BPDS), meeting all these requirements. The algorithm takes as input time series data, including those from network perturbations, such as knock-out mutant strains and RNAi experiments. It allows for the incorporation of prior biological knowledge while being robust to significant levels of noise in the data used for inference. It uses an evolutionary algorithm for local optimization with an encoding of the mathematical models as BPDS. The BPDS framework allows an effective representation of the search space for algebraic dynamic models that improves computational performance. The algorithm is validated with both simulated and experimental microarray expression profile data. Robustness to noise is tested using a published mathematical model of the segment polarity gene network in Drosophila melanogaster. Benchmarking of the algorithm is done by comparison with a spectrum of state-of-the-art network inference methods on data from the synthetic IRMA network to demonstrate that our method has good precision and recall for the network reconstruction task, while also predicting several of the dynamic patterns present in the network. Boolean polynomial dynamical systems provide a powerful modeling framework for the reverse engineering of gene regulatory networks, that enables a rich mathematical structure on the model search space. A C++ implementation of the method, distributed under LPGL license, is available, together with the source code, at http://www.paola-vera-licona.net/Software/EARevEng/REACT.html.

An evolutionary morphological approach for software development cost estimation.

PubMed

Araújo, Ricardo de A; Oliveira, Adriano L I; Soares, Sergio; Meira, Silvio

2012-08-01

In this work we present an evolutionary morphological approach to solve the software development cost estimation (SDCE) problem. The proposed approach consists of a hybrid artificial neuron based on framework of mathematical morphology (MM) with algebraic foundations in the complete lattice theory (CLT), referred to as dilation-erosion perceptron (DEP). Also, we present an evolutionary learning process, called DEP(MGA), using a modified genetic algorithm (MGA) to design the DEP model, because a drawback arises from the gradient estimation of morphological operators in the classical learning process of the DEP, since they are not differentiable in the usual way. Furthermore, an experimental analysis is conducted with the proposed model using five complex SDCE problems and three well-known performance metrics, demonstrating good performance of the DEP model to solve SDCE problems. Copyright © 2012 Elsevier Ltd. All rights reserved.

Sensor fault detection and isolation system for a condensation process.

PubMed

Castro, M A López; Escobar, R F; Torres, L; Aguilar, J F Gómez; Hernández, J A; Olivares-Peregrino, V H

2016-11-01

This article presents the design of a sensor Fault Detection and Isolation (FDI) system for a condensation process based on a nonlinear model. The condenser is modeled by dynamic and thermodynamic equations. For this work, the dynamic equations are described by three pairs of differential equations which represent the energy balance between the fluids. The thermodynamic equations consist in algebraic heat transfer equations and empirical equations, that allow for the estimation of heat transfer coefficients. The FDI system consists of a bank of two nonlinear high-gain observers, in order to detect, estimate and to isolate the fault in any of both outlet temperature sensors. The main contributions of this work were the experimental validation of the condenser nonlinear model and the FDI system. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Quantum decay model with exact explicit analytical solution

NASA Astrophysics Data System (ADS)

Marchewka, Avi; Granot, Er'El

2009-01-01

A simple decay model is introduced. The model comprises a point potential well, which experiences an abrupt change. Due to the temporal variation, the initial quantum state can either escape from the well or stay localized as a new bound state. The model allows for an exact analytical solution while having the necessary features of a decay process. The results show that the decay is never exponential, as classical dynamics predicts. Moreover, at short times the decay has a fractional power law, which differs from perturbation quantum method predictions. At long times the decay includes oscillations with an envelope that decays algebraically. This is a model where the final state can be either continuous or localized, and that has an exact analytical solution.

Modeling Simple Telescope Optics in Secondary Mathematics Classrooms

NASA Astrophysics Data System (ADS)

Siegel, Lauren; Dickinson, G.; Hooper, E. J.; Daniels, M.

2007-12-01

This presentation describes the results of collaboration between instructors in the UTeach teacher preparation program at the University of Texas at Austin, and an astronomer teaching at the university as part of a National Science Foundation Astronomy and Astrophysics Postdoctoral Fellowship. The astronomer provided training to give pre-service teachers an authentic understanding of the principles of telescope optics. This made it possible for the preservice teachers to include real design constraints and optical properties into lessons developed as part of a collaborative field experience to teach astronomical telescope design and construction to high school Algebra II students. One result is a sequence of investigations designed to explore how and why the physical and mathematical properties of parabolic mirrors both enable and constrain our ability to build and use telescopes to focus light from distant objects. Various approaches, including generating and exploring computer models, traditional proofs, even making paper models, are all woven together into a coherent set of eleven investigations for use in mathematics and science classrooms. The presentation will include a description of the suite of investigations, as well as a discussion of the collaborative process which generated the work and resulted in an article submission to a preeminent teaching journal. Teaching Algebra and Geometry Concepts by Modeling Telescope Optics, 2008, Mathematics Teacher is currently in press. Many thanks to the University of Texas UTeach Program for sponsorship of this submission.

What is special about the group of the standard model?

NASA Astrophysics Data System (ADS)

Nielsen, H. B.; Brene, N.

1989-06-01

The standard model is based on the algebra of U 1×SU 2×SU 3. The systematics of charges of the fundamental fermions seems to suggest the importance of a particular group having this algebra, viz. S(U 2×U 3). This group is distinguished from all other connected compact non semisimple groups with dimensionality up to 12 by a characteristic property: it is very “skew”. By this we mean that the group has relatively few “generalised outer automorphisms”. One may speculate about physical reasons for this fact.

A non-symmetric Yang-Baxter algebra for the quantum nonlinear Schrödinger model

NASA Astrophysics Data System (ADS)

Vlaar, Bart

2013-06-01

We study certain non-symmetric wavefunctions associated with the quantum nonlinear Schrödinger model, introduced by Komori and Hikami using Gutkin’s propagation operator, which involves representations of the degenerate affine Hecke algebra. We highlight how these functions can be generated using a vertex-type operator formalism similar to the recursion defining the symmetric (Bethe) wavefunction in the quantum inverse scattering method. Furthermore, some of the commutation relations encoded in the Yang-Baxter equation for the relevant monodromy matrix are generalized to the non-symmetric case.

Improved Linear Algebra Methods for Redshift Computation from Limited Spectrum Data - II

NASA Technical Reports Server (NTRS)

Foster, Leslie; Waagen, Alex; Aijaz, Nabella; Hurley, Michael; Luis, Apolo; Rinsky, Joel; Satyavolu, Chandrika; Gazis, Paul; Srivastava, Ashok; Way, Michael

2008-01-01

Given photometric broadband measurements of a galaxy, Gaussian processes may be used with a training set to solve the regression problem of approximating the redshift of this galaxy. However, in practice solving the traditional Gaussian processes equation is too slow and requires too much memory. We employed several methods to avoid this difficulty using algebraic manipulation and low-rank approximation, and were able to quickly approximate the redshifts in our testing data within 17 percent of the known true values using limited computational resources. The accuracy of one method, the V Formulation, is comparable to the accuracy of the best methods currently used for this problem.

Performance assessment in algebra learning process

NASA Astrophysics Data System (ADS)

Lestariani, Ida; Sujadi, Imam; Pramudya, Ikrar

2017-12-01

The purpose of research to describe the implementation of performance assessment on algebra learning process. The subject in this research is math educator of SMAN 1 Ngawi class X. This research includes descriptive qualitative research type. Techniques of data collecting are done by observation method, interview, and documentation. Data analysis technique is done by data reduction, data presentation, and conclusion. The results showed any indication that the steps taken by the educator in applying the performance assessment are 1) preparing individual worksheets and group worksheets, 2) preparing rubric assessments for independent worksheets and groups and 3) making performance assessments rubric to learners’ performance results with individual or groups task.

Structuring students’ analogical reasoning in solving algebra problem

NASA Astrophysics Data System (ADS)

Lailiyah, S.; Nusantara, T.; Sa'dijah, C.; Irawan, E. B.; Kusaeri; Asyhar, A. H.

2018-01-01

The average achievement of Indonesian students’ mathematics skills according to Benchmark International Trends in Mathematics and Science Study (TIMSS) is ranked at the 38th out of 42 countries and according to the survey result in Program for International Student Assessment (PISA) is ranked at the 64th out of 65 countries. The low mathematics skill of Indonesian student has become an important reason to research more deeply about reasoning and algebra in mathematics. Analogical reasoning is a very important component in mathematics because it is the key to creativity and it can make the learning process in the classroom become effective. The major part of the analogical reasoning is about structuring including the processes of inferencing and decision-making happens. Those processes involve base domain and target domain. Methodologically, the subjects of this research were 42 students from class XII. The sources of data were derived from the results of thinks aloud, the transcribed interviews, and the videos taken while the subject working on the instruments and interviews. The collected data were analyzed using qualitative techniques. The result of this study described the structuring characteristics of students’ analogical reasoning in solving algebra problems from all the research subjects.

Development of abstract mathematical reasoning: the case of algebra

PubMed Central

Susac, Ana; Bubic, Andreja; Vrbanc, Andrija; Planinic, Maja

2014-01-01

Algebra typically represents the students’ first encounter with abstract mathematical reasoning and it therefore causes significant difficulties for students who still reason concretely. The aim of the present study was to investigate the developmental trajectory of the students’ ability to solve simple algebraic equations. 311 participants between the ages of 13 and 17 were given a computerized test of equation rearrangement. Equations consisted of an unknown and two other elements (numbers or letters), and the operations of multiplication/division. The obtained results showed that younger participants are less accurate and slower in solving equations with letters (symbols) than those with numbers. This difference disappeared for older participants (16–17 years), suggesting that they had reached an abstract reasoning level, at least for this simple task. A corresponding conclusion arises from the analysis of their strategies which suggests that younger participants mostly used concrete strategies such as inserting numbers, while older participants typically used more abstract, rule-based strategies. These results indicate that the development of algebraic thinking is a process which unfolds over a long period of time. In agreement with previous research, we can conclude that, on average, children at the age of 15–16 transition from using concrete to abstract strategies while solving the algebra problems addressed within the present study. A better understanding of the timing and speed of students’ transition from concrete arithmetic reasoning to abstract algebraic reasoning might help in designing better curricula and teaching materials that would ease that transition. PMID:25228874

Development of abstract mathematical reasoning: the case of algebra.

