Sample records for classical mathematical models

  1. Mathematical model of the SH-3G helicopter

    NASA Technical Reports Server (NTRS)

    Phillips, J. D.

    1982-01-01

    A mathematical model of the Sikorsky SH-3G helicopter based on classical nonlinear, quasi-steady rotor theory was developed. The model was validated statically and dynamically by comparison with Navy flight-test data. The model incorporates ad hoc revisions which address the ideal assumptions of classical rotor theory and improve the static trim characteristics to provide a more realistic simulation, while retaining the simplicity of the classical model.

  2. A Unified Mathematical Definition of Classical Information Retrieval.

    ERIC Educational Resources Information Center

    Dominich, Sandor

    2000-01-01

    Presents a unified mathematical definition for the classical models of information retrieval and identifies a mathematical structure behind relevance feedback. Highlights include vector information retrieval; probabilistic information retrieval; and similarity information retrieval. (Contains 118 references.) (Author/LRW)

  3. Will the digital computer transform classical mathematics?

    PubMed

    Rotman, Brian

    2003-08-15

    Mathematics and machines have influenced each other for millennia. The advent of the digital computer introduced a powerfully new element that promises to transform the relation between them. This paper outlines the thesis that the effect of the digital computer on mathematics, already widespread, is likely to be radical and far-reaching. To articulate this claim, an abstract model of doing mathematics is introduced based on a triad of actors of which one, the 'agent', corresponds to the function performed by the computer. The model is used to frame two sorts of transformation. The first is pragmatic and involves the alterations and progressive colonization of the content and methods of enquiry of various mathematical fields brought about by digital methods. The second is conceptual and concerns a fundamental antagonism between the infinity enshrined in classical mathematics and physics (continuity, real numbers, asymptotic definitions) and the inherently real and material limit of processes associated with digital computation. An example which lies in the intersection of classical mathematics and computer science, the P=NP problem, is analysed in the light of this latter issue.

  4. The Nature of Quantum Truth: Logic, Set Theory, & Mathematics in the Context of Quantum Theory

    NASA Astrophysics Data System (ADS)

    Frey, Kimberly

    The purpose of this dissertation is to construct a radically new type of mathematics whose underlying logic differs from the ordinary classical logic used in standard mathematics, and which we feel may be more natural for applications in quantum mechanics. Specifically, we begin by constructing a first order quantum logic, the development of which closely parallels that of ordinary (classical) first order logic --- the essential differences are in the nature of the logical axioms, which, in our construction, are motivated by quantum theory. After showing that the axiomatic first order logic we develop is sound and complete (with respect to a particular class of models), this logic is then used as a foundation on which to build (axiomatic) mathematical systems --- and we refer to the resulting new mathematics as "quantum mathematics." As noted above, the hope is that this form of mathematics is more natural than classical mathematics for the description of quantum systems, and will enable us to address some foundational aspects of quantum theory which are still troublesome --- e.g. the measurement problem --- as well as possibly even inform our thinking about quantum gravity. After constructing the underlying logic, we investigate properties of several mathematical systems --- e.g. axiom systems for abstract algebras, group theory, linear algebra, etc. --- in the presence of this quantum logic. In the process, we demonstrate that the resulting quantum mathematical systems have some strange, but very interesting features, which indicates a richness in the structure of mathematics that is classically inaccessible. Moreover, some of these features do indeed suggest possible applications to foundational questions in quantum theory. We continue our investigation of quantum mathematics by constructing an axiomatic quantum set theory, which we show satisfies certain desirable criteria. Ultimately, we hope that such a set theory will lead to a foundation for quantum mathematics in a sense which parallels the foundational role of classical set theory in classical mathematics. One immediate application of the quantum set theory we develop is to provide a foundation on which to construct quantum natural numbers, which are the quantum analog of the classical counting numbers. It turns out that in a special class of models, there exists a 1-1 correspondence between the quantum natural numbers and bounded observables in quantum theory whose eigenvalues are (ordinary) natural numbers. This 1-1 correspondence is remarkably satisfying, and not only gives us great confidence in our quantum set theory, but indicates the naturalness of such models for quantum theory itself. We go on to develop a Peano-like arithmetic for these new "numbers," as well as consider some of its consequences. Finally, we conclude by summarizing our results, and discussing directions for future work.

  5. A survey on hysteresis modeling, identification and control

    NASA Astrophysics Data System (ADS)

    Hassani, Vahid; Tjahjowidodo, Tegoeh; Do, Thanh Nho

    2014-12-01

    The various mathematical models for hysteresis such as Preisach, Krasnosel'skii-Pokrovskii (KP), Prandtl-Ishlinskii (PI), Maxwell-Slip, Bouc-Wen and Duhem are surveyed in terms of their applications in modeling, control and identification of dynamical systems. In the first step, the classical formalisms of the models are presented to the reader, and more broadly, the utilization of the classical models is considered for development of more comprehensive models and appropriate controllers for corresponding systems. In addition, the authors attempt to encourage the reader to follow the existing mathematical models of hysteresis to resolve the open problems.

  6. Molecular modeling: An open invitation for applied mathematics

    NASA Astrophysics Data System (ADS)

    Mezey, Paul G.

    2013-10-01

    Molecular modeling methods provide a very wide range of challenges for innovative mathematical and computational techniques, where often high dimensionality, large sets of data, and complicated interrelations imply a multitude of iterative approximations. The physical and chemical basis of these methodologies involves quantum mechanics with several non-intuitive aspects, where classical interpretation and classical analogies are often misleading or outright wrong. Hence, instead of the everyday, common sense approaches which work so well in engineering, in molecular modeling one often needs to rely on rather abstract mathematical constraints and conditions, again emphasizing the high level of reliance on applied mathematics. Yet, the interdisciplinary aspects of the field of molecular modeling also generates some inertia and perhaps too conservative reliance on tried and tested methodologies, that is at least partially caused by the less than up-to-date involvement in the newest developments in applied mathematics. It is expected that as more applied mathematicians take up the challenge of employing the latest advances of their field in molecular modeling, important breakthroughs may follow. In this presentation some of the current challenges of molecular modeling are discussed.

  7. Mathematical Model of Armed Helicopter vs Tank Duel

    DTIC Science & Technology

    The purpose of this thesis is to mathematically model a duel between the armed helicopter and the tank. In addition to providing a parametric...analysis of B. O. Koopman’s classical Detection-Destruction Duel , two additional models were constructed and analyzed. All three models stem from stochastic

  8. Evaluation of the mathematical and economic basis for conversion processes in the LEAP energy-economy model

    NASA Astrophysics Data System (ADS)

    Oblow, E. M.

    1982-10-01

    An evaluation was made of the mathematical and economic basis for conversion processes in the Long-term Energy Analysis Program (LEAP) energy economy model. Conversion processes are the main modeling subunit in LEAP used to represent energy conversion industries and are supposedly based on the classical economic theory of the firm. Questions about uniqueness and existence of LEAP solutions and their relation to classical equilibrium economic theory prompted the study. An analysis of classical theory and LEAP model equations was made to determine their exact relationship. The conclusions drawn from this analysis were that LEAP theory is not consistent with the classical theory of the firm. Specifically, the capacity factor formalism used by LEAP does not support a classical interpretation in terms of a technological production function for energy conversion processes. The economic implications of this inconsistency are suboptimal process operation and short term negative profits in years where plant operation should be terminated. A new capacity factor formalism, which retains the behavioral features of the original model, is proposed to resolve these discrepancies.

  9. The need for data science in epidemic modelling. Comment on: "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al.

    NASA Astrophysics Data System (ADS)

    Danon, Leon; Brooks-Pollock, Ellen

    2016-09-01

    In their review, Chowell et al. consider the ability of mathematical models to predict early epidemic growth [1]. In particular, they question the central prediction of classical differential equation models that the number of cases grows exponentially during the early stages of an epidemic. Using examples including HIV and Ebola, they argue that classical models fail to capture key qualitative features of early growth and describe a selection of models that do capture non-exponential epidemic growth. An implication of this failure is that predictions may be inaccurate and unusable, highlighting the need for care when embarking upon modelling using classical methodology. There remains a lack of understanding of the mechanisms driving many observed epidemic patterns; we argue that data science should form a fundamental component of epidemic modelling, providing a rigorous methodology for data-driven approaches, rather than trying to enforce established frameworks. The need for refinement of classical models provides a strong argument for the use of data science, to identify qualitative characteristics and pinpoint the mechanisms responsible for the observed epidemic patterns.

  10. Quantum Bohmian model for financial market

    NASA Astrophysics Data System (ADS)

    Choustova, Olga Al.

    2007-01-01

    We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. The Hamiltonian formalism on the price/price-change phase space describes the classical-like evolution of prices. This classical dynamics of prices is determined by “hard” conditions (natural resources, industrial production, services and so on). These conditions are mathematically described by the classical financial potential V(q), where q=(q1,…,qn) is the vector of prices of various shares. But the information exchange and market psychology play important (and sometimes determining) role in price dynamics. We propose to describe such behavioral financial factors by using the pilot wave (Bohmian) model of quantum mechanics. The theory of financial behavioral waves takes into account the market psychology. The real trajectories of prices are determined (through the financial analogue of the second Newton law) by two financial potentials: classical-like V(q) (“hard” market conditions) and quantum-like U(q) (behavioral market conditions).

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

    Du, Qiang

    The rational design of materials, the development of accurate and efficient material simulation algorithms, and the determination of the response of materials to environments and loads occurring in practice all require an understanding of mechanics at disparate spatial and temporal scales. The project addresses mathematical and numerical analyses for material problems for which relevant scales range from those usually treated by molecular dynamics all the way up to those most often treated by classical elasticity. The prevalent approach towards developing a multiscale material model couples two or more well known models, e.g., molecular dynamics and classical elasticity, each of whichmore » is useful at a different scale, creating a multiscale multi-model. However, the challenges behind such a coupling are formidable and largely arise because the atomistic and continuum models employ nonlocal and local models of force, respectively. The project focuses on a multiscale analysis of the peridynamics materials model. Peridynamics can be used as a transition between molecular dynamics and classical elasticity so that the difficulties encountered when directly coupling those two models are mitigated. In addition, in some situations, peridynamics can be used all by itself as a material model that accurately and efficiently captures the behavior of materials over a wide range of spatial and temporal scales. Peridynamics is well suited to these purposes because it employs a nonlocal model of force, analogous to that of molecular dynamics; furthermore, at sufficiently large length scales and assuming smooth deformation, peridynamics can be approximated by classical elasticity. The project will extend the emerging mathematical and numerical analysis of peridynamics. One goal is to develop a peridynamics-enabled multiscale multi-model that potentially provides a new and more extensive mathematical basis for coupling classical elasticity and molecular dynamics, thus enabling next generation atomistic-to-continuum multiscale simulations. In addition, a rigorous studyof nite element discretizations of peridynamics will be considered. Using the fact that peridynamics is spatially derivative free, we will also characterize the space of admissible peridynamic solutions and carry out systematic analyses of the models, in particular rigorously showing how peridynamics encompasses fracture and other failure phenomena. Additional aspects of the project include the mathematical and numerical analysis of peridynamics applied to stochastic peridynamics models. In summary, the project will make feasible mathematically consistent multiscale models for the analysis and design of advanced materials.« less

  12. Mathematical modeling improves EC50 estimations from classical dose-response curves.

    PubMed

    Nyman, Elin; Lindgren, Isa; Lövfors, William; Lundengård, Karin; Cervin, Ida; Sjöström, Theresia Arbring; Altimiras, Jordi; Cedersund, Gunnar

    2015-03-01

    The β-adrenergic response is impaired in failing hearts. When studying β-adrenergic function in vitro, the half-maximal effective concentration (EC50 ) is an important measure of ligand response. We previously measured the in vitro contraction force response of chicken heart tissue to increasing concentrations of adrenaline, and observed a decreasing response at high concentrations. The classical interpretation of such data is to assume a maximal response before the decrease, and to fit a sigmoid curve to the remaining data to determine EC50 . Instead, we have applied a mathematical modeling approach to interpret the full dose-response curve in a new way. The developed model predicts a non-steady-state caused by a short resting time between increased concentrations of agonist, which affect the dose-response characterization. Therefore, an improved estimate of EC50 may be calculated using steady-state simulations of the model. The model-based estimation of EC50 is further refined using additional time-resolved data to decrease the uncertainty of the prediction. The resulting model-based EC50 (180-525 nm) is higher than the classically interpreted EC50 (46-191 nm). Mathematical modeling thus makes it possible to re-interpret previously obtained datasets, and to make accurate estimates of EC50 even when steady-state measurements are not experimentally feasible. The mathematical models described here have been submitted to the JWS Online Cellular Systems Modelling Database, and may be accessed at http://jjj.bio.vu.nl/database/nyman. © 2015 FEBS.

  13. Mathematical intelligence developed in math learning with classical backsound music of the classical era

    NASA Astrophysics Data System (ADS)

    Karlimah

    2018-05-01

    This study examines the application of classical music backsound in mathematics learning. The method used is quasi experimental design nonequivalent pretest-posttest control group in elementary school students in Tasikmalaya city, Indonesia. The results showed that classical music contributed significantly to the mathematical intelligence of elementary school students. The mathematical intelligence shown is in the cognitive ability ranging from the level of knowledge to evaluation. High level mathematical intelligence is shown by students in reading and writing integers with words and numbers. The low level of mathematical intelligence exists in projecting the story into a mathematical problem. The implication of this research is the use of classical music backsound on learning mathematics should pay attention to the level of difficulty of mathematics material being studied.

  14. Urns and Chameleons: two metaphors for two different types of measurements

    NASA Astrophysics Data System (ADS)

    Accardi, Luigi

    2013-09-01

    The awareness of the physical possibility of models of space, alternative with respect to the Euclidean one, begun to emerge towards the end of the 19-th century. At the end of the 20-th century a similar awareness emerged concerning the physical possibility of models of the laws of chance alternative with respect to the classical probabilistic models (Kolmogorov model). In geometry the mathematical construction of several non-Euclidean models of space preceded of about one century their applications in physics, which came with the theory of relativity. In physics the opposite situation took place. In fact, while the first example of non Kolmogorov probabilistic models emerged in quantum physics approximately one century ago, at the beginning of 1900, the awareness of the fact that this new mathematical formalism reflected a new mathematical model of the laws of chance had to wait until the early 1980's. In this long time interval the classical and the new probabilistic models were both used in the description and the interpretation of quantum phenomena and negatively interfered with each other because of the absence (for many decades) of a mathematical theory that clearly delimited the respective domains of application. The result of this interference was the emergence of the so-called the "paradoxes of quantum theory". For several decades there have been many different attempts to solve these paradoxes giving rise to what K. Popper baptized "the great quantum muddle": a debate which has been at the core of the philosophy of science for more than 50 years. However these attempts have led to contradictions between the two fundamental theories of the contemporary physical: the quantum theory and the theory of the relativity. Quantum probability identifies the reason of the emergence of non Kolmogorov models, and therefore of the so-called the paradoxes of quantum theory, in the difference between the notion of passive measurements like "reading pre-existent properties" (urn metaphor) and measurements consisting in reading "a response to an interaction" (chameleon metaphor). The non-trivial point is that one can prove that, while the urn scheme cannot lead to empirical data outside of classic probability, response based measurements can give rise to non classical statistics. The talk will include entirely classical examples of non classical statistics and potential applications to economic, sociological or biomedical phenomena.

  15. CDM: Teaching Discrete Mathematics to Computer Science Majors

    ERIC Educational Resources Information Center

    Sutner, Klaus

    2005-01-01

    CDM, for computational discrete mathematics, is a course that attempts to teach a number of topics in discrete mathematics to computer science majors. The course abandons the classical definition-theorem-proof model, and instead relies heavily on computation as a source of motivation and also for experimentation and illustration. The emphasis on…

  16. Inquiry Based-Computational Experiment, Acquisition of Threshold Concepts and Argumentation in Science and Mathematics Education

    ERIC Educational Resources Information Center

    Psycharis, Sarantos

    2016-01-01

    Computational experiment approach considers models as the fundamental instructional units of Inquiry Based Science and Mathematics Education (IBSE) and STEM Education, where the model take the place of the "classical" experimental set-up and simulation replaces the experiment. Argumentation in IBSE and STEM education is related to the…

  17. Modelling Of Flotation Processes By Classical Mathematical Methods - A Review

    NASA Astrophysics Data System (ADS)

    Jovanović, Ivana; Miljanović, Igor

    2015-12-01

    Flotation process modelling is not a simple task, mostly because of the process complexity, i.e. the presence of a large number of variables that (to a lesser or a greater extent) affect the final outcome of the mineral particles separation based on the differences in their surface properties. The attempts toward the development of the quantitative predictive model that would fully describe the operation of an industrial flotation plant started in the middle of past century and it lasts to this day. This paper gives a review of published research activities directed toward the development of flotation models based on the classical mathematical rules. The description and systematization of classical flotation models were performed according to the available references, with emphasize exclusively given to the flotation process modelling, regardless of the model application in a certain control system. In accordance with the contemporary considerations, models were classified as the empirical, probabilistic, kinetic and population balance types. Each model type is presented through the aspects of flotation modelling at the macro and micro process levels.

  18. Mathematics in the Making: Mapping Verbal Discourse in Polya's "Let Us Teach Guessing" Lesson

    ERIC Educational Resources Information Center

    Truxaw, Mary P.; DeFranco, Thomas C.

    2007-01-01

    This paper describes a detailed analysis of verbal discourse within an exemplary mathematics lesson--that is, George Polya teaching in the Mathematics Association of America [MAA] video classic, "Let Us Teach Guessing" (1966). The results of the analysis reveal an inductive model of teaching that represents recursive cycles rather than linear…

  19. Quantum correlations and dynamics from classical random fields valued in complex Hilbert spaces

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

    Khrennikov, Andrei

    2010-08-15

    One of the crucial differences between mathematical models of classical and quantum mechanics (QM) is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an ensemble of classical composite systems, one uses random variables taking values in the Cartesian product of the state spaces of subsystems.) We show that, nevertheless, it is possible to establish a natural correspondence between the classical and the quantum probabilistic descriptions of composite systems. Quantum averages for composite systems (including entangled) can be represented as averages with respect to classical randommore » fields. It is essentially what Albert Einstein dreamed of. QM is represented as classical statistical mechanics with infinite-dimensional phase space. While the mathematical construction is completely rigorous, its physical interpretation is a complicated problem. We present the basic physical interpretation of prequantum classical statistical field theory in Sec. II. However, this is only the first step toward real physical theory.« less

  20. Equilibriumizing all food chain chaos through reproductive efficiency.

    PubMed

    Deng, Bo

    2006-12-01

    The intraspecific interference of a top-predator is incorporated into a classical mathematical model for three-trophic food chains. All chaos types known to the classical model are shown to exist for this comprehensive model. It is further demonstrated that if the top-predator reproduces at high efficiency, then all chaotic dynamics will change to a stable coexisting equilibrium, a novel property not found in the classical model. This finding gives a mechanistic explanation to the question of why food chain chaos is rare in the field. It also suggests that high reproductive efficiency of top-predators tends to stabilize food chains.

  1. A stochastic differential equation analysis of cerebrospinal fluid dynamics.

    PubMed

    Raman, Kalyan

    2011-01-18

    Clinical measurements of intracranial pressure (ICP) over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data. The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE) that accommodates the fluctuations in ICP. The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise. Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.

  2. Mathematical modeling of fluxgate magnetic gradiometers

    NASA Astrophysics Data System (ADS)

    Milovzorov, D. G.; Yasoveev, V. Kh.

    2017-07-01

    Issues of designing fluxgate magnetic gradiometers are considered. The areas of application of fluxgate magnetic gradiometers are determined. The structure and layout of a two-component fluxgate magnetic gradiometer are presented. It is assumed that the fluxgates are strictly coaxial in the gradiometer body. Elements of the classical approach to the mathematical modeling of the spatial arrangement of solids are considered. The bases of the gradiometer body and their transformations during spatial displacement of the gradiometer are given. The problems of mathematical modeling of gradiometers are formulated, basic mathematical models of a two-component fluxgate gradiometer are developed, and the mathematical models are analyzed. A computer experiment was performed. Difference signals from the gradiometer fluxgates for the vertical and horizontal position of the gradiometer body are shown graphically as functions of the magnitude and direction of the geomagnetic field strength vector.

  3. Performance evaluation of coherent Ising machines against classical neural networks

    NASA Astrophysics Data System (ADS)

    Haribara, Yoshitaka; Ishikawa, Hitoshi; Utsunomiya, Shoko; Aihara, Kazuyuki; Yamamoto, Yoshihisa

    2017-12-01

    The coherent Ising machine is expected to find a near-optimal solution in various combinatorial optimization problems, which has been experimentally confirmed with optical parametric oscillators and a field programmable gate array circuit. The similar mathematical models were proposed three decades ago by Hopfield et al in the context of classical neural networks. In this article, we compare the computational performance of both models.

  4. Special relativity from observer's mathematics point of view

    NASA Astrophysics Data System (ADS)

    Khots, Boris; Khots, Dmitriy

    2015-09-01

    When we create mathematical models for quantum theory of light we assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of "infinitely small" and "infinitely large" quantities in arithmetic and the use of Newton - Cauchy definitions of a limit and derivative in analysis. We believe that is where the main problem lies in contemporary study of nature. We have introduced a new concept of Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. We use Einstein special relativity principles and get the analogue of classical Lorentz transformation. This work considers this transformation from Observer's Mathematics point of view.

  5. Current problems in applied mathematics and mathematical physics

    NASA Astrophysics Data System (ADS)

    Samarskii, A. A.

    Papers are presented on such topics as mathematical models in immunology, mathematical problems of medical computer tomography, classical orthogonal polynomials depending on a discrete variable, and boundary layer methods for singular perturbation problems in partial derivatives. Consideration is also given to the computer simulation of supernova explosion, nonstationary internal waves in a stratified fluid, the description of turbulent flows by unsteady solutions of the Navier-Stokes equations, and the reduced Galerkin method for external diffraction problems using the spline approximation of fields.

  6. The Multiphoton Interaction of Lambda Model Atom and Two-Mode Fields

    NASA Technical Reports Server (NTRS)

    Liu, Tang-Kun

    1996-01-01

    The system of two-mode fields interacting with atom by means of multiphotons is addressed, and the non-classical statistic quality of two-mode fields with interaction is discussed. Through mathematical calculation, some new rules of non-classical effects of two-mode fields which evolue with time, are established.

  7. Linear regression analysis and its application to multivariate chromatographic calibration for the quantitative analysis of two-component mixtures.

    PubMed

    Dinç, Erdal; Ozdemir, Abdil

    2005-01-01

    Multivariate chromatographic calibration technique was developed for the quantitative analysis of binary mixtures enalapril maleate (EA) and hydrochlorothiazide (HCT) in tablets in the presence of losartan potassium (LST). The mathematical algorithm of multivariate chromatographic calibration technique is based on the use of the linear regression equations constructed using relationship between concentration and peak area at the five-wavelength set. The algorithm of this mathematical calibration model having a simple mathematical content was briefly described. This approach is a powerful mathematical tool for an optimum chromatographic multivariate calibration and elimination of fluctuations coming from instrumental and experimental conditions. This multivariate chromatographic calibration contains reduction of multivariate linear regression functions to univariate data set. The validation of model was carried out by analyzing various synthetic binary mixtures and using the standard addition technique. Developed calibration technique was applied to the analysis of the real pharmaceutical tablets containing EA and HCT. The obtained results were compared with those obtained by classical HPLC method. It was observed that the proposed multivariate chromatographic calibration gives better results than classical HPLC.

  8. Thinking is believing.

    PubMed

    Kasturirangan, Rajesh

    2008-01-01

    Philosophers as well lay people often think of beliefs as psychological states with dubious epistemic properties. Beliefs are conceptualized as unregulated conceptual structures, for the most part hypothetical and often fanciful or deluded. Thinking and reasoning on the other hand are seen as rational activities regulated by rules and governed by norms. Computational modeling of the mind has focused on rule-governed behavior, ultimately trying to reduce them to rules of logic. What if thinking is less like reasoning and more like believing? I argue that the classical model of thought as rational is mistaken and that thinking is fundamentally constituted by believing. This new approach forces us to re-evaluate classical epistemic concepts like "truth", "justification" etc. Furthermore, if thinking is believing, then it is not clear how thoughts can be modeled computationally. We need new mathematical ideas to model thought, ideas that are quite different from traditional logic-based mathematical structures.

  9. An asymptotic Reissner-Mindlin plate model

    NASA Astrophysics Data System (ADS)

    Licht, Christian; Weller, Thibaut

    2018-06-01

    A mathematical study via variational convergence of a periodic distribution of classical linearly elastic thin plates softly abutted together shows that it is not necessary to use a different continuum model nor to make constitutive symmetry hypothesis as starting points to deduce the Reissner-Mindlin plate model.

  10. A Cognitive Diagnostic Modeling of Attribute Mastery in Massachusetts, Minnesota, and the U.S. National Sample Using the TIMSS 2007

    ERIC Educational Resources Information Center

    Lee, Young-Sun; Park, Yoon Soo; Taylan, Didem

    2011-01-01

    Studies of international mathematics achievement such as the Trends in Mathematics and Science Study (TIMSS) have employed classical test theory and item response theory to rank individuals within a latent ability continuum. Although these approaches have provided insights into comparisons between countries, they have yet to examine how specific…

  11. Temperature-Dependent Kinetic Prediction for Reactions Described by Isothermal Mathematics

    DOE PAGES

    Dinh, L. N.; Sun, T. C.; McLean, W.

    2016-09-12

    Most kinetic models are expressed in isothermal mathematics. In addition, this may lead unaware scientists either to the misconception that classical isothermal kinetic models cannot be used for any chemical process in an environment with a time-dependent temperature profile or, even worse, to a misuse of them. In reality, classical isothermal models can be employed to make kinetic predictions for reactions in environments with time-dependent temperature profiles, provided that there is a continuity/conservation in the reaction extent at every temperature–time step. In this article, fundamental analyses, illustrations, guiding tables, and examples are given to help the interested readers using eithermore » conventional isothermal reacted fraction curves or rate equations to make proper kinetic predictions for chemical reactions in environments with temperature profiles that vary, even arbitrarily, with time simply by the requirement of continuity/conservation of reaction extent whenever there is an external temperature change.« less

  12. A novel approach for inventory problem in the pharmaceutical supply chain.

    PubMed

    Candan, Gökçe; Yazgan, Harun Reşit

    2016-02-24

    In pharmaceutical enterprises, keeping up with global market conditions is possible with properly selected supply chain management policies. Generally; demand-driven classical supply chain model is used in the pharmaceutical industry. In this study, a new mathematical model is developed to solve an inventory problem in the pharmaceutical supply chain. Unlike the studies in literature, the "shelf life and product transition times" constraints are considered, simultaneously, first time in the pharmaceutical production inventory problem. The problem is formulated as a mixed-integer linear programming (MILP) model with a hybrid time representation. The objective is to maximize total net profit. Effectiveness of the proposed model is illustrated considering a classical and a vendor managed inventory (VMI) supply chain on an experimental study. To show the effectiveness of the model, an experimental study is performed; which contains 2 different supply chain policy (Classical and VMI), 24 and 30 months planning horizon, 10 and 15 different cephalosporin products. Finally the mathematical model is compared to another model in literature and the results show that proposed model is superior. This study suggest a novel approach for solving pharmaceutical inventory problem. The developed model is maximizing total net profit while determining optimal production plan under shelf life and product transition constraints in the pharmaceutical industry. And we believe that the proposed model is much more closed to real life unlike the other studies in literature.

  13. Mathematical interpretation of Brownian motor model: Limit cycles and directed transport phenomena

    NASA Astrophysics Data System (ADS)

    Yang, Jianqiang; Ma, Hong; Zhong, Suchuang

    2018-03-01

    In this article, we first suggest that the attractor of Brownian motor model is one of the reasons for the directed transport phenomenon of Brownian particle. We take the classical Smoluchowski-Feynman (SF) ratchet model as an example to investigate the relationship between limit cycles and directed transport phenomenon of the Brownian particle. We study the existence and variation rule of limit cycles of SF ratchet model at changing parameters through mathematical methods. The influences of these parameters on the directed transport phenomenon of a Brownian particle are then analyzed through numerical simulations. Reasonable mathematical explanations for the directed transport phenomenon of Brownian particle in SF ratchet model are also formulated on the basis of the existence and variation rule of the limit cycles and numerical simulations. These mathematical explanations provide a theoretical basis for applying these theories in physics, biology, chemistry, and engineering.

  14. Formal verification of mathematical software

    NASA Technical Reports Server (NTRS)

    Sutherland, D.

    1984-01-01

    Methods are investigated for formally specifying and verifying the correctness of mathematical software (software which uses floating point numbers and arithmetic). Previous work in the field was reviewed. A new model of floating point arithmetic called the asymptotic paradigm was developed and formalized. Two different conceptual approaches to program verification, the classical Verification Condition approach and the more recently developed Programming Logic approach, were adapted to use the asymptotic paradigm. These approaches were then used to verify several programs; the programs chosen were simplified versions of actual mathematical software.

  15. Global stability and periodic solution of the viral dynamics

    NASA Astrophysics Data System (ADS)

    Song, Xinyu; Neumann, Avidan U.

    2007-05-01

    It is well known that the mathematical models provide very important information for the research of human immunodeficiency virus-type 1 and hepatitis C virus (HCV). However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T cells and the viral particles. In this paper, we consider the classical mathematical model with saturation response of the infection rate. By stability analysis we obtain sufficient conditions on the parameters for the global stability of the infected steady state and the infection-free steady state. We also obtain the conditions for the existence of an orbitally asymptotically stable periodic solution. Numerical simulations are presented to illustrate the results.

  16. Why physics needs mathematics

    NASA Astrophysics Data System (ADS)

    Rohrlich, Fritz

    2011-12-01

    Classical and the quantum mechanical sciences are in essential need of mathematics. Only thus can the laws of nature be formulated quantitatively permitting quantitative predictions. Mathematics also facilitates extrapolations. But classical and quantum sciences differ in essential ways: they follow different laws of logic, Aristotelian and non-Aristotelian logics, respectively. These are explicated.

  17. The Effectiveness of Project Based Learning in Trigonometry

    NASA Astrophysics Data System (ADS)

    Gerhana, M. T. C.; Mardiyana, M.; Pramudya, I.

    2017-09-01

    This research aimed to explore the effectiveness of Project-Based Learning (PjBL) with scientific approach viewed from interpersonal intelligence toward students’ achievement learning in mathematics. This research employed quasi experimental research. The subjects of this research were grade X MIPA students in Sleman Yogyakarta. The result of the research showed that project-based learning model is more effective to generate students’ mathematics learning achievement that classical model with scientific approach. This is because in PjBL model students are more able to think actively and creatively. Students are faced with a pleasant atmosphere to solve a problem in everyday life. The use of project-based learning model is expected to be the choice of teachers to improve mathematics education.

  18. Application of quantum master equation for long-term prognosis of asset-prices

    NASA Astrophysics Data System (ADS)

    Khrennikova, Polina

    2016-05-01

    This study combines the disciplines of behavioral finance and an extension of econophysics, namely the concepts and mathematical structure of quantum physics. We apply the formalism of quantum theory to model the dynamics of some correlated financial assets, where the proposed model can be potentially applied for developing a long-term prognosis of asset price formation. At the informational level, the asset price states interact with each other by the means of a ;financial bath;. The latter is composed of agents' expectations about the future developments of asset prices on the finance market, as well as financially important information from mass-media, society, and politicians. One of the essential behavioral factors leading to the quantum-like dynamics of asset prices is the irrationality of agents' expectations operating on the finance market. These expectations lead to a deeper type of uncertainty concerning the future price dynamics of the assets, than given by a classical probability theory, e.g., in the framework of the classical financial mathematics, which is based on the theory of stochastic processes. The quantum dimension of the uncertainty in price dynamics is expressed in the form of the price-states superposition and entanglement between the prices of the different financial assets. In our model, the resolution of this deep quantum uncertainty is mathematically captured with the aid of the quantum master equation (its quantum Markov approximation). We illustrate our model of preparation of a future asset price prognosis by a numerical simulation, involving two correlated assets. Their returns interact more intensively, than understood by a classical statistical correlation. The model predictions can be extended to more complex models to obtain price configuration for multiple assets and portfolios.

  19. A mathematical model of a steady flow through the Kaplan turbine - The existence of a weak solution in the case of an arbitrarily large inflow

    NASA Astrophysics Data System (ADS)

    Neustupa, Tomáš

    2017-07-01

    The paper presents the mathematical model of a steady 2-dimensional viscous incompressible flow through a radial blade machine. The corresponding boundary value problem is studied in the rotating frame. We provide the classical and weak formulation of the problem. Using a special form of the so called "artificial" or "natural" boundary condition on the outflow, we prove the existence of a weak solution for an arbitrarily large inflow.

  20. A Toy Model of Electrodynamics in (1 + 1) Dimensions

    ERIC Educational Resources Information Center

    Boozer, A. D.

    2007-01-01

    A model is presented that describes a scalar field interacting with a point particle in (1+1) dimensions. The model exhibits many of the same phenomena that appear in classical electrodynamics, such as radiation and radiation damping, yet has a much simpler mathematical structure. By studying these phenomena in a highly simplified model, the…

  1. Theoretical Foundations of Study of Cartography

    NASA Astrophysics Data System (ADS)

    Talhofer, Václav; Hošková-Mayerová, Šárka

    2018-05-01

    Cartography and geoinformatics are technical-based fields which deal with modelling and visualization of landscape in the form of a map. The theoretical foundation is necessary to obtain during study of cartography and geoinformatics based mainly on mathematics. For the given subjects, mathematics is necessary for understanding of many procedures that are connected to modelling of the Earth as a celestial body, to ways of its projection into a plane, to methods and procedures of modelling of landscape and phenomena in society and visualization of these models in the form of electronic as well as classic paper maps. Not only general mathematics, but also its extension of differential geometry of curves and surfaces, ways of approximation of lines and surfaces of functional surfaces, mathematical statistics and multi-criterial analyses seem to be suitable and necessary. Underestimation of the significance of mathematical education in cartography and geoinformatics is inappropriate and lowers competence of cartographers and professionals in geographic information science and technology to solve problems.

  2. Mathematical and information-geometrical entropy for phenomenological Fourier and non-Fourier heat conduction

    NASA Astrophysics Data System (ADS)

    Li, Shu-Nan; Cao, Bing-Yang

    2017-09-01

    The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.

  3. Study on the tumor-induced angiogenesis using mathematical models.

    PubMed

    Suzuki, Takashi; Minerva, Dhisa; Nishiyama, Koichi; Koshikawa, Naohiko; Chaplain, Mark Andrew Joseph

    2018-01-01

    We studied angiogenesis using mathematical models describing the dynamics of tip cells. We reviewed the basic ideas of angiogenesis models and its numerical simulation technique to produce realistic computer graphics images of sprouting angiogenesis. We examined the classical model of Anderson-Chaplain using fundamental concepts of mass transport and chemical reaction with ECM degradation included. We then constructed two types of numerical schemes, model-faithful and model-driven ones, where new techniques of numerical simulation are introduced, such as transient probability, particle velocity, and Boolean variables. © 2017 The Authors. Cancer Science published by John Wiley & Sons Australia, Ltd on behalf of Japanese Cancer Association.

  4. The Pythagorean Proposition, Classics in Mathematics Education Series.

    ERIC Educational Resources Information Center

    Loomis, Elisha Scott

    This book is a reissue of the second edition which appeared in 1940. It has the distinction of being the first vintage mathematical work published in the NCTM series "Classics in Mathematics Education." The text includes a biography of Pythagoras and an account of historical data pertaining to his proposition. The remainder of the book shows 370…

  5. The role of a posteriori mathematics in physics

    NASA Astrophysics Data System (ADS)

    MacKinnon, Edward

    2018-05-01

    The calculus that co-evolved with classical mechanics relied on definitions of functions and differentials that accommodated physical intuitions. In the early nineteenth century mathematicians began the rigorous reformulation of calculus and eventually succeeded in putting almost all of mathematics on a set-theoretic foundation. Physicists traditionally ignore this rigorous mathematics. Physicists often rely on a posteriori math, a practice of using physical considerations to determine mathematical formulations. This is illustrated by examples from classical and quantum physics. A justification of such practice stems from a consideration of the role of phenomenological theories in classical physics and effective theories in contemporary physics. This relates to the larger question of how physical theories should be interpreted.

  6. Studying Reliability of Open Ended Mathematics Items According to the Classical Test Theory and Generalizability Theory

    ERIC Educational Resources Information Center

    Guler, Nese; Gelbal, Selahattin

    2010-01-01

    In this study, the Classical test theory and generalizability theory were used for determination to reliability of scores obtained from measurement tool of mathematics success. 24 open-ended mathematics question of the TIMSS-1999 was applied to 203 students in 2007-spring semester. Internal consistency of scores was found as 0.92. For…

  7. Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth

    PubMed Central

    Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M. L.; Hlatky, Lynn; Hahnfeldt, Philip

    2014-01-01

    Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic. PMID:25167199

  8. Classical mathematical models for description and prediction of experimental tumor growth.

    PubMed

    Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M L; Hlatky, Lynn; Hahnfeldt, Philip

    2014-08-01

    Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.

  9. Are quantum-mechanical-like models possible, or necessary, outside quantum physics?

    NASA Astrophysics Data System (ADS)

    Plotnitsky, Arkady

    2014-12-01

    This article examines some experimental conditions that invite and possibly require recourse to quantum-mechanical-like mathematical models (QMLMs), models based on the key mathematical features of quantum mechanics, in scientific fields outside physics, such as biology, cognitive psychology, or economics. In particular, I consider whether the following two correlative features of quantum phenomena that were decisive for establishing the mathematical formalism of quantum mechanics play similarly important roles in QMLMs elsewhere. The first is the individuality and discreteness of quantum phenomena, and the second is the irreducibly probabilistic nature of our predictions concerning them, coupled to the particular character of the probabilities involved, as different from the character of probabilities found in classical physics. I also argue that these features could be interpreted in terms of a particular form of epistemology that suspends and even precludes a causal and, in the first place, realist description of quantum objects and processes. This epistemology limits the descriptive capacity of quantum theory to the description, classical in nature, of the observed quantum phenomena manifested in measuring instruments. Quantum mechanics itself only provides descriptions, probabilistic in nature, concerning numerical data pertaining to such phenomena, without offering a physical description of quantum objects and processes. While QMLMs share their use of the quantum-mechanical or analogous mathematical formalism, they may differ by the roles, if any, the two features in question play in them and by different ways of interpreting the phenomena they considered and this formalism itself. This article will address those differences as well.

  10. The evolution of utility functions and psychological altruism.

    PubMed

    Clavien, Christine; Chapuisat, Michel

    2016-04-01

    Numerous studies show that humans tend to be more cooperative than expected given the assumption that they are rational maximizers of personal gain. As a result, theoreticians have proposed elaborated formal representations of human decision-making, in which utility functions including "altruistic" or "moral" preferences replace the purely self-oriented "Homo economicus" function. Here we review mathematical approaches that provide insights into the mathematical stability of alternative utility functions. Candidate utility functions may be evaluated with help of game theory, classical modeling of social evolution that focuses on behavioral strategies, and modeling of social evolution that focuses directly on utility functions. We present the advantages of the latter form of investigation and discuss one surprisingly precise result: "Homo economicus" as well as "altruistic" utility functions are less stable than a function containing a preference for the common welfare that is only expressed in social contexts composed of individuals with similar preferences. We discuss the contribution of mathematical models to our understanding of human other-oriented behavior, with a focus on the classical debate over psychological altruism. We conclude that human can be psychologically altruistic, but that psychological altruism evolved because it was generally expressed towards individuals that contributed to the actor's fitness, such as own children, romantic partners and long term reciprocators. Copyright © 2015 Elsevier Ltd. All rights reserved.

  11. A general consumer-resource population model

    USGS Publications Warehouse

    Lafferty, Kevin D.; DeLeo, Giulio; Briggs, Cheryl J.; Dobson, Andrew P.; Gross, Thilo; Kuris, Armand M.

    2015-01-01

    Food-web dynamics arise from predator-prey, parasite-host, and herbivore-plant interactions. Models for such interactions include up to three consumer activity states (questing, attacking, consuming) and up to four resource response states (susceptible, exposed, ingested, resistant). Articulating these states into a general model allows for dissecting, comparing, and deriving consumer-resource models. We specify this general model for 11 generic consumer strategies that group mathematically into predators, parasites, and micropredators and then derive conditions for consumer success, including a universal saturating functional response. We further show how to use this framework to create simple models with a common mathematical lineage and transparent assumptions. Underlying assumptions, missing elements, and composite parameters are revealed when classic consumer-resource models are derived from the general model.

  12. The Modulus of Rupture from a Mathematical Point of View

    NASA Astrophysics Data System (ADS)

    Quintela, P.; Sánchez, M. T.

    2007-04-01

    The goal of this work is to present a complete mathematical study about the three-point bending experiments and the modulus of rupture of brittle materials. We will present the mathematical model associated to three-point bending experiments and we will use the asymptotic expansion method to obtain a new formula to calculate the modulus of rupture. We will compare the modulus of rupture of porcelain obtained with the previous formula with that obtained by using the classic theoretical formula. Finally, we will also present one and three-dimensional numerical simulations to compute the modulus of rupture.

  13. Sifting noisy data for truths about noisy systems. Comment on "Extracting physics of life at the molecular level: A review of single-molecule data analyses" by W. Colomb and S.K. Sarkar

    NASA Astrophysics Data System (ADS)

    Flyvbjerg, Henrik; Mortensen, Kim I.

    2015-06-01

    With each new aspect of nature that becomes accessible to quantitative science, new needs arise for data analysis and mathematical modeling. The classical example is Tycho Brahe's accurate and comprehensive observations of planets, which made him hire Kepler for his mathematical skills to assist with the data analysis. We all learned what that lead to: Kepler's three laws of planetary motion, phenomenology in purely mathematical form. Newton built on this, and the scientific revolution was over, completed.

  14. A comparison of mixed-integer linear programming models for workforce scheduling with position-dependent processing times

    NASA Astrophysics Data System (ADS)

    Moreno-Camacho, Carlos A.; Montoya-Torres, Jairo R.; Vélez-Gallego, Mario C.

    2018-06-01

    Only a few studies in the available scientific literature address the problem of having a group of workers that do not share identical levels of productivity during the planning horizon. This study considers a workforce scheduling problem in which the actual processing time is a function of the scheduling sequence to represent the decline in workers' performance, evaluating two classical performance measures separately: makespan and maximum tardiness. Several mathematical models are compared with each other to highlight the advantages of each approach. The mathematical models are tested with randomly generated instances available from a public e-library.

  15. Challenges of Electronic Medical Surveillance Systems

    DTIC Science & Technology

    2004-06-01

    More sophisticated approaches, such as regression models and classical autoregressive moving average ( ARIMA ) models that make estimates based on...with those predicted by a mathematical model . The primary benefit of ARIMA models is their ability to correct for local trends in the data so that...works well, for example, during a particularly severe flu season, where prolonged periods of high visit rates are adjusted to by the ARIMA model , thus

  16. A System Computational Model of Implicit Emotional Learning

    PubMed Central

    Puviani, Luca; Rama, Sidita

    2016-01-01

    Nowadays, the experimental study of emotional learning is commonly based on classical conditioning paradigms and models, which have been thoroughly investigated in the last century. Unluckily, models based on classical conditioning are unable to explain or predict important psychophysiological phenomena, such as the failure of the extinction of emotional responses in certain circumstances (for instance, those observed in evaluative conditioning, in post-traumatic stress disorders and in panic attacks). In this manuscript, starting from the experimental results available from the literature, a computational model of implicit emotional learning based both on prediction errors computation and on statistical inference is developed. The model quantitatively predicts (a) the occurrence of evaluative conditioning, (b) the dynamics and the resistance-to-extinction of the traumatic emotional responses, (c) the mathematical relation between classical conditioning and unconditioned stimulus revaluation. Moreover, we discuss how the derived computational model can lead to the development of new animal models for resistant-to-extinction emotional reactions and novel methodologies of emotions modulation. PMID:27378898

  17. A System Computational Model of Implicit Emotional Learning.

    PubMed

    Puviani, Luca; Rama, Sidita

    2016-01-01

    Nowadays, the experimental study of emotional learning is commonly based on classical conditioning paradigms and models, which have been thoroughly investigated in the last century. Unluckily, models based on classical conditioning are unable to explain or predict important psychophysiological phenomena, such as the failure of the extinction of emotional responses in certain circumstances (for instance, those observed in evaluative conditioning, in post-traumatic stress disorders and in panic attacks). In this manuscript, starting from the experimental results available from the literature, a computational model of implicit emotional learning based both on prediction errors computation and on statistical inference is developed. The model quantitatively predicts (a) the occurrence of evaluative conditioning, (b) the dynamics and the resistance-to-extinction of the traumatic emotional responses, (c) the mathematical relation between classical conditioning and unconditioned stimulus revaluation. Moreover, we discuss how the derived computational model can lead to the development of new animal models for resistant-to-extinction emotional reactions and novel methodologies of emotions modulation.

  18. The Computer Simulation of Liquids by Molecular Dynamics.

    ERIC Educational Resources Information Center

    Smith, W.

    1987-01-01

    Proposes a mathematical computer model for the behavior of liquids using the classical dynamic principles of Sir Isaac Newton and the molecular dynamics method invented by other scientists. Concludes that other applications will be successful using supercomputers to go beyond simple Newtonian physics. (CW)

  19. ECOLOGICAL THEORY. A general consumer-resource population model.

    PubMed

    Lafferty, Kevin D; DeLeo, Giulio; Briggs, Cheryl J; Dobson, Andrew P; Gross, Thilo; Kuris, Armand M

    2015-08-21

    Food-web dynamics arise from predator-prey, parasite-host, and herbivore-plant interactions. Models for such interactions include up to three consumer activity states (questing, attacking, consuming) and up to four resource response states (susceptible, exposed, ingested, resistant). Articulating these states into a general model allows for dissecting, comparing, and deriving consumer-resource models. We specify this general model for 11 generic consumer strategies that group mathematically into predators, parasites, and micropredators and then derive conditions for consumer success, including a universal saturating functional response. We further show how to use this framework to create simple models with a common mathematical lineage and transparent assumptions. Underlying assumptions, missing elements, and composite parameters are revealed when classic consumer-resource models are derived from the general model. Copyright © 2015, American Association for the Advancement of Science.

  20. Conditionally prepared photon and quantum imaging

    NASA Astrophysics Data System (ADS)

    Lvovsky, Alexander I.; Aichele, Thomas

    2004-10-01

    We discuss a classical model allowing one to visualize and characterize the optical mode of the single photon generated by means of a conditional measurement on a biphoton produced in parametric down-conversion. The model is based on Klyshko's advanced wave interpretation, but extends beyond it, providing a precise mathematical description of the advanced wave. The optical mode of the conditional photon is shown to be identical to the mode of the classical difference-frequency field generated due to nonlinear interaction of the partially coherent advanced wave with the pump pulse. With this "nonlinear advanced wave model" most coherence properties of the conditional photon become manifest, which permits one to intuitively understand many recent results, in particular, in quantum imaging.

  1. A note on powers in finite fields

    NASA Astrophysics Data System (ADS)

    Aabrandt, Andreas; Lundsgaard Hansen, Vagn

    2016-08-01

    The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years, the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analysis, system theory, coding theory and cryptology. In this connection, it is of interest to know criteria for the existence of squares and other powers in arbitrary finite fields. Making good use of polynomial division in polynomial rings over finite fields, we have examined a classical criterion of Euler for squares in odd prime fields, giving it a formulation that is apt for generalization to arbitrary finite fields and powers. Our proof uses algebra rather than classical number theory, which makes it convenient when presenting basic methods of applied algebra in the classroom.

  2. Estimation of the dynamics and rate of transmission of classical swine fever (hog cholera) in wild pigs.

    PubMed Central

    Hone, J.; Pech, R.; Yip, P.

    1992-01-01

    Infectious diseases establish in a population of wildlife hosts when the number of secondary infections is greater than or equal to one. To estimate whether establishment will occur requires extensive experience or a mathematical model of disease dynamics and estimates of the parameters of the disease model. The latter approach is explored here. Methods for estimating key model parameters, the transmission coefficient (beta) and the basic reproductive rate (RDRS), are described using classical swine fever (hog cholera) in wild pigs as an example. The tentative results indicate that an acute infection of classical swine fever will establish in a small population of wild pigs. Data required for estimation of disease transmission rates are reviewed and sources of bias and alternative methods discussed. A comprehensive evaluation of the biases and efficiencies of the methods is needed. PMID:1582476

  3. Which Kind of Mathematics for Quantum Mechanics? the Relevance of H. Weyl's Program of Research

    NASA Astrophysics Data System (ADS)

    Drago, Antonino

    In 1918 Weyl's book Das Kontinuum planned to found anew mathematics upon more conservative bases than both rigorous mathematics and set theory. It gave birth to the so-called Weyl's elementary mathematics, i.e. an intermediate mathematics between the mathematics rejecting at all actual infinity and the classical one including it almost freely. The present paper scrutinises the subsequent Weyl's book Gruppentheorie und Quantenmechanik (1928) as a program for founding anew theoretical physics - through quantum theory - and at the same time developing his mathematics through an improvement of group theory; which, according to Weyl, is a mathematical theory effacing the old distinction between discrete and continuous mathematics. Evidence from Weyl's writings is collected for supporting this interpretation. Then Weyl's program is evaluated as unsuccessful, owing to some crucial difficulties of both physical and mathematical nature. The present clear-cut knowledge of Weyl's elementary mathematics allows us to re-evaluate Weyl's program in order to look for more adequate formulations of quantum mechanics in any weaker kind of mathematics than the classical one.

  4. Statistical Mechanics of Disordered Systems - Series: Cambridge Series in Statistical and Probabilistic Mathematics (No. 18)

    NASA Astrophysics Data System (ADS)

    Bovier, Anton

    2006-06-01

    Our mathematical understanding of the statistical mechanics of disordered systems is going through a period of stunning progress. This self-contained book is a graduate-level introduction for mathematicians and for physicists interested in the mathematical foundations of the field, and can be used as a textbook for a two-semester course on mathematical statistical mechanics. It assumes only basic knowledge of classical physics and, on the mathematics side, a good working knowledge of graduate-level probability theory. The book starts with a concise introduction to statistical mechanics, proceeds to disordered lattice spin systems, and concludes with a presentation of the latest developments in the mathematical understanding of mean-field spin glass models. In particular, recent progress towards a rigorous understanding of the replica symmetry-breaking solutions of the Sherrington-Kirkpatrick spin glass models, due to Guerra, Aizenman-Sims-Starr and Talagrand, is reviewed in some detail. Comprehensive introduction to an active and fascinating area of research Clear exposition that builds to the state of the art in the mathematics of spin glasses Written by a well-known and active researcher in the field

  5. Mechanisms explaining Coulomb's electric force & Lorentz's magnetic force from a classical perspective

    NASA Astrophysics Data System (ADS)

    Correnti, Dan S.

    2018-06-01

    The underlying mechanisms of the fundamental electric and magnetic forces are not clear in current models; they are mainly mathematical constructs. This study examines the underlying physics from a classical viewpoint to explain Coulomb's electric force and Lorentz's magnetic force. This is accomplished by building upon already established physics. Although no new physics is introduced, extension of existing models is made by close examination. We all know that an electron carries a bound cylindrical B-field (CBF) as it translates. Here, we show how the electron CBF plays an intrinsic role in the generation of the electric and magnetic forces.

  6. Mathematical modeling of damage in unidirectional composites

    NASA Technical Reports Server (NTRS)

    Goree, J. G.; Dharani, L. R.; Jones, W. F.

    1981-01-01

    A review of some approximate analytical models for damaged, fiber reinforced composite materials is presented. Using the classical shear lag stress displacement assumption, solutions are presented for a unidirectional laminate containing a notch, a rectangular cut-out, and a circular hole. The models account for longitudinal matrix yielding and splitting as well as transverse matrix yielding and fiber breakage. The constraining influence of a cover sheet on the unidirectional laminate is also modeled.

  7. The Real and the Mathematical in Quantum Modeling: From Principles to Models and from Models to Principles

    NASA Astrophysics Data System (ADS)

    Plotnitsky, Arkady

    2017-06-01

    The history of mathematical modeling outside physics has been dominated by the use of classical mathematical models, C-models, primarily those of a probabilistic or statistical nature. More recently, however, quantum mathematical models, Q-models, based in the mathematical formalism of quantum theory have become more prominent in psychology, economics, and decision science. The use of Q-models in these fields remains controversial, in part because it is not entirely clear whether Q-models are necessary for dealing with the phenomena in question or whether C-models would still suffice. My aim, however, is not to assess the necessity of Q-models in these fields, but instead to reflect on what the possible applicability of Q-models may tell us about the corresponding phenomena there, vis-à-vis quantum phenomena in physics. In order to do so, I shall first discuss the key reasons for the use of Q-models in physics. In particular, I shall examine the fundamental principles that led to the development of quantum mechanics. Then I shall consider a possible role of similar principles in using Q-models outside physics. Psychology, economics, and decision science borrow already available Q-models from quantum theory, rather than derive them from their own internal principles, while quantum mechanics was derived from such principles, because there was no readily available mathematical model to handle quantum phenomena, although the mathematics ultimately used in quantum did in fact exist then. I shall argue, however, that the principle perspective on mathematical modeling outside physics might help us to understand better the role of Q-models in these fields and possibly to envision new models, conceptually analogous to but mathematically different from those of quantum theory, helpful or even necessary there or in physics itself. I shall suggest one possible type of such models, singularized probabilistic, SP, models, some of which are time-dependent, TDSP-models. The necessity of using such models may change the nature of mathematical modeling in science and, thus, the nature of science, as it happened in the case of Q-models, which not only led to a revolutionary transformation of physics but also opened new possibilities for scientific thinking and mathematical modeling beyond physics.

  8. Ensembles and Experiments in Classical and Quantum Physics

    NASA Astrophysics Data System (ADS)

    Neumaier, Arnold

    A philosophically consistent axiomatic approach to classical and quantum mechanics is given. The approach realizes a strong formal implementation of Bohr's correspondence principle. In all instances, classical and quantum concepts are fully parallel: the same general theory has a classical realization and a quantum realization. Extending the ''probability via expectation'' approach of Whittle to noncommuting quantities, this paper defines quantities, ensembles, and experiments as mathematical concepts and shows how to model complementarity, uncertainty, probability, nonlocality and dynamics in these terms. The approach carries no connotation of unlimited repeatability; hence it can be applied to unique systems such as the universe. Consistent experiments provide an elegant solution to the reality problem, confirming the insistence of the orthodox Copenhagen interpretation on that there is nothing but ensembles, while avoiding its elusive reality picture. The weak law of large numbers explains the emergence of classical properties for macroscopic systems.

  9. Quantum Social Science

    NASA Astrophysics Data System (ADS)

    Haven, Emmanuel; Khrennikov, Andrei

    2013-01-01

    Preface; Part I. Physics Concepts in Social Science? A Discussion: 1. Classical, statistical and quantum mechanics: all in one; 2. Econophysics: statistical physics and social science; 3. Quantum social science: a non-mathematical motivation; Part II. Mathematics and Physics Preliminaries: 4. Vector calculus and other mathematical preliminaries; 5. Basic elements of quantum mechanics; 6. Basic elements of Bohmian mechanics; Part III. Quantum Probabilistic Effects in Psychology: Basic Questions and Answers: 7. A brief overview; 8. Interference effects in psychology - an introduction; 9. A quantum-like model of decision making; Part IV. Other Quantum Probabilistic Effects in Economics, Finance and Brain Sciences: 10. Financial/economic theory in crisis; 11. Bohmian mechanics in finance and economics; 12. The Bohm-Vigier Model and path simulation; 13. Other applications to economic/financial theory; 14. The neurophysiological sources of quantum-like processing in the brain; Conclusion; Glossary; Index.

  10. A Brief Historical Development of Classical Mathematics before the Renaissance

    ERIC Educational Resources Information Center

    Debnath, Lokenath

    2011-01-01

    This article deals with a short history of mathematics and mathematical scientists during the ancient and medieval periods. Included are some major developments of the ancient, Indian, Arabic, Egyptian, Greek and medieval mathematics and their significant impact on the Renaissance mathematics. Special attention is given to many results, theorems,…

  11. Development and validation of a piloted simulation of a helicopter and external sling load

    NASA Technical Reports Server (NTRS)

    Shaughnessy, J. D.; Deaux, T. N.; Yenni, K. R.