PubMed

Susac, Ana; Bubic, Andreja; Vrbanc, Andrija; Planinic, Maja

2014-01-01

Algebra typically represents the students' first encounter with abstract mathematical reasoning and it therefore causes significant difficulties for students who still reason concretely. The aim of the present study was to investigate the developmental trajectory of the students' ability to solve simple algebraic equations. 311 participants between the ages of 13 and 17 were given a computerized test of equation rearrangement. Equations consisted of an unknown and two other elements (numbers or letters), and the operations of multiplication/division. The obtained results showed that younger participants are less accurate and slower in solving equations with letters (symbols) than those with numbers. This difference disappeared for older participants (16-17 years), suggesting that they had reached an abstract reasoning level, at least for this simple task. A corresponding conclusion arises from the analysis of their strategies which suggests that younger participants mostly used concrete strategies such as inserting numbers, while older participants typically used more abstract, rule-based strategies. These results indicate that the development of algebraic thinking is a process which unfolds over a long period of time. In agreement with previous research, we can conclude that, on average, children at the age of 15-16 transition from using concrete to abstract strategies while solving the algebra problems addressed within the present study. A better understanding of the timing and speed of students' transition from concrete arithmetic reasoning to abstract algebraic reasoning might help in designing better curricula and teaching materials that would ease that transition.

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.

Interaction in Balanced Cross Nested Designs

NASA Astrophysics Data System (ADS)

Ramos, Paulo; Mexia, João T.; Carvalho, Francisco; Covas, Ricardo

2011-09-01

Commutative Jordan Algebras, CJA, are used in the study of mixed models obtained, through crossing and nesting, from simpler ones. In the study of cross nested models the interaction between nested factors have been systematically discarded. However this can constitutes an artificial simplification of the models. We point out that, when two crossed factors interact, such interaction is symmetric, both factors playing in it equivalent roles, while when two nested factors interact, the interaction is determined by the nesting factor. These interactions will be called interactions with nesting. In this work we present a coherent formulation of the algebraic structure of models enabling the choice of families of interactions between cross and nested factors using binary operations on CJA.

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

PubMed

Yang, Xian; Han, Rui; Guo, Yike; Bradley, Jeremy; Cox, Benita; Dickinson, Robert; Kitney, Richard

2012-01-01

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

Abstract numeric relations and the visual structure of algebra.

PubMed

Landy, David; Brookes, David; Smout, Ryan

2014-09-01

Formal algebras are among the most powerful and general mechanisms for expressing quantitative relational statements; yet, even university engineering students, who are relatively proficient with algebraic manipulation, struggle with and often fail to correctly deploy basic aspects of algebraic notation (Clement, 1982). In the cognitive tradition, it has often been assumed that skilled users of these formalisms treat situations in terms of semantic properties encoded in an abstract syntax that governs the use of notation without particular regard to the details of the physical structure of the equation itself (Anderson, 2005; Hegarty, Mayer, & Monk, 1995). We explore how the notational structure of verbal descriptions or algebraic equations (e.g., the spatial proximity of certain words or the visual alignment of numbers and symbols in an equation) plays a role in the process of interpreting or constructing symbolic equations. We propose in particular that construction processes involve an alignment of notational structures across representation systems, biasing reasoners toward the selection of formal notations that maintain the visuospatial structure of source representations. For example, in the statement "There are 5 elephants for every 3 rhinoceroses," the spatial proximity of 5 and elephants and 3 and rhinoceroses will bias reasoners to write the incorrect expression 5E = 3R, because that expression maintains the spatial relationships encoded in the source representation. In 3 experiments, participants constructed equations with given structure, based on story problems with a variety of phrasings. We demonstrate how the notational alignment approach accounts naturally for a variety of previously reported phenomena in equation construction and successfully predicts error patterns that are not accounted for by prior explanations, such as the left to right transcription heuristic.

The geometric semantics of algebraic quantum mechanics.

PubMed

Cruz Morales, John Alexander; Zilber, Boris

2015-08-06

In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Integrals of motion from quantum toroidal algebras

NASA Astrophysics Data System (ADS)

Feigin, B.; Jimbo, M.; Mukhin, E.

2017-11-01

We identify the Taylor coefficients of the transfer matrices corresponding to quantum toroidal algebras with the elliptic local and non-local integrals of motion introduced by Kojima, Shiraishi, Watanabe, and one of the authors. That allows us to prove the Litvinov conjectures on the Intermediate Long Wave model. We also discuss the ({gl_m, {gl_n) duality of XXZ models in quantum toroidal setting and the implications for the quantum KdV model. In particular, we conjecture that the spectrum of non-local integrals of motion of Bazhanov, Lukyanov, and Zamolodchikov is described by Gaudin Bethe ansatz equations associated to affine {sl}2 . Dedicated to the memory of Petr Petrovich Kulish.

Resolving Phase Ambiguities in the Calibration of Redundant Interferometric Arrays: Implications for Array Design

DTIC Science & Technology

2016-03-04

summary of the linear algebra involved. As we have seen, the RSC process begins with the interferometric phase measurement β, which due to wrapping will...mentary Divisors) in Section 2 and the following defi- nition of the matrix determinant. This definition is given in many linear algebra texts (see...principle solve for a particular solution of this system by arbitrarily setting two object phases (whose spatial frequencies are not co- linear ) and one

An algebraic method for constructing stable and consistent autoregressive filters

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

Harlim, John, E-mail: jharlim@psu.edu; Department of Meteorology, the Pennsylvania State University, University Park, PA 16802; Hong, Hoon, E-mail: hong@ncsu.edu

2015-02-15

In this paper, we introduce an algebraic method to construct stable and consistent univariate autoregressive (AR) models of low order for filtering and predicting nonlinear turbulent signals with memory depth. By stable, we refer to the classical stability condition for the AR model. By consistent, we refer to the classical consistency constraints of Adams–Bashforth methods of order-two. One attractive feature of this algebraic method is that the model parameters can be obtained without directly knowing any training data set as opposed to many standard, regression-based parameterization methods. It takes only long-time average statistics as inputs. The proposed method provides amore » discretization time step interval which guarantees the existence of stable and consistent AR model and simultaneously produces the parameters for the AR models. In our numerical examples with two chaotic time series with different characteristics of decaying time scales, we find that the proposed AR models produce significantly more accurate short-term predictive skill and comparable filtering skill relative to the linear regression-based AR models. These encouraging results are robust across wide ranges of discretization times, observation times, and observation noise variances. Finally, we also find that the proposed model produces an improved short-time prediction relative to the linear regression-based AR-models in forecasting a data set that characterizes the variability of the Madden–Julian Oscillation, a dominant tropical atmospheric wave pattern.« less

Effects of sources on time-domain finite difference models.

PubMed

Botts, Jonathan; Savioja, Lauri

2014-07-01

Recent work on excitation mechanisms in acoustic finite difference models focuses primarily on physical interpretations of observed phenomena. This paper offers an alternative view by examining the properties of models from the perspectives of linear algebra and signal processing. Interpretation of a simulation as matrix exponentiation clarifies the separate roles of sources as boundaries and signals. Boundary conditions modify the matrix and thus its modal structure, and initial conditions or source signals shape the solution, but not the modal structure. Low-frequency artifacts are shown to follow from eigenvalues and eigenvectors of the matrix, and previously reported artifacts are predicted from eigenvalue estimates. The role of source signals is also briefly discussed.

On Some Nonclassical Algebraic Properties of Interval-Valued Fuzzy Soft Sets

PubMed Central

2014-01-01

Interval-valued fuzzy soft sets realize a hybrid soft computing model in a general framework. Both Molodtsov's soft sets and interval-valued fuzzy sets can be seen as special cases of interval-valued fuzzy soft sets. In this study, we first compare four different types of interval-valued fuzzy soft subsets and reveal the relations among them. Then we concentrate on investigating some nonclassical algebraic properties of interval-valued fuzzy soft sets under the soft product operations. We show that some fundamental algebraic properties including the commutative and associative laws do not hold in the conventional sense, but hold in weaker forms characterized in terms of the relation =L. We obtain a number of algebraic inequalities of interval-valued fuzzy soft sets characterized by interval-valued fuzzy soft inclusions. We also establish the weak idempotent law and the weak absorptive law of interval-valued fuzzy soft sets using interval-valued fuzzy soft J-equal relations. It is revealed that the soft product operations ∧ and ∨ of interval-valued fuzzy soft sets do not always have similar algebraic properties. Moreover, we find that only distributive inequalities described by the interval-valued fuzzy soft L-inclusions hold for interval-valued fuzzy soft sets. PMID:25143964

On some nonclassical algebraic properties of interval-valued fuzzy soft sets.

PubMed

Liu, Xiaoyan; Feng, Feng; Zhang, Hui

2014-01-01

Interval-valued fuzzy soft sets realize a hybrid soft computing model in a general framework. Both Molodtsov's soft sets and interval-valued fuzzy sets can be seen as special cases of interval-valued fuzzy soft sets. In this study, we first compare four different types of interval-valued fuzzy soft subsets and reveal the relations among them. Then we concentrate on investigating some nonclassical algebraic properties of interval-valued fuzzy soft sets under the soft product operations. We show that some fundamental algebraic properties including the commutative and associative laws do not hold in the conventional sense, but hold in weaker forms characterized in terms of the relation = L . We obtain a number of algebraic inequalities of interval-valued fuzzy soft sets characterized by interval-valued fuzzy soft inclusions. We also establish the weak idempotent law and the weak absorptive law of interval-valued fuzzy soft sets using interval-valued fuzzy soft J-equal relations. It is revealed that the soft product operations ∧ and ∨ of interval-valued fuzzy soft sets do not always have similar algebraic properties. Moreover, we find that only distributive inequalities described by the interval-valued fuzzy soft L-inclusions hold for interval-valued fuzzy soft sets.

Diagnosing students' misconceptions in algebra: results from an experimental pilot study.

PubMed

Russell, Michael; O'Dwyer, Laura M; Miranda, Helena

2009-05-01

Computer-based diagnostic assessment systems hold potential to help teachers identify sources of poor performance and to connect teachers and students to learning activities designed to help advance students' conceptual understandings. The present article presents findings from a study that examined how students' performance in algebra and their overcoming of common algebraic misconceptions were affected by the use of a diagnostic assessment system that focused on important algebra concepts. This study used a four-group randomized cluster trial design in which teachers were assigned randomly to one of four groups: a "business as usual" control group, a partial intervention group that was provided with access to diagnostic tests results, a partial intervention group that was provided with access to the learning activities, and a full intervention group that was given access to the test results and learning activities. Data were collected from 905 students (6th-12th grade) nested within 44 teachers. We used hierarchical linear modeling techniques to compare the effects of full, partial, and no (control) intervention on students' algebraic ability and misconceptions. The analyses indicate that full intervention had a net positive effect on ability and misconception measures.