    1979-01-01

    A generalized, real time, piloted, visual simulation of a single rotor helicopter, suspension system, and external load is described and validated for the full flight envelope of the U.S. Army CH-54 helicopter and cargo container as an example. The mathematical model described uses modified nonlinear classical rotor theory for both the main rotor and tail rotor, nonlinear fuselage aerodynamics, an elastic suspension system, nonlinear load aerodynamics, and a loadground contact model. The implementation of the mathematical model on a large digital computing system is described, and validation of the simulation is discussed. The mathematical model is validated by comparing measured flight data with simulated data, by comparing linearized system matrices, eigenvalues, and eigenvectors with manufacturers' data, and by the subjective comparison of handling characteristics by experienced pilots. A visual landing display system for use in simulation which generates the pilot's forward looking real world display was examined and a special head up, down looking load/landing zone display is described.

  12. Mathematical modeling of unicellular microalgae and cyanobacteria metabolism for biofuel production.

    PubMed

    Baroukh, Caroline; Muñoz-Tamayo, Rafael; Bernard, Olivier; Steyer, Jean-Philippe

    2015-06-01

    The conversion of microalgae lipids and cyanobacteria carbohydrates into biofuels appears to be a promising source of renewable energy. This requires a thorough understanding of their carbon metabolism, supported by mathematical models, in order to optimize biofuel production. However, unlike heterotrophic microorganisms that utilize the same substrate as sources of energy and carbon, photoautotrophic microorganisms require light for energy and CO2 as carbon source. Furthermore, they are submitted to permanent fluctuating light environments due to outdoor cultivation or mixing inducing a flashing effect. Although, modeling these nonstandard organisms is a major challenge for which classical tools are often inadequate, this step remains a prerequisite towards efficient optimization of outdoor biofuel production at an industrial scale. Copyright © 2015 Elsevier Ltd. All rights reserved.

  13. On mathematical modelling of aeroelastic problems with finite element method

    NASA Astrophysics Data System (ADS)

    Sváček, Petr

    2018-06-01

    This paper is interested in solution of two-dimensional aeroelastic problems. Two mathematical models are compared for a benchmark problem. First, the classical approach of linearized aerodynamical forces is described to determine the aeroelastic instability and the aeroelastic response in terms of frequency and damping coefficient. This approach is compared to the coupled fluid-structure model solved with the aid of finite element method used for approximation of the incompressible Navier-Stokes equations. The finite element approximations are coupled to the non-linear motion equations of a flexibly supported airfoil. Both methods are first compared for the case of small displacement, where the linearized approach can be well adopted. The influence of nonlinearities for the case of post-critical regime is discussed.

  14. Semisolid Metal Processing Consortium

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

    Apelian,Diran

    Mathematical modeling and simulations of semisolid filling processes remains a critical issue in understanding and optimizing the process. Semisolid slurries are non-Newtonian materials that exhibit complex rheological behavior. There the way these slurries flow in cavities is very different from the way liquid in classical casting fills cavities. Actually filling in semisolid processing is often counter intuitive

  15. On the Reasonable and Unreasonable Effectiveness of Mathematics in Classical and Quantum Physics

    NASA Astrophysics Data System (ADS)

    Plotnitsky, Arkady

    2011-03-01

    The point of departure for this article is Werner Heisenberg's remark, made in 1929: "It is not surprising that our language [or conceptuality] should be incapable of describing processes occurring within atoms, for … it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. … Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme—the quantum theory [quantum mechanics]—which seems entirely adequate for the treatment of atomic processes." The cost of this discovery, at least in Heisenberg's and related interpretations of quantum mechanics (such as that of Niels Bohr), is that, in contrast to classical mechanics, the mathematical scheme in question no longer offers a description, even an idealized one, of quantum objects and processes. This scheme only enables predictions, in general, probabilistic in character, of the outcomes of quantum experiments. As a result, a new type of the relationships between mathematics and physics is established, which, in the language of Eugene Wigner adopted in my title, indeed makes the effectiveness of mathematics unreasonable in quantum but, as I shall explain, not in classical physics. The article discusses these new relationships between mathematics and physics in quantum theory and their implications for theoretical physics—past, present, and future.

  16. Ignorance is a bliss: Mathematical structure of many-box models

    NASA Astrophysics Data System (ADS)

    Tylec, Tomasz I.; Kuś, Marek

    2018-03-01

    We show that the propositional system of a many-box model is always a set-representable effect algebra. In particular cases of 2-box and 1-box models, it is an orthomodular poset and an orthomodular lattice, respectively. We discuss the relation of the obtained results with the so-called Local Orthogonality principle. We argue that non-classical properties of box models are the result of a dual enrichment of the set of states caused by the impoverishment of the set of propositions. On the other hand, quantum mechanical models always have more propositions as well as more states than the classical ones. Consequently, we show that the box models cannot be considered as generalizations of quantum mechanical models and seeking additional principles that could allow us to "recover quantum correlations" in box models are, at least from the fundamental point of view, pointless.

  17. Abstract quantum computing machines and quantum computational logics

    NASA Astrophysics Data System (ADS)

    Chiara, Maria Luisa Dalla; Giuntini, Roberto; Sergioli, Giuseppe; Leporini, Roberto

    2016-06-01

    Classical and quantum parallelism are deeply different, although it is sometimes claimed that quantum Turing machines are nothing but special examples of classical probabilistic machines. We introduce the concepts of deterministic state machine, classical probabilistic state machine and quantum state machine. On this basis, we discuss the question: To what extent can quantum state machines be simulated by classical probabilistic state machines? Each state machine is devoted to a single task determined by its program. Real computers, however, behave differently, being able to solve different kinds of problems. This capacity can be modeled, in the quantum case, by the mathematical notion of abstract quantum computing machine, whose different programs determine different quantum state machines. The computations of abstract quantum computing machines can be linguistically described by the formulas of a particular form of quantum logic, termed quantum computational logic.

  18. Modeling of delays in PKPD: classical approaches and a tutorial for delay differential equations.

    PubMed

    Koch, Gilbert; Krzyzanski, Wojciech; Pérez-Ruixo, Juan Jose; Schropp, Johannes

    2014-08-01

    In pharmacokinetics/pharmacodynamics (PKPD) the measured response is often delayed relative to drug administration, individuals in a population have a certain lifespan until they maturate or the change of biomarkers does not immediately affects the primary endpoint. The classical approach in PKPD is to apply transit compartment models (TCM) based on ordinary differential equations to handle such delays. However, an alternative approach to deal with delays are delay differential equations (DDE). DDEs feature additional flexibility and properties, realize more complex dynamics and can complementary be used together with TCMs. We introduce several delay based PKPD models and investigate mathematical properties of general DDE based models, which serve as subunits in order to build larger PKPD models. Finally, we review current PKPD software with respect to the implementation of DDEs for PKPD analysis.

  19. A modified elastance model to control mock ventricles in real-time: numerical and experimental validation.

    PubMed

    Colacino, Francesco Maria; Moscato, Francesco; Piedimonte, Fabio; Danieli, Guido; Nicosia, Salvatore; Arabia, Maurizio

    2008-01-01

    This article describes an elastance-based mock ventricle able to reproduce the correct ventricular pressure-volume relationship and its correct interaction with the hydraulic circuit connected to it. A real-time control of the mock ventricle was obtained by a new left ventricular mathematical model including resistive and inductive terms added to the classical Suga-Sagawa elastance model throughout the whole cardiac cycle. A valved piston pump was used to mimic the left ventricle. The pressure measured into the pump chamber was fed back into the mathematical model and the calculated reference left ventricular volume was used to drive the piston. Results show that the classical model is very sensitive to pressure disturbances, especially during the filling phase, while the modified model is able to filter out the oscillations thus eliminating their detrimental effects. The presented model is thus suitable to control mock ventricles in real-time, where sudden pressure disturbances represent a key issue and are not negligible. This real-time controlled mock ventricle is able to reproduce the elastance mechanism of a natural ventricle by mimicking its preload (mean atrial pressure) and afterload (mean aortic pressure) sensitivity, i.e., the Starling law. Therefore, it can be used for designing and testing cardiovascular prostheses due to its capability to reproduce the correct ventricle-vascular system interaction.

  20. Mathematical Modeling of Torsional Surface Wave Propagation in a Non-Homogeneous Transverse Isotropic Elastic Solid Semi-Infinite Medium Under a Layer

    NASA Astrophysics Data System (ADS)

    Sethi, M.; Sharma, A.; Vasishth, A.

    2017-05-01

    The present paper deals with the mathematical modeling of the propagation of torsional surface waves in a non-homogeneous transverse isotropic elastic half-space under a rigid layer. Both rigidities and density of the half-space are assumed to vary inversely linearly with depth. Separation of variable method has been used to get the analytical solutions for the dispersion equation of the torsional surface waves. Also, the effects of nonhomogeneities on the phase velocity of torsional surface waves have been shown graphically. Also, dispersion equations have been derived for some particular cases, which are in complete agreement with some classical results.

  1. Extraction of decision rules via imprecise probabilities

    NASA Astrophysics Data System (ADS)

    Abellán, Joaquín; López, Griselda; Garach, Laura; Castellano, Javier G.

    2017-05-01

    Data analysis techniques can be applied to discover important relations among features. This is the main objective of the Information Root Node Variation (IRNV) technique, a new method to extract knowledge from data via decision trees. The decision trees used by the original method were built using classic split criteria. The performance of new split criteria based on imprecise probabilities and uncertainty measures, called credal split criteria, differs significantly from the performance obtained using the classic criteria. This paper extends the IRNV method using two credal split criteria: one based on a mathematical parametric model, and other one based on a non-parametric model. The performance of the method is analyzed using a case study of traffic accident data to identify patterns related to the severity of an accident. We found that a larger number of rules is generated, significantly supplementing the information obtained using the classic split criteria.

  2. Resolution of quantum singularities

    NASA Astrophysics Data System (ADS)

    Konkowski, Deborah; Helliwell, Thomas

    2017-01-01

    A review of quantum singularities in static and conformally static spacetimes is given. A spacetime is said to be quantum mechanically non-singular if a quantum wave packet does not feel, in some sense, the presence of a singularity; mathematically, this means that the wave operator is essentially self-adjoint on the space of square integrable functions. Spacetimes with classical mild singularities (quasiregular ones) to spacetimes with classical strong curvature singularities have been tested. Here we discuss the similarities and differences between classical singularities that are healed quantum mechanically and those that are not. Possible extensions of the mathematical technique to more physically realistic spacetimes are discussed.

  3. A Mathematical Model for Railway Control Systems

    NASA Technical Reports Server (NTRS)

    Hoover, D. N.

    1996-01-01

    We present a general method for modeling safety aspects of railway control systems. Using our modeling method, one can progressively refine an abstract railway safety model, sucessively adding layers of detail about how a real system actually operates, while maintaining a safety property that refines the original abstract safety property. This method supports a top-down approach to specification of railway control systems and to proof of a variety of safety-related properties. We demonstrate our method by proving safety of the classical block control system.

  4. Black-Scholes model under subordination

    NASA Astrophysics Data System (ADS)

    Stanislavsky, A. A.

    2003-02-01

    In this paper, we consider a new mathematical extension of the Black-Scholes (BS) model in which the stochastic time and stock share price evolution is described by two independent random processes. The parent process is Brownian, and the directing process is inverse to the totally skewed, strictly α-stable process. The subordinated process represents the Brownian motion indexed by an independent, continuous and increasing process. This allows us to introduce the long-term memory effects in the classical BS model.

  5. Mathematical Modeling of Intestinal Iron Absorption Using Genetic Programming

    PubMed Central

    Colins, Andrea; Gerdtzen, Ziomara P.; Nuñez, Marco T.; Salgado, J. Cristian

    2017-01-01

    Iron is a trace metal, key for the development of living organisms. Its absorption process is complex and highly regulated at the transcriptional, translational and systemic levels. Recently, the internalization of the DMT1 transporter has been proposed as an additional regulatory mechanism at the intestinal level, associated to the mucosal block phenomenon. The short-term effect of iron exposure in apical uptake and initial absorption rates was studied in Caco-2 cells at different apical iron concentrations, using both an experimental approach and a mathematical modeling framework. This is the first report of short-term studies for this system. A non-linear behavior in the apical uptake dynamics was observed, which does not follow the classic saturation dynamics of traditional biochemical models. We propose a method for developing mathematical models for complex systems, based on a genetic programming algorithm. The algorithm is aimed at obtaining models with a high predictive capacity, and considers an additional parameter fitting stage and an additional Jackknife stage for estimating the generalization error. We developed a model for the iron uptake system with a higher predictive capacity than classic biochemical models. This was observed both with the apical uptake dataset used for generating the model and with an independent initial rates dataset used to test the predictive capacity of the model. The model obtained is a function of time and the initial apical iron concentration, with a linear component that captures the global tendency of the system, and a non-linear component that can be associated to the movement of DMT1 transporters. The model presented in this paper allows the detailed analysis, interpretation of experimental data, and identification of key relevant components for this complex biological process. This general method holds great potential for application to the elucidation of biological mechanisms and their key components in other complex systems. PMID:28072870

  6. Information transmission in microbial and fungal communication: from classical to quantum.

    PubMed

    Majumdar, Sarangam; Pal, Sukla

    2018-06-01

    Microbes have their own communication systems. Secretion and reception of chemical signaling molecules and ion-channels mediated electrical signaling mechanism are yet observed two special ways of information transmission in microbial community. In this article, we address the aspects of various crucial machineries which set the backbone of microbial cell-to-cell communication process such as quorum sensing mechanism (bacterial and fungal), quorum sensing regulated biofilm formation, gene expression, virulence, swarming, quorum quenching, role of noise in quorum sensing, mathematical models (therapy model, evolutionary model, molecular mechanism model and many more), synthetic bacterial communication, bacterial ion-channels, bacterial nanowires and electrical communication. In particular, we highlight bacterial collective behavior with classical and quantum mechanical approaches (including quantum information). Moreover, we shed a new light to introduce the concept of quantum synthetic biology and possible cellular quantum Turing test.

  7. Generalized Ehrenfest Relations, Deformation Quantization, and the Geometry of Inter-model Reduction

    NASA Astrophysics Data System (ADS)

    Rosaler, Joshua

    2018-03-01

    This study attempts to spell out more explicitly than has been done previously the connection between two types of formal correspondence that arise in the study of quantum-classical relations: one the one hand, deformation quantization and the associated continuity between quantum and classical algebras of observables in the limit \\hbar → 0, and, on the other, a certain generalization of Ehrenfest's Theorem and the result that expectation values of position and momentum evolve approximately classically for narrow wave packet states. While deformation quantization establishes a direct continuity between the abstract algebras of quantum and classical observables, the latter result makes in-eliminable reference to the quantum and classical state spaces on which these structures act—specifically, via restriction to narrow wave packet states. Here, we describe a certain geometrical re-formulation and extension of the result that expectation values evolve approximately classically for narrow wave packet states, which relies essentially on the postulates of deformation quantization, but describes a relationship between the actions of quantum and classical algebras and groups over their respective state spaces that is non-trivially distinct from deformation quantization. The goals of the discussion are partly pedagogical in that it aims to provide a clear, explicit synthesis of known results; however, the particular synthesis offered aspires to some novelty in its emphasis on a certain general type of mathematical and physical relationship between the state spaces of different models that represent the same physical system, and in the explicitness with which it details the above-mentioned connection between quantum and classical models.

  8. System analysis of a piston steam engine employing the uniflow principle, a study in optimized performance

    NASA Technical Reports Server (NTRS)

    Peoples, J. A.

    1975-01-01

    Results are reported which were obtained from a mathematical model of a generalized piston steam engine configuration employing the uniflow principal. The model accounted for the effects of clearance volume, compression work, and release volume. A simple solution is presented which characterizes optimum performance of the steam engine, based on miles per gallon. Development of the mathematical model is presented. The relationship between efficiency and miles per gallon is developed. An approach to steam car analysis and design is presented which has purpose rather than lucky hopefulness. A practical engine design is proposed which correlates to the definition of the type engine used. This engine integrates several system components into the engine structure. All conclusions relate to the classical Rankine Cycle.

  9. Instability of the Null Steady State: The Fundamental Problem of Inhibiting Malignant Cell Growth

    NASA Astrophysics Data System (ADS)

    Varfolomeev, S. D.; Lukovenkov, A. V.

    2018-07-01

    Mathematical modeling of the process of inhibiting malignant growth by common chemotherapeutic agents and biological therapeutics is used to investigate the effect kinetic parameters of the model have on the outcome of treatment. It is shown that the ultimate suppression of growth, i.e., the formation of a stable steady-state with no cancer cells, cannot be attained if only the means of classical chemotherapy are used.

  10. Biological control via "ecological" damping: An approach that attenuates non-target effects.

    PubMed

    Parshad, Rana D; Quansah, Emmanuel; Black, Kelly; Beauregard, Matthew

    2016-03-01

    In this work we develop and analyze a mathematical model of biological control to prevent or attenuate the explosive increase of an invasive species population, that functions as a top predator, in a three-species food chain. We allow for finite time blow-up in the model as a mathematical construct to mimic the explosive increase in population, enabling the species to reach "disastrous", and uncontrollable population levels, in a finite time. We next improve the mathematical model and incorporate controls that are shown to drive down the invasive population growth and, in certain cases, eliminate blow-up. Hence, the population does not reach an uncontrollable level. The controls avoid chemical treatments and/or natural enemy introduction, thus eliminating various non-target effects associated with such classical methods. We refer to these new controls as "ecological damping", as their inclusion dampens the invasive species population growth. Further, we improve prior results on the regularity and Turing instability of the three-species model that were derived in Parshad et al. (2014). Lastly, we confirm the existence of spatiotemporal chaos. Copyright © 2016 Elsevier Inc. All rights reserved.

  11. Modeling of the financial market using the two-dimensional anisotropic Ising model

    NASA Astrophysics Data System (ADS)

    Lima, L. S.

    2017-09-01

    We have used the two-dimensional classical anisotropic Ising model in an external field and with an ion single anisotropy term as a mathematical model for the price dynamics of the financial market. The model presented allows us to test within the same framework the comparative explanatory power of rational agents versus irrational agents with respect to the facts of financial markets. We have obtained the mean price in terms of the strong of the site anisotropy term Δ which reinforces the sensitivity of the agent's sentiment to external news.

  12. A Problem on Optimal Transportation

    ERIC Educational Resources Information Center

    Cechlarova, Katarina

    2005-01-01

    Mathematical optimization problems are not typical in the classical curriculum of mathematics. In this paper we show how several generalizations of an easy problem on optimal transportation were solved by gifted secondary school pupils in a correspondence mathematical seminar, how they can be used in university courses of linear programming and…

  13. Mathematical Model of Three Species Food Chain Interaction with Mixed Functional Response

    NASA Astrophysics Data System (ADS)

    Ws, Mada Sanjaya; Mohd, Ismail Bin; Mamat, Mustafa; Salleh, Zabidin

    In this paper, we study mathematical model of ecology with a tritrophic food chain composed of a classical Lotka-Volterra functional response for prey and predator, and a Holling type-III functional response for predator and super predator. There are two equilibrium points of the system. In the parameter space, there are passages from instability to stability, which are called Hopf bifurcation points. For the first equilibrium point, it is possible to find bifurcation points analytically and to prove that the system has periodic solutions around these points. Furthermore the dynamical behaviors of this model are investigated. Models for biologically reasonable parameter values, exhibits stable, unstable periodic and limit cycles. The dynamical behavior is found to be very sensitive to parameter values as well as the parameters of the practical life. Computer simulations are carried out to explain the analytical findings.

  14. Mathematical methods of studying physical phenomena

    NASA Astrophysics Data System (ADS)

    Man'ko, Margarita A.

    2013-03-01

    In recent decades, substantial theoretical and experimental progress was achieved in understanding the quantum nature of physical phenomena that serves as the foundation of present and future quantum technologies. Quantum correlations like the entanglement of the states of composite systems, the phenomenon of quantum discord, which captures other aspects of quantum correlations, quantum contextuality and, connected with these phenomena, uncertainty relations for conjugate variables and entropies, like Shannon and Rényi entropies, and the inequalities for spin states, like Bell inequalities, reflect the recently understood quantum properties of micro and macro systems. The mathematical methods needed to describe all quantum phenomena mentioned above were also the subject of intense studies in the end of the last, and beginning of the new, century. In this section of CAMOP 'Mathematical Methods of Studying Physical Phenomena' new results and new trends in the rapidly developing domain of quantum (and classical) physics are presented. Among the particular topics under discussion there are some reviews on the problems of dynamical invariants and their relations with symmetries of the physical systems. In fact, this is a very old problem of both classical and quantum systems, e.g. the systems of parametric oscillators with time-dependent parameters, like Ermakov systems, which have specific constants of motion depending linearly or quadratically on the oscillator positions and momenta. Such dynamical invariants play an important role in studying the dynamical Casimir effect, the essence of the effect being the creation of photons from the vacuum in a cavity with moving boundaries due to the presence of purely quantum fluctuations of the electromagnetic field in the vacuum. It is remarkable that this effect was recently observed experimentally. The other new direction in developing the mathematical approach in physics is quantum tomography that provides a new vision of quantum states. In the tomographic picture of quantum mechanics, the states are identified with fair conditional probability distributions, which contain the same information on the states as the wave function or the density matrix. The mathematical methods of the tomographic approach are based on studying the star-product (associative product) quantization scheme. The tomographic star-product technique provides an additional understanding of the associative product, which is connected with the existence of specific pairs of operators called quantizers and dequantizers. These operators code information on the kernels of all the star-product schemes, including the traditional phase-space Weyl-Wigner-Moyal picture describing the quantum-system evolution. The new equation to find quantizers, if the kernel of the star product of functions is given, is presented in this CAMOP section. For studying classical systems, the mathematical methods developed in quantum mechanics can also be used. The case of paraxial-radiation beams propagating in waveguides is a known example of describing a purely classical phenomenon by means of quantum-like equations. Thus, some quantum phenomenon like the entanglement can be mimicked by the properties of classical beams, for example, Gaussian modes. The mathematical structures and relations to the symplectic symmetry group are analogous for both classical and quantum phenomena. Such analogies of the mathematical classical and quantum methods used in research on quantum-like communication channels provide new tools for constructing a theoretical basis of the new information-transmission technologies. The conventional quantum mechanics and its relation to classical mechanics contain mathematical recipes of the correspondence principle and quantization rules. Attempts to find rules for deriving the quantum-mechanical formalism starting from the classical field theory, taking into account the influence of classical fluctuations of the field, is considered in these papers. The methods to solve quantum equations and formulate the boundary conditions in the problems with singular potentials are connected with the mathematical problems of self-adjointness of the Hamiltonians. The progress and some new results in this direction are reflected in this CAMOP section. The Gaussian states of the photons play an important role in quantum optics. The multimode electromagnetic field and quantum correlations in the Gaussian states are considered in this section. The new results in the statistical properties of the laser radiation discussed here are based on applications of mathematical methods in this traditional domain of physics. It is worth stressing that the universality of the mathematical procedures permitted to consider the physical phenomena in the ocean is on the same footing as the phenomena in the microworld. In this CAMOP section, there are also papers devoted to traditional problems of solving the Schrödinger equation for interesting quantum systems. Recently obtained results related to different domains of theoretical physics are united by applying mathematical methods and tools, that provide new possibilities to better understand the theoretical foundations needed to develop new quantum technologies like quantum computing and quantum communications. The papers are arranged alphabetically by the name of the first author. We are grateful to all authors who accepted our invitation to contribute to this CAMOP section.

  15. KvN mechanics approach to the time-dependent frequency harmonic oscillator.

    PubMed

    Ramos-Prieto, Irán; Urzúa-Pineda, Alejandro R; Soto-Eguibar, Francisco; Moya-Cessa, Héctor M

    2018-05-30

    Using the Ermakov-Lewis invariants appearing in KvN mechanics, the time-dependent frequency harmonic oscillator is studied. The analysis builds upon the operational dynamical model, from which it is possible to infer quantum or classical dynamics; thus, the mathematical structure governing the evolution will be the same in both cases. The Liouville operator associated with the time-dependent frequency harmonic oscillator can be transformed using an Ermakov-Lewis invariant, which is also time dependent and commutes with itself at any time. Finally, because the solution of the Ermakov equation is involved in the evolution of the classical state vector, we explore some analytical and numerical solutions.

  16. Computational approach to Thornley's problem by bivariate operational calculus

    NASA Astrophysics Data System (ADS)

    Bazhlekova, E.; Dimovski, I.

    2012-10-01

    Thornley's problem is an initial-boundary value problem with a nonlocal boundary condition for linear onedimensional reaction-diffusion equation, used as a mathematical model of spiral phyllotaxis in botany. Applying a bivariate operational calculus we find explicit representation of the solution, containing two convolution products of special solutions and the arbitrary initial and boundary functions. We use a non-classical convolution with respect to the space variable, extending in this way the classical Duhamel principle. The special solutions involved are represented in the form of fast convergent series. Numerical examples are considered to show the application of the present technique and to analyze the character of the solution.

  17. Modeling non-homologous end joining.

    PubMed

    Li, Yongfeng; Cucinotta, Francis A

    2011-08-21

    Non-homologous end joining (NHEJ) is an important DNA repair pathway for DNA double-strand breaks. Several proteins, including Ku, DNA-PKcs, Artemis, XRCC4/Ligase IV and XLF, are involved in the NHEJ for the DNA damage detection, DNA free end processing and ligation. The classical model of NHEJ is a sequential model in which DNA-PKcs is first recruited by the Ku bound DNA prior to any other repair proteins. Recent experimental study (McElhinny et al., 2000; Costantini et al., 2007; Mari et al., 2006; Yano and Chen, 2008) suggested that the recruitment ordering is not crucial. In this work, by proposing a mathematical model in terms of biochemical reaction network and performing stability and related analysis, we demonstrate theoretically that if DSB repair pathway independent of DNA-PKcs exists, then the classical sequential model and new two-phase model are essentially indistinguishable in the sense that DSB can be repaired thoroughly in both models when the repair proteins are sufficient. Published by Elsevier Ltd.

  18. Vibration of rotating-shaft design spindles with flexible bases

    NASA Astrophysics Data System (ADS)

    Tseng, Chaw-Wu

    The purpose of this study is to demonstrate an accurate mathematical model predicting forced vibration of rotating-shaft HDD spindle motors with flexible stationary parts. The mathematical model consists of three parts: a rotating part, a stationary part, and bearings. The rotating part includes a flexible hub, a flexible shaft press-fit into the hub, and N elastic disks mounted on the hub. The stationary part can include motor bracket (stator), base casting, and top cover. The bearings under consideration can be ball bearings or hydrodynamic bearings (HDB). The rotating disks are modelled through the classical plate theory. The rotating part (except the disks) and the stationary part are modelled through finite element analyses (FEA). With mode shapes and natural frequencies obtained from FEA, the kinetic and potential energies of the rotating and stationary parts are formulated and discretized to compensate for the gyroscopic effects from rotation. Finally, use of Lagrange equation results in the equations of motion. To verify the mathematical model, frequency response functions are measured experimentally for an HDB spindle carrying two identical disks at motor and drive levels. Experimental measurements agree very well with theoretical predictions not only in resonance frequency but also in resonance amplitude.

  19. Finding exact constants in a Markov model of Zipfs law generation

    NASA Astrophysics Data System (ADS)

    Bochkarev, V. V.; Lerner, E. Yu.; Nikiforov, A. A.; Pismenskiy, A. A.

    2017-12-01

    According to the classical Zipfs law, the word frequency is a power function of the word rank with an exponent -1. The objective of this work is to find multiplicative constant in a Markov model of word generation. Previously, the case of independent letters was mathematically strictly investigated in [Bochkarev V V and Lerner E Yu 2017 International Journal of Mathematics and Mathematical Sciences Article ID 914374]. Unfortunately, the methods used in this paper cannot be generalized in case of Markov chains. The search of the correct formulation of the Markov generalization of this results was performed using experiments with different ergodic matrices of transition probability P. Combinatory technique allowed taking into account all the words with probability of more than e -300 in case of 2 by 2 matrices. It was experimentally proved that the required constant in the limit is equal to the value reciprocal to conditional entropy of matrix row P with weights presenting the elements of the vector π of the stationary distribution of the Markov chain.

  20. Self-organization in the limb: a Turing mechanism for digit development.

    PubMed

    Cooper, Kimberly L

    2015-06-01

    The statistician George E. P. Box stated, 'Essentially all models are wrong, but some are useful.' (Box GEP, Draper NR: Empirical Model-Building and Response Surfaces. Wiley; 1987). Modeling biological processes is challenging for many of the reasons classically trained developmental biologists often resist the idea that black and white equations can explain the grayscale subtleties of living things. Although a simplified mathematical model of development will undoubtedly fall short of precision, a good model is exceedingly useful if it raises at least as many testable questions as it answers. Self-organizing Turing models that simulate the pattern of digits in the hand replicate events that have not yet been explained by classical approaches. The union of theory and experimentation has recently identified and validated the minimal components of a Turing network for digit pattern and triggered a cascade of questions that will undoubtedly be well-served by the continued merging of disciplines. Copyright © 2015 Elsevier Ltd. All rights reserved.

  1. Public and Private School Distinction, Regional Development Differences, and Other Factors Influencing the Success of Primary School Students in Turkey

    ERIC Educational Resources Information Center

    Sulku, Seher Nur; Abdioglu, Zehra

    2015-01-01

    This study investigates the factors influencing the success of students in primary schools in Turkey. TIMSS 2011 data for Turkey, measuring the success of eighth-grade students in the field of mathematics, were used in an econometric analysis, performed using classical linear regression models. Two hundred thirty-nine schools participated in the…

  2. A consistent modelling methodology for secondary settling tanks in wastewater treatment.

    PubMed

    Bürger, Raimund; Diehl, Stefan; Nopens, Ingmar

    2011-03-01

    The aim of this contribution is partly to build consensus on a consistent modelling methodology (CMM) of complex real processes in wastewater treatment by combining classical concepts with results from applied mathematics, and partly to apply it to the clarification-thickening process in the secondary settling tank. In the CMM, the real process should be approximated by a mathematical model (process model; ordinary or partial differential equation (ODE or PDE)), which in turn is approximated by a simulation model (numerical method) implemented on a computer. These steps have often not been carried out in a correct way. The secondary settling tank was chosen as a case since this is one of the most complex processes in a wastewater treatment plant and simulation models developed decades ago have no guarantee of satisfying fundamental mathematical and physical properties. Nevertheless, such methods are still used in commercial tools to date. This particularly becomes of interest as the state-of-the-art practice is moving towards plant-wide modelling. Then all submodels interact and errors propagate through the model and severely hamper any calibration effort and, hence, the predictive purpose of the model. The CMM is described by applying it first to a simple conversion process in the biological reactor yielding an ODE solver, and then to the solid-liquid separation in the secondary settling tank, yielding a PDE solver. Time has come to incorporate established mathematical techniques into environmental engineering, and wastewater treatment modelling in particular, and to use proven reliable and consistent simulation models. Copyright © 2011 Elsevier Ltd. All rights reserved.

  3. From classical to quantum mechanics: ``How to translate physical ideas into mathematical language''

    NASA Astrophysics Data System (ADS)

    Bergeron, H.

    2001-09-01

    Following previous works by E. Prugovečki [Physica A 91A, 202 (1978) and Stochastic Quantum Mechanics and Quantum Space-time (Reidel, Dordrecht, 1986)] on common features of classical and quantum mechanics, we develop a unified mathematical framework for classical and quantum mechanics (based on L2-spaces over classical phase space), in order to investigate to what extent quantum mechanics can be obtained as a simple modification of classical mechanics (on both logical and analytical levels). To obtain this unified framework, we split quantum theory in two parts: (i) general quantum axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoints operators, and so on) and (ii) quantum mechanics proper that specifies the Hilbert space as L2(Rn); the Heisenberg rule [pi,qj]=-iℏδij with p=-iℏ∇, the free Hamiltonian H=-ℏ2Δ/2m and so on. We show that general quantum axiomatics (up to a supplementary "axiom of classicity") can be used as a nonstandard mathematical ground to formulate physical ideas and equations of ordinary classical statistical mechanics. So, the question of a "true quantization" with "ℏ" must be seen as an independent physical problem not directly related with quantum formalism. At this stage, we show that this nonstandard formulation of classical mechanics exhibits a new kind of operation that has no classical counterpart: this operation is related to the "quantization process," and we show why quantization physically depends on group theory (the Galilei group). This analytical procedure of quantization replaces the "correspondence principle" (or canonical quantization) and allows us to map classical mechanics into quantum mechanics, giving all operators of quantum dynamics and the Schrödinger equation. The great advantage of this point of view is that quantization is based on concrete physical arguments and not derived from some "pure algebraic rule" (we exhibit also some limit of the correspondence principle). Moreover spins for particles are naturally generated, including an approximation of their interaction with magnetic fields. We also recover by this approach the semi-classical formalism developed by E. Prugovečki [Stochastic Quantum Mechanics and Quantum Space-time (Reidel, Dordrecht, 1986)].

  4. [Influence of music on a decision of mathematical logic tasks].

    PubMed

    Pavlygina, R A; Karamysheva, N N; Sakharov, D S; Davydov, V I

    2012-01-01

    Accompaniment of a decision of mathematical logical tasks by music (different style and power) influenced on the time of the decision. Classical music 35 and 65 dB and roc-music 65 and 85 dB decreased the time of the decision. More powerful classical music (85 dB) did not effect like that. The decision without the musical accompaniment led to increasing of coherent values especially in beta1, beta2, gamma frequency ranges in EEG of occipital cortex. The intrahemispheric and the interhemispheric coherences of frontal EEG increased and EEG asymmetry (in a number of Coh-connections in left and right hemispheres) arose during the tasks decision accompanied by music. Application of classical music 35 and 65 dB caused left-side asymmetry in EEG. Using of more powerful classical or rock music led to prevalence of quantity of Coh-connections in a right hemisphere.

  5. Dynamical insurance models with investment: Constrained singular problems for integrodifferential equations

    NASA Astrophysics Data System (ADS)

    Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.

    2016-01-01

    Previous and new results are used to compare two mathematical insurance models with identical insurance company strategies in a financial market, namely, when the entire current surplus or its constant fraction is invested in risky assets (stocks), while the rest of the surplus is invested in a risk-free asset (bank account). Model I is the classical Cramér-Lundberg risk model with an exponential claim size distribution. Model II is a modification of the classical risk model (risk process with stochastic premiums) with exponential distributions of claim and premium sizes. For the survival probability of an insurance company over infinite time (as a function of its initial surplus), there arise singular problems for second-order linear integrodifferential equations (IDEs) defined on a semiinfinite interval and having nonintegrable singularities at zero: model I leads to a singular constrained initial value problem for an IDE with a Volterra integral operator, while II model leads to a more complicated nonlocal constrained problem for an IDE with a non-Volterra integral operator. A brief overview of previous results for these two problems depending on several positive parameters is given, and new results are presented. Additional results are concerned with the formulation, analysis, and numerical study of "degenerate" problems for both models, i.e., problems in which some of the IDE parameters vanish; moreover, passages to the limit with respect to the parameters through which we proceed from the original problems to the degenerate ones are singular for small and/or large argument values. Such problems are of mathematical and practical interest in themselves. Along with insurance models without investment, they describe the case of surplus completely invested in risk-free assets, as well as some noninsurance models of surplus dynamics, for example, charity-type models.

  6. Research Prototype: Automated Analysis of Scientific and Engineering Semantics

    NASA Technical Reports Server (NTRS)

    Stewart, Mark E. M.; Follen, Greg (Technical Monitor)

    2001-01-01

    Physical and mathematical formulae and concepts are fundamental elements of scientific and engineering software. These classical equations and methods are time tested, universally accepted, and relatively unambiguous. The existence of this classical ontology suggests an ideal problem for automated comprehension. This problem is further motivated by the pervasive use of scientific code and high code development costs. To investigate code comprehension in this classical knowledge domain, a research prototype has been developed. The prototype incorporates scientific domain knowledge to recognize code properties (including units, physical, and mathematical quantity). Also, the procedure implements programming language semantics to propagate these properties through the code. This prototype's ability to elucidate code and detect errors will be demonstrated with state of the art scientific codes.

  7. Neurotech for Neuroscience: Unifying Concepts, Organizing Principles, and Emerging Tools

    PubMed Central

    Silver, Rae; Boahen, Kwabena; Grillner, Sten; Kopell, Nancy; Olsen, Kathie L.

    2012-01-01

    The ability to tackle analysis of the brain at multiple levels simultaneously is emerging from rapid methodological developments. The classical research strategies of “measure,” “model,” and “make” are being applied to the exploration of nervous system function. These include novel conceptual and theoretical approaches, creative use of mathematical modeling, and attempts to build brain-like devices and systems, as well as other developments including instrumentation and statistical modeling (not covered here). Increasingly, these efforts require teams of scientists from a variety of traditional scientific disciplines to work together. The potential of such efforts for understanding directed motor movement, emergence of cognitive function from neuronal activity, and development of neuromimetic computers are described by a team that includes individuals experienced in behavior and neuroscience, mathematics, and engineering. Funding agencies, including the National Science Foundation, explore the potential of these changing frontiers of research for developing research policies and long-term planning. PMID:17978017

  8. Heat and Mass Transfer with Condensation in Capillary Porous Bodies

    PubMed Central

    2014-01-01

    The purpose of this present work is related to wetting process analysis caused by condensation phenomena in capillary porous material by using a numerical simulation. Special emphasis is given to the study of the mechanism involved and the evaluation of classical theoretical models used as a predictive tool. A further discussion will be given for the distribution of the liquid phase for both its pendular and its funicular state and its consequence on diffusion coefficients of the mathematical model used. Beyond the complexity of the interaction effects between vaporisation-condensation processes on the gas-liquid interfaces, the comparison between experimental and numerical simulations permits to identify the specific contribution and the relative part of mass and energy transport parameters. This analysis allows us to understand the contribution of each part of the mathematical model used and to simplify the study. PMID:24688366

  9. Using Predictor-Corrector Methods in Numerical Solutions to Mathematical Problems of Motion

    ERIC Educational Resources Information Center

    Lewis, Jerome

    2005-01-01

    In this paper, the author looks at some classic problems in mathematics that involve motion in the plane. Many case problems like these are difficult and beyond the mathematical skills of most undergraduates, but computational approaches often require less insight into the subtleties of the problems and can be used to obtain reliable solutions.…

  10. Development of Modified Incompressible Ideal Gas Model for Natural Draft Cooling Tower Flow Simulation

    NASA Astrophysics Data System (ADS)

    Hyhlík, Tomáš

    2018-06-01

    The article deals with the development of incompressible ideal gas like model, which can be used as a part of mathematical model describing natural draft wet-cooling tower flow, heat and mass transfer. It is shown, based on the results of a complex mathematical model of natural draft wet-cooling tower flow, that behaviour of pressure, temperature and density is very similar to the case of hydrostatics of moist air, where heat and mass transfer in the fill zone must be taken into account. The behaviour inside the cooling tower is documented using density, pressure and temperature distributions. The proposed equation for the density is based on the same idea like the incompressible ideal gas model, which is only dependent on temperature, specific humidity and in this case on elevation. It is shown that normalized density difference of the density based on proposed model and density based on the nonsimplified model is in the order of 10-4. The classical incompressible ideal gas model, Boussinesq model and generalised Boussinesq model are also tested. These models show deviation in percentages.

  11. Quantum-like Modeling of Cognition

    NASA Astrophysics Data System (ADS)

    Khrennikov, Andrei

    2015-09-01

    This paper begins with a historical review of the mutual influence of physics and psychology, from Freud's invention of psychic energy inspired by von Boltzmann' thermodynamics to the enrichment quantum physics gained from the side of psychology by the notion of complementarity (the invention of Niels Bohr who was inspired by William James), besides we consider the resonance of the correspondence between Wolfgang Pauli and Carl Jung in both physics and psychology. Then we turn to the problem of development of mathematical models for laws of thought starting with Boolean logic and progressing towards foundations of classical probability theory. Interestingly, the laws of classical logic and probability are routinely violated not only by quantum statistical phenomena but by cognitive phenomena as well. This is yet another common feature between quantum physics and psychology. In particular, cognitive data can exhibit a kind of the probabilistic interference effect. This similarity with quantum physics convinced a multi-disciplinary group of scientists (physicists, psychologists, economists, sociologists) to apply the mathematical apparatus of quantum mechanics to modeling of cognition. We illustrate this activity by considering a few concrete phenomena: the order and disjunction effects, recognition of ambiguous figures, categorization-decision making. In Appendix 1 we briefly present essentials of theory of contextual probability and a method of representations of contextual probabilities by complex probability amplitudes (solution of the ``inverse Born's problem'') based on a quantum-like representation algorithm (QLRA).

  12. Optimization of numerical weather/wave prediction models based on information geometry and computational techniques

    NASA Astrophysics Data System (ADS)

    Galanis, George; Famelis, Ioannis; Kalogeri, Christina

    2014-10-01

    The last years a new highly demanding framework has been set for environmental sciences and applied mathematics as a result of the needs posed by issues that are of interest not only of the scientific community but of today's society in general: global warming, renewable resources of energy, natural hazards can be listed among them. Two are the main directions that the research community follows today in order to address the above problems: The utilization of environmental observations obtained from in situ or remote sensing sources and the meteorological-oceanographic simulations based on physical-mathematical models. In particular, trying to reach credible local forecasts the two previous data sources are combined by algorithms that are essentially based on optimization processes. The conventional approaches in this framework usually neglect the topological-geometrical properties of the space of the data under study by adopting least square methods based on classical Euclidean geometry tools. In the present work new optimization techniques are discussed making use of methodologies from a rapidly advancing branch of applied Mathematics, the Information Geometry. The latter prove that the distributions of data sets are elements of non-Euclidean structures in which the underlying geometry may differ significantly from the classical one. Geometrical entities like Riemannian metrics, distances, curvature and affine connections are utilized in order to define the optimum distributions fitting to the environmental data at specific areas and to form differential systems that describes the optimization procedures. The methodology proposed is clarified by an application for wind speed forecasts in the Kefaloniaisland, Greece.

  13. Liquid spreading under partial wetting conditions

    NASA Astrophysics Data System (ADS)

    Chen, M.; Pahlavan, A. A.; Cueto-Felgueroso, L.; McKinley, G. H.; Juanes, R.

    2013-12-01

    Traditional mathematical descriptions of multiphase flow in porous media rely on a multiphase extension of Darcy's law, and lead to nonlinear second-order (advection-diffusion) partial differential equations for fluid saturations. Here, we study horizontal redistribution of immiscible fluids. The traditional Darcy-flow model predicts that the spreading of a finite amount of liquid in a horizontal porous medium never stops; a prediction that is not substantiated by observation. To help guide the development of new models of multiphase flow in porous media [1], we draw an analogy with the flow of thin films. The flow of thin films over flat surfaces has been the subject of much theoretical, experimental and computational research [2]. Under the lubrication approximation, the classical mathematical model for these flows takes the form of a nonlinear fourth-order PDE, where the fourth-order term models the effect of surface tension [3]. This classical model, however, effectively assumes that the film is perfectly wetting to the substrate and, therefore, does not capture the partial wetting regime. Partial wetting is responsible for stopping the spread of a liquid puddle. Here, we present experiments of (large-volume) liquid spreading over a flat horizontal substrate in the partial wetting regime, and characterize the four spreading regimes that we observe. We extend our previous theoretical work of two-phase flow in a capillary tube [4], and develop a macroscopic phase-field modeling of thin-film flows with partial wetting. Our model naturally accounts for the dynamic contact angle at the contact line, and therefore permits modeling thin-film flows without invoking a precursor film, leading to compactly-supported solutions that reproduce the spreading dynamics and the static equilibrium configuration observed in the experiments. We anticipate that this modeling approach will provide a natural mathematical framework to describe spreading and redistribution of immiscible fluids in porous media. [1] L. Cueto-Felgueroso and R. Juanes, Phys. Rev. Lett. 101, 244504 (2008). [2] D. Bonn et al., Rev. Mod. Phys. 81, 739-805 (2009). [3] H. E. Huppert, Nature 300, 427-429 (1982). [4] L. Cueto-Felgueroso and R. Juanes, Phys. Rev. Lett. 108, 144502 (2012).

  14. Dirac(-Pauli), Fokker-Planck equations and exceptional Laguerre polynomials

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

    Ho, Choon-Lin, E-mail: hcl@mail.tku.edu.tw

    2011-04-15

    Research Highlights: > Physical examples involving exceptional orthogonal polynomials. > Exceptional polynomials as deformations of classical orthogonal polynomials. > Exceptional polynomials from Darboux-Crum transformation. - Abstract: An interesting discovery in the last two years in the field of mathematical physics has been the exceptional X{sub l} Laguerre and Jacobi polynomials. Unlike the well-known classical orthogonal polynomials which start with constant terms, these new polynomials have lowest degree l = 1, 2, and ..., and yet they form complete set with respect to some positive-definite measure. While the mathematical properties of these new X{sub l} polynomials deserve further analysis, it ismore » also of interest to see if they play any role in physical systems. In this paper we indicate some physical models in which these new polynomials appear as the main part of the eigenfunctions. The systems we consider include the Dirac equations coupled minimally and non-minimally with some external fields, and the Fokker-Planck equations. The systems presented here have enlarged the number of exactly solvable physical systems known so far.« less

  15. Choosing Between Public and Private Providers of Depot Maintenance: A Proposed New Approach

    DTIC Science & Technology

    1997-09-01

    Appendix A Mathematical Form of the Model Appendix B Assumed Distributions for Evaluation Factors vm Contents Appendix C Trial Evaluation Workbook ...Figure 4-2. Revised Factor Scale Anchors 4-5 Figure 4-3. Workbook Display Establishing Relevance of Factor 4-5 Figure 4-4. Comparing Results of...Introduction process. To fill voids we conducted additional research in the areas of classical microeconomics , transaction cost economics, public

  16. Mechanism of Determination of Effectiveness of Spending Assets of Endowment Funds on the Basis of Mathematical Models

    ERIC Educational Resources Information Center

    Sazonov, Sergey; Kharlamova, Ekaterina; Chekhovskaya, Irina; Polyanskaya, Elena

    2017-01-01

    Purpose: Economic problems of the system of education were the object of interest of classics of economic science--A. Smith and A. Marshall--who viewed education as a source of public capital, and acquired skills and competences--as a part of national wealth. These ideas were further developed in the theory of human capital by T. Schultz, G.S.…

  17. Power law incidence rate in epidemic models. Comment on: "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al.

    NASA Astrophysics Data System (ADS)

    Allen, Linda J. S.

    2016-09-01

    Dr. Chowell and colleagues emphasize the importance of considering a variety of modeling approaches to characterize the growth of an epidemic during the early stages [1]. A fit of data from the 2009 H1N1 influenza pandemic and the 2014-2015 Ebola outbreak to models indicates sub-exponential growth, in contrast to the classic, homogeneous-mixing SIR model with exponential growth. With incidence rate βSI / N and S approximately equal to the total population size N, the number of new infections in an SIR epidemic model grows exponentially as in the differential equation,

  18. [Risk factor analysis of the patients with solitary pulmonary nodules and establishment of a prediction model for the probability of malignancy].

    PubMed

    Wang, X; Xu, Y H; Du, Z Y; Qian, Y J; Xu, Z H; Chen, R; Shi, M H

    2018-02-23

    Objective: This study aims to analyze the relationship among the clinical features, radiologic characteristics and pathological diagnosis in patients with solitary pulmonary nodules, and establish a prediction model for the probability of malignancy. Methods: Clinical data of 372 patients with solitary pulmonary nodules who underwent surgical resection with definite postoperative pathological diagnosis were retrospectively analyzed. In these cases, we collected clinical and radiologic features including gender, age, smoking history, history of tumor, family history of cancer, the location of lesion, ground-glass opacity, maximum diameter, calcification, vessel convergence sign, vacuole sign, pleural indentation, speculation and lobulation. The cases were divided to modeling group (268 cases) and validation group (104 cases). A new prediction model was established by logistic regression analying the data from modeling group. Then the data of validation group was planned to validate the efficiency of the new model, and was compared with three classical models(Mayo model, VA model and LiYun model). With the calculated probability values for each model from validation group, SPSS 22.0 was used to draw the receiver operating characteristic curve, to assess the predictive value of this new model. Results: 112 benign SPNs and 156 malignant SPNs were included in modeling group. Multivariable logistic regression analysis showed that gender, age, history of tumor, ground -glass opacity, maximum diameter, and speculation were independent predictors of malignancy in patients with SPN( P <0.05). We calculated a prediction model for the probability of malignancy as follow: p =e(x)/(1+ e(x)), x=-4.8029-0.743×gender+ 0.057×age+ 1.306×history of tumor+ 1.305×ground-glass opacity+ 0.051×maximum diameter+ 1.043×speculation. When the data of validation group was added to the four-mathematical prediction model, The area under the curve of our mathematical prediction model was 0.742, which is greater than other models (Mayo 0.696, VA 0.634, LiYun 0.681), while the differences between any two of the four models were not significant ( P >0.05). Conclusions: Age of patient, gender, history of tumor, ground-glass opacity, maximum diameter and speculation are independent predictors of malignancy in patients with solitary pulmonary nodule. This logistic regression prediction mathematic model is not inferior to those classical models in estimating the prognosis of SPNs.

  19. A model for one-dimensional morphoelasticity and its application to fibroblast-populated collagen lattices.

    PubMed

    Menon, Shakti N; Hall, Cameron L; McCue, Scott W; McElwain, D L Sean

    2017-10-01

    The mechanical behaviour of solid biological tissues has long been described using models based on classical continuum mechanics. However, the classical continuum theories of elasticity and viscoelasticity cannot easily capture the continual remodelling and associated structural changes in biological tissues. Furthermore, models drawn from plasticity theory are difficult to apply and interpret in this context, where there is no equivalent of a yield stress or flow rule. In this work, we describe a novel one-dimensional mathematical model of tissue remodelling based on the multiplicative decomposition of the deformation gradient. We express the mechanical effects of remodelling as an evolution equation for the effective strain, a measure of the difference between the current state and a hypothetical mechanically relaxed state of the tissue. This morphoelastic model combines the simplicity and interpretability of classical viscoelastic models with the versatility of plasticity theory. A novel feature of our model is that while most models describe growth as a continuous quantity, here we begin with discrete cells and develop a continuum representation of lattice remodelling based on an appropriate limit of the behaviour of discrete cells. To demonstrate the utility of our approach, we use this framework to capture qualitative aspects of the continual remodelling observed in fibroblast-populated collagen lattices, in particular its contraction and its subsequent sudden re-expansion when remodelling is interrupted.

  20. From the limits of the classical model of sensitometric curves to a realistic model based on the percolation theory for GafChromic EBT films.

    PubMed

    del Moral, F; Vázquez, J A; Ferrero, J J; Willisch, P; Ramírez, R D; Teijeiro, A; López Medina, A; Andrade, B; Vázquez, J; Salvador, F; Medal, D; Salgado, M; Muñoz, V

    2009-09-01

    Modern radiotherapy uses complex treatments that necessitate more complex quality assurance procedures. As a continuous medium, GafChromic EBT films offer suitable features for such verification. However, its sensitometric curve is not fully understood in terms of classical theoretical models. In fact, measured optical densities and those predicted by the classical models differ significantly. This difference increases systematically with wider dose ranges. Thus, achieving the accuracy required for intensity-modulated radiotherapy (IMRT) by classical methods is not possible, plecluding their use. As a result, experimental parametrizations, such as polynomial fits, are replacing phenomenological expressions in modern investigations. This article focuses on identifying new theoretical ways to describe sensitometric curves and on evaluating the quality of fit for experimental data based on four proposed models. A whole mathematical formalism starting with a geometrical version of the classical theory is used to develop new expressions for the sensitometric curves. General results from the percolation theory are also used. A flat-bed-scanner-based method was chosen for the film analysis. Different tests were performed, such as consistency of the numeric results for the proposed model and double examination using data from independent researchers. Results show that the percolation-theory-based model provides the best theoretical explanation for the sensitometric behavior of GafChromic films. The different sizes of active centers or monomer crystals of the film are the basis of this model, allowing acquisition of information about the internal structure of the films. Values for the mean size of the active centers were obtained in accordance with technical specifications. In this model, the dynamics of the interaction between the active centers of GafChromic film and radiation is also characterized by means of its interaction cross-section value. The percolation model fulfills the accuracy requirements for quality-control procedures when large ranges of doses are used and offers a physical explanation for the film response.

  1. Motivation and engagement in mathematics: a qualitative framework for teacher-student interactions

    NASA Astrophysics Data System (ADS)

    Durksen, Tracy L.; Way, Jennifer; Bobis, Janette; Anderson, Judy; Skilling, Karen; Martin, Andrew J.

    2017-02-01

    We started with a classic research question (How do teachers motivate and engage middle year students in mathematics?) that is solidly underpinned and guided by an integration of two theoretical and multidimensional models. In particular, the current study illustrates how theory is important for guiding qualitative analytical approaches to motivation and engagement in mathematics. With little research on how teachers of mathematics are able to maintain high levels of student motivation and engagement, we focused on developing a qualitative framework that highlights the influence of teacher-student interactions. Participants were six teachers (upper primary and secondary) that taught students with higher-than-average levels of motivation and engagement in mathematics. Data sources included one video-recorded lesson and associated transcripts from pre- and post-lesson interviews with each teacher. Overall, effective classroom organisation stood out as a priority when promoting motivation and engagement in mathematics. Results on classroom organisation revealed four key indicators within teacher-student interactions deemed important for motivation and engagement in mathematics—confidence, climate, contact, and connection. Since much of the effect of teachers on student learning relies on interactions, and given the universal trend of declining mathematical performance during the middle years of schooling, future research and intervention studies might be assisted by our qualitative framework.

  2. Adam Smith's invisible hand is unstable: physics and dynamics reasoning applied to economic theorizing

    NASA Astrophysics Data System (ADS)

    McCauley, Joseph L.

    2002-11-01

    Neo-classical economic theory is based on the postulated, nonempiric notion of utility. Neo-classical economists assume that prices, dynamics, and market equilibria are supposed to be derived from utility. The results are supposed to represent mathematically the stabilizing action of Adam Smith's invisible hand. In deterministic excess demand dynamics, however, a utility function generally does not exist mathematically due to nonintegrability. Price as a function of demand does not exist and all equilibria are unstable. Qualitatively, and empirically, the neo-classical prediction of price as a function of demand describes neither consumer nor trader demand. We also discuss five inconsistent definitions of equilibrium used in economics and finance, only one of which is correct, and then explain the fallacy in the economists’ notion of ‘temporary price equilibria’.

  3. Physical Concepts and Mathematical Symbols

    NASA Astrophysics Data System (ADS)

    Grelland, Hans Herlof

    2007-12-01

    According to traditional empiricist philosophy of science, concepts and meaning grow out of sense experience, and the mathematical structure of a physical theory is nothing but a formalisation of a given meaning-content. This view seems to work well in classical mechanics. But it breaks down in quantum physics, where we have a self-supported mathematical structure which resists any conceptual or pictorial interpretation in the traditional sense. Thus, traditional empiricism is flawed. Quantum physics teaches us that mathematics is a language in itself which extends beyond ordinary language. To understand the meaning of this extended language, we have to explore how new concepts and intuitions grow out of mathematics, not the other way around. The symbolic structure is prior to its meaning. This point of view is called linguistic empiricism, to stress that the connection with experience is still crucial. As cases, I compare the concept of stiffness in classical mechanics and the concept of electron density in quantum mechanics. The last case demonstrates that the wave function has a richer interpretation than the probabilistic one concerning measurement of position.

  4. Least Squares Procedures.

    ERIC Educational Resources Information Center

    Hester, Yvette

    Least squares methods are sophisticated mathematical curve fitting procedures used in all classical parametric methods. The linear least squares approximation is most often associated with finding the "line of best fit" or the regression line. Since all statistical analyses are correlational and all classical parametric methods are least…

  5. Methods for Multiloop Identification of Visual and Neuromuscular Pilot Responses.

    PubMed

    Olivari, Mario; Nieuwenhuizen, Frank M; Venrooij, Joost; Bülthoff, Heinrich H; Pollini, Lorenzo

    2015-12-01

    In this paper, identification methods are proposed to estimate the neuromuscular and visual responses of a multiloop pilot model. A conventional and widely used technique for simultaneous identification of the neuromuscular and visual systems makes use of cross-spectral density estimates. This paper shows that this technique requires a specific noninterference hypothesis, often implicitly assumed, that may be difficult to meet during actual experimental designs. A mathematical justification of the necessity of the noninterference hypothesis is given. Furthermore, two methods are proposed that do not have the same limitations. The first method is based on autoregressive models with exogenous inputs, whereas the second one combines cross-spectral estimators with interpolation in the frequency domain. The two identification methods are validated by offline simulations and contrasted to the classic method. The results reveal that the classic method fails when the noninterference hypothesis is not fulfilled; on the contrary, the two proposed techniques give reliable estimates. Finally, the three identification methods are applied to experimental data from a closed-loop control task with pilots. The two proposed techniques give comparable estimates, different from those obtained by the classic method. The differences match those found with the simulations. Thus, the two identification methods provide a good alternative to the classic method and make it possible to simultaneously estimate human's neuromuscular and visual responses in cases where the classic method fails.

  6. A model of adaptive decision-making from representation of information environment by quantum fields.

    PubMed

    Bagarello, F; Haven, E; Khrennikov, A

    2017-11-13

    We present the mathematical model of decision-making (DM) of agents acting in a complex and uncertain environment (combining huge variety of economical, financial, behavioural and geopolitical factors). To describe interaction of agents with it, we apply the formalism of quantum field theory (QTF). Quantum fields are a purely informational nature. The QFT model can be treated as a far relative of the expected utility theory, where the role of utility is played by adaptivity to an environment (bath). However, this sort of utility-adaptivity cannot be represented simply as a numerical function. The operator representation in Hilbert space is used and adaptivity is described as in quantum dynamics. We are especially interested in stabilization of solutions for sufficiently large time. The outputs of this stabilization process, probabilities for possible choices, are treated in the framework of classical DM. To connect classical and quantum DM, we appeal to Quantum Bayesianism. We demonstrate the quantum-like interference effect in DM, which is exhibited as a violation of the formula of total probability, and hence the classical Bayesian inference scheme.This article is part of the themed issue 'Second quantum revolution: foundational questions'. © 2017 The Author(s).

  7. A model of adaptive decision-making from representation of information environment by quantum fields

    NASA Astrophysics Data System (ADS)

    Bagarello, F.; Haven, E.; Khrennikov, A.

    2017-10-01

    We present the mathematical model of decision-making (DM) of agents acting in a complex and uncertain environment (combining huge variety of economical, financial, behavioural and geopolitical factors). To describe interaction of agents with it, we apply the formalism of quantum field theory (QTF). Quantum fields are a purely informational nature. The QFT model can be treated as a far relative of the expected utility theory, where the role of utility is played by adaptivity to an environment (bath). However, this sort of utility-adaptivity cannot be represented simply as a numerical function. The operator representation in Hilbert space is used and adaptivity is described as in quantum dynamics. We are especially interested in stabilization of solutions for sufficiently large time. The outputs of this stabilization process, probabilities for possible choices, are treated in the framework of classical DM. To connect classical and quantum DM, we appeal to Quantum Bayesianism. We demonstrate the quantum-like interference effect in DM, which is exhibited as a violation of the formula of total probability, and hence the classical Bayesian inference scheme. This article is part of the themed issue `Second quantum revolution: foundational questions'.

  8. Multi-scale modelling of rubber-like materials and soft tissues: an appraisal

    PubMed Central

    Puglisi, G.

    2016-01-01

    We survey, in a partial way, multi-scale approaches for the modelling of rubber-like and soft tissues and compare them with classical macroscopic phenomenological models. Our aim is to show how it is possible to obtain practical mathematical models for the mechanical behaviour of these materials incorporating mesoscopic (network scale) information. Multi-scale approaches are crucial for the theoretical comprehension and prediction of the complex mechanical response of these materials. Moreover, such models are fundamental in the perspective of the design, through manipulation at the micro- and nano-scales, of new polymeric and bioinspired materials with exceptional macroscopic properties. PMID:27118927

  9. On the Effects of Artificial Feeding on Bee Colony Dynamics: A Mathematical Model

    PubMed Central

    Paiva, Juliana Pereira Lisboa Mohallem; Paiva, Henrique Mohallem; Esposito, Elisa; Morais, Michelle Manfrini

    2016-01-01

    This paper proposes a new mathematical model to evaluate the effects of artificial feeding on bee colony population dynamics. The proposed model is based on a classical framework and contains differential equations that describe the changes in the number of hive bees, forager bees, and brood cells, as a function of amounts of natural and artificial food. The model includes the following elements to characterize the artificial feeding scenario: a function to model the preference of the bees for natural food over artificial food; parameters to quantify the quality and palatability of artificial diets; a function to account for the efficiency of the foragers in gathering food under different environmental conditions; and a function to represent different approaches used by the beekeeper to feed the hive with artificial food. Simulated results are presented to illustrate the main characteristics of the model and its behavior under different scenarios. The model results are validated with experimental data from the literature involving four different artificial diets. A good match between simulated and experimental results was achieved. PMID:27875589

  10. Canonical partition functions: ideal quantum gases, interacting classical gases, and interacting quantum gases

    NASA Astrophysics Data System (ADS)

    Zhou, Chi-Chun; Dai, Wu-Sheng

    2018-02-01

    In statistical mechanics, for a system with a fixed number of particles, e.g. a finite-size system, strictly speaking, the thermodynamic quantity needs to be calculated in the canonical ensemble. Nevertheless, the calculation of the canonical partition function is difficult. In this paper, based on the mathematical theory of the symmetric function, we suggest a method for the calculation of the canonical partition function of ideal quantum gases, including ideal Bose, Fermi, and Gentile gases. Moreover, we express the canonical partition functions of interacting classical and quantum gases given by the classical and quantum cluster expansion methods in terms of the Bell polynomial in mathematics. The virial coefficients of ideal Bose, Fermi, and Gentile gases are calculated from the exact canonical partition function. The virial coefficients of interacting classical and quantum gases are calculated from the canonical partition function by using the expansion of the Bell polynomial, rather than calculated from the grand canonical potential.

  11. Cascade aeroacoustics including steady loading effects

    NASA Astrophysics Data System (ADS)

    Chiang, Hsiao-Wei D.; Fleeter, Sanford

    A mathematical model is developed to analyze the effects of airfoil and cascade geometry, steady aerodynamic loading, and the characteristics of the unsteady flow field on the discrete frequency noise generation of a blade row in an incompressible flow. The unsteady lift which generates the noise is predicted with a complex first-order cascade convected gust analysis. This model was then applied to the Gostelow airfoil cascade and variations, demonstrating that steady loading, cascade solidity, and the gust direction are significant. Also, even at zero incidence, the classical flat plate cascade predictions are unacceptable.

  12. Postbuckling analysis of shear deformable composite flat panels taking into account geometrical imperfections

    NASA Technical Reports Server (NTRS)

    Librescu, L.; Stein, M.

    1990-01-01

    The effects of initial geometrical imperfections on the postbuckling response of flat laminated composite panels to uniaxial and biaxial compressive loading are investigated analytically. The derivation of the mathematical model on the basis of first-order transverse shear deformation theory is outlined, and numerical results for perfect and imperfect, single-layer and three-layer square plates with free-free, clamped-clamped, or free-clamped edges are presented in graphs and briefly characterized. The present approach is shown to be more accurate than analyses based on the classical Kirchhoff plate model.

  13. Inflation and acceleration of the universe by nonlinear magnetic monopole fields

    NASA Astrophysics Data System (ADS)

    Övgün, A.

    2017-02-01

    Despite impressive phenomenological success, cosmological models are incomplete without an understanding of what happened at the big bang singularity. Maxwell electrodynamics, considered as a source of the classical Einstein field equations, leads to the singular isotropic Friedmann solutions. In the context of Friedmann-Robertson-Walker (FRW) spacetime, we show that singular behavior does not occur for a class of nonlinear generalizations of the electromagnetic theory for strong fields. A new mathematical model is proposed for which the analytical nonsingular extension of FRW solutions is obtained by using the nonlinear magnetic monopole fields.

  14. Recreating History with Archimedes and Pi

    ERIC Educational Resources Information Center

    Santucci, Lora C.

    2011-01-01

    Using modern technology to examine classical mathematics problems at the high school level can reduce difficult computations and encourage generalizations. When teachers combine historical context with access to technology, they challenge advanced students to think deeply, spark interest in students whose primary interest is not mathematics, and…

  15. Nonlinear Wave Propagation

    DTIC Science & Technology

    1984-09-01

    Asymptotic Results for a Model Equation for Low Reynolds Number Flow, SIAM J. Appi. Math., 35, July 1978. 3. A. S. Yokes : Group Theoretical Aspects of...Quadratic and Cubic Invariants in’ Classical Mechanics, J. Math. Anal. Appl.,’ 74, 342, (1980). 5. A. S. Pokas , P. A. Lagerstrom: On the Use of Lie...Mathematical Methods in Hydrodynamics and %Integrability in Dynamical System, pp. 237-241. 24. 14. J. Ablovitz and A. S. Pokas : A Direct Linearization

  16. PREFACE: Physics and Mathematics of Nonlinear Phenomena 2013 (PMNP2013)

    NASA Astrophysics Data System (ADS)

    Konopelchenko, B. G.; Landolfi, G.; Martina, L.; Vitolo, R.

    2014-03-01

    Modern theory of nonlinear integrable equations is nowdays an important and effective tool of study for numerous nonlinear phenomena in various branches of physics from hydrodynamics and optics to quantum filed theory and gravity. It includes the study of nonlinear partial differential and discrete equations, regular and singular behaviour of their solutions, Hamitonian and bi- Hamitonian structures, their symmetries, associated deformations of algebraic and geometrical structures with applications to various models in physics and mathematics. The PMNP 2013 conference focused on recent advances and developments in Continuous and discrete, classical and quantum integrable systems Hamiltonian, critical and geometric structures of nonlinear integrable equations Integrable systems in quantum field theory and matrix models Models of nonlinear phenomena in physics Applications of nonlinear integrable systems in physics The Scientific Committee of the conference was formed by Francesco Calogero (University of Rome `La Sapienza', Italy) Boris A Dubrovin (SISSA, Italy) Yuji Kodama (Ohio State University, USA) Franco Magri (University of Milan `Bicocca', Italy) Vladimir E Zakharov (University of Arizona, USA, and Landau Institute for Theoretical Physics, Russia) The Organizing Committee: Boris G Konopelchenko, Giulio Landolfi, Luigi Martina, Department of Mathematics and Physics `E De Giorgi' and the Istituto Nazionale di Fisica Nucleare, and Raffaele Vitolo, Department of Mathematics and Physics `E De Giorgi'. A list of sponsors, speakers, talks, participants and the conference photograph are given in the PDF. Conference photograph

  17. General solution for diffusion-controlled dissolution of spherical particles. 1. Theory.

    PubMed

    Wang, J; Flanagan, D R

    1999-07-01

    Three classical particle dissolution rate expressions are commonly used to interpret particle dissolution rate phenomena. Our analysis shows that an assumption used in the derivation of the traditional cube-root law may not be accurate under all conditions for diffusion-controlled particle dissolution. Mathematical analysis shows that the three classical particle dissolution rate expressions are approximate solutions to a general diffusion layer model. The cube-root law is most appropriate when particle size is much larger than the diffusion layer thickness, the two-thirds-root expression applies when the particle size is much smaller than the diffusion layer thickness. The square-root expression is intermediate between these two models. A general solution to the diffusion layer model for monodispersed spherical particles dissolution was derived for sink and nonsink conditions. Constant diffusion layer thickness was assumed in the derivation. Simulated dissolution data showed that the ratio between particle size and diffusion layer thickness (a0/h) is an important factor in controlling the shape of particle dissolution profiles. A new semiempirical general particle dissolution equation is also discussed which encompasses the three classical particle dissolution expressions. The success of the general equation in explaining limitations of traditional particle dissolution expressions demonstrates the usefulness of the general diffusion layer model.

  18. Using CAS to Solve Classical Mathematics Problems

    ERIC Educational Resources Information Center

    Burke, Maurice J.; Burroughs, Elizabeth A.

    2009-01-01

    Historically, calculus has displaced many algebraic methods for solving classical problems. This article illustrates an algebraic method for finding the zeros of polynomial functions that is closely related to Newton's method (devised in 1669, published in 1711), which is encountered in calculus. By exploring this problem, precalculus students…

  19. Cutting Cakes Carefully

    ERIC Educational Resources Information Center

    Hill, Theodore P.; Morrison, Kent E.

    2010-01-01

    This paper surveys the fascinating mathematics of fair division, and provides a suite of examples using basic ideas from algebra, calculus, and probability which can be used to examine and test new and sometimes complex mathematical theories and claims involving fair division. Conversely, the classical cut-and-choose and moving-knife algorithms…

  20. Stable time filtering of strongly unstable spatially extended systems

    PubMed Central

    Grote, Marcus J.; Majda, Andrew J.

    2006-01-01

    Many contemporary problems in science involve making predictions based on partial observation of extremely complicated spatially extended systems with many degrees of freedom and with physical instabilities on both large and small scale. Various new ensemble filtering strategies have been developed recently for these applications, and new mathematical issues arise. Because ensembles are extremely expensive to generate, one such issue is whether it is possible under appropriate circumstances to take long time steps in an explicit difference scheme and violate the classical Courant–Friedrichs–Lewy (CFL)-stability condition yet obtain stable accurate filtering by using the observations. These issues are explored here both through elementary mathematical theory, which provides simple guidelines, and the detailed study of a prototype model. The prototype model involves an unstable finite difference scheme for a convection–diffusion equation, and it is demonstrated below that appropriate observations can result in stable accurate filtering of this strongly unstable spatially extended system. PMID:16682626

  1. Stable time filtering of strongly unstable spatially extended systems.

    PubMed

    Grote, Marcus J; Majda, Andrew J

    2006-05-16

    Many contemporary problems in science involve making predictions based on partial observation of extremely complicated spatially extended systems with many degrees of freedom and with physical instabilities on both large and small scale. Various new ensemble filtering strategies have been developed recently for these applications, and new mathematical issues arise. Because ensembles are extremely expensive to generate, one such issue is whether it is possible under appropriate circumstances to take long time steps in an explicit difference scheme and violate the classical Courant-Friedrichs-Lewy (CFL)-stability condition yet obtain stable accurate filtering by using the observations. These issues are explored here both through elementary mathematical theory, which provides simple guidelines, and the detailed study of a prototype model. The prototype model involves an unstable finite difference scheme for a convection-diffusion equation, and it is demonstrated below that appropriate observations can result in stable accurate filtering of this strongly unstable spatially extended system.

  2. Merging economics and epidemiology to improve the prediction and management of infectious disease.

    PubMed

    Perrings, Charles; Castillo-Chavez, Carlos; Chowell, Gerardo; Daszak, Peter; Fenichel, Eli P; Finnoff, David; Horan, Richard D; Kilpatrick, A Marm; Kinzig, Ann P; Kuminoff, Nicolai V; Levin, Simon; Morin, Benjamin; Smith, Katherine F; Springborn, Michael

    2014-12-01

    Mathematical epidemiology, one of the oldest and richest areas in mathematical biology, has significantly enhanced our understanding of how pathogens emerge, evolve, and spread. Classical epidemiological models, the standard for predicting and managing the spread of infectious disease, assume that contacts between susceptible and infectious individuals depend on their relative frequency in the population. The behavioral factors that underpin contact rates are not generally addressed. There is, however, an emerging a class of models that addresses the feedbacks between infectious disease dynamics and the behavioral decisions driving host contact. Referred to as "economic epidemiology" or "epidemiological economics," the approach explores the determinants of decisions about the number and type of contacts made by individuals, using insights and methods from economics. We show how the approach has the potential both to improve predictions of the course of infectious disease, and to support development of novel approaches to infectious disease management.

  3. Some general remarks on hyperplasticity modelling and its extension to partially saturated soils

    NASA Astrophysics Data System (ADS)

    Lei, Xiaoqin; Wong, Henry; Fabbri, Antonin; Bui, Tuan Anh; Limam, Ali

    2016-06-01

    The essential ideas and equations of classic plasticity and hyperplasticity are successively recalled and compared, in order to highlight their differences and complementarities. The former is based on the mathematical framework proposed by Hill (The mathematical theory of plasticity. Oxford University Press, Oxford, 1950), whereas the latter is founded on the orthogonality hypothesis of Ziegler (An introduction to thermomechanics. Elsevier, North-Holland, 1983). The main drawback of classic plasticity is the possibility of violating the second principle of thermodynamics, while the relative ease to conjecture the yield function in order to approach experimental results is its main advantage. By opposition, the a priori satisfaction of thermodynamic principles constitutes the chief advantage of hyperplasticity theory. Noteworthy is also the fact that this latter approach allows a finer energy partition; in particular, the existence of frozen energy emerges as a natural consequence from its theoretical formulation. On the other hand, the relative difficulty to conjecture an efficient dissipation function to produce accurate predictions is its main drawback. The two theories are thus better viewed as two complementary approaches. Following this comparative study, a methodology to extend the hyperplasticity approach initially developed for dry or saturated materials to the case of partially saturated materials, accounting for interface energies and suction effects, is developed. A particular example based on the yield function of modified Cam-Clay model is then presented. It is shown that the approach developed leads to a model consistent with other existing works.

  4. Self-Supervised Dynamical Systems

    NASA Technical Reports Server (NTRS)

    Zak, Michail

    2003-01-01

    Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and metal aspects of a monad is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. This feedback is what makes the evolution of probability densities nonlinear. The deviation from linear evolution can be characterized, in a sense, as an expression of free will. It has been demonstrated that probability densities can approach prescribed attractors while exhibiting such patterns as shock waves, solitons, and chaos in probability space. The concept of self-supervised dynamical systems has been considered for application to diverse phenomena, including information-based neural networks, cooperation, competition, deception, games, and control of chaos. In addition, a formal similarity between the mathematical structures of self-supervised dynamical systems and of quantum-mechanical systems has been investigated.

  5. Investigating Mathematics with PentaBlocks.

    ERIC Educational Resources Information Center

    Berman, Sheldon; Plummer, Gary A.; Scheuer, Don

    These classic pattern blocks were introduced in the early 1960s as part of the Elementary Science Study materials developed by the Educational Development Center (EDC). The six classic shapes share one common characteristic: all of the angle measurements are multiplies of 30 degrees. Shapes include the regular triangle, square, and hexagon; the…

  6. Revisiting competition in a classic model system using formal links between theory and data.

    PubMed

    Hart, Simon P; Burgin, Jacqueline R; Marshall, Dustin J

    2012-09-01

    Formal links between theory and data are a critical goal for ecology. However, while our current understanding of competition provides the foundation for solving many derived ecological problems, this understanding is fractured because competition theory and data are rarely unified. Conclusions from seminal studies in space-limited benthic marine systems, in particular, have been very influential for our general understanding of competition, but rely on traditional empirical methods with limited inferential power and compatibility with theory. Here we explicitly link mathematical theory with experimental field data to provide a more sophisticated understanding of competition in this classic model system. In contrast to predictions from conceptual models, our estimates of competition coefficients show that a dominant space competitor can be equally affected by interspecific competition with a poor competitor (traditionally defined) as it is by intraspecific competition. More generally, the often-invoked competitive hierarchies and intransitivities in this system might be usefully revisited using more sophisticated empirical and analytical approaches.

  7. 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.

  8. Psychology in Mathematics Education: Past, Present, and Future

    ERIC Educational Resources Information Center

    Steffe, Leslie P.

    2017-01-01

    Starting with Woodworth and Thorndike's classical experiment published in 1901, major periods in mathematics education throughout 20th century and on into the current century are reviewed in terms of competing epistemological and psychological paradigms that were operating within as well as across the major periods. The periods were marked by…

  9. Control Engineering, System Theory and Mathematics: The Teacher's Challenge

    ERIC Educational Resources Information Center

    Zenger, K.

    2007-01-01

    The principles, difficulties and challenges in control education are discussed and compared to the similar problems in the teaching of mathematics and systems science in general. The difficulties of today's students to appreciate the classical teaching of engineering disciplines, which are based on rigorous and scientifically sound grounds, are…

  10. The Need for Alternative Paradigms in Science and Engineering Education

    ERIC Educational Resources Information Center

    Baggi, Dennis L.

    2007-01-01

    There are two main claims in this article. First, that the classic pillars of engineering education, namely, traditional mathematics and differential equations, are merely a particular, if not old-fashioned, representation of a broader mathematical vision, which spans from Turing machine programming and symbolic productions sets to sub-symbolic…

  11. Curriculum Forms: On the Assumed Shapes of Knowing and Knowledge.

    ERIC Educational Resources Information Center

    Davis, Brent; Sumara, Dennis J.

    2000-01-01

    Draws on the new field of mathematical study called fractal geometry. Illustrates the pervasiveness and constraining tendencies of classical geometries. Suggests that fractal geometry is a mathematical analogue to fields such as post-modernism, post-structuralism, and ecological theory. Examines how fractal geometry can complement other emergent…

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

    Sadovskii, V. M., E-mail: sadov@icm.krasn.ru; Sadovskaya, O. V., E-mail: o-sadov@icm.krasn.ru

    Based on the generalized rheological method, the mathematical model describing small deformations of a single-phase porous medium without regard to the effects of a fluid or gas in pores is constructed. The change in resistance of a material to the external mechanical impacts at the moment of pore collapse is taken into account by means of the von Mises–Schleicher strength condition. In order to consider irreversible deformations, alongside with the classical yield conditions by von Mises and Tresca– Saint-Venant, the special condition modeling the plastic loss of stability of a porous skeleton is used. The random nature of the poremore » size distribution is taken into account. It is shown that the proposed mathematical model satisfies the principles of thermodynamics of irreversible processes. Phenomenological parameters of the model are determined on the basis of the approximate calculation of the problem on quasi-static loading of a cubic periodicity cell with spherical voids. In the framework of the obtained model, the process of propagation of plane longitudinal waves of the compression in a homogenous porous medium, accompanied by the plastic deformation of a skeleton and the collapse of pores, is analyzed.« less

  13. Behavioral variability of choices versus structural inconsistency of preferences.

    PubMed

    Regenwetter, Michel; Davis-Stober, Clintin P

    2012-04-01

    Theories of rational choice often make the structural consistency assumption that every decision maker's binary strict preference among choice alternatives forms a strict weak order. Likewise, the very concept of a utility function over lotteries in normative, prescriptive, and descriptive theory is mathematically equivalent to strict weak order preferences over those lotteries, while intransitive heuristic models violate such weak orders. Using new quantitative interdisciplinary methodologies, we dissociate the variability of choices from the structural inconsistency of preferences. We show that laboratory choice behavior among stimuli of a classical "intransitivity" paradigm is, in fact, consistent with variable strict weak order preferences. We find that decision makers act in accordance with a restrictive mathematical model that, for the behavioral sciences, is extraordinarily parsimonious. Our findings suggest that the best place to invest future behavioral decision research is not in the development of new intransitive decision models but rather in the specification of parsimonious models consistent with strict weak order(s), as well as heuristics and other process models that explain why preferences appear to be weakly ordered.

  14. Is cancer a pure growth curve or does it follow a kinetics of dynamical structural transformation?

    PubMed

    González, Maraelys Morales; Joa, Javier Antonio González; Cabrales, Luis Enrique Bergues; Pupo, Ana Elisa Bergues; Schneider, Baruch; Kondakci, Suleyman; Ciria, Héctor Manuel Camué; Reyes, Juan Bory; Jarque, Manuel Verdecia; Mateus, Miguel Angel O'Farril; González, Tamara Rubio; Brooks, Soraida Candida Acosta; Cáceres, José Luis Hernández; González, Gustavo Victoriano Sierra

    2017-03-07

    Unperturbed tumor growth kinetics is one of the more studied cancer topics; however, it is poorly understood. Mathematical modeling is a useful tool to elucidate new mechanisms involved in tumor growth kinetics, which can be relevant to understand cancer genesis and select the most suitable treatment. The classical Kolmogorov-Johnson-Mehl-Avrami as well as the modified Kolmogorov-Johnson-Mehl-Avrami models to describe unperturbed fibrosarcoma Sa-37 tumor growth are used and compared with the Gompertz modified and Logistic models. Viable tumor cells (1×10 5 ) are inoculated to 28 BALB/c male mice. Modified Gompertz, Logistic, Kolmogorov-Johnson-Mehl-Avrami classical and modified Kolmogorov-Johnson-Mehl-Avrami models fit well to the experimental data and agree with one another. A jump in the time behaviors of the instantaneous slopes of classical and modified Kolmogorov-Johnson-Mehl-Avrami models and high values of these instantaneous slopes at very early stages of tumor growth kinetics are observed. The modified Kolmogorov-Johnson-Mehl-Avrami equation can be used to describe unperturbed fibrosarcoma Sa-37 tumor growth. It reveals that diffusion-controlled nucleation/growth and impingement mechanisms are involved in tumor growth kinetics. On the other hand, tumor development kinetics reveals dynamical structural transformations rather than a pure growth curve. Tumor fractal property prevails during entire TGK.

  15. The Five Key Questions of Human Performance Modeling.

    PubMed

    Wu, Changxu

    2018-01-01

    Via building computational (typically mathematical and computer simulation) models, human performance modeling (HPM) quantifies, predicts, and maximizes human performance, human-machine system productivity and safety. This paper describes and summarizes the five key questions of human performance modeling: 1) Why we build models of human performance; 2) What the expectations of a good human performance model are; 3) What the procedures and requirements in building and verifying a human performance model are; 4) How we integrate a human performance model with system design; and 5) What the possible future directions of human performance modeling research are. Recent and classic HPM findings are addressed in the five questions to provide new thinking in HPM's motivations, expectations, procedures, system integration and future directions.

  16. On the limitations of standard statistical modeling in biological systems: a full Bayesian approach for biology.

    PubMed

    Gomez-Ramirez, Jaime; Sanz, Ricardo

    2013-09-01

    One of the most important scientific challenges today is the quantitative and predictive understanding of biological function. Classical mathematical and computational approaches have been enormously successful in modeling inert matter, but they may be inadequate to address inherent features of biological systems. We address the conceptual and methodological obstacles that lie in the inverse problem in biological systems modeling. We introduce a full Bayesian approach (FBA), a theoretical framework to study biological function, in which probability distributions are conditional on biophysical information that physically resides in the biological system that is studied by the scientist. Copyright © 2013 Elsevier Ltd. All rights reserved.

  17. Constructivized Calculus in College Mathematics

    ERIC Educational Resources Information Center

    Lawrence, Barbara Ann

    2012-01-01

    The purpose of this study is to present some of the classical concepts, definitions, and theorems of calculus from the constructivists' point of view in the spirit of the philosophies of L.E.J. Brouwer and Errett Bishop. This presentation will compare the classical statements to the constructivized statements. The method focuses on giving…

  18. Louis Guttman's Contributions to Classical Test Theory

    ERIC Educational Resources Information Center

    Zimmerman, Donald W.; Williams, Richard H.; Zumbo, Bruno D.; Ross, Donald

    2005-01-01

    This article focuses on Louis Guttman's contributions to the classical theory of educational and psychological tests, one of the lesser known of his many contributions to quantitative methods in the social sciences. Guttman's work in this field provided a rigorous mathematical basis for ideas that, for many decades after Spearman's initial work,…

  19. The Classical Version of Stokes' Theorem Revisited

    ERIC Educational Resources Information Center

    Markvorsen, Steen

    2008-01-01

    Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…

  20. Software-aided discussion about classical picture of Mach-Zehnder interferometer

    NASA Astrophysics Data System (ADS)

    Cavalcanti, C. J. H.; Ostermann, F.; Lima, N. W.; Netto, J. S.

    2017-11-01

    The Mach-Zehnder interferometer has played an important role both in quantum and classical physics research over the years. In physics education, it has been used as a didactic tool for quantum physics teaching, allowing fundamental concepts, such as particle-wave duality, to be addressed from the very beginning. For a student to understand the novelties of the quantum scenario, it is first worth introducing the classical picture. In this paper, we introduce a new version of the software developed by our research group to deepen the discussion on the classical picture of the Mach-Zehnder interferometer. We present its equivalence with the double slit experiment and we derive the mathematical expressions relating to the interference pattern. We also explore the concept of visibility (which is very important for understanding wave-particle complementarity in quantum physics) to help students become familiar with this experiment and to enhance their knowledge of its counterintuitive aspects. We use the software articulated by the mathematical formalism and phenomenological features. We also present excerpts of the discursive interactions of students using the software in didactic situations.

  1. Growing-Making Mathematics: A Dynamic Perspective on People, Materials, and Movement in Classrooms

    ERIC Educational Resources Information Center

    Roth, Wolff-Michael

    2016-01-01

    Recent theoretical advances on learning (mathematics) emphasize the fact that what results from engagement with curriculum materials is not entirely in the control of the students in the way classical theories of knowing and learning suggest. These new theories distinguish themselves by either invoking distributed agency, some of which is…

  2. Focus in High School Mathematics: Reasoning and Sense Making in Geometry

    ERIC Educational Resources Information Center

    National Council of Teachers of Mathematics, 2010

    2010-01-01

    Classically, geometry has been the subject in which students encounter mathematical proof based on formal deduction. Attention to proof in the geometry curriculum is strengthened by a focus on reasoning and sense making. This book examines the four key elements (conjecturing about geometric objects, construction and evaluation of geometric…

  3. Designers workbench: toward real-time immersive modeling

    NASA Astrophysics Data System (ADS)

    Kuester, Falko; Duchaineau, Mark A.; Hamann, Bernd; Joy, Kenneth I.; Ma, Kwan-Liu

    2000-05-01

    This paper introduces the Designers Workbench, a semi- immersive virtual environment for two-handed modeling, sculpting and analysis tasks. The paper outlines the fundamental tools, design metaphors and hardware components required for an intuitive real-time modeling system. As companies focus on streamlining productivity to cope with global competition, the migration to computer-aided design (CAD), computer-aided manufacturing, and computer-aided engineering systems has established a new backbone of modern industrial product development. However, traditionally a product design frequently originates form a clay model that, after digitization, forms the basis for the numerical description of CAD primitives. The Designers Workbench aims at closing this technology or 'digital gap' experienced by design and CAD engineers by transforming the classical design paradigm into its fully integrate digital and virtual analog allowing collaborative development in a semi- immersive virtual environment. This project emphasizes two key components form the classical product design cycle: freeform modeling and analysis. In the freedom modeling stage, content creation in the form of two-handed sculpting of arbitrary objects using polygonal, volumetric or mathematically defined primitives is emphasized, whereas the analysis component provides the tools required for pre- and post-processing steps for finite element analysis tasks applied to the created models.

  4. Quantum Sheaf Cohomology on Grassmannians

    NASA Astrophysics Data System (ADS)

    Guo, Jirui; Lu, Zhentao; Sharpe, Eric

    2017-05-01

    In this paper we study the quantum sheaf cohomology of Grassmannians with deformations of the tangent bundle. Quantum sheaf cohomology is a (0,2) deformation of the ordinary quantum cohomology ring, realized as the OPE ring in A/2-twisted theories. Quantum sheaf cohomology has previously been computed for abelian gauged linear sigma models (GLSMs); here, we study (0,2) deformations of nonabelian GLSMs, for which previous methods have been intractable. Combined with the classical result, the quantum ring structure is derived from the one-loop effective potential. We also utilize recent advances in supersymmetric localization to compute A/2 correlation functions and check the general result in examples. In this paper we focus on physics derivations and examples; in a companion paper, we will provide a mathematically rigorous derivation of the classical sheaf cohomology ring.

  5. Mathematical modeling and experimental testing of three bioreactor configurations based on windkessel models

    PubMed Central

    Ruel, Jean; Lachance, Geneviève

    2010-01-01

    This paper presents an experimental study of three bioreactor configurations. The bioreactor is intended to be used for the development of tissue-engineered heart valve substitutes. Therefore it must be able to reproduce physiological flow and pressure waveforms accurately. A detailed analysis of three bioreactor arrangements is presented using mathematical models based on the windkessel (WK) approach. First, a review of the many applications of this approach in medical studies enhances its fundamental nature and its usefulness. Then the models are developed with reference to the actual components of the bioreactor. This study emphasizes different conflicting issues arising in the design process of a bioreactor for biomedical purposes, where an optimization process is essential to reach a compromise satisfying all conditions. Two important aspects are the need for a simple system providing ease of use and long-term sterility, opposed to the need for an advanced (thus more complex) architecture capable of a more accurate reproduction of the physiological environment. Three classic WK architectures are analyzed, and experimental results enhance the advantages and limitations of each one. PMID:21977286

  6. On Mathematical Modeling Of Quantum Systems

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

    Achuthan, P.; Dept. of Mathematics, Indian Institute of Technology, Madras, 600 036; Narayanankutty, Karuppath

    2009-07-02

    The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM,more » though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.« less

  7. Quantum descriptions of singularities leading to pair creation. [of gravitons

    NASA Technical Reports Server (NTRS)

    Misner, C. W.

    1974-01-01

    A class of cosmological models is analyzed which provide a mathematically convenient (but idealized) description of a cosmological singularity that develops into a pair creation epoch and terminates in an adiabatic expansion with redshifting particle energies. This class of models was obtained by Gowdy (1971, 1974) as a set of exact solutions of the classical empty space Einstein equations describing inhomogeneous universes populated only by gravitational waves. It is shown that these models can be used to exhibit simplified models of quantized gravitational fields, and that a quantum description can be given arbitrarily near a cosmological singularity. Graviton pair creation occurs, and can be seen to convert anisotropic expansion rates into the energy of graviton pairs.

  8. Capacity on wireless quantum cellular communication system

    NASA Astrophysics Data System (ADS)

    Zhou, Xiang-Zhen; Yu, Xu-Tao; Zhang, Zai-Chen

    2018-03-01

    Quantum technology is making excellent prospects in future communication networks. Entanglement generation and purification are two major components in quantum networks. Combining these two techniques with classical cellular mobile communication, we proposed a novel wireless quantum cellular(WQC) communication system which is possible to realize commercial mobile quantum communication. In this paper, the architecture and network topology of WQC communication system are discussed, the mathematical model of WQC system is extracted and the serving capacity, indicating the ability to serve customers, is defined and calculated under certain circumstances.

  9. The formal de Rham complex

    NASA Astrophysics Data System (ADS)

    Zharinov, V. V.

    2013-02-01

    We propose a formal construction generalizing the classic de Rham complex to a wide class of models in mathematical physics and analysis. The presentation is divided into a sequence of definitions and elementary, easily verified statements; proofs are therefore given only in the key case. Linear operations are everywhere performed over a fixed number field {F} = {R},{C}. All linear spaces, algebras, and modules, although not stipulated explicitly, are by definition or by construction endowed with natural locally convex topologies, and their morphisms are continuous.

  10. An Introduction to Turbulent Flow

    NASA Astrophysics Data System (ADS)

    Mathieu, Jean; Scott, Julian

    2000-06-01

    In recent years, turbulence has become a very lively area of scientific research and application, attracting many newcomers who need a basic introduction to the subject. Turbulent Flows ably meets this need, developing both physical insight and the mathematical framework needed to express the theory. The authors present basic theory and illustrate it with examples of simple turbulent flows and classical models of jets, wakes, and boundary layers. A deeper understanding of turbulence dynamics is provided by their treatment of spectral analysis and its applications.

  11. Bidirectional Classical Stochastic Processes with Measurements and Feedback

    NASA Technical Reports Server (NTRS)

    Hahne, G. E.

    2005-01-01

    A measurement on a quantum system is said to cause the "collapse" of the quantum state vector or density matrix. An analogous collapse occurs with measurements on a classical stochastic process. This paper addresses the question of describing the response of a classical stochastic process when there is feedback from the output of a measurement to the input, and is intended to give a model for quantum-mechanical processes that occur along a space-like reaction coordinate. The classical system can be thought of in physical terms as two counterflowing probability streams, which stochastically exchange probability currents in a way that the net probability current, and hence the overall probability, suitably interpreted, is conserved. The proposed formalism extends the . mathematics of those stochastic processes describable with linear, single-step, unidirectional transition probabilities, known as Markov chains and stochastic matrices. It is shown that a certain rearrangement and combination of the input and output of two stochastic matrices of the same order yields another matrix of the same type. Each measurement causes the partial collapse of the probability current distribution in the midst of such a process, giving rise to calculable, but non-Markov, values for the ensuing modification of the system's output probability distribution. The paper concludes with an analysis of a classical probabilistic version of the so-called grandfather paradox.

  12. The knowledge instinct, cognitive algorithms, modeling of language and cultural evolution

    NASA Astrophysics Data System (ADS)

    Perlovsky, Leonid I.

    2008-04-01

    The talk discusses mechanisms of the mind and their engineering applications. The past attempts at designing "intelligent systems" encountered mathematical difficulties related to algorithmic complexity. The culprit turned out to be logic, which in one way or another was used not only in logic rule systems, but also in statistical, neural, and fuzzy systems. Algorithmic complexity is related to Godel's theory, a most fundamental mathematical result. These difficulties were overcome by replacing logic with a dynamic process "from vague to crisp," dynamic logic. It leads to algorithms overcoming combinatorial complexity, and resulting in orders of magnitude improvement in classical problems of detection, tracking, fusion, and prediction in noise. I present engineering applications to pattern recognition, detection, tracking, fusion, financial predictions, and Internet search engines. Mathematical and engineering efficiency of dynamic logic can also be understood as cognitive algorithm, which describes fundamental property of the mind, the knowledge instinct responsible for all our higher cognitive functions: concepts, perception, cognition, instincts, imaginations, intuitions, emotions, including emotions of the beautiful. I present our latest results in modeling evolution of languages and cultures, their interactions in these processes, and role of music in cultural evolution. Experimental data is presented that support the theory. Future directions are outlined.

  13. A Primer on Elliptic Functions with Applications in Classical Mechanics

    ERIC Educational Resources Information Center

    Brizard, Alain J.

    2009-01-01

    The Jacobi and Weierstrass elliptic functions used to be part of the standard mathematical arsenal of physics students. They appear as solutions of many important problems in classical mechanics: the motion of a planar pendulum (Jacobi), the motion of a force-free asymmetric top (Jacobi), the motion of a spherical pendulum (Weierstrass) and the…

  14. Mathematical modeling of climate change and malaria transmission dynamics: a historical review.

    PubMed

    Eikenberry, Steffen E; Gumel, Abba B

    2018-04-24

    Malaria, one of the greatest historical killers of mankind, continues to claim around half a million lives annually, with almost all deaths occurring in children under the age of five living in tropical Africa. The range of this disease is limited by climate to the warmer regions of the globe, and so anthropogenic global warming (and climate change more broadly) now threatens to alter the geographic area for potential malaria transmission, as both the Plasmodium malaria parasite and Anopheles mosquito vector have highly temperature-dependent lifecycles, while the aquatic immature Anopheles habitats are also strongly dependent upon rainfall and local hydrodynamics. A wide variety of process-based (or mechanistic) mathematical models have thus been proposed for the complex, highly nonlinear weather-driven Anopheles lifecycle and malaria transmission dynamics, but have reached somewhat disparate conclusions as to optimum temperatures for transmission, and the possible effect of increasing temperatures upon (potential) malaria distribution, with some projecting a large increase in the area at risk for malaria, but others predicting primarily a shift in the disease's geographic range. More generally, both global and local environmental changes drove the initial emergence of P. falciparum as a major human pathogen in tropical Africa some 10,000 years ago, and the disease has a long and deep history through the present. It is the goal of this paper to review major aspects of malaria biology, methods for formalizing these into mathematical forms, uncertainties and controversies in proper modeling methodology, and to provide a timeline of some major modeling efforts from the classical works of Sir Ronald Ross and George Macdonald through recent climate-focused modeling studies. Finally, we attempt to place such mathematical work within a broader historical context for the "million-murdering Death" of malaria.

  15. Building "Consciousness and Legacies": Integrating Community, Critical, and Classical Knowledge Bases in a Precalculus Class

    ERIC Educational Resources Information Center

    Gutierrez, Rodrigo Jorge

    2013-01-01

    Grounded in Freire's (1970) notion that the purpose of education in an unjust society is to bring about equality and justice, Critical Mathematics (CM) scholars consider mathematics to be a tool to understand, critique, and change the world by deconstructing power structures that marginalize certain groups. In particular, Gutstein's (2006)…

  16. Mathematical analysis of compressive/tensile molecular and nuclear structures

    NASA Astrophysics Data System (ADS)

    Wang, Dayu

    Mathematical analysis in chemistry is a fascinating and critical tool to explain experimental observations. In this dissertation, mathematical methods to present chemical bonding and other structures for many-particle systems are discussed at different levels (molecular, atomic, and nuclear). First, the tetrahedral geometry of single, double, or triple carbon-carbon bonds gives an unsatisfying demonstration of bond lengths, compared to experimental trends. To correct this, Platonic solids and Archimedean solids were evaluated as atoms in covalent carbon or nitrogen bond systems in order to find the best solids for geometric fitting. Pentagonal solids, e.g. the dodecahedron and icosidodecahedron, give the best fit with experimental bond lengths; an ideal pyramidal solid which models covalent bonds was also generated. Second, the macroscopic compression/tension architectural approach was applied to forces at the molecular level, considering atomic interactions as compressive (repulsive) and tensile (attractive) forces. Two particle interactions were considered, followed by a model of the dihydrogen molecule (H2; two protons and two electrons). Dihydrogen was evaluated as two different types of compression/tension structures: a coaxial spring model and a ring model. Using similar methods, covalent diatomic molecules (made up of C, N, O, or F) were evaluated. Finally, the compression/tension model was extended to the nuclear level, based on the observation that nuclei with certain numbers of protons/neutrons (magic numbers) have extra stability compared to other nucleon ratios. A hollow spherical model was developed that combines elements of the classic nuclear shell model and liquid drop model. Nuclear structure and the trend of the "island of stability" for the current and extended periodic table were studied.

  17. Cournot games with network effects for electric power markets

    NASA Astrophysics Data System (ADS)

    Spezia, Carl John

    The electric utility industry is moving from regulated monopolies with protected service areas to an open market with many wholesale suppliers competing for consumer load. This market is typically modeled by a Cournot game oligopoly where suppliers compete by selecting profit maximizing quantities. The classical Cournot model can produce multiple solutions when the problem includes typical power system constraints. This work presents a mathematical programming formulation of oligopoly that produces unique solutions when constraints limit the supplier outputs. The formulation casts the game as a supply maximization problem with power system physical limits and supplier incremental profit functions as constraints. The formulation gives Cournot solutions identical to other commonly used algorithms when suppliers operate within the constraints. Numerical examples demonstrate the feasibility of the theory. The results show that the maximization formulation will give system operators more transmission capacity when compared to the actions of suppliers in a classical constrained Cournot game. The results also show that the profitability of suppliers in constrained networks depends on their location relative to the consumers' load concentration.

  18. A Particle Model Explaining Mass and Relativity in a Physical Way

    NASA Astrophysics Data System (ADS)

    Giese, Albrecht

    Physicists' understanding of relativity and the way it is handled is up to present days dominated by the interpretation of Albert Einstein, who related relativity to specific properties of space and time. The principal alternative to Einstein's interpretation is based on a concept proposed by Hendrik A. Lorentz, which uses knowledge of classical physics alone to explain relativistic phenomena. In this paper, we will show that on the one hand the Lorentz-based interpretation provides a simpler mathematical way of arriving at the known results for both Special and General Relativity. On the other hand, it is able to solve problems which have remained open to this day. Furthermore, a particle model will be presented, based on Lorentzian relativity and the quantum mechanical concept of Louis de Broglie, which explains the origin of mass without the use of the Higgs mechanism. It is based on the finiteness of the speed of light and provides classical results for particle properties which are currently only accessible through quantum mechanics.

  19. Dispersive shock waves and modulation theory

    NASA Astrophysics Data System (ADS)

    El, G. A.; Hoefer, M. A.

    2016-10-01

    There is growing physical and mathematical interest in the hydrodynamics of dissipationless/dispersive media. Since G.B. Whitham's seminal publication fifty years ago that ushered in the mathematical study of dispersive hydrodynamics, there has been a significant body of work in this area. However, there has been no comprehensive survey of the field of dispersive hydrodynamics. Utilizing Whitham's averaging theory as the primary mathematical tool, we review the rich mathematical developments over the past fifty years with an emphasis on physical applications. The fundamental, large scale, coherent excitation in dispersive hydrodynamic systems is an expanding, oscillatory dispersive shock wave or DSW. Both the macroscopic and microscopic properties of DSWs are analyzed in detail within the context of the universal, integrable, and foundational models for uni-directional (Korteweg-de Vries equation) and bi-directional (Nonlinear Schrödinger equation) dispersive hydrodynamics. A DSW fitting procedure that does not rely upon integrable structure yet reveals important macroscopic DSW properties is described. DSW theory is then applied to a number of physical applications: superfluids, nonlinear optics, geophysics, and fluid dynamics. Finally, we survey some of the more recent developments including non-classical DSWs, DSW interactions, DSWs in perturbed and inhomogeneous environments, and two-dimensional, oblique DSWs.

  20. Multiple Scenarios of Transition to Chaos in the Alternative Splicing Model

    NASA Astrophysics Data System (ADS)

    Kogai, Vladislav V.; Likhoshvai, Vitaly A.; Fadeev, Stanislav I.; Khlebodarova, Tamara M.

    We have investigated the scenarios of transition to chaos in the mathematical model of a genetic system constituted by a single transcription factor-encoding gene, the expression of which is self-regulated by a feedback loop that involves protein isoforms. Alternative splicing results in the synthesis of protein isoforms providing opposite regulatory outcomes — activation or repression. The model is represented by a differential equation with two delayed arguments. The possibility of transition to chaos dynamics via all classical scenarios: a cascade of period-doubling bifurcations, quasiperiodicity and type-I, type-II and type-III intermittencies, has been numerically demonstrated. The parametric features of each type of transition to chaos have been described.

  1. On the mathematical analysis of Ebola hemorrhagic fever: deathly infection disease in West African countries.

    PubMed

    Atangana, Abdon; Goufo, Emile Franc Doungmo

    2014-01-01

    For a given West African country, we constructed a model describing the spread of the deathly disease called Ebola hemorrhagic fever. The model was first constructed using the classical derivative and then converted to the generalized version using the beta-derivative. We studied in detail the endemic equilibrium points and provided the Eigen values associated using the Jacobian method. We furthered our investigation by solving the model numerically using an iteration method. The simulations were done in terms of time and beta. The study showed that, for small portion of infected individuals, the whole country could die out in a very short period of time in case there is not good prevention.

  2. The Origin of Mathematics and Number Sense in the Cerebellum: with Implications for Finger Counting and Dyscalculia.

    PubMed

    Vandervert, Larry

    2017-01-01

    Mathematicians and scientists have struggled to adequately describe the ultimate foundations of mathematics. Nobel laureates Albert Einstein and Eugene Wigner were perplexed by this issue, with Wigner concluding that the workability of mathematics in the real world is a mystery we cannot explain. In response to this classic enigma, the major purpose of this article is to provide a theoretical model of the ultimate origin of mathematics and "number sense" (as defined by S. Dehaene) that is proposed to involve the learning of inverse dynamics models through the collaboration of the cerebellum and the cerebral cortex (but prominently cerebellum-driven). This model is based upon (1) the modern definition of mathematics as the "science of patterns," (2) cerebellar sequence (pattern) detection, and (3) findings that the manipulation of numbers is automated in the cerebellum. This cerebro-cerebellar approach does not necessarily conflict with mathematics or number sense models that focus on brain functions associated with especially the intraparietal sulcus region of the cerebral cortex. A direct corollary purpose of this article is to offer a cerebellar inner speech explanation for difficulty in developing "number sense" in developmental dyscalculia. It is argued that during infancy the cerebellum learns (1) a first tier of internal models for a primitive physics that constitutes the foundations of visual-spatial working memory, and (2) a second (and more abstract) tier of internal models based on (1) that learns "number" and relationships among dimensions across the primitive physics of the first tier. Within this context it is further argued that difficulty in the early development of the second tier of abstraction (and "number sense") is based on the more demanding attentional requirements imposed on cerebellar inner speech executive control during the learning of cerebellar inverse dynamics models. Finally, it is argued that finger counting improves (does not originate) "number sense" by extending focus of attention in executive control of silent cerebellar inner speech. It is suggested that (1) the origin of mathematics has historically been an enigma only because it is learned below the level of conscious awareness in cerebellar internal models, (2) understandings of the development of "number sense" and developmental dyscalculia can be advanced by first understanding the ultimate foundations of number and mathematics do not simply originate in the cerebral cortex, but rather in cerebro-cerebellar collaboration (predominately driven by the cerebellum). It is concluded that difficulty with "number sense" results from the extended demands on executive control in learning inverse dynamics models associated with cerebellar inner speech related to the second tier of abstraction (numbers) of the infant's primitive physics.

  3. On the modeling and nonlinear dynamics of autonomous Silva-Young type chaotic oscillators with flat power spectrum

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

    Kengne, Jacques; Kenmogne, Fabien

    2014-12-15

    The nonlinear dynamics of fourth-order Silva-Young type chaotic oscillators with flat power spectrum recently introduced by Tamaseviciute and collaborators is considered. In this type of oscillators, a pair of semiconductor diodes in an anti-parallel connection acts as the nonlinear component necessary for generating chaotic oscillations. Based on the Shockley diode equation and an appropriate selection of the state variables, a smooth mathematical model (involving hyperbolic sine and cosine functions) is derived for a better description of both the regular and chaotic dynamics of the system. The complex behavior of the oscillator is characterized in terms of its parameters by usingmore » time series, bifurcation diagrams, Lyapunov exponents' plots, Poincaré sections, and frequency spectra. It is shown that the onset of chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. Some PSPICE simulations of the nonlinear dynamics of the oscillator are presented in order to confirm the ability of the proposed mathematical model to accurately describe/predict both the regular and chaotic behaviors of the oscillator.« less

  4. Hybrid semi-parametric mathematical systems: bridging the gap between systems biology and process engineering.

    PubMed

    Teixeira, Ana P; Carinhas, Nuno; Dias, João M L; Cruz, Pedro; Alves, Paula M; Carrondo, Manuel J T; Oliveira, Rui

    2007-12-01

    Systems biology is an integrative science that aims at the global characterization of biological systems. Huge amounts of data regarding gene expression, proteins activity and metabolite concentrations are collected by designing systematic genetic or environmental perturbations. Then the challenge is to integrate such data in a global model in order to provide a global picture of the cell. The analysis of these data is largely dominated by nonparametric modelling tools. In contrast, classical bioprocess engineering has been primarily founded on first principles models, but it has systematically overlooked the details of the embedded biological system. The full complexity of biological systems is currently assumed by systems biology and this knowledge can now be taken by engineers to decide how to optimally design and operate their processes. This paper discusses possible methodologies for the integration of systems biology and bioprocess engineering with emphasis on applications involving animal cell cultures. At the mathematical systems level, the discussion is focused on hybrid semi-parametric systems as a way to bridge systems biology and bioprocess engineering.

  5. Cytochrome P450 metabolism of the post-lanosterol intermediates explains enigmas of cholesterol synthesis

    NASA Astrophysics Data System (ADS)

    Ačimovič, Jure; Goyal, Sandeep; Košir, Rok; Goličnik, Marko; Perše, Martina; Belič, Ales; Urlep, Žiga; Guengerich, F. Peter; Rozman, Damjana

    2016-06-01

    Cholesterol synthesis is among the oldest metabolic pathways, consisting of the Bloch and Kandutch-Russell branches. Following lanosterol, sterols of both branches are proposed to be dedicated to cholesterol. We challenge this dogma by mathematical modeling and with experimental evidence. It was not possible to explain the sterol profile of testis in cAMP responsive element modulator tau (Crem τ) knockout mice with mathematical models based on textbook pathways of cholesterol synthesis. Our model differs in the inclusion of virtual sterol metabolizing enzymes branching from the pathway. We tested the hypothesis that enzymes from the cytochrome P450 (CYP) superfamily can participate in the catalysis of non-classical reactions. We show that CYP enzymes can metabolize multiple sterols in vitro, establishing novel branching points of cholesterol synthesis. In conclusion, sterols of cholesterol synthesis can be oxidized further to metabolites not dedicated to production of cholesterol. Additionally, CYP7A1, CYP11A1, CYP27A1, and CYP46A1 are parts of a broader cholesterol synthesis network.

  6. Cytochrome P450 metabolism of the post-lanosterol intermediates explains enigmas of cholesterol synthesis.

    PubMed

    Ačimovič, Jure; Goyal, Sandeep; Košir, Rok; Goličnik, Marko; Perše, Martina; Belič, Ales; Urlep, Žiga; Guengerich, F Peter; Rozman, Damjana

    2016-06-23

    Cholesterol synthesis is among the oldest metabolic pathways, consisting of the Bloch and Kandutch-Russell branches. Following lanosterol, sterols of both branches are proposed to be dedicated to cholesterol. We challenge this dogma by mathematical modeling and with experimental evidence. It was not possible to explain the sterol profile of testis in cAMP responsive element modulator tau (Crem τ) knockout mice with mathematical models based on textbook pathways of cholesterol synthesis. Our model differs in the inclusion of virtual sterol metabolizing enzymes branching from the pathway. We tested the hypothesis that enzymes from the cytochrome P450 (CYP) superfamily can participate in the catalysis of non-classical reactions. We show that CYP enzymes can metabolize multiple sterols in vitro, establishing novel branching points of cholesterol synthesis. In conclusion, sterols of cholesterol synthesis can be oxidized further to metabolites not dedicated to production of cholesterol. Additionally, CYP7A1, CYP11A1, CYP27A1, and CYP46A1 are parts of a broader cholesterol synthesis network.

  7. Population Biology of Schistosoma Mating, Aggregation, and Transmission Breakpoints: More Reliable Model Analysis for the End-Game in Communities at Risk

    PubMed Central

    Gurarie, David; King, Charles H.

    2014-01-01

    Mathematical modeling is widely used for predictive analysis of control options for infectious agents. Challenging problems arise for modeling host-parasite systems having complex life-cycles and transmission environments. Macroparasites, like Schistosoma, inhabit highly fragmented habitats that shape their reproductive success and distribution. Overdispersion and mating success are important factors to consider in modeling control options for such systems. Simpler models based on mean worm burden (MWB) formulations do not take these into account and overestimate transmission. Proposed MWB revisions have employed prescribed distributions and mating factor corrections to derive modified MWB models that have qualitatively different equilibria, including ‘breakpoints’ below which the parasite goes to extinction, suggesting the possibility of elimination via long-term mass-treatment control. Despite common use, no one has attempted to validate the scope and hypotheses underlying such MWB approaches. We conducted a systematic analysis of both the classical MWB and more recent “stratified worm burden” (SWB) modeling that accounts for mating and reproductive hurdles (Allee effect). Our analysis reveals some similarities, including breakpoints, between MWB and SWB, but also significant differences between the two types of model. We show the classic MWB has inherent inconsistencies, and propose SWB as a reliable alternative for projection of long-term control outcomes. PMID:25549362

  8. Modeling Flow in Porous Media with Double Porosity/Permeability.

    NASA Astrophysics Data System (ADS)

    Seyed Joodat, S. H.; Nakshatrala, K. B.; Ballarini, R.

    2016-12-01

    Although several continuum models are available to study the flow of fluids in porous media with two pore-networks [1], they lack a firm theoretical basis. In this poster presentation, we will present a mathematical model with firm thermodynamic basis and a robust computational framework for studying flow in porous media that exhibit double porosity/permeability. The mathematical model will be derived by appealing to the maximization of rate of dissipation hypothesis, which ensures that the model is in accord with the second law of thermodynamics. We will also present important properties that the solutions under the model satisfy, along with an analytical solution procedure based on the Green's function method. On the computational front, a stabilized mixed finite element formulation will be derived based on the variational multi-scale formalism. The equal-order interpolation, which is computationally the most convenient, is stable under this formulation. The performance of this formulation will be demonstrated using patch tests, numerical convergence study, and representative problems. It will be shown that the pressure and velocity profiles under the double porosity/permeability model are qualitatively and quantitatively different from the corresponding ones under the classical Darcy equations. Finally, it will be illustrated that the surface pore-structure is not sufficient in characterizing the flow through a complex porous medium, which pitches a case for using advanced characterization tools like micro-CT. References [1] G. I. Barenblatt, I. P. Zheltov, and I. N. Kochina, "Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata]," Journal of Applied Mathematics and Mechanics, vol. 24, pp. 1286-1303, 1960.

  9. Peirce's cenopythagorean categories, Merleau-Ponty's chiasmatic entrelacs and Grothendieck's Résumé.

    PubMed

    Zalamea, Fernando

    2015-12-01

    We present Peirce's cenopythagorean categories and Merleau-Ponty's entrelacs and chiasma, as universal phenomenological tools, particularly useful for a better understanding of dynamic, non-classical, non-separated contemporary mathematics. As a case study, we revisit Grothendieck's Résumé, and we explore its extremely rich mathematical, semiotical and phenomenological entanglements. Copyright © 2015 Elsevier Ltd. All rights reserved.