Deformed quantum double realization of the toric code and beyond

NASA Astrophysics Data System (ADS)

Padmanabhan, Pramod; Ibieta-Jimenez, Juan Pablo; Bernabe Ferreira, Miguel Jorge; Teotonio-Sobrinho, Paulo

2016-09-01

Quantum double models, such as the toric code, can be constructed from transfer matrices of lattice gauge theories with discrete gauge groups and parametrized by the center of the gauge group algebra and its dual. For general choices of these parameters the transfer matrix contains operators acting on links which can also be thought of as perturbations to the quantum double model driving it out of its topological phase and destroying the exact solvability of the quantum double model. We modify these transfer matrices with perturbations and extract exactly solvable models which remain in a quantum phase, thus nullifying the effect of the perturbation. The algebra of the modified vertex and plaquette operators now obey a deformed version of the quantum double algebra. The Abelian cases are shown to be in the quantum double phase whereas the non-Abelian phases are shown to be in a modified phase of the corresponding quantum double phase. These are illustrated with the groups Zn and S3. The quantum phases are determined by studying the excitations of these systems namely their fusion rules and the statistics. We then go further to construct a transfer matrix which contains the other Z2 phase namely the double semion phase. More generally for other discrete groups these transfer matrices contain the twisted quantum double models. These transfer matrices can be thought of as being obtained by introducing extra parameters into the transfer matrix of lattice gauge theories. These parameters are central elements belonging to the tensor products of the algebra and its dual and are associated to vertices and volumes of the three dimensional lattice. As in the case of the lattice gauge theories we construct the operators creating the excitations in this case and study their braiding and fusion properties.

Development of a GNSS water vapour tomography system using algebraic reconstruction techniques

NASA Astrophysics Data System (ADS)

Bender, Michael; Dick, Galina; Ge, Maorong; Deng, Zhiguo; Wickert, Jens; Kahle, Hans-Gert; Raabe, Armin; Tetzlaff, Gerd

2011-05-01

A GNSS water vapour tomography system developed to reconstruct spatially resolved humidity fields in the troposphere is described. The tomography system was designed to process the slant path delays of about 270 German GNSS stations in near real-time with a temporal resolution of 30 min, a horizontal resolution of 40 km and a vertical resolution of 500 m or better. After a short introduction to the GPS slant delay processing the framework of the GNSS tomography is described in detail. Different implementations of the iterative algebraic reconstruction techniques (ART) used to invert the linear inverse problem are discussed. It was found that the multiplicative techniques (MART) provide the best results with least processing time, i.e., a tomographic reconstruction of about 26,000 slant delays on a 8280 cell grid can be obtained in less than 10 min. Different iterative reconstruction techniques are compared with respect to their convergence behaviour and some numerical parameters. The inversion can be considerably stabilized by using additional non-GNSS observations and implementing various constraints. Different strategies for initialising the tomography and utilizing extra information are discussed. At last an example of a reconstructed field of the wet refractivity is presented and compared to the corresponding distribution of the integrated water vapour, an analysis of a numerical weather model (COSMO-DE) and some radiosonde profiles.

Numerical algebraic geometry for model selection and its application to the life sciences

PubMed Central

Gross, Elizabeth; Davis, Brent; Ho, Kenneth L.; Bates, Daniel J.

2016-01-01

Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation and model selection. These are all optimization problems, well known to be challenging due to nonlinearity, non-convexity and multiple local optima. Furthermore, the challenges are compounded when only partial data are available. Here, we consider polynomial models (e.g. mass-action chemical reaction networks at steady state) and describe a framework for their analysis based on optimization using numerical algebraic geometry. Specifically, we use probability-one polynomial homotopy continuation methods to compute all critical points of the objective function, then filter to recover the global optima. Our approach exploits the geometrical structures relating models and data, and we demonstrate its utility on examples from cell signalling, synthetic biology and epidemiology. PMID:27733697

A framework for modeling and optimizing dynamic systems under uncertainty

DOE PAGES

Nicholson, Bethany; Siirola, John

2017-11-11

Algebraic modeling languages (AMLs) have drastically simplified the implementation of algebraic optimization problems. However, there are still many classes of optimization problems that are not easily represented in most AMLs. These classes of problems are typically reformulated before implementation, which requires significant effort and time from the modeler and obscures the original problem structure or context. In this work we demonstrate how the Pyomo AML can be used to represent complex optimization problems using high-level modeling constructs. We focus on the operation of dynamic systems under uncertainty and demonstrate the combination of Pyomo extensions for dynamic optimization and stochastic programming.more » We use a dynamic semibatch reactor model and a large-scale bubbling fluidized bed adsorber model as test cases.« less

A framework for modeling and optimizing dynamic systems under uncertainty

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

Nicholson, Bethany; Siirola, John

Algebraic modeling languages (AMLs) have drastically simplified the implementation of algebraic optimization problems. However, there are still many classes of optimization problems that are not easily represented in most AMLs. These classes of problems are typically reformulated before implementation, which requires significant effort and time from the modeler and obscures the original problem structure or context. In this work we demonstrate how the Pyomo AML can be used to represent complex optimization problems using high-level modeling constructs. We focus on the operation of dynamic systems under uncertainty and demonstrate the combination of Pyomo extensions for dynamic optimization and stochastic programming.more » We use a dynamic semibatch reactor model and a large-scale bubbling fluidized bed adsorber model as test cases.« less

An Algebra-Based Introductory Computational Neuroscience Course with Lab.

PubMed

Fink, Christian G

2017-01-01

A course in computational neuroscience has been developed at Ohio Wesleyan University which requires no previous experience with calculus or computer programming, and which exposes students to theoretical models of neural information processing and techniques for analyzing neural data. The exploration of theoretical models of neural processes is conducted in the classroom portion of the course, while data analysis techniques are covered in lab. Students learn to program in MATLAB and are offered the opportunity to conclude the course with a final project in which they explore a topic of their choice within computational neuroscience. Results from a questionnaire administered at the beginning and end of the course indicate significant gains in student facility with core concepts in computational neuroscience, as well as with analysis techniques applied to neural data.

Reactive solute transport in streams: 1. Development of an equilibrium- based model

USGS Publications Warehouse

Runkel, Robert L.; Bencala, Kenneth E.; Broshears, Robert E.; Chapra, Steven C.

1996-01-01

An equilibrium-based solute transport model is developed for the simulation of trace metal fate and transport in streams. The model is formed by coupling a solute transport model with a chemical equilibrium submodel based on MINTEQ. The solute transport model considers the physical processes of advection, dispersion, lateral inflow, and transient storage, while the equilibrium submodel considers the speciation and complexation of aqueous species, precipitation/dissolution and sorption. Within the model, reactions in the water column may result in the formation of solid phases (precipitates and sorbed species) that are subject to downstream transport and settling processes. Solid phases on the streambed may also interact with the water column through dissolution and sorption/desorption reactions. Consideration of both mobile (water-borne) and immobile (streambed) solid phases requires a unique set of governing differential equations and solution techniques that are developed herein. The partial differential equations describing physical transport and the algebraic equations describing chemical equilibria are coupled using the sequential iteration approach.

Multimedia modeling of engineered nanoparticles with SimpleBox4nano: model definition and evaluation.

PubMed

Meesters, Johannes A J; Koelmans, Albert A; Quik, Joris T K; Hendriks, A Jan; van de Meent, Dik

2014-05-20

Screening level models for environmental assessment of engineered nanoparticles (ENP) are not generally available. Here, we present SimpleBox4Nano (SB4N) as the first model of this type, assess its validity, and evaluate it by comparisons with a known material flow model. SB4N expresses ENP transport and concentrations in and across air, rain, surface waters, soil, and sediment, accounting for nanospecific processes such as aggregation, attachment, and dissolution. The model solves simultaneous mass balance equations (MBE) using simple matrix algebra. The MBEs link all concentrations and transfer processes using first-order rate constants for all processes known to be relevant for ENPs. The first-order rate constants are obtained from the literature. The output of SB4N is mass concentrations of ENPs as free dispersive species, heteroaggregates with natural colloids, and larger natural particles in each compartment in time and at steady state. Known scenario studies for Switzerland were used to demonstrate the impact of the transport processes included in SB4N on the prediction of environmental concentrations. We argue that SB4N-predicted environmental concentrations are useful as background concentrations in environmental risk assessment.

Hardware implementation of fuzzy Petri net as a controller.

PubMed

Gniewek, Lesław; Kluska, Jacek

2004-06-01

The paper presents a new approach to fuzzy Petri net (FPN) and its hardware implementation. The authors' motivation is as follows. Complex industrial processes can be often decomposed into many parallelly working subprocesses, which can, in turn, be modeled using Petri nets. If all the process variables (or events) are assumed to be two-valued signals, then it is possible to obtain a hardware or software control device, which works according to the algorithm described by conventional Petri net. However, the values of real signals are contained in some bounded interval and can be interpreted as events which are not only true or false, but rather true in some degree from the interval [0, 1]. Such a natural interpretation from multivalued logic (fuzzy logic) point of view, concerns sensor outputs, control signals, time expiration, etc. It leads to the idea of FPN as a controller, which one can rather simply obtain, and which would be able to process both analog, and binary signals. In the paper both graphical, and algebraic representations of the proposed FPN are given. The conditions under which transitions can be fired are described. The algebraic description of the net and a theorem which enables computation of new marking in the net, based on current marking, are formulated. Hardware implementation of the FPN, which uses fuzzy JK flip-flops and fuzzy gates, are proposed. An example illustrating usefulness of the proposed FPN for control algorithm description and its synthesis as a controller device for the concrete production process are presented.

Smooth function approximation using neural networks.

PubMed

Ferrari, Silvia; Stengel, Robert F

2005-01-01

An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is presented. In this paper, the approach is implemented for the approximation of smooth batch data containing the function's input, output, and possibly, gradient information. The training set is associated to the network adjustable parameters by nonlinear weight equations. The cascade structure of these equations reveals that they can be treated as sets of linear systems. Hence, the training process and the network approximation properties can be investigated via linear algebra. Four algorithms are developed to achieve exact or approximate matching of input-output and/or gradient-based training sets. Their application to the design of forward and feedback neurocontrollers shows that algebraic training is characterized by faster execution speeds and better generalization properties than contemporary optimization techniques.