  10. Equilibrium Fluid Interface Behavior Under Low- and Zero-Gravity Conditions. 2

    NASA Technical Reports Server (NTRS)

    Concus, Paul; Finn, Robert

    1996-01-01

    The mathematical basis for the forthcoming Angular Liquid Bridge investigation on board Mir is described. Our mathematical work is based on the classical Young-Laplace-Gauss formulation for an equilibrium free surface of liquid partly filling a container or otherwise in contact with solid support surfaces. The anticipated liquid behavior used in the apparatus design is also illustrated.

  11. Towards the Solution of Abysmal Performance in Mathematics in Junior High Schools: Comparing the Pedagogical Potential of Two Designed Interventions

    ERIC Educational Resources Information Center

    Sarfo, Frederick Kwaku; Eshun, Grace; Elen, Jan; Adentwi, Kobina Impraim

    2014-01-01

    Introduction: In this study, the effectiveness of two different interventions was investigated. The effects of a concrete abstract intervention and a regular method of teaching intervention were compared. Both interventions were designed in line with the specifications of classical principles of instructional design for learning mathematics in the…

  12. Complete Systematic Error Model of SSR for Sensor Registration in ATC Surveillance Networks

    PubMed Central

    Besada, Juan A.

    2017-01-01

    In this paper, a complete and rigorous mathematical model for secondary surveillance radar systematic errors (biases) is developed. The model takes into account the physical effects systematically affecting the measurement processes. The azimuth biases are calculated from the physical error of the antenna calibration and the errors of the angle determination dispositive. Distance bias is calculated from the delay of the signal produced by the refractivity index of the atmosphere, and from clock errors, while the altitude bias is calculated taking into account the atmosphere conditions (pressure and temperature). It will be shown, using simulated and real data, that adapting a classical bias estimation process to use the complete parametrized model results in improved accuracy in the bias estimation. PMID:28934157

  13. Dynamics of a prey-predator system under Poisson white noise excitation

    NASA Astrophysics Data System (ADS)

    Pan, Shan-Shan; Zhu, Wei-Qiu

    2014-10-01

    The classical Lotka-Volterra (LV) model is a well-known mathematical model for prey-predator ecosystems. In the present paper, the pulse-type version of stochastic LV model, in which the effect of a random natural environment has been modeled as Poisson white noise, is investigated by using the stochastic averaging method. The averaged generalized Itô stochastic differential equation and Fokker-Planck-Kolmogorov (FPK) equation are derived for prey-predator ecosystem driven by Poisson white noise. Approximate stationary solution for the averaged generalized FPK equation is obtained by using the perturbation method. The effect of prey self-competition parameter ɛ2 s on ecosystem behavior is evaluated. The analytical result is confirmed by corresponding Monte Carlo (MC) simulation.

  14. Designers Workbench: Towards Real-Time Immersive Modeling

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

    Kuester, F; Duchaineau, M A; Hamann, B

    2001-10-03

    This paper introduces the DesignersWorkbench, a semi-immersive virtual environment for two-handed modeling, sculpting and analysis tasks. The paper outlines the fundamental tools, design metaphors and hardware components required for an intuitive real-time modeling system. As companies focus on streamlining productivity to cope with global competition, the migration to computer-aided design (CAD), computer-aided manufacturing (CAM), and computer-aided engineering (CAE) systems has established a new backbone of modern industrial product development. However, traditionally a product design frequently originates from a clay model that, after digitization, forms the basis for the numerical description of CAD primitives. The DesignersWorkbench aims at closing this technologymore » or ''digital gap'' experienced by design and CAD engineers by transforming the classical design paradigm into its filly integrated digital and virtual analog allowing collaborative development in a semi-immersive virtual environment. This project emphasizes two key components from the classical product design cycle: freeform modeling and analysis. In the freeform modeling stage, content creation in the form of two-handed sculpting of arbitrary objects using polygonal, volumetric or mathematically defined primitives is emphasized, whereas the analysis component provides the tools required for pre- and post-processing steps for finite element analysis tasks applied to the created models.« less

  15. Prequantum classical statistical field theory: background field as a source of everything?

    NASA Astrophysics Data System (ADS)

    Khrennikov, Andrei

    2011-07-01

    Prequantum classical statistical field theory (PCSFT) is a new attempt to consider quantum mechanics (QM) as an emergent phenomenon, cf. with De Broglie's "double solution" approach, Bohmian mechanics, stochastic electrodynamics (SED), Nelson's stochastic QM and its generalization by Davidson, 't Hooft's models and their development by Elze. PCSFT is a comeback to a purely wave viewpoint on QM, cf. with early Schrodinger. There is no quantum particles at all, only waves. In particular, photons are simply wave-pulses of the classical electromagnetic field, cf. SED. Moreover, even massive particles are special "prequantum fields": the electron field, the neutron field, and so on. PCSFT claims that (sooner or later) people will be able to measure components of these fields: components of the "photonic field" (the classical electromagnetic field of low intensity), electronic field, neutronic field, and so on. At the moment we are able to produce quantum correlations as correlations of classical Gaussian random fields. In this paper we are interested in mathematical and physical reasons of usage of Gaussian fields. We consider prequantum signals (corresponding to quantum systems) as composed of a huge number of wave-pulses (on very fine prequantum time scale). We speculate that the prequantum background field (the field of "vacuum fluctuations") might play the role of a source of such pulses, i.e., the source of everything.

  16. A mathematical model of fluid and gas flow in nanoporous media.

    PubMed

    Monteiro, Paulo J M; Rycroft, Chris H; Barenblatt, Grigory Isaakovich

    2012-12-11

    The mathematical modeling of the flow in nanoporous rocks (e.g., shales) becomes an important new branch of subterranean fluid mechanics. The classic approach that was successfully used in the construction of the technology to develop oil and gas deposits in the United States, Canada, and the Union of Soviet Socialist Republics becomes insufficient for deposits in shales. In the present article a mathematical model of the flow in nanoporous rocks is proposed. The model assumes the rock consists of two components: (i) a matrix, which is more or less an ordinary porous or fissurized-porous medium, and (ii) specific organic inclusions composed of kerogen. These inclusions may have substantial porosity but, due to the nanoscale of pores, tubes, and channels, have extremely low permeability on the order of a nanodarcy (~109-²¹ m² ) or less. These inclusions contain the majority of fluid: oil and gas. Our model is based on the hypothesis that the permeability of the inclusions substantially depends on the pressure gradient. At the beginning of the development of the deposit, boundary layers are formed at the boundaries of the low-permeable inclusions, where the permeability is strongly increased and intensive flow from inclusions to the matrix occurs. The resulting formulae for the production rate of the deposit are presented in explicit form. The formulae demonstrate that the production rate of deposits decays with time following a power law whose exponent lies between -1/2 and -1. Processing of experimental data obtained from various oil and gas deposits in shales demonstrated an instructive agreement with the prediction of the model.

  17. Inverters for interfacing of solar cells with the power grid

    NASA Astrophysics Data System (ADS)

    Karamanzanis, G. N.; Jackson, R. D.

    In this work, based on a research course in the Engineering Dep. Cambridge University, some non-classical inverter circuits are studied. They can be used for interfacing solar cells with the power grid at low voltage (230V) and at low power level. They are based on d.c. choppers which have a fast switching transistor. Their theoretical efficiency is 100 percent and they provide a satisfactory output current waveform in phase to the a.c. line voltage. The problems of control are also studied using a suitable mathematical model.

  18. Open problems in mathematical physics

    NASA Astrophysics Data System (ADS)

    Coley, Alan A.

    2017-09-01

    We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of mathematical physics, particularly in the topical fields of classical general relativity, cosmology and the quantum realm. This list is motivated by the recent article proposing 42 fundamental questions (in physics) which must be answered on the road to full enlightenment (Allen and Lidstrom 2017 Phys. Scr. 92 012501). But paraphrasing a famous quote by the British football manager Bill Shankly, in response to the question of whether mathematics can answer the Ultimate Question of Life, the Universe, and Everything, mathematics is, of course, much more important than that.

  19. Thermodynamically accurate modeling of the catalytic cycle of photosynthetic oxygen evolution: a mathematical solution to asymmetric Markov chains.

    PubMed

    Vinyard, David J; Zachary, Chase E; Ananyev, Gennady; Dismukes, G Charles

    2013-07-01

    Forty-three years ago, Kok and coworkers introduced a phenomenological model describing period-four oscillations in O2 flash yields during photosynthetic water oxidation (WOC), which had been first reported by Joliot and coworkers. The original two-parameter Kok model was subsequently extended in its level of complexity to better simulate diverse data sets, including intact cells and isolated PSII-WOCs, but at the expense of introducing physically unrealistic assumptions necessary to enable numerical solutions. To date, analytical solutions have been found only for symmetric Kok models (inefficiencies are equally probable for all intermediates, called "S-states"). However, it is widely accepted that S-state reaction steps are not identical and some are not reversible (by thermodynamic restraints) thereby causing asymmetric cycles. We have developed a mathematically more rigorous foundation that eliminates unphysical assumptions known to be in conflict with experiments and adopts a new experimental constraint on solutions. This new algorithm termed STEAMM for S-state Transition Eigenvalues of Asymmetric Markov Models enables solutions to models having fewer adjustable parameters and uses automated fitting to experimental data sets, yielding higher accuracy and precision than the classic Kok or extended Kok models. This new tool provides a general mathematical framework for analyzing damped oscillations arising from any cycle period using any appropriate Markov model, regardless of symmetry. We illustrate applications of STEAMM that better describe the intrinsic inefficiencies for photon-to-charge conversion within PSII-WOCs that are responsible for damped period-four and period-two oscillations of flash O2 yields across diverse species, while using simpler Markov models free from unrealistic assumptions. Copyright © 2013 Elsevier B.V. All rights reserved.

  20. Quantitative model analysis with diverse biological data: applications in developmental pattern formation.

    PubMed

    Pargett, Michael; Umulis, David M

    2013-07-15

    Mathematical modeling of transcription factor and signaling networks is widely used to understand if and how a mechanism works, and to infer regulatory interactions that produce a model consistent with the observed data. Both of these approaches to modeling are informed by experimental data, however, much of the data available or even acquirable are not quantitative. Data that is not strictly quantitative cannot be used by classical, quantitative, model-based analyses that measure a difference between the measured observation and the model prediction for that observation. To bridge the model-to-data gap, a variety of techniques have been developed to measure model "fitness" and provide numerical values that can subsequently be used in model optimization or model inference studies. Here, we discuss a selection of traditional and novel techniques to transform data of varied quality and enable quantitative comparison with mathematical models. This review is intended to both inform the use of these model analysis methods, focused on parameter estimation, and to help guide the choice of method to use for a given study based on the type of data available. Applying techniques such as normalization or optimal scaling may significantly improve the utility of current biological data in model-based study and allow greater integration between disparate types of data. Copyright © 2013 Elsevier Inc. All rights reserved.

  1. Mathematical model for cell competition: Predator-prey interactions at the interface between two groups of cells in monolayer tissue.

    PubMed

    Nishikawa, Seiya; Takamatsu, Atsuko; Ohsawa, Shizue; Igaki, Tatsushi

    2016-09-07

    The phenomenon of 'cell competition' has been implicated in the normal development and maintenance of organs, such as in the regulation of organ size and suppression of neoplastic development. In cell competition, one group of cells competes with another group through an interaction at their interface. Which cell group "wins" is governed by a certain relative fitness within the cells. However, this idea of cellular fitness has not been clearly defined. We construct two types of mathematical models to describe this phenomenon of cell competition by considering the interaction at the interface as a predator-prey type interaction in a monolayer tissue such as epithelium. Both of these models can reproduce several typical experimental observations involving systems of mutant cells (losers) and normal cells (winners). By analyzing one of the model and defining an index for the degree of fitness in groups of cells, we show that the fate of each group mainly depends on the relative carrying capacities of certain resources and the strength of the predator-prey interaction at the interface. This contradicts the classical hypothesis in which the relative proliferation rate determines the winner. Copyright © 2016 Elsevier Ltd. All rights reserved.

  2. Physics of Life: A Model for Non-Newtonian Properties of Living Systems

    NASA Technical Reports Server (NTRS)

    Zak, Michail

    2010-01-01

    This innovation proposes the reconciliation of the evolution of life with the second law of thermodynamics via the introduction of the First Principle for modeling behavior of living systems. The structure of the model is quantum-inspired: it acquires the topology of the Madelung equation in which the quantum potential is replaced with the information potential. As a result, the model captures the most fundamental property of life: the progressive evolution; i.e. the ability to evolve from disorder to order without any external interference. The mathematical structure of the model can be obtained from the Newtonian equations of motion (representing the motor dynamics) coupled with the corresponding Liouville equation (representing the mental dynamics) via information forces. All these specific non-Newtonian properties equip the model with the levels of complexity that matches the complexity of life, and that makes the model applicable for description of behaviors of ecological, social, and economical systems. Rather than addressing the six aspects of life (organization, metabolism, growth, adaptation, response to stimuli, and reproduction), this work focuses only on biosignature ; i.e. the mechanical invariants of life, and in particular, the geometry and kinematics of behavior of living things. Living things obey the First Principles of Newtonian mechanics. One main objective of this model is to extend the First Principles of classical physics to include phenomenological behavior on living systems; to develop a new mathematical formalism within the framework of classical dynamics that would allow one to capture the specific properties of natural or artificial living systems such as formation of the collective mind based upon abstract images of the selves and non-selves; exploitation of this collective mind for communications and predictions of future expected characteristics of evolution; and for making decisions and implementing the corresponding corrections if the expected scenario is different from the originally planned one. This approach postulates that even a primitive living species possesses additional, non-Newtonian properties that are not included in the laws of Newtonian or statistical mechanics. These properties follow from a privileged ability of living systems to possess a self-image (a concept introduced in psychology) and to interact with it. The proposed mathematical system is based on the coupling of the classical dynamical system representing the motor dynamics with the corresponding Liouville equation describing the evolution of initial uncertainties in terms of the probability density and representing the mental dynamics. The coupling is implemented by the information-based supervising forces that can be associated with self-awareness. These forces fundamentally change the pattern of the probability evolution, and therefore, lead to a major departure of the behavior of living systems from the patterns of both Newtonian and statistical mechanics. This innovation is meant to capture the signature of life based only on observable behavior, not on any biochemistry. This will not prevent the use of this model for developing artificial living systems, as well as for studying some general properties of behavior of natural, living systems.

  3. An Examination in Turkey: Error Analysis of Mathematics Students on Group Theory

    ERIC Educational Resources Information Center

    Arikan, Elif Esra; Ozkan, Ayten; Ozkan, E. Mehmet

    2015-01-01

    The aim of this study is to analyze the mistakes that have been made in the group theory underlying the algebra mathematics. The 100 students taking algebra math 1 class and studying at the 2nd grade at a state university in Istanbul participated in this study. The related findings were prepared as a classical exam of 6 questions which have been…

  4. A Rhythmic Approach to Mathematics. Classics in Mathematics Education, Volume 5.

    ERIC Educational Resources Information Center

    Somervell, Edith L.

    This book is a reproduction of a monograph written in 1906 to advocate the use of curve stitching in the early school years. The book was originally accompanied by a set of punched cards depicting geometric shapes; each card could be used in the construction of many varied designs. The book's preface is written by Mary Boole, to whom the technique…

  5. Phototransduction early steps model based on Beer-Lambert optical law.

    PubMed

    Salido, Ezequiel M; Servalli, Leonardo N; Gomez, Juan Carlos; Verrastro, Claudio

    2017-02-01

    The amount of available rhodopsin on the photoreceptor outer segment and its change over time is not considered in classic models of phototransduction. Thus, those models do not take into account the absorptance variation of the outer segment under different brightness conditions. The relationship between the light absorbed by a medium and its absorptance is well described by the Beer-Lambert law. This newly proposed model implements the absorptance variation phenomenon in a set of equations that admit photons per second as input and results in active rhodopsins per second as output. This study compares the classic model of phototransduction developed by Forti et al. (1989) to this new model by using different light stimuli to measure active rhodopsin and photocurrent. The results show a linear relationship between light stimulus and active rhodopsin in the Forti model and an exponential saturation in the new model. Further, photocurrent values have shown that the new model behaves equivalently to the experimental and theoretical data as published by Forti in dark-adapted rods, but fits significantly better under light-adapted conditions. The new model successfully introduced a physics optical law to the standard model of phototransduction adding a new processing layer that had not been mathematically implemented before. In addition, it describes the physiological concept of saturation and delivers outputs in concordance to input magnitudes. Copyright © 2017 Elsevier Ltd. All rights reserved.

  6. Statistical Mechanics of Coherent Ising Machine — The Case of Ferromagnetic and Finite-Loading Hopfield Models —

    NASA Astrophysics Data System (ADS)

    Aonishi, Toru; Mimura, Kazushi; Utsunomiya, Shoko; Okada, Masato; Yamamoto, Yoshihisa

    2017-10-01

    The coherent Ising machine (CIM) has attracted attention as one of the most effective Ising computing architectures for solving large scale optimization problems because of its scalability and high-speed computational ability. However, it is difficult to implement the Ising computation in the CIM because the theories and techniques of classical thermodynamic equilibrium Ising spin systems cannot be directly applied to the CIM. This means we have to adapt these theories and techniques to the CIM. Here we focus on a ferromagnetic model and a finite loading Hopfield model, which are canonical models sharing a common mathematical structure with almost all other Ising models. We derive macroscopic equations to capture nonequilibrium phase transitions in these models. The statistical mechanical methods developed here constitute a basis for constructing evaluation methods for other Ising computation models.

  7. A Stochastic-Variational Model for Soft Mumford-Shah Segmentation

    PubMed Central

    2006-01-01

    In contemporary image and vision analysis, stochastic approaches demonstrate great flexibility in representing and modeling complex phenomena, while variational-PDE methods gain enormous computational advantages over Monte Carlo or other stochastic algorithms. In combination, the two can lead to much more powerful novel models and efficient algorithms. In the current work, we propose a stochastic-variational model for soft (or fuzzy) Mumford-Shah segmentation of mixture image patterns. Unlike the classical hard Mumford-Shah segmentation, the new model allows each pixel to belong to each image pattern with some probability. Soft segmentation could lead to hard segmentation, and hence is more general. The modeling procedure, mathematical analysis on the existence of optimal solutions, and computational implementation of the new model are explored in detail, and numerical examples of both synthetic and natural images are presented. PMID:23165059

  8. The Betting Odds Rating System: Using soccer forecasts to forecast soccer.

    PubMed

    Wunderlich, Fabian; Memmert, Daniel

    2018-01-01

    Betting odds are frequently found to outperform mathematical models in sports related forecasting tasks, however the factors contributing to betting odds are not fully traceable and in contrast to rating-based forecasts no straightforward measure of team-specific quality is deducible from the betting odds. The present study investigates the approach of combining the methods of mathematical models and the information included in betting odds. A soccer forecasting model based on the well-known ELO rating system and taking advantage of betting odds as a source of information is presented. Data from almost 15.000 soccer matches (seasons 2007/2008 until 2016/2017) are used, including both domestic matches (English Premier League, German Bundesliga, Spanish Primera Division and Italian Serie A) and international matches (UEFA Champions League, UEFA Europe League). The novel betting odds based ELO model is shown to outperform classic ELO models, thus demonstrating that betting odds prior to a match contain more relevant information than the result of the match itself. It is shown how the novel model can help to gain valuable insights into the quality of soccer teams and its development over time, thus having a practical benefit in performance analysis. Moreover, it is argued that network based approaches might help in further improving rating and forecasting methods.

  9. Helicopter mathematical models and control law development for handling qualities research

    NASA Technical Reports Server (NTRS)

    Chen, Robert T. N.; Lebacqz, J. Victor; Aiken, Edwin W.; Tischler, Mark B.

    1988-01-01

    Progress made in joint NASA/Army research concerning rotorcraft flight-dynamics modeling, design methodologies for rotorcraft flight-control laws, and rotorcraft parameter identification is reviewed. Research into these interactive disciplines is needed to develop the analytical tools necessary to conduct flying qualities investigations using both the ground-based and in-flight simulators, and to permit an efficient means of performing flight test evaluation of rotorcraft flying qualities for specification compliance. The need for the research is particularly acute for rotorcraft because of their mathematical complexity, high order dynamic characteristics, and demanding mission requirements. The research in rotorcraft flight-dynamics modeling is pursued along two general directions: generic nonlinear models and nonlinear models for specific rotorcraft. In addition, linear models are generated that extend their utilization from 1-g flight to high-g maneuvers and expand their frequency range of validity for the design analysis of high-gain flight control systems. A variety of methods ranging from classical frequency-domain approaches to modern time-domain control methodology that are used in the design of rotorcraft flight control laws is reviewed. Also reviewed is a study conducted to investigate the design details associated with high-gain, digital flight control systems for combat rotorcraft. Parameter identification techniques developed for rotorcraft applications are reviewed.

  10. The Betting Odds Rating System: Using soccer forecasts to forecast soccer

    PubMed Central

    Memmert, Daniel

    2018-01-01

    Betting odds are frequently found to outperform mathematical models in sports related forecasting tasks, however the factors contributing to betting odds are not fully traceable and in contrast to rating-based forecasts no straightforward measure of team-specific quality is deducible from the betting odds. The present study investigates the approach of combining the methods of mathematical models and the information included in betting odds. A soccer forecasting model based on the well-known ELO rating system and taking advantage of betting odds as a source of information is presented. Data from almost 15.000 soccer matches (seasons 2007/2008 until 2016/2017) are used, including both domestic matches (English Premier League, German Bundesliga, Spanish Primera Division and Italian Serie A) and international matches (UEFA Champions League, UEFA Europe League). The novel betting odds based ELO model is shown to outperform classic ELO models, thus demonstrating that betting odds prior to a match contain more relevant information than the result of the match itself. It is shown how the novel model can help to gain valuable insights into the quality of soccer teams and its development over time, thus having a practical benefit in performance analysis. Moreover, it is argued that network based approaches might help in further improving rating and forecasting methods. PMID:29870554

  11. Pair interactions of heavy vortices in quantum fluids

    NASA Astrophysics Data System (ADS)

    Pshenichnyuk, Ivan A.

    2018-02-01

    The dynamics of quantum vortex pairs carrying heavy doping matter trapped inside their cores is studied. The nonlinear classical matter field formalism is used to build a universal mathematical model of a heavy vortex applicable to different types of quantum mixtures. It is shown how the usual vortex dynamics typical for undoped pairs qualitatively changes when heavy dopants are used: heavy vortices with opposite topological charges (chiralities) attract each other, while vortices with the same charge are repelled. The force responsible for such behavior appears as a result of superposition of vortices velocity fields in the presence of doping substance and can be considered as a special realization of the Magnus effect. The force is evaluated quantitatively and its inverse proportionality to the distance is demonstrated. The mechanism described in this paper gives an example of how a light nonlinear classical field may realize repulsive and attractive interactions between embedded heavy impurities.

  12. Neuromodulated Spike-Timing-Dependent Plasticity, and Theory of Three-Factor Learning Rules.

    PubMed

    Frémaux, Nicolas; Gerstner, Wulfram

    2015-01-01

    Classical Hebbian learning puts the emphasis on joint pre- and postsynaptic activity, but neglects the potential role of neuromodulators. Since neuromodulators convey information about novelty or reward, the influence of neuromodulators on synaptic plasticity is useful not just for action learning in classical conditioning, but also to decide "when" to create new memories in response to a flow of sensory stimuli. In this review, we focus on timing requirements for pre- and postsynaptic activity in conjunction with one or several phasic neuromodulatory signals. While the emphasis of the text is on conceptual models and mathematical theories, we also discuss some experimental evidence for neuromodulation of Spike-Timing-Dependent Plasticity. We highlight the importance of synaptic mechanisms in bridging the temporal gap between sensory stimulation and neuromodulatory signals, and develop a framework for a class of neo-Hebbian three-factor learning rules that depend on presynaptic activity, postsynaptic variables as well as the influence of neuromodulators.

  13. Self-reference and predictive, normative and prescriptive approaches in applications of systems thinking in social sciences—(Survey)

    NASA Astrophysics Data System (ADS)

    Mesjasz, Czesław

    2000-05-01

    Cybernetics, systems thinking or systems theory, have been viewed as instruments of enhancing predictive, normative and prescriptive capabilities of the social sciences, beginning from microscale-management and ending with various reference to the global system. Descriptions, explanations and predictions achieved thanks to various systems ideas were also viewed as supportive for potential governance of social phenomena. The main aim of the paper is to examine what could be the possible applications of modern systems thinking in predictive, normative and prescriptive approaches in modern social sciences, beginning from management theory and ending with global studies. Attention is paid not only to "classical" mathematical systems models but also to the role of predictive, normative and prescriptive interpretations of analogies and metaphors associated with application of the classical ("first order cybernetics") and modern ("second order cybernetics", "complexity theory") systems thinking in social sciences.

  14. Relativity Based on Physical Processes Rather Than Space-Time

    NASA Astrophysics Data System (ADS)

    Giese, Albrecht

    2013-09-01

    Physicists' understanding of relativity and the way it is handled is at present dominated by the interpretation of Albert Einstein, who related relativity to specific properties of space and time. The principal alternative to Einstein's interpretation is based on a concept proposed by Hendrik A. Lorentz, which uses knowledge of classical physics to explain relativistic phenomena. In this paper, we will show that on the one hand the Lorentz-based interpretation provides a simpler mathematical way of arriving at the known results for both Special and General Relativity. On the other hand, it is able to solve problems which have remained open to this day. Furthermore, a particle model will be presented, based on Lorentzian relativity, which explains the origin of mass without the use of the Higgs mechanism, based on the finiteness of the speed of light, and which provides the classical results for particle properties that are currently only accessible through quantum mechanics.

  15. Chaotic sources of noise in machine acoustics

    NASA Astrophysics Data System (ADS)

    Moon, F. C., Prof.; Broschart, Dipl.-Ing. T.

    1994-05-01

    In this paper a model is posited for deterministic, random-like noise in machines with sliding rigid parts impacting linear continuous machine structures. Such problems occur in gear transmission systems. A mathematical model is proposed to explain the random-like structure-borne and air-borne noise from such systems when the input is a periodic deterministic excitation of the quasi-rigid impacting parts. An experimental study is presented which supports the model. A thin circular plate is impacted by a chaotically vibrating mass excited by a sinusoidal moving base. The results suggest that the plate vibrations might be predicted by replacing the chaotic vibrating mass with a probabilistic forcing function. Prechaotic vibrations of the impacting mass show classical period doubling phenomena.

  16. Nonlinear versus Ordinary Adaptive Control of Continuous Stirred-Tank Reactor

    PubMed Central

    Dostal, Petr

    2015-01-01

    Unfortunately, the major group of the systems in industry has nonlinear behavior and control of such processes with conventional control approaches with fixed parameters causes problems and suboptimal or unstable control results. An adaptive control is one way to how we can cope with nonlinearity of the system. This contribution compares classic adaptive control and its modification with Wiener system. This configuration divides nonlinear controller into the dynamic linear part and the static nonlinear part. The dynamic linear part is constructed with the use of polynomial synthesis together with the pole-placement method and the spectral factorization. The static nonlinear part uses static analysis of the controlled plant for introducing the mathematical nonlinear description of the relation between the controlled output and the change of the control input. Proposed controller is tested by the simulations on the mathematical model of the continuous stirred-tank reactor with cooling in the jacket as a typical nonlinear system. PMID:26346878

  17. Optimal Shakedown of the Thin-Wall Metal Structures Under Strength and Stiffness Constraints

    NASA Astrophysics Data System (ADS)

    Alawdin, Piotr; Liepa, Liudas

    2017-06-01

    Classical optimization problems of metal structures confined mainly with 1st class cross-sections. But in practice it is common to use the cross-sections of higher classes. In this paper, a new mathematical model for described shakedown optimization problem for metal structures, which elements are designed from 1st to 4th class cross-sections, under variable quasi-static loads is presented. The features of limited plastic redistribution of forces in the structure with thin-walled elements there are taken into account. Authors assume the elastic-plastic flexural buckling in one plane without lateral torsional buckling behavior of members. Design formulae for Methods 1 and 2 for members are analyzed. Structures stiffness constrains are also incorporated in order to satisfy the limit serviceability state requirements. With the help of mathematical programming theory and extreme principles the structure optimization algorithm is developed and justified with the numerical experiment for the metal plane frames.

  18. Conservation laws with coinciding smooth solutions but different conserved variables

    NASA Astrophysics Data System (ADS)

    Colombo, Rinaldo M.; Guerra, Graziano

    2018-04-01

    Consider two hyperbolic systems of conservation laws in one space dimension with the same eigenvalues and (right) eigenvectors. We prove that solutions to Cauchy problems with the same initial data differ at third order in the total variation of the initial datum. As a first application, relying on the classical Glimm-Lax result (Glimm and Lax in Decay of solutions of systems of nonlinear hyperbolic conservation laws. Memoirs of the American Mathematical Society, No. 101. American Mathematical Society, Providence, 1970), we obtain estimates improving those in Saint-Raymond (Arch Ration Mech Anal 155(3):171-199, 2000) on the distance between solutions to the isentropic and non-isentropic inviscid compressible Euler equations, under general equations of state. Further applications are to the general scalar case, where rather precise estimates are obtained, to an approximation by Di Perna of the p-system and to a traffic model.

  19. Locality and universality of quantum memory effects.

    PubMed

    Liu, B-H; Wißmann, S; Hu, X-M; Zhang, C; Huang, Y-F; Li, C-F; Guo, G-C; Karlsson, A; Piilo, J; Breuer, H-P

    2014-09-11

    The modeling and analysis of the dynamics of complex systems often requires to employ non-Markovian stochastic processes. While there is a clear and well-established mathematical definition for non-Markovianity in the case of classical systems, the extension to the quantum regime recently caused a vivid debate, leading to many different proposals for the characterization and quantification of memory effects in the dynamics of open quantum systems. Here, we derive a mathematical representation for the non-Markovianity measure based on the exchange of information between the open system and its environment, which reveals the locality and universality of non-Markovianity in the quantum state space and substantially simplifies its numerical and experimental determination. We further illustrate the application of this representation by means of an all-optical experiment which allows the measurement of the degree of memory effects in a photonic quantum process with high accuracy.

  20. Searching fundamental information in ordinary differential equations. Nondimensionalization technique.

    PubMed

    Sánchez Pérez, J F; Conesa, M; Alhama, I; Alhama, F; Cánovas, M

    2017-01-01

    Classical dimensional analysis and nondimensionalization are assumed to be two similar approaches in the search for dimensionless groups. Both techniques, simplify the study of many problems. The first approach does not need to know the mathematical model, being sufficient a deep understanding of the physical phenomenon involved, while the second one begins with the governing equations and reduces them to their dimensionless form by simple mathematical manipulations. In this work, a formal protocol is proposed for applying the nondimensionalization process to ordinary differential equations, linear or not, leading to dimensionless normalized equations from which the resulting dimensionless groups have two inherent properties: In one hand, they are physically interpreted as balances between counteracting quantities in the problem, and on the other hand, they are of the order of magnitude unity. The solutions provided by nondimensionalization are more precise in every case than those from dimensional analysis, as it is illustrated by the applications studied in this work.

  1. Shearlet Features for Registration of Remotely Sensed Multitemporal Images

    NASA Technical Reports Server (NTRS)

    Murphy, James M.; Le Moigne, Jacqueline

    2015-01-01

    We investigate the role of anisotropic feature extraction methods for automatic image registration of remotely sensed multitemporal images. Building on the classical use of wavelets in image registration, we develop an algorithm based on shearlets, a mathematical generalization of wavelets that offers increased directional sensitivity. Initial experimental results on LANDSAT images are presented, which indicate superior performance of the shearlet algorithm when compared to classical wavelet algorithms.

  2. A single-cell spiking model for the origin of grid-cell patterns

    PubMed Central

    Kempter, Richard

    2017-01-01

    Spatial cognition in mammals is thought to rely on the activity of grid cells in the entorhinal cortex, yet the fundamental principles underlying the origin of grid-cell firing are still debated. Grid-like patterns could emerge via Hebbian learning and neuronal adaptation, but current computational models remained too abstract to allow direct confrontation with experimental data. Here, we propose a single-cell spiking model that generates grid firing fields via spike-rate adaptation and spike-timing dependent plasticity. Through rigorous mathematical analysis applicable in the linear limit, we quantitatively predict the requirements for grid-pattern formation, and we establish a direct link to classical pattern-forming systems of the Turing type. Our study lays the groundwork for biophysically-realistic models of grid-cell activity. PMID:28968386

  3. Unifying models of dialect spread and extinction using surface tension dynamics

    PubMed Central

    2018-01-01

    We provide a unified mathematical explanation of two classical forms of spatial linguistic spread. The wave model describes the radiation of linguistic change outwards from a central focus. Changes can also jump between population centres in a process known as hierarchical diffusion. It has recently been proposed that the spatial evolution of dialects can be understood using surface tension at linguistic boundaries. Here we show that the inclusion of long-range interactions in the surface tension model generates both wave-like spread, and hierarchical diffusion, and that it is surface tension that is the dominant effect in deciding the stable distribution of dialect patterns. We generalize the model to allow population mixing which can induce shrinkage of linguistic domains, or destroy dialect regions from within. PMID:29410847

  4. The Use of Mathematical Symbolism in Problem Solving: An Empirical Study Carried out in Grade One in the French Community of Belgium

    ERIC Educational Resources Information Center

    Fagnant, Annick

    2005-01-01

    This article relates to an empirical study based on the use of mathematical symbolism in problem solving, twenty-five pupils were interviewed individually at the end of grade one; each of them was asked to solve and symbolize 14 different problems. In their classical curriculum, these pupils have received a traditional education based on a…

  5. Solving the water jugs problem by an integer sequence approach

    NASA Astrophysics Data System (ADS)

    Man, Yiu-Kwong

    2012-01-01

    In this article, we present an integer sequence approach to solve the classic water jugs problem. The solution steps can be obtained easily by additions and subtractions only, which is suitable for manual calculation or programming by computer. This approach can be introduced to secondary and undergraduate students, and also to teachers and lecturers involved in teaching mathematical problem solving, recreational mathematics, or elementary number theory.

  6. A whole-body mathematical model for intracranial pressure dynamics.

    PubMed

    Lakin, William D; Stevens, Scott A; Tranmer, Bruce I; Penar, Paul L

    2003-04-01

    Most attempts to study intracranial pressure using lumped-parameter models have adopted the classical "Kellie-Monro Doctrine," which considers the intracranial space to be a closed system that is confined within the nearly-rigid skull, conserves mass, and has equal inflow and outflow. The present work revokes this Doctrine and develops a mathematical model for the dynamics of intracranial pressures, volumes, and flows that embeds the intracranial system in extensive whole-body physiology. The new model consistently introduces compartments representing the tissues and vasculature of the extradural portions of the body, including both the thoracic region and the lower extremities. In addition to vascular connections, a spinal-subarachnoid cerebrospinal fluid (CSF) compartment bridges intracranial and extracranial physiology allowing explict buffering of intracranial pressure fluctuations by the spinal theca. The model contains cerebrovascular autoregulation, regulation of systemic vascular pressures by the sympathetic nervous system, regulation of CSF production in the choroid plexus, a lymphatic system, colloid osmotic pressure effects, and realistic descriptions of cardiac output. To validate the model in situations involving normal physiology, the model's response to a realistic pulsatile cardiac output is examined. A well-known experimentally-derived intracranial pressure-volume relationship is recovered by using the model to simulate CSF infusion tests, and the effect on cerebral blood flow of a change in body position is also examined. Cardiac arrest and hemorrhagic shock are simulated to demonstrate the predictive capabilities of the model in pathological conditions.

  7. Multiporosity flow in fractured low-permeability rocks: Extension to shale hydrocarbon reservoirs

    DOE PAGES

    Kuhlman, Kristopher L.; Malama, Bwalya; Heath, Jason E.

    2015-02-05

    We presented a multiporosity extension of classical double and triple-porosity fractured rock flow models for slightly compressible fluids. The multiporosity model is an adaptation of the multirate solute transport model of Haggerty and Gorelick (1995) to viscous flow in fractured rock reservoirs. It is a generalization of both pseudo steady state and transient interporosity flow double-porosity models. The model includes a fracture continuum and an overlapping distribution of multiple rock matrix continua, whose fracture-matrix exchange coefficients are specified through a discrete probability mass function. Semianalytical cylindrically symmetric solutions to the multiporosity mathematical model are developed using the Laplace transform tomore » illustrate its behavior. Furthermore, the multiporosity model presented here is conceptually simple, yet flexible enough to simulate common conceptualizations of double and triple-porosity flow. This combination of generality and simplicity makes the multiporosity model a good choice for flow modelling in low-permeability fractured rocks.« less

  8. Mathematical modeling of a dynamic thin plate deformation in acoustoelasticity problems

    NASA Astrophysics Data System (ADS)

    Badriev, I. B.; Paimuhin, V. N.

    2018-01-01

    The coupled problem of planar acoustic wave propagation through a composite plate covered with a second damping layer with a large logarithmic decrement of oscillations is formulated. The aerohydrodynamic interaction of a plate with external acoustic environment is described by three-dimensional wave equations and the mechanical behavior of a two-layer plate by the classical Kirchhoff-Love model. An exact analytic solution of the problem is found for the case of hinged support of the edges of a plate. On the basis of this, the parameters of the covering damping layer were found, under which it is possible to achieve a practically complete damping of the plate vibration under resonant modes of its acoustic loading.

  9. Modelling of the production of gaseous by-products in anaerobic digestion.

    PubMed

    Strik, D P; Domnanovich, A M; Pfeiffer, B; Karlovitz, M; Zani, L; Braun, R; Holubar, P

    2003-01-01

    Goal of the EU-Project AMONCO (Advanced Prediction, Monitoring and Controlling of Anaerobic Digestion Processes Behaviour towards Biogas Usage in Fuel Cells) is demonstration of the practical use of biogas in fuel cells. The right precondition is a biogas quality which fits into the fuel cells tolerances. Therefore the mission of the workgroup Environmental biotechnology is to control anaerobic digestion in a way that production of potential harmful by-products for fuel cells is reduced. A good understanding of the production of these by products is essential for an applicable decision support tool. This poster presents the modelling of hydrogen sulfide by means of hierarchical neural networks and a classical mathematical method.

  10. Multiobjective optimization in a pseudometric objective space as applied to a general model of business activities

    NASA Astrophysics Data System (ADS)

    Khachaturov, R. V.

    2016-09-01

    It is shown that finding the equivalence set for solving multiobjective discrete optimization problems is advantageous over finding the set of Pareto optimal decisions. An example of a set of key parameters characterizing the economic efficiency of a commercial firm is proposed, and a mathematical model of its activities is constructed. In contrast to the classical problem of finding the maximum profit for any business, this study deals with a multiobjective optimization problem. A method for solving inverse multiobjective problems in a multidimensional pseudometric space is proposed for finding the best project of firm's activities. The solution of a particular problem of this type is presented.

  11. A DPL model of photo-thermal interaction in an infinite semiconductor material containing a spherical hole

    NASA Astrophysics Data System (ADS)

    Hobiny, Aatef D.; Abbas, Ibrahim A.

    2018-01-01

    The dual phase lag (DPL) heat transfer model is applied to study the photo-thermal interaction in an infinite semiconductor medium containing a spherical hole. The inner surface of the cavity was traction free and loaded thermally by pulse heat flux. By using the eigenvalue approach methodology and Laplace's transform, the physical variable solutions are obtained analytically. The numerical computations for the silicon-like semiconductor material are obtained. The comparison among the theories, i.e., dual phase lag (DPL), Lord and Shulman's (LS) and the classically coupled thermoelastic (CT) theory is presented graphically. The results further show that the analytical scheme can overcome mathematical problems by analyzing these problems.

  12. A Unified Model of Geostrophic Adjustment and Frontogenesis

    NASA Astrophysics Data System (ADS)

    Taylor, John; Shakespeare, Callum

    2013-11-01

    Fronts, or regions with strong horizontal density gradients, are ubiquitous and dynamically important features of the ocean and atmosphere. In the ocean, fronts are associated with enhanced air-sea fluxes, turbulence, and biological productivity, while atmospheric fronts are associated with some of the most extreme weather events. Here, we describe a new mathematical framework for describing the formation of fronts, or frontogenesis. This framework unifies two classical problems in geophysical fluid dynamics, geostrophic adjustment and strain-driven frontogenesis, and provides a number of important extensions beyond previous efforts. The model solutions closely match numerical simulations during the early stages of frontogenesis, and provide a means to describe the development of turbulence at mature fronts.

  13. Colombeau algebra as a mathematical tool for investigating step load and step deformation of systems of nonlinear springs and dashpots

    NASA Astrophysics Data System (ADS)

    Průša, Vít; Řehoř, Martin; Tůma, Karel

    2017-02-01

    The response of mechanical systems composed of springs and dashpots to a step input is of eminent interest in the applications. If the system is formed by linear elements, then its response is governed by a system of linear ordinary differential equations. In the linear case, the mathematical method of choice for the analysis of the response is the classical theory of distributions. However, if the system contains nonlinear elements, then the classical theory of distributions is of no use, since it is strictly limited to the linear setting. Consequently, a question arises whether it is even possible or reasonable to study the response of nonlinear systems to step inputs. The answer is positive. A mathematical theory that can handle the challenge is the so-called Colombeau algebra. Building on the abstract result by Průša and Rajagopal (Int J Non-Linear Mech 81:207-221, 2016), we show how to use the theory in the analysis of response of nonlinear spring-dashpot and spring-dashpot-mass systems.

  14. Mathematical Model of Solid Food Pasteurization by Ohmic Heating: Influence of Process Parameters

    PubMed Central

    2014-01-01

    Pasteurization of a solid food undergoing ohmic heating has been analysed by means of a mathematical model, involving the simultaneous solution of Laplace's equation, which describes the distribution of electrical potential within a food, the heat transfer equation, using a source term involving the displacement of electrical potential, the kinetics of inactivation of microorganisms likely to be contaminating the product. In the model, thermophysical and electrical properties as function of temperature are used. Previous works have shown the occurrence of heat loss from food products to the external environment during ohmic heating. The current model predicts that, when temperature gradients are established in the proximity of the outer ohmic cell surface, more cold areas are present at junctions of electrodes with lateral sample surface. For these reasons, colder external shells are the critical areas to be monitored, instead of internal points (typically geometrical center) as in classical pure conductive heat transfer. Analysis is carried out in order to understand the influence of pasteurisation process parameters on this temperature distribution. A successful model helps to improve understanding of these processing phenomenon, which in turn will help to reduce the magnitude of the temperature differential within the product and ultimately provide a more uniformly pasteurized product. PMID:24574874

  15. Mathematical model of solid food pasteurization by ohmic heating: influence of process parameters.

    PubMed

    Marra, Francesco

    2014-01-01

    Pasteurization of a solid food undergoing ohmic heating has been analysed by means of a mathematical model, involving the simultaneous solution of Laplace's equation, which describes the distribution of electrical potential within a food, the heat transfer equation, using a source term involving the displacement of electrical potential, the kinetics of inactivation of microorganisms likely to be contaminating the product. In the model, thermophysical and electrical properties as function of temperature are used. Previous works have shown the occurrence of heat loss from food products to the external environment during ohmic heating. The current model predicts that, when temperature gradients are established in the proximity of the outer ohmic cell surface, more cold areas are present at junctions of electrodes with lateral sample surface. For these reasons, colder external shells are the critical areas to be monitored, instead of internal points (typically geometrical center) as in classical pure conductive heat transfer. Analysis is carried out in order to understand the influence of pasteurisation process parameters on this temperature distribution. A successful model helps to improve understanding of these processing phenomenon, which in turn will help to reduce the magnitude of the temperature differential within the product and ultimately provide a more uniformly pasteurized product.

  16. A mathematical model of “Gone with the Wind”

    NASA Astrophysics Data System (ADS)

    Rinaldi, Sergio; Della Rossa, Fabio; Landi, Pietro

    2013-08-01

    We develop a mathematical model for mimicking the love story between Scarlett and Rhett described in “Gone with the Wind”. In line with tradition in classical physics, the model is composed of two Ordinary Differential Equations, one for Scarlett and one for Rhett, which encapsulate their main psycho-physical characteristics. The two lovers are described as so-called insecure individuals because they respond very strongly to small involvements of the partner but then attenuate their reaction when the pressure exerted by the partner becomes too high. These characteristics of Scarlett and Rhett clearly emerge during the first part of the film and are sufficient to develop a model that perfectly predicts the complex evolution and the dramatic end of the love story. Since the predicted evolution of the romantic relationship is a direct consequence of the characters of the two individuals, the agreement between the model and the film supports the high credibility of the story. Although credibility of a fictitious story is not necessary from a purely artistic point of view, in most cases it is very appreciated, at the point of being essential in making the film popular. In conclusion, we can say that we have explained with a scientific approach why “Gone with the Wind” has become one of the most successful films of all times.

  17. Convective flows of generalized time-nonlocal nanofluids through a vertical rectangular channel

    NASA Astrophysics Data System (ADS)

    Ahmed, Najma; Vieru, Dumitru; Fetecau, Constantin; Shah, Nehad Ali

    2018-05-01

    Time-nonlocal generalized model of the natural convection heat transfer and nanofluid flows through a rectangular vertical channel with wall conditions of the Robin type are studied. The generalized mathematical model with time-nonlocality is developed by considering the fractional constitutive equations for the shear stress and thermal flux defined with the time-fractional Caputo derivative. The Caputo power-law non-local kernel provides the damping to the velocity and temperature gradient; therefore, transport processes are influenced by the histories at all past and present times. Analytical solutions for dimensionless velocity and temperature fields are obtained by using the Laplace transform coupled with the finite sine-cosine Fourier transform which is suitable to problems with boundary conditions of the Robin type. Particularizing the fractional thermal and velocity parameters, solutions for three simplified models are obtained (classical linear momentum equation with damped thermal flux; fractional shear stress constitutive equation with classical Fourier's law for thermal flux; classical shear stress and thermal flux constitutive equations). It is found that the thermal histories strongly influence the thermal transport for small values of time t. Also, the thermal transport can be enhanced if the thermal fractional parameter decreases or by increasing the nanoparticles' volume fraction. The velocity field is influenced on the one hand by the temperature of the fluid and on the other by the damping of the velocity gradient introduced by the fractional derivative. Also, the transport motions of the channel walls influence the motion of the fluid layers located near them.

  18. Quantum Hamilton equations of motion for bound states of one-dimensional quantum systems

    NASA Astrophysics Data System (ADS)

    Köppe, J.; Patzold, M.; Grecksch, W.; Paul, W.

    2018-06-01

    On the basis of Nelson's stochastic mechanics derivation of the Schrödinger equation, a formal mathematical structure of non-relativistic quantum mechanics equivalent to the one in classical analytical mechanics has been established in the literature. We recently were able to augment this structure by deriving quantum Hamilton equations of motion by finding the Nash equilibrium of a stochastic optimal control problem, which is the generalization of Hamilton's principle of classical mechanics to quantum systems. We showed that these equations allow a description and numerical determination of the ground state of quantum problems without using the Schrödinger equation. We extend this approach here to deliver the complete discrete energy spectrum and related eigenfunctions for bound states of one-dimensional stationary quantum systems. We exemplify this analytically for the one-dimensional harmonic oscillator and numerically by analyzing a quartic double-well potential, a model of broad importance in many areas of physics. We furthermore point out a relation between the tunnel splitting of such models and mean first passage time concepts applied to Nelson's diffusion paths in the ground state.

  19. Quantum mechanics over sets

    NASA Astrophysics Data System (ADS)

    Ellerman, David

    2014-03-01

    In models of QM over finite fields (e.g., Schumacher's ``modal quantum theory'' MQT), one finite field stands out, Z2, since Z2 vectors represent sets. QM (finite-dimensional) mathematics can be transported to sets resulting in quantum mechanics over sets or QM/sets. This gives a full probability calculus (unlike MQT with only zero-one modalities) that leads to a fulsome theory of QM/sets including ``logical'' models of the double-slit experiment, Bell's Theorem, QIT, and QC. In QC over Z2 (where gates are non-singular matrices as in MQT), a simple quantum algorithm (one gate plus one function evaluation) solves the Parity SAT problem (finding the parity of the sum of all values of an n-ary Boolean function). Classically, the Parity SAT problem requires 2n function evaluations in contrast to the one function evaluation required in the quantum algorithm. This is quantum speedup but with all the calculations over Z2 just like classical computing. This shows definitively that the source of quantum speedup is not in the greater power of computing over the complex numbers, and confirms the idea that the source is in superposition.

  20. Bond Graph Model of Cerebral Circulation: Toward Clinically Feasible Systemic Blood Flow Simulations.

    PubMed

    Safaei, Soroush; Blanco, Pablo J; Müller, Lucas O; Hellevik, Leif R; Hunter, Peter J

    2018-01-01

    We propose a detailed CellML model of the human cerebral circulation that runs faster than real time on a desktop computer and is designed for use in clinical settings when the speed of response is important. A lumped parameter mathematical model, which is based on a one-dimensional formulation of the flow of an incompressible fluid in distensible vessels, is constructed using a bond graph formulation to ensure mass conservation and energy conservation. The model includes arterial vessels with geometric and anatomical data based on the ADAN circulation model. The peripheral beds are represented by lumped parameter compartments. We compare the hemodynamics predicted by the bond graph formulation of the cerebral circulation with that given by a classical one-dimensional Navier-Stokes model working on top of the whole-body ADAN model. Outputs from the bond graph model, including the pressure and flow signatures and blood volumes, are compared with physiological data.

  1. A mechanistic investigation of the algae growth "Droop" model.

    PubMed

    Lemesle, V; Mailleret, L

    2008-06-01

    In this work a mechanistic explanation of the classical algae growth model built by M. R. Droop in the late sixties is proposed. We first recall the history of the construction of the "predictive" variable yield Droop model as well as the meaning of the introduced cell quota. We then introduce some theoretical hypotheses on the biological phenomena involved in nutrient storage by the algae that lead us to a "conceptual" model. Though more complex than Droop's one, our model remains accessible to a complete mathematical study: its confrontation to the Droop model shows both have the same asymptotic behavior. However, while Droop's cell quota comes from experimental bio-chemical measurements not related to intra-cellular biological phenomena, its analogous in our model directly follows our theoretical hypotheses. This new model should then be looked at as a re-interpretation of Droop's work from a theoretical biologist's point of view.

  2. One Approach to the Synthesis, Design and Manufacture of Hyperboloid Gear Sets With Face Mating Gears. Part 1: Basic Theoretical and Cad Experience

    NASA Astrophysics Data System (ADS)

    Abadjiev, Valentin; Abadjieva, Emilia

    2016-06-01

    Hyperboloid gear drives with face mating gears are used to transform rotations between shafts with non-parallel and non-intersecting axes. A special case of these transmissions are Spiroid and Helicon gear drives. The classical gear drives of this type are the Archimedean ones. The objective of this study are hyperboloid gear drives with face meshing, when the pinion possesses threads of conic convolute, Archimedean and involute types, or the pinion has threads of cylindrical convolute, Archimedean and involute types. For simplicity, all three types transmis- sions with face mating gears and a conic pinion are titled Spiroid and all three types transmissions with face mating gears and a cylindrical pinion are titled Helicon. Principles of the mathematical modelling of tooth contact synthesis are discussed in this study. The presented research shows that the synthesis is realized by application of two mathematical models: pitch contact point and mesh region models. Two approaches for synthesis of the gear drives in accordance with Olivier's principles are illustrated. The algorithms and computer programs for optimization synthesis and design of the studied hyperboloid gear drives are presented.

  3. Hidden physics models: Machine learning of nonlinear partial differential equations

    NASA Astrophysics Data System (ADS)

    Raissi, Maziar; Karniadakis, George Em

    2018-03-01

    While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier-Stokes, Schrödinger, Kuramoto-Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data.

  4. Finite element solution of torsion and other 2-D Poisson equations

    NASA Technical Reports Server (NTRS)

    Everstine, G. C.

    1982-01-01

    The NASTRAN structural analysis computer program may be used, without modification, to solve two dimensional Poisson equations such as arise in the classical Saint Venant torsion problem. The nonhomogeneous term (the right-hand side) in the Poisson equation can be handled conveniently by specifying a gravitational load in a "structural" analysis. The use of an analogy between the equations of elasticity and those of classical mathematical physics is summarized in detail.

  5. Economic decision-making compared with an equivalent motor task.

    PubMed

    Wu, Shih-Wei; Delgado, Mauricio R; Maloney, Laurence T

    2009-04-14

    There is considerable evidence that human economic decision-making deviates from the predictions of expected utility theory (EUT) and that human performance conforms to EUT in many perceptual and motor decision tasks. It is possible that these results reflect a real difference in decision-making in the 2 domains but it is also possible that the observed discrepancy simply reflects typical differences in experimental design. We developed a motor task that is mathematically equivalent to choosing between lotteries and used it to compare how the same subject chose between classical economic lotteries and the same lotteries presented in equivalent motor form. In experiment 1, we found that subjects are more risk seeking in deciding between motor lotteries. In experiment 2, we used cumulative prospect theory to model choice and separately estimated the probability weighting functions and the value functions for each subject carrying out each task. We found no patterned differences in how subjects represented outcome value in the motor and the classical tasks. However, the probability weighting functions for motor and classical tasks were markedly and significantly different. Those for the classical task showed a typical tendency to overweight small probabilities and underweight large probabilities, and those for the motor task showed the opposite pattern of probability distortion. This outcome also accounts for the increased risk-seeking observed in the motor tasks of experiment 1. We conclude that the same subject distorts probability, but not value, differently in making identical decisions in motor and classical form.

  6. Geometric Theory of Reduction of Nonlinear Control Systems

    NASA Astrophysics Data System (ADS)

    Elkin, V. I.

    2018-02-01

    The foundations of a differential geometric theory of nonlinear control systems are described on the basis of categorical concepts (isomorphism, factorization, restrictions) by analogy with classical mathematical theories (of linear spaces, groups, etc.).

  7. Coherence and decoherence in the brain

    NASA Astrophysics Data System (ADS)

    Hepp, K.

    2012-09-01

    This review provides many entry points to controversies in neuroscience, where input from mathematical physics could be fruitful, especially about coherence and decoherence in the brain, both on the level of classical and quantum mechanics.

  8. [Decision of mathematical logical tasks in sensory enriched environment (classical music)].

    PubMed

    Pavlygina, R A; Karamysheva, N N; Tutushkina, M V; Sakharov, D S; Davydov, V I

    2012-01-01

    The time of a decision of mathematical logical tasks (MLT) was decreased during classical musical accompaniment (power 35 and 65 dB). Music 85 dB did not influence on the process of decision of MLT. Decision without the musical accompaniment led to increasing of coherent function values in beta1, beta2, gamma frequency ranges in EEG of occipital areas with prevalence in a left hemisphere. A coherence of potentials was decreased in EEG of frontal cortex. Music decreasing of making-decision time enhanced left-sided EEG asymmetry The intrahemispheric and the interhemispheric coherences of frontal cortex were increased during the decision of MLT accompanied by music. Using of musical accompaniment 85 dB produced a right-side asymmetry in EEG and formed a focus of coherent connections in EEG of temporal area of a right hemisphere.

  9. Modeling biofiltration of VOC mixtures under steady-state conditions

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

    Baltzis, B.C.; Wojdyla, S.M.; Zarook, S.M.

    1997-06-01

    Treatment of air streams contaminated with binary volatile organic compound (VOC) mixtures in classical biofilters under steady-state conditions of operation was described with a general mathematical model. The model accounts for potential kinetic interactions among the pollutants, effects of oxygen availability on biodegradation, and biomass diversification in the filter bed. While the effects of oxygen were always taken into account, two distinct cases were considered for the experimental model validation. The first involves kinetic interactions, but no biomass differentiation, used for describing data from biofiltration of benzene/toluene mixtures. The second case assumes that each pollutant is treated by a differentmore » type of biomass. Each biomass type is assumed to form separate patches of biofilm on the solid packing material, thus kinetic interference does not occur. This model was used for describing biofiltration of ethanol/butanol mixtures. Experiments were performed with classical biofilters packed with mixtures of peat moss and perlite (2:3, volume:volume). The model equations were solved through the use of computer codes based on the fourth-order Runge-Kutta technique for the gas-phase mass balances and the method of orthogonal collocation for the concentration profiles in the biofilms. Good agreement between model predictions and experimental data was found in almost all cases. Oxygen was found to be extremely important in the case of polar VOCs (ethanol/butanol).« less

  10. Newton's Metaphysics of Space as God's Emanative Effect

    NASA Astrophysics Data System (ADS)

    Jacquette, Dale

    2014-09-01

    In several of his writings, Isaac Newton proposed that physical space is God's "emanative effect" or "sensorium," revealing something interesting about the metaphysics underlying his mathematical physics. Newton's conjectures depart from Plato and Aristotle's metaphysics of space and from classical and Cambridge Neoplatonism. Present-day philosophical concepts of supervenience clarify Newton's ideas about space and offer a portrait of Newton not only as a mathematical physicist but an independent-minded rationalist philosopher.

  11. Fire suppression as a thermal implosion

    NASA Astrophysics Data System (ADS)

    Novozhilov, Vasily

    2017-01-01

    The present paper discusses the possibility of the thermal implosion scenario. This process would be a reverse of the well known thermal explosion (autoignition) phenomenon. The mechanism for thermal implosion scenario is proposed which involves quick suppression of the turbulent diffusion flame. Classical concept of the thermal explosion is discussed first. Then a possible scenario for the reverse process (thermal implosion) is discussed and illustrated by a relevant mathematical model. Based on the arguments presented in the paper, thermal implosion may be observed as an unstable equilibrium point on the generalized Semenov diagram for turbulent flame, however this hypothesis requires ultimate experimental confirmation.

  12. An intermediate-level course on Biological Physics

    NASA Astrophysics Data System (ADS)

    Nelson, Phil

    2004-03-01

    I describe both undergraduate and graduate 1-semester courses designed to give a survey of Biological Physics. The courses cover classical as well as recent topics. The undergraduate version requires calculus-based first-year physics as its prerequisite. With this level of assumed background, we can arrive at topics such as molecular motors, manipulation of single molecules, and the propagation of nerve impulses. Students majoring in physics, chemistry, biochemistry, and every engineering major (as well as a few in biology), end up taking this course. The graduate course covers the same material but includes exercises with symbolic mathematics packages and data modeling.

  13. Implementation and validation of an economic module in the Be-FAST model to predict costs generated by livestock disease epidemics: Application to classical swine fever epidemics in Spain.

    PubMed

    Fernández-Carrión, E; Ivorra, B; Martínez-López, B; Ramos, A M; Sánchez-Vizcaíno, J M

    2016-04-01

    Be-FAST is a computer program based on a time-spatial stochastic spread mathematical model for studying the transmission of infectious livestock diseases within and between farms. The present work describes a new module integrated into Be-FAST to model the economic consequences of the spreading of classical swine fever (CSF) and other infectious livestock diseases within and between farms. CSF is financially one of the most damaging diseases in the swine industry worldwide. Specifically in Spain, the economic costs in the two last CSF epidemics (1997 and 2001) reached jointly more than 108 million euros. The present analysis suggests that severe CSF epidemics are associated with significant economic costs, approximately 80% of which are related to animal culling. Direct costs associated with control measures are strongly associated with the number of infected farms, while indirect costs are more strongly associated with epidemic duration. The economic model has been validated with economic information around the last outbreaks in Spain. These results suggest that our economic module may be useful for analysing and predicting economic consequences of livestock disease epidemics. Copyright © 2016 Elsevier B.V. All rights reserved.

  14. Unfolding an electronic integrate-and-fire circuit.

    PubMed

    Carrillo, Humberto; Hoppensteadt, Frank

    2010-01-01

    Many physical and biological phenomena involve accumulation and discharge processes that can occur on significantly different time scales. Models of these processes have contributed to understand excitability self-sustained oscillations and synchronization in arrays of oscillators. Integrate-and-fire (I+F) models are popular minimal fill-and-flush mathematical models. They are used in neuroscience to study spiking and phase locking in single neuron membranes, large scale neural networks, and in a variety of applications in physics and electrical engineering. We show here how the classical first-order I+F model fits into the theory of nonlinear oscillators of van der Pol type by demonstrating that a particular second-order oscillator having small parameters converges in a singular perturbation limit to the I+F model. In this sense, our study provides a novel unfolding of such models and it identifies a constructible electronic circuit that is closely related to I+F.

  15. An elastic-plastic contact model for line contact structures

    NASA Astrophysics Data System (ADS)

    Zhu, Haibin; Zhao, Yingtao; He, Zhifeng; Zhang, Ruinan; Ma, Shaopeng

    2018-06-01

    Although numerical simulation tools are now very powerful, the development of analytical models is very important for the prediction of the mechanical behaviour of line contact structures for deeply understanding contact problems and engineering applications. For the line contact structures widely used in the engineering field, few analytical models are available for predicting the mechanical behaviour when the structures deform plastically, as the classic Hertz's theory would be invalid. Thus, the present study proposed an elastic-plastic model for line contact structures based on the understanding of the yield mechanism. A mathematical expression describing the global relationship between load history and contact width evolution of line contact structures was obtained. The proposed model was verified through an actual line contact test and a corresponding numerical simulation. The results confirmed that this model can be used to accurately predict the elastic-plastic mechanical behaviour of a line contact structure.

  16. Biofilm community succession: a neutral perspective.

    PubMed

    Woodcock, Stephen; Sloan, William T

    2017-05-22

    Although biofilms represent one of the dominant forms of life in aqueous environments, our understanding of the assembly and development of their microbial communities remains relatively poor. In recent years, several studies have addressed this and have extended the concepts of succession theory in classical ecology into microbial systems. From these datasets, niche-based conceptual models have been developed explaining observed biodiversity patterns and their dynamics. These models have not, however, been formulated mathematically and so remain untested. Here, we further develop spatially resolved neutral community models and demonstrate that these can also explain these patterns and offer alternative explanations of microbial succession. The success of neutral models suggests that stochastic effects alone may have a much greater influence on microbial community succession than previously acknowledged. Furthermore, such models are much more readily parameterised and can be used as the foundation of more complex and realistic models of microbial community succession.

  17. Dynamic Modeling and Simulation of an Underactuated System

    NASA Astrophysics Data System (ADS)

    Libardo Duarte Madrid, Juan; Ospina Henao, P. A.; González Querubín, E.

    2017-06-01

    In this paper, is used the Lagrangian classical mechanics for modeling the dynamics of an underactuated system, specifically a rotary inverted pendulum that will have two equations of motion. A basic design of the system is proposed in SOLIDWORKS 3D CAD software, which based on the material and dimensions of the model provides some physical variables necessary for modeling. In order to verify the results obtained, a comparison the CAD model simulated in the environment SimMechanics of MATLAB software with the mathematical model who was consisting of Euler-Lagrange’s equations implemented in Simulink MATLAB, solved with the ODE23tb method, included in the MATLAB libraries for the solution of systems of equations of the type and order obtained. This article also has a topological analysis of pendulum trajectories through a phase space diagram, which allows the identification of stable and unstable regions of the system.

  18. A novel approach to the experimental study on methane/steam reforming kinetics using the Orthogonal Least Squares method

    NASA Astrophysics Data System (ADS)

    Sciazko, Anna; Komatsu, Yosuke; Brus, Grzegorz; Kimijima, Shinji; Szmyd, Janusz S.

    2014-09-01

    For a mathematical model based on the result of physical measurements, it becomes possible to determine their influence on the final solution and its accuracy. However, in classical approaches, the influence of different model simplifications on the reliability of the obtained results are usually not comprehensively discussed. This paper presents a novel approach to the study of methane/steam reforming kinetics based on an advanced methodology called the Orthogonal Least Squares method. The kinetics of the reforming process published earlier are divergent among themselves. To obtain the most probable values of kinetic parameters and enable direct and objective model verification, an appropriate calculation procedure needs to be proposed. The applied Generalized Least Squares (GLS) method includes all the experimental results into the mathematical model which becomes internally contradicted, as the number of equations is greater than number of unknown variables. The GLS method is adopted to select the most probable values of results and simultaneously determine the uncertainty coupled with all the variables in the system. In this paper, the evaluation of the reaction rate after the pre-determination of the reaction rate, which was made by preliminary calculation based on the obtained experimental results over a Nickel/Yttria-stabilized Zirconia catalyst, was performed.

  19. Thermodynamic analysis of biofuels as fuels for high temperature fuel cells

    NASA Astrophysics Data System (ADS)

    Milewski, Jarosław; Bujalski, Wojciech; Lewandowski, Janusz

    2011-11-01

    Based on mathematical modeling and numerical simulations, applicativity of various biofuels on high temperature fuel cell performance are presented. Governing equations of high temperature fuel cell modeling are given. Adequate simulators of both solid oxide fuel cell (SOFC) and molten carbonate fuel cell (MCFC) have been done and described. Performance of these fuel cells with different biofuels is shown. Some characteristics are given and described. Advantages and disadvantages of various biofuels from the system performance point of view are pointed out. An analysis of various biofuels as potential fuels for SOFC and MCFC is presented. The results are compared with both methane and hydrogen as the reference fuels. The biofuels are characterized by both lower efficiency and lower fuel utilization factors compared with methane. The presented results are based on a 0D mathematical model in the design point calculation. The governing equations of the model are also presented. Technical and financial analysis of high temperature fuel cells (SOFC and MCFC) are shown. High temperature fuel cells can be fed by biofuels like: biogas, bioethanol, and biomethanol. Operational costs and possible incomes of those installation types were estimated and analyzed. A comparison against classic power generation units is shown. A basic indicator net present value (NPV) for projects was estimated and commented.

  20. Thermodynamic analysis of biofuels as fuels for high temperature fuel cells

    NASA Astrophysics Data System (ADS)

    Milewski, Jarosław; Bujalski, Wojciech; Lewandowski, Janusz

    2013-02-01

    Based on mathematical modeling and numerical simulations, applicativity of various biofuels on high temperature fuel cell performance are presented. Governing equations of high temperature fuel cell modeling are given. Adequate simulators of both solid oxide fuel cell (SOFC) and molten carbonate fuel cell (MCFC) have been done and described. Performance of these fuel cells with different biofuels is shown. Some characteristics are given and described. Advantages and disadvantages of various biofuels from the system performance point of view are pointed out. An analysis of various biofuels as potential fuels for SOFC and MCFC is presented. The results are compared with both methane and hydrogen as the reference fuels. The biofuels are characterized by both lower efficiency and lower fuel utilization factors compared with methane. The presented results are based on a 0D mathematical model in the design point calculation. The governing equations of the model are also presented. Technical and financial analysis of high temperature fuel cells (SOFC and MCFC) are shown. High temperature fuel cells can be fed by biofuels like: biogas, bioethanol, and biomethanol. Operational costs and possible incomes of those installation types were estimated and analyzed. A comparison against classic power generation units is shown. A basic indicator net present value (NPV) for projects was estimated and commented.

  1. Monitoring and decision making by people in man machine systems

    NASA Technical Reports Server (NTRS)

    Johannsen, G.

    1979-01-01

    The analysis of human monitoring and decision making behavior as well as its modeling are described. Classic and optimal control theoretical, monitoring models are surveyed. The relationship between attention allocation and eye movements is discussed. As an example of applications, the evaluation of predictor displays by means of the optimal control model is explained. Fault detection involving continuous signals and decision making behavior of a human operator engaged in fault diagnosis during different operation and maintenance situations are illustrated. Computer aided decision making is considered as a queueing problem. It is shown to what extent computer aids can be based on the state of human activity as measured by psychophysiological quantities. Finally, management information systems for different application areas are mentioned. The possibilities of mathematical modeling of human behavior in complex man machine systems are also critically assessed.

  2. The Physics of Vibration

    NASA Astrophysics Data System (ADS)

    Pippard, A. B.

    1989-11-01

    The study of vibration in physical systems is an important part of almost all fields in physics and engineering. This work, originally published in two volumes, examines the classical aspects in Part I and the quantum oscillator in Part II. The classical linear vibrator is treated first and the underlying unity of all linear oscillations in electrical, mechanical and acoustic systems is emphasized. Following this the book turns to the treatment of nonlinear vibrations, a field with which engineers and physicists are generally less familiar. In Part II the emphasis turns to quantum systems, that is those systems which can only be adequately described by quantum mechanics. The treatment concentrates on vibrations in atoms and molecules and their interaction with electromagnetic radiation. The similarities of classical and quantum methods are stressed and the limits of the classical treatment are examined. Throughout the book, each phenomenon discussed is illustrated with many examples and theory and experiment are compared. Although the reader may find that the physics discussed is demanding and the concepts are subtle in places, all mathematics used is familiar to both engineers and experimental scientists. Although not a textbook this is a useful introduction to the more advanced mathematical treatment of vibrations as it bridges the gap between the basic principles and more specialized concepts. It will be of great interest to advanced undergraduates and postgraduates as well as applied mathematicians, physicists and engineers in university and industry.

  3. A characterization of linearly repetitive cut and project sets

    NASA Astrophysics Data System (ADS)

    Haynes, Alan; Koivusalo, Henna; Walton, James

    2018-02-01

    For the development of a mathematical theory which can be used to rigorously investigate physical properties of quasicrystals, it is necessary to understand regularity of patterns in special classes of aperiodic point sets in Euclidean space. In one dimension, prototypical mathematical models for quasicrystals are provided by Sturmian sequences and by point sets generated by substitution rules. Regularity properties of such sets are well understood, thanks mostly to well known results by Morse and Hedlund, and physicists have used this understanding to study one dimensional random Schrödinger operators and lattice gas models. A key fact which plays an important role in these problems is the existence of a subadditive ergodic theorem, which is guaranteed when the corresponding point set is linearly repetitive. In this paper we extend the one-dimensional model to cut and project sets, which generalize Sturmian sequences in higher dimensions, and which are frequently used in mathematical and physical literature as models for higher dimensional quasicrystals. By using a combination of algebraic, geometric, and dynamical techniques, together with input from higher dimensional Diophantine approximation, we give a complete characterization of all linearly repetitive cut and project sets with cubical windows. We also prove that these are precisely the collection of such sets which satisfy subadditive ergodic theorems. The results are explicit enough to allow us to apply them to known classical models, and to construct linearly repetitive cut and project sets in all pairs of dimensions and codimensions in which they exist. Research supported by EPSRC grants EP/L001462, EP/J00149X, EP/M023540. HK also gratefully acknowledges the support of the Osk. Huttunen foundation.

  4. Integrating Antimicrobial Therapy with Host Immunity to Fight Drug-Resistant Infections: Classical vs. Adaptive Treatment

    PubMed Central

    Gjini, Erida; Brito, Patricia H.

    2016-01-01

    Antimicrobial resistance of infectious agents is a growing problem worldwide. To prevent the continuing selection and spread of drug resistance, rational design of antibiotic treatment is needed, and the question of aggressive vs. moderate therapies is currently heatedly debated. Host immunity is an important, but often-overlooked factor in the clearance of drug-resistant infections. In this work, we compare aggressive and moderate antibiotic treatment, accounting for host immunity effects. We use mathematical modelling of within-host infection dynamics to study the interplay between pathogen-dependent host immune responses and antibiotic treatment. We compare classical (fixed dose and duration) and adaptive (coupled to pathogen load) treatment regimes, exploring systematically infection outcomes such as time to clearance, immunopathology, host immunization, and selection of resistant bacteria. Our analysis and simulations uncover effective treatment strategies that promote synergy between the host immune system and the antimicrobial drug in clearing infection. Both in classical and adaptive treatment, we quantify how treatment timing and the strength of the immune response determine the success of moderate therapies. We explain key parameters and dimensions, where an adaptive regime differs from classical treatment, bringing new insight into the ongoing debate of resistance management. Emphasizing the sensitivity of treatment outcomes to the balance between external antibiotic intervention and endogenous natural defenses, our study calls for more empirical attention to host immunity processes. PMID:27078624

  5. Fundamental theories of waves and particles formulated without classical mass

    NASA Astrophysics Data System (ADS)

    Fry, J. L.; Musielak, Z. E.

    2010-12-01

    Quantum and classical mechanics are two conceptually and mathematically different theories of physics, and yet they do use the same concept of classical mass that was originally introduced by Newton in his formulation of the laws of dynamics. In this paper, physical consequences of using the classical mass by both theories are explored, and a novel approach that allows formulating fundamental (Galilean invariant) theories of waves and particles without formally introducing the classical mass is presented. In this new formulation, the theories depend only on one common parameter called 'wave mass', which is deduced from experiments for selected elementary particles and for the classical mass of one kilogram. It is shown that quantum theory with the wave mass is independent of the Planck constant and that higher accuracy of performing calculations can be attained by such theory. Natural units in connection with the presented approach are also discussed and justification beyond dimensional analysis is given for the particular choice of such units.

  6. Interacting Winds in Eclipsing Symbiotic Systems - The Case Study of EG Andromedae

    NASA Astrophysics Data System (ADS)

    Calabrò, Emanuele

    2014-03-01

    We report the mathematical representation of the so called eccentric eclipse model, whose numerical solutions can be used to obtain the physical parameters of a quiescent eclipsing symbiotic system. Indeed the nebular region produced by the collision of the stellar winds should be shifted to the orbital axis because of the orbital motion of the system. This mechanism is not negligible, and it led us to modify the classical concept of an eclipse. The orbital elements obtained from spectroscopy and photometry of the symbiotic EG Andromedae were used to test the eccentric eclipse model. Consistent values for the unknown orbital elements of this symbiotic were obtained. The physical parameters are in agreement with those obtained by means of other simulations for this system.

  7. Optimization of the Bridgman crystal growth process

    NASA Astrophysics Data System (ADS)

    Margulies, M.; Witomski, P.; Duffar, T.

    2004-05-01

    A numerical optimization method of the vertical Bridgman growth configuration is presented and developed. It permits to optimize the furnace temperature field and the pulling rate versus time in order to decrease the radial thermal gradients in the sample. Some constraints are also included in order to insure physically realistic results. The model includes the two classical non-linearities associated to crystal growth processes, the radiative thermal exchange and the release of latent heat at the solid-liquid interface. The mathematical analysis and development of the problem is shortly described. On some examples, it is shown that the method works in a satisfactory way; however the results are dependent on the numerical parameters. Improvements of the optimization model, on the physical and numerical point of view, are suggested.

  8. Discrete Dynamical Systems Meet the Classic Monkey-and-the-Bananas Problem.

    ERIC Educational Resources Information Center

    Gannon, Gerald E.; Martelli, Mario U.

    2001-01-01

    Presents a solution of the three-sailors-and-the-bananas problem and attempts a generalization. Introduces an interesting way of looking at the mathematics with an idea drawn from discrete dynamical systems. (KHR)

  9. From correspondence to complementarity: The emergence of Bohr's Copenhagen interpretation of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Tanona, Scott Daniel

    I develop a new analysis of Niels Bohr's Copenhagen interpretation of quantum mechanics by examining the development of his views from his earlier use of the correspondence principle in the so-called 'old quantum theory' to his articulation of the idea of complementarity in the context of the novel mathematical formalism of quantum mechanics. I argue that Bohr was motivated not by controversial and perhaps dispensable epistemological ideas---positivism or neo-Kantianism, for example---but by his own unique perspective on the difficulties of creating a new working physics of the internal structure of the atom. Bohr's use of the correspondence principle in the old quantum theory was associated with an empirical methodology that used this principle as an epistemological bridge to connect empirical phenomena with quantum models. The application of the correspondence principle required that one determine the validity of the idealizations and approximations necessary for the judicious use of classical physics within quantum theory. Bohr's interpretation of the new quantum mechanics then focused on the largely unexamined ways in which the developing abstract mathematical formalism is given empirical content by precisely this process of approximation. Significant consistency between his later interpretive framework and his forms of argument with the correspondence principle indicate that complementarity is best understood as a relationship among the various approximations and idealizations that must be made when one connects otherwise meaningless quantum mechanical symbols to empirical situations or 'experimental arrangements' described using concepts from classical physics. We discover that this relationship is unavoidable not through any sort of a priori analysis of the priority of classical concepts, but because quantum mechanics incorporates the correspondence approach in the way in which it represents quantum properties with matrices of transition probabilities, the empirical meaning of which depend on the situation but in general are tied to the correspondence connection to the spectra. For Bohr, it is then the commutation relations, which arise from the formalism, which inform us of the complementary nature of this approximate representation of quantum properties via the classical equations through which we connect them to experiments.

  10. A stochastic evolution model for residue Insertion-Deletion Independent from Substitution.

    PubMed

    Lèbre, Sophie; Michel, Christian J

    2010-12-01

    We develop here a new class of stochastic models of gene evolution based on residue Insertion-Deletion Independent from Substitution (IDIS). Indeed, in contrast to all existing evolution models, insertions and deletions are modeled here by a concept in population dynamics. Therefore, they are not only independent from each other, but also independent from the substitution process. After a separate stochastic analysis of the substitution and the insertion-deletion processes, we obtain a matrix differential equation combining these two processes defining the IDIS model. By deriving a general solution, we give an analytical expression of the residue occurrence probability at evolution time t as a function of a substitution rate matrix, an insertion rate vector, a deletion rate and an initial residue probability vector. Various mathematical properties of the IDIS model in relation with time t are derived: time scale, time step, time inversion and sequence length. Particular expressions of the nucleotide occurrence probability at time t are given for classical substitution rate matrices in various biological contexts: equal insertion rate, insertion-deletion only and substitution only. All these expressions can be directly used for biological evolutionary applications. The IDIS model shows a strongly different stochastic behavior from the classical substitution only model when compared on a gene dataset. Indeed, by considering three processes of residue insertion, deletion and substitution independently from each other, it allows a more realistic representation of gene evolution and opens new directions and applications in this research field. Copyright © 2010 Elsevier Ltd. All rights reserved.

  11. Cortical circuits for mathematical knowledge: evidence for a major subdivision within the brain's semantic networks.

    PubMed

    Amalric, Marie; Dehaene, Stanislas

    2017-02-19

    Is mathematical language similar to natural language? Are language areas used by mathematicians when they do mathematics? And does the brain comprise a generic semantic system that stores mathematical knowledge alongside knowledge of history, geography or famous people? Here, we refute those views by reviewing three functional MRI studies of the representation and manipulation of high-level mathematical knowledge in professional mathematicians. The results reveal that brain activity during professional mathematical reflection spares perisylvian language-related brain regions as well as temporal lobe areas classically involved in general semantic knowledge. Instead, mathematical reflection recycles bilateral intraparietal and ventral temporal regions involved in elementary number sense. Even simple fact retrieval, such as remembering that 'the sine function is periodical' or that 'London buses are red', activates dissociated areas for math versus non-math knowledge. Together with other fMRI and recent intracranial studies, our results indicated a major separation between two brain networks for mathematical and non-mathematical semantics, which goes a long way to explain a variety of facts in neuroimaging, neuropsychology and developmental disorders.This article is part of a discussion meeting issue 'The origins of numerical abilities'. © 2017 The Author(s).

  12. Divergence thrust loss calculations for convergent-divergent nozzles: Extensions to the classical case

    NASA Technical Reports Server (NTRS)

    Berton, Jeffrey J.

    1991-01-01

    The analytical derivations of the non-axial thrust divergence losses for convergent-divergent nozzles are described as well as how these calculations are embodied in the Navy/NASA engine computer program. The convergent-divergent geometries considered are simple classic axisymmetric nozzles, two dimensional rectangular nozzles, and axisymmetric and two dimensional plug nozzles. A simple, traditional, inviscid mathematical approach is used to deduce the influence of the ineffectual non-axial thrust as a function of the nozzle exit divergence angle.

  13. Survey of Quantification and Distance Functions Used for Internet-based Weak-link Sociological Phenomena

    DTIC Science & Technology

    2016-03-01

    well as the Yahoo search engine and a classic SearchKing HIST algorithm. The co-PI immersed herself in the sociology literature for the relevant...Google matrix, PageRank as well as the Yahoo search engine and a classic SearchKing HIST algorithm. The co-PI immersed herself in the sociology...The PI studied all mathematical literature he can find related to the Google search engine, Google matrix, PageRank as well as the Yahoo search

  14. Modeling and simulation of protein elution in linear pH and salt gradients on weak, strong and mixed cation exchange resins applying an extended Donnan ion exchange model.

    PubMed

    Wittkopp, Felix; Peeck, Lars; Hafner, Mathias; Frech, Christian

    2018-04-13

    Process development and characterization based on mathematic modeling provides several advantages and has been applied more frequently over the last few years. In this work, a Donnan equilibrium ion exchange (DIX) model is applied for modelling and simulation of ion exchange chromatography of a monoclonal antibody in linear chromatography. Four different cation exchange resin prototypes consisting of weak, strong and mixed ligands are characterized using pH and salt gradient elution experiments applying the extended DIX model. The modelling results are compared with the results using a classic stoichiometric displacement model. The Donnan equilibrium model is able to describe all four prototype resins while the stoichiometric displacement model fails for the weak and mixed weak/strong ligands. Finally, in silico chromatogram simulations of pH and pH/salt dual gradients are performed to verify the results and to show the consistency of the developed model. Copyright © 2018 Elsevier B.V. All rights reserved.

  15. Causal implications of viscous damping in compressible fluid flows

    PubMed

    Jordan; Meyer; Puri

    2000-12-01

    Classically, a compressible, isothermal, viscous fluid is regarded as a mathematical continuum and its motion is governed by the linearized continuity, Navier-Stokes, and state equations. Unfortunately, solutions of this system are of a diffusive nature and hence do not satisfy causality. However, in the case of a half-space of fluid set to motion by a harmonically vibrating plate the classical equation of motion can, under suitable conditions, be approximated by the damped wave equation. Since this equation is hyperbolic, the resulting solutions satisfy causal requirements. In this work the Laplace transform and other analytical and numerical tools are used to investigate this apparent contradiction. To this end the exact solutions, as well as their special and limiting cases, are found and compared for the two models. The effects of the physical parameters on the solutions and associated quantities are also studied. It is shown that propagating wave fronts are only possible under the hyperbolic model and that the concept of phase speed has different meanings in the two formulations. In addition, discontinuities and shock waves are noted and a physical system is modeled under both formulations. Overall, it is shown that the hyperbolic form gives a more realistic description of the physical problem than does the classical theory. Lastly, a simple mechanical analog is given and connections to viscoelastic fluids are noted. In particular, the research presented here supports the notion that linear compressible, isothermal, viscous fluids can, at least in terms of causality, be better characterized as a type of viscoelastic fluid.

  16. Modeling Loop Entropy

    PubMed Central

    Chirikjian, Gregory S.

    2011-01-01

    Proteins fold from a highly disordered state into a highly ordered one. Traditionally, the folding problem has been stated as one of predicting ‘the’ tertiary structure from sequential information. However, new evidence suggests that the ensemble of unfolded forms may not be as disordered as once believed, and that the native form of many proteins may not be described by a single conformation, but rather an ensemble of its own. Quantifying the relative disorder in the folded and unfolded ensembles as an entropy difference may therefore shed light on the folding process. One issue that clouds discussions of ‘entropy’ is that many different kinds of entropy can be defined: entropy associated with overall translational and rotational Brownian motion, configurational entropy, vibrational entropy, conformational entropy computed in internal or Cartesian coordinates (which can even be different from each other), conformational entropy computed on a lattice; each of the above with different solvation and solvent models; thermodynamic entropy measured experimentally, etc. The focus of this work is the conformational entropy of coil/loop regions in proteins. New mathematical modeling tools for the approximation of changes in conformational entropy during transition from unfolded to folded ensembles are introduced. In particular, models for computing lower and upper bounds on entropy for polymer models of polypeptide coils both with and without end constraints are presented. The methods reviewed here include kinematics (the mathematics of rigid-body motions), classical statistical mechanics and information theory. PMID:21187223

  17. Qualitative and quantitative descriptions of glenohumeral motion.

    PubMed

    Hill, A M; Bull, A M J; Wallace, A L; Johnson, G R

    2008-02-01

    Joint modelling plays an important role in qualitative and quantitative descriptions of both normal and abnormal joints, as well as predicting outcomes of alterations to joints in orthopaedic practice and research. Contemporary efforts in modelling have focussed upon the major articulations of the lower limb. Well-constrained arthrokinematics can form the basis of manageable kinetic and dynamic mathematical predictions. In order to contain computation of shoulder complex modelling, glenohumeral joint representations in both limited and complete shoulder girdle models have undergone a generic simplification. As such, glenohumeral joint models are often based upon kinematic descriptions of inadequate degrees of freedom (DOF) for clinical purposes and applications. Qualitative descriptions of glenohumeral motion range from the parody of a hinge joint to the complex realism of a spatial joint. In developing a model, a clear idea of intention is required in order to achieve a required application. Clinical applicability of a model requires both descriptive and predictive output potentials, and as such, a high level of validation is required. Without sufficient appreciation of the clinical intention of the arthrokinematic foundation to a model, error is all too easily introduced. Mathematical description of joint motion serves to quantify all relevant clinical parameters. Commonly, both the Euler angle and helical (screw) axis methods have been applied to the glenohumeral joint, although concordance between these methods and classical anatomical appreciation of joint motion is limited, resulting in miscommunication between clinician and engineer. Compounding these inconsistencies in motion quantification is gimbal lock and sequence dependency.

  18. Quantum-like dynamics applied to cognition: a consideration of available options

    NASA Astrophysics Data System (ADS)

    Broekaert, Jan; Basieva, Irina; Blasiak, Pawel; Pothos, Emmanuel M.

    2017-10-01

    Quantum probability theory (QPT) has provided a novel, rich mathematical framework for cognitive modelling, especially for situations which appear paradoxical from classical perspectives. This work concerns the dynamical aspects of QPT, as relevant to cognitive modelling. We aspire to shed light on how the mind's driving potentials (encoded in Hamiltonian and Lindbladian operators) impact the evolution of a mental state. Some existing QPT cognitive models do employ dynamical aspects when considering how a mental state changes with time, but it is often the case that several simplifying assumptions are introduced. What kind of modelling flexibility does QPT dynamics offer without any simplifying assumptions and is it likely that such flexibility will be relevant in cognitive modelling? We consider a series of nested QPT dynamical models, constructed with a view to accommodate results from a simple, hypothetical experimental paradigm on decision-making. We consider Hamiltonians more complex than the ones which have traditionally been employed with a view to explore the putative explanatory value of this additional complexity. We then proceed to compare simple models with extensions regarding both the initial state (e.g. a mixed state with a specific orthogonal decomposition; a general mixed state) and the dynamics (by introducing Hamiltonians which destroy the separability of the initial structure and by considering an open-system extension). We illustrate the relations between these models mathematically and numerically. This article is part of the themed issue `Second quantum revolution: foundational questions'.

  19. Disease Progression Modeling to Evaluate the Effects of Enzyme Replacement Therapy on Kidney Function in Adult Patients with the Classic Phenotype of Fabry Disease.

    PubMed

    Nowak, Albina; Koch, Gilbert; Huynh-Do, Uyen; Siegenthaler, Martin; Marti, Hans-Peter; Pfister, Marc

    2017-01-01

    Fabry disease (FD) is a rare inherited lysosomal storage disease with common and serious kidney complications. Enzyme replacement therapies (ERT) with agalsidase-α and -β were investigated to characterize their therapeutic effect on kidney function in FD patients with Classic phenotype. The prospective FD cohort consisted of 98 genetically confirmed patients (females, n = 61, males, n = 37). The median [interquartile range] follow-up time (time difference from first to last visit) was 9 [6, 12] years. The median age of ERT start was 36 [21 - 54] years for females and 39 [28 - 49] years for males. A disease progression model was developed to (i) characterize the time course of estimated glomerular filtration rate (eGFR) and (ii) evaluate therapeutic effects of ERT on kidney function. Change in eGFR over time was best described by the linear model. Females had stable kidney function with and without ERT (eGFR slopes of -0.07 ml/min/1.73m^2 per year and 0.52 ml/min/1.73m^2 per year, respectively). Males with ERT showed an eGFR decrease of -3.07 ml/min/1.73m^2 per year. Mathematical disease progression modeling indicates that there is no clear therapeutic effect of ERT on kidney function in adult patients with Classic Phenotype of FD. Interpretation of these findings should take into account that the study is not randomized and lacks a placebo controlled group. Further investigations are warranted to clarify whether earlier ERT initiation before 18 years of age, higher ERT dose or more intensive therapies can preserve kidney function. © 2017 The Author(s)Published by S. Karger AG, Basel.

  20. Exceptional point in a simple textbook example

    NASA Astrophysics Data System (ADS)

    Fernández, Francisco M.

    2018-07-01

    We propose to introduce the concept of exceptional points in intermediate courses on mathematics and classical mechanics by means of simple textbook examples. The first one is an ordinary second-order differential equation with constant coefficients. The second one is the well-known damped harmonic oscillator. From a strict mathematical viewpoint both are the same problem that enables one to connect the occurrence of linearly dependent exponential solutions with a defective matrix which cannot be diagonalized but can be transformed into a Jordan canonical form.

  1. Neuromodulated Spike-Timing-Dependent Plasticity, and Theory of Three-Factor Learning Rules

    PubMed Central

    Frémaux, Nicolas; Gerstner, Wulfram

    2016-01-01

    Classical Hebbian learning puts the emphasis on joint pre- and postsynaptic activity, but neglects the potential role of neuromodulators. Since neuromodulators convey information about novelty or reward, the influence of neuromodulators on synaptic plasticity is useful not just for action learning in classical conditioning, but also to decide “when” to create new memories in response to a flow of sensory stimuli. In this review, we focus on timing requirements for pre- and postsynaptic activity in conjunction with one or several phasic neuromodulatory signals. While the emphasis of the text is on conceptual models and mathematical theories, we also discuss some experimental evidence for neuromodulation of Spike-Timing-Dependent Plasticity. We highlight the importance of synaptic mechanisms in bridging the temporal gap between sensory stimulation and neuromodulatory signals, and develop a framework for a class of neo-Hebbian three-factor learning rules that depend on presynaptic activity, postsynaptic variables as well as the influence of neuromodulators. PMID:26834568

  2. Space-time models based on random fields with local interactions

    NASA Astrophysics Data System (ADS)

    Hristopulos, Dionissios T.; Tsantili, Ivi C.

    2016-08-01

    The analysis of space-time data from complex, real-life phenomena requires the use of flexible and physically motivated covariance functions. In most cases, it is not possible to explicitly solve the equations of motion for the fields or the respective covariance functions. In the statistical literature, covariance functions are often based on mathematical constructions. In this paper, we propose deriving space-time covariance functions by solving “effective equations of motion”, which can be used as statistical representations of systems with diffusive behavior. In particular, we propose to formulate space-time covariance functions based on an equilibrium effective Hamiltonian using the linear response theory. The effective space-time dynamics is then generated by a stochastic perturbation around the equilibrium point of the classical field Hamiltonian leading to an associated Langevin equation. We employ a Hamiltonian which extends the classical Gaussian field theory by including a curvature term and leads to a diffusive Langevin equation. Finally, we derive new forms of space-time covariance functions.

  3. A new problem in mathematical physics associated with the problem of coherent phase transformation

    NASA Astrophysics Data System (ADS)

    Grinfeld, M. A.

    1985-06-01

    The description of heterogeneous coherent phase equilibria in an elastic single component system is shown to lead, in the approximation of small intrinsic deformation, to a new problem in mathematical physics with an unknown bound. The low order terms of the resulting system of equilibrium equations coincide with the equations of the classical linear theory of elasticity (generally speaking, anisotropic); however, the problem remains strongly nonlinear overall, inasmuch as it contains an unknown bound and a boundary condition on it which is quadratic with respect to translation. The formulas obtained are used to find certain explicit solutions to the boundary problems. As an example, the problem of heterogeneous equilibria in an infinite rectangular isotropic beam with free faces and constant loading on the surfaces x squared = const can be examined. A modeling problem for the asymptote of small intrinsic deformation during coherent phase transformation is presented as a scalar analog of the vector problem considered initially.

  4. Nonlinear scalar forcing based on a reaction analogy

    NASA Astrophysics Data System (ADS)

    Daniel, Don; Livescu, Daniel

    2017-11-01

    We present a novel reaction analogy (RA) based forcing method for generating stationary passive scalar fields in incompressible turbulence. The new method can produce more general scalar PDFs (e.g. double-delta) than current methods, while ensuring that scalar fields remain bounded, unlike existent forcing methodologies that can potentially violate naturally existing bounds. Such features are useful for generating initial fields in non-premixed combustion or for studying non-Gaussian scalar turbulence. The RA method mathematically models hypothetical chemical reactions that convert reactants in a mixed state back into its pure unmixed components. Various types of chemical reactions are formulated and the corresponding mathematical expressions derived. For large values of the scalar dissipation rate, the method produces statistically steady double-delta scalar PDFs. Gaussian scalar statistics are recovered for small values of the scalar dissipation rate. In contrast, classical forcing methods consistently produce unimodal Gaussian scalar fields. The ability of the new method to produce fully developed scalar fields is discussed using 2563, 5123, and 10243 periodic box simulations.

  5. Combined Numerical/Analytical Perturbation Solutions of the Navier-Stokes Equations for Aerodynamic Ejector/Mixer Nozzle Flows

    NASA Technical Reports Server (NTRS)

    DeChant, Lawrence Justin

    1998-01-01

    In spite of rapid advances in both scalar and parallel computational tools, the large number of variables involved in both design and inverse problems make the use of sophisticated fluid flow models impractical, With this restriction, it is concluded that an important family of methods for mathematical/computational development are reduced or approximate fluid flow models. In this study a combined perturbation/numerical modeling methodology is developed which provides a rigorously derived family of solutions. The mathematical model is computationally more efficient than classical boundary layer but provides important two-dimensional information not available using quasi-1-d approaches. An additional strength of the current methodology is its ability to locally predict static pressure fields in a manner analogous to more sophisticated parabolized Navier Stokes (PNS) formulations. To resolve singular behavior, the model utilizes classical analytical solution techniques. Hence, analytical methods have been combined with efficient numerical methods to yield an efficient hybrid fluid flow model. In particular, the main objective of this research has been to develop a system of analytical and numerical ejector/mixer nozzle models, which require minimal empirical input. A computer code, DREA Differential Reduced Ejector/mixer Analysis has been developed with the ability to run sufficiently fast so that it may be used either as a subroutine or called by an design optimization routine. Models are of direct use to the High Speed Civil Transport Program (a joint government/industry project seeking to develop an economically.viable U.S. commercial supersonic transport vehicle) and are currently being adopted by both NASA and industry. Experimental validation of these models is provided by comparison to results obtained from open literature and Limited Exclusive Right Distribution (LERD) sources, as well as dedicated experiments performed at Texas A&M. These experiments have been performed using a hydraulic/gas flow analog. Results of comparisons of DREA computations with experimental data, which include entrainment, thrust, and local profile information, are overall good. Computational time studies indicate that DREA provides considerably more information at a lower computational cost than contemporary ejector nozzle design models. Finally. physical limitations of the method, deviations from experimental data, potential improvements and alternative formulations are described. This report represents closure to the NASA Graduate Researchers Program. Versions of the DREA code and a user's guide may be obtained from the NASA Lewis Research Center.

  6. Perseveration effects in detection tasks with correlated decision intervals. [applied to pilot collision avoidance

    NASA Technical Reports Server (NTRS)

    Gai, E. G.; Curry, R. E.

    1978-01-01

    An investigation of the behavior of the human decisionmaker is described for a task related to the problem of a pilot using a traffic situation display to avoid collisions. This sequential signal detection task is characterized by highly correlated signals with time varying strength. Experimental results are presented and the behavior of the observers is analyzed using the theory of Markov processes and classical signal detection theory. Mathematical models are developed which describe the main result of the experiment: that correlation in sequential signals induced perseveration in the observer response and a strong tendency to repeat their previous decision, even when they were wrong.

  7. Adiabatic dynamics of one-dimensional classical Hamiltonian dissipative systems

    NASA Astrophysics Data System (ADS)

    Pritula, G. M.; Petrenko, E. V.; Usatenko, O. V.

    2018-02-01

    A linearized plane pendulum with the slowly varying mass and length of string and the suspension point moving at a slowly varying speed is presented as an example of a simple 1D mechanical system described by the generalized harmonic oscillator equation, which is a basic model in discussion of the adiabatic dynamics and geometric phase. The expression for the pendulum geometric phase is obtained by three different methods. The pendulum is shown to be canonically equivalent to the damped harmonic oscillator. This supports the mathematical conclusion, not widely accepted in physical community, of no difference between the dissipative and Hamiltonian 1D systems.

  8. Unitals and ovals of symmetric block designs in LDPC and space-time coding

    NASA Astrophysics Data System (ADS)

    Andriamanalimanana, Bruno R.

    2004-08-01

    An approach to the design of LDPC (low density parity check) error-correction and space-time modulation codes involves starting with known mathematical and combinatorial structures, and deriving code properties from structure properties. This paper reports on an investigation of unital and oval configurations within generic symmetric combinatorial designs, not just classical projective planes, as the underlying structure for classes of space-time LDPC outer codes. Of particular interest are the encoding and iterative (sum-product) decoding gains that these codes may provide. Various small-length cases have been numerically implemented in Java and Matlab for a number of channel models.

  9. A useful demonstration of calculus in a physics high school laboratory

    NASA Astrophysics Data System (ADS)

    Alvarez, Gustavo; Schulte, Jurgen; Stockton, Geoffrey; Wheeler, David

    2018-01-01

    The real power of calculus is revealed when it is applied to actual physical problems. In this paper, we present a calculus inspired physics experiment suitable for high school and undergraduate programs. A model for the theory of the terminal velocity of a falling body subject to a resistive force is developed and its validity tested in an experiment of a falling magnet in a column of self-induced eddy currents. The presented method combines multiple physics concepts such as 1D kinematics, classical mechanics, electromagnetism and non-trivial mathematics. It offers the opportunity for lateral as well as project-based learning.

  10. 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.

  11. Delay-induced Turing-like waves for one-species reaction-diffusion model on a network

    NASA Astrophysics Data System (ADS)

    Petit, Julien; Carletti, Timoteo; Asllani, Malbor; Fanelli, Duccio

    2015-09-01

    A one-species time-delay reaction-diffusion system defined on a complex network is studied. Traveling waves are predicted to occur following a symmetry-breaking instability of a homogeneous stationary stable solution, subject to an external nonhomogeneous perturbation. These are generalized Turing-like waves that materialize in a single-species populations dynamics model, as the unexpected byproduct of the imposed delay in the diffusion part. Sufficient conditions for the onset of the instability are mathematically provided by performing a linear stability analysis adapted to time-delayed differential equations. The method here developed exploits the properties of the Lambert W-function. The prediction of the theory are confirmed by direct numerical simulation carried out for a modified version of the classical Fisher model, defined on a Watts-Strogatz network and with the inclusion of the delay.

  12. Applications of graph theory in protein structure identification

    PubMed Central

    2011-01-01

    There is a growing interest in the identification of proteins on the proteome wide scale. Among different kinds of protein structure identification methods, graph-theoretic methods are very sharp ones. Due to their lower costs, higher effectiveness and many other advantages, they have drawn more and more researchers’ attention nowadays. Specifically, graph-theoretic methods have been widely used in homology identification, side-chain cluster identification, peptide sequencing and so on. This paper reviews several methods in solving protein structure identification problems using graph theory. We mainly introduce classical methods and mathematical models including homology modeling based on clique finding, identification of side-chain clusters in protein structures upon graph spectrum, and de novo peptide sequencing via tandem mass spectrometry using the spectrum graph model. In addition, concluding remarks and future priorities of each method are given. PMID:22165974

  13. Contact Forces between Single Metal Oxide Nanoparticles in Gas-Phase Applications and Processes.

    PubMed

    Salameh, Samir; van der Veen, Monique A; Kappl, Michael; van Ommen, J Ruud

    2017-03-14

    In this work we present a comprehensive experimental study to determine the contact forces between individual metal oxide nanoparticles in the gas-phase using atomic force microscopy. In addition, we determined the amount of physisorbed water for each type of particle surface. By comparing our results with mathematical models of the interaction forces, we could demonstrate that classical continuum models of van der Waals and capillary forces alone cannot sufficiently describe the experimental findings. Rather, the discrete nature of the molecules has to be considered, which leads to ordering at the interface and the occurrence of solvation forces. We demonstrate that inclusion of solvation forces in the model leads to quantitative agreement with experimental data and that tuning of the molecular order by addition of isopropanol vapor allows us to control the interaction forces between the nanoparticles.

  14. Sine-Gordon equation and its application to tectonic stress transfer

    NASA Astrophysics Data System (ADS)

    Bykov, Victor G.

    2014-07-01

    An overview is given on remarkable progress that has been made in theoretical studies of solitons and other nonlinear wave patterns, excited during the deformation of fault block (fragmented) geological media. The models that are compliant with the classical and perturbed sine-Gordon equations have only been chosen. In these mathematical models, the rotation angle of blocks (fragments) and their translatory displacement of the medium are used as dynamic variables. A brief description of the known models and their geophysical and geodynamic applications is given. These models reproduce the kinematic and dynamic features of the traveling deformation front (kink, soliton) generated in the fragmented media. It is demonstrated that the sine-Gordon equation is applicable to the description of series of the observed seismic data, modeling of strain waves, as well as the features related to fault dynamics and the subduction slab, including slow earthquakes, periodicity of episodic tremor and slow slip (ETS) events, and migration pattern of tremors. The study shows that simple heuristic models and analytical and numerical computations can explain triggering of seismicity by transient processes, such as stress changes associated with solitary strain waves in crustal faults. The need to develop the above-mentioned new (nonlinear) mathematical models of the deformed fault and fragmented media was caused by the reason that it is impossible to explain a lot of the observed effects, particularly, slow redistribution and migration of stresses in the lithosphere, within the framework of the linear elasticity theory.

  15. Mathematical modeling of HIV-like particle assembly in vitro.

    PubMed

    Liu, Yuewu; Zou, Xiufen

    2017-06-01

    In vitro, the recombinant HIV-1 Gag protein can generate spherical particles with a diameter of 25-30 nm in a fully defined system. It has approximately 80 building blocks, and its intermediates for assembly are abundant in geometry. Accordingly, there are a large number of nonlinear equations in the classical model. Therefore, it is difficult to compute values of geometry parameters for intermediates and make the mathematical analysis using the model. In this work, we develop a new model of HIV-like particle assembly in vitro by using six-fold symmetry of HIV-like particle assembly to decrease the number of geometry parameters. This method will greatly reduce computational costs and facilitate the application of the model. Then, we prove the existence and uniqueness of the positive equilibrium solution for this model with 79 nonlinear equations. Based on this model, we derive the interesting result that concentrations of all intermediates at equilibrium are independent of three important parameters, including two microscopic on-rate constants and the size of nucleating structure. Before equilibrium, these three parameters influence the concentration variation rates of all intermediates. We also analyze the relationship between the initial concentration of building blocks and concentrations of all intermediates. Furthermore, the bounds of concentrations of free building blocks and HIV-like particles are estimated. These results will be helpful to guide HIV-like particle assembly experiments and improve our understanding of the assembly dynamics of HIV-like particles in vitro. Copyright © 2017 Elsevier Inc. All rights reserved.

  16. A Mathematical Framework for Critical Transitions: Normal Forms, Variance and Applications

    NASA Astrophysics Data System (ADS)

    Kuehn, Christian

    2013-06-01

    Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast-subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension-two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.

  17. Electrohydrodynamic fibrillation governed enhanced thermal transport in dielectric colloids under a field stimulus.

    PubMed

    Dhar, Purbarun; Maganti, Lakshmi Sirisha; Harikrishnan, A R

    2018-05-30

    Electrorheological (ER) fluids are known to exhibit enhanced viscous effects under an electric field stimulus. The present article reports the hitherto unreported phenomenon of greatly enhanced thermal conductivity in such electro-active colloidal dispersions in the presence of an externally applied electric field. Typical ER fluids are synthesized employing dielectric fluids and nanoparticles and experiments are performed employing an in-house designed setup. Greatly augmented thermal conductivity under a field's influence was observed. Enhanced thermal conduction along the fibril structures under the field effect is theorized as the crux of the mechanism. The formation of fibril structures has also been experimentally verified employing microscopy. Based on classical models for ER fluids, a mathematical formalism has been developed to predict the propensity of chain formation and statistically feasible chain dynamics at given Mason numbers. Further, a thermal resistance network model is employed to computationally predict the enhanced thermal conduction across the fibrillary colloid microstructure. Good agreement between the mathematical model and the experimental observations is achieved. The domineering role of thermal conductivity over relative permittivity has been shown by proposing a modified Hashin-Shtrikman (HS) formalism. The findings have implications towards better physical understanding and design of ER fluids from both 'smart' viscoelastic as well as thermally active materials points of view.

  18. A DG approach to the numerical solution of the Stein-Stein stochastic volatility option pricing model

    NASA Astrophysics Data System (ADS)

    Hozman, J.; Tichý, T.

    2017-12-01

    Stochastic volatility models enable to capture the real world features of the options better than the classical Black-Scholes treatment. Here we focus on pricing of European-style options under the Stein-Stein stochastic volatility model when the option value depends on the time, on the price of the underlying asset and on the volatility as a function of a mean reverting Orstein-Uhlenbeck process. A standard mathematical approach to this model leads to the non-stationary second-order degenerate partial differential equation of two spatial variables completed by the system of boundary and terminal conditions. In order to improve the numerical valuation process for a such pricing equation, we propose a numerical technique based on the discontinuous Galerkin method and the Crank-Nicolson scheme. Finally, reference numerical experiments on real market data illustrate comprehensive empirical findings on options with stochastic volatility.

  19. Sliding mode control of outbreaks of emerging infectious diseases.

    PubMed

    Xiao, Yanni; Xu, Xiaxia; Tang, Sanyi

    2012-10-01

    This paper proposes and analyzes a mathematical model of an infectious disease system with a piecewise control function concerning threshold policy for disease management strategy. The proposed models extend the classic models by including a piecewise incidence rate to represent control or precautionary measures being triggered once the number of infected individuals exceeds a threshold level. The long-term behaviour of the proposed non-smooth system under this strategy consists of the so-called sliding motion-a very rapid switching between application and interruption of the control action. Model solutions ultimately approach either one of two endemic states for two structures or the sliding equilibrium on the switching surface, depending on the threshold level. Our findings suggest that proper combinations of threshold densities and control intensities based on threshold policy can either preclude outbreaks or lead the number of infected to a previously chosen level.

  20. Employment of CB models for non-linear dynamic analysis

    NASA Technical Reports Server (NTRS)

    Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.

    1990-01-01

    The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.

  1. Theoretical ecology without species

    NASA Astrophysics Data System (ADS)

    Tikhonov, Mikhail

    The sequencing-driven revolution in microbial ecology demonstrated that discrete ``species'' are an inadequate description of the vast majority of life on our planet. Developing a novel theoretical language that, unlike classical ecology, would not require postulating the existence of species, is a challenge of tremendous medical and environmental significance, and an exciting direction for theoretical physics. Here, it is proposed that community dynamics can be described in a naturally hierarchical way in terms of population fluctuation eigenmodes. The approach is applied to a simple model of division of labor in a multi-species community. In one regime, effective species with a core and accessory genome are shown to naturally appear as emergent concepts. However, the same model allows a transition into a regime where the species formalism becomes inadequate, but the eigenmode description remains well-defined. Treating a community as a black box that expresses enzymes in response to resources reveals mathematically exact parallels between a community and a single coherent organism with its own fitness function. This coherence is a generic consequence of division of labor, requires no cooperative interactions, and can be expected to be widespread in microbial ecosystems. Harvard Center of Mathematical Sciences and Applications;John A. Paulson School of Engineering and Applied Sciences.

  2. Bond Graph Model of Cerebral Circulation: Toward Clinically Feasible Systemic Blood Flow Simulations

    PubMed Central

    Safaei, Soroush; Blanco, Pablo J.; Müller, Lucas O.; Hellevik, Leif R.; Hunter, Peter J.

    2018-01-01

    We propose a detailed CellML model of the human cerebral circulation that runs faster than real time on a desktop computer and is designed for use in clinical settings when the speed of response is important. A lumped parameter mathematical model, which is based on a one-dimensional formulation of the flow of an incompressible fluid in distensible vessels, is constructed using a bond graph formulation to ensure mass conservation and energy conservation. The model includes arterial vessels with geometric and anatomical data based on the ADAN circulation model. The peripheral beds are represented by lumped parameter compartments. We compare the hemodynamics predicted by the bond graph formulation of the cerebral circulation with that given by a classical one-dimensional Navier-Stokes model working on top of the whole-body ADAN model. Outputs from the bond graph model, including the pressure and flow signatures and blood volumes, are compared with physiological data. PMID:29551979

  3. The information geometry of chaos

    NASA Astrophysics Data System (ADS)

    Cafaro, Carlo

    2008-10-01

    In this Thesis, we propose a new theoretical information-geometric framework (IGAC, Information Geometrodynamical Approach to Chaos) suitable to characterize chaotic dynamical behavior of arbitrary complex systems. First, the problem being investigated is defined; its motivation and relevance are discussed. The basic tools of information physics and the relevant mathematical tools employed in this work are introduced. The basic aspects of Entropic Dynamics (ED) are reviewed. ED is an information-constrained dynamics developed by Ariel Caticha to investigate the possibility that laws of physics---either classical or quantum---may emerge as macroscopic manifestations of underlying microscopic statistical structures. ED is of primary importance in our IGAC. The notion of chaos in classical and quantum physics is introduced. Special focus is devoted to the conventional Riemannian geometrodynamical approach to chaos (Jacobi geometrodynamics) and to the Zurek-Paz quantum chaos criterion of linear entropy growth. After presenting this background material, we show that the ED formalism is not purely an abstract mathematical framework, but is indeed a general theoretical scheme from which conventional Newtonian dynamics is obtained as a special limiting case. The major elements of our IGAC and the novel notion of information geometrodynamical entropy (IGE) are introduced by studying two "toy models". To illustrate the potential power of our IGAC, one application is presented. An information-geometric analogue of the Zurek-Paz quantum chaos criterion of linear entropy growth is suggested. Finally, concluding remarks emphasizing strengths and weak points of our approach are presented and possible further research directions are addressed. At this stage of its development, IGAC remains an ambitious unifying information-geometric theoretical construct for the study of chaotic dynamics with several unsolved problems. However, based on our recent findings, we believe it already provides an interesting, innovative and potentially powerful way to study and understand the very important and challenging problems of classical and quantum chaos.

  4. Automated data processing and radioassays.

    PubMed

    Samols, E; Barrows, G H

    1978-04-01

    Radioassays include (1) radioimmunoassays, (2) competitive protein-binding assays based on competition for limited antibody or specific binding protein, (3) immunoradiometric assay, based on competition for excess labeled antibody, and (4) radioreceptor assays. Most mathematical models describing the relationship between labeled ligand binding and unlabeled ligand concentration have been based on the law of mass action or the isotope dilution principle. These models provide useful data reduction programs, but are theoretically unfactory because competitive radioassay usually is not based on classical dilution principles, labeled and unlabeled ligand do not have to be identical, antibodies (or receptors) are frequently heterogenous, equilibrium usually is not reached, and there is probably steric and cooperative influence on binding. An alternative, more flexible mathematical model based on the probability or binding collisions being restricted by the surface area of reactive divalent sites on antibody and on univalent antigen has been derived. Application of these models to automated data reduction allows standard curves to be fitted by a mathematical expression, and unknown values are calculated from binding data. The vitrues and pitfalls are presented of point-to-point data reduction, linear transformations, and curvilinear fitting approaches. A third-order polynomial using the square root of concentration closely approximates the mathematical model based on probability, and in our experience this method provides the most acceptable results with all varieties of radioassays. With this curvilinear system, linear point connection should be used between the zero standard and the beginning of significant dose response, and also towards saturation. The importance is stressed of limiting the range of reported automated assay results to that portion of the standard curve that delivers optimal sensitivity. Published methods for automated data reduction of Scatchard plots for radioreceptor assay are limited by calculation of a single mean K value. The quality of the input data is generally the limiting factor in achieving good precision with automated as it is with manual data reduction. The major advantages of computerized curve fitting include: (1) handling large amounts of data rapidly and without computational error; (2) providing useful quality-control data; (3) indicating within-batch variance of the test results; (4) providing ongoing quality-control charts and between assay variance.