A Reduced Model for the Magnetorotational Instability

NASA Astrophysics Data System (ADS)

Jamroz, Ben; Julien, Keith; Knobloch, Edgar

2008-11-01

The magnetorotational instability is investigated within the shearing box approximation in the large Elsasser number regime. In this regime, which is of fundamental importance to astrophysical accretion disk theory, shear is the dominant source of energy, but the instability itself requires the presence of a weaker vertical magnetic field. Dissipative effects are weaker still. However, they are sufficiently large to permit a nonlinear feedback mechanism whereby the turbulent stresses generated by the MRI act on and modify the local background shear in the angular velocity profile. To date this response has been omitted in shearing box simulations and is captured by a reduced pde model derived here from the global MHD fluid equations using multiscale asymptotic perturbation theory. Results from numerical simulations of the reduced pde model indicate a linear phase of exponential growth followed by a nonlinear adjustment to algebraic growth and decay in the fluctuating quantities. Remarkably, the velocity and magnetic field correlations associated with these algebraic growth and decay laws conspire to achieve saturation of the angular momentum transport. The inclusion of subdominant ohmic dissipation arrests the algebraic growth of the fluctuations on a longer, dissipative time scale.

Deformation Theory and Physics Model Building

NASA Astrophysics Data System (ADS)

Sternheimer, Daniel

2006-08-01

The mathematical theory of deformations has proved to be a powerful tool in modeling physical reality. We start with a short historical and philosophical review of the context and concentrate this rapid presentation on a few interrelated directions where deformation theory is essential in bringing a new framework - which has then to be developed using adapted tools, some of which come from the deformation aspect. Minkowskian space-time can be deformed into Anti de Sitter, where massless particles become composite (also dynamically): this opens new perspectives in particle physics, at least at the electroweak level, including prediction of new mesons. Nonlinear group representations and covariant field equations, coming from interactions, can be viewed as some deformation of their linear (free) part: recognizing this fact can provide a good framework for treating problems in this area, in particular global solutions. Last but not least, (algebras associated with) classical mechanics (and field theory) on a Poisson phase space can be deformed to (algebras associated with) quantum mechanics (and quantum field theory). That is now a frontier domain in mathematics and theoretical physics called deformation quantization, with multiple ramifications, avatars and connections in both mathematics and physics. These include representation theory, quantum groups (when considering Hopf algebras instead of associative or Lie algebras), noncommutative geometry and manifolds, algebraic geometry, number theory, and of course what is regrouped under the name of M-theory. We shall here look at these from the unifying point of view of deformation theory and refer to a limited number of papers as a starting point for further study.

Mathematical model for Dengue with three states of infection

NASA Astrophysics Data System (ADS)

Hincapie, Doracelly; Ospina, Juan

2012-06-01

A mathematical model for dengue with three states of infection is proposed and analyzed. The model consists in a system of differential equations. The three states of infection are respectively asymptomatic, partially asymptomatic and fully asymptomatic. The model is analyzed using computer algebra software, specifically Maple, and the corresponding basic reproductive number and the epidemic threshold are computed. The resulting basic reproductive number is an algebraic synthesis of all epidemic parameters and it makes clear the possible control measures. The microscopic structure of the epidemic parameters is established using the quantum theory of the interactions between the atoms and radiation. In such approximation, the human individual is represented by an atom and the mosquitoes are represented by radiation. The force of infection from the mosquitoes to the humans is considered as the transition probability from the fundamental state of atom to excited states. The combination of computer algebra software and quantum theory provides a very complete formula for the basic reproductive number and the possible control measures tending to stop the propagation of the disease. It is claimed that such result may be important in military medicine and the proposed method can be applied to other vector-borne diseases.

Sensor-based monitoring and inspection of surface morphology in ultraprecision manufacturing processes

NASA Astrophysics Data System (ADS)

Rao, Prahalad Krishna

This research proposes approaches for monitoring and inspection of surface morphology with respect to two ultraprecision/nanomanufacturing processes, namely, ultraprecision machining (UPM) and chemical mechanical planarization (CMP). The methods illustrated in this dissertation are motivated from the compelling need for in situ process monitoring in nanomanufacturing and invoke concepts from diverse scientific backgrounds, such as artificial neural networks, Bayesian learning, and algebraic graph theory. From an engineering perspective, this work has the following contributions: 1. A combined neural network and Bayesian learning approach for early detection of UPM process anomalies by integrating data from multiple heterogeneous in situ sensors (force, vibration, and acoustic emission) is developed. The approach captures process drifts in UPM of aluminum 6061 discs within 15 milliseconds of their inception and is therefore valuable for minimizing yield losses. 2. CMP process dynamics are mathematically represented using a deterministic multi-scale hierarchical nonlinear differential equation model. This process-machine inter-action (PMI) model is evocative of the various physio-mechanical aspects in CMP and closely emulates experimentally acquired vibration signal patterns, including complex nonlinear dynamics manifest in the process. By combining the PMI model predictions with features gathered from wirelessly acquired CMP vibration signal patterns, CMP process anomalies, such as pad wear, and drifts in polishing were identified in their nascent stage with high fidelity (R2 ~ 75%). 3. An algebraic graph theoretic approach for quantifying nano-surface morphology from optical micrograph images is developed. The approach enables a parsimonious representation of the topological relationships between heterogeneous nano-surface fea-tures, which are enshrined in graph theoretic entities, namely, the similarity, degree, and Laplacian matrices. Topological invariant measures (e.g., Fiedler number, Kirchoff index) extracted from these matrices are shown to be sensitive to evolving nano-surface morphology. For instance, we observed that prominent nanoscale morphological changes on CMP processed Cu wafers, although discernible visually, could not be tractably quantified using statistical metrology parameters, such as arithmetic average roughness (Sa), root mean square roughness (Sq), etc. In contrast, CMP induced nanoscale surface variations were captured on invoking graph theoretic topological invariants. Consequently, the graph theoretic approach can enable timely, non-contact, and in situ metrology of semiconductor wafers by obviating the need for reticent profile mapping techniques (e.g., AFM, SEM, etc.), and thereby prevent the propagation of yield losses over long production runs.

A Quantitative Study Analyzing Predictive Factors That Affect Achievement on Florida's Algebra I End-of-Course Exam (EOC)

ERIC Educational Resources Information Center

Holley, Hope D.

2017-01-01

Despite research that high-stakes tests do not improve knowledge, Florida requires students to pass an Algebra I End-of-Course exam (EOC) to earn a high school diploma. Test passing scores are determined by a raw score to t-score to scale score analysis. This method ultimately results as a comparative test model where students' passage is…

On boundary fusion and functional relations in the Baxterized affine Hecke algebra

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

Babichenko, A., E-mail: babichen@weizmann.ac.il; Regelskis, V., E-mail: v.regelskis@surrey.ac.uk

2014-04-15

We construct boundary type operators satisfying fused reflection equation for arbitrary representations of the Baxterized affine Hecke algebra. These operators are analogues of the fused reflection matrices in solvable half-line spin chain models. We show that these operators lead to a family of commuting transfer matrices of Sklyanin type. We derive fusion type functional relations for these operators for two families of representations.

Explaining Gender Gaps in English Composition and College Algebra in College: The Mediating Role of Psychosocial Factors

ERIC Educational Resources Information Center

Ndum, Edwin; Allen, Jeff; Way, Jason; Casillas, Alex

2018-01-01

We examined the role of six psychosocial factors (PSFs) in explaining gender gaps in English Composition (n = 8,633) and College Algebra (n = 2,261) using data of first-year female (55%) and male students from 42 colleges. Using a multilevel model and controlling for prior achievement, we found that PSFs mediated between 3% and 41% of the gender…

Teaching Linear Functions in Context with Graphics Calculators: Students' Responses and the Impact of the Approach on Their Use of Algebraic Symbols

ERIC Educational Resources Information Center

Bardini, Caroline; Pierce, Robyn U.; Stacey, Kaye

2004-01-01

This study analyses some of the consequences of adopting a functional/modelling approach to the teaching of algebra. The teaching of one class of 17 students was observed over five weeks, with 15 students undertaking both pre- and post-tests and 6 students and the teacher being interviewed individually. Use of graphics calculators made the…

Resolving phase ambiguities in the calibration of redundant interferometric arrays: implications for array design

DTIC Science & Technology

2015-11-30

matrix determinant. This definition is given in many linear algebra texts (see e.g. Bretscher (2001)). Definition 3.1 : Suppose we have an n-by-n...Processing, 2, 767 Blanchard P., Greenaway A., Anderton R., Appleby R., 1996, J. Opt. Soc. Am. A, 13, 1593 Bretscher O., 2001, Linear Algebra with...frequencies are not co- linear ) and one piston phase. This particular solution will then differ from the true solution by a phase ramp in the Fourier

Quantization of Poisson Manifolds from the Integrability of the Modular Function

NASA Astrophysics Data System (ADS)

Bonechi, F.; Ciccoli, N.; Qiu, J.; Tarlini, M.

2014-10-01

We discuss a framework for quantizing a Poisson manifold via the quantization of its symplectic groupoid, combining the tools of geometric quantization with the results of Renault's theory of groupoid C*-algebras. This setting allows very singular polarizations. In particular, we consider the case when the modular function is multiplicatively integrable, i.e., when the space of leaves of the polarization inherits a groupoid structure. If suitable regularity conditions are satisfied, then one can define the quantum algebra as the convolution algebra of the subgroupoid of leaves satisfying the Bohr-Sommerfeld conditions. We apply this procedure to the case of a family of Poisson structures on , seen as Poisson homogeneous spaces of the standard Poisson-Lie group SU( n + 1). We show that a bihamiltonian system on defines a multiplicative integrable model on the symplectic groupoid; we compute the Bohr-Sommerfeld groupoid and show that it satisfies the needed properties for applying Renault theory. We recover and extend Sheu's description of quantum homogeneous spaces as groupoid C*-algebras.

Algebraic Thinking in Solving Linier Program at High School Level: Female Student’s Field Independent Cognitive Style

NASA Astrophysics Data System (ADS)

Hardiani, N.; Budayasa, I. K.; Juniati, D.

2018-01-01

The aim of this study was to describe algebraic thinking of high school female student’s field independent cognitive style in solving linier program problem by revealing deeply the female students’ responses. Subjects in this study were 7 female students having field independent cognitive style in class 11. The type of this research was descriptive qualitative. The method of data collection used was observation, documentation, and interview. Data analysis technique was by reduction, presentation, and conclusion. The results of this study showed that the female students with field independent cognitive style in solving the linier program problem had the ability to represent algebraic ideas from the narrative question that had been read by manipulating symbols and variables presented in tabular form, creating and building mathematical models in two variables linear inequality system which represented algebraic ideas, and interpreting the solutions as variables obtained from the point of intersection in the solution area to obtain maximum benefit.

Final Report: Subcontract B623868 Algebraic Multigrid solvers for coupled PDE systems

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

Brannick, J.

The Pennsylvania State University (“Subcontractor”) continued to work on the design of algebraic multigrid solvers for coupled systems of partial differential equations (PDEs) arising in numerical modeling of various applications, with a main focus on solving the Dirac equation arising in Quantum Chromodynamics (QCD). The goal of the proposed work was to develop combined geometric and algebraic multilevel solvers that are robust and lend themselves to efficient implementation on massively parallel heterogeneous computers for these QCD systems. The research in these areas built on previous works, focusing on the following three topics: (1) the development of parallel full-multigrid (PFMG) andmore » non-Galerkin coarsening techniques in this frame work for solving the Wilson Dirac system; (2) the use of these same Wilson MG solvers for preconditioning the Overlap and Domain Wall formulations of the Dirac equation; and (3) the design and analysis of algebraic coarsening algorithms for coupled PDE systems including Stokes equation, Maxwell equation and linear elasticity.« less

Investigation of formation of cut off layers and productivity of screw milling process

NASA Astrophysics Data System (ADS)

Ambrosimov, S. K.; Morozova, A. V.

2018-03-01

The article presents studies of a new method for complex milling surfaces with a screw feed motion. Using the apparatus of algebra of logic, the process of formation of cut metal layers and processing capacity is presented.

High level language-based robotic control system

NASA Technical Reports Server (NTRS)

Rodriguez, Guillermo (Inventor); Kruetz, Kenneth K. (Inventor); Jain, Abhinandan (Inventor)

1994-01-01

This invention is a robot control system based on a high level language implementing a spatial operator algebra. There are two high level languages included within the system. At the highest level, applications programs can be written in a robot-oriented applications language including broad operators such as MOVE and GRASP. The robot-oriented applications language statements are translated into statements in the spatial operator algebra language. Programming can also take place using the spatial operator algebra language. The statements in the spatial operator algebra language from either source are then translated into machine language statements for execution by a digital control computer. The system also includes the capability of executing the control code sequences in a simulation mode before actual execution to assure proper action at execution time. The robot's environment is checked as part of the process and dynamic reconfiguration is also possible. The languages and system allow the programming and control of multiple arms and the use of inward/outward spatial recursions in which every computational step can be related to a transformation from one point in the mechanical robot to another point to name two major advantages.

High level language-based robotic control system

NASA Technical Reports Server (NTRS)

Rodriguez, Guillermo (Inventor); Kreutz, Kenneth K. (Inventor); Jain, Abhinandan (Inventor)

1996-01-01

This invention is a robot control system based on a high level language implementing a spatial operator algebra. There are two high level languages included within the system. At the highest level, applications programs can be written in a robot-oriented applications language including broad operators such as MOVE and GRASP. The robot-oriented applications language statements are translated into statements in the spatial operator algebra language. Programming can also take place using the spatial operator algebra language. The statements in the spatial operator algebra language from either source are then translated into machine language statements for execution by a digital control computer. The system also includes the capability of executing the control code sequences in a simulation mode before actual execution to assure proper action at execution time. The robot's environment is checked as part of the process and dynamic reconfiguration is also possible. The languages and system allow the programming and control of multiple arms and the use of inward/outward spatial recursions in which every computational step can be related to a transformation from one point in the mechanical robot to another point to name two major advantages.

Special issue on cluster algebras in mathematical physics

NASA Astrophysics Data System (ADS)

Di Francesco, Philippe; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

2013-10-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics. Editorial policy The Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki. The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutations cluster structure on Poisson varieties cluster algebras and soliton interactions cluster positivity conjecture Y-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjecture T-system of transfer matrices of integrable lattice models dilogarithm identities in conformal field theory wall crossing in 4d N = 2 supersymmetric gauge theories 4d N = 1 quiver gauge theories described by networks scattering amplitudes of 4d N = 4 theories 3d N = 2 gauge theories described by flat connections on 3-manifolds integrability of dimer/Ising models on graphs. All contributions will be refereed and processed according to the usual procedure of the journal. Guidelines for preparation of contributions The deadline for contributed papers is 31 March 2014. This deadline will allow the special issue to appear at the end of 2014. There is no strict regulation on article size, but as a guide the preferable size is 15-30 pages for contributed papers and 40-60 pages for reviews. Further advice on publishing your work in Journal of Physics A may be found at iopscience.iop.org/jphysa. Contributions to the special issue should be submitted by web upload via authors.iop.org/, or by email to jphysa@iop.org, quoting 'JPhysA special issue on cluster algebras in mathematical physics'. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. The special issue will be published in the print and online versions of the journal.

Uncertainties in Atomic Data and Their Propagation Through Spectral Models. I.

NASA Technical Reports Server (NTRS)

Bautista, M. A.; Fivet, V.; Quinet, P.; Dunn, J.; Gull, T. R.; Kallman, T. R.; Mendoza, C.

2013-01-01

We present a method for computing uncertainties in spectral models, i.e., level populations, line emissivities, and emission line ratios, based upon the propagation of uncertainties originating from atomic data.We provide analytic expressions, in the form of linear sets of algebraic equations, for the coupled uncertainties among all levels. These equations can be solved efficiently for any set of physical conditions and uncertainties in the atomic data. We illustrate our method applied to spectral models of Oiii and Fe ii and discuss the impact of the uncertainties on atomic systems under different physical conditions. As to intrinsic uncertainties in theoretical atomic data, we propose that these uncertainties can be estimated from the dispersion in the results from various independent calculations. This technique provides excellent results for the uncertainties in A-values of forbidden transitions in [Fe ii]. Key words: atomic data - atomic processes - line: formation - methods: data analysis - molecular data - molecular processes - techniques: spectroscopic

A framework for optimization and quantification of uncertainty and sensitivity for developing carbon capture systems

DOE PAGES

Eslick, John C.; Ng, Brenda; Gao, Qianwen; ...

2014-12-31

Under the auspices of the U.S. Department of Energy’s Carbon Capture Simulation Initiative (CCSI), a Framework for Optimization and Quantification of Uncertainty and Sensitivity (FOQUS) has been developed. This tool enables carbon capture systems to be rapidly synthesized and rigorously optimized, in an environment that accounts for and propagates uncertainties in parameters and models. FOQUS currently enables (1) the development of surrogate algebraic models utilizing the ALAMO algorithm, which can be used for superstructure optimization to identify optimal process configurations, (2) simulation-based optimization utilizing derivative free optimization (DFO) algorithms with detailed black-box process models, and (3) rigorous uncertainty quantification throughmore » PSUADE. FOQUS utilizes another CCSI technology, the Turbine Science Gateway, to manage the thousands of simulated runs necessary for optimization and UQ. Thus, this computational framework has been demonstrated for the design and analysis of a solid sorbent based carbon capture system.« less

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)

A Julia set model of field-directed morphogenesis: developmental biology and artificial life.

PubMed

Levin, M

1994-04-01

One paradigm used in understanding the control of morphogenetic events is the concept of positional information, where sub-organismic components (such as cells) act in response to positional cues. It is important to determine what kinds of spatiotemporal patterns may be obtained by such a method, and what the characteristics of such a morphogenetic process might be. This paper presents a computer model of morphogenesis based on gene activity driven by interpreting a positional information field. In this model, the interactions of mutually regulating developmental genes are viewed as a map from R2 to R2, and are modeled by the complex number algebra. Functions in complex variables are used to simulate genetic interactions resulting in position-dependent differentiation. This is shown to be equivalent to computing modified Julia sets, and is seen to be sufficient to produce a very rich set of morphologies which are similar in appearance and several important characteristics to those of real organisms. The properties of this model can be used to study the potential role of fields and positional information as guiding factors in morphogenesis, as the model facilitates the study of static images, time-series (movies) and experimental alterations of the developmental process. It is thus shown that gene interactions can be modeled as a multi-dimensional algebra, and that only two interacting genes are sufficient for (i) complex pattern formation, (ii) chaotic differentiation behavior, and (iii) production of sharp edges from a continuous positional information field. This model is meant to elucidate the properties of the process of positional information-guided biomorphogenesis, not to serve as a simulation of any particular organism's development. Good quantitative data are not currently available on the interplay of gene products in morphogenesis. Thus, no attempt is made to link the images produced with actual pictures of any particular real organism. A brief introduction to top-down models and positional information is followed by the formal definition of the model. Then, the implications of the resulting morphologies to biological development are discussed, in terms of static shapes, parametrization studies, time series (movies made from individual frames), and behavior of the model in light of experimental perturbations. All figures (in grayscale), formulas and parameter values needed to re-create the figures and movies are included.

From integrability to conformal symmetry: Bosonic superconformal Toda theories

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

Bo-Yu Hou; Liu Chao

In this paper the authors study the conformal integrable models obtained from conformal reductions of WZNW theory associated with second order constraints. These models are called bosonic superconformal Toda models due to their conformal spectra and their resemblance to the usual Toda theories. From the reduction procedure they get the equations of motion and the linearized Lax equations in a generic Z gradation of the underlying Lie algebra. Then, in the special case of principal gradation, they derive the classical r matrix, fundamental Poisson relation, exchange algebra of chiral operators and find out the classical vertex operators. The result showsmore » that their model is very similar to the ordinary Toda theories in that one can obtain various conformal properties of the model from its integrability.« less

A rigorous approach to facilitate and guarantee the correctness of the genetic testing management in human genome information systems.