  5. Characterizing the topology of probabilistic biological networks.

    PubMed

    Todor, Andrei; Dobra, Alin; Kahveci, Tamer

    2013-01-01

    Biological interactions are often uncertain events, that may or may not take place with some probability. This uncertainty leads to a massive number of alternative interaction topologies for each such network. The existing studies analyze the degree distribution of biological networks by assuming that all the given interactions take place under all circumstances. This strong and often incorrect assumption can lead to misleading results. In this paper, we address this problem and develop a sound mathematical basis to characterize networks in the presence of uncertain interactions. Using our mathematical representation, we develop a method that can accurately describe the degree distribution of such networks. We also take one more step and extend our method to accurately compute the joint-degree distributions of node pairs connected by edges. The number of possible network topologies grows exponentially with the number of uncertain interactions. However, the mathematical model we develop allows us to compute these degree distributions in polynomial time in the number of interactions. Our method works quickly even for entire protein-protein interaction (PPI) networks. It also helps us find an adequate mathematical model using MLE. We perform a comparative study of node-degree and joint-degree distributions in two types of biological networks: the classical deterministic networks and the more flexible probabilistic networks. Our results confirm that power-law and log-normal models best describe degree distributions for both probabilistic and deterministic networks. Moreover, the inverse correlation of degrees of neighboring nodes shows that, in probabilistic networks, nodes with large number of interactions prefer to interact with those with small number of interactions more frequently than expected. We also show that probabilistic networks are more robust for node-degree distribution computation than the deterministic ones. all the data sets used, the software implemented and the alignments found in this paper are available at http://bioinformatics.cise.ufl.edu/projects/probNet/.

  6. Qualitative methods in quantum theory

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

    Migdal, A.B.

    The author feels that the solution of most problems in theoretical physics begins with the application of qualitative methods - dimensional estimates and estimates made from simple models, the investigation of limiting cases, the use of the analytic properties of physical quantities, etc. This book proceeds in this spirit, rather than in a formal, mathematical way with no traces of the sweat involved in the original work left to show. The chapters are entitled Dimensional and model approximations, Various types of perturbation theory, The quasi-classical approximation, Analytic properties of physical quantities, Methods in the many-body problem, and Qualitative methods inmore » quantum field theory. Each chapter begins with a detailed introduction, in which the physical meaning of the results obtained in that chapter is explained in a simple way. 61 figures. (RWR)« less

  7. Periodic and chaotic host-parasite interactions in human malaria.

    PubMed Central

    Kwiatkowski, D; Nowak, M

    1991-01-01

    It has been recognized since ancient times that malaria fever is highly periodic but the mechanism has been poorly understood. Malaria fever is related to the parasite growth cycle in erythrocytes. After a fixed period of replication, a mature parasite (schizont) causes the infected erythrocyte to rupture, releasing progeny that quickly invade other erythrocytes. Simultaneous rupture of a large number of schizonts stimulates a host fever response. Febrile temperatures are damaging to Plasmodium falciparum, particularly in the second half of its 48-hr replicative cycle. Using a mathematical model, we show that these interactions naturally tend to generate periodic fever. The model predicts chaotic parasite population dynamics at high multiplication rates, consistent with the classical observation that P. falciparum causes less regular fever than other species of parasite. PMID:2052590

  8. Phase space explorations in time dependent density functional theory

    NASA Astrophysics Data System (ADS)

    Rajam, Aruna K.

    Time dependent density functional theory (TDDFT) is one of the useful tools for the study of the dynamic behavior of correlated electronic systems under the influence of external potentials. The success of this formally exact theory practically relies on approximations for the exchange-correlation potential which is a complicated functional of the co-ordinate density, non-local in space and time. Adiabatic approximations (such as ALDA), which are local in time, are most commonly used in the increasing applications of the field. Going beyond ALDA, has been proved difficult leading to mathematical inconsistencies. We explore the regions where the theory faces challenges, and try to answer some of them via the insights from two electron model systems. In this thesis work we propose a phase-space extension of the TDDFT. We want to answer the challenges the theory is facing currently by exploring the one-body phase-space. We give a general introduction to this theory and its mathematical background in the first chapter. In second chapter, we carryout a detailed study of instantaneous phase-space densities and argue that the functionals of distributions can be a better alternative to the nonlocality issue of the exchange-correlation potentials. For this we study in detail the interacting and the non-interacting phase-space distributions for Hookes atom model. The applicability of ALDA-based TDDFT for the dynamics in strongfields can become severely problematic due to the failure of single-Slater determinant picture.. In the third chapter, we analyze how the phase-space distributions can shine some light into this problem. We do a comparative study of Kohn-Sham and interacting phase-space and momentum distributions for single ionization and double ionization systems. Using a simple model of two-electron systems, we have showed that the momentum distribution computed directly from the exact KS system contains spurious oscillations: a non-classical description of the essentially classical two-electron dynamics. In Time dependent density matrix functional theory (TDDMFT), the evolution scheme of the 1RDM (first order reduced density matrix) contains second-order reduced density matrix (2RDM), which has to be expressed in terms of 1RDMs. Any non-correlated approximations (Hartree-Fock) for 2RDM would fail to capture the natural occupations of the system. In our fourth chapter, we show that by applying the quasi-classical and semi-classical approximations one can capture the natural occupations of the excited systems. We study a time-dependent Moshinsky atom model for this. The fifth chapter contains a comparative work on the existing non-local exchange-correlation kernels that are based on current density response frame work and the co-moving frame work. We show that the two approaches though coinciding with each other in linear response regime, actually turn out to be different in non-linear regime.

  9. The complexity of proving chaoticity and the Church-Turing thesis

    NASA Astrophysics Data System (ADS)

    Calude, Cristian S.; Calude, Elena; Svozil, Karl

    2010-09-01

    Proving the chaoticity of some dynamical systems is equivalent to solving the hardest problems in mathematics. Conversely, classical physical systems may "compute the hard or even the incomputable" by measuring observables which correspond to computationally hard or even incomputable problems.

  10. Chance, determinism and the classical theory of probability.

    PubMed

    Vasudevan, Anubav

    2018-02-01

    This paper situates the metaphysical antinomy between chance and determinism in the historical context of some of the earliest developments in the mathematical theory of probability. Since Hacking's seminal work on the subject, it has been a widely held view that the classical theorists of probability were guilty of an unwitting equivocation between a subjective, or epistemic, interpretation of probability, on the one hand, and an objective, or statistical, interpretation, on the other. While there is some truth to this account, I argue that the tension at the heart of the classical theory of probability is not best understood in terms of the duality between subjective and objective interpretations of probability. Rather, the apparent paradox of chance and determinism, when viewed through the lens of the classical theory of probability, manifests itself in a much deeper ambivalence on the part of the classical probabilists as to the rational commensurability of causal and probabilistic reasoning. Copyright © 2017 Elsevier Ltd. All rights reserved.

  11. A model of gene expression based on random dynamical systems reveals modularity properties of gene regulatory networks.

    PubMed

    Antoneli, Fernando; Ferreira, Renata C; Briones, Marcelo R S

    2016-06-01

    Here we propose a new approach to modeling gene expression based on the theory of random dynamical systems (RDS) that provides a general coupling prescription between the nodes of any given regulatory network given the dynamics of each node is modeled by a RDS. The main virtues of this approach are the following: (i) it provides a natural way to obtain arbitrarily large networks by coupling together simple basic pieces, thus revealing the modularity of regulatory networks; (ii) the assumptions about the stochastic processes used in the modeling are fairly general, in the sense that the only requirement is stationarity; (iii) there is a well developed mathematical theory, which is a blend of smooth dynamical systems theory, ergodic theory and stochastic analysis that allows one to extract relevant dynamical and statistical information without solving the system; (iv) one may obtain the classical rate equations form the corresponding stochastic version by averaging the dynamic random variables (small noise limit). It is important to emphasize that unlike the deterministic case, where coupling two equations is a trivial matter, coupling two RDS is non-trivial, specially in our case, where the coupling is performed between a state variable of one gene and the switching stochastic process of another gene and, hence, it is not a priori true that the resulting coupled system will satisfy the definition of a random dynamical system. We shall provide the necessary arguments that ensure that our coupling prescription does indeed furnish a coupled regulatory network of random dynamical systems. Finally, the fact that classical rate equations are the small noise limit of our stochastic model ensures that any validation or prediction made on the basis of the classical theory is also a validation or prediction of our model. We illustrate our framework with some simple examples of single-gene system and network motifs. Copyright © 2016 Elsevier Inc. All rights reserved.

  12. JOURNAL SCOPE GUIDELINES: Paper classification scheme

    NASA Astrophysics Data System (ADS)

    2005-06-01

    This scheme is used to clarify the journal's scope and enable authors and readers to more easily locate the appropriate section for their work. For each of the sections listed in the scope statement we suggest some more detailed subject areas which help define that subject area. These lists are by no means exhaustive and are intended only as a guide to the type of papers we envisage appearing in each section. We acknowledge that no classification scheme can be perfect and that there are some papers which might be placed in more than one section. We are happy to provide further advice on paper classification to authors upon request (please email jphysa@iop.org). 1. Statistical physics numerical and computational methods statistical mechanics, phase transitions and critical phenomena quantum condensed matter theory Bose-Einstein condensation strongly correlated electron systems exactly solvable models in statistical mechanics lattice models, random walks and combinatorics field-theoretical models in statistical mechanics disordered systems, spin glasses and neural networks nonequilibrium systems network theory 2. Chaotic and complex systems nonlinear dynamics and classical chaos fractals and multifractals quantum chaos classical and quantum transport cellular automata granular systems and self-organization pattern formation biophysical models 3. Mathematical physics combinatorics algebraic structures and number theory matrix theory classical and quantum groups, symmetry and representation theory Lie algebras, special functions and orthogonal polynomials ordinary and partial differential equations difference and functional equations integrable systems soliton theory functional analysis and operator theory inverse problems geometry, differential geometry and topology numerical approximation and analysis geometric integration computational methods 4. Quantum mechanics and quantum information theory coherent states eigenvalue problems supersymmetric quantum mechanics scattering theory relativistic quantum mechanics semiclassical approximations foundations of quantum mechanics and measurement theory entanglement and quantum nonlocality geometric phases and quantum tomography quantum tunnelling decoherence and open systems quantum cryptography, communication and computation theoretical quantum optics 5. Classical and quantum field theory quantum field theory gauge and conformal field theory quantum electrodynamics and quantum chromodynamics Casimir effect integrable field theory random matrix theory applications in field theory string theory and its developments classical field theory and electromagnetism metamaterials 6. Fluid and plasma theory turbulence fundamental plasma physics kinetic theory magnetohydrodynamics and multifluid descriptions strongly coupled plasmas one-component plasmas non-neutral plasmas astrophysical and dusty plasmas

  13. Semi-classical Electrodynamics

    NASA Astrophysics Data System (ADS)

    Lestone, John

    2016-03-01

    Quantum electrodynamics is complex and its associated mathematics can appear overwhelming for those not trained in this field. We describe semi-classical approaches that can be used to obtain a more intuitive physical feel for several QED processes including electro-statics, Compton scattering, pair annihilation, the anomalous magnetic moment, and the Lamb shift, that could be taught easily to undergraduate students. Any physicist who brings their laptop to the talk will be able to build spread sheets in less than 10 minutes to calculate g/2 =1.001160 and a Lamb shift of 1057 MHz.

  14. Combining Empirical and Stochastic Models for Extreme Floods Estimation

    NASA Astrophysics Data System (ADS)

    Zemzami, M.; Benaabidate, L.

    2013-12-01

    Hydrological models can be defined as physical, mathematical or empirical. The latter class uses mathematical equations independent of the physical processes involved in the hydrological system. The linear regression and Gradex (Gradient of Extreme values) are classic examples of empirical models. However, conventional empirical models are still used as a tool for hydrological analysis by probabilistic approaches. In many regions in the world, watersheds are not gauged. This is true even in developed countries where the gauging network has continued to decline as a result of the lack of human and financial resources. Indeed, the obvious lack of data in these watersheds makes it impossible to apply some basic empirical models for daily forecast. So we had to find a combination of rainfall-runoff models in which it would be possible to create our own data and use them to estimate the flow. The estimated design floods would be a good choice to illustrate the difficulties facing the hydrologist for the construction of a standard empirical model in basins where hydrological information is rare. The construction of the climate-hydrological model, which is based on frequency analysis, was established to estimate the design flood in the Anseghmir catchments, Morocco. The choice of using this complex model returns to its ability to be applied in watersheds where hydrological information is not sufficient. It was found that this method is a powerful tool for estimating the design flood of the watershed and also other hydrological elements (runoff, volumes of water...).The hydrographic characteristics and climatic parameters were used to estimate the runoff, water volumes and design flood for different return periods.

  15. Developing group investigation-based book on numerical analysis to increase critical thinking student’s ability

    NASA Astrophysics Data System (ADS)

    Maharani, S.; Suprapto, E.

    2018-03-01

    Critical thinking is very important in Mathematics; it can make student more understanding mathematics concept. Critical thinking is also needed in numerical analysis. The Numerical analysis's book is not yet including critical thinking in them. This research aims to develop group investigation-based book on numerical analysis to increase critical thinking student’s ability, to know the quality of the group investigation-based book on numerical analysis is valid, practical, and effective. The research method is Research and Development (R&D) with the subject are 30 student college department of Mathematics education at Universitas PGRI Madiun. The development model used is 4-D modified to 3-D until the stage development. The type of data used is descriptive qualitative data. Instruments used are sheets of validation, test, and questionnaire. Development results indicate that group investigation-based book on numerical analysis in the category of valid a value 84.25%. Students response to the books very positive, so group investigation-based book on numerical analysis category practical, i.e., 86.00%. The use of group investigation-based book on numerical analysis has been meeting the completeness criteria classical learning that is 84.32 %. Based on research result of this study concluded that group investigation-based book on numerical analysis is feasible because it meets the criteria valid, practical, and effective. So, the book can be used by every mathematics academician. The next research can be observed that book based group investigation in other subjects.

  16. Mathematical formula recognition using graph grammar

    NASA Astrophysics Data System (ADS)

    Lavirotte, Stephane; Pottier, Loic

    1998-04-01

    This paper describes current results of Ofr, a system for extracting and understanding mathematical expressions in documents. Such a tool could be really useful to be able to re-use knowledge in scientific books which are not available in electronic form. We currently also study use of this system for direct input of formulas with a graphical tablet for computer algebra system softwares. Existing solutions for mathematical recognition have problems to analyze 2D expressions like vectors and matrices. This is because they often try to use extended classical grammar to analyze formulas, relatively to baseline. But a lot of mathematical notations do not respect rules for such a parsing and that is the reason why they fail to extend text parsing technic. We investigate graph grammar and graph rewriting as a solution to recognize 2D mathematical notations. Graph grammar provide a powerful formalism to describe structural manipulations of multi-dimensional data. The main two problems to solve are ambiguities between rules of grammar and construction of graph.

  17. Comparative evolution of the inverse problems (Introduction to an interdisciplinary study of the inverse problems)

    NASA Technical Reports Server (NTRS)

    Sabatier, P. C.

    1972-01-01

    The progressive realization of the consequences of nonuniqueness imply an evolution of both the methods and the centers of interest in inverse problems. This evolution is schematically described together with the various mathematical methods used. A comparative description is given of inverse methods in scientific research, with examples taken from mathematics, quantum and classical physics, seismology, transport theory, radiative transfer, electromagnetic scattering, electrocardiology, etc. It is hoped that this paper will pave the way for an interdisciplinary study of inverse problems.

  18. Quantum deformations of conformal algebras with mass-like deformation parameters

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

    Frydryszak, Andrzej; Lukierski, Jerzy; Mozrzymas, Marek

    1998-12-15

    We recall the mathematical apparatus necessary for the quantum deformation of Lie algebras, namely the notions of coboundary Lie algebras, classical r-matrices, classical Yang-Baxter equations (CYBE), Froebenius algebras and parabolic subalgebras. Then we construct the quantum deformation of D=1, D=2 and D=3 conformal algebras, showing that this quantization introduce fundamental mass parameters. Finally we consider with more details the quantization of D=4 conformal algebra. We build three classes of sl(4,C) classical r-matrices, satisfying CYBE and depending respectively on 8, 10 and 12 generators of parabolic subalgebras. We show that only the 8-dimensional r-matrices allow to impose the D=4 conformal o(4,2){approx_equal}su(2,2)more » reality conditions. Weyl reflections and Dynkin diagram automorphisms for o(4,2) define the class of admissible bases for given classical r-matrices.« less

  19. Ψ-model of micro- and macrosystems

    NASA Astrophysics Data System (ADS)

    Perepelkin, E. E.; Sadovnikov, B. I.; Inozemtseva, N. G.

    2017-08-01

    A mathematical model (referred as Ψ-model for convenience) has been developed, which allows describing certain class of micro- and macrosystems. Ψ-model is based on quantum mechanics and classical mechanics of continuous media. Ψ-model describes micro- and macrosystems, in which vector field of velocities of probability flows, charge, mass has specific spiral structure. The field of velocities has spiral structure on concentric spherical surfaces. The velocity field is not defined and has a characteristic property on the poles of sphere and on the axis and tends to zero at infinity. The behavior of Ψ-model can be described in the general case with time-dependent periodic singular solution of the Schrödinger equation. The goal of this paper is to choose a particular probability flux in the continuity equation which we solve in this paper and deduce from it the solution of the Schrödinger equation. For example, in the frame of approach the problem with modified Coulomb potential was considered.

  20. Application of neural models as controllers in mobile robot velocity control loop

    NASA Astrophysics Data System (ADS)

    Cerkala, Jakub; Jadlovska, Anna

    2017-01-01

    This paper presents the application of an inverse neural models used as controllers in comparison to classical PI controllers for velocity tracking control task used in two-wheel, differentially driven mobile robot. The PI controller synthesis is based on linear approximation of actuators with equivalent load. In order to obtain relevant datasets for training of feed-forward multi-layer perceptron based neural network used as neural model, the mathematical model of mobile robot, that combines its kinematic and dynamic properties such as chassis dimensions, center of gravity offset, friction and actuator parameters is used. Neural models are trained off-line to act as an inverse dynamics of DC motors with particular load using data collected in simulation experiment for motor input voltage step changes within bounded operating area. The performances of PI controllers versus inverse neural models in mobile robot internal velocity control loops are demonstrated and compared in simulation experiment of navigation control task for line segment motion in plane.

  1. Inhibition, Conflict Detection, and Number Conservation

    ERIC Educational Resources Information Center

    Lubin, Amélie; Simon, Grégory; Houdé, Olivier; De Neys, Wim

    2015-01-01

    The acquisition of number conservation is a critical step in children's numerical and mathematical development. Classic developmental studies have established that children's number conservation is often biased by misleading intuitions. However, the precise nature of these conservation errors is not clear. A key question is whether conservation…

  2. Web Sitings.

    ERIC Educational Resources Information Center

    Lo, Erika

    2001-01-01

    Presents seven mathematics games, located on the World Wide Web, for elementary students, including: Absurd Math: Pre-Algebra from Another Dimension; The Little Animals Activity Centre; MathDork Game Room (classic video games focusing on algebra); Lemonade Stand (students practice math and business skills); Math Cats (teaches the artistic beauty…

  3. Probability and Statistics: A Prelude.

    ERIC Educational Resources Information Center

    Goodman, A. F.; Blischke, W. R.

    Probability and statistics have become indispensable to scientific, technical, and management progress. They serve as essential dialects of mathematics, the classical language of science, and as instruments necessary for intelligent generation and analysis of information. A prelude to probability and statistics is presented by examination of the…

  4. A dynamic subgrid scale model for Large Eddy Simulations based on the Mori-Zwanzig formalism

    NASA Astrophysics Data System (ADS)

    Parish, Eric J.; Duraisamy, Karthik

    2017-11-01

    The development of reduced models for complex multiscale problems remains one of the principal challenges in computational physics. The optimal prediction framework of Chorin et al. [1], which is a reformulation of the Mori-Zwanzig (M-Z) formalism of non-equilibrium statistical mechanics, provides a framework for the development of mathematically-derived reduced models of dynamical systems. Several promising models have emerged from the optimal prediction community and have found application in molecular dynamics and turbulent flows. In this work, a new M-Z-based closure model that addresses some of the deficiencies of existing methods is developed. The model is constructed by exploiting similarities between two levels of coarse-graining via the Germano identity of fluid mechanics and by assuming that memory effects have a finite temporal support. The appeal of the proposed model, which will be referred to as the 'dynamic-MZ-τ' model, is that it is parameter-free and has a structural form imposed by the mathematics of the coarse-graining process (rather than the phenomenological assumptions made by the modeler, such as in classical subgrid scale models). To promote the applicability of M-Z models in general, two procedures are presented to compute the resulting model form, helping to bypass the tedious error-prone algebra that has proven to be a hindrance to the construction of M-Z-based models for complex dynamical systems. While the new formulation is applicable to the solution of general partial differential equations, demonstrations are presented in the context of Large Eddy Simulation closures for the Burgers equation, decaying homogeneous turbulence, and turbulent channel flow. The performance of the model and validity of the underlying assumptions are investigated in detail.

  5. Quantum-Like Model for Decision Making Process in Two Players Game. A Non-Kolmogorovian Model

    NASA Astrophysics Data System (ADS)

    Asano, Masanari; Ohya, Masanori; Khrennikov, Andrei

    2011-03-01

    In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of Khrennikov (Information Dynamics in Cognitive, Psychological and Anomalous Phenomena. Fundamental Theories of Physics, Kluwer Academic, Norwell, 2004; Fuzzy Sets Syst. 155:4-17, 2005; Biosystems 84:225-241, 2006; Found. Phys. 35(10):1655-1693, 2005; in QP-PQ Quantum Probability and White Noise Analysis, vol. XXIV, pp. 105-117, 2009), it was pointed out that statistics collected in such the experiments have "quantum-like" properties, which can not be explained in classical probability theory. In this paper, we design a simple quantum-like model describing a decision-making process in a two-players game and try to explain a mechanism of the irrational behavior of players. Finally we discuss a mathematical frame of non-Kolmogorovian system in terms of liftings (Accardi and Ohya, in Appl. Math. Optim. 39:33-59, 1999).

  6. Wave propagation in viscoelastic horns using a fractional calculus rheology model

    NASA Astrophysics Data System (ADS)

    Margulies, Timothy

    2003-10-01

    The complex mechanical behavior of materials are characterized by fluid and solid models with fractional calculus differentials to relate stress and strain fields. Fractional derivatives have been shown to describe the viscoelastic stress from polymer chain theory for molecular solutions [Rouse and Sittel, J. Appl. Phys. 24, 690 (1953)]. Here the propagation of infinitesimal waves in one dimensional horns with a small cross-sectional area change along the longitudinal axis are examined. In particular, the linear, conical, exponential, and catenoidal shapes are studied. The wave amplitudes versus frequency are solved analytically and predicted with mathematical computation. Fractional rheology data from Bagley [J. Rheol. 27, 201 (1983); Bagley and Torvik, J. Rheol. 30, 133 (1986)] are incorporated in the simulations. Classical elastic and fluid ``Webster equations'' are recovered in the appropriate limits. Horns with real materials that employ fractional calculus representations can be modeled to examine design trade-offs for engineering or for scientific application.

  7. Prediction and optimization of the laccase-mediated synthesis of the antimicrobial compound iodine (I2).

    PubMed

    Schubert, M; Fey, A; Ihssen, J; Civardi, C; Schwarze, F W M R; Mourad, S

    2015-01-10

    An artificial neural network (ANN) and genetic algorithm (GA) were applied to improve the laccase-mediated oxidation of iodide (I(-)) to elemental iodine (I2). Biosynthesis of iodine (I2) was studied with a 5-level-4-factor central composite design (CCD). The generated ANN network was mathematically evaluated by several statistical indices and revealed better results than a classical quadratic response surface (RS) model. Determination of the relative significance of model input parameters, ranking the process parameters in order of importance (pH>laccase>mediator>iodide), was performed by sensitivity analysis. ANN-GA methodology was used to optimize the input space of the neural network model to find optimal settings for the laccase-mediated synthesis of iodine. ANN-GA optimized parameters resulted in a 9.9% increase in the conversion rate. Copyright © 2014 Elsevier B.V. All rights reserved.

  8. From direct-space discrepancy functions to crystallographic least squares.

    PubMed

    Giacovazzo, Carmelo

    2015-01-01

    Crystallographic least squares are a fundamental tool for crystal structure analysis. In this paper their properties are derived from functions estimating the degree of similarity between two electron-density maps. The new approach leads also to modifications of the standard least-squares procedures, potentially able to improve their efficiency. The role of the scaling factor between observed and model amplitudes is analysed: the concept of unlocated model is discussed and its scattering contribution is combined with that arising from the located model. Also, the possible use of an ancillary parameter, to be associated with the classical weight related to the variance of the observed amplitudes, is studied. The crystallographic discrepancy factors, basic tools often combined with least-squares procedures in phasing approaches, are analysed. The mathematical approach here described includes, as a special case, the so-called vector refinement, used when accurate estimates of the target phases are available.

  9. Analytical solution of Luedeking-Piret equation for a batch fermentation obeying Monod growth kinetics.

    PubMed

    Garnier, Alain; Gaillet, Bruno

    2015-12-01

    Not so many fermentation mathematical models allow analytical solutions of batch process dynamics. The most widely used is the combination of the logistic microbial growth kinetics with Luedeking-Piret bioproduct synthesis relation. However, the logistic equation is principally based on formalistic similarities and only fits a limited range of fermentation types. In this article, we have developed an analytical solution for the combination of Monod growth kinetics with Luedeking-Piret relation, which can be identified by linear regression and used to simulate batch fermentation evolution. Two classical examples are used to show the quality of fit and the simplicity of the method proposed. A solution for the combination of Haldane substrate-limited growth model combined with Luedeking-Piret relation is also provided. These models could prove useful for the analysis of fermentation data in industry as well as academia. © 2015 Wiley Periodicals, Inc.

  10. Quantum Brownian motion model for the stock market

    NASA Astrophysics Data System (ADS)

    Meng, Xiangyi; Zhang, Jian-Wei; Guo, Hong

    2016-06-01

    It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysical framework for the stock market, based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system-a quantum Brownian particle. In particular, the irrationality of stock transactions is quantitatively considered as the Planck constant within Heisenberg's uncertainty relationship of quantum mechanics in an analogous manner. We analyze real stock data of Shanghai Stock Exchange of China and investigate fat-tail phenomena and non-Markovian behaviors of the stock index with the assistance of the quantum Brownian motion model, thereby interpreting and studying the limitations of the classical Brownian motion model for the efficient market hypothesis from a new perspective of quantum open system dynamics.

  11. Contact Forces between Single Metal Oxide Nanoparticles in Gas-Phase Applications and Processes

    PubMed Central

    2017-01-01

    In this work we present a comprehensive experimental study to determine the contact forces between individual metal oxide nanoparticles in the gas-phase using atomic force microscopy. In addition, we determined the amount of physisorbed water for each type of particle surface. By comparing our results with mathematical models of the interaction forces, we could demonstrate that classical continuum models of van der Waals and capillary forces alone cannot sufficiently describe the experimental findings. Rather, the discrete nature of the molecules has to be considered, which leads to ordering at the interface and the occurrence of solvation forces. We demonstrate that inclusion of solvation forces in the model leads to quantitative agreement with experimental data and that tuning of the molecular order by addition of isopropanol vapor allows us to control the interaction forces between the nanoparticles. PMID:28186771

  12. The analysis of mathematics literacy on PMRI learning with media schoology of junior high school students

    NASA Astrophysics Data System (ADS)

    Wardono; Mariani, S.

    2018-03-01

    Indonesia as a developing country in the future will have high competitiveness if its students have high mathematics literacy ability. The current reality from year to year rankings of PISA mathematics literacy Indonesian students are still not good. This research is motivated by the importance and low ability of the mathematics literacy. The purpose of this study is to: (1) analyze the effectiveness of PMRI learning with media Schoology, (2) describe the ability of students' mathematics literacy on PMRI learning with media Schoology which is reviewed based on seven components of mathematics literacy, namely communication, mathematizing, representation, reasoning, devising strategies, using symbols, and using mathematics tool. The method used in this research is the method of sequential design method mix. Techniques of data collection using observation, interviews, tests, and documentation. Data analysis techniques use proportion test, appellate test, and use descriptive analysis. Based on the data analysis, it can be concluded; (1) PMRI learning with media Schoology effectively improve the ability of mathematics literacy because of the achievement of classical completeness, students' mathematics literacy ability in PMRI learning with media Schoology is higher than expository learning, and there is increasing ability of mathematics literacy in PMRI learning with media Schoology of 30%. (2) Highly capable students attain excellent mathematics literacy skills, can work using broad thinking with appropriate resolution strategies. Students who are capable of achieving good mathematics literacy skills can summarize information, present problem-solving processes, and interpret solutions. low-ability students have reached the level of ability of mathematics literacy good enough that can solve the problem in a simple way.

  13. Quantum-inspired algorithm for estimating the permanent of positive semidefinite matrices

    NASA Astrophysics Data System (ADS)

    Chakhmakhchyan, L.; Cerf, N. J.; Garcia-Patron, R.

    2017-08-01

    We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the permanent of a Hermitian positive semidefinite matrix can be expressed in terms of the expected value of a random variable, which stands for a specific photon-counting probability when measuring a linear-optically evolved random multimode coherent state. Our algorithm then approximates the matrix permanent from the corresponding sample mean and is shown to run in polynomial time for various sets of Hermitian positive semidefinite matrices, achieving a precision that improves over known techniques. This work illustrates how quantum optics may benefit algorithm development.

  14. Minimization search method for data inversion

    NASA Technical Reports Server (NTRS)

    Fymat, A. L.

    1975-01-01

    Technique has been developed for determining values of selected subsets of independent variables in mathematical formulations. Required computation time increases with first power of the number of variables. This is in contrast with classical minimization methods for which computational time increases with third power of the number of variables.

  15. The Use of Force Sensors and a Computer System to Introduce the Concept of Inertia at a School

    ERIC Educational Resources Information Center

    Bogacz, Bogdan F.; Pedziwiatr, Antoni T.

    2014-01-01

    A classical experiment used to introduce the concept of body inertia, breaking of a thread below and above a hanging weight, is described mathematically and presented in a new way, using force sensors and a computer system.

  16. Computational Thinking Concepts for Grade School

    ERIC Educational Resources Information Center

    Sanford, John F.; Naidu, Jaideep T.

    2016-01-01

    Early education has classically introduced reading, writing, and mathematics. Recent literature discusses the importance of adding "computational thinking" as a core ability that every child must learn. The goal is to develop students by making them equally comfortable with computational thinking as they are with other core areas of…

  17. Brain Stretchers Book 4--Advanced.

    ERIC Educational Resources Information Center

    Anderson, Carolyn

    This book provides puzzles, games, and mathematical activities for students in elementary grades. Number concepts and arithmetic are common topics. These classic math, logic, and word-problem activities encourage students to become flexible, creative thinkers while teaching them to draw valid conclusions based on logic and evidence. Each activity…

  18. Factors Influencing Learning of Classical Mechanics.

    ERIC Educational Resources Information Center

    Champagne, Audrey B.; And Others

    Beginning college physics students' misconceptions about moving objects, their mathematics skills, and formal reasoning ability, are all believed to be related to their achievement in physics. It is hypothesized that students whose knowledge structures include misconceptions that are in conflict with concepts in the lectures and text will have…

  19. Mathematical analysis of a power-law form time dependent vector-borne disease transmission model.

    PubMed

    Sardar, Tridip; Saha, Bapi

    2017-06-01

    In the last few years, fractional order derivatives have been used in epidemiology to capture the memory phenomena. However, these models do not have proper biological justification in most of the cases and lack a derivation from a stochastic process. In this present manuscript, using theory of a stochastic process, we derived a general time dependent single strain vector borne disease model. It is shown that under certain choice of time dependent transmission kernel this model can be converted into the classical integer order system. When the time-dependent transmission follows a power law form, we showed that the model converted into a vector borne disease model with fractional order transmission. We explicitly derived the disease-free and endemic equilibrium of this new fractional order vector borne disease model. Using mathematical properties of nonlinear Volterra type integral equation it is shown that the unique disease-free state is globally asymptotically stable under certain condition. We define a threshold quantity which is epidemiologically known as the basic reproduction number (R 0 ). It is shown that if R 0 > 1, then the derived fractional order model has a unique endemic equilibrium. We analytically derived the condition for the local stability of the endemic equilibrium. To test the model capability to capture real epidemic, we calibrated our newly proposed model to weekly dengue incidence data of San Juan, Puerto Rico for the time period 30th April 1994 to 23rd April 1995. We estimated several parameters, including the order of the fractional derivative of the proposed model using aforesaid data. It is shown that our proposed fractional order model can nicely capture real epidemic. Copyright © 2017 Elsevier Inc. All rights reserved.

  20. Analytical solutions for benchmarking cold regions subsurface water flow and energy transport models: one-dimensional soil thaw with conduction and advection

    USGS Publications Warehouse

    Kurylyk, Barret L.; McKenzie, Jeffrey M; MacQuarrie, Kerry T. B.; Voss, Clifford I.

    2014-01-01

    Numerous cold regions water flow and energy transport models have emerged in recent years. Dissimilarities often exist in their mathematical formulations and/or numerical solution techniques, but few analytical solutions exist for benchmarking flow and energy transport models that include pore water phase change. This paper presents a detailed derivation of the Lunardini solution, an approximate analytical solution for predicting soil thawing subject to conduction, advection, and phase change. Fifteen thawing scenarios are examined by considering differences in porosity, surface temperature, Darcy velocity, and initial temperature. The accuracy of the Lunardini solution is shown to be proportional to the Stefan number. The analytical solution results obtained for soil thawing scenarios with water flow and advection are compared to those obtained from the finite element model SUTRA. Three problems, two involving the Lunardini solution and one involving the classic Neumann solution, are recommended as standard benchmarks for future model development and testing.

  1. Modeling the interference of vortex-induced vibration and galloping for a slender rectangular prism

    NASA Astrophysics Data System (ADS)

    Mannini, Claudio; Massai, Tommaso; Marra, Antonino Maria

    2018-04-01

    Several bluff bodies in an airflow, such as rectangular cylinders with moderate side ratio, in particular conditions of mass and damping can experience the interference of vortex-induced vibration (VIV) and galloping. This promotes a combined instability, which one may call "unsteady galloping", with peculiar features and possibly large vibration amplitudes in flow speed ranges where no excitation is predicted by classical theories. The mathematical model proposed between the 70's and the 80's by Prof. Y. Tamura to simulate this phenomenon was considered here for the case study of a two-dimensional rectangular cylinder with a side ratio of 1.5, having the shorter section side perpendicular to the smooth airflow. This wake-oscillator model relies on the linear superposition of the unsteady wake force producing VIV excitation and the quasi-steady force that is responsible for galloping. The model formulation was slightly modified, and the way to determine a crucial parameter was changed, revealing a previously unexplored behavior of the equations. In the present form, the model is able to predict the dynamic response of the rectangular cylinder with a satisfactory qualitative and, to a certain extent, quantitative agreement with the experimental data, although the limitations of the present approach are clearly highlighted in the paper. The mathematical modeling of unsteady galloping and the analysis of the results offer a deep insight into this complicated phenomenon and its nonlinear features. The model also represents a useful engineering tool to estimate the vibration of a structure or structural element for which the interference of VIV and galloping is envisaged.

  2. Introduction to focus issue: quantitative approaches to genetic networks.

    PubMed

    Albert, Réka; Collins, James J; Glass, Leon

    2013-06-01

    All cells of living organisms contain similar genetic instructions encoded in the organism's DNA. In any particular cell, the control of the expression of each different gene is regulated, in part, by binding of molecular complexes to specific regions of the DNA. The molecular complexes are composed of protein molecules, called transcription factors, combined with various other molecules such as hormones and drugs. Since transcription factors are coded by genes, cellular function is partially determined by genetic networks. Recent research is making large strides to understand both the structure and the function of these networks. Further, the emerging discipline of synthetic biology is engineering novel gene circuits with specific dynamic properties to advance both basic science and potential practical applications. Although there is not yet a universally accepted mathematical framework for studying the properties of genetic networks, the strong analogies between the activation and inhibition of gene expression and electric circuits suggest frameworks based on logical switching circuits. This focus issue provides a selection of papers reflecting current research directions in the quantitative analysis of genetic networks. The work extends from molecular models for the binding of proteins, to realistic detailed models of cellular metabolism. Between these extremes are simplified models in which genetic dynamics are modeled using classical methods of systems engineering, Boolean switching networks, differential equations that are continuous analogues of Boolean switching networks, and differential equations in which control is based on power law functions. The mathematical techniques are applied to study: (i) naturally occurring gene networks in living organisms including: cyanobacteria, Mycoplasma genitalium, fruit flies, immune cells in mammals; (ii) synthetic gene circuits in Escherichia coli and yeast; and (iii) electronic circuits modeling genetic networks using field-programmable gate arrays. Mathematical analyses will be essential for understanding naturally occurring genetic networks in diverse organisms and for providing a foundation for the improved development of synthetic genetic networks.

  3. Introduction to Focus Issue: Quantitative Approaches to Genetic Networks

    NASA Astrophysics Data System (ADS)

    Albert, Réka; Collins, James J.; Glass, Leon

    2013-06-01

    All cells of living organisms contain similar genetic instructions encoded in the organism's DNA. In any particular cell, the control of the expression of each different gene is regulated, in part, by binding of molecular complexes to specific regions of the DNA. The molecular complexes are composed of protein molecules, called transcription factors, combined with various other molecules such as hormones and drugs. Since transcription factors are coded by genes, cellular function is partially determined by genetic networks. Recent research is making large strides to understand both the structure and the function of these networks. Further, the emerging discipline of synthetic biology is engineering novel gene circuits with specific dynamic properties to advance both basic science and potential practical applications. Although there is not yet a universally accepted mathematical framework for studying the properties of genetic networks, the strong analogies between the activation and inhibition of gene expression and electric circuits suggest frameworks based on logical switching circuits. This focus issue provides a selection of papers reflecting current research directions in the quantitative analysis of genetic networks. The work extends from molecular models for the binding of proteins, to realistic detailed models of cellular metabolism. Between these extremes are simplified models in which genetic dynamics are modeled using classical methods of systems engineering, Boolean switching networks, differential equations that are continuous analogues of Boolean switching networks, and differential equations in which control is based on power law functions. The mathematical techniques are applied to study: (i) naturally occurring gene networks in living organisms including: cyanobacteria, Mycoplasma genitalium, fruit flies, immune cells in mammals; (ii) synthetic gene circuits in Escherichia coli and yeast; and (iii) electronic circuits modeling genetic networks using field-programmable gate arrays. Mathematical analyses will be essential for understanding naturally occurring genetic networks in diverse organisms and for providing a foundation for the improved development of synthetic genetic networks.

  4. A robust interpolation method for constructing digital elevation models from remote sensing data

    NASA Astrophysics Data System (ADS)

    Chen, Chuanfa; Liu, Fengying; Li, Yanyan; Yan, Changqing; Liu, Guolin

    2016-09-01

    A digital elevation model (DEM) derived from remote sensing data often suffers from outliers due to various reasons such as the physical limitation of sensors and low contrast of terrain textures. In order to reduce the effect of outliers on DEM construction, a robust algorithm of multiquadric (MQ) methodology based on M-estimators (MQ-M) was proposed. MQ-M adopts an adaptive weight function with three-parts. The weight function is null for large errors, one for small errors and quadric for others. A mathematical surface was employed to comparatively analyze the robustness of MQ-M, and its performance was compared with those of the classical MQ and a recently developed robust MQ method based on least absolute deviation (MQ-L). Numerical tests show that MQ-M is comparative to the classical MQ and superior to MQ-L when sample points follow normal and Laplace distributions, and under the presence of outliers the former is more accurate than the latter. A real-world example of DEM construction using stereo images indicates that compared with the classical interpolation methods, such as natural neighbor (NN), ordinary kriging (OK), ANUDEM, MQ-L and MQ, MQ-M has a better ability of preserving subtle terrain features. MQ-M replaces thin plate spline for reference DEM construction to assess the contribution to our recently developed multiresolution hierarchical classification method (MHC). Classifying the 15 groups of benchmark datasets provided by the ISPRS Commission demonstrates that MQ-M-based MHC is more accurate than MQ-L-based and TPS-based MHCs. MQ-M has high potential for DEM construction.

  5. Detecting Moving Targets by Use of Soliton Resonances

    NASA Technical Reports Server (NTRS)

    Zak, Michael; Kulikov, Igor

    2003-01-01

    A proposed method of detecting moving targets in scenes that include cluttered or noisy backgrounds is based on a soliton-resonance mathematical model. The model is derived from asymptotic solutions of the cubic Schroedinger equation for a one-dimensional system excited by a position-and-time-dependent externally applied potential. The cubic Schroedinger equation has general significance for time-dependent dispersive waves. It has been used to approximate several phenomena in classical as well as quantum physics, including modulated beams in nonlinear optics, and superfluids (in particular, Bose-Einstein condensates). In the proposed method, one would take advantage of resonant interactions between (1) a soliton excited by the position-and-time-dependent potential associated with a moving target and (2) eigen-solitons, which represent dispersive waves and are solutions of the cubic Schroedinger equation for a time-independent potential.

  6. Studying the complex spectral line profiles in the spectra of hot emission stars and quasars .

    NASA Astrophysics Data System (ADS)

    Danezis, E.; Lyratzi, E.; Antoniou, A.; Popović, L. Č.; Dimitrijević, M. S.

    Some Hot Emission Stars and AGNs present peculiar spectral line profiles which are due to DACs and SACs phenomena. The origin and the mechanisms which are responsible for the creation of DACs/SACs is an important problem that has been studied by many researchers. This paper is a review of our efforts to study the origin and the mechanisms of these phenomena. At first we present a theoretic ad hoc picture for the structure of the plasma that surrounds the specific category of hot emission stars that present DACs or SACs. Then we present the mathematical model that we constructed, which is based on the properties of the above ad hoc theoretical structure. Finally, we present some results from our statistical studies that prove the consistency of our model with the classical physical theory.

  7. Asymptotic theory of neutral stability of the Couette flow of a vibrationally excited gas

    NASA Astrophysics Data System (ADS)

    Grigor'ev, Yu. N.; Ershov, I. V.

    2017-01-01

    An asymptotic theory of the neutral stability curve for a supersonic plane Couette flow of a vibrationally excited gas is developed. The initial mathematical model consists of equations of two-temperature viscous gas dynamics, which are used to derive a spectral problem for a linear system of eighth-order ordinary differential equations within the framework of the classical linear stability theory. Unified transformations of the system for all shear flows are performed in accordance with the classical Lin scheme. The problem is reduced to an algebraic secular equation with separation into the "inviscid" and "viscous" parts, which is solved numerically. It is shown that the thus-calculated neutral stability curves agree well with the previously obtained results of the direct numerical solution of the original spectral problem. In particular, the critical Reynolds number increases with excitation enhancement, and the neutral stability curve is shifted toward the domain of higher wave numbers. This is also confirmed by means of solving an asymptotic equation for the critical Reynolds number at the Mach number M ≤ 4.

  8. The Dreaded "Work" Problems Revisited: Connections through Problem Solving from Basic Fractions to Calculus

    ERIC Educational Resources Information Center

    Shore, Felice S.; Pascal, Matthew

    2008-01-01

    This article describes several distinct approaches taken by preservice elementary teachers to solving a classic rate problem. Their approaches incorporate a variety of mathematical concepts, ranging from proportions to infinite series, and illustrate the power of all five NCTM Process Standards. (Contains 8 figures.)

  9. Increasing Math Achievement through Use of Music.

    ERIC Educational Resources Information Center

    Bryant-Jones, Marian; Shimmins, Kymberley J.; Vega, Jill D.

    This report describes a program for increasing math achievement through the use of musical interventions including repeated exposure to Mozart classical music and School House Rock, and introduction to teacher-made songs that introduce mathematical concepts in the music classroom. The students of the targeted second and fourth grade classes…

  10. Solving Optimization Problems with Spreadsheets

    ERIC Educational Resources Information Center

    Beigie, Darin

    2017-01-01

    Spreadsheets provide a rich setting for first-year algebra students to solve problems. Individual spreadsheet cells play the role of variables, and creating algebraic expressions for a spreadsheet to perform a task allows students to achieve a glimpse of how mathematics is used to program a computer and solve problems. Classic optimization…

  11. Past Is Prologue: The Classics Today.

    ERIC Educational Resources Information Center

    Lukes, Alana Karalius

    1992-01-01

    Stresses the relevance of Greek and Roman cultures and languages to the study of contemporary U.S. culture. Architecture, science, government, drama, mathematics, religion, and music are compared and contrasted. Faculty and students participate in this interdisciplinary approach to develop new awareness of links between past and present cultures.…

  12. The Prisoner Problem--A Generalization.

    ERIC Educational Resources Information Center

    Gannon, Gerald E.; Martelli, Mario U.

    2000-01-01

    Presents a generalization to the classic prisoner problem, which is inherently interesting and has a solution within the reach of most high school mathematics students. Suggests the problem as a way to emphasize to students the final step in a problem-solver's tool kit, considering possible generalizations when a particular problem has been…

  13. Enzyme Kinetics and the Michaelis-Menten Equation

    ERIC Educational Resources Information Center

    Biaglow, Andrew; Erickson, Keith; McMurran, Shawnee

    2010-01-01

    The concepts presented in this article represent the cornerstone of classical mathematical biology. The central problem of the article relates to enzyme kinetics, which is a biochemical system. However, the theoretical underpinnings that lead to the formation of systems of time-dependent ordinary differential equations have been applied widely to…

  14. Conjecturing via Reconceived Classical Analogy

    ERIC Educational Resources Information Center

    Lee, Kyeong-Hwa; Sriraman, Bharath

    2011-01-01

    Analogical reasoning is believed to be an efficient means of problem solving and construction of knowledge during the search for and the analysis of new mathematical objects. However, there is growing concern that despite everyday usage, learners are unable to transfer analogical reasoning to learning situations. This study aims at facilitating…

  15. Hermann-Bernoulli-Laplace-Hamilton-Runge-Lenz Vector.

    ERIC Educational Resources Information Center

    Subramanian, P. R.; And Others

    1991-01-01

    A way for students to refresh and use their knowledge in both mathematics and physics is presented. By the study of the properties of the "Runge-Lenz" vector the subjects of algebra, analytical geometry, calculus, classical mechanics, differential equations, matrices, quantum mechanics, trigonometry, and vector analysis can be reviewed. (KR)

  16. Procedural Quantum Programming

    NASA Astrophysics Data System (ADS)

    Ömer, Bernhard

    2002-09-01

    While classical computing science has developed a variety of methods and programming languages around the concept of the universal computer, the typical description of quantum algorithms still uses a purely mathematical, non-constructive formalism which makes no difference between a hydrogen atom and a quantum computer. This paper investigates, how the concept of procedural programming languages, the most widely used classical formalism for describing and implementing algorithms, can be adopted to the field of quantum computing, and how non-classical features like the reversibility of unitary transformations, the non-observability of quantum states or the lack of copy and erase operations can be reflected semantically. It introduces the key concepts of procedural quantum programming (hybrid target architecture, operator hierarchy, quantum data types, memory management, etc.) and presents the experimental language QCL, which implements these principles.

  17. 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.

  18. Restriction-Modification systems interplay causes avoidance of GATC site in prokaryotic genomes.

    PubMed

    Ershova, Anna; Rusinov, Ivan; Vasiliev, Mikhail; Spirin, Sergey; Karyagina, Anna

    2016-04-01

    Palindromes are frequently underrepresented in prokaryotic genomes. Palindromic 5[Formula: see text]-GATC-3[Formula: see text] site is a recognition site of different Restriction-Modification (R-M) systems, as well as solitary methyltransferase Dam. Classical GATC-specific R-M systems methylate GATC and cleave unmethylated GATC. On the contrary, methyl-directed Type II restriction endonucleases cleave methylated GATC. Methylation of GATC by Dam methyltransferase is involved in the regulation of different cellular processes. The diversity of functions of GATC-recognizing proteins makes GATC sequence a good model for studying the reasons of palindrome avoidance in prokaryotic genomes. In this work, the influence of R-M systems and solitary proteins on the GATC site avoidance is described by a mathematical model. GATC avoidance is strongly associated with the presence of alternate (methyl-directed or classical Type II R-M system) genes in different strains of the same species, as we have shown for Streptococcus pneumoniae, Neisseria meningitidis, Eubacterium rectale, and Moraxella catarrhalis. We hypothesize that GATC avoidance can result from a DNA exchange between strains with different methylation status of GATC site within the process of natural transformation. If this hypothesis is correct, the GATC avoidance is a sign of a DNA exchange between bacteria with different methylation status in a mixed population.

  19. Solution of the equations for one-dimensional, two-phase, immiscible flow by geometric methods

    NASA Astrophysics Data System (ADS)

    Boronin, Ivan; Shevlyakov, Andrey

    2018-03-01

    Buckley-Leverett equations describe non viscous, immiscible, two-phase filtration, which is often of interest in modelling of oil production. For many parameters and initial conditions, the solutions of these equations exhibit non-smooth behaviour, namely discontinuities in form of shock waves. In this paper we obtain a novel method for the solution of Buckley-Leverett equations, which is based on geometry of differential equations. This method is fast, accurate, stable, and describes non-smooth phenomena. The main idea of the method is that classic discontinuous solutions correspond to the continuous surfaces in the space of jets - the so-called multi-valued solutions (Bocharov et al., Symmetries and conservation laws for differential equations of mathematical physics. American Mathematical Society, Providence, 1998). A mapping of multi-valued solutions from the jet space onto the plane of the independent variables is constructed. This mapping is not one-to-one, and its singular points form a curve on the plane of the independent variables, which is called the caustic. The real shock occurs at the points close to the caustic and is determined by the Rankine-Hugoniot conditions.

  20. The solids-flux theory--confirmation and extension by using partial differential equations.

    PubMed

    Diehl, Stefan

    2008-12-01

    The solids-flux theory has been used for half a century as a tool for estimating concentration and fluxes in the design and operation of secondary settling tanks during stationary conditions. The flux theory means that the conservation of mass is used in one dimension together with the batch-settling flux function according to the Kynch assumption. The flux theory results correspond to stationary solutions of a partial differential equation, a conservation law, with discontinuous coefficients modelling the continuous-sedimentation process in one dimension. The mathematical analysis of such an equation is intricate, partly since it cannot be interpreted in the classical sense. Recent results, however, make it possible to partly confirm and extend the previous flux theory statements, partly draw new conclusions also on the dynamic behaviour and the possibilities and limitations for control. We use here a single example of an ideal settling tank and a given batch-settling flux in a whole series of calculations. The mathematical results are adapted towards the application and many of them are conveniently presented in terms of operating charts.

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

    Morales, George J.; Maggs, James E.

    The project expanded and developed mathematical descriptions, and corresponding numerical modeling, of non-diffusive transport to incorporate new perspectives derived from basic transport experiments performed in the LAPD device at UCLA, and at fusion devices throughout the world. By non-diffusive it is meant that the transport of fundamental macroscopic parameters of a system, such as temperature and density, does not follow the standard diffusive behavior predicted by a classical Fokker-Planck equation. The appearance of non-diffusive behavior is often related to underlying microscopic processes that cause the value of a system parameter, at one spatial position, to be linked to distant events,more » i.e., non-locality. In the LAPD experiments the underlying process was traced to large amplitude, coherent drift-waves that give rise to chaotic trajectories. Significant advances were made in this project. The results have lead to a new perspective about the fundamentals of edge transport in magnetically confined plasmas; the insight has important consequences for worldwide studies in fusion devices. Progress was also made in advancing the mathematical techniques used to describe fractional diffusion.« less

  2. Neo-classical theory of competition or Adam Smith's hand as mathematized ideology

    NASA Astrophysics Data System (ADS)

    McCauley, Joseph L.

    2001-10-01

    Orthodox economic theory (utility maximization, rational agents, efficient markets in equilibrium) is based on arbitrarily postulated, nonempiric notions. The disagreement between economic reality and a key feature of neo-classical economic theory was criticized empirically by Osborne. I show that the orthodox theory is internally self-inconsistent for the very reason suggested by Osborne: lack of invertibility of demand and supply as functions of price to obtain price as functions of supply and demand. The reason for the noninvertibililty arises from nonintegrable excess demand dynamics, a feature of their theory completely ignored by economists.

  3. Counterfactual Definiteness and Bell's Inequality

    NASA Astrophysics Data System (ADS)

    Hess, Karl; Raedt, Hans De; Michielsen, Kristel

    Counterfactual definiteness must be used as at least one of the postulates or axioms that are necessary to derive Bell-type inequalities. It is considered by many to be a postulate that is not only commensurate with classical physics (as for example Einstein's special relativity), but also separates and distinguishes classical physics from quantum mechanics. It is the purpose of this paper to show that Bell's choice of mathematical functions and independent variables implicitly includes counterfactual definiteness and reduces the generality of the physics of Bell-type theories so significantly that no meaningful comparison of these theories with actual Einstein-Podolsky-Rosen experiments can be made.

  4. Leaky GFD problems

    NASA Astrophysics Data System (ADS)

    Chumakova, Lyubov; Rzeznik, Andrew; Rosales, Rodolfo R.

    2017-11-01

    In many dispersive/conservative wave problems, waves carry energy outside of the domain of interest and never return. Inside the domain of interest, this wave leakage acts as an effective dissipation mechanism, causing solutions to decay. In classical geophysical fluid dynamics problems this scenario occurs in the troposphere, if one assumes a homogeneous stratosphere. In this talk we present several classic GFD problems, where we seek the solution in the troposphere alone. Assuming that upward propagating waves that reach the stratosphere never return, we demonstrate how classic baroclinic modes become leaky, with characteristic decay time-scales that can be calculated. We also show how damping due to wave leakage changes the classic baroclinic instability problem in the presence of shear. This presentation is a part of a joint project. The mathematical approach used here relies on extending the classical concept of group velocity to leaky waves with complex wavenumber and frequency, which will be presented at this meeting by A. Rzeznik in the talk ``Group Velocity for Leaky Waves''. This research is funded by the Royal Soc. of Edinburgh, Scottish Government, and NSF.

  5. Statistical mechanics in the context of special relativity. II.

    PubMed

    Kaniadakis, G

    2005-09-01

    The special relativity laws emerge as one-parameter (light speed) generalizations of the corresponding laws of classical physics. These generalizations, imposed by the Lorentz transformations, affect both the definition of the various physical observables (e.g., momentum, energy, etc.), as well as the mathematical apparatus of the theory. Here, following the general lines of [Phys. Rev. E 66, 056125 (2002)], we show that the Lorentz transformations impose also a proper one-parameter generalization of the classical Boltzmann-Gibbs-Shannon entropy. The obtained relativistic entropy permits us to construct a coherent and self-consistent relativistic statistical theory, preserving the main features of the ordinary statistical theory, which is recovered in the classical limit. The predicted distribution function is a one-parameter continuous deformation of the classical Maxwell-Boltzmann distribution and has a simple analytic form, showing power law tails in accordance with the experimental evidence. Furthermore, this statistical mechanics can be obtained as the stationary case of a generalized kinetic theory governed by an evolution equation obeying the H theorem and reproducing the Boltzmann equation of the ordinary kinetics in the classical limit.