PubMed

Araújo, Luciano V; Malkowski, Simon; Braghetto, Kelly R; Passos-Bueno, Maria R; Zatz, Mayana; Pu, Calton; Ferreira, João E

2011-12-22

Recent medical and biological technology advances have stimulated the development of new testing systems that have been providing huge, varied amounts of molecular and clinical data. Growing data volumes pose significant challenges for information processing systems in research centers. Additionally, the routines of genomics laboratory are typically characterized by high parallelism in testing and constant procedure changes. This paper describes a formal approach to address this challenge through the implementation of a genetic testing management system applied to human genome laboratory. We introduced the Human Genome Research Center Information System (CEGH) in Brazil, a system that is able to support constant changes in human genome testing and can provide patients updated results based on the most recent and validated genetic knowledge. Our approach uses a common repository for process planning to ensure reusability, specification, instantiation, monitoring, and execution of processes, which are defined using a relational database and rigorous control flow specifications based on process algebra (ACP). The main difference between our approach and related works is that we were able to join two important aspects: 1) process scalability achieved through relational database implementation, and 2) correctness of processes using process algebra. Furthermore, the software allows end users to define genetic testing without requiring any knowledge about business process notation or process algebra. This paper presents the CEGH information system that is a Laboratory Information Management System (LIMS) based on a formal framework to support genetic testing management for Mendelian disorder studies. We have proved the feasibility and showed usability benefits of a rigorous approach that is able to specify, validate, and perform genetic testing using easy end user interfaces.

A rigorous approach to facilitate and guarantee the correctness of the genetic testing management in human genome information systems

PubMed Central

2011-01-01

Background Recent medical and biological technology advances have stimulated the development of new testing systems that have been providing huge, varied amounts of molecular and clinical data. Growing data volumes pose significant challenges for information processing systems in research centers. Additionally, the routines of genomics laboratory are typically characterized by high parallelism in testing and constant procedure changes. Results This paper describes a formal approach to address this challenge through the implementation of a genetic testing management system applied to human genome laboratory. We introduced the Human Genome Research Center Information System (CEGH) in Brazil, a system that is able to support constant changes in human genome testing and can provide patients updated results based on the most recent and validated genetic knowledge. Our approach uses a common repository for process planning to ensure reusability, specification, instantiation, monitoring, and execution of processes, which are defined using a relational database and rigorous control flow specifications based on process algebra (ACP). The main difference between our approach and related works is that we were able to join two important aspects: 1) process scalability achieved through relational database implementation, and 2) correctness of processes using process algebra. Furthermore, the software allows end users to define genetic testing without requiring any knowledge about business process notation or process algebra. Conclusions This paper presents the CEGH information system that is a Laboratory Information Management System (LIMS) based on a formal framework to support genetic testing management for Mendelian disorder studies. We have proved the feasibility and showed usability benefits of a rigorous approach that is able to specify, validate, and perform genetic testing using easy end user interfaces. PMID:22369688

FAST TRACK COMMUNICATION: \\ {P}\\ {T}-symmetry, Cartan decompositions, Lie triple systems and Krein space-related Clifford algebras

NASA Astrophysics Data System (ADS)

Günther, Uwe; Kuzhel, Sergii

2010-10-01

Gauged \\ {P}\\ {T} quantum mechanics (PTQM) and corresponding Krein space setups are studied. For models with constant non-Abelian gauge potentials and extended parity inversions compact and noncompact Lie group components are analyzed via Cartan decompositions. A Lie-triple structure is found and an interpretation as \\ {P}\\ {T}-symmetrically generalized Jaynes-Cummings model is possible with close relation to recently studied cavity QED setups with transmon states in multilevel artificial atoms. For models with Abelian gauge potentials a hidden Clifford algebra structure is found and used to obtain the fundamental symmetry of Krein space-related J-self-adjoint extensions for PTQM setups with ultra-localized potentials.

Application of the algebraic RNG model for transition simulation. [renormalization group theory

NASA Technical Reports Server (NTRS)

Lund, Thomas S.

1990-01-01

The algebraic form of the RNG model of Yakhot and Orszag (1986) is investigated as a transition model for the Reynolds averaged boundary layer equations. It is found that the cubic equation for the eddy viscosity contains both a jump discontinuity and one spurious root. A yet unpublished transformation to a quartic equation is shown to remove the numerical difficulties associated with the discontinuity, but only at the expense of merging both the physical and spurious root of the cubic. Jumps between the branches of the resulting multiple-valued solution are found to lead to oscillations in flat plate transition calculations. Aside from the oscillations, the transition behavior is qualitatively correct.

Genomic signal processing: from matrix algebra to genetic networks.

PubMed

Alter, Orly

2007-01-01

DNA microarrays make it possible, for the first time, to record the complete genomic signals that guide the progression of cellular processes. Future discovery in biology and medicine will come from the mathematical modeling of these data, which hold the key to fundamental understanding of life on the molecular level, as well as answers to questions regarding diagnosis, treatment, and drug development. This chapter reviews the first data-driven models that were created from these genome-scale data, through adaptations and generalizations of mathematical frameworks from matrix algebra that have proven successful in describing the physical world, in such diverse areas as mechanics and perception: the singular value decomposition model, the generalized singular value decomposition model comparative model, and the pseudoinverse projection integrative model. These models provide mathematical descriptions of the genetic networks that generate and sense the measured data, where the mathematical variables and operations represent biological reality. The variables, patterns uncovered in the data, correlate with activities of cellular elements such as regulators or transcription factors that drive the measured signals and cellular states where these elements are active. The operations, such as data reconstruction, rotation, and classification in subspaces of selected patterns, simulate experimental observation of only the cellular programs that these patterns represent. These models are illustrated in the analyses of RNA expression data from yeast and human during their cell cycle programs and DNA-binding data from yeast cell cycle transcription factors and replication initiation proteins. Two alternative pictures of RNA expression oscillations during the cell cycle that emerge from these analyses, which parallel well-known designs of physical oscillators, convey the capacity of the models to elucidate the design principles of cellular systems, as well as guide the design of synthetic ones. In these analyses, the power of the models to predict previously unknown biological principles is demonstrated with a prediction of a novel mechanism of regulation that correlates DNA replication initiation with cell cycle-regulated RNA transcription in yeast. These models may become the foundation of a future in which biological systems are modeled as physical systems are today.

Renormalization group flows and continual Lie algebras

NASA Astrophysics Data System (ADS)

Bakas, Ioannis

2003-08-01

We study the renormalization group flows of two-dimensional metrics in sigma models using the one-loop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the world-sheet length scale, t, is interpreted as Dynkin parameter on the root system of a novel continual Lie algebra, denoted by Script G(d/dt;1), with anti-symmetric Cartan kernel K(t,t') = delta'(t-t'); as such, it coincides with the Cartan matrix of the superalgebra sl(N|N+1) in the large-N limit. The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time, t. We provide the general solution of the renormalization group flows in terms of free fields, via Bäcklund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Zn to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra Script G(d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown.

A note on derivations of Murray-von Neumann algebras.

PubMed

Kadison, Richard V; Liu, Zhe

2014-02-11

A Murray-von Neumann algebra is the algebra of operators affiliated with a finite von Neumann algebra. In this article, we first present a brief introduction to the theory of derivations of operator algebras from both the physical and mathematical points of view. We then describe our recent work on derivations of Murray-von Neumann algebras. We show that the "extended derivations" of a Murray-von Neumann algebra, those that map the associated finite von Neumann algebra into itself, are inner. In particular, we prove that the only derivation that maps a Murray-von Neumann algebra associated with a factor of type II1 into that factor is 0. Those results are extensions of Singer's seminal result answering a question of Kaplansky, as applied to von Neumann algebras: The algebra may be noncommutative and may even contain unbounded elements.

Blooms' separation of the final exam of Engineering Mathematics II: Item reliability using Rasch measurement model

NASA Astrophysics Data System (ADS)

Fuaad, Norain Farhana Ahmad; Nopiah, Zulkifli Mohd; Tawil, Norgainy Mohd; Othman, Haliza; Asshaari, Izamarlina; Osman, Mohd Hanif; Ismail, Nur Arzilah

2014-06-01

In engineering studies and researches, Mathematics is one of the main elements which express physical, chemical and engineering laws. Therefore, it is essential for engineering students to have a strong knowledge in the fundamental of mathematics in order to apply the knowledge to real life issues. However, based on the previous results of Mathematics Pre-Test, it shows that the engineering students lack the fundamental knowledge in certain topics in mathematics. Due to this, apart from making improvements in the methods of teaching and learning, studies on the construction of questions (items) should also be emphasized. The purpose of this study is to assist lecturers in the process of item development and to monitor the separation of items based on Blooms' Taxonomy and to measure the reliability of the items itself usingRasch Measurement Model as a tool. By using Rasch Measurement Model, the final exam questions of Engineering Mathematics II (Linear Algebra) for semester 2 sessions 2012/2013 were analysed and the results will provide the details onthe extent to which the content of the item providesuseful information about students' ability. This study reveals that the items used in Engineering Mathematics II (Linear Algebra) final exam are well constructed but the separation of the items raises concern as it is argued that it needs further attention, as there is abig gap between items at several levels of Blooms' cognitive skill.

Minimal models of compact symplectic semitoric manifolds

NASA Astrophysics Data System (ADS)

Kane, D. M.; Palmer, J.; Pelayo, Á.

2018-02-01

A symplectic semitoric manifold is a symplectic 4-manifold endowed with a Hamiltonian (S1 × R) -action satisfying certain conditions. The goal of this paper is to construct a new symplectic invariant of symplectic semitoric manifolds, the helix, and give applications. The helix is a symplectic analogue of the fan of a nonsingular complete toric variety in algebraic geometry, that takes into account the effects of the monodromy near focus-focus singularities. We give two applications of the helix: first, we use it to give a classification of the minimal models of symplectic semitoric manifolds, where "minimal" is in the sense of not admitting any blowdowns. The second application is an extension to the compact case of a well known result of Vũ Ngọc about the constraints posed on a symplectic semitoric manifold by the existence of focus-focus singularities. The helix permits to translate a symplectic geometric problem into an algebraic problem, and the paper describes a method to solve this type of algebraic problem.

Quantum trilogy: discrete Toda, Y-system and chaos

NASA Astrophysics Data System (ADS)

Yamazaki, Masahito

2018-02-01

We discuss a discretization of the quantum Toda field theory associated with a semisimple finite-dimensional Lie algebra or a tamely-laced infinite-dimensional Kac-Moody algebra G, generalizing the previous construction of discrete quantum Liouville theory for the case G  =  A 1. The model is defined on a discrete two-dimensional lattice, whose spatial direction is of length L. In addition we also find a ‘discretized extra dimension’ whose width is given by the rank r of G, which decompactifies in the large r limit. For the case of G  =  A N or AN-1(1) , we find a symmetry exchanging L and N under appropriate spatial boundary conditions. The dynamical time evolution rule of the model is quantizations of the so-called Y-system, and the theory can be well described by the quantum cluster algebra. We discuss possible implications for recent discussions of quantum chaos, and comment on the relation with the quantum higher Teichmüller theory of type A N .

Banach Synaptic Algebras

NASA Astrophysics Data System (ADS)

Foulis, David J.; Pulmannov, Sylvia

2018-04-01

Using a representation theorem of Erik Alfsen, Frederic Schultz, and Erling Størmer for special JB-algebras, we prove that a synaptic algebra is norm complete (i.e., Banach) if and only if it is isomorphic to the self-adjoint part of a Rickart C∗-algebra. Also, we give conditions on a Banach synaptic algebra that are equivalent to the condition that it is isomorphic to the self-adjoint part of an AW∗-algebra. Moreover, we study some relationships between synaptic algebras and so-called generalized Hermitian algebras.

Numerical stability in problems of linear algebra.

NASA Technical Reports Server (NTRS)

Babuska, I.

1972-01-01

Mathematical problems are introduced as mappings from the space of input data to that of the desired output information. Then a numerical process is defined as a prescribed recurrence of elementary operations creating the mapping of the underlying mathematical problem. The ratio of the error committed by executing the operations of the numerical process (the roundoff errors) to the error introduced by perturbations of the input data (initial error) gives rise to the concept of lambda-stability. As examples, several processes are analyzed from this point of view, including, especially, old and new processes for solving systems of linear algebraic equations with tridiagonal matrices. In particular, it is shown how such a priori information can be utilized as, for instance, a knowledge of the row sums of the matrix. Information of this type is frequently available where the system arises in connection with the numerical solution of differential equations.

Quantum processes: A Whiteheadian interpretation of quantum field theory

NASA Astrophysics Data System (ADS)

Bain, Jonathan

Quantum processes: A Whiteheadian interpretation of quantum field theory is an ambitious and thought-provoking exercise in physics and metaphysics, combining an erudite study of the very complex metaphysics of A.N. Whitehead with a well-informed discussion of contemporary issues in the philosophy of algebraic quantum field theory. Hättich's overall goal is to construct an interpretation of quantum field theory. He does this by translating key concepts in Whitehead's metaphysics into the language of algebraic quantum field theory. In brief, this Hättich-Whitehead (H-W, hereafter) interpretation takes "actual occasions" as the fundamental ontological entities of quantum field theory. An actual occasion is the result of two types of processes: a "transition process" in which a set of initial possibly-possessed properties for the occasion (in the form of "eternal objects") is localized to a space-time region; and a "concrescence process" in which a subset of these initial possibly-possessed properties is selected and actualized to produce the occasion. Essential to these processes is the "underlying activity", which conditions the way in which properties are initially selected and subsequently actualized. In short, under the H-W interpretation of quantum field theory, an initial set of possibly-possessed eternal objects is represented by a Boolean sublattice of the lattice of projection operators determined by a von Neumann algebra R (O) associated with a region O of Minkowski space-time, and the underlying activity is represented by a state on R (O) obtained by conditionalizing off of the vacuum state. The details associated with the H-W interpretation involve imposing constraints on these representations motivated by principles found in Whitehead's metaphysics. These details are spelled out in the three sections of the book. The first section is a summary and critique of Whitehead's metaphysics, the second section introduces the formalism of algebraic quantum field theory, and the third section consists of a translation between the first two sections. This review will concentrate on the first and third sections, with an eye on making explicit the essential characteristics of the H-W interpretation.

Experimental evaluation of four infiltration models for calcareous soil irrigated with treated untreated grey water and fresh water

NASA Astrophysics Data System (ADS)

Gharaibeh, M. A.; Eltaif, N. I.; Alrababah, M. A.; Alhamad, M. N.

2009-04-01

Infiltration is vital for both irrigated and rainfed agriculture. The knowledge of infiltration characteristics of a soil is the basic information required for designing an efficient irrigation system. The objective of the present study was to model soil infiltration using four models: Green and Ampt, Horton, Kostaikov and modified Kostiakov. Infiltration tests were conducted on field plot irrigated with treated, untreated greywater and fresh water. The field water infiltration data used in these models were based on double ring infiltrometer tests conducted for 4 h. The algebraic parameters of the infiltration models and nonlinear least squares regression were fitted using measured infiltration time [I (t)] data. Among process-based infiltration models, the Horton model performed best and matched the measured I (t) data with lower sum of squares (SS).

An Integrity Framework for Image-Based Navigation Systems

DTIC Science & Technology

2010-06-01

Anton H. and Rorres C. Elementary Linear Algebra . New York, NY: John Wiley & Sons, Inc., 2000. 4. Arthur T. “The Disparity of Parity, Determining...107. Spilker , James J.J. Digital Communications by Satellite. Englewood Cliffs NJ: Prentice Hall, 1977. 108. Strang G. Linear Algebra and its...2.3 The Linearized and Extended Kalman Filters . . . . . . 22 2.3.1 State and Measurement Model Equations . . . 23 2.3.2 The Linearized Kalman Filter

Algebraic approach to solve ttbar dilepton equations

NASA Astrophysics Data System (ADS)

Sonnenschein, Lars

2006-01-01

The set of non-linear equations describing the Standard Model kinematics of the top quark an- tiqark production system in the dilepton decay channel has at most a four-fold ambiguity due to two not fully reconstructed neutrinos. Its most precise and robust solution is of major importance for measurements of top quark properties like the top quark mass and t t spin correlations. Simple algebraic operations allow to transform the non-linear equations into a system of two polynomial equations with two unknowns. These two polynomials of multidegree eight can in turn be an- alytically reduced to one polynomial with one unknown by means of resultants. The obtained univariate polynomial is of degree sixteen and the coefficients are free of any singularity. The number of its real solutions is determined analytically by means of Sturm’s theorem, which is as well used to isolate each real solution into a unique pairwise disjoint interval. The solutions are polished by seeking the sign change of the polynomial in a given interval through binary brack- eting. Further a new Ansatz - exploiting an accidental cancelation in the process of transforming the equations - is presented. It permits to transform the initial system of equations into two poly- nomial equations with two unknowns. These two polynomials of multidegree two can be reduced to one univariate polynomial of degree four by means of resultants. The obtained quartic equation can be solved analytically. The analytical solution has singularities which can be circumvented by the algebraic approach described above.

Efficient computer algebra algorithms for polynomial matrices in control design

NASA Technical Reports Server (NTRS)

Baras, J. S.; Macenany, D. C.; Munach, R.

1989-01-01

The theory of polynomial matrices plays a key role in the design and analysis of multi-input multi-output control and communications systems using frequency domain methods. Examples include coprime factorizations of transfer functions, cannonical realizations from matrix fraction descriptions, and the transfer function design of feedback compensators. Typically, such problems abstract in a natural way to the need to solve systems of Diophantine equations or systems of linear equations over polynomials. These and other problems involving polynomial matrices can in turn be reduced to polynomial matrix triangularization procedures, a result which is not surprising given the importance of matrix triangularization techniques in numerical linear algebra. Matrices with entries from a field and Gaussian elimination play a fundamental role in understanding the triangularization process. In the case of polynomial matrices, matrices with entries from a ring for which Gaussian elimination is not defined and triangularization is accomplished by what is quite properly called Euclidean elimination. Unfortunately, the numerical stability and sensitivity issues which accompany floating point approaches to Euclidean elimination are not very well understood. New algorithms are presented which circumvent entirely such numerical issues through the use of exact, symbolic methods in computer algebra. The use of such error-free algorithms guarantees that the results are accurate to within the precision of the model data--the best that can be hoped for. Care must be taken in the design of such algorithms due to the phenomenon of intermediate expressions swell.

The Unitality of Quantum B-algebras

NASA Astrophysics Data System (ADS)

Han, Shengwei; Xu, Xiaoting; Qin, Feng

2018-02-01

Quantum B-algebras as a generalization of quantales were introduced by Rump and Yang, which cover the majority of implicational algebras and provide a unified semantic for a wide class of substructural logics. Unital quantum B-algebras play an important role in the classification of implicational algebras. The main purpose of this paper is to construct unital quantum B-algebras from non-unital quantum B-algebras.

Quantum incompatibility of channels with general outcome operator algebras

NASA Astrophysics Data System (ADS)

Kuramochi, Yui

2018-04-01

A pair of quantum channels is said to be incompatible if they cannot be realized as marginals of a single channel. This paper addresses the general structure of the incompatibility of completely positive channels with a fixed quantum input space and with general outcome operator algebras. We define a compatibility relation for such channels by identifying the composite outcome space as the maximal (projective) C*-tensor product of outcome algebras. We show theorems that characterize this compatibility relation in terms of the concatenation and conjugation of channels, generalizing the recent result for channels with quantum outcome spaces. These results are applied to the positive operator valued measures (POVMs) by identifying each of them with the corresponding quantum-classical (QC) channel. We also give a characterization of the maximality of a POVM with respect to the post-processing preorder in terms of the conjugate channel of the QC channel. We consider another definition of compatibility of normal channels by identifying the composite outcome space with the normal tensor product of the outcome von Neumann algebras. We prove that for a given normal channel, the class of normally compatible channels is upper bounded by a special class of channels called tensor conjugate channels. We show the inequivalence of the C*- and normal compatibility relations for QC channels, which originates from the possibility and impossibility of copying operations for commutative von Neumann algebras in C*- and normal compatibility relations, respectively.

Generalizing the bms3 and 2D-conformal algebras by expanding the Virasoro algebra

NASA Astrophysics Data System (ADS)

Caroca, Ricardo; Concha, Patrick; Rodríguez, Evelyn; Salgado-Rebolledo, Patricio

2018-03-01

By means of the Lie algebra expansion method, the centrally extended conformal algebra in two dimensions and the bms3 algebra are obtained from the Virasoro algebra. We extend this result to construct new families of expanded Virasoro algebras that turn out to be infinite-dimensional lifts of the so-called Bk, Ck and Dk algebras recently introduced in the literature in the context of (super)gravity. We also show how some of these new infinite-dimensional symmetries can be obtained from expanded Kač-Moody algebras using modified Sugawara constructions. Applications in the context of three-dimensional gravity are briefly discussed.

Linear-scaling density-functional simulations of charged point defects in Al2O3 using hierarchical sparse matrix algebra.