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

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

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

    2016-07-07

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

  7. Can modeling of HIV treatment processes improve outcomes? Capitalizing on an operations research approach to the global pandemic

    PubMed Central

    Xiong, Wei; Hupert, Nathaniel; Hollingsworth, Eric B; O'Brien, Megan E; Fast, Jessica; Rodriguez, William R

    2008-01-01

    Background Mathematical modeling has been applied to a range of policy-level decisions on resource allocation for HIV care and treatment. We describe the application of classic operations research (OR) techniques to address logistical and resource management challenges in HIV treatment scale-up activities in resource-limited countries. Methods We review and categorize several of the major logistical and operational problems encountered over the last decade in the global scale-up of HIV care and antiretroviral treatment for people with AIDS. While there are unique features of HIV care and treatment that pose significant challenges to effective modeling and service improvement, we identify several analogous OR-based solutions that have been developed in the service, industrial, and health sectors. Results HIV treatment scale-up includes many processes that are amenable to mathematical and simulation modeling, including forecasting future demand for services; locating and sizing facilities for maximal efficiency; and determining optimal staffing levels at clinical centers. Optimization of clinical and logistical processes through modeling may improve outcomes, but successful OR-based interventions will require contextualization of response strategies, including appreciation of both existing health care systems and limitations in local health workforces. Conclusion The modeling techniques developed in the engineering field of operations research have wide potential application to the variety of logistical problems encountered in HIV treatment scale-up in resource-limited settings. Increasing the number of cross-disciplinary collaborations between engineering and public health will help speed the appropriate development and application of these tools. PMID:18680594

  8. Systems Toxicology: From Basic Research to Risk Assessment

    PubMed Central

    2014-01-01

    Systems Toxicology is the integration of classical toxicology with quantitative analysis of large networks of molecular and functional changes occurring across multiple levels of biological organization. Society demands increasingly close scrutiny of the potential health risks associated with exposure to chemicals present in our everyday life, leading to an increasing need for more predictive and accurate risk-assessment approaches. Developing such approaches requires a detailed mechanistic understanding of the ways in which xenobiotic substances perturb biological systems and lead to adverse outcomes. Thus, Systems Toxicology approaches offer modern strategies for gaining such mechanistic knowledge by combining advanced analytical and computational tools. Furthermore, Systems Toxicology is a means for the identification and application of biomarkers for improved safety assessments. In Systems Toxicology, quantitative systems-wide molecular changes in the context of an exposure are measured, and a causal chain of molecular events linking exposures with adverse outcomes (i.e., functional and apical end points) is deciphered. Mathematical models are then built to describe these processes in a quantitative manner. The integrated data analysis leads to the identification of how biological networks are perturbed by the exposure and enables the development of predictive mathematical models of toxicological processes. This perspective integrates current knowledge regarding bioanalytical approaches, computational analysis, and the potential for improved risk assessment. PMID:24446777

  9. Shaping the micromechanical behavior of multi-phase composites for bone tissue engineering.

    PubMed

    Ranganathan, Shivakumar I; Yoon, Diana M; Henslee, Allan M; Nair, Manitha B; Smid, Christine; Kasper, F Kurtis; Tasciotti, Ennio; Mikos, Antonios G; Decuzzi, Paolo; Ferrari, Mauro

    2010-09-01

    Mechanical stiffness is a fundamental parameter in the rational design of composites for bone tissue engineering in that it affects both the mechanical stability and the osteo-regeneration process at the fracture site. A mathematical model is presented for predicting the effective Young's modulus (E) and shear modulus (G) of a multi-phase biocomposite as a function of the geometry, material properties and volume concentration of each individual phase. It is demonstrated that the shape of the reinforcing particles may dramatically affect the mechanical stiffness: E and G can be maximized by employing particles with large geometrical anisotropy, such as thin platelet-like or long fibrillar-like particles. For a porous poly(propylene fumarate) (60% porosity) scaffold reinforced with silicon particles (10% volume concentration) the Young's (shear) modulus could be increased by more than 10 times by just using thin platelet-like as opposed to classical spherical particles, achieving an effective modulus E approximately 8 GPa (G approximately 3.5 GPa). The mathematical model proposed provides results in good agreement with several experimental test cases and could help in identifying the proper formulation of bone scaffolds, reducing the development time and guiding the experimental testing. 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

  10. Systems toxicology: from basic research to risk assessment.

    PubMed

    Sturla, Shana J; Boobis, Alan R; FitzGerald, Rex E; Hoeng, Julia; Kavlock, Robert J; Schirmer, Kristin; Whelan, Maurice; Wilks, Martin F; Peitsch, Manuel C

    2014-03-17

    Systems Toxicology is the integration of classical toxicology with quantitative analysis of large networks of molecular and functional changes occurring across multiple levels of biological organization. Society demands increasingly close scrutiny of the potential health risks associated with exposure to chemicals present in our everyday life, leading to an increasing need for more predictive and accurate risk-assessment approaches. Developing such approaches requires a detailed mechanistic understanding of the ways in which xenobiotic substances perturb biological systems and lead to adverse outcomes. Thus, Systems Toxicology approaches offer modern strategies for gaining such mechanistic knowledge by combining advanced analytical and computational tools. Furthermore, Systems Toxicology is a means for the identification and application of biomarkers for improved safety assessments. In Systems Toxicology, quantitative systems-wide molecular changes in the context of an exposure are measured, and a causal chain of molecular events linking exposures with adverse outcomes (i.e., functional and apical end points) is deciphered. Mathematical models are then built to describe these processes in a quantitative manner. The integrated data analysis leads to the identification of how biological networks are perturbed by the exposure and enables the development of predictive mathematical models of toxicological processes. This perspective integrates current knowledge regarding bioanalytical approaches, computational analysis, and the potential for improved risk assessment.

  11. A relativistically interacting exactly solvable multi-time model for two massless Dirac particles in 1 + 1 dimensions

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

    Lienert, Matthias, E-mail: lienert@math.lmu.de

    2015-04-15

    The question how to Lorentz transform an N-particle wave function naturally leads to the concept of a so-called multi-time wave function, i.e., a map from (space-time){sup N} to a spin space. This concept was originally proposed by Dirac as the basis of relativistic quantum mechanics. In such a view, interaction potentials are mathematically inconsistent. This fact motivates the search for new mechanisms for relativistic interactions. In this paper, we explore the idea that relativistic interaction can be described by boundary conditions on the set of coincidence points of two particles in space-time. This extends ideas from zero-range physics to amore » relativistic setting. We illustrate the idea at the simplest model which still possesses essential physical properties like Lorentz invariance and a positive definite density: two-time equations for massless Dirac particles in 1 + 1 dimensions. In order to deal with a spatio-temporally non-trivial domain, a necessity in the multi-time picture, we develop a new method to prove existence and uniqueness of classical solutions: a generalized version of the method of characteristics. Both mathematical and physical considerations are combined to precisely formulate and answer the questions of probability conservation, Lorentz invariance, interaction, and antisymmetry.« less

  12. A brief historical development of classical mathematics before the Renaissance

    NASA Astrophysics Data System (ADS)

    Debnath, Lokenath

    2011-07-01

    'If you wish to foresee the future of mathematics our proper course is to study the history and present condition of the science.' Henri Poincaré 'It is India that gave us the ingenious method of expressing all numbers by ten symbols, each symbol receiving a value of position, as well as an absolute value. We shall appreciate the grandeur of the achievement when we remember that it escaped the genius of Archimedes and Apollonius.' P.S. Laplace 'The Greeks were the first mathematicians who are still 'real' to us today. Oriental mathematics may be an interesting curiosity, but Greek mathematics is the real thing. The Greek first spoke of a language which modern mathematicians can understand.' G.H. Hardy This article deals with a short history of mathematics and mathematical scientists during the ancient and medieval periods. Included are some major developments of the ancient, Indian, Arabic, Egyptian, Greek and medieval mathematics and their significant impact on the Renaissance mathematics. Special attention is given to many results, theorems, generalizations, and new discoveries of arithmetic, algebra, number theory, geometry and astronomy during the above periods. A number of exciting applications of the above areas is discussed in some detail. It also contains a wide variety of important material accessible to college and even high school students and teachers at all levels. Included also is mathematical information that puts the professionals and prospective mathematical scientists at the forefront of current research.

  13. An economic order quantity model with shortage and inflation

    NASA Astrophysics Data System (ADS)

    Wulan, Elis Ratna; Nurjaman, Wildan

    2015-09-01

    The effect of inflation has become a persistent characteristic and more significant problem of many developing economies especially in the third world countries. While making effort to achieve optimal quantity of product to be produced or purchased using the simplest and on the shelf classical EOQ model, the non-inclusion of conflicting economic realities as shortage and inflation has rendered its result quite uneconomical and hence the purpose for this study. Mathematical expression was developed for each of the cost components the sum of which become the total inventory model over the period (0,L) ((TIC(0,L)). L is planning horizon and TIC(0,L) is total inventory cost over a period of (0,L). Significant savings with increase in quantity was achieved based on deference in the varying price regime. With the assumptions considered and subject to the availability of reliable inventory cost element, the developed model is found to produce a feasible, and economic inventory stock-level with the numerical example of a material supply of a manufacturing company.

  14. The Fisher-KPP problem with doubly nonlinear diffusion

    NASA Astrophysics Data System (ADS)

    Audrito, Alessandro; Vázquez, Juan Luis

    2017-12-01

    The famous Fisher-KPP reaction-diffusion model combines linear diffusion with the typical KPP reaction term, and appears in a number of relevant applications in biology and chemistry. It is remarkable as a mathematical model since it possesses a family of travelling waves that describe the asymptotic behaviour of a large class solutions 0 ≤ u (x , t) ≤ 1 of the problem posed in the real line. The existence of propagation waves with finite speed has been confirmed in some related models and disproved in others. We investigate here the corresponding theory when the linear diffusion is replaced by the "slow" doubly nonlinear diffusion and we find travelling waves that represent the wave propagation of more general solutions even when we extend the study to several space dimensions. A similar study is performed in the critical case that we call "pseudo-linear", i.e., when the operator is still nonlinear but has homogeneity one. With respect to the classical model and the "pseudo-linear" case, the "slow" travelling waves exhibit free boundaries.

  15. Integrating the automatic and the controlled: Strategies in Semantic Priming in an Attractor Network with Latching Dynamics

    PubMed Central

    Lerner, Itamar; Bentin, Shlomo; Shriki, Oren

    2014-01-01

    Semantic priming has long been recognized to reflect, along with automatic semantic mechanisms, the contribution of controlled strategies. However, previous theories of controlled priming were mostly qualitative, lacking common grounds with modern mathematical models of automatic priming based on neural networks. Recently, we have introduced a novel attractor network model of automatic semantic priming with latching dynamics. Here, we extend this work to show how the same model can also account for important findings regarding controlled processes. Assuming the rate of semantic transitions in the network can be adapted using simple reinforcement learning, we show how basic findings attributed to controlled processes in priming can be achieved, including their dependency on stimulus onset asynchrony and relatedness proportion and their unique effect on associative, category-exemplar, mediated and backward prime-target relations. We discuss how our mechanism relates to the classic expectancy theory and how it can be further extended in future developments of the model. PMID:24890261

  16. On the role of visual experience in mathematical development: Evidence from blind mathematicians.

    PubMed

    Amalric, Marie; Denghien, Isabelle; Dehaene, Stanislas

    2018-04-01

    Advanced mathematical reasoning, regardless of domain or difficulty, activates a reproducible set of bilateral brain areas including intraparietal, inferior temporal and dorsal prefrontal cortex. The respective roles of genetics, experience and education in the development of this math-responsive network, however, remain unresolved. Here, we investigate the role of visual experience by studying the exceptional case of three professional mathematicians who were blind from birth (n=1) or became blind during childhood (n=2). Subjects were scanned with fMRI while they judged the truth value of spoken mathematical and nonmathematical statements. Blind mathematicians activated the classical network of math-related areas during mathematical reflection, similar to that found in a group of sighted professional mathematicians. Thus, brain networks for advanced mathematical reasoning can develop in the absence of visual experience. Additional activations were found in occipital cortex, even in individuals who became blind during childhood, suggesting that either mental imagery or a more radical repurposing of visual cortex may occur in blind mathematicians. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

  17. An Implementation of RC4+ Algorithm and Zig-zag Algorithm in a Super Encryption Scheme for Text Security

    NASA Astrophysics Data System (ADS)

    Budiman, M. A.; Amalia; Chayanie, N. I.

    2018-03-01

    Cryptography is the art and science of using mathematical methods to preserve message security. There are two types of cryptography, namely classical and modern cryptography. Nowadays, most people would rather use modern cryptography than classical cryptography because it is harder to break than the classical one. One of classical algorithm is the Zig-zag algorithm that uses the transposition technique: the original message is unreadable unless the person has the key to decrypt the message. To improve the security, the Zig-zag Cipher is combined with RC4+ Cipher which is one of the symmetric key algorithms in the form of stream cipher. The two algorithms are combined to make a super-encryption. By combining these two algorithms, the message will be harder to break by a cryptanalyst. The result showed that complexity of the combined algorithm is θ(n2 ), while the complexity of Zig-zag Cipher and RC4+ Cipher are θ(n2 ) and θ(n), respectively.

  18. Complexity for Survival of Living Systems

    NASA Technical Reports Server (NTRS)

    Zak, Michail

    2009-01-01

    A logical connection between the survivability of living systems and the complexity of their behavior (equivalently, mental complexity) has been established. This connection is an important intermediate result of continuing research on mathematical models that could constitute a unified representation of the evolution of both living and non-living systems. Earlier results of this research were reported in several prior NASA Tech Briefs articles, the two most relevant being Characteristics of Dynamics of Intelligent Systems (NPO- 21037), NASA Tech Briefs, Vol. 26, No. 12 (December 2002), page 48; and Self-Supervised Dynamical Systems (NPO- 30634) NASA Tech Briefs, Vol. 27, No. 3 (March 2003), page 72. As used here, living systems is synonymous with active systems and intelligent systems. The quoted terms can signify artificial agents (e.g., suitably programmed computers) or natural biological systems ranging from single-cell organisms at one extreme to the whole of human society at the other extreme. One of the requirements that must be satisfied in mathematical modeling of living systems is reconciliation of evolution of life with the second law of thermodynamics. In the approach followed in this research, this reconciliation is effected by means of a model, inspired partly by quantum mechanics, in which the quantum potential is replaced with an information potential. The model captures the most fundamental property of life - the ability to evolve from disorder to order without any external interference. The model incorporates the equations of classical dynamics, including Newton s equations of motion and equations for random components caused by uncertainties in initial conditions and by Langevin forces. The equations of classical dynamics are coupled with corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces that are gradients of the information potential, which, in turn, is a function of the probability densities. The probability densities are associated with mental images both self-image and nonself images (images of external objects that can include other agents). The evolution of the probability densities represents mental dynamics. Then the interaction between the physical and metal aspects of behavior is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. The interaction of a system with its self and nonself images affords unlimited capacity for increase of complexity. There is a biological basis for this model of mental dynamics in the discovery of mirror neurons that learn by imitation. The levels of complexity attained by use of this model match those observed in living systems. To establish a mechanism for increasing the complexity of dynamics of an active system, the model enables exploitation of a chain of reflections exemplified by questions of the form, "What do you think that I think that you think...?" Mathematically, each level of reflection is represented in the form of an attractor performing the corresponding level of abstraction with more details removed from higher levels. The model can be used to describe the behaviors, not only of biological systems, but also of ecological, social, and economics ones.

  19. Example-Based Learning in Heuristic Domains: A Cognitive Load Theory Account

    ERIC Educational Resources Information Center

    Renkl, Alexander; Hilbert, Tatjana; Schworm, Silke

    2009-01-01

    One classical instructional effect of cognitive load theory (CLT) is the worked-example effect. Although the vast majority of studies have focused on well-structured and algorithmic sub-domains of mathematics or physics, more recent studies have also analyzed learning with examples from complex domains in which only heuristic solution strategies…

  20. Advanced classical thermodynamics

    NASA Astrophysics Data System (ADS)

    Emanuel, George

    The theoretical and mathematical foundations of thermodynamics are presented in an advanced text intended for graduate engineering students. Chapters are devoted to definitions and postulates, the fundamental equation, equilibrium, the application of Jacobian theory to thermodynamics, the Maxwell equations, stability, the theory of real gases, critical-point theory, and chemical thermodynamics. Diagrams, graphs, tables, and sample problems are provided.

  1. Adolescents' Homework Performance in Mathematics and Science: Personal Factors and Teaching Practices

    ERIC Educational Resources Information Center

    Fernández-Alonso, Rubén; Suárez-Álvarez, Javier; Muñiz, José

    2015-01-01

    Classical educational research provides empirical evidence of the positive effect of doing homework on academic results. Nonetheless, when this effect is analyzed in detail there are inconsistent, and in some cases, contradictory results. The central aim of this study was to systematically investigate the effect of homework on performance of…

  2. The Electrostatic Potential of a Uniformly Charged Ring

    ERIC Educational Resources Information Center

    Ciftja, Orion; Babineaux, Arica; Hafeez, Nadia

    2009-01-01

    When faced with mathematical methods, undergraduate students have difficulty in grasping the reality of various approaches and special functions. It is only when they take a more specialized course such as classical electromagnetism that they finally see the connection. A problem that we believe illustrates very well the depth and variety of…

  3. MendelWeb: An Electronic Science/Math/History Resource for the WWW.

    ERIC Educational Resources Information Center

    Blumberg, Roger B.

    This paper describes a hypermedia resource, called MendelWeb that integrates elementary biology, discrete mathematics, and the history of science. MendelWeb is constructed from Gregor Menders 1865 paper, "Experiments in Plant Hybridization". An English translation of Mendel's paper, which is considered to mark the birth of classical and…

  4. Prior Knowledge of Mechanics amongst First Year Engineering Students

    ERIC Educational Resources Information Center

    Clements, Dick

    2007-01-01

    In the last 25 years, A-level Mathematics syllabi have changed very considerably, introducing a broader range of application areas but reducing the previous emphasis on classical mechanics. This article describes a baseline survey undertaken to establish in detail the entry levels in mechanics for the cohort of students entering Engineering…

  5. Developing a Questionnaire to Assess the Probability Content Knowledge of Prospective Primary School Teachers

    ERIC Educational Resources Information Center

    Gómez-Torres, Emilse; Batanero, Carmen; Díaz, Carmen; Contreras, José Miguel

    2016-01-01

    In this paper we describe the development of a questionnaire designed to assess the probability content knowledge of prospective primary school teachers. Three components of mathematical knowledge for teaching and three different meanings of probability (classical, frequentist and subjective) are considered. The questionnaire content is based on…

  6. Collateral Learning and Mathematical Education of Teachers

    ERIC Educational Resources Information Center

    Abramovich, Sergei

    2012-01-01

    This article explores the notion of collateral learning in the context of classic ideas about the summation of powers of the first "n" counting numbers. Proceeding from the well-known legend about young Gauss, this article demonstrates the value of reflection under the guidance of "the more knowledgeable other" as a pedagogical method of making…

  7. Particle in a Box: An Experiential Environment for Learning Introductory Quantum Mechanics

    ERIC Educational Resources Information Center

    Anupam, Aditya; Gupta, Ridhima; Naeemi, Azad; JafariNaimi, Nassim

    2018-01-01

    Quantum mechanics (QMs) is a foundational subject in many science and engineering fields. It is difficult to teach, however, as it requires a fundamental revision of the assumptions and laws of classical physics and probability. Furthermore, introductory QM courses and texts predominantly focus on the mathematical formulations of the subject and…

  8. Solving Optimization Problems with Dynamic Geometry Software: The Airport Problem

    ERIC Educational Resources Information Center

    Contreras, José

    2014-01-01

    This paper describes how the author's students (in-service and pre-service secondary mathematics teachers) enrolled in college geometry courses use the Geometers' Sketchpad (GSP) to gain insight to formulate, confirm, test, and refine conjectures to solve the classical airport problem for triangles. The students are then provided with strategic…

  9. Understanding the antiangiogenic effect of metronomic chemotherapy through a simple mathematical model

    NASA Astrophysics Data System (ADS)

    Rodrigues, Diego S.; Mancera, Paulo F. A.; Pinho, Suani T. R.

    2016-12-01

    Despite the current and increasingly successful fight against cancer, there are some important questions concerning the efficiency of its treatment - in particular, the design of oncology chemotherapy protocols. Seeking efficiency, schedules based on more frequent, low-doses of drugs, known as metronomic chemotherapy, have been proposed as an alternative to the classical standard protocol of chemotherapy administration. The in silico approach may be very useful for providing a comparative analysis of these two kinds of protocols. In so doing, we found that metronomic schedules are more effective in eliminating tumour cells mainly due to their chemotherapeutic action on endothelial cells and that more frequent, low drug doses also entail outcomes in which the survival time of patient is increased.

  10. Fractional calculus in hydrologic modeling: A numerical perspective

    PubMed Central

    Benson, David A.; Meerschaert, Mark M.; Revielle, Jordan

    2013-01-01

    Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Lévy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus. PMID:23524449

  11. Physical models of biological information and adaptation.

    PubMed

    Stuart, C I

    1985-04-07

    The bio-informational equivalence asserts that biological processes reduce to processes of information transfer. In this paper, that equivalence is treated as a metaphor with deeply anthropomorphic content of a sort that resists constitutive-analytical definition, including formulation within mathematical theories of information. It is argued that continuance of the metaphor, as a quasi-theoretical perspective in biology, must entail a methodological dislocation between biological and physical science. It is proposed that a general class of functions, drawn from classical physics, can serve to eliminate the anthropomorphism. Further considerations indicate that the concept of biological adaptation is central to the general applicability of the informational idea in biology; a non-anthropomorphic treatment of adaptive phenomena is suggested in terms of variational principles.

  12. Theory of Neutron Chain Reactions: Extracts from Volume I, Diffusion and Slowing Down of Neutrons: Chapter I. Elementary Theory of Neutron Diffusion. Chapter II. Second Order Diffusion Theory. Chapter III. Slowing Down of Neutrons

    DOE R&D Accomplishments Database

    Weinberg, Alvin M.; Noderer, L. C.

    1951-05-15

    The large scale release of nuclear energy in a uranium fission chain reaction involves two essentially distinct physical phenomena. On the one hand there are the individual nuclear processes such as fission, neutron capture, and neutron scattering. These are essentially quantum mechanical in character, and their theory is non-classical. On the other hand, there is the process of diffusion -- in particular, diffusion of neutrons, which is of fundamental importance in a nuclear chain reaction. This process is classical; insofar as the theory of the nuclear chain reaction depends on the theory of neutron diffusion, the mathematical study of chain reactions is an application of classical, not quantum mechanical, techniques.

  13. The origin of three-cocycles in quantum field theory

    NASA Astrophysics Data System (ADS)

    Carey, A. L.

    1987-08-01

    When quantising a classical field theory it is not automatic that a group of symmetries of the classical system is preserved as a symmetry of the quantum system. Apart from the phenomenon of symmetry breaking it can also happen (as in Faddeev's Gauss law anomaly) that only an extension of the classical group acts as a symmetry group of the quantum system. We show here that rather than signalling a failure of the associative law as has been suggested in the literature, the occurrence of a non-trivial three-cocycle on the local gauge group is an ``anomaly'' or obstruction to the existence of an extension of the local gauge group acting as a symmetry group of the quantum system. Permanent address: Department of Pure Mathematics, University of Adelaide, G.P.O. Box 498, Adelaide, SA 5000, Australia.

  14. Chaotic Behaviuor of the Navier-Stokes Solutions, Gyroscopes and Storm Surging

    NASA Astrophysics Data System (ADS)

    Tchiguirinskaia, Ioulia; Schertzer, Daniel

    2015-04-01

    Storm surges are phenomena inflicting wide damages all over the planet. Unfortunately they are badly represented in classical forecast model schemes because their multiscale nature is at odd with the scale truncation of these models. For similar reasons, classical data analysis often compelled to considered them as 'outliers' of the normal atmospheric activity, whereas as in fact they result from the same physical mechanisms that create less extreme behavior. A better representation of storm surges requires a multicale understanding of how a cascade of seemingly harmless instabilities can generate major ones. This correspond to the conjectured, outstanding intermittency.of the chaotic behaviour of the Navier-Stokes solutions. However, our limited, mathematical understanding of the Navier-Stokes equations prevent us to directly use them to investigate this question. We therefore use the most relevant cascade model to theoretically tackle this question of intermittency, i.e. the Scaling Gyroscopes Cascade (SGC). Indeed, this model is obtained with the help of a non trivial tree-decomposition of the Lie structure of the Navier-Stokes equations. the SGC model is deduced from these equations by preserving only a certain type of direct interactions, while the resulting indirect interactions are built dynamically along the tree-structure of the cascade. Because its fundamental element corresponds to a 'top' -i.e., an object with which almost anyone began to discover the puzzling nonlinear properties of rotation!- the SGC model remains rather simple, yet not simplistic! In particular, the SGC model enables us to investigate in details the occurrence of the critical singularity of a first order multifractal phase transition, which theoretically define storm surges. Overall, these theoretical findings could significantly reduce numerous uncertainties of environmental risk assessments.

  15. VirtualLeaf: an open-source framework for cell-based modeling of plant tissue growth and development.

    PubMed

    Merks, Roeland M H; Guravage, Michael; Inzé, Dirk; Beemster, Gerrit T S

    2011-02-01

    Plant organs, including leaves and roots, develop by means of a multilevel cross talk between gene regulation, patterned cell division and cell expansion, and tissue mechanics. The multilevel regulatory mechanisms complicate classic molecular genetics or functional genomics approaches to biological development, because these methodologies implicitly assume a direct relation between genes and traits at the level of the whole plant or organ. Instead, understanding gene function requires insight into the roles of gene products in regulatory networks, the conditions of gene expression, etc. This interplay is impossible to understand intuitively. Mathematical and computer modeling allows researchers to design new hypotheses and produce experimentally testable insights. However, the required mathematics and programming experience makes modeling poorly accessible to experimental biologists. Problem-solving environments provide biologically intuitive in silico objects ("cells", "regulation networks") required for setting up a simulation and present those to the user in terms of familiar, biological terminology. Here, we introduce the cell-based computer modeling framework VirtualLeaf for plant tissue morphogenesis. The current version defines a set of biologically intuitive C++ objects, including cells, cell walls, and diffusing and reacting chemicals, that provide useful abstractions for building biological simulations of developmental processes. We present a step-by-step introduction to building models with VirtualLeaf, providing basic example models of leaf venation and meristem development. VirtualLeaf-based models provide a means for plant researchers to analyze the function of developmental genes in the context of the biophysics of growth and patterning. VirtualLeaf is an ongoing open-source software project (http://virtualleaf.googlecode.com) that runs on Windows, Mac, and Linux.

  16. On the stability of the exact solutions of the dual-phase lagging model of heat conduction.

    PubMed

    Ordonez-Miranda, Jose; Alvarado-Gil, Juan Jose

    2011-04-13

    The dual-phase lagging (DPL) model has been considered as one of the most promising theoretical approaches to generalize the classical Fourier law for heat conduction involving short time and space scales. Its applicability, potential, equivalences, and possible drawbacks have been discussed in the current literature. In this study, the implications of solving the exact DPL model of heat conduction in a three-dimensional bounded domain solution are explored. Based on the principle of causality, it is shown that the temperature gradient must be always the cause and the heat flux must be the effect in the process of heat transfer under the dual-phase model. This fact establishes explicitly that the single- and DPL models with different physical origins are mathematically equivalent. In addition, taking into account the properties of the Lambert W function and by requiring that the temperature remains stable, in such a way that it does not go to infinity when the time increases, it is shown that the DPL model in its exact form cannot provide a general description of the heat conduction phenomena.

  17. Application of different variants of the BEM in numerical modeling of bioheat transfer problems.

    PubMed

    Majchrzak, Ewa

    2013-09-01

    Heat transfer processes proceeding in the living organisms are described by the different mathematical models. In particular, the typical continuous model of bioheat transfer bases on the most popular Pennes equation, but the Cattaneo-Vernotte equation and the dual phase lag equation are also used. It should be pointed out that in parallel are also examined the vascular models, and then for the large blood vessels and tissue domain the energy equations are formulated separately. In the paper the different variants of the boundary element method as a tool of numerical solution of bioheat transfer problems are discussed. For the steady state problems and the vascular models the classical BEM algorithm and also the multiple reciprocity BEM are presented. For the transient problems connected with the heating of tissue, the various tissue models are considered for which the 1st scheme of the BEM, the BEM using discretization in time and the general BEM are applied. Examples of computations illustrate the possibilities of practical applications of boundary element method in the scope of bioheat transfer problems.

  18. Quantum-like model of unconscious–conscious dynamics

    PubMed Central

    Khrennikov, Andrei

    2015-01-01

    We present a quantum-like model of sensation–perception dynamics (originated in Helmholtz theory of unconscious inference) based on the theory of quantum apparatuses and instruments. We illustrate our approach with the model of bistable perception of a particular ambiguous figure, the Schröder stair. This is a concrete model for unconscious and conscious processing of information and their interaction. The starting point of our quantum-like journey was the observation that perception dynamics is essentially contextual which implies impossibility of (straightforward) embedding of experimental statistical data in the classical (Kolmogorov, 1933) framework of probability theory. This motivates application of nonclassical probabilistic schemes. And the quantum formalism provides a variety of the well-approved and mathematically elegant probabilistic schemes to handle results of measurements. The theory of quantum apparatuses and instruments is the most general quantum scheme describing measurements and it is natural to explore it to model the sensation–perception dynamics. In particular, this theory provides the scheme of indirect quantum measurements which we apply to model unconscious inference leading to transition from sensations to perceptions. PMID:26283979

  19. In vitro ovine articular chondrocyte proliferation: experiments and modelling.

    PubMed

    Mancuso, L; Liuzzo, M I; Fadda, S; Pisu, M; Cincotti, A; Arras, M; La Nasa, G; Concas, A; Cao, G

    2010-06-01

    This study focuses on analysis of in vitro cultures of chondrocytes from ovine articular cartilage. Isolated cells were seeded in Petri dishes, then expanded to confluence and phenotypically characterized by flow cytometry. The sigmoidal temporal profile of total counts was obtained by classic haemocytometry and corresponding cell size distributions were measured electronically using a Coulter Counter. A mathematical model recently proposed (1) was adopted for quantitative interpretation of these experimental data. The model is based on a 1-D (that is, mass-structured), single-staged population balance approach capable of taking into account contact inhibition at confluence. The model's parameters were determined by fitting measured total cell counts and size distributions. Model reliability was verified by predicting cell proliferation counts and corresponding size distributions at culture times longer than those used when tuning the model's parameters. It was found that adoption of cell mass as the intrinsic characteristic of a growing chondrocyte population enables sigmoidal temporal profiles of total counts in the Petri dish, as well as cell size distributions at 'balanced growth', to be adequately predicted.

  20. PREFACE: X Mexican School on Gravitation and Mathematical Physics: ''Reaching a Century: Classical and Modified General Relativity's Attempts to explain de evolution of the Universe''

    NASA Astrophysics Data System (ADS)

    Bárcenas, R. B.; Hernández, H. H. H.; Sabido, M.

    2015-11-01

    The collection of papers in this volume was presented during the X Mexican School on Gravitation and Mathematical Physics, which was held in Playa del Carmen, Quintana Roo, México, December 1-5, 2014. The Mexican School on Gravitation and Mathematical Physics is a series of conferences sponsored by the Mexican Physical Society that started in 1994 with the purposes of discussing and exchanging current ideas in gravitational physics. Each Mexican School has been devoted to a particular subject, and these have included supergravity, branes, black holes, the early Universe, observational cosmology, quantum gravity and numerical relativity. In this ocasion the theme of the school was Reaching a Century: Classical and Modified General Relativity's Attempts to explain the evolution of the Universe, which focused on the discussion of classical and modified aspects of general relativity. Following our previous Schools, world leaders in the field were invited to give courses and plenary lectures. More specialized talks were also presented in parallel sessions, and some of them have been included in these proceedings. The contributions in this volume have been reviewed and represent some of the courses, plenary talks and contributed talks presented during our X School. We are indebted to the contributors of these proceedings as well as to the rest of the participants in our Mexican School all for making of it a complete success. As for financial support we should mention the Mexican National Science and Technology Council (CONACyT), the Royal Society of London (UK), the Mexican Physical Society (SMF), as well as several Institutions including: Centro de Investigación y Estudios Avanzados (CINVESTAV), Universidad Autónoma Metropolitana Iztapalapa (UAM-I), Universidad de Guanajuato (UG), and Universidad Nacional Autónoma de México (UNAM).

  1. A Conserving Discretization for the Free Boundary in a Two-Dimensional Stefan Problem

    NASA Astrophysics Data System (ADS)

    Segal, Guus; Vuik, Kees; Vermolen, Fred

    1998-03-01

    The dissolution of a disk-likeAl2Cuparticle is considered. A characteristic property is that initially the particle has a nonsmooth boundary. The mathematical model of this dissolution process contains a description of the particle interface, of which the position varies in time. Such a model is called a Stefan problem. It is impossible to obtain an analytical solution for a general two-dimensional Stefan problem, so we use the finite element method to solve this problem numerically. First, we apply a classical moving mesh method. Computations show that after some time steps the predicted particle interface becomes very unrealistic. Therefore, we derive a new method for the displacement of the free boundary based on the balance of atoms. This method leads to good results, also, for nonsmooth boundaries. Some numerical experiments are given for the dissolution of anAl2Cuparticle in anAl-Cualloy.

  2. [Diffusion and diffusion-osmosis models of the charged macromolecule transfer in barriers of biosystems].

    PubMed

    Varakin, A I; Mazur, V V; Arkhipova, N V; Serianov, Iu V

    2009-01-01

    Mathematical models of the transfer of charged macromolecules have been constructed on the basis of the classical equations of electromigration diffusion of Helmholtz-Smolukhovskii, Goldman, and Goldman-Hodgkin-Katz. It was shown that ion transfer in placental (mimicking lipid-protein barriers) and muscle barriers occurs by different mechanisms. In placental barriers, the electromigration diffusion occurs along lipid-protein channels formed due to the conformational deformation of phospholipid and protein molecules with the coefficients of diffusion D = (2.6-3.6) x 10(-8) cm2/s. The transfer in muscle barriers is due to the migration across charged interfibrillar channels with the negative diffusion activation energy, which is explained by changes in the structure of muscle fibers and expenditures of thermal energy for the extrusion of Cl- from channel walls with the diffusion coefficient D = (6.0-10.0) x 10(-6) cm2/s.

  3. A New TS Algorithm for Solving Low-Carbon Logistics Vehicle Routing Problem with Split Deliveries by Backpack-From a Green Operation Perspective.

    PubMed

    Xia, Yangkun; Fu, Zhuo; Tsai, Sang-Bing; Wang, Jiangtao

    2018-05-10

    In order to promote the development of low-carbon logistics and economize logistics distribution costs, the vehicle routing problem with split deliveries by backpack is studied. With the help of the model of classical capacitated vehicle routing problem, in this study, a form of discrete split deliveries was designed in which the customer demand can be split only by backpack. A double-objective mathematical model and the corresponding adaptive tabu search (TS) algorithm were constructed for solving this problem. By embedding the adaptive penalty mechanism, and adopting the random neighborhood selection strategy and reinitialization principle, the global optimization ability of the new algorithm was enhanced. Comparisons with the results in the literature show the effectiveness of the proposed algorithm. The proposed method can save the costs of low-carbon logistics and reduce carbon emissions, which is conducive to the sustainable development of low-carbon logistics.

  4. Improved color constancy in honey bees enabled by parallel visual projections from dorsal ocelli.

    PubMed

    Garcia, Jair E; Hung, Yu-Shan; Greentree, Andrew D; Rosa, Marcello G P; Endler, John A; Dyer, Adrian G

    2017-07-18

    How can a pollinator, like the honey bee, perceive the same colors on visited flowers, despite continuous and rapid changes in ambient illumination and background color? A hundred years ago, von Kries proposed an elegant solution to this problem, color constancy, which is currently incorporated in many imaging and technological applications. However, empirical evidence on how this method can operate on animal brains remains tenuous. Our mathematical modeling proposes that the observed spectral tuning of simple ocellar photoreceptors in the honey bee allows for the necessary input for an optimal color constancy solution to most natural light environments. The model is fully supported by our detailed description of a neural pathway allowing for the integration of signals originating from the ocellar photoreceptors to the information processing regions in the bee brain. These findings reveal a neural implementation to the classic color constancy problem that can be easily translated into artificial color imaging systems.

  5. A flooding algorithm for multirobot exploration.

    PubMed

    Cabrera-Mora, Flavio; Xiao, Jizhong

    2012-06-01

    In this paper, we present a multirobot exploration algorithm that aims at reducing the exploration time and to minimize the overall traverse distance of the robots by coordinating the movement of the robots performing the exploration. Modeling the environment as a tree, we consider a coordination model that restricts the number of robots allowed to traverse an edge and to enter a vertex during each step. This coordination is achieved in a decentralized manner by the robots using a set of active landmarks that are dropped by them at explored vertices. We mathematically analyze the algorithm on trees, obtaining its main properties and specifying its bounds on the exploration time. We also define three metrics of performance for multirobot algorithms. We simulate and compare the performance of this new algorithm with those of our multirobot depth first search (MR-DFS) approach presented in our recent paper and classic single-robot DFS.

  6. Some new ideas for the study of the complex spectral line profiles of hot emission stars and quasars

    NASA Astrophysics Data System (ADS)

    Danezis, E.

    2013-01-01

    Some Hot Emission Stars and AGNs present peculiar spectral line profiles which are due to DACs and SACs phenomena. The origin and the mechanisms which are responsible for the creation of DACs/SACs is an important problem that has been studied by many researchers. This paper is a review of our efforts to study the origin and the mechanisms of these phenomena. At first we present a theoretic ad hoc picture for the structure of the plasma that surrounds the specific category of hot emission stars that present DACs or SACs. Then we present the mathematical model that we constructed, which is based on the properties of the above ad hoc theoretical structure. Finally, we present some results from our statistical studies that prove the consistency of our model with the classical physical theory.

  7. New efficient optimizing techniques for Kalman filters and numerical weather prediction models

    NASA Astrophysics Data System (ADS)

    Famelis, Ioannis; Galanis, George; Liakatas, Aristotelis

    2016-06-01

    The need for accurate local environmental predictions and simulations beyond the classical meteorological forecasts are increasing the last years due to the great number of applications that are directly or not affected: renewable energy resource assessment, natural hazards early warning systems, global warming and questions on the climate change can be listed among them. Within this framework the utilization of numerical weather and wave prediction systems in conjunction with advanced statistical techniques that support the elimination of the model bias and the reduction of the error variability may successfully address the above issues. In the present work, new optimization methods are studied and tested in selected areas of Greece where the use of renewable energy sources is of critical. The added value of the proposed work is due to the solid mathematical background adopted making use of Information Geometry and Statistical techniques, new versions of Kalman filters and state of the art numerical analysis tools.

  8. Maintenance of Mitochondrial Oxygen Homeostasis by Cosubstrate Compensation

    PubMed Central

    Kueh, Hao Yuan; Niethammer, Philipp; Mitchison, Timothy J.

    2013-01-01

    Mitochondria maintain a constant rate of aerobic respiration over a wide range of oxygen levels. However, the control strategies underlying oxygen homeostasis are still unclear. Using mathematical modeling, we found that the mitochondrial electron transport chain (ETC) responds to oxygen level changes by undergoing compensatory changes in reduced electron carrier levels. This emergent behavior, which we named cosubstrate compensation (CSC), enables the ETC to maintain homeostasis over a wide of oxygen levels. When performing CSC, our ETC models recapitulated a classic scaling relationship discovered by Chance [Chance B (1965) J. Gen. Physiol. 49:163-165] relating the extent of oxygen homeostasis to the kinetics of mitochondrial electron transport. Analysis of an in silico mitochondrial respiratory system further showed evidence that CSC constitutes the dominant control strategy for mitochondrial oxygen homeostasis during active respiration. Our findings indicate that CSC constitutes a robust control strategy for homeostasis and adaptation in cellular biochemical networks. PMID:23528093

  9. Development of a percutaneous penetration predictive model by SR-FTIR.

    PubMed

    Jungman, E; Laugel, C; Rutledge, D N; Dumas, P; Baillet-Guffroy, A

    2013-01-30

    This work focused on developing a new evaluation criterion of percutaneous penetration, in complement to Log Pow and MW and based on high spatial resolution Fourier transformed infrared (FTIR) microspectroscopy with a synchrotron source (SR-FTIR). Classic Franz cell experiments were run and after 22 h molecule distribution in skin was determined either by HPLC or by SR-FTIR. HPLC data served as reference. HPLC and SR-FTIR results were compared and a new predictive criterion based from SR-FTIR results, named S(index), was determined using a multi-block data analysis technique (ComDim). A predictive cartography of the distribution of molecules in the skin was built and compared to OECD predictive cartography. This new criterion S(index) and the cartography using SR-FTIR/HPLC results provides relevant information for risk analysis regarding prediction of percutaneous penetration and could be used to build a new mathematical model. Copyright © 2012 Elsevier B.V. All rights reserved.

  10. Validation of Blockage Interference Corrections in the National Transonic Facility

    NASA Technical Reports Server (NTRS)

    Walker, Eric L.

    2007-01-01

    A validation test has recently been constructed for wall interference methods as applied to the National Transonic Facility (NTF). The goal of this study was to begin to address the uncertainty of wall-induced-blockage interference corrections, which will make it possible to address the overall quality of data generated by the facility. The validation test itself is not specific to any particular modeling. For this present effort, the Transonic Wall Interference Correction System (TWICS) as implemented at the NTF is the mathematical model being tested. TWICS uses linear, potential boundary conditions that must first be calibrated. These boundary conditions include three different classical, linear. homogeneous forms that have been historically used to approximate the physical behavior of longitudinally slotted test section walls. Results of the application of the calibrated wall boundary conditions are discussed in the context of the validation test.

  11. A Novel Discrete Differential Evolution Algorithm for the Vehicle Routing Problem in B2C E-Commerce

    NASA Astrophysics Data System (ADS)

    Xia, Chao; Sheng, Ying; Jiang, Zhong-Zhong; Tan, Chunqiao; Huang, Min; He, Yuanjian

    2015-12-01

    In this paper, a novel discrete differential evolution (DDE) algorithm is proposed to solve the vehicle routing problems (VRP) in B2C e-commerce, in which VRP is modeled by the incomplete graph based on the actual urban road system. First, a variant of classical VRP is described and a mathematical programming model for the variant is given. Second, the DDE is presented, where individuals are represented as the sequential encoding scheme, and a novel reparation operator is employed to repair the infeasible solutions. Furthermore, a FLOYD operator for dealing with the shortest route is embedded in the proposed DDE. Finally, an extensive computational study is carried out in comparison with the predatory search algorithm and genetic algorithm, and the results show that the proposed DDE is an effective algorithm for VRP in B2C e-commerce.

  12. Theory and applications survey of decentralized control methods

    NASA Technical Reports Server (NTRS)

    Athans, M.

    1975-01-01

    A nonmathematical overview is presented of trends in the general area of decentralized control strategies which are suitable for hierarchical systems. Advances in decentralized system theory are closely related to advances in the so-called stochastic control problem with nonclassical information pattern. The basic assumptions and mathematical tools pertaining to the classical stochastic control problem are outlined. Particular attention is devoted to pitfalls in the mathematical problem formulation for decentralized control. Major conclusions are that any purely deterministic approach to multilevel hierarchical dynamic systems is unlikely to lead to realistic theories or designs, that the flow of measurements and decisions in a decentralized system should not be instantaneous and error-free, and that delays in information exchange in a decentralized system lead to reasonable approaches to decentralized control. A mathematically precise notion of aggregating information is not yet available.

  13. Horace Lamb and the circumstances of his appointment at Owens College

    PubMed Central

    Launder, Brian

    2013-01-01

    This paper examines a succession of incidents at a critical juncture in the life of Professor Horace Lamb FRS, a highly regarded classical fluid mechanicist, who, over a period of some 35 years at Manchester, made notable contributions in research, in education and in wise administration at both national and university levels. Drawing on archived documents from the universities of Manchester and Adelaide, the article presents the unusual sequence of events that led to his removing from Adelaide, South Australia, where he had served for nine years as the Elder Professor of Mathematics, to Manchester. In 1885 he was initially appointed to the vacant Chair of Pure Mathematics at Owens College and then, in 1888, as an outcome of his proposal for rearranging professorial responsibilities, to the Beyer Professorship of Pure and Applied Mathematics.

  14. Mathematization Competencies of Pre-Service Elementary Mathematics Teachers in the Mathematical Modelling Process

    ERIC Educational Resources Information Center

    Yilmaz, Suha; Tekin-Dede, Ayse

    2016-01-01

    Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified…

  15. From Newton to Einstein; Ask the physicist about mechanics and relativity

    NASA Astrophysics Data System (ADS)

    Baker, F. Todd

    2014-12-01

    Since 2006 the author has run a web site, WWW.AskThePhysicist.com, where he answers questions about physics. The site is not intended for answering highly technical questions; rather the purpose is to answer, with as little mathematics and formalism as possible, questions from intelligent and curious laypersons. This book is about classical mechanics. Usually `classical' calls to mind Newtonian mechanics and that is indeed where modern physics started. The bulk of the book is devoted to sections which will contain mainly categorized groups of Q&As from the web site, sort of a Best of Ask the Physicist.

  16. Exact analytical solution of a classical Josephson tunnel junction problem

    NASA Astrophysics Data System (ADS)

    Kuplevakhsky, S. V.; Glukhov, A. M.

    2010-10-01

    We give an exact and complete analytical solution of the classical problem of a Josephson tunnel junction of arbitrary length W ɛ(0,∞) in the presence of external magnetic fields and transport currents. Contrary to a wide-spread belief, the exact analytical solution unambiguously proves that there is no qualitative difference between so-called "small" (W≪1) and "large" junctions (W≫1). Another unexpected physical implication of the exact analytical solution is the existence (in the current-carrying state) of unquantized Josephson vortices carrying fractional flux and located near one of the edges of the junction. We also refine the mathematical definition of critical transport current.

  17. An Arbitrary First Order Theory Can Be Represented by a Program: A Theorem

    NASA Technical Reports Server (NTRS)

    Hosheleva, Olga

    1997-01-01

    How can we represent knowledge inside a computer? For formalized knowledge, classical logic seems to be the most adequate tool. Classical logic is behind all formalisms of classical mathematics, and behind many formalisms used in Artificial Intelligence. There is only one serious problem with classical logic: due to the famous Godel's theorem, classical logic is algorithmically undecidable; as a result, when the knowledge is represented in the form of logical statements, it is very difficult to check whether, based on this statement, a given query is true or not. To make knowledge representations more algorithmic, a special field of logic programming was invented. An important portion of logic programming is algorithmically decidable. To cover knowledge that cannot be represented in this portion, several extensions of the decidable fragments have been proposed. In the spirit of logic programming, these extensions are usually introduced in such a way that even if a general algorithm is not available, good heuristic methods exist. It is important to check whether the already proposed extensions are sufficient, or further extensions is necessary. In the present paper, we show that one particular extension, namely, logic programming with classical negation, introduced by M. Gelfond and V. Lifschitz, can represent (in some reasonable sense) an arbitrary first order logical theory.

  18. Moving-Boundary Problems Associated with Lyopreservation

    NASA Astrophysics Data System (ADS)

    Gruber, Christopher Andrew

    The work presented in this Dissertation is motivated by research into the preservation of biological specimens by way of vitrification, a technique known as lyopreservation. The operative principle behind lyopreservation is that a glassy material forms as a solution of sugar and water is desiccated. The microstructure of this glass impedes transport within the material, thereby slowing metabolism and effectively halting the aging processes in a biospecimen. This Dissertation is divided into two segments. The first concerns the nature of diffusive transport within a glassy state. Experimental studies suggest that diffusion within a glass is anomalously slow. Scaled Brownian motion (SBM) is proposed as a mathematical model which captures the qualitative features of anomalously slow diffusion while minimizing computational expense. This model is applied to several moving-boundary problems and the results are compared to a more well-established model, fractional anomalous diffusion (FAD). The virtues of SBM are based on the model's relative mathematical simplicity: the governing equation under FAD dynamics involves a fractional derivative operator, which precludes the use of analytical methods in almost all circumstances and also entails great computational expense. In some geometries, SBM allows similarity solutions, though computational methods are generally required. The use of SBM as an approximation to FAD when a system is "nearly classical'' is also explored. The second portion of this Dissertation concerns spin-drying, which is an experimental approach to biopreservation in a laboratory setting. A biospecimen is adhered to a glass wafer and this substrate is covered with sugar solution and rapidly spun on a turntable while water is evaporated from the film surface. The mathematical model for the spin-drying process includes diffusion, viscous fluid flow, and evaporation, among other contributions to the dynamics. Lubrication theory is applied to the model and an expansion in orthogonal polynomials is applied. The resulting system of equations is solved computationally. The influence of various experimental parameters upon the system dynamics is investigated, particularly the role of the spin rate. A convergence study of the solution verifies that the polynomial expansion method yields accurate results.

  19. On the Relation between Mathematics, Natural Sciences, and Scientific Inquiry

    NASA Astrophysics Data System (ADS)

    Christianto, Victor; Smarandache, Florentin

    2011-10-01

    In this article, we will shortly review a few old thoughts and recent thoughts on the relation between Mathematics and the Natural Sciences. Of course, the classic references to this open problem will include Wigner's paper (1964); a more recent review article is Darvas (2008). But it appears that this issue is partly on the domain of natural philosophy and also philosophy of inquiry. Therefore we will begin with a review on some known thoughts of Kant, Bacon, Popper, etc. Our hope here is to find out clues to reveal the hidden structure of Nature, just as what Planck did a century ago.

  20. Practical results from a mathematical analysis of guard patrols

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

    Indusi, Joseph P.

    1978-12-01

    Using guard patrols as a primary detection mechanism is not generally viewed as a highly efficient detection method when compared to electronic means. Many factors such as visibility, alertness, and the space-time coincidence of guard and adversary presence all have an effect on the probability of detection. Mathematical analysis of the guard patrol detection problem is related to that of classical search theory originally developed for naval search operations. The results of this analysis tend to support the current practice of using guard forces to assess and respond to previously detected intrusions and not as the primary detection mechanism. 6more » refs.« less

  1. Graph Structure Theory: Proceedings of a Joint Summer Research Conference on Graph Minors Held June 22 to July 5, 1991, at the University of Washington, Seattle. Contemporary Mathematics 147

    DTIC Science & Technology

    1991-01-01

    aspects of classical field theory, 1992 131 L A. Bokut’, Yu. L Ershov, and A. I. Kostrikin, Editors, Proceedings of the International Conference on Algebra...should be addressed to the Manager of Editorial Services , American Mathematical Society, P.O. Box 6248, Providence, Rhode Island 02940-6248. The...dominant edges in T, and b(T) as the number of dominant edges not in T, for the fixed enumeration U. In [2] a(T) is called the " internal activity" and b(T

  2. Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

    ERIC Educational Resources Information Center

    Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem

    2014-01-01

    Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…

  3. Elementary Preservice Teachers' and Elementary Inservice Teachers' Knowledge of Mathematical Modeling

    ERIC Educational Resources Information Center

    Schwerdtfeger, Sara

    2017-01-01

    This study examined the differences in knowledge of mathematical modeling between a group of elementary preservice teachers and a group of elementary inservice teachers. Mathematical modeling has recently come to the forefront of elementary mathematics classrooms because of the call to add mathematical modeling tasks in mathematics classes through…

  4. A Case Study of Teachers' Development of Well-Structured Mathematical Modelling Activities

    ERIC Educational Resources Information Center

    Stohlmann, Micah; Maiorca, Cathrine; Allen, Charlie

    2017-01-01

    This case study investigated how three teachers developed mathematical modelling activities integrated with content standards through participation in a course on mathematical modelling. The class activities involved experiencing a mathematical modelling activity, reading and rating example mathematical modelling activities, reading articles about…

  5. A polynomial-chaos-expansion-based building block approach for stochastic analysis of photonic circuits

    NASA Astrophysics Data System (ADS)

    Waqas, Abi; Melati, Daniele; Manfredi, Paolo; Grassi, Flavia; Melloni, Andrea

    2018-02-01

    The Building Block (BB) approach has recently emerged in photonic as a suitable strategy for the analysis and design of complex circuits. Each BB can be foundry related and contains a mathematical macro-model of its functionality. As well known, statistical variations in fabrication processes can have a strong effect on their functionality and ultimately affect the yield. In order to predict the statistical behavior of the circuit, proper analysis of the uncertainties effects is crucial. This paper presents a method to build a novel class of Stochastic Process Design Kits for the analysis of photonic circuits. The proposed design kits directly store the information on the stochastic behavior of each building block in the form of a generalized-polynomial-chaos-based augmented macro-model obtained by properly exploiting stochastic collocation and Galerkin methods. Using this approach, we demonstrate that the augmented macro-models of the BBs can be calculated once and stored in a BB (foundry dependent) library and then used for the analysis of any desired circuit. The main advantage of this approach, shown here for the first time in photonics, is that the stochastic moments of an arbitrary photonic circuit can be evaluated by a single simulation only, without the need for repeated simulations. The accuracy and the significant speed-up with respect to the classical Monte Carlo analysis are verified by means of classical photonic circuit example with multiple uncertain variables.

  6. Spike solutions in Gierer#x2013;Meinhardt model with a time dependent anomaly exponent

    NASA Astrophysics Data System (ADS)

    Nec, Yana

    2018-01-01

    Experimental evidence of complex dispersion regimes in natural systems, where the growth of the mean square displacement in time cannot be characterised by a single power, has been accruing for the past two decades. In such processes the exponent γ(t) in ⟨r2⟩ ∼ tγ(t) at times might be approximated by a piecewise constant function, or it can be a continuous function. Variable order differential equations are an emerging mathematical tool with a strong potential to model these systems. However, variable order differential equations are not tractable by the classic differential equations theory. This contribution illustrates how a classic method can be adapted to gain insight into a system of this type. Herein a variable order Gierer-Meinhardt model is posed, a generic reaction- diffusion system of a chemical origin. With a fixed order this system possesses a solution in the form of a constellation of arbitrarily situated localised pulses, when the components' diffusivity ratio is asymptotically small. The pattern was shown to exist subject to multiple step-like transitions between normal diffusion and sub-diffusion, as well as between distinct sub-diffusive regimes. The analytical approximation obtained permits qualitative analysis of the impact thereof. Numerical solution for typical cross-over scenarios revealed such features as earlier equilibration and non-monotonic excursions before attainment of equilibrium. The method is general and allows for an approximate numerical solution with any reasonably behaved γ(t).

  7. Energy Models for One-Carrier Transport in Semiconductor Devices

    NASA Technical Reports Server (NTRS)

    Jerome, Joseph W.; Shu, Chi-Wang

    1991-01-01

    Moment models of carrier transport, derived from the Boltzmann equation, made possible the simulation of certain key effects through such realistic assumptions as energy dependent mobility functions. This type of global dependence permits the observation of velocity overshoot in the vicinity of device junctions, not discerned via classical drift-diffusion models, which are primarily local in nature. It was found that a critical role is played in the hydrodynamic model by the heat conduction term. When ignored, the overshoot is inappropriately damped. When the standard choice of the Wiedemann-Franz law is made for the conductivity, spurious overshoot is observed. Agreement with Monte-Carlo simulation in this regime required empirical modification of this law, or nonstandard choices. Simulations of the hydrodynamic model in one and two dimensions, as well as simulations of a newly developed energy model, the RT model, are presented. The RT model, intermediate between the hydrodynamic and drift-diffusion model, was developed to eliminate the parabolic energy band and Maxwellian distribution assumptions, and to reduce the spurious overshoot with physically consistent assumptions. The algorithms employed for both models are the essentially non-oscillatory shock capturing algorithms. Some mathematical results are presented and contrasted with the highly developed state of the drift-diffusion model.

  8. [Mathematics - astronomy - astrology special library].

    PubMed

    Gluch, Sibylle

    2011-01-01

    About 1560 Elector August of Saxony created an unusual library--one distinguished within its period by both its specialization and location. Situated within the Kunstkammer this library was mostly dedicated to the mathematical sciences and related disciplines. It contained works by the most important authors on mathematics, astronomy, and astrology from the classical, medieval, and early modern periods. This essay traces the formation and composition of August's library, and examines its function: What kind of relationship existed between the library and the Kunstkammer? In what way did the library mirror the interests of the Elector, and to what extend does it permit inferences regarding the Elector's knowledge of mathematics? From the analysis August emerges not as a specialist with a deep understanding of mathematics, but as a particular aficionado of mathematical applications. As a practitioner and general follower of the mathematical arts he took part in a far-reaching intellectual network the center of which lay in the University of Wittenberg. Here, Melanchthon had effectively strengthened the importance of the mathematical disciplines within the university curriculum. He regarded mathematics as the foremost science, arguing that before all other disciplines its method enabled man to recognize the harmonic order of the world, and to discern divine providence. Thus, mathematics offered consoling stability and support in an often seemingly chaotic world torn by religious controversies. This kind of esteem for the mathematical sciences did not presuppose expert knowledge. Hence, the fact that August does not appear to have read the mathematical books he collected does not come as a contradiction. On the contrary, for August it sufficed to recognize the potential of the mathematical sciences, which he brought into life through the creation of a specialized library that developed a rhetoric of its own. The collection of his Kunstkammer library spoke of a harmonically ordered world while at the same time memorializing August as a lover of mathematics and an important figure within the group of mathematical experts and enthusiasts.