PubMed

Hine, N D M; Haynes, P D; Mostofi, A A; Payne, M C

2010-09-21

We present calculations of formation energies of defects in an ionic solid (Al(2)O(3)) extrapolated to the dilute limit, corresponding to a simulation cell of infinite size. The large-scale calculations required for this extrapolation are enabled by developments in the approach to parallel sparse matrix algebra operations, which are central to linear-scaling density-functional theory calculations. The computational cost of manipulating sparse matrices, whose sizes are determined by the large number of basis functions present, is greatly improved with this new approach. We present details of the sparse algebra scheme implemented in the ONETEP code using hierarchical sparsity patterns, and demonstrate its use in calculations on a wide range of systems, involving thousands of atoms on hundreds to thousands of parallel processes.

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

Suh, Uhi Rinn, E-mail: uhrisu1@math.snu.ac.kr

We introduce a classical BRST complex (See Definition 3.2.) and show that one can construct a classical affine W-algebra via the complex. This definition clarifies that classical affine W-algebras can be considered as quasi-classical limits of quantum affine W-algebras. We also give a definition of a classical affine fractional W-algebra as a Poisson vertex algebra. As in the classical affine case, a classical affine fractional W-algebra has two compatible λ-brackets and is isomorphic to an algebra of differential polynomials as a differential algebra. When a classical affine fractional W-algebra is associated to a minimal nilpotent, we describe explicit forms ofmore » free generators and compute λ-brackets between them. Provided some assumptions on a classical affine fractional W-algebra, we find an infinite sequence of integrable systems related to the algebra, using the generalized Drinfel’d and Sokolov reduction.« less

A note on derivations of Murray–von Neumann algebras

PubMed Central

Kadison, Richard V.; Liu, Zhe

2014-01-01

A Murray–von Neumann algebra is the algebra of operators affiliated with a finite von Neumann algebra. In this article, we first present a brief introduction to the theory of derivations of operator algebras from both the physical and mathematical points of view. We then describe our recent work on derivations of Murray–von Neumann algebras. We show that the “extended derivations” of a Murray–von Neumann algebra, those that map the associated finite von Neumann algebra into itself, are inner. In particular, we prove that the only derivation that maps a Murray–von Neumann algebra associated with a factor of type II1 into that factor is 0. Those results are extensions of Singer’s seminal result answering a question of Kaplansky, as applied to von Neumann algebras: The algebra may be noncommutative and may even contain unbounded elements. PMID:24469831

A double commutant theorem for Murray–von Neumann algebras

PubMed Central

Liu, Zhe

2012-01-01

Murray–von Neumann algebras are algebras of operators affiliated with finite von Neumann algebras. In this article, we study commutativity and affiliation of self-adjoint operators (possibly unbounded). We show that a maximal abelian self-adjoint subalgebra of the Murray–von Neumann algebra associated with a finite von Neumann algebra is the Murray–von Neumann algebra , where is a maximal abelian self-adjoint subalgebra of and, in addition, is . We also prove that the Murray–von Neumann algebra with the center of is the center of the Murray–von Neumann algebra . Von Neumann’s celebrated double commutant theorem characterizes von Neumann algebras as those for which , where , the commutant of , is the set of bounded operators on the Hilbert space that commute with all operators in . At the end of this article, we present a double commutant theorem for Murray–von Neumann algebras. PMID:22543165

Passive acoustic measurement of bedload grain size distribution using self-generated noise

NASA Astrophysics Data System (ADS)

Petrut, Teodor; Geay, Thomas; Gervaise, Cédric; Belleudy, Philippe; Zanker, Sebastien

2018-01-01

Monitoring sediment transport processes in rivers is of particular interest to engineers and scientists to assess the stability of rivers and hydraulic structures. Various methods for sediment transport process description were proposed using conventional or surrogate measurement techniques. This paper addresses the topic of the passive acoustic monitoring of bedload transport in rivers and especially the estimation of the bedload grain size distribution from self-generated noise. It discusses the feasibility of linking the acoustic signal spectrum shape to bedload grain sizes involved in elastic impacts with the river bed treated as a massive slab. Bedload grain size distribution is estimated by a regularized algebraic inversion scheme fed with the power spectrum density of river noise estimated from one hydrophone. The inversion methodology relies upon a physical model that predicts the acoustic field generated by the collision between rigid bodies. Here we proposed an analytic model of the acoustic energy spectrum generated by the impacts between a sphere and a slab. The proposed model computes the power spectral density of bedload noise using a linear system of analytic energy spectra weighted by the grain size distribution. The algebraic system of equations is then solved by least square optimization and solution regularization methods. The result of inversion leads directly to the estimation of the bedload grain size distribution. The inversion method was applied to real acoustic data from passive acoustics experiments realized on the Isère River, in France. The inversion of in situ measured spectra reveals good estimations of grain size distribution, fairly close to what was estimated by physical sampling instruments. These results illustrate the potential of the hydrophone technique to be used as a standalone method that could ensure high spatial and temporal resolution measurements for sediment transport in rivers.

Algebraic Reasoning in Solving Mathematical Problem Based on Learning Style

NASA Astrophysics Data System (ADS)

Indraswari, N. F.; Budayasa, I. K.; Ekawati, R.

2018-01-01

This study aimed to describe algebraic reasoning of secondary school’s pupils with different learning styles in solving mathematical problem. This study begins by giving the questionnaire to find out the learning styles and followed by mathematical ability test to get three subjects of 8th-grade whereas the learning styles of each pupil is visual, auditory, kinesthetic and had similar mathematical abilities. Then it continued with given algebraic problems and interviews. The data is validated using triangulation of time. The result showed that in the pattern of seeking indicator, subjects identified the things that were known and asked based on them observations. The visual and kinesthetic learners represented the known information in a chart, whereas the auditory learner in a table. In addition, they found the elements which makes the pattern and made a relationship between two quantities. In the pattern recognition indicator, they created conjectures on the relationship between two quantities and proved it. In the generalization indicator, they were determining the general rule of pattern found on each element of pattern using algebraic symbols and created a mathematical model. Visual and kinesthetic learners determined the general rule of equations which was used to solve problems using algebraic symbols, but auditory learner in a sentence.

Optimal control in a model of malaria with differential susceptibility

NASA Astrophysics Data System (ADS)

Hincapié, Doracelly; Ospina, Juan

2014-06-01

A malaria model with differential susceptibility is analyzed using the optimal control technique. In the model the human population is classified as susceptible, infected and recovered. Susceptibility is assumed dependent on genetic, physiological, or social characteristics that vary between individuals. The model is described by a system of differential equations that relate the human and vector populations, so that the infection is transmitted to humans by vectors, and the infection is transmitted to vectors by humans. The model considered is analyzed using the optimal control method when the control consists in using of insecticide-treated nets and educational campaigns; and the optimality criterion is to minimize the number of infected humans, while keeping the cost as low as is possible. One first goal is to determine the effects of differential susceptibility in the proposed control mechanism; and the second goal is to determine the algebraic form of the basic reproductive number of the model. All computations are performed using computer algebra, specifically Maple. It is claimed that the analytical results obtained are important for the design and implementation of control measures for malaria. It is suggested some future investigations such as the application of the method to other vector-borne diseases such as dengue or yellow fever; and also it is suggested the possible application of free software of computer algebra like Maxima.

On the intersection of irreducible components of the space of finite-dimensional Lie algebras

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

Gorbatsevich, Vladimir V

2012-07-31

The irreducible components of the space of n-dimensional Lie algebras are investigated. The properties of Lie algebras belonging to the intersection of all the irreducible components of this kind are studied (these Lie algebras are said to be basic or founding Lie algebras). It is proved that all Lie algebras of this kind are nilpotent and each of these Lie algebras has an Abelian ideal of codimension one. Specific examples of founding Lie algebras of arbitrary dimension are described and, to describe the Lie algebras in general, we state a conjecture. The concept of spectrum of a Lie algebra ismore » considered and some of the most elementary properties of the spectrum are studied. Bibliography: 6 titles.« less

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.

From simplicial Lie algebras and hypercrossed complexes to differential graded Lie algebras via 1-jets

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

2012-12-01

Let g be a simplicial Lie algebra with Moore complex Ng of length k. Let G be the simplicial Lie group integrating g, such that each Gn is simply connected. We use the 1-jet of the classifying space W¯ G to construct, starting from g, a Lie k-algebra L. The so constructed Lie k-algebra L is actually a differential graded Lie algebra. The differential and the brackets are explicitly described in terms (of a part) of the corresponding k-hypercrossed complex structure of Ng. The result can be seen as a geometric interpretation of Quillen's (purely algebraic) construction of the adjunction between simplicial Lie algebras and dg-Lie algebras.

Multicriterion problem of allocation of resources in the heterogeneous distributed information processing systems

NASA Astrophysics Data System (ADS)

Antamoshkin, O. A.; Kilochitskaya, T. R.; Ontuzheva, G. A.; Stupina, A. A.; Tynchenko, V. S.

2018-05-01

This study reviews the problem of allocation of resources in the heterogeneous distributed information processing systems, which may be formalized in the form of a multicriterion multi-index problem with the linear constraints of the transport type. The algorithms for solution of this problem suggest a search for the entire set of Pareto-optimal solutions. For some classes of hierarchical systems, it is possible to significantly speed up the procedure of verification of a system of linear algebraic inequalities for consistency due to the reducibility of them to the stream models or the application of other solution schemes (for strongly connected structures) that take into account the specifics of the hierarchies under consideration.

Quantum Structure in Cognition and the Foundations of Human Reasoning

NASA Astrophysics Data System (ADS)

Aerts, Diederik; Sozzo, Sandro; Veloz, Tomas

2015-12-01

Traditional cognitive science rests on a foundation of classical logic and probability theory. This foundation has been seriously challenged by several findings in experimental psychology on human decision making. Meanwhile, the formalism of quantum theory has provided an efficient resource for modeling these classically problematical situations. In this paper, we start from our successful quantum-theoretic approach to the modeling of concept combinations to formulate a unifying explanatory hypothesis. In it, human reasoning is the superposition of two processes - a conceptual reasoning, whose nature is emergence of new conceptuality, and a logical reasoning, founded on an algebraic calculus of the logical type. In most cognitive processes however, the former reasoning prevails over the latter. In this perspective, the observed deviations from classical logical reasoning should not be interpreted as biases but, rather, as natural expressions of emergence in its deepest form.