  9. A Simple Mathematical Model Inspired by the Purkinje Cells: From Delayed Travelling Waves to Fractional Diffusion.

    PubMed

    Dipierro, Serena; Valdinoci, Enrico

    2018-07-01

    Recently, several experiments have demonstrated the existence of fractional diffusion in the neuronal transmission occurring in the Purkinje cells, whose malfunctioning is known to be related to the lack of voluntary coordination and the appearance of tremors. Also, a classical mathematical feature is that (fractional) parabolic equations possess smoothing effects, in contrast with the case of hyperbolic equations, which typically exhibit shocks and discontinuities. In this paper, we show how a simple toy-model of a highly ramified structure, somehow inspired by that of the Purkinje cells, may produce a fractional diffusion via the superposition of travelling waves that solve a hyperbolic equation. This could suggest that the high ramification of the Purkinje cells might have provided an evolutionary advantage of "smoothing" the transmission of signals and avoiding shock propagations (at the price of slowing a bit such transmission). Although an experimental confirmation of the possibility of such evolutionary advantage goes well beyond the goals of this paper, we think that it is intriguing, as a mathematical counterpart, to consider the time fractional diffusion as arising from the superposition of delayed travelling waves in highly ramified transmission media. The case of a travelling concave parabola with sufficiently small curvature is explicitly computed. The new link that we propose between time fractional diffusion and hyperbolic equation also provides a novelty with respect to the usual paradigm relating time fractional diffusion with parabolic equations in the limit. This paper is written in such a way as to be of interest to both biologists and mathematician alike. In order to accomplish this aim, both complete explanations of the objects considered and detailed lists of references are provided.

  10. Bernhard Riemann, a(rche)typical mathematical-physicist?

    NASA Astrophysics Data System (ADS)

    Elizalde, Emilio

    2013-09-01

    The work of Bernhard Riemann is discussed under the perspective of present day mathematics and physics, and with a prospective view towards the future, too. Against the (unfortunately rather widespread) trend---which predominantly dominated national scientific societies in Europe during the last Century---of strictly classifying the work of scientists with the aim to constrain them to separated domains of knowledge, without any possible interaction among those and often even fighting against each other (and which, no doubt, was in part responsible for the decline of European in favor of American science), it will be here argued, using Riemann as a model, archetypical example, that good research transcends any classification. Its uses and applications arguably permeate all domains, subjects and disciplines one can possibly define, to the point that it can be considered to be universally useful. After providing a very concise review of the main publications of Bernhard Riemann on physical problems, some connections between Riemann's papers and contemporary physics will be considered: (i) the uses of Riemann's work on the zeta function for devising applications to the regularization of quantum field theories in curved space-time, in particular, of quantum vacuum fluctuations; (ii) the uses of the Riemann tensor in general relativity and in recent generalizations of this theory, which aim at understanding the presently observed acceleration of the universe expansion (the dark energy issue). Finally, it will be argued that mathematical physics, which was yet not long ago a model paradigm for interdisciplinary activity---and had a very important pioneering role in this sense---is now quickly being surpassed by the extraordinarily fruitful interconnections which seem to pop up from nothing every day and simultaneously involve several disciplines, in the classical sense, including genetics, combinatorics, nanoelectronics, biochemistry, medicine, and even ps

  11. Mathematical Modelling Approach in Mathematics Education

    ERIC Educational Resources Information Center

    Arseven, Ayla

    2015-01-01

    The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

  12. Mathematical Modelling in the Junior Secondary Years: An Approach Incorporating Mathematical Technology

    ERIC Educational Resources Information Center

    Lowe, James; Carter, Merilyn; Cooper, Tom

    2018-01-01

    Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…

  13. Mathematics teachers' conceptions about modelling activities and its reflection on their beliefs about mathematics

    NASA Astrophysics Data System (ADS)

    Shahbari, Juhaina Awawdeh

    2018-07-01

    The current study examines whether the engagement of mathematics teachers in modelling activities and subsequent changes in their conceptions about these activities affect their beliefs about mathematics. The sample comprised 52 mathematics teachers working in small groups in four modelling activities. The data were collected from teachers' Reports about features of each activity, interviews and questionnaires on teachers' beliefs about mathematics. The findings indicated changes in teachers' conceptions about the modelling activities. Most teachers referred to the first activity as a mathematical problem but emphasized only the mathematical notions or the mathematical operations in the modelling process; changes in their conceptions were gradual. Most of the teachers referred to the fourth activity as a mathematical problem and emphasized features of the whole modelling process. The results of the interviews indicated that changes in the teachers' conceptions can be attributed to structure of the activities, group discussions, solution paths and elicited models. These changes about modelling activities were reflected in teachers' beliefs about mathematics. The quantitative findings indicated that the teachers developed more constructive beliefs about mathematics after engagement in the modelling activities and that the difference was significant, however there was no significant difference regarding changes in their traditional beliefs.

  14. Exploiting temporal collateral sensitivity in tumor clonal evolution

    PubMed Central

    Zhao, Boyang; Sedlak, Joseph C.; Srinivas, Raja; Creixell, Pau; Pritchard, Justin R.; Tidor, Bruce; Lauffenburger, Douglas A.; Hemann, Michael T.

    2016-01-01

    SUMMARY The prevailing approach to addressing secondary drug resistance in cancer focuses on treating the resistance mechanisms at relapse. However, the dynamic nature of clonal evolution, along with potential fitness costs and cost compensations, may present exploitable vulnerabilities; a notion that we term ‘temporal collateral sensitivity’. Using a combined pharmacological screen and drug resistance selection approach in a murine model of Ph+ acute lymphoblastic leukemia, we indeed find that temporal and/or persistent collateral sensitivity to non-classical BCR-ABL1 drugs arises in emergent tumor subpopulations during the evolution of resistance toward initial treatment with BCR-ABL1 targeted inhibitors. We determined the sensitization mechanism via genotypic, phenotypic, signaling, and binding measurements in combination with computational models, and demonstrated significant overall survival extension in mice. Additional stochastic mathematical models and small molecule screens extended our insights, indicating the value of focusing on evolutionary trajectories and pharmacological profiles to identify new strategies to treat dynamic tumor vulnerabilities. PMID:26924578

  15. Exploiting Temporal Collateral Sensitivity in Tumor Clonal Evolution.

    PubMed

    Zhao, Boyang; Sedlak, Joseph C; Srinivas, Raja; Creixell, Pau; Pritchard, Justin R; Tidor, Bruce; Lauffenburger, Douglas A; Hemann, Michael T

    2016-03-24

    The prevailing approach to addressing secondary drug resistance in cancer focuses on treating the resistance mechanisms at relapse. However, the dynamic nature of clonal evolution, along with potential fitness costs and cost compensations, may present exploitable vulnerabilities-a notion that we term "temporal collateral sensitivity." Using a combined pharmacological screen and drug resistance selection approach in a murine model of Ph(+) acute lymphoblastic leukemia, we indeed find that temporal and/or persistent collateral sensitivity to non-classical BCR-ABL1 drugs arises in emergent tumor subpopulations during the evolution of resistance toward initial treatment with BCR-ABL1-targeted inhibitors. We determined the sensitization mechanism via genotypic, phenotypic, signaling, and binding measurements in combination with computational models and demonstrated significant overall survival extension in mice. Additional stochastic mathematical models and small-molecule screens extended our insights, indicating the value of focusing on evolutionary trajectories and pharmacological profiles to identify new strategies to treat dynamic tumor vulnerabilities. Copyright © 2016 Elsevier Inc. All rights reserved.

  16. On the implications of the classical ergodic theorems: analysis of developmental processes has to focus on intra-individual variation.

    PubMed

    Molenaar, Peter C M

    2008-01-01

    It is argued that general mathematical-statistical theorems imply that standard statistical analysis techniques of inter-individual variation are invalid to investigate developmental processes. Developmental processes have to be analyzed at the level of individual subjects, using time series data characterizing the patterns of intra-individual variation. It is shown that standard statistical techniques based on the analysis of inter-individual variation appear to be insensitive to the presence of arbitrary large degrees of inter-individual heterogeneity in the population. An important class of nonlinear epigenetic models of neural growth is described which can explain the occurrence of such heterogeneity in brain structures and behavior. Links with models of developmental instability are discussed. A simulation study based on a chaotic growth model illustrates the invalidity of standard analysis of inter-individual variation, whereas time series analysis of intra-individual variation is able to recover the true state of affairs. (c) 2007 Wiley Periodicals, Inc.

  17. Jamming Attack in Wireless Sensor Network: From Time to Space

    NASA Astrophysics Data System (ADS)

    Sun, Yanqiang; Wang, Xiaodong; Zhou, Xingming

    Classical jamming attack models in the time domain have been proposed, such as constant jammer, random jammer, and reactive jammer. In this letter, we consider a new problem: given k jammers, how does the attacker minimize the pair-wise connectivity among the nodes in a Wireless Sensor Network (WSN)? We call this problem k-Jammer Deployment Problem (k-JDP). To the best of our knowledge, this is the first attempt at considering the position-critical jamming attack against wireless sensor network. We mainly make three contributions. First, we prove that the decision version of k-JDP is NP-complete even in the ideal situation where the attacker has full knowledge of the topology information of sensor network. Second, we propose a mathematical formulation based on Integer Programming (IP) model which yields an optimal solution. Third, we present a heuristic algorithm HAJDP, and compare it with the IP model. Numerical results show that our heuristic algorithm is computationally efficient.

  18. From public outrage to the burst of public violence: An epidemic-like model

    NASA Astrophysics Data System (ADS)

    Nizamani, Sarwat; Memon, Nasrullah; Galam, Serge

    2014-12-01

    This study extends classical models of spreading epidemics to describe the phenomenon of contagious public outrage, which eventually leads to the spread of violence following a disclosure of some unpopular political decisions and/or activity. Accordingly, a mathematical model is proposed to simulate from the start, the internal dynamics by which an external event is turned into internal violence within a population. Five kinds of agents are considered: “Upset” (U), “Violent” (V), “Sensitive” (S), “Immune” (I), and “Relaxed” (R), leading to a set of ordinary differential equations, which in turn yield the dynamics of spreading of each type of agents among the population. The process is stopped with the deactivation of the associated issue. Conditions coinciding with a twofold spreading of public violence are singled out. The results shed new light to understand terror activity and provides some hint on how to curb the spreading of violence within population globally sensitive to specific world issues. Recent violent events in the world are discussed.

  19. On the necessity of U-shaped learning.

    PubMed

    Carlucci, Lorenzo; Case, John

    2013-01-01

    A U-shaped curve in a cognitive-developmental trajectory refers to a three-step process: good performance followed by bad performance followed by good performance once again. U-shaped curves have been observed in a wide variety of cognitive-developmental and learning contexts. U-shaped learning seems to contradict the idea that learning is a monotonic, cumulative process and thus constitutes a challenge for competing theories of cognitive development and learning. U-shaped behavior in language learning (in particular in learning English past tense) has become a central topic in the Cognitive Science debate about learning models. Antagonist models (e.g., connectionism versus nativism) are often judged on their ability of modeling or accounting for U-shaped behavior. The prior literature is mostly occupied with explaining how U-shaped behavior occurs. Instead, we are interested in the necessity of this kind of apparently inefficient strategy. We present and discuss a body of results in the abstract mathematical setting of (extensions of) Gold-style computational learning theory addressing a mathematically precise version of the following question: Are there learning tasks that require U-shaped behavior? All notions considered are learning in the limit from positive data. We present results about the necessity of U-shaped learning in classical models of learning as well as in models with bounds on the memory of the learner. The pattern emerges that, for parameterized, cognitively relevant learning criteria, beyond very few initial parameter values, U-shapes are necessary for full learning power! We discuss the possible relevance of the above results for the Cognitive Science debate about learning models as well as directions for future research. Copyright © 2013 Cognitive Science Society, Inc.

  20. Modeling Non-homologous End Joining

    NASA Technical Reports Server (NTRS)

    Li, Yongfeng

    2013-01-01

    Non-homologous end joining (NHEJ) is the dominant DNA double strand break (DSB) repair pathway and involves several NHEJ proteins such as Ku, DNA-PKcs, XRCC4, Ligase IV and so on. Once DSBs are generated, Ku is first recruited to the DNA end, followed by other NHEJ proteins for DNA end processing and ligation. Because of the direct ligation of break ends without the need for a homologous template, NHEJ turns out to be an error-prone but efficient repair pathway. Some mechanisms have been proposed of how the efficiency of NHEJ repair is affected. The type of DNA damage is an important factor of NHEJ repair. For instance, the length of DNA fragment may determine the recruitment efficiency of NHEJ protein such as Ku [1], or the complexity of the DNA breaks [2] is accounted for the choice of NHEJ proteins and subpathway of NHEJ repair. On the other hand, the chromatin structure also plays a role of the accessibility of NHEJ protein to the DNA damage site. In this talk, some mathematical models of NHEJ, that consist of series of biochemical reactions complying with the laws of chemical reaction (e.g. mass action, etc.), will be introduced. By mathematical and numerical analysis and parameter estimation, the models are able to capture the qualitative biological features and show good agreement with experimental data. As conclusions, from the viewpoint of modeling, how the NHEJ proteins are recruited will be first discussed for connection between the classical sequential model [4] and recently proposed two-phase model [5]. Then how the NHEJ repair pathway is affected, by the length of DNA fragment [6], the complexity of DNA damage [7] and the chromatin structure [8], will be addressed

  1. An Extension of the Mean Value Theorem for Integrals

    ERIC Educational Resources Information Center

    Khalili, Parviz; Vasiliu, Daniel

    2010-01-01

    In this note we present an extension of the mean value theorem for integrals. The extension we consider is motivated by an older result (here referred as Corollary 2), which is quite classical for the literature of Mathematical Analysis or Calculus. We also show an interesting application for computing the sum of a harmonic series.

  2. Diophantine Equations as a Context for Technology-Enhanced Training in Conjecturing and Proving

    ERIC Educational Resources Information Center

    Abramovich, Sergei; Sugden, Stephen J.

    2008-01-01

    Solving indeterminate algebraic equations in integers is a classic topic in the mathematics curricula across grades. At the undergraduate level, the study of solutions of non-linear equations of this kind can be motivated by the use of technology. This article shows how the unity of geometric contextualization and spreadsheet-based amplification…

  3. A Pedagogical Approach to the Boltzmann Factor through Experiments and Simulations

    ERIC Educational Resources Information Center

    Battaglia, O. R.; Bonura, A.; Sperandeo-Mineo, R. M.

    2009-01-01

    The Boltzmann factor is the basis of a huge amount of thermodynamic and statistical physics, both classical and quantum. It governs the behaviour of all systems in nature that are exchanging energy with their environment. To understand why the expression has this specific form involves a deep mathematical analysis, whose flow of logic is hard to…

  4. Why Do Gestures Matter? Sensuous Cognition and the Palpability of Mathematical Meanings

    ERIC Educational Resources Information Center

    Radford, Luis

    2009-01-01

    The goal of this article is to present a sketch of what, following the German social theorist Arnold Gehlen, may be termed "sensuous cognition." The starting point of this alternative approach to classical mental-oriented views of cognition is a multimodal "material" conception of thinking. The very texture of thinking, it is suggested, cannot be…

  5. Conceptualizing Vectors in College Geometry: A New Framework for Analysis of Student Approaches and Difficulties

    ERIC Educational Resources Information Center

    Kwon, Oh Hoon

    2012-01-01

    This dissertation documents a new way of conceptualizing vectors in college mathematics, especially in geometry. First, I will introduce three problems to show the complexity and subtlety of the construct of vectors with the classical vector representations. These highlight the need for a new framework that: (1) differentiates abstraction from a…

  6. On One Unusual Method of Computation of Limits of Rational Functions in the Program Mathematica[R

    ERIC Educational Resources Information Center

    Hora, Jaroslav; Pech, Pavel

    2005-01-01

    Computing limits of functions is a traditional part of mathematical analysis which is very difficult for students. Now an algorithm for the elimination of quantifiers in the field of real numbers is implemented in the program Mathematica. This offers a non-traditional view on this classical theme. (Contains 1 table.)

  7. The Logical Heart of a Classic Proof Revisited: A Guide to Godel's "Incompleteness" Theorems

    ERIC Educational Resources Information Center

    Padula, Janice

    2011-01-01

    The study of Kurt Godel's proof of the "incompleteness" of a formal system such as "Principia Mathematica" is a great way to stimulate students' thinking and creative processes and interest in mathematics and its important developments. This article describes salient features of the proof together with ways to deal with potential difficulties for…

  8. A Binomial Modeling Approach for Upscaling Colloid Transport Under Unfavorable Attachment Conditions: Emergent Prediction of Nonmonotonic Retention Profiles

    NASA Astrophysics Data System (ADS)

    Hilpert, Markus; Johnson, William P.

    2018-01-01

    We used a recently developed simple mathematical network model to upscale pore-scale colloid transport information determined under unfavorable attachment conditions. Classical log-linear and nonmonotonic retention profiles, both well-reported under favorable and unfavorable attachment conditions, respectively, emerged from our upscaling. The primary attribute of the network is colloid transfer between bulk pore fluid, the near-surface fluid domain (NSFD), and attachment (treated as irreversible). The network model accounts for colloid transfer to the NSFD of downgradient grains and for reentrainment to bulk pore fluid via diffusion or via expulsion at rear flow stagnation zones (RFSZs). The model describes colloid transport by a sequence of random trials in a one-dimensional (1-D) network of Happel cells, which contain a grain and a pore. Using combinatorial analysis that capitalizes on the binomial coefficient, we derived from the pore-scale information the theoretical residence time distribution of colloids in the network. The transition from log-linear to nonmonotonic retention profiles occurs when the conditions underlying classical filtration theory are not fulfilled, i.e., when an NSFD colloid population is maintained. Then, nonmonotonic retention profiles result potentially both for attached and NSFD colloids. The concentration maxima shift downgradient depending on specific parameter choice. The concentration maxima were also shown to shift downgradient temporally (with continued elution) under conditions where attachment is negligible, explaining experimentally observed downgradient transport of retained concentration maxima of adhesion-deficient bacteria. For the case of zero reentrainment, we develop closed-form, analytical expressions for the shape, and the maximum of the colloid retention profile.

  9. Toward quantum-like modeling of financial processes

    NASA Astrophysics Data System (ADS)

    Choustova, Olga

    2007-05-01

    We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. We propose to describe behavioral financial factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model of quantum mechanics. Trajectories of prices are determined by two financial potentials: classical-like V(q) ("hard" market conditions, e.g., natural resources) and quantum-like U(q) (behavioral market conditions). On the one hand, our Bohmian model is a quantum-like model for the financial market, cf. with works of W. Segal, I. E. Segal, E. Haven, E. W. Piotrowski, J. Sladkowski. On the other hand, (since Bohmian mechanics provides the possibility to describe individual price trajectories) it belongs to the domain of extended research on deterministic dynamics for financial assets (C.W.J. Granger, W.A. Barnett, A. J. Benhabib, W.A. Brock, C. Sayers, J. Y. Campbell, A. W. Lo, A. C. MacKinlay, A. Serletis, S. Kuchta, M. Frank, R. Gencay, T. Stengos, M. J. Hinich, D. Patterson, D. A. Hsieh, D. T. Caplan, J.A. Scheinkman, B. LeBaron and many others).

  10. 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.

  11. The 24-Hour Mathematical Modeling Challenge

    ERIC Educational Resources Information Center

    Galluzzo, Benjamin J.; Wendt, Theodore J.

    2015-01-01

    Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…

  12. Probability Distributome: A Web Computational Infrastructure for Exploring the Properties, Interrelations, and Applications of Probability Distributions.

    PubMed

    Dinov, Ivo D; Siegrist, Kyle; Pearl, Dennis K; Kalinin, Alexandr; Christou, Nicolas

    2016-06-01

    Probability distributions are useful for modeling, simulation, analysis, and inference on varieties of natural processes and physical phenomena. There are uncountably many probability distributions. However, a few dozen families of distributions are commonly defined and are frequently used in practice for problem solving, experimental applications, and theoretical studies. In this paper, we present a new computational and graphical infrastructure, the Distributome , which facilitates the discovery, exploration and application of diverse spectra of probability distributions. The extensible Distributome infrastructure provides interfaces for (human and machine) traversal, search, and navigation of all common probability distributions. It also enables distribution modeling, applications, investigation of inter-distribution relations, as well as their analytical representations and computational utilization. The entire Distributome framework is designed and implemented as an open-source, community-built, and Internet-accessible infrastructure. It is portable, extensible and compatible with HTML5 and Web2.0 standards (http://Distributome.org). We demonstrate two types of applications of the probability Distributome resources: computational research and science education. The Distributome tools may be employed to address five complementary computational modeling applications (simulation, data-analysis and inference, model-fitting, examination of the analytical, mathematical and computational properties of specific probability distributions, and exploration of the inter-distributional relations). Many high school and college science, technology, engineering and mathematics (STEM) courses may be enriched by the use of modern pedagogical approaches and technology-enhanced methods. The Distributome resources provide enhancements for blended STEM education by improving student motivation, augmenting the classical curriculum with interactive webapps, and overhauling the learning assessment protocols.

  13. Probability Distributome: A Web Computational Infrastructure for Exploring the Properties, Interrelations, and Applications of Probability Distributions

    PubMed Central

    Dinov, Ivo D.; Siegrist, Kyle; Pearl, Dennis K.; Kalinin, Alexandr; Christou, Nicolas

    2015-01-01

    Probability distributions are useful for modeling, simulation, analysis, and inference on varieties of natural processes and physical phenomena. There are uncountably many probability distributions. However, a few dozen families of distributions are commonly defined and are frequently used in practice for problem solving, experimental applications, and theoretical studies. In this paper, we present a new computational and graphical infrastructure, the Distributome, which facilitates the discovery, exploration and application of diverse spectra of probability distributions. The extensible Distributome infrastructure provides interfaces for (human and machine) traversal, search, and navigation of all common probability distributions. It also enables distribution modeling, applications, investigation of inter-distribution relations, as well as their analytical representations and computational utilization. The entire Distributome framework is designed and implemented as an open-source, community-built, and Internet-accessible infrastructure. It is portable, extensible and compatible with HTML5 and Web2.0 standards (http://Distributome.org). We demonstrate two types of applications of the probability Distributome resources: computational research and science education. The Distributome tools may be employed to address five complementary computational modeling applications (simulation, data-analysis and inference, model-fitting, examination of the analytical, mathematical and computational properties of specific probability distributions, and exploration of the inter-distributional relations). Many high school and college science, technology, engineering and mathematics (STEM) courses may be enriched by the use of modern pedagogical approaches and technology-enhanced methods. The Distributome resources provide enhancements for blended STEM education by improving student motivation, augmenting the classical curriculum with interactive webapps, and overhauling the learning assessment protocols. PMID:27158191

  14. A [32P]-NAD+-based method to identify and quantitate long residence time enoyl-ACP reductase inhibitors

    PubMed Central

    Yu, Weixuan; Neckles, Carla; Chang, Andrew; Bommineni, Gopal Reddy; Spagnuolo, Lauren; Zhang, Zhuo; Liu, Nina; Lai, Christina; Truglio, James; Tonge, Peter J.

    2015-01-01

    The classical methods for quantifying drug-target residence time (tR) use loss or regain of enzyme activity in progress curve kinetic assays. However, such methods become imprecise at very long residence times, mitigating the use of alternative strategies. Using the NAD(P)H-dependent FabI enoyl-ACP reductase as a model system, we developed a Penefsky column-based method for direct measurement of tR, where the off-rate of the drug was determined with radiolabeled [adenylate-32P] NAD(P+) cofactor. Twenty-three FabI inhibitors were analyzed and a mathematical model was used to estimate limits to the tR values of each inhibitor based on percent drug-target complex recovery following gel filtration. In general, this method showed good agreement with the classical steady state kinetic methods for compounds with tR values of 10-100 min. In addition, we were able to identify seven long tR inhibitors (100-1500 min) and to accurately determine their tR values. The method was then used to measure tR as a function of temperature, an analysis not previously possible using the standard kinetic approach due to decreased NAD(P)H stability at elevated temperatures. In general, a 4-fold difference in tR was observed when the temperature was increased from 25 °C to 37 °C . PMID:25684450

  15. A faster numerical scheme for a coupled system modeling soil erosion and sediment transport

    NASA Astrophysics Data System (ADS)

    Le, M.-H.; Cordier, S.; Lucas, C.; Cerdan, O.

    2015-02-01

    Overland flow and soil erosion play an essential role in water quality and soil degradation. Such processes, involving the interactions between water flow and the bed sediment, are classically described by a well-established system coupling the shallow water equations and the Hairsine-Rose model. Numerical approximation of this coupled system requires advanced methods to preserve some important physical and mathematical properties; in particular, the steady states and the positivity of both water depth and sediment concentration. Recently, finite volume schemes based on Roe's solver have been proposed by Heng et al. (2009) and Kim et al. (2013) for one and two-dimensional problems. In their approach, an additional and artificial restriction on the time step is required to guarantee the positivity of sediment concentration. This artificial condition can lead the computation to be costly when dealing with very shallow flow and wet/dry fronts. The main result of this paper is to propose a new and faster scheme for which only the CFL condition of the shallow water equations is sufficient to preserve the positivity of sediment concentration. In addition, the numerical procedure of the erosion part can be used with any well-balanced and positivity preserving scheme of the shallow water equations. The proposed method is tested on classical benchmarks and also on a realistic configuration.

  16. The Gibbs paradox and the physical criteria for indistinguishability of identical particles

    NASA Astrophysics Data System (ADS)

    Unnikrishnan, C. S.

    2016-08-01

    Gibbs paradox in the context of statistical mechanics addresses the issue of additivity of entropy of mixing gases. The usual discussion attributes the paradoxical situation to classical distinguishability of identical particles and credits quantum theory for enabling indistinguishability of identical particles to solve the problem. We argue that indistinguishability of identical particles is already a feature in classical mechanics and this is clearly brought out when the problem is treated in the language of information and associated entropy. We pinpoint the physical criteria for indistinguishability that is crucial for the treatment of the Gibbs’ problem and the consistency of its solution with conventional thermodynamics. Quantum mechanics provides a quantitative criterion, not possible in the classical picture, for the degree of indistinguishability in terms of visibility of quantum interference, or overlap of the states as pointed out by von Neumann, thereby endowing the entropy expression with mathematical continuity and physical reasonableness.

  17. Implementation of quantum and classical discrete fractional Fourier transforms.

    PubMed

    Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander

    2016-03-23

    Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

  18. Implementation of quantum and classical discrete fractional Fourier transforms

    PubMed Central

    Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander

    2016-01-01

    Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089

  19. Revisiting the positive DC corona discharge theory: Beyond Peek's and Townsend's law

    NASA Astrophysics Data System (ADS)

    Monrolin, Nicolas; Praud, Olivier; Plouraboué, Franck

    2018-06-01

    The classical positive Corona Discharge theory in a cylindrical axisymmetric configuration is revisited in order to find analytically the influence of gas properties and thermodynamic conditions on the corona current. The matched asymptotic expansion of Durbin and Turyn [J. Phys. D: Appl. Phys. 20, 1490-1495 (1987)] of a simplified but self-consistent problem is performed and explicit analytical solutions are derived. The mathematical derivation enables us to express a new positive DC corona current-voltage characteristic, choosing either a dimensionless or dimensional formulation. In dimensional variables, the current voltage law and the corona inception voltage explicitly depend on the electrode size and physical gas properties such as ionization and photoionization parameters. The analytical predictions are successfully confronted with experiments and Peek's and Townsend's laws. An analytical expression of the corona inception voltage φ o n is proposed, which depends on the known values of physical parameters without adjustable parameters. As a proof of consistency, the classical Townsend current-voltage law I = C φ ( φ - φ o n ) is retrieved by linearizing the non-dimensional analytical solution. A brief parametric study showcases the interest in this analytical current model, especially for exploring small corona wires or considering various thermodynamic conditions.

  20. The Relationship between Students' Performance on Conventional Standardized Mathematics Assessments and Complex Mathematical Modeling Problems

    ERIC Educational Resources Information Center

    Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.

    2016-01-01

    Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

  1. Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics

    ERIC Educational Resources Information Center

    Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.

    2016-01-01

    Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…

  2. Spreaders and Sponges define metastasis in lung cancer: A Markov chain Monte Carlo Mathematical Model

    PubMed Central

    Newton, Paul K.; Mason, Jeremy; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Norton, Larry; Kuhn, Peter

    2013-01-01

    The classic view of metastatic cancer progression is that it is a unidirectional process initiated at the primary tumor site, progressing to variably distant metastatic sites in a fairly predictable, though not perfectly understood, fashion. A Markov chain Monte Carlo mathematical approach can determine a pathway diagram that classifies metastatic tumors as ‘spreaders’ or ‘sponges’ and orders the timescales of progression from site to site. In light of recent experimental evidence highlighting the potential significance of self-seeding of primary tumors, we use a Markov chain Monte Carlo (MCMC) approach, based on large autopsy data sets, to quantify the stochastic, systemic, and often multi-directional aspects of cancer progression. We quantify three types of multi-directional mechanisms of progression: (i) self-seeding of the primary tumor; (ii) re-seeding of the primary tumor from a metastatic site (primary re-seeding); and (iii) re-seeding of metastatic tumors (metastasis re-seeding). The model shows that the combined characteristics of the primary and the first metastatic site to which it spreads largely determine the future pathways and timescales of systemic disease. For lung cancer, the main ‘spreaders’ of systemic disease are the adrenal gland and kidney, whereas the main ‘sponges’ are regional lymph nodes, liver, and bone. Lung is a significant self-seeder, although it is a ‘sponge’ site with respect to progression characteristics. PMID:23447576

  3. Mathematical Modeling: A Bridge to STEM Education

    ERIC Educational Resources Information Center

    Kertil, Mahmut; Gurel, Cem

    2016-01-01

    The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…

  4. Jones index, secret sharing and total quantum dimension

    NASA Astrophysics Data System (ADS)

    Fiedler, Leander; Naaijkens, Pieter; Osborne, Tobias J.

    2017-02-01

    We study the total quantum dimension in the thermodynamic limit of topologically ordered systems. In particular, using the anyons (or superselection sectors) of such models, we define a secret sharing scheme, storing information invisible to a malicious party, and argue that the total quantum dimension quantifies how well we can perform this task. We then argue that this can be made mathematically rigorous using the index theory of subfactors, originally due to Jones and later extended by Kosaki and Longo. This theory provides us with a ‘relative entropy’ of two von Neumann algebras and a quantum channel, and we argue how these can be used to quantify how much classical information two parties can hide form an adversary. We also review the total quantum dimension in finite systems, in particular how it relates to topological entanglement entropy. It is known that the latter also has an interpretation in terms of secret sharing schemes, although this is shown by completely different methods from ours. Our work provides a different and independent take on this, which at the same time is completely mathematically rigorous. This complementary point of view might be beneficial, for example, when studying the stability of the total quantum dimension when the system is perturbed.

  5. The influence of mathematics learning using SAVI approach on junior high school students’ mathematical modelling ability

    NASA Astrophysics Data System (ADS)

    Khusna, H.; Heryaningsih, N. Y.

    2018-01-01

    The aim of this research was to examine mathematical modeling ability who learn mathematics by using SAVI approach. This research was a quasi-experimental research with non-equivalent control group designed by using purposive sampling technique. The population of this research was the state junior high school students in Lembang while the sample consisted of two class at 8th grade. The instrument used in this research was mathematical modeling ability. Data analysis of this research was conducted by using SPSS 20 by Windows. The result showed that students’ ability of mathematical modeling who learn mathematics by using SAVI approach was better than students’ ability of mathematical modeling who learn mathematics using conventional learning.

  6. Beyond Motivation: Exploring Mathematical Modeling as a Context for Deepening Students' Understandings of Curricular Mathematics

    ERIC Educational Resources Information Center

    Zbiek, Rose Mary; Conner, Annamarie

    2006-01-01

    Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical…

  7. An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers

    ERIC Educational Resources Information Center

    Thrasher, Emily Plunkett

    2016-01-01

    The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…

  8. Experimental identification and mathematical modeling of viscoplastic material behavior

    NASA Astrophysics Data System (ADS)

    Haupt, P.; Lion, A.

    1995-03-01

    Uniaxial torsion and biaxial torsion-tension experiments on thin-walled tubes were carried out to investigate the viscoplastic behavior of stainless steel XCrNi18.9. A series of monotonic tests under strain and stress control shows nonlinear rate dependence and suggests the existence of equilibrium states, which are asymptotically approached during relaxation and creep processes. Strain controlled cyclic experiments display various hardening and softening phenomena that depend on strain amplitude and mean strain. All experiments indicate that the equilibrium states within the material depend on the history of the input process, whereas the history-dependence of the relaxation and creep behavior appears less significant. From the experiments the design of a constitutive model of viscoplasticity is motivated: The basic assumption is a decomposition of the total stress into an equilibrium stress and a non-equilibrium overstress: At constant strain, the overstress relaxes to zero, where the relaxation time depends on the overstress in order to account for the nonlinear rate-dependence. The equilibrium stress is assumed to be a rate independent functional of the total strain history. Classical plasticity is utilized with a kinematic hardening rule of the Armstrong-Frederick type. In order to incorporate the amplitude-dependent hardening and softening behavior, a generalized arc length representation is applied [14]. The introduction of an additional kinematic hardening variable facilitates consideration of additional hardening effects resulting from the non-radiality of the input process. Apart from the common yield and loading criterion of classical plasticity, the proposed constitutive model does not contain any further distinction of different cases. The experimental data are sufficient to identify the material parameters of the constitutive model. The results of the identification procedure demonstrate the ability of the model to represent the observed phenomena with satisfactory approximation.

  9. Composing chaotic music from the letter m

    NASA Astrophysics Data System (ADS)

    Sotiropoulos, Anastasios D.

    Chaotic music is composed from a proposed iterative map depicting the letter m, relating the pitch, duration and loudness of successive steps. Each of the two curves of the letter m is based on the classical logistic map. Thus, the generating map is xn+1 = r xn(1/2 - xn) for xn between 0 and 1/2 defining the first curve, and xn+1 = r (xn - 1/2)(1 - xn) for xn between 1/2 and 1 representing the second curve. The parameter r which determines the height(s) of the letter m varies from 2 to 16, the latter value ensuring fully developed chaotic solutions for the whole letter m; r = 8 yielding full chaotic solutions only for its first curve. The m-model yields fixed points, bifurcation points and chaotic regions for each separate curve, as well as values of the parameter r greater than 8 which produce inter-fixed points, inter-bifurcation points and inter-chaotic regions from the interplay of the two curves. Based on this, music is composed from mapping the m- recurrence model solutions onto actual notes. The resulting musical score strongly depends on the sequence of notes chosen by the composer to define the musical range corresponding to the range of the chaotic mathematical solutions x from 0 to 1. Here, two musical ranges are used; one is the middle chromatic scale and the other is the seven- octaves range. At the composer's will and, for aesthetics, within the same composition, notes can be the outcome of different values of r and/or shifted in any octave. Compositions with endings of non-repeating note patterns result from values of r in the m-model that do not produce bifurcations. Scores of chaotic music composed from the m-model and the classical logistic model are presented.

  10. Reflective Modeling in Teacher Education.

    ERIC Educational Resources Information Center

    Shealy, Barry E.

    This paper describes mathematical modeling activities from a secondary mathematics teacher education course taken by fourth-year university students. Experiences with mathematical modeling are viewed as important in helping teachers develop a more intuitive understanding of mathematics, generate and evaluate mathematical interpretations, and…

  11. Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling

    ERIC Educational Resources Information Center

    Karali, Diren; Durmus, Soner

    2015-01-01

    The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…

  12. Automation of closed environments in space for human comfort and safety

    NASA Technical Reports Server (NTRS)

    Cogley, Allen C.; Tucker, Nathan P.

    1992-01-01

    For prolonged missions into space and colonization outside the Earth's atmosphere, development of Environmental Control and Life Support Systems (ECLSS) are essential to provide astronauts with habitable environments. The Kansas State University Advanced Design Team have researched and designed a control system for an ECLSS like that on Space Station Freedom. The following milestones have been accomplished: (1) completed computer simulation of the CO2 Removal Assembly; (2) created a set of rules for the expert control system of the CO2 Removal Assembly; (3) created a classical controls system for the CO2 Removal Assembly; (4) established a means of communication between the mathematical model and the two controls systems; and (5) analyzed the dynamic response of the simulation and compared the two methods of control.

  13. The sympathy of two pendulum clocks: beyond Huygens' observations.

    PubMed

    Peña Ramirez, Jonatan; Olvera, Luis Alberto; Nijmeijer, Henk; Alvarez, Joaquin

    2016-03-29

    This paper introduces a modern version of the classical Huygens' experiment on synchronization of pendulum clocks. The version presented here consists of two monumental pendulum clocks--ad hoc designed and fabricated--which are coupled through a wooden structure. It is demonstrated that the coupled clocks exhibit 'sympathetic' motion, i.e. the pendula of the clocks oscillate in consonance and in the same direction. Interestingly, when the clocks are synchronized, the common oscillation frequency decreases, i.e. the clocks become slow and inaccurate. In order to rigorously explain these findings, a mathematical model for the coupled clocks is obtained by using well-established physical and mechanical laws and likewise, a theoretical analysis is conducted. Ultimately, the sympathy of two monumental pendulum clocks, interacting via a flexible coupling structure, is experimentally, numerically, and analytically demonstrated.

  14. Pulse Phase Dynamic Thermal Tomography Investigation on the Defects of the Solid-Propellant Missile Engine Cladding Layer

    NASA Astrophysics Data System (ADS)

    Peng, Wei; Wang, Fei; Liu, Jun-yan; Xiao, Peng; Wang, Yang; Dai, Jing-min

    2018-04-01

    Pulse phase dynamic thermal tomography (PP-DTT) was introduced as a nondestructive inspection technique to detect the defects of the solid-propellant missile engine cladding layer. One-dimensional thermal wave mathematical model stimulated by pulse signal was developed and employed to investigate the thermal wave transmission characteristics. The pulse phase algorithm was used to extract the thermal wave characteristic of thermal radiation. Depth calibration curve was obtained by fuzzy c-means algorithm. Moreover, PP-DTT, a depth-resolved photothermal imaging modality, was employed to enable three-dimensional (3D) visualization of cladding layer defects. The comparison experiment between PP-DTT and classical dynamic thermal tomography was investigated. The results showed that PP-DTT can reconstruct the 3D topography of defects in a high quality.

  15. The Iodine Spectrum: A New Look at an Old Topic

    NASA Astrophysics Data System (ADS)

    Long, George; Sauder, Deborah; Shalhoub, George M.; Stout, Roland; Hamby Towns, Marcy; Zielinski, Theresa Julia

    1999-06-01

    This paper describes a new approach to the traditional iodine gas absorption spectrum experiment often performed in undergraduate physical chemistry labs. The approach is student centered and designed to emphasize the conceptual richness in this classic experiment. It gives students the opportunity to examine the conceptual and mathematical connections between spectroscopic data and quantum models by organizing the material in conceptual chunks, which they work through sequentially. Students use symbolic mathematics software, Mathcad, to expedite the sophisticated numerical calculations required. The curricular chunks were specifically constructed to make the sophisticated concepts embedded in the project accessible. The focus activities remind the students of information they already know and require them to employ both paper and pencil and computer worksheets to complete calculations. Five Mathcad templates provide a rich mathematical treatment of the topics in this experiment. This paper describes how the documents MorsePotential.mcd, BirgeSponer.mcd, IodineSpectrum.mcd, FranckCondonBackground.mcd, and FranckCondonComputation.mcd are used during the three weeks in which this experiment can be performed by a typical physical chemistry student. Although originally designed to use the WWW to disseminate information and promote interaction among physical chemistry students at geographically dispersed institutions, this segmented focus-question approach to the iodine experiment has also been used by a physical chemistry class at a single campus. In both formats, faculty noticed decreased anxiety of the students towards the experiment and an increase in the quality of laboratory reports that indicated better understanding of the chemical concepts.

  16. 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.

  17. Non-Kolmogorovian Approach to the Context-Dependent Systems Breaking the Classical Probability Law

    NASA Astrophysics Data System (ADS)

    Asano, Masanari; Basieva, Irina; Khrennikov, Andrei; Ohya, Masanori; Yamato, Ichiro

    2013-07-01

    There exist several phenomena breaking the classical probability laws. The systems related to such phenomena are context-dependent, so that they are adaptive to other systems. In this paper, we present a new mathematical formalism to compute the joint probability distribution for two event-systems by using concepts of the adaptive dynamics and quantum information theory, e.g., quantum channels and liftings. In physics the basic example of the context-dependent phenomena is the famous double-slit experiment. Recently similar examples have been found in biological and psychological sciences. Our approach is an extension of traditional quantum probability theory, and it is general enough to describe aforementioned contextual phenomena outside of quantum physics.

  18. Canonical methods in classical and quantum gravity: An invitation to canonical LQG

    NASA Astrophysics Data System (ADS)

    Reyes, Juan D.

    2018-04-01

    Loop Quantum Gravity (LQG) is a candidate quantum theory of gravity still under construction. LQG was originally conceived as a background independent canonical quantization of Einstein’s general relativity theory. This contribution provides some physical motivations and an overview of some mathematical tools employed in canonical Loop Quantum Gravity. First, Hamiltonian classical methods are reviewed from a geometric perspective. Canonical Dirac quantization of general gauge systems is sketched next. The Hamiltonian formultation of gravity in geometric ADM and connection-triad variables is then presented to finally lay down the canonical loop quantization program. The presentation is geared toward advanced undergradute or graduate students in physics and/or non-specialists curious about LQG.

  19. The Identification of the Mediterranean cyclones main classical trajectories towards Romania by using objective methods based on mathematical algorithms

    NASA Astrophysics Data System (ADS)

    Oana, Catrina; Parding, Kajsa Maria; Stefan, Sabina

    2017-04-01

    The importance of knowledge on the trajectories that Mediterranean cyclones follows toward Romania is fundamental because most of the times the weather phenomena that accompany them determine significant economic damage and not only. In the specialized literature, the principal classic trajectories on which the Mediterranean cyclones pass toward the south-east of Europe and by default toward Romania, causing in these areas a crucial weather conditions change in all aspects at any time during the year, have been determined in subjectively mode, many years ago, by C. Sorodoc (1962) E. I. Bordei (1983). Starting from the known 9 classic trajectories determined subjectively, in this study it was aimed and subsequently carried out their identification by this date, but objectively, using the method based on mathematic algorithms developed by Rasmus E. Benestad, Abdelkader Mezghani, and Kajsa M. Parding (2006). The study was carried out between January 2003 and December 2015, taking into account the fact that the presence of the Mediterranean cyclones may be established almost every month, these representing important links of the atmosphere movement over Europe. The data used by the daily review have contained values, in grid points, of the mean pressure field at sea level (MSLP), with spatial resolution of 0.75° x 0.75° and 6 hours temporal coverage, originating from ECMWF, ERA-Interim project (2006), and the chosen field of interest was between 15°W - 40°E and 30°N - 50°N. Of the total number of Mediterranean cyclones identified objectively, that followed trajectories toward Romania, were randomly selected only a few cases, which indicates the similarity between the paths of classic subjectively determined and those determined objectively. Validation of the results consisted in the first phase in a comparison between the trajectories identified with the classic trajectories determined subjectively, then was carried out a second validation, by analysis of the MSLP field, geopotential height and potential vorticity. As a conclusion, the results obtained highlights certainly reliability but especially the usefulness of the objective method used, in particular in carrying out the complex Mediterranean climatology studies and not only.

  20. Towards a Policy Social Psychology: Teacher Engagement with Policy Enactment and the Core Concept of Affective Disruption

    ERIC Educational Resources Information Center

    Sheikh, Irfan; Bagley, Carl

    2018-01-01

    The article uncovers the complex process of educational policy enactment and the impact this process has on teachers as policy actors as they undertake the task of introducing a new mathematics curriculum in a Canadian secondary school. The three year study based on in-depth qualitative interviews adopts a classic grounded theory approach of…

  1. Legacy of the Ancient World: An Educational Guide. Understanding Ancient Culture through Art at the Tampa Museum of Art.

    ERIC Educational Resources Information Center

    Whitelaw, R. Lynn

    Among the many contributions made by Ancient Greeks and Romans to contemporary life, are those which influence art, architecture, literature, philosophy, mathematics and science, theater, athletics, religion, and the founding of democracy. The Tampa Museum of Art's classical collection offers a unique opportunity to learn about Ancient Greeks and…

  2. Solving the Sailors and the Coconuts Problem via Diagrammatic Approach

    ERIC Educational Resources Information Center

    Man, Yiu-Kwong

    2010-01-01

    In this article, we discuss how to use a diagrammatic approach to solve the classic sailors and the coconuts problem. It provides us an insight on how to tackle this type of problem in a novel and intuitive way. This problem-solving approach will be found useful to mathematics teachers or lecturers involved in teaching elementary number theory,…

  3. The Foundations of Einstein's Theory of Gravitation

    NASA Astrophysics Data System (ADS)

    Freundlich, Erwin; Brose, Translated by Henry L.; Einstein, Preface by Albert; Turner, Introduction by H. H.

    2011-06-01

    Introduction; 1. The special theory of relativity as a stepping-stone to the general theory of relativity; 2. Two fundamental postulates in the mathematical formulation of physical laws; 3. Concerning the fulfilment of the two postulates; 4. The difficulties in the principles of classical mechanics; 5. Einstein's theory of gravitation; 6. The verification of the new theory by actual experience; Appendix; Index.

  4. The implementation of multiple intelligences based teaching model to improve mathematical problem solving ability for student of junior high school

    NASA Astrophysics Data System (ADS)

    Fasni, Nurli; Fatimah, Siti; Yulanda, Syerli

    2017-05-01

    This research aims to achieve some purposes such as: to know whether mathematical problem solving ability of students who have learned mathematics using Multiple Intelligences based teaching model is higher than the student who have learned mathematics using cooperative learning; to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using Multiple Intelligences based teaching model., to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using cooperative learning; to know the attitude of the students to Multiple Intelligences based teaching model. The method employed here is quasi-experiment which is controlled by pre-test and post-test. The population of this research is all of VII grade in SMP Negeri 14 Bandung even-term 2013/2014, later on two classes of it were taken for the samples of this research. A class was taught using Multiple Intelligences based teaching model and the other one was taught using cooperative learning. The data of this research were gotten from the test in mathematical problem solving, scale questionnaire of the student attitudes, and observation. The results show the mathematical problem solving of the students who have learned mathematics using Multiple Intelligences based teaching model learning is higher than the student who have learned mathematics using cooperative learning, the mathematical problem solving ability of the student who have learned mathematics using cooperative learning and Multiple Intelligences based teaching model are in intermediate level, and the students showed the positive attitude in learning mathematics using Multiple Intelligences based teaching model. As for the recommendation for next author, Multiple Intelligences based teaching model can be tested on other subject and other ability.

  5. Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

    ERIC Educational Resources Information Center

    Mumcu, Hayal Yavuz

    2016-01-01

    The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

  6. Modulation theory, dispersive shock waves and Gerald Beresford Whitham

    NASA Astrophysics Data System (ADS)

    Minzoni, A. A.; Smyth, Noel F.

    2016-10-01

    Gerald Beresford (GB) Whitham, FRS, (13th December, 1927-26th January, 2014) was one of the leading applied mathematicians of the twentieth century whose work over forty years had a profound, formative impact on research on wave motion across a broad range of areas. Many of the ideas and techniques he developed have now become the standard tools used to analyse and understand wave motion, as the papers of this special issue of Physica D testify. Many of the techniques pioneered by GB Whitham have spread beyond wave propagation into other applied mathematics areas, such as reaction-diffusion, and even into theoretical physics and pure mathematics, in which Whitham modulation theory is an active area of research. GB Whitham's classic textbook Linear and Nonlinear Waves, published in 1974, is still the standard reference for the applied mathematics of wave motion. In honour of his scientific achievements, GB Whitham was elected a Fellow of the American Academy of Arts and Sciences in 1959 and a Fellow of the Royal Society in 1965. He was awarded the Norbert Wiener Prize for Applied Mathematics in 1980.

  7. Quantum non-objectivity from performativity of quantum phenomena

    NASA Astrophysics Data System (ADS)

    Khrennikov, Andrei; Schumann, Andrew

    2014-12-01

    We analyze the logical foundations of quantum mechanics (QM) by stressing non-objectivity of quantum observables, which is a consequence of the absence of logical atoms in QM. We argue that the matter of quantum non-objectivity is that, on the one hand, the formalism of QM constructed as a mathematical theory is self-consistent, but, on the other hand, quantum phenomena as results of experimenters’ performances are not self-consistent. This self-inconsistency is an effect of the language of QM differing greatly from the language of human performances. The former is the language of a mathematical theory that uses some Aristotelian and Russellian assumptions (e.g., the assumption that there are logical atoms). The latter language consists of performative propositions that are self-inconsistent only from the viewpoint of conventional mathematical theory, but they satisfy another logic that is non-Aristotelian. Hence, the representation of quantum reality in linguistic terms may be different: the difference between a mathematical theory and a logic of performative propositions. To solve quantum self-inconsistency, we apply the formalism of non-classical self-referent logics.

  8. Scientific Assistant Virtual Laboratory (SAVL)

    NASA Astrophysics Data System (ADS)

    Alaghband, Gita; Fardi, Hamid; Gnabasik, David

    2007-03-01

    The Scientific Assistant Virtual Laboratory (SAVL) is a scientific discovery environment, an interactive simulated virtual laboratory, for learning physics and mathematics. The purpose of this computer-assisted intervention is to improve middle and high school student interest, insight and scores in physics and mathematics. SAVL develops scientific and mathematical imagination in a visual, symbolic, and experimental simulation environment. It directly addresses the issues of scientific and technological competency by providing critical thinking training through integrated modules. This on-going research provides a virtual laboratory environment in which the student directs the building of the experiment rather than observing a packaged simulation. SAVL: * Engages the persistent interest of young minds in physics and math by visually linking simulation objects and events with mathematical relations. * Teaches integrated concepts by the hands-on exploration and focused visualization of classic physics experiments within software. * Systematically and uniformly assesses and scores students by their ability to answer their own questions within the context of a Master Question Network. We will demonstrate how the Master Question Network uses polymorphic interfaces and C# lambda expressions to manage simulation objects.

  9. Systems modelling methodology for the analysis of apoptosis signal transduction and cell death decisions.

    PubMed

    Rehm, Markus; Prehn, Jochen H M

    2013-06-01

    Systems biology and systems medicine, i.e. the application of systems biology in a clinical context, is becoming of increasing importance in biology, drug discovery and health care. Systems biology incorporates knowledge and methods that are applied in mathematics, physics and engineering, but may not be part of classical training in biology. We here provide an introduction to basic concepts and methods relevant to the construction and application of systems models for apoptosis research. We present the key methods relevant to the representation of biochemical processes in signal transduction models, with a particular reference to apoptotic processes. We demonstrate how such models enable a quantitative and temporal analysis of changes in molecular entities in response to an apoptosis-inducing stimulus, and provide information on cell survival and cell death decisions. We introduce methods for analyzing the spatial propagation of cell death signals, and discuss the concepts of sensitivity analyses that enable a prediction of network responses to disturbances of single or multiple parameters. Copyright © 2013 Elsevier Inc. All rights reserved.

  10. Mathematical modeling of polymer flooding using the unstructured Voronoi grid

    NASA Astrophysics Data System (ADS)

    Kireev, T. F.; Bulgakova, G. T.; Khatmullin, I. F.

    2017-12-01

    Effective recovery of unconventional oil reserves necessitates development of enhanced oil recovery techniques such as polymer flooding. The study investigated the model of polymer flooding with effects of adsorption and water salinity. The model takes into account six components that include elements of the classic black oil model. These components are polymer, salt, water, dead oil, dry gas and dissolved gas. Solution of the problem is obtained by finite volume method on unstructured Voronoi grid using fully implicit scheme and the Newton’s method. To compare several different grid configurations numerical simulation of polymer flooding is performed. The oil rates obtained by a hexagonal locally refined Voronoi grid are shown to be more accurate than the oil rates obtained by a rectangular grid with the same number of cells. The latter effect is caused by high solution accuracy near the wells due to the local grid refinement. Minimization of the grid orientation effect caused by the hexagonal pattern is also demonstrated. However, in the inter-well regions with large Voronoi cells flood front tends to flatten and the water breakthrough moment is smoothed.

  11. Global Regularity of 2D Density Patches for Inhomogeneous Navier-Stokes

    NASA Astrophysics Data System (ADS)

    Gancedo, Francisco; García-Juárez, Eduardo

    2018-07-01

    This paper is about Lions' open problem on density patches (Lions in Mathematical topics in fluid mechanics. Vol. 1, volume 3 of Oxford Lecture series in mathematics and its applications, Clarendon Press, Oxford University Press, New York, 1996): whether or not inhomogeneous incompressible Navier-Stokes equations preserve the initial regularity of the free boundary given by density patches. Using classical Sobolev spaces for the velocity, we first establish the propagation of {C^{1+γ}} regularity with {0 < γ < 1} in the case of positive density. Furthermore, we go beyond this to show the persistence of a geometrical quantity such as the curvature. In addition, we obtain a proof for {C^{2+γ}} regularity.

  12. Pre-Service Teachers' Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

    ERIC Educational Resources Information Center

    Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc

    2016-01-01

    Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…

  13. Evolution of Mathematics Teachers' Pedagogical Knowledge When They Are Teaching through Modeling

    ERIC Educational Resources Information Center

    Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat; Alacaci, Cengiz; Cakiroglu, Erdinc; Cetinkaya, Bulent

    2017-01-01

    Use of mathematical modeling in mathematics education has been receiving significant attention as a way to develop students' mathematical knowledge and skills. As effective use of modeling in classes depends on the competencies of teachers we need to know more about the nature of teachers' knowledge to use modeling in mathematics education and how…

  14. Mathematical Modeling in Science: Using Spreadsheets to Create Mathematical Models and Address Scientific Inquiry

    ERIC Educational Resources Information Center

    Horton, Robert M.; Leonard, William H.

    2005-01-01

    In science, inquiry is used as students explore important and interesting questions concerning the world around them. In mathematics, one contemporary inquiry approach is to create models that describe real phenomena. Creating mathematical models using spreadsheets can help students learn at deep levels in both science and mathematics, and give…

  15. Mathematical Modeling and Pure Mathematics

    ERIC Educational Resources Information Center

    Usiskin, Zalman

    2015-01-01

    Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

  16. Understanding Prospective Teachers' Mathematical Modeling Processes in the Context of a Mathematical Modeling Course

    ERIC Educational Resources Information Center

    Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat

    2017-01-01

    This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…

  17. Introducing Modeling Transition Diagrams as a Tool to Connect Mathematical Modeling to Mathematical Thinking

    ERIC Educational Resources Information Center

    Czocher, Jennifer A.

    2016-01-01

    This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…

  18. An Experimental Approach to Mathematical Modeling in Biology

    ERIC Educational Resources Information Center

    Ledder, Glenn

    2008-01-01

    The simplest age-structured population models update a population vector via multiplication by a matrix. These linear models offer an opportunity to introduce mathematical modeling to students of limited mathematical sophistication and background. We begin with a detailed discussion of mathematical modeling, particularly in a biological context.…

  19. Mathematical Modeling with Middle School Students: The Robot Art Model-Eliciting Activity

    ERIC Educational Resources Information Center

    Stohlmann, Micah S.

    2017-01-01

    Internationally mathematical modeling is garnering more attention for the benefits associated with it. Mathematical modeling can develop students' communication skills and the ability to demonstrate understanding through different representations. With the increased attention on mathematical modeling, there is a need for more curricula to be…

  20. The Music of Mathematics: Toward a New Problem Typology

    NASA Astrophysics Data System (ADS)

    Quarfoot, David

    Halmos (1980) once described problems and their solutions as "the heart of mathematics". Following this line of thinking, one might naturally ask: "What, then, is the heart of problems?". In this work, I attempt to answer this question using techniques from statistics, information visualization, and machine learning. I begin the journey by cataloging the features of problems delineated by the mathematics and mathematics education communities. These dimensions are explored in a large data set of students working thousands of problems at the Art of Problem Solving, an online company that provides adaptive mathematical training for students around the world. This analysis is able to concretely show how the fabric of mathematical problems changes across different subjects, difficulty levels, and students. Furthermore, it locates problems that stand out in the crowd -- those that synergize cognitive engagement, learning, and difficulty. This quantitatively-heavy side of the dissertation is partnered with a qualitatively-inspired portion that involves human scoring of 105 problems and their solutions. In this setting, I am able to capture elusive features of mathematical problems and derive a fuller picture of the space of mathematical problems. Using correlation matrices, principal components analysis, and clustering techniques, I explore the relationships among those features frequently discussed in mathematics problems (e.g., difficulty, creativity, novelty, affective engagement, authenticity). Along the way, I define a new set of uncorrelated features in problems and use these as the basis for a New Mathematical Problem Typology (NMPT). Grounded in the terminology of classical music, the NMPT works to quickly convey the essence and value of a problem, just as terms like "etude" and "mazurka" do for musicians. Taken together, these quantitative and qualitative analyses seek to terraform the landscape of mathematical problems and, concomitantly, the current thinking about that world. Most importantly, this work highlights and names the panoply of problems that exist, expanding the myopic vision of contemporary mathematical problem solving.

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